%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ITP155^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:24:23 AM UTC 2026
% Result : Theorem 45.82s 7.95s
% Output : CNFRefutation 45.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 107
% Syntax : Number of formulae : 1715 ( 617 unt; 0 typ; 0 def)
% Number of atoms : 14024 (4515 equ; 0 cnn)
% Maximal formula atoms : 9 ( 8 avg)
% Number of connectives : 27356 (4430 ~;4227 |; 111 &;18033 @)
% ( 0 <=>; 555 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Number of types : 15 ( 14 usr)
% Number of type conns : 332 ( 332 >; 0 *; 0 +; 0 <<)
% Number of symbols : 115 ( 112 usr; 13 con; 0-4 aty)
% Number of variables : 5012 ( 130 ^;4864 !; 18 ?;5012 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_nat,type,
nat: $tType ).
thf(tp_produc1404140509_a_nat,type,
produc1404140509_a_nat: $tType ).
thf(tp_produc1463940355_set_a,type,
produc1463940355_set_a: $tType ).
thf(tp_produc1572603623od_a_a,type,
produc1572603623od_a_a: $tType ).
thf(tp_produc1691597095_set_a,type,
produc1691597095_set_a: $tType ).
thf(tp_product_prod_a_a,type,
product_prod_a_a: $tType ).
thf(tp_product_prod_nat_nat,type,
product_prod_nat_nat: $tType ).
thf(tp_set_Pr1948701895od_a_a,type,
set_Pr1948701895od_a_a: $tType ).
thf(tp_set_Pr1986765409at_nat,type,
set_Pr1986765409at_nat: $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_nat,type,
set_nat: $tType ).
thf(tp_set_set_a,type,
set_set_a: $tType ).
thf(tp_bot_bo1293121322_a_a_o,type,
bot_bo1293121322_a_a_o: product_prod_a_a > $o ).
thf(tp_bot_bo1519632275_set_a,type,
bot_bo1519632275_set_a: produc1691597095_set_a ).
thf(tp_bot_bo2131659635od_a_a,type,
bot_bo2131659635od_a_a: set_Product_prod_a_a ).
thf(tp_bot_bot_a_o,type,
bot_bot_a_o: a > $o ).
thf(tp_bot_bot_nat,type,
bot_bot_nat: nat ).
thf(tp_bot_bot_nat_o,type,
bot_bot_nat_o: nat > $o ).
thf(tp_bot_bot_set_a,type,
bot_bot_set_a: set_a ).
thf(tp_bot_bot_set_nat,type,
bot_bot_set_nat: set_nat ).
thf(tp_bot_bot_set_set_a,type,
bot_bot_set_set_a: set_set_a ).
thf(tp_carrier,type,
carrier: set_a ).
thf(tp_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_nat,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(tp_finite1481642319od_a_a,type,
finite1481642319od_a_a: set_Product_prod_a_a > nat ).
thf(tp_finite1664988688od_a_a,type,
finite1664988688od_a_a: set_Pr1948701895od_a_a > $o ).
thf(tp_finite179568208od_a_a,type,
finite179568208od_a_a: set_Product_prod_a_a > $o ).
thf(tp_finite772653738at_nat,type,
finite772653738at_nat: set_Pr1986765409at_nat > $o ).
thf(tp_finite_card_a,type,
finite_card_a: set_a > nat ).
thf(tp_finite_card_nat,type,
finite_card_nat: set_nat > nat ).
thf(tp_finite_finite_a,type,
finite_finite_a: set_a > $o ).
thf(tp_finite_finite_nat,type,
finite_finite_nat: set_nat > $o ).
thf(tp_finite_finite_set_a,type,
finite_finite_set_a: set_set_a > $o ).
thf(tp_is_empty_a,type,
is_empty_a: set_a > $o ).
thf(tp_member2057358096od_a_a,type,
member2057358096od_a_a: produc1572603623od_a_a > set_Pr1948701895od_a_a > $o ).
thf(tp_member449909584od_a_a,type,
member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
thf(tp_member701585322at_nat,type,
member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
thf(tp_member_a,type,
member_a: a > set_a > $o ).
thf(tp_member_nat,type,
member_nat: nat > set_nat > $o ).
thf(tp_member_set_a,type,
member_set_a: set_a > set_set_a > $o ).
thf(tp_ord_le1302190241at_nat,type,
ord_le1302190241at_nat: product_prod_nat_nat > product_prod_nat_nat > $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_le486764743_set_a,type,
ord_le486764743_set_a: produc1691597095_set_a > produc1691597095_set_a > $o ).
thf(tp_ord_le781360189_a_nat,type,
ord_le781360189_a_nat: produc1404140509_a_nat > produc1404140509_a_nat > $o ).
thf(tp_ord_le841160035_set_a,type,
ord_le841160035_set_a: produc1463940355_set_a > produc1463940355_set_a > $o ).
thf(tp_ord_less_eq_nat,type,
ord_less_eq_nat: nat > nat > $o ).
thf(tp_ord_less_eq_set_a,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(tp_ord_less_eq_set_nat,type,
ord_less_eq_set_nat: set_nat > set_nat > $o ).
thf(tp_ord_less_nat,type,
ord_less_nat: nat > nat > $o ).
thf(tp_order_1150839801on_nat,type,
order_1150839801on_nat: set_nat > set_Pr1986765409at_nat > $o ).
thf(tp_order_359341630od_a_a,type,
order_359341630od_a_a: set_Product_prod_a_a > set_Pr1948701895od_a_a > $o ).
thf(tp_order_preorder_on_a,type,
order_preorder_on_a: set_a > set_Product_prod_a_a > $o ).
thf(tp_prefer1147844220ce_nat,type,
prefer1147844220ce_nat: set_nat > set_Pr1986765409at_nat > $o ).
thf(tp_prefer1292084992ence_a,type,
prefer1292084992ence_a: set_a > set_Product_prod_a_a > $o ).
thf(tp_prefer1293349710ce_nat,type,
prefer1293349710ce_nat: set_nat > set_Pr1986765409at_nat > $o ).
thf(tp_prefer1338892073od_a_a,type,
prefer1338892073od_a_a: set_Product_prod_a_a > set_Pr1948701895od_a_a > $o ).
thf(tp_prefer1498087410od_a_a,type,
prefer1498087410od_a_a: product_prod_a_a > set_Product_prod_a_a > set_Pr1948701895od_a_a > set_Product_prod_a_a ).
thf(tp_prefer161218362good_a,type,
prefer161218362good_a: a > set_a > set_Product_prod_a_a > set_a ).
thf(tp_prefer1672638789an_nat,type,
prefer1672638789an_nat: nat > set_nat > set_Pr1986765409at_nat > set_nat ).
thf(tp_prefer1676310729than_a,type,
prefer1676310729than_a: a > set_a > set_Product_prod_a_a > set_a ).
thf(tp_prefer1936906324as_nat,type,
prefer1936906324as_nat: nat > set_nat > set_Pr1986765409at_nat > set_nat ).
thf(tp_prefer436369274d_as_a,type,
prefer436369274d_as_a: a > set_a > set_Product_prod_a_a > set_a ).
thf(tp_prefer477097315od_a_a,type,
prefer477097315od_a_a: product_prod_a_a > set_Product_prod_a_a > set_Pr1948701895od_a_a > set_Product_prod_a_a ).
thf(tp_prefer563798164od_nat,type,
prefer563798164od_nat: nat > set_nat > set_Pr1986765409at_nat > set_nat ).
thf(tp_prefer580340847ioms_a,type,
prefer580340847ioms_a: set_a > set_Product_prod_a_a > $o ).
thf(tp_prefer697821563od_a_a,type,
prefer697821563od_a_a: set_Product_prod_a_a > set_Pr1948701895od_a_a > $o ).
thf(tp_prefer719835986ence_a,type,
prefer719835986ence_a: set_a > set_Product_prod_a_a > $o ).
thf(tp_prefer74720675od_a_a,type,
prefer74720675od_a_a: product_prod_a_a > set_Product_prod_a_a > set_Pr1948701895od_a_a > set_Product_prod_a_a ).
thf(tp_produc1450889781_set_a,type,
produc1450889781_set_a: nat > set_a > produc1463940355_set_a ).
thf(tp_produc1474507607od_a_a,type,
produc1474507607od_a_a: product_prod_a_a > product_prod_a_a > produc1572603623od_a_a ).
thf(tp_produc1928581911_set_a,type,
produc1928581911_set_a: set_a > set_a > produc1691597095_set_a ).
thf(tp_produc515611863_a_nat,type,
produc515611863_a_nat: set_a > nat > produc1404140509_a_nat ).
thf(tp_product_Pair_a_a,type,
product_Pair_a_a: a > a > product_prod_a_a ).
thf(tp_product_Pair_nat_nat,type,
product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
thf(tp_refl_o1298442278od_a_a,type,
refl_o1298442278od_a_a: set_Product_prod_a_a > set_Pr1948701895od_a_a > $o ).
thf(tp_refl_on_a,type,
refl_on_a: set_a > set_Product_prod_a_a > $o ).
thf(tp_refl_on_nat,type,
refl_on_nat: set_nat > set_Pr1986765409at_nat > $o ).
thf(tp_relation,type,
relation: set_Product_prod_a_a ).
thf(tp_sK10_SY475,type,
sK10_SY475: set_a > set_set_a > set_a ).
thf(tp_sK11_SY329,type,
sK11_SY329: set_set_a > set_a ).
thf(tp_sK12_SY517,type,
sK12_SY517: set_a > set_set_a > set_a ).
thf(tp_sK13_SY625,type,
sK13_SY625: set_a > set_a > a ).
thf(tp_sK14_SY630,type,
sK14_SY630: set_a > set_a > a ).
thf(tp_sK15_SY585,type,
sK15_SY585: set_a > nat > set_a > ( set_a > nat ) > set_a ).
thf(tp_sK16_SY513,type,
sK16_SY513: set_a > set_a > set_a > ( set_a > set_a ) > set_a ).
thf(tp_sK17_SY594,type,
sK17_SY594: set_a > nat > set_a > ( set_a > nat ) > set_a ).
thf(tp_sK18_SY597,type,
sK18_SY597: set_a > set_a > set_a > ( set_a > set_a ) > set_a ).
thf(tp_sK19_SY540,type,
sK19_SY540: set_a > set_a > nat > ( set_a > nat ) > set_a ).
thf(tp_sK1_SY360,type,
sK1_SY360: set_a > a ).
thf(tp_sK20_SY605,type,
sK20_SY605: nat > set_a > nat > ( nat > set_a ) > nat ).
thf(tp_sK21_SY608,type,
sK21_SY608: set_a > set_a > set_a > ( set_a > set_a ) > set_a ).
thf(tp_sK22_SY556,type,
sK22_SY556: set_a > set_a > nat > ( set_a > nat ) > set_a ).
thf(tp_sK23_SY560,type,
sK23_SY560: nat > nat > set_a > ( nat > set_a ) > nat ).
thf(tp_sK24_SY617,type,
sK24_SY617: nat > set_a > nat > ( nat > set_a ) > nat ).
thf(tp_sK25_SY569,type,
sK25_SY569: set_a > set_a > set_a > ( set_a > set_a ) > set_a ).
thf(tp_sK26_SY575,type,
sK26_SY575: nat > nat > set_a > ( nat > set_a ) > nat ).
thf(tp_sK27_SY655,type,
sK27_SY655: ( set_a > nat ) > set_a > nat > set_a > set_a ).
thf(tp_sK28_SY656,type,
sK28_SY656: ( set_a > set_a ) > set_a > set_a > set_a > set_a ).
thf(tp_sK29_SY657,type,
sK29_SY657: ( set_a > nat ) > set_a > nat > set_a > set_a ).
thf(tp_sK2_SY497,type,
sK2_SY497: set_a > set_a > a ).
thf(tp_sK30_SY658,type,
sK30_SY658: ( set_a > set_a ) > set_a > set_a > set_a > set_a ).
thf(tp_sK31_SY659,type,
sK31_SY659: ( set_a > nat ) > nat > set_a > set_a > set_a ).
thf(tp_sK32_SY660,type,
sK32_SY660: ( nat > set_a ) > nat > set_a > nat > nat ).
thf(tp_sK33_SY661,type,
sK33_SY661: ( set_a > set_a ) > set_a > set_a > set_a > set_a ).
thf(tp_sK34_SY662,type,
sK34_SY662: ( set_a > nat ) > nat > set_a > set_a > set_a ).
thf(tp_sK35_SY663,type,
sK35_SY663: ( nat > set_a ) > set_a > nat > nat > nat ).
thf(tp_sK36_SY664,type,
sK36_SY664: ( nat > set_a ) > nat > set_a > nat > nat ).
thf(tp_sK37_SY665,type,
sK37_SY665: ( set_a > set_a ) > set_a > set_a > set_a > set_a ).
thf(tp_sK38_SY666,type,
sK38_SY666: ( nat > set_a ) > set_a > nat > nat > nat ).
thf(tp_sK3_SY508,type,
sK3_SY508: ( a > $o ) > ( a > $o ) > a ).
thf(tp_sK4_SY543,type,
sK4_SY543: nat > set_a > set_a ).
thf(tp_sK5_SY489,type,
sK5_SY489: nat > set_a > set_a ).
thf(tp_sK6_SY490,type,
sK6_SY490: nat > set_a > set_a ).
thf(tp_sK7_SY542,type,
sK7_SY542: ( a > $o ) > ( a > $o ) > a ).
thf(tp_sK8_SY552,type,
sK8_SY552: set_a > nat > set_a ).
thf(tp_sK9_SY294,type,
sK9_SY294: set_set_a > set_a ).
thf(tp_total_1490170027od_a_a,type,
total_1490170027od_a_a: set_Product_prod_a_a > set_Pr1948701895od_a_a > $o ).
thf(tp_total_on_a,type,
total_on_a: set_a > set_Product_prod_a_a > $o ).
thf(tp_total_on_nat,type,
total_on_nat: set_nat > set_Pr1986765409at_nat > $o ).
thf(tp_trans_a,type,
trans_a: set_Product_prod_a_a > $o ).
thf(tp_x,type,
x: a ).
thf(tp_y,type,
y: a ).
thf(tp_zero_zero_nat,type,
zero_zero_nat: nat ).
thf(23,axiom,
trans_a @ relation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_transitivity) ).
thf(33,axiom,
! [A2: set_a] :
( ! [X4: a] :
~ ( member_a @ X4 @ A2 )
=> ( ord_less_eq_set_a @ A2 @ bot_bot_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_subset__emptyI) ).
thf(65,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_bot_Oextremum) ).
thf(67,axiom,
! [A: set_a] :
( ( ord_less_eq_set_a @ A @ bot_bot_set_a )
= ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_bot_Oextremum__unique) ).
thf(69,axiom,
! [A: set_a] :
( ( ord_less_eq_set_a @ A @ bot_bot_set_a )
=> ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_bot_Oextremum__uniqueI) ).
thf(78,axiom,
! [A: nat,F2: set_a > nat,B: set_a,C: set_a] :
( ( ord_less_eq_nat @ A @ ( F2 @ B ) )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ! [X4: set_a,Y3: set_a] :
( ( ord_less_eq_set_a @ X4 @ Y3 )
=> ( ord_less_eq_nat @ ( F2 @ X4 ) @ ( F2 @ Y3 ) ) )
=> ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_order__subst1) ).
thf(79,axiom,
! [A: set_a,F2: nat > set_a,B: nat,C: nat] :
( ( ord_less_eq_set_a @ A @ ( F2 @ B ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ! [X4: nat,Y3: nat] :
( ( ord_less_eq_nat @ X4 @ Y3 )
=> ( ord_less_eq_set_a @ ( F2 @ X4 ) @ ( F2 @ Y3 ) ) )
=> ( ord_less_eq_set_a @ A @ ( F2 @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_order__subst1) ).
thf(80,axiom,
! [A: set_a,F2: set_a > set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ ( F2 @ B ) )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ! [X4: set_a,Y3: set_a] :
( ( ord_less_eq_set_a @ X4 @ Y3 )
=> ( ord_less_eq_set_a @ ( F2 @ X4 ) @ ( F2 @ Y3 ) ) )
=> ( ord_less_eq_set_a @ A @ ( F2 @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_order__subst1) ).
thf(82,axiom,
! [A: nat,B: nat,F2: nat > set_a,C: set_a] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_set_a @ ( F2 @ B ) @ C )
=> ( ! [X4: nat,Y3: nat] :
( ( ord_less_eq_nat @ X4 @ Y3 )
=> ( ord_less_eq_set_a @ ( F2 @ X4 ) @ ( F2 @ Y3 ) ) )
=> ( ord_less_eq_set_a @ ( F2 @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_order__subst2) ).
thf(83,axiom,
! [A: set_a,B: set_a,F2: set_a > nat,C: nat] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_nat @ ( F2 @ B ) @ C )
=> ( ! [X4: set_a,Y3: set_a] :
( ( ord_less_eq_set_a @ X4 @ Y3 )
=> ( ord_less_eq_nat @ ( F2 @ X4 ) @ ( F2 @ Y3 ) ) )
=> ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_order__subst2) ).
thf(84,axiom,
! [A: set_a,B: set_a,F2: set_a > set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ ( F2 @ B ) @ C )
=> ( ! [X4: set_a,Y3: set_a] :
( ( ord_less_eq_set_a @ X4 @ Y3 )
=> ( ord_less_eq_set_a @ ( F2 @ X4 ) @ ( F2 @ Y3 ) ) )
=> ( ord_less_eq_set_a @ ( F2 @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_order__subst2) ).
thf(86,axiom,
! [A: set_a,F2: nat > set_a,B: nat,C: nat] :
( ( A
= ( F2 @ B ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ! [X4: nat,Y3: nat] :
( ( ord_less_eq_nat @ X4 @ Y3 )
=> ( ord_less_eq_set_a @ ( F2 @ X4 ) @ ( F2 @ Y3 ) ) )
=> ( ord_less_eq_set_a @ A @ ( F2 @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_ord__eq__le__subst) ).
thf(87,axiom,
! [A: nat,F2: set_a > nat,B: set_a,C: set_a] :
( ( A
= ( F2 @ B ) )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ! [X4: set_a,Y3: set_a] :
( ( ord_less_eq_set_a @ X4 @ Y3 )
=> ( ord_less_eq_nat @ ( F2 @ X4 ) @ ( F2 @ Y3 ) ) )
=> ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_ord__eq__le__subst) ).
thf(88,axiom,
! [A: set_a,F2: set_a > set_a,B: set_a,C: set_a] :
( ( A
= ( F2 @ B ) )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ! [X4: set_a,Y3: set_a] :
( ( ord_less_eq_set_a @ X4 @ Y3 )
=> ( ord_less_eq_set_a @ ( F2 @ X4 ) @ ( F2 @ Y3 ) ) )
=> ( ord_less_eq_set_a @ A @ ( F2 @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_ord__eq__le__subst) ).
thf(90,axiom,
! [A: nat,B: nat,F2: nat > set_a,C: set_a] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( F2 @ B )
= C )
=> ( ! [X4: nat,Y3: nat] :
( ( ord_less_eq_nat @ X4 @ Y3 )
=> ( ord_less_eq_set_a @ ( F2 @ X4 ) @ ( F2 @ Y3 ) ) )
=> ( ord_less_eq_set_a @ ( F2 @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_ord__le__eq__subst) ).
thf(91,axiom,
! [A: set_a,B: set_a,F2: set_a > nat,C: nat] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( F2 @ B )
= C )
=> ( ! [X4: set_a,Y3: set_a] :
( ( ord_less_eq_set_a @ X4 @ Y3 )
=> ( ord_less_eq_nat @ ( F2 @ X4 ) @ ( F2 @ Y3 ) ) )
=> ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_ord__le__eq__subst) ).
thf(92,axiom,
! [A: set_a,B: set_a,F2: set_a > set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( F2 @ B )
= C )
=> ( ! [X4: set_a,Y3: set_a] :
( ( ord_less_eq_set_a @ X4 @ Y3 )
=> ( ord_less_eq_set_a @ ( F2 @ X4 ) @ ( F2 @ Y3 ) ) )
=> ( ord_less_eq_set_a @ ( F2 @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_ord__le__eq__subst) ).
thf(94,axiom,
( ( ^ [Y4: set_a,Z2: set_a] : ( Y4 = Z2 ) )
= ( ^ [X3: set_a,Y2: set_a] :
( ( ord_less_eq_set_a @ X3 @ Y2 )
& ( ord_less_eq_set_a @ Y2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_eq__iff) ).
thf(96,axiom,
! [X: set_a,Y: set_a] :
( ( ord_less_eq_set_a @ X @ Y )
=> ( ( ord_less_eq_set_a @ Y @ X )
=> ( X = Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_antisym) ).
thf(99,axiom,
! [X: set_a,Y: set_a] :
( ( X = Y )
=> ( ord_less_eq_set_a @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_eq__refl) ).
thf(102,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_order_Otrans) ).
thf(105,axiom,
! [Y: set_a,X: set_a] :
( ( ord_less_eq_set_a @ Y @ X )
=> ( ( ord_less_eq_set_a @ X @ Y )
= ( X = Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_antisym__conv) ).
thf(107,axiom,
( ( ^ [Y4: set_a,Z2: set_a] : ( Y4 = Z2 ) )
= ( ^ [A6: set_a,B8: set_a] :
( ( ord_less_eq_set_a @ A6 @ B8 )
& ( ord_less_eq_set_a @ B8 @ A6 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_order__class_Oorder_Oeq__iff) ).
thf(109,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( A = B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_ord__eq__le__trans) ).
thf(111,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_ord__le__eq__trans) ).
thf(113,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_order__class_Oorder_Oantisym) ).
thf(115,axiom,
! [X: set_a,Y: set_a,Z: set_a] :
( ( ord_less_eq_set_a @ X @ Y )
=> ( ( ord_less_eq_set_a @ Y @ Z )
=> ( ord_less_eq_set_a @ X @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_order__trans) ).
thf(117,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_dual__order_Orefl) ).
thf(120,axiom,
! [B: set_a,A: set_a,C: set_a] :
( ( ord_less_eq_set_a @ B @ A )
=> ( ( ord_less_eq_set_a @ C @ B )
=> ( ord_less_eq_set_a @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_dual__order_Otrans) ).
thf(122,axiom,
( ( ^ [Y4: set_a,Z2: set_a] : ( Y4 = Z2 ) )
= ( ^ [A6: set_a,B8: set_a] :
( ( ord_less_eq_set_a @ B8 @ A6 )
& ( ord_less_eq_set_a @ A6 @ B8 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_dual__order_Oeq__iff) ).
thf(124,axiom,
! [B: set_a,A: set_a] :
( ( ord_less_eq_set_a @ B @ A )
=> ( ( ord_less_eq_set_a @ A @ B )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_dual__order_Oantisym) ).
thf(127,axiom,
! [X: set_a] : ( ord_less_eq_set_a @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_order__refl) ).
thf(130,axiom,
! [N: nat,A2: set_a] :
( ( ord_less_eq_nat @ N @ ( finite_card_a @ A2 ) )
=> ? [S2: set_a] :
( ( ord_less_eq_set_a @ S2 @ A2 )
& ( ( finite_card_a @ S2 )
= N ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_ex__card) ).
thf(140,axiom,
! [N: nat,S: set_a] :
( ( ord_less_eq_nat @ N @ ( finite_card_a @ S ) )
=> ~ ! [T3: set_a] :
( ( ord_less_eq_set_a @ T3 @ S )
=> ( ( ( finite_card_a @ T3 )
= N )
=> ~ ( finite_finite_a @ T3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_obtain__subset__with__card__n) ).
thf(143,axiom,
! [B2: set_a,A2: set_a] :
( ( finite_finite_a @ B2 )
=> ( ( ord_less_eq_set_a @ A2 @ B2 )
=> ( ( ord_less_eq_nat @ ( finite_card_a @ B2 ) @ ( finite_card_a @ A2 ) )
=> ( A2 = B2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_card__seteq) ).
thf(146,axiom,
! [F: set_a,C2: nat] :
( ! [G: set_a] :
( ( ord_less_eq_set_a @ G @ F )
=> ( ( finite_finite_a @ G )
=> ( ord_less_eq_nat @ ( finite_card_a @ G ) @ C2 ) ) )
=> ( ( finite_finite_a @ F )
& ( ord_less_eq_nat @ ( finite_card_a @ F ) @ C2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_finite__if__finite__subsets__card__bdd) ).
thf(149,axiom,
! [A2: set_a,N: nat] :
( ~ ( finite_finite_a @ A2 )
=> ? [B4: set_a] :
( ( finite_finite_a @ B4 )
& ( ( finite_card_a @ B4 )
= N )
& ( ord_less_eq_set_a @ B4 @ A2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_infinite__arbitrarily__large) ).
thf(152,axiom,
! [B2: set_a,A2: set_a] :
( ( finite_finite_a @ B2 )
=> ( ( ord_less_eq_set_a @ A2 @ B2 )
=> ( ( ( finite_card_a @ A2 )
= ( finite_card_a @ B2 ) )
=> ( A2 = B2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_card__subset__eq) ).
thf(156,axiom,
! [A2: set_set_a] :
( ( finite_finite_set_a @ A2 )
=> ( ( A2 != bot_bot_set_set_a )
=> ? [X4: set_a] :
( ( member_set_a @ X4 @ A2 )
& ! [Xa: set_a] :
( ( member_set_a @ Xa @ A2 )
=> ( ( ord_less_eq_set_a @ X4 @ Xa )
=> ( X4 = Xa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_finite__has__maximal) ).
thf(158,axiom,
! [A2: set_set_a] :
( ( finite_finite_set_a @ A2 )
=> ( ( A2 != bot_bot_set_set_a )
=> ? [X4: set_a] :
( ( member_set_a @ X4 @ A2 )
& ! [Xa: set_a] :
( ( member_set_a @ Xa @ A2 )
=> ( ( ord_less_eq_set_a @ Xa @ X4 )
=> ( X4 = Xa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_finite__has__minimal) ).
thf(159,axiom,
! [B2: set_a,A2: set_a] :
( ( finite_finite_a @ B2 )
=> ( ( ord_less_eq_set_a @ A2 @ B2 )
=> ( finite_finite_a @ A2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_rev__finite__subset) ).
thf(162,axiom,
! [S: set_a,T2: set_a] :
( ( ord_less_eq_set_a @ S @ T2 )
=> ( ~ ( finite_finite_a @ S )
=> ~ ( finite_finite_a @ T2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_infinite__super) ).
thf(165,axiom,
! [A2: set_a,B2: set_a] :
( ( ord_less_eq_set_a @ A2 @ B2 )
=> ( ( finite_finite_a @ B2 )
=> ( finite_finite_a @ A2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_finite__subset) ).
thf(176,axiom,
! [A2: set_set_a,A: set_a] :
( ( finite_finite_set_a @ A2 )
=> ( ( member_set_a @ A @ A2 )
=> ? [X4: set_a] :
( ( member_set_a @ X4 @ A2 )
& ( ord_less_eq_set_a @ X4 @ A )
& ! [Xa: set_a] :
( ( member_set_a @ Xa @ A2 )
=> ( ( ord_less_eq_set_a @ Xa @ X4 )
=> ( X4 = Xa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_finite__has__minimal2) ).
thf(178,axiom,
! [A2: set_set_a,A: set_a] :
( ( finite_finite_set_a @ A2 )
=> ( ( member_set_a @ A @ A2 )
=> ? [X4: set_a] :
( ( member_set_a @ X4 @ A2 )
& ( ord_less_eq_set_a @ A @ X4 )
& ! [Xa: set_a] :
( ( member_set_a @ Xa @ A2 )
=> ( ( ord_less_eq_set_a @ X4 @ Xa )
=> ( X4 = Xa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_finite__has__maximal2) ).
thf(180,axiom,
! [X: nat,X5: nat,Y: set_a,Y5: set_a] :
( ( ord_less_eq_nat @ X @ X5 )
=> ( ( ord_less_eq_set_a @ Y @ Y5 )
=> ( ord_le841160035_set_a @ ( produc1450889781_set_a @ X @ Y ) @ ( produc1450889781_set_a @ X5 @ Y5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_Pair__mono) ).
thf(181,axiom,
! [X: set_a,X5: set_a,Y: nat,Y5: nat] :
( ( ord_less_eq_set_a @ X @ X5 )
=> ( ( ord_less_eq_nat @ Y @ Y5 )
=> ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ X @ Y ) @ ( produc515611863_a_nat @ X5 @ Y5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_Pair__mono) ).
thf(182,axiom,
! [X: set_a,X5: set_a,Y: set_a,Y5: set_a] :
( ( ord_less_eq_set_a @ X @ X5 )
=> ( ( ord_less_eq_set_a @ Y @ Y5 )
=> ( ord_le486764743_set_a @ ( produc1928581911_set_a @ X @ Y ) @ ( produc1928581911_set_a @ X5 @ Y5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_Pair__mono) ).
thf(196,axiom,
! [P: a > $o,Q: a > $o] :
( ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) )
= ( ! [X3: a] :
( ( P @ X3 )
=> ( Q @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_Collect__mono__iff) ).
thf(197,axiom,
( ( ^ [Y4: set_a,Z2: set_a] : ( Y4 = Z2 ) )
= ( ^ [A3: set_a,B3: set_a] :
( ( ord_less_eq_set_a @ A3 @ B3 )
& ( ord_less_eq_set_a @ B3 @ A3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_set__eq__subset) ).
thf(198,axiom,
! [A2: set_a,B2: set_a,C2: set_a] :
( ( ord_less_eq_set_a @ A2 @ B2 )
=> ( ( ord_less_eq_set_a @ B2 @ C2 )
=> ( ord_less_eq_set_a @ A2 @ C2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_subset__trans) ).
thf(199,axiom,
! [P: a > $o,Q: a > $o] :
( ! [X4: a] :
( ( P @ X4 )
=> ( Q @ X4 ) )
=> ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_Collect__mono) ).
thf(200,axiom,
! [A2: set_a] : ( ord_less_eq_set_a @ A2 @ A2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_subset__refl) ).
thf(201,axiom,
( ord_less_eq_set_a
= ( ^ [A3: set_a,B3: set_a] :
! [T: a] :
( ( member_a @ T @ A3 )
=> ( member_a @ T @ B3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_subset__iff) ).
thf(204,axiom,
! [A2: set_a,B2: set_a] :
( ( A2 = B2 )
=> ( ord_less_eq_set_a @ B2 @ A2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_equalityD2) ).
thf(205,axiom,
! [A2: set_a,B2: set_a] :
( ( A2 = B2 )
=> ( ord_less_eq_set_a @ A2 @ B2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_equalityD1) ).
thf(206,axiom,
( ord_less_eq_set_a
= ( ^ [A3: set_a,B3: set_a] :
! [X3: a] :
( ( member_a @ X3 @ A3 )
=> ( member_a @ X3 @ B3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_subset__eq) ).
thf(209,axiom,
! [A2: set_a,B2: set_a] :
( ( A2 = B2 )
=> ~ ( ( ord_less_eq_set_a @ A2 @ B2 )
=> ~ ( ord_less_eq_set_a @ B2 @ A2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_equalityE) ).
thf(210,axiom,
! [A2: set_a,B2: set_a,C: a] :
( ( ord_less_eq_set_a @ A2 @ B2 )
=> ( ( member_a @ C @ A2 )
=> ( member_a @ C @ B2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_subsetD) ).
thf(213,axiom,
! [A2: set_a,B2: set_a,X: a] :
( ( ord_less_eq_set_a @ A2 @ B2 )
=> ( ( member_a @ X @ A2 )
=> ( member_a @ X @ B2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_in__mono) ).
thf(234,axiom,
! [A2: set_a,B2: set_a] :
( ( ord_less_eq_set_a @ A2 @ B2 )
=> ( ( ord_less_eq_set_a @ B2 @ A2 )
=> ( A2 = B2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_subset__antisym) ).
thf(235,axiom,
! [A2: set_a,B2: set_a] :
( ! [X4: a] :
( ( member_a @ X4 @ A2 )
=> ( member_a @ X4 @ B2 ) )
=> ( ord_less_eq_set_a @ A2 @ B2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_subsetI) ).
thf(246,axiom,
! [B2: set_a,A2: set_a] :
( ( finite_finite_a @ B2 )
=> ( ( ord_less_eq_set_a @ A2 @ B2 )
=> ( ord_less_eq_nat @ ( finite_card_a @ A2 ) @ ( finite_card_a @ B2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_card__mono) ).
thf(249,axiom,
( ( finite_finite_a @ carrier )
=> ( finite179568208od_a_a @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_fnt__carrier__fnt__rel) ).
thf(253,axiom,
! [A: nat,B: set_a,C: nat,D: set_a] :
( ( ord_le841160035_set_a @ ( produc1450889781_set_a @ A @ B ) @ ( produc1450889781_set_a @ C @ D ) )
= ( ( ord_less_eq_nat @ A @ C )
& ( ord_less_eq_set_a @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_Pair__le) ).
thf(254,axiom,
! [A: set_a,B: nat,C: set_a,D: nat] :
( ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ A @ B ) @ ( produc515611863_a_nat @ C @ D ) )
= ( ( ord_less_eq_set_a @ A @ C )
& ( ord_less_eq_nat @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_Pair__le) ).
thf(255,axiom,
! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( ord_le486764743_set_a @ ( produc1928581911_set_a @ A @ B ) @ ( produc1928581911_set_a @ C @ D ) )
= ( ( ord_less_eq_set_a @ A @ C )
& ( ord_less_eq_set_a @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_Pair__le) ).
thf(256,axiom,
! [A2: set_a] :
( ( ord_less_eq_set_a @ A2 @ bot_bot_set_a )
= ( A2 = bot_bot_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_subset__empty) ).
thf(257,axiom,
! [A2: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_empty__subsetI) ).
thf(259,axiom,
! [Z: a,Y: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ Y ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ Z ) @ relation ) )
=> ( ( prefer161218362good_a @ Z @ carrier @ relation )
= ( prefer161218362good_a @ Y @ carrier @ relation ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_same__at__least__as__equal) ).
thf(261,axiom,
! [Carrier: set_a,Relation: set_Product_prod_a_a,Y: a,X: a] :
( ( prefer719835986ence_a @ Carrier @ Relation )
=> ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ Y @ Carrier @ Relation ) @ ( prefer1676310729than_a @ X @ Carrier @ Relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X @ Carrier @ Relation ) @ ( prefer1676310729than_a @ Y @ Carrier @ Relation ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_rational__preference_Onbt__nest) ).
thf(262,axiom,
! [Carrier: set_a,Relation: set_Product_prod_a_a,X: a] :
( ( prefer719835986ence_a @ Carrier @ Relation )
=> ( ( member_a @ X @ Carrier )
=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X @ Carrier @ Relation ) @ Carrier ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_rational__preference_Onbt__subset__carrier) ).
thf(265,axiom,
! [Carrier: set_a,Relation: set_Product_prod_a_a,X: a,Y: a] :
( ( prefer719835986ence_a @ Carrier @ Relation )
=> ( ( member_a @ X @ Carrier )
=> ( ( member_a @ Y @ Carrier )
=> ( ( member_a @ X @ ( prefer1676310729than_a @ Y @ Carrier @ Relation ) )
| ( member_a @ Y @ ( prefer1676310729than_a @ X @ Carrier @ Relation ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_rational__preference_Oxy__in__eachothers__nbt) ).
thf(268,axiom,
! [Carrier: set_a,Relation: set_Product_prod_a_a,X: a,Y: a] :
( ( prefer719835986ence_a @ Carrier @ Relation )
=> ( ( finite_finite_a @ Carrier )
=> ( ( member_a @ X @ Carrier )
=> ( ( member_a @ Y @ Carrier )
=> ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X @ Carrier @ Relation ) @ ( prefer1676310729than_a @ X @ Carrier @ Relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X @ Carrier @ Relation ) @ ( prefer1676310729than_a @ X @ Carrier @ Relation ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_rational__preference_Onbt__subset) ).
thf(271,axiom,
! [Carrier: set_a,Relation: set_Product_prod_a_a,X: a,Y: a] :
( ( prefer719835986ence_a @ Carrier @ Relation )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ Relation )
=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ Y @ Carrier @ Relation ) @ ( prefer1676310729than_a @ X @ Carrier @ Relation ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_rational__preference_Ono__better__subset__pref) ).
thf(275,axiom,
! [Carrier: set_a,Relation: set_Product_prod_a_a,X: a] :
( ( prefer719835986ence_a @ Carrier @ Relation )
=> ( ( Carrier != bot_bot_set_a )
=> ( ( member_a @ X @ Carrier )
=> ( ( prefer1676310729than_a @ X @ Carrier @ Relation )
!= bot_bot_set_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_rational__preference_Ono__better__than__nonepty) ).
thf(278,axiom,
! [Carrier: set_a,Relation: set_Product_prod_a_a] :
( ( prefer719835986ence_a @ Carrier @ Relation )
=> ( ( finite_finite_a @ Carrier )
=> ! [X2: a] :
( ( member_a @ X2 @ Carrier )
=> ( finite_finite_a @ ( prefer1676310729than_a @ X2 @ Carrier @ Relation ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_rational__preference_Ofnt__carrier__fnt__nbt) ).
thf(326,axiom,
! [X: a,Y: a] :
( ( ( member_a @ X @ carrier )
& ( member_a @ Y @ carrier ) )
=> ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_strict__not__refl__weak) ).
thf(327,axiom,
! [X: a,Y: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
=> ( member_a @ X @ carrier ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_not__outside) ).
thf(328,axiom,
! [X: a,Y: a,Z: a] :
( ( ( member_a @ X @ carrier )
& ( member_a @ Y @ carrier )
& ( member_a @ Z @ carrier ) )
=> ( ( ( 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 @ Z ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ X ) @ relation ) )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ Y ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ Z ) @ relation ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_strict__is__neg__transitive) ).
thf(329,axiom,
! [X: a,Y: a,Z: a] :
( ( ( member_a @ X @ carrier )
& ( member_a @ Y @ carrier )
& ( member_a @ Z @ carrier ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ Z ) @ relation )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Z ) @ relation ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_weak__is__transitive) ).
thf(330,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/sandbox2/benchmark/theBenchmark.p',fact_24_indifferent__imp__weak__pref_I2_J) ).
thf(331,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/sandbox2/benchmark/theBenchmark.p',fact_23_indifferent__imp__weak__pref_I1_J) ).
thf(332,axiom,
! [X: a,Y: a,Z: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ Z ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ Y ) @ relation ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Z ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ X ) @ relation ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_indiff__trans) ).
thf(333,axiom,
! [X: a,Y: a,Z: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ Z ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ Y ) @ relation ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Z ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ X ) @ relation ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_strict__trans) ).
thf(334,axiom,
! [X: a,Y: a] :
( ( member_a @ X @ carrier )
=> ( ( member_a @ Y @ carrier )
=> ( ( X != Y )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_completeD) ).
thf(335,axiom,
! [X2: a] :
( ( member_a @ X2 @ carrier )
=> ! [Xa: a] :
( ( member_a @ Xa @ carrier )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X2 @ Xa ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ Xa @ X2 ) @ relation ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_compl) ).
thf(336,axiom,
refl_on_a @ carrier @ relation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_reflexivity) ).
thf(337,axiom,
! [X: a,Y: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
=> ( member_a @ Y @ ( prefer1676310729than_a @ Y @ carrier @ relation ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_worse__in__no__better) ).
thf(338,axiom,
! [X: a,Y: a] :
( ( member_a @ X @ carrier )
=> ( ( member_a @ Y @ carrier )
=> ( ( ( member_a @ X @ ( prefer1676310729than_a @ Y @ carrier @ relation ) )
& ( member_a @ Y @ ( prefer1676310729than_a @ X @ carrier @ relation ) ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_same__nbt__same__pref) ).
thf(339,axiom,
! [X2: a] :
( ( member_a @ X2 @ carrier )
=> ( finite_finite_a @ ( prefer1676310729than_a @ X2 @ carrier @ relation ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_fnt__carrier__fnt__nbt) ).
thf(340,axiom,
total_on_a @ carrier @ relation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_total) ).
thf(341,axiom,
! [X: a] :
( ( carrier != bot_bot_set_a )
=> ( ( member_a @ X @ carrier )
=> ( ( prefer1676310729than_a @ X @ carrier @ relation )
!= bot_bot_set_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_no__better__than__nonepty) ).
thf(342,axiom,
! [X: a,Y: a] :
( ( member_a @ X @ carrier )
=> ( ( member_a @ Y @ carrier )
=> ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ Y @ carrier @ relation ) @ ( prefer1676310729than_a @ X @ carrier @ relation ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_no__better__thansubset__rel) ).
thf(343,axiom,
! [X: a,Y: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ Y @ carrier @ relation ) @ ( prefer1676310729than_a @ X @ carrier @ relation ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_no__better__subset__pref) ).
thf(344,axiom,
! [X: a,Y: a] :
( ( finite_finite_a @ carrier )
=> ( ( member_a @ X @ carrier )
=> ( ( member_a @ Y @ carrier )
=> ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X @ carrier @ relation ) @ ( prefer1676310729than_a @ X @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X @ carrier @ relation ) @ ( prefer1676310729than_a @ X @ carrier @ relation ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_nbt__subset) ).
thf(345,axiom,
order_preorder_on_a @ carrier @ relation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_trans__refl) ).
thf(346,axiom,
prefer1292084992ence_a @ carrier @ relation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_preference__axioms) ).
thf(347,axiom,
finite_finite_a @ carrier,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7__092_060open_062finite_Acarrier_092_060close_062) ).
thf(348,axiom,
prefer719835986ence_a @ carrier @ relation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_rational__preference__axioms) ).
thf(349,axiom,
! [X: a] :
( ( member_a @ X @ carrier )
=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X @ carrier @ relation ) @ carrier ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_nbt__subset__carrier) ).
thf(350,axiom,
! [Y: a,X: a] :
( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ Y @ carrier @ relation ) @ ( prefer1676310729than_a @ X @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X @ carrier @ relation ) @ ( prefer1676310729than_a @ Y @ carrier @ relation ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_nbt__nest) ).
thf(351,axiom,
ord_less_eq_nat @ ( finite_card_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) ) @ ( finite_card_a @ ( prefer1676310729than_a @ y @ carrier @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__092_060open_062card_A_Ino__better__than_Ax_Acarrier_Arelation_J_A_092_060le_062_Acard_A_Ino__better__than_Ay_Acarrier_Arelation_J_092_060close_062) ).
thf(352,axiom,
! [X: a,Y: a] :
( ( member_a @ X @ carrier )
=> ( ( member_a @ Y @ carrier )
=> ( ( member_a @ X @ ( prefer1676310729than_a @ Y @ carrier @ relation ) )
| ( member_a @ Y @ ( prefer1676310729than_a @ X @ carrier @ relation ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_xy__in__eachothers__nbt) ).
thf(353,axiom,
member_a @ x @ carrier,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_assms_I1_J) ).
thf(354,axiom,
member_a @ y @ carrier,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_assms_I2_J) ).
thf(355,conjecture,
ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ y @ carrier @ relation ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(356,negated_conjecture,
( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ y @ carrier @ relation ) )
= $false ),
inference(negate_conjecture,[status(cth)],[355]) ).
thf(357,plain,
( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ y @ carrier @ relation ) )
= $false ),
inference(unfold_def,[status(thm)],[356]) ).
thf(358,plain,
( ( trans_a @ relation )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(359,plain,
( ( ! [A2: set_a] :
( ! [X4: a] :
~ ( member_a @ X4 @ A2 )
=> ( ord_less_eq_set_a @ A2 @ bot_bot_set_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(360,plain,
( ( ! [A: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(361,plain,
( ( ! [A: set_a] :
( ( ord_less_eq_set_a @ A @ bot_bot_set_a )
= ( A = bot_bot_set_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(362,plain,
( ( ! [A: set_a] :
( ( ord_less_eq_set_a @ A @ bot_bot_set_a )
=> ( A = bot_bot_set_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(363,plain,
( ( ! [A: nat,F2: set_a > nat,B: set_a,C: set_a] :
( ( ord_less_eq_nat @ A @ ( F2 @ B ) )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ! [X4: set_a,Y3: set_a] :
( ( ord_less_eq_set_a @ X4 @ Y3 )
=> ( ord_less_eq_nat @ ( F2 @ X4 ) @ ( F2 @ Y3 ) ) )
=> ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(364,plain,
( ( ! [A: set_a,F2: nat > set_a,B: nat,C: nat] :
( ( ord_less_eq_set_a @ A @ ( F2 @ B ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ! [X4: nat,Y3: nat] :
( ( ord_less_eq_nat @ X4 @ Y3 )
=> ( ord_less_eq_set_a @ ( F2 @ X4 ) @ ( F2 @ Y3 ) ) )
=> ( ord_less_eq_set_a @ A @ ( F2 @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(365,plain,
( ( ! [A: set_a,F2: set_a > set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ ( F2 @ B ) )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ! [X4: set_a,Y3: set_a] :
( ( ord_less_eq_set_a @ X4 @ Y3 )
=> ( ord_less_eq_set_a @ ( F2 @ X4 ) @ ( F2 @ Y3 ) ) )
=> ( ord_less_eq_set_a @ A @ ( F2 @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(366,plain,
( ( ! [A: nat,B: nat,F2: nat > set_a,C: set_a] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_set_a @ ( F2 @ B ) @ C )
=> ( ! [X4: nat,Y3: nat] :
( ( ord_less_eq_nat @ X4 @ Y3 )
=> ( ord_less_eq_set_a @ ( F2 @ X4 ) @ ( F2 @ Y3 ) ) )
=> ( ord_less_eq_set_a @ ( F2 @ A ) @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(367,plain,
( ( ! [A: set_a,B: set_a,F2: set_a > nat,C: nat] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_nat @ ( F2 @ B ) @ C )
=> ( ! [X4: set_a,Y3: set_a] :
( ( ord_less_eq_set_a @ X4 @ Y3 )
=> ( ord_less_eq_nat @ ( F2 @ X4 ) @ ( F2 @ Y3 ) ) )
=> ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(368,plain,
( ( ! [A: set_a,B: set_a,F2: set_a > set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ ( F2 @ B ) @ C )
=> ( ! [X4: set_a,Y3: set_a] :
( ( ord_less_eq_set_a @ X4 @ Y3 )
=> ( ord_less_eq_set_a @ ( F2 @ X4 ) @ ( F2 @ Y3 ) ) )
=> ( ord_less_eq_set_a @ ( F2 @ A ) @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(369,plain,
( ( ! [A: set_a,F2: nat > set_a,B: nat,C: nat] :
( ( A
= ( F2 @ B ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ! [X4: nat,Y3: nat] :
( ( ord_less_eq_nat @ X4 @ Y3 )
=> ( ord_less_eq_set_a @ ( F2 @ X4 ) @ ( F2 @ Y3 ) ) )
=> ( ord_less_eq_set_a @ A @ ( F2 @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(370,plain,
( ( ! [A: nat,F2: set_a > nat,B: set_a,C: set_a] :
( ( A
= ( F2 @ B ) )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ! [X4: set_a,Y3: set_a] :
( ( ord_less_eq_set_a @ X4 @ Y3 )
=> ( ord_less_eq_nat @ ( F2 @ X4 ) @ ( F2 @ Y3 ) ) )
=> ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(371,plain,
( ( ! [A: set_a,F2: set_a > set_a,B: set_a,C: set_a] :
( ( A
= ( F2 @ B ) )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ! [X4: set_a,Y3: set_a] :
( ( ord_less_eq_set_a @ X4 @ Y3 )
=> ( ord_less_eq_set_a @ ( F2 @ X4 ) @ ( F2 @ Y3 ) ) )
=> ( ord_less_eq_set_a @ A @ ( F2 @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(372,plain,
( ( ! [A: nat,B: nat,F2: nat > set_a,C: set_a] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( F2 @ B )
= C )
=> ( ! [X4: nat,Y3: nat] :
( ( ord_less_eq_nat @ X4 @ Y3 )
=> ( ord_less_eq_set_a @ ( F2 @ X4 ) @ ( F2 @ Y3 ) ) )
=> ( ord_less_eq_set_a @ ( F2 @ A ) @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(373,plain,
( ( ! [A: set_a,B: set_a,F2: set_a > nat,C: nat] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( F2 @ B )
= C )
=> ( ! [X4: set_a,Y3: set_a] :
( ( ord_less_eq_set_a @ X4 @ Y3 )
=> ( ord_less_eq_nat @ ( F2 @ X4 ) @ ( F2 @ Y3 ) ) )
=> ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(374,plain,
( ( ! [A: set_a,B: set_a,F2: set_a > set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( F2 @ B )
= C )
=> ( ! [X4: set_a,Y3: set_a] :
( ( ord_less_eq_set_a @ X4 @ Y3 )
=> ( ord_less_eq_set_a @ ( F2 @ X4 ) @ ( F2 @ Y3 ) ) )
=> ( ord_less_eq_set_a @ ( F2 @ A ) @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(375,plain,
( ( ( ^ [Y4: set_a,Z2: set_a] : ( Y4 = Z2 ) )
= ( ^ [X3: set_a,Y2: set_a] :
( ( ord_less_eq_set_a @ X3 @ Y2 )
& ( ord_less_eq_set_a @ Y2 @ X3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(376,plain,
( ( ! [X: set_a,Y: set_a] :
( ( ord_less_eq_set_a @ X @ Y )
=> ( ( ord_less_eq_set_a @ Y @ X )
=> ( X = Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(377,plain,
( ( ! [X: set_a,Y: set_a] :
( ( X = Y )
=> ( ord_less_eq_set_a @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(378,plain,
( ( ! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(379,plain,
( ( ! [Y: set_a,X: set_a] :
( ( ord_less_eq_set_a @ Y @ X )
=> ( ( ord_less_eq_set_a @ X @ Y )
= ( X = Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(380,plain,
( ( ( ^ [Y4: set_a,Z2: set_a] : ( Y4 = Z2 ) )
= ( ^ [A6: set_a,B8: set_a] :
( ( ord_less_eq_set_a @ A6 @ B8 )
& ( ord_less_eq_set_a @ B8 @ A6 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(381,plain,
( ( ! [A: set_a,B: set_a,C: set_a] :
( ( A = B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(382,plain,
( ( ! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_set_a @ A @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(383,plain,
( ( ! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(384,plain,
( ( ! [X: set_a,Y: set_a,Z: set_a] :
( ( ord_less_eq_set_a @ X @ Y )
=> ( ( ord_less_eq_set_a @ Y @ Z )
=> ( ord_less_eq_set_a @ X @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(385,plain,
( ( ! [A: set_a] : ( ord_less_eq_set_a @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(386,plain,
( ( ! [B: set_a,A: set_a,C: set_a] :
( ( ord_less_eq_set_a @ B @ A )
=> ( ( ord_less_eq_set_a @ C @ B )
=> ( ord_less_eq_set_a @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(387,plain,
( ( ( ^ [Y4: set_a,Z2: set_a] : ( Y4 = Z2 ) )
= ( ^ [A6: set_a,B8: set_a] :
( ( ord_less_eq_set_a @ B8 @ A6 )
& ( ord_less_eq_set_a @ A6 @ B8 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(388,plain,
( ( ! [B: set_a,A: set_a] :
( ( ord_less_eq_set_a @ B @ A )
=> ( ( ord_less_eq_set_a @ A @ B )
=> ( A = B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(389,plain,
( ( ! [X: set_a] : ( ord_less_eq_set_a @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(390,plain,
( ( ! [N: nat,A2: set_a] :
( ( ord_less_eq_nat @ N @ ( finite_card_a @ A2 ) )
=> ? [S2: set_a] :
( ( ord_less_eq_set_a @ S2 @ A2 )
& ( ( finite_card_a @ S2 )
= N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(391,plain,
( ( ! [N: nat,S: set_a] :
( ( ord_less_eq_nat @ N @ ( finite_card_a @ S ) )
=> ~ ! [T3: set_a] :
( ( ord_less_eq_set_a @ T3 @ S )
=> ( ( ( finite_card_a @ T3 )
= N )
=> ~ ( finite_finite_a @ T3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(392,plain,
( ( ! [B2: set_a,A2: set_a] :
( ( finite_finite_a @ B2 )
=> ( ( ord_less_eq_set_a @ A2 @ B2 )
=> ( ( ord_less_eq_nat @ ( finite_card_a @ B2 ) @ ( finite_card_a @ A2 ) )
=> ( A2 = B2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(393,plain,
( ( ! [F: set_a,C2: nat] :
( ! [G: set_a] :
( ( ord_less_eq_set_a @ G @ F )
=> ( ( finite_finite_a @ G )
=> ( ord_less_eq_nat @ ( finite_card_a @ G ) @ C2 ) ) )
=> ( ( finite_finite_a @ F )
& ( ord_less_eq_nat @ ( finite_card_a @ F ) @ C2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(394,plain,
( ( ! [A2: set_a,N: nat] :
( ~ ( finite_finite_a @ A2 )
=> ? [B4: set_a] :
( ( finite_finite_a @ B4 )
& ( ( finite_card_a @ B4 )
= N )
& ( ord_less_eq_set_a @ B4 @ A2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(395,plain,
( ( ! [B2: set_a,A2: set_a] :
( ( finite_finite_a @ B2 )
=> ( ( ord_less_eq_set_a @ A2 @ B2 )
=> ( ( ( finite_card_a @ A2 )
= ( finite_card_a @ B2 ) )
=> ( A2 = B2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(396,plain,
( ( ! [A2: set_set_a] :
( ( finite_finite_set_a @ A2 )
=> ( ( A2 != bot_bot_set_set_a )
=> ? [X4: set_a] :
( ( member_set_a @ X4 @ A2 )
& ! [Xa: set_a] :
( ( member_set_a @ Xa @ A2 )
=> ( ( ord_less_eq_set_a @ X4 @ Xa )
=> ( X4 = Xa ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(397,plain,
( ( ! [A2: set_set_a] :
( ( finite_finite_set_a @ A2 )
=> ( ( A2 != bot_bot_set_set_a )
=> ? [X4: set_a] :
( ( member_set_a @ X4 @ A2 )
& ! [Xa: set_a] :
( ( member_set_a @ Xa @ A2 )
=> ( ( ord_less_eq_set_a @ Xa @ X4 )
=> ( X4 = Xa ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(398,plain,
( ( ! [B2: set_a,A2: set_a] :
( ( finite_finite_a @ B2 )
=> ( ( ord_less_eq_set_a @ A2 @ B2 )
=> ( finite_finite_a @ A2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(399,plain,
( ( ! [S: set_a,T2: set_a] :
( ( ord_less_eq_set_a @ S @ T2 )
=> ( ~ ( finite_finite_a @ S )
=> ~ ( finite_finite_a @ T2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(400,plain,
( ( ! [A2: set_a,B2: set_a] :
( ( ord_less_eq_set_a @ A2 @ B2 )
=> ( ( finite_finite_a @ B2 )
=> ( finite_finite_a @ A2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(401,plain,
( ( ! [A2: set_set_a,A: set_a] :
( ( finite_finite_set_a @ A2 )
=> ( ( member_set_a @ A @ A2 )
=> ? [X4: set_a] :
( ( member_set_a @ X4 @ A2 )
& ( ord_less_eq_set_a @ X4 @ A )
& ! [Xa: set_a] :
( ( member_set_a @ Xa @ A2 )
=> ( ( ord_less_eq_set_a @ Xa @ X4 )
=> ( X4 = Xa ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(402,plain,
( ( ! [A2: set_set_a,A: set_a] :
( ( finite_finite_set_a @ A2 )
=> ( ( member_set_a @ A @ A2 )
=> ? [X4: set_a] :
( ( member_set_a @ X4 @ A2 )
& ( ord_less_eq_set_a @ A @ X4 )
& ! [Xa: set_a] :
( ( member_set_a @ Xa @ A2 )
=> ( ( ord_less_eq_set_a @ X4 @ Xa )
=> ( X4 = Xa ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(403,plain,
( ( ! [X: nat,X5: nat,Y: set_a,Y5: set_a] :
( ( ord_less_eq_nat @ X @ X5 )
=> ( ( ord_less_eq_set_a @ Y @ Y5 )
=> ( ord_le841160035_set_a @ ( produc1450889781_set_a @ X @ Y ) @ ( produc1450889781_set_a @ X5 @ Y5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(404,plain,
( ( ! [X: set_a,X5: set_a,Y: nat,Y5: nat] :
( ( ord_less_eq_set_a @ X @ X5 )
=> ( ( ord_less_eq_nat @ Y @ Y5 )
=> ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ X @ Y ) @ ( produc515611863_a_nat @ X5 @ Y5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(405,plain,
( ( ! [X: set_a,X5: set_a,Y: set_a,Y5: set_a] :
( ( ord_less_eq_set_a @ X @ X5 )
=> ( ( ord_less_eq_set_a @ Y @ Y5 )
=> ( ord_le486764743_set_a @ ( produc1928581911_set_a @ X @ Y ) @ ( produc1928581911_set_a @ X5 @ Y5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(406,plain,
( ( ! [P: a > $o,Q: a > $o] :
( ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) )
= ( ! [X3: a] :
( ( P @ X3 )
=> ( Q @ X3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(407,plain,
( ( ( ^ [Y4: set_a,Z2: set_a] : ( Y4 = Z2 ) )
= ( ^ [A3: set_a,B3: set_a] :
( ( ord_less_eq_set_a @ A3 @ B3 )
& ( ord_less_eq_set_a @ B3 @ A3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[197]) ).
thf(408,plain,
( ( ! [A2: set_a,B2: set_a,C2: set_a] :
( ( ord_less_eq_set_a @ A2 @ B2 )
=> ( ( ord_less_eq_set_a @ B2 @ C2 )
=> ( ord_less_eq_set_a @ A2 @ C2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[198]) ).
thf(409,plain,
( ( ! [P: a > $o,Q: a > $o] :
( ! [X4: a] :
( ( P @ X4 )
=> ( Q @ X4 ) )
=> ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(410,plain,
( ( ! [A2: set_a] : ( ord_less_eq_set_a @ A2 @ A2 ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(411,plain,
( ( ord_less_eq_set_a
= ( ^ [A3: set_a,B3: set_a] :
! [T: a] :
( ( member_a @ T @ A3 )
=> ( member_a @ T @ B3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(412,plain,
( ( ! [A2: set_a,B2: set_a] :
( ( A2 = B2 )
=> ( ord_less_eq_set_a @ B2 @ A2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[204]) ).
thf(413,plain,
( ( ! [A2: set_a,B2: set_a] :
( ( A2 = B2 )
=> ( ord_less_eq_set_a @ A2 @ B2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[205]) ).
thf(414,plain,
( ( ord_less_eq_set_a
= ( ^ [A3: set_a,B3: set_a] :
! [X3: a] :
( ( member_a @ X3 @ A3 )
=> ( member_a @ X3 @ B3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(415,plain,
( ( ! [A2: set_a,B2: set_a] :
( ( A2 = B2 )
=> ~ ( ( ord_less_eq_set_a @ A2 @ B2 )
=> ~ ( ord_less_eq_set_a @ B2 @ A2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(416,plain,
( ( ! [A2: set_a,B2: set_a,C: a] :
( ( ord_less_eq_set_a @ A2 @ B2 )
=> ( ( member_a @ C @ A2 )
=> ( member_a @ C @ B2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(417,plain,
( ( ! [A2: set_a,B2: set_a,X: a] :
( ( ord_less_eq_set_a @ A2 @ B2 )
=> ( ( member_a @ X @ A2 )
=> ( member_a @ X @ B2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[213]) ).
thf(418,plain,
( ( ! [A2: set_a,B2: set_a] :
( ( ord_less_eq_set_a @ A2 @ B2 )
=> ( ( ord_less_eq_set_a @ B2 @ A2 )
=> ( A2 = B2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(419,plain,
( ( ! [A2: set_a,B2: set_a] :
( ! [X4: a] :
( ( member_a @ X4 @ A2 )
=> ( member_a @ X4 @ B2 ) )
=> ( ord_less_eq_set_a @ A2 @ B2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(420,plain,
( ( ! [B2: set_a,A2: set_a] :
( ( finite_finite_a @ B2 )
=> ( ( ord_less_eq_set_a @ A2 @ B2 )
=> ( ord_less_eq_nat @ ( finite_card_a @ A2 ) @ ( finite_card_a @ B2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(421,plain,
( ( ( finite_finite_a @ carrier )
=> ( finite179568208od_a_a @ relation ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(422,plain,
( ( ! [A: nat,B: set_a,C: nat,D: set_a] :
( ( ord_le841160035_set_a @ ( produc1450889781_set_a @ A @ B ) @ ( produc1450889781_set_a @ C @ D ) )
= ( ( ord_less_eq_nat @ A @ C )
& ( ord_less_eq_set_a @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(423,plain,
( ( ! [A: set_a,B: nat,C: set_a,D: nat] :
( ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ A @ B ) @ ( produc515611863_a_nat @ C @ D ) )
= ( ( ord_less_eq_set_a @ A @ C )
& ( ord_less_eq_nat @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(424,plain,
( ( ! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( ord_le486764743_set_a @ ( produc1928581911_set_a @ A @ B ) @ ( produc1928581911_set_a @ C @ D ) )
= ( ( ord_less_eq_set_a @ A @ C )
& ( ord_less_eq_set_a @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255]) ).
thf(425,plain,
( ( ! [A2: set_a] :
( ( ord_less_eq_set_a @ A2 @ bot_bot_set_a )
= ( A2 = bot_bot_set_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[256]) ).
thf(426,plain,
( ( ! [A2: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A2 ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(427,plain,
( ( ! [Z: a,Y: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ Y ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ Z ) @ relation ) )
=> ( ( prefer161218362good_a @ Z @ carrier @ relation )
= ( prefer161218362good_a @ Y @ carrier @ relation ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259]) ).
thf(428,plain,
( ( ! [Carrier: set_a,Relation: set_Product_prod_a_a,Y: a,X: a] :
( ( prefer719835986ence_a @ Carrier @ Relation )
=> ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ Y @ Carrier @ Relation ) @ ( prefer1676310729than_a @ X @ Carrier @ Relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X @ Carrier @ Relation ) @ ( prefer1676310729than_a @ Y @ Carrier @ Relation ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(429,plain,
( ( ! [Carrier: set_a,Relation: set_Product_prod_a_a,X: a] :
( ( prefer719835986ence_a @ Carrier @ Relation )
=> ( ( member_a @ X @ Carrier )
=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X @ Carrier @ Relation ) @ Carrier ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(430,plain,
( ( ! [Carrier: set_a,Relation: set_Product_prod_a_a,X: a,Y: a] :
( ( prefer719835986ence_a @ Carrier @ Relation )
=> ( ( member_a @ X @ Carrier )
=> ( ( member_a @ Y @ Carrier )
=> ( ( member_a @ X @ ( prefer1676310729than_a @ Y @ Carrier @ Relation ) )
| ( member_a @ Y @ ( prefer1676310729than_a @ X @ Carrier @ Relation ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(431,plain,
( ( ! [Carrier: set_a,Relation: set_Product_prod_a_a,X: a,Y: a] :
( ( prefer719835986ence_a @ Carrier @ Relation )
=> ( ( finite_finite_a @ Carrier )
=> ( ( member_a @ X @ Carrier )
=> ( ( member_a @ Y @ Carrier )
=> ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X @ Carrier @ Relation ) @ ( prefer1676310729than_a @ X @ Carrier @ Relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X @ Carrier @ Relation ) @ ( prefer1676310729than_a @ X @ Carrier @ Relation ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(432,plain,
( ( ! [Carrier: set_a,Relation: set_Product_prod_a_a,X: a,Y: a] :
( ( prefer719835986ence_a @ Carrier @ Relation )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ Relation )
=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ Y @ Carrier @ Relation ) @ ( prefer1676310729than_a @ X @ Carrier @ Relation ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[271]) ).
thf(433,plain,
( ( ! [Carrier: set_a,Relation: set_Product_prod_a_a,X: a] :
( ( prefer719835986ence_a @ Carrier @ Relation )
=> ( ( Carrier != bot_bot_set_a )
=> ( ( member_a @ X @ Carrier )
=> ( ( prefer1676310729than_a @ X @ Carrier @ Relation )
!= bot_bot_set_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
thf(434,plain,
( ( ! [Carrier: set_a,Relation: set_Product_prod_a_a] :
( ( prefer719835986ence_a @ Carrier @ Relation )
=> ( ( finite_finite_a @ Carrier )
=> ! [X2: a] :
( ( member_a @ X2 @ Carrier )
=> ( finite_finite_a @ ( prefer1676310729than_a @ X2 @ Carrier @ Relation ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[278]) ).
thf(435,plain,
( ( ! [X: a,Y: a] :
( ( ( member_a @ X @ carrier )
& ( member_a @ Y @ carrier ) )
=> ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[326]) ).
thf(436,plain,
( ( ! [X: a,Y: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
=> ( member_a @ X @ carrier ) ) )
= $true ),
inference(unfold_def,[status(thm)],[327]) ).
thf(437,plain,
( ( ! [X: a,Y: a,Z: a] :
( ( ( member_a @ X @ carrier )
& ( member_a @ Y @ carrier )
& ( member_a @ Z @ carrier ) )
=> ( ( ( 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 @ Z ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ X ) @ relation ) )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ Y ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ Z ) @ relation ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[328]) ).
thf(438,plain,
( ( ! [X: a,Y: a,Z: a] :
( ( ( member_a @ X @ carrier )
& ( member_a @ Y @ carrier )
& ( member_a @ Z @ carrier ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ Z ) @ relation )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Z ) @ relation ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
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)],[330]) ).
thf(440,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)],[331]) ).
thf(441,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)],[332]) ).
thf(442,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)],[333]) ).
thf(443,plain,
( ( ! [X: a,Y: a] :
( ( member_a @ X @ carrier )
=> ( ( member_a @ Y @ carrier )
=> ( ( X != Y )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(444,plain,
( ( ! [X2: a] :
( ( member_a @ X2 @ carrier )
=> ! [Xa: a] :
( ( member_a @ Xa @ carrier )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X2 @ Xa ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ Xa @ X2 ) @ relation ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(445,plain,
( ( refl_on_a @ carrier @ relation )
= $true ),
inference(unfold_def,[status(thm)],[336]) ).
thf(446,plain,
( ( ! [X: a,Y: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
=> ( member_a @ Y @ ( prefer1676310729than_a @ Y @ carrier @ relation ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[337]) ).
thf(447,plain,
( ( ! [X: a,Y: a] :
( ( member_a @ X @ carrier )
=> ( ( member_a @ Y @ carrier )
=> ( ( ( member_a @ X @ ( prefer1676310729than_a @ Y @ carrier @ relation ) )
& ( member_a @ Y @ ( prefer1676310729than_a @ X @ carrier @ relation ) ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(448,plain,
( ( ! [X2: a] :
( ( member_a @ X2 @ carrier )
=> ( finite_finite_a @ ( prefer1676310729than_a @ X2 @ carrier @ relation ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[339]) ).
thf(449,plain,
( ( total_on_a @ carrier @ relation )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(450,plain,
( ( ! [X: a] :
( ( carrier != bot_bot_set_a )
=> ( ( member_a @ X @ carrier )
=> ( ( prefer1676310729than_a @ X @ carrier @ relation )
!= bot_bot_set_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[341]) ).
thf(451,plain,
( ( ! [X: a,Y: a] :
( ( member_a @ X @ carrier )
=> ( ( member_a @ Y @ carrier )
=> ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ Y @ carrier @ relation ) @ ( prefer1676310729than_a @ X @ carrier @ relation ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(452,plain,
( ( ! [X: a,Y: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ Y @ carrier @ relation ) @ ( prefer1676310729than_a @ X @ carrier @ relation ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(453,plain,
( ( ! [X: a,Y: a] :
( ( finite_finite_a @ carrier )
=> ( ( member_a @ X @ carrier )
=> ( ( member_a @ Y @ carrier )
=> ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X @ carrier @ relation ) @ ( prefer1676310729than_a @ X @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X @ carrier @ relation ) @ ( prefer1676310729than_a @ X @ carrier @ relation ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[344]) ).
thf(454,plain,
( ( order_preorder_on_a @ carrier @ relation )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(455,plain,
( ( prefer1292084992ence_a @ carrier @ relation )
= $true ),
inference(unfold_def,[status(thm)],[346]) ).
thf(456,plain,
( ( finite_finite_a @ carrier )
= $true ),
inference(unfold_def,[status(thm)],[347]) ).
thf(457,plain,
( ( prefer719835986ence_a @ carrier @ relation )
= $true ),
inference(unfold_def,[status(thm)],[348]) ).
thf(458,plain,
( ( ! [X: a] :
( ( member_a @ X @ carrier )
=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X @ carrier @ relation ) @ carrier ) ) )
= $true ),
inference(unfold_def,[status(thm)],[349]) ).
thf(459,plain,
( ( ! [Y: a,X: a] :
( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ Y @ carrier @ relation ) @ ( prefer1676310729than_a @ X @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X @ carrier @ relation ) @ ( prefer1676310729than_a @ Y @ carrier @ relation ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[350]) ).
thf(460,plain,
( ( ord_less_eq_nat @ ( finite_card_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) ) @ ( finite_card_a @ ( prefer1676310729than_a @ y @ carrier @ relation ) ) )
= $true ),
inference(unfold_def,[status(thm)],[351]) ).
thf(461,plain,
( ( ! [X: a,Y: a] :
( ( member_a @ X @ carrier )
=> ( ( member_a @ Y @ carrier )
=> ( ( member_a @ X @ ( prefer1676310729than_a @ Y @ carrier @ relation ) )
| ( member_a @ Y @ ( prefer1676310729than_a @ X @ carrier @ relation ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(462,plain,
( ( member_a @ x @ carrier )
= $true ),
inference(unfold_def,[status(thm)],[353]) ).
thf(463,plain,
( ( member_a @ y @ carrier )
= $true ),
inference(unfold_def,[status(thm)],[354]) ).
thf(464,plain,
( ( ~ ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ y @ carrier @ relation ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[357]) ).
thf(465,plain,
( ( member_a @ y @ carrier )
= $true ),
inference(copy,[status(thm)],[463]) ).
thf(466,plain,
( ( member_a @ x @ carrier )
= $true ),
inference(copy,[status(thm)],[462]) ).
thf(467,plain,
( ( ! [X: a,Y: a] :
( ( member_a @ X @ carrier )
=> ( ( member_a @ Y @ carrier )
=> ( ( member_a @ X @ ( prefer1676310729than_a @ Y @ carrier @ relation ) )
| ( member_a @ Y @ ( prefer1676310729than_a @ X @ carrier @ relation ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[461]) ).
thf(468,plain,
( ( ord_less_eq_nat @ ( finite_card_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) ) @ ( finite_card_a @ ( prefer1676310729than_a @ y @ carrier @ relation ) ) )
= $true ),
inference(copy,[status(thm)],[460]) ).
thf(469,plain,
( ( ! [Y: a,X: a] :
( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ Y @ carrier @ relation ) @ ( prefer1676310729than_a @ X @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X @ carrier @ relation ) @ ( prefer1676310729than_a @ Y @ carrier @ relation ) ) ) )
= $true ),
inference(copy,[status(thm)],[459]) ).
thf(470,plain,
( ( ! [X: a] :
( ( member_a @ X @ carrier )
=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X @ carrier @ relation ) @ carrier ) ) )
= $true ),
inference(copy,[status(thm)],[458]) ).
thf(471,plain,
( ( prefer719835986ence_a @ carrier @ relation )
= $true ),
inference(copy,[status(thm)],[457]) ).
thf(472,plain,
( ( finite_finite_a @ carrier )
= $true ),
inference(copy,[status(thm)],[456]) ).
thf(473,plain,
( ( prefer1292084992ence_a @ carrier @ relation )
= $true ),
inference(copy,[status(thm)],[455]) ).
thf(474,plain,
( ( order_preorder_on_a @ carrier @ relation )
= $true ),
inference(copy,[status(thm)],[454]) ).
thf(475,plain,
( ( ! [X: a,Y: a] :
( ( finite_finite_a @ carrier )
=> ( ( member_a @ X @ carrier )
=> ( ( member_a @ Y @ carrier )
=> ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X @ carrier @ relation ) @ ( prefer1676310729than_a @ X @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X @ carrier @ relation ) @ ( prefer1676310729than_a @ X @ carrier @ relation ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[453]) ).
thf(476,plain,
( ( ! [X: a,Y: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ Y @ carrier @ relation ) @ ( prefer1676310729than_a @ X @ carrier @ relation ) ) ) )
= $true ),
inference(copy,[status(thm)],[452]) ).
thf(477,plain,
( ( ! [X: a,Y: a] :
( ( member_a @ X @ carrier )
=> ( ( member_a @ Y @ carrier )
=> ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ Y @ carrier @ relation ) @ ( prefer1676310729than_a @ X @ carrier @ relation ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[451]) ).
thf(478,plain,
( ( ! [X: a] :
( ( carrier != bot_bot_set_a )
=> ( ( member_a @ X @ carrier )
=> ( ( prefer1676310729than_a @ X @ carrier @ relation )
!= bot_bot_set_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[450]) ).
thf(479,plain,
( ( total_on_a @ carrier @ relation )
= $true ),
inference(copy,[status(thm)],[449]) ).
thf(480,plain,
( ( ! [X2: a] :
( ( member_a @ X2 @ carrier )
=> ( finite_finite_a @ ( prefer1676310729than_a @ X2 @ carrier @ relation ) ) ) )
= $true ),
inference(copy,[status(thm)],[448]) ).
thf(481,plain,
( ( ! [X: a,Y: a] :
( ( member_a @ X @ carrier )
=> ( ( member_a @ Y @ carrier )
=> ( ( ( member_a @ X @ ( prefer1676310729than_a @ Y @ carrier @ relation ) )
& ( member_a @ Y @ ( prefer1676310729than_a @ X @ carrier @ relation ) ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[447]) ).
thf(482,plain,
( ( ! [X: a,Y: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
=> ( member_a @ Y @ ( prefer1676310729than_a @ Y @ carrier @ relation ) ) ) )
= $true ),
inference(copy,[status(thm)],[446]) ).
thf(483,plain,
( ( refl_on_a @ carrier @ relation )
= $true ),
inference(copy,[status(thm)],[445]) ).
thf(484,plain,
( ( ! [X2: a] :
( ( member_a @ X2 @ carrier )
=> ! [Xa: a] :
( ( member_a @ Xa @ carrier )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X2 @ Xa ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ Xa @ X2 ) @ relation ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[444]) ).
thf(485,plain,
( ( ! [X: a,Y: a] :
( ( member_a @ X @ carrier )
=> ( ( member_a @ Y @ carrier )
=> ( ( X != Y )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[443]) ).
thf(486,plain,
( ( ! [X: a,Y: a,Z: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ Z ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ Y ) @ relation ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Z ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ X ) @ relation ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[442]) ).
thf(487,plain,
( ( ! [X: a,Y: a,Z: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ Z ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ Y ) @ relation ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Z ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ X ) @ relation ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[441]) ).
thf(488,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)],[440]) ).
thf(489,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(490,plain,
( ( ! [X: a,Y: a,Z: a] :
( ( ( member_a @ X @ carrier )
& ( member_a @ Y @ carrier )
& ( member_a @ Z @ carrier ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ Z ) @ relation )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Z ) @ relation ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[438]) ).
thf(491,plain,
( ( ! [X: a,Y: a,Z: a] :
( ( ( member_a @ X @ carrier )
& ( member_a @ Y @ carrier )
& ( member_a @ Z @ carrier ) )
=> ( ( ( 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 @ Z ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ X ) @ relation ) )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ Y ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ Z ) @ relation ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[437]) ).
thf(492,plain,
( ( ! [X: a,Y: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
=> ( member_a @ X @ carrier ) ) )
= $true ),
inference(copy,[status(thm)],[436]) ).
thf(493,plain,
( ( ! [X: a,Y: a] :
( ( ( member_a @ X @ carrier )
& ( member_a @ Y @ carrier ) )
=> ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[435]) ).
thf(494,plain,
( ( ! [Carrier: set_a,Relation: set_Product_prod_a_a] :
( ( prefer719835986ence_a @ Carrier @ Relation )
=> ( ( finite_finite_a @ Carrier )
=> ! [X2: a] :
( ( member_a @ X2 @ Carrier )
=> ( finite_finite_a @ ( prefer1676310729than_a @ X2 @ Carrier @ Relation ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[434]) ).
thf(495,plain,
( ( ! [Carrier: set_a,Relation: set_Product_prod_a_a,X: a] :
( ( prefer719835986ence_a @ Carrier @ Relation )
=> ( ( Carrier != bot_bot_set_a )
=> ( ( member_a @ X @ Carrier )
=> ( ( prefer1676310729than_a @ X @ Carrier @ Relation )
!= bot_bot_set_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[433]) ).
thf(496,plain,
( ( ! [Carrier: set_a,Relation: set_Product_prod_a_a,X: a,Y: a] :
( ( prefer719835986ence_a @ Carrier @ Relation )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ Relation )
=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ Y @ Carrier @ Relation ) @ ( prefer1676310729than_a @ X @ Carrier @ Relation ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[432]) ).
thf(497,plain,
( ( ! [Carrier: set_a,Relation: set_Product_prod_a_a,X: a,Y: a] :
( ( prefer719835986ence_a @ Carrier @ Relation )
=> ( ( finite_finite_a @ Carrier )
=> ( ( member_a @ X @ Carrier )
=> ( ( member_a @ Y @ Carrier )
=> ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X @ Carrier @ Relation ) @ ( prefer1676310729than_a @ X @ Carrier @ Relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X @ Carrier @ Relation ) @ ( prefer1676310729than_a @ X @ Carrier @ Relation ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[431]) ).
thf(498,plain,
( ( ! [Carrier: set_a,Relation: set_Product_prod_a_a,X: a,Y: a] :
( ( prefer719835986ence_a @ Carrier @ Relation )
=> ( ( member_a @ X @ Carrier )
=> ( ( member_a @ Y @ Carrier )
=> ( ( member_a @ X @ ( prefer1676310729than_a @ Y @ Carrier @ Relation ) )
| ( member_a @ Y @ ( prefer1676310729than_a @ X @ Carrier @ Relation ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[430]) ).
thf(499,plain,
( ( ! [Carrier: set_a,Relation: set_Product_prod_a_a,X: a] :
( ( prefer719835986ence_a @ Carrier @ Relation )
=> ( ( member_a @ X @ Carrier )
=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X @ Carrier @ Relation ) @ Carrier ) ) ) )
= $true ),
inference(copy,[status(thm)],[429]) ).
thf(500,plain,
( ( ! [Carrier: set_a,Relation: set_Product_prod_a_a,Y: a,X: a] :
( ( prefer719835986ence_a @ Carrier @ Relation )
=> ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ Y @ Carrier @ Relation ) @ ( prefer1676310729than_a @ X @ Carrier @ Relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X @ Carrier @ Relation ) @ ( prefer1676310729than_a @ Y @ Carrier @ Relation ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[428]) ).
thf(501,plain,
( ( ! [Z: a,Y: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ Y ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ Z ) @ relation ) )
=> ( ( prefer161218362good_a @ Z @ carrier @ relation )
= ( prefer161218362good_a @ Y @ carrier @ relation ) ) ) )
= $true ),
inference(copy,[status(thm)],[427]) ).
thf(502,plain,
( ( ! [A2: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A2 ) )
= $true ),
inference(copy,[status(thm)],[426]) ).
thf(503,plain,
( ( ! [A2: set_a] :
( ( ord_less_eq_set_a @ A2 @ bot_bot_set_a )
= ( A2 = bot_bot_set_a ) ) )
= $true ),
inference(copy,[status(thm)],[425]) ).
thf(504,plain,
( ( ! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( ord_le486764743_set_a @ ( produc1928581911_set_a @ A @ B ) @ ( produc1928581911_set_a @ C @ D ) )
= ( ( ord_less_eq_set_a @ A @ C )
& ( ord_less_eq_set_a @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[424]) ).
thf(505,plain,
( ( ! [A: set_a,B: nat,C: set_a,D: nat] :
( ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ A @ B ) @ ( produc515611863_a_nat @ C @ D ) )
= ( ( ord_less_eq_set_a @ A @ C )
& ( ord_less_eq_nat @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[423]) ).
thf(506,plain,
( ( ! [A: nat,B: set_a,C: nat,D: set_a] :
( ( ord_le841160035_set_a @ ( produc1450889781_set_a @ A @ B ) @ ( produc1450889781_set_a @ C @ D ) )
= ( ( ord_less_eq_nat @ A @ C )
& ( ord_less_eq_set_a @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[422]) ).
thf(507,plain,
( ( ( finite_finite_a @ carrier )
=> ( finite179568208od_a_a @ relation ) )
= $true ),
inference(copy,[status(thm)],[421]) ).
thf(508,plain,
( ( ! [B2: set_a,A2: set_a] :
( ( finite_finite_a @ B2 )
=> ( ( ord_less_eq_set_a @ A2 @ B2 )
=> ( ord_less_eq_nat @ ( finite_card_a @ A2 ) @ ( finite_card_a @ B2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[420]) ).
thf(509,plain,
( ( ! [A2: set_a,B2: set_a] :
( ! [X4: a] :
( ( member_a @ X4 @ A2 )
=> ( member_a @ X4 @ B2 ) )
=> ( ord_less_eq_set_a @ A2 @ B2 ) ) )
= $true ),
inference(copy,[status(thm)],[419]) ).
thf(510,plain,
( ( ! [A2: set_a,B2: set_a] :
( ( ord_less_eq_set_a @ A2 @ B2 )
=> ( ( ord_less_eq_set_a @ B2 @ A2 )
=> ( A2 = B2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[418]) ).
thf(511,plain,
( ( ! [A2: set_a,B2: set_a,X: a] :
( ( ord_less_eq_set_a @ A2 @ B2 )
=> ( ( member_a @ X @ A2 )
=> ( member_a @ X @ B2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[417]) ).
thf(512,plain,
( ( ! [A2: set_a,B2: set_a,C: a] :
( ( ord_less_eq_set_a @ A2 @ B2 )
=> ( ( member_a @ C @ A2 )
=> ( member_a @ C @ B2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[416]) ).
thf(513,plain,
( ( ! [A2: set_a,B2: set_a] :
( ( A2 = B2 )
=> ~ ( ( ord_less_eq_set_a @ A2 @ B2 )
=> ~ ( ord_less_eq_set_a @ B2 @ A2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[415]) ).
thf(514,plain,
( ( ord_less_eq_set_a
= ( ^ [A3: set_a,B3: set_a] :
! [X3: a] :
( ( member_a @ X3 @ A3 )
=> ( member_a @ X3 @ B3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[414]) ).
thf(515,plain,
( ( ! [A2: set_a,B2: set_a] :
( ( A2 = B2 )
=> ( ord_less_eq_set_a @ A2 @ B2 ) ) )
= $true ),
inference(copy,[status(thm)],[413]) ).
thf(516,plain,
( ( ! [A2: set_a,B2: set_a] :
( ( A2 = B2 )
=> ( ord_less_eq_set_a @ B2 @ A2 ) ) )
= $true ),
inference(copy,[status(thm)],[412]) ).
thf(517,plain,
( ( ord_less_eq_set_a
= ( ^ [A3: set_a,B3: set_a] :
! [T: a] :
( ( member_a @ T @ A3 )
=> ( member_a @ T @ B3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[411]) ).
thf(518,plain,
( ( ! [A2: set_a] : ( ord_less_eq_set_a @ A2 @ A2 ) )
= $true ),
inference(copy,[status(thm)],[410]) ).
thf(519,plain,
( ( ! [P: a > $o,Q: a > $o] :
( ! [X4: a] :
( ( P @ X4 )
=> ( Q @ X4 ) )
=> ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ) )
= $true ),
inference(copy,[status(thm)],[409]) ).
thf(520,plain,
( ( ! [A2: set_a,B2: set_a,C2: set_a] :
( ( ord_less_eq_set_a @ A2 @ B2 )
=> ( ( ord_less_eq_set_a @ B2 @ C2 )
=> ( ord_less_eq_set_a @ A2 @ C2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[408]) ).
thf(521,plain,
( ( ( ^ [Y4: set_a,Z2: set_a] : ( Y4 = Z2 ) )
= ( ^ [A3: set_a,B3: set_a] :
( ( ord_less_eq_set_a @ A3 @ B3 )
& ( ord_less_eq_set_a @ B3 @ A3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[407]) ).
thf(522,plain,
( ( ! [P: a > $o,Q: a > $o] :
( ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) )
= ( ! [X3: a] :
( ( P @ X3 )
=> ( Q @ X3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[406]) ).
thf(523,plain,
( ( ! [X: set_a,X5: set_a,Y: set_a,Y5: set_a] :
( ( ord_less_eq_set_a @ X @ X5 )
=> ( ( ord_less_eq_set_a @ Y @ Y5 )
=> ( ord_le486764743_set_a @ ( produc1928581911_set_a @ X @ Y ) @ ( produc1928581911_set_a @ X5 @ Y5 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[405]) ).
thf(524,plain,
( ( ! [X: set_a,X5: set_a,Y: nat,Y5: nat] :
( ( ord_less_eq_set_a @ X @ X5 )
=> ( ( ord_less_eq_nat @ Y @ Y5 )
=> ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ X @ Y ) @ ( produc515611863_a_nat @ X5 @ Y5 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[404]) ).
thf(525,plain,
( ( ! [X: nat,X5: nat,Y: set_a,Y5: set_a] :
( ( ord_less_eq_nat @ X @ X5 )
=> ( ( ord_less_eq_set_a @ Y @ Y5 )
=> ( ord_le841160035_set_a @ ( produc1450889781_set_a @ X @ Y ) @ ( produc1450889781_set_a @ X5 @ Y5 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(526,plain,
( ( ! [A2: set_set_a,A: set_a] :
( ( finite_finite_set_a @ A2 )
=> ( ( member_set_a @ A @ A2 )
=> ? [X4: set_a] :
( ( member_set_a @ X4 @ A2 )
& ( ord_less_eq_set_a @ A @ X4 )
& ! [Xa: set_a] :
( ( member_set_a @ Xa @ A2 )
=> ( ( ord_less_eq_set_a @ X4 @ Xa )
=> ( X4 = Xa ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[402]) ).
thf(527,plain,
( ( ! [A2: set_set_a,A: set_a] :
( ( finite_finite_set_a @ A2 )
=> ( ( member_set_a @ A @ A2 )
=> ? [X4: set_a] :
( ( member_set_a @ X4 @ A2 )
& ( ord_less_eq_set_a @ X4 @ A )
& ! [Xa: set_a] :
( ( member_set_a @ Xa @ A2 )
=> ( ( ord_less_eq_set_a @ Xa @ X4 )
=> ( X4 = Xa ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[401]) ).
thf(528,plain,
( ( ! [A2: set_a,B2: set_a] :
( ( ord_less_eq_set_a @ A2 @ B2 )
=> ( ( finite_finite_a @ B2 )
=> ( finite_finite_a @ A2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[400]) ).
thf(529,plain,
( ( ! [S: set_a,T2: set_a] :
( ( ord_less_eq_set_a @ S @ T2 )
=> ( ~ ( finite_finite_a @ S )
=> ~ ( finite_finite_a @ T2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[399]) ).
thf(530,plain,
( ( ! [B2: set_a,A2: set_a] :
( ( finite_finite_a @ B2 )
=> ( ( ord_less_eq_set_a @ A2 @ B2 )
=> ( finite_finite_a @ A2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[398]) ).
thf(531,plain,
( ( ! [A2: set_set_a] :
( ( finite_finite_set_a @ A2 )
=> ( ( A2 != bot_bot_set_set_a )
=> ? [X4: set_a] :
( ( member_set_a @ X4 @ A2 )
& ! [Xa: set_a] :
( ( member_set_a @ Xa @ A2 )
=> ( ( ord_less_eq_set_a @ Xa @ X4 )
=> ( X4 = Xa ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[397]) ).
thf(532,plain,
( ( ! [A2: set_set_a] :
( ( finite_finite_set_a @ A2 )
=> ( ( A2 != bot_bot_set_set_a )
=> ? [X4: set_a] :
( ( member_set_a @ X4 @ A2 )
& ! [Xa: set_a] :
( ( member_set_a @ Xa @ A2 )
=> ( ( ord_less_eq_set_a @ X4 @ Xa )
=> ( X4 = Xa ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[396]) ).
thf(533,plain,
( ( ! [B2: set_a,A2: set_a] :
( ( finite_finite_a @ B2 )
=> ( ( ord_less_eq_set_a @ A2 @ B2 )
=> ( ( ( finite_card_a @ A2 )
= ( finite_card_a @ B2 ) )
=> ( A2 = B2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[395]) ).
thf(534,plain,
( ( ! [A2: set_a,N: nat] :
( ~ ( finite_finite_a @ A2 )
=> ? [B4: set_a] :
( ( finite_finite_a @ B4 )
& ( ( finite_card_a @ B4 )
= N )
& ( ord_less_eq_set_a @ B4 @ A2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[394]) ).
thf(535,plain,
( ( ! [F: set_a,C2: nat] :
( ! [G: set_a] :
( ( ord_less_eq_set_a @ G @ F )
=> ( ( finite_finite_a @ G )
=> ( ord_less_eq_nat @ ( finite_card_a @ G ) @ C2 ) ) )
=> ( ( finite_finite_a @ F )
& ( ord_less_eq_nat @ ( finite_card_a @ F ) @ C2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[393]) ).
thf(536,plain,
( ( ! [B2: set_a,A2: set_a] :
( ( finite_finite_a @ B2 )
=> ( ( ord_less_eq_set_a @ A2 @ B2 )
=> ( ( ord_less_eq_nat @ ( finite_card_a @ B2 ) @ ( finite_card_a @ A2 ) )
=> ( A2 = B2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[392]) ).
thf(537,plain,
( ( ! [N: nat,S: set_a] :
( ( ord_less_eq_nat @ N @ ( finite_card_a @ S ) )
=> ~ ! [T3: set_a] :
( ( ord_less_eq_set_a @ T3 @ S )
=> ( ( ( finite_card_a @ T3 )
= N )
=> ~ ( finite_finite_a @ T3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[391]) ).
thf(538,plain,
( ( ! [N: nat,A2: set_a] :
( ( ord_less_eq_nat @ N @ ( finite_card_a @ A2 ) )
=> ? [S2: set_a] :
( ( ord_less_eq_set_a @ S2 @ A2 )
& ( ( finite_card_a @ S2 )
= N ) ) ) )
= $true ),
inference(copy,[status(thm)],[390]) ).
thf(539,plain,
( ( ! [X: set_a] : ( ord_less_eq_set_a @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[389]) ).
thf(540,plain,
( ( ! [B: set_a,A: set_a] :
( ( ord_less_eq_set_a @ B @ A )
=> ( ( ord_less_eq_set_a @ A @ B )
=> ( A = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[388]) ).
thf(541,plain,
( ( ( ^ [Y4: set_a,Z2: set_a] : ( Y4 = Z2 ) )
= ( ^ [A6: set_a,B8: set_a] :
( ( ord_less_eq_set_a @ B8 @ A6 )
& ( ord_less_eq_set_a @ A6 @ B8 ) ) ) )
= $true ),
inference(copy,[status(thm)],[387]) ).
thf(542,plain,
( ( ! [B: set_a,A: set_a,C: set_a] :
( ( ord_less_eq_set_a @ B @ A )
=> ( ( ord_less_eq_set_a @ C @ B )
=> ( ord_less_eq_set_a @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[386]) ).
thf(543,plain,
( ( ! [A: set_a] : ( ord_less_eq_set_a @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[385]) ).
thf(544,plain,
( ( ! [X: set_a,Y: set_a,Z: set_a] :
( ( ord_less_eq_set_a @ X @ Y )
=> ( ( ord_less_eq_set_a @ Y @ Z )
=> ( ord_less_eq_set_a @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[384]) ).
thf(545,plain,
( ( ! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[383]) ).
thf(546,plain,
( ( ! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_set_a @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[382]) ).
thf(547,plain,
( ( ! [A: set_a,B: set_a,C: set_a] :
( ( A = B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[381]) ).
thf(548,plain,
( ( ( ^ [Y4: set_a,Z2: set_a] : ( Y4 = Z2 ) )
= ( ^ [A6: set_a,B8: set_a] :
( ( ord_less_eq_set_a @ A6 @ B8 )
& ( ord_less_eq_set_a @ B8 @ A6 ) ) ) )
= $true ),
inference(copy,[status(thm)],[380]) ).
thf(549,plain,
( ( ! [Y: set_a,X: set_a] :
( ( ord_less_eq_set_a @ Y @ X )
=> ( ( ord_less_eq_set_a @ X @ Y )
= ( X = Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[379]) ).
thf(550,plain,
( ( ! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[378]) ).
thf(551,plain,
( ( ! [X: set_a,Y: set_a] :
( ( X = Y )
=> ( ord_less_eq_set_a @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(552,plain,
( ( ! [X: set_a,Y: set_a] :
( ( ord_less_eq_set_a @ X @ Y )
=> ( ( ord_less_eq_set_a @ Y @ X )
=> ( X = Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[376]) ).
thf(553,plain,
( ( ( ^ [Y4: set_a,Z2: set_a] : ( Y4 = Z2 ) )
= ( ^ [X3: set_a,Y2: set_a] :
( ( ord_less_eq_set_a @ X3 @ Y2 )
& ( ord_less_eq_set_a @ Y2 @ X3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[375]) ).
thf(554,plain,
( ( ! [A: set_a,B: set_a,F2: set_a > set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( F2 @ B )
= C )
=> ( ! [X4: set_a,Y3: set_a] :
( ( ord_less_eq_set_a @ X4 @ Y3 )
=> ( ord_less_eq_set_a @ ( F2 @ X4 ) @ ( F2 @ Y3 ) ) )
=> ( ord_less_eq_set_a @ ( F2 @ A ) @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[374]) ).
thf(555,plain,
( ( ! [A: set_a,B: set_a,F2: set_a > nat,C: nat] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( F2 @ B )
= C )
=> ( ! [X4: set_a,Y3: set_a] :
( ( ord_less_eq_set_a @ X4 @ Y3 )
=> ( ord_less_eq_nat @ ( F2 @ X4 ) @ ( F2 @ Y3 ) ) )
=> ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(556,plain,
( ( ! [A: nat,B: nat,F2: nat > set_a,C: set_a] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( F2 @ B )
= C )
=> ( ! [X4: nat,Y3: nat] :
( ( ord_less_eq_nat @ X4 @ Y3 )
=> ( ord_less_eq_set_a @ ( F2 @ X4 ) @ ( F2 @ Y3 ) ) )
=> ( ord_less_eq_set_a @ ( F2 @ A ) @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(557,plain,
( ( ! [A: set_a,F2: set_a > set_a,B: set_a,C: set_a] :
( ( A
= ( F2 @ B ) )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ! [X4: set_a,Y3: set_a] :
( ( ord_less_eq_set_a @ X4 @ Y3 )
=> ( ord_less_eq_set_a @ ( F2 @ X4 ) @ ( F2 @ Y3 ) ) )
=> ( ord_less_eq_set_a @ A @ ( F2 @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(558,plain,
( ( ! [A: nat,F2: set_a > nat,B: set_a,C: set_a] :
( ( A
= ( F2 @ B ) )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ! [X4: set_a,Y3: set_a] :
( ( ord_less_eq_set_a @ X4 @ Y3 )
=> ( ord_less_eq_nat @ ( F2 @ X4 ) @ ( F2 @ Y3 ) ) )
=> ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(559,plain,
( ( ! [A: set_a,F2: nat > set_a,B: nat,C: nat] :
( ( A
= ( F2 @ B ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ! [X4: nat,Y3: nat] :
( ( ord_less_eq_nat @ X4 @ Y3 )
=> ( ord_less_eq_set_a @ ( F2 @ X4 ) @ ( F2 @ Y3 ) ) )
=> ( ord_less_eq_set_a @ A @ ( F2 @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(560,plain,
( ( ! [A: set_a,B: set_a,F2: set_a > set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ ( F2 @ B ) @ C )
=> ( ! [X4: set_a,Y3: set_a] :
( ( ord_less_eq_set_a @ X4 @ Y3 )
=> ( ord_less_eq_set_a @ ( F2 @ X4 ) @ ( F2 @ Y3 ) ) )
=> ( ord_less_eq_set_a @ ( F2 @ A ) @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(561,plain,
( ( ! [A: set_a,B: set_a,F2: set_a > nat,C: nat] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_nat @ ( F2 @ B ) @ C )
=> ( ! [X4: set_a,Y3: set_a] :
( ( ord_less_eq_set_a @ X4 @ Y3 )
=> ( ord_less_eq_nat @ ( F2 @ X4 ) @ ( F2 @ Y3 ) ) )
=> ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(562,plain,
( ( ! [A: nat,B: nat,F2: nat > set_a,C: set_a] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_set_a @ ( F2 @ B ) @ C )
=> ( ! [X4: nat,Y3: nat] :
( ( ord_less_eq_nat @ X4 @ Y3 )
=> ( ord_less_eq_set_a @ ( F2 @ X4 ) @ ( F2 @ Y3 ) ) )
=> ( ord_less_eq_set_a @ ( F2 @ A ) @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(563,plain,
( ( ! [A: set_a,F2: set_a > set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ ( F2 @ B ) )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ! [X4: set_a,Y3: set_a] :
( ( ord_less_eq_set_a @ X4 @ Y3 )
=> ( ord_less_eq_set_a @ ( F2 @ X4 ) @ ( F2 @ Y3 ) ) )
=> ( ord_less_eq_set_a @ A @ ( F2 @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[365]) ).
thf(564,plain,
( ( ! [A: set_a,F2: nat > set_a,B: nat,C: nat] :
( ( ord_less_eq_set_a @ A @ ( F2 @ B ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ! [X4: nat,Y3: nat] :
( ( ord_less_eq_nat @ X4 @ Y3 )
=> ( ord_less_eq_set_a @ ( F2 @ X4 ) @ ( F2 @ Y3 ) ) )
=> ( ord_less_eq_set_a @ A @ ( F2 @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(565,plain,
( ( ! [A: nat,F2: set_a > nat,B: set_a,C: set_a] :
( ( ord_less_eq_nat @ A @ ( F2 @ B ) )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ! [X4: set_a,Y3: set_a] :
( ( ord_less_eq_set_a @ X4 @ Y3 )
=> ( ord_less_eq_nat @ ( F2 @ X4 ) @ ( F2 @ Y3 ) ) )
=> ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(566,plain,
( ( ! [A: set_a] :
( ( ord_less_eq_set_a @ A @ bot_bot_set_a )
=> ( A = bot_bot_set_a ) ) )
= $true ),
inference(copy,[status(thm)],[362]) ).
thf(567,plain,
( ( ! [A: set_a] :
( ( ord_less_eq_set_a @ A @ bot_bot_set_a )
= ( A = bot_bot_set_a ) ) )
= $true ),
inference(copy,[status(thm)],[361]) ).
thf(568,plain,
( ( ! [A: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(569,plain,
( ( ! [A2: set_a] :
( ! [X4: a] :
~ ( member_a @ X4 @ A2 )
=> ( ord_less_eq_set_a @ A2 @ bot_bot_set_a ) ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(570,plain,
( ( trans_a @ relation )
= $true ),
inference(copy,[status(thm)],[358]) ).
thf(571,plain,
( ( ~ ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ y @ carrier @ relation ) ) )
= $true ),
inference(copy,[status(thm)],[464]) ).
thf(572,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)],[486]) ).
thf(573,plain,
( ( ! [SX0: set_a,SX1: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[510]) ).
thf(574,plain,
( ( ! [SX0: set_a,SX1: set_a,SX2: nat,SX3: nat] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ SX2 @ SX3 )
| ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SX0 @ SX2 ) @ ( produc515611863_a_nat @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[524]) ).
thf(575,plain,
( ( ! [SX0: set_a,SX1: set_Product_prod_a_a] :
( ~ ( prefer719835986ence_a @ SX0 @ SX1 )
| ~ ( finite_finite_a @ SX0 )
| ! [SX2: a] :
( ~ ( member_a @ SX2 @ SX0 )
| ( finite_finite_a @ ( prefer1676310729than_a @ SX2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[494]) ).
thf(576,plain,
( ( ! [SX0: set_set_a] :
( ~ ( finite_finite_set_a @ SX0 )
| ~ ( ( SX0 != bot_bot_set_set_a ) )
| ~ ! [SX1: set_a] :
~ ~ ( ~ ( member_set_a @ SX1 @ SX0 )
| ~ ! [SX2: set_a] :
( ~ ( member_set_a @ SX2 @ SX0 )
| ~ ( ord_less_eq_set_a @ SX2 @ SX1 )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[531]) ).
thf(577,plain,
( ( ! [SX0: set_a,SX1: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ( ( ord_less_eq_set_a @ SX1 @ SX0 )
= ( SX1 = SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[549]) ).
thf(578,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ( member_a @ SX0 @ carrier )
| ~ ( member_a @ SX1 @ carrier )
| ( member_a @ SX0 @ ( prefer1676310729than_a @ SX1 @ carrier @ relation ) )
| ( member_a @ SX1 @ ( prefer1676310729than_a @ SX0 @ carrier @ relation ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[467]) ).
thf(579,plain,
( ( ! [SX0: set_set_a,SX1: set_a] :
( ~ ( finite_finite_set_a @ SX0 )
| ~ ( member_set_a @ SX1 @ SX0 )
| ~ ! [SX2: set_a] :
~ ~ ( ~ ~ ( ~ ( member_set_a @ SX2 @ SX0 )
| ~ ( ord_less_eq_set_a @ SX2 @ SX1 ) )
| ~ ! [SX3: set_a] :
( ~ ( member_set_a @ SX3 @ SX0 )
| ~ ( ord_less_eq_set_a @ SX3 @ SX2 )
| ( SX2 = SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[527]) ).
thf(580,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 ) )
| ( ( prefer161218362good_a @ SX0 @ carrier @ relation )
= ( prefer161218362good_a @ SX1 @ carrier @ relation ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[501]) ).
thf(581,plain,
( ( ! [SX0: set_a,SX1: set_a,SX2: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ( SX1 != SX2 )
| ( ord_less_eq_set_a @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[546]) ).
thf(582,plain,
( ( ! [SX0: nat,SX1: nat,SX2: set_a,SX3: set_a] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ SX2 @ SX3 )
| ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SX0 @ SX2 ) @ ( produc1450889781_set_a @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[525]) ).
thf(583,plain,
( ( ! [SX0: set_a,SX1: set_a,SX2: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ SX2 @ SX0 )
| ( ord_less_eq_set_a @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[542]) ).
thf(584,plain,
( ( ! [SX0: set_a,SX1: set_a] :
( ( SX0 != SX1 )
| ( ord_less_eq_set_a @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[515]) ).
thf(585,plain,
( ( ! [SX0: nat,SX1: set_a,SX2: nat,SX3: set_a] :
( ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SX0 @ SX1 ) @ ( produc1450889781_set_a @ SX2 @ SX3 ) )
= ( ~ ( ~ ( ord_less_eq_nat @ SX0 @ SX2 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[506]) ).
thf(586,plain,
( ( ( ^ [SX0: set_a,SX1: set_a] : ( SX0 = SX1 ) )
= ( ^ [SX0: set_a,SX1: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SX1 @ SX0 )
| ~ ( ord_less_eq_set_a @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[541]) ).
thf(587,plain,
( ( ! [SX0: set_a,SX1: set_a,SX2: set_a,SX3: set_a] :
( ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SX0 @ SX1 ) @ ( produc1928581911_set_a @ SX2 @ SX3 ) )
= ( ~ ( ~ ( ord_less_eq_set_a @ SX0 @ SX2 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[504]) ).
thf(588,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ( finite_finite_a @ carrier )
| ~ ( member_a @ SX0 @ carrier )
| ~ ( member_a @ SX1 @ carrier )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SX0 @ carrier @ relation ) @ ( prefer1676310729than_a @ SX0 @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SX0 @ carrier @ relation ) @ ( prefer1676310729than_a @ SX0 @ carrier @ relation ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[475]) ).
thf(589,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)],[489]) ).
thf(590,plain,
( ( ! [SX0: set_a,SX1: set_a,SX2: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX2 )
| ( ord_less_eq_set_a @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[520]) ).
thf(591,plain,
( ( ! [SX0: set_a,SX1: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( finite_finite_a @ SX1 )
| ( finite_finite_a @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[528]) ).
thf(592,plain,
( ( ! [SX0: a] :
( ~ ( ( carrier != bot_bot_set_a ) )
| ~ ( member_a @ SX0 @ carrier )
| ( ( prefer1676310729than_a @ SX0 @ carrier @ relation )
!= bot_bot_set_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[478]) ).
thf(593,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ( member_a @ SX0 @ carrier )
| ~ ( member_a @ SX1 @ carrier )
| ~ ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SX1 @ carrier @ relation ) @ ( prefer1676310729than_a @ SX0 @ carrier @ relation ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX1 ) @ relation ) ) )
= $true ),
inference(unfold_def,[status(thm)],[477]) ).
thf(594,plain,
( ( ! [SX0: set_a,SX1: set_a,SX2: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX2 )
| ( ord_less_eq_set_a @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[544]) ).
thf(595,plain,
( ( ! [SX0: set_a,SX1: set_a] :
( ~ ( finite_finite_a @ SX0 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX0 )
| ( ord_less_eq_nat @ ( finite_card_a @ SX1 ) @ ( finite_card_a @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[508]) ).
thf(596,plain,
( ( ! [SX0: nat,SX1: set_a] :
( ~ ( ord_less_eq_nat @ SX0 @ ( finite_card_a @ SX1 ) )
| ~ ! [SX2: set_a] :
( ~ ( ord_less_eq_set_a @ SX2 @ SX1 )
| ( ( finite_card_a @ SX2 )
!= SX0 )
| ~ ( finite_finite_a @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[537]) ).
thf(597,plain,
( ( ! [SX0: set_set_a] :
( ~ ( finite_finite_set_a @ SX0 )
| ~ ( ( SX0 != bot_bot_set_set_a ) )
| ~ ! [SX1: set_a] :
~ ~ ( ~ ( member_set_a @ SX1 @ SX0 )
| ~ ! [SX2: set_a] :
( ~ ( member_set_a @ SX2 @ SX0 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX2 )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[532]) ).
thf(598,plain,
( ( ! [SX0: set_a,SX1: set_a] :
( ~ ( finite_finite_a @ SX0 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX0 )
| ( ( finite_card_a @ SX1 )
!= ( finite_card_a @ SX0 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[533]) ).
thf(599,plain,
( ( ! [SX0: nat,SX1: set_a] :
( ~ ( ord_less_eq_nat @ SX0 @ ( finite_card_a @ SX1 ) )
| ~ ! [SX2: set_a] :
~ ~ ( ~ ( ord_less_eq_set_a @ SX2 @ SX1 )
| ( ( finite_card_a @ SX2 )
!= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[538]) ).
thf(600,plain,
( ( ! [SX0: set_a,SX1: set_a,SX2: set_a] :
( ( SX0 != SX1 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX2 )
| ( ord_less_eq_set_a @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[547]) ).
thf(601,plain,
( ( ! [SX0: set_a,SX1: nat,SX2: set_a,SX3: nat] :
( ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SX0 @ SX1 ) @ ( produc515611863_a_nat @ SX2 @ SX3 ) )
= ( ~ ( ~ ( ord_less_eq_set_a @ SX0 @ SX2 )
| ~ ( ord_less_eq_nat @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[505]) ).
thf(602,plain,
( ( ! [SX0: set_a,SX1: set_Product_prod_a_a,SX2: a] :
( ~ ( prefer719835986ence_a @ SX0 @ SX1 )
| ~ ( ( SX0 != bot_bot_set_a ) )
| ~ ( member_a @ SX2 @ SX0 )
| ( ( prefer1676310729than_a @ SX2 @ SX0 @ SX1 )
!= bot_bot_set_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[495]) ).
thf(603,plain,
( ( ! [SX0: set_a,SX1: set_a] :
( ~ ( finite_finite_a @ SX0 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX0 )
| ( finite_finite_a @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[530]) ).
thf(604,plain,
( ( ord_less_eq_set_a
= ( ^ [SX0: set_a,SX1: set_a] :
! [SX2: a] :
( ~ ( member_a @ SX2 @ SX0 )
| ( member_a @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[517]) ).
thf(605,plain,
( ( ! [SX0: set_a,SX1: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[552]) ).
thf(606,plain,
( ( ~ ( finite_finite_a @ carrier )
| ( finite179568208od_a_a @ relation ) )
= $true ),
inference(unfold_def,[status(thm)],[507]) ).
thf(607,plain,
( ( ! [SX0: set_a,SX1: set_a] :
( ~ ! [SX2: a] :
( ~ ( member_a @ SX2 @ SX0 )
| ( member_a @ SX2 @ SX1 ) )
| ( ord_less_eq_set_a @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[509]) ).
thf(608,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX1 ) @ relation )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SX1 @ carrier @ relation ) @ ( prefer1676310729than_a @ SX0 @ carrier @ relation ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[476]) ).
thf(609,plain,
( ( ! [SX0: a] :
( ~ ( member_a @ SX0 @ carrier )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SX0 @ carrier @ relation ) @ carrier ) ) )
= $true ),
inference(unfold_def,[status(thm)],[470]) ).
thf(610,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ~ ( ~ ~ ( ~ ( member_a @ SX0 @ carrier )
| ~ ( member_a @ SX1 @ carrier ) )
| ~ ( member_a @ SX2 @ carrier ) )
| ~ ~ ( ~ ( 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 @ SX2 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX0 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX1 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX2 ) @ relation ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[491]) ).
thf(611,plain,
( ( ! [SX0: set_a,SX1: set_Product_prod_a_a,SX2: a,SX3: a] :
( ~ ( prefer719835986ence_a @ SX0 @ SX1 )
| ~ ( member_a @ SX2 @ SX0 )
| ~ ( member_a @ SX3 @ SX0 )
| ( member_a @ SX2 @ ( prefer1676310729than_a @ SX3 @ SX0 @ SX1 ) )
| ( member_a @ SX3 @ ( prefer1676310729than_a @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[498]) ).
thf(612,plain,
( ( ! [SX0: set_a,SX1: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX0 )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[540]) ).
thf(613,plain,
( ( ! [SX0: a] :
( ~ ( member_a @ SX0 @ carrier )
| ( finite_finite_a @ ( prefer1676310729than_a @ SX0 @ carrier @ relation ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[480]) ).
thf(614,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ~ ( ~ ~ ( ~ ( member_a @ SX0 @ carrier )
| ~ ( member_a @ SX1 @ carrier ) )
| ~ ( member_a @ SX2 @ carrier ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX1 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX2 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX2 ) @ relation ) ) )
= $true ),
inference(unfold_def,[status(thm)],[490]) ).
thf(615,plain,
( ( ! [SX0: set_a,SX1: set_a,SX2: a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( member_a @ SX2 @ SX0 )
| ( member_a @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[511]) ).
thf(616,plain,
( ( ! [SX0: set_a,SX1: set_Product_prod_a_a,SX2: a] :
( ~ ( prefer719835986ence_a @ SX0 @ SX1 )
| ~ ( member_a @ SX2 @ SX0 )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SX2 @ SX0 @ SX1 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[499]) ).
thf(617,plain,
( ( ! [SX0: set_a] :
( ~ ! [SX1: a] :
~ ( member_a @ SX1 @ SX0 )
| ( ord_less_eq_set_a @ SX0 @ bot_bot_set_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[569]) ).
thf(618,plain,
( ( ! [SX0: set_a,SX1: set_a,SX2: set_a > nat,SX3: nat] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ( ( SX2 @ SX1 )
!= SX3 )
| ~ ! [SX4: set_a,SX5: set_a] :
( ~ ( ord_less_eq_set_a @ SX4 @ SX5 )
| ( ord_less_eq_nat @ ( SX2 @ SX4 ) @ ( SX2 @ SX5 ) ) )
| ( ord_less_eq_nat @ ( SX2 @ SX0 ) @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[555]) ).
thf(619,plain,
( ( ! [SX0: a > $o,SX1: a > $o] :
( ~ ! [SX2: a] :
( ~ ( SX0 @ SX2 )
| ( SX1 @ SX2 ) )
| ( ord_less_eq_set_a @ ( collect_a @ SX0 ) @ ( collect_a @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[519]) ).
thf(620,plain,
( ( ( ^ [SX0: set_a,SX1: set_a] : ( SX0 = SX1 ) )
= ( ^ [SX0: set_a,SX1: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[548]) ).
thf(621,plain,
( ( ! [SX0: set_a,SX1: set_a > set_a,SX2: set_a,SX3: set_a] :
( ( SX0
!= ( SX1 @ SX2 ) )
| ~ ( ord_less_eq_set_a @ SX2 @ SX3 )
| ~ ! [SX4: set_a,SX5: set_a] :
( ~ ( ord_less_eq_set_a @ SX4 @ SX5 )
| ( ord_less_eq_set_a @ ( SX1 @ SX4 ) @ ( SX1 @ SX5 ) ) )
| ( ord_less_eq_set_a @ SX0 @ ( SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[557]) ).
thf(622,plain,
( ( ! [SX0: set_a,SX1: set_a] :
( ( SX0 != SX1 )
| ( ord_less_eq_set_a @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[516]) ).
thf(623,plain,
( ( ! [SX0: set_a,SX1: set_a] :
( ~ ( finite_finite_a @ SX0 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX0 )
| ~ ( ord_less_eq_nat @ ( finite_card_a @ SX0 ) @ ( finite_card_a @ SX1 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[536]) ).
thf(624,plain,
( ( ! [SX0: set_a,SX1: set_Product_prod_a_a,SX2: a,SX3: a] :
( ~ ( prefer719835986ence_a @ SX0 @ SX1 )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SX2 @ SX0 @ SX1 ) @ ( prefer1676310729than_a @ SX3 @ SX0 @ SX1 ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SX3 @ SX0 @ SX1 ) @ ( prefer1676310729than_a @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[500]) ).
thf(625,plain,
( ( ! [SX0: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ bot_bot_set_a )
| ( SX0 = bot_bot_set_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[566]) ).
thf(626,plain,
( ( ! [SX0: set_set_a,SX1: set_a] :
( ~ ( finite_finite_set_a @ SX0 )
| ~ ( member_set_a @ SX1 @ SX0 )
| ~ ! [SX2: set_a] :
~ ~ ( ~ ~ ( ~ ( member_set_a @ SX2 @ SX0 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX2 ) )
| ~ ! [SX3: set_a] :
( ~ ( member_set_a @ SX3 @ SX0 )
| ~ ( ord_less_eq_set_a @ SX2 @ SX3 )
| ( SX2 = SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[526]) ).
thf(627,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ~ ( ~ ( member_a @ SX0 @ carrier )
| ~ ( member_a @ SX1 @ carrier ) )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX0 ) @ relation ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX1 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX0 ) @ relation ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[493]) ).
thf(628,plain,
( ( ord_less_eq_set_a
= ( ^ [SX0: set_a,SX1: set_a] :
! [SX2: a] :
( ~ ( member_a @ SX2 @ SX0 )
| ( member_a @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[514]) ).
thf(629,plain,
( ( ! [SX0: set_a,SX1: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[545]) ).
thf(630,plain,
( ( ! [SX0: set_a,SX1: set_Product_prod_a_a,SX2: a,SX3: a] :
( ~ ( prefer719835986ence_a @ SX0 @ SX1 )
| ~ ( finite_finite_a @ SX0 )
| ~ ( member_a @ SX2 @ SX0 )
| ~ ( member_a @ SX3 @ SX0 )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SX2 @ SX0 @ SX1 ) @ ( prefer1676310729than_a @ SX2 @ SX0 @ SX1 ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SX2 @ SX0 @ SX1 ) @ ( prefer1676310729than_a @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[497]) ).
thf(631,plain,
( ( ! [SX0: set_a,SX1: set_a,SX2: set_a > nat,SX3: nat] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ ( SX2 @ SX1 ) @ SX3 )
| ~ ! [SX4: set_a,SX5: set_a] :
( ~ ( ord_less_eq_set_a @ SX4 @ SX5 )
| ( ord_less_eq_nat @ ( SX2 @ SX4 ) @ ( SX2 @ SX5 ) ) )
| ( ord_less_eq_nat @ ( SX2 @ SX0 ) @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[561]) ).
thf(632,plain,
( ( ! [SX0: set_a,SX1: set_a] :
( ( SX0 != SX1 )
| ~ ( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[513]) ).
thf(633,plain,
( ( ( ^ [SX0: set_a,SX1: set_a] : ( SX0 = SX1 ) )
= ( ^ [SX0: set_a,SX1: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[553]) ).
thf(634,plain,
( ( ! [SX0: set_a,SX1: set_a,SX2: set_a > set_a,SX3: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ ( SX2 @ SX1 ) @ SX3 )
| ~ ! [SX4: set_a,SX5: set_a] :
( ~ ( ord_less_eq_set_a @ SX4 @ SX5 )
| ( ord_less_eq_set_a @ ( SX2 @ SX4 ) @ ( SX2 @ SX5 ) ) )
| ( ord_less_eq_set_a @ ( SX2 @ SX0 ) @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[560]) ).
thf(635,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ( member_a @ SX0 @ carrier )
| ~ ( member_a @ SX1 @ carrier )
| ( ( ~ ( ~ ( member_a @ SX0 @ ( prefer1676310729than_a @ SX1 @ carrier @ relation ) )
| ~ ( member_a @ SX1 @ ( prefer1676310729than_a @ SX0 @ carrier @ relation ) ) ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX1 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX0 ) @ relation ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[481]) ).
thf(636,plain,
( ( ! [SX0: set_a,SX1: set_a,SX2: set_a,SX3: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ SX2 @ SX3 )
| ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SX0 @ SX2 ) @ ( produc1928581911_set_a @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[523]) ).
thf(637,plain,
( ( ! [SX0: set_a,SX1: set_a,SX2: a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( member_a @ SX2 @ SX0 )
| ( member_a @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[512]) ).
thf(638,plain,
( ( ! [SX0: set_a,SX1: set_Product_prod_a_a,SX2: a,SX3: a] :
( ~ ( prefer719835986ence_a @ SX0 @ SX1 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SX1 )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SX3 @ SX0 @ SX1 ) @ ( prefer1676310729than_a @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[496]) ).
thf(639,plain,
( ( ! [SX0: nat,SX1: set_a > nat,SX2: set_a,SX3: set_a] :
( ( SX0
!= ( SX1 @ SX2 ) )
| ~ ( ord_less_eq_set_a @ SX2 @ SX3 )
| ~ ! [SX4: set_a,SX5: set_a] :
( ~ ( ord_less_eq_set_a @ SX4 @ SX5 )
| ( ord_less_eq_nat @ ( SX1 @ SX4 ) @ ( SX1 @ SX5 ) ) )
| ( ord_less_eq_nat @ SX0 @ ( SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[558]) ).
thf(640,plain,
( ( ! [SX0: a > $o,SX1: a > $o] :
( ( ord_less_eq_set_a @ ( collect_a @ SX0 ) @ ( collect_a @ SX1 ) )
= ( ! [SX2: a] :
( ~ ( SX0 @ SX2 )
| ( SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[522]) ).
thf(641,plain,
( ( ! [SX0: set_a,SX1: nat] :
( ~ ! [SX2: set_a] :
( ~ ( ord_less_eq_set_a @ SX2 @ SX0 )
| ~ ( finite_finite_a @ SX2 )
| ( ord_less_eq_nat @ ( finite_card_a @ SX2 ) @ SX1 ) )
| ~ ( ~ ( finite_finite_a @ SX0 )
| ~ ( ord_less_eq_nat @ ( finite_card_a @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[535]) ).
thf(642,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ( member_a @ SX0 @ carrier )
| ~ ( member_a @ SX1 @ carrier )
| ~ ( ( SX0 != SX1 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX1 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX0 ) @ relation ) ) )
= $true ),
inference(unfold_def,[status(thm)],[485]) ).
thf(643,plain,
( ( ! [SX0: set_a,SX1: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ~ ( finite_finite_a @ SX0 )
| ~ ( finite_finite_a @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[529]) ).
thf(644,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat > set_a,SX3: set_a] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ( SX2 @ SX1 )
!= SX3 )
| ~ ! [SX4: nat,SX5: nat] :
( ~ ( ord_less_eq_nat @ SX4 @ SX5 )
| ( ord_less_eq_set_a @ ( SX2 @ SX4 ) @ ( SX2 @ SX5 ) ) )
| ( ord_less_eq_set_a @ ( SX2 @ SX0 ) @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[556]) ).
thf(645,plain,
( ( ! [SX0: set_a,SX1: set_a,SX2: set_a > set_a,SX3: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ( ( SX2 @ SX1 )
!= SX3 )
| ~ ! [SX4: set_a,SX5: set_a] :
( ~ ( ord_less_eq_set_a @ SX4 @ SX5 )
| ( ord_less_eq_set_a @ ( SX2 @ SX4 ) @ ( SX2 @ SX5 ) ) )
| ( ord_less_eq_set_a @ ( SX2 @ SX0 ) @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[554]) ).
thf(646,plain,
( ( ! [SX0: set_a,SX1: nat] :
( ~ ~ ( finite_finite_a @ SX0 )
| ~ ! [SX2: set_a] :
~ ~ ( ~ ~ ( ~ ( finite_finite_a @ SX2 )
| ( ( finite_card_a @ SX2 )
!= SX1 ) )
| ~ ( ord_less_eq_set_a @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[534]) ).
thf(647,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)],[487]) ).
thf(648,plain,
( ( ! [SX0: set_a,SX1: set_a] :
( ( SX0 != SX1 )
| ( ord_less_eq_set_a @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[551]) ).
thf(649,plain,
( ( ! [SX0: nat,SX1: set_a > nat,SX2: set_a,SX3: set_a] :
( ~ ( ord_less_eq_nat @ SX0 @ ( SX1 @ SX2 ) )
| ~ ( ord_less_eq_set_a @ SX2 @ SX3 )
| ~ ! [SX4: set_a,SX5: set_a] :
( ~ ( ord_less_eq_set_a @ SX4 @ SX5 )
| ( ord_less_eq_nat @ ( SX1 @ SX4 ) @ ( SX1 @ SX5 ) ) )
| ( ord_less_eq_nat @ SX0 @ ( SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[565]) ).
thf(650,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX1 ) @ relation )
| ( member_a @ SX0 @ carrier ) ) )
= $true ),
inference(unfold_def,[status(thm)],[492]) ).
thf(651,plain,
( ( ! [SX0: set_a,SX1: nat > set_a,SX2: nat,SX3: nat] :
( ~ ( ord_less_eq_set_a @ SX0 @ ( SX1 @ SX2 ) )
| ~ ( ord_less_eq_nat @ SX2 @ SX3 )
| ~ ! [SX4: nat,SX5: nat] :
( ~ ( ord_less_eq_nat @ SX4 @ SX5 )
| ( ord_less_eq_set_a @ ( SX1 @ SX4 ) @ ( SX1 @ SX5 ) ) )
| ( ord_less_eq_set_a @ SX0 @ ( SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[564]) ).
thf(652,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX1 ) @ relation )
| ( member_a @ SX1 @ ( prefer1676310729than_a @ SX1 @ carrier @ relation ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[482]) ).
thf(653,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat > set_a,SX3: set_a] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ ( SX2 @ SX1 ) @ SX3 )
| ~ ! [SX4: nat,SX5: nat] :
( ~ ( ord_less_eq_nat @ SX4 @ SX5 )
| ( ord_less_eq_set_a @ ( SX2 @ SX4 ) @ ( SX2 @ SX5 ) ) )
| ( ord_less_eq_set_a @ ( SX2 @ SX0 ) @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[562]) ).
thf(654,plain,
( ( ! [SX0: set_a,SX1: set_a,SX2: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX2 )
| ( ord_less_eq_set_a @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[550]) ).
thf(655,plain,
( ( ! [SX0: set_a,SX1: set_a > set_a,SX2: set_a,SX3: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ ( SX1 @ SX2 ) )
| ~ ( ord_less_eq_set_a @ SX2 @ SX3 )
| ~ ! [SX4: set_a,SX5: set_a] :
( ~ ( ord_less_eq_set_a @ SX4 @ SX5 )
| ( ord_less_eq_set_a @ ( SX1 @ SX4 ) @ ( SX1 @ SX5 ) ) )
| ( ord_less_eq_set_a @ SX0 @ ( SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[563]) ).
thf(656,plain,
( ( ( ^ [SX0: set_a,SX1: set_a] : ( SX0 = SX1 ) )
= ( ^ [SX0: set_a,SX1: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[521]) ).
thf(657,plain,
( ( ! [SX0: a] :
( ~ ( member_a @ SX0 @ carrier )
| ! [SX1: a] :
( ~ ( member_a @ SX1 @ carrier )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX1 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX0 ) @ relation ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[484]) ).
thf(658,plain,
( ( ! [SX0: set_a,SX1: nat > set_a,SX2: nat,SX3: nat] :
( ( SX0
!= ( SX1 @ SX2 ) )
| ~ ( ord_less_eq_nat @ SX2 @ SX3 )
| ~ ! [SX4: nat,SX5: nat] :
( ~ ( ord_less_eq_nat @ SX4 @ SX5 )
| ( ord_less_eq_set_a @ ( SX1 @ SX4 ) @ ( SX1 @ SX5 ) ) )
| ( ord_less_eq_set_a @ SX0 @ ( SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[559]) ).
thf(659,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)],[488]) ).
thf(660,plain,
! [SV1: a] :
( ( ! [SY285: a] :
( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV1 @ carrier @ relation ) @ ( prefer1676310729than_a @ SY285 @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SY285 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV1 @ carrier @ relation ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(661,plain,
! [SV2: set_a] :
( ( ord_less_eq_set_a @ bot_bot_set_a @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(662,plain,
! [SV3: set_a] :
( ( ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
= ( SV3 = bot_bot_set_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(663,plain,
! [SV4: set_a] :
( ( ord_less_eq_set_a @ SV4 @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(664,plain,
! [SV5: set_a] :
( ( ord_less_eq_set_a @ SV5 @ SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(665,plain,
! [SV6: set_a] :
( ( ord_less_eq_set_a @ SV6 @ SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(666,plain,
! [SV7: set_a] :
( ( ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
= ( SV7 = bot_bot_set_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(667,plain,
! [SV8: set_a] :
( ( ord_less_eq_set_a @ bot_bot_set_a @ SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(668,plain,
( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ y @ carrier @ relation ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(669,plain,
! [SV9: a] :
( ( ! [SY286: a,SY287: a] :
( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SY286 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY286 @ SV9 ) @ relation ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY286 @ SY287 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY287 @ SY286 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SY287 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY287 @ SV9 ) @ relation ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(670,plain,
! [SV10: set_a] :
( ( ! [SY288: set_a] :
( ~ ( ord_less_eq_set_a @ SV10 @ SY288 )
| ~ ( ord_less_eq_set_a @ SY288 @ SV10 )
| ( SV10 = SY288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(671,plain,
! [SV11: set_a] :
( ( ! [SY289: set_a,SY290: nat,SY291: nat] :
( ~ ( ord_less_eq_set_a @ SV11 @ SY289 )
| ~ ( ord_less_eq_nat @ SY290 @ SY291 )
| ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV11 @ SY290 ) @ ( produc515611863_a_nat @ SY289 @ SY291 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(672,plain,
! [SV12: set_a] :
( ( ! [SY292: set_Product_prod_a_a] :
( ~ ( prefer719835986ence_a @ SV12 @ SY292 )
| ~ ( finite_finite_a @ SV12 )
| ! [SY293: a] :
( ~ ( member_a @ SY293 @ SV12 )
| ( finite_finite_a @ ( prefer1676310729than_a @ SY293 @ SV12 @ SY292 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(673,plain,
! [SV13: set_set_a] :
( ( ~ ( finite_finite_set_a @ SV13 )
| ~ ( ( SV13 != bot_bot_set_set_a ) )
| ~ ! [SY294: set_a] :
~ ~ ( ~ ( member_set_a @ SY294 @ SV13 )
| ~ ! [SY295: set_a] :
( ~ ( member_set_a @ SY295 @ SV13 )
| ~ ( ord_less_eq_set_a @ SY295 @ SY294 )
| ( SY294 = SY295 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(674,plain,
! [SV14: set_a] :
( ( ! [SY296: set_a] :
( ~ ( ord_less_eq_set_a @ SV14 @ SY296 )
| ( ( ord_less_eq_set_a @ SY296 @ SV14 )
= ( SY296 = SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(675,plain,
! [SV15: a] :
( ( ! [SY297: a] :
( ~ ( member_a @ SV15 @ carrier )
| ~ ( member_a @ SY297 @ carrier )
| ( member_a @ SV15 @ ( prefer1676310729than_a @ SY297 @ carrier @ relation ) )
| ( member_a @ SY297 @ ( prefer1676310729than_a @ SV15 @ carrier @ relation ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(676,plain,
! [SV16: set_set_a] :
( ( ! [SY298: set_a] :
( ~ ( finite_finite_set_a @ SV16 )
| ~ ( member_set_a @ SY298 @ SV16 )
| ~ ! [SY299: set_a] :
~ ~ ( ~ ~ ( ~ ( member_set_a @ SY299 @ SV16 )
| ~ ( ord_less_eq_set_a @ SY299 @ SY298 ) )
| ~ ! [SY300: set_a] :
( ~ ( member_set_a @ SY300 @ SV16 )
| ~ ( ord_less_eq_set_a @ SY300 @ SY299 )
| ( SY299 = SY300 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[579]) ).
thf(677,plain,
! [SV17: a] :
( ( ! [SY301: a] :
( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV17 @ SY301 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY301 @ SV17 ) @ relation ) )
| ( ( prefer161218362good_a @ SV17 @ carrier @ relation )
= ( prefer161218362good_a @ SY301 @ carrier @ relation ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(678,plain,
! [SV18: set_a] :
( ( ! [SY302: set_a,SY303: set_a] :
( ~ ( ord_less_eq_set_a @ SV18 @ SY302 )
| ( SY302 != SY303 )
| ( ord_less_eq_set_a @ SV18 @ SY303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(679,plain,
! [SV19: nat] :
( ( ! [SY304: nat,SY305: set_a,SY306: set_a] :
( ~ ( ord_less_eq_nat @ SV19 @ SY304 )
| ~ ( ord_less_eq_set_a @ SY305 @ SY306 )
| ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV19 @ SY305 ) @ ( produc1450889781_set_a @ SY304 @ SY306 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(680,plain,
! [SV20: set_a] :
( ( ! [SY307: set_a,SY308: set_a] :
( ~ ( ord_less_eq_set_a @ SV20 @ SY307 )
| ~ ( ord_less_eq_set_a @ SY308 @ SV20 )
| ( ord_less_eq_set_a @ SY308 @ SY307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(681,plain,
! [SV21: set_a] :
( ( ! [SY309: set_a] :
( ( SV21 != SY309 )
| ( ord_less_eq_set_a @ SV21 @ SY309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(682,plain,
! [SV22: nat] :
( ( ! [SY310: set_a,SY311: nat,SY312: set_a] :
( ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV22 @ SY310 ) @ ( produc1450889781_set_a @ SY311 @ SY312 ) )
= ( ~ ( ~ ( ord_less_eq_nat @ SV22 @ SY311 )
| ~ ( ord_less_eq_set_a @ SY310 @ SY312 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(683,plain,
( ( ! [SV23: set_a] :
( ( ^ [SY313: set_a] : ( SV23 = SY313 ) )
= ( ^ [SY314: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SY314 @ SV23 )
| ~ ( ord_less_eq_set_a @ SV23 @ SY314 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[586]) ).
thf(684,plain,
( ( ( ^ [SX0: set_a,SX1: set_a] : ( SX0 = SX1 ) )
= ( ^ [SX0: set_a,SX1: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SX1 @ SX0 )
| ~ ( ord_less_eq_set_a @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[586]) ).
thf(685,plain,
! [SV24: set_a] :
( ( ! [SY315: set_a,SY316: set_a,SY317: set_a] :
( ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV24 @ SY315 ) @ ( produc1928581911_set_a @ SY316 @ SY317 ) )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV24 @ SY316 )
| ~ ( ord_less_eq_set_a @ SY315 @ SY317 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(686,plain,
! [SV25: a] :
( ( ! [SY318: a] :
( ~ ( finite_finite_a @ carrier )
| ~ ( member_a @ SV25 @ carrier )
| ~ ( member_a @ SY318 @ carrier )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV25 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV25 @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV25 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV25 @ carrier @ relation ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(687,plain,
! [SV26: a] :
( ( ! [SY319: a] :
( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV26 @ SY319 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY319 @ SV26 ) @ relation ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY319 @ SV26 ) @ relation ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(688,plain,
! [SV27: set_a] :
( ( ! [SY320: set_a,SY321: set_a] :
( ~ ( ord_less_eq_set_a @ SV27 @ SY320 )
| ~ ( ord_less_eq_set_a @ SY320 @ SY321 )
| ( ord_less_eq_set_a @ SV27 @ SY321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(689,plain,
! [SV28: set_a] :
( ( ! [SY322: set_a] :
( ~ ( ord_less_eq_set_a @ SV28 @ SY322 )
| ~ ( finite_finite_a @ SY322 )
| ( finite_finite_a @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(690,plain,
! [SV29: a] :
( ( ~ ( ( carrier != bot_bot_set_a ) )
| ~ ( member_a @ SV29 @ carrier )
| ( ( prefer1676310729than_a @ SV29 @ carrier @ relation )
!= bot_bot_set_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(691,plain,
! [SV30: a] :
( ( ! [SY323: a] :
( ~ ( member_a @ SV30 @ carrier )
| ~ ( member_a @ SY323 @ carrier )
| ~ ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SY323 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV30 @ carrier @ relation ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV30 @ SY323 ) @ relation ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(692,plain,
! [SV31: set_a] :
( ( ! [SY324: set_a,SY325: set_a] :
( ~ ( ord_less_eq_set_a @ SV31 @ SY324 )
| ~ ( ord_less_eq_set_a @ SY324 @ SY325 )
| ( ord_less_eq_set_a @ SV31 @ SY325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(693,plain,
! [SV32: set_a] :
( ( ! [SY326: set_a] :
( ~ ( finite_finite_a @ SV32 )
| ~ ( ord_less_eq_set_a @ SY326 @ SV32 )
| ( ord_less_eq_nat @ ( finite_card_a @ SY326 ) @ ( finite_card_a @ SV32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(694,plain,
! [SV33: nat] :
( ( ! [SY327: set_a] :
( ~ ( ord_less_eq_nat @ SV33 @ ( finite_card_a @ SY327 ) )
| ~ ! [SY328: set_a] :
( ~ ( ord_less_eq_set_a @ SY328 @ SY327 )
| ( ( finite_card_a @ SY328 )
!= SV33 )
| ~ ( finite_finite_a @ SY328 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(695,plain,
! [SV34: set_set_a] :
( ( ~ ( finite_finite_set_a @ SV34 )
| ~ ( ( SV34 != bot_bot_set_set_a ) )
| ~ ! [SY329: set_a] :
~ ~ ( ~ ( member_set_a @ SY329 @ SV34 )
| ~ ! [SY330: set_a] :
( ~ ( member_set_a @ SY330 @ SV34 )
| ~ ( ord_less_eq_set_a @ SY329 @ SY330 )
| ( SY329 = SY330 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(696,plain,
! [SV35: set_a] :
( ( ! [SY331: set_a] :
( ~ ( finite_finite_a @ SV35 )
| ~ ( ord_less_eq_set_a @ SY331 @ SV35 )
| ( ( finite_card_a @ SY331 )
!= ( finite_card_a @ SV35 ) )
| ( SY331 = SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(697,plain,
! [SV36: nat] :
( ( ! [SY332: set_a] :
( ~ ( ord_less_eq_nat @ SV36 @ ( finite_card_a @ SY332 ) )
| ~ ! [SY333: set_a] :
~ ~ ( ~ ( ord_less_eq_set_a @ SY333 @ SY332 )
| ( ( finite_card_a @ SY333 )
!= SV36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(698,plain,
! [SV37: set_a] :
( ( ! [SY334: set_a,SY335: set_a] :
( ( SV37 != SY334 )
| ~ ( ord_less_eq_set_a @ SY334 @ SY335 )
| ( ord_less_eq_set_a @ SV37 @ SY335 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(699,plain,
! [SV38: set_a] :
( ( ! [SY336: nat,SY337: set_a,SY338: nat] :
( ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV38 @ SY336 ) @ ( produc515611863_a_nat @ SY337 @ SY338 ) )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV38 @ SY337 )
| ~ ( ord_less_eq_nat @ SY336 @ SY338 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(700,plain,
! [SV39: set_a] :
( ( ! [SY339: set_Product_prod_a_a,SY340: a] :
( ~ ( prefer719835986ence_a @ SV39 @ SY339 )
| ~ ( ( SV39 != bot_bot_set_a ) )
| ~ ( member_a @ SY340 @ SV39 )
| ( ( prefer1676310729than_a @ SY340 @ SV39 @ SY339 )
!= bot_bot_set_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(701,plain,
! [SV40: set_a] :
( ( ! [SY341: set_a] :
( ~ ( finite_finite_a @ SV40 )
| ~ ( ord_less_eq_set_a @ SY341 @ SV40 )
| ( finite_finite_a @ SY341 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(702,plain,
( ( ! [SV41: set_a] :
( ( ord_less_eq_set_a @ SV41 )
= ( ^ [SY342: set_a] :
! [SY343: a] :
( ~ ( member_a @ SY343 @ SV41 )
| ( member_a @ SY343 @ SY342 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[604]) ).
thf(703,plain,
( ( ord_less_eq_set_a
= ( ^ [SX0: set_a,SX1: set_a] :
! [SX2: a] :
( ~ ( member_a @ SX2 @ SX0 )
| ( member_a @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[604]) ).
thf(704,plain,
! [SV42: set_a] :
( ( ! [SY344: set_a] :
( ~ ( ord_less_eq_set_a @ SV42 @ SY344 )
| ~ ( ord_less_eq_set_a @ SY344 @ SV42 )
| ( SV42 = SY344 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[605]) ).
thf(705,plain,
( ( ( ~ ( finite_finite_a @ carrier ) )
= $true )
| ( ( finite179568208od_a_a @ relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[606]) ).
thf(706,plain,
! [SV43: set_a] :
( ( ! [SY345: set_a] :
( ~ ! [SY346: a] :
( ~ ( member_a @ SY346 @ SV43 )
| ( member_a @ SY346 @ SY345 ) )
| ( ord_less_eq_set_a @ SV43 @ SY345 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(707,plain,
! [SV44: a] :
( ( ! [SY347: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV44 @ SY347 ) @ relation )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SY347 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV44 @ carrier @ relation ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(708,plain,
! [SV45: a] :
( ( ~ ( member_a @ SV45 @ carrier )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV45 @ carrier @ relation ) @ carrier ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(709,plain,
! [SV46: a] :
( ( ! [SY348: a,SY349: a] :
( ~ ~ ( ~ ~ ( ~ ( member_a @ SV46 @ carrier )
| ~ ( member_a @ SY348 @ carrier ) )
| ~ ( member_a @ SY349 @ carrier ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SY348 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY348 @ SV46 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SY349 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY349 @ SV46 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY349 @ SY348 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY348 @ SY349 ) @ relation ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(710,plain,
! [SV47: set_a] :
( ( ! [SY350: set_Product_prod_a_a,SY351: a,SY352: a] :
( ~ ( prefer719835986ence_a @ SV47 @ SY350 )
| ~ ( member_a @ SY351 @ SV47 )
| ~ ( member_a @ SY352 @ SV47 )
| ( member_a @ SY351 @ ( prefer1676310729than_a @ SY352 @ SV47 @ SY350 ) )
| ( member_a @ SY352 @ ( prefer1676310729than_a @ SY351 @ SV47 @ SY350 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(711,plain,
! [SV48: set_a] :
( ( ! [SY353: set_a] :
( ~ ( ord_less_eq_set_a @ SV48 @ SY353 )
| ~ ( ord_less_eq_set_a @ SY353 @ SV48 )
| ( SY353 = SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(712,plain,
! [SV49: a] :
( ( ~ ( member_a @ SV49 @ carrier )
| ( finite_finite_a @ ( prefer1676310729than_a @ SV49 @ carrier @ relation ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(713,plain,
! [SV50: a] :
( ( ! [SY354: a,SY355: a] :
( ~ ~ ( ~ ~ ( ~ ( member_a @ SV50 @ carrier )
| ~ ( member_a @ SY354 @ carrier ) )
| ~ ( member_a @ SY355 @ carrier ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV50 @ SY354 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY354 @ SY355 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV50 @ SY355 ) @ relation ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(714,plain,
! [SV51: set_a] :
( ( ! [SY356: set_a,SY357: a] :
( ~ ( ord_less_eq_set_a @ SV51 @ SY356 )
| ~ ( member_a @ SY357 @ SV51 )
| ( member_a @ SY357 @ SY356 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(715,plain,
! [SV52: set_a] :
( ( ! [SY358: set_Product_prod_a_a,SY359: a] :
( ~ ( prefer719835986ence_a @ SV52 @ SY358 )
| ~ ( member_a @ SY359 @ SV52 )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SY359 @ SV52 @ SY358 ) @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(716,plain,
! [SV53: set_a] :
( ( ~ ! [SY360: a] :
~ ( member_a @ SY360 @ SV53 )
| ( ord_less_eq_set_a @ SV53 @ bot_bot_set_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(717,plain,
! [SV54: set_a] :
( ( ! [SY361: set_a,SY362: set_a > nat,SY363: nat] :
( ~ ( ord_less_eq_set_a @ SV54 @ SY361 )
| ( ( SY362 @ SY361 )
!= SY363 )
| ~ ! [SX4: set_a,SX5: set_a] :
( ~ ( ord_less_eq_set_a @ SX4 @ SX5 )
| ( ord_less_eq_nat @ ( SY362 @ SX4 ) @ ( SY362 @ SX5 ) ) )
| ( ord_less_eq_nat @ ( SY362 @ SV54 ) @ SY363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(718,plain,
! [SV55: a > $o] :
( ( ! [SY366: a > $o] :
( ~ ! [SY367: a] :
( ~ ( SV55 @ SY367 )
| ( SY366 @ SY367 ) )
| ( ord_less_eq_set_a @ ( collect_a @ SV55 ) @ ( collect_a @ SY366 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(719,plain,
( ( ! [SV56: set_a] :
( ( ^ [SY368: set_a] : ( SV56 = SY368 ) )
= ( ^ [SY369: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SV56 @ SY369 )
| ~ ( ord_less_eq_set_a @ SY369 @ SV56 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[620]) ).
thf(720,plain,
( ( ( ^ [SX0: set_a,SX1: set_a] : ( SX0 = SX1 ) )
= ( ^ [SX0: set_a,SX1: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[620]) ).
thf(721,plain,
! [SV57: set_a] :
( ( ! [SY370: set_a > set_a,SY371: set_a,SY372: set_a] :
( ( SV57
!= ( SY370 @ SY371 ) )
| ~ ( ord_less_eq_set_a @ SY371 @ SY372 )
| ~ ! [SX4: set_a,SX5: set_a] :
( ~ ( ord_less_eq_set_a @ SX4 @ SX5 )
| ( ord_less_eq_set_a @ ( SY370 @ SX4 ) @ ( SY370 @ SX5 ) ) )
| ( ord_less_eq_set_a @ SV57 @ ( SY370 @ SY372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(722,plain,
! [SV58: set_a] :
( ( ! [SY375: set_a] :
( ( SV58 != SY375 )
| ( ord_less_eq_set_a @ SY375 @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(723,plain,
! [SV59: set_a] :
( ( ! [SY376: set_a] :
( ~ ( finite_finite_a @ SV59 )
| ~ ( ord_less_eq_set_a @ SY376 @ SV59 )
| ~ ( ord_less_eq_nat @ ( finite_card_a @ SV59 ) @ ( finite_card_a @ SY376 ) )
| ( SY376 = SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(724,plain,
! [SV60: set_a] :
( ( ! [SY377: set_Product_prod_a_a,SY378: a,SY379: a] :
( ~ ( prefer719835986ence_a @ SV60 @ SY377 )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SY378 @ SV60 @ SY377 ) @ ( prefer1676310729than_a @ SY379 @ SV60 @ SY377 ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SY379 @ SV60 @ SY377 ) @ ( prefer1676310729than_a @ SY378 @ SV60 @ SY377 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(725,plain,
! [SV61: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV61 @ bot_bot_set_a )
| ( SV61 = bot_bot_set_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(726,plain,
! [SV62: set_set_a] :
( ( ! [SY380: set_a] :
( ~ ( finite_finite_set_a @ SV62 )
| ~ ( member_set_a @ SY380 @ SV62 )
| ~ ! [SY381: set_a] :
~ ~ ( ~ ~ ( ~ ( member_set_a @ SY381 @ SV62 )
| ~ ( ord_less_eq_set_a @ SY380 @ SY381 ) )
| ~ ! [SY382: set_a] :
( ~ ( member_set_a @ SY382 @ SV62 )
| ~ ( ord_less_eq_set_a @ SY381 @ SY382 )
| ( SY381 = SY382 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(727,plain,
! [SV63: a] :
( ( ! [SY383: a] :
( ~ ~ ( ~ ( member_a @ SV63 @ carrier )
| ~ ( member_a @ SY383 @ carrier ) )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY383 @ SV63 ) @ relation ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SY383 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY383 @ SV63 ) @ relation ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(728,plain,
( ( ! [SV64: set_a] :
( ( ord_less_eq_set_a @ SV64 )
= ( ^ [SY384: set_a] :
! [SY385: a] :
( ~ ( member_a @ SY385 @ SV64 )
| ( member_a @ SY385 @ SY384 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[628]) ).
thf(729,plain,
( ( ord_less_eq_set_a
= ( ^ [SX0: set_a,SX1: set_a] :
! [SX2: a] :
( ~ ( member_a @ SX2 @ SX0 )
| ( member_a @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[628]) ).
thf(730,plain,
! [SV65: set_a] :
( ( ! [SY386: set_a] :
( ~ ( ord_less_eq_set_a @ SV65 @ SY386 )
| ~ ( ord_less_eq_set_a @ SY386 @ SV65 )
| ( SV65 = SY386 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(731,plain,
! [SV66: set_a] :
( ( ! [SY387: set_Product_prod_a_a,SY388: a,SY389: a] :
( ~ ( prefer719835986ence_a @ SV66 @ SY387 )
| ~ ( finite_finite_a @ SV66 )
| ~ ( member_a @ SY388 @ SV66 )
| ~ ( member_a @ SY389 @ SV66 )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SY388 @ SV66 @ SY387 ) @ ( prefer1676310729than_a @ SY388 @ SV66 @ SY387 ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SY388 @ SV66 @ SY387 ) @ ( prefer1676310729than_a @ SY388 @ SV66 @ SY387 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(732,plain,
! [SV67: set_a] :
( ( ! [SY390: set_a,SY391: set_a > nat,SY392: nat] :
( ~ ( ord_less_eq_set_a @ SV67 @ SY390 )
| ~ ( ord_less_eq_nat @ ( SY391 @ SY390 ) @ SY392 )
| ~ ! [SX4: set_a,SX5: set_a] :
( ~ ( ord_less_eq_set_a @ SX4 @ SX5 )
| ( ord_less_eq_nat @ ( SY391 @ SX4 ) @ ( SY391 @ SX5 ) ) )
| ( ord_less_eq_nat @ ( SY391 @ SV67 ) @ SY392 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(733,plain,
! [SV68: set_a] :
( ( ! [SY395: set_a] :
( ( SV68 != SY395 )
| ~ ( ~ ( ord_less_eq_set_a @ SV68 @ SY395 )
| ~ ( ord_less_eq_set_a @ SY395 @ SV68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(734,plain,
( ( ! [SV69: set_a] :
( ( ^ [SY396: set_a] : ( SV69 = SY396 ) )
= ( ^ [SY397: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SV69 @ SY397 )
| ~ ( ord_less_eq_set_a @ SY397 @ SV69 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[633]) ).
thf(735,plain,
( ( ( ^ [SX0: set_a,SX1: set_a] : ( SX0 = SX1 ) )
= ( ^ [SX0: set_a,SX1: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[633]) ).
thf(736,plain,
! [SV70: set_a] :
( ( ! [SY398: set_a,SY399: set_a > set_a,SY400: set_a] :
( ~ ( ord_less_eq_set_a @ SV70 @ SY398 )
| ~ ( ord_less_eq_set_a @ ( SY399 @ SY398 ) @ SY400 )
| ~ ! [SX4: set_a,SX5: set_a] :
( ~ ( ord_less_eq_set_a @ SX4 @ SX5 )
| ( ord_less_eq_set_a @ ( SY399 @ SX4 ) @ ( SY399 @ SX5 ) ) )
| ( ord_less_eq_set_a @ ( SY399 @ SV70 ) @ SY400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(737,plain,
! [SV71: a] :
( ( ! [SY403: a] :
( ~ ( member_a @ SV71 @ carrier )
| ~ ( member_a @ SY403 @ carrier )
| ( ( ~ ( ~ ( member_a @ SV71 @ ( prefer1676310729than_a @ SY403 @ carrier @ relation ) )
| ~ ( member_a @ SY403 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SY403 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY403 @ SV71 ) @ relation ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(738,plain,
! [SV72: set_a] :
( ( ! [SY404: set_a,SY405: set_a,SY406: set_a] :
( ~ ( ord_less_eq_set_a @ SV72 @ SY404 )
| ~ ( ord_less_eq_set_a @ SY405 @ SY406 )
| ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV72 @ SY405 ) @ ( produc1928581911_set_a @ SY404 @ SY406 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(739,plain,
! [SV73: set_a] :
( ( ! [SY407: set_a,SY408: a] :
( ~ ( ord_less_eq_set_a @ SV73 @ SY407 )
| ~ ( member_a @ SY408 @ SV73 )
| ( member_a @ SY408 @ SY407 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(740,plain,
! [SV74: set_a] :
( ( ! [SY409: set_Product_prod_a_a,SY410: a,SY411: a] :
( ~ ( prefer719835986ence_a @ SV74 @ SY409 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY410 @ SY411 ) @ SY409 )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SY411 @ SV74 @ SY409 ) @ ( prefer1676310729than_a @ SY410 @ SV74 @ SY409 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(741,plain,
! [SV75: nat] :
( ( ! [SY412: set_a > nat,SY413: set_a,SY414: set_a] :
( ( SV75
!= ( SY412 @ SY413 ) )
| ~ ( ord_less_eq_set_a @ SY413 @ SY414 )
| ~ ! [SX4: set_a,SX5: set_a] :
( ~ ( ord_less_eq_set_a @ SX4 @ SX5 )
| ( ord_less_eq_nat @ ( SY412 @ SX4 ) @ ( SY412 @ SX5 ) ) )
| ( ord_less_eq_nat @ SV75 @ ( SY412 @ SY414 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(742,plain,
! [SV76: a > $o] :
( ( ! [SY417: a > $o] :
( ( ord_less_eq_set_a @ ( collect_a @ SV76 ) @ ( collect_a @ SY417 ) )
= ( ! [SY418: a] :
( ~ ( SV76 @ SY418 )
| ( SY417 @ SY418 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(743,plain,
! [SV77: set_a] :
( ( ! [SY419: nat] :
( ~ ! [SY420: set_a] :
( ~ ( ord_less_eq_set_a @ SY420 @ SV77 )
| ~ ( finite_finite_a @ SY420 )
| ( ord_less_eq_nat @ ( finite_card_a @ SY420 ) @ SY419 ) )
| ~ ( ~ ( finite_finite_a @ SV77 )
| ~ ( ord_less_eq_nat @ ( finite_card_a @ SV77 ) @ SY419 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(744,plain,
! [SV78: a] :
( ( ! [SY421: a] :
( ~ ( member_a @ SV78 @ carrier )
| ~ ( member_a @ SY421 @ carrier )
| ~ ( ( SV78 != SY421 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV78 @ SY421 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY421 @ SV78 ) @ relation ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(745,plain,
! [SV79: set_a] :
( ( ! [SY422: set_a] :
( ~ ( ord_less_eq_set_a @ SV79 @ SY422 )
| ~ ~ ( finite_finite_a @ SV79 )
| ~ ( finite_finite_a @ SY422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(746,plain,
! [SV80: nat] :
( ( ! [SY423: nat,SY424: nat > set_a,SY425: set_a] :
( ~ ( ord_less_eq_nat @ SV80 @ SY423 )
| ( ( SY424 @ SY423 )
!= SY425 )
| ~ ! [SX4: nat,SX5: nat] :
( ~ ( ord_less_eq_nat @ SX4 @ SX5 )
| ( ord_less_eq_set_a @ ( SY424 @ SX4 ) @ ( SY424 @ SX5 ) ) )
| ( ord_less_eq_set_a @ ( SY424 @ SV80 ) @ SY425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(747,plain,
! [SV81: set_a] :
( ( ! [SY428: set_a,SY429: set_a > set_a,SY430: set_a] :
( ~ ( ord_less_eq_set_a @ SV81 @ SY428 )
| ( ( SY429 @ SY428 )
!= SY430 )
| ~ ! [SX4: set_a,SX5: set_a] :
( ~ ( ord_less_eq_set_a @ SX4 @ SX5 )
| ( ord_less_eq_set_a @ ( SY429 @ SX4 ) @ ( SY429 @ SX5 ) ) )
| ( ord_less_eq_set_a @ ( SY429 @ SV81 ) @ SY430 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(748,plain,
! [SV82: set_a] :
( ( ! [SY433: nat] :
( ~ ~ ( finite_finite_a @ SV82 )
| ~ ! [SY434: set_a] :
~ ~ ( ~ ~ ( ~ ( finite_finite_a @ SY434 )
| ( ( finite_card_a @ SY434 )
!= SY433 ) )
| ~ ( ord_less_eq_set_a @ SY434 @ SV82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(749,plain,
! [SV83: a] :
( ( ! [SY435: a,SY436: a] :
( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SY435 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY435 @ SV83 ) @ relation ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY435 @ SY436 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY436 @ SY435 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SY436 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY436 @ SV83 ) @ relation ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(750,plain,
! [SV84: set_a] :
( ( ! [SY437: set_a] :
( ( SV84 != SY437 )
| ( ord_less_eq_set_a @ SV84 @ SY437 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(751,plain,
! [SV85: nat] :
( ( ! [SY438: set_a > nat,SY439: set_a,SY440: set_a] :
( ~ ( ord_less_eq_nat @ SV85 @ ( SY438 @ SY439 ) )
| ~ ( ord_less_eq_set_a @ SY439 @ SY440 )
| ~ ! [SX4: set_a,SX5: set_a] :
( ~ ( ord_less_eq_set_a @ SX4 @ SX5 )
| ( ord_less_eq_nat @ ( SY438 @ SX4 ) @ ( SY438 @ SX5 ) ) )
| ( ord_less_eq_nat @ SV85 @ ( SY438 @ SY440 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(752,plain,
! [SV86: a] :
( ( ! [SY443: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV86 @ SY443 ) @ relation )
| ( member_a @ SV86 @ carrier ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(753,plain,
! [SV87: set_a] :
( ( ! [SY444: nat > set_a,SY445: nat,SY446: nat] :
( ~ ( ord_less_eq_set_a @ SV87 @ ( SY444 @ SY445 ) )
| ~ ( ord_less_eq_nat @ SY445 @ SY446 )
| ~ ! [SX4: nat,SX5: nat] :
( ~ ( ord_less_eq_nat @ SX4 @ SX5 )
| ( ord_less_eq_set_a @ ( SY444 @ SX4 ) @ ( SY444 @ SX5 ) ) )
| ( ord_less_eq_set_a @ SV87 @ ( SY444 @ SY446 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(754,plain,
! [SV88: a] :
( ( ! [SY449: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SY449 ) @ relation )
| ( member_a @ SY449 @ ( prefer1676310729than_a @ SY449 @ carrier @ relation ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(755,plain,
! [SV89: nat] :
( ( ! [SY450: nat,SY451: nat > set_a,SY452: set_a] :
( ~ ( ord_less_eq_nat @ SV89 @ SY450 )
| ~ ( ord_less_eq_set_a @ ( SY451 @ SY450 ) @ SY452 )
| ~ ! [SX4: nat,SX5: nat] :
( ~ ( ord_less_eq_nat @ SX4 @ SX5 )
| ( ord_less_eq_set_a @ ( SY451 @ SX4 ) @ ( SY451 @ SX5 ) ) )
| ( ord_less_eq_set_a @ ( SY451 @ SV89 ) @ SY452 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(756,plain,
! [SV90: set_a] :
( ( ! [SY455: set_a,SY456: set_a] :
( ~ ( ord_less_eq_set_a @ SV90 @ SY455 )
| ~ ( ord_less_eq_set_a @ SY455 @ SY456 )
| ( ord_less_eq_set_a @ SV90 @ SY456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(757,plain,
! [SV91: set_a] :
( ( ! [SY457: set_a > set_a,SY458: set_a,SY459: set_a] :
( ~ ( ord_less_eq_set_a @ SV91 @ ( SY457 @ SY458 ) )
| ~ ( ord_less_eq_set_a @ SY458 @ SY459 )
| ~ ! [SX4: set_a,SX5: set_a] :
( ~ ( ord_less_eq_set_a @ SX4 @ SX5 )
| ( ord_less_eq_set_a @ ( SY457 @ SX4 ) @ ( SY457 @ SX5 ) ) )
| ( ord_less_eq_set_a @ SV91 @ ( SY457 @ SY459 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(758,plain,
( ( ! [SV92: set_a] :
( ( ^ [SY462: set_a] : ( SV92 = SY462 ) )
= ( ^ [SY463: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SV92 @ SY463 )
| ~ ( ord_less_eq_set_a @ SY463 @ SV92 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[656]) ).
thf(759,plain,
( ( ( ^ [SX0: set_a,SX1: set_a] : ( SX0 = SX1 ) )
= ( ^ [SX0: set_a,SX1: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[656]) ).
thf(760,plain,
! [SV93: a] :
( ( ~ ( member_a @ SV93 @ carrier )
| ! [SY464: a] :
( ~ ( member_a @ SY464 @ carrier )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV93 @ SY464 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY464 @ SV93 ) @ relation ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(761,plain,
! [SV94: set_a] :
( ( ! [SY465: nat > set_a,SY466: nat,SY467: nat] :
( ( SV94
!= ( SY465 @ SY466 ) )
| ~ ( ord_less_eq_nat @ SY466 @ SY467 )
| ~ ! [SX4: nat,SX5: nat] :
( ~ ( ord_less_eq_nat @ SX4 @ SX5 )
| ( ord_less_eq_set_a @ ( SY465 @ SX4 ) @ ( SY465 @ SX5 ) ) )
| ( ord_less_eq_set_a @ SV94 @ ( SY465 @ SY467 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(762,plain,
! [SV95: a] :
( ( ! [SY470: a] :
( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV95 @ SY470 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY470 @ SV95 ) @ relation ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV95 @ SY470 ) @ relation ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(763,plain,
! [SV96: a,SV1: a] :
( ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV1 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV96 @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV96 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV1 @ carrier @ relation ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(764,plain,
! [SV3: set_a] :
( ( ~ ( ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
| ( SV3 = bot_bot_set_a ) )
| ~ ( ~ ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
| ( SV3 != bot_bot_set_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[662]) ).
thf(765,plain,
! [SV3: set_a] :
( ( ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
= ( SV3 = bot_bot_set_a ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[662]) ).
thf(766,plain,
! [SV7: set_a] :
( ( ~ ( ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
| ( SV7 = bot_bot_set_a ) )
| ~ ( ~ ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
| ( SV7 != bot_bot_set_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[666]) ).
thf(767,plain,
! [SV7: set_a] :
( ( ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
= ( SV7 = bot_bot_set_a ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[666]) ).
thf(768,plain,
! [SV97: a,SV9: a] :
( ( ! [SY471: a] :
( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV97 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV9 ) @ relation ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SY471 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SV97 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SY471 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SV9 ) @ relation ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(769,plain,
! [SV98: set_a,SV10: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV10 @ SV98 )
| ~ ( ord_less_eq_set_a @ SV98 @ SV10 )
| ( SV10 = SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(770,plain,
! [SV99: set_a,SV11: set_a] :
( ( ! [SY472: nat,SY473: nat] :
( ~ ( ord_less_eq_set_a @ SV11 @ SV99 )
| ~ ( ord_less_eq_nat @ SY472 @ SY473 )
| ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV11 @ SY472 ) @ ( produc515611863_a_nat @ SV99 @ SY473 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(771,plain,
! [SV100: set_Product_prod_a_a,SV12: set_a] :
( ( ~ ( prefer719835986ence_a @ SV12 @ SV100 )
| ~ ( finite_finite_a @ SV12 )
| ! [SY474: a] :
( ~ ( member_a @ SY474 @ SV12 )
| ( finite_finite_a @ ( prefer1676310729than_a @ SY474 @ SV12 @ SV100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(772,plain,
! [SV13: set_set_a] :
( ( ( ~ ( finite_finite_set_a @ SV13 ) )
= $true )
| ( ( ~ ( ( SV13 != bot_bot_set_set_a ) )
| ~ ! [SY294: set_a] :
~ ~ ( ~ ( member_set_a @ SY294 @ SV13 )
| ~ ! [SY295: set_a] :
( ~ ( member_set_a @ SY295 @ SV13 )
| ~ ( ord_less_eq_set_a @ SY295 @ SY294 )
| ( SY294 = SY295 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[673]) ).
thf(773,plain,
! [SV101: set_a,SV14: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV14 @ SV101 )
| ( ( ord_less_eq_set_a @ SV101 @ SV14 )
= ( SV101 = SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(774,plain,
! [SV102: a,SV15: a] :
( ( ~ ( member_a @ SV15 @ carrier )
| ~ ( member_a @ SV102 @ carrier )
| ( member_a @ SV15 @ ( prefer1676310729than_a @ SV102 @ carrier @ relation ) )
| ( member_a @ SV102 @ ( prefer1676310729than_a @ SV15 @ carrier @ relation ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(775,plain,
! [SV103: set_a,SV16: set_set_a] :
( ( ~ ( finite_finite_set_a @ SV16 )
| ~ ( member_set_a @ SV103 @ SV16 )
| ~ ! [SY475: set_a] :
~ ~ ( ~ ~ ( ~ ( member_set_a @ SY475 @ SV16 )
| ~ ( ord_less_eq_set_a @ SY475 @ SV103 ) )
| ~ ! [SY300: set_a] :
( ~ ( member_set_a @ SY300 @ SV16 )
| ~ ( ord_less_eq_set_a @ SY300 @ SY475 )
| ( SY475 = SY300 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(776,plain,
! [SV104: a,SV17: a] :
( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV17 @ SV104 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV104 @ SV17 ) @ relation ) )
| ( ( prefer161218362good_a @ SV17 @ carrier @ relation )
= ( prefer161218362good_a @ SV104 @ carrier @ relation ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(777,plain,
! [SV105: set_a,SV18: set_a] :
( ( ! [SY477: set_a] :
( ~ ( ord_less_eq_set_a @ SV18 @ SV105 )
| ( SV105 != SY477 )
| ( ord_less_eq_set_a @ SV18 @ SY477 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(778,plain,
! [SV106: nat,SV19: nat] :
( ( ! [SY478: set_a,SY479: set_a] :
( ~ ( ord_less_eq_nat @ SV19 @ SV106 )
| ~ ( ord_less_eq_set_a @ SY478 @ SY479 )
| ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV19 @ SY478 ) @ ( produc1450889781_set_a @ SV106 @ SY479 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(779,plain,
! [SV107: set_a,SV20: set_a] :
( ( ! [SY480: set_a] :
( ~ ( ord_less_eq_set_a @ SV20 @ SV107 )
| ~ ( ord_less_eq_set_a @ SY480 @ SV20 )
| ( ord_less_eq_set_a @ SY480 @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(780,plain,
! [SV108: set_a,SV21: set_a] :
( ( ( SV21 != SV108 )
| ( ord_less_eq_set_a @ SV21 @ SV108 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(781,plain,
! [SV109: set_a,SV22: nat] :
( ( ! [SY481: nat,SY482: set_a] :
( ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV22 @ SV109 ) @ ( produc1450889781_set_a @ SY481 @ SY482 ) )
= ( ~ ( ~ ( ord_less_eq_nat @ SV22 @ SY481 )
| ~ ( ord_less_eq_set_a @ SV109 @ SY482 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(782,plain,
! [SV110: set_a] :
( ( ( ^ [SY483: set_a] : ( SV110 = SY483 ) )
= ( ^ [SY484: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SY484 @ SV110 )
| ~ ( ord_less_eq_set_a @ SV110 @ SY484 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(783,plain,
! [SV111: set_a,SV24: set_a] :
( ( ! [SY485: set_a,SY486: set_a] :
( ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV24 @ SV111 ) @ ( produc1928581911_set_a @ SY485 @ SY486 ) )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV24 @ SY485 )
| ~ ( ord_less_eq_set_a @ SV111 @ SY486 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(784,plain,
! [SV112: a,SV25: a] :
( ( ~ ( finite_finite_a @ carrier )
| ~ ( member_a @ SV25 @ carrier )
| ~ ( member_a @ SV112 @ carrier )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV25 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV25 @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV25 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV25 @ carrier @ relation ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(785,plain,
! [SV113: a,SV26: a] :
( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV26 @ SV113 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV113 @ SV26 ) @ relation ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV113 @ SV26 ) @ relation ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(786,plain,
! [SV114: set_a,SV27: set_a] :
( ( ! [SY487: set_a] :
( ~ ( ord_less_eq_set_a @ SV27 @ SV114 )
| ~ ( ord_less_eq_set_a @ SV114 @ SY487 )
| ( ord_less_eq_set_a @ SV27 @ SY487 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(787,plain,
! [SV115: set_a,SV28: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV28 @ SV115 )
| ~ ( finite_finite_a @ SV115 )
| ( finite_finite_a @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(788,plain,
! [SV29: a] :
( ( ( ~ ( ( carrier != bot_bot_set_a ) ) )
= $true )
| ( ( ~ ( member_a @ SV29 @ carrier )
| ( ( prefer1676310729than_a @ SV29 @ carrier @ relation )
!= bot_bot_set_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[690]) ).
thf(789,plain,
! [SV116: a,SV30: a] :
( ( ~ ( member_a @ SV30 @ carrier )
| ~ ( member_a @ SV116 @ carrier )
| ~ ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV116 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV30 @ carrier @ relation ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV30 @ SV116 ) @ relation ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(790,plain,
! [SV117: set_a,SV31: set_a] :
( ( ! [SY488: set_a] :
( ~ ( ord_less_eq_set_a @ SV31 @ SV117 )
| ~ ( ord_less_eq_set_a @ SV117 @ SY488 )
| ( ord_less_eq_set_a @ SV31 @ SY488 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(791,plain,
! [SV118: set_a,SV32: set_a] :
( ( ~ ( finite_finite_a @ SV32 )
| ~ ( ord_less_eq_set_a @ SV118 @ SV32 )
| ( ord_less_eq_nat @ ( finite_card_a @ SV118 ) @ ( finite_card_a @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(792,plain,
! [SV119: set_a,SV33: nat] :
( ( ~ ( ord_less_eq_nat @ SV33 @ ( finite_card_a @ SV119 ) )
| ~ ! [SY489: set_a] :
( ~ ( ord_less_eq_set_a @ SY489 @ SV119 )
| ( ( finite_card_a @ SY489 )
!= SV33 )
| ~ ( finite_finite_a @ SY489 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(793,plain,
! [SV34: set_set_a] :
( ( ( ~ ( finite_finite_set_a @ SV34 ) )
= $true )
| ( ( ~ ( ( SV34 != bot_bot_set_set_a ) )
| ~ ! [SY329: set_a] :
~ ~ ( ~ ( member_set_a @ SY329 @ SV34 )
| ~ ! [SY330: set_a] :
( ~ ( member_set_a @ SY330 @ SV34 )
| ~ ( ord_less_eq_set_a @ SY329 @ SY330 )
| ( SY329 = SY330 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[695]) ).
thf(794,plain,
! [SV120: set_a,SV35: set_a] :
( ( ~ ( finite_finite_a @ SV35 )
| ~ ( ord_less_eq_set_a @ SV120 @ SV35 )
| ( ( finite_card_a @ SV120 )
!= ( finite_card_a @ SV35 ) )
| ( SV120 = SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(795,plain,
! [SV121: set_a,SV36: nat] :
( ( ~ ( ord_less_eq_nat @ SV36 @ ( finite_card_a @ SV121 ) )
| ~ ! [SY490: set_a] :
~ ~ ( ~ ( ord_less_eq_set_a @ SY490 @ SV121 )
| ( ( finite_card_a @ SY490 )
!= SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(796,plain,
! [SV122: set_a,SV37: set_a] :
( ( ! [SY491: set_a] :
( ( SV37 != SV122 )
| ~ ( ord_less_eq_set_a @ SV122 @ SY491 )
| ( ord_less_eq_set_a @ SV37 @ SY491 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(797,plain,
! [SV123: nat,SV38: set_a] :
( ( ! [SY492: set_a,SY493: nat] :
( ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV38 @ SV123 ) @ ( produc515611863_a_nat @ SY492 @ SY493 ) )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV38 @ SY492 )
| ~ ( ord_less_eq_nat @ SV123 @ SY493 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(798,plain,
! [SV124: set_Product_prod_a_a,SV39: set_a] :
( ( ! [SY494: a] :
( ~ ( prefer719835986ence_a @ SV39 @ SV124 )
| ~ ( ( SV39 != bot_bot_set_a ) )
| ~ ( member_a @ SY494 @ SV39 )
| ( ( prefer1676310729than_a @ SY494 @ SV39 @ SV124 )
!= bot_bot_set_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(799,plain,
! [SV125: set_a,SV40: set_a] :
( ( ~ ( finite_finite_a @ SV40 )
| ~ ( ord_less_eq_set_a @ SV125 @ SV40 )
| ( finite_finite_a @ SV125 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(800,plain,
! [SV126: set_a] :
( ( ( ord_less_eq_set_a @ SV126 )
= ( ^ [SY495: set_a] :
! [SY496: a] :
( ~ ( member_a @ SY496 @ SV126 )
| ( member_a @ SY496 @ SY495 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(801,plain,
! [SV127: set_a,SV42: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV42 @ SV127 )
| ~ ( ord_less_eq_set_a @ SV127 @ SV42 )
| ( SV42 = SV127 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(802,plain,
( ( ( finite_finite_a @ carrier )
= $false )
| ( ( finite179568208od_a_a @ relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[705]) ).
thf(803,plain,
! [SV128: set_a,SV43: set_a] :
( ( ~ ! [SY497: a] :
( ~ ( member_a @ SY497 @ SV43 )
| ( member_a @ SY497 @ SV128 ) )
| ( ord_less_eq_set_a @ SV43 @ SV128 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(804,plain,
! [SV129: a,SV44: a] :
( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV44 @ SV129 ) @ relation )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV129 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV44 @ carrier @ relation ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(805,plain,
! [SV45: a] :
( ( ( ~ ( member_a @ SV45 @ carrier ) )
= $true )
| ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV45 @ carrier @ relation ) @ carrier )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[708]) ).
thf(806,plain,
! [SV130: a,SV46: a] :
( ( ! [SY498: a] :
( ~ ~ ( ~ ~ ( ~ ( member_a @ SV46 @ carrier )
| ~ ( member_a @ SV130 @ carrier ) )
| ~ ( member_a @ SY498 @ carrier ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SY498 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY498 @ SV46 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY498 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SY498 ) @ relation ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(807,plain,
! [SV131: set_Product_prod_a_a,SV47: set_a] :
( ( ! [SY499: a,SY500: a] :
( ~ ( prefer719835986ence_a @ SV47 @ SV131 )
| ~ ( member_a @ SY499 @ SV47 )
| ~ ( member_a @ SY500 @ SV47 )
| ( member_a @ SY499 @ ( prefer1676310729than_a @ SY500 @ SV47 @ SV131 ) )
| ( member_a @ SY500 @ ( prefer1676310729than_a @ SY499 @ SV47 @ SV131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(808,plain,
! [SV132: set_a,SV48: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV48 @ SV132 )
| ~ ( ord_less_eq_set_a @ SV132 @ SV48 )
| ( SV132 = SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(809,plain,
! [SV49: a] :
( ( ( ~ ( member_a @ SV49 @ carrier ) )
= $true )
| ( ( finite_finite_a @ ( prefer1676310729than_a @ SV49 @ carrier @ relation ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[712]) ).
thf(810,plain,
! [SV133: a,SV50: a] :
( ( ! [SY501: a] :
( ~ ~ ( ~ ~ ( ~ ( member_a @ SV50 @ carrier )
| ~ ( member_a @ SV133 @ carrier ) )
| ~ ( member_a @ SY501 @ carrier ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV50 @ SV133 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV133 @ SY501 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV50 @ SY501 ) @ relation ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(811,plain,
! [SV134: set_a,SV51: set_a] :
( ( ! [SY502: a] :
( ~ ( ord_less_eq_set_a @ SV51 @ SV134 )
| ~ ( member_a @ SY502 @ SV51 )
| ( member_a @ SY502 @ SV134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(812,plain,
! [SV135: set_Product_prod_a_a,SV52: set_a] :
( ( ! [SY503: a] :
( ~ ( prefer719835986ence_a @ SV52 @ SV135 )
| ~ ( member_a @ SY503 @ SV52 )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SY503 @ SV52 @ SV135 ) @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(813,plain,
! [SV53: set_a] :
( ( ( ~ ! [SY360: a] :
~ ( member_a @ SY360 @ SV53 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV53 @ bot_bot_set_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[716]) ).
thf(814,plain,
! [SV136: set_a,SV54: set_a] :
( ( ! [SY504: set_a > nat,SY505: nat] :
( ~ ( ord_less_eq_set_a @ SV54 @ SV136 )
| ( ( SY504 @ SV136 )
!= SY505 )
| ~ ! [SX4: set_a,SX5: set_a] :
( ~ ( ord_less_eq_set_a @ SX4 @ SX5 )
| ( ord_less_eq_nat @ ( SY504 @ SX4 ) @ ( SY504 @ SX5 ) ) )
| ( ord_less_eq_nat @ ( SY504 @ SV54 ) @ SY505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(815,plain,
! [SV137: a > $o,SV55: a > $o] :
( ( ~ ! [SY508: a] :
( ~ ( SV55 @ SY508 )
| ( SV137 @ SY508 ) )
| ( ord_less_eq_set_a @ ( collect_a @ SV55 ) @ ( collect_a @ SV137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(816,plain,
! [SV138: set_a] :
( ( ( ^ [SY509: set_a] : ( SV138 = SY509 ) )
= ( ^ [SY510: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SV138 @ SY510 )
| ~ ( ord_less_eq_set_a @ SY510 @ SV138 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(817,plain,
! [SV139: set_a > set_a,SV57: set_a] :
( ( ! [SY511: set_a,SY512: set_a] :
( ( SV57
!= ( SV139 @ SY511 ) )
| ~ ( ord_less_eq_set_a @ SY511 @ SY512 )
| ~ ! [SY513: set_a,SY514: set_a] :
( ~ ( ord_less_eq_set_a @ SY513 @ SY514 )
| ( ord_less_eq_set_a @ ( SV139 @ SY513 ) @ ( SV139 @ SY514 ) ) )
| ( ord_less_eq_set_a @ SV57 @ ( SV139 @ SY512 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(818,plain,
! [SV140: set_a,SV58: set_a] :
( ( ( SV58 != SV140 )
| ( ord_less_eq_set_a @ SV140 @ SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(819,plain,
! [SV141: set_a,SV59: set_a] :
( ( ~ ( finite_finite_a @ SV59 )
| ~ ( ord_less_eq_set_a @ SV141 @ SV59 )
| ~ ( ord_less_eq_nat @ ( finite_card_a @ SV59 ) @ ( finite_card_a @ SV141 ) )
| ( SV141 = SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(820,plain,
! [SV142: set_Product_prod_a_a,SV60: set_a] :
( ( ! [SY515: a,SY516: a] :
( ~ ( prefer719835986ence_a @ SV60 @ SV142 )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SY515 @ SV60 @ SV142 ) @ ( prefer1676310729than_a @ SY516 @ SV60 @ SV142 ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SY516 @ SV60 @ SV142 ) @ ( prefer1676310729than_a @ SY515 @ SV60 @ SV142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(821,plain,
! [SV61: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV61 @ bot_bot_set_a ) )
= $true )
| ( ( SV61 = bot_bot_set_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[725]) ).
thf(822,plain,
! [SV143: set_a,SV62: set_set_a] :
( ( ~ ( finite_finite_set_a @ SV62 )
| ~ ( member_set_a @ SV143 @ SV62 )
| ~ ! [SY517: set_a] :
~ ~ ( ~ ~ ( ~ ( member_set_a @ SY517 @ SV62 )
| ~ ( ord_less_eq_set_a @ SV143 @ SY517 ) )
| ~ ! [SY382: set_a] :
( ~ ( member_set_a @ SY382 @ SV62 )
| ~ ( ord_less_eq_set_a @ SY517 @ SY382 )
| ( SY517 = SY382 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(823,plain,
! [SV144: a,SV63: a] :
( ( ~ ~ ( ~ ( member_a @ SV63 @ carrier )
| ~ ( member_a @ SV144 @ carrier ) )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(824,plain,
! [SV145: set_a] :
( ( ( ord_less_eq_set_a @ SV145 )
= ( ^ [SY519: set_a] :
! [SY520: a] :
( ~ ( member_a @ SY520 @ SV145 )
| ( member_a @ SY520 @ SY519 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(825,plain,
! [SV146: set_a,SV65: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV65 @ SV146 )
| ~ ( ord_less_eq_set_a @ SV146 @ SV65 )
| ( SV65 = SV146 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(826,plain,
! [SV147: set_Product_prod_a_a,SV66: set_a] :
( ( ! [SY521: a,SY522: a] :
( ~ ( prefer719835986ence_a @ SV66 @ SV147 )
| ~ ( finite_finite_a @ SV66 )
| ~ ( member_a @ SY521 @ SV66 )
| ~ ( member_a @ SY522 @ SV66 )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SY521 @ SV66 @ SV147 ) @ ( prefer1676310729than_a @ SY521 @ SV66 @ SV147 ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SY521 @ SV66 @ SV147 ) @ ( prefer1676310729than_a @ SY521 @ SV66 @ SV147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(827,plain,
! [SV148: set_a,SV67: set_a] :
( ( ! [SY523: set_a > nat,SY524: nat] :
( ~ ( ord_less_eq_set_a @ SV67 @ SV148 )
| ~ ( ord_less_eq_nat @ ( SY523 @ SV148 ) @ SY524 )
| ~ ! [SX4: set_a,SX5: set_a] :
( ~ ( ord_less_eq_set_a @ SX4 @ SX5 )
| ( ord_less_eq_nat @ ( SY523 @ SX4 ) @ ( SY523 @ SX5 ) ) )
| ( ord_less_eq_nat @ ( SY523 @ SV67 ) @ SY524 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(828,plain,
! [SV149: set_a,SV68: set_a] :
( ( ( SV68 != SV149 )
| ~ ( ~ ( ord_less_eq_set_a @ SV68 @ SV149 )
| ~ ( ord_less_eq_set_a @ SV149 @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(829,plain,
! [SV150: set_a] :
( ( ( ^ [SY527: set_a] : ( SV150 = SY527 ) )
= ( ^ [SY528: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SV150 @ SY528 )
| ~ ( ord_less_eq_set_a @ SY528 @ SV150 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(830,plain,
! [SV151: set_a,SV70: set_a] :
( ( ! [SY529: set_a > set_a,SY530: set_a] :
( ~ ( ord_less_eq_set_a @ SV70 @ SV151 )
| ~ ( ord_less_eq_set_a @ ( SY529 @ SV151 ) @ SY530 )
| ~ ! [SX4: set_a,SX5: set_a] :
( ~ ( ord_less_eq_set_a @ SX4 @ SX5 )
| ( ord_less_eq_set_a @ ( SY529 @ SX4 ) @ ( SY529 @ SX5 ) ) )
| ( ord_less_eq_set_a @ ( SY529 @ SV70 ) @ SY530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(831,plain,
! [SV152: a,SV71: a] :
( ( ~ ( member_a @ SV71 @ carrier )
| ~ ( member_a @ SV152 @ carrier )
| ( ( ~ ( ~ ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
| ~ ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(832,plain,
! [SV153: set_a,SV72: set_a] :
( ( ! [SY533: set_a,SY534: set_a] :
( ~ ( ord_less_eq_set_a @ SV72 @ SV153 )
| ~ ( ord_less_eq_set_a @ SY533 @ SY534 )
| ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV72 @ SY533 ) @ ( produc1928581911_set_a @ SV153 @ SY534 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(833,plain,
! [SV154: set_a,SV73: set_a] :
( ( ! [SY535: a] :
( ~ ( ord_less_eq_set_a @ SV73 @ SV154 )
| ~ ( member_a @ SY535 @ SV73 )
| ( member_a @ SY535 @ SV154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(834,plain,
! [SV155: set_Product_prod_a_a,SV74: set_a] :
( ( ! [SY536: a,SY537: a] :
( ~ ( prefer719835986ence_a @ SV74 @ SV155 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY536 @ SY537 ) @ SV155 )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SY537 @ SV74 @ SV155 ) @ ( prefer1676310729than_a @ SY536 @ SV74 @ SV155 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(835,plain,
! [SV156: set_a > nat,SV75: nat] :
( ( ! [SY538: set_a,SY539: set_a] :
( ( SV75
!= ( SV156 @ SY538 ) )
| ~ ( ord_less_eq_set_a @ SY538 @ SY539 )
| ~ ! [SY540: set_a,SY541: set_a] :
( ~ ( ord_less_eq_set_a @ SY540 @ SY541 )
| ( ord_less_eq_nat @ ( SV156 @ SY540 ) @ ( SV156 @ SY541 ) ) )
| ( ord_less_eq_nat @ SV75 @ ( SV156 @ SY539 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(836,plain,
! [SV157: a > $o,SV76: a > $o] :
( ( ( ord_less_eq_set_a @ ( collect_a @ SV76 ) @ ( collect_a @ SV157 ) )
= ( ! [SY542: a] :
( ~ ( SV76 @ SY542 )
| ( SV157 @ SY542 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(837,plain,
! [SV158: nat,SV77: set_a] :
( ( ~ ! [SY543: set_a] :
( ~ ( ord_less_eq_set_a @ SY543 @ SV77 )
| ~ ( finite_finite_a @ SY543 )
| ( ord_less_eq_nat @ ( finite_card_a @ SY543 ) @ SV158 ) )
| ~ ( ~ ( finite_finite_a @ SV77 )
| ~ ( ord_less_eq_nat @ ( finite_card_a @ SV77 ) @ SV158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(838,plain,
! [SV159: a,SV78: a] :
( ( ~ ( member_a @ SV78 @ carrier )
| ~ ( member_a @ SV159 @ carrier )
| ~ ( ( SV78 != SV159 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV78 @ SV159 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV159 @ SV78 ) @ relation ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(839,plain,
! [SV160: set_a,SV79: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV79 @ SV160 )
| ~ ~ ( finite_finite_a @ SV79 )
| ~ ( finite_finite_a @ SV160 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(840,plain,
! [SV161: nat,SV80: nat] :
( ( ! [SY544: nat > set_a,SY545: set_a] :
( ~ ( ord_less_eq_nat @ SV80 @ SV161 )
| ( ( SY544 @ SV161 )
!= SY545 )
| ~ ! [SX4: nat,SX5: nat] :
( ~ ( ord_less_eq_nat @ SX4 @ SX5 )
| ( ord_less_eq_set_a @ ( SY544 @ SX4 ) @ ( SY544 @ SX5 ) ) )
| ( ord_less_eq_set_a @ ( SY544 @ SV80 ) @ SY545 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(841,plain,
! [SV162: set_a,SV81: set_a] :
( ( ! [SY548: set_a > set_a,SY549: set_a] :
( ~ ( ord_less_eq_set_a @ SV81 @ SV162 )
| ( ( SY548 @ SV162 )
!= SY549 )
| ~ ! [SX4: set_a,SX5: set_a] :
( ~ ( ord_less_eq_set_a @ SX4 @ SX5 )
| ( ord_less_eq_set_a @ ( SY548 @ SX4 ) @ ( SY548 @ SX5 ) ) )
| ( ord_less_eq_set_a @ ( SY548 @ SV81 ) @ SY549 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(842,plain,
! [SV163: nat,SV82: set_a] :
( ( ~ ~ ( finite_finite_a @ SV82 )
| ~ ! [SY552: set_a] :
~ ~ ( ~ ~ ( ~ ( finite_finite_a @ SY552 )
| ( ( finite_card_a @ SY552 )
!= SV163 ) )
| ~ ( ord_less_eq_set_a @ SY552 @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(843,plain,
! [SV164: a,SV83: a] :
( ( ! [SY553: a] :
( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SV164 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV83 ) @ relation ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SY553 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY553 @ SV164 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SY553 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY553 @ SV83 ) @ relation ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(844,plain,
! [SV165: set_a,SV84: set_a] :
( ( ( SV84 != SV165 )
| ( ord_less_eq_set_a @ SV84 @ SV165 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(845,plain,
! [SV166: set_a > nat,SV85: nat] :
( ( ! [SY554: set_a,SY555: set_a] :
( ~ ( ord_less_eq_nat @ SV85 @ ( SV166 @ SY554 ) )
| ~ ( ord_less_eq_set_a @ SY554 @ SY555 )
| ~ ! [SY556: set_a,SY557: set_a] :
( ~ ( ord_less_eq_set_a @ SY556 @ SY557 )
| ( ord_less_eq_nat @ ( SV166 @ SY556 ) @ ( SV166 @ SY557 ) ) )
| ( ord_less_eq_nat @ SV85 @ ( SV166 @ SY555 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(846,plain,
! [SV167: a,SV86: a] :
( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV86 @ SV167 ) @ relation )
| ( member_a @ SV86 @ carrier ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(847,plain,
! [SV168: nat > set_a,SV87: set_a] :
( ( ! [SY558: nat,SY559: nat] :
( ~ ( ord_less_eq_set_a @ SV87 @ ( SV168 @ SY558 ) )
| ~ ( ord_less_eq_nat @ SY558 @ SY559 )
| ~ ! [SY560: nat,SY561: nat] :
( ~ ( ord_less_eq_nat @ SY560 @ SY561 )
| ( ord_less_eq_set_a @ ( SV168 @ SY560 ) @ ( SV168 @ SY561 ) ) )
| ( ord_less_eq_set_a @ SV87 @ ( SV168 @ SY559 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(848,plain,
! [SV169: a,SV88: a] :
( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV169 ) @ relation )
| ( member_a @ SV169 @ ( prefer1676310729than_a @ SV169 @ carrier @ relation ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(849,plain,
! [SV170: nat,SV89: nat] :
( ( ! [SY562: nat > set_a,SY563: set_a] :
( ~ ( ord_less_eq_nat @ SV89 @ SV170 )
| ~ ( ord_less_eq_set_a @ ( SY562 @ SV170 ) @ SY563 )
| ~ ! [SX4: nat,SX5: nat] :
( ~ ( ord_less_eq_nat @ SX4 @ SX5 )
| ( ord_less_eq_set_a @ ( SY562 @ SX4 ) @ ( SY562 @ SX5 ) ) )
| ( ord_less_eq_set_a @ ( SY562 @ SV89 ) @ SY563 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(850,plain,
! [SV171: set_a,SV90: set_a] :
( ( ! [SY566: set_a] :
( ~ ( ord_less_eq_set_a @ SV90 @ SV171 )
| ~ ( ord_less_eq_set_a @ SV171 @ SY566 )
| ( ord_less_eq_set_a @ SV90 @ SY566 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(851,plain,
! [SV172: set_a > set_a,SV91: set_a] :
( ( ! [SY567: set_a,SY568: set_a] :
( ~ ( ord_less_eq_set_a @ SV91 @ ( SV172 @ SY567 ) )
| ~ ( ord_less_eq_set_a @ SY567 @ SY568 )
| ~ ! [SY569: set_a,SY570: set_a] :
( ~ ( ord_less_eq_set_a @ SY569 @ SY570 )
| ( ord_less_eq_set_a @ ( SV172 @ SY569 ) @ ( SV172 @ SY570 ) ) )
| ( ord_less_eq_set_a @ SV91 @ ( SV172 @ SY568 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(852,plain,
! [SV173: set_a] :
( ( ( ^ [SY571: set_a] : ( SV173 = SY571 ) )
= ( ^ [SY572: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SV173 @ SY572 )
| ~ ( ord_less_eq_set_a @ SY572 @ SV173 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(853,plain,
! [SV93: a] :
( ( ( ~ ( member_a @ SV93 @ carrier ) )
= $true )
| ( ( ! [SY464: a] :
( ~ ( member_a @ SY464 @ carrier )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV93 @ SY464 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY464 @ SV93 ) @ relation ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[760]) ).
thf(854,plain,
! [SV174: nat > set_a,SV94: set_a] :
( ( ! [SY573: nat,SY574: nat] :
( ( SV94
!= ( SV174 @ SY573 ) )
| ~ ( ord_less_eq_nat @ SY573 @ SY574 )
| ~ ! [SY575: nat,SY576: nat] :
( ~ ( ord_less_eq_nat @ SY575 @ SY576 )
| ( ord_less_eq_set_a @ ( SV174 @ SY575 ) @ ( SV174 @ SY576 ) ) )
| ( ord_less_eq_set_a @ SV94 @ ( SV174 @ SY574 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(855,plain,
! [SV175: a,SV95: a] :
( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV95 @ SV175 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV175 @ SV95 ) @ relation ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV95 @ SV175 ) @ relation ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(856,plain,
! [SV96: a,SV1: a] :
( ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV1 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV96 @ carrier @ relation ) )
= $true )
| ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV96 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV1 @ carrier @ relation ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[763]) ).
thf(857,plain,
! [SV3: set_a] :
( ( ( ~ ( ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
| ( SV3 = bot_bot_set_a ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
| ( SV3 != bot_bot_set_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[764]) ).
thf(858,plain,
! [SV7: set_a] :
( ( ( ~ ( ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
| ( SV7 = bot_bot_set_a ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
| ( SV7 != bot_bot_set_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[766]) ).
thf(859,plain,
! [SV176: a,SV97: a,SV9: a] :
( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV97 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV9 ) @ relation ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV176 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV97 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV176 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV9 ) @ relation ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(860,plain,
! [SV98: set_a,SV10: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV10 @ SV98 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV98 @ SV10 )
| ( SV10 = SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[769]) ).
thf(861,plain,
! [SV177: nat,SV99: set_a,SV11: set_a] :
( ( ! [SY577: nat] :
( ~ ( ord_less_eq_set_a @ SV11 @ SV99 )
| ~ ( ord_less_eq_nat @ SV177 @ SY577 )
| ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV11 @ SV177 ) @ ( produc515611863_a_nat @ SV99 @ SY577 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(862,plain,
! [SV100: set_Product_prod_a_a,SV12: set_a] :
( ( ( ~ ( prefer719835986ence_a @ SV12 @ SV100 ) )
= $true )
| ( ( ~ ( finite_finite_a @ SV12 )
| ! [SY474: a] :
( ~ ( member_a @ SY474 @ SV12 )
| ( finite_finite_a @ ( prefer1676310729than_a @ SY474 @ SV12 @ SV100 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[771]) ).
thf(863,plain,
! [SV13: set_set_a] :
( ( ( finite_finite_set_a @ SV13 )
= $false )
| ( ( ~ ( ( SV13 != bot_bot_set_set_a ) )
| ~ ! [SY294: set_a] :
~ ~ ( ~ ( member_set_a @ SY294 @ SV13 )
| ~ ! [SY295: set_a] :
( ~ ( member_set_a @ SY295 @ SV13 )
| ~ ( ord_less_eq_set_a @ SY295 @ SY294 )
| ( SY294 = SY295 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[772]) ).
thf(864,plain,
! [SV101: set_a,SV14: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV14 @ SV101 ) )
= $true )
| ( ( ( ord_less_eq_set_a @ SV101 @ SV14 )
= ( SV101 = SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[773]) ).
thf(865,plain,
! [SV102: a,SV15: a] :
( ( ( ~ ( member_a @ SV15 @ carrier ) )
= $true )
| ( ( ~ ( member_a @ SV102 @ carrier )
| ( member_a @ SV15 @ ( prefer1676310729than_a @ SV102 @ carrier @ relation ) )
| ( member_a @ SV102 @ ( prefer1676310729than_a @ SV15 @ carrier @ relation ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[774]) ).
thf(866,plain,
! [SV103: set_a,SV16: set_set_a] :
( ( ( ~ ( finite_finite_set_a @ SV16 ) )
= $true )
| ( ( ~ ( member_set_a @ SV103 @ SV16 )
| ~ ! [SY475: set_a] :
~ ~ ( ~ ~ ( ~ ( member_set_a @ SY475 @ SV16 )
| ~ ( ord_less_eq_set_a @ SY475 @ SV103 ) )
| ~ ! [SY300: set_a] :
( ~ ( member_set_a @ SY300 @ SV16 )
| ~ ( ord_less_eq_set_a @ SY300 @ SY475 )
| ( SY475 = SY300 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[775]) ).
thf(867,plain,
! [SV104: a,SV17: a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV17 @ SV104 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV104 @ SV17 ) @ relation ) ) )
= $true )
| ( ( ( prefer161218362good_a @ SV17 @ carrier @ relation )
= ( prefer161218362good_a @ SV104 @ carrier @ relation ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[776]) ).
thf(868,plain,
! [SV178: set_a,SV105: set_a,SV18: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV18 @ SV105 )
| ( SV105 != SV178 )
| ( ord_less_eq_set_a @ SV18 @ SV178 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(869,plain,
! [SV179: set_a,SV106: nat,SV19: nat] :
( ( ! [SY578: set_a] :
( ~ ( ord_less_eq_nat @ SV19 @ SV106 )
| ~ ( ord_less_eq_set_a @ SV179 @ SY578 )
| ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV19 @ SV179 ) @ ( produc1450889781_set_a @ SV106 @ SY578 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(870,plain,
! [SV180: set_a,SV107: set_a,SV20: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV20 @ SV107 )
| ~ ( ord_less_eq_set_a @ SV180 @ SV20 )
| ( ord_less_eq_set_a @ SV180 @ SV107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(871,plain,
! [SV108: set_a,SV21: set_a] :
( ( ( SV21 != SV108 )
= $true )
| ( ( ord_less_eq_set_a @ SV21 @ SV108 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[780]) ).
thf(872,plain,
! [SV181: nat,SV109: set_a,SV22: nat] :
( ( ! [SY579: set_a] :
( ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV22 @ SV109 ) @ ( produc1450889781_set_a @ SV181 @ SY579 ) )
= ( ~ ( ~ ( ord_less_eq_nat @ SV22 @ SV181 )
| ~ ( ord_less_eq_set_a @ SV109 @ SY579 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(873,plain,
! [SV110: set_a] :
( ( ! [SV182: set_a] :
( ( SV110 = SV182 )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV182 @ SV110 )
| ~ ( ord_less_eq_set_a @ SV110 @ SV182 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[782]) ).
thf(874,plain,
! [SV110: set_a] :
( ( ( ^ [SY483: set_a] : ( SV110 = SY483 ) )
= ( ^ [SY484: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SY484 @ SV110 )
| ~ ( ord_less_eq_set_a @ SV110 @ SY484 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[782]) ).
thf(875,plain,
! [SV183: set_a,SV111: set_a,SV24: set_a] :
( ( ! [SY580: set_a] :
( ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV24 @ SV111 ) @ ( produc1928581911_set_a @ SV183 @ SY580 ) )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV24 @ SV183 )
| ~ ( ord_less_eq_set_a @ SV111 @ SY580 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(876,plain,
! [SV112: a,SV25: a] :
( ( ( ~ ( finite_finite_a @ carrier ) )
= $true )
| ( ( ~ ( member_a @ SV25 @ carrier )
| ~ ( member_a @ SV112 @ carrier )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV25 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV25 @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV25 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV25 @ carrier @ relation ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[784]) ).
thf(877,plain,
! [SV113: a,SV26: a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV26 @ SV113 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV113 @ SV26 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV113 @ SV26 ) @ relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[785]) ).
thf(878,plain,
! [SV184: set_a,SV114: set_a,SV27: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV27 @ SV114 )
| ~ ( ord_less_eq_set_a @ SV114 @ SV184 )
| ( ord_less_eq_set_a @ SV27 @ SV184 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(879,plain,
! [SV115: set_a,SV28: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV28 @ SV115 ) )
= $true )
| ( ( ~ ( finite_finite_a @ SV115 )
| ( finite_finite_a @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[787]) ).
thf(880,plain,
! [SV29: a] :
( ( ( carrier != bot_bot_set_a )
= $false )
| ( ( ~ ( member_a @ SV29 @ carrier )
| ( ( prefer1676310729than_a @ SV29 @ carrier @ relation )
!= bot_bot_set_a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[788]) ).
thf(881,plain,
! [SV116: a,SV30: a] :
( ( ( ~ ( member_a @ SV30 @ carrier ) )
= $true )
| ( ( ~ ( member_a @ SV116 @ carrier )
| ~ ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV116 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV30 @ carrier @ relation ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV30 @ SV116 ) @ relation ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[789]) ).
thf(882,plain,
! [SV185: set_a,SV117: set_a,SV31: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV31 @ SV117 )
| ~ ( ord_less_eq_set_a @ SV117 @ SV185 )
| ( ord_less_eq_set_a @ SV31 @ SV185 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(883,plain,
! [SV118: set_a,SV32: set_a] :
( ( ( ~ ( finite_finite_a @ SV32 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV118 @ SV32 )
| ( ord_less_eq_nat @ ( finite_card_a @ SV118 ) @ ( finite_card_a @ SV32 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[791]) ).
thf(884,plain,
! [SV119: set_a,SV33: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV33 @ ( finite_card_a @ SV119 ) ) )
= $true )
| ( ( ~ ! [SY489: set_a] :
( ~ ( ord_less_eq_set_a @ SY489 @ SV119 )
| ( ( finite_card_a @ SY489 )
!= SV33 )
| ~ ( finite_finite_a @ SY489 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[792]) ).
thf(885,plain,
! [SV34: set_set_a] :
( ( ( finite_finite_set_a @ SV34 )
= $false )
| ( ( ~ ( ( SV34 != bot_bot_set_set_a ) )
| ~ ! [SY329: set_a] :
~ ~ ( ~ ( member_set_a @ SY329 @ SV34 )
| ~ ! [SY330: set_a] :
( ~ ( member_set_a @ SY330 @ SV34 )
| ~ ( ord_less_eq_set_a @ SY329 @ SY330 )
| ( SY329 = SY330 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[793]) ).
thf(886,plain,
! [SV120: set_a,SV35: set_a] :
( ( ( ~ ( finite_finite_a @ SV35 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV120 @ SV35 )
| ( ( finite_card_a @ SV120 )
!= ( finite_card_a @ SV35 ) )
| ( SV120 = SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[794]) ).
thf(887,plain,
! [SV121: set_a,SV36: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV36 @ ( finite_card_a @ SV121 ) ) )
= $true )
| ( ( ~ ! [SY490: set_a] :
~ ~ ( ~ ( ord_less_eq_set_a @ SY490 @ SV121 )
| ( ( finite_card_a @ SY490 )
!= SV36 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[795]) ).
thf(888,plain,
! [SV186: set_a,SV122: set_a,SV37: set_a] :
( ( ( SV37 != SV122 )
| ~ ( ord_less_eq_set_a @ SV122 @ SV186 )
| ( ord_less_eq_set_a @ SV37 @ SV186 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(889,plain,
! [SV187: set_a,SV123: nat,SV38: set_a] :
( ( ! [SY581: nat] :
( ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV38 @ SV123 ) @ ( produc515611863_a_nat @ SV187 @ SY581 ) )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV38 @ SV187 )
| ~ ( ord_less_eq_nat @ SV123 @ SY581 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(890,plain,
! [SV188: a,SV124: set_Product_prod_a_a,SV39: set_a] :
( ( ~ ( prefer719835986ence_a @ SV39 @ SV124 )
| ~ ( ( SV39 != bot_bot_set_a ) )
| ~ ( member_a @ SV188 @ SV39 )
| ( ( prefer1676310729than_a @ SV188 @ SV39 @ SV124 )
!= bot_bot_set_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(891,plain,
! [SV125: set_a,SV40: set_a] :
( ( ( ~ ( finite_finite_a @ SV40 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV125 @ SV40 )
| ( finite_finite_a @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[799]) ).
thf(892,plain,
! [SV126: set_a] :
( ( ! [SV189: set_a] :
( ( ord_less_eq_set_a @ SV126 @ SV189 )
= ( ! [SY582: a] :
( ~ ( member_a @ SY582 @ SV126 )
| ( member_a @ SY582 @ SV189 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[800]) ).
thf(893,plain,
! [SV126: set_a] :
( ( ( ord_less_eq_set_a @ SV126 )
= ( ^ [SY495: set_a] :
! [SY496: a] :
( ~ ( member_a @ SY496 @ SV126 )
| ( member_a @ SY496 @ SY495 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[800]) ).
thf(894,plain,
! [SV127: set_a,SV42: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV42 @ SV127 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV127 @ SV42 )
| ( SV42 = SV127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[801]) ).
thf(895,plain,
! [SV128: set_a,SV43: set_a] :
( ( ( ~ ! [SY497: a] :
( ~ ( member_a @ SY497 @ SV43 )
| ( member_a @ SY497 @ SV128 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV43 @ SV128 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[803]) ).
thf(896,plain,
! [SV129: a,SV44: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV44 @ SV129 ) @ relation ) )
= $true )
| ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV129 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV44 @ carrier @ relation ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[804]) ).
thf(897,plain,
! [SV45: a] :
( ( ( member_a @ SV45 @ carrier )
= $false )
| ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV45 @ carrier @ relation ) @ carrier )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[805]) ).
thf(898,plain,
! [SV190: a,SV130: a,SV46: a] :
( ( ~ ~ ( ~ ~ ( ~ ( member_a @ SV46 @ carrier )
| ~ ( member_a @ SV130 @ carrier ) )
| ~ ( member_a @ SV190 @ carrier ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV190 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV46 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV190 ) @ relation ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(899,plain,
! [SV191: a,SV131: set_Product_prod_a_a,SV47: set_a] :
( ( ! [SY583: a] :
( ~ ( prefer719835986ence_a @ SV47 @ SV131 )
| ~ ( member_a @ SV191 @ SV47 )
| ~ ( member_a @ SY583 @ SV47 )
| ( member_a @ SV191 @ ( prefer1676310729than_a @ SY583 @ SV47 @ SV131 ) )
| ( member_a @ SY583 @ ( prefer1676310729than_a @ SV191 @ SV47 @ SV131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(900,plain,
! [SV132: set_a,SV48: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV48 @ SV132 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV132 @ SV48 )
| ( SV132 = SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[808]) ).
thf(901,plain,
! [SV49: a] :
( ( ( member_a @ SV49 @ carrier )
= $false )
| ( ( finite_finite_a @ ( prefer1676310729than_a @ SV49 @ carrier @ relation ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[809]) ).
thf(902,plain,
! [SV192: a,SV133: a,SV50: a] :
( ( ~ ~ ( ~ ~ ( ~ ( member_a @ SV50 @ carrier )
| ~ ( member_a @ SV133 @ carrier ) )
| ~ ( member_a @ SV192 @ carrier ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV50 @ SV133 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV133 @ SV192 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV50 @ SV192 ) @ relation ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(903,plain,
! [SV193: a,SV134: set_a,SV51: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV51 @ SV134 )
| ~ ( member_a @ SV193 @ SV51 )
| ( member_a @ SV193 @ SV134 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(904,plain,
! [SV194: a,SV135: set_Product_prod_a_a,SV52: set_a] :
( ( ~ ( prefer719835986ence_a @ SV52 @ SV135 )
| ~ ( member_a @ SV194 @ SV52 )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV194 @ SV52 @ SV135 ) @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(905,plain,
! [SV53: set_a] :
( ( ( ! [SY360: a] :
~ ( member_a @ SY360 @ SV53 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV53 @ bot_bot_set_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[813]) ).
thf(906,plain,
! [SV195: set_a > nat,SV136: set_a,SV54: set_a] :
( ( ! [SY584: nat] :
( ~ ( ord_less_eq_set_a @ SV54 @ SV136 )
| ( ( SV195 @ SV136 )
!= SY584 )
| ~ ! [SY585: set_a,SY586: set_a] :
( ~ ( ord_less_eq_set_a @ SY585 @ SY586 )
| ( ord_less_eq_nat @ ( SV195 @ SY585 ) @ ( SV195 @ SY586 ) ) )
| ( ord_less_eq_nat @ ( SV195 @ SV54 ) @ SY584 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(907,plain,
! [SV137: a > $o,SV55: a > $o] :
( ( ( ~ ! [SY508: a] :
( ~ ( SV55 @ SY508 )
| ( SV137 @ SY508 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ ( collect_a @ SV55 ) @ ( collect_a @ SV137 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[815]) ).
thf(908,plain,
! [SV138: set_a] :
( ( ! [SV196: set_a] :
( ( SV138 = SV196 )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV138 @ SV196 )
| ~ ( ord_less_eq_set_a @ SV196 @ SV138 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[816]) ).
thf(909,plain,
! [SV138: set_a] :
( ( ( ^ [SY509: set_a] : ( SV138 = SY509 ) )
= ( ^ [SY510: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SV138 @ SY510 )
| ~ ( ord_less_eq_set_a @ SY510 @ SV138 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[816]) ).
thf(910,plain,
! [SV197: set_a,SV139: set_a > set_a,SV57: set_a] :
( ( ! [SY587: set_a] :
( ( SV57
!= ( SV139 @ SV197 ) )
| ~ ( ord_less_eq_set_a @ SV197 @ SY587 )
| ~ ! [SY513: set_a,SY514: set_a] :
( ~ ( ord_less_eq_set_a @ SY513 @ SY514 )
| ( ord_less_eq_set_a @ ( SV139 @ SY513 ) @ ( SV139 @ SY514 ) ) )
| ( ord_less_eq_set_a @ SV57 @ ( SV139 @ SY587 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(911,plain,
! [SV140: set_a,SV58: set_a] :
( ( ( SV58 != SV140 )
= $true )
| ( ( ord_less_eq_set_a @ SV140 @ SV58 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[818]) ).
thf(912,plain,
! [SV141: set_a,SV59: set_a] :
( ( ( ~ ( finite_finite_a @ SV59 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV141 @ SV59 )
| ~ ( ord_less_eq_nat @ ( finite_card_a @ SV59 ) @ ( finite_card_a @ SV141 ) )
| ( SV141 = SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[819]) ).
thf(913,plain,
! [SV198: a,SV142: set_Product_prod_a_a,SV60: set_a] :
( ( ! [SY590: a] :
( ~ ( prefer719835986ence_a @ SV60 @ SV142 )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV198 @ SV60 @ SV142 ) @ ( prefer1676310729than_a @ SY590 @ SV60 @ SV142 ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SY590 @ SV60 @ SV142 ) @ ( prefer1676310729than_a @ SV198 @ SV60 @ SV142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(914,plain,
! [SV61: set_a] :
( ( ( ord_less_eq_set_a @ SV61 @ bot_bot_set_a )
= $false )
| ( ( SV61 = bot_bot_set_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[821]) ).
thf(915,plain,
! [SV143: set_a,SV62: set_set_a] :
( ( ( ~ ( finite_finite_set_a @ SV62 ) )
= $true )
| ( ( ~ ( member_set_a @ SV143 @ SV62 )
| ~ ! [SY517: set_a] :
~ ~ ( ~ ~ ( ~ ( member_set_a @ SY517 @ SV62 )
| ~ ( ord_less_eq_set_a @ SV143 @ SY517 ) )
| ~ ! [SY382: set_a] :
( ~ ( member_set_a @ SY382 @ SV62 )
| ~ ( ord_less_eq_set_a @ SY517 @ SY382 )
| ( SY517 = SY382 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[822]) ).
thf(916,plain,
! [SV144: a,SV63: a] :
( ( ( ~ ~ ( ~ ( member_a @ SV63 @ carrier )
| ~ ( member_a @ SV144 @ carrier ) ) )
= $true )
| ( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[823]) ).
thf(917,plain,
! [SV145: set_a] :
( ( ! [SV199: set_a] :
( ( ord_less_eq_set_a @ SV145 @ SV199 )
= ( ! [SY591: a] :
( ~ ( member_a @ SY591 @ SV145 )
| ( member_a @ SY591 @ SV199 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[824]) ).
thf(918,plain,
! [SV145: set_a] :
( ( ( ord_less_eq_set_a @ SV145 )
= ( ^ [SY519: set_a] :
! [SY520: a] :
( ~ ( member_a @ SY520 @ SV145 )
| ( member_a @ SY520 @ SY519 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[824]) ).
thf(919,plain,
! [SV146: set_a,SV65: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV65 @ SV146 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV146 @ SV65 )
| ( SV65 = SV146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[825]) ).
thf(920,plain,
! [SV200: a,SV147: set_Product_prod_a_a,SV66: set_a] :
( ( ! [SY592: a] :
( ~ ( prefer719835986ence_a @ SV66 @ SV147 )
| ~ ( finite_finite_a @ SV66 )
| ~ ( member_a @ SV200 @ SV66 )
| ~ ( member_a @ SY592 @ SV66 )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(921,plain,
! [SV201: set_a > nat,SV148: set_a,SV67: set_a] :
( ( ! [SY593: nat] :
( ~ ( ord_less_eq_set_a @ SV67 @ SV148 )
| ~ ( ord_less_eq_nat @ ( SV201 @ SV148 ) @ SY593 )
| ~ ! [SY594: set_a,SY595: set_a] :
( ~ ( ord_less_eq_set_a @ SY594 @ SY595 )
| ( ord_less_eq_nat @ ( SV201 @ SY594 ) @ ( SV201 @ SY595 ) ) )
| ( ord_less_eq_nat @ ( SV201 @ SV67 ) @ SY593 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(922,plain,
! [SV149: set_a,SV68: set_a] :
( ( ( SV68 != SV149 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV68 @ SV149 )
| ~ ( ord_less_eq_set_a @ SV149 @ SV68 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[828]) ).
thf(923,plain,
! [SV150: set_a] :
( ( ! [SV202: set_a] :
( ( SV150 = SV202 )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV150 @ SV202 )
| ~ ( ord_less_eq_set_a @ SV202 @ SV150 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[829]) ).
thf(924,plain,
! [SV150: set_a] :
( ( ( ^ [SY527: set_a] : ( SV150 = SY527 ) )
= ( ^ [SY528: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SV150 @ SY528 )
| ~ ( ord_less_eq_set_a @ SY528 @ SV150 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[829]) ).
thf(925,plain,
! [SV203: set_a > set_a,SV151: set_a,SV70: set_a] :
( ( ! [SY596: set_a] :
( ~ ( ord_less_eq_set_a @ SV70 @ SV151 )
| ~ ( ord_less_eq_set_a @ ( SV203 @ SV151 ) @ SY596 )
| ~ ! [SY597: set_a,SY598: set_a] :
( ~ ( ord_less_eq_set_a @ SY597 @ SY598 )
| ( ord_less_eq_set_a @ ( SV203 @ SY597 ) @ ( SV203 @ SY598 ) ) )
| ( ord_less_eq_set_a @ ( SV203 @ SV70 ) @ SY596 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(926,plain,
! [SV152: a,SV71: a] :
( ( ( ~ ( member_a @ SV71 @ carrier ) )
= $true )
| ( ( ~ ( member_a @ SV152 @ carrier )
| ( ( ~ ( ~ ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
| ~ ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[831]) ).
thf(927,plain,
! [SV204: set_a,SV153: set_a,SV72: set_a] :
( ( ! [SY599: set_a] :
( ~ ( ord_less_eq_set_a @ SV72 @ SV153 )
| ~ ( ord_less_eq_set_a @ SV204 @ SY599 )
| ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV72 @ SV204 ) @ ( produc1928581911_set_a @ SV153 @ SY599 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(928,plain,
! [SV205: a,SV154: set_a,SV73: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV73 @ SV154 )
| ~ ( member_a @ SV205 @ SV73 )
| ( member_a @ SV205 @ SV154 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(929,plain,
! [SV206: a,SV155: set_Product_prod_a_a,SV74: set_a] :
( ( ! [SY600: a] :
( ~ ( prefer719835986ence_a @ SV74 @ SV155 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV206 @ SY600 ) @ SV155 )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SY600 @ SV74 @ SV155 ) @ ( prefer1676310729than_a @ SV206 @ SV74 @ SV155 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(930,plain,
! [SV207: set_a,SV156: set_a > nat,SV75: nat] :
( ( ! [SY601: set_a] :
( ( SV75
!= ( SV156 @ SV207 ) )
| ~ ( ord_less_eq_set_a @ SV207 @ SY601 )
| ~ ! [SY540: set_a,SY541: set_a] :
( ~ ( ord_less_eq_set_a @ SY540 @ SY541 )
| ( ord_less_eq_nat @ ( SV156 @ SY540 ) @ ( SV156 @ SY541 ) ) )
| ( ord_less_eq_nat @ SV75 @ ( SV156 @ SY601 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(931,plain,
! [SV157: a > $o,SV76: a > $o] :
( ( ~ ( ( ord_less_eq_set_a @ ( collect_a @ SV76 ) @ ( collect_a @ SV157 ) )
| ! [SY542: a] :
( ~ ( SV76 @ SY542 )
| ( SV157 @ SY542 ) ) )
| ~ ( ~ ( ord_less_eq_set_a @ ( collect_a @ SV76 ) @ ( collect_a @ SV157 ) )
| ~ ! [SY542: a] :
( ~ ( SV76 @ SY542 )
| ( SV157 @ SY542 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[836]) ).
thf(932,plain,
! [SV157: a > $o,SV76: a > $o] :
( ( ( ord_less_eq_set_a @ ( collect_a @ SV76 ) @ ( collect_a @ SV157 ) )
= ( ! [SY542: a] :
( ~ ( SV76 @ SY542 )
| ( SV157 @ SY542 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[836]) ).
thf(933,plain,
! [SV158: nat,SV77: set_a] :
( ( ( ~ ! [SY543: set_a] :
( ~ ( ord_less_eq_set_a @ SY543 @ SV77 )
| ~ ( finite_finite_a @ SY543 )
| ( ord_less_eq_nat @ ( finite_card_a @ SY543 ) @ SV158 ) ) )
= $true )
| ( ( ~ ( ~ ( finite_finite_a @ SV77 )
| ~ ( ord_less_eq_nat @ ( finite_card_a @ SV77 ) @ SV158 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[837]) ).
thf(934,plain,
! [SV159: a,SV78: a] :
( ( ( ~ ( member_a @ SV78 @ carrier ) )
= $true )
| ( ( ~ ( member_a @ SV159 @ carrier )
| ~ ( ( SV78 != SV159 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV78 @ SV159 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV159 @ SV78 ) @ relation ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[838]) ).
thf(935,plain,
! [SV160: set_a,SV79: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV79 @ SV160 ) )
= $true )
| ( ( ~ ~ ( finite_finite_a @ SV79 )
| ~ ( finite_finite_a @ SV160 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[839]) ).
thf(936,plain,
! [SV208: nat > set_a,SV161: nat,SV80: nat] :
( ( ! [SY604: set_a] :
( ~ ( ord_less_eq_nat @ SV80 @ SV161 )
| ( ( SV208 @ SV161 )
!= SY604 )
| ~ ! [SY605: nat,SY606: nat] :
( ~ ( ord_less_eq_nat @ SY605 @ SY606 )
| ( ord_less_eq_set_a @ ( SV208 @ SY605 ) @ ( SV208 @ SY606 ) ) )
| ( ord_less_eq_set_a @ ( SV208 @ SV80 ) @ SY604 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(937,plain,
! [SV209: set_a > set_a,SV162: set_a,SV81: set_a] :
( ( ! [SY607: set_a] :
( ~ ( ord_less_eq_set_a @ SV81 @ SV162 )
| ( ( SV209 @ SV162 )
!= SY607 )
| ~ ! [SY608: set_a,SY609: set_a] :
( ~ ( ord_less_eq_set_a @ SY608 @ SY609 )
| ( ord_less_eq_set_a @ ( SV209 @ SY608 ) @ ( SV209 @ SY609 ) ) )
| ( ord_less_eq_set_a @ ( SV209 @ SV81 ) @ SY607 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(938,plain,
! [SV163: nat,SV82: set_a] :
( ( ( ~ ~ ( finite_finite_a @ SV82 ) )
= $true )
| ( ( ~ ! [SY552: set_a] :
~ ~ ( ~ ~ ( ~ ( finite_finite_a @ SY552 )
| ( ( finite_card_a @ SY552 )
!= SV163 ) )
| ~ ( ord_less_eq_set_a @ SY552 @ SV82 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[842]) ).
thf(939,plain,
! [SV210: a,SV164: a,SV83: a] :
( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SV164 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV83 ) @ relation ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV210 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV210 @ SV164 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SV210 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV210 @ SV83 ) @ relation ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(940,plain,
! [SV165: set_a,SV84: set_a] :
( ( ( SV84 != SV165 )
= $true )
| ( ( ord_less_eq_set_a @ SV84 @ SV165 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[844]) ).
thf(941,plain,
! [SV211: set_a,SV166: set_a > nat,SV85: nat] :
( ( ! [SY610: set_a] :
( ~ ( ord_less_eq_nat @ SV85 @ ( SV166 @ SV211 ) )
| ~ ( ord_less_eq_set_a @ SV211 @ SY610 )
| ~ ! [SY556: set_a,SY557: set_a] :
( ~ ( ord_less_eq_set_a @ SY556 @ SY557 )
| ( ord_less_eq_nat @ ( SV166 @ SY556 ) @ ( SV166 @ SY557 ) ) )
| ( ord_less_eq_nat @ SV85 @ ( SV166 @ SY610 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(942,plain,
! [SV167: a,SV86: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV86 @ SV167 ) @ relation ) )
= $true )
| ( ( member_a @ SV86 @ carrier )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[846]) ).
thf(943,plain,
! [SV212: nat,SV168: nat > set_a,SV87: set_a] :
( ( ! [SY613: nat] :
( ~ ( ord_less_eq_set_a @ SV87 @ ( SV168 @ SV212 ) )
| ~ ( ord_less_eq_nat @ SV212 @ SY613 )
| ~ ! [SY560: nat,SY561: nat] :
( ~ ( ord_less_eq_nat @ SY560 @ SY561 )
| ( ord_less_eq_set_a @ ( SV168 @ SY560 ) @ ( SV168 @ SY561 ) ) )
| ( ord_less_eq_set_a @ SV87 @ ( SV168 @ SY613 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(944,plain,
! [SV169: a,SV88: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV169 ) @ relation ) )
= $true )
| ( ( member_a @ SV169 @ ( prefer1676310729than_a @ SV169 @ carrier @ relation ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[848]) ).
thf(945,plain,
! [SV213: nat > set_a,SV170: nat,SV89: nat] :
( ( ! [SY616: set_a] :
( ~ ( ord_less_eq_nat @ SV89 @ SV170 )
| ~ ( ord_less_eq_set_a @ ( SV213 @ SV170 ) @ SY616 )
| ~ ! [SY617: nat,SY618: nat] :
( ~ ( ord_less_eq_nat @ SY617 @ SY618 )
| ( ord_less_eq_set_a @ ( SV213 @ SY617 ) @ ( SV213 @ SY618 ) ) )
| ( ord_less_eq_set_a @ ( SV213 @ SV89 ) @ SY616 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(946,plain,
! [SV214: set_a,SV171: set_a,SV90: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV90 @ SV171 )
| ~ ( ord_less_eq_set_a @ SV171 @ SV214 )
| ( ord_less_eq_set_a @ SV90 @ SV214 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(947,plain,
! [SV215: set_a,SV172: set_a > set_a,SV91: set_a] :
( ( ! [SY619: set_a] :
( ~ ( ord_less_eq_set_a @ SV91 @ ( SV172 @ SV215 ) )
| ~ ( ord_less_eq_set_a @ SV215 @ SY619 )
| ~ ! [SY569: set_a,SY570: set_a] :
( ~ ( ord_less_eq_set_a @ SY569 @ SY570 )
| ( ord_less_eq_set_a @ ( SV172 @ SY569 ) @ ( SV172 @ SY570 ) ) )
| ( ord_less_eq_set_a @ SV91 @ ( SV172 @ SY619 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[851]) ).
thf(948,plain,
! [SV173: set_a] :
( ( ! [SV216: set_a] :
( ( SV173 = SV216 )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV173 @ SV216 )
| ~ ( ord_less_eq_set_a @ SV216 @ SV173 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[852]) ).
thf(949,plain,
! [SV173: set_a] :
( ( ( ^ [SY571: set_a] : ( SV173 = SY571 ) )
= ( ^ [SY572: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SV173 @ SY572 )
| ~ ( ord_less_eq_set_a @ SY572 @ SV173 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[852]) ).
thf(950,plain,
! [SV93: a] :
( ( ( member_a @ SV93 @ carrier )
= $false )
| ( ( ! [SY464: a] :
( ~ ( member_a @ SY464 @ carrier )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV93 @ SY464 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY464 @ SV93 ) @ relation ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[853]) ).
thf(951,plain,
! [SV217: nat,SV174: nat > set_a,SV94: set_a] :
( ( ! [SY622: nat] :
( ( SV94
!= ( SV174 @ SV217 ) )
| ~ ( ord_less_eq_nat @ SV217 @ SY622 )
| ~ ! [SY575: nat,SY576: nat] :
( ~ ( ord_less_eq_nat @ SY575 @ SY576 )
| ( ord_less_eq_set_a @ ( SV174 @ SY575 ) @ ( SV174 @ SY576 ) ) )
| ( ord_less_eq_set_a @ SV94 @ ( SV174 @ SY622 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(952,plain,
! [SV175: a,SV95: a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV95 @ SV175 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV175 @ SV95 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV95 @ SV175 ) @ relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[855]) ).
thf(953,plain,
! [SV3: set_a] :
( ( ( ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
| ( SV3 = bot_bot_set_a ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
| ( SV3 != bot_bot_set_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[857]) ).
thf(954,plain,
! [SV7: set_a] :
( ( ( ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
| ( SV7 = bot_bot_set_a ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
| ( SV7 != bot_bot_set_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[858]) ).
thf(955,plain,
! [SV176: a,SV97: a,SV9: a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV97 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV9 ) @ relation ) ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV176 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV97 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV176 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV9 ) @ relation ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[859]) ).
thf(956,plain,
! [SV98: set_a,SV10: set_a] :
( ( ( ord_less_eq_set_a @ SV10 @ SV98 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV98 @ SV10 )
| ( SV10 = SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[860]) ).
thf(957,plain,
! [SV218: nat,SV177: nat,SV99: set_a,SV11: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV11 @ SV99 )
| ~ ( ord_less_eq_nat @ SV177 @ SV218 )
| ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV11 @ SV177 ) @ ( produc515611863_a_nat @ SV99 @ SV218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(958,plain,
! [SV100: set_Product_prod_a_a,SV12: set_a] :
( ( ( prefer719835986ence_a @ SV12 @ SV100 )
= $false )
| ( ( ~ ( finite_finite_a @ SV12 )
| ! [SY474: a] :
( ~ ( member_a @ SY474 @ SV12 )
| ( finite_finite_a @ ( prefer1676310729than_a @ SY474 @ SV12 @ SV100 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[862]) ).
thf(959,plain,
! [SV13: set_set_a] :
( ( ( ~ ( ( SV13 != bot_bot_set_set_a ) ) )
= $true )
| ( ( ~ ! [SY294: set_a] :
~ ~ ( ~ ( member_set_a @ SY294 @ SV13 )
| ~ ! [SY295: set_a] :
( ~ ( member_set_a @ SY295 @ SV13 )
| ~ ( ord_less_eq_set_a @ SY295 @ SY294 )
| ( SY294 = SY295 ) ) ) )
= $true )
| ( ( finite_finite_set_a @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[863]) ).
thf(960,plain,
! [SV101: set_a,SV14: set_a] :
( ( ( ord_less_eq_set_a @ SV14 @ SV101 )
= $false )
| ( ( ( ord_less_eq_set_a @ SV101 @ SV14 )
= ( SV101 = SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[864]) ).
thf(961,plain,
! [SV102: a,SV15: a] :
( ( ( member_a @ SV15 @ carrier )
= $false )
| ( ( ~ ( member_a @ SV102 @ carrier )
| ( member_a @ SV15 @ ( prefer1676310729than_a @ SV102 @ carrier @ relation ) )
| ( member_a @ SV102 @ ( prefer1676310729than_a @ SV15 @ carrier @ relation ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[865]) ).
thf(962,plain,
! [SV103: set_a,SV16: set_set_a] :
( ( ( finite_finite_set_a @ SV16 )
= $false )
| ( ( ~ ( member_set_a @ SV103 @ SV16 )
| ~ ! [SY475: set_a] :
~ ~ ( ~ ~ ( ~ ( member_set_a @ SY475 @ SV16 )
| ~ ( ord_less_eq_set_a @ SY475 @ SV103 ) )
| ~ ! [SY300: set_a] :
( ~ ( member_set_a @ SY300 @ SV16 )
| ~ ( ord_less_eq_set_a @ SY300 @ SY475 )
| ( SY475 = SY300 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[866]) ).
thf(963,plain,
! [SV104: a,SV17: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV17 @ SV104 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV104 @ SV17 ) @ relation ) ) )
= $false )
| ( ( ( prefer161218362good_a @ SV17 @ carrier @ relation )
= ( prefer161218362good_a @ SV104 @ carrier @ relation ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[867]) ).
thf(964,plain,
! [SV178: set_a,SV105: set_a,SV18: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV18 @ SV105 ) )
= $true )
| ( ( ( SV105 != SV178 )
| ( ord_less_eq_set_a @ SV18 @ SV178 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[868]) ).
thf(965,plain,
! [SV219: set_a,SV179: set_a,SV106: nat,SV19: nat] :
( ( ~ ( ord_less_eq_nat @ SV19 @ SV106 )
| ~ ( ord_less_eq_set_a @ SV179 @ SV219 )
| ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV19 @ SV179 ) @ ( produc1450889781_set_a @ SV106 @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(966,plain,
! [SV180: set_a,SV107: set_a,SV20: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV20 @ SV107 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV180 @ SV20 )
| ( ord_less_eq_set_a @ SV180 @ SV107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[870]) ).
thf(967,plain,
! [SV108: set_a,SV21: set_a] :
( ( ( SV21 = SV108 )
= $false )
| ( ( ord_less_eq_set_a @ SV21 @ SV108 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[871]) ).
thf(968,plain,
! [SV220: set_a,SV181: nat,SV109: set_a,SV22: nat] :
( ( ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV22 @ SV109 ) @ ( produc1450889781_set_a @ SV181 @ SV220 ) )
= ( ~ ( ~ ( ord_less_eq_nat @ SV22 @ SV181 )
| ~ ( ord_less_eq_set_a @ SV109 @ SV220 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[872]) ).
thf(969,plain,
! [SV221: set_a,SV110: set_a] :
( ( ( SV110 = SV221 )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV221 @ SV110 )
| ~ ( ord_less_eq_set_a @ SV110 @ SV221 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[873]) ).
thf(970,plain,
! [SV222: set_a,SV183: set_a,SV111: set_a,SV24: set_a] :
( ( ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV24 @ SV111 ) @ ( produc1928581911_set_a @ SV183 @ SV222 ) )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV24 @ SV183 )
| ~ ( ord_less_eq_set_a @ SV111 @ SV222 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(971,plain,
! [SV112: a,SV25: a] :
( ( ( finite_finite_a @ carrier )
= $false )
| ( ( ~ ( member_a @ SV25 @ carrier )
| ~ ( member_a @ SV112 @ carrier )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV25 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV25 @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV25 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV25 @ carrier @ relation ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[876]) ).
thf(972,plain,
! [SV113: a,SV26: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV26 @ SV113 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV113 @ SV26 ) @ relation ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV113 @ SV26 ) @ relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[877]) ).
thf(973,plain,
! [SV184: set_a,SV114: set_a,SV27: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV27 @ SV114 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV114 @ SV184 )
| ( ord_less_eq_set_a @ SV27 @ SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[878]) ).
thf(974,plain,
! [SV115: set_a,SV28: set_a] :
( ( ( ord_less_eq_set_a @ SV28 @ SV115 )
= $false )
| ( ( ~ ( finite_finite_a @ SV115 )
| ( finite_finite_a @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[879]) ).
thf(975,plain,
! [SV29: a] :
( ( ( carrier = bot_bot_set_a )
= $true )
| ( ( ~ ( member_a @ SV29 @ carrier )
| ( ( prefer1676310729than_a @ SV29 @ carrier @ relation )
!= bot_bot_set_a ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[880]) ).
thf(976,plain,
! [SV116: a,SV30: a] :
( ( ( member_a @ SV30 @ carrier )
= $false )
| ( ( ~ ( member_a @ SV116 @ carrier )
| ~ ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV116 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV30 @ carrier @ relation ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV30 @ SV116 ) @ relation ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[881]) ).
thf(977,plain,
! [SV185: set_a,SV117: set_a,SV31: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV31 @ SV117 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV117 @ SV185 )
| ( ord_less_eq_set_a @ SV31 @ SV185 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[882]) ).
thf(978,plain,
! [SV118: set_a,SV32: set_a] :
( ( ( finite_finite_a @ SV32 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV118 @ SV32 )
| ( ord_less_eq_nat @ ( finite_card_a @ SV118 ) @ ( finite_card_a @ SV32 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[883]) ).
thf(979,plain,
! [SV119: set_a,SV33: nat] :
( ( ( ord_less_eq_nat @ SV33 @ ( finite_card_a @ SV119 ) )
= $false )
| ( ( ~ ! [SY489: set_a] :
( ~ ( ord_less_eq_set_a @ SY489 @ SV119 )
| ( ( finite_card_a @ SY489 )
!= SV33 )
| ~ ( finite_finite_a @ SY489 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[884]) ).
thf(980,plain,
! [SV34: set_set_a] :
( ( ( ~ ( ( SV34 != bot_bot_set_set_a ) ) )
= $true )
| ( ( ~ ! [SY329: set_a] :
~ ~ ( ~ ( member_set_a @ SY329 @ SV34 )
| ~ ! [SY330: set_a] :
( ~ ( member_set_a @ SY330 @ SV34 )
| ~ ( ord_less_eq_set_a @ SY329 @ SY330 )
| ( SY329 = SY330 ) ) ) )
= $true )
| ( ( finite_finite_set_a @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[885]) ).
thf(981,plain,
! [SV120: set_a,SV35: set_a] :
( ( ( finite_finite_a @ SV35 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV120 @ SV35 )
| ( ( finite_card_a @ SV120 )
!= ( finite_card_a @ SV35 ) )
| ( SV120 = SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[886]) ).
thf(982,plain,
! [SV121: set_a,SV36: nat] :
( ( ( ord_less_eq_nat @ SV36 @ ( finite_card_a @ SV121 ) )
= $false )
| ( ( ~ ! [SY490: set_a] :
~ ~ ( ~ ( ord_less_eq_set_a @ SY490 @ SV121 )
| ( ( finite_card_a @ SY490 )
!= SV36 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[887]) ).
thf(983,plain,
! [SV186: set_a,SV122: set_a,SV37: set_a] :
( ( ( SV37 != SV122 )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV122 @ SV186 )
| ( ord_less_eq_set_a @ SV37 @ SV186 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[888]) ).
thf(984,plain,
! [SV223: nat,SV187: set_a,SV123: nat,SV38: set_a] :
( ( ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV38 @ SV123 ) @ ( produc515611863_a_nat @ SV187 @ SV223 ) )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV38 @ SV187 )
| ~ ( ord_less_eq_nat @ SV123 @ SV223 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(985,plain,
! [SV188: a,SV124: set_Product_prod_a_a,SV39: set_a] :
( ( ( ~ ( prefer719835986ence_a @ SV39 @ SV124 ) )
= $true )
| ( ( ~ ( ( SV39 != bot_bot_set_a ) )
| ~ ( member_a @ SV188 @ SV39 )
| ( ( prefer1676310729than_a @ SV188 @ SV39 @ SV124 )
!= bot_bot_set_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[890]) ).
thf(986,plain,
! [SV125: set_a,SV40: set_a] :
( ( ( finite_finite_a @ SV40 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV125 @ SV40 )
| ( finite_finite_a @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[891]) ).
thf(987,plain,
! [SV224: set_a,SV126: set_a] :
( ( ( ord_less_eq_set_a @ SV126 @ SV224 )
= ( ! [SY625: a] :
( ~ ( member_a @ SY625 @ SV126 )
| ( member_a @ SY625 @ SV224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[892]) ).
thf(988,plain,
! [SV127: set_a,SV42: set_a] :
( ( ( ord_less_eq_set_a @ SV42 @ SV127 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV127 @ SV42 )
| ( SV42 = SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[894]) ).
thf(989,plain,
! [SV128: set_a,SV43: set_a] :
( ( ( ! [SY497: a] :
( ~ ( member_a @ SY497 @ SV43 )
| ( member_a @ SY497 @ SV128 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV43 @ SV128 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[895]) ).
thf(990,plain,
! [SV129: a,SV44: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV44 @ SV129 ) @ relation )
= $false )
| ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV129 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV44 @ carrier @ relation ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[896]) ).
thf(991,plain,
! [SV190: a,SV130: a,SV46: a] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member_a @ SV46 @ carrier )
| ~ ( member_a @ SV130 @ carrier ) )
| ~ ( member_a @ SV190 @ carrier ) ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV190 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV46 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV190 ) @ relation ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[898]) ).
thf(992,plain,
! [SV225: a,SV191: a,SV131: set_Product_prod_a_a,SV47: set_a] :
( ( ~ ( prefer719835986ence_a @ SV47 @ SV131 )
| ~ ( member_a @ SV191 @ SV47 )
| ~ ( member_a @ SV225 @ SV47 )
| ( member_a @ SV191 @ ( prefer1676310729than_a @ SV225 @ SV47 @ SV131 ) )
| ( member_a @ SV225 @ ( prefer1676310729than_a @ SV191 @ SV47 @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(993,plain,
! [SV132: set_a,SV48: set_a] :
( ( ( ord_less_eq_set_a @ SV48 @ SV132 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV132 @ SV48 )
| ( SV132 = SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[900]) ).
thf(994,plain,
! [SV192: a,SV133: a,SV50: a] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member_a @ SV50 @ carrier )
| ~ ( member_a @ SV133 @ carrier ) )
| ~ ( member_a @ SV192 @ carrier ) ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV50 @ SV133 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV133 @ SV192 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV50 @ SV192 ) @ relation ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[902]) ).
thf(995,plain,
! [SV193: a,SV134: set_a,SV51: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV51 @ SV134 ) )
= $true )
| ( ( ~ ( member_a @ SV193 @ SV51 )
| ( member_a @ SV193 @ SV134 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[903]) ).
thf(996,plain,
! [SV194: a,SV135: set_Product_prod_a_a,SV52: set_a] :
( ( ( ~ ( prefer719835986ence_a @ SV52 @ SV135 ) )
= $true )
| ( ( ~ ( member_a @ SV194 @ SV52 )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV194 @ SV52 @ SV135 ) @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[904]) ).
thf(997,plain,
! [SV53: set_a] :
( ( ( ~ ( member_a @ ( sK1_SY360 @ SV53 ) @ SV53 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV53 @ bot_bot_set_a )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[905]) ).
thf(998,plain,
! [SV226: nat,SV195: set_a > nat,SV136: set_a,SV54: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV54 @ SV136 )
| ( ( SV195 @ SV136 )
!= SV226 )
| ~ ! [SY585: set_a,SY586: set_a] :
( ~ ( ord_less_eq_set_a @ SY585 @ SY586 )
| ( ord_less_eq_nat @ ( SV195 @ SY585 ) @ ( SV195 @ SY586 ) ) )
| ( ord_less_eq_nat @ ( SV195 @ SV54 ) @ SV226 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[906]) ).
thf(999,plain,
! [SV137: a > $o,SV55: a > $o] :
( ( ( ! [SY508: a] :
( ~ ( SV55 @ SY508 )
| ( SV137 @ SY508 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( collect_a @ SV55 ) @ ( collect_a @ SV137 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[907]) ).
thf(1000,plain,
! [SV227: set_a,SV138: set_a] :
( ( ( SV138 = SV227 )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV138 @ SV227 )
| ~ ( ord_less_eq_set_a @ SV227 @ SV138 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[908]) ).
thf(1001,plain,
! [SV228: set_a,SV197: set_a,SV139: set_a > set_a,SV57: set_a] :
( ( ( SV57
!= ( SV139 @ SV197 ) )
| ~ ( ord_less_eq_set_a @ SV197 @ SV228 )
| ~ ! [SY513: set_a,SY514: set_a] :
( ~ ( ord_less_eq_set_a @ SY513 @ SY514 )
| ( ord_less_eq_set_a @ ( SV139 @ SY513 ) @ ( SV139 @ SY514 ) ) )
| ( ord_less_eq_set_a @ SV57 @ ( SV139 @ SV228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(1002,plain,
! [SV140: set_a,SV58: set_a] :
( ( ( SV58 = SV140 )
= $false )
| ( ( ord_less_eq_set_a @ SV140 @ SV58 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[911]) ).
thf(1003,plain,
! [SV141: set_a,SV59: set_a] :
( ( ( finite_finite_a @ SV59 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV141 @ SV59 )
| ~ ( ord_less_eq_nat @ ( finite_card_a @ SV59 ) @ ( finite_card_a @ SV141 ) )
| ( SV141 = SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[912]) ).
thf(1004,plain,
! [SV229: a,SV198: a,SV142: set_Product_prod_a_a,SV60: set_a] :
( ( ~ ( prefer719835986ence_a @ SV60 @ SV142 )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV198 @ SV60 @ SV142 ) @ ( prefer1676310729than_a @ SV229 @ SV60 @ SV142 ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV229 @ SV60 @ SV142 ) @ ( prefer1676310729than_a @ SV198 @ SV60 @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[913]) ).
thf(1005,plain,
! [SV143: set_a,SV62: set_set_a] :
( ( ( finite_finite_set_a @ SV62 )
= $false )
| ( ( ~ ( member_set_a @ SV143 @ SV62 )
| ~ ! [SY517: set_a] :
~ ~ ( ~ ~ ( ~ ( member_set_a @ SY517 @ SV62 )
| ~ ( ord_less_eq_set_a @ SV143 @ SY517 ) )
| ~ ! [SY382: set_a] :
( ~ ( member_set_a @ SY382 @ SV62 )
| ~ ( ord_less_eq_set_a @ SY517 @ SY382 )
| ( SY517 = SY382 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[915]) ).
thf(1006,plain,
! [SV144: a,SV63: a] :
( ( ( ~ ( ~ ( member_a @ SV63 @ carrier )
| ~ ( member_a @ SV144 @ carrier ) ) )
= $false )
| ( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[916]) ).
thf(1007,plain,
! [SV230: set_a,SV145: set_a] :
( ( ( ord_less_eq_set_a @ SV145 @ SV230 )
= ( ! [SY630: a] :
( ~ ( member_a @ SY630 @ SV145 )
| ( member_a @ SY630 @ SV230 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[917]) ).
thf(1008,plain,
! [SV146: set_a,SV65: set_a] :
( ( ( ord_less_eq_set_a @ SV65 @ SV146 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV146 @ SV65 )
| ( SV65 = SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[919]) ).
thf(1009,plain,
! [SV231: a,SV200: a,SV147: set_Product_prod_a_a,SV66: set_a] :
( ( ~ ( prefer719835986ence_a @ SV66 @ SV147 )
| ~ ( finite_finite_a @ SV66 )
| ~ ( member_a @ SV200 @ SV66 )
| ~ ( member_a @ SV231 @ SV66 )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(1010,plain,
! [SV232: nat,SV201: set_a > nat,SV148: set_a,SV67: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV67 @ SV148 )
| ~ ( ord_less_eq_nat @ ( SV201 @ SV148 ) @ SV232 )
| ~ ! [SY594: set_a,SY595: set_a] :
( ~ ( ord_less_eq_set_a @ SY594 @ SY595 )
| ( ord_less_eq_nat @ ( SV201 @ SY594 ) @ ( SV201 @ SY595 ) ) )
| ( ord_less_eq_nat @ ( SV201 @ SV67 ) @ SV232 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(1011,plain,
! [SV149: set_a,SV68: set_a] :
( ( ( SV68 = SV149 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV68 @ SV149 )
| ~ ( ord_less_eq_set_a @ SV149 @ SV68 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[922]) ).
thf(1012,plain,
! [SV233: set_a,SV150: set_a] :
( ( ( SV150 = SV233 )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV150 @ SV233 )
| ~ ( ord_less_eq_set_a @ SV233 @ SV150 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[923]) ).
thf(1013,plain,
! [SV234: set_a,SV203: set_a > set_a,SV151: set_a,SV70: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV70 @ SV151 )
| ~ ( ord_less_eq_set_a @ ( SV203 @ SV151 ) @ SV234 )
| ~ ! [SY597: set_a,SY598: set_a] :
( ~ ( ord_less_eq_set_a @ SY597 @ SY598 )
| ( ord_less_eq_set_a @ ( SV203 @ SY597 ) @ ( SV203 @ SY598 ) ) )
| ( ord_less_eq_set_a @ ( SV203 @ SV70 ) @ SV234 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(1014,plain,
! [SV152: a,SV71: a] :
( ( ( member_a @ SV71 @ carrier )
= $false )
| ( ( ~ ( member_a @ SV152 @ carrier )
| ( ( ~ ( ~ ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
| ~ ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[926]) ).
thf(1015,plain,
! [SV235: set_a,SV204: set_a,SV153: set_a,SV72: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV72 @ SV153 )
| ~ ( ord_less_eq_set_a @ SV204 @ SV235 )
| ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV72 @ SV204 ) @ ( produc1928581911_set_a @ SV153 @ SV235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(1016,plain,
! [SV205: a,SV154: set_a,SV73: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV73 @ SV154 ) )
= $true )
| ( ( ~ ( member_a @ SV205 @ SV73 )
| ( member_a @ SV205 @ SV154 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[928]) ).
thf(1017,plain,
! [SV236: a,SV206: a,SV155: set_Product_prod_a_a,SV74: set_a] :
( ( ~ ( prefer719835986ence_a @ SV74 @ SV155 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV206 @ SV236 ) @ SV155 )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV236 @ SV74 @ SV155 ) @ ( prefer1676310729than_a @ SV206 @ SV74 @ SV155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(1018,plain,
! [SV237: set_a,SV207: set_a,SV156: set_a > nat,SV75: nat] :
( ( ( SV75
!= ( SV156 @ SV207 ) )
| ~ ( ord_less_eq_set_a @ SV207 @ SV237 )
| ~ ! [SY540: set_a,SY541: set_a] :
( ~ ( ord_less_eq_set_a @ SY540 @ SY541 )
| ( ord_less_eq_nat @ ( SV156 @ SY540 ) @ ( SV156 @ SY541 ) ) )
| ( ord_less_eq_nat @ SV75 @ ( SV156 @ SV237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[930]) ).
thf(1019,plain,
! [SV157: a > $o,SV76: a > $o] :
( ( ( ~ ( ( ord_less_eq_set_a @ ( collect_a @ SV76 ) @ ( collect_a @ SV157 ) )
| ! [SY542: a] :
( ~ ( SV76 @ SY542 )
| ( SV157 @ SY542 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ ( collect_a @ SV76 ) @ ( collect_a @ SV157 ) )
| ~ ! [SY542: a] :
( ~ ( SV76 @ SY542 )
| ( SV157 @ SY542 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[931]) ).
thf(1020,plain,
! [SV158: nat,SV77: set_a] :
( ( ( ! [SY543: set_a] :
( ~ ( ord_less_eq_set_a @ SY543 @ SV77 )
| ~ ( finite_finite_a @ SY543 )
| ( ord_less_eq_nat @ ( finite_card_a @ SY543 ) @ SV158 ) ) )
= $false )
| ( ( ~ ( ~ ( finite_finite_a @ SV77 )
| ~ ( ord_less_eq_nat @ ( finite_card_a @ SV77 ) @ SV158 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[933]) ).
thf(1021,plain,
! [SV159: a,SV78: a] :
( ( ( member_a @ SV78 @ carrier )
= $false )
| ( ( ~ ( member_a @ SV159 @ carrier )
| ~ ( ( SV78 != SV159 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV78 @ SV159 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV159 @ SV78 ) @ relation ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[934]) ).
thf(1022,plain,
! [SV160: set_a,SV79: set_a] :
( ( ( ord_less_eq_set_a @ SV79 @ SV160 )
= $false )
| ( ( ~ ~ ( finite_finite_a @ SV79 )
| ~ ( finite_finite_a @ SV160 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[935]) ).
thf(1023,plain,
! [SV238: set_a,SV208: nat > set_a,SV161: nat,SV80: nat] :
( ( ~ ( ord_less_eq_nat @ SV80 @ SV161 )
| ( ( SV208 @ SV161 )
!= SV238 )
| ~ ! [SY605: nat,SY606: nat] :
( ~ ( ord_less_eq_nat @ SY605 @ SY606 )
| ( ord_less_eq_set_a @ ( SV208 @ SY605 ) @ ( SV208 @ SY606 ) ) )
| ( ord_less_eq_set_a @ ( SV208 @ SV80 ) @ SV238 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1024,plain,
! [SV239: set_a,SV209: set_a > set_a,SV162: set_a,SV81: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV81 @ SV162 )
| ( ( SV209 @ SV162 )
!= SV239 )
| ~ ! [SY608: set_a,SY609: set_a] :
( ~ ( ord_less_eq_set_a @ SY608 @ SY609 )
| ( ord_less_eq_set_a @ ( SV209 @ SY608 ) @ ( SV209 @ SY609 ) ) )
| ( ord_less_eq_set_a @ ( SV209 @ SV81 ) @ SV239 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[937]) ).
thf(1025,plain,
! [SV163: nat,SV82: set_a] :
( ( ( ~ ( finite_finite_a @ SV82 ) )
= $false )
| ( ( ~ ! [SY552: set_a] :
~ ~ ( ~ ~ ( ~ ( finite_finite_a @ SY552 )
| ( ( finite_card_a @ SY552 )
!= SV163 ) )
| ~ ( ord_less_eq_set_a @ SY552 @ SV82 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[938]) ).
thf(1026,plain,
! [SV210: a,SV164: a,SV83: a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SV164 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV83 ) @ relation ) ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV210 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV210 @ SV164 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SV210 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV210 @ SV83 ) @ relation ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[939]) ).
thf(1027,plain,
! [SV165: set_a,SV84: set_a] :
( ( ( SV84 = SV165 )
= $false )
| ( ( ord_less_eq_set_a @ SV84 @ SV165 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[940]) ).
thf(1028,plain,
! [SV240: set_a,SV211: set_a,SV166: set_a > nat,SV85: nat] :
( ( ~ ( ord_less_eq_nat @ SV85 @ ( SV166 @ SV211 ) )
| ~ ( ord_less_eq_set_a @ SV211 @ SV240 )
| ~ ! [SY556: set_a,SY557: set_a] :
( ~ ( ord_less_eq_set_a @ SY556 @ SY557 )
| ( ord_less_eq_nat @ ( SV166 @ SY556 ) @ ( SV166 @ SY557 ) ) )
| ( ord_less_eq_nat @ SV85 @ ( SV166 @ SV240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[941]) ).
thf(1029,plain,
! [SV167: a,SV86: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV86 @ SV167 ) @ relation )
= $false )
| ( ( member_a @ SV86 @ carrier )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[942]) ).
thf(1030,plain,
! [SV241: nat,SV212: nat,SV168: nat > set_a,SV87: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV87 @ ( SV168 @ SV212 ) )
| ~ ( ord_less_eq_nat @ SV212 @ SV241 )
| ~ ! [SY560: nat,SY561: nat] :
( ~ ( ord_less_eq_nat @ SY560 @ SY561 )
| ( ord_less_eq_set_a @ ( SV168 @ SY560 ) @ ( SV168 @ SY561 ) ) )
| ( ord_less_eq_set_a @ SV87 @ ( SV168 @ SV241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(1031,plain,
! [SV169: a,SV88: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV169 ) @ relation )
= $false )
| ( ( member_a @ SV169 @ ( prefer1676310729than_a @ SV169 @ carrier @ relation ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[944]) ).
thf(1032,plain,
! [SV242: set_a,SV213: nat > set_a,SV170: nat,SV89: nat] :
( ( ~ ( ord_less_eq_nat @ SV89 @ SV170 )
| ~ ( ord_less_eq_set_a @ ( SV213 @ SV170 ) @ SV242 )
| ~ ! [SY617: nat,SY618: nat] :
( ~ ( ord_less_eq_nat @ SY617 @ SY618 )
| ( ord_less_eq_set_a @ ( SV213 @ SY617 ) @ ( SV213 @ SY618 ) ) )
| ( ord_less_eq_set_a @ ( SV213 @ SV89 ) @ SV242 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(1033,plain,
! [SV214: set_a,SV171: set_a,SV90: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV90 @ SV171 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV171 @ SV214 )
| ( ord_less_eq_set_a @ SV90 @ SV214 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[946]) ).
thf(1034,plain,
! [SV243: set_a,SV215: set_a,SV172: set_a > set_a,SV91: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV91 @ ( SV172 @ SV215 ) )
| ~ ( ord_less_eq_set_a @ SV215 @ SV243 )
| ~ ! [SY569: set_a,SY570: set_a] :
( ~ ( ord_less_eq_set_a @ SY569 @ SY570 )
| ( ord_less_eq_set_a @ ( SV172 @ SY569 ) @ ( SV172 @ SY570 ) ) )
| ( ord_less_eq_set_a @ SV91 @ ( SV172 @ SV243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(1035,plain,
! [SV244: set_a,SV173: set_a] :
( ( ( SV173 = SV244 )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV173 @ SV244 )
| ~ ( ord_less_eq_set_a @ SV244 @ SV173 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(1036,plain,
! [SV93: a,SV245: a] :
( ( ( ~ ( member_a @ SV245 @ carrier )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV93 @ SV245 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV245 @ SV93 ) @ relation ) )
= $true )
| ( ( member_a @ SV93 @ carrier )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(1037,plain,
! [SV246: nat,SV217: nat,SV174: nat > set_a,SV94: set_a] :
( ( ( SV94
!= ( SV174 @ SV217 ) )
| ~ ( ord_less_eq_nat @ SV217 @ SV246 )
| ~ ! [SY575: nat,SY576: nat] :
( ~ ( ord_less_eq_nat @ SY575 @ SY576 )
| ( ord_less_eq_set_a @ ( SV174 @ SY575 ) @ ( SV174 @ SY576 ) ) )
| ( ord_less_eq_set_a @ SV94 @ ( SV174 @ SV246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(1038,plain,
! [SV175: a,SV95: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV95 @ SV175 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV175 @ SV95 ) @ relation ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV95 @ SV175 ) @ relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[952]) ).
thf(1039,plain,
! [SV3: set_a] :
( ( ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
| ( SV3 != bot_bot_set_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[953]) ).
thf(1040,plain,
! [SV3: set_a] :
( ( ( SV3 = bot_bot_set_a )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
| ( SV3 != bot_bot_set_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[953]) ).
thf(1041,plain,
! [SV7: set_a] :
( ( ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
| ( SV7 != bot_bot_set_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[954]) ).
thf(1042,plain,
! [SV7: set_a] :
( ( ( SV7 = bot_bot_set_a )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
| ( SV7 != bot_bot_set_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[954]) ).
thf(1043,plain,
! [SV176: a,SV97: a,SV9: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV97 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV9 ) @ relation ) ) )
= $false )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV176 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV97 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV176 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV9 ) @ relation ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[955]) ).
thf(1044,plain,
! [SV10: set_a,SV98: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV98 @ SV10 ) )
= $true )
| ( ( SV10 = SV98 )
= $true )
| ( ( ord_less_eq_set_a @ SV10 @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[956]) ).
thf(1045,plain,
! [SV218: nat,SV177: nat,SV99: set_a,SV11: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV11 @ SV99 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV177 @ SV218 )
| ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV11 @ SV177 ) @ ( produc515611863_a_nat @ SV99 @ SV218 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[957]) ).
thf(1046,plain,
! [SV100: set_Product_prod_a_a,SV12: set_a] :
( ( ( ~ ( finite_finite_a @ SV12 ) )
= $true )
| ( ( ! [SY474: a] :
( ~ ( member_a @ SY474 @ SV12 )
| ( finite_finite_a @ ( prefer1676310729than_a @ SY474 @ SV12 @ SV100 ) ) ) )
= $true )
| ( ( prefer719835986ence_a @ SV12 @ SV100 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[958]) ).
thf(1047,plain,
! [SV13: set_set_a] :
( ( ( SV13 != bot_bot_set_set_a )
= $false )
| ( ( ~ ! [SY294: set_a] :
~ ~ ( ~ ( member_set_a @ SY294 @ SV13 )
| ~ ! [SY295: set_a] :
( ~ ( member_set_a @ SY295 @ SV13 )
| ~ ( ord_less_eq_set_a @ SY295 @ SY294 )
| ( SY294 = SY295 ) ) ) )
= $true )
| ( ( finite_finite_set_a @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[959]) ).
thf(1048,plain,
! [SV14: set_a,SV101: set_a] :
( ( ( ~ ( ( ord_less_eq_set_a @ SV101 @ SV14 )
| ( SV101 = SV14 ) )
| ~ ( ~ ( ord_less_eq_set_a @ SV101 @ SV14 )
| ( SV101 != SV14 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV14 @ SV101 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[960]) ).
thf(1049,plain,
! [SV14: set_a,SV101: set_a] :
( ( ( ( ord_less_eq_set_a @ SV101 @ SV14 )
= ( SV101 = SV14 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV14 @ SV101 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[960]) ).
thf(1050,plain,
! [SV15: a,SV102: a] :
( ( ( ~ ( member_a @ SV102 @ carrier ) )
= $true )
| ( ( ( member_a @ SV15 @ ( prefer1676310729than_a @ SV102 @ carrier @ relation ) )
| ( member_a @ SV102 @ ( prefer1676310729than_a @ SV15 @ carrier @ relation ) ) )
= $true )
| ( ( member_a @ SV15 @ carrier )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[961]) ).
thf(1051,plain,
! [SV16: set_set_a,SV103: set_a] :
( ( ( ~ ( member_set_a @ SV103 @ SV16 ) )
= $true )
| ( ( ~ ! [SY475: set_a] :
~ ~ ( ~ ~ ( ~ ( member_set_a @ SY475 @ SV16 )
| ~ ( ord_less_eq_set_a @ SY475 @ SV103 ) )
| ~ ! [SY300: set_a] :
( ~ ( member_set_a @ SY300 @ SV16 )
| ~ ( ord_less_eq_set_a @ SY300 @ SY475 )
| ( SY475 = SY300 ) ) ) )
= $true )
| ( ( finite_finite_set_a @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[962]) ).
thf(1052,plain,
! [SV104: a,SV17: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV17 @ SV104 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV104 @ SV17 ) @ relation ) )
= $true )
| ( ( ( prefer161218362good_a @ SV17 @ carrier @ relation )
= ( prefer161218362good_a @ SV104 @ carrier @ relation ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[963]) ).
thf(1053,plain,
! [SV178: set_a,SV105: set_a,SV18: set_a] :
( ( ( ord_less_eq_set_a @ SV18 @ SV105 )
= $false )
| ( ( ( SV105 != SV178 )
| ( ord_less_eq_set_a @ SV18 @ SV178 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[964]) ).
thf(1054,plain,
! [SV219: set_a,SV179: set_a,SV106: nat,SV19: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV19 @ SV106 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV179 @ SV219 )
| ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV19 @ SV179 ) @ ( produc1450889781_set_a @ SV106 @ SV219 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[965]) ).
thf(1055,plain,
! [SV180: set_a,SV107: set_a,SV20: set_a] :
( ( ( ord_less_eq_set_a @ SV20 @ SV107 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV180 @ SV20 )
| ( ord_less_eq_set_a @ SV180 @ SV107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[966]) ).
thf(1056,plain,
! [SV220: set_a,SV181: nat,SV109: set_a,SV22: nat] :
( ( ~ ( ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV22 @ SV109 ) @ ( produc1450889781_set_a @ SV181 @ SV220 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV22 @ SV181 )
| ~ ( ord_less_eq_set_a @ SV109 @ SV220 ) ) )
| ~ ( ~ ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV22 @ SV109 ) @ ( produc1450889781_set_a @ SV181 @ SV220 ) )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV22 @ SV181 )
| ~ ( ord_less_eq_set_a @ SV109 @ SV220 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[968]) ).
thf(1057,plain,
! [SV220: set_a,SV181: nat,SV109: set_a,SV22: nat] :
( ( ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV22 @ SV109 ) @ ( produc1450889781_set_a @ SV181 @ SV220 ) )
= ( ~ ( ~ ( ord_less_eq_nat @ SV22 @ SV181 )
| ~ ( ord_less_eq_set_a @ SV109 @ SV220 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[968]) ).
thf(1058,plain,
! [SV221: set_a,SV110: set_a] :
( ( ~ ( ( SV110 = SV221 )
| ~ ( ~ ( ord_less_eq_set_a @ SV221 @ SV110 )
| ~ ( ord_less_eq_set_a @ SV110 @ SV221 ) ) )
| ~ ( ( SV110 != SV221 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV221 @ SV110 )
| ~ ( ord_less_eq_set_a @ SV110 @ SV221 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[969]) ).
thf(1059,plain,
! [SV221: set_a,SV110: set_a] :
( ( ( SV110 = SV221 )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV221 @ SV110 )
| ~ ( ord_less_eq_set_a @ SV110 @ SV221 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[969]) ).
thf(1060,plain,
! [SV222: set_a,SV183: set_a,SV111: set_a,SV24: set_a] :
( ( ~ ( ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV24 @ SV111 ) @ ( produc1928581911_set_a @ SV183 @ SV222 ) )
| ~ ( ~ ( ord_less_eq_set_a @ SV24 @ SV183 )
| ~ ( ord_less_eq_set_a @ SV111 @ SV222 ) ) )
| ~ ( ~ ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV24 @ SV111 ) @ ( produc1928581911_set_a @ SV183 @ SV222 ) )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV24 @ SV183 )
| ~ ( ord_less_eq_set_a @ SV111 @ SV222 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[970]) ).
thf(1061,plain,
! [SV222: set_a,SV183: set_a,SV111: set_a,SV24: set_a] :
( ( ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV24 @ SV111 ) @ ( produc1928581911_set_a @ SV183 @ SV222 ) )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV24 @ SV183 )
| ~ ( ord_less_eq_set_a @ SV111 @ SV222 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[970]) ).
thf(1062,plain,
! [SV112: a,SV25: a] :
( ( ( ~ ( member_a @ SV25 @ carrier ) )
= $true )
| ( ( ~ ( member_a @ SV112 @ carrier )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV25 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV25 @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV25 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV25 @ carrier @ relation ) ) )
= $true )
| ( ( finite_finite_a @ carrier )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[971]) ).
thf(1063,plain,
! [SV113: a,SV26: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV26 @ SV113 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV113 @ SV26 ) @ relation ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV113 @ SV26 ) @ relation )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[972]) ).
thf(1064,plain,
! [SV184: set_a,SV114: set_a,SV27: set_a] :
( ( ( ord_less_eq_set_a @ SV27 @ SV114 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV114 @ SV184 )
| ( ord_less_eq_set_a @ SV27 @ SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[973]) ).
thf(1065,plain,
! [SV28: set_a,SV115: set_a] :
( ( ( ~ ( finite_finite_a @ SV115 ) )
= $true )
| ( ( finite_finite_a @ SV28 )
= $true )
| ( ( ord_less_eq_set_a @ SV28 @ SV115 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[974]) ).
thf(1066,plain,
! [SV29: a] :
( ( ( ~ ( member_a @ SV29 @ carrier ) )
= $true )
| ( ( ( prefer1676310729than_a @ SV29 @ carrier @ relation )
!= bot_bot_set_a )
= $true )
| ( ( carrier = bot_bot_set_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[975]) ).
thf(1067,plain,
! [SV30: a,SV116: a] :
( ( ( ~ ( member_a @ SV116 @ carrier ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV116 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV30 @ carrier @ relation ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV30 @ SV116 ) @ relation ) )
= $true )
| ( ( member_a @ SV30 @ carrier )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[976]) ).
thf(1068,plain,
! [SV185: set_a,SV117: set_a,SV31: set_a] :
( ( ( ord_less_eq_set_a @ SV31 @ SV117 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV117 @ SV185 )
| ( ord_less_eq_set_a @ SV31 @ SV185 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[977]) ).
thf(1069,plain,
! [SV32: set_a,SV118: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV118 @ SV32 ) )
= $true )
| ( ( ord_less_eq_nat @ ( finite_card_a @ SV118 ) @ ( finite_card_a @ SV32 ) )
= $true )
| ( ( finite_finite_a @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[978]) ).
thf(1070,plain,
! [SV33: nat,SV119: set_a] :
( ( ( ! [SY489: set_a] :
( ~ ( ord_less_eq_set_a @ SY489 @ SV119 )
| ( ( finite_card_a @ SY489 )
!= SV33 )
| ~ ( finite_finite_a @ SY489 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV33 @ ( finite_card_a @ SV119 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[979]) ).
thf(1071,plain,
! [SV34: set_set_a] :
( ( ( SV34 != bot_bot_set_set_a )
= $false )
| ( ( ~ ! [SY329: set_a] :
~ ~ ( ~ ( member_set_a @ SY329 @ SV34 )
| ~ ! [SY330: set_a] :
( ~ ( member_set_a @ SY330 @ SV34 )
| ~ ( ord_less_eq_set_a @ SY329 @ SY330 )
| ( SY329 = SY330 ) ) ) )
= $true )
| ( ( finite_finite_set_a @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[980]) ).
thf(1072,plain,
! [SV35: set_a,SV120: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV120 @ SV35 ) )
= $true )
| ( ( ( ( finite_card_a @ SV120 )
!= ( finite_card_a @ SV35 ) )
| ( SV120 = SV35 ) )
= $true )
| ( ( finite_finite_a @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[981]) ).
thf(1073,plain,
! [SV36: nat,SV121: set_a] :
( ( ( ! [SY490: set_a] :
~ ~ ( ~ ( ord_less_eq_set_a @ SY490 @ SV121 )
| ( ( finite_card_a @ SY490 )
!= SV36 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV36 @ ( finite_card_a @ SV121 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(1074,plain,
! [SV186: set_a,SV122: set_a,SV37: set_a] :
( ( ( SV37 = SV122 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV122 @ SV186 )
| ( ord_less_eq_set_a @ SV37 @ SV186 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[983]) ).
thf(1075,plain,
! [SV223: nat,SV187: set_a,SV123: nat,SV38: set_a] :
( ( ~ ( ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV38 @ SV123 ) @ ( produc515611863_a_nat @ SV187 @ SV223 ) )
| ~ ( ~ ( ord_less_eq_set_a @ SV38 @ SV187 )
| ~ ( ord_less_eq_nat @ SV123 @ SV223 ) ) )
| ~ ( ~ ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV38 @ SV123 ) @ ( produc515611863_a_nat @ SV187 @ SV223 ) )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV38 @ SV187 )
| ~ ( ord_less_eq_nat @ SV123 @ SV223 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[984]) ).
thf(1076,plain,
! [SV223: nat,SV187: set_a,SV123: nat,SV38: set_a] :
( ( ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV38 @ SV123 ) @ ( produc515611863_a_nat @ SV187 @ SV223 ) )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV38 @ SV187 )
| ~ ( ord_less_eq_nat @ SV123 @ SV223 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[984]) ).
thf(1077,plain,
! [SV188: a,SV124: set_Product_prod_a_a,SV39: set_a] :
( ( ( prefer719835986ence_a @ SV39 @ SV124 )
= $false )
| ( ( ~ ( ( SV39 != bot_bot_set_a ) )
| ~ ( member_a @ SV188 @ SV39 )
| ( ( prefer1676310729than_a @ SV188 @ SV39 @ SV124 )
!= bot_bot_set_a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[985]) ).
thf(1078,plain,
! [SV40: set_a,SV125: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV125 @ SV40 ) )
= $true )
| ( ( finite_finite_a @ SV125 )
= $true )
| ( ( finite_finite_a @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[986]) ).
thf(1079,plain,
! [SV224: set_a,SV126: set_a] :
( ( ~ ( ( ord_less_eq_set_a @ SV126 @ SV224 )
| ! [SY625: a] :
( ~ ( member_a @ SY625 @ SV126 )
| ( member_a @ SY625 @ SV224 ) ) )
| ~ ( ~ ( ord_less_eq_set_a @ SV126 @ SV224 )
| ~ ! [SY625: a] :
( ~ ( member_a @ SY625 @ SV126 )
| ( member_a @ SY625 @ SV224 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[987]) ).
thf(1080,plain,
! [SV224: set_a,SV126: set_a] :
( ( ( ord_less_eq_set_a @ SV126 @ SV224 )
= ( ! [SY625: a] :
( ~ ( member_a @ SY625 @ SV126 )
| ( member_a @ SY625 @ SV224 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[987]) ).
thf(1081,plain,
! [SV42: set_a,SV127: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV127 @ SV42 ) )
= $true )
| ( ( SV42 = SV127 )
= $true )
| ( ( ord_less_eq_set_a @ SV42 @ SV127 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[988]) ).
thf(1082,plain,
! [SV43: set_a,SV128: set_a] :
( ( ( ~ ( member_a @ ( sK2_SY497 @ SV128 @ SV43 ) @ SV43 )
| ( member_a @ ( sK2_SY497 @ SV128 @ SV43 ) @ SV128 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV43 @ SV128 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[989]) ).
thf(1083,plain,
! [SV190: a,SV130: a,SV46: a] :
( ( ( ~ ( ~ ~ ( ~ ( member_a @ SV46 @ carrier )
| ~ ( member_a @ SV130 @ carrier ) )
| ~ ( member_a @ SV190 @ carrier ) ) )
= $false )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV190 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV46 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV190 ) @ relation ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[991]) ).
thf(1084,plain,
! [SV225: a,SV191: a,SV131: set_Product_prod_a_a,SV47: set_a] :
( ( ( ~ ( prefer719835986ence_a @ SV47 @ SV131 ) )
= $true )
| ( ( ~ ( member_a @ SV191 @ SV47 )
| ~ ( member_a @ SV225 @ SV47 )
| ( member_a @ SV191 @ ( prefer1676310729than_a @ SV225 @ SV47 @ SV131 ) )
| ( member_a @ SV225 @ ( prefer1676310729than_a @ SV191 @ SV47 @ SV131 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[992]) ).
thf(1085,plain,
! [SV48: set_a,SV132: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV132 @ SV48 ) )
= $true )
| ( ( SV132 = SV48 )
= $true )
| ( ( ord_less_eq_set_a @ SV48 @ SV132 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[993]) ).
thf(1086,plain,
! [SV192: a,SV133: a,SV50: a] :
( ( ( ~ ( ~ ~ ( ~ ( member_a @ SV50 @ carrier )
| ~ ( member_a @ SV133 @ carrier ) )
| ~ ( member_a @ SV192 @ carrier ) ) )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV50 @ SV133 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV133 @ SV192 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV50 @ SV192 ) @ relation ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[994]) ).
thf(1087,plain,
! [SV193: a,SV134: set_a,SV51: set_a] :
( ( ( ord_less_eq_set_a @ SV51 @ SV134 )
= $false )
| ( ( ~ ( member_a @ SV193 @ SV51 )
| ( member_a @ SV193 @ SV134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[995]) ).
thf(1088,plain,
! [SV194: a,SV135: set_Product_prod_a_a,SV52: set_a] :
( ( ( prefer719835986ence_a @ SV52 @ SV135 )
= $false )
| ( ( ~ ( member_a @ SV194 @ SV52 )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV194 @ SV52 @ SV135 ) @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[996]) ).
thf(1089,plain,
! [SV53: set_a] :
( ( ( member_a @ ( sK1_SY360 @ SV53 ) @ SV53 )
= $true )
| ( ( ord_less_eq_set_a @ SV53 @ bot_bot_set_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[997]) ).
thf(1090,plain,
! [SV226: nat,SV195: set_a > nat,SV136: set_a,SV54: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV54 @ SV136 ) )
= $true )
| ( ( ( ( SV195 @ SV136 )
!= SV226 )
| ~ ! [SY585: set_a,SY586: set_a] :
( ~ ( ord_less_eq_set_a @ SY585 @ SY586 )
| ( ord_less_eq_nat @ ( SV195 @ SY585 ) @ ( SV195 @ SY586 ) ) )
| ( ord_less_eq_nat @ ( SV195 @ SV54 ) @ SV226 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[998]) ).
thf(1091,plain,
! [SV137: a > $o,SV55: a > $o] :
( ( ( ~ ( SV55 @ ( sK3_SY508 @ SV137 @ SV55 ) )
| ( SV137 @ ( sK3_SY508 @ SV137 @ SV55 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( collect_a @ SV55 ) @ ( collect_a @ SV137 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[999]) ).
thf(1092,plain,
! [SV227: set_a,SV138: set_a] :
( ( ~ ( ( SV138 = SV227 )
| ~ ( ~ ( ord_less_eq_set_a @ SV138 @ SV227 )
| ~ ( ord_less_eq_set_a @ SV227 @ SV138 ) ) )
| ~ ( ( SV138 != SV227 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV138 @ SV227 )
| ~ ( ord_less_eq_set_a @ SV227 @ SV138 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1000]) ).
thf(1093,plain,
! [SV227: set_a,SV138: set_a] :
( ( ( SV138 = SV227 )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV138 @ SV227 )
| ~ ( ord_less_eq_set_a @ SV227 @ SV138 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1000]) ).
thf(1094,plain,
! [SV228: set_a,SV197: set_a,SV139: set_a > set_a,SV57: set_a] :
( ( ( SV57
!= ( SV139 @ SV197 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV197 @ SV228 )
| ~ ! [SY513: set_a,SY514: set_a] :
( ~ ( ord_less_eq_set_a @ SY513 @ SY514 )
| ( ord_less_eq_set_a @ ( SV139 @ SY513 ) @ ( SV139 @ SY514 ) ) )
| ( ord_less_eq_set_a @ SV57 @ ( SV139 @ SV228 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1001]) ).
thf(1095,plain,
! [SV59: set_a,SV141: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV141 @ SV59 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ ( finite_card_a @ SV59 ) @ ( finite_card_a @ SV141 ) )
| ( SV141 = SV59 ) )
= $true )
| ( ( finite_finite_a @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1003]) ).
thf(1096,plain,
! [SV229: a,SV198: a,SV142: set_Product_prod_a_a,SV60: set_a] :
( ( ( ~ ( prefer719835986ence_a @ SV60 @ SV142 ) )
= $true )
| ( ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV198 @ SV60 @ SV142 ) @ ( prefer1676310729than_a @ SV229 @ SV60 @ SV142 ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV229 @ SV60 @ SV142 ) @ ( prefer1676310729than_a @ SV198 @ SV60 @ SV142 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1004]) ).
thf(1097,plain,
! [SV62: set_set_a,SV143: set_a] :
( ( ( ~ ( member_set_a @ SV143 @ SV62 ) )
= $true )
| ( ( ~ ! [SY517: set_a] :
~ ~ ( ~ ~ ( ~ ( member_set_a @ SY517 @ SV62 )
| ~ ( ord_less_eq_set_a @ SV143 @ SY517 ) )
| ~ ! [SY382: set_a] :
( ~ ( member_set_a @ SY382 @ SV62 )
| ~ ( ord_less_eq_set_a @ SY517 @ SY382 )
| ( SY517 = SY382 ) ) ) )
= $true )
| ( ( finite_finite_set_a @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1005]) ).
thf(1098,plain,
! [SV144: a,SV63: a] :
( ( ( ~ ( member_a @ SV63 @ carrier )
| ~ ( member_a @ SV144 @ carrier ) )
= $true )
| ( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1006]) ).
thf(1099,plain,
! [SV230: set_a,SV145: set_a] :
( ( ~ ( ( ord_less_eq_set_a @ SV145 @ SV230 )
| ! [SY630: a] :
( ~ ( member_a @ SY630 @ SV145 )
| ( member_a @ SY630 @ SV230 ) ) )
| ~ ( ~ ( ord_less_eq_set_a @ SV145 @ SV230 )
| ~ ! [SY630: a] :
( ~ ( member_a @ SY630 @ SV145 )
| ( member_a @ SY630 @ SV230 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1007]) ).
thf(1100,plain,
! [SV230: set_a,SV145: set_a] :
( ( ( ord_less_eq_set_a @ SV145 @ SV230 )
= ( ! [SY630: a] :
( ~ ( member_a @ SY630 @ SV145 )
| ( member_a @ SY630 @ SV230 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1007]) ).
thf(1101,plain,
! [SV65: set_a,SV146: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV146 @ SV65 ) )
= $true )
| ( ( SV65 = SV146 )
= $true )
| ( ( ord_less_eq_set_a @ SV65 @ SV146 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1008]) ).
thf(1102,plain,
! [SV231: a,SV200: a,SV147: set_Product_prod_a_a,SV66: set_a] :
( ( ( ~ ( prefer719835986ence_a @ SV66 @ SV147 ) )
= $true )
| ( ( ~ ( finite_finite_a @ SV66 )
| ~ ( member_a @ SV200 @ SV66 )
| ~ ( member_a @ SV231 @ SV66 )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1009]) ).
thf(1103,plain,
! [SV232: nat,SV201: set_a > nat,SV148: set_a,SV67: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV67 @ SV148 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ ( SV201 @ SV148 ) @ SV232 )
| ~ ! [SY594: set_a,SY595: set_a] :
( ~ ( ord_less_eq_set_a @ SY594 @ SY595 )
| ( ord_less_eq_nat @ ( SV201 @ SY594 ) @ ( SV201 @ SY595 ) ) )
| ( ord_less_eq_nat @ ( SV201 @ SV67 ) @ SV232 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1010]) ).
thf(1104,plain,
! [SV149: set_a,SV68: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV68 @ SV149 )
| ~ ( ord_less_eq_set_a @ SV149 @ SV68 ) )
= $false )
| ( ( SV68 = SV149 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1011]) ).
thf(1105,plain,
! [SV233: set_a,SV150: set_a] :
( ( ~ ( ( SV150 = SV233 )
| ~ ( ~ ( ord_less_eq_set_a @ SV150 @ SV233 )
| ~ ( ord_less_eq_set_a @ SV233 @ SV150 ) ) )
| ~ ( ( SV150 != SV233 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV150 @ SV233 )
| ~ ( ord_less_eq_set_a @ SV233 @ SV150 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1012]) ).
thf(1106,plain,
! [SV233: set_a,SV150: set_a] :
( ( ( SV150 = SV233 )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV150 @ SV233 )
| ~ ( ord_less_eq_set_a @ SV233 @ SV150 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1012]) ).
thf(1107,plain,
! [SV234: set_a,SV203: set_a > set_a,SV151: set_a,SV70: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV70 @ SV151 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ ( SV203 @ SV151 ) @ SV234 )
| ~ ! [SY597: set_a,SY598: set_a] :
( ~ ( ord_less_eq_set_a @ SY597 @ SY598 )
| ( ord_less_eq_set_a @ ( SV203 @ SY597 ) @ ( SV203 @ SY598 ) ) )
| ( ord_less_eq_set_a @ ( SV203 @ SV70 ) @ SV234 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1013]) ).
thf(1108,plain,
! [SV71: a,SV152: a] :
( ( ( ~ ( member_a @ SV152 @ carrier ) )
= $true )
| ( ( ( ~ ( ~ ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
| ~ ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1014]) ).
thf(1109,plain,
! [SV235: set_a,SV204: set_a,SV153: set_a,SV72: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV72 @ SV153 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV204 @ SV235 )
| ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV72 @ SV204 ) @ ( produc1928581911_set_a @ SV153 @ SV235 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1015]) ).
thf(1110,plain,
! [SV205: a,SV154: set_a,SV73: set_a] :
( ( ( ord_less_eq_set_a @ SV73 @ SV154 )
= $false )
| ( ( ~ ( member_a @ SV205 @ SV73 )
| ( member_a @ SV205 @ SV154 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1016]) ).
thf(1111,plain,
! [SV236: a,SV206: a,SV155: set_Product_prod_a_a,SV74: set_a] :
( ( ( ~ ( prefer719835986ence_a @ SV74 @ SV155 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV206 @ SV236 ) @ SV155 )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV236 @ SV74 @ SV155 ) @ ( prefer1676310729than_a @ SV206 @ SV74 @ SV155 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1017]) ).
thf(1112,plain,
! [SV237: set_a,SV207: set_a,SV156: set_a > nat,SV75: nat] :
( ( ( SV75
!= ( SV156 @ SV207 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV207 @ SV237 )
| ~ ! [SY540: set_a,SY541: set_a] :
( ~ ( ord_less_eq_set_a @ SY540 @ SY541 )
| ( ord_less_eq_nat @ ( SV156 @ SY540 ) @ ( SV156 @ SY541 ) ) )
| ( ord_less_eq_nat @ SV75 @ ( SV156 @ SV237 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1018]) ).
thf(1113,plain,
! [SV157: a > $o,SV76: a > $o] :
( ( ( ( ord_less_eq_set_a @ ( collect_a @ SV76 ) @ ( collect_a @ SV157 ) )
| ! [SY542: a] :
( ~ ( SV76 @ SY542 )
| ( SV157 @ SY542 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ ( collect_a @ SV76 ) @ ( collect_a @ SV157 ) )
| ~ ! [SY542: a] :
( ~ ( SV76 @ SY542 )
| ( SV157 @ SY542 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1019]) ).
thf(1114,plain,
! [SV77: set_a,SV158: nat] :
( ( ( ~ ( ord_less_eq_set_a @ ( sK4_SY543 @ SV158 @ SV77 ) @ SV77 )
| ~ ( finite_finite_a @ ( sK4_SY543 @ SV158 @ SV77 ) )
| ( ord_less_eq_nat @ ( finite_card_a @ ( sK4_SY543 @ SV158 @ SV77 ) ) @ SV158 ) )
= $false )
| ( ( ~ ( ~ ( finite_finite_a @ SV77 )
| ~ ( ord_less_eq_nat @ ( finite_card_a @ SV77 ) @ SV158 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1020]) ).
thf(1115,plain,
! [SV78: a,SV159: a] :
( ( ( ~ ( member_a @ SV159 @ carrier ) )
= $true )
| ( ( ~ ( ( SV78 != SV159 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV78 @ SV159 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV159 @ SV78 ) @ relation ) )
= $true )
| ( ( member_a @ SV78 @ carrier )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1021]) ).
thf(1116,plain,
! [SV160: set_a,SV79: set_a] :
( ( ( ~ ~ ( finite_finite_a @ SV79 ) )
= $true )
| ( ( ~ ( finite_finite_a @ SV160 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV79 @ SV160 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1022]) ).
thf(1117,plain,
! [SV238: set_a,SV208: nat > set_a,SV161: nat,SV80: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV80 @ SV161 ) )
= $true )
| ( ( ( ( SV208 @ SV161 )
!= SV238 )
| ~ ! [SY605: nat,SY606: nat] :
( ~ ( ord_less_eq_nat @ SY605 @ SY606 )
| ( ord_less_eq_set_a @ ( SV208 @ SY605 ) @ ( SV208 @ SY606 ) ) )
| ( ord_less_eq_set_a @ ( SV208 @ SV80 ) @ SV238 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1023]) ).
thf(1118,plain,
! [SV239: set_a,SV209: set_a > set_a,SV162: set_a,SV81: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV81 @ SV162 ) )
= $true )
| ( ( ( ( SV209 @ SV162 )
!= SV239 )
| ~ ! [SY608: set_a,SY609: set_a] :
( ~ ( ord_less_eq_set_a @ SY608 @ SY609 )
| ( ord_less_eq_set_a @ ( SV209 @ SY608 ) @ ( SV209 @ SY609 ) ) )
| ( ord_less_eq_set_a @ ( SV209 @ SV81 ) @ SV239 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1024]) ).
thf(1119,plain,
! [SV163: nat,SV82: set_a] :
( ( ( finite_finite_a @ SV82 )
= $true )
| ( ( ~ ! [SY552: set_a] :
~ ~ ( ~ ~ ( ~ ( finite_finite_a @ SY552 )
| ( ( finite_card_a @ SY552 )
!= SV163 ) )
| ~ ( ord_less_eq_set_a @ SY552 @ SV82 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1025]) ).
thf(1120,plain,
! [SV210: a,SV164: a,SV83: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SV164 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV83 ) @ relation ) ) )
= $false )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV210 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV210 @ SV164 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SV210 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV210 @ SV83 ) @ relation ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1026]) ).
thf(1121,plain,
! [SV240: set_a,SV211: set_a,SV166: set_a > nat,SV85: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV85 @ ( SV166 @ SV211 ) ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV211 @ SV240 )
| ~ ! [SY556: set_a,SY557: set_a] :
( ~ ( ord_less_eq_set_a @ SY556 @ SY557 )
| ( ord_less_eq_nat @ ( SV166 @ SY556 ) @ ( SV166 @ SY557 ) ) )
| ( ord_less_eq_nat @ SV85 @ ( SV166 @ SV240 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1028]) ).
thf(1122,plain,
! [SV241: nat,SV212: nat,SV168: nat > set_a,SV87: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV87 @ ( SV168 @ SV212 ) ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV212 @ SV241 )
| ~ ! [SY560: nat,SY561: nat] :
( ~ ( ord_less_eq_nat @ SY560 @ SY561 )
| ( ord_less_eq_set_a @ ( SV168 @ SY560 ) @ ( SV168 @ SY561 ) ) )
| ( ord_less_eq_set_a @ SV87 @ ( SV168 @ SV241 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1030]) ).
thf(1123,plain,
! [SV242: set_a,SV213: nat > set_a,SV170: nat,SV89: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV89 @ SV170 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ ( SV213 @ SV170 ) @ SV242 )
| ~ ! [SY617: nat,SY618: nat] :
( ~ ( ord_less_eq_nat @ SY617 @ SY618 )
| ( ord_less_eq_set_a @ ( SV213 @ SY617 ) @ ( SV213 @ SY618 ) ) )
| ( ord_less_eq_set_a @ ( SV213 @ SV89 ) @ SV242 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1032]) ).
thf(1124,plain,
! [SV214: set_a,SV171: set_a,SV90: set_a] :
( ( ( ord_less_eq_set_a @ SV90 @ SV171 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV171 @ SV214 )
| ( ord_less_eq_set_a @ SV90 @ SV214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1033]) ).
thf(1125,plain,
! [SV243: set_a,SV215: set_a,SV172: set_a > set_a,SV91: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV91 @ ( SV172 @ SV215 ) ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV215 @ SV243 )
| ~ ! [SY569: set_a,SY570: set_a] :
( ~ ( ord_less_eq_set_a @ SY569 @ SY570 )
| ( ord_less_eq_set_a @ ( SV172 @ SY569 ) @ ( SV172 @ SY570 ) ) )
| ( ord_less_eq_set_a @ SV91 @ ( SV172 @ SV243 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1034]) ).
thf(1126,plain,
! [SV244: set_a,SV173: set_a] :
( ( ~ ( ( SV173 = SV244 )
| ~ ( ~ ( ord_less_eq_set_a @ SV173 @ SV244 )
| ~ ( ord_less_eq_set_a @ SV244 @ SV173 ) ) )
| ~ ( ( SV173 != SV244 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV173 @ SV244 )
| ~ ( ord_less_eq_set_a @ SV244 @ SV173 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1035]) ).
thf(1127,plain,
! [SV244: set_a,SV173: set_a] :
( ( ( SV173 = SV244 )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV173 @ SV244 )
| ~ ( ord_less_eq_set_a @ SV244 @ SV173 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1035]) ).
thf(1128,plain,
! [SV93: a,SV245: a] :
( ( ( ~ ( member_a @ SV245 @ carrier ) )
= $true )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV93 @ SV245 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV245 @ SV93 ) @ relation ) )
= $true )
| ( ( member_a @ SV93 @ carrier )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1036]) ).
thf(1129,plain,
! [SV246: nat,SV217: nat,SV174: nat > set_a,SV94: set_a] :
( ( ( SV94
!= ( SV174 @ SV217 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV217 @ SV246 )
| ~ ! [SY575: nat,SY576: nat] :
( ~ ( ord_less_eq_nat @ SY575 @ SY576 )
| ( ord_less_eq_set_a @ ( SV174 @ SY575 ) @ ( SV174 @ SY576 ) ) )
| ( ord_less_eq_set_a @ SV94 @ ( SV174 @ SV246 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1037]) ).
thf(1130,plain,
! [SV175: a,SV95: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV95 @ SV175 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV175 @ SV95 ) @ relation ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV95 @ SV175 ) @ relation )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1038]) ).
thf(1131,plain,
! [SV3: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
| ( SV3 != bot_bot_set_a ) )
= $false )
| ( ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1039]) ).
thf(1132,plain,
! [SV3: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
| ( SV3 != bot_bot_set_a ) )
= $false )
| ( ( SV3 = bot_bot_set_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1040]) ).
thf(1133,plain,
! [SV7: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
| ( SV7 != bot_bot_set_a ) )
= $false )
| ( ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1041]) ).
thf(1134,plain,
! [SV7: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
| ( SV7 != bot_bot_set_a ) )
= $false )
| ( ( SV7 = bot_bot_set_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1042]) ).
thf(1135,plain,
! [SV176: a,SV97: a,SV9: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV97 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV9 ) @ relation ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV176 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV97 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV176 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV9 ) @ relation ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1043]) ).
thf(1136,plain,
! [SV10: set_a,SV98: set_a] :
( ( ( ord_less_eq_set_a @ SV98 @ SV10 )
= $false )
| ( ( SV10 = SV98 )
= $true )
| ( ( ord_less_eq_set_a @ SV10 @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1044]) ).
thf(1137,plain,
! [SV218: nat,SV177: nat,SV99: set_a,SV11: set_a] :
( ( ( ord_less_eq_set_a @ SV11 @ SV99 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV177 @ SV218 )
| ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV11 @ SV177 ) @ ( produc515611863_a_nat @ SV99 @ SV218 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1045]) ).
thf(1138,plain,
! [SV100: set_Product_prod_a_a,SV12: set_a] :
( ( ( finite_finite_a @ SV12 )
= $false )
| ( ( ! [SY474: a] :
( ~ ( member_a @ SY474 @ SV12 )
| ( finite_finite_a @ ( prefer1676310729than_a @ SY474 @ SV12 @ SV100 ) ) ) )
= $true )
| ( ( prefer719835986ence_a @ SV12 @ SV100 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1046]) ).
thf(1139,plain,
! [SV13: set_set_a] :
( ( ( SV13 = bot_bot_set_set_a )
= $true )
| ( ( ~ ! [SY294: set_a] :
~ ~ ( ~ ( member_set_a @ SY294 @ SV13 )
| ~ ! [SY295: set_a] :
( ~ ( member_set_a @ SY295 @ SV13 )
| ~ ( ord_less_eq_set_a @ SY295 @ SY294 )
| ( SY294 = SY295 ) ) ) )
= $true )
| ( ( finite_finite_set_a @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1047]) ).
thf(1140,plain,
! [SV14: set_a,SV101: set_a] :
( ( ( ~ ( ( ord_less_eq_set_a @ SV101 @ SV14 )
| ( SV101 = SV14 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV101 @ SV14 )
| ( SV101 != SV14 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV14 @ SV101 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1048]) ).
thf(1141,plain,
! [SV15: a,SV102: a] :
( ( ( member_a @ SV102 @ carrier )
= $false )
| ( ( ( member_a @ SV15 @ ( prefer1676310729than_a @ SV102 @ carrier @ relation ) )
| ( member_a @ SV102 @ ( prefer1676310729than_a @ SV15 @ carrier @ relation ) ) )
= $true )
| ( ( member_a @ SV15 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1050]) ).
thf(1142,plain,
! [SV16: set_set_a,SV103: set_a] :
( ( ( member_set_a @ SV103 @ SV16 )
= $false )
| ( ( ~ ! [SY475: set_a] :
~ ~ ( ~ ~ ( ~ ( member_set_a @ SY475 @ SV16 )
| ~ ( ord_less_eq_set_a @ SY475 @ SV103 ) )
| ~ ! [SY300: set_a] :
( ~ ( member_set_a @ SY300 @ SV16 )
| ~ ( ord_less_eq_set_a @ SY300 @ SY475 )
| ( SY475 = SY300 ) ) ) )
= $true )
| ( ( finite_finite_set_a @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1051]) ).
thf(1143,plain,
! [SV104: a,SV17: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV17 @ SV104 ) @ relation ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV104 @ SV17 ) @ relation ) )
= $true )
| ( ( ( prefer161218362good_a @ SV17 @ carrier @ relation )
= ( prefer161218362good_a @ SV104 @ carrier @ relation ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1052]) ).
thf(1144,plain,
! [SV18: set_a,SV178: set_a,SV105: set_a] :
( ( ( SV105 != SV178 )
= $true )
| ( ( ord_less_eq_set_a @ SV18 @ SV178 )
= $true )
| ( ( ord_less_eq_set_a @ SV18 @ SV105 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1053]) ).
thf(1145,plain,
! [SV219: set_a,SV179: set_a,SV106: nat,SV19: nat] :
( ( ( ord_less_eq_nat @ SV19 @ SV106 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV179 @ SV219 )
| ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV19 @ SV179 ) @ ( produc1450889781_set_a @ SV106 @ SV219 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1054]) ).
thf(1146,plain,
! [SV107: set_a,SV20: set_a,SV180: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV180 @ SV20 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV180 @ SV107 )
= $true )
| ( ( ord_less_eq_set_a @ SV20 @ SV107 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1055]) ).
thf(1147,plain,
! [SV220: set_a,SV181: nat,SV109: set_a,SV22: nat] :
( ( ( ~ ( ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV22 @ SV109 ) @ ( produc1450889781_set_a @ SV181 @ SV220 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV22 @ SV181 )
| ~ ( ord_less_eq_set_a @ SV109 @ SV220 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV22 @ SV109 ) @ ( produc1450889781_set_a @ SV181 @ SV220 ) )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV22 @ SV181 )
| ~ ( ord_less_eq_set_a @ SV109 @ SV220 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1056]) ).
thf(1148,plain,
! [SV221: set_a,SV110: set_a] :
( ( ( ~ ( ( SV110 = SV221 )
| ~ ( ~ ( ord_less_eq_set_a @ SV221 @ SV110 )
| ~ ( ord_less_eq_set_a @ SV110 @ SV221 ) ) ) )
= $true )
| ( ( ~ ( ( SV110 != SV221 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV221 @ SV110 )
| ~ ( ord_less_eq_set_a @ SV110 @ SV221 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1058]) ).
thf(1149,plain,
! [SV222: set_a,SV183: set_a,SV111: set_a,SV24: set_a] :
( ( ( ~ ( ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV24 @ SV111 ) @ ( produc1928581911_set_a @ SV183 @ SV222 ) )
| ~ ( ~ ( ord_less_eq_set_a @ SV24 @ SV183 )
| ~ ( ord_less_eq_set_a @ SV111 @ SV222 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV24 @ SV111 ) @ ( produc1928581911_set_a @ SV183 @ SV222 ) )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV24 @ SV183 )
| ~ ( ord_less_eq_set_a @ SV111 @ SV222 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1060]) ).
thf(1150,plain,
! [SV112: a,SV25: a] :
( ( ( member_a @ SV25 @ carrier )
= $false )
| ( ( ~ ( member_a @ SV112 @ carrier )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV25 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV25 @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV25 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV25 @ carrier @ relation ) ) )
= $true )
| ( ( finite_finite_a @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1062]) ).
thf(1151,plain,
! [SV113: a,SV26: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV26 @ SV113 ) @ relation ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV113 @ SV26 ) @ relation ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV113 @ SV26 ) @ relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1063]) ).
thf(1152,plain,
! [SV27: set_a,SV184: set_a,SV114: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV114 @ SV184 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV27 @ SV184 )
= $true )
| ( ( ord_less_eq_set_a @ SV27 @ SV114 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1064]) ).
thf(1153,plain,
! [SV28: set_a,SV115: set_a] :
( ( ( finite_finite_a @ SV115 )
= $false )
| ( ( finite_finite_a @ SV28 )
= $true )
| ( ( ord_less_eq_set_a @ SV28 @ SV115 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1065]) ).
thf(1154,plain,
! [SV29: a] :
( ( ( member_a @ SV29 @ carrier )
= $false )
| ( ( ( prefer1676310729than_a @ SV29 @ carrier @ relation )
!= bot_bot_set_a )
= $true )
| ( ( carrier = bot_bot_set_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1066]) ).
thf(1155,plain,
! [SV30: a,SV116: a] :
( ( ( member_a @ SV116 @ carrier )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV116 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV30 @ carrier @ relation ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV30 @ SV116 ) @ relation ) )
= $true )
| ( ( member_a @ SV30 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1067]) ).
thf(1156,plain,
! [SV31: set_a,SV185: set_a,SV117: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV117 @ SV185 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV31 @ SV185 )
= $true )
| ( ( ord_less_eq_set_a @ SV31 @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1068]) ).
thf(1157,plain,
! [SV32: set_a,SV118: set_a] :
( ( ( ord_less_eq_set_a @ SV118 @ SV32 )
= $false )
| ( ( ord_less_eq_nat @ ( finite_card_a @ SV118 ) @ ( finite_card_a @ SV32 ) )
= $true )
| ( ( finite_finite_a @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1069]) ).
thf(1158,plain,
! [SV119: set_a,SV33: nat] :
( ( ( ~ ( ord_less_eq_set_a @ ( sK5_SY489 @ SV33 @ SV119 ) @ SV119 )
| ( ( finite_card_a @ ( sK5_SY489 @ SV33 @ SV119 ) )
!= SV33 )
| ~ ( finite_finite_a @ ( sK5_SY489 @ SV33 @ SV119 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV33 @ ( finite_card_a @ SV119 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1070]) ).
thf(1159,plain,
! [SV34: set_set_a] :
( ( ( SV34 = bot_bot_set_set_a )
= $true )
| ( ( ~ ! [SY329: set_a] :
~ ~ ( ~ ( member_set_a @ SY329 @ SV34 )
| ~ ! [SY330: set_a] :
( ~ ( member_set_a @ SY330 @ SV34 )
| ~ ( ord_less_eq_set_a @ SY329 @ SY330 )
| ( SY329 = SY330 ) ) ) )
= $true )
| ( ( finite_finite_set_a @ SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1071]) ).
thf(1160,plain,
! [SV35: set_a,SV120: set_a] :
( ( ( ord_less_eq_set_a @ SV120 @ SV35 )
= $false )
| ( ( ( ( finite_card_a @ SV120 )
!= ( finite_card_a @ SV35 ) )
| ( SV120 = SV35 ) )
= $true )
| ( ( finite_finite_a @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1072]) ).
thf(1161,plain,
! [SV121: set_a,SV36: nat] :
( ( ( ~ ~ ( ~ ( ord_less_eq_set_a @ ( sK6_SY490 @ SV36 @ SV121 ) @ SV121 )
| ( ( finite_card_a @ ( sK6_SY490 @ SV36 @ SV121 ) )
!= SV36 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV36 @ ( finite_card_a @ SV121 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1073]) ).
thf(1162,plain,
! [SV37: set_a,SV186: set_a,SV122: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV122 @ SV186 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV37 @ SV186 )
= $true )
| ( ( SV37 = SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1074]) ).
thf(1163,plain,
! [SV223: nat,SV187: set_a,SV123: nat,SV38: set_a] :
( ( ( ~ ( ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV38 @ SV123 ) @ ( produc515611863_a_nat @ SV187 @ SV223 ) )
| ~ ( ~ ( ord_less_eq_set_a @ SV38 @ SV187 )
| ~ ( ord_less_eq_nat @ SV123 @ SV223 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV38 @ SV123 ) @ ( produc515611863_a_nat @ SV187 @ SV223 ) )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV38 @ SV187 )
| ~ ( ord_less_eq_nat @ SV123 @ SV223 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1075]) ).
thf(1164,plain,
! [SV124: set_Product_prod_a_a,SV188: a,SV39: set_a] :
( ( ( ~ ( ( SV39 != bot_bot_set_a ) ) )
= $true )
| ( ( ~ ( member_a @ SV188 @ SV39 )
| ( ( prefer1676310729than_a @ SV188 @ SV39 @ SV124 )
!= bot_bot_set_a ) )
= $true )
| ( ( prefer719835986ence_a @ SV39 @ SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1077]) ).
thf(1165,plain,
! [SV40: set_a,SV125: set_a] :
( ( ( ord_less_eq_set_a @ SV125 @ SV40 )
= $false )
| ( ( finite_finite_a @ SV125 )
= $true )
| ( ( finite_finite_a @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1078]) ).
thf(1166,plain,
! [SV224: set_a,SV126: set_a] :
( ( ( ~ ( ( ord_less_eq_set_a @ SV126 @ SV224 )
| ! [SY625: a] :
( ~ ( member_a @ SY625 @ SV126 )
| ( member_a @ SY625 @ SV224 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV126 @ SV224 )
| ~ ! [SY625: a] :
( ~ ( member_a @ SY625 @ SV126 )
| ( member_a @ SY625 @ SV224 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1079]) ).
thf(1167,plain,
! [SV42: set_a,SV127: set_a] :
( ( ( ord_less_eq_set_a @ SV127 @ SV42 )
= $false )
| ( ( SV42 = SV127 )
= $true )
| ( ( ord_less_eq_set_a @ SV42 @ SV127 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1081]) ).
thf(1168,plain,
! [SV43: set_a,SV128: set_a] :
( ( ( ~ ( member_a @ ( sK2_SY497 @ SV128 @ SV43 ) @ SV43 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV43 @ SV128 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1082]) ).
thf(1169,plain,
! [SV43: set_a,SV128: set_a] :
( ( ( member_a @ ( sK2_SY497 @ SV128 @ SV43 ) @ SV128 )
= $false )
| ( ( ord_less_eq_set_a @ SV43 @ SV128 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1082]) ).
thf(1170,plain,
! [SV190: a,SV130: a,SV46: a] :
( ( ( ~ ~ ( ~ ( member_a @ SV46 @ carrier )
| ~ ( member_a @ SV130 @ carrier ) )
| ~ ( member_a @ SV190 @ carrier ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV190 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV46 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV190 ) @ relation ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1083]) ).
thf(1171,plain,
! [SV225: a,SV191: a,SV131: set_Product_prod_a_a,SV47: set_a] :
( ( ( prefer719835986ence_a @ SV47 @ SV131 )
= $false )
| ( ( ~ ( member_a @ SV191 @ SV47 )
| ~ ( member_a @ SV225 @ SV47 )
| ( member_a @ SV191 @ ( prefer1676310729than_a @ SV225 @ SV47 @ SV131 ) )
| ( member_a @ SV225 @ ( prefer1676310729than_a @ SV191 @ SV47 @ SV131 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1084]) ).
thf(1172,plain,
! [SV48: set_a,SV132: set_a] :
( ( ( ord_less_eq_set_a @ SV132 @ SV48 )
= $false )
| ( ( SV132 = SV48 )
= $true )
| ( ( ord_less_eq_set_a @ SV48 @ SV132 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1085]) ).
thf(1173,plain,
! [SV192: a,SV133: a,SV50: a] :
( ( ( ~ ~ ( ~ ( member_a @ SV50 @ carrier )
| ~ ( member_a @ SV133 @ carrier ) )
| ~ ( member_a @ SV192 @ carrier ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV50 @ SV133 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV133 @ SV192 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV50 @ SV192 ) @ relation ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1086]) ).
thf(1174,plain,
! [SV134: set_a,SV51: set_a,SV193: a] :
( ( ( ~ ( member_a @ SV193 @ SV51 ) )
= $true )
| ( ( member_a @ SV193 @ SV134 )
= $true )
| ( ( ord_less_eq_set_a @ SV51 @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1087]) ).
thf(1175,plain,
! [SV135: set_Product_prod_a_a,SV52: set_a,SV194: a] :
( ( ( ~ ( member_a @ SV194 @ SV52 ) )
= $true )
| ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV194 @ SV52 @ SV135 ) @ SV52 )
= $true )
| ( ( prefer719835986ence_a @ SV52 @ SV135 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1088]) ).
thf(1176,plain,
! [SV226: nat,SV195: set_a > nat,SV136: set_a,SV54: set_a] :
( ( ( ord_less_eq_set_a @ SV54 @ SV136 )
= $false )
| ( ( ( ( SV195 @ SV136 )
!= SV226 )
| ~ ! [SY585: set_a,SY586: set_a] :
( ~ ( ord_less_eq_set_a @ SY585 @ SY586 )
| ( ord_less_eq_nat @ ( SV195 @ SY585 ) @ ( SV195 @ SY586 ) ) )
| ( ord_less_eq_nat @ ( SV195 @ SV54 ) @ SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1090]) ).
thf(1177,plain,
! [SV137: a > $o,SV55: a > $o] :
( ( ( ~ ( SV55 @ ( sK3_SY508 @ SV137 @ SV55 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( collect_a @ SV55 ) @ ( collect_a @ SV137 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1091]) ).
thf(1178,plain,
! [SV55: a > $o,SV137: a > $o] :
( ( ( SV137 @ ( sK3_SY508 @ SV137 @ SV55 ) )
= $false )
| ( ( ord_less_eq_set_a @ ( collect_a @ SV55 ) @ ( collect_a @ SV137 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1091]) ).
thf(1179,plain,
! [SV227: set_a,SV138: set_a] :
( ( ( ~ ( ( SV138 = SV227 )
| ~ ( ~ ( ord_less_eq_set_a @ SV138 @ SV227 )
| ~ ( ord_less_eq_set_a @ SV227 @ SV138 ) ) ) )
= $true )
| ( ( ~ ( ( SV138 != SV227 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV138 @ SV227 )
| ~ ( ord_less_eq_set_a @ SV227 @ SV138 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1092]) ).
thf(1180,plain,
! [SV228: set_a,SV197: set_a,SV139: set_a > set_a,SV57: set_a] :
( ( ( SV57
= ( SV139 @ SV197 ) )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV197 @ SV228 )
| ~ ! [SY513: set_a,SY514: set_a] :
( ~ ( ord_less_eq_set_a @ SY513 @ SY514 )
| ( ord_less_eq_set_a @ ( SV139 @ SY513 ) @ ( SV139 @ SY514 ) ) )
| ( ord_less_eq_set_a @ SV57 @ ( SV139 @ SV228 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1094]) ).
thf(1181,plain,
! [SV59: set_a,SV141: set_a] :
( ( ( ord_less_eq_set_a @ SV141 @ SV59 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ ( finite_card_a @ SV59 ) @ ( finite_card_a @ SV141 ) )
| ( SV141 = SV59 ) )
= $true )
| ( ( finite_finite_a @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1095]) ).
thf(1182,plain,
! [SV229: a,SV198: a,SV142: set_Product_prod_a_a,SV60: set_a] :
( ( ( prefer719835986ence_a @ SV60 @ SV142 )
= $false )
| ( ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV198 @ SV60 @ SV142 ) @ ( prefer1676310729than_a @ SV229 @ SV60 @ SV142 ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV229 @ SV60 @ SV142 ) @ ( prefer1676310729than_a @ SV198 @ SV60 @ SV142 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1096]) ).
thf(1183,plain,
! [SV62: set_set_a,SV143: set_a] :
( ( ( member_set_a @ SV143 @ SV62 )
= $false )
| ( ( ~ ! [SY517: set_a] :
~ ~ ( ~ ~ ( ~ ( member_set_a @ SY517 @ SV62 )
| ~ ( ord_less_eq_set_a @ SV143 @ SY517 ) )
| ~ ! [SY382: set_a] :
( ~ ( member_set_a @ SY382 @ SV62 )
| ~ ( ord_less_eq_set_a @ SY517 @ SY382 )
| ( SY517 = SY382 ) ) ) )
= $true )
| ( ( finite_finite_set_a @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1097]) ).
thf(1184,plain,
! [SV144: a,SV63: a] :
( ( ( ~ ( member_a @ SV63 @ carrier ) )
= $true )
| ( ( ~ ( member_a @ SV144 @ carrier ) )
= $true )
| ( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1098]) ).
thf(1185,plain,
! [SV230: set_a,SV145: set_a] :
( ( ( ~ ( ( ord_less_eq_set_a @ SV145 @ SV230 )
| ! [SY630: a] :
( ~ ( member_a @ SY630 @ SV145 )
| ( member_a @ SY630 @ SV230 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV145 @ SV230 )
| ~ ! [SY630: a] :
( ~ ( member_a @ SY630 @ SV145 )
| ( member_a @ SY630 @ SV230 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1099]) ).
thf(1186,plain,
! [SV65: set_a,SV146: set_a] :
( ( ( ord_less_eq_set_a @ SV146 @ SV65 )
= $false )
| ( ( SV65 = SV146 )
= $true )
| ( ( ord_less_eq_set_a @ SV65 @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1101]) ).
thf(1187,plain,
! [SV231: a,SV200: a,SV147: set_Product_prod_a_a,SV66: set_a] :
( ( ( prefer719835986ence_a @ SV66 @ SV147 )
= $false )
| ( ( ~ ( finite_finite_a @ SV66 )
| ~ ( member_a @ SV200 @ SV66 )
| ~ ( member_a @ SV231 @ SV66 )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1102]) ).
thf(1188,plain,
! [SV232: nat,SV201: set_a > nat,SV148: set_a,SV67: set_a] :
( ( ( ord_less_eq_set_a @ SV67 @ SV148 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ ( SV201 @ SV148 ) @ SV232 )
| ~ ! [SY594: set_a,SY595: set_a] :
( ~ ( ord_less_eq_set_a @ SY594 @ SY595 )
| ( ord_less_eq_nat @ ( SV201 @ SY594 ) @ ( SV201 @ SY595 ) ) )
| ( ord_less_eq_nat @ ( SV201 @ SV67 ) @ SV232 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1103]) ).
thf(1189,plain,
! [SV149: set_a,SV68: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV68 @ SV149 ) )
= $false )
| ( ( SV68 = SV149 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1104]) ).
thf(1190,plain,
! [SV68: set_a,SV149: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV149 @ SV68 ) )
= $false )
| ( ( SV68 = SV149 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1104]) ).
thf(1191,plain,
! [SV233: set_a,SV150: set_a] :
( ( ( ~ ( ( SV150 = SV233 )
| ~ ( ~ ( ord_less_eq_set_a @ SV150 @ SV233 )
| ~ ( ord_less_eq_set_a @ SV233 @ SV150 ) ) ) )
= $true )
| ( ( ~ ( ( SV150 != SV233 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV150 @ SV233 )
| ~ ( ord_less_eq_set_a @ SV233 @ SV150 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1105]) ).
thf(1192,plain,
! [SV234: set_a,SV203: set_a > set_a,SV151: set_a,SV70: set_a] :
( ( ( ord_less_eq_set_a @ SV70 @ SV151 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ ( SV203 @ SV151 ) @ SV234 )
| ~ ! [SY597: set_a,SY598: set_a] :
( ~ ( ord_less_eq_set_a @ SY597 @ SY598 )
| ( ord_less_eq_set_a @ ( SV203 @ SY597 ) @ ( SV203 @ SY598 ) ) )
| ( ord_less_eq_set_a @ ( SV203 @ SV70 ) @ SV234 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1107]) ).
thf(1193,plain,
! [SV71: a,SV152: a] :
( ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( ( ~ ( ~ ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
| ~ ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1108]) ).
thf(1194,plain,
! [SV235: set_a,SV204: set_a,SV153: set_a,SV72: set_a] :
( ( ( ord_less_eq_set_a @ SV72 @ SV153 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV204 @ SV235 )
| ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV72 @ SV204 ) @ ( produc1928581911_set_a @ SV153 @ SV235 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1109]) ).
thf(1195,plain,
! [SV154: set_a,SV73: set_a,SV205: a] :
( ( ( ~ ( member_a @ SV205 @ SV73 ) )
= $true )
| ( ( member_a @ SV205 @ SV154 )
= $true )
| ( ( ord_less_eq_set_a @ SV73 @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1110]) ).
thf(1196,plain,
! [SV236: a,SV206: a,SV155: set_Product_prod_a_a,SV74: set_a] :
( ( ( prefer719835986ence_a @ SV74 @ SV155 )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV206 @ SV236 ) @ SV155 )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV236 @ SV74 @ SV155 ) @ ( prefer1676310729than_a @ SV206 @ SV74 @ SV155 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1111]) ).
thf(1197,plain,
! [SV237: set_a,SV207: set_a,SV156: set_a > nat,SV75: nat] :
( ( ( SV75
= ( SV156 @ SV207 ) )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV207 @ SV237 )
| ~ ! [SY540: set_a,SY541: set_a] :
( ~ ( ord_less_eq_set_a @ SY540 @ SY541 )
| ( ord_less_eq_nat @ ( SV156 @ SY540 ) @ ( SV156 @ SY541 ) ) )
| ( ord_less_eq_nat @ SV75 @ ( SV156 @ SV237 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1112]) ).
thf(1198,plain,
! [SV157: a > $o,SV76: a > $o] :
( ( ( ord_less_eq_set_a @ ( collect_a @ SV76 ) @ ( collect_a @ SV157 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ ( collect_a @ SV76 ) @ ( collect_a @ SV157 ) )
| ~ ! [SY542: a] :
( ~ ( SV76 @ SY542 )
| ( SV157 @ SY542 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1113]) ).
thf(1199,plain,
! [SV157: a > $o,SV76: a > $o] :
( ( ( ! [SY542: a] :
( ~ ( SV76 @ SY542 )
| ( SV157 @ SY542 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ ( collect_a @ SV76 ) @ ( collect_a @ SV157 ) )
| ~ ! [SY542: a] :
( ~ ( SV76 @ SY542 )
| ( SV157 @ SY542 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1113]) ).
thf(1200,plain,
! [SV77: set_a,SV158: nat] :
( ( ( ~ ( ord_less_eq_set_a @ ( sK4_SY543 @ SV158 @ SV77 ) @ SV77 ) )
= $false )
| ( ( ~ ( ~ ( finite_finite_a @ SV77 )
| ~ ( ord_less_eq_nat @ ( finite_card_a @ SV77 ) @ SV158 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1114]) ).
thf(1201,plain,
! [SV77: set_a,SV158: nat] :
( ( ( ~ ( finite_finite_a @ ( sK4_SY543 @ SV158 @ SV77 ) )
| ( ord_less_eq_nat @ ( finite_card_a @ ( sK4_SY543 @ SV158 @ SV77 ) ) @ SV158 ) )
= $false )
| ( ( ~ ( ~ ( finite_finite_a @ SV77 )
| ~ ( ord_less_eq_nat @ ( finite_card_a @ SV77 ) @ SV158 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1114]) ).
thf(1202,plain,
! [SV78: a,SV159: a] :
( ( ( member_a @ SV159 @ carrier )
= $false )
| ( ( ~ ( ( SV78 != SV159 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV78 @ SV159 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV159 @ SV78 ) @ relation ) )
= $true )
| ( ( member_a @ SV78 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1115]) ).
thf(1203,plain,
! [SV160: set_a,SV79: set_a] :
( ( ( ~ ( finite_finite_a @ SV79 ) )
= $false )
| ( ( ~ ( finite_finite_a @ SV160 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV79 @ SV160 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1116]) ).
thf(1204,plain,
! [SV238: set_a,SV208: nat > set_a,SV161: nat,SV80: nat] :
( ( ( ord_less_eq_nat @ SV80 @ SV161 )
= $false )
| ( ( ( ( SV208 @ SV161 )
!= SV238 )
| ~ ! [SY605: nat,SY606: nat] :
( ~ ( ord_less_eq_nat @ SY605 @ SY606 )
| ( ord_less_eq_set_a @ ( SV208 @ SY605 ) @ ( SV208 @ SY606 ) ) )
| ( ord_less_eq_set_a @ ( SV208 @ SV80 ) @ SV238 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1117]) ).
thf(1205,plain,
! [SV239: set_a,SV209: set_a > set_a,SV162: set_a,SV81: set_a] :
( ( ( ord_less_eq_set_a @ SV81 @ SV162 )
= $false )
| ( ( ( ( SV209 @ SV162 )
!= SV239 )
| ~ ! [SY608: set_a,SY609: set_a] :
( ~ ( ord_less_eq_set_a @ SY608 @ SY609 )
| ( ord_less_eq_set_a @ ( SV209 @ SY608 ) @ ( SV209 @ SY609 ) ) )
| ( ord_less_eq_set_a @ ( SV209 @ SV81 ) @ SV239 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1118]) ).
thf(1206,plain,
! [SV82: set_a,SV163: nat] :
( ( ( ! [SY552: set_a] :
~ ~ ( ~ ~ ( ~ ( finite_finite_a @ SY552 )
| ( ( finite_card_a @ SY552 )
!= SV163 ) )
| ~ ( ord_less_eq_set_a @ SY552 @ SV82 ) ) )
= $false )
| ( ( finite_finite_a @ SV82 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1119]) ).
thf(1207,plain,
! [SV210: a,SV164: a,SV83: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SV164 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV83 ) @ relation ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV210 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV210 @ SV164 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SV210 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV210 @ SV83 ) @ relation ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1120]) ).
thf(1208,plain,
! [SV240: set_a,SV211: set_a,SV166: set_a > nat,SV85: nat] :
( ( ( ord_less_eq_nat @ SV85 @ ( SV166 @ SV211 ) )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV211 @ SV240 )
| ~ ! [SY556: set_a,SY557: set_a] :
( ~ ( ord_less_eq_set_a @ SY556 @ SY557 )
| ( ord_less_eq_nat @ ( SV166 @ SY556 ) @ ( SV166 @ SY557 ) ) )
| ( ord_less_eq_nat @ SV85 @ ( SV166 @ SV240 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1121]) ).
thf(1209,plain,
! [SV241: nat,SV212: nat,SV168: nat > set_a,SV87: set_a] :
( ( ( ord_less_eq_set_a @ SV87 @ ( SV168 @ SV212 ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV212 @ SV241 )
| ~ ! [SY560: nat,SY561: nat] :
( ~ ( ord_less_eq_nat @ SY560 @ SY561 )
| ( ord_less_eq_set_a @ ( SV168 @ SY560 ) @ ( SV168 @ SY561 ) ) )
| ( ord_less_eq_set_a @ SV87 @ ( SV168 @ SV241 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1122]) ).
thf(1210,plain,
! [SV242: set_a,SV213: nat > set_a,SV170: nat,SV89: nat] :
( ( ( ord_less_eq_nat @ SV89 @ SV170 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ ( SV213 @ SV170 ) @ SV242 )
| ~ ! [SY617: nat,SY618: nat] :
( ~ ( ord_less_eq_nat @ SY617 @ SY618 )
| ( ord_less_eq_set_a @ ( SV213 @ SY617 ) @ ( SV213 @ SY618 ) ) )
| ( ord_less_eq_set_a @ ( SV213 @ SV89 ) @ SV242 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1123]) ).
thf(1211,plain,
! [SV90: set_a,SV214: set_a,SV171: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV171 @ SV214 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV90 @ SV214 )
= $true )
| ( ( ord_less_eq_set_a @ SV90 @ SV171 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1124]) ).
thf(1212,plain,
! [SV243: set_a,SV215: set_a,SV172: set_a > set_a,SV91: set_a] :
( ( ( ord_less_eq_set_a @ SV91 @ ( SV172 @ SV215 ) )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV215 @ SV243 )
| ~ ! [SY569: set_a,SY570: set_a] :
( ~ ( ord_less_eq_set_a @ SY569 @ SY570 )
| ( ord_less_eq_set_a @ ( SV172 @ SY569 ) @ ( SV172 @ SY570 ) ) )
| ( ord_less_eq_set_a @ SV91 @ ( SV172 @ SV243 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1125]) ).
thf(1213,plain,
! [SV244: set_a,SV173: set_a] :
( ( ( ~ ( ( SV173 = SV244 )
| ~ ( ~ ( ord_less_eq_set_a @ SV173 @ SV244 )
| ~ ( ord_less_eq_set_a @ SV244 @ SV173 ) ) ) )
= $true )
| ( ( ~ ( ( SV173 != SV244 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV173 @ SV244 )
| ~ ( ord_less_eq_set_a @ SV244 @ SV173 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1126]) ).
thf(1214,plain,
! [SV93: a,SV245: a] :
( ( ( member_a @ SV245 @ carrier )
= $false )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV93 @ SV245 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV245 @ SV93 ) @ relation ) )
= $true )
| ( ( member_a @ SV93 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1128]) ).
thf(1215,plain,
! [SV246: nat,SV217: nat,SV174: nat > set_a,SV94: set_a] :
( ( ( SV94
= ( SV174 @ SV217 ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV217 @ SV246 )
| ~ ! [SY575: nat,SY576: nat] :
( ~ ( ord_less_eq_nat @ SY575 @ SY576 )
| ( ord_less_eq_set_a @ ( SV174 @ SY575 ) @ ( SV174 @ SY576 ) ) )
| ( ord_less_eq_set_a @ SV94 @ ( SV174 @ SV246 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1129]) ).
thf(1216,plain,
! [SV175: a,SV95: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV95 @ SV175 ) @ relation ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV175 @ SV95 ) @ relation ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV95 @ SV175 ) @ relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1130]) ).
thf(1217,plain,
! [SV3: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a ) )
= $false )
| ( ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1131]) ).
thf(1218,plain,
! [SV3: set_a] :
( ( ( SV3 != bot_bot_set_a )
= $false )
| ( ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1131]) ).
thf(1219,plain,
! [SV3: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a ) )
= $false )
| ( ( SV3 = bot_bot_set_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1132]) ).
thf(1220,plain,
! [SV3: set_a] :
( ( ( SV3 != bot_bot_set_a )
= $false )
| ( ( SV3 = bot_bot_set_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1132]) ).
thf(1221,plain,
! [SV7: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a ) )
= $false )
| ( ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1133]) ).
thf(1222,plain,
! [SV7: set_a] :
( ( ( SV7 != bot_bot_set_a )
= $false )
| ( ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1133]) ).
thf(1223,plain,
! [SV7: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a ) )
= $false )
| ( ( SV7 = bot_bot_set_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1134]) ).
thf(1224,plain,
! [SV7: set_a] :
( ( ( SV7 != bot_bot_set_a )
= $false )
| ( ( SV7 = bot_bot_set_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1134]) ).
thf(1225,plain,
! [SV176: a,SV97: a,SV9: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV97 ) @ relation ) )
= $true )
| ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV9 ) @ relation ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV176 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV97 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV176 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV9 ) @ relation ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1135]) ).
thf(1226,plain,
! [SV99: set_a,SV11: set_a,SV218: nat,SV177: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV177 @ SV218 ) )
= $true )
| ( ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV11 @ SV177 ) @ ( produc515611863_a_nat @ SV99 @ SV218 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV11 @ SV99 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1137]) ).
thf(1227,plain,
! [SV100: set_Product_prod_a_a,SV12: set_a,SV247: a] :
( ( ( ~ ( member_a @ SV247 @ SV12 )
| ( finite_finite_a @ ( prefer1676310729than_a @ SV247 @ SV12 @ SV100 ) ) )
= $true )
| ( ( finite_finite_a @ SV12 )
= $false )
| ( ( prefer719835986ence_a @ SV12 @ SV100 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1138]) ).
thf(1228,plain,
! [SV13: set_set_a] :
( ( ( ! [SY294: set_a] :
~ ~ ( ~ ( member_set_a @ SY294 @ SV13 )
| ~ ! [SY295: set_a] :
( ~ ( member_set_a @ SY295 @ SV13 )
| ~ ( ord_less_eq_set_a @ SY295 @ SY294 )
| ( SY294 = SY295 ) ) ) )
= $false )
| ( ( SV13 = bot_bot_set_set_a )
= $true )
| ( ( finite_finite_set_a @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1139]) ).
thf(1229,plain,
! [SV14: set_a,SV101: set_a] :
( ( ( ( ord_less_eq_set_a @ SV101 @ SV14 )
| ( SV101 = SV14 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV101 @ SV14 )
| ( SV101 != SV14 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV14 @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1140]) ).
thf(1230,plain,
! [SV102: a,SV15: a] :
( ( ( member_a @ SV15 @ ( prefer1676310729than_a @ SV102 @ carrier @ relation ) )
= $true )
| ( ( member_a @ SV102 @ ( prefer1676310729than_a @ SV15 @ carrier @ relation ) )
= $true )
| ( ( member_a @ SV102 @ carrier )
= $false )
| ( ( member_a @ SV15 @ carrier )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1141]) ).
thf(1231,plain,
! [SV103: set_a,SV16: set_set_a] :
( ( ( ! [SY475: set_a] :
~ ~ ( ~ ~ ( ~ ( member_set_a @ SY475 @ SV16 )
| ~ ( ord_less_eq_set_a @ SY475 @ SV103 ) )
| ~ ! [SY300: set_a] :
( ~ ( member_set_a @ SY300 @ SV16 )
| ~ ( ord_less_eq_set_a @ SY300 @ SY475 )
| ( SY475 = SY300 ) ) ) )
= $false )
| ( ( member_set_a @ SV103 @ SV16 )
= $false )
| ( ( finite_finite_set_a @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1142]) ).
thf(1232,plain,
! [SV104: a,SV17: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV17 @ SV104 ) @ relation )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV104 @ SV17 ) @ relation ) )
= $true )
| ( ( ( prefer161218362good_a @ SV17 @ carrier @ relation )
= ( prefer161218362good_a @ SV104 @ carrier @ relation ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1143]) ).
thf(1233,plain,
! [SV18: set_a,SV178: set_a,SV105: set_a] :
( ( ( SV105 = SV178 )
= $false )
| ( ( ord_less_eq_set_a @ SV18 @ SV178 )
= $true )
| ( ( ord_less_eq_set_a @ SV18 @ SV105 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1144]) ).
thf(1234,plain,
! [SV106: nat,SV19: nat,SV219: set_a,SV179: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV179 @ SV219 ) )
= $true )
| ( ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV19 @ SV179 ) @ ( produc1450889781_set_a @ SV106 @ SV219 ) )
= $true )
| ( ( ord_less_eq_nat @ SV19 @ SV106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1145]) ).
thf(1235,plain,
! [SV107: set_a,SV20: set_a,SV180: set_a] :
( ( ( ord_less_eq_set_a @ SV180 @ SV20 )
= $false )
| ( ( ord_less_eq_set_a @ SV180 @ SV107 )
= $true )
| ( ( ord_less_eq_set_a @ SV20 @ SV107 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1146]) ).
thf(1236,plain,
! [SV220: set_a,SV181: nat,SV109: set_a,SV22: nat] :
( ( ( ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV22 @ SV109 ) @ ( produc1450889781_set_a @ SV181 @ SV220 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV22 @ SV181 )
| ~ ( ord_less_eq_set_a @ SV109 @ SV220 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV22 @ SV109 ) @ ( produc1450889781_set_a @ SV181 @ SV220 ) )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV22 @ SV181 )
| ~ ( ord_less_eq_set_a @ SV109 @ SV220 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1147]) ).
thf(1237,plain,
! [SV221: set_a,SV110: set_a] :
( ( ( ( SV110 = SV221 )
| ~ ( ~ ( ord_less_eq_set_a @ SV221 @ SV110 )
| ~ ( ord_less_eq_set_a @ SV110 @ SV221 ) ) )
= $false )
| ( ( ~ ( ( SV110 != SV221 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV221 @ SV110 )
| ~ ( ord_less_eq_set_a @ SV110 @ SV221 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1148]) ).
thf(1238,plain,
! [SV222: set_a,SV183: set_a,SV111: set_a,SV24: set_a] :
( ( ( ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV24 @ SV111 ) @ ( produc1928581911_set_a @ SV183 @ SV222 ) )
| ~ ( ~ ( ord_less_eq_set_a @ SV24 @ SV183 )
| ~ ( ord_less_eq_set_a @ SV111 @ SV222 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV24 @ SV111 ) @ ( produc1928581911_set_a @ SV183 @ SV222 ) )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV24 @ SV183 )
| ~ ( ord_less_eq_set_a @ SV111 @ SV222 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1149]) ).
thf(1239,plain,
! [SV25: a,SV112: a] :
( ( ( ~ ( member_a @ SV112 @ carrier ) )
= $true )
| ( ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV25 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV25 @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV25 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV25 @ carrier @ relation ) ) )
= $true )
| ( ( member_a @ SV25 @ carrier )
= $false )
| ( ( finite_finite_a @ carrier )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1150]) ).
thf(1240,plain,
! [SV113: a,SV26: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV26 @ SV113 ) @ relation )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV113 @ SV26 ) @ relation ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV113 @ SV26 ) @ relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1151]) ).
thf(1241,plain,
! [SV27: set_a,SV184: set_a,SV114: set_a] :
( ( ( ord_less_eq_set_a @ SV114 @ SV184 )
= $false )
| ( ( ord_less_eq_set_a @ SV27 @ SV184 )
= $true )
| ( ( ord_less_eq_set_a @ SV27 @ SV114 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1152]) ).
thf(1242,plain,
! [SV29: a] :
( ( ( ( prefer1676310729than_a @ SV29 @ carrier @ relation )
= bot_bot_set_a )
= $false )
| ( ( member_a @ SV29 @ carrier )
= $false )
| ( ( carrier = bot_bot_set_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1154]) ).
thf(1243,plain,
! [SV30: a,SV116: a] :
( ( ( ~ ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV116 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV30 @ carrier @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV30 @ SV116 ) @ relation )
= $true )
| ( ( member_a @ SV116 @ carrier )
= $false )
| ( ( member_a @ SV30 @ carrier )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1155]) ).
thf(1244,plain,
! [SV31: set_a,SV185: set_a,SV117: set_a] :
( ( ( ord_less_eq_set_a @ SV117 @ SV185 )
= $false )
| ( ( ord_less_eq_set_a @ SV31 @ SV185 )
= $true )
| ( ( ord_less_eq_set_a @ SV31 @ SV117 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1156]) ).
thf(1245,plain,
! [SV119: set_a,SV33: nat] :
( ( ( ~ ( ord_less_eq_set_a @ ( sK5_SY489 @ SV33 @ SV119 ) @ SV119 ) )
= $false )
| ( ( ord_less_eq_nat @ SV33 @ ( finite_card_a @ SV119 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1158]) ).
thf(1246,plain,
! [SV119: set_a,SV33: nat] :
( ( ( ( ( finite_card_a @ ( sK5_SY489 @ SV33 @ SV119 ) )
!= SV33 )
| ~ ( finite_finite_a @ ( sK5_SY489 @ SV33 @ SV119 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV33 @ ( finite_card_a @ SV119 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1158]) ).
thf(1247,plain,
! [SV34: set_set_a] :
( ( ( ! [SY329: set_a] :
~ ~ ( ~ ( member_set_a @ SY329 @ SV34 )
| ~ ! [SY330: set_a] :
( ~ ( member_set_a @ SY330 @ SV34 )
| ~ ( ord_less_eq_set_a @ SY329 @ SY330 )
| ( SY329 = SY330 ) ) ) )
= $false )
| ( ( SV34 = bot_bot_set_set_a )
= $true )
| ( ( finite_finite_set_a @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1159]) ).
thf(1248,plain,
! [SV35: set_a,SV120: set_a] :
( ( ( ( finite_card_a @ SV120 )
!= ( finite_card_a @ SV35 ) )
= $true )
| ( ( SV120 = SV35 )
= $true )
| ( ( ord_less_eq_set_a @ SV120 @ SV35 )
= $false )
| ( ( finite_finite_a @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1160]) ).
thf(1249,plain,
! [SV121: set_a,SV36: nat] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ ( sK6_SY490 @ SV36 @ SV121 ) @ SV121 )
| ( ( finite_card_a @ ( sK6_SY490 @ SV36 @ SV121 ) )
!= SV36 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV36 @ ( finite_card_a @ SV121 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1161]) ).
thf(1250,plain,
! [SV37: set_a,SV186: set_a,SV122: set_a] :
( ( ( ord_less_eq_set_a @ SV122 @ SV186 )
= $false )
| ( ( ord_less_eq_set_a @ SV37 @ SV186 )
= $true )
| ( ( SV37 = SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1162]) ).
thf(1251,plain,
! [SV223: nat,SV187: set_a,SV123: nat,SV38: set_a] :
( ( ( ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV38 @ SV123 ) @ ( produc515611863_a_nat @ SV187 @ SV223 ) )
| ~ ( ~ ( ord_less_eq_set_a @ SV38 @ SV187 )
| ~ ( ord_less_eq_nat @ SV123 @ SV223 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV38 @ SV123 ) @ ( produc515611863_a_nat @ SV187 @ SV223 ) )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV38 @ SV187 )
| ~ ( ord_less_eq_nat @ SV123 @ SV223 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1163]) ).
thf(1252,plain,
! [SV124: set_Product_prod_a_a,SV188: a,SV39: set_a] :
( ( ( SV39 != bot_bot_set_a )
= $false )
| ( ( ~ ( member_a @ SV188 @ SV39 )
| ( ( prefer1676310729than_a @ SV188 @ SV39 @ SV124 )
!= bot_bot_set_a ) )
= $true )
| ( ( prefer719835986ence_a @ SV39 @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1164]) ).
thf(1253,plain,
! [SV224: set_a,SV126: set_a] :
( ( ( ( ord_less_eq_set_a @ SV126 @ SV224 )
| ! [SY625: a] :
( ~ ( member_a @ SY625 @ SV126 )
| ( member_a @ SY625 @ SV224 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV126 @ SV224 )
| ~ ! [SY625: a] :
( ~ ( member_a @ SY625 @ SV126 )
| ( member_a @ SY625 @ SV224 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1166]) ).
thf(1254,plain,
! [SV43: set_a,SV128: set_a] :
( ( ( member_a @ ( sK2_SY497 @ SV128 @ SV43 ) @ SV43 )
= $true )
| ( ( ord_less_eq_set_a @ SV43 @ SV128 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1168]) ).
thf(1255,plain,
! [SV190: a,SV130: a,SV46: a] :
( ( ( ~ ~ ( ~ ( member_a @ SV46 @ carrier )
| ~ ( member_a @ SV130 @ carrier ) ) )
= $true )
| ( ( ~ ( member_a @ SV190 @ carrier ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV190 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV46 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV190 ) @ relation ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1170]) ).
thf(1256,plain,
! [SV131: set_Product_prod_a_a,SV225: a,SV47: set_a,SV191: a] :
( ( ( ~ ( member_a @ SV191 @ SV47 ) )
= $true )
| ( ( ~ ( member_a @ SV225 @ SV47 )
| ( member_a @ SV191 @ ( prefer1676310729than_a @ SV225 @ SV47 @ SV131 ) )
| ( member_a @ SV225 @ ( prefer1676310729than_a @ SV191 @ SV47 @ SV131 ) ) )
= $true )
| ( ( prefer719835986ence_a @ SV47 @ SV131 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1171]) ).
thf(1257,plain,
! [SV192: a,SV133: a,SV50: a] :
( ( ( ~ ~ ( ~ ( member_a @ SV50 @ carrier )
| ~ ( member_a @ SV133 @ carrier ) ) )
= $true )
| ( ( ~ ( member_a @ SV192 @ carrier ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV50 @ SV133 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV133 @ SV192 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV50 @ SV192 ) @ relation ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1173]) ).
thf(1258,plain,
! [SV134: set_a,SV51: set_a,SV193: a] :
( ( ( member_a @ SV193 @ SV51 )
= $false )
| ( ( member_a @ SV193 @ SV134 )
= $true )
| ( ( ord_less_eq_set_a @ SV51 @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1174]) ).
thf(1259,plain,
! [SV135: set_Product_prod_a_a,SV52: set_a,SV194: a] :
( ( ( member_a @ SV194 @ SV52 )
= $false )
| ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV194 @ SV52 @ SV135 ) @ SV52 )
= $true )
| ( ( prefer719835986ence_a @ SV52 @ SV135 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1175]) ).
thf(1260,plain,
! [SV54: set_a,SV226: nat,SV136: set_a,SV195: set_a > nat] :
( ( ( ( SV195 @ SV136 )
!= SV226 )
= $true )
| ( ( ~ ! [SY585: set_a,SY586: set_a] :
( ~ ( ord_less_eq_set_a @ SY585 @ SY586 )
| ( ord_less_eq_nat @ ( SV195 @ SY585 ) @ ( SV195 @ SY586 ) ) )
| ( ord_less_eq_nat @ ( SV195 @ SV54 ) @ SV226 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV54 @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1176]) ).
thf(1261,plain,
! [SV137: a > $o,SV55: a > $o] :
( ( ( SV55 @ ( sK3_SY508 @ SV137 @ SV55 ) )
= $true )
| ( ( ord_less_eq_set_a @ ( collect_a @ SV55 ) @ ( collect_a @ SV137 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1177]) ).
thf(1262,plain,
! [SV227: set_a,SV138: set_a] :
( ( ( ( SV138 = SV227 )
| ~ ( ~ ( ord_less_eq_set_a @ SV138 @ SV227 )
| ~ ( ord_less_eq_set_a @ SV227 @ SV138 ) ) )
= $false )
| ( ( ~ ( ( SV138 != SV227 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV138 @ SV227 )
| ~ ( ord_less_eq_set_a @ SV227 @ SV138 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1179]) ).
thf(1263,plain,
! [SV57: set_a,SV139: set_a > set_a,SV228: set_a,SV197: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV197 @ SV228 ) )
= $true )
| ( ( ~ ! [SY513: set_a,SY514: set_a] :
( ~ ( ord_less_eq_set_a @ SY513 @ SY514 )
| ( ord_less_eq_set_a @ ( SV139 @ SY513 ) @ ( SV139 @ SY514 ) ) )
| ( ord_less_eq_set_a @ SV57 @ ( SV139 @ SV228 ) ) )
= $true )
| ( ( SV57
= ( SV139 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1180]) ).
thf(1264,plain,
! [SV141: set_a,SV59: set_a] :
( ( ( ~ ( ord_less_eq_nat @ ( finite_card_a @ SV59 ) @ ( finite_card_a @ SV141 ) ) )
= $true )
| ( ( SV141 = SV59 )
= $true )
| ( ( ord_less_eq_set_a @ SV141 @ SV59 )
= $false )
| ( ( finite_finite_a @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1181]) ).
thf(1265,plain,
! [SV229: a,SV142: set_Product_prod_a_a,SV60: set_a,SV198: a] :
( ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV198 @ SV60 @ SV142 ) @ ( prefer1676310729than_a @ SV229 @ SV60 @ SV142 ) )
= $true )
| ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV229 @ SV60 @ SV142 ) @ ( prefer1676310729than_a @ SV198 @ SV60 @ SV142 ) )
= $true )
| ( ( prefer719835986ence_a @ SV60 @ SV142 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1182]) ).
thf(1266,plain,
! [SV143: set_a,SV62: set_set_a] :
( ( ( ! [SY517: set_a] :
~ ~ ( ~ ~ ( ~ ( member_set_a @ SY517 @ SV62 )
| ~ ( ord_less_eq_set_a @ SV143 @ SY517 ) )
| ~ ! [SY382: set_a] :
( ~ ( member_set_a @ SY382 @ SV62 )
| ~ ( ord_less_eq_set_a @ SY517 @ SY382 )
| ( SY517 = SY382 ) ) ) )
= $false )
| ( ( member_set_a @ SV143 @ SV62 )
= $false )
| ( ( finite_finite_set_a @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1183]) ).
thf(1267,plain,
! [SV144: a,SV63: a] :
( ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( ~ ( member_a @ SV144 @ carrier ) )
= $true )
| ( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1184]) ).
thf(1268,plain,
! [SV230: set_a,SV145: set_a] :
( ( ( ( ord_less_eq_set_a @ SV145 @ SV230 )
| ! [SY630: a] :
( ~ ( member_a @ SY630 @ SV145 )
| ( member_a @ SY630 @ SV230 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV145 @ SV230 )
| ~ ! [SY630: a] :
( ~ ( member_a @ SY630 @ SV145 )
| ( member_a @ SY630 @ SV230 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1185]) ).
thf(1269,plain,
! [SV147: set_Product_prod_a_a,SV231: a,SV200: a,SV66: set_a] :
( ( ( ~ ( finite_finite_a @ SV66 ) )
= $true )
| ( ( ~ ( member_a @ SV200 @ SV66 )
| ~ ( member_a @ SV231 @ SV66 )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) ) )
= $true )
| ( ( prefer719835986ence_a @ SV66 @ SV147 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1187]) ).
thf(1270,plain,
! [SV67: set_a,SV232: nat,SV148: set_a,SV201: set_a > nat] :
( ( ( ~ ( ord_less_eq_nat @ ( SV201 @ SV148 ) @ SV232 ) )
= $true )
| ( ( ~ ! [SY594: set_a,SY595: set_a] :
( ~ ( ord_less_eq_set_a @ SY594 @ SY595 )
| ( ord_less_eq_nat @ ( SV201 @ SY594 ) @ ( SV201 @ SY595 ) ) )
| ( ord_less_eq_nat @ ( SV201 @ SV67 ) @ SV232 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV67 @ SV148 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1188]) ).
thf(1271,plain,
! [SV149: set_a,SV68: set_a] :
( ( ( ord_less_eq_set_a @ SV68 @ SV149 )
= $true )
| ( ( SV68 = SV149 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1189]) ).
thf(1272,plain,
! [SV68: set_a,SV149: set_a] :
( ( ( ord_less_eq_set_a @ SV149 @ SV68 )
= $true )
| ( ( SV68 = SV149 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1190]) ).
thf(1273,plain,
! [SV233: set_a,SV150: set_a] :
( ( ( ( SV150 = SV233 )
| ~ ( ~ ( ord_less_eq_set_a @ SV150 @ SV233 )
| ~ ( ord_less_eq_set_a @ SV233 @ SV150 ) ) )
= $false )
| ( ( ~ ( ( SV150 != SV233 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV150 @ SV233 )
| ~ ( ord_less_eq_set_a @ SV233 @ SV150 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1191]) ).
thf(1274,plain,
! [SV70: set_a,SV234: set_a,SV151: set_a,SV203: set_a > set_a] :
( ( ( ~ ( ord_less_eq_set_a @ ( SV203 @ SV151 ) @ SV234 ) )
= $true )
| ( ( ~ ! [SY597: set_a,SY598: set_a] :
( ~ ( ord_less_eq_set_a @ SY597 @ SY598 )
| ( ord_less_eq_set_a @ ( SV203 @ SY597 ) @ ( SV203 @ SY598 ) ) )
| ( ord_less_eq_set_a @ ( SV203 @ SV70 ) @ SV234 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV70 @ SV151 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1192]) ).
thf(1275,plain,
! [SV152: a,SV71: a] :
( ( ( ~ ( ~ ( ~ ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
| ~ ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation ) ) )
| ~ ( ~ ~ ( ~ ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
| ~ ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1193]) ).
thf(1276,plain,
! [SV152: a,SV71: a] :
( ( ( ( ~ ( ~ ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
| ~ ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1193]) ).
thf(1277,plain,
! [SV153: set_a,SV72: set_a,SV235: set_a,SV204: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV204 @ SV235 ) )
= $true )
| ( ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV72 @ SV204 ) @ ( produc1928581911_set_a @ SV153 @ SV235 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV72 @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1194]) ).
thf(1278,plain,
! [SV154: set_a,SV73: set_a,SV205: a] :
( ( ( member_a @ SV205 @ SV73 )
= $false )
| ( ( member_a @ SV205 @ SV154 )
= $true )
| ( ( ord_less_eq_set_a @ SV73 @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1195]) ).
thf(1279,plain,
! [SV74: set_a,SV155: set_Product_prod_a_a,SV236: a,SV206: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV206 @ SV236 ) @ SV155 ) )
= $true )
| ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV236 @ SV74 @ SV155 ) @ ( prefer1676310729than_a @ SV206 @ SV74 @ SV155 ) )
= $true )
| ( ( prefer719835986ence_a @ SV74 @ SV155 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1196]) ).
thf(1280,plain,
! [SV75: nat,SV156: set_a > nat,SV237: set_a,SV207: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV207 @ SV237 ) )
= $true )
| ( ( ~ ! [SY540: set_a,SY541: set_a] :
( ~ ( ord_less_eq_set_a @ SY540 @ SY541 )
| ( ord_less_eq_nat @ ( SV156 @ SY540 ) @ ( SV156 @ SY541 ) ) )
| ( ord_less_eq_nat @ SV75 @ ( SV156 @ SV237 ) ) )
= $true )
| ( ( SV75
= ( SV156 @ SV207 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1197]) ).
thf(1281,plain,
! [SV157: a > $o,SV76: a > $o] :
( ( ( ~ ( ord_less_eq_set_a @ ( collect_a @ SV76 ) @ ( collect_a @ SV157 ) )
| ~ ! [SY542: a] :
( ~ ( SV76 @ SY542 )
| ( SV157 @ SY542 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( collect_a @ SV76 ) @ ( collect_a @ SV157 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1198]) ).
thf(1282,plain,
! [SV157: a > $o,SV76: a > $o] :
( ( ( ~ ( SV76 @ ( sK7_SY542 @ SV157 @ SV76 ) )
| ( SV157 @ ( sK7_SY542 @ SV157 @ SV76 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ ( collect_a @ SV76 ) @ ( collect_a @ SV157 ) )
| ~ ! [SY542: a] :
( ~ ( SV76 @ SY542 )
| ( SV157 @ SY542 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1199]) ).
thf(1283,plain,
! [SV77: set_a,SV158: nat] :
( ( ( ord_less_eq_set_a @ ( sK4_SY543 @ SV158 @ SV77 ) @ SV77 )
= $true )
| ( ( ~ ( ~ ( finite_finite_a @ SV77 )
| ~ ( ord_less_eq_nat @ ( finite_card_a @ SV77 ) @ SV158 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1200]) ).
thf(1284,plain,
! [SV77: set_a,SV158: nat] :
( ( ( ~ ( finite_finite_a @ ( sK4_SY543 @ SV158 @ SV77 ) ) )
= $false )
| ( ( ~ ( ~ ( finite_finite_a @ SV77 )
| ~ ( ord_less_eq_nat @ ( finite_card_a @ SV77 ) @ SV158 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1201]) ).
thf(1285,plain,
! [SV77: set_a,SV158: nat] :
( ( ( ord_less_eq_nat @ ( finite_card_a @ ( sK4_SY543 @ SV158 @ SV77 ) ) @ SV158 )
= $false )
| ( ( ~ ( ~ ( finite_finite_a @ SV77 )
| ~ ( ord_less_eq_nat @ ( finite_card_a @ SV77 ) @ SV158 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1201]) ).
thf(1286,plain,
! [SV159: a,SV78: a] :
( ( ( ~ ( ( SV78 != SV159 ) ) )
= $true )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV78 @ SV159 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV159 @ SV78 ) @ relation ) )
= $true )
| ( ( member_a @ SV159 @ carrier )
= $false )
| ( ( member_a @ SV78 @ carrier )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1202]) ).
thf(1287,plain,
! [SV160: set_a,SV79: set_a] :
( ( ( finite_finite_a @ SV79 )
= $true )
| ( ( ~ ( finite_finite_a @ SV160 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV79 @ SV160 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1203]) ).
thf(1288,plain,
! [SV80: nat,SV238: set_a,SV161: nat,SV208: nat > set_a] :
( ( ( ( SV208 @ SV161 )
!= SV238 )
= $true )
| ( ( ~ ! [SY605: nat,SY606: nat] :
( ~ ( ord_less_eq_nat @ SY605 @ SY606 )
| ( ord_less_eq_set_a @ ( SV208 @ SY605 ) @ ( SV208 @ SY606 ) ) )
| ( ord_less_eq_set_a @ ( SV208 @ SV80 ) @ SV238 ) )
= $true )
| ( ( ord_less_eq_nat @ SV80 @ SV161 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1204]) ).
thf(1289,plain,
! [SV81: set_a,SV239: set_a,SV162: set_a,SV209: set_a > set_a] :
( ( ( ( SV209 @ SV162 )
!= SV239 )
= $true )
| ( ( ~ ! [SY608: set_a,SY609: set_a] :
( ~ ( ord_less_eq_set_a @ SY608 @ SY609 )
| ( ord_less_eq_set_a @ ( SV209 @ SY608 ) @ ( SV209 @ SY609 ) ) )
| ( ord_less_eq_set_a @ ( SV209 @ SV81 ) @ SV239 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV81 @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1205]) ).
thf(1290,plain,
! [SV163: nat,SV82: set_a] :
( ( ( ~ ~ ( ~ ~ ( ~ ( finite_finite_a @ ( sK8_SY552 @ SV82 @ SV163 ) )
| ( ( finite_card_a @ ( sK8_SY552 @ SV82 @ SV163 ) )
!= SV163 ) )
| ~ ( ord_less_eq_set_a @ ( sK8_SY552 @ SV82 @ SV163 ) @ SV82 ) ) )
= $false )
| ( ( finite_finite_a @ SV82 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1206]) ).
thf(1291,plain,
! [SV210: a,SV164: a,SV83: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SV164 ) @ relation ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV83 ) @ relation ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV210 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV210 @ SV164 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SV210 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV210 @ SV83 ) @ relation ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1207]) ).
thf(1292,plain,
! [SV85: nat,SV166: set_a > nat,SV240: set_a,SV211: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV211 @ SV240 ) )
= $true )
| ( ( ~ ! [SY556: set_a,SY557: set_a] :
( ~ ( ord_less_eq_set_a @ SY556 @ SY557 )
| ( ord_less_eq_nat @ ( SV166 @ SY556 ) @ ( SV166 @ SY557 ) ) )
| ( ord_less_eq_nat @ SV85 @ ( SV166 @ SV240 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV85 @ ( SV166 @ SV211 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1208]) ).
thf(1293,plain,
! [SV87: set_a,SV168: nat > set_a,SV241: nat,SV212: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV212 @ SV241 ) )
= $true )
| ( ( ~ ! [SY560: nat,SY561: nat] :
( ~ ( ord_less_eq_nat @ SY560 @ SY561 )
| ( ord_less_eq_set_a @ ( SV168 @ SY560 ) @ ( SV168 @ SY561 ) ) )
| ( ord_less_eq_set_a @ SV87 @ ( SV168 @ SV241 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV87 @ ( SV168 @ SV212 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1209]) ).
thf(1294,plain,
! [SV89: nat,SV242: set_a,SV170: nat,SV213: nat > set_a] :
( ( ( ~ ( ord_less_eq_set_a @ ( SV213 @ SV170 ) @ SV242 ) )
= $true )
| ( ( ~ ! [SY617: nat,SY618: nat] :
( ~ ( ord_less_eq_nat @ SY617 @ SY618 )
| ( ord_less_eq_set_a @ ( SV213 @ SY617 ) @ ( SV213 @ SY618 ) ) )
| ( ord_less_eq_set_a @ ( SV213 @ SV89 ) @ SV242 ) )
= $true )
| ( ( ord_less_eq_nat @ SV89 @ SV170 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1210]) ).
thf(1295,plain,
! [SV90: set_a,SV214: set_a,SV171: set_a] :
( ( ( ord_less_eq_set_a @ SV171 @ SV214 )
= $false )
| ( ( ord_less_eq_set_a @ SV90 @ SV214 )
= $true )
| ( ( ord_less_eq_set_a @ SV90 @ SV171 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1211]) ).
thf(1296,plain,
! [SV91: set_a,SV172: set_a > set_a,SV243: set_a,SV215: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV215 @ SV243 ) )
= $true )
| ( ( ~ ! [SY569: set_a,SY570: set_a] :
( ~ ( ord_less_eq_set_a @ SY569 @ SY570 )
| ( ord_less_eq_set_a @ ( SV172 @ SY569 ) @ ( SV172 @ SY570 ) ) )
| ( ord_less_eq_set_a @ SV91 @ ( SV172 @ SV243 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV91 @ ( SV172 @ SV215 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1212]) ).
thf(1297,plain,
! [SV244: set_a,SV173: set_a] :
( ( ( ( SV173 = SV244 )
| ~ ( ~ ( ord_less_eq_set_a @ SV173 @ SV244 )
| ~ ( ord_less_eq_set_a @ SV244 @ SV173 ) ) )
= $false )
| ( ( ~ ( ( SV173 != SV244 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV173 @ SV244 )
| ~ ( ord_less_eq_set_a @ SV244 @ SV173 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1213]) ).
thf(1298,plain,
! [SV245: a,SV93: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV93 @ SV245 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV245 @ SV93 ) @ relation )
= $true )
| ( ( member_a @ SV245 @ carrier )
= $false )
| ( ( member_a @ SV93 @ carrier )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1214]) ).
thf(1299,plain,
! [SV94: set_a,SV174: nat > set_a,SV246: nat,SV217: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV217 @ SV246 ) )
= $true )
| ( ( ~ ! [SY575: nat,SY576: nat] :
( ~ ( ord_less_eq_nat @ SY575 @ SY576 )
| ( ord_less_eq_set_a @ ( SV174 @ SY575 ) @ ( SV174 @ SY576 ) ) )
| ( ord_less_eq_set_a @ SV94 @ ( SV174 @ SV246 ) ) )
= $true )
| ( ( SV94
= ( SV174 @ SV217 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1215]) ).
thf(1300,plain,
! [SV175: a,SV95: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV95 @ SV175 ) @ relation )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV175 @ SV95 ) @ relation ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV95 @ SV175 ) @ relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1216]) ).
thf(1301,plain,
! [SV3: set_a] :
( ( ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1217]) ).
thf(1302,plain,
! [SV3: set_a] :
( ( ( SV3 = bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1218]) ).
thf(1303,plain,
! [SV3: set_a] :
( ( ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
= $true )
| ( ( SV3 = bot_bot_set_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1219]) ).
thf(1304,plain,
! [SV3: set_a] :
( ( ( SV3 = bot_bot_set_a )
= $true )
| ( ( SV3 = bot_bot_set_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1220]) ).
thf(1305,plain,
! [SV7: set_a] :
( ( ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1221]) ).
thf(1306,plain,
! [SV7: set_a] :
( ( ( SV7 = bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1222]) ).
thf(1307,plain,
! [SV7: set_a] :
( ( ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
= $true )
| ( ( SV7 = bot_bot_set_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1223]) ).
thf(1308,plain,
! [SV7: set_a] :
( ( ( SV7 = bot_bot_set_a )
= $true )
| ( ( SV7 = bot_bot_set_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1224]) ).
thf(1309,plain,
! [SV176: a,SV97: a,SV9: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV97 ) @ relation )
= $false )
| ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV9 ) @ relation ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV176 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV97 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV176 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV9 ) @ relation ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1225]) ).
thf(1310,plain,
! [SV99: set_a,SV11: set_a,SV218: nat,SV177: nat] :
( ( ( ord_less_eq_nat @ SV177 @ SV218 )
= $false )
| ( ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV11 @ SV177 ) @ ( produc515611863_a_nat @ SV99 @ SV218 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV11 @ SV99 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1226]) ).
thf(1311,plain,
! [SV100: set_Product_prod_a_a,SV12: set_a,SV247: a] :
( ( ( ~ ( member_a @ SV247 @ SV12 ) )
= $true )
| ( ( finite_finite_a @ ( prefer1676310729than_a @ SV247 @ SV12 @ SV100 ) )
= $true )
| ( ( finite_finite_a @ SV12 )
= $false )
| ( ( prefer719835986ence_a @ SV12 @ SV100 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1227]) ).
thf(1312,plain,
! [SV13: set_set_a] :
( ( ( ~ ~ ( ~ ( member_set_a @ ( sK9_SY294 @ SV13 ) @ SV13 )
| ~ ! [SY651: set_a] :
( ~ ( member_set_a @ SY651 @ SV13 )
| ~ ( ord_less_eq_set_a @ SY651 @ ( sK9_SY294 @ SV13 ) )
| ( ( sK9_SY294 @ SV13 )
= SY651 ) ) ) )
= $false )
| ( ( SV13 = bot_bot_set_set_a )
= $true )
| ( ( finite_finite_set_a @ SV13 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1228]) ).
thf(1313,plain,
! [SV14: set_a,SV101: set_a] :
( ( ( ord_less_eq_set_a @ SV101 @ SV14 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV101 @ SV14 )
| ( SV101 != SV14 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV14 @ SV101 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1229]) ).
thf(1314,plain,
! [SV14: set_a,SV101: set_a] :
( ( ( SV101 = SV14 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV101 @ SV14 )
| ( SV101 != SV14 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV14 @ SV101 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1229]) ).
thf(1315,plain,
! [SV16: set_set_a,SV103: set_a] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member_set_a @ ( sK10_SY475 @ SV103 @ SV16 ) @ SV16 )
| ~ ( ord_less_eq_set_a @ ( sK10_SY475 @ SV103 @ SV16 ) @ SV103 ) )
| ~ ! [SY652: set_a] :
( ~ ( member_set_a @ SY652 @ SV16 )
| ~ ( ord_less_eq_set_a @ SY652 @ ( sK10_SY475 @ SV103 @ SV16 ) )
| ( ( sK10_SY475 @ SV103 @ SV16 )
= SY652 ) ) ) )
= $false )
| ( ( member_set_a @ SV103 @ SV16 )
= $false )
| ( ( finite_finite_set_a @ SV16 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1231]) ).
thf(1316,plain,
! [SV17: a,SV104: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV104 @ SV17 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV17 @ SV104 ) @ relation )
= $false )
| ( ( ( prefer161218362good_a @ SV17 @ carrier @ relation )
= ( prefer161218362good_a @ SV104 @ carrier @ relation ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1232]) ).
thf(1317,plain,
! [SV106: nat,SV19: nat,SV219: set_a,SV179: set_a] :
( ( ( ord_less_eq_set_a @ SV179 @ SV219 )
= $false )
| ( ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV19 @ SV179 ) @ ( produc1450889781_set_a @ SV106 @ SV219 ) )
= $true )
| ( ( ord_less_eq_nat @ SV19 @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1234]) ).
thf(1318,plain,
! [SV220: set_a,SV181: nat,SV109: set_a,SV22: nat] :
( ( ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV22 @ SV109 ) @ ( produc1450889781_set_a @ SV181 @ SV220 ) )
= $false )
| ( ( ~ ( ~ ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV22 @ SV109 ) @ ( produc1450889781_set_a @ SV181 @ SV220 ) )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV22 @ SV181 )
| ~ ( ord_less_eq_set_a @ SV109 @ SV220 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1236]) ).
thf(1319,plain,
! [SV220: set_a,SV109: set_a,SV181: nat,SV22: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV22 @ SV181 )
| ~ ( ord_less_eq_set_a @ SV109 @ SV220 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV22 @ SV109 ) @ ( produc1450889781_set_a @ SV181 @ SV220 ) )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV22 @ SV181 )
| ~ ( ord_less_eq_set_a @ SV109 @ SV220 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1236]) ).
thf(1320,plain,
! [SV221: set_a,SV110: set_a] :
( ( ( SV110 = SV221 )
= $false )
| ( ( ~ ( ( SV110 != SV221 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV221 @ SV110 )
| ~ ( ord_less_eq_set_a @ SV110 @ SV221 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1237]) ).
thf(1321,plain,
! [SV110: set_a,SV221: set_a] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ SV221 @ SV110 )
| ~ ( ord_less_eq_set_a @ SV110 @ SV221 ) ) )
= $false )
| ( ( ~ ( ( SV110 != SV221 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV221 @ SV110 )
| ~ ( ord_less_eq_set_a @ SV110 @ SV221 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1237]) ).
thf(1322,plain,
! [SV222: set_a,SV183: set_a,SV111: set_a,SV24: set_a] :
( ( ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV24 @ SV111 ) @ ( produc1928581911_set_a @ SV183 @ SV222 ) )
= $false )
| ( ( ~ ( ~ ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV24 @ SV111 ) @ ( produc1928581911_set_a @ SV183 @ SV222 ) )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV24 @ SV183 )
| ~ ( ord_less_eq_set_a @ SV111 @ SV222 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1238]) ).
thf(1323,plain,
! [SV222: set_a,SV111: set_a,SV183: set_a,SV24: set_a] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ SV24 @ SV183 )
| ~ ( ord_less_eq_set_a @ SV111 @ SV222 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV24 @ SV111 ) @ ( produc1928581911_set_a @ SV183 @ SV222 ) )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV24 @ SV183 )
| ~ ( ord_less_eq_set_a @ SV111 @ SV222 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1238]) ).
thf(1324,plain,
! [SV25: a,SV112: a] :
( ( ( member_a @ SV112 @ carrier )
= $false )
| ( ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV25 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV25 @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV25 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV25 @ carrier @ relation ) ) )
= $true )
| ( ( member_a @ SV25 @ carrier )
= $false )
| ( ( finite_finite_a @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1239]) ).
thf(1325,plain,
! [SV26: a,SV113: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV113 @ SV26 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV26 @ SV113 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV113 @ SV26 ) @ relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1240]) ).
thf(1326,plain,
! [SV30: a,SV116: a] :
( ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV116 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV30 @ carrier @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV30 @ SV116 ) @ relation )
= $true )
| ( ( member_a @ SV116 @ carrier )
= $false )
| ( ( member_a @ SV30 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1243]) ).
thf(1327,plain,
! [SV119: set_a,SV33: nat] :
( ( ( ord_less_eq_set_a @ ( sK5_SY489 @ SV33 @ SV119 ) @ SV119 )
= $true )
| ( ( ord_less_eq_nat @ SV33 @ ( finite_card_a @ SV119 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1245]) ).
thf(1328,plain,
! [SV119: set_a,SV33: nat] :
( ( ( ( finite_card_a @ ( sK5_SY489 @ SV33 @ SV119 ) )
!= SV33 )
= $false )
| ( ( ord_less_eq_nat @ SV33 @ ( finite_card_a @ SV119 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1246]) ).
thf(1329,plain,
! [SV119: set_a,SV33: nat] :
( ( ( ~ ( finite_finite_a @ ( sK5_SY489 @ SV33 @ SV119 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV33 @ ( finite_card_a @ SV119 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1246]) ).
thf(1330,plain,
! [SV34: set_set_a] :
( ( ( ~ ~ ( ~ ( member_set_a @ ( sK11_SY329 @ SV34 ) @ SV34 )
| ~ ! [SY653: set_a] :
( ~ ( member_set_a @ SY653 @ SV34 )
| ~ ( ord_less_eq_set_a @ ( sK11_SY329 @ SV34 ) @ SY653 )
| ( ( sK11_SY329 @ SV34 )
= SY653 ) ) ) )
= $false )
| ( ( SV34 = bot_bot_set_set_a )
= $true )
| ( ( finite_finite_set_a @ SV34 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1247]) ).
thf(1331,plain,
! [SV35: set_a,SV120: set_a] :
( ( ( ( finite_card_a @ SV120 )
= ( finite_card_a @ SV35 ) )
= $false )
| ( ( SV120 = SV35 )
= $true )
| ( ( ord_less_eq_set_a @ SV120 @ SV35 )
= $false )
| ( ( finite_finite_a @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1248]) ).
thf(1332,plain,
! [SV121: set_a,SV36: nat] :
( ( ( ~ ( ord_less_eq_set_a @ ( sK6_SY490 @ SV36 @ SV121 ) @ SV121 )
| ( ( finite_card_a @ ( sK6_SY490 @ SV36 @ SV121 ) )
!= SV36 ) )
= $false )
| ( ( ord_less_eq_nat @ SV36 @ ( finite_card_a @ SV121 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1249]) ).
thf(1333,plain,
! [SV223: nat,SV187: set_a,SV123: nat,SV38: set_a] :
( ( ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV38 @ SV123 ) @ ( produc515611863_a_nat @ SV187 @ SV223 ) )
= $false )
| ( ( ~ ( ~ ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV38 @ SV123 ) @ ( produc515611863_a_nat @ SV187 @ SV223 ) )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV38 @ SV187 )
| ~ ( ord_less_eq_nat @ SV123 @ SV223 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1251]) ).
thf(1334,plain,
! [SV223: nat,SV123: nat,SV187: set_a,SV38: set_a] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ SV38 @ SV187 )
| ~ ( ord_less_eq_nat @ SV123 @ SV223 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV38 @ SV123 ) @ ( produc515611863_a_nat @ SV187 @ SV223 ) )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV38 @ SV187 )
| ~ ( ord_less_eq_nat @ SV123 @ SV223 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1251]) ).
thf(1335,plain,
! [SV124: set_Product_prod_a_a,SV188: a,SV39: set_a] :
( ( ( SV39 = bot_bot_set_a )
= $true )
| ( ( ~ ( member_a @ SV188 @ SV39 )
| ( ( prefer1676310729than_a @ SV188 @ SV39 @ SV124 )
!= bot_bot_set_a ) )
= $true )
| ( ( prefer719835986ence_a @ SV39 @ SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1252]) ).
thf(1336,plain,
! [SV224: set_a,SV126: set_a] :
( ( ( ord_less_eq_set_a @ SV126 @ SV224 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV126 @ SV224 )
| ~ ! [SY625: a] :
( ~ ( member_a @ SY625 @ SV126 )
| ( member_a @ SY625 @ SV224 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1253]) ).
thf(1337,plain,
! [SV224: set_a,SV126: set_a] :
( ( ( ! [SY625: a] :
( ~ ( member_a @ SY625 @ SV126 )
| ( member_a @ SY625 @ SV224 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV126 @ SV224 )
| ~ ! [SY625: a] :
( ~ ( member_a @ SY625 @ SV126 )
| ( member_a @ SY625 @ SV224 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1253]) ).
thf(1338,plain,
! [SV190: a,SV130: a,SV46: a] :
( ( ( ~ ( ~ ( member_a @ SV46 @ carrier )
| ~ ( member_a @ SV130 @ carrier ) ) )
= $false )
| ( ( ~ ( member_a @ SV190 @ carrier ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV190 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV46 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV190 ) @ relation ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1255]) ).
thf(1339,plain,
! [SV131: set_Product_prod_a_a,SV225: a,SV47: set_a,SV191: a] :
( ( ( member_a @ SV191 @ SV47 )
= $false )
| ( ( ~ ( member_a @ SV225 @ SV47 )
| ( member_a @ SV191 @ ( prefer1676310729than_a @ SV225 @ SV47 @ SV131 ) )
| ( member_a @ SV225 @ ( prefer1676310729than_a @ SV191 @ SV47 @ SV131 ) ) )
= $true )
| ( ( prefer719835986ence_a @ SV47 @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1256]) ).
thf(1340,plain,
! [SV192: a,SV133: a,SV50: a] :
( ( ( ~ ( ~ ( member_a @ SV50 @ carrier )
| ~ ( member_a @ SV133 @ carrier ) ) )
= $false )
| ( ( ~ ( member_a @ SV192 @ carrier ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV50 @ SV133 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV133 @ SV192 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV50 @ SV192 ) @ relation ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1257]) ).
thf(1341,plain,
! [SV54: set_a,SV226: nat,SV136: set_a,SV195: set_a > nat] :
( ( ( ( SV195 @ SV136 )
= SV226 )
= $false )
| ( ( ~ ! [SY585: set_a,SY586: set_a] :
( ~ ( ord_less_eq_set_a @ SY585 @ SY586 )
| ( ord_less_eq_nat @ ( SV195 @ SY585 ) @ ( SV195 @ SY586 ) ) )
| ( ord_less_eq_nat @ ( SV195 @ SV54 ) @ SV226 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV54 @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1260]) ).
thf(1342,plain,
! [SV227: set_a,SV138: set_a] :
( ( ( SV138 = SV227 )
= $false )
| ( ( ~ ( ( SV138 != SV227 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV138 @ SV227 )
| ~ ( ord_less_eq_set_a @ SV227 @ SV138 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1262]) ).
thf(1343,plain,
! [SV227: set_a,SV138: set_a] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ SV138 @ SV227 )
| ~ ( ord_less_eq_set_a @ SV227 @ SV138 ) ) )
= $false )
| ( ( ~ ( ( SV138 != SV227 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV138 @ SV227 )
| ~ ( ord_less_eq_set_a @ SV227 @ SV138 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1262]) ).
thf(1344,plain,
! [SV57: set_a,SV139: set_a > set_a,SV228: set_a,SV197: set_a] :
( ( ( ord_less_eq_set_a @ SV197 @ SV228 )
= $false )
| ( ( ~ ! [SY513: set_a,SY514: set_a] :
( ~ ( ord_less_eq_set_a @ SY513 @ SY514 )
| ( ord_less_eq_set_a @ ( SV139 @ SY513 ) @ ( SV139 @ SY514 ) ) )
| ( ord_less_eq_set_a @ SV57 @ ( SV139 @ SV228 ) ) )
= $true )
| ( ( SV57
= ( SV139 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1263]) ).
thf(1345,plain,
! [SV141: set_a,SV59: set_a] :
( ( ( ord_less_eq_nat @ ( finite_card_a @ SV59 ) @ ( finite_card_a @ SV141 ) )
= $false )
| ( ( SV141 = SV59 )
= $true )
| ( ( ord_less_eq_set_a @ SV141 @ SV59 )
= $false )
| ( ( finite_finite_a @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1264]) ).
thf(1346,plain,
! [SV62: set_set_a,SV143: set_a] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member_set_a @ ( sK12_SY517 @ SV143 @ SV62 ) @ SV62 )
| ~ ( ord_less_eq_set_a @ SV143 @ ( sK12_SY517 @ SV143 @ SV62 ) ) )
| ~ ! [SY654: set_a] :
( ~ ( member_set_a @ SY654 @ SV62 )
| ~ ( ord_less_eq_set_a @ ( sK12_SY517 @ SV143 @ SV62 ) @ SY654 )
| ( ( sK12_SY517 @ SV143 @ SV62 )
= SY654 ) ) ) )
= $false )
| ( ( member_set_a @ SV143 @ SV62 )
= $false )
| ( ( finite_finite_set_a @ SV62 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1266]) ).
thf(1347,plain,
! [SV63: a,SV144: a] :
( ( ( member_a @ SV144 @ carrier )
= $false )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1267]) ).
thf(1348,plain,
! [SV230: set_a,SV145: set_a] :
( ( ( ord_less_eq_set_a @ SV145 @ SV230 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV145 @ SV230 )
| ~ ! [SY630: a] :
( ~ ( member_a @ SY630 @ SV145 )
| ( member_a @ SY630 @ SV230 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1268]) ).
thf(1349,plain,
! [SV230: set_a,SV145: set_a] :
( ( ( ! [SY630: a] :
( ~ ( member_a @ SY630 @ SV145 )
| ( member_a @ SY630 @ SV230 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV145 @ SV230 )
| ~ ! [SY630: a] :
( ~ ( member_a @ SY630 @ SV145 )
| ( member_a @ SY630 @ SV230 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1268]) ).
thf(1350,plain,
! [SV147: set_Product_prod_a_a,SV231: a,SV200: a,SV66: set_a] :
( ( ( finite_finite_a @ SV66 )
= $false )
| ( ( ~ ( member_a @ SV200 @ SV66 )
| ~ ( member_a @ SV231 @ SV66 )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) ) )
= $true )
| ( ( prefer719835986ence_a @ SV66 @ SV147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1269]) ).
thf(1351,plain,
! [SV67: set_a,SV232: nat,SV148: set_a,SV201: set_a > nat] :
( ( ( ord_less_eq_nat @ ( SV201 @ SV148 ) @ SV232 )
= $false )
| ( ( ~ ! [SY594: set_a,SY595: set_a] :
( ~ ( ord_less_eq_set_a @ SY594 @ SY595 )
| ( ord_less_eq_nat @ ( SV201 @ SY594 ) @ ( SV201 @ SY595 ) ) )
| ( ord_less_eq_nat @ ( SV201 @ SV67 ) @ SV232 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV67 @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1270]) ).
thf(1352,plain,
! [SV233: set_a,SV150: set_a] :
( ( ( SV150 = SV233 )
= $false )
| ( ( ~ ( ( SV150 != SV233 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV150 @ SV233 )
| ~ ( ord_less_eq_set_a @ SV233 @ SV150 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1273]) ).
thf(1353,plain,
! [SV233: set_a,SV150: set_a] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ SV150 @ SV233 )
| ~ ( ord_less_eq_set_a @ SV233 @ SV150 ) ) )
= $false )
| ( ( ~ ( ( SV150 != SV233 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV150 @ SV233 )
| ~ ( ord_less_eq_set_a @ SV233 @ SV150 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1273]) ).
thf(1354,plain,
! [SV70: set_a,SV234: set_a,SV151: set_a,SV203: set_a > set_a] :
( ( ( ord_less_eq_set_a @ ( SV203 @ SV151 ) @ SV234 )
= $false )
| ( ( ~ ! [SY597: set_a,SY598: set_a] :
( ~ ( ord_less_eq_set_a @ SY597 @ SY598 )
| ( ord_less_eq_set_a @ ( SV203 @ SY597 ) @ ( SV203 @ SY598 ) ) )
| ( ord_less_eq_set_a @ ( SV203 @ SV70 ) @ SV234 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV70 @ SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1274]) ).
thf(1355,plain,
! [SV152: a,SV71: a] :
( ( ( ~ ( ~ ( ~ ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
| ~ ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
| ~ ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1275]) ).
thf(1356,plain,
! [SV153: set_a,SV72: set_a,SV235: set_a,SV204: set_a] :
( ( ( ord_less_eq_set_a @ SV204 @ SV235 )
= $false )
| ( ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV72 @ SV204 ) @ ( produc1928581911_set_a @ SV153 @ SV235 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV72 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1277]) ).
thf(1357,plain,
! [SV74: set_a,SV155: set_Product_prod_a_a,SV236: a,SV206: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV206 @ SV236 ) @ SV155 )
= $false )
| ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV236 @ SV74 @ SV155 ) @ ( prefer1676310729than_a @ SV206 @ SV74 @ SV155 ) )
= $true )
| ( ( prefer719835986ence_a @ SV74 @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1279]) ).
thf(1358,plain,
! [SV75: nat,SV156: set_a > nat,SV237: set_a,SV207: set_a] :
( ( ( ord_less_eq_set_a @ SV207 @ SV237 )
= $false )
| ( ( ~ ! [SY540: set_a,SY541: set_a] :
( ~ ( ord_less_eq_set_a @ SY540 @ SY541 )
| ( ord_less_eq_nat @ ( SV156 @ SY540 ) @ ( SV156 @ SY541 ) ) )
| ( ord_less_eq_nat @ SV75 @ ( SV156 @ SV237 ) ) )
= $true )
| ( ( SV75
= ( SV156 @ SV207 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1280]) ).
thf(1359,plain,
! [SV157: a > $o,SV76: a > $o] :
( ( ( ~ ( ord_less_eq_set_a @ ( collect_a @ SV76 ) @ ( collect_a @ SV157 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( collect_a @ SV76 ) @ ( collect_a @ SV157 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1281]) ).
thf(1360,plain,
! [SV157: a > $o,SV76: a > $o] :
( ( ( ~ ! [SY542: a] :
( ~ ( SV76 @ SY542 )
| ( SV157 @ SY542 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( collect_a @ SV76 ) @ ( collect_a @ SV157 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1281]) ).
thf(1361,plain,
! [SV157: a > $o,SV76: a > $o] :
( ( ( ~ ( SV76 @ ( sK7_SY542 @ SV157 @ SV76 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ ( collect_a @ SV76 ) @ ( collect_a @ SV157 ) )
| ~ ! [SY542: a] :
( ~ ( SV76 @ SY542 )
| ( SV157 @ SY542 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1282]) ).
thf(1362,plain,
! [SV76: a > $o,SV157: a > $o] :
( ( ( SV157 @ ( sK7_SY542 @ SV157 @ SV76 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ ( collect_a @ SV76 ) @ ( collect_a @ SV157 ) )
| ~ ! [SY542: a] :
( ~ ( SV76 @ SY542 )
| ( SV157 @ SY542 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1282]) ).
thf(1363,plain,
! [SV158: nat,SV77: set_a] :
( ( ( ~ ( finite_finite_a @ SV77 )
| ~ ( ord_less_eq_nat @ ( finite_card_a @ SV77 ) @ SV158 ) )
= $false )
| ( ( ord_less_eq_set_a @ ( sK4_SY543 @ SV158 @ SV77 ) @ SV77 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1283]) ).
thf(1364,plain,
! [SV77: set_a,SV158: nat] :
( ( ( finite_finite_a @ ( sK4_SY543 @ SV158 @ SV77 ) )
= $true )
| ( ( ~ ( ~ ( finite_finite_a @ SV77 )
| ~ ( ord_less_eq_nat @ ( finite_card_a @ SV77 ) @ SV158 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1284]) ).
thf(1365,plain,
! [SV158: nat,SV77: set_a] :
( ( ( ~ ( finite_finite_a @ SV77 )
| ~ ( ord_less_eq_nat @ ( finite_card_a @ SV77 ) @ SV158 ) )
= $false )
| ( ( ord_less_eq_nat @ ( finite_card_a @ ( sK4_SY543 @ SV158 @ SV77 ) ) @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1285]) ).
thf(1366,plain,
! [SV159: a,SV78: a] :
( ( ( SV78 != SV159 )
= $false )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV78 @ SV159 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV159 @ SV78 ) @ relation ) )
= $true )
| ( ( member_a @ SV159 @ carrier )
= $false )
| ( ( member_a @ SV78 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1286]) ).
thf(1367,plain,
! [SV79: set_a,SV160: set_a] :
( ( ( finite_finite_a @ SV160 )
= $false )
| ( ( finite_finite_a @ SV79 )
= $true )
| ( ( ord_less_eq_set_a @ SV79 @ SV160 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1287]) ).
thf(1368,plain,
! [SV80: nat,SV238: set_a,SV161: nat,SV208: nat > set_a] :
( ( ( ( SV208 @ SV161 )
= SV238 )
= $false )
| ( ( ~ ! [SY605: nat,SY606: nat] :
( ~ ( ord_less_eq_nat @ SY605 @ SY606 )
| ( ord_less_eq_set_a @ ( SV208 @ SY605 ) @ ( SV208 @ SY606 ) ) )
| ( ord_less_eq_set_a @ ( SV208 @ SV80 ) @ SV238 ) )
= $true )
| ( ( ord_less_eq_nat @ SV80 @ SV161 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1288]) ).
thf(1369,plain,
! [SV81: set_a,SV239: set_a,SV162: set_a,SV209: set_a > set_a] :
( ( ( ( SV209 @ SV162 )
= SV239 )
= $false )
| ( ( ~ ! [SY608: set_a,SY609: set_a] :
( ~ ( ord_less_eq_set_a @ SY608 @ SY609 )
| ( ord_less_eq_set_a @ ( SV209 @ SY608 ) @ ( SV209 @ SY609 ) ) )
| ( ord_less_eq_set_a @ ( SV209 @ SV81 ) @ SV239 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV81 @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1289]) ).
thf(1370,plain,
! [SV163: nat,SV82: set_a] :
( ( ( ~ ( ~ ~ ( ~ ( finite_finite_a @ ( sK8_SY552 @ SV82 @ SV163 ) )
| ( ( finite_card_a @ ( sK8_SY552 @ SV82 @ SV163 ) )
!= SV163 ) )
| ~ ( ord_less_eq_set_a @ ( sK8_SY552 @ SV82 @ SV163 ) @ SV82 ) ) )
= $true )
| ( ( finite_finite_a @ SV82 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1290]) ).
thf(1371,plain,
! [SV210: a,SV164: a,SV83: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SV164 ) @ relation )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV83 ) @ relation ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV210 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV210 @ SV164 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SV210 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV210 @ SV83 ) @ relation ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1291]) ).
thf(1372,plain,
! [SV85: nat,SV166: set_a > nat,SV240: set_a,SV211: set_a] :
( ( ( ord_less_eq_set_a @ SV211 @ SV240 )
= $false )
| ( ( ~ ! [SY556: set_a,SY557: set_a] :
( ~ ( ord_less_eq_set_a @ SY556 @ SY557 )
| ( ord_less_eq_nat @ ( SV166 @ SY556 ) @ ( SV166 @ SY557 ) ) )
| ( ord_less_eq_nat @ SV85 @ ( SV166 @ SV240 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV85 @ ( SV166 @ SV211 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1292]) ).
thf(1373,plain,
! [SV87: set_a,SV168: nat > set_a,SV241: nat,SV212: nat] :
( ( ( ord_less_eq_nat @ SV212 @ SV241 )
= $false )
| ( ( ~ ! [SY560: nat,SY561: nat] :
( ~ ( ord_less_eq_nat @ SY560 @ SY561 )
| ( ord_less_eq_set_a @ ( SV168 @ SY560 ) @ ( SV168 @ SY561 ) ) )
| ( ord_less_eq_set_a @ SV87 @ ( SV168 @ SV241 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV87 @ ( SV168 @ SV212 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1293]) ).
thf(1374,plain,
! [SV89: nat,SV242: set_a,SV170: nat,SV213: nat > set_a] :
( ( ( ord_less_eq_set_a @ ( SV213 @ SV170 ) @ SV242 )
= $false )
| ( ( ~ ! [SY617: nat,SY618: nat] :
( ~ ( ord_less_eq_nat @ SY617 @ SY618 )
| ( ord_less_eq_set_a @ ( SV213 @ SY617 ) @ ( SV213 @ SY618 ) ) )
| ( ord_less_eq_set_a @ ( SV213 @ SV89 ) @ SV242 ) )
= $true )
| ( ( ord_less_eq_nat @ SV89 @ SV170 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1294]) ).
thf(1375,plain,
! [SV91: set_a,SV172: set_a > set_a,SV243: set_a,SV215: set_a] :
( ( ( ord_less_eq_set_a @ SV215 @ SV243 )
= $false )
| ( ( ~ ! [SY569: set_a,SY570: set_a] :
( ~ ( ord_less_eq_set_a @ SY569 @ SY570 )
| ( ord_less_eq_set_a @ ( SV172 @ SY569 ) @ ( SV172 @ SY570 ) ) )
| ( ord_less_eq_set_a @ SV91 @ ( SV172 @ SV243 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV91 @ ( SV172 @ SV215 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1296]) ).
thf(1376,plain,
! [SV244: set_a,SV173: set_a] :
( ( ( SV173 = SV244 )
= $false )
| ( ( ~ ( ( SV173 != SV244 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV173 @ SV244 )
| ~ ( ord_less_eq_set_a @ SV244 @ SV173 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1297]) ).
thf(1377,plain,
! [SV244: set_a,SV173: set_a] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ SV173 @ SV244 )
| ~ ( ord_less_eq_set_a @ SV244 @ SV173 ) ) )
= $false )
| ( ( ~ ( ( SV173 != SV244 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV173 @ SV244 )
| ~ ( ord_less_eq_set_a @ SV244 @ SV173 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1297]) ).
thf(1378,plain,
! [SV94: set_a,SV174: nat > set_a,SV246: nat,SV217: nat] :
( ( ( ord_less_eq_nat @ SV217 @ SV246 )
= $false )
| ( ( ~ ! [SY575: nat,SY576: nat] :
( ~ ( ord_less_eq_nat @ SY575 @ SY576 )
| ( ord_less_eq_set_a @ ( SV174 @ SY575 ) @ ( SV174 @ SY576 ) ) )
| ( ord_less_eq_set_a @ SV94 @ ( SV174 @ SV246 ) ) )
= $true )
| ( ( SV94
= ( SV174 @ SV217 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1299]) ).
thf(1379,plain,
! [SV95: a,SV175: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV175 @ SV95 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV95 @ SV175 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV95 @ SV175 ) @ relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1300]) ).
thf(1380,plain,
! [SV176: a,SV9: a,SV97: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV9 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV97 ) @ relation )
= $false )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV176 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV97 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV176 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV9 ) @ relation ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1309]) ).
thf(1381,plain,
! [SV100: set_Product_prod_a_a,SV12: set_a,SV247: a] :
( ( ( member_a @ SV247 @ SV12 )
= $false )
| ( ( finite_finite_a @ ( prefer1676310729than_a @ SV247 @ SV12 @ SV100 ) )
= $true )
| ( ( finite_finite_a @ SV12 )
= $false )
| ( ( prefer719835986ence_a @ SV12 @ SV100 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1311]) ).
thf(1382,plain,
! [SV13: set_set_a] :
( ( ( ~ ( ~ ( member_set_a @ ( sK9_SY294 @ SV13 ) @ SV13 )
| ~ ! [SY651: set_a] :
( ~ ( member_set_a @ SY651 @ SV13 )
| ~ ( ord_less_eq_set_a @ SY651 @ ( sK9_SY294 @ SV13 ) )
| ( ( sK9_SY294 @ SV13 )
= SY651 ) ) ) )
= $true )
| ( ( SV13 = bot_bot_set_set_a )
= $true )
| ( ( finite_finite_set_a @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1312]) ).
thf(1383,plain,
! [SV14: set_a,SV101: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV101 @ SV14 )
| ( SV101 != SV14 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV101 @ SV14 )
= $false )
| ( ( ord_less_eq_set_a @ SV14 @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1313]) ).
thf(1384,plain,
! [SV14: set_a,SV101: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV101 @ SV14 )
| ( SV101 != SV14 ) )
= $false )
| ( ( SV101 = SV14 )
= $false )
| ( ( ord_less_eq_set_a @ SV14 @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1314]) ).
thf(1385,plain,
! [SV16: set_set_a,SV103: set_a] :
( ( ( ~ ( ~ ~ ( ~ ( member_set_a @ ( sK10_SY475 @ SV103 @ SV16 ) @ SV16 )
| ~ ( ord_less_eq_set_a @ ( sK10_SY475 @ SV103 @ SV16 ) @ SV103 ) )
| ~ ! [SY652: set_a] :
( ~ ( member_set_a @ SY652 @ SV16 )
| ~ ( ord_less_eq_set_a @ SY652 @ ( sK10_SY475 @ SV103 @ SV16 ) )
| ( ( sK10_SY475 @ SV103 @ SV16 )
= SY652 ) ) ) )
= $true )
| ( ( member_set_a @ SV103 @ SV16 )
= $false )
| ( ( finite_finite_set_a @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1315]) ).
thf(1386,plain,
! [SV220: set_a,SV181: nat,SV109: set_a,SV22: nat] :
( ( ( ~ ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV22 @ SV109 ) @ ( produc1450889781_set_a @ SV181 @ SV220 ) )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV22 @ SV181 )
| ~ ( ord_less_eq_set_a @ SV109 @ SV220 ) ) )
= $false )
| ( ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV22 @ SV109 ) @ ( produc1450889781_set_a @ SV181 @ SV220 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1318]) ).
thf(1387,plain,
! [SV220: set_a,SV109: set_a,SV181: nat,SV22: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV22 @ SV181 )
| ~ ( ord_less_eq_set_a @ SV109 @ SV220 ) )
= $true )
| ( ( ~ ( ~ ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV22 @ SV109 ) @ ( produc1450889781_set_a @ SV181 @ SV220 ) )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV22 @ SV181 )
| ~ ( ord_less_eq_set_a @ SV109 @ SV220 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1319]) ).
thf(1388,plain,
! [SV221: set_a,SV110: set_a] :
( ( ( ( SV110 != SV221 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV221 @ SV110 )
| ~ ( ord_less_eq_set_a @ SV110 @ SV221 ) ) )
= $false )
| ( ( SV110 = SV221 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1320]) ).
thf(1389,plain,
! [SV110: set_a,SV221: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV221 @ SV110 )
| ~ ( ord_less_eq_set_a @ SV110 @ SV221 ) )
= $true )
| ( ( ~ ( ( SV110 != SV221 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV221 @ SV110 )
| ~ ( ord_less_eq_set_a @ SV110 @ SV221 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1321]) ).
thf(1390,plain,
! [SV222: set_a,SV183: set_a,SV111: set_a,SV24: set_a] :
( ( ( ~ ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV24 @ SV111 ) @ ( produc1928581911_set_a @ SV183 @ SV222 ) )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV24 @ SV183 )
| ~ ( ord_less_eq_set_a @ SV111 @ SV222 ) ) )
= $false )
| ( ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV24 @ SV111 ) @ ( produc1928581911_set_a @ SV183 @ SV222 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1322]) ).
thf(1391,plain,
! [SV222: set_a,SV111: set_a,SV183: set_a,SV24: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV24 @ SV183 )
| ~ ( ord_less_eq_set_a @ SV111 @ SV222 ) )
= $true )
| ( ( ~ ( ~ ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV24 @ SV111 ) @ ( produc1928581911_set_a @ SV183 @ SV222 ) )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV24 @ SV183 )
| ~ ( ord_less_eq_set_a @ SV111 @ SV222 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1323]) ).
thf(1392,plain,
! [SV112: a,SV25: a] :
( ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV25 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV25 @ carrier @ relation ) )
= $true )
| ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV25 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV25 @ carrier @ relation ) )
= $true )
| ( ( member_a @ SV112 @ carrier )
= $false )
| ( ( member_a @ SV25 @ carrier )
= $false )
| ( ( finite_finite_a @ carrier )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1324]) ).
thf(1393,plain,
! [SV119: set_a,SV33: nat] :
( ( ( ( finite_card_a @ ( sK5_SY489 @ SV33 @ SV119 ) )
= SV33 )
= $true )
| ( ( ord_less_eq_nat @ SV33 @ ( finite_card_a @ SV119 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1328]) ).
thf(1394,plain,
! [SV119: set_a,SV33: nat] :
( ( ( finite_finite_a @ ( sK5_SY489 @ SV33 @ SV119 ) )
= $true )
| ( ( ord_less_eq_nat @ SV33 @ ( finite_card_a @ SV119 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1329]) ).
thf(1395,plain,
! [SV34: set_set_a] :
( ( ( ~ ( ~ ( member_set_a @ ( sK11_SY329 @ SV34 ) @ SV34 )
| ~ ! [SY653: set_a] :
( ~ ( member_set_a @ SY653 @ SV34 )
| ~ ( ord_less_eq_set_a @ ( sK11_SY329 @ SV34 ) @ SY653 )
| ( ( sK11_SY329 @ SV34 )
= SY653 ) ) ) )
= $true )
| ( ( SV34 = bot_bot_set_set_a )
= $true )
| ( ( finite_finite_set_a @ SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1330]) ).
thf(1396,plain,
! [SV121: set_a,SV36: nat] :
( ( ( ~ ( ord_less_eq_set_a @ ( sK6_SY490 @ SV36 @ SV121 ) @ SV121 ) )
= $false )
| ( ( ord_less_eq_nat @ SV36 @ ( finite_card_a @ SV121 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1332]) ).
thf(1397,plain,
! [SV121: set_a,SV36: nat] :
( ( ( ( finite_card_a @ ( sK6_SY490 @ SV36 @ SV121 ) )
!= SV36 )
= $false )
| ( ( ord_less_eq_nat @ SV36 @ ( finite_card_a @ SV121 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1332]) ).
thf(1398,plain,
! [SV223: nat,SV187: set_a,SV123: nat,SV38: set_a] :
( ( ( ~ ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV38 @ SV123 ) @ ( produc515611863_a_nat @ SV187 @ SV223 ) )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV38 @ SV187 )
| ~ ( ord_less_eq_nat @ SV123 @ SV223 ) ) )
= $false )
| ( ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV38 @ SV123 ) @ ( produc515611863_a_nat @ SV187 @ SV223 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1333]) ).
thf(1399,plain,
! [SV223: nat,SV123: nat,SV187: set_a,SV38: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV38 @ SV187 )
| ~ ( ord_less_eq_nat @ SV123 @ SV223 ) )
= $true )
| ( ( ~ ( ~ ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV38 @ SV123 ) @ ( produc515611863_a_nat @ SV187 @ SV223 ) )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV38 @ SV187 )
| ~ ( ord_less_eq_nat @ SV123 @ SV223 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1334]) ).
thf(1400,plain,
! [SV124: set_Product_prod_a_a,SV39: set_a,SV188: a] :
( ( ( ~ ( member_a @ SV188 @ SV39 ) )
= $true )
| ( ( ( prefer1676310729than_a @ SV188 @ SV39 @ SV124 )
!= bot_bot_set_a )
= $true )
| ( ( SV39 = bot_bot_set_a )
= $true )
| ( ( prefer719835986ence_a @ SV39 @ SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1335]) ).
thf(1401,plain,
! [SV224: set_a,SV126: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV126 @ SV224 )
| ~ ! [SY625: a] :
( ~ ( member_a @ SY625 @ SV126 )
| ( member_a @ SY625 @ SV224 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV126 @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1336]) ).
thf(1402,plain,
! [SV126: set_a,SV224: set_a] :
( ( ( ~ ( member_a @ ( sK13_SY625 @ SV224 @ SV126 ) @ SV126 )
| ( member_a @ ( sK13_SY625 @ SV224 @ SV126 ) @ SV224 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV126 @ SV224 )
| ~ ! [SY625: a] :
( ~ ( member_a @ SY625 @ SV126 )
| ( member_a @ SY625 @ SV224 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1337]) ).
thf(1403,plain,
! [SV190: a,SV130: a,SV46: a] :
( ( ( ~ ( member_a @ SV46 @ carrier )
| ~ ( member_a @ SV130 @ carrier ) )
= $true )
| ( ( ~ ( member_a @ SV190 @ carrier ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV190 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV46 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV190 ) @ relation ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1338]) ).
thf(1404,plain,
! [SV131: set_Product_prod_a_a,SV191: a,SV47: set_a,SV225: a] :
( ( ( ~ ( member_a @ SV225 @ SV47 ) )
= $true )
| ( ( ( member_a @ SV191 @ ( prefer1676310729than_a @ SV225 @ SV47 @ SV131 ) )
| ( member_a @ SV225 @ ( prefer1676310729than_a @ SV191 @ SV47 @ SV131 ) ) )
= $true )
| ( ( member_a @ SV191 @ SV47 )
= $false )
| ( ( prefer719835986ence_a @ SV47 @ SV131 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1339]) ).
thf(1405,plain,
! [SV192: a,SV133: a,SV50: a] :
( ( ( ~ ( member_a @ SV50 @ carrier )
| ~ ( member_a @ SV133 @ carrier ) )
= $true )
| ( ( ~ ( member_a @ SV192 @ carrier ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV50 @ SV133 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV133 @ SV192 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV50 @ SV192 ) @ relation ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1340]) ).
thf(1406,plain,
! [SV136: set_a,SV226: nat,SV54: set_a,SV195: set_a > nat] :
( ( ( ~ ! [SY585: set_a,SY586: set_a] :
( ~ ( ord_less_eq_set_a @ SY585 @ SY586 )
| ( ord_less_eq_nat @ ( SV195 @ SY585 ) @ ( SV195 @ SY586 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ ( SV195 @ SV54 ) @ SV226 )
= $true )
| ( ( ( SV195 @ SV136 )
= SV226 )
= $false )
| ( ( ord_less_eq_set_a @ SV54 @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1341]) ).
thf(1407,plain,
! [SV227: set_a,SV138: set_a] :
( ( ( ( SV138 != SV227 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV138 @ SV227 )
| ~ ( ord_less_eq_set_a @ SV227 @ SV138 ) ) )
= $false )
| ( ( SV138 = SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1342]) ).
thf(1408,plain,
! [SV227: set_a,SV138: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV138 @ SV227 )
| ~ ( ord_less_eq_set_a @ SV227 @ SV138 ) )
= $true )
| ( ( ~ ( ( SV138 != SV227 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV138 @ SV227 )
| ~ ( ord_less_eq_set_a @ SV227 @ SV138 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1343]) ).
thf(1409,plain,
! [SV197: set_a,SV228: set_a,SV57: set_a,SV139: set_a > set_a] :
( ( ( ~ ! [SY513: set_a,SY514: set_a] :
( ~ ( ord_less_eq_set_a @ SY513 @ SY514 )
| ( ord_less_eq_set_a @ ( SV139 @ SY513 ) @ ( SV139 @ SY514 ) ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV57 @ ( SV139 @ SV228 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV197 @ SV228 )
= $false )
| ( ( SV57
= ( SV139 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1344]) ).
thf(1410,plain,
! [SV62: set_set_a,SV143: set_a] :
( ( ( ~ ( ~ ~ ( ~ ( member_set_a @ ( sK12_SY517 @ SV143 @ SV62 ) @ SV62 )
| ~ ( ord_less_eq_set_a @ SV143 @ ( sK12_SY517 @ SV143 @ SV62 ) ) )
| ~ ! [SY654: set_a] :
( ~ ( member_set_a @ SY654 @ SV62 )
| ~ ( ord_less_eq_set_a @ ( sK12_SY517 @ SV143 @ SV62 ) @ SY654 )
| ( ( sK12_SY517 @ SV143 @ SV62 )
= SY654 ) ) ) )
= $true )
| ( ( member_set_a @ SV143 @ SV62 )
= $false )
| ( ( finite_finite_set_a @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1346]) ).
thf(1411,plain,
! [SV63: a,SV144: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) ) )
| ~ ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( member_a @ SV144 @ carrier )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1347]) ).
thf(1412,plain,
! [SV63: a,SV144: a] :
( ( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( member_a @ SV144 @ carrier )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1347]) ).
thf(1413,plain,
! [SV230: set_a,SV145: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV145 @ SV230 )
| ~ ! [SY630: a] :
( ~ ( member_a @ SY630 @ SV145 )
| ( member_a @ SY630 @ SV230 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV145 @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1348]) ).
thf(1414,plain,
! [SV145: set_a,SV230: set_a] :
( ( ( ~ ( member_a @ ( sK14_SY630 @ SV230 @ SV145 ) @ SV145 )
| ( member_a @ ( sK14_SY630 @ SV230 @ SV145 ) @ SV230 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV145 @ SV230 )
| ~ ! [SY630: a] :
( ~ ( member_a @ SY630 @ SV145 )
| ( member_a @ SY630 @ SV230 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1349]) ).
thf(1415,plain,
! [SV147: set_Product_prod_a_a,SV231: a,SV66: set_a,SV200: a] :
( ( ( ~ ( member_a @ SV200 @ SV66 ) )
= $true )
| ( ( ~ ( member_a @ SV231 @ SV66 )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) ) )
= $true )
| ( ( finite_finite_a @ SV66 )
= $false )
| ( ( prefer719835986ence_a @ SV66 @ SV147 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1350]) ).
thf(1416,plain,
! [SV148: set_a,SV232: nat,SV67: set_a,SV201: set_a > nat] :
( ( ( ~ ! [SY594: set_a,SY595: set_a] :
( ~ ( ord_less_eq_set_a @ SY594 @ SY595 )
| ( ord_less_eq_nat @ ( SV201 @ SY594 ) @ ( SV201 @ SY595 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ ( SV201 @ SV67 ) @ SV232 )
= $true )
| ( ( ord_less_eq_nat @ ( SV201 @ SV148 ) @ SV232 )
= $false )
| ( ( ord_less_eq_set_a @ SV67 @ SV148 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1351]) ).
thf(1417,plain,
! [SV233: set_a,SV150: set_a] :
( ( ( ( SV150 != SV233 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV150 @ SV233 )
| ~ ( ord_less_eq_set_a @ SV233 @ SV150 ) ) )
= $false )
| ( ( SV150 = SV233 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1352]) ).
thf(1418,plain,
! [SV233: set_a,SV150: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV150 @ SV233 )
| ~ ( ord_less_eq_set_a @ SV233 @ SV150 ) )
= $true )
| ( ( ~ ( ( SV150 != SV233 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV150 @ SV233 )
| ~ ( ord_less_eq_set_a @ SV233 @ SV150 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1353]) ).
thf(1419,plain,
! [SV151: set_a,SV234: set_a,SV70: set_a,SV203: set_a > set_a] :
( ( ( ~ ! [SY597: set_a,SY598: set_a] :
( ~ ( ord_less_eq_set_a @ SY597 @ SY598 )
| ( ord_less_eq_set_a @ ( SV203 @ SY597 ) @ ( SV203 @ SY598 ) ) ) )
= $true )
| ( ( ord_less_eq_set_a @ ( SV203 @ SV70 ) @ SV234 )
= $true )
| ( ( ord_less_eq_set_a @ ( SV203 @ SV151 ) @ SV234 )
= $false )
| ( ( ord_less_eq_set_a @ SV70 @ SV151 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1354]) ).
thf(1420,plain,
! [SV152: a,SV71: a] :
( ( ( ~ ( ~ ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
| ~ ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
| ~ ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1355]) ).
thf(1421,plain,
! [SV207: set_a,SV237: set_a,SV75: nat,SV156: set_a > nat] :
( ( ( ~ ! [SY540: set_a,SY541: set_a] :
( ~ ( ord_less_eq_set_a @ SY540 @ SY541 )
| ( ord_less_eq_nat @ ( SV156 @ SY540 ) @ ( SV156 @ SY541 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV75 @ ( SV156 @ SV237 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV207 @ SV237 )
= $false )
| ( ( SV75
= ( SV156 @ SV207 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1358]) ).
thf(1422,plain,
! [SV157: a > $o,SV76: a > $o] :
( ( ( ord_less_eq_set_a @ ( collect_a @ SV76 ) @ ( collect_a @ SV157 ) )
= $true )
| ( ( ord_less_eq_set_a @ ( collect_a @ SV76 ) @ ( collect_a @ SV157 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1359]) ).
thf(1423,plain,
! [SV157: a > $o,SV76: a > $o] :
( ( ( ! [SY542: a] :
( ~ ( SV76 @ SY542 )
| ( SV157 @ SY542 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ ( collect_a @ SV76 ) @ ( collect_a @ SV157 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1360]) ).
thf(1424,plain,
! [SV157: a > $o,SV76: a > $o] :
( ( ( SV76 @ ( sK7_SY542 @ SV157 @ SV76 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ ( collect_a @ SV76 ) @ ( collect_a @ SV157 ) )
| ~ ! [SY542: a] :
( ~ ( SV76 @ SY542 )
| ( SV157 @ SY542 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1361]) ).
thf(1425,plain,
! [SV157: a > $o,SV76: a > $o] :
( ( ( ~ ( ord_less_eq_set_a @ ( collect_a @ SV76 ) @ ( collect_a @ SV157 ) )
| ~ ! [SY542: a] :
( ~ ( SV76 @ SY542 )
| ( SV157 @ SY542 ) ) )
= $false )
| ( ( SV157 @ ( sK7_SY542 @ SV157 @ SV76 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1362]) ).
thf(1426,plain,
! [SV158: nat,SV77: set_a] :
( ( ( ~ ( finite_finite_a @ SV77 ) )
= $false )
| ( ( ord_less_eq_set_a @ ( sK4_SY543 @ SV158 @ SV77 ) @ SV77 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1363]) ).
thf(1427,plain,
! [SV158: nat,SV77: set_a] :
( ( ( ~ ( ord_less_eq_nat @ ( finite_card_a @ SV77 ) @ SV158 ) )
= $false )
| ( ( ord_less_eq_set_a @ ( sK4_SY543 @ SV158 @ SV77 ) @ SV77 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1363]) ).
thf(1428,plain,
! [SV158: nat,SV77: set_a] :
( ( ( ~ ( finite_finite_a @ SV77 )
| ~ ( ord_less_eq_nat @ ( finite_card_a @ SV77 ) @ SV158 ) )
= $false )
| ( ( finite_finite_a @ ( sK4_SY543 @ SV158 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1364]) ).
thf(1429,plain,
! [SV158: nat,SV77: set_a] :
( ( ( ~ ( finite_finite_a @ SV77 ) )
= $false )
| ( ( ord_less_eq_nat @ ( finite_card_a @ ( sK4_SY543 @ SV158 @ SV77 ) ) @ SV158 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1365]) ).
thf(1430,plain,
! [SV158: nat,SV77: set_a] :
( ( ( ~ ( ord_less_eq_nat @ ( finite_card_a @ SV77 ) @ SV158 ) )
= $false )
| ( ( ord_less_eq_nat @ ( finite_card_a @ ( sK4_SY543 @ SV158 @ SV77 ) ) @ SV158 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1365]) ).
thf(1431,plain,
! [SV159: a,SV78: a] :
( ( ( SV78 = SV159 )
= $true )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV78 @ SV159 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV159 @ SV78 ) @ relation ) )
= $true )
| ( ( member_a @ SV159 @ carrier )
= $false )
| ( ( member_a @ SV78 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1366]) ).
thf(1432,plain,
! [SV161: nat,SV238: set_a,SV80: nat,SV208: nat > set_a] :
( ( ( ~ ! [SY605: nat,SY606: nat] :
( ~ ( ord_less_eq_nat @ SY605 @ SY606 )
| ( ord_less_eq_set_a @ ( SV208 @ SY605 ) @ ( SV208 @ SY606 ) ) ) )
= $true )
| ( ( ord_less_eq_set_a @ ( SV208 @ SV80 ) @ SV238 )
= $true )
| ( ( ( SV208 @ SV161 )
= SV238 )
= $false )
| ( ( ord_less_eq_nat @ SV80 @ SV161 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1368]) ).
thf(1433,plain,
! [SV162: set_a,SV239: set_a,SV81: set_a,SV209: set_a > set_a] :
( ( ( ~ ! [SY608: set_a,SY609: set_a] :
( ~ ( ord_less_eq_set_a @ SY608 @ SY609 )
| ( ord_less_eq_set_a @ ( SV209 @ SY608 ) @ ( SV209 @ SY609 ) ) ) )
= $true )
| ( ( ord_less_eq_set_a @ ( SV209 @ SV81 ) @ SV239 )
= $true )
| ( ( ( SV209 @ SV162 )
= SV239 )
= $false )
| ( ( ord_less_eq_set_a @ SV81 @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1369]) ).
thf(1434,plain,
! [SV163: nat,SV82: set_a] :
( ( ( ~ ~ ( ~ ( finite_finite_a @ ( sK8_SY552 @ SV82 @ SV163 ) )
| ( ( finite_card_a @ ( sK8_SY552 @ SV82 @ SV163 ) )
!= SV163 ) )
| ~ ( ord_less_eq_set_a @ ( sK8_SY552 @ SV82 @ SV163 ) @ SV82 ) )
= $false )
| ( ( finite_finite_a @ SV82 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1370]) ).
thf(1435,plain,
! [SV210: a,SV83: a,SV164: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV83 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SV164 ) @ relation )
= $false )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV210 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV210 @ SV164 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SV210 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV210 @ SV83 ) @ relation ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1371]) ).
thf(1436,plain,
! [SV211: set_a,SV240: set_a,SV85: nat,SV166: set_a > nat] :
( ( ( ~ ! [SY556: set_a,SY557: set_a] :
( ~ ( ord_less_eq_set_a @ SY556 @ SY557 )
| ( ord_less_eq_nat @ ( SV166 @ SY556 ) @ ( SV166 @ SY557 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV85 @ ( SV166 @ SV240 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV211 @ SV240 )
= $false )
| ( ( ord_less_eq_nat @ SV85 @ ( SV166 @ SV211 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1372]) ).
thf(1437,plain,
! [SV212: nat,SV241: nat,SV87: set_a,SV168: nat > set_a] :
( ( ( ~ ! [SY560: nat,SY561: nat] :
( ~ ( ord_less_eq_nat @ SY560 @ SY561 )
| ( ord_less_eq_set_a @ ( SV168 @ SY560 ) @ ( SV168 @ SY561 ) ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV87 @ ( SV168 @ SV241 ) )
= $true )
| ( ( ord_less_eq_nat @ SV212 @ SV241 )
= $false )
| ( ( ord_less_eq_set_a @ SV87 @ ( SV168 @ SV212 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1373]) ).
thf(1438,plain,
! [SV170: nat,SV242: set_a,SV89: nat,SV213: nat > set_a] :
( ( ( ~ ! [SY617: nat,SY618: nat] :
( ~ ( ord_less_eq_nat @ SY617 @ SY618 )
| ( ord_less_eq_set_a @ ( SV213 @ SY617 ) @ ( SV213 @ SY618 ) ) ) )
= $true )
| ( ( ord_less_eq_set_a @ ( SV213 @ SV89 ) @ SV242 )
= $true )
| ( ( ord_less_eq_set_a @ ( SV213 @ SV170 ) @ SV242 )
= $false )
| ( ( ord_less_eq_nat @ SV89 @ SV170 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1374]) ).
thf(1439,plain,
! [SV215: set_a,SV243: set_a,SV91: set_a,SV172: set_a > set_a] :
( ( ( ~ ! [SY569: set_a,SY570: set_a] :
( ~ ( ord_less_eq_set_a @ SY569 @ SY570 )
| ( ord_less_eq_set_a @ ( SV172 @ SY569 ) @ ( SV172 @ SY570 ) ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV91 @ ( SV172 @ SV243 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV215 @ SV243 )
= $false )
| ( ( ord_less_eq_set_a @ SV91 @ ( SV172 @ SV215 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1375]) ).
thf(1440,plain,
! [SV244: set_a,SV173: set_a] :
( ( ( ( SV173 != SV244 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV173 @ SV244 )
| ~ ( ord_less_eq_set_a @ SV244 @ SV173 ) ) )
= $false )
| ( ( SV173 = SV244 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1376]) ).
thf(1441,plain,
! [SV244: set_a,SV173: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV173 @ SV244 )
| ~ ( ord_less_eq_set_a @ SV244 @ SV173 ) )
= $true )
| ( ( ~ ( ( SV173 != SV244 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV173 @ SV244 )
| ~ ( ord_less_eq_set_a @ SV244 @ SV173 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1377]) ).
thf(1442,plain,
! [SV217: nat,SV246: nat,SV94: set_a,SV174: nat > set_a] :
( ( ( ~ ! [SY575: nat,SY576: nat] :
( ~ ( ord_less_eq_nat @ SY575 @ SY576 )
| ( ord_less_eq_set_a @ ( SV174 @ SY575 ) @ ( SV174 @ SY576 ) ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV94 @ ( SV174 @ SV246 ) )
= $true )
| ( ( ord_less_eq_nat @ SV217 @ SV246 )
= $false )
| ( ( SV94
= ( SV174 @ SV217 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1378]) ).
thf(1443,plain,
! [SV176: a,SV9: a,SV97: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV9 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV97 ) @ relation )
= $false )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV176 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV97 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV176 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV9 ) @ relation ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1380]) ).
thf(1444,plain,
! [SV13: set_set_a] :
( ( ( ~ ( member_set_a @ ( sK9_SY294 @ SV13 ) @ SV13 )
| ~ ! [SY651: set_a] :
( ~ ( member_set_a @ SY651 @ SV13 )
| ~ ( ord_less_eq_set_a @ SY651 @ ( sK9_SY294 @ SV13 ) )
| ( ( sK9_SY294 @ SV13 )
= SY651 ) ) )
= $false )
| ( ( SV13 = bot_bot_set_set_a )
= $true )
| ( ( finite_finite_set_a @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1382]) ).
thf(1445,plain,
! [SV14: set_a,SV101: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV101 @ SV14 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV101 @ SV14 )
= $false )
| ( ( ord_less_eq_set_a @ SV14 @ SV101 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1383]) ).
thf(1446,plain,
! [SV14: set_a,SV101: set_a] :
( ( ( SV101 != SV14 )
= $false )
| ( ( ord_less_eq_set_a @ SV101 @ SV14 )
= $false )
| ( ( ord_less_eq_set_a @ SV14 @ SV101 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1383]) ).
thf(1447,plain,
! [SV14: set_a,SV101: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV101 @ SV14 ) )
= $false )
| ( ( SV101 = SV14 )
= $false )
| ( ( ord_less_eq_set_a @ SV14 @ SV101 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1384]) ).
thf(1448,plain,
! [SV14: set_a,SV101: set_a] :
( ( ( SV101 != SV14 )
= $false )
| ( ( SV101 = SV14 )
= $false )
| ( ( ord_less_eq_set_a @ SV14 @ SV101 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1384]) ).
thf(1449,plain,
! [SV16: set_set_a,SV103: set_a] :
( ( ( ~ ~ ( ~ ( member_set_a @ ( sK10_SY475 @ SV103 @ SV16 ) @ SV16 )
| ~ ( ord_less_eq_set_a @ ( sK10_SY475 @ SV103 @ SV16 ) @ SV103 ) )
| ~ ! [SY652: set_a] :
( ~ ( member_set_a @ SY652 @ SV16 )
| ~ ( ord_less_eq_set_a @ SY652 @ ( sK10_SY475 @ SV103 @ SV16 ) )
| ( ( sK10_SY475 @ SV103 @ SV16 )
= SY652 ) ) )
= $false )
| ( ( member_set_a @ SV103 @ SV16 )
= $false )
| ( ( finite_finite_set_a @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1385]) ).
thf(1450,plain,
! [SV220: set_a,SV181: nat,SV109: set_a,SV22: nat] :
( ( ( ~ ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV22 @ SV109 ) @ ( produc1450889781_set_a @ SV181 @ SV220 ) ) )
= $false )
| ( ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV22 @ SV109 ) @ ( produc1450889781_set_a @ SV181 @ SV220 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1386]) ).
thf(1451,plain,
! [SV220: set_a,SV109: set_a,SV181: nat,SV22: nat] :
( ( ( ~ ~ ( ~ ( ord_less_eq_nat @ SV22 @ SV181 )
| ~ ( ord_less_eq_set_a @ SV109 @ SV220 ) ) )
= $false )
| ( ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV22 @ SV109 ) @ ( produc1450889781_set_a @ SV181 @ SV220 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1386]) ).
thf(1452,plain,
! [SV220: set_a,SV109: set_a,SV181: nat,SV22: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV22 @ SV181 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV109 @ SV220 ) )
= $true )
| ( ( ~ ( ~ ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV22 @ SV109 ) @ ( produc1450889781_set_a @ SV181 @ SV220 ) )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV22 @ SV181 )
| ~ ( ord_less_eq_set_a @ SV109 @ SV220 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1387]) ).
thf(1453,plain,
! [SV221: set_a,SV110: set_a] :
( ( ( SV110 != SV221 )
= $false )
| ( ( SV110 = SV221 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1388]) ).
thf(1454,plain,
! [SV110: set_a,SV221: set_a] :
( ( ( ~ ~ ( ~ ( ord_less_eq_set_a @ SV221 @ SV110 )
| ~ ( ord_less_eq_set_a @ SV110 @ SV221 ) ) )
= $false )
| ( ( SV110 = SV221 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1388]) ).
thf(1455,plain,
! [SV110: set_a,SV221: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV221 @ SV110 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV110 @ SV221 ) )
= $true )
| ( ( ~ ( ( SV110 != SV221 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV221 @ SV110 )
| ~ ( ord_less_eq_set_a @ SV110 @ SV221 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1389]) ).
thf(1456,plain,
! [SV222: set_a,SV183: set_a,SV111: set_a,SV24: set_a] :
( ( ( ~ ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV24 @ SV111 ) @ ( produc1928581911_set_a @ SV183 @ SV222 ) ) )
= $false )
| ( ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV24 @ SV111 ) @ ( produc1928581911_set_a @ SV183 @ SV222 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1390]) ).
thf(1457,plain,
! [SV222: set_a,SV111: set_a,SV183: set_a,SV24: set_a] :
( ( ( ~ ~ ( ~ ( ord_less_eq_set_a @ SV24 @ SV183 )
| ~ ( ord_less_eq_set_a @ SV111 @ SV222 ) ) )
= $false )
| ( ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV24 @ SV111 ) @ ( produc1928581911_set_a @ SV183 @ SV222 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1390]) ).
thf(1458,plain,
! [SV222: set_a,SV111: set_a,SV183: set_a,SV24: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV24 @ SV183 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV111 @ SV222 ) )
= $true )
| ( ( ~ ( ~ ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV24 @ SV111 ) @ ( produc1928581911_set_a @ SV183 @ SV222 ) )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV24 @ SV183 )
| ~ ( ord_less_eq_set_a @ SV111 @ SV222 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1391]) ).
thf(1459,plain,
! [SV34: set_set_a] :
( ( ( ~ ( member_set_a @ ( sK11_SY329 @ SV34 ) @ SV34 )
| ~ ! [SY653: set_a] :
( ~ ( member_set_a @ SY653 @ SV34 )
| ~ ( ord_less_eq_set_a @ ( sK11_SY329 @ SV34 ) @ SY653 )
| ( ( sK11_SY329 @ SV34 )
= SY653 ) ) )
= $false )
| ( ( SV34 = bot_bot_set_set_a )
= $true )
| ( ( finite_finite_set_a @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1395]) ).
thf(1460,plain,
! [SV121: set_a,SV36: nat] :
( ( ( ord_less_eq_set_a @ ( sK6_SY490 @ SV36 @ SV121 ) @ SV121 )
= $true )
| ( ( ord_less_eq_nat @ SV36 @ ( finite_card_a @ SV121 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1396]) ).
thf(1461,plain,
! [SV121: set_a,SV36: nat] :
( ( ( ( finite_card_a @ ( sK6_SY490 @ SV36 @ SV121 ) )
= SV36 )
= $true )
| ( ( ord_less_eq_nat @ SV36 @ ( finite_card_a @ SV121 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1397]) ).
thf(1462,plain,
! [SV223: nat,SV187: set_a,SV123: nat,SV38: set_a] :
( ( ( ~ ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV38 @ SV123 ) @ ( produc515611863_a_nat @ SV187 @ SV223 ) ) )
= $false )
| ( ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV38 @ SV123 ) @ ( produc515611863_a_nat @ SV187 @ SV223 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1398]) ).
thf(1463,plain,
! [SV223: nat,SV123: nat,SV187: set_a,SV38: set_a] :
( ( ( ~ ~ ( ~ ( ord_less_eq_set_a @ SV38 @ SV187 )
| ~ ( ord_less_eq_nat @ SV123 @ SV223 ) ) )
= $false )
| ( ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV38 @ SV123 ) @ ( produc515611863_a_nat @ SV187 @ SV223 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1398]) ).
thf(1464,plain,
! [SV223: nat,SV123: nat,SV187: set_a,SV38: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV38 @ SV187 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV123 @ SV223 ) )
= $true )
| ( ( ~ ( ~ ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV38 @ SV123 ) @ ( produc515611863_a_nat @ SV187 @ SV223 ) )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV38 @ SV187 )
| ~ ( ord_less_eq_nat @ SV123 @ SV223 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1399]) ).
thf(1465,plain,
! [SV124: set_Product_prod_a_a,SV39: set_a,SV188: a] :
( ( ( member_a @ SV188 @ SV39 )
= $false )
| ( ( ( prefer1676310729than_a @ SV188 @ SV39 @ SV124 )
!= bot_bot_set_a )
= $true )
| ( ( SV39 = bot_bot_set_a )
= $true )
| ( ( prefer719835986ence_a @ SV39 @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1400]) ).
thf(1466,plain,
! [SV224: set_a,SV126: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV126 @ SV224 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV126 @ SV224 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1401]) ).
thf(1467,plain,
! [SV224: set_a,SV126: set_a] :
( ( ( ~ ! [SY625: a] :
( ~ ( member_a @ SY625 @ SV126 )
| ( member_a @ SY625 @ SV224 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV126 @ SV224 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1401]) ).
thf(1468,plain,
! [SV126: set_a,SV224: set_a] :
( ( ( ~ ( member_a @ ( sK13_SY625 @ SV224 @ SV126 ) @ SV126 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV126 @ SV224 )
| ~ ! [SY625: a] :
( ~ ( member_a @ SY625 @ SV126 )
| ( member_a @ SY625 @ SV224 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1402]) ).
thf(1469,plain,
! [SV126: set_a,SV224: set_a] :
( ( ( member_a @ ( sK13_SY625 @ SV224 @ SV126 ) @ SV224 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV126 @ SV224 )
| ~ ! [SY625: a] :
( ~ ( member_a @ SY625 @ SV126 )
| ( member_a @ SY625 @ SV224 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1402]) ).
thf(1470,plain,
! [SV190: a,SV130: a,SV46: a] :
( ( ( ~ ( member_a @ SV46 @ carrier ) )
= $true )
| ( ( ~ ( member_a @ SV130 @ carrier ) )
= $true )
| ( ( ~ ( member_a @ SV190 @ carrier ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV190 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV46 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV190 ) @ relation ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1403]) ).
thf(1471,plain,
! [SV131: set_Product_prod_a_a,SV191: a,SV47: set_a,SV225: a] :
( ( ( member_a @ SV225 @ SV47 )
= $false )
| ( ( ( member_a @ SV191 @ ( prefer1676310729than_a @ SV225 @ SV47 @ SV131 ) )
| ( member_a @ SV225 @ ( prefer1676310729than_a @ SV191 @ SV47 @ SV131 ) ) )
= $true )
| ( ( member_a @ SV191 @ SV47 )
= $false )
| ( ( prefer719835986ence_a @ SV47 @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1404]) ).
thf(1472,plain,
! [SV192: a,SV133: a,SV50: a] :
( ( ( ~ ( member_a @ SV50 @ carrier ) )
= $true )
| ( ( ~ ( member_a @ SV133 @ carrier ) )
= $true )
| ( ( ~ ( member_a @ SV192 @ carrier ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV50 @ SV133 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV133 @ SV192 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV50 @ SV192 ) @ relation ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1405]) ).
thf(1473,plain,
! [SV136: set_a,SV226: nat,SV54: set_a,SV195: set_a > nat] :
( ( ( ! [SY585: set_a,SY586: set_a] :
( ~ ( ord_less_eq_set_a @ SY585 @ SY586 )
| ( ord_less_eq_nat @ ( SV195 @ SY585 ) @ ( SV195 @ SY586 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( SV195 @ SV54 ) @ SV226 )
= $true )
| ( ( ( SV195 @ SV136 )
= SV226 )
= $false )
| ( ( ord_less_eq_set_a @ SV54 @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1406]) ).
thf(1474,plain,
! [SV227: set_a,SV138: set_a] :
( ( ( SV138 != SV227 )
= $false )
| ( ( SV138 = SV227 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1407]) ).
thf(1475,plain,
! [SV227: set_a,SV138: set_a] :
( ( ( ~ ~ ( ~ ( ord_less_eq_set_a @ SV138 @ SV227 )
| ~ ( ord_less_eq_set_a @ SV227 @ SV138 ) ) )
= $false )
| ( ( SV138 = SV227 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1407]) ).
thf(1476,plain,
! [SV227: set_a,SV138: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV138 @ SV227 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV227 @ SV138 ) )
= $true )
| ( ( ~ ( ( SV138 != SV227 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV138 @ SV227 )
| ~ ( ord_less_eq_set_a @ SV227 @ SV138 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1408]) ).
thf(1477,plain,
! [SV197: set_a,SV228: set_a,SV57: set_a,SV139: set_a > set_a] :
( ( ( ! [SY513: set_a,SY514: set_a] :
( ~ ( ord_less_eq_set_a @ SY513 @ SY514 )
| ( ord_less_eq_set_a @ ( SV139 @ SY513 ) @ ( SV139 @ SY514 ) ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV57 @ ( SV139 @ SV228 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV197 @ SV228 )
= $false )
| ( ( SV57
= ( SV139 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1409]) ).
thf(1478,plain,
! [SV62: set_set_a,SV143: set_a] :
( ( ( ~ ~ ( ~ ( member_set_a @ ( sK12_SY517 @ SV143 @ SV62 ) @ SV62 )
| ~ ( ord_less_eq_set_a @ SV143 @ ( sK12_SY517 @ SV143 @ SV62 ) ) )
| ~ ! [SY654: set_a] :
( ~ ( member_set_a @ SY654 @ SV62 )
| ~ ( ord_less_eq_set_a @ ( sK12_SY517 @ SV143 @ SV62 ) @ SY654 )
| ( ( sK12_SY517 @ SV143 @ SV62 )
= SY654 ) ) )
= $false )
| ( ( member_set_a @ SV143 @ SV62 )
= $false )
| ( ( finite_finite_set_a @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1410]) ).
thf(1479,plain,
! [SV63: a,SV144: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( member_a @ SV144 @ carrier )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1411]) ).
thf(1480,plain,
! [SV230: set_a,SV145: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV145 @ SV230 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV145 @ SV230 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1413]) ).
thf(1481,plain,
! [SV230: set_a,SV145: set_a] :
( ( ( ~ ! [SY630: a] :
( ~ ( member_a @ SY630 @ SV145 )
| ( member_a @ SY630 @ SV230 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV145 @ SV230 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1413]) ).
thf(1482,plain,
! [SV145: set_a,SV230: set_a] :
( ( ( ~ ( member_a @ ( sK14_SY630 @ SV230 @ SV145 ) @ SV145 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV145 @ SV230 )
| ~ ! [SY630: a] :
( ~ ( member_a @ SY630 @ SV145 )
| ( member_a @ SY630 @ SV230 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1414]) ).
thf(1483,plain,
! [SV145: set_a,SV230: set_a] :
( ( ( member_a @ ( sK14_SY630 @ SV230 @ SV145 ) @ SV230 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV145 @ SV230 )
| ~ ! [SY630: a] :
( ~ ( member_a @ SY630 @ SV145 )
| ( member_a @ SY630 @ SV230 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1414]) ).
thf(1484,plain,
! [SV147: set_Product_prod_a_a,SV231: a,SV66: set_a,SV200: a] :
( ( ( member_a @ SV200 @ SV66 )
= $false )
| ( ( ~ ( member_a @ SV231 @ SV66 )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) ) )
= $true )
| ( ( finite_finite_a @ SV66 )
= $false )
| ( ( prefer719835986ence_a @ SV66 @ SV147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1415]) ).
thf(1485,plain,
! [SV148: set_a,SV232: nat,SV67: set_a,SV201: set_a > nat] :
( ( ( ! [SY594: set_a,SY595: set_a] :
( ~ ( ord_less_eq_set_a @ SY594 @ SY595 )
| ( ord_less_eq_nat @ ( SV201 @ SY594 ) @ ( SV201 @ SY595 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( SV201 @ SV67 ) @ SV232 )
= $true )
| ( ( ord_less_eq_nat @ ( SV201 @ SV148 ) @ SV232 )
= $false )
| ( ( ord_less_eq_set_a @ SV67 @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1416]) ).
thf(1486,plain,
! [SV233: set_a,SV150: set_a] :
( ( ( SV150 != SV233 )
= $false )
| ( ( SV150 = SV233 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1417]) ).
thf(1487,plain,
! [SV233: set_a,SV150: set_a] :
( ( ( ~ ~ ( ~ ( ord_less_eq_set_a @ SV150 @ SV233 )
| ~ ( ord_less_eq_set_a @ SV233 @ SV150 ) ) )
= $false )
| ( ( SV150 = SV233 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1417]) ).
thf(1488,plain,
! [SV233: set_a,SV150: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV150 @ SV233 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV233 @ SV150 ) )
= $true )
| ( ( ~ ( ( SV150 != SV233 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV150 @ SV233 )
| ~ ( ord_less_eq_set_a @ SV233 @ SV150 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1418]) ).
thf(1489,plain,
! [SV151: set_a,SV234: set_a,SV70: set_a,SV203: set_a > set_a] :
( ( ( ! [SY597: set_a,SY598: set_a] :
( ~ ( ord_less_eq_set_a @ SY597 @ SY598 )
| ( ord_less_eq_set_a @ ( SV203 @ SY597 ) @ ( SV203 @ SY598 ) ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( SV203 @ SV70 ) @ SV234 )
= $true )
| ( ( ord_less_eq_set_a @ ( SV203 @ SV151 ) @ SV234 )
= $false )
| ( ( ord_less_eq_set_a @ SV70 @ SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1419]) ).
thf(1490,plain,
! [SV152: a,SV71: a] :
( ( ( ~ ( ~ ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
| ~ ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
| ~ ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1420]) ).
thf(1491,plain,
! [SV152: a,SV71: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
| ~ ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1420]) ).
thf(1492,plain,
! [SV207: set_a,SV237: set_a,SV75: nat,SV156: set_a > nat] :
( ( ( ! [SY540: set_a,SY541: set_a] :
( ~ ( ord_less_eq_set_a @ SY540 @ SY541 )
| ( ord_less_eq_nat @ ( SV156 @ SY540 ) @ ( SV156 @ SY541 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV75 @ ( SV156 @ SV237 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV207 @ SV237 )
= $false )
| ( ( SV75
= ( SV156 @ SV207 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1421]) ).
thf(1493,plain,
! [SV157: a > $o,SV248: a,SV76: a > $o] :
( ( ( ~ ( SV76 @ SV248 )
| ( SV157 @ SV248 ) )
= $true )
| ( ( ord_less_eq_set_a @ ( collect_a @ SV76 ) @ ( collect_a @ SV157 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1423]) ).
thf(1494,plain,
! [SV157: a > $o,SV76: a > $o] :
( ( ( ~ ( ord_less_eq_set_a @ ( collect_a @ SV76 ) @ ( collect_a @ SV157 ) )
| ~ ! [SY542: a] :
( ~ ( SV76 @ SY542 )
| ( SV157 @ SY542 ) ) )
= $false )
| ( ( SV76 @ ( sK7_SY542 @ SV157 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1424]) ).
thf(1495,plain,
! [SV157: a > $o,SV76: a > $o] :
( ( ( ~ ( ord_less_eq_set_a @ ( collect_a @ SV76 ) @ ( collect_a @ SV157 ) ) )
= $false )
| ( ( SV157 @ ( sK7_SY542 @ SV157 @ SV76 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1425]) ).
thf(1496,plain,
! [SV157: a > $o,SV76: a > $o] :
( ( ( ~ ! [SY542: a] :
( ~ ( SV76 @ SY542 )
| ( SV157 @ SY542 ) ) )
= $false )
| ( ( SV157 @ ( sK7_SY542 @ SV157 @ SV76 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1425]) ).
thf(1497,plain,
! [SV158: nat,SV77: set_a] :
( ( ( finite_finite_a @ SV77 )
= $true )
| ( ( ord_less_eq_set_a @ ( sK4_SY543 @ SV158 @ SV77 ) @ SV77 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1426]) ).
thf(1498,plain,
! [SV158: nat,SV77: set_a] :
( ( ( ord_less_eq_nat @ ( finite_card_a @ SV77 ) @ SV158 )
= $true )
| ( ( ord_less_eq_set_a @ ( sK4_SY543 @ SV158 @ SV77 ) @ SV77 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1427]) ).
thf(1499,plain,
! [SV158: nat,SV77: set_a] :
( ( ( ~ ( finite_finite_a @ SV77 ) )
= $false )
| ( ( finite_finite_a @ ( sK4_SY543 @ SV158 @ SV77 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1428]) ).
thf(1500,plain,
! [SV158: nat,SV77: set_a] :
( ( ( ~ ( ord_less_eq_nat @ ( finite_card_a @ SV77 ) @ SV158 ) )
= $false )
| ( ( finite_finite_a @ ( sK4_SY543 @ SV158 @ SV77 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1428]) ).
thf(1501,plain,
! [SV158: nat,SV77: set_a] :
( ( ( finite_finite_a @ SV77 )
= $true )
| ( ( ord_less_eq_nat @ ( finite_card_a @ ( sK4_SY543 @ SV158 @ SV77 ) ) @ SV158 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1429]) ).
thf(1502,plain,
! [SV158: nat,SV77: set_a] :
( ( ( ord_less_eq_nat @ ( finite_card_a @ SV77 ) @ SV158 )
= $true )
| ( ( ord_less_eq_nat @ ( finite_card_a @ ( sK4_SY543 @ SV158 @ SV77 ) ) @ SV158 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1430]) ).
thf(1503,plain,
! [SV159: a,SV78: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV78 @ SV159 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV159 @ SV78 ) @ relation )
= $true )
| ( ( SV78 = SV159 )
= $true )
| ( ( member_a @ SV159 @ carrier )
= $false )
| ( ( member_a @ SV78 @ carrier )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1431]) ).
thf(1504,plain,
! [SV161: nat,SV238: set_a,SV80: nat,SV208: nat > set_a] :
( ( ( ! [SY605: nat,SY606: nat] :
( ~ ( ord_less_eq_nat @ SY605 @ SY606 )
| ( ord_less_eq_set_a @ ( SV208 @ SY605 ) @ ( SV208 @ SY606 ) ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( SV208 @ SV80 ) @ SV238 )
= $true )
| ( ( ( SV208 @ SV161 )
= SV238 )
= $false )
| ( ( ord_less_eq_nat @ SV80 @ SV161 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1432]) ).
thf(1505,plain,
! [SV162: set_a,SV239: set_a,SV81: set_a,SV209: set_a > set_a] :
( ( ( ! [SY608: set_a,SY609: set_a] :
( ~ ( ord_less_eq_set_a @ SY608 @ SY609 )
| ( ord_less_eq_set_a @ ( SV209 @ SY608 ) @ ( SV209 @ SY609 ) ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( SV209 @ SV81 ) @ SV239 )
= $true )
| ( ( ( SV209 @ SV162 )
= SV239 )
= $false )
| ( ( ord_less_eq_set_a @ SV81 @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1433]) ).
thf(1506,plain,
! [SV163: nat,SV82: set_a] :
( ( ( ~ ~ ( ~ ( finite_finite_a @ ( sK8_SY552 @ SV82 @ SV163 ) )
| ( ( finite_card_a @ ( sK8_SY552 @ SV82 @ SV163 ) )
!= SV163 ) ) )
= $false )
| ( ( finite_finite_a @ SV82 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1434]) ).
thf(1507,plain,
! [SV163: nat,SV82: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ ( sK8_SY552 @ SV82 @ SV163 ) @ SV82 ) )
= $false )
| ( ( finite_finite_a @ SV82 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1434]) ).
thf(1508,plain,
! [SV83: a,SV210: a,SV164: a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV210 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV210 @ SV164 ) @ relation ) ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SV210 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV210 @ SV83 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SV164 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV83 ) @ relation )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1435]) ).
thf(1509,plain,
! [SV211: set_a,SV240: set_a,SV85: nat,SV166: set_a > nat] :
( ( ( ! [SY556: set_a,SY557: set_a] :
( ~ ( ord_less_eq_set_a @ SY556 @ SY557 )
| ( ord_less_eq_nat @ ( SV166 @ SY556 ) @ ( SV166 @ SY557 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV85 @ ( SV166 @ SV240 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV211 @ SV240 )
= $false )
| ( ( ord_less_eq_nat @ SV85 @ ( SV166 @ SV211 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1436]) ).
thf(1510,plain,
! [SV212: nat,SV241: nat,SV87: set_a,SV168: nat > set_a] :
( ( ( ! [SY560: nat,SY561: nat] :
( ~ ( ord_less_eq_nat @ SY560 @ SY561 )
| ( ord_less_eq_set_a @ ( SV168 @ SY560 ) @ ( SV168 @ SY561 ) ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV87 @ ( SV168 @ SV241 ) )
= $true )
| ( ( ord_less_eq_nat @ SV212 @ SV241 )
= $false )
| ( ( ord_less_eq_set_a @ SV87 @ ( SV168 @ SV212 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1437]) ).
thf(1511,plain,
! [SV170: nat,SV242: set_a,SV89: nat,SV213: nat > set_a] :
( ( ( ! [SY617: nat,SY618: nat] :
( ~ ( ord_less_eq_nat @ SY617 @ SY618 )
| ( ord_less_eq_set_a @ ( SV213 @ SY617 ) @ ( SV213 @ SY618 ) ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( SV213 @ SV89 ) @ SV242 )
= $true )
| ( ( ord_less_eq_set_a @ ( SV213 @ SV170 ) @ SV242 )
= $false )
| ( ( ord_less_eq_nat @ SV89 @ SV170 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1438]) ).
thf(1512,plain,
! [SV215: set_a,SV243: set_a,SV91: set_a,SV172: set_a > set_a] :
( ( ( ! [SY569: set_a,SY570: set_a] :
( ~ ( ord_less_eq_set_a @ SY569 @ SY570 )
| ( ord_less_eq_set_a @ ( SV172 @ SY569 ) @ ( SV172 @ SY570 ) ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV91 @ ( SV172 @ SV243 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV215 @ SV243 )
= $false )
| ( ( ord_less_eq_set_a @ SV91 @ ( SV172 @ SV215 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1439]) ).
thf(1513,plain,
! [SV244: set_a,SV173: set_a] :
( ( ( SV173 != SV244 )
= $false )
| ( ( SV173 = SV244 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1440]) ).
thf(1514,plain,
! [SV244: set_a,SV173: set_a] :
( ( ( ~ ~ ( ~ ( ord_less_eq_set_a @ SV173 @ SV244 )
| ~ ( ord_less_eq_set_a @ SV244 @ SV173 ) ) )
= $false )
| ( ( SV173 = SV244 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1440]) ).
thf(1515,plain,
! [SV244: set_a,SV173: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV173 @ SV244 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV244 @ SV173 ) )
= $true )
| ( ( ~ ( ( SV173 != SV244 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV173 @ SV244 )
| ~ ( ord_less_eq_set_a @ SV244 @ SV173 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1441]) ).
thf(1516,plain,
! [SV217: nat,SV246: nat,SV94: set_a,SV174: nat > set_a] :
( ( ( ! [SY575: nat,SY576: nat] :
( ~ ( ord_less_eq_nat @ SY575 @ SY576 )
| ( ord_less_eq_set_a @ ( SV174 @ SY575 ) @ ( SV174 @ SY576 ) ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV94 @ ( SV174 @ SV246 ) )
= $true )
| ( ( ord_less_eq_nat @ SV217 @ SV246 )
= $false )
| ( ( SV94
= ( SV174 @ SV217 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1442]) ).
thf(1517,plain,
! [SV9: a,SV176: a,SV97: a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV176 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV97 ) @ relation ) ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV176 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV9 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV97 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV9 ) @ relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1443]) ).
thf(1518,plain,
! [SV13: set_set_a] :
( ( ( ~ ( member_set_a @ ( sK9_SY294 @ SV13 ) @ SV13 ) )
= $false )
| ( ( SV13 = bot_bot_set_set_a )
= $true )
| ( ( finite_finite_set_a @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1444]) ).
thf(1519,plain,
! [SV13: set_set_a] :
( ( ( ~ ! [SY651: set_a] :
( ~ ( member_set_a @ SY651 @ SV13 )
| ~ ( ord_less_eq_set_a @ SY651 @ ( sK9_SY294 @ SV13 ) )
| ( ( sK9_SY294 @ SV13 )
= SY651 ) ) )
= $false )
| ( ( SV13 = bot_bot_set_set_a )
= $true )
| ( ( finite_finite_set_a @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1444]) ).
thf(1520,plain,
! [SV14: set_a,SV101: set_a] :
( ( ( ord_less_eq_set_a @ SV101 @ SV14 )
= $true )
| ( ( ord_less_eq_set_a @ SV101 @ SV14 )
= $false )
| ( ( ord_less_eq_set_a @ SV14 @ SV101 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1445]) ).
thf(1521,plain,
! [SV14: set_a,SV101: set_a] :
( ( ( SV101 = SV14 )
= $true )
| ( ( ord_less_eq_set_a @ SV101 @ SV14 )
= $false )
| ( ( ord_less_eq_set_a @ SV14 @ SV101 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1446]) ).
thf(1522,plain,
! [SV14: set_a,SV101: set_a] :
( ( ( ord_less_eq_set_a @ SV101 @ SV14 )
= $true )
| ( ( SV101 = SV14 )
= $false )
| ( ( ord_less_eq_set_a @ SV14 @ SV101 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1447]) ).
thf(1523,plain,
! [SV14: set_a,SV101: set_a] :
( ( ( SV101 = SV14 )
= $true )
| ( ( SV101 = SV14 )
= $false )
| ( ( ord_less_eq_set_a @ SV14 @ SV101 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1448]) ).
thf(1524,plain,
! [SV16: set_set_a,SV103: set_a] :
( ( ( ~ ~ ( ~ ( member_set_a @ ( sK10_SY475 @ SV103 @ SV16 ) @ SV16 )
| ~ ( ord_less_eq_set_a @ ( sK10_SY475 @ SV103 @ SV16 ) @ SV103 ) ) )
= $false )
| ( ( member_set_a @ SV103 @ SV16 )
= $false )
| ( ( finite_finite_set_a @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1449]) ).
thf(1525,plain,
! [SV103: set_a,SV16: set_set_a] :
( ( ( ~ ! [SY652: set_a] :
( ~ ( member_set_a @ SY652 @ SV16 )
| ~ ( ord_less_eq_set_a @ SY652 @ ( sK10_SY475 @ SV103 @ SV16 ) )
| ( ( sK10_SY475 @ SV103 @ SV16 )
= SY652 ) ) )
= $false )
| ( ( member_set_a @ SV103 @ SV16 )
= $false )
| ( ( finite_finite_set_a @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1449]) ).
thf(1526,plain,
! [SV220: set_a,SV181: nat,SV109: set_a,SV22: nat] :
( ( ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV22 @ SV109 ) @ ( produc1450889781_set_a @ SV181 @ SV220 ) )
= $true )
| ( ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV22 @ SV109 ) @ ( produc1450889781_set_a @ SV181 @ SV220 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1450]) ).
thf(1527,plain,
! [SV220: set_a,SV109: set_a,SV181: nat,SV22: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV22 @ SV181 )
| ~ ( ord_less_eq_set_a @ SV109 @ SV220 ) ) )
= $true )
| ( ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV22 @ SV109 ) @ ( produc1450889781_set_a @ SV181 @ SV220 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1451]) ).
thf(1528,plain,
! [SV220: set_a,SV109: set_a,SV181: nat,SV22: nat] :
( ( ( ord_less_eq_nat @ SV22 @ SV181 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV109 @ SV220 ) )
= $true )
| ( ( ~ ( ~ ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV22 @ SV109 ) @ ( produc1450889781_set_a @ SV181 @ SV220 ) )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV22 @ SV181 )
| ~ ( ord_less_eq_set_a @ SV109 @ SV220 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1452]) ).
thf(1529,plain,
! [SV221: set_a,SV110: set_a] :
( ( ( SV110 = SV221 )
= $true )
| ( ( SV110 = SV221 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1453]) ).
thf(1530,plain,
! [SV110: set_a,SV221: set_a] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ SV221 @ SV110 )
| ~ ( ord_less_eq_set_a @ SV110 @ SV221 ) ) )
= $true )
| ( ( SV110 = SV221 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1454]) ).
thf(1531,plain,
! [SV110: set_a,SV221: set_a] :
( ( ( ord_less_eq_set_a @ SV221 @ SV110 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV110 @ SV221 ) )
= $true )
| ( ( ~ ( ( SV110 != SV221 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV221 @ SV110 )
| ~ ( ord_less_eq_set_a @ SV110 @ SV221 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1455]) ).
thf(1532,plain,
! [SV222: set_a,SV183: set_a,SV111: set_a,SV24: set_a] :
( ( ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV24 @ SV111 ) @ ( produc1928581911_set_a @ SV183 @ SV222 ) )
= $true )
| ( ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV24 @ SV111 ) @ ( produc1928581911_set_a @ SV183 @ SV222 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1456]) ).
thf(1533,plain,
! [SV222: set_a,SV111: set_a,SV183: set_a,SV24: set_a] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ SV24 @ SV183 )
| ~ ( ord_less_eq_set_a @ SV111 @ SV222 ) ) )
= $true )
| ( ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV24 @ SV111 ) @ ( produc1928581911_set_a @ SV183 @ SV222 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1457]) ).
thf(1534,plain,
! [SV222: set_a,SV111: set_a,SV183: set_a,SV24: set_a] :
( ( ( ord_less_eq_set_a @ SV24 @ SV183 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV111 @ SV222 ) )
= $true )
| ( ( ~ ( ~ ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV24 @ SV111 ) @ ( produc1928581911_set_a @ SV183 @ SV222 ) )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV24 @ SV183 )
| ~ ( ord_less_eq_set_a @ SV111 @ SV222 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1458]) ).
thf(1535,plain,
! [SV34: set_set_a] :
( ( ( ~ ( member_set_a @ ( sK11_SY329 @ SV34 ) @ SV34 ) )
= $false )
| ( ( SV34 = bot_bot_set_set_a )
= $true )
| ( ( finite_finite_set_a @ SV34 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1459]) ).
thf(1536,plain,
! [SV34: set_set_a] :
( ( ( ~ ! [SY653: set_a] :
( ~ ( member_set_a @ SY653 @ SV34 )
| ~ ( ord_less_eq_set_a @ ( sK11_SY329 @ SV34 ) @ SY653 )
| ( ( sK11_SY329 @ SV34 )
= SY653 ) ) )
= $false )
| ( ( SV34 = bot_bot_set_set_a )
= $true )
| ( ( finite_finite_set_a @ SV34 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1459]) ).
thf(1537,plain,
! [SV223: nat,SV187: set_a,SV123: nat,SV38: set_a] :
( ( ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV38 @ SV123 ) @ ( produc515611863_a_nat @ SV187 @ SV223 ) )
= $true )
| ( ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV38 @ SV123 ) @ ( produc515611863_a_nat @ SV187 @ SV223 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1462]) ).
thf(1538,plain,
! [SV223: nat,SV123: nat,SV187: set_a,SV38: set_a] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ SV38 @ SV187 )
| ~ ( ord_less_eq_nat @ SV123 @ SV223 ) ) )
= $true )
| ( ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV38 @ SV123 ) @ ( produc515611863_a_nat @ SV187 @ SV223 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1463]) ).
thf(1539,plain,
! [SV223: nat,SV123: nat,SV187: set_a,SV38: set_a] :
( ( ( ord_less_eq_set_a @ SV38 @ SV187 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV123 @ SV223 ) )
= $true )
| ( ( ~ ( ~ ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV38 @ SV123 ) @ ( produc515611863_a_nat @ SV187 @ SV223 ) )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV38 @ SV187 )
| ~ ( ord_less_eq_nat @ SV123 @ SV223 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1464]) ).
thf(1540,plain,
! [SV124: set_Product_prod_a_a,SV39: set_a,SV188: a] :
( ( ( ( prefer1676310729than_a @ SV188 @ SV39 @ SV124 )
= bot_bot_set_a )
= $false )
| ( ( member_a @ SV188 @ SV39 )
= $false )
| ( ( SV39 = bot_bot_set_a )
= $true )
| ( ( prefer719835986ence_a @ SV39 @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1465]) ).
thf(1541,plain,
! [SV224: set_a,SV126: set_a] :
( ( ( ord_less_eq_set_a @ SV126 @ SV224 )
= $true )
| ( ( ord_less_eq_set_a @ SV126 @ SV224 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1466]) ).
thf(1542,plain,
! [SV224: set_a,SV126: set_a] :
( ( ( ! [SY625: a] :
( ~ ( member_a @ SY625 @ SV126 )
| ( member_a @ SY625 @ SV224 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV126 @ SV224 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1467]) ).
thf(1543,plain,
! [SV126: set_a,SV224: set_a] :
( ( ( member_a @ ( sK13_SY625 @ SV224 @ SV126 ) @ SV126 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV126 @ SV224 )
| ~ ! [SY625: a] :
( ~ ( member_a @ SY625 @ SV126 )
| ( member_a @ SY625 @ SV224 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1468]) ).
thf(1544,plain,
! [SV224: set_a,SV126: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV126 @ SV224 )
| ~ ! [SY625: a] :
( ~ ( member_a @ SY625 @ SV126 )
| ( member_a @ SY625 @ SV224 ) ) )
= $false )
| ( ( member_a @ ( sK13_SY625 @ SV224 @ SV126 ) @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1469]) ).
thf(1545,plain,
! [SV190: a,SV130: a,SV46: a] :
( ( ( member_a @ SV46 @ carrier )
= $false )
| ( ( ~ ( member_a @ SV130 @ carrier ) )
= $true )
| ( ( ~ ( member_a @ SV190 @ carrier ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV190 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV46 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV190 ) @ relation ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1470]) ).
thf(1546,plain,
! [SV131: set_Product_prod_a_a,SV47: set_a,SV225: a,SV191: a] :
( ( ( member_a @ SV191 @ ( prefer1676310729than_a @ SV225 @ SV47 @ SV131 ) )
= $true )
| ( ( member_a @ SV225 @ ( prefer1676310729than_a @ SV191 @ SV47 @ SV131 ) )
= $true )
| ( ( member_a @ SV225 @ SV47 )
= $false )
| ( ( member_a @ SV191 @ SV47 )
= $false )
| ( ( prefer719835986ence_a @ SV47 @ SV131 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1471]) ).
thf(1547,plain,
! [SV192: a,SV133: a,SV50: a] :
( ( ( member_a @ SV50 @ carrier )
= $false )
| ( ( ~ ( member_a @ SV133 @ carrier ) )
= $true )
| ( ( ~ ( member_a @ SV192 @ carrier ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV50 @ SV133 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV133 @ SV192 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV50 @ SV192 ) @ relation ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1472]) ).
thf(1548,plain,
! [SV195: set_a > nat,SV54: set_a,SV226: nat,SV136: set_a] :
( ( ( ! [SY655: set_a] :
( ~ ( ord_less_eq_set_a @ ( sK15_SY585 @ SV136 @ SV226 @ SV54 @ SV195 ) @ SY655 )
| ( ord_less_eq_nat @ ( SV195 @ ( sK15_SY585 @ SV136 @ SV226 @ SV54 @ SV195 ) ) @ ( SV195 @ SY655 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( SV195 @ SV54 ) @ SV226 )
= $true )
| ( ( ( SV195 @ SV136 )
= SV226 )
= $false )
| ( ( ord_less_eq_set_a @ SV54 @ SV136 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1473]) ).
thf(1549,plain,
! [SV227: set_a,SV138: set_a] :
( ( ( SV138 = SV227 )
= $true )
| ( ( SV138 = SV227 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1474]) ).
thf(1550,plain,
! [SV227: set_a,SV138: set_a] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ SV138 @ SV227 )
| ~ ( ord_less_eq_set_a @ SV227 @ SV138 ) ) )
= $true )
| ( ( SV138 = SV227 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1475]) ).
thf(1551,plain,
! [SV227: set_a,SV138: set_a] :
( ( ( ord_less_eq_set_a @ SV138 @ SV227 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV227 @ SV138 ) )
= $true )
| ( ( ~ ( ( SV138 != SV227 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV138 @ SV227 )
| ~ ( ord_less_eq_set_a @ SV227 @ SV138 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1476]) ).
thf(1552,plain,
! [SV139: set_a > set_a,SV57: set_a,SV228: set_a,SV197: set_a] :
( ( ( ! [SY656: set_a] :
( ~ ( ord_less_eq_set_a @ ( sK16_SY513 @ SV197 @ SV228 @ SV57 @ SV139 ) @ SY656 )
| ( ord_less_eq_set_a @ ( SV139 @ ( sK16_SY513 @ SV197 @ SV228 @ SV57 @ SV139 ) ) @ ( SV139 @ SY656 ) ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV57 @ ( SV139 @ SV228 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV197 @ SV228 )
= $false )
| ( ( SV57
= ( SV139 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1477]) ).
thf(1553,plain,
! [SV62: set_set_a,SV143: set_a] :
( ( ( ~ ~ ( ~ ( member_set_a @ ( sK12_SY517 @ SV143 @ SV62 ) @ SV62 )
| ~ ( ord_less_eq_set_a @ SV143 @ ( sK12_SY517 @ SV143 @ SV62 ) ) ) )
= $false )
| ( ( member_set_a @ SV143 @ SV62 )
= $false )
| ( ( finite_finite_set_a @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1478]) ).
thf(1554,plain,
! [SV143: set_a,SV62: set_set_a] :
( ( ( ~ ! [SY654: set_a] :
( ~ ( member_set_a @ SY654 @ SV62 )
| ~ ( ord_less_eq_set_a @ ( sK12_SY517 @ SV143 @ SV62 ) @ SY654 )
| ( ( sK12_SY517 @ SV143 @ SV62 )
= SY654 ) ) )
= $false )
| ( ( member_set_a @ SV143 @ SV62 )
= $false )
| ( ( finite_finite_set_a @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1478]) ).
thf(1555,plain,
! [SV63: a,SV144: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) ) )
= $false )
| ( ( ~ ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( member_a @ SV144 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1479]) ).
thf(1556,plain,
! [SV230: set_a,SV145: set_a] :
( ( ( ord_less_eq_set_a @ SV145 @ SV230 )
= $true )
| ( ( ord_less_eq_set_a @ SV145 @ SV230 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1480]) ).
thf(1557,plain,
! [SV230: set_a,SV145: set_a] :
( ( ( ! [SY630: a] :
( ~ ( member_a @ SY630 @ SV145 )
| ( member_a @ SY630 @ SV230 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV145 @ SV230 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1481]) ).
thf(1558,plain,
! [SV145: set_a,SV230: set_a] :
( ( ( member_a @ ( sK14_SY630 @ SV230 @ SV145 ) @ SV145 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV145 @ SV230 )
| ~ ! [SY630: a] :
( ~ ( member_a @ SY630 @ SV145 )
| ( member_a @ SY630 @ SV230 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1482]) ).
thf(1559,plain,
! [SV230: set_a,SV145: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV145 @ SV230 )
| ~ ! [SY630: a] :
( ~ ( member_a @ SY630 @ SV145 )
| ( member_a @ SY630 @ SV230 ) ) )
= $false )
| ( ( member_a @ ( sK14_SY630 @ SV230 @ SV145 ) @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1483]) ).
thf(1560,plain,
! [SV147: set_Product_prod_a_a,SV200: a,SV66: set_a,SV231: a] :
( ( ( ~ ( member_a @ SV231 @ SV66 ) )
= $true )
| ( ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) ) )
= $true )
| ( ( member_a @ SV200 @ SV66 )
= $false )
| ( ( finite_finite_a @ SV66 )
= $false )
| ( ( prefer719835986ence_a @ SV66 @ SV147 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1484]) ).
thf(1561,plain,
! [SV201: set_a > nat,SV67: set_a,SV232: nat,SV148: set_a] :
( ( ( ! [SY657: set_a] :
( ~ ( ord_less_eq_set_a @ ( sK17_SY594 @ SV148 @ SV232 @ SV67 @ SV201 ) @ SY657 )
| ( ord_less_eq_nat @ ( SV201 @ ( sK17_SY594 @ SV148 @ SV232 @ SV67 @ SV201 ) ) @ ( SV201 @ SY657 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( SV201 @ SV67 ) @ SV232 )
= $true )
| ( ( ord_less_eq_nat @ ( SV201 @ SV148 ) @ SV232 )
= $false )
| ( ( ord_less_eq_set_a @ SV67 @ SV148 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1485]) ).
thf(1562,plain,
! [SV233: set_a,SV150: set_a] :
( ( ( SV150 = SV233 )
= $true )
| ( ( SV150 = SV233 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1486]) ).
thf(1563,plain,
! [SV233: set_a,SV150: set_a] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ SV150 @ SV233 )
| ~ ( ord_less_eq_set_a @ SV233 @ SV150 ) ) )
= $true )
| ( ( SV150 = SV233 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1487]) ).
thf(1564,plain,
! [SV233: set_a,SV150: set_a] :
( ( ( ord_less_eq_set_a @ SV150 @ SV233 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV233 @ SV150 ) )
= $true )
| ( ( ~ ( ( SV150 != SV233 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV150 @ SV233 )
| ~ ( ord_less_eq_set_a @ SV233 @ SV150 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1488]) ).
thf(1565,plain,
! [SV203: set_a > set_a,SV70: set_a,SV234: set_a,SV151: set_a] :
( ( ( ! [SY658: set_a] :
( ~ ( ord_less_eq_set_a @ ( sK18_SY597 @ SV151 @ SV234 @ SV70 @ SV203 ) @ SY658 )
| ( ord_less_eq_set_a @ ( SV203 @ ( sK18_SY597 @ SV151 @ SV234 @ SV70 @ SV203 ) ) @ ( SV203 @ SY658 ) ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( SV203 @ SV70 ) @ SV234 )
= $true )
| ( ( ord_less_eq_set_a @ ( SV203 @ SV151 ) @ SV234 )
= $false )
| ( ( ord_less_eq_set_a @ SV70 @ SV151 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1489]) ).
thf(1566,plain,
! [SV152: a,SV71: a] :
( ( ( ~ ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
| ~ ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
| ~ ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1490]) ).
thf(1567,plain,
! [SV152: a,SV71: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
| ~ ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1491]) ).
thf(1568,plain,
! [SV156: set_a > nat,SV75: nat,SV237: set_a,SV207: set_a] :
( ( ( ! [SY659: set_a] :
( ~ ( ord_less_eq_set_a @ ( sK19_SY540 @ SV207 @ SV237 @ SV75 @ SV156 ) @ SY659 )
| ( ord_less_eq_nat @ ( SV156 @ ( sK19_SY540 @ SV207 @ SV237 @ SV75 @ SV156 ) ) @ ( SV156 @ SY659 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV75 @ ( SV156 @ SV237 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV207 @ SV237 )
= $false )
| ( ( SV75
= ( SV156 @ SV207 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1492]) ).
thf(1569,plain,
! [SV157: a > $o,SV248: a,SV76: a > $o] :
( ( ( ~ ( SV76 @ SV248 ) )
= $true )
| ( ( SV157 @ SV248 )
= $true )
| ( ( ord_less_eq_set_a @ ( collect_a @ SV76 ) @ ( collect_a @ SV157 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1493]) ).
thf(1570,plain,
! [SV157: a > $o,SV76: a > $o] :
( ( ( ~ ( ord_less_eq_set_a @ ( collect_a @ SV76 ) @ ( collect_a @ SV157 ) ) )
= $false )
| ( ( SV76 @ ( sK7_SY542 @ SV157 @ SV76 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1494]) ).
thf(1571,plain,
! [SV157: a > $o,SV76: a > $o] :
( ( ( ~ ! [SY542: a] :
( ~ ( SV76 @ SY542 )
| ( SV157 @ SY542 ) ) )
= $false )
| ( ( SV76 @ ( sK7_SY542 @ SV157 @ SV76 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1494]) ).
thf(1572,plain,
! [SV157: a > $o,SV76: a > $o] :
( ( ( ord_less_eq_set_a @ ( collect_a @ SV76 ) @ ( collect_a @ SV157 ) )
= $true )
| ( ( SV157 @ ( sK7_SY542 @ SV157 @ SV76 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1495]) ).
thf(1573,plain,
! [SV157: a > $o,SV76: a > $o] :
( ( ( ! [SY542: a] :
( ~ ( SV76 @ SY542 )
| ( SV157 @ SY542 ) ) )
= $true )
| ( ( SV157 @ ( sK7_SY542 @ SV157 @ SV76 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1496]) ).
thf(1574,plain,
! [SV158: nat,SV77: set_a] :
( ( ( finite_finite_a @ SV77 )
= $true )
| ( ( finite_finite_a @ ( sK4_SY543 @ SV158 @ SV77 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1499]) ).
thf(1575,plain,
! [SV158: nat,SV77: set_a] :
( ( ( ord_less_eq_nat @ ( finite_card_a @ SV77 ) @ SV158 )
= $true )
| ( ( finite_finite_a @ ( sK4_SY543 @ SV158 @ SV77 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1500]) ).
thf(1576,plain,
! [SV208: nat > set_a,SV80: nat,SV238: set_a,SV161: nat] :
( ( ( ! [SY660: nat] :
( ~ ( ord_less_eq_nat @ ( sK20_SY605 @ SV161 @ SV238 @ SV80 @ SV208 ) @ SY660 )
| ( ord_less_eq_set_a @ ( SV208 @ ( sK20_SY605 @ SV161 @ SV238 @ SV80 @ SV208 ) ) @ ( SV208 @ SY660 ) ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( SV208 @ SV80 ) @ SV238 )
= $true )
| ( ( ( SV208 @ SV161 )
= SV238 )
= $false )
| ( ( ord_less_eq_nat @ SV80 @ SV161 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1504]) ).
thf(1577,plain,
! [SV209: set_a > set_a,SV81: set_a,SV239: set_a,SV162: set_a] :
( ( ( ! [SY661: set_a] :
( ~ ( ord_less_eq_set_a @ ( sK21_SY608 @ SV162 @ SV239 @ SV81 @ SV209 ) @ SY661 )
| ( ord_less_eq_set_a @ ( SV209 @ ( sK21_SY608 @ SV162 @ SV239 @ SV81 @ SV209 ) ) @ ( SV209 @ SY661 ) ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( SV209 @ SV81 ) @ SV239 )
= $true )
| ( ( ( SV209 @ SV162 )
= SV239 )
= $false )
| ( ( ord_less_eq_set_a @ SV81 @ SV162 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1505]) ).
thf(1578,plain,
! [SV163: nat,SV82: set_a] :
( ( ( ~ ( ~ ( finite_finite_a @ ( sK8_SY552 @ SV82 @ SV163 ) )
| ( ( finite_card_a @ ( sK8_SY552 @ SV82 @ SV163 ) )
!= SV163 ) ) )
= $true )
| ( ( finite_finite_a @ SV82 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1506]) ).
thf(1579,plain,
! [SV163: nat,SV82: set_a] :
( ( ( ord_less_eq_set_a @ ( sK8_SY552 @ SV82 @ SV163 ) @ SV82 )
= $true )
| ( ( finite_finite_a @ SV82 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1507]) ).
thf(1580,plain,
! [SV83: a,SV210: a,SV164: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV210 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV210 @ SV164 ) @ relation ) ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SV210 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV210 @ SV83 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SV164 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV83 ) @ relation )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1508]) ).
thf(1581,plain,
! [SV166: set_a > nat,SV85: nat,SV240: set_a,SV211: set_a] :
( ( ( ! [SY662: set_a] :
( ~ ( ord_less_eq_set_a @ ( sK22_SY556 @ SV211 @ SV240 @ SV85 @ SV166 ) @ SY662 )
| ( ord_less_eq_nat @ ( SV166 @ ( sK22_SY556 @ SV211 @ SV240 @ SV85 @ SV166 ) ) @ ( SV166 @ SY662 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV85 @ ( SV166 @ SV240 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV211 @ SV240 )
= $false )
| ( ( ord_less_eq_nat @ SV85 @ ( SV166 @ SV211 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1509]) ).
thf(1582,plain,
! [SV168: nat > set_a,SV87: set_a,SV241: nat,SV212: nat] :
( ( ( ! [SY663: nat] :
( ~ ( ord_less_eq_nat @ ( sK23_SY560 @ SV212 @ SV241 @ SV87 @ SV168 ) @ SY663 )
| ( ord_less_eq_set_a @ ( SV168 @ ( sK23_SY560 @ SV212 @ SV241 @ SV87 @ SV168 ) ) @ ( SV168 @ SY663 ) ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV87 @ ( SV168 @ SV241 ) )
= $true )
| ( ( ord_less_eq_nat @ SV212 @ SV241 )
= $false )
| ( ( ord_less_eq_set_a @ SV87 @ ( SV168 @ SV212 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1510]) ).
thf(1583,plain,
! [SV213: nat > set_a,SV89: nat,SV242: set_a,SV170: nat] :
( ( ( ! [SY664: nat] :
( ~ ( ord_less_eq_nat @ ( sK24_SY617 @ SV170 @ SV242 @ SV89 @ SV213 ) @ SY664 )
| ( ord_less_eq_set_a @ ( SV213 @ ( sK24_SY617 @ SV170 @ SV242 @ SV89 @ SV213 ) ) @ ( SV213 @ SY664 ) ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( SV213 @ SV89 ) @ SV242 )
= $true )
| ( ( ord_less_eq_set_a @ ( SV213 @ SV170 ) @ SV242 )
= $false )
| ( ( ord_less_eq_nat @ SV89 @ SV170 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1511]) ).
thf(1584,plain,
! [SV172: set_a > set_a,SV91: set_a,SV243: set_a,SV215: set_a] :
( ( ( ! [SY665: set_a] :
( ~ ( ord_less_eq_set_a @ ( sK25_SY569 @ SV215 @ SV243 @ SV91 @ SV172 ) @ SY665 )
| ( ord_less_eq_set_a @ ( SV172 @ ( sK25_SY569 @ SV215 @ SV243 @ SV91 @ SV172 ) ) @ ( SV172 @ SY665 ) ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV91 @ ( SV172 @ SV243 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV215 @ SV243 )
= $false )
| ( ( ord_less_eq_set_a @ SV91 @ ( SV172 @ SV215 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1512]) ).
thf(1585,plain,
! [SV244: set_a,SV173: set_a] :
( ( ( SV173 = SV244 )
= $true )
| ( ( SV173 = SV244 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1513]) ).
thf(1586,plain,
! [SV244: set_a,SV173: set_a] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ SV173 @ SV244 )
| ~ ( ord_less_eq_set_a @ SV244 @ SV173 ) ) )
= $true )
| ( ( SV173 = SV244 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1514]) ).
thf(1587,plain,
! [SV244: set_a,SV173: set_a] :
( ( ( ord_less_eq_set_a @ SV173 @ SV244 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV244 @ SV173 ) )
= $true )
| ( ( ~ ( ( SV173 != SV244 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV173 @ SV244 )
| ~ ( ord_less_eq_set_a @ SV244 @ SV173 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1515]) ).
thf(1588,plain,
! [SV174: nat > set_a,SV94: set_a,SV246: nat,SV217: nat] :
( ( ( ! [SY666: nat] :
( ~ ( ord_less_eq_nat @ ( sK26_SY575 @ SV217 @ SV246 @ SV94 @ SV174 ) @ SY666 )
| ( ord_less_eq_set_a @ ( SV174 @ ( sK26_SY575 @ SV217 @ SV246 @ SV94 @ SV174 ) ) @ ( SV174 @ SY666 ) ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV94 @ ( SV174 @ SV246 ) )
= $true )
| ( ( ord_less_eq_nat @ SV217 @ SV246 )
= $false )
| ( ( SV94
= ( SV174 @ SV217 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1516]) ).
thf(1589,plain,
! [SV9: a,SV176: a,SV97: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV176 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV97 ) @ relation ) ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV176 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV9 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV97 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV9 ) @ relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1517]) ).
thf(1590,plain,
! [SV13: set_set_a] :
( ( ( member_set_a @ ( sK9_SY294 @ SV13 ) @ SV13 )
= $true )
| ( ( SV13 = bot_bot_set_set_a )
= $true )
| ( ( finite_finite_set_a @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1518]) ).
thf(1591,plain,
! [SV13: set_set_a] :
( ( ( ! [SY651: set_a] :
( ~ ( member_set_a @ SY651 @ SV13 )
| ~ ( ord_less_eq_set_a @ SY651 @ ( sK9_SY294 @ SV13 ) )
| ( ( sK9_SY294 @ SV13 )
= SY651 ) ) )
= $true )
| ( ( SV13 = bot_bot_set_set_a )
= $true )
| ( ( finite_finite_set_a @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1519]) ).
thf(1592,plain,
! [SV16: set_set_a,SV103: set_a] :
( ( ( ~ ( ~ ( member_set_a @ ( sK10_SY475 @ SV103 @ SV16 ) @ SV16 )
| ~ ( ord_less_eq_set_a @ ( sK10_SY475 @ SV103 @ SV16 ) @ SV103 ) ) )
= $true )
| ( ( member_set_a @ SV103 @ SV16 )
= $false )
| ( ( finite_finite_set_a @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1524]) ).
thf(1593,plain,
! [SV103: set_a,SV16: set_set_a] :
( ( ( ! [SY652: set_a] :
( ~ ( member_set_a @ SY652 @ SV16 )
| ~ ( ord_less_eq_set_a @ SY652 @ ( sK10_SY475 @ SV103 @ SV16 ) )
| ( ( sK10_SY475 @ SV103 @ SV16 )
= SY652 ) ) )
= $true )
| ( ( member_set_a @ SV103 @ SV16 )
= $false )
| ( ( finite_finite_set_a @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1525]) ).
thf(1594,plain,
! [SV220: set_a,SV109: set_a,SV181: nat,SV22: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV22 @ SV181 )
| ~ ( ord_less_eq_set_a @ SV109 @ SV220 ) )
= $false )
| ( ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV22 @ SV109 ) @ ( produc1450889781_set_a @ SV181 @ SV220 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1527]) ).
thf(1595,plain,
! [SV181: nat,SV22: nat,SV220: set_a,SV109: set_a] :
( ( ( ord_less_eq_set_a @ SV109 @ SV220 )
= $false )
| ( ( ord_less_eq_nat @ SV22 @ SV181 )
= $false )
| ( ( ~ ( ~ ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV22 @ SV109 ) @ ( produc1450889781_set_a @ SV181 @ SV220 ) )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV22 @ SV181 )
| ~ ( ord_less_eq_set_a @ SV109 @ SV220 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1528]) ).
thf(1596,plain,
! [SV110: set_a,SV221: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV221 @ SV110 )
| ~ ( ord_less_eq_set_a @ SV110 @ SV221 ) )
= $false )
| ( ( SV110 = SV221 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1530]) ).
thf(1597,plain,
! [SV221: set_a,SV110: set_a] :
( ( ( ord_less_eq_set_a @ SV110 @ SV221 )
= $false )
| ( ( ord_less_eq_set_a @ SV221 @ SV110 )
= $false )
| ( ( ~ ( ( SV110 != SV221 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV221 @ SV110 )
| ~ ( ord_less_eq_set_a @ SV110 @ SV221 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1531]) ).
thf(1598,plain,
! [SV222: set_a,SV111: set_a,SV183: set_a,SV24: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV24 @ SV183 )
| ~ ( ord_less_eq_set_a @ SV111 @ SV222 ) )
= $false )
| ( ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV24 @ SV111 ) @ ( produc1928581911_set_a @ SV183 @ SV222 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1533]) ).
thf(1599,plain,
! [SV183: set_a,SV24: set_a,SV222: set_a,SV111: set_a] :
( ( ( ord_less_eq_set_a @ SV111 @ SV222 )
= $false )
| ( ( ord_less_eq_set_a @ SV24 @ SV183 )
= $false )
| ( ( ~ ( ~ ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV24 @ SV111 ) @ ( produc1928581911_set_a @ SV183 @ SV222 ) )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV24 @ SV183 )
| ~ ( ord_less_eq_set_a @ SV111 @ SV222 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1534]) ).
thf(1600,plain,
! [SV34: set_set_a] :
( ( ( member_set_a @ ( sK11_SY329 @ SV34 ) @ SV34 )
= $true )
| ( ( SV34 = bot_bot_set_set_a )
= $true )
| ( ( finite_finite_set_a @ SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1535]) ).
thf(1601,plain,
! [SV34: set_set_a] :
( ( ( ! [SY653: set_a] :
( ~ ( member_set_a @ SY653 @ SV34 )
| ~ ( ord_less_eq_set_a @ ( sK11_SY329 @ SV34 ) @ SY653 )
| ( ( sK11_SY329 @ SV34 )
= SY653 ) ) )
= $true )
| ( ( SV34 = bot_bot_set_set_a )
= $true )
| ( ( finite_finite_set_a @ SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1536]) ).
thf(1602,plain,
! [SV223: nat,SV123: nat,SV187: set_a,SV38: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV38 @ SV187 )
| ~ ( ord_less_eq_nat @ SV123 @ SV223 ) )
= $false )
| ( ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV38 @ SV123 ) @ ( produc515611863_a_nat @ SV187 @ SV223 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1538]) ).
thf(1603,plain,
! [SV187: set_a,SV38: set_a,SV223: nat,SV123: nat] :
( ( ( ord_less_eq_nat @ SV123 @ SV223 )
= $false )
| ( ( ord_less_eq_set_a @ SV38 @ SV187 )
= $false )
| ( ( ~ ( ~ ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV38 @ SV123 ) @ ( produc515611863_a_nat @ SV187 @ SV223 ) )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV38 @ SV187 )
| ~ ( ord_less_eq_nat @ SV123 @ SV223 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1539]) ).
thf(1604,plain,
! [SV224: set_a,SV126: set_a,SV249: a] :
( ( ( ~ ( member_a @ SV249 @ SV126 )
| ( member_a @ SV249 @ SV224 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV126 @ SV224 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1542]) ).
thf(1605,plain,
! [SV224: set_a,SV126: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV126 @ SV224 )
| ~ ! [SY625: a] :
( ~ ( member_a @ SY625 @ SV126 )
| ( member_a @ SY625 @ SV224 ) ) )
= $false )
| ( ( member_a @ ( sK13_SY625 @ SV224 @ SV126 ) @ SV126 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1543]) ).
thf(1606,plain,
! [SV224: set_a,SV126: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV126 @ SV224 ) )
= $false )
| ( ( member_a @ ( sK13_SY625 @ SV224 @ SV126 ) @ SV224 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1544]) ).
thf(1607,plain,
! [SV224: set_a,SV126: set_a] :
( ( ( ~ ! [SY625: a] :
( ~ ( member_a @ SY625 @ SV126 )
| ( member_a @ SY625 @ SV224 ) ) )
= $false )
| ( ( member_a @ ( sK13_SY625 @ SV224 @ SV126 ) @ SV224 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1544]) ).
thf(1608,plain,
! [SV190: a,SV46: a,SV130: a] :
( ( ( member_a @ SV130 @ carrier )
= $false )
| ( ( member_a @ SV46 @ carrier )
= $false )
| ( ( ~ ( member_a @ SV190 @ carrier ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV190 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV46 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV190 ) @ relation ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1545]) ).
thf(1609,plain,
! [SV192: a,SV50: a,SV133: a] :
( ( ( member_a @ SV133 @ carrier )
= $false )
| ( ( member_a @ SV50 @ carrier )
= $false )
| ( ( ~ ( member_a @ SV192 @ carrier ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV50 @ SV133 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV133 @ SV192 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV50 @ SV192 ) @ relation ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1547]) ).
thf(1610,plain,
! [SV195: set_a > nat,SV54: set_a,SV226: nat,SV136: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ ( sK15_SY585 @ SV136 @ SV226 @ SV54 @ SV195 ) @ ( sK27_SY655 @ SV195 @ SV54 @ SV226 @ SV136 ) )
| ( ord_less_eq_nat @ ( SV195 @ ( sK15_SY585 @ SV136 @ SV226 @ SV54 @ SV195 ) ) @ ( SV195 @ ( sK27_SY655 @ SV195 @ SV54 @ SV226 @ SV136 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( SV195 @ SV54 ) @ SV226 )
= $true )
| ( ( ( SV195 @ SV136 )
= SV226 )
= $false )
| ( ( ord_less_eq_set_a @ SV54 @ SV136 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1548]) ).
thf(1611,plain,
! [SV227: set_a,SV138: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV138 @ SV227 )
| ~ ( ord_less_eq_set_a @ SV227 @ SV138 ) )
= $false )
| ( ( SV138 = SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1550]) ).
thf(1612,plain,
! [SV138: set_a,SV227: set_a] :
( ( ( ord_less_eq_set_a @ SV227 @ SV138 )
= $false )
| ( ( ord_less_eq_set_a @ SV138 @ SV227 )
= $false )
| ( ( ~ ( ( SV138 != SV227 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV138 @ SV227 )
| ~ ( ord_less_eq_set_a @ SV227 @ SV138 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1551]) ).
thf(1613,plain,
! [SV139: set_a > set_a,SV57: set_a,SV228: set_a,SV197: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ ( sK16_SY513 @ SV197 @ SV228 @ SV57 @ SV139 ) @ ( sK28_SY656 @ SV139 @ SV57 @ SV228 @ SV197 ) )
| ( ord_less_eq_set_a @ ( SV139 @ ( sK16_SY513 @ SV197 @ SV228 @ SV57 @ SV139 ) ) @ ( SV139 @ ( sK28_SY656 @ SV139 @ SV57 @ SV228 @ SV197 ) ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV57 @ ( SV139 @ SV228 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV197 @ SV228 )
= $false )
| ( ( SV57
= ( SV139 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1552]) ).
thf(1614,plain,
! [SV62: set_set_a,SV143: set_a] :
( ( ( ~ ( ~ ( member_set_a @ ( sK12_SY517 @ SV143 @ SV62 ) @ SV62 )
| ~ ( ord_less_eq_set_a @ SV143 @ ( sK12_SY517 @ SV143 @ SV62 ) ) ) )
= $true )
| ( ( member_set_a @ SV143 @ SV62 )
= $false )
| ( ( finite_finite_set_a @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1553]) ).
thf(1615,plain,
! [SV143: set_a,SV62: set_set_a] :
( ( ( ! [SY654: set_a] :
( ~ ( member_set_a @ SY654 @ SV62 )
| ~ ( ord_less_eq_set_a @ ( sK12_SY517 @ SV143 @ SV62 ) @ SY654 )
| ( ( sK12_SY517 @ SV143 @ SV62 )
= SY654 ) ) )
= $true )
| ( ( member_set_a @ SV143 @ SV62 )
= $false )
| ( ( finite_finite_set_a @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1554]) ).
thf(1616,plain,
! [SV63: a,SV144: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) )
= $false )
| ( ( ~ ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( member_a @ SV144 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1555]) ).
thf(1617,plain,
! [SV144: a,SV63: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) ) )
= $false )
| ( ( ~ ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( member_a @ SV144 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1555]) ).
thf(1618,plain,
! [SV230: set_a,SV145: set_a,SV250: a] :
( ( ( ~ ( member_a @ SV250 @ SV145 )
| ( member_a @ SV250 @ SV230 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV145 @ SV230 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1557]) ).
thf(1619,plain,
! [SV230: set_a,SV145: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV145 @ SV230 )
| ~ ! [SY630: a] :
( ~ ( member_a @ SY630 @ SV145 )
| ( member_a @ SY630 @ SV230 ) ) )
= $false )
| ( ( member_a @ ( sK14_SY630 @ SV230 @ SV145 ) @ SV145 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1558]) ).
thf(1620,plain,
! [SV230: set_a,SV145: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV145 @ SV230 ) )
= $false )
| ( ( member_a @ ( sK14_SY630 @ SV230 @ SV145 ) @ SV230 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1559]) ).
thf(1621,plain,
! [SV230: set_a,SV145: set_a] :
( ( ( ~ ! [SY630: a] :
( ~ ( member_a @ SY630 @ SV145 )
| ( member_a @ SY630 @ SV230 ) ) )
= $false )
| ( ( member_a @ ( sK14_SY630 @ SV230 @ SV145 ) @ SV230 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1559]) ).
thf(1622,plain,
! [SV147: set_Product_prod_a_a,SV200: a,SV66: set_a,SV231: a] :
( ( ( member_a @ SV231 @ SV66 )
= $false )
| ( ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) ) )
= $true )
| ( ( member_a @ SV200 @ SV66 )
= $false )
| ( ( finite_finite_a @ SV66 )
= $false )
| ( ( prefer719835986ence_a @ SV66 @ SV147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1560]) ).
thf(1623,plain,
! [SV201: set_a > nat,SV67: set_a,SV232: nat,SV148: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ ( sK17_SY594 @ SV148 @ SV232 @ SV67 @ SV201 ) @ ( sK29_SY657 @ SV201 @ SV67 @ SV232 @ SV148 ) )
| ( ord_less_eq_nat @ ( SV201 @ ( sK17_SY594 @ SV148 @ SV232 @ SV67 @ SV201 ) ) @ ( SV201 @ ( sK29_SY657 @ SV201 @ SV67 @ SV232 @ SV148 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( SV201 @ SV67 ) @ SV232 )
= $true )
| ( ( ord_less_eq_nat @ ( SV201 @ SV148 ) @ SV232 )
= $false )
| ( ( ord_less_eq_set_a @ SV67 @ SV148 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1561]) ).
thf(1624,plain,
! [SV233: set_a,SV150: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV150 @ SV233 )
| ~ ( ord_less_eq_set_a @ SV233 @ SV150 ) )
= $false )
| ( ( SV150 = SV233 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1563]) ).
thf(1625,plain,
! [SV150: set_a,SV233: set_a] :
( ( ( ord_less_eq_set_a @ SV233 @ SV150 )
= $false )
| ( ( ord_less_eq_set_a @ SV150 @ SV233 )
= $false )
| ( ( ~ ( ( SV150 != SV233 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV150 @ SV233 )
| ~ ( ord_less_eq_set_a @ SV233 @ SV150 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1564]) ).
thf(1626,plain,
! [SV203: set_a > set_a,SV70: set_a,SV234: set_a,SV151: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ ( sK18_SY597 @ SV151 @ SV234 @ SV70 @ SV203 ) @ ( sK30_SY658 @ SV203 @ SV70 @ SV234 @ SV151 ) )
| ( ord_less_eq_set_a @ ( SV203 @ ( sK18_SY597 @ SV151 @ SV234 @ SV70 @ SV203 ) ) @ ( SV203 @ ( sK30_SY658 @ SV203 @ SV70 @ SV234 @ SV151 ) ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( SV203 @ SV70 ) @ SV234 )
= $true )
| ( ( ord_less_eq_set_a @ ( SV203 @ SV151 ) @ SV234 )
= $false )
| ( ( ord_less_eq_set_a @ SV70 @ SV151 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1565]) ).
thf(1627,plain,
! [SV152: a,SV71: a] :
( ( ( ~ ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) ) )
= $true )
| ( ( ~ ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
| ~ ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1566]) ).
thf(1628,plain,
! [SV152: a,SV71: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
| ~ ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1567]) ).
thf(1629,plain,
! [SV156: set_a > nat,SV75: nat,SV237: set_a,SV207: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ ( sK19_SY540 @ SV207 @ SV237 @ SV75 @ SV156 ) @ ( sK31_SY659 @ SV156 @ SV75 @ SV237 @ SV207 ) )
| ( ord_less_eq_nat @ ( SV156 @ ( sK19_SY540 @ SV207 @ SV237 @ SV75 @ SV156 ) ) @ ( SV156 @ ( sK31_SY659 @ SV156 @ SV75 @ SV237 @ SV207 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV75 @ ( SV156 @ SV237 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV207 @ SV237 )
= $false )
| ( ( SV75
= ( SV156 @ SV207 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1568]) ).
thf(1630,plain,
! [SV157: a > $o,SV248: a,SV76: a > $o] :
( ( ( SV76 @ SV248 )
= $false )
| ( ( SV157 @ SV248 )
= $true )
| ( ( ord_less_eq_set_a @ ( collect_a @ SV76 ) @ ( collect_a @ SV157 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1569]) ).
thf(1631,plain,
! [SV157: a > $o,SV76: a > $o] :
( ( ( ord_less_eq_set_a @ ( collect_a @ SV76 ) @ ( collect_a @ SV157 ) )
= $true )
| ( ( SV76 @ ( sK7_SY542 @ SV157 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1570]) ).
thf(1632,plain,
! [SV157: a > $o,SV76: a > $o] :
( ( ( ! [SY542: a] :
( ~ ( SV76 @ SY542 )
| ( SV157 @ SY542 ) ) )
= $true )
| ( ( SV76 @ ( sK7_SY542 @ SV157 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1571]) ).
thf(1633,plain,
! [SV157: a > $o,SV251: a,SV76: a > $o] :
( ( ( ~ ( SV76 @ SV251 )
| ( SV157 @ SV251 ) )
= $true )
| ( ( SV157 @ ( sK7_SY542 @ SV157 @ SV76 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1573]) ).
thf(1634,plain,
! [SV208: nat > set_a,SV80: nat,SV238: set_a,SV161: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( sK20_SY605 @ SV161 @ SV238 @ SV80 @ SV208 ) @ ( sK32_SY660 @ SV208 @ SV80 @ SV238 @ SV161 ) )
| ( ord_less_eq_set_a @ ( SV208 @ ( sK20_SY605 @ SV161 @ SV238 @ SV80 @ SV208 ) ) @ ( SV208 @ ( sK32_SY660 @ SV208 @ SV80 @ SV238 @ SV161 ) ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( SV208 @ SV80 ) @ SV238 )
= $true )
| ( ( ( SV208 @ SV161 )
= SV238 )
= $false )
| ( ( ord_less_eq_nat @ SV80 @ SV161 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1576]) ).
thf(1635,plain,
! [SV209: set_a > set_a,SV81: set_a,SV239: set_a,SV162: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ ( sK21_SY608 @ SV162 @ SV239 @ SV81 @ SV209 ) @ ( sK33_SY661 @ SV209 @ SV81 @ SV239 @ SV162 ) )
| ( ord_less_eq_set_a @ ( SV209 @ ( sK21_SY608 @ SV162 @ SV239 @ SV81 @ SV209 ) ) @ ( SV209 @ ( sK33_SY661 @ SV209 @ SV81 @ SV239 @ SV162 ) ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( SV209 @ SV81 ) @ SV239 )
= $true )
| ( ( ( SV209 @ SV162 )
= SV239 )
= $false )
| ( ( ord_less_eq_set_a @ SV81 @ SV162 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1577]) ).
thf(1636,plain,
! [SV163: nat,SV82: set_a] :
( ( ( ~ ( finite_finite_a @ ( sK8_SY552 @ SV82 @ SV163 ) )
| ( ( finite_card_a @ ( sK8_SY552 @ SV82 @ SV163 ) )
!= SV163 ) )
= $false )
| ( ( finite_finite_a @ SV82 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1578]) ).
thf(1637,plain,
! [SV83: a,SV210: a,SV164: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV210 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV210 @ SV164 ) @ relation ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SV210 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV210 @ SV83 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SV164 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV83 ) @ relation )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1580]) ).
thf(1638,plain,
! [SV166: set_a > nat,SV85: nat,SV240: set_a,SV211: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ ( sK22_SY556 @ SV211 @ SV240 @ SV85 @ SV166 ) @ ( sK34_SY662 @ SV166 @ SV85 @ SV240 @ SV211 ) )
| ( ord_less_eq_nat @ ( SV166 @ ( sK22_SY556 @ SV211 @ SV240 @ SV85 @ SV166 ) ) @ ( SV166 @ ( sK34_SY662 @ SV166 @ SV85 @ SV240 @ SV211 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV85 @ ( SV166 @ SV240 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV211 @ SV240 )
= $false )
| ( ( ord_less_eq_nat @ SV85 @ ( SV166 @ SV211 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1581]) ).
thf(1639,plain,
! [SV168: nat > set_a,SV87: set_a,SV241: nat,SV212: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( sK23_SY560 @ SV212 @ SV241 @ SV87 @ SV168 ) @ ( sK35_SY663 @ SV168 @ SV87 @ SV241 @ SV212 ) )
| ( ord_less_eq_set_a @ ( SV168 @ ( sK23_SY560 @ SV212 @ SV241 @ SV87 @ SV168 ) ) @ ( SV168 @ ( sK35_SY663 @ SV168 @ SV87 @ SV241 @ SV212 ) ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV87 @ ( SV168 @ SV241 ) )
= $true )
| ( ( ord_less_eq_nat @ SV212 @ SV241 )
= $false )
| ( ( ord_less_eq_set_a @ SV87 @ ( SV168 @ SV212 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1582]) ).
thf(1640,plain,
! [SV213: nat > set_a,SV89: nat,SV242: set_a,SV170: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( sK24_SY617 @ SV170 @ SV242 @ SV89 @ SV213 ) @ ( sK36_SY664 @ SV213 @ SV89 @ SV242 @ SV170 ) )
| ( ord_less_eq_set_a @ ( SV213 @ ( sK24_SY617 @ SV170 @ SV242 @ SV89 @ SV213 ) ) @ ( SV213 @ ( sK36_SY664 @ SV213 @ SV89 @ SV242 @ SV170 ) ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( SV213 @ SV89 ) @ SV242 )
= $true )
| ( ( ord_less_eq_set_a @ ( SV213 @ SV170 ) @ SV242 )
= $false )
| ( ( ord_less_eq_nat @ SV89 @ SV170 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1583]) ).
thf(1641,plain,
! [SV172: set_a > set_a,SV91: set_a,SV243: set_a,SV215: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ ( sK25_SY569 @ SV215 @ SV243 @ SV91 @ SV172 ) @ ( sK37_SY665 @ SV172 @ SV91 @ SV243 @ SV215 ) )
| ( ord_less_eq_set_a @ ( SV172 @ ( sK25_SY569 @ SV215 @ SV243 @ SV91 @ SV172 ) ) @ ( SV172 @ ( sK37_SY665 @ SV172 @ SV91 @ SV243 @ SV215 ) ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV91 @ ( SV172 @ SV243 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV215 @ SV243 )
= $false )
| ( ( ord_less_eq_set_a @ SV91 @ ( SV172 @ SV215 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1584]) ).
thf(1642,plain,
! [SV244: set_a,SV173: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV173 @ SV244 )
| ~ ( ord_less_eq_set_a @ SV244 @ SV173 ) )
= $false )
| ( ( SV173 = SV244 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1586]) ).
thf(1643,plain,
! [SV173: set_a,SV244: set_a] :
( ( ( ord_less_eq_set_a @ SV244 @ SV173 )
= $false )
| ( ( ord_less_eq_set_a @ SV173 @ SV244 )
= $false )
| ( ( ~ ( ( SV173 != SV244 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV173 @ SV244 )
| ~ ( ord_less_eq_set_a @ SV244 @ SV173 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1587]) ).
thf(1644,plain,
! [SV174: nat > set_a,SV94: set_a,SV246: nat,SV217: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( sK26_SY575 @ SV217 @ SV246 @ SV94 @ SV174 ) @ ( sK38_SY666 @ SV174 @ SV94 @ SV246 @ SV217 ) )
| ( ord_less_eq_set_a @ ( SV174 @ ( sK26_SY575 @ SV217 @ SV246 @ SV94 @ SV174 ) ) @ ( SV174 @ ( sK38_SY666 @ SV174 @ SV94 @ SV246 @ SV217 ) ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV94 @ ( SV174 @ SV246 ) )
= $true )
| ( ( ord_less_eq_nat @ SV217 @ SV246 )
= $false )
| ( ( SV94
= ( SV174 @ SV217 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1588]) ).
thf(1645,plain,
! [SV9: a,SV176: a,SV97: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV176 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV97 ) @ relation ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV176 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV9 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV97 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV9 ) @ relation )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1589]) ).
thf(1646,plain,
! [SV13: set_set_a,SV252: set_a] :
( ( ( ~ ( member_set_a @ SV252 @ SV13 )
| ~ ( ord_less_eq_set_a @ SV252 @ ( sK9_SY294 @ SV13 ) )
| ( ( sK9_SY294 @ SV13 )
= SV252 ) )
= $true )
| ( ( SV13 = bot_bot_set_set_a )
= $true )
| ( ( finite_finite_set_a @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1591]) ).
thf(1647,plain,
! [SV16: set_set_a,SV103: set_a] :
( ( ( ~ ( member_set_a @ ( sK10_SY475 @ SV103 @ SV16 ) @ SV16 )
| ~ ( ord_less_eq_set_a @ ( sK10_SY475 @ SV103 @ SV16 ) @ SV103 ) )
= $false )
| ( ( member_set_a @ SV103 @ SV16 )
= $false )
| ( ( finite_finite_set_a @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1592]) ).
thf(1648,plain,
! [SV103: set_a,SV16: set_set_a,SV253: set_a] :
( ( ( ~ ( member_set_a @ SV253 @ SV16 )
| ~ ( ord_less_eq_set_a @ SV253 @ ( sK10_SY475 @ SV103 @ SV16 ) )
| ( ( sK10_SY475 @ SV103 @ SV16 )
= SV253 ) )
= $true )
| ( ( member_set_a @ SV103 @ SV16 )
= $false )
| ( ( finite_finite_set_a @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1593]) ).
thf(1649,plain,
! [SV220: set_a,SV109: set_a,SV181: nat,SV22: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV22 @ SV181 ) )
= $false )
| ( ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV22 @ SV109 ) @ ( produc1450889781_set_a @ SV181 @ SV220 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1594]) ).
thf(1650,plain,
! [SV181: nat,SV22: nat,SV220: set_a,SV109: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV109 @ SV220 ) )
= $false )
| ( ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV22 @ SV109 ) @ ( produc1450889781_set_a @ SV181 @ SV220 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1594]) ).
thf(1651,plain,
! [SV220: set_a,SV181: nat,SV109: set_a,SV22: nat] :
( ( ( ~ ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV22 @ SV109 ) @ ( produc1450889781_set_a @ SV181 @ SV220 ) )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV22 @ SV181 )
| ~ ( ord_less_eq_set_a @ SV109 @ SV220 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV22 @ SV181 )
= $false )
| ( ( ord_less_eq_set_a @ SV109 @ SV220 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1595]) ).
thf(1652,plain,
! [SV110: set_a,SV221: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV221 @ SV110 ) )
= $false )
| ( ( SV110 = SV221 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1596]) ).
thf(1653,plain,
! [SV221: set_a,SV110: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV110 @ SV221 ) )
= $false )
| ( ( SV110 = SV221 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1596]) ).
thf(1654,plain,
! [SV221: set_a,SV110: set_a] :
( ( ( ( SV110 != SV221 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV221 @ SV110 )
| ~ ( ord_less_eq_set_a @ SV110 @ SV221 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV221 @ SV110 )
= $false )
| ( ( ord_less_eq_set_a @ SV110 @ SV221 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1597]) ).
thf(1655,plain,
! [SV222: set_a,SV111: set_a,SV183: set_a,SV24: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV24 @ SV183 ) )
= $false )
| ( ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV24 @ SV111 ) @ ( produc1928581911_set_a @ SV183 @ SV222 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1598]) ).
thf(1656,plain,
! [SV183: set_a,SV24: set_a,SV222: set_a,SV111: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV111 @ SV222 ) )
= $false )
| ( ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV24 @ SV111 ) @ ( produc1928581911_set_a @ SV183 @ SV222 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1598]) ).
thf(1657,plain,
! [SV222: set_a,SV183: set_a,SV111: set_a,SV24: set_a] :
( ( ( ~ ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV24 @ SV111 ) @ ( produc1928581911_set_a @ SV183 @ SV222 ) )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV24 @ SV183 )
| ~ ( ord_less_eq_set_a @ SV111 @ SV222 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV24 @ SV183 )
= $false )
| ( ( ord_less_eq_set_a @ SV111 @ SV222 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1599]) ).
thf(1658,plain,
! [SV34: set_set_a,SV254: set_a] :
( ( ( ~ ( member_set_a @ SV254 @ SV34 )
| ~ ( ord_less_eq_set_a @ ( sK11_SY329 @ SV34 ) @ SV254 )
| ( ( sK11_SY329 @ SV34 )
= SV254 ) )
= $true )
| ( ( SV34 = bot_bot_set_set_a )
= $true )
| ( ( finite_finite_set_a @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1601]) ).
thf(1659,plain,
! [SV223: nat,SV123: nat,SV187: set_a,SV38: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV38 @ SV187 ) )
= $false )
| ( ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV38 @ SV123 ) @ ( produc515611863_a_nat @ SV187 @ SV223 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1602]) ).
thf(1660,plain,
! [SV187: set_a,SV38: set_a,SV223: nat,SV123: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV123 @ SV223 ) )
= $false )
| ( ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV38 @ SV123 ) @ ( produc515611863_a_nat @ SV187 @ SV223 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1602]) ).
thf(1661,plain,
! [SV223: nat,SV187: set_a,SV123: nat,SV38: set_a] :
( ( ( ~ ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV38 @ SV123 ) @ ( produc515611863_a_nat @ SV187 @ SV223 ) )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV38 @ SV187 )
| ~ ( ord_less_eq_nat @ SV123 @ SV223 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV38 @ SV187 )
= $false )
| ( ( ord_less_eq_nat @ SV123 @ SV223 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1603]) ).
thf(1662,plain,
! [SV224: set_a,SV126: set_a,SV249: a] :
( ( ( ~ ( member_a @ SV249 @ SV126 ) )
= $true )
| ( ( member_a @ SV249 @ SV224 )
= $true )
| ( ( ord_less_eq_set_a @ SV126 @ SV224 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1604]) ).
thf(1663,plain,
! [SV224: set_a,SV126: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV126 @ SV224 ) )
= $false )
| ( ( member_a @ ( sK13_SY625 @ SV224 @ SV126 ) @ SV126 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1605]) ).
thf(1664,plain,
! [SV224: set_a,SV126: set_a] :
( ( ( ~ ! [SY625: a] :
( ~ ( member_a @ SY625 @ SV126 )
| ( member_a @ SY625 @ SV224 ) ) )
= $false )
| ( ( member_a @ ( sK13_SY625 @ SV224 @ SV126 ) @ SV126 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1605]) ).
thf(1665,plain,
! [SV224: set_a,SV126: set_a] :
( ( ( ord_less_eq_set_a @ SV126 @ SV224 )
= $true )
| ( ( member_a @ ( sK13_SY625 @ SV224 @ SV126 ) @ SV224 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1606]) ).
thf(1666,plain,
! [SV224: set_a,SV126: set_a] :
( ( ( ! [SY625: a] :
( ~ ( member_a @ SY625 @ SV126 )
| ( member_a @ SY625 @ SV224 ) ) )
= $true )
| ( ( member_a @ ( sK13_SY625 @ SV224 @ SV126 ) @ SV224 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1607]) ).
thf(1667,plain,
! [SV130: a,SV46: a,SV190: a] :
( ( ( member_a @ SV190 @ carrier )
= $false )
| ( ( member_a @ SV46 @ carrier )
= $false )
| ( ( member_a @ SV130 @ carrier )
= $false )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV190 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV46 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV190 ) @ relation ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1608]) ).
thf(1668,plain,
! [SV133: a,SV50: a,SV192: a] :
( ( ( member_a @ SV192 @ carrier )
= $false )
| ( ( member_a @ SV50 @ carrier )
= $false )
| ( ( member_a @ SV133 @ carrier )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV50 @ SV133 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV133 @ SV192 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV50 @ SV192 ) @ relation ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1609]) ).
thf(1669,plain,
! [SV195: set_a > nat,SV54: set_a,SV226: nat,SV136: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ ( sK15_SY585 @ SV136 @ SV226 @ SV54 @ SV195 ) @ ( sK27_SY655 @ SV195 @ SV54 @ SV226 @ SV136 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( SV195 @ SV54 ) @ SV226 )
= $true )
| ( ( ( SV195 @ SV136 )
= SV226 )
= $false )
| ( ( ord_less_eq_set_a @ SV54 @ SV136 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1610]) ).
thf(1670,plain,
! [SV54: set_a,SV226: nat,SV136: set_a,SV195: set_a > nat] :
( ( ( ord_less_eq_nat @ ( SV195 @ ( sK15_SY585 @ SV136 @ SV226 @ SV54 @ SV195 ) ) @ ( SV195 @ ( sK27_SY655 @ SV195 @ SV54 @ SV226 @ SV136 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( SV195 @ SV54 ) @ SV226 )
= $true )
| ( ( ( SV195 @ SV136 )
= SV226 )
= $false )
| ( ( ord_less_eq_set_a @ SV54 @ SV136 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1610]) ).
thf(1671,plain,
! [SV227: set_a,SV138: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV138 @ SV227 ) )
= $false )
| ( ( SV138 = SV227 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1611]) ).
thf(1672,plain,
! [SV138: set_a,SV227: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV227 @ SV138 ) )
= $false )
| ( ( SV138 = SV227 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1611]) ).
thf(1673,plain,
! [SV227: set_a,SV138: set_a] :
( ( ( ( SV138 != SV227 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV138 @ SV227 )
| ~ ( ord_less_eq_set_a @ SV227 @ SV138 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV138 @ SV227 )
= $false )
| ( ( ord_less_eq_set_a @ SV227 @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1612]) ).
thf(1674,plain,
! [SV139: set_a > set_a,SV57: set_a,SV228: set_a,SV197: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ ( sK16_SY513 @ SV197 @ SV228 @ SV57 @ SV139 ) @ ( sK28_SY656 @ SV139 @ SV57 @ SV228 @ SV197 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV57 @ ( SV139 @ SV228 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV197 @ SV228 )
= $false )
| ( ( SV57
= ( SV139 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1613]) ).
thf(1675,plain,
! [SV57: set_a,SV228: set_a,SV197: set_a,SV139: set_a > set_a] :
( ( ( ord_less_eq_set_a @ ( SV139 @ ( sK16_SY513 @ SV197 @ SV228 @ SV57 @ SV139 ) ) @ ( SV139 @ ( sK28_SY656 @ SV139 @ SV57 @ SV228 @ SV197 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV57 @ ( SV139 @ SV228 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV197 @ SV228 )
= $false )
| ( ( SV57
= ( SV139 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1613]) ).
thf(1676,plain,
! [SV62: set_set_a,SV143: set_a] :
( ( ( ~ ( member_set_a @ ( sK12_SY517 @ SV143 @ SV62 ) @ SV62 )
| ~ ( ord_less_eq_set_a @ SV143 @ ( sK12_SY517 @ SV143 @ SV62 ) ) )
= $false )
| ( ( member_set_a @ SV143 @ SV62 )
= $false )
| ( ( finite_finite_set_a @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1614]) ).
thf(1677,plain,
! [SV143: set_a,SV62: set_set_a,SV255: set_a] :
( ( ( ~ ( member_set_a @ SV255 @ SV62 )
| ~ ( ord_less_eq_set_a @ ( sK12_SY517 @ SV143 @ SV62 ) @ SV255 )
| ( ( sK12_SY517 @ SV143 @ SV62 )
= SV255 ) )
= $true )
| ( ( member_set_a @ SV143 @ SV62 )
= $false )
| ( ( finite_finite_set_a @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1615]) ).
thf(1678,plain,
! [SV63: a,SV144: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
= $true )
| ( ( ~ ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( member_a @ SV144 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1616]) ).
thf(1679,plain,
! [SV144: a,SV63: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) )
= $true )
| ( ( ~ ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( member_a @ SV144 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1617]) ).
thf(1680,plain,
! [SV230: set_a,SV145: set_a,SV250: a] :
( ( ( ~ ( member_a @ SV250 @ SV145 ) )
= $true )
| ( ( member_a @ SV250 @ SV230 )
= $true )
| ( ( ord_less_eq_set_a @ SV145 @ SV230 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1618]) ).
thf(1681,plain,
! [SV230: set_a,SV145: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV145 @ SV230 ) )
= $false )
| ( ( member_a @ ( sK14_SY630 @ SV230 @ SV145 ) @ SV145 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1619]) ).
thf(1682,plain,
! [SV230: set_a,SV145: set_a] :
( ( ( ~ ! [SY630: a] :
( ~ ( member_a @ SY630 @ SV145 )
| ( member_a @ SY630 @ SV230 ) ) )
= $false )
| ( ( member_a @ ( sK14_SY630 @ SV230 @ SV145 ) @ SV145 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1619]) ).
thf(1683,plain,
! [SV230: set_a,SV145: set_a] :
( ( ( ord_less_eq_set_a @ SV145 @ SV230 )
= $true )
| ( ( member_a @ ( sK14_SY630 @ SV230 @ SV145 ) @ SV230 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1620]) ).
thf(1684,plain,
! [SV230: set_a,SV145: set_a] :
( ( ( ! [SY630: a] :
( ~ ( member_a @ SY630 @ SV145 )
| ( member_a @ SY630 @ SV230 ) ) )
= $true )
| ( ( member_a @ ( sK14_SY630 @ SV230 @ SV145 ) @ SV230 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1621]) ).
thf(1685,plain,
! [SV231: a,SV147: set_Product_prod_a_a,SV66: set_a,SV200: a] :
( ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) )
= $true )
| ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) @ ( prefer1676310729than_a @ SV200 @ SV66 @ SV147 ) )
= $true )
| ( ( member_a @ SV231 @ SV66 )
= $false )
| ( ( member_a @ SV200 @ SV66 )
= $false )
| ( ( finite_finite_a @ SV66 )
= $false )
| ( ( prefer719835986ence_a @ SV66 @ SV147 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1622]) ).
thf(1686,plain,
! [SV201: set_a > nat,SV67: set_a,SV232: nat,SV148: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ ( sK17_SY594 @ SV148 @ SV232 @ SV67 @ SV201 ) @ ( sK29_SY657 @ SV201 @ SV67 @ SV232 @ SV148 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( SV201 @ SV67 ) @ SV232 )
= $true )
| ( ( ord_less_eq_nat @ ( SV201 @ SV148 ) @ SV232 )
= $false )
| ( ( ord_less_eq_set_a @ SV67 @ SV148 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1623]) ).
thf(1687,plain,
! [SV67: set_a,SV232: nat,SV148: set_a,SV201: set_a > nat] :
( ( ( ord_less_eq_nat @ ( SV201 @ ( sK17_SY594 @ SV148 @ SV232 @ SV67 @ SV201 ) ) @ ( SV201 @ ( sK29_SY657 @ SV201 @ SV67 @ SV232 @ SV148 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( SV201 @ SV67 ) @ SV232 )
= $true )
| ( ( ord_less_eq_nat @ ( SV201 @ SV148 ) @ SV232 )
= $false )
| ( ( ord_less_eq_set_a @ SV67 @ SV148 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1623]) ).
thf(1688,plain,
! [SV233: set_a,SV150: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV150 @ SV233 ) )
= $false )
| ( ( SV150 = SV233 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1624]) ).
thf(1689,plain,
! [SV150: set_a,SV233: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV233 @ SV150 ) )
= $false )
| ( ( SV150 = SV233 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1624]) ).
thf(1690,plain,
! [SV233: set_a,SV150: set_a] :
( ( ( ( SV150 != SV233 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV150 @ SV233 )
| ~ ( ord_less_eq_set_a @ SV233 @ SV150 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV150 @ SV233 )
= $false )
| ( ( ord_less_eq_set_a @ SV233 @ SV150 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1625]) ).
thf(1691,plain,
! [SV203: set_a > set_a,SV70: set_a,SV234: set_a,SV151: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ ( sK18_SY597 @ SV151 @ SV234 @ SV70 @ SV203 ) @ ( sK30_SY658 @ SV203 @ SV70 @ SV234 @ SV151 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( SV203 @ SV70 ) @ SV234 )
= $true )
| ( ( ord_less_eq_set_a @ ( SV203 @ SV151 ) @ SV234 )
= $false )
| ( ( ord_less_eq_set_a @ SV70 @ SV151 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1626]) ).
thf(1692,plain,
! [SV70: set_a,SV234: set_a,SV151: set_a,SV203: set_a > set_a] :
( ( ( ord_less_eq_set_a @ ( SV203 @ ( sK18_SY597 @ SV151 @ SV234 @ SV70 @ SV203 ) ) @ ( SV203 @ ( sK30_SY658 @ SV203 @ SV70 @ SV234 @ SV151 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( SV203 @ SV70 ) @ SV234 )
= $true )
| ( ( ord_less_eq_set_a @ ( SV203 @ SV151 ) @ SV234 )
= $false )
| ( ( ord_less_eq_set_a @ SV70 @ SV151 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1626]) ).
thf(1693,plain,
! [SV152: a,SV71: a] :
( ( ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
= $false )
| ( ( ~ ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
| ~ ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1627]) ).
thf(1694,plain,
! [SV152: a,SV71: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
| ~ ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1628]) ).
thf(1695,plain,
! [SV156: set_a > nat,SV75: nat,SV237: set_a,SV207: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ ( sK19_SY540 @ SV207 @ SV237 @ SV75 @ SV156 ) @ ( sK31_SY659 @ SV156 @ SV75 @ SV237 @ SV207 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV75 @ ( SV156 @ SV237 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV207 @ SV237 )
= $false )
| ( ( SV75
= ( SV156 @ SV207 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1629]) ).
thf(1696,plain,
! [SV75: nat,SV237: set_a,SV207: set_a,SV156: set_a > nat] :
( ( ( ord_less_eq_nat @ ( SV156 @ ( sK19_SY540 @ SV207 @ SV237 @ SV75 @ SV156 ) ) @ ( SV156 @ ( sK31_SY659 @ SV156 @ SV75 @ SV237 @ SV207 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV75 @ ( SV156 @ SV237 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV207 @ SV237 )
= $false )
| ( ( SV75
= ( SV156 @ SV207 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1629]) ).
thf(1697,plain,
! [SV157: a > $o,SV256: a,SV76: a > $o] :
( ( ( ~ ( SV76 @ SV256 )
| ( SV157 @ SV256 ) )
= $true )
| ( ( SV76 @ ( sK7_SY542 @ SV157 @ SV76 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1632]) ).
thf(1698,plain,
! [SV157: a > $o,SV251: a,SV76: a > $o] :
( ( ( ~ ( SV76 @ SV251 ) )
= $true )
| ( ( SV157 @ SV251 )
= $true )
| ( ( SV157 @ ( sK7_SY542 @ SV157 @ SV76 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1633]) ).
thf(1699,plain,
! [SV208: nat > set_a,SV80: nat,SV238: set_a,SV161: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( sK20_SY605 @ SV161 @ SV238 @ SV80 @ SV208 ) @ ( sK32_SY660 @ SV208 @ SV80 @ SV238 @ SV161 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( SV208 @ SV80 ) @ SV238 )
= $true )
| ( ( ( SV208 @ SV161 )
= SV238 )
= $false )
| ( ( ord_less_eq_nat @ SV80 @ SV161 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1634]) ).
thf(1700,plain,
! [SV80: nat,SV238: set_a,SV161: nat,SV208: nat > set_a] :
( ( ( ord_less_eq_set_a @ ( SV208 @ ( sK20_SY605 @ SV161 @ SV238 @ SV80 @ SV208 ) ) @ ( SV208 @ ( sK32_SY660 @ SV208 @ SV80 @ SV238 @ SV161 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( SV208 @ SV80 ) @ SV238 )
= $true )
| ( ( ( SV208 @ SV161 )
= SV238 )
= $false )
| ( ( ord_less_eq_nat @ SV80 @ SV161 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1634]) ).
thf(1701,plain,
! [SV209: set_a > set_a,SV81: set_a,SV239: set_a,SV162: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ ( sK21_SY608 @ SV162 @ SV239 @ SV81 @ SV209 ) @ ( sK33_SY661 @ SV209 @ SV81 @ SV239 @ SV162 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( SV209 @ SV81 ) @ SV239 )
= $true )
| ( ( ( SV209 @ SV162 )
= SV239 )
= $false )
| ( ( ord_less_eq_set_a @ SV81 @ SV162 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1635]) ).
thf(1702,plain,
! [SV81: set_a,SV239: set_a,SV162: set_a,SV209: set_a > set_a] :
( ( ( ord_less_eq_set_a @ ( SV209 @ ( sK21_SY608 @ SV162 @ SV239 @ SV81 @ SV209 ) ) @ ( SV209 @ ( sK33_SY661 @ SV209 @ SV81 @ SV239 @ SV162 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( SV209 @ SV81 ) @ SV239 )
= $true )
| ( ( ( SV209 @ SV162 )
= SV239 )
= $false )
| ( ( ord_less_eq_set_a @ SV81 @ SV162 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1635]) ).
thf(1703,plain,
! [SV163: nat,SV82: set_a] :
( ( ( ~ ( finite_finite_a @ ( sK8_SY552 @ SV82 @ SV163 ) ) )
= $false )
| ( ( finite_finite_a @ SV82 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1636]) ).
thf(1704,plain,
! [SV163: nat,SV82: set_a] :
( ( ( ( finite_card_a @ ( sK8_SY552 @ SV82 @ SV163 ) )
!= SV163 )
= $false )
| ( ( finite_finite_a @ SV82 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1636]) ).
thf(1705,plain,
! [SV83: a,SV210: a,SV164: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV210 ) @ relation ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV210 @ SV164 ) @ relation ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SV210 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV210 @ SV83 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SV164 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV83 ) @ relation )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1637]) ).
thf(1706,plain,
! [SV166: set_a > nat,SV85: nat,SV240: set_a,SV211: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ ( sK22_SY556 @ SV211 @ SV240 @ SV85 @ SV166 ) @ ( sK34_SY662 @ SV166 @ SV85 @ SV240 @ SV211 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV85 @ ( SV166 @ SV240 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV211 @ SV240 )
= $false )
| ( ( ord_less_eq_nat @ SV85 @ ( SV166 @ SV211 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1638]) ).
thf(1707,plain,
! [SV85: nat,SV240: set_a,SV211: set_a,SV166: set_a > nat] :
( ( ( ord_less_eq_nat @ ( SV166 @ ( sK22_SY556 @ SV211 @ SV240 @ SV85 @ SV166 ) ) @ ( SV166 @ ( sK34_SY662 @ SV166 @ SV85 @ SV240 @ SV211 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV85 @ ( SV166 @ SV240 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV211 @ SV240 )
= $false )
| ( ( ord_less_eq_nat @ SV85 @ ( SV166 @ SV211 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1638]) ).
thf(1708,plain,
! [SV168: nat > set_a,SV87: set_a,SV241: nat,SV212: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( sK23_SY560 @ SV212 @ SV241 @ SV87 @ SV168 ) @ ( sK35_SY663 @ SV168 @ SV87 @ SV241 @ SV212 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV87 @ ( SV168 @ SV241 ) )
= $true )
| ( ( ord_less_eq_nat @ SV212 @ SV241 )
= $false )
| ( ( ord_less_eq_set_a @ SV87 @ ( SV168 @ SV212 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1639]) ).
thf(1709,plain,
! [SV87: set_a,SV241: nat,SV212: nat,SV168: nat > set_a] :
( ( ( ord_less_eq_set_a @ ( SV168 @ ( sK23_SY560 @ SV212 @ SV241 @ SV87 @ SV168 ) ) @ ( SV168 @ ( sK35_SY663 @ SV168 @ SV87 @ SV241 @ SV212 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV87 @ ( SV168 @ SV241 ) )
= $true )
| ( ( ord_less_eq_nat @ SV212 @ SV241 )
= $false )
| ( ( ord_less_eq_set_a @ SV87 @ ( SV168 @ SV212 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1639]) ).
thf(1710,plain,
! [SV213: nat > set_a,SV89: nat,SV242: set_a,SV170: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( sK24_SY617 @ SV170 @ SV242 @ SV89 @ SV213 ) @ ( sK36_SY664 @ SV213 @ SV89 @ SV242 @ SV170 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( SV213 @ SV89 ) @ SV242 )
= $true )
| ( ( ord_less_eq_set_a @ ( SV213 @ SV170 ) @ SV242 )
= $false )
| ( ( ord_less_eq_nat @ SV89 @ SV170 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1640]) ).
thf(1711,plain,
! [SV89: nat,SV242: set_a,SV170: nat,SV213: nat > set_a] :
( ( ( ord_less_eq_set_a @ ( SV213 @ ( sK24_SY617 @ SV170 @ SV242 @ SV89 @ SV213 ) ) @ ( SV213 @ ( sK36_SY664 @ SV213 @ SV89 @ SV242 @ SV170 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( SV213 @ SV89 ) @ SV242 )
= $true )
| ( ( ord_less_eq_set_a @ ( SV213 @ SV170 ) @ SV242 )
= $false )
| ( ( ord_less_eq_nat @ SV89 @ SV170 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1640]) ).
thf(1712,plain,
! [SV172: set_a > set_a,SV91: set_a,SV243: set_a,SV215: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ ( sK25_SY569 @ SV215 @ SV243 @ SV91 @ SV172 ) @ ( sK37_SY665 @ SV172 @ SV91 @ SV243 @ SV215 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV91 @ ( SV172 @ SV243 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV215 @ SV243 )
= $false )
| ( ( ord_less_eq_set_a @ SV91 @ ( SV172 @ SV215 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1641]) ).
thf(1713,plain,
! [SV91: set_a,SV243: set_a,SV215: set_a,SV172: set_a > set_a] :
( ( ( ord_less_eq_set_a @ ( SV172 @ ( sK25_SY569 @ SV215 @ SV243 @ SV91 @ SV172 ) ) @ ( SV172 @ ( sK37_SY665 @ SV172 @ SV91 @ SV243 @ SV215 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV91 @ ( SV172 @ SV243 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV215 @ SV243 )
= $false )
| ( ( ord_less_eq_set_a @ SV91 @ ( SV172 @ SV215 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1641]) ).
thf(1714,plain,
! [SV244: set_a,SV173: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV173 @ SV244 ) )
= $false )
| ( ( SV173 = SV244 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1642]) ).
thf(1715,plain,
! [SV173: set_a,SV244: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV244 @ SV173 ) )
= $false )
| ( ( SV173 = SV244 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1642]) ).
thf(1716,plain,
! [SV244: set_a,SV173: set_a] :
( ( ( ( SV173 != SV244 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV173 @ SV244 )
| ~ ( ord_less_eq_set_a @ SV244 @ SV173 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV173 @ SV244 )
= $false )
| ( ( ord_less_eq_set_a @ SV244 @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1643]) ).
thf(1717,plain,
! [SV174: nat > set_a,SV94: set_a,SV246: nat,SV217: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( sK26_SY575 @ SV217 @ SV246 @ SV94 @ SV174 ) @ ( sK38_SY666 @ SV174 @ SV94 @ SV246 @ SV217 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV94 @ ( SV174 @ SV246 ) )
= $true )
| ( ( ord_less_eq_nat @ SV217 @ SV246 )
= $false )
| ( ( SV94
= ( SV174 @ SV217 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1644]) ).
thf(1718,plain,
! [SV94: set_a,SV246: nat,SV217: nat,SV174: nat > set_a] :
( ( ( ord_less_eq_set_a @ ( SV174 @ ( sK26_SY575 @ SV217 @ SV246 @ SV94 @ SV174 ) ) @ ( SV174 @ ( sK38_SY666 @ SV174 @ SV94 @ SV246 @ SV217 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV94 @ ( SV174 @ SV246 ) )
= $true )
| ( ( ord_less_eq_nat @ SV217 @ SV246 )
= $false )
| ( ( SV94
= ( SV174 @ SV217 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1644]) ).
thf(1719,plain,
! [SV9: a,SV176: a,SV97: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV176 ) @ relation ) )
= $true )
| ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV97 ) @ relation ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV176 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV9 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV97 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV9 ) @ relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1645]) ).
thf(1720,plain,
! [SV13: set_set_a,SV252: set_a] :
( ( ( ~ ( member_set_a @ SV252 @ SV13 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV252 @ ( sK9_SY294 @ SV13 ) )
| ( ( sK9_SY294 @ SV13 )
= SV252 ) )
= $true )
| ( ( SV13 = bot_bot_set_set_a )
= $true )
| ( ( finite_finite_set_a @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1646]) ).
thf(1721,plain,
! [SV16: set_set_a,SV103: set_a] :
( ( ( ~ ( member_set_a @ ( sK10_SY475 @ SV103 @ SV16 ) @ SV16 ) )
= $false )
| ( ( member_set_a @ SV103 @ SV16 )
= $false )
| ( ( finite_finite_set_a @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1647]) ).
thf(1722,plain,
! [SV16: set_set_a,SV103: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ ( sK10_SY475 @ SV103 @ SV16 ) @ SV103 ) )
= $false )
| ( ( member_set_a @ SV103 @ SV16 )
= $false )
| ( ( finite_finite_set_a @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1647]) ).
thf(1723,plain,
! [SV103: set_a,SV16: set_set_a,SV253: set_a] :
( ( ( ~ ( member_set_a @ SV253 @ SV16 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV253 @ ( sK10_SY475 @ SV103 @ SV16 ) )
| ( ( sK10_SY475 @ SV103 @ SV16 )
= SV253 ) )
= $true )
| ( ( member_set_a @ SV103 @ SV16 )
= $false )
| ( ( finite_finite_set_a @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1648]) ).
thf(1724,plain,
! [SV220: set_a,SV109: set_a,SV181: nat,SV22: nat] :
( ( ( ord_less_eq_nat @ SV22 @ SV181 )
= $true )
| ( ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV22 @ SV109 ) @ ( produc1450889781_set_a @ SV181 @ SV220 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1649]) ).
thf(1725,plain,
! [SV181: nat,SV22: nat,SV220: set_a,SV109: set_a] :
( ( ( ord_less_eq_set_a @ SV109 @ SV220 )
= $true )
| ( ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV22 @ SV109 ) @ ( produc1450889781_set_a @ SV181 @ SV220 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1650]) ).
thf(1726,plain,
! [SV220: set_a,SV181: nat,SV109: set_a,SV22: nat] :
( ( ( ~ ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV22 @ SV109 ) @ ( produc1450889781_set_a @ SV181 @ SV220 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV22 @ SV181 )
= $false )
| ( ( ord_less_eq_set_a @ SV109 @ SV220 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1651]) ).
thf(1727,plain,
! [SV220: set_a,SV109: set_a,SV181: nat,SV22: nat] :
( ( ( ~ ~ ( ~ ( ord_less_eq_nat @ SV22 @ SV181 )
| ~ ( ord_less_eq_set_a @ SV109 @ SV220 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV22 @ SV181 )
= $false )
| ( ( ord_less_eq_set_a @ SV109 @ SV220 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1651]) ).
thf(1728,plain,
! [SV110: set_a,SV221: set_a] :
( ( ( ord_less_eq_set_a @ SV221 @ SV110 )
= $true )
| ( ( SV110 = SV221 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1652]) ).
thf(1729,plain,
! [SV221: set_a,SV110: set_a] :
( ( ( ord_less_eq_set_a @ SV110 @ SV221 )
= $true )
| ( ( SV110 = SV221 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1653]) ).
thf(1730,plain,
! [SV221: set_a,SV110: set_a] :
( ( ( SV110 != SV221 )
= $false )
| ( ( ord_less_eq_set_a @ SV221 @ SV110 )
= $false )
| ( ( ord_less_eq_set_a @ SV110 @ SV221 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1654]) ).
thf(1731,plain,
! [SV110: set_a,SV221: set_a] :
( ( ( ~ ~ ( ~ ( ord_less_eq_set_a @ SV221 @ SV110 )
| ~ ( ord_less_eq_set_a @ SV110 @ SV221 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV221 @ SV110 )
= $false )
| ( ( ord_less_eq_set_a @ SV110 @ SV221 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1654]) ).
thf(1732,plain,
! [SV222: set_a,SV111: set_a,SV183: set_a,SV24: set_a] :
( ( ( ord_less_eq_set_a @ SV24 @ SV183 )
= $true )
| ( ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV24 @ SV111 ) @ ( produc1928581911_set_a @ SV183 @ SV222 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1655]) ).
thf(1733,plain,
! [SV183: set_a,SV24: set_a,SV222: set_a,SV111: set_a] :
( ( ( ord_less_eq_set_a @ SV111 @ SV222 )
= $true )
| ( ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV24 @ SV111 ) @ ( produc1928581911_set_a @ SV183 @ SV222 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1656]) ).
thf(1734,plain,
! [SV222: set_a,SV183: set_a,SV111: set_a,SV24: set_a] :
( ( ( ~ ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV24 @ SV111 ) @ ( produc1928581911_set_a @ SV183 @ SV222 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV24 @ SV183 )
= $false )
| ( ( ord_less_eq_set_a @ SV111 @ SV222 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1657]) ).
thf(1735,plain,
! [SV222: set_a,SV111: set_a,SV183: set_a,SV24: set_a] :
( ( ( ~ ~ ( ~ ( ord_less_eq_set_a @ SV24 @ SV183 )
| ~ ( ord_less_eq_set_a @ SV111 @ SV222 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV24 @ SV183 )
= $false )
| ( ( ord_less_eq_set_a @ SV111 @ SV222 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1657]) ).
thf(1736,plain,
! [SV34: set_set_a,SV254: set_a] :
( ( ( ~ ( member_set_a @ SV254 @ SV34 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ ( sK11_SY329 @ SV34 ) @ SV254 )
| ( ( sK11_SY329 @ SV34 )
= SV254 ) )
= $true )
| ( ( SV34 = bot_bot_set_set_a )
= $true )
| ( ( finite_finite_set_a @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1658]) ).
thf(1737,plain,
! [SV223: nat,SV123: nat,SV187: set_a,SV38: set_a] :
( ( ( ord_less_eq_set_a @ SV38 @ SV187 )
= $true )
| ( ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV38 @ SV123 ) @ ( produc515611863_a_nat @ SV187 @ SV223 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1659]) ).
thf(1738,plain,
! [SV187: set_a,SV38: set_a,SV223: nat,SV123: nat] :
( ( ( ord_less_eq_nat @ SV123 @ SV223 )
= $true )
| ( ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV38 @ SV123 ) @ ( produc515611863_a_nat @ SV187 @ SV223 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1660]) ).
thf(1739,plain,
! [SV223: nat,SV187: set_a,SV123: nat,SV38: set_a] :
( ( ( ~ ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV38 @ SV123 ) @ ( produc515611863_a_nat @ SV187 @ SV223 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV38 @ SV187 )
= $false )
| ( ( ord_less_eq_nat @ SV123 @ SV223 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1661]) ).
thf(1740,plain,
! [SV223: nat,SV123: nat,SV187: set_a,SV38: set_a] :
( ( ( ~ ~ ( ~ ( ord_less_eq_set_a @ SV38 @ SV187 )
| ~ ( ord_less_eq_nat @ SV123 @ SV223 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV38 @ SV187 )
= $false )
| ( ( ord_less_eq_nat @ SV123 @ SV223 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1661]) ).
thf(1741,plain,
! [SV224: set_a,SV126: set_a,SV249: a] :
( ( ( member_a @ SV249 @ SV126 )
= $false )
| ( ( member_a @ SV249 @ SV224 )
= $true )
| ( ( ord_less_eq_set_a @ SV126 @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1662]) ).
thf(1742,plain,
! [SV224: set_a,SV126: set_a] :
( ( ( ord_less_eq_set_a @ SV126 @ SV224 )
= $true )
| ( ( member_a @ ( sK13_SY625 @ SV224 @ SV126 ) @ SV126 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1663]) ).
thf(1743,plain,
! [SV224: set_a,SV126: set_a] :
( ( ( ! [SY625: a] :
( ~ ( member_a @ SY625 @ SV126 )
| ( member_a @ SY625 @ SV224 ) ) )
= $true )
| ( ( member_a @ ( sK13_SY625 @ SV224 @ SV126 ) @ SV126 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1664]) ).
thf(1744,plain,
! [SV224: set_a,SV126: set_a,SV257: a] :
( ( ( ~ ( member_a @ SV257 @ SV126 )
| ( member_a @ SV257 @ SV224 ) )
= $true )
| ( ( member_a @ ( sK13_SY625 @ SV224 @ SV126 ) @ SV224 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1666]) ).
thf(1745,plain,
! [SV190: a,SV130: a,SV46: a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation ) ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV190 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV46 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV190 ) @ relation ) ) )
= $true )
| ( ( member_a @ SV130 @ carrier )
= $false )
| ( ( member_a @ SV46 @ carrier )
= $false )
| ( ( member_a @ SV190 @ carrier )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1667]) ).
thf(1746,plain,
! [SV192: a,SV133: a,SV50: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV50 @ SV133 ) @ relation ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV133 @ SV192 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV50 @ SV192 ) @ relation ) )
= $true )
| ( ( member_a @ SV133 @ carrier )
= $false )
| ( ( member_a @ SV50 @ carrier )
= $false )
| ( ( member_a @ SV192 @ carrier )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1668]) ).
thf(1747,plain,
! [SV195: set_a > nat,SV54: set_a,SV226: nat,SV136: set_a] :
( ( ( ord_less_eq_set_a @ ( sK15_SY585 @ SV136 @ SV226 @ SV54 @ SV195 ) @ ( sK27_SY655 @ SV195 @ SV54 @ SV226 @ SV136 ) )
= $true )
| ( ( ord_less_eq_nat @ ( SV195 @ SV54 ) @ SV226 )
= $true )
| ( ( ( SV195 @ SV136 )
= SV226 )
= $false )
| ( ( ord_less_eq_set_a @ SV54 @ SV136 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1669]) ).
thf(1748,plain,
! [SV227: set_a,SV138: set_a] :
( ( ( ord_less_eq_set_a @ SV138 @ SV227 )
= $true )
| ( ( SV138 = SV227 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1671]) ).
thf(1749,plain,
! [SV138: set_a,SV227: set_a] :
( ( ( ord_less_eq_set_a @ SV227 @ SV138 )
= $true )
| ( ( SV138 = SV227 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1672]) ).
thf(1750,plain,
! [SV227: set_a,SV138: set_a] :
( ( ( SV138 != SV227 )
= $false )
| ( ( ord_less_eq_set_a @ SV138 @ SV227 )
= $false )
| ( ( ord_less_eq_set_a @ SV227 @ SV138 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1673]) ).
thf(1751,plain,
! [SV227: set_a,SV138: set_a] :
( ( ( ~ ~ ( ~ ( ord_less_eq_set_a @ SV138 @ SV227 )
| ~ ( ord_less_eq_set_a @ SV227 @ SV138 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV138 @ SV227 )
= $false )
| ( ( ord_less_eq_set_a @ SV227 @ SV138 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1673]) ).
thf(1752,plain,
! [SV139: set_a > set_a,SV57: set_a,SV228: set_a,SV197: set_a] :
( ( ( ord_less_eq_set_a @ ( sK16_SY513 @ SV197 @ SV228 @ SV57 @ SV139 ) @ ( sK28_SY656 @ SV139 @ SV57 @ SV228 @ SV197 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV57 @ ( SV139 @ SV228 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV197 @ SV228 )
= $false )
| ( ( SV57
= ( SV139 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1674]) ).
thf(1753,plain,
! [SV62: set_set_a,SV143: set_a] :
( ( ( ~ ( member_set_a @ ( sK12_SY517 @ SV143 @ SV62 ) @ SV62 ) )
= $false )
| ( ( member_set_a @ SV143 @ SV62 )
= $false )
| ( ( finite_finite_set_a @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1676]) ).
thf(1754,plain,
! [SV62: set_set_a,SV143: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV143 @ ( sK12_SY517 @ SV143 @ SV62 ) ) )
= $false )
| ( ( member_set_a @ SV143 @ SV62 )
= $false )
| ( ( finite_finite_set_a @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1676]) ).
thf(1755,plain,
! [SV143: set_a,SV62: set_set_a,SV255: set_a] :
( ( ( ~ ( member_set_a @ SV255 @ SV62 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ ( sK12_SY517 @ SV143 @ SV62 ) @ SV255 )
| ( ( sK12_SY517 @ SV143 @ SV62 )
= SV255 ) )
= $true )
| ( ( member_set_a @ SV143 @ SV62 )
= $false )
| ( ( finite_finite_set_a @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1677]) ).
thf(1756,plain,
! [SV63: a,SV144: a] :
( ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
= $true )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( member_a @ SV144 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1678]) ).
thf(1757,plain,
! [SV144: a,SV63: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation ) )
= $true )
| ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) )
= $true )
| ( ( ~ ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( member_a @ SV144 @ carrier )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1679]) ).
thf(1758,plain,
! [SV230: set_a,SV145: set_a,SV250: a] :
( ( ( member_a @ SV250 @ SV145 )
= $false )
| ( ( member_a @ SV250 @ SV230 )
= $true )
| ( ( ord_less_eq_set_a @ SV145 @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1680]) ).
thf(1759,plain,
! [SV230: set_a,SV145: set_a] :
( ( ( ord_less_eq_set_a @ SV145 @ SV230 )
= $true )
| ( ( member_a @ ( sK14_SY630 @ SV230 @ SV145 ) @ SV145 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1681]) ).
thf(1760,plain,
! [SV230: set_a,SV145: set_a] :
( ( ( ! [SY630: a] :
( ~ ( member_a @ SY630 @ SV145 )
| ( member_a @ SY630 @ SV230 ) ) )
= $true )
| ( ( member_a @ ( sK14_SY630 @ SV230 @ SV145 ) @ SV145 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1682]) ).
thf(1761,plain,
! [SV230: set_a,SV145: set_a,SV258: a] :
( ( ( ~ ( member_a @ SV258 @ SV145 )
| ( member_a @ SV258 @ SV230 ) )
= $true )
| ( ( member_a @ ( sK14_SY630 @ SV230 @ SV145 ) @ SV230 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1684]) ).
thf(1762,plain,
! [SV201: set_a > nat,SV67: set_a,SV232: nat,SV148: set_a] :
( ( ( ord_less_eq_set_a @ ( sK17_SY594 @ SV148 @ SV232 @ SV67 @ SV201 ) @ ( sK29_SY657 @ SV201 @ SV67 @ SV232 @ SV148 ) )
= $true )
| ( ( ord_less_eq_nat @ ( SV201 @ SV67 ) @ SV232 )
= $true )
| ( ( ord_less_eq_nat @ ( SV201 @ SV148 ) @ SV232 )
= $false )
| ( ( ord_less_eq_set_a @ SV67 @ SV148 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1686]) ).
thf(1763,plain,
! [SV233: set_a,SV150: set_a] :
( ( ( ord_less_eq_set_a @ SV150 @ SV233 )
= $true )
| ( ( SV150 = SV233 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1688]) ).
thf(1764,plain,
! [SV150: set_a,SV233: set_a] :
( ( ( ord_less_eq_set_a @ SV233 @ SV150 )
= $true )
| ( ( SV150 = SV233 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1689]) ).
thf(1765,plain,
! [SV233: set_a,SV150: set_a] :
( ( ( SV150 != SV233 )
= $false )
| ( ( ord_less_eq_set_a @ SV150 @ SV233 )
= $false )
| ( ( ord_less_eq_set_a @ SV233 @ SV150 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1690]) ).
thf(1766,plain,
! [SV233: set_a,SV150: set_a] :
( ( ( ~ ~ ( ~ ( ord_less_eq_set_a @ SV150 @ SV233 )
| ~ ( ord_less_eq_set_a @ SV233 @ SV150 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV150 @ SV233 )
= $false )
| ( ( ord_less_eq_set_a @ SV233 @ SV150 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1690]) ).
thf(1767,plain,
! [SV203: set_a > set_a,SV70: set_a,SV234: set_a,SV151: set_a] :
( ( ( ord_less_eq_set_a @ ( sK18_SY597 @ SV151 @ SV234 @ SV70 @ SV203 ) @ ( sK30_SY658 @ SV203 @ SV70 @ SV234 @ SV151 ) )
= $true )
| ( ( ord_less_eq_set_a @ ( SV203 @ SV70 ) @ SV234 )
= $true )
| ( ( ord_less_eq_set_a @ ( SV203 @ SV151 ) @ SV234 )
= $false )
| ( ( ord_less_eq_set_a @ SV70 @ SV151 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1691]) ).
thf(1768,plain,
! [SV71: a,SV152: a] :
( ( ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) )
= $false )
| ( ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
| ~ ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1693]) ).
thf(1769,plain,
! [SV71: a,SV152: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
| ~ ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1694]) ).
thf(1770,plain,
! [SV156: set_a > nat,SV75: nat,SV237: set_a,SV207: set_a] :
( ( ( ord_less_eq_set_a @ ( sK19_SY540 @ SV207 @ SV237 @ SV75 @ SV156 ) @ ( sK31_SY659 @ SV156 @ SV75 @ SV237 @ SV207 ) )
= $true )
| ( ( ord_less_eq_nat @ SV75 @ ( SV156 @ SV237 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV207 @ SV237 )
= $false )
| ( ( SV75
= ( SV156 @ SV207 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1695]) ).
thf(1771,plain,
! [SV157: a > $o,SV256: a,SV76: a > $o] :
( ( ( ~ ( SV76 @ SV256 ) )
= $true )
| ( ( SV157 @ SV256 )
= $true )
| ( ( SV76 @ ( sK7_SY542 @ SV157 @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1697]) ).
thf(1772,plain,
! [SV157: a > $o,SV251: a,SV76: a > $o] :
( ( ( SV76 @ SV251 )
= $false )
| ( ( SV157 @ SV251 )
= $true )
| ( ( SV157 @ ( sK7_SY542 @ SV157 @ SV76 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1698]) ).
thf(1773,plain,
! [SV208: nat > set_a,SV80: nat,SV238: set_a,SV161: nat] :
( ( ( ord_less_eq_nat @ ( sK20_SY605 @ SV161 @ SV238 @ SV80 @ SV208 ) @ ( sK32_SY660 @ SV208 @ SV80 @ SV238 @ SV161 ) )
= $true )
| ( ( ord_less_eq_set_a @ ( SV208 @ SV80 ) @ SV238 )
= $true )
| ( ( ( SV208 @ SV161 )
= SV238 )
= $false )
| ( ( ord_less_eq_nat @ SV80 @ SV161 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1699]) ).
thf(1774,plain,
! [SV209: set_a > set_a,SV81: set_a,SV239: set_a,SV162: set_a] :
( ( ( ord_less_eq_set_a @ ( sK21_SY608 @ SV162 @ SV239 @ SV81 @ SV209 ) @ ( sK33_SY661 @ SV209 @ SV81 @ SV239 @ SV162 ) )
= $true )
| ( ( ord_less_eq_set_a @ ( SV209 @ SV81 ) @ SV239 )
= $true )
| ( ( ( SV209 @ SV162 )
= SV239 )
= $false )
| ( ( ord_less_eq_set_a @ SV81 @ SV162 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1701]) ).
thf(1775,plain,
! [SV163: nat,SV82: set_a] :
( ( ( finite_finite_a @ ( sK8_SY552 @ SV82 @ SV163 ) )
= $true )
| ( ( finite_finite_a @ SV82 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1703]) ).
thf(1776,plain,
! [SV163: nat,SV82: set_a] :
( ( ( ( finite_card_a @ ( sK8_SY552 @ SV82 @ SV163 ) )
= SV163 )
= $true )
| ( ( finite_finite_a @ SV82 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1704]) ).
thf(1777,plain,
! [SV83: a,SV210: a,SV164: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV210 ) @ relation )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV210 @ SV164 ) @ relation ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SV210 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV210 @ SV83 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SV164 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV83 ) @ relation )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1705]) ).
thf(1778,plain,
! [SV166: set_a > nat,SV85: nat,SV240: set_a,SV211: set_a] :
( ( ( ord_less_eq_set_a @ ( sK22_SY556 @ SV211 @ SV240 @ SV85 @ SV166 ) @ ( sK34_SY662 @ SV166 @ SV85 @ SV240 @ SV211 ) )
= $true )
| ( ( ord_less_eq_nat @ SV85 @ ( SV166 @ SV240 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV211 @ SV240 )
= $false )
| ( ( ord_less_eq_nat @ SV85 @ ( SV166 @ SV211 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1706]) ).
thf(1779,plain,
! [SV168: nat > set_a,SV87: set_a,SV241: nat,SV212: nat] :
( ( ( ord_less_eq_nat @ ( sK23_SY560 @ SV212 @ SV241 @ SV87 @ SV168 ) @ ( sK35_SY663 @ SV168 @ SV87 @ SV241 @ SV212 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV87 @ ( SV168 @ SV241 ) )
= $true )
| ( ( ord_less_eq_nat @ SV212 @ SV241 )
= $false )
| ( ( ord_less_eq_set_a @ SV87 @ ( SV168 @ SV212 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1708]) ).
thf(1780,plain,
! [SV213: nat > set_a,SV89: nat,SV242: set_a,SV170: nat] :
( ( ( ord_less_eq_nat @ ( sK24_SY617 @ SV170 @ SV242 @ SV89 @ SV213 ) @ ( sK36_SY664 @ SV213 @ SV89 @ SV242 @ SV170 ) )
= $true )
| ( ( ord_less_eq_set_a @ ( SV213 @ SV89 ) @ SV242 )
= $true )
| ( ( ord_less_eq_set_a @ ( SV213 @ SV170 ) @ SV242 )
= $false )
| ( ( ord_less_eq_nat @ SV89 @ SV170 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1710]) ).
thf(1781,plain,
! [SV172: set_a > set_a,SV91: set_a,SV243: set_a,SV215: set_a] :
( ( ( ord_less_eq_set_a @ ( sK25_SY569 @ SV215 @ SV243 @ SV91 @ SV172 ) @ ( sK37_SY665 @ SV172 @ SV91 @ SV243 @ SV215 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV91 @ ( SV172 @ SV243 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV215 @ SV243 )
= $false )
| ( ( ord_less_eq_set_a @ SV91 @ ( SV172 @ SV215 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1712]) ).
thf(1782,plain,
! [SV244: set_a,SV173: set_a] :
( ( ( ord_less_eq_set_a @ SV173 @ SV244 )
= $true )
| ( ( SV173 = SV244 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1714]) ).
thf(1783,plain,
! [SV173: set_a,SV244: set_a] :
( ( ( ord_less_eq_set_a @ SV244 @ SV173 )
= $true )
| ( ( SV173 = SV244 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1715]) ).
thf(1784,plain,
! [SV244: set_a,SV173: set_a] :
( ( ( SV173 != SV244 )
= $false )
| ( ( ord_less_eq_set_a @ SV173 @ SV244 )
= $false )
| ( ( ord_less_eq_set_a @ SV244 @ SV173 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1716]) ).
thf(1785,plain,
! [SV244: set_a,SV173: set_a] :
( ( ( ~ ~ ( ~ ( ord_less_eq_set_a @ SV173 @ SV244 )
| ~ ( ord_less_eq_set_a @ SV244 @ SV173 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV173 @ SV244 )
= $false )
| ( ( ord_less_eq_set_a @ SV244 @ SV173 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1716]) ).
thf(1786,plain,
! [SV174: nat > set_a,SV94: set_a,SV246: nat,SV217: nat] :
( ( ( ord_less_eq_nat @ ( sK26_SY575 @ SV217 @ SV246 @ SV94 @ SV174 ) @ ( sK38_SY666 @ SV174 @ SV94 @ SV246 @ SV217 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV94 @ ( SV174 @ SV246 ) )
= $true )
| ( ( ord_less_eq_nat @ SV217 @ SV246 )
= $false )
| ( ( SV94
= ( SV174 @ SV217 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1717]) ).
thf(1787,plain,
! [SV9: a,SV176: a,SV97: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV176 ) @ relation )
= $false )
| ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV97 ) @ relation ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV176 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV9 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV97 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV9 ) @ relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1719]) ).
thf(1788,plain,
! [SV13: set_set_a,SV252: set_a] :
( ( ( member_set_a @ SV252 @ SV13 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV252 @ ( sK9_SY294 @ SV13 ) )
| ( ( sK9_SY294 @ SV13 )
= SV252 ) )
= $true )
| ( ( SV13 = bot_bot_set_set_a )
= $true )
| ( ( finite_finite_set_a @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1720]) ).
thf(1789,plain,
! [SV16: set_set_a,SV103: set_a] :
( ( ( member_set_a @ ( sK10_SY475 @ SV103 @ SV16 ) @ SV16 )
= $true )
| ( ( member_set_a @ SV103 @ SV16 )
= $false )
| ( ( finite_finite_set_a @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1721]) ).
thf(1790,plain,
! [SV16: set_set_a,SV103: set_a] :
( ( ( ord_less_eq_set_a @ ( sK10_SY475 @ SV103 @ SV16 ) @ SV103 )
= $true )
| ( ( member_set_a @ SV103 @ SV16 )
= $false )
| ( ( finite_finite_set_a @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1722]) ).
thf(1791,plain,
! [SV103: set_a,SV16: set_set_a,SV253: set_a] :
( ( ( member_set_a @ SV253 @ SV16 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV253 @ ( sK10_SY475 @ SV103 @ SV16 ) )
| ( ( sK10_SY475 @ SV103 @ SV16 )
= SV253 ) )
= $true )
| ( ( member_set_a @ SV103 @ SV16 )
= $false )
| ( ( finite_finite_set_a @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1723]) ).
thf(1792,plain,
! [SV220: set_a,SV181: nat,SV109: set_a,SV22: nat] :
( ( ( ord_le841160035_set_a @ ( produc1450889781_set_a @ SV22 @ SV109 ) @ ( produc1450889781_set_a @ SV181 @ SV220 ) )
= $true )
| ( ( ord_less_eq_nat @ SV22 @ SV181 )
= $false )
| ( ( ord_less_eq_set_a @ SV109 @ SV220 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1726]) ).
thf(1793,plain,
! [SV220: set_a,SV109: set_a,SV181: nat,SV22: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV22 @ SV181 )
| ~ ( ord_less_eq_set_a @ SV109 @ SV220 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV22 @ SV181 )
= $false )
| ( ( ord_less_eq_set_a @ SV109 @ SV220 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1727]) ).
thf(1794,plain,
! [SV221: set_a,SV110: set_a] :
( ( ( SV110 = SV221 )
= $true )
| ( ( ord_less_eq_set_a @ SV221 @ SV110 )
= $false )
| ( ( ord_less_eq_set_a @ SV110 @ SV221 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1730]) ).
thf(1795,plain,
! [SV110: set_a,SV221: set_a] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ SV221 @ SV110 )
| ~ ( ord_less_eq_set_a @ SV110 @ SV221 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV221 @ SV110 )
= $false )
| ( ( ord_less_eq_set_a @ SV110 @ SV221 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1731]) ).
thf(1796,plain,
! [SV222: set_a,SV183: set_a,SV111: set_a,SV24: set_a] :
( ( ( ord_le486764743_set_a @ ( produc1928581911_set_a @ SV24 @ SV111 ) @ ( produc1928581911_set_a @ SV183 @ SV222 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV24 @ SV183 )
= $false )
| ( ( ord_less_eq_set_a @ SV111 @ SV222 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1734]) ).
thf(1797,plain,
! [SV222: set_a,SV111: set_a,SV183: set_a,SV24: set_a] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ SV24 @ SV183 )
| ~ ( ord_less_eq_set_a @ SV111 @ SV222 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV24 @ SV183 )
= $false )
| ( ( ord_less_eq_set_a @ SV111 @ SV222 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1735]) ).
thf(1798,plain,
! [SV34: set_set_a,SV254: set_a] :
( ( ( member_set_a @ SV254 @ SV34 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ ( sK11_SY329 @ SV34 ) @ SV254 )
| ( ( sK11_SY329 @ SV34 )
= SV254 ) )
= $true )
| ( ( SV34 = bot_bot_set_set_a )
= $true )
| ( ( finite_finite_set_a @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1736]) ).
thf(1799,plain,
! [SV223: nat,SV187: set_a,SV123: nat,SV38: set_a] :
( ( ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ SV38 @ SV123 ) @ ( produc515611863_a_nat @ SV187 @ SV223 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV38 @ SV187 )
= $false )
| ( ( ord_less_eq_nat @ SV123 @ SV223 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1739]) ).
thf(1800,plain,
! [SV223: nat,SV123: nat,SV187: set_a,SV38: set_a] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ SV38 @ SV187 )
| ~ ( ord_less_eq_nat @ SV123 @ SV223 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV38 @ SV187 )
= $false )
| ( ( ord_less_eq_nat @ SV123 @ SV223 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1740]) ).
thf(1801,plain,
! [SV224: set_a,SV126: set_a,SV259: a] :
( ( ( ~ ( member_a @ SV259 @ SV126 )
| ( member_a @ SV259 @ SV224 ) )
= $true )
| ( ( member_a @ ( sK13_SY625 @ SV224 @ SV126 ) @ SV126 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1743]) ).
thf(1802,plain,
! [SV224: set_a,SV126: set_a,SV257: a] :
( ( ( ~ ( member_a @ SV257 @ SV126 ) )
= $true )
| ( ( member_a @ SV257 @ SV224 )
= $true )
| ( ( member_a @ ( sK13_SY625 @ SV224 @ SV126 ) @ SV224 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1744]) ).
thf(1803,plain,
! [SV190: a,SV130: a,SV46: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation ) ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV190 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV46 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV190 ) @ relation ) ) )
= $true )
| ( ( member_a @ SV130 @ carrier )
= $false )
| ( ( member_a @ SV46 @ carrier )
= $false )
| ( ( member_a @ SV190 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1745]) ).
thf(1804,plain,
! [SV192: a,SV133: a,SV50: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV50 @ SV133 ) @ relation )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV133 @ SV192 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV50 @ SV192 ) @ relation ) )
= $true )
| ( ( member_a @ SV133 @ carrier )
= $false )
| ( ( member_a @ SV50 @ carrier )
= $false )
| ( ( member_a @ SV192 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1746]) ).
thf(1805,plain,
! [SV227: set_a,SV138: set_a] :
( ( ( SV138 = SV227 )
= $true )
| ( ( ord_less_eq_set_a @ SV138 @ SV227 )
= $false )
| ( ( ord_less_eq_set_a @ SV227 @ SV138 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1750]) ).
thf(1806,plain,
! [SV227: set_a,SV138: set_a] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ SV138 @ SV227 )
| ~ ( ord_less_eq_set_a @ SV227 @ SV138 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV138 @ SV227 )
= $false )
| ( ( ord_less_eq_set_a @ SV227 @ SV138 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1751]) ).
thf(1807,plain,
! [SV62: set_set_a,SV143: set_a] :
( ( ( member_set_a @ ( sK12_SY517 @ SV143 @ SV62 ) @ SV62 )
= $true )
| ( ( member_set_a @ SV143 @ SV62 )
= $false )
| ( ( finite_finite_set_a @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1753]) ).
thf(1808,plain,
! [SV62: set_set_a,SV143: set_a] :
( ( ( ord_less_eq_set_a @ SV143 @ ( sK12_SY517 @ SV143 @ SV62 ) )
= $true )
| ( ( member_set_a @ SV143 @ SV62 )
= $false )
| ( ( finite_finite_set_a @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1754]) ).
thf(1809,plain,
! [SV143: set_a,SV62: set_set_a,SV255: set_a] :
( ( ( member_set_a @ SV255 @ SV62 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ ( sK12_SY517 @ SV143 @ SV62 ) @ SV255 )
| ( ( sK12_SY517 @ SV143 @ SV62 )
= SV255 ) )
= $true )
| ( ( member_set_a @ SV143 @ SV62 )
= $false )
| ( ( finite_finite_set_a @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1755]) ).
thf(1810,plain,
! [SV63: a,SV144: a] :
( ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
= $true )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( member_a @ SV144 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1756]) ).
thf(1811,plain,
! [SV144: a,SV63: a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
= $true )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( member_a @ SV144 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1756]) ).
thf(1812,plain,
! [SV144: a,SV63: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
= $false )
| ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) )
= $true )
| ( ( ~ ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( member_a @ SV144 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1757]) ).
thf(1813,plain,
! [SV230: set_a,SV145: set_a,SV260: a] :
( ( ( ~ ( member_a @ SV260 @ SV145 )
| ( member_a @ SV260 @ SV230 ) )
= $true )
| ( ( member_a @ ( sK14_SY630 @ SV230 @ SV145 ) @ SV145 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1760]) ).
thf(1814,plain,
! [SV230: set_a,SV145: set_a,SV258: a] :
( ( ( ~ ( member_a @ SV258 @ SV145 ) )
= $true )
| ( ( member_a @ SV258 @ SV230 )
= $true )
| ( ( member_a @ ( sK14_SY630 @ SV230 @ SV145 ) @ SV230 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1761]) ).
thf(1815,plain,
! [SV233: set_a,SV150: set_a] :
( ( ( SV150 = SV233 )
= $true )
| ( ( ord_less_eq_set_a @ SV150 @ SV233 )
= $false )
| ( ( ord_less_eq_set_a @ SV233 @ SV150 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1765]) ).
thf(1816,plain,
! [SV233: set_a,SV150: set_a] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ SV150 @ SV233 )
| ~ ( ord_less_eq_set_a @ SV233 @ SV150 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV150 @ SV233 )
= $false )
| ( ( ord_less_eq_set_a @ SV233 @ SV150 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1766]) ).
thf(1817,plain,
! [SV152: a,SV71: a] :
( ( ( ~ ~ ( ~ ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
| ~ ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation ) ) )
= $false )
| ( ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
= $false )
| ( ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) )
= $false )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1768]) ).
thf(1818,plain,
! [SV152: a,SV71: a] :
( ( ( ~ ~ ( ~ ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
| ~ ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation )
= $false )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1769]) ).
thf(1819,plain,
! [SV157: a > $o,SV256: a,SV76: a > $o] :
( ( ( SV76 @ SV256 )
= $false )
| ( ( SV157 @ SV256 )
= $true )
| ( ( SV76 @ ( sK7_SY542 @ SV157 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1771]) ).
thf(1820,plain,
! [SV83: a,SV164: a,SV210: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV210 @ SV164 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV210 ) @ relation )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SV210 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV210 @ SV83 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SV164 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV83 ) @ relation )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1777]) ).
thf(1821,plain,
! [SV244: set_a,SV173: set_a] :
( ( ( SV173 = SV244 )
= $true )
| ( ( ord_less_eq_set_a @ SV173 @ SV244 )
= $false )
| ( ( ord_less_eq_set_a @ SV244 @ SV173 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1784]) ).
thf(1822,plain,
! [SV244: set_a,SV173: set_a] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ SV173 @ SV244 )
| ~ ( ord_less_eq_set_a @ SV244 @ SV173 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV173 @ SV244 )
= $false )
| ( ( ord_less_eq_set_a @ SV244 @ SV173 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1785]) ).
thf(1823,plain,
! [SV9: a,SV97: a,SV176: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV97 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV176 ) @ relation )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV176 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV9 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV97 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV9 ) @ relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1787]) ).
thf(1824,plain,
! [SV13: set_set_a,SV252: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV252 @ ( sK9_SY294 @ SV13 ) ) )
= $true )
| ( ( ( sK9_SY294 @ SV13 )
= SV252 )
= $true )
| ( ( member_set_a @ SV252 @ SV13 )
= $false )
| ( ( SV13 = bot_bot_set_set_a )
= $true )
| ( ( finite_finite_set_a @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1788]) ).
thf(1825,plain,
! [SV16: set_set_a,SV103: set_a,SV253: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV253 @ ( sK10_SY475 @ SV103 @ SV16 ) ) )
= $true )
| ( ( ( sK10_SY475 @ SV103 @ SV16 )
= SV253 )
= $true )
| ( ( member_set_a @ SV253 @ SV16 )
= $false )
| ( ( member_set_a @ SV103 @ SV16 )
= $false )
| ( ( finite_finite_set_a @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1791]) ).
thf(1826,plain,
! [SV220: set_a,SV109: set_a,SV181: nat,SV22: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV22 @ SV181 )
| ~ ( ord_less_eq_set_a @ SV109 @ SV220 ) )
= $false )
| ( ( ord_less_eq_nat @ SV22 @ SV181 )
= $false )
| ( ( ord_less_eq_set_a @ SV109 @ SV220 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1793]) ).
thf(1827,plain,
! [SV110: set_a,SV221: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV221 @ SV110 )
| ~ ( ord_less_eq_set_a @ SV110 @ SV221 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV221 @ SV110 )
= $false )
| ( ( ord_less_eq_set_a @ SV110 @ SV221 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1795]) ).
thf(1828,plain,
! [SV222: set_a,SV111: set_a,SV183: set_a,SV24: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV24 @ SV183 )
| ~ ( ord_less_eq_set_a @ SV111 @ SV222 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV24 @ SV183 )
= $false )
| ( ( ord_less_eq_set_a @ SV111 @ SV222 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1797]) ).
thf(1829,plain,
! [SV254: set_a,SV34: set_set_a] :
( ( ( ~ ( ord_less_eq_set_a @ ( sK11_SY329 @ SV34 ) @ SV254 ) )
= $true )
| ( ( ( sK11_SY329 @ SV34 )
= SV254 )
= $true )
| ( ( member_set_a @ SV254 @ SV34 )
= $false )
| ( ( SV34 = bot_bot_set_set_a )
= $true )
| ( ( finite_finite_set_a @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1798]) ).
thf(1830,plain,
! [SV223: nat,SV123: nat,SV187: set_a,SV38: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV38 @ SV187 )
| ~ ( ord_less_eq_nat @ SV123 @ SV223 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV38 @ SV187 )
= $false )
| ( ( ord_less_eq_nat @ SV123 @ SV223 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1800]) ).
thf(1831,plain,
! [SV224: set_a,SV126: set_a,SV259: a] :
( ( ( ~ ( member_a @ SV259 @ SV126 ) )
= $true )
| ( ( member_a @ SV259 @ SV224 )
= $true )
| ( ( member_a @ ( sK13_SY625 @ SV224 @ SV126 ) @ SV126 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1801]) ).
thf(1832,plain,
! [SV224: set_a,SV126: set_a,SV257: a] :
( ( ( member_a @ SV257 @ SV126 )
= $false )
| ( ( member_a @ SV257 @ SV224 )
= $true )
| ( ( member_a @ ( sK13_SY625 @ SV224 @ SV126 ) @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1802]) ).
thf(1833,plain,
! [SV190: a,SV130: a,SV46: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV190 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV46 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV190 ) @ relation ) ) )
= $true )
| ( ( member_a @ SV130 @ carrier )
= $false )
| ( ( member_a @ SV46 @ carrier )
= $false )
| ( ( member_a @ SV190 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1803]) ).
thf(1834,plain,
! [SV50: a,SV192: a,SV133: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV133 @ SV192 ) @ relation ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV50 @ SV192 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV50 @ SV133 ) @ relation )
= $false )
| ( ( member_a @ SV133 @ carrier )
= $false )
| ( ( member_a @ SV50 @ carrier )
= $false )
| ( ( member_a @ SV192 @ carrier )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1804]) ).
thf(1835,plain,
! [SV227: set_a,SV138: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV138 @ SV227 )
| ~ ( ord_less_eq_set_a @ SV227 @ SV138 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV138 @ SV227 )
= $false )
| ( ( ord_less_eq_set_a @ SV227 @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1806]) ).
thf(1836,plain,
! [SV255: set_a,SV62: set_set_a,SV143: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ ( sK12_SY517 @ SV143 @ SV62 ) @ SV255 ) )
= $true )
| ( ( ( sK12_SY517 @ SV143 @ SV62 )
= SV255 )
= $true )
| ( ( member_set_a @ SV255 @ SV62 )
= $false )
| ( ( member_set_a @ SV143 @ SV62 )
= $false )
| ( ( finite_finite_set_a @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1809]) ).
thf(1837,plain,
! [SV63: a,SV144: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
= $true )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( member_a @ SV144 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1810]) ).
thf(1838,plain,
! [SV144: a,SV63: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
= $true )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( member_a @ SV144 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1811]) ).
thf(1839,plain,
! [SV63: a,SV144: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
= $false )
| ( ( ~ ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( member_a @ SV144 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1812]) ).
thf(1840,plain,
! [SV230: set_a,SV145: set_a,SV260: a] :
( ( ( ~ ( member_a @ SV260 @ SV145 ) )
= $true )
| ( ( member_a @ SV260 @ SV230 )
= $true )
| ( ( member_a @ ( sK14_SY630 @ SV230 @ SV145 ) @ SV145 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1813]) ).
thf(1841,plain,
! [SV230: set_a,SV145: set_a,SV258: a] :
( ( ( member_a @ SV258 @ SV145 )
= $false )
| ( ( member_a @ SV258 @ SV230 )
= $true )
| ( ( member_a @ ( sK14_SY630 @ SV230 @ SV145 ) @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1814]) ).
thf(1842,plain,
! [SV233: set_a,SV150: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV150 @ SV233 )
| ~ ( ord_less_eq_set_a @ SV233 @ SV150 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV150 @ SV233 )
= $false )
| ( ( ord_less_eq_set_a @ SV233 @ SV150 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1816]) ).
thf(1843,plain,
! [SV152: a,SV71: a] :
( ( ( ~ ~ ( ~ ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
| ~ ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) ) )
= $false )
| ( ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
= $false )
| ( ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) )
= $false )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1817]) ).
thf(1844,plain,
! [SV152: a,SV71: a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation ) ) )
= $false )
| ( ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
= $false )
| ( ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) )
= $false )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1817]) ).
thf(1845,plain,
! [SV152: a,SV71: a] :
( ( ( ~ ~ ( ~ ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
| ~ ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation )
= $false )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1818]) ).
thf(1846,plain,
! [SV152: a,SV71: a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation )
= $false )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1818]) ).
thf(1847,plain,
! [SV164: a,SV210: a,SV83: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SV210 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV210 @ SV83 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV210 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV210 @ SV164 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SV164 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV83 ) @ relation )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1820]) ).
thf(1848,plain,
! [SV244: set_a,SV173: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV173 @ SV244 )
| ~ ( ord_less_eq_set_a @ SV244 @ SV173 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV173 @ SV244 )
= $false )
| ( ( ord_less_eq_set_a @ SV244 @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1822]) ).
thf(1849,plain,
! [SV9: a,SV97: a,SV176: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV97 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV176 ) @ relation )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV176 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV9 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV97 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV9 ) @ relation )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1823]) ).
thf(1850,plain,
! [SV13: set_set_a,SV252: set_a] :
( ( ( ord_less_eq_set_a @ SV252 @ ( sK9_SY294 @ SV13 ) )
= $false )
| ( ( ( sK9_SY294 @ SV13 )
= SV252 )
= $true )
| ( ( member_set_a @ SV252 @ SV13 )
= $false )
| ( ( SV13 = bot_bot_set_set_a )
= $true )
| ( ( finite_finite_set_a @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1824]) ).
thf(1851,plain,
! [SV16: set_set_a,SV103: set_a,SV253: set_a] :
( ( ( ord_less_eq_set_a @ SV253 @ ( sK10_SY475 @ SV103 @ SV16 ) )
= $false )
| ( ( ( sK10_SY475 @ SV103 @ SV16 )
= SV253 )
= $true )
| ( ( member_set_a @ SV253 @ SV16 )
= $false )
| ( ( member_set_a @ SV103 @ SV16 )
= $false )
| ( ( finite_finite_set_a @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1825]) ).
thf(1852,plain,
! [SV220: set_a,SV109: set_a,SV181: nat,SV22: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV22 @ SV181 ) )
= $false )
| ( ( ord_less_eq_nat @ SV22 @ SV181 )
= $false )
| ( ( ord_less_eq_set_a @ SV109 @ SV220 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1826]) ).
thf(1853,plain,
! [SV181: nat,SV22: nat,SV220: set_a,SV109: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV109 @ SV220 ) )
= $false )
| ( ( ord_less_eq_nat @ SV22 @ SV181 )
= $false )
| ( ( ord_less_eq_set_a @ SV109 @ SV220 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1826]) ).
thf(1854,plain,
! [SV110: set_a,SV221: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV221 @ SV110 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV221 @ SV110 )
= $false )
| ( ( ord_less_eq_set_a @ SV110 @ SV221 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1827]) ).
thf(1855,plain,
! [SV221: set_a,SV110: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV110 @ SV221 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV221 @ SV110 )
= $false )
| ( ( ord_less_eq_set_a @ SV110 @ SV221 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1827]) ).
thf(1856,plain,
! [SV222: set_a,SV111: set_a,SV183: set_a,SV24: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV24 @ SV183 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV24 @ SV183 )
= $false )
| ( ( ord_less_eq_set_a @ SV111 @ SV222 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1828]) ).
thf(1857,plain,
! [SV183: set_a,SV24: set_a,SV222: set_a,SV111: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV111 @ SV222 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV24 @ SV183 )
= $false )
| ( ( ord_less_eq_set_a @ SV111 @ SV222 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1828]) ).
thf(1858,plain,
! [SV254: set_a,SV34: set_set_a] :
( ( ( ord_less_eq_set_a @ ( sK11_SY329 @ SV34 ) @ SV254 )
= $false )
| ( ( ( sK11_SY329 @ SV34 )
= SV254 )
= $true )
| ( ( member_set_a @ SV254 @ SV34 )
= $false )
| ( ( SV34 = bot_bot_set_set_a )
= $true )
| ( ( finite_finite_set_a @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1829]) ).
thf(1859,plain,
! [SV223: nat,SV123: nat,SV187: set_a,SV38: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV38 @ SV187 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV38 @ SV187 )
= $false )
| ( ( ord_less_eq_nat @ SV123 @ SV223 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1830]) ).
thf(1860,plain,
! [SV187: set_a,SV38: set_a,SV223: nat,SV123: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV123 @ SV223 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV38 @ SV187 )
= $false )
| ( ( ord_less_eq_nat @ SV123 @ SV223 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1830]) ).
thf(1861,plain,
! [SV224: set_a,SV126: set_a,SV259: a] :
( ( ( member_a @ SV259 @ SV126 )
= $false )
| ( ( member_a @ SV259 @ SV224 )
= $true )
| ( ( member_a @ ( sK13_SY625 @ SV224 @ SV126 ) @ SV126 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1831]) ).
thf(1862,plain,
! [SV190: a,SV130: a,SV46: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation ) )
= $true )
| ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV190 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV46 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV190 ) @ relation ) ) )
= $true )
| ( ( member_a @ SV130 @ carrier )
= $false )
| ( ( member_a @ SV46 @ carrier )
= $false )
| ( ( member_a @ SV190 @ carrier )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1833]) ).
thf(1863,plain,
! [SV50: a,SV192: a,SV133: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV133 @ SV192 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV50 @ SV192 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV50 @ SV133 ) @ relation )
= $false )
| ( ( member_a @ SV133 @ carrier )
= $false )
| ( ( member_a @ SV50 @ carrier )
= $false )
| ( ( member_a @ SV192 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1834]) ).
thf(1864,plain,
! [SV227: set_a,SV138: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV138 @ SV227 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV138 @ SV227 )
= $false )
| ( ( ord_less_eq_set_a @ SV227 @ SV138 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1835]) ).
thf(1865,plain,
! [SV138: set_a,SV227: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV227 @ SV138 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV138 @ SV227 )
= $false )
| ( ( ord_less_eq_set_a @ SV227 @ SV138 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1835]) ).
thf(1866,plain,
! [SV255: set_a,SV62: set_set_a,SV143: set_a] :
( ( ( ord_less_eq_set_a @ ( sK12_SY517 @ SV143 @ SV62 ) @ SV255 )
= $false )
| ( ( ( sK12_SY517 @ SV143 @ SV62 )
= SV255 )
= $true )
| ( ( member_set_a @ SV255 @ SV62 )
= $false )
| ( ( member_set_a @ SV143 @ SV62 )
= $false )
| ( ( finite_finite_set_a @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1836]) ).
thf(1867,plain,
! [SV63: a,SV144: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
= $true )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( member_a @ SV144 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1837]) ).
thf(1868,plain,
! [SV144: a,SV63: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
= $true )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( member_a @ SV144 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1838]) ).
thf(1869,plain,
! [SV63: a,SV144: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
= $false )
| ( ( ~ ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( member_a @ SV144 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1839]) ).
thf(1870,plain,
! [SV230: set_a,SV145: set_a,SV260: a] :
( ( ( member_a @ SV260 @ SV145 )
= $false )
| ( ( member_a @ SV260 @ SV230 )
= $true )
| ( ( member_a @ ( sK14_SY630 @ SV230 @ SV145 ) @ SV145 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1840]) ).
thf(1871,plain,
! [SV233: set_a,SV150: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV150 @ SV233 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV150 @ SV233 )
= $false )
| ( ( ord_less_eq_set_a @ SV233 @ SV150 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1842]) ).
thf(1872,plain,
! [SV150: set_a,SV233: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV233 @ SV150 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV150 @ SV233 )
= $false )
| ( ( ord_less_eq_set_a @ SV233 @ SV150 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1842]) ).
thf(1873,plain,
! [SV152: a,SV71: a] :
( ( ( ~ ( ~ ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
| ~ ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) ) )
= $true )
| ( ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
= $false )
| ( ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) )
= $false )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1843]) ).
thf(1874,plain,
! [SV152: a,SV71: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation ) ) )
= $true )
| ( ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
= $false )
| ( ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) )
= $false )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1844]) ).
thf(1875,plain,
! [SV152: a,SV71: a] :
( ( ( ~ ( ~ ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
| ~ ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation )
= $false )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1845]) ).
thf(1876,plain,
! [SV152: a,SV71: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation )
= $false )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1846]) ).
thf(1877,plain,
! [SV164: a,SV210: a,SV83: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SV210 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV210 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV210 @ SV164 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SV164 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV83 ) @ relation )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1847]) ).
thf(1878,plain,
! [SV164: a,SV83: a,SV210: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV210 @ SV83 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV210 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV210 @ SV164 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SV164 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV83 ) @ relation )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1847]) ).
thf(1879,plain,
! [SV244: set_a,SV173: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV173 @ SV244 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV173 @ SV244 )
= $false )
| ( ( ord_less_eq_set_a @ SV244 @ SV173 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1848]) ).
thf(1880,plain,
! [SV173: set_a,SV244: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV244 @ SV173 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV173 @ SV244 )
= $false )
| ( ( ord_less_eq_set_a @ SV244 @ SV173 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1848]) ).
thf(1881,plain,
! [SV97: a,SV176: a,SV9: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV176 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV9 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV176 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV97 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV97 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV9 ) @ relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1849]) ).
thf(1882,plain,
! [SV220: set_a,SV109: set_a,SV181: nat,SV22: nat] :
( ( ( ord_less_eq_nat @ SV22 @ SV181 )
= $true )
| ( ( ord_less_eq_nat @ SV22 @ SV181 )
= $false )
| ( ( ord_less_eq_set_a @ SV109 @ SV220 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1852]) ).
thf(1883,plain,
! [SV181: nat,SV22: nat,SV220: set_a,SV109: set_a] :
( ( ( ord_less_eq_set_a @ SV109 @ SV220 )
= $true )
| ( ( ord_less_eq_nat @ SV22 @ SV181 )
= $false )
| ( ( ord_less_eq_set_a @ SV109 @ SV220 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1853]) ).
thf(1884,plain,
! [SV110: set_a,SV221: set_a] :
( ( ( ord_less_eq_set_a @ SV221 @ SV110 )
= $true )
| ( ( ord_less_eq_set_a @ SV221 @ SV110 )
= $false )
| ( ( ord_less_eq_set_a @ SV110 @ SV221 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1854]) ).
thf(1885,plain,
! [SV221: set_a,SV110: set_a] :
( ( ( ord_less_eq_set_a @ SV110 @ SV221 )
= $true )
| ( ( ord_less_eq_set_a @ SV221 @ SV110 )
= $false )
| ( ( ord_less_eq_set_a @ SV110 @ SV221 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1855]) ).
thf(1886,plain,
! [SV222: set_a,SV111: set_a,SV183: set_a,SV24: set_a] :
( ( ( ord_less_eq_set_a @ SV24 @ SV183 )
= $true )
| ( ( ord_less_eq_set_a @ SV24 @ SV183 )
= $false )
| ( ( ord_less_eq_set_a @ SV111 @ SV222 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1856]) ).
thf(1887,plain,
! [SV183: set_a,SV24: set_a,SV222: set_a,SV111: set_a] :
( ( ( ord_less_eq_set_a @ SV111 @ SV222 )
= $true )
| ( ( ord_less_eq_set_a @ SV24 @ SV183 )
= $false )
| ( ( ord_less_eq_set_a @ SV111 @ SV222 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1857]) ).
thf(1888,plain,
! [SV223: nat,SV123: nat,SV187: set_a,SV38: set_a] :
( ( ( ord_less_eq_set_a @ SV38 @ SV187 )
= $true )
| ( ( ord_less_eq_set_a @ SV38 @ SV187 )
= $false )
| ( ( ord_less_eq_nat @ SV123 @ SV223 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1859]) ).
thf(1889,plain,
! [SV187: set_a,SV38: set_a,SV223: nat,SV123: nat] :
( ( ( ord_less_eq_nat @ SV123 @ SV223 )
= $true )
| ( ( ord_less_eq_set_a @ SV38 @ SV187 )
= $false )
| ( ( ord_less_eq_nat @ SV123 @ SV223 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1860]) ).
thf(1890,plain,
! [SV190: a,SV130: a,SV46: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
= $false )
| ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV190 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV46 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV190 ) @ relation ) ) )
= $true )
| ( ( member_a @ SV130 @ carrier )
= $false )
| ( ( member_a @ SV46 @ carrier )
= $false )
| ( ( member_a @ SV190 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1862]) ).
thf(1891,plain,
! [SV227: set_a,SV138: set_a] :
( ( ( ord_less_eq_set_a @ SV138 @ SV227 )
= $true )
| ( ( ord_less_eq_set_a @ SV138 @ SV227 )
= $false )
| ( ( ord_less_eq_set_a @ SV227 @ SV138 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1864]) ).
thf(1892,plain,
! [SV138: set_a,SV227: set_a] :
( ( ( ord_less_eq_set_a @ SV227 @ SV138 )
= $true )
| ( ( ord_less_eq_set_a @ SV138 @ SV227 )
= $false )
| ( ( ord_less_eq_set_a @ SV227 @ SV138 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1865]) ).
thf(1893,plain,
! [SV144: a,SV63: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
= $true )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( member_a @ SV144 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1868]) ).
thf(1894,plain,
! [SV63: a,SV144: a] :
( ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
= $true )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( member_a @ SV144 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1868]) ).
thf(1895,plain,
! [SV63: a,SV144: a] :
( ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
= $true )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( member_a @ SV144 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1869]) ).
thf(1896,plain,
! [SV233: set_a,SV150: set_a] :
( ( ( ord_less_eq_set_a @ SV150 @ SV233 )
= $true )
| ( ( ord_less_eq_set_a @ SV150 @ SV233 )
= $false )
| ( ( ord_less_eq_set_a @ SV233 @ SV150 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1871]) ).
thf(1897,plain,
! [SV150: set_a,SV233: set_a] :
( ( ( ord_less_eq_set_a @ SV233 @ SV150 )
= $true )
| ( ( ord_less_eq_set_a @ SV150 @ SV233 )
= $false )
| ( ( ord_less_eq_set_a @ SV233 @ SV150 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1872]) ).
thf(1898,plain,
! [SV152: a,SV71: a] :
( ( ( ~ ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
| ~ ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) )
= $false )
| ( ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
= $false )
| ( ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) )
= $false )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1873]) ).
thf(1899,plain,
! [SV152: a,SV71: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation ) )
= $false )
| ( ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
= $false )
| ( ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) )
= $false )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1874]) ).
thf(1900,plain,
! [SV152: a,SV71: a] :
( ( ( ~ ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
| ~ ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation )
= $false )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1875]) ).
thf(1901,plain,
! [SV152: a,SV71: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation )
= $false )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1876]) ).
thf(1902,plain,
! [SV164: a,SV210: a,SV83: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SV210 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV210 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV210 @ SV164 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SV164 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV83 ) @ relation )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1877]) ).
thf(1903,plain,
! [SV164: a,SV83: a,SV210: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV210 @ SV83 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV210 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV210 @ SV164 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV83 @ SV164 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV164 @ SV83 ) @ relation )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1878]) ).
thf(1904,plain,
! [SV244: set_a,SV173: set_a] :
( ( ( ord_less_eq_set_a @ SV173 @ SV244 )
= $true )
| ( ( ord_less_eq_set_a @ SV173 @ SV244 )
= $false )
| ( ( ord_less_eq_set_a @ SV244 @ SV173 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1879]) ).
thf(1905,plain,
! [SV173: set_a,SV244: set_a] :
( ( ( ord_less_eq_set_a @ SV244 @ SV173 )
= $true )
| ( ( ord_less_eq_set_a @ SV173 @ SV244 )
= $false )
| ( ( ord_less_eq_set_a @ SV244 @ SV173 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1880]) ).
thf(1906,plain,
! [SV97: a,SV176: a,SV9: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV176 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV176 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV97 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV97 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV9 ) @ relation )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1881]) ).
thf(1907,plain,
! [SV97: a,SV9: a,SV176: a] :
( ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV9 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV176 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV97 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV97 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV9 ) @ relation )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1881]) ).
thf(1908,plain,
! [SV190: a,SV46: a,SV130: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV190 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV46 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV190 ) @ relation ) ) )
= $true )
| ( ( member_a @ SV130 @ carrier )
= $false )
| ( ( member_a @ SV46 @ carrier )
= $false )
| ( ( member_a @ SV190 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1890]) ).
thf(1909,plain,
! [SV144: a,SV63: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
= $true )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( member_a @ SV144 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1893]) ).
thf(1910,plain,
! [SV63: a,SV144: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
= $true )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( member_a @ SV144 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1894]) ).
thf(1911,plain,
! [SV63: a,SV144: a] :
( ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
= $true )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( member_a @ SV144 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1895]) ).
thf(1912,plain,
! [SV144: a,SV63: a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
= $true )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( member_a @ SV144 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1895]) ).
thf(1913,plain,
! [SV152: a,SV71: a] :
( ( ( ~ ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) ) )
= $false )
| ( ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
= $false )
| ( ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) )
= $false )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1898]) ).
thf(1914,plain,
! [SV71: a,SV152: a] :
( ( ( ~ ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) )
= $false )
| ( ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
= $false )
| ( ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) )
= $false )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1898]) ).
thf(1915,plain,
! [SV152: a,SV71: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation ) )
= $false )
| ( ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
= $false )
| ( ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) )
= $false )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1899]) ).
thf(1916,plain,
! [SV71: a,SV152: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation ) )
= $false )
| ( ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
= $false )
| ( ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) )
= $false )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1899]) ).
thf(1917,plain,
! [SV152: a,SV71: a] :
( ( ( ~ ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation )
= $false )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1900]) ).
thf(1918,plain,
! [SV71: a,SV152: a] :
( ( ( ~ ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation )
= $false )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1900]) ).
thf(1919,plain,
! [SV152: a,SV71: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation )
= $false )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1901]) ).
thf(1920,plain,
! [SV71: a,SV152: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation )
= $false )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1901]) ).
thf(1921,plain,
! [SV97: a,SV176: a,SV9: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV176 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV176 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV97 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV97 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV9 ) @ relation )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1906]) ).
thf(1922,plain,
! [SV97: a,SV9: a,SV176: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV9 ) @ relation ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV176 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV97 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV97 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV9 ) @ relation )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1907]) ).
thf(1923,plain,
! [SV190: a,SV46: a,SV130: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV190 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV46 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV190 ) @ relation ) ) )
= $true )
| ( ( member_a @ SV130 @ carrier )
= $false )
| ( ( member_a @ SV46 @ carrier )
= $false )
| ( ( member_a @ SV190 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1908]) ).
thf(1924,plain,
! [SV63: a,SV144: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
= $true )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( member_a @ SV144 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1910]) ).
thf(1925,plain,
! [SV63: a,SV144: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
= $true )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( member_a @ SV144 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1911]) ).
thf(1926,plain,
! [SV144: a,SV63: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
= $true )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( member_a @ SV144 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1912]) ).
thf(1927,plain,
! [SV152: a,SV71: a] :
( ( ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
= $true )
| ( ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
= $false )
| ( ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) )
= $false )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1913]) ).
thf(1928,plain,
! [SV71: a,SV152: a] :
( ( ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) )
= $true )
| ( ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
= $false )
| ( ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) )
= $false )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1914]) ).
thf(1929,plain,
! [SV152: a,SV71: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
= $true )
| ( ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
= $false )
| ( ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) )
= $false )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1915]) ).
thf(1930,plain,
! [SV71: a,SV152: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation )
= $true )
| ( ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
= $false )
| ( ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) )
= $false )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1916]) ).
thf(1931,plain,
! [SV152: a,SV71: a] :
( ( ( member_a @ SV71 @ ( prefer1676310729than_a @ SV152 @ carrier @ relation ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation )
= $false )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1917]) ).
thf(1932,plain,
! [SV71: a,SV152: a] :
( ( ( member_a @ SV152 @ ( prefer1676310729than_a @ SV71 @ carrier @ relation ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation )
= $false )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1918]) ).
thf(1933,plain,
! [SV152: a,SV71: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation )
= $false )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1919]) ).
thf(1934,plain,
! [SV71: a,SV152: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV152 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV152 @ SV71 ) @ relation )
= $false )
| ( ( member_a @ SV152 @ carrier )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1920]) ).
thf(1935,plain,
! [SV97: a,SV9: a,SV176: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV9 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV176 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV176 @ SV97 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV97 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SV9 ) @ relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1922]) ).
thf(1936,plain,
! [SV130: a,SV190: a,SV46: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV190 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV46 ) @ relation ) ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV190 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation )
= $true )
| ( ( member_a @ SV130 @ carrier )
= $false )
| ( ( member_a @ SV46 @ carrier )
= $false )
| ( ( member_a @ SV190 @ carrier )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1923]) ).
thf(1937,plain,
! [SV63: a,SV144: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
= $true )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( member_a @ SV144 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1925]) ).
thf(1938,plain,
! [SV144: a,SV63: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
= $true )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( member_a @ SV144 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1926]) ).
thf(1939,plain,
! [SV130: a,SV190: a,SV46: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV190 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV46 ) @ relation ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV190 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation )
= $true )
| ( ( member_a @ SV130 @ carrier )
= $false )
| ( ( member_a @ SV46 @ carrier )
= $false )
| ( ( member_a @ SV190 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1936]) ).
thf(1940,plain,
! [SV144: a,SV63: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
= $true )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( member_a @ SV144 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1938]) ).
thf(1941,plain,
! [SV63: a,SV144: a] :
( ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
= $true )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( member_a @ SV144 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1938]) ).
thf(1942,plain,
! [SV130: a,SV190: a,SV46: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV190 ) @ relation ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV190 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation )
= $true )
| ( ( member_a @ SV130 @ carrier )
= $false )
| ( ( member_a @ SV46 @ carrier )
= $false )
| ( ( member_a @ SV190 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1939]) ).
thf(1943,plain,
! [SV130: a,SV46: a,SV190: a] :
( ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV46 ) @ relation ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV190 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation )
= $true )
| ( ( member_a @ SV130 @ carrier )
= $false )
| ( ( member_a @ SV46 @ carrier )
= $false )
| ( ( member_a @ SV190 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1939]) ).
thf(1944,plain,
! [SV144: a,SV63: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
= $true )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( member_a @ SV144 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1940]) ).
thf(1945,plain,
! [SV63: a,SV144: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
= $true )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( member_a @ SV144 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1941]) ).
thf(1946,plain,
! [SV130: a,SV190: a,SV46: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV190 ) @ relation )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV190 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation )
= $true )
| ( ( member_a @ SV130 @ carrier )
= $false )
| ( ( member_a @ SV46 @ carrier )
= $false )
| ( ( member_a @ SV190 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1942]) ).
thf(1947,plain,
! [SV130: a,SV46: a,SV190: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV46 ) @ relation ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV190 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation )
= $true )
| ( ( member_a @ SV130 @ carrier )
= $false )
| ( ( member_a @ SV46 @ carrier )
= $false )
| ( ( member_a @ SV190 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1943]) ).
thf(1948,plain,
! [SV63: a,SV144: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV63 @ SV144 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV144 @ SV63 ) @ relation )
= $true )
| ( ( member_a @ SV63 @ carrier )
= $false )
| ( ( member_a @ SV144 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1945]) ).
thf(1949,plain,
! [SV46: a,SV130: a,SV190: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV190 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV190 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation )
= $true )
| ( ( member_a @ SV130 @ carrier )
= $false )
| ( ( member_a @ SV46 @ carrier )
= $false )
| ( ( member_a @ SV190 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1946]) ).
thf(1950,plain,
! [SV130: a,SV46: a,SV190: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV46 ) @ relation )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV190 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation )
= $true )
| ( ( member_a @ SV130 @ carrier )
= $false )
| ( ( member_a @ SV46 @ carrier )
= $false )
| ( ( member_a @ SV190 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1947]) ).
thf(1951,plain,
! [SV46: a,SV130: a,SV190: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV130 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV190 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation )
= $true )
| ( ( member_a @ SV130 @ carrier )
= $false )
| ( ( member_a @ SV46 @ carrier )
= $false )
| ( ( member_a @ SV190 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1949]) ).
thf(1952,plain,
! [SV46: a,SV190: a,SV130: a] :
( ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV190 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV190 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation )
= $true )
| ( ( member_a @ SV130 @ carrier )
= $false )
| ( ( member_a @ SV46 @ carrier )
= $false )
| ( ( member_a @ SV190 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1949]) ).
thf(1953,plain,
! [SV46: a,SV130: a,SV190: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV130 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV190 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV46 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation )
= $true )
| ( ( member_a @ SV130 @ carrier )
= $false )
| ( ( member_a @ SV46 @ carrier )
= $false )
| ( ( member_a @ SV190 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1950]) ).
thf(1954,plain,
! [SV46: a,SV130: a,SV190: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV130 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV190 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation )
= $true )
| ( ( member_a @ SV130 @ carrier )
= $false )
| ( ( member_a @ SV46 @ carrier )
= $false )
| ( ( member_a @ SV190 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1951]) ).
thf(1955,plain,
! [SV46: a,SV190: a,SV130: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV190 ) @ relation ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV190 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation )
= $true )
| ( ( member_a @ SV130 @ carrier )
= $false )
| ( ( member_a @ SV46 @ carrier )
= $false )
| ( ( member_a @ SV190 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1952]) ).
thf(1956,plain,
! [SV46: a,SV130: a,SV190: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV130 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV46 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation )
= $true )
| ( ( member_a @ SV130 @ carrier )
= $false )
| ( ( member_a @ SV46 @ carrier )
= $false )
| ( ( member_a @ SV190 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1953]) ).
thf(1957,plain,
! [SV46: a,SV190: a,SV130: a] :
( ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV190 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV46 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation )
= $true )
| ( ( member_a @ SV130 @ carrier )
= $false )
| ( ( member_a @ SV46 @ carrier )
= $false )
| ( ( member_a @ SV190 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1953]) ).
thf(1958,plain,
! [SV46: a,SV190: a,SV130: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV190 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV190 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation )
= $true )
| ( ( member_a @ SV130 @ carrier )
= $false )
| ( ( member_a @ SV46 @ carrier )
= $false )
| ( ( member_a @ SV190 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1955]) ).
thf(1959,plain,
! [SV46: a,SV130: a,SV190: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV130 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV46 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation )
= $true )
| ( ( member_a @ SV130 @ carrier )
= $false )
| ( ( member_a @ SV46 @ carrier )
= $false )
| ( ( member_a @ SV190 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1956]) ).
thf(1960,plain,
! [SV46: a,SV190: a,SV130: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV190 ) @ relation ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV46 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation )
= $true )
| ( ( member_a @ SV130 @ carrier )
= $false )
| ( ( member_a @ SV46 @ carrier )
= $false )
| ( ( member_a @ SV190 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1957]) ).
thf(1961,plain,
! [SV46: a,SV190: a,SV130: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV190 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV190 @ SV46 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV46 @ SV130 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV46 ) @ relation )
= $true )
| ( ( member_a @ SV130 @ carrier )
= $false )
| ( ( member_a @ SV46 @ carrier )
= $false )
| ( ( member_a @ SV190 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1960]) ).
thf(1962,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[465,1961,1959,1958,1954,1948,1944,1937,1935,1934,1933,1932,1931,1930,1929,1928,1927,1924,1921,1909,1905,1904,1903,1902,1897,1896,1892,1891,1889,1888,1887,1886,1885,1884,1883,1882,1870,1867,1866,1863,1861,1858,1851,1850,1841,1832,1821,1819,1815,1808,1807,1805,1799,1796,1794,1792,1790,1789,1786,1783,1782,1781,1780,1779,1778,1776,1775,1774,1773,1772,1770,1767,1764,1763,1762,1759,1758,1752,1749,1748,1747,1742,1741,1738,1737,1733,1732,1729,1728,1725,1724,1718,1713,1711,1709,1707,1702,1700,1696,1692,1687,1685,1683,1675,1670,1665,1631,1630,1600,1590,1585,1579,1575,1574,1572,1562,1556,1549,1546,1541,1540,1537,1532,1529,1526,1523,1522,1521,1520,1503,1502,1501,1498,1497,1461,1460,1422,1412,1394,1393,1392,1381,1379,1367,1357,1356,1345,1331,1327,1326,1325,1317,1316,1310,1308,1307,1306,1305,1304,1303,1302,1301,1298,1295,1278,1276,1272,1271,1265,1261,1259,1258,1254,1250,1244,1242,1241,1235,1233,1230,1186,1178,1172,1169,1167,1165,1157,1153,1136,1127,1106,1100,1093,1089,1080,1076,1061,1059,1057,1049,1031,1029,1027,1002,990,967,949,932,924,918,914,909,901,897,893,874,856,802,767,765,759,735,729,720,703,684,668,667,665,664,663,661,570,483,479,474,473,472,471,468,466]) ).
thf(1963,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1962]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP155^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.20 % Computer : n018.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Oct 6 11:21:06 UTC 2026
% 0.07/0.21 % CPUTime :
% 0.07/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 45.82/7.95 ..
% 45.82/7.95
% 45.82/7.95 No.of.Axioms: 106
% 45.82/7.95
% 45.82/7.95 Length.of.Defs: 0
% 45.82/7.95
% 45.82/7.95 Contains.Choice.Funs: false
% 45.82/7.95 .........................................................
% 45.82/7.95
% 45.82/7.95 ********************************
% 45.82/7.95 * All subproblems solved! *
% 45.82/7.95 ********************************
% 45.82/7.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:106,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:1962,loop_count:0,foatp_calls:1,translation:fof_full)
% 45.82/7.95
% 45.82/7.95 %**** Beginning of derivation protocol ****
% 45.82/7.95 % SZS output start CNFRefutation
% See solution above
% 45.82/7.98
% 45.82/7.98 %**** End of derivation protocol ****
% 45.82/7.98 %**** no. of clauses in derivation: 1715 ****
% 45.82/7.98 %**** clause counter: 1962 ****
% 45.82/7.98
% 45.82/7.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:106,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:1962,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------