%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU180+2 : TPTP v9.3.1. Released v3.3.0.
% 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 : n007.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 10:43:17 AM UTC 2026
% Result : Theorem 87.04s 14.75s
% Output : CNFRefutation 87.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 66
% Syntax : Number of formulae : 2760 ( 901 unt; 0 typ; 0 def)
% Number of atoms : 24499 (8995 equ; 0 cnn)
% Maximal formula atoms : 11 ( 8 avg)
% Number of connectives : 53936 (13964 ~;9030 |; 183 &;30463 @)
% ( 140 <=>; 156 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 116 ( 113 usr; 8 con; 0-5 aty)
% Number of variables : 9238 ( 0 ^;9198 !; 40 ?;9238 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_are_equipotent,type,
are_equipotent: $i > $i > $o ).
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_cast_to_subset,type,
cast_to_subset: $i > $i ).
thf(tp_complements_of_subsets,type,
complements_of_subsets: $i > $i > $i ).
thf(tp_disjoint,type,
disjoint: $i > $i > $o ).
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_meet_of_subsets,type,
meet_of_subsets: $i > $i > $i ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_proper_subset,type,
proper_subset: $i > $i > $o ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_dom,type,
relation_dom: $i > $i ).
thf(tp_relation_field,type,
relation_field: $i > $i ).
thf(tp_relation_rng,type,
relation_rng: $i > $i ).
thf(tp_sK10_SY262,type,
sK10_SY262: $i > $i ).
thf(tp_sK11_SY297,type,
sK11_SY297: $i > $i > $i ).
thf(tp_sK12_SY303,type,
sK12_SY303: $i > $i > $i ).
thf(tp_sK13_SY305,type,
sK13_SY305: $i > $i > $i ).
thf(tp_sK14_SY331,type,
sK14_SY331: $i > $i > $i ).
thf(tp_sK15_SY359,type,
sK15_SY359: $i > $i > $i > $i ).
thf(tp_sK16_SY365,type,
sK16_SY365: $i > $i > $i > $i ).
thf(tp_sK17_SY371,type,
sK17_SY371: $i > $i > $i > $i ).
thf(tp_sK18_SY373,type,
sK18_SY373: $i > $i > $i > $i ).
thf(tp_sK19_SY382,type,
sK19_SY382: $i > $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_SY388,type,
sK20_SY388: $i > $i > $i ).
thf(tp_sK21_SY394,type,
sK21_SY394: $i > $i > $i ).
thf(tp_sK22_SY313,type,
sK22_SY313: $i > $i > $i ).
thf(tp_sK23_SY350,type,
sK23_SY350: $i > $i > $i ).
thf(tp_sK24_SY397,type,
sK24_SY397: $i > $i > $i ).
thf(tp_sK25_SY335,type,
sK25_SY335: $i > $i > $i ).
thf(tp_sK26_SY424,type,
sK26_SY424: $i > $i > $i ).
thf(tp_sK27_SY401,type,
sK27_SY401: $i > $i > $i > $i ).
thf(tp_sK28_SY405,type,
sK28_SY405: $i > $i > $i > $i > $i ).
thf(tp_sK29_SY413,type,
sK29_SY413: $i > $i > $i > $i ).
thf(tp_sK2_SY155,type,
sK2_SY155: $i ).
thf(tp_sK30_SY421,type,
sK30_SY421: $i > $i > $i ).
thf(tp_sK31_SY417,type,
sK31_SY417: $i > $i > $i > $i ).
thf(tp_sK32_SY404,type,
sK32_SY404: $i > $i > $i ).
thf(tp_sK33_SY432,type,
sK33_SY432: $i > $i > $i > $i > $i ).
thf(tp_sK34_SY411,type,
sK34_SY411: $i > $i > $i > $i ).
thf(tp_sK35_SY428,type,
sK35_SY428: $i > $i > $i ).
thf(tp_sK36_SY416,type,
sK36_SY416: $i > $i > $i ).
thf(tp_sK37_SY427,type,
sK37_SY427: $i > $i > $i > $i ).
thf(tp_sK38_SY420,type,
sK38_SY420: $i > $i > $i ).
thf(tp_sK39_SY416,type,
sK39_SY416: $i > $i > $i > $i ).
thf(tp_sK3_SY157,type,
sK3_SY157: $i ).
thf(tp_sK40_SY435,type,
sK40_SY435: $i > $i > $i > $i ).
thf(tp_sK41_SY420,type,
sK41_SY420: $i > $i > $i > $i ).
thf(tp_sK42_SY404,type,
sK42_SY404: $i > $i > $i > $i ).
thf(tp_sK43_SY411,type,
sK43_SY411: $i > $i > $i > $i > $i > $i ).
thf(tp_sK44_SY436,type,
sK44_SY436: $i > $i > $i > $i > $i > $i ).
thf(tp_sK45_SX0,type,
sK45_SX0: $i ).
thf(tp_sK46_SY444,type,
sK46_SY444: $i > $i ).
thf(tp_sK47_SY499,type,
sK47_SY499: $i > $i ).
thf(tp_sK48_SY613,type,
sK48_SY613: $i > $i > $i ).
thf(tp_sK49_SY631,type,
sK49_SY631: $i > $i > $i ).
thf(tp_sK4_SX0,type,
sK4_SX0: $i ).
thf(tp_sK50_SY493,type,
sK50_SY493: $i > $i ).
thf(tp_sK51_SY568,type,
sK51_SY568: $i > $i ).
thf(tp_sK52_SY580,type,
sK52_SY580: $i > $i > $i ).
thf(tp_sK53_SY590,type,
sK53_SY590: $i > $i > $i ).
thf(tp_sK54_SY599,type,
sK54_SY599: $i > $i > $i ).
thf(tp_sK55_SY615,type,
sK55_SY615: $i > $i > $i ).
thf(tp_sK56_SY634,type,
sK56_SY634: $i > $i > $i > $i ).
thf(tp_sK57_SY643,type,
sK57_SY643: $i > $i > $i > $i ).
thf(tp_sK58_SY650,type,
sK58_SY650: $i > $i > $i > $i ).
thf(tp_sK59_SY652,type,
sK59_SY652: $i > $i > $i > $i ).
thf(tp_sK5_SY160,type,
sK5_SY160: $i > $i ).
thf(tp_sK60_SY659,type,
sK60_SY659: $i > $i > $i > $i ).
thf(tp_sK61_SY667,type,
sK61_SY667: $i > $i > $i ).
thf(tp_sK62_SY673,type,
sK62_SY673: $i > $i > $i ).
thf(tp_sK63_SY601,type,
sK63_SY601: $i > $i > $i ).
thf(tp_sK64_SY628,type,
sK64_SY628: $i > $i > $i ).
thf(tp_sK65_SY676,type,
sK65_SY676: $i > $i > $i ).
thf(tp_sK66_SY584,type,
sK66_SY584: $i > $i > $i ).
thf(tp_sK67_SY703,type,
sK67_SY703: $i > $i > $i ).
thf(tp_sK68_SY680,type,
sK68_SY680: $i > $i > $i > $i ).
thf(tp_sK69_SY684,type,
sK69_SY684: $i > $i > $i > $i > $i ).
thf(tp_sK6_SY251,type,
sK6_SY251: $i > $i ).
thf(tp_sK70_SY700,type,
sK70_SY700: $i > $i > $i ).
thf(tp_sK71_SY692,type,
sK71_SY692: $i > $i > $i > $i ).
thf(tp_sK72_SY696,type,
sK72_SY696: $i > $i > $i > $i ).
thf(tp_sK73_SY683,type,
sK73_SY683: $i > $i > $i ).
thf(tp_sK74_SY707,type,
sK74_SY707: $i > $i > $i ).
thf(tp_sK75_SY711,type,
sK75_SY711: $i > $i > $i > $i > $i ).
thf(tp_sK76_SY690,type,
sK76_SY690: $i > $i > $i > $i ).
thf(tp_sK77_SY706,type,
sK77_SY706: $i > $i > $i > $i ).
thf(tp_sK78_SY695,type,
sK78_SY695: $i > $i > $i ).
thf(tp_sK79_SY699,type,
sK79_SY699: $i > $i > $i ).
thf(tp_sK7_SY306,type,
sK7_SY306: $i > $i > $i ).
thf(tp_sK80_SY695,type,
sK80_SY695: $i > $i > $i > $i ).
thf(tp_sK81_SY714,type,
sK81_SY714: $i > $i > $i > $i ).
thf(tp_sK82_SY699,type,
sK82_SY699: $i > $i > $i > $i ).
thf(tp_sK83_SY683,type,
sK83_SY683: $i > $i > $i > $i ).
thf(tp_sK84_SY690,type,
sK84_SY690: $i > $i > $i > $i > $i > $i ).
thf(tp_sK85_SY715,type,
sK85_SY715: $i > $i > $i > $i > $i > $i ).
thf(tp_sK8_SY307,type,
sK8_SY307: $i > $i > $i ).
thf(tp_sK9_SY197,type,
sK9_SY197: $i > $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_set_intersection2,type,
set_intersection2: $i > $i > $i ).
thf(tp_set_meet,type,
set_meet: $i > $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subset_complement,type,
subset_complement: $i > $i > $i ).
thf(tp_subset_difference,type,
subset_difference: $i > $i > $i > $i ).
thf(tp_union,type,
union: $i > $i ).
thf(tp_union_of_subsets,type,
union_of_subsets: $i > $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(1,axiom,
! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
( ( subset @ E @ C )
=> ( in @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_tarski) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(24,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_relat_1) ).
thf(36,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(40,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(45,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(46,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(47,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(48,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_tarski) ).
thf(50,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_relat_1) ).
thf(51,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(52,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(53,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(55,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(56,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(57,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(58,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(59,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_setfam_1) ).
thf(60,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(64,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_1) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
thf(67,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
thf(71,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_dom @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(73,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
=> ( ( element @ B @ A )
<=> ( in @ B @ A ) ) )
& ( ( empty @ A )
=> ( ( element @ B @ A )
<=> ( empty @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(79,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(80,axiom,
! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(81,axiom,
! [A: $i,B: $i] :
( ( ( A != empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ! [D: $i] :
( ( in @ D @ A )
=> ( in @ C @ D ) ) ) ) )
& ( ( A = empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ( B = empty_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_setfam_1) ).
thf(82,axiom,
! [A: $i] :
( ( relation @ A )
<=> ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
thf(88,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(91,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(98,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
= A )
<=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ~ ( ( in @ B @ ( subset_complement @ A @ C ) )
& ( in @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_subset_1) ).
thf(103,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(107,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_zfmisc_1) ).
thf(113,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( in @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
& ( disjoint @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ C )
& ( in @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).
thf(117,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(120,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(125,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) )
& ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relat_1) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_dom @ C ) )
& ( in @ B @ ( relation_rng @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_relat_1) ).
thf(132,axiom,
! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( powerset @ C ) @ B ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_zfmisc_1) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
thf(138,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l71_subset_1) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
thf(140,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l50_zfmisc_1) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_zfmisc_1) ).
thf(143,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_subset_1) ).
thf(145,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(146,axiom,
! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
thf(147,axiom,
! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l25_zfmisc_1) ).
thf(148,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l23_zfmisc_1) ).
thf(150,conjecture,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_field @ C ) )
& ( in @ B @ ( relation_field @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_relat_1) ).
thf(151,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_field @ C ) )
& ( in @ B @ ( relation_field @ C ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[150]) ).
thf(152,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_field @ C ) )
& ( in @ B @ ( relation_field @ C ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[151]) ).
thf(153,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
( ( subset @ E @ C )
=> ( in @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(154,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(155,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(156,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(157,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(158,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(159,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(160,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(161,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(162,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(163,plain,
$true = $true,
inference(unfold_def,[status(thm)],[40]) ).
thf(164,plain,
$true = $true,
inference(unfold_def,[status(thm)],[45]) ).
thf(165,plain,
$true = $true,
inference(unfold_def,[status(thm)],[46]) ).
thf(166,plain,
$true = $true,
inference(unfold_def,[status(thm)],[47]) ).
thf(167,plain,
$true = $true,
inference(unfold_def,[status(thm)],[48]) ).
thf(168,plain,
$true = $true,
inference(unfold_def,[status(thm)],[50]) ).
thf(169,plain,
$true = $true,
inference(unfold_def,[status(thm)],[51]) ).
thf(170,plain,
$true = $true,
inference(unfold_def,[status(thm)],[52]) ).
thf(171,plain,
$true = $true,
inference(unfold_def,[status(thm)],[53]) ).
thf(172,plain,
$true = $true,
inference(unfold_def,[status(thm)],[55]) ).
thf(173,plain,
$true = $true,
inference(unfold_def,[status(thm)],[56]) ).
thf(174,plain,
$true = $true,
inference(unfold_def,[status(thm)],[57]) ).
thf(175,plain,
$true = $true,
inference(unfold_def,[status(thm)],[58]) ).
thf(176,plain,
$true = $true,
inference(unfold_def,[status(thm)],[59]) ).
thf(177,plain,
$true = $true,
inference(unfold_def,[status(thm)],[60]) ).
thf(178,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(179,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(180,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(181,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(182,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(183,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_dom @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(184,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(185,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(186,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(187,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(188,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(189,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
=> ( ( element @ B @ A )
<=> ( in @ B @ A ) ) )
& ( ( empty @ A )
=> ( ( element @ B @ A )
<=> ( empty @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(190,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(191,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(192,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(193,plain,
( ( ! [A: $i,B: $i] :
( ( ( A != empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ! [D: $i] :
( ( in @ D @ A )
=> ( in @ C @ D ) ) ) ) )
& ( ( A = empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ( B = empty_set ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(194,plain,
( ( ! [A: $i] :
( ( relation @ A )
<=> ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(195,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(196,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(197,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
= A )
<=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(198,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ~ ( ( in @ B @ ( subset_complement @ A @ C ) )
& ( in @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(199,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(200,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(201,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( in @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
& ( disjoint @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(202,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ C )
& ( in @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(203,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(204,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(205,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) )
& ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(206,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_dom @ C ) )
& ( in @ B @ ( relation_rng @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(207,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( powerset @ C ) @ B ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(208,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(209,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(210,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(211,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(212,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(213,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(214,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(215,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(216,plain,
( ( ! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(217,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(218,plain,
( ( ! [SY155: $i,SY156: $i] :
( ( relation @ SY156 )
=> ( ( in @ ( ordered_pair @ sK1_A @ SY155 ) @ SY156 )
=> ( ( in @ sK1_A @ ( relation_field @ SY156 ) )
& ( in @ SY155 @ ( relation_field @ SY156 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[152]) ).
thf(219,plain,
( ( ! [SY157: $i] :
( ( relation @ SY157 )
=> ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY155 ) @ SY157 )
=> ( ( in @ sK1_A @ ( relation_field @ SY157 ) )
& ( in @ sK2_SY155 @ ( relation_field @ SY157 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[218]) ).
thf(220,plain,
( ( ( relation @ sK3_SY157 )
=> ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY155 ) @ sK3_SY157 )
=> ( ( in @ sK1_A @ ( relation_field @ sK3_SY157 ) )
& ( in @ sK2_SY155 @ ( relation_field @ sK3_SY157 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[219]) ).
thf(221,plain,
( ( relation @ sK3_SY157 )
= $true ),
inference(standard_cnf,[status(thm)],[220]) ).
thf(222,plain,
( ( in @ ( ordered_pair @ sK1_A @ sK2_SY155 ) @ sK3_SY157 )
= $true ),
inference(standard_cnf,[status(thm)],[220]) ).
thf(223,plain,
( ( ( in @ sK1_A @ ( relation_field @ sK3_SY157 ) )
& ( in @ sK2_SY155 @ ( relation_field @ sK3_SY157 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[220]) ).
thf(224,plain,
( ( in @ sK1_A @ ( relation_field @ sK3_SY157 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[223]) ).
thf(225,plain,
( ( in @ sK2_SY155 @ ( relation_field @ sK3_SY157 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[223]) ).
thf(226,plain,
( ( ~ ( in @ sK1_A @ ( relation_field @ sK3_SY157 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[224]) ).
thf(227,plain,
( ( ~ ( in @ sK2_SY155 @ ( relation_field @ sK3_SY157 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[225]) ).
thf(228,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(229,plain,
( ( ! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(230,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[215]) ).
thf(231,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[214]) ).
thf(232,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[213]) ).
thf(233,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[212]) ).
thf(234,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[211]) ).
thf(235,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(236,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(237,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[208]) ).
thf(238,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( powerset @ C ) @ B ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[207]) ).
thf(239,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_dom @ C ) )
& ( in @ B @ ( relation_rng @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[206]) ).
thf(240,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) )
& ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[205]) ).
thf(241,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) )
= $true ),
inference(copy,[status(thm)],[204]) ).
thf(242,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[203]) ).
thf(243,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ C )
& ( in @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[202]) ).
thf(244,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( in @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
& ( disjoint @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(245,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[200]) ).
thf(246,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[199]) ).
thf(247,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ~ ( ( in @ B @ ( subset_complement @ A @ C ) )
& ( in @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[198]) ).
thf(248,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
= A )
<=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[197]) ).
thf(249,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[196]) ).
thf(250,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(251,plain,
( ( ! [A: $i] :
( ( relation @ A )
<=> ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[194]) ).
thf(252,plain,
( ( ! [A: $i,B: $i] :
( ( ( A != empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ! [D: $i] :
( ( in @ D @ A )
=> ( in @ C @ D ) ) ) ) )
& ( ( A = empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ( B = empty_set ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[193]) ).
thf(253,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(copy,[status(thm)],[192]) ).
thf(254,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[191]) ).
thf(255,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[190]) ).
thf(256,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
=> ( ( element @ B @ A )
<=> ( in @ B @ A ) ) )
& ( ( empty @ A )
=> ( ( element @ B @ A )
<=> ( empty @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[189]) ).
thf(257,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[188]) ).
thf(258,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[187]) ).
thf(259,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[186]) ).
thf(260,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[185]) ).
thf(261,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[184]) ).
thf(262,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_dom @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[183]) ).
thf(263,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[182]) ).
thf(264,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[181]) ).
thf(265,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[180]) ).
thf(266,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[179]) ).
thf(267,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[178]) ).
thf(268,plain,
$true = $true,
inference(copy,[status(thm)],[177]) ).
thf(269,plain,
$true = $true,
inference(copy,[status(thm)],[176]) ).
thf(270,plain,
$true = $true,
inference(copy,[status(thm)],[175]) ).
thf(271,plain,
$true = $true,
inference(copy,[status(thm)],[174]) ).
thf(272,plain,
$true = $true,
inference(copy,[status(thm)],[173]) ).
thf(273,plain,
$true = $true,
inference(copy,[status(thm)],[172]) ).
thf(274,plain,
$true = $true,
inference(copy,[status(thm)],[171]) ).
thf(275,plain,
$true = $true,
inference(copy,[status(thm)],[170]) ).
thf(276,plain,
$true = $true,
inference(copy,[status(thm)],[169]) ).
thf(277,plain,
$true = $true,
inference(copy,[status(thm)],[168]) ).
thf(278,plain,
$true = $true,
inference(copy,[status(thm)],[167]) ).
thf(279,plain,
$true = $true,
inference(copy,[status(thm)],[166]) ).
thf(280,plain,
$true = $true,
inference(copy,[status(thm)],[165]) ).
thf(281,plain,
$true = $true,
inference(copy,[status(thm)],[164]) ).
thf(282,plain,
$true = $true,
inference(copy,[status(thm)],[163]) ).
thf(283,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[162]) ).
thf(284,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[161]) ).
thf(285,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[160]) ).
thf(286,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[159]) ).
thf(287,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[158]) ).
thf(288,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[157]) ).
thf(289,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[156]) ).
thf(290,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[155]) ).
thf(291,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[154]) ).
thf(292,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
( ( subset @ E @ C )
=> ( in @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[153]) ).
thf(293,plain,
( ( in @ ( ordered_pair @ sK1_A @ sK2_SY155 ) @ sK3_SY157 )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(294,plain,
( ( relation @ sK3_SY157 )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(295,plain,
( ( ~ ( in @ sK1_A @ ( relation_field @ sK3_SY157 ) ) )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(296,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ( subset @ SX3 @ SX2 ) )
| ( in @ SX3 @ SX1 ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ ( powerset @ SX2 ) @ SX1 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SX2 @ SX1 )
| ~ ~ ( are_equipotent @ SX2 @ SX1 ) )
| ~ ~ ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(297,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX1
!= ( union @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[263]) ).
thf(298,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ SX1 )
| ( empty @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287]) ).
thf(299,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ SX2 ) ) )
| ~ ( empty @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(300,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(301,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) )
| ~ ( ~ ~ ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(302,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
~ ( ~ ( ( SX1
!= ( relation_rng @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( relation_rng @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(303,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(304,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_field @ SX0 )
= ( set_union2 @ ( relation_dom @ SX0 ) @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[267]) ).
thf(305,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX1
!= ( powerset @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255]) ).
thf(306,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(307,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(308,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( set_union2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(309,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) )
| ~ ( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(310,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( in @ SX2 @ SX0 )
| ( subset @ SX0 @ ( set_difference @ SX1 @ ( singleton @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[233]) ).
thf(311,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( set_intersection2 @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( set_intersection2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(312,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 )
| ~ ( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX2 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX2 ) )
| ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[243]) ).
thf(313,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SX0 @ SX1 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) ) )
| ~ ~ ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[244]) ).
thf(314,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( ( set_union2 @ ( singleton @ SX0 ) @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[228]) ).
thf(315,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( cartesian_product2 @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 ) )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 ) )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 ) )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 ) )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( cartesian_product2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259]) ).
thf(316,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( set_union2 @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ( ~ ( ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ( ~ ( ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( set_union2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(317,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ~ ( ~ ( in @ SX0 @ ( relation_dom @ SX2 ) )
| ~ ( in @ SX1 @ ( relation_rng @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(318,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( disjoint @ ( singleton @ SX0 ) @ SX1 )
| ~ ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229]) ).
thf(319,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX1
!= ( singleton @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) )
| ~ ( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) )
| ~ ( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(320,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ( SX0 != empty_set ) )
| ~ ( ~ ( ( SX1
!= ( set_meet @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
| ~ ( ( SX0 != empty_set )
| ~ ( ~ ( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) )
| ~ ( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[252]) ).
thf(321,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( in @ SX0 @ SX1 )
| ( disjoint @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[230]) ).
thf(322,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ~ ( ~ ( subset @ ( relation_dom @ SX0 ) @ ( relation_dom @ SX1 ) )
| ~ ( subset @ ( relation_rng @ SX0 ) @ ( relation_rng @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(323,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ SX0 @ ( union @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(324,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ~ ( empty @ SX0 )
| ~ ( ~ ( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) )
| ~ ( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
| ~ ( ~ ( empty @ SX0 )
| ~ ( ~ ( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) )
| ~ ( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[256]) ).
thf(325,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ SX0 @ ( union @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(326,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( unordered_pair @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ( ~ ( ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ( ~ ( ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( unordered_pair @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(327,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( ( set_union2 @ ( singleton @ SX0 ) @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(328,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[285]) ).
thf(329,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(330,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(331,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ( subset @ SX3 @ SX2 ) )
| ( in @ SX3 @ SX1 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SX1 )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) ) ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SX2 @ SX1 )
| ~ ~ ( are_equipotent @ SX2 @ SX1 ) )
| ~ ~ ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(332,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286]) ).
thf(333,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( relation @ SX0 )
| ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ! [SX2: $i,SX3: $i] :
( SX1
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
| ~ ( ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ! [SX2: $i,SX3: $i] :
( SX1
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(334,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( ordered_pair @ SX0 @ SX1 )
!= ( ordered_pair @ SX2 @ SX3 ) )
| ~ ( ( SX0 != SX2 )
| ( SX1 != SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[241]) ).
thf(335,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ SX2 ) ) )
| ( element @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(336,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
~ ( ~ ( ( SX1
!= ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( relation_dom @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(337,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( set_difference @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( set_difference @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(338,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( element @ SX2 @ ( powerset @ SX0 ) )
| ~ ~ ( ~ ( in @ SX1 @ ( subset_complement @ SX0 @ SX2 ) )
| ~ ( in @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(339,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ~ ( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 ) )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[237]) ).
thf(340,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) )
| ~ ( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(341,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) )
| ~ ( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[242]) ).
thf(342,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SX0 @ SX1 )
| ~ ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ~ ~ ( ~ ~ ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(343,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ~ ( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 ) )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(344,plain,
! [SV1: $i] :
( ( ! [SY158: $i] :
( ( ordered_pair @ SV1 @ SY158 )
= ( unordered_pair @ ( unordered_pair @ SV1 @ SY158 ) @ ( singleton @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(345,plain,
! [SV2: $i] :
( ( ! [SY159: $i] :
~ ( empty @ ( ordered_pair @ SV2 @ SY159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(346,plain,
( ( in @ sK1_A @ ( relation_field @ sK3_SY157 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(347,plain,
! [SV3: $i] :
( ( ~ ! [SY160: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV3 @ SY160 )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY160 )
| ~ ( subset @ SX3 @ SX2 ) )
| ( in @ SX3 @ SY160 ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY160 )
| ( in @ ( powerset @ SX2 ) @ SY160 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SX2 @ SY160 )
| ~ ~ ( are_equipotent @ SX2 @ SY160 ) )
| ~ ~ ( in @ SX2 @ SY160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(348,plain,
! [SV4: $i] :
( ( ! [SY165: $i] :
~ ( ~ ( ( SY165
!= ( union @ SV4 ) )
| ! [SY166: $i] :
~ ( ~ ( ~ ( in @ SY166 @ SY165 )
| ~ ! [SY167: $i] :
~ ~ ( ~ ( in @ SY166 @ SY167 )
| ~ ( in @ SY167 @ SV4 ) ) )
| ~ ( ~ ~ ! [SY168: $i] :
~ ~ ( ~ ( in @ SY166 @ SY168 )
| ~ ( in @ SY168 @ SV4 ) )
| ( in @ SY166 @ SY165 ) ) ) )
| ~ ( ~ ! [SY169: $i] :
~ ( ~ ( ~ ( in @ SY169 @ SY165 )
| ~ ! [SY170: $i] :
~ ~ ( ~ ( in @ SY169 @ SY170 )
| ~ ( in @ SY170 @ SV4 ) ) )
| ~ ( ~ ~ ! [SY171: $i] :
~ ~ ( ~ ( in @ SY169 @ SY171 )
| ~ ( in @ SY171 @ SV4 ) )
| ( in @ SY169 @ SY165 ) ) )
| ( SY165
= ( union @ SV4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(349,plain,
! [SV5: $i] :
( ( ! [SY172: $i] :
( ~ ( element @ SV5 @ SY172 )
| ( empty @ SY172 )
| ( in @ SV5 @ SY172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(350,plain,
! [SV6: $i] :
( ( ! [SY173: $i,SY174: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV6 @ SY173 )
| ~ ( element @ SY173 @ ( powerset @ SY174 ) ) )
| ~ ( empty @ SY174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(351,plain,
! [SV7: $i] :
( ( ! [SY175: $i] :
( ~ ( element @ SY175 @ ( powerset @ SV7 ) )
| ! [SY176: $i] :
( ~ ( in @ SY176 @ SY175 )
| ( in @ SY176 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(352,plain,
! [SV8: $i] :
( ( ! [SY177: $i] :
~ ( ~ ( ( ( set_difference @ SV8 @ ( singleton @ SY177 ) )
!= SV8 )
| ~ ( in @ SY177 @ SV8 ) )
| ~ ( ~ ~ ( in @ SY177 @ SV8 )
| ( ( set_difference @ SV8 @ ( singleton @ SY177 ) )
= SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(353,plain,
! [SV9: $i] :
( ( ~ ( relation @ SV9 )
| ! [SY178: $i] :
~ ( ~ ( ( SY178
!= ( relation_rng @ SV9 ) )
| ! [SY179: $i] :
~ ( ~ ( ~ ( in @ SY179 @ SY178 )
| ~ ! [SY180: $i] :
~ ( in @ ( ordered_pair @ SY180 @ SY179 ) @ SV9 ) )
| ~ ( ~ ~ ! [SY181: $i] :
~ ( in @ ( ordered_pair @ SY181 @ SY179 ) @ SV9 )
| ( in @ SY179 @ SY178 ) ) ) )
| ~ ( ~ ! [SY182: $i] :
~ ( ~ ( ~ ( in @ SY182 @ SY178 )
| ~ ! [SY183: $i] :
~ ( in @ ( ordered_pair @ SY183 @ SY182 ) @ SV9 ) )
| ~ ( ~ ~ ! [SY184: $i] :
~ ( in @ ( ordered_pair @ SY184 @ SY182 ) @ SV9 )
| ( in @ SY182 @ SY178 ) ) )
| ( SY178
= ( relation_rng @ SV9 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(354,plain,
! [SV10: $i] :
( ( ! [SY185: $i] :
~ ( ~ ( ~ ( subset @ SV10 @ SY185 )
| ! [SY186: $i] :
( ~ ( in @ SY186 @ SV10 )
| ( in @ SY186 @ SY185 ) ) )
| ~ ( ~ ! [SY187: $i] :
( ~ ( in @ SY187 @ SV10 )
| ( in @ SY187 @ SY185 ) )
| ( subset @ SV10 @ SY185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(355,plain,
! [SV11: $i] :
( ( ~ ( relation @ SV11 )
| ( ( relation_field @ SV11 )
= ( set_union2 @ ( relation_dom @ SV11 ) @ ( relation_rng @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(356,plain,
! [SV12: $i] :
( ( ! [SY188: $i] :
~ ( ~ ( ( SY188
!= ( powerset @ SV12 ) )
| ! [SY189: $i] :
~ ( ~ ( ~ ( in @ SY189 @ SY188 )
| ( subset @ SY189 @ SV12 ) )
| ~ ( ~ ( subset @ SY189 @ SV12 )
| ( in @ SY189 @ SY188 ) ) ) )
| ~ ( ~ ! [SY190: $i] :
~ ( ~ ( ~ ( in @ SY190 @ SY188 )
| ( subset @ SY190 @ SV12 ) )
| ~ ( ~ ( subset @ SY190 @ SV12 )
| ( in @ SY190 @ SY188 ) ) )
| ( SY188
= ( powerset @ SV12 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(357,plain,
! [SV13: $i] :
( ( ! [SY191: $i] :
( ~ ! [SY192: $i] :
( ~ ( in @ SY192 @ SV13 )
| ( in @ SY192 @ SY191 ) )
| ( element @ SV13 @ ( powerset @ SY191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(358,plain,
! [SV14: $i] :
( ( ! [SY193: $i] :
( ~ ! [SY194: $i] :
~ ( ~ ( ~ ( in @ SY194 @ SV14 )
| ( in @ SY194 @ SY193 ) )
| ~ ( ~ ( in @ SY194 @ SY193 )
| ( in @ SY194 @ SV14 ) ) )
| ( SV14 = SY193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(359,plain,
! [SV15: $i] :
( ( ! [SY195: $i] :
( ~ ~ ( ~ ( relation @ SV15 )
| ~ ( relation @ SY195 ) )
| ( relation @ ( set_union2 @ SV15 @ SY195 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(360,plain,
! [SV16: $i] :
( ( ~ ( ~ ( ( SV16 != empty_set )
| ! [SY196: $i] :
~ ( in @ SY196 @ SV16 ) )
| ~ ( ~ ! [SY197: $i] :
~ ( in @ SY197 @ SV16 )
| ( SV16 = empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(361,plain,
! [SV17: $i] :
( ( ! [SY198: $i,SY199: $i] :
( ~ ( subset @ SV17 @ SY198 )
| ( in @ SY199 @ SV17 )
| ( subset @ SV17 @ ( set_difference @ SY198 @ ( singleton @ SY199 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(362,plain,
! [SV18: $i] :
( ( ! [SY200: $i,SY201: $i] :
~ ( ~ ( ( SY201
!= ( set_intersection2 @ SV18 @ SY200 ) )
| ! [SY202: $i] :
~ ( ~ ( ~ ( in @ SY202 @ SY201 )
| ~ ( ~ ( in @ SY202 @ SV18 )
| ~ ( in @ SY202 @ SY200 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY202 @ SV18 )
| ~ ( in @ SY202 @ SY200 ) )
| ( in @ SY202 @ SY201 ) ) ) )
| ~ ( ~ ! [SY203: $i] :
~ ( ~ ( ~ ( in @ SY203 @ SY201 )
| ~ ( ~ ( in @ SY203 @ SV18 )
| ~ ( in @ SY203 @ SY200 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY203 @ SV18 )
| ~ ( in @ SY203 @ SY200 ) )
| ( in @ SY203 @ SY201 ) ) )
| ( SY201
= ( set_intersection2 @ SV18 @ SY200 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(363,plain,
! [SV19: $i] :
( ( ! [SY204: $i,SY205: $i] :
~ ( ~ ( ~ ( subset @ ( unordered_pair @ SV19 @ SY204 ) @ SY205 )
| ~ ( ~ ( in @ SV19 @ SY205 )
| ~ ( in @ SY204 @ SY205 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV19 @ SY205 )
| ~ ( in @ SY204 @ SY205 ) )
| ( subset @ ( unordered_pair @ SV19 @ SY204 ) @ SY205 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(364,plain,
! [SV20: $i] :
( ( ! [SY206: $i] :
~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SV20 @ SY206 )
| ~ ! [SY207: $i] :
~ ~ ( ~ ( in @ SY207 @ SV20 )
| ~ ( in @ SY207 @ SY206 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY208: $i] :
~ ~ ( ~ ( in @ SY208 @ SV20 )
| ~ ( in @ SY208 @ SY206 ) )
| ~ ( disjoint @ SV20 @ SY206 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(365,plain,
! [SV21: $i] :
( ( ! [SY209: $i] :
( ~ ( in @ SV21 @ SY209 )
| ( ( set_union2 @ ( singleton @ SV21 ) @ SY209 )
= SY209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(366,plain,
! [SV22: $i] :
( ( ! [SY210: $i,SY211: $i] :
~ ( ~ ( ( SY211
!= ( cartesian_product2 @ SV22 @ SY210 ) )
| ! [SY212: $i] :
~ ( ~ ( ~ ( in @ SY212 @ SY211 )
| ~ ! [SY213: $i] :
~ ~ ! [SY214: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY213 @ SV22 )
| ~ ( in @ SY214 @ SY210 ) )
| ( SY212
!= ( ordered_pair @ SY213 @ SY214 ) ) ) )
| ~ ( ~ ~ ! [SY215: $i] :
~ ~ ! [SY216: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY215 @ SV22 )
| ~ ( in @ SY216 @ SY210 ) )
| ( SY212
!= ( ordered_pair @ SY215 @ SY216 ) ) )
| ( in @ SY212 @ SY211 ) ) ) )
| ~ ( ~ ! [SY217: $i] :
~ ( ~ ( ~ ( in @ SY217 @ SY211 )
| ~ ! [SY218: $i] :
~ ~ ! [SY219: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY218 @ SV22 )
| ~ ( in @ SY219 @ SY210 ) )
| ( SY217
!= ( ordered_pair @ SY218 @ SY219 ) ) ) )
| ~ ( ~ ~ ! [SY220: $i] :
~ ~ ! [SY221: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY220 @ SV22 )
| ~ ( in @ SY221 @ SY210 ) )
| ( SY217
!= ( ordered_pair @ SY220 @ SY221 ) ) )
| ( in @ SY217 @ SY211 ) ) )
| ( SY211
= ( cartesian_product2 @ SV22 @ SY210 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(367,plain,
! [SV23: $i] :
( ( ! [SY222: $i,SY223: $i] :
~ ( ~ ( ( SY223
!= ( set_union2 @ SV23 @ SY222 ) )
| ! [SY224: $i] :
~ ( ~ ( ~ ( in @ SY224 @ SY223 )
| ( in @ SY224 @ SV23 )
| ( in @ SY224 @ SY222 ) )
| ~ ( ~ ( ( in @ SY224 @ SV23 )
| ( in @ SY224 @ SY222 ) )
| ( in @ SY224 @ SY223 ) ) ) )
| ~ ( ~ ! [SY225: $i] :
~ ( ~ ( ~ ( in @ SY225 @ SY223 )
| ( in @ SY225 @ SV23 )
| ( in @ SY225 @ SY222 ) )
| ~ ( ~ ( ( in @ SY225 @ SV23 )
| ( in @ SY225 @ SY222 ) )
| ( in @ SY225 @ SY223 ) ) )
| ( SY223
= ( set_union2 @ SV23 @ SY222 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(368,plain,
! [SV24: $i] :
( ( ! [SY226: $i,SY227: $i] :
( ~ ( relation @ SY227 )
| ~ ( in @ ( ordered_pair @ SV24 @ SY226 ) @ SY227 )
| ~ ( ~ ( in @ SV24 @ ( relation_dom @ SY227 ) )
| ~ ( in @ SY226 @ ( relation_rng @ SY227 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(369,plain,
! [SV25: $i] :
( ( ! [SY228: $i] :
~ ~ ( ~ ( disjoint @ ( singleton @ SV25 ) @ SY228 )
| ~ ( in @ SV25 @ SY228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(370,plain,
! [SV26: $i] :
( ( ! [SY229: $i] :
~ ( ~ ( ( SY229
!= ( singleton @ SV26 ) )
| ! [SY230: $i] :
~ ( ~ ( ~ ( in @ SY230 @ SY229 )
| ( SY230 = SV26 ) )
| ~ ( ( SY230 != SV26 )
| ( in @ SY230 @ SY229 ) ) ) )
| ~ ( ~ ! [SY231: $i] :
~ ( ~ ( ~ ( in @ SY231 @ SY229 )
| ( SY231 = SV26 ) )
| ~ ( ( SY231 != SV26 )
| ( in @ SY231 @ SY229 ) ) )
| ( SY229
= ( singleton @ SV26 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(371,plain,
! [SV27: $i] :
( ( ! [SY232: $i] :
~ ( ~ ( ~ ( ( SV27 != empty_set ) )
| ~ ( ~ ( ( SY232
!= ( set_meet @ SV27 ) )
| ! [SY233: $i] :
~ ( ~ ( ~ ( in @ SY233 @ SY232 )
| ! [SY234: $i] :
( ~ ( in @ SY234 @ SV27 )
| ( in @ SY233 @ SY234 ) ) )
| ~ ( ~ ! [SY235: $i] :
( ~ ( in @ SY235 @ SV27 )
| ( in @ SY233 @ SY235 ) )
| ( in @ SY233 @ SY232 ) ) ) )
| ~ ( ~ ! [SY236: $i] :
~ ( ~ ( ~ ( in @ SY236 @ SY232 )
| ! [SY237: $i] :
( ~ ( in @ SY237 @ SV27 )
| ( in @ SY236 @ SY237 ) ) )
| ~ ( ~ ! [SY238: $i] :
( ~ ( in @ SY238 @ SV27 )
| ( in @ SY236 @ SY238 ) )
| ( in @ SY236 @ SY232 ) ) )
| ( SY232
= ( set_meet @ SV27 ) ) ) ) )
| ~ ( ( SV27 != empty_set )
| ~ ( ~ ( ( SY232
!= ( set_meet @ SV27 ) )
| ( SY232 = empty_set ) )
| ~ ( ( SY232 != empty_set )
| ( SY232
= ( set_meet @ SV27 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(372,plain,
! [SV28: $i] :
( ( ! [SY239: $i] :
( ~ ~ ( in @ SV28 @ SY239 )
| ( disjoint @ ( singleton @ SV28 ) @ SY239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(373,plain,
! [SV29: $i] :
( ( ~ ( relation @ SV29 )
| ! [SY240: $i] :
( ~ ( relation @ SY240 )
| ~ ( subset @ SV29 @ SY240 )
| ~ ( ~ ( subset @ ( relation_dom @ SV29 ) @ ( relation_dom @ SY240 ) )
| ~ ( subset @ ( relation_rng @ SV29 ) @ ( relation_rng @ SY240 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(374,plain,
! [SV30: $i] :
( ( ! [SY241: $i] :
( ~ ( in @ SV30 @ SY241 )
| ( subset @ SV30 @ ( union @ SY241 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(375,plain,
! [SV31: $i] :
( ( ! [SY242: $i] :
~ ( ~ ( ~ ~ ( empty @ SV31 )
| ~ ( ~ ( ~ ( element @ SY242 @ SV31 )
| ( in @ SY242 @ SV31 ) )
| ~ ( ~ ( in @ SY242 @ SV31 )
| ( element @ SY242 @ SV31 ) ) ) )
| ~ ( ~ ( empty @ SV31 )
| ~ ( ~ ( ~ ( element @ SY242 @ SV31 )
| ( empty @ SY242 ) )
| ~ ( ~ ( empty @ SY242 )
| ( element @ SY242 @ SV31 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(376,plain,
! [SV32: $i] :
( ( ! [SY243: $i] :
( ~ ( in @ SV32 @ SY243 )
| ( subset @ SV32 @ ( union @ SY243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(377,plain,
! [SV33: $i] :
( ( ! [SY244: $i,SY245: $i] :
~ ( ~ ( ( SY245
!= ( unordered_pair @ SV33 @ SY244 ) )
| ! [SY246: $i] :
~ ( ~ ( ~ ( in @ SY246 @ SY245 )
| ( SY246 = SV33 )
| ( SY246 = SY244 ) )
| ~ ( ~ ( ( SY246 = SV33 )
| ( SY246 = SY244 ) )
| ( in @ SY246 @ SY245 ) ) ) )
| ~ ( ~ ! [SY247: $i] :
~ ( ~ ( ~ ( in @ SY247 @ SY245 )
| ( SY247 = SV33 )
| ( SY247 = SY244 ) )
| ~ ( ~ ( ( SY247 = SV33 )
| ( SY247 = SY244 ) )
| ( in @ SY247 @ SY245 ) ) )
| ( SY245
= ( unordered_pair @ SV33 @ SY244 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(378,plain,
! [SV34: $i] :
( ( ! [SY248: $i] :
( ~ ( in @ SV34 @ SY248 )
| ( ( set_union2 @ ( singleton @ SV34 ) @ SY248 )
= SY248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(379,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(380,plain,
! [SV35: $i] :
( ( ! [SY249: $i] :
~ ~ ( ~ ( in @ SV35 @ SY249 )
| ~ ( empty @ SY249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(381,plain,
! [SV36: $i] :
( ( ! [SY250: $i] :
( ~ ( in @ SV36 @ SY250 )
| ~ ( in @ SY250 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(382,plain,
! [SV37: $i] :
( ( ~ ! [SY251: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV37 @ SY251 )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY251 )
| ~ ( subset @ SX3 @ SX2 ) )
| ( in @ SX3 @ SY251 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SY251 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SY251 )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) ) ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SX2 @ SY251 )
| ~ ~ ( are_equipotent @ SX2 @ SY251 ) )
| ~ ~ ( in @ SX2 @ SY251 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(383,plain,
! [SV38: $i] :
( ( ! [SY258: $i] :
( ~ ( in @ SV38 @ SY258 )
| ( element @ SV38 @ SY258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(384,plain,
! [SV39: $i] :
( ( ~ ( ~ ( ~ ( relation @ SV39 )
| ! [SY259: $i] :
~ ~ ( ~ ( in @ SY259 @ SV39 )
| ~ ! [SX2: $i,SX3: $i] :
( SY259
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
| ~ ( ~ ! [SY262: $i] :
~ ~ ( ~ ( in @ SY262 @ SV39 )
| ~ ! [SX2: $i,SX3: $i] :
( SY262
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SV39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(385,plain,
! [SV40: $i] :
( ( ! [SY265: $i,SY266: $i,SY267: $i] :
( ( ( ordered_pair @ SV40 @ SY265 )
!= ( ordered_pair @ SY266 @ SY267 ) )
| ~ ( ( SV40 != SY266 )
| ( SY265 != SY267 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(386,plain,
! [SV41: $i] :
( ( ! [SY268: $i,SY269: $i] :
( ~ ~ ( ~ ( in @ SV41 @ SY268 )
| ~ ( element @ SY268 @ ( powerset @ SY269 ) ) )
| ( element @ SV41 @ SY269 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[335]) ).
thf(387,plain,
! [SV42: $i] :
( ( ~ ( relation @ SV42 )
| ! [SY270: $i] :
~ ( ~ ( ( SY270
!= ( relation_dom @ SV42 ) )
| ! [SY271: $i] :
~ ( ~ ( ~ ( in @ SY271 @ SY270 )
| ~ ! [SY272: $i] :
~ ( in @ ( ordered_pair @ SY271 @ SY272 ) @ SV42 ) )
| ~ ( ~ ~ ! [SY273: $i] :
~ ( in @ ( ordered_pair @ SY271 @ SY273 ) @ SV42 )
| ( in @ SY271 @ SY270 ) ) ) )
| ~ ( ~ ! [SY274: $i] :
~ ( ~ ( ~ ( in @ SY274 @ SY270 )
| ~ ! [SY275: $i] :
~ ( in @ ( ordered_pair @ SY274 @ SY275 ) @ SV42 ) )
| ~ ( ~ ~ ! [SY276: $i] :
~ ( in @ ( ordered_pair @ SY274 @ SY276 ) @ SV42 )
| ( in @ SY274 @ SY270 ) ) )
| ( SY270
= ( relation_dom @ SV42 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(388,plain,
! [SV43: $i] :
( ( ! [SY277: $i,SY278: $i] :
~ ( ~ ( ( SY278
!= ( set_difference @ SV43 @ SY277 ) )
| ! [SY279: $i] :
~ ( ~ ( ~ ( in @ SY279 @ SY278 )
| ~ ( ~ ( in @ SY279 @ SV43 )
| ~ ~ ( in @ SY279 @ SY277 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY279 @ SV43 )
| ~ ~ ( in @ SY279 @ SY277 ) )
| ( in @ SY279 @ SY278 ) ) ) )
| ~ ( ~ ! [SY280: $i] :
~ ( ~ ( ~ ( in @ SY280 @ SY278 )
| ~ ( ~ ( in @ SY280 @ SV43 )
| ~ ~ ( in @ SY280 @ SY277 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY280 @ SV43 )
| ~ ~ ( in @ SY280 @ SY277 ) )
| ( in @ SY280 @ SY278 ) ) )
| ( SY278
= ( set_difference @ SV43 @ SY277 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(389,plain,
! [SV44: $i] :
( ( ! [SY281: $i,SY282: $i] :
( ~ ( element @ SY282 @ ( powerset @ SV44 ) )
| ~ ~ ( ~ ( in @ SY281 @ ( subset_complement @ SV44 @ SY282 ) )
| ~ ( in @ SY281 @ SY282 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(390,plain,
! [SV45: $i] :
( ( ! [SY283: $i,SY284: $i,SY285: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV45 @ SY283 ) @ ( cartesian_product2 @ SY284 @ SY285 ) )
| ~ ( ~ ( in @ SV45 @ SY284 )
| ~ ( in @ SY283 @ SY285 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV45 @ SY284 )
| ~ ( in @ SY283 @ SY285 ) )
| ( in @ ( ordered_pair @ SV45 @ SY283 ) @ ( cartesian_product2 @ SY284 @ SY285 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(391,plain,
! [SV46: $i] :
( ( ! [SY286: $i] :
~ ( ~ ( ~ ( subset @ ( singleton @ SV46 ) @ SY286 )
| ( in @ SV46 @ SY286 ) )
| ~ ( ~ ( in @ SV46 @ SY286 )
| ( subset @ ( singleton @ SV46 ) @ SY286 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(392,plain,
! [SV47: $i] :
( ( ! [SY287: $i] :
~ ( ~ ( ~ ( subset @ ( singleton @ SV47 ) @ SY287 )
| ( in @ SV47 @ SY287 ) )
| ~ ( ~ ( in @ SV47 @ SY287 )
| ( subset @ ( singleton @ SV47 ) @ SY287 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(393,plain,
! [SV48: $i] :
( ( ! [SY288: $i] :
~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SV48 @ SY288 )
| ~ ! [SY289: $i] :
~ ( in @ SY289 @ ( set_intersection2 @ SV48 @ SY288 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY290: $i] :
~ ( in @ SY290 @ ( set_intersection2 @ SV48 @ SY288 ) )
| ~ ( disjoint @ SV48 @ SY288 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(394,plain,
! [SV49: $i] :
( ( ! [SY291: $i,SY292: $i,SY293: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV49 @ SY291 ) @ ( cartesian_product2 @ SY292 @ SY293 ) )
| ~ ( ~ ( in @ SV49 @ SY292 )
| ~ ( in @ SY291 @ SY293 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV49 @ SY292 )
| ~ ( in @ SY291 @ SY293 ) )
| ( in @ ( ordered_pair @ SV49 @ SY291 ) @ ( cartesian_product2 @ SY292 @ SY293 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(395,plain,
! [SV50: $i,SV1: $i] :
( ( ( ordered_pair @ SV1 @ SV50 )
= ( unordered_pair @ ( unordered_pair @ SV1 @ SV50 ) @ ( singleton @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(396,plain,
! [SV51: $i,SV2: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV2 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(397,plain,
! [SV3: $i] :
( ( ! [SY160: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV3 @ SY160 )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY160 )
| ~ ( subset @ SX3 @ SX2 ) )
| ( in @ SX3 @ SY160 ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY160 )
| ( in @ ( powerset @ SX2 ) @ SY160 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SX2 @ SY160 )
| ~ ~ ( are_equipotent @ SX2 @ SY160 ) )
| ~ ~ ( in @ SX2 @ SY160 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(398,plain,
! [SV4: $i,SV52: $i] :
( ( ~ ( ~ ( ( SV52
!= ( union @ SV4 ) )
| ! [SY294: $i] :
~ ( ~ ( ~ ( in @ SY294 @ SV52 )
| ~ ! [SY167: $i] :
~ ~ ( ~ ( in @ SY294 @ SY167 )
| ~ ( in @ SY167 @ SV4 ) ) )
| ~ ( ~ ~ ! [SY168: $i] :
~ ~ ( ~ ( in @ SY294 @ SY168 )
| ~ ( in @ SY168 @ SV4 ) )
| ( in @ SY294 @ SV52 ) ) ) )
| ~ ( ~ ! [SY297: $i] :
~ ( ~ ( ~ ( in @ SY297 @ SV52 )
| ~ ! [SY170: $i] :
~ ~ ( ~ ( in @ SY297 @ SY170 )
| ~ ( in @ SY170 @ SV4 ) ) )
| ~ ( ~ ~ ! [SY171: $i] :
~ ~ ( ~ ( in @ SY297 @ SY171 )
| ~ ( in @ SY171 @ SV4 ) )
| ( in @ SY297 @ SV52 ) ) )
| ( SV52
= ( union @ SV4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(399,plain,
! [SV53: $i,SV5: $i] :
( ( ~ ( element @ SV5 @ SV53 )
| ( empty @ SV53 )
| ( in @ SV5 @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(400,plain,
! [SV54: $i,SV6: $i] :
( ( ! [SY300: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV6 @ SV54 )
| ~ ( element @ SV54 @ ( powerset @ SY300 ) ) )
| ~ ( empty @ SY300 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(401,plain,
! [SV7: $i,SV55: $i] :
( ( ~ ( element @ SV55 @ ( powerset @ SV7 ) )
| ! [SY301: $i] :
( ~ ( in @ SY301 @ SV55 )
| ( in @ SY301 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(402,plain,
! [SV56: $i,SV8: $i] :
( ( ~ ( ~ ( ( ( set_difference @ SV8 @ ( singleton @ SV56 ) )
!= SV8 )
| ~ ( in @ SV56 @ SV8 ) )
| ~ ( ~ ~ ( in @ SV56 @ SV8 )
| ( ( set_difference @ SV8 @ ( singleton @ SV56 ) )
= SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(403,plain,
! [SV9: $i] :
( ( ( ~ ( relation @ SV9 ) )
= $true )
| ( ( ! [SY178: $i] :
~ ( ~ ( ( SY178
!= ( relation_rng @ SV9 ) )
| ! [SY179: $i] :
~ ( ~ ( ~ ( in @ SY179 @ SY178 )
| ~ ! [SY180: $i] :
~ ( in @ ( ordered_pair @ SY180 @ SY179 ) @ SV9 ) )
| ~ ( ~ ~ ! [SY181: $i] :
~ ( in @ ( ordered_pair @ SY181 @ SY179 ) @ SV9 )
| ( in @ SY179 @ SY178 ) ) ) )
| ~ ( ~ ! [SY182: $i] :
~ ( ~ ( ~ ( in @ SY182 @ SY178 )
| ~ ! [SY183: $i] :
~ ( in @ ( ordered_pair @ SY183 @ SY182 ) @ SV9 ) )
| ~ ( ~ ~ ! [SY184: $i] :
~ ( in @ ( ordered_pair @ SY184 @ SY182 ) @ SV9 )
| ( in @ SY182 @ SY178 ) ) )
| ( SY178
= ( relation_rng @ SV9 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[353]) ).
thf(404,plain,
! [SV57: $i,SV10: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV10 @ SV57 )
| ! [SY302: $i] :
( ~ ( in @ SY302 @ SV10 )
| ( in @ SY302 @ SV57 ) ) )
| ~ ( ~ ! [SY303: $i] :
( ~ ( in @ SY303 @ SV10 )
| ( in @ SY303 @ SV57 ) )
| ( subset @ SV10 @ SV57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(405,plain,
! [SV11: $i] :
( ( ( ~ ( relation @ SV11 ) )
= $true )
| ( ( ( relation_field @ SV11 )
= ( set_union2 @ ( relation_dom @ SV11 ) @ ( relation_rng @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[355]) ).
thf(406,plain,
! [SV12: $i,SV58: $i] :
( ( ~ ( ~ ( ( SV58
!= ( powerset @ SV12 ) )
| ! [SY304: $i] :
~ ( ~ ( ~ ( in @ SY304 @ SV58 )
| ( subset @ SY304 @ SV12 ) )
| ~ ( ~ ( subset @ SY304 @ SV12 )
| ( in @ SY304 @ SV58 ) ) ) )
| ~ ( ~ ! [SY305: $i] :
~ ( ~ ( ~ ( in @ SY305 @ SV58 )
| ( subset @ SY305 @ SV12 ) )
| ~ ( ~ ( subset @ SY305 @ SV12 )
| ( in @ SY305 @ SV58 ) ) )
| ( SV58
= ( powerset @ SV12 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(407,plain,
! [SV59: $i,SV13: $i] :
( ( ~ ! [SY306: $i] :
( ~ ( in @ SY306 @ SV13 )
| ( in @ SY306 @ SV59 ) )
| ( element @ SV13 @ ( powerset @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[357]) ).
thf(408,plain,
! [SV60: $i,SV14: $i] :
( ( ~ ! [SY307: $i] :
~ ( ~ ( ~ ( in @ SY307 @ SV14 )
| ( in @ SY307 @ SV60 ) )
| ~ ( ~ ( in @ SY307 @ SV60 )
| ( in @ SY307 @ SV14 ) ) )
| ( SV14 = SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(409,plain,
! [SV61: $i,SV15: $i] :
( ( ~ ~ ( ~ ( relation @ SV15 )
| ~ ( relation @ SV61 ) )
| ( relation @ ( set_union2 @ SV15 @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(410,plain,
! [SV16: $i] :
( ( ~ ( ( SV16 != empty_set )
| ! [SY196: $i] :
~ ( in @ SY196 @ SV16 ) )
| ~ ( ~ ! [SY197: $i] :
~ ( in @ SY197 @ SV16 )
| ( SV16 = empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(411,plain,
! [SV62: $i,SV17: $i] :
( ( ! [SY308: $i] :
( ~ ( subset @ SV17 @ SV62 )
| ( in @ SY308 @ SV17 )
| ( subset @ SV17 @ ( set_difference @ SV62 @ ( singleton @ SY308 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(412,plain,
! [SV63: $i,SV18: $i] :
( ( ! [SY309: $i] :
~ ( ~ ( ( SY309
!= ( set_intersection2 @ SV18 @ SV63 ) )
| ! [SY310: $i] :
~ ( ~ ( ~ ( in @ SY310 @ SY309 )
| ~ ( ~ ( in @ SY310 @ SV18 )
| ~ ( in @ SY310 @ SV63 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY310 @ SV18 )
| ~ ( in @ SY310 @ SV63 ) )
| ( in @ SY310 @ SY309 ) ) ) )
| ~ ( ~ ! [SY311: $i] :
~ ( ~ ( ~ ( in @ SY311 @ SY309 )
| ~ ( ~ ( in @ SY311 @ SV18 )
| ~ ( in @ SY311 @ SV63 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY311 @ SV18 )
| ~ ( in @ SY311 @ SV63 ) )
| ( in @ SY311 @ SY309 ) ) )
| ( SY309
= ( set_intersection2 @ SV18 @ SV63 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(413,plain,
! [SV64: $i,SV19: $i] :
( ( ! [SY312: $i] :
~ ( ~ ( ~ ( subset @ ( unordered_pair @ SV19 @ SV64 ) @ SY312 )
| ~ ( ~ ( in @ SV19 @ SY312 )
| ~ ( in @ SV64 @ SY312 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV19 @ SY312 )
| ~ ( in @ SV64 @ SY312 ) )
| ( subset @ ( unordered_pair @ SV19 @ SV64 ) @ SY312 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(414,plain,
! [SV65: $i,SV20: $i] :
( ( ~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SV20 @ SV65 )
| ~ ! [SY313: $i] :
~ ~ ( ~ ( in @ SY313 @ SV20 )
| ~ ( in @ SY313 @ SV65 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY314: $i] :
~ ~ ( ~ ( in @ SY314 @ SV20 )
| ~ ( in @ SY314 @ SV65 ) )
| ~ ( disjoint @ SV20 @ SV65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(415,plain,
! [SV66: $i,SV21: $i] :
( ( ~ ( in @ SV21 @ SV66 )
| ( ( set_union2 @ ( singleton @ SV21 ) @ SV66 )
= SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(416,plain,
! [SV67: $i,SV22: $i] :
( ( ! [SY315: $i] :
~ ( ~ ( ( SY315
!= ( cartesian_product2 @ SV22 @ SV67 ) )
| ! [SY316: $i] :
~ ( ~ ( ~ ( in @ SY316 @ SY315 )
| ~ ! [SY317: $i] :
~ ~ ! [SY318: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY317 @ SV22 )
| ~ ( in @ SY318 @ SV67 ) )
| ( SY316
!= ( ordered_pair @ SY317 @ SY318 ) ) ) )
| ~ ( ~ ~ ! [SY319: $i] :
~ ~ ! [SY320: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY319 @ SV22 )
| ~ ( in @ SY320 @ SV67 ) )
| ( SY316
!= ( ordered_pair @ SY319 @ SY320 ) ) )
| ( in @ SY316 @ SY315 ) ) ) )
| ~ ( ~ ! [SY321: $i] :
~ ( ~ ( ~ ( in @ SY321 @ SY315 )
| ~ ! [SY322: $i] :
~ ~ ! [SY323: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY322 @ SV22 )
| ~ ( in @ SY323 @ SV67 ) )
| ( SY321
!= ( ordered_pair @ SY322 @ SY323 ) ) ) )
| ~ ( ~ ~ ! [SY324: $i] :
~ ~ ! [SY325: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY324 @ SV22 )
| ~ ( in @ SY325 @ SV67 ) )
| ( SY321
!= ( ordered_pair @ SY324 @ SY325 ) ) )
| ( in @ SY321 @ SY315 ) ) )
| ( SY315
= ( cartesian_product2 @ SV22 @ SV67 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(417,plain,
! [SV68: $i,SV23: $i] :
( ( ! [SY326: $i] :
~ ( ~ ( ( SY326
!= ( set_union2 @ SV23 @ SV68 ) )
| ! [SY327: $i] :
~ ( ~ ( ~ ( in @ SY327 @ SY326 )
| ( in @ SY327 @ SV23 )
| ( in @ SY327 @ SV68 ) )
| ~ ( ~ ( ( in @ SY327 @ SV23 )
| ( in @ SY327 @ SV68 ) )
| ( in @ SY327 @ SY326 ) ) ) )
| ~ ( ~ ! [SY328: $i] :
~ ( ~ ( ~ ( in @ SY328 @ SY326 )
| ( in @ SY328 @ SV23 )
| ( in @ SY328 @ SV68 ) )
| ~ ( ~ ( ( in @ SY328 @ SV23 )
| ( in @ SY328 @ SV68 ) )
| ( in @ SY328 @ SY326 ) ) )
| ( SY326
= ( set_union2 @ SV23 @ SV68 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(418,plain,
! [SV69: $i,SV24: $i] :
( ( ! [SY329: $i] :
( ~ ( relation @ SY329 )
| ~ ( in @ ( ordered_pair @ SV24 @ SV69 ) @ SY329 )
| ~ ( ~ ( in @ SV24 @ ( relation_dom @ SY329 ) )
| ~ ( in @ SV69 @ ( relation_rng @ SY329 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(419,plain,
! [SV70: $i,SV25: $i] :
( ( ~ ~ ( ~ ( disjoint @ ( singleton @ SV25 ) @ SV70 )
| ~ ( in @ SV25 @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(420,plain,
! [SV26: $i,SV71: $i] :
( ( ~ ( ~ ( ( SV71
!= ( singleton @ SV26 ) )
| ! [SY330: $i] :
~ ( ~ ( ~ ( in @ SY330 @ SV71 )
| ( SY330 = SV26 ) )
| ~ ( ( SY330 != SV26 )
| ( in @ SY330 @ SV71 ) ) ) )
| ~ ( ~ ! [SY331: $i] :
~ ( ~ ( ~ ( in @ SY331 @ SV71 )
| ( SY331 = SV26 ) )
| ~ ( ( SY331 != SV26 )
| ( in @ SY331 @ SV71 ) ) )
| ( SV71
= ( singleton @ SV26 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(421,plain,
! [SV72: $i,SV27: $i] :
( ( ~ ( ~ ( ~ ( ( SV27 != empty_set ) )
| ~ ( ~ ( ( SV72
!= ( set_meet @ SV27 ) )
| ! [SY332: $i] :
~ ( ~ ( ~ ( in @ SY332 @ SV72 )
| ! [SY234: $i] :
( ~ ( in @ SY234 @ SV27 )
| ( in @ SY332 @ SY234 ) ) )
| ~ ( ~ ! [SY235: $i] :
( ~ ( in @ SY235 @ SV27 )
| ( in @ SY332 @ SY235 ) )
| ( in @ SY332 @ SV72 ) ) ) )
| ~ ( ~ ! [SY335: $i] :
~ ( ~ ( ~ ( in @ SY335 @ SV72 )
| ! [SY237: $i] :
( ~ ( in @ SY237 @ SV27 )
| ( in @ SY335 @ SY237 ) ) )
| ~ ( ~ ! [SY238: $i] :
( ~ ( in @ SY238 @ SV27 )
| ( in @ SY335 @ SY238 ) )
| ( in @ SY335 @ SV72 ) ) )
| ( SV72
= ( set_meet @ SV27 ) ) ) ) )
| ~ ( ( SV27 != empty_set )
| ~ ( ~ ( ( SV72
!= ( set_meet @ SV27 ) )
| ( SV72 = empty_set ) )
| ~ ( ( SV72 != empty_set )
| ( SV72
= ( set_meet @ SV27 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(422,plain,
! [SV73: $i,SV28: $i] :
( ( ~ ~ ( in @ SV28 @ SV73 )
| ( disjoint @ ( singleton @ SV28 ) @ SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(423,plain,
! [SV29: $i] :
( ( ( ~ ( relation @ SV29 ) )
= $true )
| ( ( ! [SY240: $i] :
( ~ ( relation @ SY240 )
| ~ ( subset @ SV29 @ SY240 )
| ~ ( ~ ( subset @ ( relation_dom @ SV29 ) @ ( relation_dom @ SY240 ) )
| ~ ( subset @ ( relation_rng @ SV29 ) @ ( relation_rng @ SY240 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[373]) ).
thf(424,plain,
! [SV74: $i,SV30: $i] :
( ( ~ ( in @ SV30 @ SV74 )
| ( subset @ SV30 @ ( union @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(425,plain,
! [SV75: $i,SV31: $i] :
( ( ~ ( ~ ( ~ ~ ( empty @ SV31 )
| ~ ( ~ ( ~ ( element @ SV75 @ SV31 )
| ( in @ SV75 @ SV31 ) )
| ~ ( ~ ( in @ SV75 @ SV31 )
| ( element @ SV75 @ SV31 ) ) ) )
| ~ ( ~ ( empty @ SV31 )
| ~ ( ~ ( ~ ( element @ SV75 @ SV31 )
| ( empty @ SV75 ) )
| ~ ( ~ ( empty @ SV75 )
| ( element @ SV75 @ SV31 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(426,plain,
! [SV76: $i,SV32: $i] :
( ( ~ ( in @ SV32 @ SV76 )
| ( subset @ SV32 @ ( union @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(427,plain,
! [SV77: $i,SV33: $i] :
( ( ! [SY338: $i] :
~ ( ~ ( ( SY338
!= ( unordered_pair @ SV33 @ SV77 ) )
| ! [SY339: $i] :
~ ( ~ ( ~ ( in @ SY339 @ SY338 )
| ( SY339 = SV33 )
| ( SY339 = SV77 ) )
| ~ ( ~ ( ( SY339 = SV33 )
| ( SY339 = SV77 ) )
| ( in @ SY339 @ SY338 ) ) ) )
| ~ ( ~ ! [SY340: $i] :
~ ( ~ ( ~ ( in @ SY340 @ SY338 )
| ( SY340 = SV33 )
| ( SY340 = SV77 ) )
| ~ ( ~ ( ( SY340 = SV33 )
| ( SY340 = SV77 ) )
| ( in @ SY340 @ SY338 ) ) )
| ( SY338
= ( unordered_pair @ SV33 @ SV77 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(428,plain,
! [SV78: $i,SV34: $i] :
( ( ~ ( in @ SV34 @ SV78 )
| ( ( set_union2 @ ( singleton @ SV34 ) @ SV78 )
= SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(429,plain,
( ( ~ ~ ( ~ ( empty @ sK4_SX0 )
| ~ ( relation @ sK4_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[379]) ).
thf(430,plain,
! [SV79: $i,SV35: $i] :
( ( ~ ~ ( ~ ( in @ SV35 @ SV79 )
| ~ ( empty @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(431,plain,
! [SV80: $i,SV36: $i] :
( ( ~ ( in @ SV36 @ SV80 )
| ~ ( in @ SV80 @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(432,plain,
! [SV37: $i] :
( ( ! [SY251: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV37 @ SY251 )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY251 )
| ~ ( subset @ SX3 @ SX2 ) )
| ( in @ SX3 @ SY251 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SY251 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SY251 )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) ) ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SX2 @ SY251 )
| ~ ~ ( are_equipotent @ SX2 @ SY251 ) )
| ~ ~ ( in @ SX2 @ SY251 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(433,plain,
! [SV81: $i,SV38: $i] :
( ( ~ ( in @ SV38 @ SV81 )
| ( element @ SV38 @ SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(434,plain,
! [SV39: $i] :
( ( ~ ( ~ ( relation @ SV39 )
| ! [SY259: $i] :
~ ~ ( ~ ( in @ SY259 @ SV39 )
| ~ ! [SX2: $i,SX3: $i] :
( SY259
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
| ~ ( ~ ! [SY262: $i] :
~ ~ ( ~ ( in @ SY262 @ SV39 )
| ~ ! [SX2: $i,SX3: $i] :
( SY262
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SV39 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(435,plain,
! [SV82: $i,SV40: $i] :
( ( ! [SY341: $i,SY342: $i] :
( ( ( ordered_pair @ SV40 @ SV82 )
!= ( ordered_pair @ SY341 @ SY342 ) )
| ~ ( ( SV40 != SY341 )
| ( SV82 != SY342 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(436,plain,
! [SV83: $i,SV41: $i] :
( ( ! [SY343: $i] :
( ~ ~ ( ~ ( in @ SV41 @ SV83 )
| ~ ( element @ SV83 @ ( powerset @ SY343 ) ) )
| ( element @ SV41 @ SY343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(437,plain,
! [SV42: $i] :
( ( ( ~ ( relation @ SV42 ) )
= $true )
| ( ( ! [SY270: $i] :
~ ( ~ ( ( SY270
!= ( relation_dom @ SV42 ) )
| ! [SY271: $i] :
~ ( ~ ( ~ ( in @ SY271 @ SY270 )
| ~ ! [SY272: $i] :
~ ( in @ ( ordered_pair @ SY271 @ SY272 ) @ SV42 ) )
| ~ ( ~ ~ ! [SY273: $i] :
~ ( in @ ( ordered_pair @ SY271 @ SY273 ) @ SV42 )
| ( in @ SY271 @ SY270 ) ) ) )
| ~ ( ~ ! [SY274: $i] :
~ ( ~ ( ~ ( in @ SY274 @ SY270 )
| ~ ! [SY275: $i] :
~ ( in @ ( ordered_pair @ SY274 @ SY275 ) @ SV42 ) )
| ~ ( ~ ~ ! [SY276: $i] :
~ ( in @ ( ordered_pair @ SY274 @ SY276 ) @ SV42 )
| ( in @ SY274 @ SY270 ) ) )
| ( SY270
= ( relation_dom @ SV42 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[387]) ).
thf(438,plain,
! [SV84: $i,SV43: $i] :
( ( ! [SY344: $i] :
~ ( ~ ( ( SY344
!= ( set_difference @ SV43 @ SV84 ) )
| ! [SY345: $i] :
~ ( ~ ( ~ ( in @ SY345 @ SY344 )
| ~ ( ~ ( in @ SY345 @ SV43 )
| ~ ~ ( in @ SY345 @ SV84 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY345 @ SV43 )
| ~ ~ ( in @ SY345 @ SV84 ) )
| ( in @ SY345 @ SY344 ) ) ) )
| ~ ( ~ ! [SY346: $i] :
~ ( ~ ( ~ ( in @ SY346 @ SY344 )
| ~ ( ~ ( in @ SY346 @ SV43 )
| ~ ~ ( in @ SY346 @ SV84 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY346 @ SV43 )
| ~ ~ ( in @ SY346 @ SV84 ) )
| ( in @ SY346 @ SY344 ) ) )
| ( SY344
= ( set_difference @ SV43 @ SV84 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(439,plain,
! [SV85: $i,SV44: $i] :
( ( ! [SY347: $i] :
( ~ ( element @ SY347 @ ( powerset @ SV44 ) )
| ~ ~ ( ~ ( in @ SV85 @ ( subset_complement @ SV44 @ SY347 ) )
| ~ ( in @ SV85 @ SY347 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(440,plain,
! [SV86: $i,SV45: $i] :
( ( ! [SY348: $i,SY349: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV45 @ SV86 ) @ ( cartesian_product2 @ SY348 @ SY349 ) )
| ~ ( ~ ( in @ SV45 @ SY348 )
| ~ ( in @ SV86 @ SY349 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV45 @ SY348 )
| ~ ( in @ SV86 @ SY349 ) )
| ( in @ ( ordered_pair @ SV45 @ SV86 ) @ ( cartesian_product2 @ SY348 @ SY349 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(441,plain,
! [SV87: $i,SV46: $i] :
( ( ~ ( ~ ( ~ ( subset @ ( singleton @ SV46 ) @ SV87 )
| ( in @ SV46 @ SV87 ) )
| ~ ( ~ ( in @ SV46 @ SV87 )
| ( subset @ ( singleton @ SV46 ) @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(442,plain,
! [SV88: $i,SV47: $i] :
( ( ~ ( ~ ( ~ ( subset @ ( singleton @ SV47 ) @ SV88 )
| ( in @ SV47 @ SV88 ) )
| ~ ( ~ ( in @ SV47 @ SV88 )
| ( subset @ ( singleton @ SV47 ) @ SV88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(443,plain,
! [SV89: $i,SV48: $i] :
( ( ~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SV48 @ SV89 )
| ~ ! [SY350: $i] :
~ ( in @ SY350 @ ( set_intersection2 @ SV48 @ SV89 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY351: $i] :
~ ( in @ SY351 @ ( set_intersection2 @ SV48 @ SV89 ) )
| ~ ( disjoint @ SV48 @ SV89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(444,plain,
! [SV90: $i,SV49: $i] :
( ( ! [SY352: $i,SY353: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV49 @ SV90 ) @ ( cartesian_product2 @ SY352 @ SY353 ) )
| ~ ( ~ ( in @ SV49 @ SY352 )
| ~ ( in @ SV90 @ SY353 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV49 @ SY352 )
| ~ ( in @ SV90 @ SY353 ) )
| ( in @ ( ordered_pair @ SV49 @ SV90 ) @ ( cartesian_product2 @ SY352 @ SY353 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(445,plain,
! [SV51: $i,SV2: $i] :
( ( empty @ ( ordered_pair @ SV2 @ SV51 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(446,plain,
! [SV3: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV3 @ ( sK5_SY160 @ SV3 ) )
| ~ ! [SY354: $i,SY355: $i] :
( ~ ~ ( ~ ( in @ SY354 @ ( sK5_SY160 @ SV3 ) )
| ~ ( subset @ SY355 @ SY354 ) )
| ( in @ SY355 @ ( sK5_SY160 @ SV3 ) ) ) )
| ~ ! [SY356: $i] :
( ~ ( in @ SY356 @ ( sK5_SY160 @ SV3 ) )
| ( in @ ( powerset @ SY356 ) @ ( sK5_SY160 @ SV3 ) ) ) )
| ~ ! [SY357: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY357 @ ( sK5_SY160 @ SV3 ) )
| ~ ~ ( are_equipotent @ SY357 @ ( sK5_SY160 @ SV3 ) ) )
| ~ ~ ( in @ SY357 @ ( sK5_SY160 @ SV3 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[397]) ).
thf(447,plain,
! [SV4: $i,SV52: $i] :
( ( ~ ( ( SV52
!= ( union @ SV4 ) )
| ! [SY294: $i] :
~ ( ~ ( ~ ( in @ SY294 @ SV52 )
| ~ ! [SY167: $i] :
~ ~ ( ~ ( in @ SY294 @ SY167 )
| ~ ( in @ SY167 @ SV4 ) ) )
| ~ ( ~ ~ ! [SY168: $i] :
~ ~ ( ~ ( in @ SY294 @ SY168 )
| ~ ( in @ SY168 @ SV4 ) )
| ( in @ SY294 @ SV52 ) ) ) )
| ~ ( ~ ! [SY297: $i] :
~ ( ~ ( ~ ( in @ SY297 @ SV52 )
| ~ ! [SY170: $i] :
~ ~ ( ~ ( in @ SY297 @ SY170 )
| ~ ( in @ SY170 @ SV4 ) ) )
| ~ ( ~ ~ ! [SY171: $i] :
~ ~ ( ~ ( in @ SY297 @ SY171 )
| ~ ( in @ SY171 @ SV4 ) )
| ( in @ SY297 @ SV52 ) ) )
| ( SV52
= ( union @ SV4 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(448,plain,
! [SV53: $i,SV5: $i] :
( ( ( ~ ( element @ SV5 @ SV53 ) )
= $true )
| ( ( ( empty @ SV53 )
| ( in @ SV5 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[399]) ).
thf(449,plain,
! [SV91: $i,SV54: $i,SV6: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( in @ SV6 @ SV54 )
| ~ ( element @ SV54 @ ( powerset @ SV91 ) ) )
| ~ ( empty @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(450,plain,
! [SV7: $i,SV55: $i] :
( ( ( ~ ( element @ SV55 @ ( powerset @ SV7 ) ) )
= $true )
| ( ( ! [SY301: $i] :
( ~ ( in @ SY301 @ SV55 )
| ( in @ SY301 @ SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[401]) ).
thf(451,plain,
! [SV56: $i,SV8: $i] :
( ( ~ ( ( ( set_difference @ SV8 @ ( singleton @ SV56 ) )
!= SV8 )
| ~ ( in @ SV56 @ SV8 ) )
| ~ ( ~ ~ ( in @ SV56 @ SV8 )
| ( ( set_difference @ SV8 @ ( singleton @ SV56 ) )
= SV8 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[402]) ).
thf(452,plain,
! [SV9: $i] :
( ( ( relation @ SV9 )
= $false )
| ( ( ! [SY178: $i] :
~ ( ~ ( ( SY178
!= ( relation_rng @ SV9 ) )
| ! [SY179: $i] :
~ ( ~ ( ~ ( in @ SY179 @ SY178 )
| ~ ! [SY180: $i] :
~ ( in @ ( ordered_pair @ SY180 @ SY179 ) @ SV9 ) )
| ~ ( ~ ~ ! [SY181: $i] :
~ ( in @ ( ordered_pair @ SY181 @ SY179 ) @ SV9 )
| ( in @ SY179 @ SY178 ) ) ) )
| ~ ( ~ ! [SY182: $i] :
~ ( ~ ( ~ ( in @ SY182 @ SY178 )
| ~ ! [SY183: $i] :
~ ( in @ ( ordered_pair @ SY183 @ SY182 ) @ SV9 ) )
| ~ ( ~ ~ ! [SY184: $i] :
~ ( in @ ( ordered_pair @ SY184 @ SY182 ) @ SV9 )
| ( in @ SY182 @ SY178 ) ) )
| ( SY178
= ( relation_rng @ SV9 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(453,plain,
! [SV57: $i,SV10: $i] :
( ( ~ ( ~ ( subset @ SV10 @ SV57 )
| ! [SY302: $i] :
( ~ ( in @ SY302 @ SV10 )
| ( in @ SY302 @ SV57 ) ) )
| ~ ( ~ ! [SY303: $i] :
( ~ ( in @ SY303 @ SV10 )
| ( in @ SY303 @ SV57 ) )
| ( subset @ SV10 @ SV57 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[404]) ).
thf(454,plain,
! [SV11: $i] :
( ( ( relation @ SV11 )
= $false )
| ( ( ( relation_field @ SV11 )
= ( set_union2 @ ( relation_dom @ SV11 ) @ ( relation_rng @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(455,plain,
! [SV12: $i,SV58: $i] :
( ( ~ ( ( SV58
!= ( powerset @ SV12 ) )
| ! [SY304: $i] :
~ ( ~ ( ~ ( in @ SY304 @ SV58 )
| ( subset @ SY304 @ SV12 ) )
| ~ ( ~ ( subset @ SY304 @ SV12 )
| ( in @ SY304 @ SV58 ) ) ) )
| ~ ( ~ ! [SY305: $i] :
~ ( ~ ( ~ ( in @ SY305 @ SV58 )
| ( subset @ SY305 @ SV12 ) )
| ~ ( ~ ( subset @ SY305 @ SV12 )
| ( in @ SY305 @ SV58 ) ) )
| ( SV58
= ( powerset @ SV12 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(456,plain,
! [SV59: $i,SV13: $i] :
( ( ( ~ ! [SY306: $i] :
( ~ ( in @ SY306 @ SV13 )
| ( in @ SY306 @ SV59 ) ) )
= $true )
| ( ( element @ SV13 @ ( powerset @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[407]) ).
thf(457,plain,
! [SV60: $i,SV14: $i] :
( ( ( ~ ! [SY307: $i] :
~ ( ~ ( ~ ( in @ SY307 @ SV14 )
| ( in @ SY307 @ SV60 ) )
| ~ ( ~ ( in @ SY307 @ SV60 )
| ( in @ SY307 @ SV14 ) ) ) )
= $true )
| ( ( SV14 = SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[408]) ).
thf(458,plain,
! [SV61: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV15 )
| ~ ( relation @ SV61 ) ) )
= $true )
| ( ( relation @ ( set_union2 @ SV15 @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[409]) ).
thf(459,plain,
! [SV16: $i] :
( ( ~ ( ( SV16 != empty_set )
| ! [SY196: $i] :
~ ( in @ SY196 @ SV16 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[410]) ).
thf(460,plain,
! [SV16: $i] :
( ( ~ ( ~ ! [SY197: $i] :
~ ( in @ SY197 @ SV16 )
| ( SV16 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[410]) ).
thf(461,plain,
! [SV92: $i,SV62: $i,SV17: $i] :
( ( ~ ( subset @ SV17 @ SV62 )
| ( in @ SV92 @ SV17 )
| ( subset @ SV17 @ ( set_difference @ SV62 @ ( singleton @ SV92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(462,plain,
! [SV63: $i,SV18: $i,SV93: $i] :
( ( ~ ( ~ ( ( SV93
!= ( set_intersection2 @ SV18 @ SV63 ) )
| ! [SY358: $i] :
~ ( ~ ( ~ ( in @ SY358 @ SV93 )
| ~ ( ~ ( in @ SY358 @ SV18 )
| ~ ( in @ SY358 @ SV63 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY358 @ SV18 )
| ~ ( in @ SY358 @ SV63 ) )
| ( in @ SY358 @ SV93 ) ) ) )
| ~ ( ~ ! [SY359: $i] :
~ ( ~ ( ~ ( in @ SY359 @ SV93 )
| ~ ( ~ ( in @ SY359 @ SV18 )
| ~ ( in @ SY359 @ SV63 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY359 @ SV18 )
| ~ ( in @ SY359 @ SV63 ) )
| ( in @ SY359 @ SV93 ) ) )
| ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(463,plain,
! [SV94: $i,SV64: $i,SV19: $i] :
( ( ~ ( ~ ( ~ ( subset @ ( unordered_pair @ SV19 @ SV64 ) @ SV94 )
| ~ ( ~ ( in @ SV19 @ SV94 )
| ~ ( in @ SV64 @ SV94 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV19 @ SV94 )
| ~ ( in @ SV64 @ SV94 ) )
| ( subset @ ( unordered_pair @ SV19 @ SV64 ) @ SV94 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(464,plain,
! [SV65: $i,SV20: $i] :
( ( ~ ~ ~ ( ~ ~ ( disjoint @ SV20 @ SV65 )
| ~ ! [SY313: $i] :
~ ~ ( ~ ( in @ SY313 @ SV20 )
| ~ ( in @ SY313 @ SV65 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY314: $i] :
~ ~ ( ~ ( in @ SY314 @ SV20 )
| ~ ( in @ SY314 @ SV65 ) )
| ~ ( disjoint @ SV20 @ SV65 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(465,plain,
! [SV66: $i,SV21: $i] :
( ( ( ~ ( in @ SV21 @ SV66 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV21 ) @ SV66 )
= SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(466,plain,
! [SV67: $i,SV22: $i,SV95: $i] :
( ( ~ ( ~ ( ( SV95
!= ( cartesian_product2 @ SV22 @ SV67 ) )
| ! [SY360: $i] :
~ ( ~ ( ~ ( in @ SY360 @ SV95 )
| ~ ! [SY317: $i] :
~ ~ ! [SY318: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY317 @ SV22 )
| ~ ( in @ SY318 @ SV67 ) )
| ( SY360
!= ( ordered_pair @ SY317 @ SY318 ) ) ) )
| ~ ( ~ ~ ! [SY319: $i] :
~ ~ ! [SY320: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY319 @ SV22 )
| ~ ( in @ SY320 @ SV67 ) )
| ( SY360
!= ( ordered_pair @ SY319 @ SY320 ) ) )
| ( in @ SY360 @ SV95 ) ) ) )
| ~ ( ~ ! [SY365: $i] :
~ ( ~ ( ~ ( in @ SY365 @ SV95 )
| ~ ! [SY322: $i] :
~ ~ ! [SY323: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY322 @ SV22 )
| ~ ( in @ SY323 @ SV67 ) )
| ( SY365
!= ( ordered_pair @ SY322 @ SY323 ) ) ) )
| ~ ( ~ ~ ! [SY324: $i] :
~ ~ ! [SY325: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY324 @ SV22 )
| ~ ( in @ SY325 @ SV67 ) )
| ( SY365
!= ( ordered_pair @ SY324 @ SY325 ) ) )
| ( in @ SY365 @ SV95 ) ) )
| ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(467,plain,
! [SV68: $i,SV23: $i,SV96: $i] :
( ( ~ ( ~ ( ( SV96
!= ( set_union2 @ SV23 @ SV68 ) )
| ! [SY370: $i] :
~ ( ~ ( ~ ( in @ SY370 @ SV96 )
| ( in @ SY370 @ SV23 )
| ( in @ SY370 @ SV68 ) )
| ~ ( ~ ( ( in @ SY370 @ SV23 )
| ( in @ SY370 @ SV68 ) )
| ( in @ SY370 @ SV96 ) ) ) )
| ~ ( ~ ! [SY371: $i] :
~ ( ~ ( ~ ( in @ SY371 @ SV96 )
| ( in @ SY371 @ SV23 )
| ( in @ SY371 @ SV68 ) )
| ~ ( ~ ( ( in @ SY371 @ SV23 )
| ( in @ SY371 @ SV68 ) )
| ( in @ SY371 @ SV96 ) ) )
| ( SV96
= ( set_union2 @ SV23 @ SV68 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(468,plain,
! [SV69: $i,SV24: $i,SV97: $i] :
( ( ~ ( relation @ SV97 )
| ~ ( in @ ( ordered_pair @ SV24 @ SV69 ) @ SV97 )
| ~ ( ~ ( in @ SV24 @ ( relation_dom @ SV97 ) )
| ~ ( in @ SV69 @ ( relation_rng @ SV97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(469,plain,
! [SV70: $i,SV25: $i] :
( ( ~ ( ~ ( disjoint @ ( singleton @ SV25 ) @ SV70 )
| ~ ( in @ SV25 @ SV70 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(470,plain,
! [SV26: $i,SV71: $i] :
( ( ~ ( ( SV71
!= ( singleton @ SV26 ) )
| ! [SY330: $i] :
~ ( ~ ( ~ ( in @ SY330 @ SV71 )
| ( SY330 = SV26 ) )
| ~ ( ( SY330 != SV26 )
| ( in @ SY330 @ SV71 ) ) ) )
| ~ ( ~ ! [SY331: $i] :
~ ( ~ ( ~ ( in @ SY331 @ SV71 )
| ( SY331 = SV26 ) )
| ~ ( ( SY331 != SV26 )
| ( in @ SY331 @ SV71 ) ) )
| ( SV71
= ( singleton @ SV26 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(471,plain,
! [SV72: $i,SV27: $i] :
( ( ~ ( ~ ( ( SV27 != empty_set ) )
| ~ ( ~ ( ( SV72
!= ( set_meet @ SV27 ) )
| ! [SY332: $i] :
~ ( ~ ( ~ ( in @ SY332 @ SV72 )
| ! [SY234: $i] :
( ~ ( in @ SY234 @ SV27 )
| ( in @ SY332 @ SY234 ) ) )
| ~ ( ~ ! [SY235: $i] :
( ~ ( in @ SY235 @ SV27 )
| ( in @ SY332 @ SY235 ) )
| ( in @ SY332 @ SV72 ) ) ) )
| ~ ( ~ ! [SY335: $i] :
~ ( ~ ( ~ ( in @ SY335 @ SV72 )
| ! [SY237: $i] :
( ~ ( in @ SY237 @ SV27 )
| ( in @ SY335 @ SY237 ) ) )
| ~ ( ~ ! [SY238: $i] :
( ~ ( in @ SY238 @ SV27 )
| ( in @ SY335 @ SY238 ) )
| ( in @ SY335 @ SV72 ) ) )
| ( SV72
= ( set_meet @ SV27 ) ) ) ) )
| ~ ( ( SV27 != empty_set )
| ~ ( ~ ( ( SV72
!= ( set_meet @ SV27 ) )
| ( SV72 = empty_set ) )
| ~ ( ( SV72 != empty_set )
| ( SV72
= ( set_meet @ SV27 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(472,plain,
! [SV73: $i,SV28: $i] :
( ( ( ~ ~ ( in @ SV28 @ SV73 ) )
= $true )
| ( ( disjoint @ ( singleton @ SV28 ) @ SV73 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[422]) ).
thf(473,plain,
! [SV29: $i] :
( ( ( relation @ SV29 )
= $false )
| ( ( ! [SY240: $i] :
( ~ ( relation @ SY240 )
| ~ ( subset @ SV29 @ SY240 )
| ~ ( ~ ( subset @ ( relation_dom @ SV29 ) @ ( relation_dom @ SY240 ) )
| ~ ( subset @ ( relation_rng @ SV29 ) @ ( relation_rng @ SY240 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[423]) ).
thf(474,plain,
! [SV74: $i,SV30: $i] :
( ( ( ~ ( in @ SV30 @ SV74 ) )
= $true )
| ( ( subset @ SV30 @ ( union @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[424]) ).
thf(475,plain,
! [SV75: $i,SV31: $i] :
( ( ~ ( ~ ~ ( empty @ SV31 )
| ~ ( ~ ( ~ ( element @ SV75 @ SV31 )
| ( in @ SV75 @ SV31 ) )
| ~ ( ~ ( in @ SV75 @ SV31 )
| ( element @ SV75 @ SV31 ) ) ) )
| ~ ( ~ ( empty @ SV31 )
| ~ ( ~ ( ~ ( element @ SV75 @ SV31 )
| ( empty @ SV75 ) )
| ~ ( ~ ( empty @ SV75 )
| ( element @ SV75 @ SV31 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(476,plain,
! [SV76: $i,SV32: $i] :
( ( ( ~ ( in @ SV32 @ SV76 ) )
= $true )
| ( ( subset @ SV32 @ ( union @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[426]) ).
thf(477,plain,
! [SV77: $i,SV33: $i,SV98: $i] :
( ( ~ ( ~ ( ( SV98
!= ( unordered_pair @ SV33 @ SV77 ) )
| ! [SY372: $i] :
~ ( ~ ( ~ ( in @ SY372 @ SV98 )
| ( SY372 = SV33 )
| ( SY372 = SV77 ) )
| ~ ( ~ ( ( SY372 = SV33 )
| ( SY372 = SV77 ) )
| ( in @ SY372 @ SV98 ) ) ) )
| ~ ( ~ ! [SY373: $i] :
~ ( ~ ( ~ ( in @ SY373 @ SV98 )
| ( SY373 = SV33 )
| ( SY373 = SV77 ) )
| ~ ( ~ ( ( SY373 = SV33 )
| ( SY373 = SV77 ) )
| ( in @ SY373 @ SV98 ) ) )
| ( SV98
= ( unordered_pair @ SV33 @ SV77 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(478,plain,
! [SV78: $i,SV34: $i] :
( ( ( ~ ( in @ SV34 @ SV78 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV34 ) @ SV78 )
= SV78 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[428]) ).
thf(479,plain,
( ( ~ ( ~ ( empty @ sK4_SX0 )
| ~ ( relation @ sK4_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[429]) ).
thf(480,plain,
! [SV79: $i,SV35: $i] :
( ( ~ ( ~ ( in @ SV35 @ SV79 )
| ~ ( empty @ SV79 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(481,plain,
! [SV80: $i,SV36: $i] :
( ( ( ~ ( in @ SV36 @ SV80 ) )
= $true )
| ( ( ~ ( in @ SV80 @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[431]) ).
thf(482,plain,
! [SV37: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV37 @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SY374: $i,SY375: $i] :
( ~ ~ ( ~ ( in @ SY374 @ ( sK6_SY251 @ SV37 ) )
| ~ ( subset @ SY375 @ SY374 ) )
| ( in @ SY375 @ ( sK6_SY251 @ SV37 ) ) ) )
| ~ ! [SY376: $i] :
~ ~ ( ~ ( in @ SY376 @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SY377: $i] :
~ ~ ( ~ ( in @ SY377 @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY376 )
| ( in @ SX4 @ SY377 ) ) ) ) )
| ~ ! [SY379: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY379 @ ( sK6_SY251 @ SV37 ) )
| ~ ~ ( are_equipotent @ SY379 @ ( sK6_SY251 @ SV37 ) ) )
| ~ ~ ( in @ SY379 @ ( sK6_SY251 @ SV37 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[432]) ).
thf(483,plain,
! [SV81: $i,SV38: $i] :
( ( ( ~ ( in @ SV38 @ SV81 ) )
= $true )
| ( ( element @ SV38 @ SV81 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[433]) ).
thf(484,plain,
! [SV39: $i] :
( ( ~ ( ~ ( relation @ SV39 )
| ! [SY259: $i] :
~ ~ ( ~ ( in @ SY259 @ SV39 )
| ~ ! [SX2: $i,SX3: $i] :
( SY259
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[434]) ).
thf(485,plain,
! [SV39: $i] :
( ( ~ ( ~ ! [SY262: $i] :
~ ~ ( ~ ( in @ SY262 @ SV39 )
| ~ ! [SX2: $i,SX3: $i] :
( SY262
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SV39 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[434]) ).
thf(486,plain,
! [SV99: $i,SV82: $i,SV40: $i] :
( ( ! [SY380: $i] :
( ( ( ordered_pair @ SV40 @ SV82 )
!= ( ordered_pair @ SV99 @ SY380 ) )
| ~ ( ( SV40 != SV99 )
| ( SV82 != SY380 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(487,plain,
! [SV100: $i,SV83: $i,SV41: $i] :
( ( ~ ~ ( ~ ( in @ SV41 @ SV83 )
| ~ ( element @ SV83 @ ( powerset @ SV100 ) ) )
| ( element @ SV41 @ SV100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(488,plain,
! [SV42: $i] :
( ( ( relation @ SV42 )
= $false )
| ( ( ! [SY270: $i] :
~ ( ~ ( ( SY270
!= ( relation_dom @ SV42 ) )
| ! [SY271: $i] :
~ ( ~ ( ~ ( in @ SY271 @ SY270 )
| ~ ! [SY272: $i] :
~ ( in @ ( ordered_pair @ SY271 @ SY272 ) @ SV42 ) )
| ~ ( ~ ~ ! [SY273: $i] :
~ ( in @ ( ordered_pair @ SY271 @ SY273 ) @ SV42 )
| ( in @ SY271 @ SY270 ) ) ) )
| ~ ( ~ ! [SY274: $i] :
~ ( ~ ( ~ ( in @ SY274 @ SY270 )
| ~ ! [SY275: $i] :
~ ( in @ ( ordered_pair @ SY274 @ SY275 ) @ SV42 ) )
| ~ ( ~ ~ ! [SY276: $i] :
~ ( in @ ( ordered_pair @ SY274 @ SY276 ) @ SV42 )
| ( in @ SY274 @ SY270 ) ) )
| ( SY270
= ( relation_dom @ SV42 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(489,plain,
! [SV84: $i,SV43: $i,SV101: $i] :
( ( ~ ( ~ ( ( SV101
!= ( set_difference @ SV43 @ SV84 ) )
| ! [SY381: $i] :
~ ( ~ ( ~ ( in @ SY381 @ SV101 )
| ~ ( ~ ( in @ SY381 @ SV43 )
| ~ ~ ( in @ SY381 @ SV84 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY381 @ SV43 )
| ~ ~ ( in @ SY381 @ SV84 ) )
| ( in @ SY381 @ SV101 ) ) ) )
| ~ ( ~ ! [SY382: $i] :
~ ( ~ ( ~ ( in @ SY382 @ SV101 )
| ~ ( ~ ( in @ SY382 @ SV43 )
| ~ ~ ( in @ SY382 @ SV84 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY382 @ SV43 )
| ~ ~ ( in @ SY382 @ SV84 ) )
| ( in @ SY382 @ SV101 ) ) )
| ( SV101
= ( set_difference @ SV43 @ SV84 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(490,plain,
! [SV85: $i,SV44: $i,SV102: $i] :
( ( ~ ( element @ SV102 @ ( powerset @ SV44 ) )
| ~ ~ ( ~ ( in @ SV85 @ ( subset_complement @ SV44 @ SV102 ) )
| ~ ( in @ SV85 @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(491,plain,
! [SV103: $i,SV86: $i,SV45: $i] :
( ( ! [SY383: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV45 @ SV86 ) @ ( cartesian_product2 @ SV103 @ SY383 ) )
| ~ ( ~ ( in @ SV45 @ SV103 )
| ~ ( in @ SV86 @ SY383 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV45 @ SV103 )
| ~ ( in @ SV86 @ SY383 ) )
| ( in @ ( ordered_pair @ SV45 @ SV86 ) @ ( cartesian_product2 @ SV103 @ SY383 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(492,plain,
! [SV87: $i,SV46: $i] :
( ( ~ ( ~ ( subset @ ( singleton @ SV46 ) @ SV87 )
| ( in @ SV46 @ SV87 ) )
| ~ ( ~ ( in @ SV46 @ SV87 )
| ( subset @ ( singleton @ SV46 ) @ SV87 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[441]) ).
thf(493,plain,
! [SV88: $i,SV47: $i] :
( ( ~ ( ~ ( subset @ ( singleton @ SV47 ) @ SV88 )
| ( in @ SV47 @ SV88 ) )
| ~ ( ~ ( in @ SV47 @ SV88 )
| ( subset @ ( singleton @ SV47 ) @ SV88 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[442]) ).
thf(494,plain,
! [SV89: $i,SV48: $i] :
( ( ~ ~ ~ ( ~ ~ ( disjoint @ SV48 @ SV89 )
| ~ ! [SY350: $i] :
~ ( in @ SY350 @ ( set_intersection2 @ SV48 @ SV89 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY351: $i] :
~ ( in @ SY351 @ ( set_intersection2 @ SV48 @ SV89 ) )
| ~ ( disjoint @ SV48 @ SV89 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[443]) ).
thf(495,plain,
! [SV104: $i,SV90: $i,SV49: $i] :
( ( ! [SY384: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV49 @ SV90 ) @ ( cartesian_product2 @ SV104 @ SY384 ) )
| ~ ( ~ ( in @ SV49 @ SV104 )
| ~ ( in @ SV90 @ SY384 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV49 @ SV104 )
| ~ ( in @ SV90 @ SY384 ) )
| ( in @ ( ordered_pair @ SV49 @ SV90 ) @ ( cartesian_product2 @ SV104 @ SY384 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(496,plain,
! [SV3: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV3 @ ( sK5_SY160 @ SV3 ) )
| ~ ! [SY354: $i,SY355: $i] :
( ~ ~ ( ~ ( in @ SY354 @ ( sK5_SY160 @ SV3 ) )
| ~ ( subset @ SY355 @ SY354 ) )
| ( in @ SY355 @ ( sK5_SY160 @ SV3 ) ) ) )
| ~ ! [SY356: $i] :
( ~ ( in @ SY356 @ ( sK5_SY160 @ SV3 ) )
| ( in @ ( powerset @ SY356 ) @ ( sK5_SY160 @ SV3 ) ) ) )
| ~ ! [SY357: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY357 @ ( sK5_SY160 @ SV3 ) )
| ~ ~ ( are_equipotent @ SY357 @ ( sK5_SY160 @ SV3 ) ) )
| ~ ~ ( in @ SY357 @ ( sK5_SY160 @ SV3 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[446]) ).
thf(497,plain,
! [SV4: $i,SV52: $i] :
( ( ~ ( ( SV52
!= ( union @ SV4 ) )
| ! [SY294: $i] :
~ ( ~ ( ~ ( in @ SY294 @ SV52 )
| ~ ! [SY167: $i] :
~ ~ ( ~ ( in @ SY294 @ SY167 )
| ~ ( in @ SY167 @ SV4 ) ) )
| ~ ( ~ ~ ! [SY168: $i] :
~ ~ ( ~ ( in @ SY294 @ SY168 )
| ~ ( in @ SY168 @ SV4 ) )
| ( in @ SY294 @ SV52 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[447]) ).
thf(498,plain,
! [SV4: $i,SV52: $i] :
( ( ~ ( ~ ! [SY297: $i] :
~ ( ~ ( ~ ( in @ SY297 @ SV52 )
| ~ ! [SY170: $i] :
~ ~ ( ~ ( in @ SY297 @ SY170 )
| ~ ( in @ SY170 @ SV4 ) ) )
| ~ ( ~ ~ ! [SY171: $i] :
~ ~ ( ~ ( in @ SY297 @ SY171 )
| ~ ( in @ SY171 @ SV4 ) )
| ( in @ SY297 @ SV52 ) ) )
| ( SV52
= ( union @ SV4 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[447]) ).
thf(499,plain,
! [SV53: $i,SV5: $i] :
( ( ( element @ SV5 @ SV53 )
= $false )
| ( ( ( empty @ SV53 )
| ( in @ SV5 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(500,plain,
! [SV91: $i,SV54: $i,SV6: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV6 @ SV54 )
| ~ ( element @ SV54 @ ( powerset @ SV91 ) ) )
| ~ ( empty @ SV91 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[449]) ).
thf(501,plain,
! [SV7: $i,SV55: $i] :
( ( ( element @ SV55 @ ( powerset @ SV7 ) )
= $false )
| ( ( ! [SY301: $i] :
( ~ ( in @ SY301 @ SV55 )
| ( in @ SY301 @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(502,plain,
! [SV56: $i,SV8: $i] :
( ( ~ ( ( ( set_difference @ SV8 @ ( singleton @ SV56 ) )
!= SV8 )
| ~ ( in @ SV56 @ SV8 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[451]) ).
thf(503,plain,
! [SV8: $i,SV56: $i] :
( ( ~ ( ~ ~ ( in @ SV56 @ SV8 )
| ( ( set_difference @ SV8 @ ( singleton @ SV56 ) )
= SV8 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[451]) ).
thf(504,plain,
! [SV9: $i,SV105: $i] :
( ( ( ~ ( ~ ( ( SV105
!= ( relation_rng @ SV9 ) )
| ! [SY385: $i] :
~ ( ~ ( ~ ( in @ SY385 @ SV105 )
| ~ ! [SY180: $i] :
~ ( in @ ( ordered_pair @ SY180 @ SY385 ) @ SV9 ) )
| ~ ( ~ ~ ! [SY181: $i] :
~ ( in @ ( ordered_pair @ SY181 @ SY385 ) @ SV9 )
| ( in @ SY385 @ SV105 ) ) ) )
| ~ ( ~ ! [SY388: $i] :
~ ( ~ ( ~ ( in @ SY388 @ SV105 )
| ~ ! [SY183: $i] :
~ ( in @ ( ordered_pair @ SY183 @ SY388 ) @ SV9 ) )
| ~ ( ~ ~ ! [SY184: $i] :
~ ( in @ ( ordered_pair @ SY184 @ SY388 ) @ SV9 )
| ( in @ SY388 @ SV105 ) ) )
| ( SV105
= ( relation_rng @ SV9 ) ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(505,plain,
! [SV57: $i,SV10: $i] :
( ( ~ ( ~ ( subset @ SV10 @ SV57 )
| ! [SY302: $i] :
( ~ ( in @ SY302 @ SV10 )
| ( in @ SY302 @ SV57 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[453]) ).
thf(506,plain,
! [SV57: $i,SV10: $i] :
( ( ~ ( ~ ! [SY303: $i] :
( ~ ( in @ SY303 @ SV10 )
| ( in @ SY303 @ SV57 ) )
| ( subset @ SV10 @ SV57 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[453]) ).
thf(507,plain,
! [SV12: $i,SV58: $i] :
( ( ~ ( ( SV58
!= ( powerset @ SV12 ) )
| ! [SY304: $i] :
~ ( ~ ( ~ ( in @ SY304 @ SV58 )
| ( subset @ SY304 @ SV12 ) )
| ~ ( ~ ( subset @ SY304 @ SV12 )
| ( in @ SY304 @ SV58 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[455]) ).
thf(508,plain,
! [SV12: $i,SV58: $i] :
( ( ~ ( ~ ! [SY305: $i] :
~ ( ~ ( ~ ( in @ SY305 @ SV58 )
| ( subset @ SY305 @ SV12 ) )
| ~ ( ~ ( subset @ SY305 @ SV12 )
| ( in @ SY305 @ SV58 ) ) )
| ( SV58
= ( powerset @ SV12 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[455]) ).
thf(509,plain,
! [SV59: $i,SV13: $i] :
( ( ( ! [SY306: $i] :
( ~ ( in @ SY306 @ SV13 )
| ( in @ SY306 @ SV59 ) ) )
= $false )
| ( ( element @ SV13 @ ( powerset @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(510,plain,
! [SV60: $i,SV14: $i] :
( ( ( ! [SY307: $i] :
~ ( ~ ( ~ ( in @ SY307 @ SV14 )
| ( in @ SY307 @ SV60 ) )
| ~ ( ~ ( in @ SY307 @ SV60 )
| ( in @ SY307 @ SV14 ) ) ) )
= $false )
| ( ( SV14 = SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[457]) ).
thf(511,plain,
! [SV61: $i,SV15: $i] :
( ( ( ~ ( ~ ( relation @ SV15 )
| ~ ( relation @ SV61 ) ) )
= $false )
| ( ( relation @ ( set_union2 @ SV15 @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[458]) ).
thf(512,plain,
! [SV16: $i] :
( ( ( SV16 != empty_set )
| ! [SY196: $i] :
~ ( in @ SY196 @ SV16 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[459]) ).
thf(513,plain,
! [SV16: $i] :
( ( ~ ! [SY197: $i] :
~ ( in @ SY197 @ SV16 )
| ( SV16 = empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[460]) ).
thf(514,plain,
! [SV92: $i,SV62: $i,SV17: $i] :
( ( ( ~ ( subset @ SV17 @ SV62 ) )
= $true )
| ( ( ( in @ SV92 @ SV17 )
| ( subset @ SV17 @ ( set_difference @ SV62 @ ( singleton @ SV92 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(515,plain,
! [SV63: $i,SV18: $i,SV93: $i] :
( ( ~ ( ( SV93
!= ( set_intersection2 @ SV18 @ SV63 ) )
| ! [SY358: $i] :
~ ( ~ ( ~ ( in @ SY358 @ SV93 )
| ~ ( ~ ( in @ SY358 @ SV18 )
| ~ ( in @ SY358 @ SV63 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY358 @ SV18 )
| ~ ( in @ SY358 @ SV63 ) )
| ( in @ SY358 @ SV93 ) ) ) )
| ~ ( ~ ! [SY359: $i] :
~ ( ~ ( ~ ( in @ SY359 @ SV93 )
| ~ ( ~ ( in @ SY359 @ SV18 )
| ~ ( in @ SY359 @ SV63 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY359 @ SV18 )
| ~ ( in @ SY359 @ SV63 ) )
| ( in @ SY359 @ SV93 ) ) )
| ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(516,plain,
! [SV94: $i,SV64: $i,SV19: $i] :
( ( ~ ( ~ ( subset @ ( unordered_pair @ SV19 @ SV64 ) @ SV94 )
| ~ ( ~ ( in @ SV19 @ SV94 )
| ~ ( in @ SV64 @ SV94 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV19 @ SV94 )
| ~ ( in @ SV64 @ SV94 ) )
| ( subset @ ( unordered_pair @ SV19 @ SV64 ) @ SV94 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[463]) ).
thf(517,plain,
! [SV65: $i,SV20: $i] :
( ( ~ ~ ~ ( ~ ~ ( disjoint @ SV20 @ SV65 )
| ~ ! [SY313: $i] :
~ ~ ( ~ ( in @ SY313 @ SV20 )
| ~ ( in @ SY313 @ SV65 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[464]) ).
thf(518,plain,
! [SV65: $i,SV20: $i] :
( ( ~ ~ ~ ( ~ ~ ! [SY314: $i] :
~ ~ ( ~ ( in @ SY314 @ SV20 )
| ~ ( in @ SY314 @ SV65 ) )
| ~ ( disjoint @ SV20 @ SV65 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[464]) ).
thf(519,plain,
! [SV66: $i,SV21: $i] :
( ( ( in @ SV21 @ SV66 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV21 ) @ SV66 )
= SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(520,plain,
! [SV67: $i,SV22: $i,SV95: $i] :
( ( ~ ( ( SV95
!= ( cartesian_product2 @ SV22 @ SV67 ) )
| ! [SY360: $i] :
~ ( ~ ( ~ ( in @ SY360 @ SV95 )
| ~ ! [SY317: $i] :
~ ~ ! [SY318: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY317 @ SV22 )
| ~ ( in @ SY318 @ SV67 ) )
| ( SY360
!= ( ordered_pair @ SY317 @ SY318 ) ) ) )
| ~ ( ~ ~ ! [SY319: $i] :
~ ~ ! [SY320: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY319 @ SV22 )
| ~ ( in @ SY320 @ SV67 ) )
| ( SY360
!= ( ordered_pair @ SY319 @ SY320 ) ) )
| ( in @ SY360 @ SV95 ) ) ) )
| ~ ( ~ ! [SY365: $i] :
~ ( ~ ( ~ ( in @ SY365 @ SV95 )
| ~ ! [SY322: $i] :
~ ~ ! [SY323: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY322 @ SV22 )
| ~ ( in @ SY323 @ SV67 ) )
| ( SY365
!= ( ordered_pair @ SY322 @ SY323 ) ) ) )
| ~ ( ~ ~ ! [SY324: $i] :
~ ~ ! [SY325: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY324 @ SV22 )
| ~ ( in @ SY325 @ SV67 ) )
| ( SY365
!= ( ordered_pair @ SY324 @ SY325 ) ) )
| ( in @ SY365 @ SV95 ) ) )
| ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[466]) ).
thf(521,plain,
! [SV68: $i,SV23: $i,SV96: $i] :
( ( ~ ( ( SV96
!= ( set_union2 @ SV23 @ SV68 ) )
| ! [SY370: $i] :
~ ( ~ ( ~ ( in @ SY370 @ SV96 )
| ( in @ SY370 @ SV23 )
| ( in @ SY370 @ SV68 ) )
| ~ ( ~ ( ( in @ SY370 @ SV23 )
| ( in @ SY370 @ SV68 ) )
| ( in @ SY370 @ SV96 ) ) ) )
| ~ ( ~ ! [SY371: $i] :
~ ( ~ ( ~ ( in @ SY371 @ SV96 )
| ( in @ SY371 @ SV23 )
| ( in @ SY371 @ SV68 ) )
| ~ ( ~ ( ( in @ SY371 @ SV23 )
| ( in @ SY371 @ SV68 ) )
| ( in @ SY371 @ SV96 ) ) )
| ( SV96
= ( set_union2 @ SV23 @ SV68 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[467]) ).
thf(522,plain,
! [SV69: $i,SV24: $i,SV97: $i] :
( ( ( ~ ( relation @ SV97 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV24 @ SV69 ) @ SV97 )
| ~ ( ~ ( in @ SV24 @ ( relation_dom @ SV97 ) )
| ~ ( in @ SV69 @ ( relation_rng @ SV97 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[468]) ).
thf(523,plain,
! [SV70: $i,SV25: $i] :
( ( ~ ( disjoint @ ( singleton @ SV25 ) @ SV70 )
| ~ ( in @ SV25 @ SV70 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[469]) ).
thf(524,plain,
! [SV26: $i,SV71: $i] :
( ( ~ ( ( SV71
!= ( singleton @ SV26 ) )
| ! [SY330: $i] :
~ ( ~ ( ~ ( in @ SY330 @ SV71 )
| ( SY330 = SV26 ) )
| ~ ( ( SY330 != SV26 )
| ( in @ SY330 @ SV71 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[470]) ).
thf(525,plain,
! [SV26: $i,SV71: $i] :
( ( ~ ( ~ ! [SY331: $i] :
~ ( ~ ( ~ ( in @ SY331 @ SV71 )
| ( SY331 = SV26 ) )
| ~ ( ( SY331 != SV26 )
| ( in @ SY331 @ SV71 ) ) )
| ( SV71
= ( singleton @ SV26 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[470]) ).
thf(526,plain,
! [SV72: $i,SV27: $i] :
( ( ~ ( ~ ( ( SV27 != empty_set ) )
| ~ ( ~ ( ( SV72
!= ( set_meet @ SV27 ) )
| ! [SY332: $i] :
~ ( ~ ( ~ ( in @ SY332 @ SV72 )
| ! [SY234: $i] :
( ~ ( in @ SY234 @ SV27 )
| ( in @ SY332 @ SY234 ) ) )
| ~ ( ~ ! [SY235: $i] :
( ~ ( in @ SY235 @ SV27 )
| ( in @ SY332 @ SY235 ) )
| ( in @ SY332 @ SV72 ) ) ) )
| ~ ( ~ ! [SY335: $i] :
~ ( ~ ( ~ ( in @ SY335 @ SV72 )
| ! [SY237: $i] :
( ~ ( in @ SY237 @ SV27 )
| ( in @ SY335 @ SY237 ) ) )
| ~ ( ~ ! [SY238: $i] :
( ~ ( in @ SY238 @ SV27 )
| ( in @ SY335 @ SY238 ) )
| ( in @ SY335 @ SV72 ) ) )
| ( SV72
= ( set_meet @ SV27 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[471]) ).
thf(527,plain,
! [SV72: $i,SV27: $i] :
( ( ~ ( ( SV27 != empty_set )
| ~ ( ~ ( ( SV72
!= ( set_meet @ SV27 ) )
| ( SV72 = empty_set ) )
| ~ ( ( SV72 != empty_set )
| ( SV72
= ( set_meet @ SV27 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[471]) ).
thf(528,plain,
! [SV73: $i,SV28: $i] :
( ( ( ~ ( in @ SV28 @ SV73 ) )
= $false )
| ( ( disjoint @ ( singleton @ SV28 ) @ SV73 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[472]) ).
thf(529,plain,
! [SV29: $i,SV106: $i] :
( ( ( ~ ( relation @ SV106 )
| ~ ( subset @ SV29 @ SV106 )
| ~ ( ~ ( subset @ ( relation_dom @ SV29 ) @ ( relation_dom @ SV106 ) )
| ~ ( subset @ ( relation_rng @ SV29 ) @ ( relation_rng @ SV106 ) ) ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(530,plain,
! [SV74: $i,SV30: $i] :
( ( ( in @ SV30 @ SV74 )
= $false )
| ( ( subset @ SV30 @ ( union @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[474]) ).
thf(531,plain,
! [SV75: $i,SV31: $i] :
( ( ~ ( ~ ~ ( empty @ SV31 )
| ~ ( ~ ( ~ ( element @ SV75 @ SV31 )
| ( in @ SV75 @ SV31 ) )
| ~ ( ~ ( in @ SV75 @ SV31 )
| ( element @ SV75 @ SV31 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[475]) ).
thf(532,plain,
! [SV75: $i,SV31: $i] :
( ( ~ ( ~ ( empty @ SV31 )
| ~ ( ~ ( ~ ( element @ SV75 @ SV31 )
| ( empty @ SV75 ) )
| ~ ( ~ ( empty @ SV75 )
| ( element @ SV75 @ SV31 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[475]) ).
thf(533,plain,
! [SV76: $i,SV32: $i] :
( ( ( in @ SV32 @ SV76 )
= $false )
| ( ( subset @ SV32 @ ( union @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[476]) ).
thf(534,plain,
! [SV77: $i,SV33: $i,SV98: $i] :
( ( ~ ( ( SV98
!= ( unordered_pair @ SV33 @ SV77 ) )
| ! [SY372: $i] :
~ ( ~ ( ~ ( in @ SY372 @ SV98 )
| ( SY372 = SV33 )
| ( SY372 = SV77 ) )
| ~ ( ~ ( ( SY372 = SV33 )
| ( SY372 = SV77 ) )
| ( in @ SY372 @ SV98 ) ) ) )
| ~ ( ~ ! [SY373: $i] :
~ ( ~ ( ~ ( in @ SY373 @ SV98 )
| ( SY373 = SV33 )
| ( SY373 = SV77 ) )
| ~ ( ~ ( ( SY373 = SV33 )
| ( SY373 = SV77 ) )
| ( in @ SY373 @ SV98 ) ) )
| ( SV98
= ( unordered_pair @ SV33 @ SV77 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[477]) ).
thf(535,plain,
! [SV78: $i,SV34: $i] :
( ( ( in @ SV34 @ SV78 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV34 ) @ SV78 )
= SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[478]) ).
thf(536,plain,
( ( ~ ( empty @ sK4_SX0 )
| ~ ( relation @ sK4_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(537,plain,
! [SV79: $i,SV35: $i] :
( ( ~ ( in @ SV35 @ SV79 )
| ~ ( empty @ SV79 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[480]) ).
thf(538,plain,
! [SV80: $i,SV36: $i] :
( ( ( in @ SV36 @ SV80 )
= $false )
| ( ( ~ ( in @ SV80 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[481]) ).
thf(539,plain,
! [SV37: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV37 @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SY374: $i,SY375: $i] :
( ~ ~ ( ~ ( in @ SY374 @ ( sK6_SY251 @ SV37 ) )
| ~ ( subset @ SY375 @ SY374 ) )
| ( in @ SY375 @ ( sK6_SY251 @ SV37 ) ) ) )
| ~ ! [SY376: $i] :
~ ~ ( ~ ( in @ SY376 @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SY377: $i] :
~ ~ ( ~ ( in @ SY377 @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY376 )
| ( in @ SX4 @ SY377 ) ) ) ) )
| ~ ! [SY379: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY379 @ ( sK6_SY251 @ SV37 ) )
| ~ ~ ( are_equipotent @ SY379 @ ( sK6_SY251 @ SV37 ) ) )
| ~ ~ ( in @ SY379 @ ( sK6_SY251 @ SV37 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[482]) ).
thf(540,plain,
! [SV81: $i,SV38: $i] :
( ( ( in @ SV38 @ SV81 )
= $false )
| ( ( element @ SV38 @ SV81 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[483]) ).
thf(541,plain,
! [SV39: $i] :
( ( ~ ( relation @ SV39 )
| ! [SY259: $i] :
~ ~ ( ~ ( in @ SY259 @ SV39 )
| ~ ! [SX2: $i,SX3: $i] :
( SY259
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[484]) ).
thf(542,plain,
! [SV39: $i] :
( ( ~ ! [SY262: $i] :
~ ~ ( ~ ( in @ SY262 @ SV39 )
| ~ ! [SX2: $i,SX3: $i] :
( SY262
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SV39 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[485]) ).
thf(543,plain,
! [SV107: $i,SV99: $i,SV82: $i,SV40: $i] :
( ( ( ( ordered_pair @ SV40 @ SV82 )
!= ( ordered_pair @ SV99 @ SV107 ) )
| ~ ( ( SV40 != SV99 )
| ( SV82 != SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(544,plain,
! [SV100: $i,SV83: $i,SV41: $i] :
( ( ( ~ ~ ( ~ ( in @ SV41 @ SV83 )
| ~ ( element @ SV83 @ ( powerset @ SV100 ) ) ) )
= $true )
| ( ( element @ SV41 @ SV100 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[487]) ).
thf(545,plain,
! [SV42: $i,SV108: $i] :
( ( ( ~ ( ~ ( ( SV108
!= ( relation_dom @ SV42 ) )
| ! [SY391: $i] :
~ ( ~ ( ~ ( in @ SY391 @ SV108 )
| ~ ! [SY272: $i] :
~ ( in @ ( ordered_pair @ SY391 @ SY272 ) @ SV42 ) )
| ~ ( ~ ~ ! [SY273: $i] :
~ ( in @ ( ordered_pair @ SY391 @ SY273 ) @ SV42 )
| ( in @ SY391 @ SV108 ) ) ) )
| ~ ( ~ ! [SY394: $i] :
~ ( ~ ( ~ ( in @ SY394 @ SV108 )
| ~ ! [SY275: $i] :
~ ( in @ ( ordered_pair @ SY394 @ SY275 ) @ SV42 ) )
| ~ ( ~ ~ ! [SY276: $i] :
~ ( in @ ( ordered_pair @ SY394 @ SY276 ) @ SV42 )
| ( in @ SY394 @ SV108 ) ) )
| ( SV108
= ( relation_dom @ SV42 ) ) ) ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(546,plain,
! [SV84: $i,SV43: $i,SV101: $i] :
( ( ~ ( ( SV101
!= ( set_difference @ SV43 @ SV84 ) )
| ! [SY381: $i] :
~ ( ~ ( ~ ( in @ SY381 @ SV101 )
| ~ ( ~ ( in @ SY381 @ SV43 )
| ~ ~ ( in @ SY381 @ SV84 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY381 @ SV43 )
| ~ ~ ( in @ SY381 @ SV84 ) )
| ( in @ SY381 @ SV101 ) ) ) )
| ~ ( ~ ! [SY382: $i] :
~ ( ~ ( ~ ( in @ SY382 @ SV101 )
| ~ ( ~ ( in @ SY382 @ SV43 )
| ~ ~ ( in @ SY382 @ SV84 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY382 @ SV43 )
| ~ ~ ( in @ SY382 @ SV84 ) )
| ( in @ SY382 @ SV101 ) ) )
| ( SV101
= ( set_difference @ SV43 @ SV84 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[489]) ).
thf(547,plain,
! [SV85: $i,SV44: $i,SV102: $i] :
( ( ( ~ ( element @ SV102 @ ( powerset @ SV44 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( in @ SV85 @ ( subset_complement @ SV44 @ SV102 ) )
| ~ ( in @ SV85 @ SV102 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[490]) ).
thf(548,plain,
! [SV109: $i,SV103: $i,SV86: $i,SV45: $i] :
( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV45 @ SV86 ) @ ( cartesian_product2 @ SV103 @ SV109 ) )
| ~ ( ~ ( in @ SV45 @ SV103 )
| ~ ( in @ SV86 @ SV109 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV45 @ SV103 )
| ~ ( in @ SV86 @ SV109 ) )
| ( in @ ( ordered_pair @ SV45 @ SV86 ) @ ( cartesian_product2 @ SV103 @ SV109 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(549,plain,
! [SV87: $i,SV46: $i] :
( ( ~ ( ~ ( subset @ ( singleton @ SV46 ) @ SV87 )
| ( in @ SV46 @ SV87 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[492]) ).
thf(550,plain,
! [SV87: $i,SV46: $i] :
( ( ~ ( ~ ( in @ SV46 @ SV87 )
| ( subset @ ( singleton @ SV46 ) @ SV87 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[492]) ).
thf(551,plain,
! [SV88: $i,SV47: $i] :
( ( ~ ( ~ ( subset @ ( singleton @ SV47 ) @ SV88 )
| ( in @ SV47 @ SV88 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[493]) ).
thf(552,plain,
! [SV88: $i,SV47: $i] :
( ( ~ ( ~ ( in @ SV47 @ SV88 )
| ( subset @ ( singleton @ SV47 ) @ SV88 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[493]) ).
thf(553,plain,
! [SV89: $i,SV48: $i] :
( ( ~ ~ ~ ( ~ ~ ( disjoint @ SV48 @ SV89 )
| ~ ! [SY350: $i] :
~ ( in @ SY350 @ ( set_intersection2 @ SV48 @ SV89 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[494]) ).
thf(554,plain,
! [SV89: $i,SV48: $i] :
( ( ~ ~ ~ ( ~ ~ ! [SY351: $i] :
~ ( in @ SY351 @ ( set_intersection2 @ SV48 @ SV89 ) )
| ~ ( disjoint @ SV48 @ SV89 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[494]) ).
thf(555,plain,
! [SV110: $i,SV104: $i,SV90: $i,SV49: $i] :
( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV49 @ SV90 ) @ ( cartesian_product2 @ SV104 @ SV110 ) )
| ~ ( ~ ( in @ SV49 @ SV104 )
| ~ ( in @ SV90 @ SV110 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV49 @ SV104 )
| ~ ( in @ SV90 @ SV110 ) )
| ( in @ ( ordered_pair @ SV49 @ SV90 ) @ ( cartesian_product2 @ SV104 @ SV110 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(556,plain,
! [SV3: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( in @ SV3 @ ( sK5_SY160 @ SV3 ) )
| ~ ! [SY354: $i,SY355: $i] :
( ~ ~ ( ~ ( in @ SY354 @ ( sK5_SY160 @ SV3 ) )
| ~ ( subset @ SY355 @ SY354 ) )
| ( in @ SY355 @ ( sK5_SY160 @ SV3 ) ) ) )
| ~ ! [SY356: $i] :
( ~ ( in @ SY356 @ ( sK5_SY160 @ SV3 ) )
| ( in @ ( powerset @ SY356 ) @ ( sK5_SY160 @ SV3 ) ) ) )
| ~ ! [SY357: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY357 @ ( sK5_SY160 @ SV3 ) )
| ~ ~ ( are_equipotent @ SY357 @ ( sK5_SY160 @ SV3 ) ) )
| ~ ~ ( in @ SY357 @ ( sK5_SY160 @ SV3 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(557,plain,
! [SV4: $i,SV52: $i] :
( ( ( SV52
!= ( union @ SV4 ) )
| ! [SY294: $i] :
~ ( ~ ( ~ ( in @ SY294 @ SV52 )
| ~ ! [SY167: $i] :
~ ~ ( ~ ( in @ SY294 @ SY167 )
| ~ ( in @ SY167 @ SV4 ) ) )
| ~ ( ~ ~ ! [SY168: $i] :
~ ~ ( ~ ( in @ SY294 @ SY168 )
| ~ ( in @ SY168 @ SV4 ) )
| ( in @ SY294 @ SV52 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[497]) ).
thf(558,plain,
! [SV4: $i,SV52: $i] :
( ( ~ ! [SY297: $i] :
~ ( ~ ( ~ ( in @ SY297 @ SV52 )
| ~ ! [SY170: $i] :
~ ~ ( ~ ( in @ SY297 @ SY170 )
| ~ ( in @ SY170 @ SV4 ) ) )
| ~ ( ~ ~ ! [SY171: $i] :
~ ~ ( ~ ( in @ SY297 @ SY171 )
| ~ ( in @ SY171 @ SV4 ) )
| ( in @ SY297 @ SV52 ) ) )
| ( SV52
= ( union @ SV4 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[498]) ).
thf(559,plain,
! [SV5: $i,SV53: $i] :
( ( ( empty @ SV53 )
= $true )
| ( ( in @ SV5 @ SV53 )
= $true )
| ( ( element @ SV5 @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[499]) ).
thf(560,plain,
! [SV91: $i,SV54: $i,SV6: $i] :
( ( ~ ~ ( ~ ( in @ SV6 @ SV54 )
| ~ ( element @ SV54 @ ( powerset @ SV91 ) ) )
| ~ ( empty @ SV91 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[500]) ).
thf(561,plain,
! [SV7: $i,SV55: $i,SV111: $i] :
( ( ( ~ ( in @ SV111 @ SV55 )
| ( in @ SV111 @ SV7 ) )
= $true )
| ( ( element @ SV55 @ ( powerset @ SV7 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(562,plain,
! [SV56: $i,SV8: $i] :
( ( ( ( set_difference @ SV8 @ ( singleton @ SV56 ) )
!= SV8 )
| ~ ( in @ SV56 @ SV8 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[502]) ).
thf(563,plain,
! [SV8: $i,SV56: $i] :
( ( ~ ~ ( in @ SV56 @ SV8 )
| ( ( set_difference @ SV8 @ ( singleton @ SV56 ) )
= SV8 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[503]) ).
thf(564,plain,
! [SV9: $i,SV105: $i] :
( ( ( ~ ( ( SV105
!= ( relation_rng @ SV9 ) )
| ! [SY385: $i] :
~ ( ~ ( ~ ( in @ SY385 @ SV105 )
| ~ ! [SY180: $i] :
~ ( in @ ( ordered_pair @ SY180 @ SY385 ) @ SV9 ) )
| ~ ( ~ ~ ! [SY181: $i] :
~ ( in @ ( ordered_pair @ SY181 @ SY385 ) @ SV9 )
| ( in @ SY385 @ SV105 ) ) ) )
| ~ ( ~ ! [SY388: $i] :
~ ( ~ ( ~ ( in @ SY388 @ SV105 )
| ~ ! [SY183: $i] :
~ ( in @ ( ordered_pair @ SY183 @ SY388 ) @ SV9 ) )
| ~ ( ~ ~ ! [SY184: $i] :
~ ( in @ ( ordered_pair @ SY184 @ SY388 ) @ SV9 )
| ( in @ SY388 @ SV105 ) ) )
| ( SV105
= ( relation_rng @ SV9 ) ) ) )
= $false )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(565,plain,
! [SV57: $i,SV10: $i] :
( ( ~ ( subset @ SV10 @ SV57 )
| ! [SY302: $i] :
( ~ ( in @ SY302 @ SV10 )
| ( in @ SY302 @ SV57 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[505]) ).
thf(566,plain,
! [SV57: $i,SV10: $i] :
( ( ~ ! [SY303: $i] :
( ~ ( in @ SY303 @ SV10 )
| ( in @ SY303 @ SV57 ) )
| ( subset @ SV10 @ SV57 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[506]) ).
thf(567,plain,
! [SV12: $i,SV58: $i] :
( ( ( SV58
!= ( powerset @ SV12 ) )
| ! [SY304: $i] :
~ ( ~ ( ~ ( in @ SY304 @ SV58 )
| ( subset @ SY304 @ SV12 ) )
| ~ ( ~ ( subset @ SY304 @ SV12 )
| ( in @ SY304 @ SV58 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[507]) ).
thf(568,plain,
! [SV12: $i,SV58: $i] :
( ( ~ ! [SY305: $i] :
~ ( ~ ( ~ ( in @ SY305 @ SV58 )
| ( subset @ SY305 @ SV12 ) )
| ~ ( ~ ( subset @ SY305 @ SV12 )
| ( in @ SY305 @ SV58 ) ) )
| ( SV58
= ( powerset @ SV12 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[508]) ).
thf(569,plain,
! [SV13: $i,SV59: $i] :
( ( ( ~ ( in @ ( sK7_SY306 @ SV59 @ SV13 ) @ SV13 )
| ( in @ ( sK7_SY306 @ SV59 @ SV13 ) @ SV59 ) )
= $false )
| ( ( element @ SV13 @ ( powerset @ SV59 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[509]) ).
thf(570,plain,
! [SV14: $i,SV60: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV14 )
| ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV60 ) )
| ~ ( ~ ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV60 )
| ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV14 ) ) ) )
= $false )
| ( ( SV14 = SV60 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[510]) ).
thf(571,plain,
! [SV61: $i,SV15: $i] :
( ( ( ~ ( relation @ SV15 )
| ~ ( relation @ SV61 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV15 @ SV61 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[511]) ).
thf(572,plain,
! [SV16: $i] :
( ( ( SV16 != empty_set )
= $true )
| ( ( ! [SY196: $i] :
~ ( in @ SY196 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[512]) ).
thf(573,plain,
! [SV16: $i] :
( ( ( ~ ! [SY197: $i] :
~ ( in @ SY197 @ SV16 ) )
= $true )
| ( ( SV16 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[513]) ).
thf(574,plain,
! [SV92: $i,SV62: $i,SV17: $i] :
( ( ( subset @ SV17 @ SV62 )
= $false )
| ( ( ( in @ SV92 @ SV17 )
| ( subset @ SV17 @ ( set_difference @ SV62 @ ( singleton @ SV92 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[514]) ).
thf(575,plain,
! [SV63: $i,SV18: $i,SV93: $i] :
( ( ~ ( ( SV93
!= ( set_intersection2 @ SV18 @ SV63 ) )
| ! [SY358: $i] :
~ ( ~ ( ~ ( in @ SY358 @ SV93 )
| ~ ( ~ ( in @ SY358 @ SV18 )
| ~ ( in @ SY358 @ SV63 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY358 @ SV18 )
| ~ ( in @ SY358 @ SV63 ) )
| ( in @ SY358 @ SV93 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[515]) ).
thf(576,plain,
! [SV63: $i,SV18: $i,SV93: $i] :
( ( ~ ( ~ ! [SY359: $i] :
~ ( ~ ( ~ ( in @ SY359 @ SV93 )
| ~ ( ~ ( in @ SY359 @ SV18 )
| ~ ( in @ SY359 @ SV63 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY359 @ SV18 )
| ~ ( in @ SY359 @ SV63 ) )
| ( in @ SY359 @ SV93 ) ) )
| ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[515]) ).
thf(577,plain,
! [SV94: $i,SV64: $i,SV19: $i] :
( ( ~ ( ~ ( subset @ ( unordered_pair @ SV19 @ SV64 ) @ SV94 )
| ~ ( ~ ( in @ SV19 @ SV94 )
| ~ ( in @ SV64 @ SV94 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[516]) ).
thf(578,plain,
! [SV64: $i,SV94: $i,SV19: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV19 @ SV94 )
| ~ ( in @ SV64 @ SV94 ) )
| ( subset @ ( unordered_pair @ SV19 @ SV64 ) @ SV94 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[516]) ).
thf(579,plain,
! [SV65: $i,SV20: $i] :
( ( ~ ~ ( ~ ~ ( disjoint @ SV20 @ SV65 )
| ~ ! [SY313: $i] :
~ ~ ( ~ ( in @ SY313 @ SV20 )
| ~ ( in @ SY313 @ SV65 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[517]) ).
thf(580,plain,
! [SV65: $i,SV20: $i] :
( ( ~ ~ ( ~ ~ ! [SY314: $i] :
~ ~ ( ~ ( in @ SY314 @ SV20 )
| ~ ( in @ SY314 @ SV65 ) )
| ~ ( disjoint @ SV20 @ SV65 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[518]) ).
thf(581,plain,
! [SV67: $i,SV22: $i,SV95: $i] :
( ( ~ ( ( SV95
!= ( cartesian_product2 @ SV22 @ SV67 ) )
| ! [SY360: $i] :
~ ( ~ ( ~ ( in @ SY360 @ SV95 )
| ~ ! [SY317: $i] :
~ ~ ! [SY318: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY317 @ SV22 )
| ~ ( in @ SY318 @ SV67 ) )
| ( SY360
!= ( ordered_pair @ SY317 @ SY318 ) ) ) )
| ~ ( ~ ~ ! [SY319: $i] :
~ ~ ! [SY320: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY319 @ SV22 )
| ~ ( in @ SY320 @ SV67 ) )
| ( SY360
!= ( ordered_pair @ SY319 @ SY320 ) ) )
| ( in @ SY360 @ SV95 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[520]) ).
thf(582,plain,
! [SV67: $i,SV22: $i,SV95: $i] :
( ( ~ ( ~ ! [SY365: $i] :
~ ( ~ ( ~ ( in @ SY365 @ SV95 )
| ~ ! [SY322: $i] :
~ ~ ! [SY323: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY322 @ SV22 )
| ~ ( in @ SY323 @ SV67 ) )
| ( SY365
!= ( ordered_pair @ SY322 @ SY323 ) ) ) )
| ~ ( ~ ~ ! [SY324: $i] :
~ ~ ! [SY325: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY324 @ SV22 )
| ~ ( in @ SY325 @ SV67 ) )
| ( SY365
!= ( ordered_pair @ SY324 @ SY325 ) ) )
| ( in @ SY365 @ SV95 ) ) )
| ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[520]) ).
thf(583,plain,
! [SV68: $i,SV23: $i,SV96: $i] :
( ( ~ ( ( SV96
!= ( set_union2 @ SV23 @ SV68 ) )
| ! [SY370: $i] :
~ ( ~ ( ~ ( in @ SY370 @ SV96 )
| ( in @ SY370 @ SV23 )
| ( in @ SY370 @ SV68 ) )
| ~ ( ~ ( ( in @ SY370 @ SV23 )
| ( in @ SY370 @ SV68 ) )
| ( in @ SY370 @ SV96 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[521]) ).
thf(584,plain,
! [SV68: $i,SV23: $i,SV96: $i] :
( ( ~ ( ~ ! [SY371: $i] :
~ ( ~ ( ~ ( in @ SY371 @ SV96 )
| ( in @ SY371 @ SV23 )
| ( in @ SY371 @ SV68 ) )
| ~ ( ~ ( ( in @ SY371 @ SV23 )
| ( in @ SY371 @ SV68 ) )
| ( in @ SY371 @ SV96 ) ) )
| ( SV96
= ( set_union2 @ SV23 @ SV68 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[521]) ).
thf(585,plain,
! [SV69: $i,SV24: $i,SV97: $i] :
( ( ( relation @ SV97 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV24 @ SV69 ) @ SV97 )
| ~ ( ~ ( in @ SV24 @ ( relation_dom @ SV97 ) )
| ~ ( in @ SV69 @ ( relation_rng @ SV97 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[522]) ).
thf(586,plain,
! [SV70: $i,SV25: $i] :
( ( ( ~ ( disjoint @ ( singleton @ SV25 ) @ SV70 ) )
= $true )
| ( ( ~ ( in @ SV25 @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[523]) ).
thf(587,plain,
! [SV26: $i,SV71: $i] :
( ( ( SV71
!= ( singleton @ SV26 ) )
| ! [SY330: $i] :
~ ( ~ ( ~ ( in @ SY330 @ SV71 )
| ( SY330 = SV26 ) )
| ~ ( ( SY330 != SV26 )
| ( in @ SY330 @ SV71 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[524]) ).
thf(588,plain,
! [SV26: $i,SV71: $i] :
( ( ~ ! [SY331: $i] :
~ ( ~ ( ~ ( in @ SY331 @ SV71 )
| ( SY331 = SV26 ) )
| ~ ( ( SY331 != SV26 )
| ( in @ SY331 @ SV71 ) ) )
| ( SV71
= ( singleton @ SV26 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[525]) ).
thf(589,plain,
! [SV72: $i,SV27: $i] :
( ( ~ ( ( SV27 != empty_set ) )
| ~ ( ~ ( ( SV72
!= ( set_meet @ SV27 ) )
| ! [SY332: $i] :
~ ( ~ ( ~ ( in @ SY332 @ SV72 )
| ! [SY234: $i] :
( ~ ( in @ SY234 @ SV27 )
| ( in @ SY332 @ SY234 ) ) )
| ~ ( ~ ! [SY235: $i] :
( ~ ( in @ SY235 @ SV27 )
| ( in @ SY332 @ SY235 ) )
| ( in @ SY332 @ SV72 ) ) ) )
| ~ ( ~ ! [SY335: $i] :
~ ( ~ ( ~ ( in @ SY335 @ SV72 )
| ! [SY237: $i] :
( ~ ( in @ SY237 @ SV27 )
| ( in @ SY335 @ SY237 ) ) )
| ~ ( ~ ! [SY238: $i] :
( ~ ( in @ SY238 @ SV27 )
| ( in @ SY335 @ SY238 ) )
| ( in @ SY335 @ SV72 ) ) )
| ( SV72
= ( set_meet @ SV27 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[526]) ).
thf(590,plain,
! [SV72: $i,SV27: $i] :
( ( ( SV27 != empty_set )
| ~ ( ~ ( ( SV72
!= ( set_meet @ SV27 ) )
| ( SV72 = empty_set ) )
| ~ ( ( SV72 != empty_set )
| ( SV72
= ( set_meet @ SV27 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[527]) ).
thf(591,plain,
! [SV73: $i,SV28: $i] :
( ( ( in @ SV28 @ SV73 )
= $true )
| ( ( disjoint @ ( singleton @ SV28 ) @ SV73 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[528]) ).
thf(592,plain,
! [SV29: $i,SV106: $i] :
( ( ( ~ ( relation @ SV106 ) )
= $true )
| ( ( ~ ( subset @ SV29 @ SV106 )
| ~ ( ~ ( subset @ ( relation_dom @ SV29 ) @ ( relation_dom @ SV106 ) )
| ~ ( subset @ ( relation_rng @ SV29 ) @ ( relation_rng @ SV106 ) ) ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[529]) ).
thf(593,plain,
! [SV75: $i,SV31: $i] :
( ( ~ ~ ( empty @ SV31 )
| ~ ( ~ ( ~ ( element @ SV75 @ SV31 )
| ( in @ SV75 @ SV31 ) )
| ~ ( ~ ( in @ SV75 @ SV31 )
| ( element @ SV75 @ SV31 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[531]) ).
thf(594,plain,
! [SV75: $i,SV31: $i] :
( ( ~ ( empty @ SV31 )
| ~ ( ~ ( ~ ( element @ SV75 @ SV31 )
| ( empty @ SV75 ) )
| ~ ( ~ ( empty @ SV75 )
| ( element @ SV75 @ SV31 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[532]) ).
thf(595,plain,
! [SV77: $i,SV33: $i,SV98: $i] :
( ( ~ ( ( SV98
!= ( unordered_pair @ SV33 @ SV77 ) )
| ! [SY372: $i] :
~ ( ~ ( ~ ( in @ SY372 @ SV98 )
| ( SY372 = SV33 )
| ( SY372 = SV77 ) )
| ~ ( ~ ( ( SY372 = SV33 )
| ( SY372 = SV77 ) )
| ( in @ SY372 @ SV98 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[534]) ).
thf(596,plain,
! [SV77: $i,SV33: $i,SV98: $i] :
( ( ~ ( ~ ! [SY373: $i] :
~ ( ~ ( ~ ( in @ SY373 @ SV98 )
| ( SY373 = SV33 )
| ( SY373 = SV77 ) )
| ~ ( ~ ( ( SY373 = SV33 )
| ( SY373 = SV77 ) )
| ( in @ SY373 @ SV98 ) ) )
| ( SV98
= ( unordered_pair @ SV33 @ SV77 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[534]) ).
thf(597,plain,
( ( ~ ( empty @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[536]) ).
thf(598,plain,
( ( ~ ( relation @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[536]) ).
thf(599,plain,
! [SV79: $i,SV35: $i] :
( ( ( ~ ( in @ SV35 @ SV79 ) )
= $true )
| ( ( ~ ( empty @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[537]) ).
thf(600,plain,
! [SV36: $i,SV80: $i] :
( ( ( in @ SV80 @ SV36 )
= $false )
| ( ( in @ SV36 @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[538]) ).
thf(601,plain,
! [SV37: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( in @ SV37 @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SY374: $i,SY375: $i] :
( ~ ~ ( ~ ( in @ SY374 @ ( sK6_SY251 @ SV37 ) )
| ~ ( subset @ SY375 @ SY374 ) )
| ( in @ SY375 @ ( sK6_SY251 @ SV37 ) ) ) )
| ~ ! [SY376: $i] :
~ ~ ( ~ ( in @ SY376 @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SY377: $i] :
~ ~ ( ~ ( in @ SY377 @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY376 )
| ( in @ SX4 @ SY377 ) ) ) ) )
| ~ ! [SY379: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY379 @ ( sK6_SY251 @ SV37 ) )
| ~ ~ ( are_equipotent @ SY379 @ ( sK6_SY251 @ SV37 ) ) )
| ~ ~ ( in @ SY379 @ ( sK6_SY251 @ SV37 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[539]) ).
thf(602,plain,
! [SV39: $i] :
( ( ( ~ ( relation @ SV39 ) )
= $true )
| ( ( ! [SY259: $i] :
~ ~ ( ~ ( in @ SY259 @ SV39 )
| ~ ! [SX2: $i,SX3: $i] :
( SY259
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[541]) ).
thf(603,plain,
! [SV39: $i] :
( ( ( ~ ! [SY262: $i] :
~ ~ ( ~ ( in @ SY262 @ SV39 )
| ~ ! [SX2: $i,SX3: $i] :
( SY262
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $true )
| ( ( relation @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[542]) ).
thf(604,plain,
! [SV107: $i,SV99: $i,SV82: $i,SV40: $i] :
( ( ( ( ordered_pair @ SV40 @ SV82 )
!= ( ordered_pair @ SV99 @ SV107 ) )
= $true )
| ( ( ~ ( ( SV40 != SV99 )
| ( SV82 != SV107 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[543]) ).
thf(605,plain,
! [SV100: $i,SV83: $i,SV41: $i] :
( ( ( ~ ( ~ ( in @ SV41 @ SV83 )
| ~ ( element @ SV83 @ ( powerset @ SV100 ) ) ) )
= $false )
| ( ( element @ SV41 @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[544]) ).
thf(606,plain,
! [SV42: $i,SV108: $i] :
( ( ( ~ ( ( SV108
!= ( relation_dom @ SV42 ) )
| ! [SY391: $i] :
~ ( ~ ( ~ ( in @ SY391 @ SV108 )
| ~ ! [SY272: $i] :
~ ( in @ ( ordered_pair @ SY391 @ SY272 ) @ SV42 ) )
| ~ ( ~ ~ ! [SY273: $i] :
~ ( in @ ( ordered_pair @ SY391 @ SY273 ) @ SV42 )
| ( in @ SY391 @ SV108 ) ) ) )
| ~ ( ~ ! [SY394: $i] :
~ ( ~ ( ~ ( in @ SY394 @ SV108 )
| ~ ! [SY275: $i] :
~ ( in @ ( ordered_pair @ SY394 @ SY275 ) @ SV42 ) )
| ~ ( ~ ~ ! [SY276: $i] :
~ ( in @ ( ordered_pair @ SY394 @ SY276 ) @ SV42 )
| ( in @ SY394 @ SV108 ) ) )
| ( SV108
= ( relation_dom @ SV42 ) ) ) )
= $false )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[545]) ).
thf(607,plain,
! [SV84: $i,SV43: $i,SV101: $i] :
( ( ~ ( ( SV101
!= ( set_difference @ SV43 @ SV84 ) )
| ! [SY381: $i] :
~ ( ~ ( ~ ( in @ SY381 @ SV101 )
| ~ ( ~ ( in @ SY381 @ SV43 )
| ~ ~ ( in @ SY381 @ SV84 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY381 @ SV43 )
| ~ ~ ( in @ SY381 @ SV84 ) )
| ( in @ SY381 @ SV101 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[546]) ).
thf(608,plain,
! [SV84: $i,SV43: $i,SV101: $i] :
( ( ~ ( ~ ! [SY382: $i] :
~ ( ~ ( ~ ( in @ SY382 @ SV101 )
| ~ ( ~ ( in @ SY382 @ SV43 )
| ~ ~ ( in @ SY382 @ SV84 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY382 @ SV43 )
| ~ ~ ( in @ SY382 @ SV84 ) )
| ( in @ SY382 @ SV101 ) ) )
| ( SV101
= ( set_difference @ SV43 @ SV84 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[546]) ).
thf(609,plain,
! [SV85: $i,SV44: $i,SV102: $i] :
( ( ( element @ SV102 @ ( powerset @ SV44 ) )
= $false )
| ( ( ~ ~ ( ~ ( in @ SV85 @ ( subset_complement @ SV44 @ SV102 ) )
| ~ ( in @ SV85 @ SV102 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[547]) ).
thf(610,plain,
! [SV109: $i,SV103: $i,SV86: $i,SV45: $i] :
( ( ~ ( ~ ( in @ ( ordered_pair @ SV45 @ SV86 ) @ ( cartesian_product2 @ SV103 @ SV109 ) )
| ~ ( ~ ( in @ SV45 @ SV103 )
| ~ ( in @ SV86 @ SV109 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV45 @ SV103 )
| ~ ( in @ SV86 @ SV109 ) )
| ( in @ ( ordered_pair @ SV45 @ SV86 ) @ ( cartesian_product2 @ SV103 @ SV109 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[548]) ).
thf(611,plain,
! [SV87: $i,SV46: $i] :
( ( ~ ( subset @ ( singleton @ SV46 ) @ SV87 )
| ( in @ SV46 @ SV87 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[549]) ).
thf(612,plain,
! [SV87: $i,SV46: $i] :
( ( ~ ( in @ SV46 @ SV87 )
| ( subset @ ( singleton @ SV46 ) @ SV87 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[550]) ).
thf(613,plain,
! [SV88: $i,SV47: $i] :
( ( ~ ( subset @ ( singleton @ SV47 ) @ SV88 )
| ( in @ SV47 @ SV88 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[551]) ).
thf(614,plain,
! [SV88: $i,SV47: $i] :
( ( ~ ( in @ SV47 @ SV88 )
| ( subset @ ( singleton @ SV47 ) @ SV88 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[552]) ).
thf(615,plain,
! [SV89: $i,SV48: $i] :
( ( ~ ~ ( ~ ~ ( disjoint @ SV48 @ SV89 )
| ~ ! [SY350: $i] :
~ ( in @ SY350 @ ( set_intersection2 @ SV48 @ SV89 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[553]) ).
thf(616,plain,
! [SV89: $i,SV48: $i] :
( ( ~ ~ ( ~ ~ ! [SY351: $i] :
~ ( in @ SY351 @ ( set_intersection2 @ SV48 @ SV89 ) )
| ~ ( disjoint @ SV48 @ SV89 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[554]) ).
thf(617,plain,
! [SV110: $i,SV104: $i,SV90: $i,SV49: $i] :
( ( ~ ( ~ ( in @ ( ordered_pair @ SV49 @ SV90 ) @ ( cartesian_product2 @ SV104 @ SV110 ) )
| ~ ( ~ ( in @ SV49 @ SV104 )
| ~ ( in @ SV90 @ SV110 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV49 @ SV104 )
| ~ ( in @ SV90 @ SV110 ) )
| ( in @ ( ordered_pair @ SV49 @ SV90 ) @ ( cartesian_product2 @ SV104 @ SV110 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[555]) ).
thf(618,plain,
! [SV3: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( in @ SV3 @ ( sK5_SY160 @ SV3 ) )
| ~ ! [SY354: $i,SY355: $i] :
( ~ ~ ( ~ ( in @ SY354 @ ( sK5_SY160 @ SV3 ) )
| ~ ( subset @ SY355 @ SY354 ) )
| ( in @ SY355 @ ( sK5_SY160 @ SV3 ) ) ) )
| ~ ! [SY356: $i] :
( ~ ( in @ SY356 @ ( sK5_SY160 @ SV3 ) )
| ( in @ ( powerset @ SY356 ) @ ( sK5_SY160 @ SV3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[556]) ).
thf(619,plain,
! [SV3: $i] :
( ( ~ ! [SY357: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY357 @ ( sK5_SY160 @ SV3 ) )
| ~ ~ ( are_equipotent @ SY357 @ ( sK5_SY160 @ SV3 ) ) )
| ~ ~ ( in @ SY357 @ ( sK5_SY160 @ SV3 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[556]) ).
thf(620,plain,
! [SV4: $i,SV52: $i] :
( ( ( SV52
!= ( union @ SV4 ) )
= $true )
| ( ( ! [SY294: $i] :
~ ( ~ ( ~ ( in @ SY294 @ SV52 )
| ~ ! [SY167: $i] :
~ ~ ( ~ ( in @ SY294 @ SY167 )
| ~ ( in @ SY167 @ SV4 ) ) )
| ~ ( ~ ~ ! [SY168: $i] :
~ ~ ( ~ ( in @ SY294 @ SY168 )
| ~ ( in @ SY168 @ SV4 ) )
| ( in @ SY294 @ SV52 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[557]) ).
thf(621,plain,
! [SV4: $i,SV52: $i] :
( ( ( ~ ! [SY297: $i] :
~ ( ~ ( ~ ( in @ SY297 @ SV52 )
| ~ ! [SY170: $i] :
~ ~ ( ~ ( in @ SY297 @ SY170 )
| ~ ( in @ SY170 @ SV4 ) ) )
| ~ ( ~ ~ ! [SY171: $i] :
~ ~ ( ~ ( in @ SY297 @ SY171 )
| ~ ( in @ SY171 @ SV4 ) )
| ( in @ SY297 @ SV52 ) ) ) )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[558]) ).
thf(622,plain,
! [SV91: $i,SV54: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( in @ SV6 @ SV54 )
| ~ ( element @ SV54 @ ( powerset @ SV91 ) ) ) )
= $true )
| ( ( ~ ( empty @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[560]) ).
thf(623,plain,
! [SV7: $i,SV55: $i,SV111: $i] :
( ( ( ~ ( in @ SV111 @ SV55 ) )
= $true )
| ( ( in @ SV111 @ SV7 )
= $true )
| ( ( element @ SV55 @ ( powerset @ SV7 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[561]) ).
thf(624,plain,
! [SV56: $i,SV8: $i] :
( ( ( ( set_difference @ SV8 @ ( singleton @ SV56 ) )
!= SV8 )
= $true )
| ( ( ~ ( in @ SV56 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[562]) ).
thf(625,plain,
! [SV8: $i,SV56: $i] :
( ( ( ~ ~ ( in @ SV56 @ SV8 ) )
= $true )
| ( ( ( set_difference @ SV8 @ ( singleton @ SV56 ) )
= SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[563]) ).
thf(626,plain,
! [SV9: $i,SV105: $i] :
( ( ( ~ ( ( SV105
!= ( relation_rng @ SV9 ) )
| ! [SY385: $i] :
~ ( ~ ( ~ ( in @ SY385 @ SV105 )
| ~ ! [SY180: $i] :
~ ( in @ ( ordered_pair @ SY180 @ SY385 ) @ SV9 ) )
| ~ ( ~ ~ ! [SY181: $i] :
~ ( in @ ( ordered_pair @ SY181 @ SY385 ) @ SV9 )
| ( in @ SY385 @ SV105 ) ) ) ) )
= $false )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[564]) ).
thf(627,plain,
! [SV9: $i,SV105: $i] :
( ( ( ~ ( ~ ! [SY388: $i] :
~ ( ~ ( ~ ( in @ SY388 @ SV105 )
| ~ ! [SY183: $i] :
~ ( in @ ( ordered_pair @ SY183 @ SY388 ) @ SV9 ) )
| ~ ( ~ ~ ! [SY184: $i] :
~ ( in @ ( ordered_pair @ SY184 @ SY388 ) @ SV9 )
| ( in @ SY388 @ SV105 ) ) )
| ( SV105
= ( relation_rng @ SV9 ) ) ) )
= $false )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[564]) ).
thf(628,plain,
! [SV57: $i,SV10: $i] :
( ( ( ~ ( subset @ SV10 @ SV57 ) )
= $true )
| ( ( ! [SY302: $i] :
( ~ ( in @ SY302 @ SV10 )
| ( in @ SY302 @ SV57 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[565]) ).
thf(629,plain,
! [SV57: $i,SV10: $i] :
( ( ( ~ ! [SY303: $i] :
( ~ ( in @ SY303 @ SV10 )
| ( in @ SY303 @ SV57 ) ) )
= $true )
| ( ( subset @ SV10 @ SV57 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[566]) ).
thf(630,plain,
! [SV12: $i,SV58: $i] :
( ( ( SV58
!= ( powerset @ SV12 ) )
= $true )
| ( ( ! [SY304: $i] :
~ ( ~ ( ~ ( in @ SY304 @ SV58 )
| ( subset @ SY304 @ SV12 ) )
| ~ ( ~ ( subset @ SY304 @ SV12 )
| ( in @ SY304 @ SV58 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[567]) ).
thf(631,plain,
! [SV12: $i,SV58: $i] :
( ( ( ~ ! [SY305: $i] :
~ ( ~ ( ~ ( in @ SY305 @ SV58 )
| ( subset @ SY305 @ SV12 ) )
| ~ ( ~ ( subset @ SY305 @ SV12 )
| ( in @ SY305 @ SV58 ) ) ) )
= $true )
| ( ( SV58
= ( powerset @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[568]) ).
thf(632,plain,
! [SV13: $i,SV59: $i] :
( ( ( ~ ( in @ ( sK7_SY306 @ SV59 @ SV13 ) @ SV13 ) )
= $false )
| ( ( element @ SV13 @ ( powerset @ SV59 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[569]) ).
thf(633,plain,
! [SV13: $i,SV59: $i] :
( ( ( in @ ( sK7_SY306 @ SV59 @ SV13 ) @ SV59 )
= $false )
| ( ( element @ SV13 @ ( powerset @ SV59 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[569]) ).
thf(634,plain,
! [SV14: $i,SV60: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV14 )
| ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV60 ) )
| ~ ( ~ ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV60 )
| ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV14 ) ) )
= $true )
| ( ( SV14 = SV60 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[570]) ).
thf(635,plain,
! [SV61: $i,SV15: $i] :
( ( ( ~ ( relation @ SV15 ) )
= $true )
| ( ( ~ ( relation @ SV61 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV15 @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[571]) ).
thf(636,plain,
! [SV16: $i] :
( ( ( SV16 = empty_set )
= $false )
| ( ( ! [SY196: $i] :
~ ( in @ SY196 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[572]) ).
thf(637,plain,
! [SV16: $i] :
( ( ( ! [SY197: $i] :
~ ( in @ SY197 @ SV16 ) )
= $false )
| ( ( SV16 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[573]) ).
thf(638,plain,
! [SV62: $i,SV17: $i,SV92: $i] :
( ( ( in @ SV92 @ SV17 )
= $true )
| ( ( subset @ SV17 @ ( set_difference @ SV62 @ ( singleton @ SV92 ) ) )
= $true )
| ( ( subset @ SV17 @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[574]) ).
thf(639,plain,
! [SV63: $i,SV18: $i,SV93: $i] :
( ( ( SV93
!= ( set_intersection2 @ SV18 @ SV63 ) )
| ! [SY358: $i] :
~ ( ~ ( ~ ( in @ SY358 @ SV93 )
| ~ ( ~ ( in @ SY358 @ SV18 )
| ~ ( in @ SY358 @ SV63 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY358 @ SV18 )
| ~ ( in @ SY358 @ SV63 ) )
| ( in @ SY358 @ SV93 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[575]) ).
thf(640,plain,
! [SV63: $i,SV18: $i,SV93: $i] :
( ( ~ ! [SY359: $i] :
~ ( ~ ( ~ ( in @ SY359 @ SV93 )
| ~ ( ~ ( in @ SY359 @ SV18 )
| ~ ( in @ SY359 @ SV63 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY359 @ SV18 )
| ~ ( in @ SY359 @ SV63 ) )
| ( in @ SY359 @ SV93 ) ) )
| ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[576]) ).
thf(641,plain,
! [SV94: $i,SV64: $i,SV19: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV19 @ SV64 ) @ SV94 )
| ~ ( ~ ( in @ SV19 @ SV94 )
| ~ ( in @ SV64 @ SV94 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[577]) ).
thf(642,plain,
! [SV64: $i,SV94: $i,SV19: $i] :
( ( ~ ~ ( ~ ( in @ SV19 @ SV94 )
| ~ ( in @ SV64 @ SV94 ) )
| ( subset @ ( unordered_pair @ SV19 @ SV64 ) @ SV94 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[578]) ).
thf(643,plain,
! [SV65: $i,SV20: $i] :
( ( ~ ( ~ ~ ( disjoint @ SV20 @ SV65 )
| ~ ! [SY313: $i] :
~ ~ ( ~ ( in @ SY313 @ SV20 )
| ~ ( in @ SY313 @ SV65 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[579]) ).
thf(644,plain,
! [SV65: $i,SV20: $i] :
( ( ~ ( ~ ~ ! [SY314: $i] :
~ ~ ( ~ ( in @ SY314 @ SV20 )
| ~ ( in @ SY314 @ SV65 ) )
| ~ ( disjoint @ SV20 @ SV65 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[580]) ).
thf(645,plain,
! [SV67: $i,SV22: $i,SV95: $i] :
( ( ( SV95
!= ( cartesian_product2 @ SV22 @ SV67 ) )
| ! [SY360: $i] :
~ ( ~ ( ~ ( in @ SY360 @ SV95 )
| ~ ! [SY317: $i] :
~ ~ ! [SY318: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY317 @ SV22 )
| ~ ( in @ SY318 @ SV67 ) )
| ( SY360
!= ( ordered_pair @ SY317 @ SY318 ) ) ) )
| ~ ( ~ ~ ! [SY319: $i] :
~ ~ ! [SY320: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY319 @ SV22 )
| ~ ( in @ SY320 @ SV67 ) )
| ( SY360
!= ( ordered_pair @ SY319 @ SY320 ) ) )
| ( in @ SY360 @ SV95 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[581]) ).
thf(646,plain,
! [SV67: $i,SV22: $i,SV95: $i] :
( ( ~ ! [SY365: $i] :
~ ( ~ ( ~ ( in @ SY365 @ SV95 )
| ~ ! [SY322: $i] :
~ ~ ! [SY323: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY322 @ SV22 )
| ~ ( in @ SY323 @ SV67 ) )
| ( SY365
!= ( ordered_pair @ SY322 @ SY323 ) ) ) )
| ~ ( ~ ~ ! [SY324: $i] :
~ ~ ! [SY325: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY324 @ SV22 )
| ~ ( in @ SY325 @ SV67 ) )
| ( SY365
!= ( ordered_pair @ SY324 @ SY325 ) ) )
| ( in @ SY365 @ SV95 ) ) )
| ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[582]) ).
thf(647,plain,
! [SV68: $i,SV23: $i,SV96: $i] :
( ( ( SV96
!= ( set_union2 @ SV23 @ SV68 ) )
| ! [SY370: $i] :
~ ( ~ ( ~ ( in @ SY370 @ SV96 )
| ( in @ SY370 @ SV23 )
| ( in @ SY370 @ SV68 ) )
| ~ ( ~ ( ( in @ SY370 @ SV23 )
| ( in @ SY370 @ SV68 ) )
| ( in @ SY370 @ SV96 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[583]) ).
thf(648,plain,
! [SV68: $i,SV23: $i,SV96: $i] :
( ( ~ ! [SY371: $i] :
~ ( ~ ( ~ ( in @ SY371 @ SV96 )
| ( in @ SY371 @ SV23 )
| ( in @ SY371 @ SV68 ) )
| ~ ( ~ ( ( in @ SY371 @ SV23 )
| ( in @ SY371 @ SV68 ) )
| ( in @ SY371 @ SV96 ) ) )
| ( SV96
= ( set_union2 @ SV23 @ SV68 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[584]) ).
thf(649,plain,
! [SV97: $i,SV69: $i,SV24: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV24 @ SV69 ) @ SV97 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV24 @ ( relation_dom @ SV97 ) )
| ~ ( in @ SV69 @ ( relation_rng @ SV97 ) ) ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[585]) ).
thf(650,plain,
! [SV70: $i,SV25: $i] :
( ( ( disjoint @ ( singleton @ SV25 ) @ SV70 )
= $false )
| ( ( ~ ( in @ SV25 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(651,plain,
! [SV26: $i,SV71: $i] :
( ( ( SV71
!= ( singleton @ SV26 ) )
= $true )
| ( ( ! [SY330: $i] :
~ ( ~ ( ~ ( in @ SY330 @ SV71 )
| ( SY330 = SV26 ) )
| ~ ( ( SY330 != SV26 )
| ( in @ SY330 @ SV71 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[587]) ).
thf(652,plain,
! [SV26: $i,SV71: $i] :
( ( ( ~ ! [SY331: $i] :
~ ( ~ ( ~ ( in @ SY331 @ SV71 )
| ( SY331 = SV26 ) )
| ~ ( ( SY331 != SV26 )
| ( in @ SY331 @ SV71 ) ) ) )
= $true )
| ( ( SV71
= ( singleton @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[588]) ).
thf(653,plain,
! [SV72: $i,SV27: $i] :
( ( ( ~ ( ( SV27 != empty_set ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV72
!= ( set_meet @ SV27 ) )
| ! [SY332: $i] :
~ ( ~ ( ~ ( in @ SY332 @ SV72 )
| ! [SY234: $i] :
( ~ ( in @ SY234 @ SV27 )
| ( in @ SY332 @ SY234 ) ) )
| ~ ( ~ ! [SY235: $i] :
( ~ ( in @ SY235 @ SV27 )
| ( in @ SY332 @ SY235 ) )
| ( in @ SY332 @ SV72 ) ) ) )
| ~ ( ~ ! [SY335: $i] :
~ ( ~ ( ~ ( in @ SY335 @ SV72 )
| ! [SY237: $i] :
( ~ ( in @ SY237 @ SV27 )
| ( in @ SY335 @ SY237 ) ) )
| ~ ( ~ ! [SY238: $i] :
( ~ ( in @ SY238 @ SV27 )
| ( in @ SY335 @ SY238 ) )
| ( in @ SY335 @ SV72 ) ) )
| ( SV72
= ( set_meet @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[589]) ).
thf(654,plain,
! [SV72: $i,SV27: $i] :
( ( ( SV27 != empty_set )
= $true )
| ( ( ~ ( ~ ( ( SV72
!= ( set_meet @ SV27 ) )
| ( SV72 = empty_set ) )
| ~ ( ( SV72 != empty_set )
| ( SV72
= ( set_meet @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[590]) ).
thf(655,plain,
! [SV29: $i,SV106: $i] :
( ( ( relation @ SV106 )
= $false )
| ( ( ~ ( subset @ SV29 @ SV106 )
| ~ ( ~ ( subset @ ( relation_dom @ SV29 ) @ ( relation_dom @ SV106 ) )
| ~ ( subset @ ( relation_rng @ SV29 ) @ ( relation_rng @ SV106 ) ) ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[592]) ).
thf(656,plain,
! [SV75: $i,SV31: $i] :
( ( ( ~ ~ ( empty @ SV31 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( element @ SV75 @ SV31 )
| ( in @ SV75 @ SV31 ) )
| ~ ( ~ ( in @ SV75 @ SV31 )
| ( element @ SV75 @ SV31 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[593]) ).
thf(657,plain,
! [SV75: $i,SV31: $i] :
( ( ( ~ ( empty @ SV31 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( element @ SV75 @ SV31 )
| ( empty @ SV75 ) )
| ~ ( ~ ( empty @ SV75 )
| ( element @ SV75 @ SV31 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[594]) ).
thf(658,plain,
! [SV77: $i,SV33: $i,SV98: $i] :
( ( ( SV98
!= ( unordered_pair @ SV33 @ SV77 ) )
| ! [SY372: $i] :
~ ( ~ ( ~ ( in @ SY372 @ SV98 )
| ( SY372 = SV33 )
| ( SY372 = SV77 ) )
| ~ ( ~ ( ( SY372 = SV33 )
| ( SY372 = SV77 ) )
| ( in @ SY372 @ SV98 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[595]) ).
thf(659,plain,
! [SV77: $i,SV33: $i,SV98: $i] :
( ( ~ ! [SY373: $i] :
~ ( ~ ( ~ ( in @ SY373 @ SV98 )
| ( SY373 = SV33 )
| ( SY373 = SV77 ) )
| ~ ( ~ ( ( SY373 = SV33 )
| ( SY373 = SV77 ) )
| ( in @ SY373 @ SV98 ) ) )
| ( SV98
= ( unordered_pair @ SV33 @ SV77 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[596]) ).
thf(660,plain,
( ( empty @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[597]) ).
thf(661,plain,
( ( relation @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[598]) ).
thf(662,plain,
! [SV79: $i,SV35: $i] :
( ( ( in @ SV35 @ SV79 )
= $false )
| ( ( ~ ( empty @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[599]) ).
thf(663,plain,
! [SV37: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( in @ SV37 @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SY374: $i,SY375: $i] :
( ~ ~ ( ~ ( in @ SY374 @ ( sK6_SY251 @ SV37 ) )
| ~ ( subset @ SY375 @ SY374 ) )
| ( in @ SY375 @ ( sK6_SY251 @ SV37 ) ) ) )
| ~ ! [SY376: $i] :
~ ~ ( ~ ( in @ SY376 @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SY377: $i] :
~ ~ ( ~ ( in @ SY377 @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY376 )
| ( in @ SX4 @ SY377 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[601]) ).
thf(664,plain,
! [SV37: $i] :
( ( ~ ! [SY379: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY379 @ ( sK6_SY251 @ SV37 ) )
| ~ ~ ( are_equipotent @ SY379 @ ( sK6_SY251 @ SV37 ) ) )
| ~ ~ ( in @ SY379 @ ( sK6_SY251 @ SV37 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[601]) ).
thf(665,plain,
! [SV39: $i] :
( ( ( relation @ SV39 )
= $false )
| ( ( ! [SY259: $i] :
~ ~ ( ~ ( in @ SY259 @ SV39 )
| ~ ! [SX2: $i,SX3: $i] :
( SY259
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[602]) ).
thf(666,plain,
! [SV39: $i] :
( ( ( ! [SY262: $i] :
~ ~ ( ~ ( in @ SY262 @ SV39 )
| ~ ! [SX2: $i,SX3: $i] :
( SY262
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $false )
| ( ( relation @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[603]) ).
thf(667,plain,
! [SV107: $i,SV99: $i,SV82: $i,SV40: $i] :
( ( ( ( ordered_pair @ SV40 @ SV82 )
= ( ordered_pair @ SV99 @ SV107 ) )
= $false )
| ( ( ~ ( ( SV40 != SV99 )
| ( SV82 != SV107 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(668,plain,
! [SV100: $i,SV83: $i,SV41: $i] :
( ( ( ~ ( in @ SV41 @ SV83 )
| ~ ( element @ SV83 @ ( powerset @ SV100 ) ) )
= $true )
| ( ( element @ SV41 @ SV100 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[605]) ).
thf(669,plain,
! [SV42: $i,SV108: $i] :
( ( ( ~ ( ( SV108
!= ( relation_dom @ SV42 ) )
| ! [SY391: $i] :
~ ( ~ ( ~ ( in @ SY391 @ SV108 )
| ~ ! [SY272: $i] :
~ ( in @ ( ordered_pair @ SY391 @ SY272 ) @ SV42 ) )
| ~ ( ~ ~ ! [SY273: $i] :
~ ( in @ ( ordered_pair @ SY391 @ SY273 ) @ SV42 )
| ( in @ SY391 @ SV108 ) ) ) ) )
= $false )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[606]) ).
thf(670,plain,
! [SV42: $i,SV108: $i] :
( ( ( ~ ( ~ ! [SY394: $i] :
~ ( ~ ( ~ ( in @ SY394 @ SV108 )
| ~ ! [SY275: $i] :
~ ( in @ ( ordered_pair @ SY394 @ SY275 ) @ SV42 ) )
| ~ ( ~ ~ ! [SY276: $i] :
~ ( in @ ( ordered_pair @ SY394 @ SY276 ) @ SV42 )
| ( in @ SY394 @ SV108 ) ) )
| ( SV108
= ( relation_dom @ SV42 ) ) ) )
= $false )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[606]) ).
thf(671,plain,
! [SV84: $i,SV43: $i,SV101: $i] :
( ( ( SV101
!= ( set_difference @ SV43 @ SV84 ) )
| ! [SY381: $i] :
~ ( ~ ( ~ ( in @ SY381 @ SV101 )
| ~ ( ~ ( in @ SY381 @ SV43 )
| ~ ~ ( in @ SY381 @ SV84 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY381 @ SV43 )
| ~ ~ ( in @ SY381 @ SV84 ) )
| ( in @ SY381 @ SV101 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[607]) ).
thf(672,plain,
! [SV84: $i,SV43: $i,SV101: $i] :
( ( ~ ! [SY382: $i] :
~ ( ~ ( ~ ( in @ SY382 @ SV101 )
| ~ ( ~ ( in @ SY382 @ SV43 )
| ~ ~ ( in @ SY382 @ SV84 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY382 @ SV43 )
| ~ ~ ( in @ SY382 @ SV84 ) )
| ( in @ SY382 @ SV101 ) ) )
| ( SV101
= ( set_difference @ SV43 @ SV84 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[608]) ).
thf(673,plain,
! [SV102: $i,SV44: $i,SV85: $i] :
( ( ( ~ ( ~ ( in @ SV85 @ ( subset_complement @ SV44 @ SV102 ) )
| ~ ( in @ SV85 @ SV102 ) ) )
= $false )
| ( ( element @ SV102 @ ( powerset @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[609]) ).
thf(674,plain,
! [SV109: $i,SV103: $i,SV86: $i,SV45: $i] :
( ( ~ ( ~ ( in @ ( ordered_pair @ SV45 @ SV86 ) @ ( cartesian_product2 @ SV103 @ SV109 ) )
| ~ ( ~ ( in @ SV45 @ SV103 )
| ~ ( in @ SV86 @ SV109 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[610]) ).
thf(675,plain,
! [SV109: $i,SV86: $i,SV103: $i,SV45: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV45 @ SV103 )
| ~ ( in @ SV86 @ SV109 ) )
| ( in @ ( ordered_pair @ SV45 @ SV86 ) @ ( cartesian_product2 @ SV103 @ SV109 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[610]) ).
thf(676,plain,
! [SV87: $i,SV46: $i] :
( ( ( ~ ( subset @ ( singleton @ SV46 ) @ SV87 ) )
= $true )
| ( ( in @ SV46 @ SV87 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[611]) ).
thf(677,plain,
! [SV87: $i,SV46: $i] :
( ( ( ~ ( in @ SV46 @ SV87 ) )
= $true )
| ( ( subset @ ( singleton @ SV46 ) @ SV87 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[612]) ).
thf(678,plain,
! [SV88: $i,SV47: $i] :
( ( ( ~ ( subset @ ( singleton @ SV47 ) @ SV88 ) )
= $true )
| ( ( in @ SV47 @ SV88 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[613]) ).
thf(679,plain,
! [SV88: $i,SV47: $i] :
( ( ( ~ ( in @ SV47 @ SV88 ) )
= $true )
| ( ( subset @ ( singleton @ SV47 ) @ SV88 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[614]) ).
thf(680,plain,
! [SV89: $i,SV48: $i] :
( ( ~ ( ~ ~ ( disjoint @ SV48 @ SV89 )
| ~ ! [SY350: $i] :
~ ( in @ SY350 @ ( set_intersection2 @ SV48 @ SV89 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[615]) ).
thf(681,plain,
! [SV89: $i,SV48: $i] :
( ( ~ ( ~ ~ ! [SY351: $i] :
~ ( in @ SY351 @ ( set_intersection2 @ SV48 @ SV89 ) )
| ~ ( disjoint @ SV48 @ SV89 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[616]) ).
thf(682,plain,
! [SV110: $i,SV104: $i,SV90: $i,SV49: $i] :
( ( ~ ( ~ ( in @ ( ordered_pair @ SV49 @ SV90 ) @ ( cartesian_product2 @ SV104 @ SV110 ) )
| ~ ( ~ ( in @ SV49 @ SV104 )
| ~ ( in @ SV90 @ SV110 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[617]) ).
thf(683,plain,
! [SV110: $i,SV90: $i,SV104: $i,SV49: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV49 @ SV104 )
| ~ ( in @ SV90 @ SV110 ) )
| ( in @ ( ordered_pair @ SV49 @ SV90 ) @ ( cartesian_product2 @ SV104 @ SV110 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[617]) ).
thf(684,plain,
! [SV3: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV3 @ ( sK5_SY160 @ SV3 ) )
| ~ ! [SY354: $i,SY355: $i] :
( ~ ~ ( ~ ( in @ SY354 @ ( sK5_SY160 @ SV3 ) )
| ~ ( subset @ SY355 @ SY354 ) )
| ( in @ SY355 @ ( sK5_SY160 @ SV3 ) ) ) )
| ~ ! [SY356: $i] :
( ~ ( in @ SY356 @ ( sK5_SY160 @ SV3 ) )
| ( in @ ( powerset @ SY356 ) @ ( sK5_SY160 @ SV3 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[618]) ).
thf(685,plain,
! [SV3: $i] :
( ( ! [SY357: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY357 @ ( sK5_SY160 @ SV3 ) )
| ~ ~ ( are_equipotent @ SY357 @ ( sK5_SY160 @ SV3 ) ) )
| ~ ~ ( in @ SY357 @ ( sK5_SY160 @ SV3 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[619]) ).
thf(686,plain,
! [SV4: $i,SV52: $i] :
( ( ( SV52
= ( union @ SV4 ) )
= $false )
| ( ( ! [SY294: $i] :
~ ( ~ ( ~ ( in @ SY294 @ SV52 )
| ~ ! [SY167: $i] :
~ ~ ( ~ ( in @ SY294 @ SY167 )
| ~ ( in @ SY167 @ SV4 ) ) )
| ~ ( ~ ~ ! [SY168: $i] :
~ ~ ( ~ ( in @ SY294 @ SY168 )
| ~ ( in @ SY168 @ SV4 ) )
| ( in @ SY294 @ SV52 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[620]) ).
thf(687,plain,
! [SV4: $i,SV52: $i] :
( ( ( ! [SY297: $i] :
~ ( ~ ( ~ ( in @ SY297 @ SV52 )
| ~ ! [SY170: $i] :
~ ~ ( ~ ( in @ SY297 @ SY170 )
| ~ ( in @ SY170 @ SV4 ) ) )
| ~ ( ~ ~ ! [SY171: $i] :
~ ~ ( ~ ( in @ SY297 @ SY171 )
| ~ ( in @ SY171 @ SV4 ) )
| ( in @ SY297 @ SV52 ) ) ) )
= $false )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[621]) ).
thf(688,plain,
! [SV91: $i,SV54: $i,SV6: $i] :
( ( ( ~ ( ~ ( in @ SV6 @ SV54 )
| ~ ( element @ SV54 @ ( powerset @ SV91 ) ) ) )
= $false )
| ( ( ~ ( empty @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[622]) ).
thf(689,plain,
! [SV7: $i,SV55: $i,SV111: $i] :
( ( ( in @ SV111 @ SV55 )
= $false )
| ( ( in @ SV111 @ SV7 )
= $true )
| ( ( element @ SV55 @ ( powerset @ SV7 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[623]) ).
thf(690,plain,
! [SV56: $i,SV8: $i] :
( ( ( ( set_difference @ SV8 @ ( singleton @ SV56 ) )
= SV8 )
= $false )
| ( ( ~ ( in @ SV56 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[624]) ).
thf(691,plain,
! [SV8: $i,SV56: $i] :
( ( ( ~ ( in @ SV56 @ SV8 ) )
= $false )
| ( ( ( set_difference @ SV8 @ ( singleton @ SV56 ) )
= SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[625]) ).
thf(692,plain,
! [SV9: $i,SV105: $i] :
( ( ( ( SV105
!= ( relation_rng @ SV9 ) )
| ! [SY385: $i] :
~ ( ~ ( ~ ( in @ SY385 @ SV105 )
| ~ ! [SY180: $i] :
~ ( in @ ( ordered_pair @ SY180 @ SY385 ) @ SV9 ) )
| ~ ( ~ ~ ! [SY181: $i] :
~ ( in @ ( ordered_pair @ SY181 @ SY385 ) @ SV9 )
| ( in @ SY385 @ SV105 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[626]) ).
thf(693,plain,
! [SV9: $i,SV105: $i] :
( ( ( ~ ! [SY388: $i] :
~ ( ~ ( ~ ( in @ SY388 @ SV105 )
| ~ ! [SY183: $i] :
~ ( in @ ( ordered_pair @ SY183 @ SY388 ) @ SV9 ) )
| ~ ( ~ ~ ! [SY184: $i] :
~ ( in @ ( ordered_pair @ SY184 @ SY388 ) @ SV9 )
| ( in @ SY388 @ SV105 ) ) )
| ( SV105
= ( relation_rng @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[627]) ).
thf(694,plain,
! [SV57: $i,SV10: $i] :
( ( ( subset @ SV10 @ SV57 )
= $false )
| ( ( ! [SY302: $i] :
( ~ ( in @ SY302 @ SV10 )
| ( in @ SY302 @ SV57 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[628]) ).
thf(695,plain,
! [SV57: $i,SV10: $i] :
( ( ( ! [SY303: $i] :
( ~ ( in @ SY303 @ SV10 )
| ( in @ SY303 @ SV57 ) ) )
= $false )
| ( ( subset @ SV10 @ SV57 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[629]) ).
thf(696,plain,
! [SV12: $i,SV58: $i] :
( ( ( SV58
= ( powerset @ SV12 ) )
= $false )
| ( ( ! [SY304: $i] :
~ ( ~ ( ~ ( in @ SY304 @ SV58 )
| ( subset @ SY304 @ SV12 ) )
| ~ ( ~ ( subset @ SY304 @ SV12 )
| ( in @ SY304 @ SV58 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[630]) ).
thf(697,plain,
! [SV12: $i,SV58: $i] :
( ( ( ! [SY305: $i] :
~ ( ~ ( ~ ( in @ SY305 @ SV58 )
| ( subset @ SY305 @ SV12 ) )
| ~ ( ~ ( subset @ SY305 @ SV12 )
| ( in @ SY305 @ SV58 ) ) ) )
= $false )
| ( ( SV58
= ( powerset @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[631]) ).
thf(698,plain,
! [SV13: $i,SV59: $i] :
( ( ( in @ ( sK7_SY306 @ SV59 @ SV13 ) @ SV13 )
= $true )
| ( ( element @ SV13 @ ( powerset @ SV59 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[632]) ).
thf(699,plain,
! [SV14: $i,SV60: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV14 )
| ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV60 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV60 )
| ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV14 ) ) )
= $true )
| ( ( SV14 = SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[634]) ).
thf(700,plain,
! [SV61: $i,SV15: $i] :
( ( ( relation @ SV15 )
= $false )
| ( ( ~ ( relation @ SV61 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV15 @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[635]) ).
thf(701,plain,
! [SV16: $i,SV112: $i] :
( ( ( ~ ( in @ SV112 @ SV16 ) )
= $true )
| ( ( SV16 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(702,plain,
! [SV16: $i] :
( ( ( ~ ( in @ ( sK9_SY197 @ SV16 ) @ SV16 ) )
= $false )
| ( ( SV16 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[637]) ).
thf(703,plain,
! [SV63: $i,SV18: $i,SV93: $i] :
( ( ( SV93
!= ( set_intersection2 @ SV18 @ SV63 ) )
= $true )
| ( ( ! [SY358: $i] :
~ ( ~ ( ~ ( in @ SY358 @ SV93 )
| ~ ( ~ ( in @ SY358 @ SV18 )
| ~ ( in @ SY358 @ SV63 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY358 @ SV18 )
| ~ ( in @ SY358 @ SV63 ) )
| ( in @ SY358 @ SV93 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[639]) ).
thf(704,plain,
! [SV63: $i,SV18: $i,SV93: $i] :
( ( ( ~ ! [SY359: $i] :
~ ( ~ ( ~ ( in @ SY359 @ SV93 )
| ~ ( ~ ( in @ SY359 @ SV18 )
| ~ ( in @ SY359 @ SV63 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY359 @ SV18 )
| ~ ( in @ SY359 @ SV63 ) )
| ( in @ SY359 @ SV93 ) ) ) )
= $true )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[640]) ).
thf(705,plain,
! [SV94: $i,SV64: $i,SV19: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV19 @ SV64 ) @ SV94 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV19 @ SV94 )
| ~ ( in @ SV64 @ SV94 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[641]) ).
thf(706,plain,
! [SV64: $i,SV94: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ( in @ SV19 @ SV94 )
| ~ ( in @ SV64 @ SV94 ) ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV19 @ SV64 ) @ SV94 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[642]) ).
thf(707,plain,
! [SV65: $i,SV20: $i] :
( ( ~ ~ ( disjoint @ SV20 @ SV65 )
| ~ ! [SY313: $i] :
~ ~ ( ~ ( in @ SY313 @ SV20 )
| ~ ( in @ SY313 @ SV65 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[643]) ).
thf(708,plain,
! [SV65: $i,SV20: $i] :
( ( ~ ~ ! [SY314: $i] :
~ ~ ( ~ ( in @ SY314 @ SV20 )
| ~ ( in @ SY314 @ SV65 ) )
| ~ ( disjoint @ SV20 @ SV65 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[644]) ).
thf(709,plain,
! [SV67: $i,SV22: $i,SV95: $i] :
( ( ( SV95
!= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true )
| ( ( ! [SY360: $i] :
~ ( ~ ( ~ ( in @ SY360 @ SV95 )
| ~ ! [SY317: $i] :
~ ~ ! [SY318: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY317 @ SV22 )
| ~ ( in @ SY318 @ SV67 ) )
| ( SY360
!= ( ordered_pair @ SY317 @ SY318 ) ) ) )
| ~ ( ~ ~ ! [SY319: $i] :
~ ~ ! [SY320: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY319 @ SV22 )
| ~ ( in @ SY320 @ SV67 ) )
| ( SY360
!= ( ordered_pair @ SY319 @ SY320 ) ) )
| ( in @ SY360 @ SV95 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[645]) ).
thf(710,plain,
! [SV67: $i,SV22: $i,SV95: $i] :
( ( ( ~ ! [SY365: $i] :
~ ( ~ ( ~ ( in @ SY365 @ SV95 )
| ~ ! [SY322: $i] :
~ ~ ! [SY323: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY322 @ SV22 )
| ~ ( in @ SY323 @ SV67 ) )
| ( SY365
!= ( ordered_pair @ SY322 @ SY323 ) ) ) )
| ~ ( ~ ~ ! [SY324: $i] :
~ ~ ! [SY325: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY324 @ SV22 )
| ~ ( in @ SY325 @ SV67 ) )
| ( SY365
!= ( ordered_pair @ SY324 @ SY325 ) ) )
| ( in @ SY365 @ SV95 ) ) ) )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[646]) ).
thf(711,plain,
! [SV68: $i,SV23: $i,SV96: $i] :
( ( ( SV96
!= ( set_union2 @ SV23 @ SV68 ) )
= $true )
| ( ( ! [SY370: $i] :
~ ( ~ ( ~ ( in @ SY370 @ SV96 )
| ( in @ SY370 @ SV23 )
| ( in @ SY370 @ SV68 ) )
| ~ ( ~ ( ( in @ SY370 @ SV23 )
| ( in @ SY370 @ SV68 ) )
| ( in @ SY370 @ SV96 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[647]) ).
thf(712,plain,
! [SV68: $i,SV23: $i,SV96: $i] :
( ( ( ~ ! [SY371: $i] :
~ ( ~ ( ~ ( in @ SY371 @ SV96 )
| ( in @ SY371 @ SV23 )
| ( in @ SY371 @ SV68 ) )
| ~ ( ~ ( ( in @ SY371 @ SV23 )
| ( in @ SY371 @ SV68 ) )
| ( in @ SY371 @ SV96 ) ) ) )
= $true )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[648]) ).
thf(713,plain,
! [SV97: $i,SV69: $i,SV24: $i] :
( ( ( in @ ( ordered_pair @ SV24 @ SV69 ) @ SV97 )
= $false )
| ( ( ~ ( ~ ( in @ SV24 @ ( relation_dom @ SV97 ) )
| ~ ( in @ SV69 @ ( relation_rng @ SV97 ) ) ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[649]) ).
thf(714,plain,
! [SV70: $i,SV25: $i] :
( ( ( in @ SV25 @ SV70 )
= $false )
| ( ( disjoint @ ( singleton @ SV25 ) @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[650]) ).
thf(715,plain,
! [SV26: $i,SV71: $i] :
( ( ( SV71
= ( singleton @ SV26 ) )
= $false )
| ( ( ! [SY330: $i] :
~ ( ~ ( ~ ( in @ SY330 @ SV71 )
| ( SY330 = SV26 ) )
| ~ ( ( SY330 != SV26 )
| ( in @ SY330 @ SV71 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[651]) ).
thf(716,plain,
! [SV26: $i,SV71: $i] :
( ( ( ! [SY331: $i] :
~ ( ~ ( ~ ( in @ SY331 @ SV71 )
| ( SY331 = SV26 ) )
| ~ ( ( SY331 != SV26 )
| ( in @ SY331 @ SV71 ) ) ) )
= $false )
| ( ( SV71
= ( singleton @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[652]) ).
thf(717,plain,
! [SV72: $i,SV27: $i] :
( ( ( SV27 != empty_set )
= $false )
| ( ( ~ ( ~ ( ( SV72
!= ( set_meet @ SV27 ) )
| ! [SY332: $i] :
~ ( ~ ( ~ ( in @ SY332 @ SV72 )
| ! [SY234: $i] :
( ~ ( in @ SY234 @ SV27 )
| ( in @ SY332 @ SY234 ) ) )
| ~ ( ~ ! [SY235: $i] :
( ~ ( in @ SY235 @ SV27 )
| ( in @ SY332 @ SY235 ) )
| ( in @ SY332 @ SV72 ) ) ) )
| ~ ( ~ ! [SY335: $i] :
~ ( ~ ( ~ ( in @ SY335 @ SV72 )
| ! [SY237: $i] :
( ~ ( in @ SY237 @ SV27 )
| ( in @ SY335 @ SY237 ) ) )
| ~ ( ~ ! [SY238: $i] :
( ~ ( in @ SY238 @ SV27 )
| ( in @ SY335 @ SY238 ) )
| ( in @ SY335 @ SV72 ) ) )
| ( SV72
= ( set_meet @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[653]) ).
thf(718,plain,
! [SV72: $i,SV27: $i] :
( ( ( SV27 = empty_set )
= $false )
| ( ( ~ ( ~ ( ( SV72
!= ( set_meet @ SV27 ) )
| ( SV72 = empty_set ) )
| ~ ( ( SV72 != empty_set )
| ( SV72
= ( set_meet @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[654]) ).
thf(719,plain,
! [SV106: $i,SV29: $i] :
( ( ( ~ ( subset @ SV29 @ SV106 ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( relation_dom @ SV29 ) @ ( relation_dom @ SV106 ) )
| ~ ( subset @ ( relation_rng @ SV29 ) @ ( relation_rng @ SV106 ) ) ) )
= $true )
| ( ( relation @ SV106 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[655]) ).
thf(720,plain,
! [SV75: $i,SV31: $i] :
( ( ( ~ ( empty @ SV31 ) )
= $false )
| ( ( ~ ( ~ ( ~ ( element @ SV75 @ SV31 )
| ( in @ SV75 @ SV31 ) )
| ~ ( ~ ( in @ SV75 @ SV31 )
| ( element @ SV75 @ SV31 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[656]) ).
thf(721,plain,
! [SV75: $i,SV31: $i] :
( ( ( empty @ SV31 )
= $false )
| ( ( ~ ( ~ ( ~ ( element @ SV75 @ SV31 )
| ( empty @ SV75 ) )
| ~ ( ~ ( empty @ SV75 )
| ( element @ SV75 @ SV31 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[657]) ).
thf(722,plain,
! [SV77: $i,SV33: $i,SV98: $i] :
( ( ( SV98
!= ( unordered_pair @ SV33 @ SV77 ) )
= $true )
| ( ( ! [SY372: $i] :
~ ( ~ ( ~ ( in @ SY372 @ SV98 )
| ( SY372 = SV33 )
| ( SY372 = SV77 ) )
| ~ ( ~ ( ( SY372 = SV33 )
| ( SY372 = SV77 ) )
| ( in @ SY372 @ SV98 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[658]) ).
thf(723,plain,
! [SV77: $i,SV33: $i,SV98: $i] :
( ( ( ~ ! [SY373: $i] :
~ ( ~ ( ~ ( in @ SY373 @ SV98 )
| ( SY373 = SV33 )
| ( SY373 = SV77 ) )
| ~ ( ~ ( ( SY373 = SV33 )
| ( SY373 = SV77 ) )
| ( in @ SY373 @ SV98 ) ) ) )
= $true )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[659]) ).
thf(724,plain,
! [SV35: $i,SV79: $i] :
( ( ( empty @ SV79 )
= $false )
| ( ( in @ SV35 @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[662]) ).
thf(725,plain,
! [SV37: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV37 @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SY374: $i,SY375: $i] :
( ~ ~ ( ~ ( in @ SY374 @ ( sK6_SY251 @ SV37 ) )
| ~ ( subset @ SY375 @ SY374 ) )
| ( in @ SY375 @ ( sK6_SY251 @ SV37 ) ) ) )
| ~ ! [SY376: $i] :
~ ~ ( ~ ( in @ SY376 @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SY377: $i] :
~ ~ ( ~ ( in @ SY377 @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY376 )
| ( in @ SX4 @ SY377 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[663]) ).
thf(726,plain,
! [SV37: $i] :
( ( ! [SY379: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY379 @ ( sK6_SY251 @ SV37 ) )
| ~ ~ ( are_equipotent @ SY379 @ ( sK6_SY251 @ SV37 ) ) )
| ~ ~ ( in @ SY379 @ ( sK6_SY251 @ SV37 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[664]) ).
thf(727,plain,
! [SV39: $i,SV113: $i] :
( ( ( ~ ~ ( ~ ( in @ SV113 @ SV39 )
| ~ ! [SY397: $i,SY398: $i] :
( SV113
!= ( ordered_pair @ SY397 @ SY398 ) ) ) )
= $true )
| ( ( relation @ SV39 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(728,plain,
! [SV39: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK10_SY262 @ SV39 ) @ SV39 )
| ~ ! [SY399: $i,SY400: $i] :
( ( sK10_SY262 @ SV39 )
!= ( ordered_pair @ SY399 @ SY400 ) ) ) )
= $false )
| ( ( relation @ SV39 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[666]) ).
thf(729,plain,
! [SV107: $i,SV82: $i,SV99: $i,SV40: $i] :
( ( ( ( SV40 != SV99 )
| ( SV82 != SV107 ) )
= $false )
| ( ( ( ordered_pair @ SV40 @ SV82 )
= ( ordered_pair @ SV99 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[667]) ).
thf(730,plain,
! [SV100: $i,SV83: $i,SV41: $i] :
( ( ( ~ ( in @ SV41 @ SV83 ) )
= $true )
| ( ( ~ ( element @ SV83 @ ( powerset @ SV100 ) ) )
= $true )
| ( ( element @ SV41 @ SV100 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[668]) ).
thf(731,plain,
! [SV42: $i,SV108: $i] :
( ( ( ( SV108
!= ( relation_dom @ SV42 ) )
| ! [SY391: $i] :
~ ( ~ ( ~ ( in @ SY391 @ SV108 )
| ~ ! [SY272: $i] :
~ ( in @ ( ordered_pair @ SY391 @ SY272 ) @ SV42 ) )
| ~ ( ~ ~ ! [SY273: $i] :
~ ( in @ ( ordered_pair @ SY391 @ SY273 ) @ SV42 )
| ( in @ SY391 @ SV108 ) ) ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[669]) ).
thf(732,plain,
! [SV42: $i,SV108: $i] :
( ( ( ~ ! [SY394: $i] :
~ ( ~ ( ~ ( in @ SY394 @ SV108 )
| ~ ! [SY275: $i] :
~ ( in @ ( ordered_pair @ SY394 @ SY275 ) @ SV42 ) )
| ~ ( ~ ~ ! [SY276: $i] :
~ ( in @ ( ordered_pair @ SY394 @ SY276 ) @ SV42 )
| ( in @ SY394 @ SV108 ) ) )
| ( SV108
= ( relation_dom @ SV42 ) ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[670]) ).
thf(733,plain,
! [SV84: $i,SV43: $i,SV101: $i] :
( ( ( SV101
!= ( set_difference @ SV43 @ SV84 ) )
= $true )
| ( ( ! [SY381: $i] :
~ ( ~ ( ~ ( in @ SY381 @ SV101 )
| ~ ( ~ ( in @ SY381 @ SV43 )
| ~ ~ ( in @ SY381 @ SV84 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY381 @ SV43 )
| ~ ~ ( in @ SY381 @ SV84 ) )
| ( in @ SY381 @ SV101 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[671]) ).
thf(734,plain,
! [SV84: $i,SV43: $i,SV101: $i] :
( ( ( ~ ! [SY382: $i] :
~ ( ~ ( ~ ( in @ SY382 @ SV101 )
| ~ ( ~ ( in @ SY382 @ SV43 )
| ~ ~ ( in @ SY382 @ SV84 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY382 @ SV43 )
| ~ ~ ( in @ SY382 @ SV84 ) )
| ( in @ SY382 @ SV101 ) ) ) )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[672]) ).
thf(735,plain,
! [SV102: $i,SV44: $i,SV85: $i] :
( ( ( ~ ( in @ SV85 @ ( subset_complement @ SV44 @ SV102 ) )
| ~ ( in @ SV85 @ SV102 ) )
= $true )
| ( ( element @ SV102 @ ( powerset @ SV44 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[673]) ).
thf(736,plain,
! [SV109: $i,SV103: $i,SV86: $i,SV45: $i] :
( ( ~ ( in @ ( ordered_pair @ SV45 @ SV86 ) @ ( cartesian_product2 @ SV103 @ SV109 ) )
| ~ ( ~ ( in @ SV45 @ SV103 )
| ~ ( in @ SV86 @ SV109 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[674]) ).
thf(737,plain,
! [SV109: $i,SV86: $i,SV103: $i,SV45: $i] :
( ( ~ ~ ( ~ ( in @ SV45 @ SV103 )
| ~ ( in @ SV86 @ SV109 ) )
| ( in @ ( ordered_pair @ SV45 @ SV86 ) @ ( cartesian_product2 @ SV103 @ SV109 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[675]) ).
thf(738,plain,
! [SV87: $i,SV46: $i] :
( ( ( subset @ ( singleton @ SV46 ) @ SV87 )
= $false )
| ( ( in @ SV46 @ SV87 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[676]) ).
thf(739,plain,
! [SV87: $i,SV46: $i] :
( ( ( in @ SV46 @ SV87 )
= $false )
| ( ( subset @ ( singleton @ SV46 ) @ SV87 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[677]) ).
thf(740,plain,
! [SV88: $i,SV47: $i] :
( ( ( subset @ ( singleton @ SV47 ) @ SV88 )
= $false )
| ( ( in @ SV47 @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[678]) ).
thf(741,plain,
! [SV88: $i,SV47: $i] :
( ( ( in @ SV47 @ SV88 )
= $false )
| ( ( subset @ ( singleton @ SV47 ) @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[679]) ).
thf(742,plain,
! [SV89: $i,SV48: $i] :
( ( ~ ~ ( disjoint @ SV48 @ SV89 )
| ~ ! [SY350: $i] :
~ ( in @ SY350 @ ( set_intersection2 @ SV48 @ SV89 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[680]) ).
thf(743,plain,
! [SV89: $i,SV48: $i] :
( ( ~ ~ ! [SY351: $i] :
~ ( in @ SY351 @ ( set_intersection2 @ SV48 @ SV89 ) )
| ~ ( disjoint @ SV48 @ SV89 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[681]) ).
thf(744,plain,
! [SV110: $i,SV104: $i,SV90: $i,SV49: $i] :
( ( ~ ( in @ ( ordered_pair @ SV49 @ SV90 ) @ ( cartesian_product2 @ SV104 @ SV110 ) )
| ~ ( ~ ( in @ SV49 @ SV104 )
| ~ ( in @ SV90 @ SV110 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[682]) ).
thf(745,plain,
! [SV110: $i,SV90: $i,SV104: $i,SV49: $i] :
( ( ~ ~ ( ~ ( in @ SV49 @ SV104 )
| ~ ( in @ SV90 @ SV110 ) )
| ( in @ ( ordered_pair @ SV49 @ SV90 ) @ ( cartesian_product2 @ SV104 @ SV110 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[683]) ).
thf(746,plain,
! [SV3: $i] :
( ( ~ ~ ( ~ ( in @ SV3 @ ( sK5_SY160 @ SV3 ) )
| ~ ! [SY354: $i,SY355: $i] :
( ~ ~ ( ~ ( in @ SY354 @ ( sK5_SY160 @ SV3 ) )
| ~ ( subset @ SY355 @ SY354 ) )
| ( in @ SY355 @ ( sK5_SY160 @ SV3 ) ) ) )
| ~ ! [SY356: $i] :
( ~ ( in @ SY356 @ ( sK5_SY160 @ SV3 ) )
| ( in @ ( powerset @ SY356 ) @ ( sK5_SY160 @ SV3 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[684]) ).
thf(747,plain,
! [SV3: $i,SV114: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( subset @ SV114 @ ( sK5_SY160 @ SV3 ) )
| ~ ~ ( are_equipotent @ SV114 @ ( sK5_SY160 @ SV3 ) ) )
| ~ ~ ( in @ SV114 @ ( sK5_SY160 @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(748,plain,
! [SV4: $i,SV52: $i,SV115: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV115 @ SV52 )
| ~ ! [SY401: $i] :
~ ~ ( ~ ( in @ SV115 @ SY401 )
| ~ ( in @ SY401 @ SV4 ) ) )
| ~ ( ~ ~ ! [SY402: $i] :
~ ~ ( ~ ( in @ SV115 @ SY402 )
| ~ ( in @ SY402 @ SV4 ) )
| ( in @ SV115 @ SV52 ) ) ) )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(749,plain,
! [SV52: $i,SV4: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV52 )
| ~ ! [SY403: $i] :
~ ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SY403 )
| ~ ( in @ SY403 @ SV4 ) ) )
| ~ ( ~ ~ ! [SY404: $i] :
~ ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SY404 )
| ~ ( in @ SY404 @ SV4 ) )
| ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV52 ) ) ) )
= $false )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[687]) ).
thf(750,plain,
! [SV91: $i,SV54: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ SV54 )
| ~ ( element @ SV54 @ ( powerset @ SV91 ) ) )
= $true )
| ( ( ~ ( empty @ SV91 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[688]) ).
thf(751,plain,
! [SV8: $i,SV56: $i] :
( ( ( in @ SV56 @ SV8 )
= $false )
| ( ( ( set_difference @ SV8 @ ( singleton @ SV56 ) )
= SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[690]) ).
thf(752,plain,
! [SV8: $i,SV56: $i] :
( ( ( in @ SV56 @ SV8 )
= $true )
| ( ( ( set_difference @ SV8 @ ( singleton @ SV56 ) )
= SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[691]) ).
thf(753,plain,
! [SV9: $i,SV105: $i] :
( ( ( SV105
!= ( relation_rng @ SV9 ) )
= $true )
| ( ( ! [SY385: $i] :
~ ( ~ ( ~ ( in @ SY385 @ SV105 )
| ~ ! [SY180: $i] :
~ ( in @ ( ordered_pair @ SY180 @ SY385 ) @ SV9 ) )
| ~ ( ~ ~ ! [SY181: $i] :
~ ( in @ ( ordered_pair @ SY181 @ SY385 ) @ SV9 )
| ( in @ SY385 @ SV105 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[692]) ).
thf(754,plain,
! [SV9: $i,SV105: $i] :
( ( ( ~ ! [SY388: $i] :
~ ( ~ ( ~ ( in @ SY388 @ SV105 )
| ~ ! [SY183: $i] :
~ ( in @ ( ordered_pair @ SY183 @ SY388 ) @ SV9 ) )
| ~ ( ~ ~ ! [SY184: $i] :
~ ( in @ ( ordered_pair @ SY184 @ SY388 ) @ SV9 )
| ( in @ SY388 @ SV105 ) ) ) )
= $true )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[693]) ).
thf(755,plain,
! [SV57: $i,SV10: $i,SV116: $i] :
( ( ( ~ ( in @ SV116 @ SV10 )
| ( in @ SV116 @ SV57 ) )
= $true )
| ( ( subset @ SV10 @ SV57 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(756,plain,
! [SV10: $i,SV57: $i] :
( ( ( ~ ( in @ ( sK12_SY303 @ SV57 @ SV10 ) @ SV10 )
| ( in @ ( sK12_SY303 @ SV57 @ SV10 ) @ SV57 ) )
= $false )
| ( ( subset @ SV10 @ SV57 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[695]) ).
thf(757,plain,
! [SV12: $i,SV58: $i,SV117: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV117 @ SV58 )
| ( subset @ SV117 @ SV12 ) )
| ~ ( ~ ( subset @ SV117 @ SV12 )
| ( in @ SV117 @ SV58 ) ) ) )
= $true )
| ( ( SV58
= ( powerset @ SV12 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(758,plain,
! [SV58: $i,SV12: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV58 )
| ( subset @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV12 ) )
| ~ ( ~ ( subset @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV12 )
| ( in @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV58 ) ) ) )
= $false )
| ( ( SV58
= ( powerset @ SV12 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[697]) ).
thf(759,plain,
! [SV14: $i,SV60: $i] :
( ( ( ~ ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV14 )
| ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV60 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV60 )
| ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV14 ) ) )
= $true )
| ( ( SV14 = SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[699]) ).
thf(760,plain,
! [SV15: $i,SV61: $i] :
( ( ( relation @ SV61 )
= $false )
| ( ( relation @ SV15 )
= $false )
| ( ( relation @ ( set_union2 @ SV15 @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[700]) ).
thf(761,plain,
! [SV16: $i,SV112: $i] :
( ( ( in @ SV112 @ SV16 )
= $false )
| ( ( SV16 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[701]) ).
thf(762,plain,
! [SV16: $i] :
( ( ( in @ ( sK9_SY197 @ SV16 ) @ SV16 )
= $true )
| ( ( SV16 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[702]) ).
thf(763,plain,
! [SV63: $i,SV18: $i,SV93: $i] :
( ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $false )
| ( ( ! [SY358: $i] :
~ ( ~ ( ~ ( in @ SY358 @ SV93 )
| ~ ( ~ ( in @ SY358 @ SV18 )
| ~ ( in @ SY358 @ SV63 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY358 @ SV18 )
| ~ ( in @ SY358 @ SV63 ) )
| ( in @ SY358 @ SV93 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[703]) ).
thf(764,plain,
! [SV63: $i,SV18: $i,SV93: $i] :
( ( ( ! [SY359: $i] :
~ ( ~ ( ~ ( in @ SY359 @ SV93 )
| ~ ( ~ ( in @ SY359 @ SV18 )
| ~ ( in @ SY359 @ SV63 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY359 @ SV18 )
| ~ ( in @ SY359 @ SV63 ) )
| ( in @ SY359 @ SV93 ) ) ) )
= $false )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[704]) ).
thf(765,plain,
! [SV94: $i,SV64: $i,SV19: $i] :
( ( ( subset @ ( unordered_pair @ SV19 @ SV64 ) @ SV94 )
= $false )
| ( ( ~ ( ~ ( in @ SV19 @ SV94 )
| ~ ( in @ SV64 @ SV94 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[705]) ).
thf(766,plain,
! [SV64: $i,SV94: $i,SV19: $i] :
( ( ( ~ ( ~ ( in @ SV19 @ SV94 )
| ~ ( in @ SV64 @ SV94 ) ) )
= $false )
| ( ( subset @ ( unordered_pair @ SV19 @ SV64 ) @ SV94 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[706]) ).
thf(767,plain,
! [SV65: $i,SV20: $i] :
( ( ( ~ ~ ( disjoint @ SV20 @ SV65 ) )
= $true )
| ( ( ~ ! [SY313: $i] :
~ ~ ( ~ ( in @ SY313 @ SV20 )
| ~ ( in @ SY313 @ SV65 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[707]) ).
thf(768,plain,
! [SV65: $i,SV20: $i] :
( ( ( ~ ~ ! [SY314: $i] :
~ ~ ( ~ ( in @ SY314 @ SV20 )
| ~ ( in @ SY314 @ SV65 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV20 @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[708]) ).
thf(769,plain,
! [SV67: $i,SV22: $i,SV95: $i] :
( ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false )
| ( ( ! [SY360: $i] :
~ ( ~ ( ~ ( in @ SY360 @ SV95 )
| ~ ! [SY317: $i] :
~ ~ ! [SY318: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY317 @ SV22 )
| ~ ( in @ SY318 @ SV67 ) )
| ( SY360
!= ( ordered_pair @ SY317 @ SY318 ) ) ) )
| ~ ( ~ ~ ! [SY319: $i] :
~ ~ ! [SY320: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY319 @ SV22 )
| ~ ( in @ SY320 @ SV67 ) )
| ( SY360
!= ( ordered_pair @ SY319 @ SY320 ) ) )
| ( in @ SY360 @ SV95 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[709]) ).
thf(770,plain,
! [SV67: $i,SV22: $i,SV95: $i] :
( ( ( ! [SY365: $i] :
~ ( ~ ( ~ ( in @ SY365 @ SV95 )
| ~ ! [SY322: $i] :
~ ~ ! [SY323: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY322 @ SV22 )
| ~ ( in @ SY323 @ SV67 ) )
| ( SY365
!= ( ordered_pair @ SY322 @ SY323 ) ) ) )
| ~ ( ~ ~ ! [SY324: $i] :
~ ~ ! [SY325: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY324 @ SV22 )
| ~ ( in @ SY325 @ SV67 ) )
| ( SY365
!= ( ordered_pair @ SY324 @ SY325 ) ) )
| ( in @ SY365 @ SV95 ) ) ) )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[710]) ).
thf(771,plain,
! [SV68: $i,SV23: $i,SV96: $i] :
( ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $false )
| ( ( ! [SY370: $i] :
~ ( ~ ( ~ ( in @ SY370 @ SV96 )
| ( in @ SY370 @ SV23 )
| ( in @ SY370 @ SV68 ) )
| ~ ( ~ ( ( in @ SY370 @ SV23 )
| ( in @ SY370 @ SV68 ) )
| ( in @ SY370 @ SV96 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[711]) ).
thf(772,plain,
! [SV68: $i,SV23: $i,SV96: $i] :
( ( ( ! [SY371: $i] :
~ ( ~ ( ~ ( in @ SY371 @ SV96 )
| ( in @ SY371 @ SV23 )
| ( in @ SY371 @ SV68 ) )
| ~ ( ~ ( ( in @ SY371 @ SV23 )
| ( in @ SY371 @ SV68 ) )
| ( in @ SY371 @ SV96 ) ) ) )
= $false )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[712]) ).
thf(773,plain,
! [SV69: $i,SV97: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ ( relation_dom @ SV97 ) )
| ~ ( in @ SV69 @ ( relation_rng @ SV97 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV24 @ SV69 ) @ SV97 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[713]) ).
thf(774,plain,
! [SV26: $i,SV71: $i,SV118: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV118 @ SV71 )
| ( SV118 = SV26 ) )
| ~ ( ( SV118 != SV26 )
| ( in @ SV118 @ SV71 ) ) ) )
= $true )
| ( ( SV71
= ( singleton @ SV26 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(775,plain,
! [SV71: $i,SV26: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK14_SY331 @ SV26 @ SV71 ) @ SV71 )
| ( ( sK14_SY331 @ SV26 @ SV71 )
= SV26 ) )
| ~ ( ( ( sK14_SY331 @ SV26 @ SV71 )
!= SV26 )
| ( in @ ( sK14_SY331 @ SV26 @ SV71 ) @ SV71 ) ) ) )
= $false )
| ( ( SV71
= ( singleton @ SV26 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[716]) ).
thf(776,plain,
! [SV72: $i,SV27: $i] :
( ( ( SV27 = empty_set )
= $true )
| ( ( ~ ( ~ ( ( SV72
!= ( set_meet @ SV27 ) )
| ! [SY332: $i] :
~ ( ~ ( ~ ( in @ SY332 @ SV72 )
| ! [SY234: $i] :
( ~ ( in @ SY234 @ SV27 )
| ( in @ SY332 @ SY234 ) ) )
| ~ ( ~ ! [SY235: $i] :
( ~ ( in @ SY235 @ SV27 )
| ( in @ SY332 @ SY235 ) )
| ( in @ SY332 @ SV72 ) ) ) )
| ~ ( ~ ! [SY335: $i] :
~ ( ~ ( ~ ( in @ SY335 @ SV72 )
| ! [SY237: $i] :
( ~ ( in @ SY237 @ SV27 )
| ( in @ SY335 @ SY237 ) ) )
| ~ ( ~ ! [SY238: $i] :
( ~ ( in @ SY238 @ SV27 )
| ( in @ SY335 @ SY238 ) )
| ( in @ SY335 @ SV72 ) ) )
| ( SV72
= ( set_meet @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[717]) ).
thf(777,plain,
! [SV27: $i,SV72: $i] :
( ( ( ~ ( ( SV72
!= ( set_meet @ SV27 ) )
| ( SV72 = empty_set ) )
| ~ ( ( SV72 != empty_set )
| ( SV72
= ( set_meet @ SV27 ) ) ) )
= $false )
| ( ( SV27 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[718]) ).
thf(778,plain,
! [SV106: $i,SV29: $i] :
( ( ( subset @ SV29 @ SV106 )
= $false )
| ( ( ~ ( ~ ( subset @ ( relation_dom @ SV29 ) @ ( relation_dom @ SV106 ) )
| ~ ( subset @ ( relation_rng @ SV29 ) @ ( relation_rng @ SV106 ) ) ) )
= $true )
| ( ( relation @ SV106 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[719]) ).
thf(779,plain,
! [SV75: $i,SV31: $i] :
( ( ( empty @ SV31 )
= $true )
| ( ( ~ ( ~ ( ~ ( element @ SV75 @ SV31 )
| ( in @ SV75 @ SV31 ) )
| ~ ( ~ ( in @ SV75 @ SV31 )
| ( element @ SV75 @ SV31 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[720]) ).
thf(780,plain,
! [SV31: $i,SV75: $i] :
( ( ( ~ ( ~ ( element @ SV75 @ SV31 )
| ( empty @ SV75 ) )
| ~ ( ~ ( empty @ SV75 )
| ( element @ SV75 @ SV31 ) ) )
= $false )
| ( ( empty @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[721]) ).
thf(781,plain,
! [SV77: $i,SV33: $i,SV98: $i] :
( ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $false )
| ( ( ! [SY372: $i] :
~ ( ~ ( ~ ( in @ SY372 @ SV98 )
| ( SY372 = SV33 )
| ( SY372 = SV77 ) )
| ~ ( ~ ( ( SY372 = SV33 )
| ( SY372 = SV77 ) )
| ( in @ SY372 @ SV98 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[722]) ).
thf(782,plain,
! [SV77: $i,SV33: $i,SV98: $i] :
( ( ( ! [SY373: $i] :
~ ( ~ ( ~ ( in @ SY373 @ SV98 )
| ( SY373 = SV33 )
| ( SY373 = SV77 ) )
| ~ ( ~ ( ( SY373 = SV33 )
| ( SY373 = SV77 ) )
| ( in @ SY373 @ SV98 ) ) ) )
= $false )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[723]) ).
thf(783,plain,
! [SV37: $i] :
( ( ~ ~ ( ~ ( in @ SV37 @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SY374: $i,SY375: $i] :
( ~ ~ ( ~ ( in @ SY374 @ ( sK6_SY251 @ SV37 ) )
| ~ ( subset @ SY375 @ SY374 ) )
| ( in @ SY375 @ ( sK6_SY251 @ SV37 ) ) ) )
| ~ ! [SY376: $i] :
~ ~ ( ~ ( in @ SY376 @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SY377: $i] :
~ ~ ( ~ ( in @ SY377 @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY376 )
| ( in @ SX4 @ SY377 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[725]) ).
thf(784,plain,
! [SV37: $i,SV119: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( subset @ SV119 @ ( sK6_SY251 @ SV37 ) )
| ~ ~ ( are_equipotent @ SV119 @ ( sK6_SY251 @ SV37 ) ) )
| ~ ~ ( in @ SV119 @ ( sK6_SY251 @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(785,plain,
! [SV39: $i,SV113: $i] :
( ( ( ~ ( ~ ( in @ SV113 @ SV39 )
| ~ ! [SY397: $i,SY398: $i] :
( SV113
!= ( ordered_pair @ SY397 @ SY398 ) ) ) )
= $false )
| ( ( relation @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[727]) ).
thf(786,plain,
! [SV39: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_SY262 @ SV39 ) @ SV39 )
| ~ ! [SY399: $i,SY400: $i] :
( ( sK10_SY262 @ SV39 )
!= ( ordered_pair @ SY399 @ SY400 ) ) ) )
= $true )
| ( ( relation @ SV39 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[728]) ).
thf(787,plain,
! [SV107: $i,SV82: $i,SV99: $i,SV40: $i] :
( ( ( SV40 != SV99 )
= $false )
| ( ( ( ordered_pair @ SV40 @ SV82 )
= ( ordered_pair @ SV99 @ SV107 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[729]) ).
thf(788,plain,
! [SV99: $i,SV40: $i,SV107: $i,SV82: $i] :
( ( ( SV82 != SV107 )
= $false )
| ( ( ( ordered_pair @ SV40 @ SV82 )
= ( ordered_pair @ SV99 @ SV107 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[729]) ).
thf(789,plain,
! [SV100: $i,SV83: $i,SV41: $i] :
( ( ( in @ SV41 @ SV83 )
= $false )
| ( ( ~ ( element @ SV83 @ ( powerset @ SV100 ) ) )
= $true )
| ( ( element @ SV41 @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[730]) ).
thf(790,plain,
! [SV42: $i,SV108: $i] :
( ( ( SV108
!= ( relation_dom @ SV42 ) )
= $true )
| ( ( ! [SY391: $i] :
~ ( ~ ( ~ ( in @ SY391 @ SV108 )
| ~ ! [SY272: $i] :
~ ( in @ ( ordered_pair @ SY391 @ SY272 ) @ SV42 ) )
| ~ ( ~ ~ ! [SY273: $i] :
~ ( in @ ( ordered_pair @ SY391 @ SY273 ) @ SV42 )
| ( in @ SY391 @ SV108 ) ) ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[731]) ).
thf(791,plain,
! [SV42: $i,SV108: $i] :
( ( ( ~ ! [SY394: $i] :
~ ( ~ ( ~ ( in @ SY394 @ SV108 )
| ~ ! [SY275: $i] :
~ ( in @ ( ordered_pair @ SY394 @ SY275 ) @ SV42 ) )
| ~ ( ~ ~ ! [SY276: $i] :
~ ( in @ ( ordered_pair @ SY394 @ SY276 ) @ SV42 )
| ( in @ SY394 @ SV108 ) ) ) )
= $true )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[732]) ).
thf(792,plain,
! [SV84: $i,SV43: $i,SV101: $i] :
( ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $false )
| ( ( ! [SY381: $i] :
~ ( ~ ( ~ ( in @ SY381 @ SV101 )
| ~ ( ~ ( in @ SY381 @ SV43 )
| ~ ~ ( in @ SY381 @ SV84 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY381 @ SV43 )
| ~ ~ ( in @ SY381 @ SV84 ) )
| ( in @ SY381 @ SV101 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[733]) ).
thf(793,plain,
! [SV84: $i,SV43: $i,SV101: $i] :
( ( ( ! [SY382: $i] :
~ ( ~ ( ~ ( in @ SY382 @ SV101 )
| ~ ( ~ ( in @ SY382 @ SV43 )
| ~ ~ ( in @ SY382 @ SV84 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY382 @ SV43 )
| ~ ~ ( in @ SY382 @ SV84 ) )
| ( in @ SY382 @ SV101 ) ) ) )
= $false )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[734]) ).
thf(794,plain,
! [SV102: $i,SV44: $i,SV85: $i] :
( ( ( ~ ( in @ SV85 @ ( subset_complement @ SV44 @ SV102 ) ) )
= $true )
| ( ( ~ ( in @ SV85 @ SV102 ) )
= $true )
| ( ( element @ SV102 @ ( powerset @ SV44 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[735]) ).
thf(795,plain,
! [SV109: $i,SV103: $i,SV86: $i,SV45: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV45 @ SV86 ) @ ( cartesian_product2 @ SV103 @ SV109 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV45 @ SV103 )
| ~ ( in @ SV86 @ SV109 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[736]) ).
thf(796,plain,
! [SV109: $i,SV86: $i,SV103: $i,SV45: $i] :
( ( ( ~ ~ ( ~ ( in @ SV45 @ SV103 )
| ~ ( in @ SV86 @ SV109 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV45 @ SV86 ) @ ( cartesian_product2 @ SV103 @ SV109 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[737]) ).
thf(797,plain,
! [SV89: $i,SV48: $i] :
( ( ( ~ ~ ( disjoint @ SV48 @ SV89 ) )
= $true )
| ( ( ~ ! [SY350: $i] :
~ ( in @ SY350 @ ( set_intersection2 @ SV48 @ SV89 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[742]) ).
thf(798,plain,
! [SV89: $i,SV48: $i] :
( ( ( ~ ~ ! [SY351: $i] :
~ ( in @ SY351 @ ( set_intersection2 @ SV48 @ SV89 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV48 @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[743]) ).
thf(799,plain,
! [SV110: $i,SV104: $i,SV90: $i,SV49: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV49 @ SV90 ) @ ( cartesian_product2 @ SV104 @ SV110 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV49 @ SV104 )
| ~ ( in @ SV90 @ SV110 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[744]) ).
thf(800,plain,
! [SV110: $i,SV90: $i,SV104: $i,SV49: $i] :
( ( ( ~ ~ ( ~ ( in @ SV49 @ SV104 )
| ~ ( in @ SV90 @ SV110 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV49 @ SV90 ) @ ( cartesian_product2 @ SV104 @ SV110 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[745]) ).
thf(801,plain,
! [SV3: $i] :
( ( ~ ~ ( ~ ( in @ SV3 @ ( sK5_SY160 @ SV3 ) )
| ~ ! [SY354: $i,SY355: $i] :
( ~ ~ ( ~ ( in @ SY354 @ ( sK5_SY160 @ SV3 ) )
| ~ ( subset @ SY355 @ SY354 ) )
| ( in @ SY355 @ ( sK5_SY160 @ SV3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[746]) ).
thf(802,plain,
! [SV3: $i] :
( ( ~ ! [SY356: $i] :
( ~ ( in @ SY356 @ ( sK5_SY160 @ SV3 ) )
| ( in @ ( powerset @ SY356 ) @ ( sK5_SY160 @ SV3 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[746]) ).
thf(803,plain,
! [SV3: $i,SV114: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV114 @ ( sK5_SY160 @ SV3 ) )
| ~ ~ ( are_equipotent @ SV114 @ ( sK5_SY160 @ SV3 ) ) )
| ~ ~ ( in @ SV114 @ ( sK5_SY160 @ SV3 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[747]) ).
thf(804,plain,
! [SV4: $i,SV52: $i,SV115: $i] :
( ( ( ~ ( ~ ( in @ SV115 @ SV52 )
| ~ ! [SY401: $i] :
~ ~ ( ~ ( in @ SV115 @ SY401 )
| ~ ( in @ SY401 @ SV4 ) ) )
| ~ ( ~ ~ ! [SY402: $i] :
~ ~ ( ~ ( in @ SV115 @ SY402 )
| ~ ( in @ SY402 @ SV4 ) )
| ( in @ SV115 @ SV52 ) ) )
= $false )
| ( ( SV52
= ( union @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[748]) ).
thf(805,plain,
! [SV52: $i,SV4: $i] :
( ( ( ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV52 )
| ~ ! [SY403: $i] :
~ ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SY403 )
| ~ ( in @ SY403 @ SV4 ) ) )
| ~ ( ~ ~ ! [SY404: $i] :
~ ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SY404 )
| ~ ( in @ SY404 @ SV4 ) )
| ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV52 ) ) )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[749]) ).
thf(806,plain,
! [SV91: $i,SV54: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ SV54 ) )
= $true )
| ( ( ~ ( element @ SV54 @ ( powerset @ SV91 ) ) )
= $true )
| ( ( ~ ( empty @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[750]) ).
thf(807,plain,
! [SV9: $i,SV105: $i] :
( ( ( SV105
= ( relation_rng @ SV9 ) )
= $false )
| ( ( ! [SY385: $i] :
~ ( ~ ( ~ ( in @ SY385 @ SV105 )
| ~ ! [SY180: $i] :
~ ( in @ ( ordered_pair @ SY180 @ SY385 ) @ SV9 ) )
| ~ ( ~ ~ ! [SY181: $i] :
~ ( in @ ( ordered_pair @ SY181 @ SY385 ) @ SV9 )
| ( in @ SY385 @ SV105 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[753]) ).
thf(808,plain,
! [SV9: $i,SV105: $i] :
( ( ( ! [SY388: $i] :
~ ( ~ ( ~ ( in @ SY388 @ SV105 )
| ~ ! [SY183: $i] :
~ ( in @ ( ordered_pair @ SY183 @ SY388 ) @ SV9 ) )
| ~ ( ~ ~ ! [SY184: $i] :
~ ( in @ ( ordered_pair @ SY184 @ SY388 ) @ SV9 )
| ( in @ SY388 @ SV105 ) ) ) )
= $false )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[754]) ).
thf(809,plain,
! [SV57: $i,SV10: $i,SV116: $i] :
( ( ( ~ ( in @ SV116 @ SV10 ) )
= $true )
| ( ( in @ SV116 @ SV57 )
= $true )
| ( ( subset @ SV10 @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[755]) ).
thf(810,plain,
! [SV10: $i,SV57: $i] :
( ( ( ~ ( in @ ( sK12_SY303 @ SV57 @ SV10 ) @ SV10 ) )
= $false )
| ( ( subset @ SV10 @ SV57 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[756]) ).
thf(811,plain,
! [SV10: $i,SV57: $i] :
( ( ( in @ ( sK12_SY303 @ SV57 @ SV10 ) @ SV57 )
= $false )
| ( ( subset @ SV10 @ SV57 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[756]) ).
thf(812,plain,
! [SV12: $i,SV58: $i,SV117: $i] :
( ( ( ~ ( ~ ( in @ SV117 @ SV58 )
| ( subset @ SV117 @ SV12 ) )
| ~ ( ~ ( subset @ SV117 @ SV12 )
| ( in @ SV117 @ SV58 ) ) )
= $false )
| ( ( SV58
= ( powerset @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[757]) ).
thf(813,plain,
! [SV58: $i,SV12: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV58 )
| ( subset @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV12 ) )
| ~ ( ~ ( subset @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV12 )
| ( in @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV58 ) ) )
= $true )
| ( ( SV58
= ( powerset @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[758]) ).
thf(814,plain,
! [SV14: $i,SV60: $i] :
( ( ( ~ ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV14 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV60 )
| ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV14 ) ) )
= $true )
| ( ( SV14 = SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[759]) ).
thf(815,plain,
! [SV14: $i,SV60: $i] :
( ( ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV60 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV60 )
| ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV14 ) ) )
= $true )
| ( ( SV14 = SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[759]) ).
thf(816,plain,
! [SV63: $i,SV18: $i,SV93: $i,SV120: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV120 @ SV93 )
| ~ ( ~ ( in @ SV120 @ SV18 )
| ~ ( in @ SV120 @ SV63 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV120 @ SV18 )
| ~ ( in @ SV120 @ SV63 ) )
| ( in @ SV120 @ SV93 ) ) ) )
= $true )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(817,plain,
! [SV93: $i,SV18: $i,SV63: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV93 )
| ~ ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
| ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
| ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 ) )
| ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV93 ) ) ) )
= $false )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[764]) ).
thf(818,plain,
! [SV64: $i,SV94: $i,SV19: $i] :
( ( ( ~ ( in @ SV19 @ SV94 )
| ~ ( in @ SV64 @ SV94 ) )
= $false )
| ( ( subset @ ( unordered_pair @ SV19 @ SV64 ) @ SV94 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[765]) ).
thf(819,plain,
! [SV64: $i,SV94: $i,SV19: $i] :
( ( ( ~ ( in @ SV19 @ SV94 )
| ~ ( in @ SV64 @ SV94 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV19 @ SV64 ) @ SV94 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[766]) ).
thf(820,plain,
! [SV65: $i,SV20: $i] :
( ( ( ~ ( disjoint @ SV20 @ SV65 ) )
= $false )
| ( ( ~ ! [SY313: $i] :
~ ~ ( ~ ( in @ SY313 @ SV20 )
| ~ ( in @ SY313 @ SV65 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[767]) ).
thf(821,plain,
! [SV65: $i,SV20: $i] :
( ( ( ~ ! [SY314: $i] :
~ ~ ( ~ ( in @ SY314 @ SV20 )
| ~ ( in @ SY314 @ SV65 ) ) )
= $false )
| ( ( ~ ( disjoint @ SV20 @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[768]) ).
thf(822,plain,
! [SV67: $i,SV22: $i,SV95: $i,SV121: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV121 @ SV95 )
| ~ ! [SY405: $i] :
~ ~ ! [SY406: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY405 @ SV22 )
| ~ ( in @ SY406 @ SV67 ) )
| ( SV121
!= ( ordered_pair @ SY405 @ SY406 ) ) ) )
| ~ ( ~ ~ ! [SY407: $i] :
~ ~ ! [SY408: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY407 @ SV22 )
| ~ ( in @ SY408 @ SV67 ) )
| ( SV121
!= ( ordered_pair @ SY407 @ SY408 ) ) )
| ( in @ SV121 @ SV95 ) ) ) )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(823,plain,
! [SV95: $i,SV22: $i,SV67: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 )
| ~ ! [SY409: $i] :
~ ~ ! [SY410: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY409 @ SV22 )
| ~ ( in @ SY410 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SY409 @ SY410 ) ) ) )
| ~ ( ~ ~ ! [SY411: $i] :
~ ~ ! [SY412: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY411 @ SV22 )
| ~ ( in @ SY412 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SY411 @ SY412 ) ) )
| ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 ) ) ) )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[770]) ).
thf(824,plain,
! [SV68: $i,SV23: $i,SV96: $i,SV122: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV122 @ SV96 )
| ( in @ SV122 @ SV23 )
| ( in @ SV122 @ SV68 ) )
| ~ ( ~ ( ( in @ SV122 @ SV23 )
| ( in @ SV122 @ SV68 ) )
| ( in @ SV122 @ SV96 ) ) ) )
= $true )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(825,plain,
! [SV96: $i,SV23: $i,SV68: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV96 )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV23 )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV68 ) )
| ~ ( ~ ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV23 )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV68 ) )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV96 ) ) ) )
= $false )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[772]) ).
thf(826,plain,
! [SV69: $i,SV97: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ ( relation_dom @ SV97 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV24 @ SV69 ) @ SV97 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[773]) ).
thf(827,plain,
! [SV24: $i,SV97: $i,SV69: $i] :
( ( ( ~ ( in @ SV69 @ ( relation_rng @ SV97 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV24 @ SV69 ) @ SV97 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[773]) ).
thf(828,plain,
! [SV26: $i,SV71: $i,SV118: $i] :
( ( ( ~ ( ~ ( in @ SV118 @ SV71 )
| ( SV118 = SV26 ) )
| ~ ( ( SV118 != SV26 )
| ( in @ SV118 @ SV71 ) ) )
= $false )
| ( ( SV71
= ( singleton @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[774]) ).
thf(829,plain,
! [SV71: $i,SV26: $i] :
( ( ( ~ ( ~ ( in @ ( sK14_SY331 @ SV26 @ SV71 ) @ SV71 )
| ( ( sK14_SY331 @ SV26 @ SV71 )
= SV26 ) )
| ~ ( ( ( sK14_SY331 @ SV26 @ SV71 )
!= SV26 )
| ( in @ ( sK14_SY331 @ SV26 @ SV71 ) @ SV71 ) ) )
= $true )
| ( ( SV71
= ( singleton @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[775]) ).
thf(830,plain,
! [SV27: $i,SV72: $i] :
( ( ( ~ ( ( SV72
!= ( set_meet @ SV27 ) )
| ! [SY332: $i] :
~ ( ~ ( ~ ( in @ SY332 @ SV72 )
| ! [SY234: $i] :
( ~ ( in @ SY234 @ SV27 )
| ( in @ SY332 @ SY234 ) ) )
| ~ ( ~ ! [SY235: $i] :
( ~ ( in @ SY235 @ SV27 )
| ( in @ SY332 @ SY235 ) )
| ( in @ SY332 @ SV72 ) ) ) )
| ~ ( ~ ! [SY335: $i] :
~ ( ~ ( ~ ( in @ SY335 @ SV72 )
| ! [SY237: $i] :
( ~ ( in @ SY237 @ SV27 )
| ( in @ SY335 @ SY237 ) ) )
| ~ ( ~ ! [SY238: $i] :
( ~ ( in @ SY238 @ SV27 )
| ( in @ SY335 @ SY238 ) )
| ( in @ SY335 @ SV72 ) ) )
| ( SV72
= ( set_meet @ SV27 ) ) ) )
= $false )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[776]) ).
thf(831,plain,
! [SV27: $i,SV72: $i] :
( ( ( ~ ( ( SV72
!= ( set_meet @ SV27 ) )
| ( SV72 = empty_set ) ) )
= $false )
| ( ( SV27 = empty_set )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[777]) ).
thf(832,plain,
! [SV27: $i,SV72: $i] :
( ( ( ~ ( ( SV72 != empty_set )
| ( SV72
= ( set_meet @ SV27 ) ) ) )
= $false )
| ( ( SV27 = empty_set )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[777]) ).
thf(833,plain,
! [SV106: $i,SV29: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV29 ) @ ( relation_dom @ SV106 ) )
| ~ ( subset @ ( relation_rng @ SV29 ) @ ( relation_rng @ SV106 ) ) )
= $false )
| ( ( subset @ SV29 @ SV106 )
= $false )
| ( ( relation @ SV106 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[778]) ).
thf(834,plain,
! [SV31: $i,SV75: $i] :
( ( ( ~ ( ~ ( element @ SV75 @ SV31 )
| ( in @ SV75 @ SV31 ) )
| ~ ( ~ ( in @ SV75 @ SV31 )
| ( element @ SV75 @ SV31 ) ) )
= $false )
| ( ( empty @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[779]) ).
thf(835,plain,
! [SV31: $i,SV75: $i] :
( ( ( ~ ( ~ ( element @ SV75 @ SV31 )
| ( empty @ SV75 ) ) )
= $false )
| ( ( empty @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[780]) ).
thf(836,plain,
! [SV31: $i,SV75: $i] :
( ( ( ~ ( ~ ( empty @ SV75 )
| ( element @ SV75 @ SV31 ) ) )
= $false )
| ( ( empty @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[780]) ).
thf(837,plain,
! [SV77: $i,SV33: $i,SV98: $i,SV123: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV123 @ SV98 )
| ( SV123 = SV33 )
| ( SV123 = SV77 ) )
| ~ ( ~ ( ( SV123 = SV33 )
| ( SV123 = SV77 ) )
| ( in @ SV123 @ SV98 ) ) ) )
= $true )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(838,plain,
! [SV98: $i,SV33: $i,SV77: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK18_SY373 @ SV77 @ SV33 @ SV98 ) @ SV98 )
| ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV33 )
| ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV77 ) )
| ~ ( ~ ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV33 )
| ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV77 ) )
| ( in @ ( sK18_SY373 @ SV77 @ SV33 @ SV98 ) @ SV98 ) ) ) )
= $false )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[782]) ).
thf(839,plain,
! [SV37: $i] :
( ( ~ ~ ( ~ ( in @ SV37 @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SY374: $i,SY375: $i] :
( ~ ~ ( ~ ( in @ SY374 @ ( sK6_SY251 @ SV37 ) )
| ~ ( subset @ SY375 @ SY374 ) )
| ( in @ SY375 @ ( sK6_SY251 @ SV37 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[783]) ).
thf(840,plain,
! [SV37: $i] :
( ( ~ ! [SY376: $i] :
~ ~ ( ~ ( in @ SY376 @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SY377: $i] :
~ ~ ( ~ ( in @ SY377 @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY376 )
| ( in @ SX4 @ SY377 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[783]) ).
thf(841,plain,
! [SV37: $i,SV119: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV119 @ ( sK6_SY251 @ SV37 ) )
| ~ ~ ( are_equipotent @ SV119 @ ( sK6_SY251 @ SV37 ) ) )
| ~ ~ ( in @ SV119 @ ( sK6_SY251 @ SV37 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[784]) ).
thf(842,plain,
! [SV39: $i,SV113: $i] :
( ( ( ~ ( in @ SV113 @ SV39 )
| ~ ! [SY397: $i,SY398: $i] :
( SV113
!= ( ordered_pair @ SY397 @ SY398 ) ) )
= $true )
| ( ( relation @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[785]) ).
thf(843,plain,
! [SV39: $i] :
( ( ( ~ ( in @ ( sK10_SY262 @ SV39 ) @ SV39 )
| ~ ! [SY399: $i,SY400: $i] :
( ( sK10_SY262 @ SV39 )
!= ( ordered_pair @ SY399 @ SY400 ) ) )
= $false )
| ( ( relation @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[786]) ).
thf(844,plain,
! [SV107: $i,SV82: $i,SV99: $i,SV40: $i] :
( ( ( SV40 = SV99 )
= $true )
| ( ( ( ordered_pair @ SV40 @ SV82 )
= ( ordered_pair @ SV99 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[787]) ).
thf(845,plain,
! [SV99: $i,SV40: $i,SV107: $i,SV82: $i] :
( ( ( SV82 = SV107 )
= $true )
| ( ( ( ordered_pair @ SV40 @ SV82 )
= ( ordered_pair @ SV99 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[788]) ).
thf(846,plain,
! [SV41: $i,SV100: $i,SV83: $i] :
( ( ( element @ SV83 @ ( powerset @ SV100 ) )
= $false )
| ( ( in @ SV41 @ SV83 )
= $false )
| ( ( element @ SV41 @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[789]) ).
thf(847,plain,
! [SV42: $i,SV108: $i] :
( ( ( SV108
= ( relation_dom @ SV42 ) )
= $false )
| ( ( ! [SY391: $i] :
~ ( ~ ( ~ ( in @ SY391 @ SV108 )
| ~ ! [SY272: $i] :
~ ( in @ ( ordered_pair @ SY391 @ SY272 ) @ SV42 ) )
| ~ ( ~ ~ ! [SY273: $i] :
~ ( in @ ( ordered_pair @ SY391 @ SY273 ) @ SV42 )
| ( in @ SY391 @ SV108 ) ) ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[790]) ).
thf(848,plain,
! [SV42: $i,SV108: $i] :
( ( ( ! [SY394: $i] :
~ ( ~ ( ~ ( in @ SY394 @ SV108 )
| ~ ! [SY275: $i] :
~ ( in @ ( ordered_pair @ SY394 @ SY275 ) @ SV42 ) )
| ~ ( ~ ~ ! [SY276: $i] :
~ ( in @ ( ordered_pair @ SY394 @ SY276 ) @ SV42 )
| ( in @ SY394 @ SV108 ) ) ) )
= $false )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[791]) ).
thf(849,plain,
! [SV84: $i,SV43: $i,SV101: $i,SV124: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV124 @ SV101 )
| ~ ( ~ ( in @ SV124 @ SV43 )
| ~ ~ ( in @ SV124 @ SV84 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV124 @ SV43 )
| ~ ~ ( in @ SV124 @ SV84 ) )
| ( in @ SV124 @ SV101 ) ) ) )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(850,plain,
! [SV101: $i,SV43: $i,SV84: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV101 )
| ~ ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
| ~ ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
| ~ ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 ) )
| ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV101 ) ) ) )
= $false )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[793]) ).
thf(851,plain,
! [SV102: $i,SV44: $i,SV85: $i] :
( ( ( in @ SV85 @ ( subset_complement @ SV44 @ SV102 ) )
= $false )
| ( ( ~ ( in @ SV85 @ SV102 ) )
= $true )
| ( ( element @ SV102 @ ( powerset @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[794]) ).
thf(852,plain,
! [SV109: $i,SV103: $i,SV86: $i,SV45: $i] :
( ( ( in @ ( ordered_pair @ SV45 @ SV86 ) @ ( cartesian_product2 @ SV103 @ SV109 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV45 @ SV103 )
| ~ ( in @ SV86 @ SV109 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[795]) ).
thf(853,plain,
! [SV109: $i,SV86: $i,SV103: $i,SV45: $i] :
( ( ( ~ ( ~ ( in @ SV45 @ SV103 )
| ~ ( in @ SV86 @ SV109 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV45 @ SV86 ) @ ( cartesian_product2 @ SV103 @ SV109 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[796]) ).
thf(854,plain,
! [SV89: $i,SV48: $i] :
( ( ( ~ ( disjoint @ SV48 @ SV89 ) )
= $false )
| ( ( ~ ! [SY350: $i] :
~ ( in @ SY350 @ ( set_intersection2 @ SV48 @ SV89 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[797]) ).
thf(855,plain,
! [SV89: $i,SV48: $i] :
( ( ( ~ ! [SY351: $i] :
~ ( in @ SY351 @ ( set_intersection2 @ SV48 @ SV89 ) ) )
= $false )
| ( ( ~ ( disjoint @ SV48 @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[798]) ).
thf(856,plain,
! [SV110: $i,SV104: $i,SV90: $i,SV49: $i] :
( ( ( in @ ( ordered_pair @ SV49 @ SV90 ) @ ( cartesian_product2 @ SV104 @ SV110 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV49 @ SV104 )
| ~ ( in @ SV90 @ SV110 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[799]) ).
thf(857,plain,
! [SV110: $i,SV90: $i,SV104: $i,SV49: $i] :
( ( ( ~ ( ~ ( in @ SV49 @ SV104 )
| ~ ( in @ SV90 @ SV110 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV49 @ SV90 ) @ ( cartesian_product2 @ SV104 @ SV110 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[800]) ).
thf(858,plain,
! [SV3: $i] :
( ( ~ ( ~ ( in @ SV3 @ ( sK5_SY160 @ SV3 ) )
| ~ ! [SY354: $i,SY355: $i] :
( ~ ~ ( ~ ( in @ SY354 @ ( sK5_SY160 @ SV3 ) )
| ~ ( subset @ SY355 @ SY354 ) )
| ( in @ SY355 @ ( sK5_SY160 @ SV3 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[801]) ).
thf(859,plain,
! [SV3: $i] :
( ( ! [SY356: $i] :
( ~ ( in @ SY356 @ ( sK5_SY160 @ SV3 ) )
| ( in @ ( powerset @ SY356 ) @ ( sK5_SY160 @ SV3 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[802]) ).
thf(860,plain,
! [SV3: $i,SV114: $i] :
( ( ~ ~ ( ~ ( subset @ SV114 @ ( sK5_SY160 @ SV3 ) )
| ~ ~ ( are_equipotent @ SV114 @ ( sK5_SY160 @ SV3 ) ) )
| ~ ~ ( in @ SV114 @ ( sK5_SY160 @ SV3 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[803]) ).
thf(861,plain,
! [SV4: $i,SV52: $i,SV115: $i] :
( ( ( ~ ( ~ ( in @ SV115 @ SV52 )
| ~ ! [SY401: $i] :
~ ~ ( ~ ( in @ SV115 @ SY401 )
| ~ ( in @ SY401 @ SV4 ) ) ) )
= $false )
| ( ( SV52
= ( union @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[804]) ).
thf(862,plain,
! [SV52: $i,SV4: $i,SV115: $i] :
( ( ( ~ ( ~ ~ ! [SY402: $i] :
~ ~ ( ~ ( in @ SV115 @ SY402 )
| ~ ( in @ SY402 @ SV4 ) )
| ( in @ SV115 @ SV52 ) ) )
= $false )
| ( ( SV52
= ( union @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[804]) ).
thf(863,plain,
! [SV52: $i,SV4: $i] :
( ( ( ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV52 )
| ~ ! [SY403: $i] :
~ ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SY403 )
| ~ ( in @ SY403 @ SV4 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY404: $i] :
~ ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SY404 )
| ~ ( in @ SY404 @ SV4 ) )
| ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV52 ) ) )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[805]) ).
thf(864,plain,
! [SV91: $i,SV54: $i,SV6: $i] :
( ( ( in @ SV6 @ SV54 )
= $false )
| ( ( ~ ( element @ SV54 @ ( powerset @ SV91 ) ) )
= $true )
| ( ( ~ ( empty @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[806]) ).
thf(865,plain,
! [SV9: $i,SV105: $i,SV125: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV125 @ SV105 )
| ~ ! [SY413: $i] :
~ ( in @ ( ordered_pair @ SY413 @ SV125 ) @ SV9 ) )
| ~ ( ~ ~ ! [SY414: $i] :
~ ( in @ ( ordered_pair @ SY414 @ SV125 ) @ SV9 )
| ( in @ SV125 @ SV105 ) ) ) )
= $true )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $false )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(866,plain,
! [SV105: $i,SV9: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK20_SY388 @ SV9 @ SV105 ) @ SV105 )
| ~ ! [SY415: $i] :
~ ( in @ ( ordered_pair @ SY415 @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 ) )
| ~ ( ~ ~ ! [SY416: $i] :
~ ( in @ ( ordered_pair @ SY416 @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 )
| ( in @ ( sK20_SY388 @ SV9 @ SV105 ) @ SV105 ) ) ) )
= $false )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[808]) ).
thf(867,plain,
! [SV57: $i,SV10: $i,SV116: $i] :
( ( ( in @ SV116 @ SV10 )
= $false )
| ( ( in @ SV116 @ SV57 )
= $true )
| ( ( subset @ SV10 @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[809]) ).
thf(868,plain,
! [SV10: $i,SV57: $i] :
( ( ( in @ ( sK12_SY303 @ SV57 @ SV10 ) @ SV10 )
= $true )
| ( ( subset @ SV10 @ SV57 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[810]) ).
thf(869,plain,
! [SV12: $i,SV58: $i,SV117: $i] :
( ( ( ~ ( ~ ( in @ SV117 @ SV58 )
| ( subset @ SV117 @ SV12 ) ) )
= $false )
| ( ( SV58
= ( powerset @ SV12 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[812]) ).
thf(870,plain,
! [SV58: $i,SV12: $i,SV117: $i] :
( ( ( ~ ( ~ ( subset @ SV117 @ SV12 )
| ( in @ SV117 @ SV58 ) ) )
= $false )
| ( ( SV58
= ( powerset @ SV12 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[812]) ).
thf(871,plain,
! [SV58: $i,SV12: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV58 )
| ( subset @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV12 ) ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV12 )
| ( in @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV58 ) ) )
= $true )
| ( ( SV58
= ( powerset @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[813]) ).
thf(872,plain,
! [SV14: $i,SV60: $i] :
( ( ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV14 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV60 )
| ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV14 ) ) )
= $true )
| ( ( SV14 = SV60 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[814]) ).
thf(873,plain,
! [SV14: $i,SV60: $i] :
( ( ( ~ ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV60 )
| ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV14 ) )
= $false )
| ( ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV60 )
= $false )
| ( ( SV14 = SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[815]) ).
thf(874,plain,
! [SV63: $i,SV18: $i,SV93: $i,SV120: $i] :
( ( ( ~ ( ~ ( in @ SV120 @ SV93 )
| ~ ( ~ ( in @ SV120 @ SV18 )
| ~ ( in @ SV120 @ SV63 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV120 @ SV18 )
| ~ ( in @ SV120 @ SV63 ) )
| ( in @ SV120 @ SV93 ) ) )
= $false )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[816]) ).
thf(875,plain,
! [SV93: $i,SV18: $i,SV63: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV93 )
| ~ ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
| ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
| ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 ) )
| ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV93 ) ) )
= $true )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[817]) ).
thf(876,plain,
! [SV64: $i,SV94: $i,SV19: $i] :
( ( ( ~ ( in @ SV19 @ SV94 ) )
= $false )
| ( ( subset @ ( unordered_pair @ SV19 @ SV64 ) @ SV94 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[818]) ).
thf(877,plain,
! [SV19: $i,SV94: $i,SV64: $i] :
( ( ( ~ ( in @ SV64 @ SV94 ) )
= $false )
| ( ( subset @ ( unordered_pair @ SV19 @ SV64 ) @ SV94 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[818]) ).
thf(878,plain,
! [SV64: $i,SV94: $i,SV19: $i] :
( ( ( ~ ( in @ SV19 @ SV94 ) )
= $true )
| ( ( ~ ( in @ SV64 @ SV94 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV19 @ SV64 ) @ SV94 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[819]) ).
thf(879,plain,
! [SV65: $i,SV20: $i] :
( ( ( disjoint @ SV20 @ SV65 )
= $true )
| ( ( ~ ! [SY313: $i] :
~ ~ ( ~ ( in @ SY313 @ SV20 )
| ~ ( in @ SY313 @ SV65 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[820]) ).
thf(880,plain,
! [SV65: $i,SV20: $i] :
( ( ( ! [SY314: $i] :
~ ~ ( ~ ( in @ SY314 @ SV20 )
| ~ ( in @ SY314 @ SV65 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV20 @ SV65 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[821]) ).
thf(881,plain,
! [SV67: $i,SV22: $i,SV95: $i,SV121: $i] :
( ( ( ~ ( ~ ( in @ SV121 @ SV95 )
| ~ ! [SY405: $i] :
~ ~ ! [SY406: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY405 @ SV22 )
| ~ ( in @ SY406 @ SV67 ) )
| ( SV121
!= ( ordered_pair @ SY405 @ SY406 ) ) ) )
| ~ ( ~ ~ ! [SY407: $i] :
~ ~ ! [SY408: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY407 @ SV22 )
| ~ ( in @ SY408 @ SV67 ) )
| ( SV121
!= ( ordered_pair @ SY407 @ SY408 ) ) )
| ( in @ SV121 @ SV95 ) ) )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[822]) ).
thf(882,plain,
! [SV95: $i,SV22: $i,SV67: $i] :
( ( ( ~ ( ~ ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 )
| ~ ! [SY409: $i] :
~ ~ ! [SY410: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY409 @ SV22 )
| ~ ( in @ SY410 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SY409 @ SY410 ) ) ) )
| ~ ( ~ ~ ! [SY411: $i] :
~ ~ ! [SY412: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY411 @ SV22 )
| ~ ( in @ SY412 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SY411 @ SY412 ) ) )
| ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 ) ) )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[823]) ).
thf(883,plain,
! [SV68: $i,SV23: $i,SV96: $i,SV122: $i] :
( ( ( ~ ( ~ ( in @ SV122 @ SV96 )
| ( in @ SV122 @ SV23 )
| ( in @ SV122 @ SV68 ) )
| ~ ( ~ ( ( in @ SV122 @ SV23 )
| ( in @ SV122 @ SV68 ) )
| ( in @ SV122 @ SV96 ) ) )
= $false )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[824]) ).
thf(884,plain,
! [SV96: $i,SV23: $i,SV68: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV96 )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV23 )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV68 ) )
| ~ ( ~ ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV23 )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV68 ) )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV96 ) ) )
= $true )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[825]) ).
thf(885,plain,
! [SV69: $i,SV97: $i,SV24: $i] :
( ( ( in @ SV24 @ ( relation_dom @ SV97 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV24 @ SV69 ) @ SV97 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[826]) ).
thf(886,plain,
! [SV24: $i,SV97: $i,SV69: $i] :
( ( ( in @ SV69 @ ( relation_rng @ SV97 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV24 @ SV69 ) @ SV97 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[827]) ).
thf(887,plain,
! [SV26: $i,SV71: $i,SV118: $i] :
( ( ( ~ ( ~ ( in @ SV118 @ SV71 )
| ( SV118 = SV26 ) ) )
= $false )
| ( ( SV71
= ( singleton @ SV26 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[828]) ).
thf(888,plain,
! [SV71: $i,SV26: $i,SV118: $i] :
( ( ( ~ ( ( SV118 != SV26 )
| ( in @ SV118 @ SV71 ) ) )
= $false )
| ( ( SV71
= ( singleton @ SV26 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[828]) ).
thf(889,plain,
! [SV71: $i,SV26: $i] :
( ( ( ~ ( ~ ( in @ ( sK14_SY331 @ SV26 @ SV71 ) @ SV71 )
| ( ( sK14_SY331 @ SV26 @ SV71 )
= SV26 ) ) )
= $true )
| ( ( ~ ( ( ( sK14_SY331 @ SV26 @ SV71 )
!= SV26 )
| ( in @ ( sK14_SY331 @ SV26 @ SV71 ) @ SV71 ) ) )
= $true )
| ( ( SV71
= ( singleton @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[829]) ).
thf(890,plain,
! [SV27: $i,SV72: $i] :
( ( ( ~ ( ( SV72
!= ( set_meet @ SV27 ) )
| ! [SY332: $i] :
~ ( ~ ( ~ ( in @ SY332 @ SV72 )
| ! [SY234: $i] :
( ~ ( in @ SY234 @ SV27 )
| ( in @ SY332 @ SY234 ) ) )
| ~ ( ~ ! [SY235: $i] :
( ~ ( in @ SY235 @ SV27 )
| ( in @ SY332 @ SY235 ) )
| ( in @ SY332 @ SV72 ) ) ) ) )
= $false )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[830]) ).
thf(891,plain,
! [SV27: $i,SV72: $i] :
( ( ( ~ ( ~ ! [SY335: $i] :
~ ( ~ ( ~ ( in @ SY335 @ SV72 )
| ! [SY237: $i] :
( ~ ( in @ SY237 @ SV27 )
| ( in @ SY335 @ SY237 ) ) )
| ~ ( ~ ! [SY238: $i] :
( ~ ( in @ SY238 @ SV27 )
| ( in @ SY335 @ SY238 ) )
| ( in @ SY335 @ SV72 ) ) )
| ( SV72
= ( set_meet @ SV27 ) ) ) )
= $false )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[830]) ).
thf(892,plain,
! [SV27: $i,SV72: $i] :
( ( ( ( SV72
!= ( set_meet @ SV27 ) )
| ( SV72 = empty_set ) )
= $true )
| ( ( SV27 = empty_set )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[831]) ).
thf(893,plain,
! [SV27: $i,SV72: $i] :
( ( ( ( SV72 != empty_set )
| ( SV72
= ( set_meet @ SV27 ) ) )
= $true )
| ( ( SV27 = empty_set )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[832]) ).
thf(894,plain,
! [SV106: $i,SV29: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV29 ) @ ( relation_dom @ SV106 ) ) )
= $false )
| ( ( subset @ SV29 @ SV106 )
= $false )
| ( ( relation @ SV106 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[833]) ).
thf(895,plain,
! [SV106: $i,SV29: $i] :
( ( ( ~ ( subset @ ( relation_rng @ SV29 ) @ ( relation_rng @ SV106 ) ) )
= $false )
| ( ( subset @ SV29 @ SV106 )
= $false )
| ( ( relation @ SV106 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[833]) ).
thf(896,plain,
! [SV31: $i,SV75: $i] :
( ( ( ~ ( ~ ( element @ SV75 @ SV31 )
| ( in @ SV75 @ SV31 ) ) )
= $false )
| ( ( empty @ SV31 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[834]) ).
thf(897,plain,
! [SV31: $i,SV75: $i] :
( ( ( ~ ( ~ ( in @ SV75 @ SV31 )
| ( element @ SV75 @ SV31 ) ) )
= $false )
| ( ( empty @ SV31 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[834]) ).
thf(898,plain,
! [SV31: $i,SV75: $i] :
( ( ( ~ ( element @ SV75 @ SV31 )
| ( empty @ SV75 ) )
= $true )
| ( ( empty @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[835]) ).
thf(899,plain,
! [SV31: $i,SV75: $i] :
( ( ( ~ ( empty @ SV75 )
| ( element @ SV75 @ SV31 ) )
= $true )
| ( ( empty @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[836]) ).
thf(900,plain,
! [SV77: $i,SV33: $i,SV98: $i,SV123: $i] :
( ( ( ~ ( ~ ( in @ SV123 @ SV98 )
| ( SV123 = SV33 )
| ( SV123 = SV77 ) )
| ~ ( ~ ( ( SV123 = SV33 )
| ( SV123 = SV77 ) )
| ( in @ SV123 @ SV98 ) ) )
= $false )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[837]) ).
thf(901,plain,
! [SV98: $i,SV33: $i,SV77: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_SY373 @ SV77 @ SV33 @ SV98 ) @ SV98 )
| ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV33 )
| ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV77 ) )
| ~ ( ~ ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV33 )
| ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV77 ) )
| ( in @ ( sK18_SY373 @ SV77 @ SV33 @ SV98 ) @ SV98 ) ) )
= $true )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[838]) ).
thf(902,plain,
! [SV37: $i] :
( ( ~ ( ~ ( in @ SV37 @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SY374: $i,SY375: $i] :
( ~ ~ ( ~ ( in @ SY374 @ ( sK6_SY251 @ SV37 ) )
| ~ ( subset @ SY375 @ SY374 ) )
| ( in @ SY375 @ ( sK6_SY251 @ SV37 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[839]) ).
thf(903,plain,
! [SV37: $i] :
( ( ! [SY376: $i] :
~ ~ ( ~ ( in @ SY376 @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SY377: $i] :
~ ~ ( ~ ( in @ SY377 @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY376 )
| ( in @ SX4 @ SY377 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[840]) ).
thf(904,plain,
! [SV37: $i,SV119: $i] :
( ( ~ ~ ( ~ ( subset @ SV119 @ ( sK6_SY251 @ SV37 ) )
| ~ ~ ( are_equipotent @ SV119 @ ( sK6_SY251 @ SV37 ) ) )
| ~ ~ ( in @ SV119 @ ( sK6_SY251 @ SV37 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[841]) ).
thf(905,plain,
! [SV39: $i,SV113: $i] :
( ( ( ~ ( in @ SV113 @ SV39 ) )
= $true )
| ( ( ~ ! [SY397: $i,SY398: $i] :
( SV113
!= ( ordered_pair @ SY397 @ SY398 ) ) )
= $true )
| ( ( relation @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[842]) ).
thf(906,plain,
! [SV39: $i] :
( ( ( ~ ( in @ ( sK10_SY262 @ SV39 ) @ SV39 ) )
= $false )
| ( ( relation @ SV39 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[843]) ).
thf(907,plain,
! [SV39: $i] :
( ( ( ~ ! [SY399: $i,SY400: $i] :
( ( sK10_SY262 @ SV39 )
!= ( ordered_pair @ SY399 @ SY400 ) ) )
= $false )
| ( ( relation @ SV39 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[843]) ).
thf(908,plain,
! [SV42: $i,SV108: $i,SV126: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV126 @ SV108 )
| ~ ! [SY417: $i] :
~ ( in @ ( ordered_pair @ SV126 @ SY417 ) @ SV42 ) )
| ~ ( ~ ~ ! [SY418: $i] :
~ ( in @ ( ordered_pair @ SV126 @ SY418 ) @ SV42 )
| ( in @ SV126 @ SV108 ) ) ) )
= $true )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $false )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(909,plain,
! [SV108: $i,SV42: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK21_SY394 @ SV42 @ SV108 ) @ SV108 )
| ~ ! [SY419: $i] :
~ ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ SY419 ) @ SV42 ) )
| ~ ( ~ ~ ! [SY420: $i] :
~ ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ SY420 ) @ SV42 )
| ( in @ ( sK21_SY394 @ SV42 @ SV108 ) @ SV108 ) ) ) )
= $false )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[848]) ).
thf(910,plain,
! [SV84: $i,SV43: $i,SV101: $i,SV124: $i] :
( ( ( ~ ( ~ ( in @ SV124 @ SV101 )
| ~ ( ~ ( in @ SV124 @ SV43 )
| ~ ~ ( in @ SV124 @ SV84 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV124 @ SV43 )
| ~ ~ ( in @ SV124 @ SV84 ) )
| ( in @ SV124 @ SV101 ) ) )
= $false )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[849]) ).
thf(911,plain,
! [SV101: $i,SV43: $i,SV84: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV101 )
| ~ ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
| ~ ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
| ~ ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 ) )
| ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV101 ) ) )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[850]) ).
thf(912,plain,
! [SV44: $i,SV102: $i,SV85: $i] :
( ( ( in @ SV85 @ SV102 )
= $false )
| ( ( in @ SV85 @ ( subset_complement @ SV44 @ SV102 ) )
= $false )
| ( ( element @ SV102 @ ( powerset @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[851]) ).
thf(913,plain,
! [SV109: $i,SV86: $i,SV103: $i,SV45: $i] :
( ( ( ~ ( in @ SV45 @ SV103 )
| ~ ( in @ SV86 @ SV109 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV45 @ SV86 ) @ ( cartesian_product2 @ SV103 @ SV109 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[852]) ).
thf(914,plain,
! [SV109: $i,SV86: $i,SV103: $i,SV45: $i] :
( ( ( ~ ( in @ SV45 @ SV103 )
| ~ ( in @ SV86 @ SV109 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV45 @ SV86 ) @ ( cartesian_product2 @ SV103 @ SV109 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[853]) ).
thf(915,plain,
! [SV89: $i,SV48: $i] :
( ( ( disjoint @ SV48 @ SV89 )
= $true )
| ( ( ~ ! [SY350: $i] :
~ ( in @ SY350 @ ( set_intersection2 @ SV48 @ SV89 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[854]) ).
thf(916,plain,
! [SV89: $i,SV48: $i] :
( ( ( ! [SY351: $i] :
~ ( in @ SY351 @ ( set_intersection2 @ SV48 @ SV89 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV48 @ SV89 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[855]) ).
thf(917,plain,
! [SV110: $i,SV90: $i,SV104: $i,SV49: $i] :
( ( ( ~ ( in @ SV49 @ SV104 )
| ~ ( in @ SV90 @ SV110 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV49 @ SV90 ) @ ( cartesian_product2 @ SV104 @ SV110 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[856]) ).
thf(918,plain,
! [SV110: $i,SV90: $i,SV104: $i,SV49: $i] :
( ( ( ~ ( in @ SV49 @ SV104 )
| ~ ( in @ SV90 @ SV110 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV49 @ SV90 ) @ ( cartesian_product2 @ SV104 @ SV110 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[857]) ).
thf(919,plain,
! [SV3: $i] :
( ( ~ ( in @ SV3 @ ( sK5_SY160 @ SV3 ) )
| ~ ! [SY354: $i,SY355: $i] :
( ~ ~ ( ~ ( in @ SY354 @ ( sK5_SY160 @ SV3 ) )
| ~ ( subset @ SY355 @ SY354 ) )
| ( in @ SY355 @ ( sK5_SY160 @ SV3 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[858]) ).
thf(920,plain,
! [SV3: $i,SV127: $i] :
( ( ~ ( in @ SV127 @ ( sK5_SY160 @ SV3 ) )
| ( in @ ( powerset @ SV127 ) @ ( sK5_SY160 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(921,plain,
! [SV3: $i,SV114: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV114 @ ( sK5_SY160 @ SV3 ) )
| ~ ~ ( are_equipotent @ SV114 @ ( sK5_SY160 @ SV3 ) ) ) )
= $true )
| ( ( ~ ~ ( in @ SV114 @ ( sK5_SY160 @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[860]) ).
thf(922,plain,
! [SV4: $i,SV52: $i,SV115: $i] :
( ( ( ~ ( in @ SV115 @ SV52 )
| ~ ! [SY401: $i] :
~ ~ ( ~ ( in @ SV115 @ SY401 )
| ~ ( in @ SY401 @ SV4 ) ) )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[861]) ).
thf(923,plain,
! [SV52: $i,SV4: $i,SV115: $i] :
( ( ( ~ ~ ! [SY402: $i] :
~ ~ ( ~ ( in @ SV115 @ SY402 )
| ~ ( in @ SY402 @ SV4 ) )
| ( in @ SV115 @ SV52 ) )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[862]) ).
thf(924,plain,
! [SV52: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV52 )
| ~ ! [SY403: $i] :
~ ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SY403 )
| ~ ( in @ SY403 @ SV4 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY404: $i] :
~ ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SY404 )
| ~ ( in @ SY404 @ SV4 ) )
| ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV52 ) ) )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[863]) ).
thf(925,plain,
! [SV6: $i,SV91: $i,SV54: $i] :
( ( ( element @ SV54 @ ( powerset @ SV91 ) )
= $false )
| ( ( in @ SV6 @ SV54 )
= $false )
| ( ( ~ ( empty @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[864]) ).
thf(926,plain,
! [SV9: $i,SV105: $i,SV125: $i] :
( ( ( ~ ( ~ ( in @ SV125 @ SV105 )
| ~ ! [SY413: $i] :
~ ( in @ ( ordered_pair @ SY413 @ SV125 ) @ SV9 ) )
| ~ ( ~ ~ ! [SY414: $i] :
~ ( in @ ( ordered_pair @ SY414 @ SV125 ) @ SV9 )
| ( in @ SV125 @ SV105 ) ) )
= $false )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $false )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[865]) ).
thf(927,plain,
! [SV105: $i,SV9: $i] :
( ( ( ~ ( ~ ( in @ ( sK20_SY388 @ SV9 @ SV105 ) @ SV105 )
| ~ ! [SY415: $i] :
~ ( in @ ( ordered_pair @ SY415 @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 ) )
| ~ ( ~ ~ ! [SY416: $i] :
~ ( in @ ( ordered_pair @ SY416 @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 )
| ( in @ ( sK20_SY388 @ SV9 @ SV105 ) @ SV105 ) ) )
= $true )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[866]) ).
thf(928,plain,
! [SV12: $i,SV58: $i,SV117: $i] :
( ( ( ~ ( in @ SV117 @ SV58 )
| ( subset @ SV117 @ SV12 ) )
= $true )
| ( ( SV58
= ( powerset @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[869]) ).
thf(929,plain,
! [SV58: $i,SV12: $i,SV117: $i] :
( ( ( ~ ( subset @ SV117 @ SV12 )
| ( in @ SV117 @ SV58 ) )
= $true )
| ( ( SV58
= ( powerset @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[870]) ).
thf(930,plain,
! [SV58: $i,SV12: $i] :
( ( ( ~ ( in @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV58 )
| ( subset @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV12 ) )
= $false )
| ( ( ~ ( ~ ( subset @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV12 )
| ( in @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV58 ) ) )
= $true )
| ( ( SV58
= ( powerset @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[871]) ).
thf(931,plain,
! [SV14: $i,SV60: $i] :
( ( ( ~ ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV60 )
| ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV14 ) )
= $false )
| ( ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV14 )
= $true )
| ( ( SV14 = SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[872]) ).
thf(932,plain,
! [SV14: $i,SV60: $i] :
( ( ( ~ ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV60 ) )
= $false )
| ( ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV60 )
= $false )
| ( ( SV14 = SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[873]) ).
thf(933,plain,
! [SV14: $i,SV60: $i] :
( ( ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV14 )
= $false )
| ( ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV60 )
= $false )
| ( ( SV14 = SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[873]) ).
thf(934,plain,
! [SV63: $i,SV18: $i,SV93: $i,SV120: $i] :
( ( ( ~ ( ~ ( in @ SV120 @ SV93 )
| ~ ( ~ ( in @ SV120 @ SV18 )
| ~ ( in @ SV120 @ SV63 ) ) ) )
= $false )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[874]) ).
thf(935,plain,
! [SV93: $i,SV63: $i,SV18: $i,SV120: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV120 @ SV18 )
| ~ ( in @ SV120 @ SV63 ) )
| ( in @ SV120 @ SV93 ) ) )
= $false )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[874]) ).
thf(936,plain,
! [SV93: $i,SV18: $i,SV63: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV93 )
| ~ ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
| ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
| ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 ) )
| ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV93 ) ) )
= $true )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[875]) ).
thf(937,plain,
! [SV64: $i,SV94: $i,SV19: $i] :
( ( ( in @ SV19 @ SV94 )
= $true )
| ( ( subset @ ( unordered_pair @ SV19 @ SV64 ) @ SV94 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[876]) ).
thf(938,plain,
! [SV19: $i,SV94: $i,SV64: $i] :
( ( ( in @ SV64 @ SV94 )
= $true )
| ( ( subset @ ( unordered_pair @ SV19 @ SV64 ) @ SV94 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[877]) ).
thf(939,plain,
! [SV64: $i,SV94: $i,SV19: $i] :
( ( ( in @ SV19 @ SV94 )
= $false )
| ( ( ~ ( in @ SV64 @ SV94 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV19 @ SV64 ) @ SV94 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[878]) ).
thf(940,plain,
! [SV65: $i,SV20: $i] :
( ( ( ! [SY313: $i] :
~ ~ ( ~ ( in @ SY313 @ SV20 )
| ~ ( in @ SY313 @ SV65 ) ) )
= $false )
| ( ( disjoint @ SV20 @ SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[879]) ).
thf(941,plain,
! [SV65: $i,SV20: $i,SV128: $i] :
( ( ( ~ ~ ( ~ ( in @ SV128 @ SV20 )
| ~ ( in @ SV128 @ SV65 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV20 @ SV65 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(942,plain,
! [SV67: $i,SV22: $i,SV95: $i,SV121: $i] :
( ( ( ~ ( ~ ( in @ SV121 @ SV95 )
| ~ ! [SY405: $i] :
~ ~ ! [SY406: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY405 @ SV22 )
| ~ ( in @ SY406 @ SV67 ) )
| ( SV121
!= ( ordered_pair @ SY405 @ SY406 ) ) ) ) )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[881]) ).
thf(943,plain,
! [SV95: $i,SV121: $i,SV67: $i,SV22: $i] :
( ( ( ~ ( ~ ~ ! [SY407: $i] :
~ ~ ! [SY408: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY407 @ SV22 )
| ~ ( in @ SY408 @ SV67 ) )
| ( SV121
!= ( ordered_pair @ SY407 @ SY408 ) ) )
| ( in @ SV121 @ SV95 ) ) )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[881]) ).
thf(944,plain,
! [SV95: $i,SV22: $i,SV67: $i] :
( ( ( ~ ( ~ ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 )
| ~ ! [SY409: $i] :
~ ~ ! [SY410: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY409 @ SV22 )
| ~ ( in @ SY410 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SY409 @ SY410 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY411: $i] :
~ ~ ! [SY412: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY411 @ SV22 )
| ~ ( in @ SY412 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SY411 @ SY412 ) ) )
| ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 ) ) )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[882]) ).
thf(945,plain,
! [SV68: $i,SV23: $i,SV96: $i,SV122: $i] :
( ( ( ~ ( ~ ( in @ SV122 @ SV96 )
| ( in @ SV122 @ SV23 )
| ( in @ SV122 @ SV68 ) ) )
= $false )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[883]) ).
thf(946,plain,
! [SV96: $i,SV68: $i,SV23: $i,SV122: $i] :
( ( ( ~ ( ~ ( ( in @ SV122 @ SV23 )
| ( in @ SV122 @ SV68 ) )
| ( in @ SV122 @ SV96 ) ) )
= $false )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[883]) ).
thf(947,plain,
! [SV96: $i,SV23: $i,SV68: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV96 )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV23 )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV68 ) ) )
= $true )
| ( ( ~ ( ~ ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV23 )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV68 ) )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV96 ) ) )
= $true )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[884]) ).
thf(948,plain,
! [SV26: $i,SV71: $i,SV118: $i] :
( ( ( ~ ( in @ SV118 @ SV71 )
| ( SV118 = SV26 ) )
= $true )
| ( ( SV71
= ( singleton @ SV26 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[887]) ).
thf(949,plain,
! [SV71: $i,SV26: $i,SV118: $i] :
( ( ( ( SV118 != SV26 )
| ( in @ SV118 @ SV71 ) )
= $true )
| ( ( SV71
= ( singleton @ SV26 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[888]) ).
thf(950,plain,
! [SV71: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK14_SY331 @ SV26 @ SV71 ) @ SV71 )
| ( ( sK14_SY331 @ SV26 @ SV71 )
= SV26 ) )
= $false )
| ( ( ~ ( ( ( sK14_SY331 @ SV26 @ SV71 )
!= SV26 )
| ( in @ ( sK14_SY331 @ SV26 @ SV71 ) @ SV71 ) ) )
= $true )
| ( ( SV71
= ( singleton @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[889]) ).
thf(951,plain,
! [SV27: $i,SV72: $i] :
( ( ( ( SV72
!= ( set_meet @ SV27 ) )
| ! [SY332: $i] :
~ ( ~ ( ~ ( in @ SY332 @ SV72 )
| ! [SY234: $i] :
( ~ ( in @ SY234 @ SV27 )
| ( in @ SY332 @ SY234 ) ) )
| ~ ( ~ ! [SY235: $i] :
( ~ ( in @ SY235 @ SV27 )
| ( in @ SY332 @ SY235 ) )
| ( in @ SY332 @ SV72 ) ) ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[890]) ).
thf(952,plain,
! [SV27: $i,SV72: $i] :
( ( ( ~ ! [SY335: $i] :
~ ( ~ ( ~ ( in @ SY335 @ SV72 )
| ! [SY237: $i] :
( ~ ( in @ SY237 @ SV27 )
| ( in @ SY335 @ SY237 ) ) )
| ~ ( ~ ! [SY238: $i] :
( ~ ( in @ SY238 @ SV27 )
| ( in @ SY335 @ SY238 ) )
| ( in @ SY335 @ SV72 ) ) )
| ( SV72
= ( set_meet @ SV27 ) ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[891]) ).
thf(953,plain,
! [SV27: $i,SV72: $i] :
( ( ( SV72
!= ( set_meet @ SV27 ) )
= $true )
| ( ( SV72 = empty_set )
= $true )
| ( ( SV27 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[892]) ).
thf(954,plain,
! [SV27: $i,SV72: $i] :
( ( ( SV72 != empty_set )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $true )
| ( ( SV27 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[893]) ).
thf(955,plain,
! [SV106: $i,SV29: $i] :
( ( ( subset @ ( relation_dom @ SV29 ) @ ( relation_dom @ SV106 ) )
= $true )
| ( ( subset @ SV29 @ SV106 )
= $false )
| ( ( relation @ SV106 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[894]) ).
thf(956,plain,
! [SV106: $i,SV29: $i] :
( ( ( subset @ ( relation_rng @ SV29 ) @ ( relation_rng @ SV106 ) )
= $true )
| ( ( subset @ SV29 @ SV106 )
= $false )
| ( ( relation @ SV106 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[895]) ).
thf(957,plain,
! [SV31: $i,SV75: $i] :
( ( ( ~ ( element @ SV75 @ SV31 )
| ( in @ SV75 @ SV31 ) )
= $true )
| ( ( empty @ SV31 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[896]) ).
thf(958,plain,
! [SV31: $i,SV75: $i] :
( ( ( ~ ( in @ SV75 @ SV31 )
| ( element @ SV75 @ SV31 ) )
= $true )
| ( ( empty @ SV31 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[897]) ).
thf(959,plain,
! [SV31: $i,SV75: $i] :
( ( ( ~ ( element @ SV75 @ SV31 ) )
= $true )
| ( ( empty @ SV75 )
= $true )
| ( ( empty @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[898]) ).
thf(960,plain,
! [SV31: $i,SV75: $i] :
( ( ( ~ ( empty @ SV75 ) )
= $true )
| ( ( element @ SV75 @ SV31 )
= $true )
| ( ( empty @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[899]) ).
thf(961,plain,
! [SV77: $i,SV33: $i,SV98: $i,SV123: $i] :
( ( ( ~ ( ~ ( in @ SV123 @ SV98 )
| ( SV123 = SV33 )
| ( SV123 = SV77 ) ) )
= $false )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[900]) ).
thf(962,plain,
! [SV98: $i,SV77: $i,SV33: $i,SV123: $i] :
( ( ( ~ ( ~ ( ( SV123 = SV33 )
| ( SV123 = SV77 ) )
| ( in @ SV123 @ SV98 ) ) )
= $false )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[900]) ).
thf(963,plain,
! [SV98: $i,SV33: $i,SV77: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_SY373 @ SV77 @ SV33 @ SV98 ) @ SV98 )
| ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV33 )
| ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV77 ) ) )
= $true )
| ( ( ~ ( ~ ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV33 )
| ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV77 ) )
| ( in @ ( sK18_SY373 @ SV77 @ SV33 @ SV98 ) @ SV98 ) ) )
= $true )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[901]) ).
thf(964,plain,
! [SV37: $i] :
( ( ~ ( in @ SV37 @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SY374: $i,SY375: $i] :
( ~ ~ ( ~ ( in @ SY374 @ ( sK6_SY251 @ SV37 ) )
| ~ ( subset @ SY375 @ SY374 ) )
| ( in @ SY375 @ ( sK6_SY251 @ SV37 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(965,plain,
! [SV37: $i,SV129: $i] :
( ( ~ ~ ( ~ ( in @ SV129 @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SY421: $i] :
~ ~ ( ~ ( in @ SY421 @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SY422: $i] :
( ~ ( subset @ SY422 @ SV129 )
| ( in @ SY422 @ SY421 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(966,plain,
! [SV37: $i,SV119: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV119 @ ( sK6_SY251 @ SV37 ) )
| ~ ~ ( are_equipotent @ SV119 @ ( sK6_SY251 @ SV37 ) ) ) )
= $true )
| ( ( ~ ~ ( in @ SV119 @ ( sK6_SY251 @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[904]) ).
thf(967,plain,
! [SV39: $i,SV113: $i] :
( ( ( in @ SV113 @ SV39 )
= $false )
| ( ( ~ ! [SY397: $i,SY398: $i] :
( SV113
!= ( ordered_pair @ SY397 @ SY398 ) ) )
= $true )
| ( ( relation @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[905]) ).
thf(968,plain,
! [SV39: $i] :
( ( ( in @ ( sK10_SY262 @ SV39 ) @ SV39 )
= $true )
| ( ( relation @ SV39 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[906]) ).
thf(969,plain,
! [SV39: $i] :
( ( ( ! [SY399: $i,SY400: $i] :
( ( sK10_SY262 @ SV39 )
!= ( ordered_pair @ SY399 @ SY400 ) ) )
= $true )
| ( ( relation @ SV39 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[907]) ).
thf(970,plain,
! [SV42: $i,SV108: $i,SV126: $i] :
( ( ( ~ ( ~ ( in @ SV126 @ SV108 )
| ~ ! [SY417: $i] :
~ ( in @ ( ordered_pair @ SV126 @ SY417 ) @ SV42 ) )
| ~ ( ~ ~ ! [SY418: $i] :
~ ( in @ ( ordered_pair @ SV126 @ SY418 ) @ SV42 )
| ( in @ SV126 @ SV108 ) ) )
= $false )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $false )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[908]) ).
thf(971,plain,
! [SV108: $i,SV42: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_SY394 @ SV42 @ SV108 ) @ SV108 )
| ~ ! [SY419: $i] :
~ ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ SY419 ) @ SV42 ) )
| ~ ( ~ ~ ! [SY420: $i] :
~ ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ SY420 ) @ SV42 )
| ( in @ ( sK21_SY394 @ SV42 @ SV108 ) @ SV108 ) ) )
= $true )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[909]) ).
thf(972,plain,
! [SV84: $i,SV43: $i,SV101: $i,SV124: $i] :
( ( ( ~ ( ~ ( in @ SV124 @ SV101 )
| ~ ( ~ ( in @ SV124 @ SV43 )
| ~ ~ ( in @ SV124 @ SV84 ) ) ) )
= $false )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[910]) ).
thf(973,plain,
! [SV101: $i,SV84: $i,SV43: $i,SV124: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV124 @ SV43 )
| ~ ~ ( in @ SV124 @ SV84 ) )
| ( in @ SV124 @ SV101 ) ) )
= $false )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[910]) ).
thf(974,plain,
! [SV101: $i,SV43: $i,SV84: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV101 )
| ~ ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
| ~ ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
| ~ ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 ) )
| ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV101 ) ) )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[911]) ).
thf(975,plain,
! [SV109: $i,SV86: $i,SV103: $i,SV45: $i] :
( ( ( ~ ( in @ SV45 @ SV103 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV45 @ SV86 ) @ ( cartesian_product2 @ SV103 @ SV109 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[913]) ).
thf(976,plain,
! [SV103: $i,SV45: $i,SV109: $i,SV86: $i] :
( ( ( ~ ( in @ SV86 @ SV109 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV45 @ SV86 ) @ ( cartesian_product2 @ SV103 @ SV109 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[913]) ).
thf(977,plain,
! [SV109: $i,SV86: $i,SV103: $i,SV45: $i] :
( ( ( ~ ( in @ SV45 @ SV103 ) )
= $true )
| ( ( ~ ( in @ SV86 @ SV109 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV45 @ SV86 ) @ ( cartesian_product2 @ SV103 @ SV109 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[914]) ).
thf(978,plain,
! [SV89: $i,SV48: $i] :
( ( ( ! [SY350: $i] :
~ ( in @ SY350 @ ( set_intersection2 @ SV48 @ SV89 ) ) )
= $false )
| ( ( disjoint @ SV48 @ SV89 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[915]) ).
thf(979,plain,
! [SV89: $i,SV48: $i,SV130: $i] :
( ( ( ~ ( in @ SV130 @ ( set_intersection2 @ SV48 @ SV89 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV48 @ SV89 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(980,plain,
! [SV110: $i,SV90: $i,SV104: $i,SV49: $i] :
( ( ( ~ ( in @ SV49 @ SV104 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV49 @ SV90 ) @ ( cartesian_product2 @ SV104 @ SV110 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[917]) ).
thf(981,plain,
! [SV104: $i,SV49: $i,SV110: $i,SV90: $i] :
( ( ( ~ ( in @ SV90 @ SV110 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV49 @ SV90 ) @ ( cartesian_product2 @ SV104 @ SV110 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[917]) ).
thf(982,plain,
! [SV110: $i,SV90: $i,SV104: $i,SV49: $i] :
( ( ( ~ ( in @ SV49 @ SV104 ) )
= $true )
| ( ( ~ ( in @ SV90 @ SV110 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV49 @ SV90 ) @ ( cartesian_product2 @ SV104 @ SV110 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[918]) ).
thf(983,plain,
! [SV3: $i] :
( ( ~ ( in @ SV3 @ ( sK5_SY160 @ SV3 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[919]) ).
thf(984,plain,
! [SV3: $i] :
( ( ~ ! [SY354: $i,SY355: $i] :
( ~ ~ ( ~ ( in @ SY354 @ ( sK5_SY160 @ SV3 ) )
| ~ ( subset @ SY355 @ SY354 ) )
| ( in @ SY355 @ ( sK5_SY160 @ SV3 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[919]) ).
thf(985,plain,
! [SV3: $i,SV127: $i] :
( ( ( ~ ( in @ SV127 @ ( sK5_SY160 @ SV3 ) ) )
= $true )
| ( ( in @ ( powerset @ SV127 ) @ ( sK5_SY160 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[920]) ).
thf(986,plain,
! [SV3: $i,SV114: $i] :
( ( ( ~ ( ~ ( subset @ SV114 @ ( sK5_SY160 @ SV3 ) )
| ~ ~ ( are_equipotent @ SV114 @ ( sK5_SY160 @ SV3 ) ) ) )
= $false )
| ( ( ~ ~ ( in @ SV114 @ ( sK5_SY160 @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[921]) ).
thf(987,plain,
! [SV4: $i,SV52: $i,SV115: $i] :
( ( ( ~ ( in @ SV115 @ SV52 ) )
= $true )
| ( ( ~ ! [SY401: $i] :
~ ~ ( ~ ( in @ SV115 @ SY401 )
| ~ ( in @ SY401 @ SV4 ) ) )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[922]) ).
thf(988,plain,
! [SV52: $i,SV4: $i,SV115: $i] :
( ( ( ~ ~ ! [SY402: $i] :
~ ~ ( ~ ( in @ SV115 @ SY402 )
| ~ ( in @ SY402 @ SV4 ) ) )
= $true )
| ( ( in @ SV115 @ SV52 )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[923]) ).
thf(989,plain,
! [SV52: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV52 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY404: $i] :
~ ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SY404 )
| ~ ( in @ SY404 @ SV4 ) )
| ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV52 ) ) )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[924]) ).
thf(990,plain,
! [SV52: $i,SV4: $i] :
( ( ( ~ ! [SY403: $i] :
~ ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SY403 )
| ~ ( in @ SY403 @ SV4 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY404: $i] :
~ ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SY404 )
| ~ ( in @ SY404 @ SV4 ) )
| ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV52 ) ) )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[924]) ).
thf(991,plain,
! [SV54: $i,SV6: $i,SV91: $i] :
( ( ( empty @ SV91 )
= $false )
| ( ( in @ SV6 @ SV54 )
= $false )
| ( ( element @ SV54 @ ( powerset @ SV91 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[925]) ).
thf(992,plain,
! [SV9: $i,SV105: $i,SV125: $i] :
( ( ( ~ ( ~ ( in @ SV125 @ SV105 )
| ~ ! [SY413: $i] :
~ ( in @ ( ordered_pair @ SY413 @ SV125 ) @ SV9 ) ) )
= $false )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $false )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[926]) ).
thf(993,plain,
! [SV105: $i,SV9: $i,SV125: $i] :
( ( ( ~ ( ~ ~ ! [SY414: $i] :
~ ( in @ ( ordered_pair @ SY414 @ SV125 ) @ SV9 )
| ( in @ SV125 @ SV105 ) ) )
= $false )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $false )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[926]) ).
thf(994,plain,
! [SV105: $i,SV9: $i] :
( ( ( ~ ( ~ ( in @ ( sK20_SY388 @ SV9 @ SV105 ) @ SV105 )
| ~ ! [SY415: $i] :
~ ( in @ ( ordered_pair @ SY415 @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY416: $i] :
~ ( in @ ( ordered_pair @ SY416 @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 )
| ( in @ ( sK20_SY388 @ SV9 @ SV105 ) @ SV105 ) ) )
= $true )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[927]) ).
thf(995,plain,
! [SV12: $i,SV58: $i,SV117: $i] :
( ( ( ~ ( in @ SV117 @ SV58 ) )
= $true )
| ( ( subset @ SV117 @ SV12 )
= $true )
| ( ( SV58
= ( powerset @ SV12 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[928]) ).
thf(996,plain,
! [SV58: $i,SV12: $i,SV117: $i] :
( ( ( ~ ( subset @ SV117 @ SV12 ) )
= $true )
| ( ( in @ SV117 @ SV58 )
= $true )
| ( ( SV58
= ( powerset @ SV12 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[929]) ).
thf(997,plain,
! [SV58: $i,SV12: $i] :
( ( ( ~ ( in @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV58 ) )
= $false )
| ( ( ~ ( ~ ( subset @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV12 )
| ( in @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV58 ) ) )
= $true )
| ( ( SV58
= ( powerset @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[930]) ).
thf(998,plain,
! [SV58: $i,SV12: $i] :
( ( ( subset @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV12 )
= $false )
| ( ( ~ ( ~ ( subset @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV12 )
| ( in @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV58 ) ) )
= $true )
| ( ( SV58
= ( powerset @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[930]) ).
thf(999,plain,
! [SV14: $i,SV60: $i] :
( ( ( ~ ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV60 ) )
= $false )
| ( ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV14 )
= $true )
| ( ( SV14 = SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[931]) ).
thf(1000,plain,
! [SV14: $i,SV60: $i] :
( ( ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV14 )
= $false )
| ( ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV14 )
= $true )
| ( ( SV14 = SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[931]) ).
thf(1001,plain,
! [SV14: $i,SV60: $i] :
( ( ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV60 )
= $true )
| ( ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV60 )
= $false )
| ( ( SV14 = SV60 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[932]) ).
thf(1002,plain,
! [SV63: $i,SV18: $i,SV93: $i,SV120: $i] :
( ( ( ~ ( in @ SV120 @ SV93 )
| ~ ( ~ ( in @ SV120 @ SV18 )
| ~ ( in @ SV120 @ SV63 ) ) )
= $true )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[934]) ).
thf(1003,plain,
! [SV93: $i,SV63: $i,SV18: $i,SV120: $i] :
( ( ( ~ ~ ( ~ ( in @ SV120 @ SV18 )
| ~ ( in @ SV120 @ SV63 ) )
| ( in @ SV120 @ SV93 ) )
= $true )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[935]) ).
thf(1004,plain,
! [SV93: $i,SV18: $i,SV63: $i] :
( ( ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV93 )
| ~ ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
| ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
| ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 ) )
| ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV93 ) ) )
= $true )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[936]) ).
thf(1005,plain,
! [SV19: $i,SV94: $i,SV64: $i] :
( ( ( in @ SV64 @ SV94 )
= $false )
| ( ( in @ SV19 @ SV94 )
= $false )
| ( ( subset @ ( unordered_pair @ SV19 @ SV64 ) @ SV94 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[939]) ).
thf(1006,plain,
! [SV20: $i,SV65: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK22_SY313 @ SV65 @ SV20 ) @ SV20 )
| ~ ( in @ ( sK22_SY313 @ SV65 @ SV20 ) @ SV65 ) ) )
= $false )
| ( ( disjoint @ SV20 @ SV65 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[940]) ).
thf(1007,plain,
! [SV65: $i,SV20: $i,SV128: $i] :
( ( ( ~ ( ~ ( in @ SV128 @ SV20 )
| ~ ( in @ SV128 @ SV65 ) ) )
= $false )
| ( ( ~ ( disjoint @ SV20 @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[941]) ).
thf(1008,plain,
! [SV67: $i,SV22: $i,SV95: $i,SV121: $i] :
( ( ( ~ ( in @ SV121 @ SV95 )
| ~ ! [SY405: $i] :
~ ~ ! [SY406: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY405 @ SV22 )
| ~ ( in @ SY406 @ SV67 ) )
| ( SV121
!= ( ordered_pair @ SY405 @ SY406 ) ) ) )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[942]) ).
thf(1009,plain,
! [SV95: $i,SV121: $i,SV67: $i,SV22: $i] :
( ( ( ~ ~ ! [SY407: $i] :
~ ~ ! [SY408: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY407 @ SV22 )
| ~ ( in @ SY408 @ SV67 ) )
| ( SV121
!= ( ordered_pair @ SY407 @ SY408 ) ) )
| ( in @ SV121 @ SV95 ) )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[943]) ).
thf(1010,plain,
! [SV95: $i,SV22: $i,SV67: $i] :
( ( ( ~ ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 )
| ~ ! [SY409: $i] :
~ ~ ! [SY410: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY409 @ SV22 )
| ~ ( in @ SY410 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SY409 @ SY410 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY411: $i] :
~ ~ ! [SY412: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY411 @ SV22 )
| ~ ( in @ SY412 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SY411 @ SY412 ) ) )
| ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 ) ) )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[944]) ).
thf(1011,plain,
! [SV68: $i,SV23: $i,SV96: $i,SV122: $i] :
( ( ( ~ ( in @ SV122 @ SV96 )
| ( in @ SV122 @ SV23 )
| ( in @ SV122 @ SV68 ) )
= $true )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[945]) ).
thf(1012,plain,
! [SV96: $i,SV68: $i,SV23: $i,SV122: $i] :
( ( ( ~ ( ( in @ SV122 @ SV23 )
| ( in @ SV122 @ SV68 ) )
| ( in @ SV122 @ SV96 ) )
= $true )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[946]) ).
thf(1013,plain,
! [SV96: $i,SV23: $i,SV68: $i] :
( ( ( ~ ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV96 )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV23 )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV68 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV23 )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV68 ) )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV96 ) ) )
= $true )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[947]) ).
thf(1014,plain,
! [SV26: $i,SV71: $i,SV118: $i] :
( ( ( ~ ( in @ SV118 @ SV71 ) )
= $true )
| ( ( SV118 = SV26 )
= $true )
| ( ( SV71
= ( singleton @ SV26 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[948]) ).
thf(1015,plain,
! [SV71: $i,SV26: $i,SV118: $i] :
( ( ( SV118 != SV26 )
= $true )
| ( ( in @ SV118 @ SV71 )
= $true )
| ( ( SV71
= ( singleton @ SV26 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[949]) ).
thf(1016,plain,
! [SV71: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK14_SY331 @ SV26 @ SV71 ) @ SV71 ) )
= $false )
| ( ( ~ ( ( ( sK14_SY331 @ SV26 @ SV71 )
!= SV26 )
| ( in @ ( sK14_SY331 @ SV26 @ SV71 ) @ SV71 ) ) )
= $true )
| ( ( SV71
= ( singleton @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[950]) ).
thf(1017,plain,
! [SV71: $i,SV26: $i] :
( ( ( ( sK14_SY331 @ SV26 @ SV71 )
= SV26 )
= $false )
| ( ( ~ ( ( ( sK14_SY331 @ SV26 @ SV71 )
!= SV26 )
| ( in @ ( sK14_SY331 @ SV26 @ SV71 ) @ SV71 ) ) )
= $true )
| ( ( SV71
= ( singleton @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[950]) ).
thf(1018,plain,
! [SV27: $i,SV72: $i] :
( ( ( SV72
!= ( set_meet @ SV27 ) )
= $true )
| ( ( ! [SY332: $i] :
~ ( ~ ( ~ ( in @ SY332 @ SV72 )
| ! [SY234: $i] :
( ~ ( in @ SY234 @ SV27 )
| ( in @ SY332 @ SY234 ) ) )
| ~ ( ~ ! [SY235: $i] :
( ~ ( in @ SY235 @ SV27 )
| ( in @ SY332 @ SY235 ) )
| ( in @ SY332 @ SV72 ) ) ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[951]) ).
thf(1019,plain,
! [SV27: $i,SV72: $i] :
( ( ( ~ ! [SY335: $i] :
~ ( ~ ( ~ ( in @ SY335 @ SV72 )
| ! [SY237: $i] :
( ~ ( in @ SY237 @ SV27 )
| ( in @ SY335 @ SY237 ) ) )
| ~ ( ~ ! [SY238: $i] :
( ~ ( in @ SY238 @ SV27 )
| ( in @ SY335 @ SY238 ) )
| ( in @ SY335 @ SV72 ) ) ) )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[952]) ).
thf(1020,plain,
! [SV27: $i,SV72: $i] :
( ( ( SV72
= ( set_meet @ SV27 ) )
= $false )
| ( ( SV72 = empty_set )
= $true )
| ( ( SV27 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[953]) ).
thf(1021,plain,
! [SV27: $i,SV72: $i] :
( ( ( SV72 = empty_set )
= $false )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $true )
| ( ( SV27 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[954]) ).
thf(1022,plain,
! [SV31: $i,SV75: $i] :
( ( ( ~ ( element @ SV75 @ SV31 ) )
= $true )
| ( ( in @ SV75 @ SV31 )
= $true )
| ( ( empty @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[957]) ).
thf(1023,plain,
! [SV31: $i,SV75: $i] :
( ( ( ~ ( in @ SV75 @ SV31 ) )
= $true )
| ( ( element @ SV75 @ SV31 )
= $true )
| ( ( empty @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[958]) ).
thf(1024,plain,
! [SV31: $i,SV75: $i] :
( ( ( element @ SV75 @ SV31 )
= $false )
| ( ( empty @ SV75 )
= $true )
| ( ( empty @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[959]) ).
thf(1025,plain,
! [SV31: $i,SV75: $i] :
( ( ( empty @ SV75 )
= $false )
| ( ( element @ SV75 @ SV31 )
= $true )
| ( ( empty @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[960]) ).
thf(1026,plain,
! [SV77: $i,SV33: $i,SV98: $i,SV123: $i] :
( ( ( ~ ( in @ SV123 @ SV98 )
| ( SV123 = SV33 )
| ( SV123 = SV77 ) )
= $true )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[961]) ).
thf(1027,plain,
! [SV98: $i,SV77: $i,SV33: $i,SV123: $i] :
( ( ( ~ ( ( SV123 = SV33 )
| ( SV123 = SV77 ) )
| ( in @ SV123 @ SV98 ) )
= $true )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[962]) ).
thf(1028,plain,
! [SV98: $i,SV33: $i,SV77: $i] :
( ( ( ~ ( in @ ( sK18_SY373 @ SV77 @ SV33 @ SV98 ) @ SV98 )
| ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV33 )
| ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV77 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV33 )
| ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV77 ) )
| ( in @ ( sK18_SY373 @ SV77 @ SV33 @ SV98 ) @ SV98 ) ) )
= $true )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[963]) ).
thf(1029,plain,
! [SV37: $i] :
( ( ~ ( in @ SV37 @ ( sK6_SY251 @ SV37 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[964]) ).
thf(1030,plain,
! [SV37: $i] :
( ( ~ ! [SY374: $i,SY375: $i] :
( ~ ~ ( ~ ( in @ SY374 @ ( sK6_SY251 @ SV37 ) )
| ~ ( subset @ SY375 @ SY374 ) )
| ( in @ SY375 @ ( sK6_SY251 @ SV37 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[964]) ).
thf(1031,plain,
! [SV37: $i,SV129: $i] :
( ( ~ ( ~ ( in @ SV129 @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SY421: $i] :
~ ~ ( ~ ( in @ SY421 @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SY422: $i] :
( ~ ( subset @ SY422 @ SV129 )
| ( in @ SY422 @ SY421 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[965]) ).
thf(1032,plain,
! [SV37: $i,SV119: $i] :
( ( ( ~ ( ~ ( subset @ SV119 @ ( sK6_SY251 @ SV37 ) )
| ~ ~ ( are_equipotent @ SV119 @ ( sK6_SY251 @ SV37 ) ) ) )
= $false )
| ( ( ~ ~ ( in @ SV119 @ ( sK6_SY251 @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[966]) ).
thf(1033,plain,
! [SV39: $i,SV113: $i] :
( ( ( ! [SY397: $i,SY398: $i] :
( SV113
!= ( ordered_pair @ SY397 @ SY398 ) ) )
= $false )
| ( ( in @ SV113 @ SV39 )
= $false )
| ( ( relation @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[967]) ).
thf(1034,plain,
! [SV131: $i,SV39: $i] :
( ( ( ! [SY423: $i] :
( ( sK10_SY262 @ SV39 )
!= ( ordered_pair @ SV131 @ SY423 ) ) )
= $true )
| ( ( relation @ SV39 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1035,plain,
! [SV42: $i,SV108: $i,SV126: $i] :
( ( ( ~ ( ~ ( in @ SV126 @ SV108 )
| ~ ! [SY417: $i] :
~ ( in @ ( ordered_pair @ SV126 @ SY417 ) @ SV42 ) ) )
= $false )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $false )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[970]) ).
thf(1036,plain,
! [SV108: $i,SV42: $i,SV126: $i] :
( ( ( ~ ( ~ ~ ! [SY418: $i] :
~ ( in @ ( ordered_pair @ SV126 @ SY418 ) @ SV42 )
| ( in @ SV126 @ SV108 ) ) )
= $false )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $false )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[970]) ).
thf(1037,plain,
! [SV108: $i,SV42: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_SY394 @ SV42 @ SV108 ) @ SV108 )
| ~ ! [SY419: $i] :
~ ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ SY419 ) @ SV42 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY420: $i] :
~ ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ SY420 ) @ SV42 )
| ( in @ ( sK21_SY394 @ SV42 @ SV108 ) @ SV108 ) ) )
= $true )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[971]) ).
thf(1038,plain,
! [SV84: $i,SV43: $i,SV101: $i,SV124: $i] :
( ( ( ~ ( in @ SV124 @ SV101 )
| ~ ( ~ ( in @ SV124 @ SV43 )
| ~ ~ ( in @ SV124 @ SV84 ) ) )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[972]) ).
thf(1039,plain,
! [SV101: $i,SV84: $i,SV43: $i,SV124: $i] :
( ( ( ~ ~ ( ~ ( in @ SV124 @ SV43 )
| ~ ~ ( in @ SV124 @ SV84 ) )
| ( in @ SV124 @ SV101 ) )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[973]) ).
thf(1040,plain,
! [SV101: $i,SV43: $i,SV84: $i] :
( ( ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV101 )
| ~ ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
| ~ ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
| ~ ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 ) )
| ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV101 ) ) )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[974]) ).
thf(1041,plain,
! [SV109: $i,SV86: $i,SV103: $i,SV45: $i] :
( ( ( in @ SV45 @ SV103 )
= $true )
| ( ( in @ ( ordered_pair @ SV45 @ SV86 ) @ ( cartesian_product2 @ SV103 @ SV109 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[975]) ).
thf(1042,plain,
! [SV103: $i,SV45: $i,SV109: $i,SV86: $i] :
( ( ( in @ SV86 @ SV109 )
= $true )
| ( ( in @ ( ordered_pair @ SV45 @ SV86 ) @ ( cartesian_product2 @ SV103 @ SV109 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[976]) ).
thf(1043,plain,
! [SV109: $i,SV86: $i,SV103: $i,SV45: $i] :
( ( ( in @ SV45 @ SV103 )
= $false )
| ( ( ~ ( in @ SV86 @ SV109 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV45 @ SV86 ) @ ( cartesian_product2 @ SV103 @ SV109 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[977]) ).
thf(1044,plain,
! [SV48: $i,SV89: $i] :
( ( ( ~ ( in @ ( sK23_SY350 @ SV89 @ SV48 ) @ ( set_intersection2 @ SV48 @ SV89 ) ) )
= $false )
| ( ( disjoint @ SV48 @ SV89 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[978]) ).
thf(1045,plain,
! [SV89: $i,SV48: $i,SV130: $i] :
( ( ( in @ SV130 @ ( set_intersection2 @ SV48 @ SV89 ) )
= $false )
| ( ( ~ ( disjoint @ SV48 @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[979]) ).
thf(1046,plain,
! [SV110: $i,SV90: $i,SV104: $i,SV49: $i] :
( ( ( in @ SV49 @ SV104 )
= $true )
| ( ( in @ ( ordered_pair @ SV49 @ SV90 ) @ ( cartesian_product2 @ SV104 @ SV110 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[980]) ).
thf(1047,plain,
! [SV104: $i,SV49: $i,SV110: $i,SV90: $i] :
( ( ( in @ SV90 @ SV110 )
= $true )
| ( ( in @ ( ordered_pair @ SV49 @ SV90 ) @ ( cartesian_product2 @ SV104 @ SV110 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[981]) ).
thf(1048,plain,
! [SV110: $i,SV90: $i,SV104: $i,SV49: $i] :
( ( ( in @ SV49 @ SV104 )
= $false )
| ( ( ~ ( in @ SV90 @ SV110 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV49 @ SV90 ) @ ( cartesian_product2 @ SV104 @ SV110 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(1049,plain,
! [SV3: $i] :
( ( in @ SV3 @ ( sK5_SY160 @ SV3 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[983]) ).
thf(1050,plain,
! [SV3: $i] :
( ( ! [SY354: $i,SY355: $i] :
( ~ ~ ( ~ ( in @ SY354 @ ( sK5_SY160 @ SV3 ) )
| ~ ( subset @ SY355 @ SY354 ) )
| ( in @ SY355 @ ( sK5_SY160 @ SV3 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[984]) ).
thf(1051,plain,
! [SV3: $i,SV127: $i] :
( ( ( in @ SV127 @ ( sK5_SY160 @ SV3 ) )
= $false )
| ( ( in @ ( powerset @ SV127 ) @ ( sK5_SY160 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[985]) ).
thf(1052,plain,
! [SV3: $i,SV114: $i] :
( ( ( ~ ( subset @ SV114 @ ( sK5_SY160 @ SV3 ) )
| ~ ~ ( are_equipotent @ SV114 @ ( sK5_SY160 @ SV3 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV114 @ ( sK5_SY160 @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[986]) ).
thf(1053,plain,
! [SV4: $i,SV52: $i,SV115: $i] :
( ( ( in @ SV115 @ SV52 )
= $false )
| ( ( ~ ! [SY401: $i] :
~ ~ ( ~ ( in @ SV115 @ SY401 )
| ~ ( in @ SY401 @ SV4 ) ) )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[987]) ).
thf(1054,plain,
! [SV52: $i,SV4: $i,SV115: $i] :
( ( ( ~ ! [SY402: $i] :
~ ~ ( ~ ( in @ SV115 @ SY402 )
| ~ ( in @ SY402 @ SV4 ) ) )
= $false )
| ( ( in @ SV115 @ SV52 )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[988]) ).
thf(1055,plain,
! [SV52: $i,SV4: $i] :
( ( ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV52 )
= $true )
| ( ( ~ ( ~ ~ ! [SY404: $i] :
~ ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SY404 )
| ~ ( in @ SY404 @ SV4 ) )
| ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV52 ) ) )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[989]) ).
thf(1056,plain,
! [SV52: $i,SV4: $i] :
( ( ( ! [SY403: $i] :
~ ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SY403 )
| ~ ( in @ SY403 @ SV4 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY404: $i] :
~ ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SY404 )
| ~ ( in @ SY404 @ SV4 ) )
| ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV52 ) ) )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[990]) ).
thf(1057,plain,
! [SV9: $i,SV105: $i,SV125: $i] :
( ( ( ~ ( in @ SV125 @ SV105 )
| ~ ! [SY413: $i] :
~ ( in @ ( ordered_pair @ SY413 @ SV125 ) @ SV9 ) )
= $true )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $false )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[992]) ).
thf(1058,plain,
! [SV105: $i,SV9: $i,SV125: $i] :
( ( ( ~ ~ ! [SY414: $i] :
~ ( in @ ( ordered_pair @ SY414 @ SV125 ) @ SV9 )
| ( in @ SV125 @ SV105 ) )
= $true )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $false )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[993]) ).
thf(1059,plain,
! [SV105: $i,SV9: $i] :
( ( ( ~ ( in @ ( sK20_SY388 @ SV9 @ SV105 ) @ SV105 )
| ~ ! [SY415: $i] :
~ ( in @ ( ordered_pair @ SY415 @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY416: $i] :
~ ( in @ ( ordered_pair @ SY416 @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 )
| ( in @ ( sK20_SY388 @ SV9 @ SV105 ) @ SV105 ) ) )
= $true )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[994]) ).
thf(1060,plain,
! [SV12: $i,SV58: $i,SV117: $i] :
( ( ( in @ SV117 @ SV58 )
= $false )
| ( ( subset @ SV117 @ SV12 )
= $true )
| ( ( SV58
= ( powerset @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[995]) ).
thf(1061,plain,
! [SV58: $i,SV12: $i,SV117: $i] :
( ( ( subset @ SV117 @ SV12 )
= $false )
| ( ( in @ SV117 @ SV58 )
= $true )
| ( ( SV58
= ( powerset @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[996]) ).
thf(1062,plain,
! [SV58: $i,SV12: $i] :
( ( ( in @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV58 )
= $true )
| ( ( ~ ( ~ ( subset @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV12 )
| ( in @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV58 ) ) )
= $true )
| ( ( SV58
= ( powerset @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[997]) ).
thf(1063,plain,
! [SV58: $i,SV12: $i] :
( ( ( ~ ( subset @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV12 )
| ( in @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV58 ) )
= $false )
| ( ( subset @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV12 )
= $false )
| ( ( SV58
= ( powerset @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[998]) ).
thf(1064,plain,
! [SV14: $i,SV60: $i] :
( ( ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV60 )
= $true )
| ( ( in @ ( sK8_SY307 @ SV60 @ SV14 ) @ SV14 )
= $true )
| ( ( SV14 = SV60 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[999]) ).
thf(1065,plain,
! [SV63: $i,SV18: $i,SV93: $i,SV120: $i] :
( ( ( ~ ( in @ SV120 @ SV93 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV120 @ SV18 )
| ~ ( in @ SV120 @ SV63 ) ) )
= $true )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1002]) ).
thf(1066,plain,
! [SV93: $i,SV63: $i,SV18: $i,SV120: $i] :
( ( ( ~ ~ ( ~ ( in @ SV120 @ SV18 )
| ~ ( in @ SV120 @ SV63 ) ) )
= $true )
| ( ( in @ SV120 @ SV93 )
= $true )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1003]) ).
thf(1067,plain,
! [SV93: $i,SV18: $i,SV63: $i] :
( ( ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV93 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
| ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 ) )
| ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV93 ) ) )
= $true )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1004]) ).
thf(1068,plain,
! [SV93: $i,SV18: $i,SV63: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
| ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
| ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 ) )
| ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV93 ) ) )
= $true )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1004]) ).
thf(1069,plain,
! [SV20: $i,SV65: $i] :
( ( ( ~ ( ~ ( in @ ( sK22_SY313 @ SV65 @ SV20 ) @ SV20 )
| ~ ( in @ ( sK22_SY313 @ SV65 @ SV20 ) @ SV65 ) ) )
= $true )
| ( ( disjoint @ SV20 @ SV65 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1006]) ).
thf(1070,plain,
! [SV65: $i,SV20: $i,SV128: $i] :
( ( ( ~ ( in @ SV128 @ SV20 )
| ~ ( in @ SV128 @ SV65 ) )
= $true )
| ( ( ~ ( disjoint @ SV20 @ SV65 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1007]) ).
thf(1071,plain,
! [SV67: $i,SV22: $i,SV95: $i,SV121: $i] :
( ( ( ~ ( in @ SV121 @ SV95 ) )
= $true )
| ( ( ~ ! [SY405: $i] :
~ ~ ! [SY406: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY405 @ SV22 )
| ~ ( in @ SY406 @ SV67 ) )
| ( SV121
!= ( ordered_pair @ SY405 @ SY406 ) ) ) )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1008]) ).
thf(1072,plain,
! [SV95: $i,SV121: $i,SV67: $i,SV22: $i] :
( ( ( ~ ~ ! [SY407: $i] :
~ ~ ! [SY408: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY407 @ SV22 )
| ~ ( in @ SY408 @ SV67 ) )
| ( SV121
!= ( ordered_pair @ SY407 @ SY408 ) ) ) )
= $true )
| ( ( in @ SV121 @ SV95 )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1009]) ).
thf(1073,plain,
! [SV95: $i,SV22: $i,SV67: $i] :
( ( ( ~ ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY411: $i] :
~ ~ ! [SY412: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY411 @ SV22 )
| ~ ( in @ SY412 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SY411 @ SY412 ) ) )
| ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 ) ) )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1010]) ).
thf(1074,plain,
! [SV95: $i,SV67: $i,SV22: $i] :
( ( ( ~ ! [SY409: $i] :
~ ~ ! [SY410: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY409 @ SV22 )
| ~ ( in @ SY410 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SY409 @ SY410 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY411: $i] :
~ ~ ! [SY412: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY411 @ SV22 )
| ~ ( in @ SY412 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SY411 @ SY412 ) ) )
| ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 ) ) )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1010]) ).
thf(1075,plain,
! [SV68: $i,SV23: $i,SV96: $i,SV122: $i] :
( ( ( ~ ( in @ SV122 @ SV96 ) )
= $true )
| ( ( ( in @ SV122 @ SV23 )
| ( in @ SV122 @ SV68 ) )
= $true )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1011]) ).
thf(1076,plain,
! [SV96: $i,SV68: $i,SV23: $i,SV122: $i] :
( ( ( ~ ( ( in @ SV122 @ SV23 )
| ( in @ SV122 @ SV68 ) ) )
= $true )
| ( ( in @ SV122 @ SV96 )
= $true )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1012]) ).
thf(1077,plain,
! [SV96: $i,SV23: $i,SV68: $i] :
( ( ( ~ ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV96 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV23 )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV68 ) )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV96 ) ) )
= $true )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1013]) ).
thf(1078,plain,
! [SV96: $i,SV23: $i,SV68: $i] :
( ( ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV23 )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV68 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV23 )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV68 ) )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV96 ) ) )
= $true )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1013]) ).
thf(1079,plain,
! [SV26: $i,SV71: $i,SV118: $i] :
( ( ( in @ SV118 @ SV71 )
= $false )
| ( ( SV118 = SV26 )
= $true )
| ( ( SV71
= ( singleton @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1014]) ).
thf(1080,plain,
! [SV71: $i,SV26: $i,SV118: $i] :
( ( ( SV118 = SV26 )
= $false )
| ( ( in @ SV118 @ SV71 )
= $true )
| ( ( SV71
= ( singleton @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1015]) ).
thf(1081,plain,
! [SV71: $i,SV26: $i] :
( ( ( in @ ( sK14_SY331 @ SV26 @ SV71 ) @ SV71 )
= $true )
| ( ( ~ ( ( ( sK14_SY331 @ SV26 @ SV71 )
!= SV26 )
| ( in @ ( sK14_SY331 @ SV26 @ SV71 ) @ SV71 ) ) )
= $true )
| ( ( SV71
= ( singleton @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1016]) ).
thf(1082,plain,
! [SV71: $i,SV26: $i] :
( ( ( ( ( sK14_SY331 @ SV26 @ SV71 )
!= SV26 )
| ( in @ ( sK14_SY331 @ SV26 @ SV71 ) @ SV71 ) )
= $false )
| ( ( ( sK14_SY331 @ SV26 @ SV71 )
= SV26 )
= $false )
| ( ( SV71
= ( singleton @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1017]) ).
thf(1083,plain,
! [SV27: $i,SV72: $i] :
( ( ( SV72
= ( set_meet @ SV27 ) )
= $false )
| ( ( ! [SY332: $i] :
~ ( ~ ( ~ ( in @ SY332 @ SV72 )
| ! [SY234: $i] :
( ~ ( in @ SY234 @ SV27 )
| ( in @ SY332 @ SY234 ) ) )
| ~ ( ~ ! [SY235: $i] :
( ~ ( in @ SY235 @ SV27 )
| ( in @ SY332 @ SY235 ) )
| ( in @ SY332 @ SV72 ) ) ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1018]) ).
thf(1084,plain,
! [SV27: $i,SV72: $i] :
( ( ( ! [SY335: $i] :
~ ( ~ ( ~ ( in @ SY335 @ SV72 )
| ! [SY237: $i] :
( ~ ( in @ SY237 @ SV27 )
| ( in @ SY335 @ SY237 ) ) )
| ~ ( ~ ! [SY238: $i] :
( ~ ( in @ SY238 @ SV27 )
| ( in @ SY335 @ SY238 ) )
| ( in @ SY335 @ SV72 ) ) ) )
= $false )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1019]) ).
thf(1085,plain,
! [SV31: $i,SV75: $i] :
( ( ( element @ SV75 @ SV31 )
= $false )
| ( ( in @ SV75 @ SV31 )
= $true )
| ( ( empty @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1022]) ).
thf(1086,plain,
! [SV31: $i,SV75: $i] :
( ( ( in @ SV75 @ SV31 )
= $false )
| ( ( element @ SV75 @ SV31 )
= $true )
| ( ( empty @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1023]) ).
thf(1087,plain,
! [SV77: $i,SV33: $i,SV98: $i,SV123: $i] :
( ( ( ~ ( in @ SV123 @ SV98 ) )
= $true )
| ( ( ( SV123 = SV33 )
| ( SV123 = SV77 ) )
= $true )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1026]) ).
thf(1088,plain,
! [SV98: $i,SV77: $i,SV33: $i,SV123: $i] :
( ( ( ~ ( ( SV123 = SV33 )
| ( SV123 = SV77 ) ) )
= $true )
| ( ( in @ SV123 @ SV98 )
= $true )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1027]) ).
thf(1089,plain,
! [SV98: $i,SV33: $i,SV77: $i] :
( ( ( ~ ( in @ ( sK18_SY373 @ SV77 @ SV33 @ SV98 ) @ SV98 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV33 )
| ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV77 ) )
| ( in @ ( sK18_SY373 @ SV77 @ SV33 @ SV98 ) @ SV98 ) ) )
= $true )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1028]) ).
thf(1090,plain,
! [SV98: $i,SV33: $i,SV77: $i] :
( ( ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV33 )
| ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV77 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV33 )
| ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV77 ) )
| ( in @ ( sK18_SY373 @ SV77 @ SV33 @ SV98 ) @ SV98 ) ) )
= $true )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1028]) ).
thf(1091,plain,
! [SV37: $i] :
( ( in @ SV37 @ ( sK6_SY251 @ SV37 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1029]) ).
thf(1092,plain,
! [SV37: $i] :
( ( ! [SY374: $i,SY375: $i] :
( ~ ~ ( ~ ( in @ SY374 @ ( sK6_SY251 @ SV37 ) )
| ~ ( subset @ SY375 @ SY374 ) )
| ( in @ SY375 @ ( sK6_SY251 @ SV37 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1030]) ).
thf(1093,plain,
! [SV37: $i,SV129: $i] :
( ( ~ ( in @ SV129 @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SY421: $i] :
~ ~ ( ~ ( in @ SY421 @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SY422: $i] :
( ~ ( subset @ SY422 @ SV129 )
| ( in @ SY422 @ SY421 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1031]) ).
thf(1094,plain,
! [SV37: $i,SV119: $i] :
( ( ( ~ ( subset @ SV119 @ ( sK6_SY251 @ SV37 ) )
| ~ ~ ( are_equipotent @ SV119 @ ( sK6_SY251 @ SV37 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV119 @ ( sK6_SY251 @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1032]) ).
thf(1095,plain,
! [SV39: $i,SV113: $i] :
( ( ( ! [SY424: $i] :
( SV113
!= ( ordered_pair @ ( sK24_SY397 @ SV39 @ SV113 ) @ SY424 ) ) )
= $false )
| ( ( in @ SV113 @ SV39 )
= $false )
| ( ( relation @ SV39 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1033]) ).
thf(1096,plain,
! [SV132: $i,SV131: $i,SV39: $i] :
( ( ( ( sK10_SY262 @ SV39 )
!= ( ordered_pair @ SV131 @ SV132 ) )
= $true )
| ( ( relation @ SV39 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1034]) ).
thf(1097,plain,
! [SV42: $i,SV108: $i,SV126: $i] :
( ( ( ~ ( in @ SV126 @ SV108 )
| ~ ! [SY417: $i] :
~ ( in @ ( ordered_pair @ SV126 @ SY417 ) @ SV42 ) )
= $true )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $false )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1035]) ).
thf(1098,plain,
! [SV108: $i,SV42: $i,SV126: $i] :
( ( ( ~ ~ ! [SY418: $i] :
~ ( in @ ( ordered_pair @ SV126 @ SY418 ) @ SV42 )
| ( in @ SV126 @ SV108 ) )
= $true )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $false )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1036]) ).
thf(1099,plain,
! [SV108: $i,SV42: $i] :
( ( ( ~ ( in @ ( sK21_SY394 @ SV42 @ SV108 ) @ SV108 )
| ~ ! [SY419: $i] :
~ ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ SY419 ) @ SV42 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY420: $i] :
~ ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ SY420 ) @ SV42 )
| ( in @ ( sK21_SY394 @ SV42 @ SV108 ) @ SV108 ) ) )
= $true )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1037]) ).
thf(1100,plain,
! [SV84: $i,SV43: $i,SV101: $i,SV124: $i] :
( ( ( ~ ( in @ SV124 @ SV101 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV124 @ SV43 )
| ~ ~ ( in @ SV124 @ SV84 ) ) )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1038]) ).
thf(1101,plain,
! [SV101: $i,SV84: $i,SV43: $i,SV124: $i] :
( ( ( ~ ~ ( ~ ( in @ SV124 @ SV43 )
| ~ ~ ( in @ SV124 @ SV84 ) ) )
= $true )
| ( ( in @ SV124 @ SV101 )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1039]) ).
thf(1102,plain,
! [SV101: $i,SV43: $i,SV84: $i] :
( ( ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV101 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
| ~ ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 ) )
| ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV101 ) ) )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1040]) ).
thf(1103,plain,
! [SV101: $i,SV43: $i,SV84: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
| ~ ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
| ~ ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 ) )
| ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV101 ) ) )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1040]) ).
thf(1104,plain,
! [SV103: $i,SV45: $i,SV109: $i,SV86: $i] :
( ( ( in @ SV86 @ SV109 )
= $false )
| ( ( in @ SV45 @ SV103 )
= $false )
| ( ( in @ ( ordered_pair @ SV45 @ SV86 ) @ ( cartesian_product2 @ SV103 @ SV109 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1043]) ).
thf(1105,plain,
! [SV48: $i,SV89: $i] :
( ( ( in @ ( sK23_SY350 @ SV89 @ SV48 ) @ ( set_intersection2 @ SV48 @ SV89 ) )
= $true )
| ( ( disjoint @ SV48 @ SV89 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1044]) ).
thf(1106,plain,
! [SV130: $i,SV89: $i,SV48: $i] :
( ( ( disjoint @ SV48 @ SV89 )
= $false )
| ( ( in @ SV130 @ ( set_intersection2 @ SV48 @ SV89 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1045]) ).
thf(1107,plain,
! [SV104: $i,SV49: $i,SV110: $i,SV90: $i] :
( ( ( in @ SV90 @ SV110 )
= $false )
| ( ( in @ SV49 @ SV104 )
= $false )
| ( ( in @ ( ordered_pair @ SV49 @ SV90 ) @ ( cartesian_product2 @ SV104 @ SV110 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1048]) ).
thf(1108,plain,
! [SV3: $i,SV133: $i] :
( ( ! [SY425: $i] :
( ~ ~ ( ~ ( in @ SV133 @ ( sK5_SY160 @ SV3 ) )
| ~ ( subset @ SY425 @ SV133 ) )
| ( in @ SY425 @ ( sK5_SY160 @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1109,plain,
! [SV3: $i,SV114: $i] :
( ( ( ~ ( subset @ SV114 @ ( sK5_SY160 @ SV3 ) ) )
= $true )
| ( ( ~ ~ ( are_equipotent @ SV114 @ ( sK5_SY160 @ SV3 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV114 @ ( sK5_SY160 @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1052]) ).
thf(1110,plain,
! [SV52: $i,SV4: $i,SV115: $i] :
( ( ( ! [SY401: $i] :
~ ~ ( ~ ( in @ SV115 @ SY401 )
| ~ ( in @ SY401 @ SV4 ) ) )
= $false )
| ( ( in @ SV115 @ SV52 )
= $false )
| ( ( SV52
= ( union @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1053]) ).
thf(1111,plain,
! [SV52: $i,SV4: $i,SV115: $i] :
( ( ( ! [SY402: $i] :
~ ~ ( ~ ( in @ SV115 @ SY402 )
| ~ ( in @ SY402 @ SV4 ) ) )
= $true )
| ( ( in @ SV115 @ SV52 )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1054]) ).
thf(1112,plain,
! [SV52: $i,SV4: $i] :
( ( ( ~ ~ ! [SY404: $i] :
~ ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SY404 )
| ~ ( in @ SY404 @ SV4 ) )
| ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV52 ) )
= $false )
| ( ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV52 )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1055]) ).
thf(1113,plain,
! [SV134: $i,SV52: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV134 )
| ~ ( in @ SV134 @ SV4 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY404: $i] :
~ ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SY404 )
| ~ ( in @ SY404 @ SV4 ) )
| ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV52 ) ) )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1114,plain,
! [SV9: $i,SV105: $i,SV125: $i] :
( ( ( ~ ( in @ SV125 @ SV105 ) )
= $true )
| ( ( ~ ! [SY413: $i] :
~ ( in @ ( ordered_pair @ SY413 @ SV125 ) @ SV9 ) )
= $true )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $false )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1057]) ).
thf(1115,plain,
! [SV105: $i,SV9: $i,SV125: $i] :
( ( ( ~ ~ ! [SY414: $i] :
~ ( in @ ( ordered_pair @ SY414 @ SV125 ) @ SV9 ) )
= $true )
| ( ( in @ SV125 @ SV105 )
= $true )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $false )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1058]) ).
thf(1116,plain,
! [SV105: $i,SV9: $i] :
( ( ( ~ ( in @ ( sK20_SY388 @ SV9 @ SV105 ) @ SV105 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY416: $i] :
~ ( in @ ( ordered_pair @ SY416 @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 )
| ( in @ ( sK20_SY388 @ SV9 @ SV105 ) @ SV105 ) ) )
= $true )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1059]) ).
thf(1117,plain,
! [SV105: $i,SV9: $i] :
( ( ( ~ ! [SY415: $i] :
~ ( in @ ( ordered_pair @ SY415 @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY416: $i] :
~ ( in @ ( ordered_pair @ SY416 @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 )
| ( in @ ( sK20_SY388 @ SV9 @ SV105 ) @ SV105 ) ) )
= $true )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1059]) ).
thf(1118,plain,
! [SV58: $i,SV12: $i] :
( ( ( ~ ( subset @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV12 )
| ( in @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV58 ) )
= $false )
| ( ( in @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV58 )
= $true )
| ( ( SV58
= ( powerset @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1062]) ).
thf(1119,plain,
! [SV58: $i,SV12: $i] :
( ( ( ~ ( subset @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV12 ) )
= $false )
| ( ( subset @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV12 )
= $false )
| ( ( SV58
= ( powerset @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1063]) ).
thf(1120,plain,
! [SV58: $i,SV12: $i] :
( ( ( in @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV58 )
= $false )
| ( ( subset @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV12 )
= $false )
| ( ( SV58
= ( powerset @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1063]) ).
thf(1121,plain,
! [SV63: $i,SV18: $i,SV93: $i,SV120: $i] :
( ( ( in @ SV120 @ SV93 )
= $false )
| ( ( ~ ( ~ ( in @ SV120 @ SV18 )
| ~ ( in @ SV120 @ SV63 ) ) )
= $true )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1065]) ).
thf(1122,plain,
! [SV93: $i,SV63: $i,SV18: $i,SV120: $i] :
( ( ( ~ ( ~ ( in @ SV120 @ SV18 )
| ~ ( in @ SV120 @ SV63 ) ) )
= $false )
| ( ( in @ SV120 @ SV93 )
= $true )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1066]) ).
thf(1123,plain,
! [SV93: $i,SV18: $i,SV63: $i] :
( ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV93 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
| ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 ) )
| ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV93 ) ) )
= $true )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1067]) ).
thf(1124,plain,
! [SV93: $i,SV18: $i,SV63: $i] :
( ( ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
| ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
| ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 ) )
| ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV93 ) ) )
= $true )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1068]) ).
thf(1125,plain,
! [SV20: $i,SV65: $i] :
( ( ( ~ ( in @ ( sK22_SY313 @ SV65 @ SV20 ) @ SV20 )
| ~ ( in @ ( sK22_SY313 @ SV65 @ SV20 ) @ SV65 ) )
= $false )
| ( ( disjoint @ SV20 @ SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1069]) ).
thf(1126,plain,
! [SV65: $i,SV20: $i,SV128: $i] :
( ( ( ~ ( in @ SV128 @ SV20 ) )
= $true )
| ( ( ~ ( in @ SV128 @ SV65 ) )
= $true )
| ( ( ~ ( disjoint @ SV20 @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1070]) ).
thf(1127,plain,
! [SV67: $i,SV22: $i,SV95: $i,SV121: $i] :
( ( ( in @ SV121 @ SV95 )
= $false )
| ( ( ~ ! [SY405: $i] :
~ ~ ! [SY406: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY405 @ SV22 )
| ~ ( in @ SY406 @ SV67 ) )
| ( SV121
!= ( ordered_pair @ SY405 @ SY406 ) ) ) )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1071]) ).
thf(1128,plain,
! [SV95: $i,SV121: $i,SV67: $i,SV22: $i] :
( ( ( ~ ! [SY407: $i] :
~ ~ ! [SY408: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY407 @ SV22 )
| ~ ( in @ SY408 @ SV67 ) )
| ( SV121
!= ( ordered_pair @ SY407 @ SY408 ) ) ) )
= $false )
| ( ( in @ SV121 @ SV95 )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1072]) ).
thf(1129,plain,
! [SV95: $i,SV22: $i,SV67: $i] :
( ( ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 )
= $true )
| ( ( ~ ( ~ ~ ! [SY411: $i] :
~ ~ ! [SY412: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY411 @ SV22 )
| ~ ( in @ SY412 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SY411 @ SY412 ) ) )
| ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 ) ) )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1073]) ).
thf(1130,plain,
! [SV95: $i,SV67: $i,SV22: $i] :
( ( ( ! [SY409: $i] :
~ ~ ! [SY410: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY409 @ SV22 )
| ~ ( in @ SY410 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SY409 @ SY410 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY411: $i] :
~ ~ ! [SY412: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY411 @ SV22 )
| ~ ( in @ SY412 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SY411 @ SY412 ) ) )
| ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 ) ) )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1074]) ).
thf(1131,plain,
! [SV68: $i,SV23: $i,SV96: $i,SV122: $i] :
( ( ( in @ SV122 @ SV96 )
= $false )
| ( ( ( in @ SV122 @ SV23 )
| ( in @ SV122 @ SV68 ) )
= $true )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1075]) ).
thf(1132,plain,
! [SV96: $i,SV68: $i,SV23: $i,SV122: $i] :
( ( ( ( in @ SV122 @ SV23 )
| ( in @ SV122 @ SV68 ) )
= $false )
| ( ( in @ SV122 @ SV96 )
= $true )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1076]) ).
thf(1133,plain,
! [SV96: $i,SV23: $i,SV68: $i] :
( ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV96 )
= $true )
| ( ( ~ ( ~ ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV23 )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV68 ) )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV96 ) ) )
= $true )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1077]) ).
thf(1134,plain,
! [SV96: $i,SV23: $i,SV68: $i] :
( ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV23 )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV23 )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV68 ) )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV96 ) ) )
= $true )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1078]) ).
thf(1135,plain,
! [SV96: $i,SV23: $i,SV68: $i] :
( ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV68 )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV23 )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV68 ) )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV96 ) ) )
= $true )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1078]) ).
thf(1136,plain,
! [SV71: $i,SV26: $i] :
( ( ( ( ( sK14_SY331 @ SV26 @ SV71 )
!= SV26 )
| ( in @ ( sK14_SY331 @ SV26 @ SV71 ) @ SV71 ) )
= $false )
| ( ( in @ ( sK14_SY331 @ SV26 @ SV71 ) @ SV71 )
= $true )
| ( ( SV71
= ( singleton @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1081]) ).
thf(1137,plain,
! [SV71: $i,SV26: $i] :
( ( ( ( sK14_SY331 @ SV26 @ SV71 )
!= SV26 )
= $false )
| ( ( ( sK14_SY331 @ SV26 @ SV71 )
= SV26 )
= $false )
| ( ( SV71
= ( singleton @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1082]) ).
thf(1138,plain,
! [SV71: $i,SV26: $i] :
( ( ( in @ ( sK14_SY331 @ SV26 @ SV71 ) @ SV71 )
= $false )
| ( ( ( sK14_SY331 @ SV26 @ SV71 )
= SV26 )
= $false )
| ( ( SV71
= ( singleton @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1082]) ).
thf(1139,plain,
! [SV27: $i,SV72: $i,SV135: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV135 @ SV72 )
| ! [SY426: $i] :
( ~ ( in @ SY426 @ SV27 )
| ( in @ SV135 @ SY426 ) ) )
| ~ ( ~ ! [SY427: $i] :
( ~ ( in @ SY427 @ SV27 )
| ( in @ SV135 @ SY427 ) )
| ( in @ SV135 @ SV72 ) ) ) )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $false )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1140,plain,
! [SV72: $i,SV27: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV72 )
| ! [SY428: $i] :
( ~ ( in @ SY428 @ SV27 )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SY428 ) ) )
| ~ ( ~ ! [SY429: $i] :
( ~ ( in @ SY429 @ SV27 )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SY429 ) )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV72 ) ) ) )
= $false )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1084]) ).
thf(1141,plain,
! [SV77: $i,SV33: $i,SV98: $i,SV123: $i] :
( ( ( in @ SV123 @ SV98 )
= $false )
| ( ( ( SV123 = SV33 )
| ( SV123 = SV77 ) )
= $true )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1087]) ).
thf(1142,plain,
! [SV98: $i,SV77: $i,SV33: $i,SV123: $i] :
( ( ( ( SV123 = SV33 )
| ( SV123 = SV77 ) )
= $false )
| ( ( in @ SV123 @ SV98 )
= $true )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1088]) ).
thf(1143,plain,
! [SV98: $i,SV33: $i,SV77: $i] :
( ( ( in @ ( sK18_SY373 @ SV77 @ SV33 @ SV98 ) @ SV98 )
= $true )
| ( ( ~ ( ~ ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV33 )
| ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV77 ) )
| ( in @ ( sK18_SY373 @ SV77 @ SV33 @ SV98 ) @ SV98 ) ) )
= $true )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1089]) ).
thf(1144,plain,
! [SV98: $i,SV33: $i,SV77: $i] :
( ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV33 )
= $false )
| ( ( ~ ( ~ ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV33 )
| ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV77 ) )
| ( in @ ( sK18_SY373 @ SV77 @ SV33 @ SV98 ) @ SV98 ) ) )
= $true )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1090]) ).
thf(1145,plain,
! [SV98: $i,SV33: $i,SV77: $i] :
( ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV77 )
= $false )
| ( ( ~ ( ~ ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV33 )
| ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV77 ) )
| ( in @ ( sK18_SY373 @ SV77 @ SV33 @ SV98 ) @ SV98 ) ) )
= $true )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1090]) ).
thf(1146,plain,
! [SV37: $i,SV136: $i] :
( ( ! [SY430: $i] :
( ~ ~ ( ~ ( in @ SV136 @ ( sK6_SY251 @ SV37 ) )
| ~ ( subset @ SY430 @ SV136 ) )
| ( in @ SY430 @ ( sK6_SY251 @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1092]) ).
thf(1147,plain,
! [SV37: $i,SV129: $i] :
( ( ( ~ ( in @ SV129 @ ( sK6_SY251 @ SV37 ) ) )
= $true )
| ( ( ~ ! [SY421: $i] :
~ ~ ( ~ ( in @ SY421 @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SY422: $i] :
( ~ ( subset @ SY422 @ SV129 )
| ( in @ SY422 @ SY421 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1093]) ).
thf(1148,plain,
! [SV37: $i,SV119: $i] :
( ( ( ~ ( subset @ SV119 @ ( sK6_SY251 @ SV37 ) ) )
= $true )
| ( ( ~ ~ ( are_equipotent @ SV119 @ ( sK6_SY251 @ SV37 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV119 @ ( sK6_SY251 @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1094]) ).
thf(1149,plain,
! [SV39: $i,SV113: $i] :
( ( ( SV113
!= ( ordered_pair @ ( sK24_SY397 @ SV39 @ SV113 ) @ ( sK26_SY424 @ SV39 @ SV113 ) ) )
= $false )
| ( ( in @ SV113 @ SV39 )
= $false )
| ( ( relation @ SV39 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1095]) ).
thf(1150,plain,
! [SV132: $i,SV131: $i,SV39: $i] :
( ( ( ( sK10_SY262 @ SV39 )
= ( ordered_pair @ SV131 @ SV132 ) )
= $false )
| ( ( relation @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1096]) ).
thf(1151,plain,
! [SV42: $i,SV108: $i,SV126: $i] :
( ( ( ~ ( in @ SV126 @ SV108 ) )
= $true )
| ( ( ~ ! [SY417: $i] :
~ ( in @ ( ordered_pair @ SV126 @ SY417 ) @ SV42 ) )
= $true )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $false )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1097]) ).
thf(1152,plain,
! [SV108: $i,SV42: $i,SV126: $i] :
( ( ( ~ ~ ! [SY418: $i] :
~ ( in @ ( ordered_pair @ SV126 @ SY418 ) @ SV42 ) )
= $true )
| ( ( in @ SV126 @ SV108 )
= $true )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $false )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1098]) ).
thf(1153,plain,
! [SV108: $i,SV42: $i] :
( ( ( ~ ( in @ ( sK21_SY394 @ SV42 @ SV108 ) @ SV108 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY420: $i] :
~ ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ SY420 ) @ SV42 )
| ( in @ ( sK21_SY394 @ SV42 @ SV108 ) @ SV108 ) ) )
= $true )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1099]) ).
thf(1154,plain,
! [SV108: $i,SV42: $i] :
( ( ( ~ ! [SY419: $i] :
~ ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ SY419 ) @ SV42 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY420: $i] :
~ ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ SY420 ) @ SV42 )
| ( in @ ( sK21_SY394 @ SV42 @ SV108 ) @ SV108 ) ) )
= $true )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1099]) ).
thf(1155,plain,
! [SV84: $i,SV43: $i,SV101: $i,SV124: $i] :
( ( ( in @ SV124 @ SV101 )
= $false )
| ( ( ~ ( ~ ( in @ SV124 @ SV43 )
| ~ ~ ( in @ SV124 @ SV84 ) ) )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1100]) ).
thf(1156,plain,
! [SV101: $i,SV84: $i,SV43: $i,SV124: $i] :
( ( ( ~ ( ~ ( in @ SV124 @ SV43 )
| ~ ~ ( in @ SV124 @ SV84 ) ) )
= $false )
| ( ( in @ SV124 @ SV101 )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1101]) ).
thf(1157,plain,
! [SV101: $i,SV43: $i,SV84: $i] :
( ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV101 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
| ~ ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 ) )
| ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV101 ) ) )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1102]) ).
thf(1158,plain,
! [SV101: $i,SV43: $i,SV84: $i] :
( ( ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
| ~ ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
| ~ ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 ) )
| ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV101 ) ) )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1103]) ).
thf(1159,plain,
! [SV137: $i,SV3: $i,SV133: $i] :
( ( ~ ~ ( ~ ( in @ SV133 @ ( sK5_SY160 @ SV3 ) )
| ~ ( subset @ SV137 @ SV133 ) )
| ( in @ SV137 @ ( sK5_SY160 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1160,plain,
! [SV3: $i,SV114: $i] :
( ( ( subset @ SV114 @ ( sK5_SY160 @ SV3 ) )
= $false )
| ( ( ~ ~ ( are_equipotent @ SV114 @ ( sK5_SY160 @ SV3 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV114 @ ( sK5_SY160 @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1109]) ).
thf(1161,plain,
! [SV4: $i,SV52: $i,SV115: $i] :
( ( ( ~ ~ ( ~ ( in @ SV115 @ ( sK27_SY401 @ SV52 @ SV4 @ SV115 ) )
| ~ ( in @ ( sK27_SY401 @ SV52 @ SV4 @ SV115 ) @ SV4 ) ) )
= $false )
| ( ( in @ SV115 @ SV52 )
= $false )
| ( ( SV52
= ( union @ SV4 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1110]) ).
thf(1162,plain,
! [SV52: $i,SV4: $i,SV138: $i,SV115: $i] :
( ( ( ~ ~ ( ~ ( in @ SV115 @ SV138 )
| ~ ( in @ SV138 @ SV4 ) ) )
= $true )
| ( ( in @ SV115 @ SV52 )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1111]) ).
thf(1163,plain,
! [SV52: $i,SV4: $i] :
( ( ( ~ ~ ! [SY404: $i] :
~ ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SY404 )
| ~ ( in @ SY404 @ SV4 ) ) )
= $false )
| ( ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV52 )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1112]) ).
thf(1164,plain,
! [SV52: $i,SV4: $i] :
( ( ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV52 )
= $false )
| ( ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV52 )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1112]) ).
thf(1165,plain,
! [SV134: $i,SV52: $i,SV4: $i] :
( ( ( ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV134 )
| ~ ( in @ SV134 @ SV4 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY404: $i] :
~ ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SY404 )
| ~ ( in @ SY404 @ SV4 ) )
| ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV52 ) ) )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1113]) ).
thf(1166,plain,
! [SV9: $i,SV105: $i,SV125: $i] :
( ( ( in @ SV125 @ SV105 )
= $false )
| ( ( ~ ! [SY413: $i] :
~ ( in @ ( ordered_pair @ SY413 @ SV125 ) @ SV9 ) )
= $true )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $false )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1114]) ).
thf(1167,plain,
! [SV105: $i,SV9: $i,SV125: $i] :
( ( ( ~ ! [SY414: $i] :
~ ( in @ ( ordered_pair @ SY414 @ SV125 ) @ SV9 ) )
= $false )
| ( ( in @ SV125 @ SV105 )
= $true )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $false )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1115]) ).
thf(1168,plain,
! [SV105: $i,SV9: $i] :
( ( ( in @ ( sK20_SY388 @ SV9 @ SV105 ) @ SV105 )
= $true )
| ( ( ~ ( ~ ~ ! [SY416: $i] :
~ ( in @ ( ordered_pair @ SY416 @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 )
| ( in @ ( sK20_SY388 @ SV9 @ SV105 ) @ SV105 ) ) )
= $true )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1116]) ).
thf(1169,plain,
! [SV105: $i,SV9: $i] :
( ( ( ! [SY415: $i] :
~ ( in @ ( ordered_pair @ SY415 @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY416: $i] :
~ ( in @ ( ordered_pair @ SY416 @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 )
| ( in @ ( sK20_SY388 @ SV9 @ SV105 ) @ SV105 ) ) )
= $true )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1117]) ).
thf(1170,plain,
! [SV58: $i,SV12: $i] :
( ( ( ~ ( subset @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV12 ) )
= $false )
| ( ( in @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV58 )
= $true )
| ( ( SV58
= ( powerset @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1118]) ).
thf(1171,plain,
! [SV58: $i,SV12: $i] :
( ( ( in @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV58 )
= $false )
| ( ( in @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV58 )
= $true )
| ( ( SV58
= ( powerset @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1118]) ).
thf(1172,plain,
! [SV58: $i,SV12: $i] :
( ( ( subset @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV12 )
= $true )
| ( ( subset @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV12 )
= $false )
| ( ( SV58
= ( powerset @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1119]) ).
thf(1173,plain,
! [SV93: $i,SV63: $i,SV18: $i,SV120: $i] :
( ( ( ~ ( in @ SV120 @ SV18 )
| ~ ( in @ SV120 @ SV63 ) )
= $false )
| ( ( in @ SV120 @ SV93 )
= $false )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1121]) ).
thf(1174,plain,
! [SV93: $i,SV63: $i,SV18: $i,SV120: $i] :
( ( ( ~ ( in @ SV120 @ SV18 )
| ~ ( in @ SV120 @ SV63 ) )
= $true )
| ( ( in @ SV120 @ SV93 )
= $true )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1122]) ).
thf(1175,plain,
! [SV93: $i,SV18: $i,SV63: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
| ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 ) )
| ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV93 ) )
= $false )
| ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV93 )
= $true )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1123]) ).
thf(1176,plain,
! [SV93: $i,SV18: $i,SV63: $i] :
( ( ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 ) )
= $true )
| ( ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
| ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 ) )
| ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV93 ) ) )
= $true )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1124]) ).
thf(1177,plain,
! [SV20: $i,SV65: $i] :
( ( ( ~ ( in @ ( sK22_SY313 @ SV65 @ SV20 ) @ SV20 ) )
= $false )
| ( ( disjoint @ SV20 @ SV65 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1125]) ).
thf(1178,plain,
! [SV20: $i,SV65: $i] :
( ( ( ~ ( in @ ( sK22_SY313 @ SV65 @ SV20 ) @ SV65 ) )
= $false )
| ( ( disjoint @ SV20 @ SV65 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1125]) ).
thf(1179,plain,
! [SV65: $i,SV20: $i,SV128: $i] :
( ( ( in @ SV128 @ SV20 )
= $false )
| ( ( ~ ( in @ SV128 @ SV65 ) )
= $true )
| ( ( ~ ( disjoint @ SV20 @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1126]) ).
thf(1180,plain,
! [SV95: $i,SV121: $i,SV67: $i,SV22: $i] :
( ( ( ! [SY405: $i] :
~ ~ ! [SY406: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY405 @ SV22 )
| ~ ( in @ SY406 @ SV67 ) )
| ( SV121
!= ( ordered_pair @ SY405 @ SY406 ) ) ) )
= $false )
| ( ( in @ SV121 @ SV95 )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1127]) ).
thf(1181,plain,
! [SV95: $i,SV121: $i,SV67: $i,SV22: $i] :
( ( ( ! [SY407: $i] :
~ ~ ! [SY408: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY407 @ SV22 )
| ~ ( in @ SY408 @ SV67 ) )
| ( SV121
!= ( ordered_pair @ SY407 @ SY408 ) ) ) )
= $true )
| ( ( in @ SV121 @ SV95 )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1128]) ).
thf(1182,plain,
! [SV95: $i,SV67: $i,SV22: $i] :
( ( ( ~ ~ ! [SY411: $i] :
~ ~ ! [SY412: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY411 @ SV22 )
| ~ ( in @ SY412 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SY411 @ SY412 ) ) )
| ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 ) )
= $false )
| ( ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1129]) ).
thf(1183,plain,
! [SV95: $i,SV67: $i,SV22: $i,SV139: $i] :
( ( ( ~ ~ ! [SY431: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV139 @ SV22 )
| ~ ( in @ SY431 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SV139 @ SY431 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY411: $i] :
~ ~ ! [SY412: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY411 @ SV22 )
| ~ ( in @ SY412 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SY411 @ SY412 ) ) )
| ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 ) ) )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1184,plain,
! [SV96: $i,SV68: $i,SV23: $i,SV122: $i] :
( ( ( in @ SV122 @ SV23 )
= $true )
| ( ( in @ SV122 @ SV68 )
= $true )
| ( ( in @ SV122 @ SV96 )
= $false )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1131]) ).
thf(1185,plain,
! [SV68: $i,SV96: $i,SV23: $i,SV122: $i] :
( ( ( in @ SV122 @ SV23 )
= $false )
| ( ( in @ SV122 @ SV96 )
= $true )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1132]) ).
thf(1186,plain,
! [SV23: $i,SV96: $i,SV68: $i,SV122: $i] :
( ( ( in @ SV122 @ SV68 )
= $false )
| ( ( in @ SV122 @ SV96 )
= $true )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1132]) ).
thf(1187,plain,
! [SV96: $i,SV23: $i,SV68: $i] :
( ( ( ~ ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV23 )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV68 ) )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV96 ) )
= $false )
| ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV96 )
= $true )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1133]) ).
thf(1188,plain,
! [SV96: $i,SV23: $i,SV68: $i] :
( ( ( ~ ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV23 )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV68 ) )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV96 ) )
= $false )
| ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV23 )
= $false )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1134]) ).
thf(1189,plain,
! [SV96: $i,SV23: $i,SV68: $i] :
( ( ( ~ ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV23 )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV68 ) )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV96 ) )
= $false )
| ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV68 )
= $false )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1135]) ).
thf(1190,plain,
! [SV71: $i,SV26: $i] :
( ( ( ( sK14_SY331 @ SV26 @ SV71 )
!= SV26 )
= $false )
| ( ( in @ ( sK14_SY331 @ SV26 @ SV71 ) @ SV71 )
= $true )
| ( ( SV71
= ( singleton @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1136]) ).
thf(1191,plain,
! [SV71: $i,SV26: $i] :
( ( ( in @ ( sK14_SY331 @ SV26 @ SV71 ) @ SV71 )
= $false )
| ( ( in @ ( sK14_SY331 @ SV26 @ SV71 ) @ SV71 )
= $true )
| ( ( SV71
= ( singleton @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1136]) ).
thf(1192,plain,
! [SV71: $i,SV26: $i] :
( ( ( ( sK14_SY331 @ SV26 @ SV71 )
= SV26 )
= $true )
| ( ( ( sK14_SY331 @ SV26 @ SV71 )
= SV26 )
= $false )
| ( ( SV71
= ( singleton @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1137]) ).
thf(1193,plain,
! [SV27: $i,SV72: $i,SV135: $i] :
( ( ( ~ ( ~ ( in @ SV135 @ SV72 )
| ! [SY426: $i] :
( ~ ( in @ SY426 @ SV27 )
| ( in @ SV135 @ SY426 ) ) )
| ~ ( ~ ! [SY427: $i] :
( ~ ( in @ SY427 @ SV27 )
| ( in @ SV135 @ SY427 ) )
| ( in @ SV135 @ SV72 ) ) )
= $false )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $false )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1139]) ).
thf(1194,plain,
! [SV72: $i,SV27: $i] :
( ( ( ~ ( ~ ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV72 )
| ! [SY428: $i] :
( ~ ( in @ SY428 @ SV27 )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SY428 ) ) )
| ~ ( ~ ! [SY429: $i] :
( ~ ( in @ SY429 @ SV27 )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SY429 ) )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV72 ) ) )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1140]) ).
thf(1195,plain,
! [SV98: $i,SV77: $i,SV33: $i,SV123: $i] :
( ( ( SV123 = SV33 )
= $true )
| ( ( SV123 = SV77 )
= $true )
| ( ( in @ SV123 @ SV98 )
= $false )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1141]) ).
thf(1196,plain,
! [SV77: $i,SV98: $i,SV33: $i,SV123: $i] :
( ( ( SV123 = SV33 )
= $false )
| ( ( in @ SV123 @ SV98 )
= $true )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1142]) ).
thf(1197,plain,
! [SV33: $i,SV98: $i,SV77: $i,SV123: $i] :
( ( ( SV123 = SV77 )
= $false )
| ( ( in @ SV123 @ SV98 )
= $true )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1142]) ).
thf(1198,plain,
! [SV98: $i,SV33: $i,SV77: $i] :
( ( ( ~ ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV33 )
| ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV77 ) )
| ( in @ ( sK18_SY373 @ SV77 @ SV33 @ SV98 ) @ SV98 ) )
= $false )
| ( ( in @ ( sK18_SY373 @ SV77 @ SV33 @ SV98 ) @ SV98 )
= $true )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1143]) ).
thf(1199,plain,
! [SV98: $i,SV33: $i,SV77: $i] :
( ( ( ~ ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV33 )
| ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV77 ) )
| ( in @ ( sK18_SY373 @ SV77 @ SV33 @ SV98 ) @ SV98 ) )
= $false )
| ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV33 )
= $false )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1144]) ).
thf(1200,plain,
! [SV98: $i,SV33: $i,SV77: $i] :
( ( ( ~ ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV33 )
| ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV77 ) )
| ( in @ ( sK18_SY373 @ SV77 @ SV33 @ SV98 ) @ SV98 ) )
= $false )
| ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV77 )
= $false )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1145]) ).
thf(1201,plain,
! [SV140: $i,SV37: $i,SV136: $i] :
( ( ~ ~ ( ~ ( in @ SV136 @ ( sK6_SY251 @ SV37 ) )
| ~ ( subset @ SV140 @ SV136 ) )
| ( in @ SV140 @ ( sK6_SY251 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1202,plain,
! [SV37: $i,SV129: $i] :
( ( ( in @ SV129 @ ( sK6_SY251 @ SV37 ) )
= $false )
| ( ( ~ ! [SY421: $i] :
~ ~ ( ~ ( in @ SY421 @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SY422: $i] :
( ~ ( subset @ SY422 @ SV129 )
| ( in @ SY422 @ SY421 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1147]) ).
thf(1203,plain,
! [SV37: $i,SV119: $i] :
( ( ( subset @ SV119 @ ( sK6_SY251 @ SV37 ) )
= $false )
| ( ( ~ ~ ( are_equipotent @ SV119 @ ( sK6_SY251 @ SV37 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV119 @ ( sK6_SY251 @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1148]) ).
thf(1204,plain,
! [SV39: $i,SV113: $i] :
( ( ( SV113
= ( ordered_pair @ ( sK24_SY397 @ SV39 @ SV113 ) @ ( sK26_SY424 @ SV39 @ SV113 ) ) )
= $true )
| ( ( in @ SV113 @ SV39 )
= $false )
| ( ( relation @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1149]) ).
thf(1205,plain,
! [SV42: $i,SV108: $i,SV126: $i] :
( ( ( in @ SV126 @ SV108 )
= $false )
| ( ( ~ ! [SY417: $i] :
~ ( in @ ( ordered_pair @ SV126 @ SY417 ) @ SV42 ) )
= $true )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $false )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1151]) ).
thf(1206,plain,
! [SV108: $i,SV42: $i,SV126: $i] :
( ( ( ~ ! [SY418: $i] :
~ ( in @ ( ordered_pair @ SV126 @ SY418 ) @ SV42 ) )
= $false )
| ( ( in @ SV126 @ SV108 )
= $true )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $false )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1152]) ).
thf(1207,plain,
! [SV108: $i,SV42: $i] :
( ( ( in @ ( sK21_SY394 @ SV42 @ SV108 ) @ SV108 )
= $true )
| ( ( ~ ( ~ ~ ! [SY420: $i] :
~ ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ SY420 ) @ SV42 )
| ( in @ ( sK21_SY394 @ SV42 @ SV108 ) @ SV108 ) ) )
= $true )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1153]) ).
thf(1208,plain,
! [SV108: $i,SV42: $i] :
( ( ( ! [SY419: $i] :
~ ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ SY419 ) @ SV42 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY420: $i] :
~ ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ SY420 ) @ SV42 )
| ( in @ ( sK21_SY394 @ SV42 @ SV108 ) @ SV108 ) ) )
= $true )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1154]) ).
thf(1209,plain,
! [SV101: $i,SV84: $i,SV43: $i,SV124: $i] :
( ( ( ~ ( in @ SV124 @ SV43 )
| ~ ~ ( in @ SV124 @ SV84 ) )
= $false )
| ( ( in @ SV124 @ SV101 )
= $false )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1155]) ).
thf(1210,plain,
! [SV101: $i,SV84: $i,SV43: $i,SV124: $i] :
( ( ( ~ ( in @ SV124 @ SV43 )
| ~ ~ ( in @ SV124 @ SV84 ) )
= $true )
| ( ( in @ SV124 @ SV101 )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1156]) ).
thf(1211,plain,
! [SV101: $i,SV43: $i,SV84: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
| ~ ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 ) )
| ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV101 ) )
= $false )
| ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV101 )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1157]) ).
thf(1212,plain,
! [SV101: $i,SV43: $i,SV84: $i] :
( ( ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 ) )
= $true )
| ( ( ~ ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
| ~ ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 ) )
| ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV101 ) ) )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1158]) ).
thf(1213,plain,
! [SV137: $i,SV3: $i,SV133: $i] :
( ( ( ~ ~ ( ~ ( in @ SV133 @ ( sK5_SY160 @ SV3 ) )
| ~ ( subset @ SV137 @ SV133 ) ) )
= $true )
| ( ( in @ SV137 @ ( sK5_SY160 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1159]) ).
thf(1214,plain,
! [SV3: $i,SV114: $i] :
( ( ( ~ ( are_equipotent @ SV114 @ ( sK5_SY160 @ SV3 ) ) )
= $false )
| ( ( subset @ SV114 @ ( sK5_SY160 @ SV3 ) )
= $false )
| ( ( ~ ~ ( in @ SV114 @ ( sK5_SY160 @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1160]) ).
thf(1215,plain,
! [SV4: $i,SV52: $i,SV115: $i] :
( ( ( ~ ( ~ ( in @ SV115 @ ( sK27_SY401 @ SV52 @ SV4 @ SV115 ) )
| ~ ( in @ ( sK27_SY401 @ SV52 @ SV4 @ SV115 ) @ SV4 ) ) )
= $true )
| ( ( in @ SV115 @ SV52 )
= $false )
| ( ( SV52
= ( union @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1161]) ).
thf(1216,plain,
! [SV52: $i,SV4: $i,SV138: $i,SV115: $i] :
( ( ( ~ ( ~ ( in @ SV115 @ SV138 )
| ~ ( in @ SV138 @ SV4 ) ) )
= $false )
| ( ( in @ SV115 @ SV52 )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1162]) ).
thf(1217,plain,
! [SV52: $i,SV4: $i] :
( ( ( ~ ! [SY404: $i] :
~ ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SY404 )
| ~ ( in @ SY404 @ SV4 ) ) )
= $true )
| ( ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV52 )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1163]) ).
thf(1218,plain,
! [SV134: $i,SV52: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV134 )
| ~ ( in @ SV134 @ SV4 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY404: $i] :
~ ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SY404 )
| ~ ( in @ SY404 @ SV4 ) )
| ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV52 ) ) )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1165]) ).
thf(1219,plain,
! [SV105: $i,SV9: $i,SV125: $i] :
( ( ( ! [SY413: $i] :
~ ( in @ ( ordered_pair @ SY413 @ SV125 ) @ SV9 ) )
= $false )
| ( ( in @ SV125 @ SV105 )
= $false )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $false )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1166]) ).
thf(1220,plain,
! [SV105: $i,SV9: $i,SV125: $i] :
( ( ( ! [SY414: $i] :
~ ( in @ ( ordered_pair @ SY414 @ SV125 ) @ SV9 ) )
= $true )
| ( ( in @ SV125 @ SV105 )
= $true )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $false )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1167]) ).
thf(1221,plain,
! [SV105: $i,SV9: $i] :
( ( ( ~ ~ ! [SY416: $i] :
~ ( in @ ( ordered_pair @ SY416 @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 )
| ( in @ ( sK20_SY388 @ SV9 @ SV105 ) @ SV105 ) )
= $false )
| ( ( in @ ( sK20_SY388 @ SV9 @ SV105 ) @ SV105 )
= $true )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1168]) ).
thf(1222,plain,
! [SV105: $i,SV9: $i,SV141: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV141 @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY416: $i] :
~ ( in @ ( ordered_pair @ SY416 @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 )
| ( in @ ( sK20_SY388 @ SV9 @ SV105 ) @ SV105 ) ) )
= $true )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1169]) ).
thf(1223,plain,
! [SV58: $i,SV12: $i] :
( ( ( subset @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV12 )
= $true )
| ( ( in @ ( sK13_SY305 @ SV12 @ SV58 ) @ SV58 )
= $true )
| ( ( SV58
= ( powerset @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1170]) ).
thf(1224,plain,
! [SV63: $i,SV93: $i,SV18: $i,SV120: $i] :
( ( ( ~ ( in @ SV120 @ SV18 ) )
= $false )
| ( ( in @ SV120 @ SV93 )
= $false )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1173]) ).
thf(1225,plain,
! [SV18: $i,SV93: $i,SV63: $i,SV120: $i] :
( ( ( ~ ( in @ SV120 @ SV63 ) )
= $false )
| ( ( in @ SV120 @ SV93 )
= $false )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1173]) ).
thf(1226,plain,
! [SV93: $i,SV63: $i,SV18: $i,SV120: $i] :
( ( ( ~ ( in @ SV120 @ SV18 ) )
= $true )
| ( ( ~ ( in @ SV120 @ SV63 ) )
= $true )
| ( ( in @ SV120 @ SV93 )
= $true )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1174]) ).
thf(1227,plain,
! [SV93: $i,SV18: $i,SV63: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
| ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 ) ) )
= $false )
| ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV93 )
= $true )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1175]) ).
thf(1228,plain,
! [SV93: $i,SV18: $i,SV63: $i] :
( ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV93 )
= $false )
| ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV93 )
= $true )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1175]) ).
thf(1229,plain,
! [SV93: $i,SV18: $i,SV63: $i] :
( ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
= $false )
| ( ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
| ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 ) )
| ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV93 ) ) )
= $true )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1176]) ).
thf(1230,plain,
! [SV20: $i,SV65: $i] :
( ( ( in @ ( sK22_SY313 @ SV65 @ SV20 ) @ SV20 )
= $true )
| ( ( disjoint @ SV20 @ SV65 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1177]) ).
thf(1231,plain,
! [SV20: $i,SV65: $i] :
( ( ( in @ ( sK22_SY313 @ SV65 @ SV20 ) @ SV65 )
= $true )
| ( ( disjoint @ SV20 @ SV65 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1178]) ).
thf(1232,plain,
! [SV20: $i,SV65: $i,SV128: $i] :
( ( ( in @ SV128 @ SV65 )
= $false )
| ( ( in @ SV128 @ SV20 )
= $false )
| ( ( ~ ( disjoint @ SV20 @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1179]) ).
thf(1233,plain,
! [SV22: $i,SV67: $i,SV121: $i,SV95: $i] :
( ( ( ~ ~ ! [SY432: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK28_SY405 @ SV95 @ SV121 @ SV67 @ SV22 ) @ SV22 )
| ~ ( in @ SY432 @ SV67 ) )
| ( SV121
!= ( ordered_pair @ ( sK28_SY405 @ SV95 @ SV121 @ SV67 @ SV22 ) @ SY432 ) ) ) )
= $false )
| ( ( in @ SV121 @ SV95 )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1180]) ).
thf(1234,plain,
! [SV95: $i,SV121: $i,SV67: $i,SV22: $i,SV142: $i] :
( ( ( ~ ~ ! [SY433: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV142 @ SV22 )
| ~ ( in @ SY433 @ SV67 ) )
| ( SV121
!= ( ordered_pair @ SV142 @ SY433 ) ) ) )
= $true )
| ( ( in @ SV121 @ SV95 )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1181]) ).
thf(1235,plain,
! [SV95: $i,SV67: $i,SV22: $i] :
( ( ( ~ ~ ! [SY411: $i] :
~ ~ ! [SY412: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY411 @ SV22 )
| ~ ( in @ SY412 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SY411 @ SY412 ) ) ) )
= $false )
| ( ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1182]) ).
thf(1236,plain,
! [SV95: $i,SV22: $i,SV67: $i] :
( ( ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 )
= $false )
| ( ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1182]) ).
thf(1237,plain,
! [SV95: $i,SV67: $i,SV22: $i,SV139: $i] :
( ( ( ~ ! [SY431: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV139 @ SV22 )
| ~ ( in @ SY431 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SV139 @ SY431 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY411: $i] :
~ ~ ! [SY412: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY411 @ SV22 )
| ~ ( in @ SY412 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SY411 @ SY412 ) ) )
| ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 ) ) )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1183]) ).
thf(1238,plain,
! [SV96: $i,SV23: $i,SV68: $i] :
( ( ( ~ ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV23 )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV68 ) ) )
= $false )
| ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV96 )
= $true )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1187]) ).
thf(1239,plain,
! [SV96: $i,SV23: $i,SV68: $i] :
( ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV96 )
= $false )
| ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV96 )
= $true )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1187]) ).
thf(1240,plain,
! [SV96: $i,SV23: $i,SV68: $i] :
( ( ( ~ ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV23 )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV68 ) ) )
= $false )
| ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV23 )
= $false )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1188]) ).
thf(1241,plain,
! [SV96: $i,SV23: $i,SV68: $i] :
( ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV96 )
= $false )
| ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV23 )
= $false )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1188]) ).
thf(1242,plain,
! [SV96: $i,SV23: $i,SV68: $i] :
( ( ( ~ ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV23 )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV68 ) ) )
= $false )
| ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV68 )
= $false )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1189]) ).
thf(1243,plain,
! [SV96: $i,SV23: $i,SV68: $i] :
( ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV96 )
= $false )
| ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV68 )
= $false )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1189]) ).
thf(1244,plain,
! [SV71: $i,SV26: $i] :
( ( ( ( sK14_SY331 @ SV26 @ SV71 )
= SV26 )
= $true )
| ( ( in @ ( sK14_SY331 @ SV26 @ SV71 ) @ SV71 )
= $true )
| ( ( SV71
= ( singleton @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1190]) ).
thf(1245,plain,
! [SV27: $i,SV72: $i,SV135: $i] :
( ( ( ~ ( ~ ( in @ SV135 @ SV72 )
| ! [SY426: $i] :
( ~ ( in @ SY426 @ SV27 )
| ( in @ SV135 @ SY426 ) ) ) )
= $false )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $false )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1193]) ).
thf(1246,plain,
! [SV72: $i,SV135: $i,SV27: $i] :
( ( ( ~ ( ~ ! [SY427: $i] :
( ~ ( in @ SY427 @ SV27 )
| ( in @ SV135 @ SY427 ) )
| ( in @ SV135 @ SV72 ) ) )
= $false )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $false )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1193]) ).
thf(1247,plain,
! [SV72: $i,SV27: $i] :
( ( ( ~ ( ~ ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV72 )
| ! [SY428: $i] :
( ~ ( in @ SY428 @ SV27 )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SY428 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY429: $i] :
( ~ ( in @ SY429 @ SV27 )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SY429 ) )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV72 ) ) )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1194]) ).
thf(1248,plain,
! [SV98: $i,SV33: $i,SV77: $i] :
( ( ( ~ ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV33 )
| ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV77 ) ) )
= $false )
| ( ( in @ ( sK18_SY373 @ SV77 @ SV33 @ SV98 ) @ SV98 )
= $true )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1198]) ).
thf(1249,plain,
! [SV98: $i,SV33: $i,SV77: $i] :
( ( ( in @ ( sK18_SY373 @ SV77 @ SV33 @ SV98 ) @ SV98 )
= $false )
| ( ( in @ ( sK18_SY373 @ SV77 @ SV33 @ SV98 ) @ SV98 )
= $true )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1198]) ).
thf(1250,plain,
! [SV98: $i,SV33: $i,SV77: $i] :
( ( ( ~ ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV33 )
| ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV77 ) ) )
= $false )
| ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV33 )
= $false )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1199]) ).
thf(1251,plain,
! [SV98: $i,SV33: $i,SV77: $i] :
( ( ( in @ ( sK18_SY373 @ SV77 @ SV33 @ SV98 ) @ SV98 )
= $false )
| ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV33 )
= $false )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1199]) ).
thf(1252,plain,
! [SV98: $i,SV33: $i,SV77: $i] :
( ( ( ~ ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV33 )
| ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV77 ) ) )
= $false )
| ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV77 )
= $false )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1200]) ).
thf(1253,plain,
! [SV98: $i,SV33: $i,SV77: $i] :
( ( ( in @ ( sK18_SY373 @ SV77 @ SV33 @ SV98 ) @ SV98 )
= $false )
| ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV77 )
= $false )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1200]) ).
thf(1254,plain,
! [SV140: $i,SV37: $i,SV136: $i] :
( ( ( ~ ~ ( ~ ( in @ SV136 @ ( sK6_SY251 @ SV37 ) )
| ~ ( subset @ SV140 @ SV136 ) ) )
= $true )
| ( ( in @ SV140 @ ( sK6_SY251 @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1201]) ).
thf(1255,plain,
! [SV129: $i,SV37: $i] :
( ( ( ! [SY421: $i] :
~ ~ ( ~ ( in @ SY421 @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SY422: $i] :
( ~ ( subset @ SY422 @ SV129 )
| ( in @ SY422 @ SY421 ) ) ) )
= $false )
| ( ( in @ SV129 @ ( sK6_SY251 @ SV37 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1202]) ).
thf(1256,plain,
! [SV37: $i,SV119: $i] :
( ( ( ~ ( are_equipotent @ SV119 @ ( sK6_SY251 @ SV37 ) ) )
= $false )
| ( ( subset @ SV119 @ ( sK6_SY251 @ SV37 ) )
= $false )
| ( ( ~ ~ ( in @ SV119 @ ( sK6_SY251 @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1203]) ).
thf(1257,plain,
! [SV108: $i,SV42: $i,SV126: $i] :
( ( ( ! [SY417: $i] :
~ ( in @ ( ordered_pair @ SV126 @ SY417 ) @ SV42 ) )
= $false )
| ( ( in @ SV126 @ SV108 )
= $false )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $false )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1205]) ).
thf(1258,plain,
! [SV108: $i,SV42: $i,SV126: $i] :
( ( ( ! [SY418: $i] :
~ ( in @ ( ordered_pair @ SV126 @ SY418 ) @ SV42 ) )
= $true )
| ( ( in @ SV126 @ SV108 )
= $true )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $false )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1206]) ).
thf(1259,plain,
! [SV108: $i,SV42: $i] :
( ( ( ~ ~ ! [SY420: $i] :
~ ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ SY420 ) @ SV42 )
| ( in @ ( sK21_SY394 @ SV42 @ SV108 ) @ SV108 ) )
= $false )
| ( ( in @ ( sK21_SY394 @ SV42 @ SV108 ) @ SV108 )
= $true )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1207]) ).
thf(1260,plain,
! [SV143: $i,SV108: $i,SV42: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ SV143 ) @ SV42 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY420: $i] :
~ ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ SY420 ) @ SV42 )
| ( in @ ( sK21_SY394 @ SV42 @ SV108 ) @ SV108 ) ) )
= $true )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1208]) ).
thf(1261,plain,
! [SV84: $i,SV101: $i,SV43: $i,SV124: $i] :
( ( ( ~ ( in @ SV124 @ SV43 ) )
= $false )
| ( ( in @ SV124 @ SV101 )
= $false )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1209]) ).
thf(1262,plain,
! [SV43: $i,SV101: $i,SV84: $i,SV124: $i] :
( ( ( ~ ~ ( in @ SV124 @ SV84 ) )
= $false )
| ( ( in @ SV124 @ SV101 )
= $false )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1209]) ).
thf(1263,plain,
! [SV101: $i,SV84: $i,SV43: $i,SV124: $i] :
( ( ( ~ ( in @ SV124 @ SV43 ) )
= $true )
| ( ( ~ ~ ( in @ SV124 @ SV84 ) )
= $true )
| ( ( in @ SV124 @ SV101 )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1210]) ).
thf(1264,plain,
! [SV101: $i,SV43: $i,SV84: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
| ~ ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 ) ) )
= $false )
| ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV101 )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1211]) ).
thf(1265,plain,
! [SV101: $i,SV43: $i,SV84: $i] :
( ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV101 )
= $false )
| ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV101 )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1211]) ).
thf(1266,plain,
! [SV101: $i,SV43: $i,SV84: $i] :
( ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
= $false )
| ( ( ~ ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
| ~ ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 ) )
| ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV101 ) ) )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1212]) ).
thf(1267,plain,
! [SV137: $i,SV3: $i,SV133: $i] :
( ( ( ~ ( ~ ( in @ SV133 @ ( sK5_SY160 @ SV3 ) )
| ~ ( subset @ SV137 @ SV133 ) ) )
= $false )
| ( ( in @ SV137 @ ( sK5_SY160 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1213]) ).
thf(1268,plain,
! [SV3: $i,SV114: $i] :
( ( ( are_equipotent @ SV114 @ ( sK5_SY160 @ SV3 ) )
= $true )
| ( ( subset @ SV114 @ ( sK5_SY160 @ SV3 ) )
= $false )
| ( ( ~ ~ ( in @ SV114 @ ( sK5_SY160 @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1214]) ).
thf(1269,plain,
! [SV4: $i,SV52: $i,SV115: $i] :
( ( ( ~ ( in @ SV115 @ ( sK27_SY401 @ SV52 @ SV4 @ SV115 ) )
| ~ ( in @ ( sK27_SY401 @ SV52 @ SV4 @ SV115 ) @ SV4 ) )
= $false )
| ( ( in @ SV115 @ SV52 )
= $false )
| ( ( SV52
= ( union @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1215]) ).
thf(1270,plain,
! [SV52: $i,SV4: $i,SV138: $i,SV115: $i] :
( ( ( ~ ( in @ SV115 @ SV138 )
| ~ ( in @ SV138 @ SV4 ) )
= $true )
| ( ( in @ SV115 @ SV52 )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1216]) ).
thf(1271,plain,
! [SV52: $i,SV4: $i] :
( ( ( ! [SY404: $i] :
~ ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SY404 )
| ~ ( in @ SY404 @ SV4 ) ) )
= $false )
| ( ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV52 )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1217]) ).
thf(1272,plain,
! [SV134: $i,SV52: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV134 ) )
= $true )
| ( ( ~ ( in @ SV134 @ SV4 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY404: $i] :
~ ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SY404 )
| ~ ( in @ SY404 @ SV4 ) )
| ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV52 ) ) )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1218]) ).
thf(1273,plain,
! [SV125: $i,SV9: $i,SV105: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK29_SY413 @ SV105 @ SV9 @ SV125 ) @ SV125 ) @ SV9 ) )
= $false )
| ( ( in @ SV125 @ SV105 )
= $false )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $false )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1219]) ).
thf(1274,plain,
! [SV105: $i,SV9: $i,SV125: $i,SV144: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV144 @ SV125 ) @ SV9 ) )
= $true )
| ( ( in @ SV125 @ SV105 )
= $true )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $false )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1220]) ).
thf(1275,plain,
! [SV105: $i,SV9: $i] :
( ( ( ~ ~ ! [SY416: $i] :
~ ( in @ ( ordered_pair @ SY416 @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 ) )
= $false )
| ( ( in @ ( sK20_SY388 @ SV9 @ SV105 ) @ SV105 )
= $true )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1221]) ).
thf(1276,plain,
! [SV105: $i,SV9: $i] :
( ( ( in @ ( sK20_SY388 @ SV9 @ SV105 ) @ SV105 )
= $false )
| ( ( in @ ( sK20_SY388 @ SV9 @ SV105 ) @ SV105 )
= $true )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1221]) ).
thf(1277,plain,
! [SV105: $i,SV9: $i,SV141: $i] :
( ( ( in @ ( ordered_pair @ SV141 @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 )
= $false )
| ( ( ~ ( ~ ~ ! [SY416: $i] :
~ ( in @ ( ordered_pair @ SY416 @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 )
| ( in @ ( sK20_SY388 @ SV9 @ SV105 ) @ SV105 ) ) )
= $true )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1222]) ).
thf(1278,plain,
! [SV63: $i,SV93: $i,SV18: $i,SV120: $i] :
( ( ( in @ SV120 @ SV18 )
= $true )
| ( ( in @ SV120 @ SV93 )
= $false )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1224]) ).
thf(1279,plain,
! [SV18: $i,SV93: $i,SV63: $i,SV120: $i] :
( ( ( in @ SV120 @ SV63 )
= $true )
| ( ( in @ SV120 @ SV93 )
= $false )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1225]) ).
thf(1280,plain,
! [SV93: $i,SV63: $i,SV18: $i,SV120: $i] :
( ( ( in @ SV120 @ SV18 )
= $false )
| ( ( ~ ( in @ SV120 @ SV63 ) )
= $true )
| ( ( in @ SV120 @ SV93 )
= $true )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1226]) ).
thf(1281,plain,
! [SV93: $i,SV18: $i,SV63: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
| ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 ) ) )
= $true )
| ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV93 )
= $true )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1227]) ).
thf(1282,plain,
! [SV93: $i,SV18: $i,SV63: $i] :
( ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 )
= $false )
| ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
| ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 ) )
| ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV93 ) ) )
= $true )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1229]) ).
thf(1283,plain,
! [SV128: $i,SV65: $i,SV20: $i] :
( ( ( disjoint @ SV20 @ SV65 )
= $false )
| ( ( in @ SV128 @ SV20 )
= $false )
| ( ( in @ SV128 @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1232]) ).
thf(1284,plain,
! [SV22: $i,SV67: $i,SV121: $i,SV95: $i] :
( ( ( ~ ! [SY432: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK28_SY405 @ SV95 @ SV121 @ SV67 @ SV22 ) @ SV22 )
| ~ ( in @ SY432 @ SV67 ) )
| ( SV121
!= ( ordered_pair @ ( sK28_SY405 @ SV95 @ SV121 @ SV67 @ SV22 ) @ SY432 ) ) ) )
= $true )
| ( ( in @ SV121 @ SV95 )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1233]) ).
thf(1285,plain,
! [SV95: $i,SV121: $i,SV67: $i,SV22: $i,SV142: $i] :
( ( ( ~ ! [SY433: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV142 @ SV22 )
| ~ ( in @ SY433 @ SV67 ) )
| ( SV121
!= ( ordered_pair @ SV142 @ SY433 ) ) ) )
= $false )
| ( ( in @ SV121 @ SV95 )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1234]) ).
thf(1286,plain,
! [SV95: $i,SV67: $i,SV22: $i] :
( ( ( ~ ! [SY411: $i] :
~ ~ ! [SY412: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY411 @ SV22 )
| ~ ( in @ SY412 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SY411 @ SY412 ) ) ) )
= $true )
| ( ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1235]) ).
thf(1287,plain,
! [SV95: $i,SV67: $i,SV22: $i,SV139: $i] :
( ( ( ! [SY431: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV139 @ SV22 )
| ~ ( in @ SY431 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SV139 @ SY431 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY411: $i] :
~ ~ ! [SY412: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY411 @ SV22 )
| ~ ( in @ SY412 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SY411 @ SY412 ) ) )
| ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 ) ) )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1237]) ).
thf(1288,plain,
! [SV96: $i,SV23: $i,SV68: $i] :
( ( ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV23 )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV68 ) )
= $true )
| ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV96 )
= $true )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1238]) ).
thf(1289,plain,
! [SV96: $i,SV23: $i,SV68: $i] :
( ( ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV23 )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV68 ) )
= $true )
| ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV23 )
= $false )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1240]) ).
thf(1290,plain,
! [SV96: $i,SV23: $i,SV68: $i] :
( ( ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV23 )
| ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV68 ) )
= $true )
| ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV68 )
= $false )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1242]) ).
thf(1291,plain,
! [SV27: $i,SV72: $i,SV135: $i] :
( ( ( ~ ( in @ SV135 @ SV72 )
| ! [SY426: $i] :
( ~ ( in @ SY426 @ SV27 )
| ( in @ SV135 @ SY426 ) ) )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $false )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1245]) ).
thf(1292,plain,
! [SV72: $i,SV135: $i,SV27: $i] :
( ( ( ~ ! [SY427: $i] :
( ~ ( in @ SY427 @ SV27 )
| ( in @ SV135 @ SY427 ) )
| ( in @ SV135 @ SV72 ) )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $false )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1246]) ).
thf(1293,plain,
! [SV72: $i,SV27: $i] :
( ( ( ~ ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV72 )
| ! [SY428: $i] :
( ~ ( in @ SY428 @ SV27 )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SY428 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY429: $i] :
( ~ ( in @ SY429 @ SV27 )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SY429 ) )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV72 ) ) )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1247]) ).
thf(1294,plain,
! [SV98: $i,SV33: $i,SV77: $i] :
( ( ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV33 )
| ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV77 ) )
= $true )
| ( ( in @ ( sK18_SY373 @ SV77 @ SV33 @ SV98 ) @ SV98 )
= $true )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1248]) ).
thf(1295,plain,
! [SV98: $i,SV33: $i,SV77: $i] :
( ( ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV33 )
| ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV77 ) )
= $true )
| ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV33 )
= $false )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1250]) ).
thf(1296,plain,
! [SV98: $i,SV33: $i,SV77: $i] :
( ( ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV33 )
| ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV77 ) )
= $true )
| ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV77 )
= $false )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1252]) ).
thf(1297,plain,
! [SV140: $i,SV37: $i,SV136: $i] :
( ( ( ~ ( ~ ( in @ SV136 @ ( sK6_SY251 @ SV37 ) )
| ~ ( subset @ SV140 @ SV136 ) ) )
= $false )
| ( ( in @ SV140 @ ( sK6_SY251 @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1254]) ).
thf(1298,plain,
! [SV37: $i,SV129: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK30_SY421 @ SV129 @ SV37 ) @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SY434: $i] :
( ~ ( subset @ SY434 @ SV129 )
| ( in @ SY434 @ ( sK30_SY421 @ SV129 @ SV37 ) ) ) ) )
= $false )
| ( ( in @ SV129 @ ( sK6_SY251 @ SV37 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1255]) ).
thf(1299,plain,
! [SV37: $i,SV119: $i] :
( ( ( are_equipotent @ SV119 @ ( sK6_SY251 @ SV37 ) )
= $true )
| ( ( subset @ SV119 @ ( sK6_SY251 @ SV37 ) )
= $false )
| ( ( ~ ~ ( in @ SV119 @ ( sK6_SY251 @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1256]) ).
thf(1300,plain,
! [SV42: $i,SV108: $i,SV126: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV126 @ ( sK31_SY417 @ SV108 @ SV42 @ SV126 ) ) @ SV42 ) )
= $false )
| ( ( in @ SV126 @ SV108 )
= $false )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $false )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1257]) ).
thf(1301,plain,
! [SV108: $i,SV42: $i,SV145: $i,SV126: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV126 @ SV145 ) @ SV42 ) )
= $true )
| ( ( in @ SV126 @ SV108 )
= $true )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $false )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1258]) ).
thf(1302,plain,
! [SV108: $i,SV42: $i] :
( ( ( ~ ~ ! [SY420: $i] :
~ ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ SY420 ) @ SV42 ) )
= $false )
| ( ( in @ ( sK21_SY394 @ SV42 @ SV108 ) @ SV108 )
= $true )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1259]) ).
thf(1303,plain,
! [SV108: $i,SV42: $i] :
( ( ( in @ ( sK21_SY394 @ SV42 @ SV108 ) @ SV108 )
= $false )
| ( ( in @ ( sK21_SY394 @ SV42 @ SV108 ) @ SV108 )
= $true )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1259]) ).
thf(1304,plain,
! [SV143: $i,SV108: $i,SV42: $i] :
( ( ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ SV143 ) @ SV42 )
= $false )
| ( ( ~ ( ~ ~ ! [SY420: $i] :
~ ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ SY420 ) @ SV42 )
| ( in @ ( sK21_SY394 @ SV42 @ SV108 ) @ SV108 ) ) )
= $true )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1260]) ).
thf(1305,plain,
! [SV84: $i,SV101: $i,SV43: $i,SV124: $i] :
( ( ( in @ SV124 @ SV43 )
= $true )
| ( ( in @ SV124 @ SV101 )
= $false )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1261]) ).
thf(1306,plain,
! [SV43: $i,SV101: $i,SV84: $i,SV124: $i] :
( ( ( ~ ( in @ SV124 @ SV84 ) )
= $true )
| ( ( in @ SV124 @ SV101 )
= $false )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1262]) ).
thf(1307,plain,
! [SV101: $i,SV84: $i,SV43: $i,SV124: $i] :
( ( ( in @ SV124 @ SV43 )
= $false )
| ( ( ~ ~ ( in @ SV124 @ SV84 ) )
= $true )
| ( ( in @ SV124 @ SV101 )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1263]) ).
thf(1308,plain,
! [SV101: $i,SV43: $i,SV84: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
| ~ ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 ) ) )
= $true )
| ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV101 )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1264]) ).
thf(1309,plain,
! [SV101: $i,SV43: $i,SV84: $i] :
( ( ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 ) )
= $false )
| ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
| ~ ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 ) )
| ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV101 ) ) )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1266]) ).
thf(1310,plain,
! [SV137: $i,SV3: $i,SV133: $i] :
( ( ( ~ ( in @ SV133 @ ( sK5_SY160 @ SV3 ) )
| ~ ( subset @ SV137 @ SV133 ) )
= $true )
| ( ( in @ SV137 @ ( sK5_SY160 @ SV3 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1267]) ).
thf(1311,plain,
! [SV3: $i,SV114: $i] :
( ( ( ~ ( in @ SV114 @ ( sK5_SY160 @ SV3 ) ) )
= $false )
| ( ( subset @ SV114 @ ( sK5_SY160 @ SV3 ) )
= $false )
| ( ( are_equipotent @ SV114 @ ( sK5_SY160 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1268]) ).
thf(1312,plain,
! [SV4: $i,SV52: $i,SV115: $i] :
( ( ( ~ ( in @ SV115 @ ( sK27_SY401 @ SV52 @ SV4 @ SV115 ) ) )
= $false )
| ( ( in @ SV115 @ SV52 )
= $false )
| ( ( SV52
= ( union @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1269]) ).
thf(1313,plain,
! [SV115: $i,SV4: $i,SV52: $i] :
( ( ( ~ ( in @ ( sK27_SY401 @ SV52 @ SV4 @ SV115 ) @ SV4 ) )
= $false )
| ( ( in @ SV115 @ SV52 )
= $false )
| ( ( SV52
= ( union @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1269]) ).
thf(1314,plain,
! [SV52: $i,SV4: $i,SV138: $i,SV115: $i] :
( ( ( ~ ( in @ SV115 @ SV138 ) )
= $true )
| ( ( ~ ( in @ SV138 @ SV4 ) )
= $true )
| ( ( in @ SV115 @ SV52 )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1270]) ).
thf(1315,plain,
! [SV52: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ ( sK32_SY404 @ SV52 @ SV4 ) )
| ~ ( in @ ( sK32_SY404 @ SV52 @ SV4 ) @ SV4 ) ) )
= $false )
| ( ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV52 )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1271]) ).
thf(1316,plain,
! [SV134: $i,SV52: $i,SV4: $i] :
( ( ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV134 )
= $false )
| ( ( ~ ( in @ SV134 @ SV4 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY404: $i] :
~ ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SY404 )
| ~ ( in @ SY404 @ SV4 ) )
| ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV52 ) ) )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1272]) ).
thf(1317,plain,
! [SV125: $i,SV9: $i,SV105: $i] :
( ( ( in @ ( ordered_pair @ ( sK29_SY413 @ SV105 @ SV9 @ SV125 ) @ SV125 ) @ SV9 )
= $true )
| ( ( in @ SV125 @ SV105 )
= $false )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $false )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1273]) ).
thf(1318,plain,
! [SV105: $i,SV9: $i,SV125: $i,SV144: $i] :
( ( ( in @ ( ordered_pair @ SV144 @ SV125 ) @ SV9 )
= $false )
| ( ( in @ SV125 @ SV105 )
= $true )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $false )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1274]) ).
thf(1319,plain,
! [SV105: $i,SV9: $i] :
( ( ( ~ ! [SY416: $i] :
~ ( in @ ( ordered_pair @ SY416 @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 ) )
= $true )
| ( ( in @ ( sK20_SY388 @ SV9 @ SV105 ) @ SV105 )
= $true )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1275]) ).
thf(1320,plain,
! [SV141: $i,SV105: $i,SV9: $i] :
( ( ( ~ ~ ! [SY416: $i] :
~ ( in @ ( ordered_pair @ SY416 @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 )
| ( in @ ( sK20_SY388 @ SV9 @ SV105 ) @ SV105 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV141 @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 )
= $false )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1277]) ).
thf(1321,plain,
! [SV93: $i,SV18: $i,SV63: $i,SV120: $i] :
( ( ( in @ SV120 @ SV63 )
= $false )
| ( ( in @ SV120 @ SV18 )
= $false )
| ( ( in @ SV120 @ SV93 )
= $true )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1280]) ).
thf(1322,plain,
! [SV93: $i,SV18: $i,SV63: $i] :
( ( ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
| ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 ) )
= $false )
| ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV93 )
= $true )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1281]) ).
thf(1323,plain,
! [SV93: $i,SV18: $i,SV63: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
| ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 ) )
| ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV93 ) )
= $false )
| ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
= $false )
| ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 )
= $false )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1282]) ).
thf(1324,plain,
! [SV22: $i,SV67: $i,SV121: $i,SV95: $i] :
( ( ( ! [SY432: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK28_SY405 @ SV95 @ SV121 @ SV67 @ SV22 ) @ SV22 )
| ~ ( in @ SY432 @ SV67 ) )
| ( SV121
!= ( ordered_pair @ ( sK28_SY405 @ SV95 @ SV121 @ SV67 @ SV22 ) @ SY432 ) ) ) )
= $false )
| ( ( in @ SV121 @ SV95 )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1284]) ).
thf(1325,plain,
! [SV95: $i,SV121: $i,SV67: $i,SV22: $i,SV142: $i] :
( ( ( ! [SY433: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV142 @ SV22 )
| ~ ( in @ SY433 @ SV67 ) )
| ( SV121
!= ( ordered_pair @ SV142 @ SY433 ) ) ) )
= $true )
| ( ( in @ SV121 @ SV95 )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1285]) ).
thf(1326,plain,
! [SV95: $i,SV67: $i,SV22: $i] :
( ( ( ! [SY411: $i] :
~ ~ ! [SY412: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY411 @ SV22 )
| ~ ( in @ SY412 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SY411 @ SY412 ) ) ) )
= $false )
| ( ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1286]) ).
thf(1327,plain,
! [SV95: $i,SV67: $i,SV146: $i,SV22: $i,SV139: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV139 @ SV22 )
| ~ ( in @ SV146 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SV139 @ SV146 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY411: $i] :
~ ~ ! [SY412: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY411 @ SV22 )
| ~ ( in @ SY412 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SY411 @ SY412 ) ) )
| ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 ) ) )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1287]) ).
thf(1328,plain,
! [SV96: $i,SV23: $i,SV68: $i] :
( ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV23 )
= $true )
| ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV68 )
= $true )
| ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV96 )
= $true )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1288]) ).
thf(1329,plain,
! [SV96: $i,SV23: $i,SV68: $i] :
( ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV23 )
= $true )
| ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV68 )
= $true )
| ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV23 )
= $false )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1289]) ).
thf(1330,plain,
! [SV96: $i,SV23: $i,SV68: $i] :
( ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV23 )
= $true )
| ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV68 )
= $true )
| ( ( in @ ( sK17_SY371 @ SV68 @ SV23 @ SV96 ) @ SV68 )
= $false )
| ( ( SV96
= ( set_union2 @ SV23 @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1290]) ).
thf(1331,plain,
! [SV27: $i,SV72: $i,SV135: $i] :
( ( ( ~ ( in @ SV135 @ SV72 ) )
= $true )
| ( ( ! [SY426: $i] :
( ~ ( in @ SY426 @ SV27 )
| ( in @ SV135 @ SY426 ) ) )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $false )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1291]) ).
thf(1332,plain,
! [SV72: $i,SV135: $i,SV27: $i] :
( ( ( ~ ! [SY427: $i] :
( ~ ( in @ SY427 @ SV27 )
| ( in @ SV135 @ SY427 ) ) )
= $true )
| ( ( in @ SV135 @ SV72 )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $false )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1292]) ).
thf(1333,plain,
! [SV72: $i,SV27: $i] :
( ( ( ~ ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV72 ) )
= $false )
| ( ( ~ ( ~ ! [SY429: $i] :
( ~ ( in @ SY429 @ SV27 )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SY429 ) )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV72 ) ) )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1293]) ).
thf(1334,plain,
! [SV72: $i,SV27: $i] :
( ( ( ! [SY428: $i] :
( ~ ( in @ SY428 @ SV27 )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SY428 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY429: $i] :
( ~ ( in @ SY429 @ SV27 )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SY429 ) )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV72 ) ) )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1293]) ).
thf(1335,plain,
! [SV98: $i,SV33: $i,SV77: $i] :
( ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV33 )
= $true )
| ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV77 )
= $true )
| ( ( in @ ( sK18_SY373 @ SV77 @ SV33 @ SV98 ) @ SV98 )
= $true )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1294]) ).
thf(1336,plain,
! [SV98: $i,SV33: $i,SV77: $i] :
( ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV33 )
= $true )
| ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV77 )
= $true )
| ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV33 )
= $false )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1295]) ).
thf(1337,plain,
! [SV98: $i,SV33: $i,SV77: $i] :
( ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV33 )
= $true )
| ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV77 )
= $true )
| ( ( ( sK18_SY373 @ SV77 @ SV33 @ SV98 )
= SV77 )
= $false )
| ( ( SV98
= ( unordered_pair @ SV33 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1296]) ).
thf(1338,plain,
! [SV140: $i,SV37: $i,SV136: $i] :
( ( ( ~ ( in @ SV136 @ ( sK6_SY251 @ SV37 ) )
| ~ ( subset @ SV140 @ SV136 ) )
= $true )
| ( ( in @ SV140 @ ( sK6_SY251 @ SV37 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1297]) ).
thf(1339,plain,
! [SV37: $i,SV129: $i] :
( ( ( ~ ( ~ ( in @ ( sK30_SY421 @ SV129 @ SV37 ) @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SY434: $i] :
( ~ ( subset @ SY434 @ SV129 )
| ( in @ SY434 @ ( sK30_SY421 @ SV129 @ SV37 ) ) ) ) )
= $true )
| ( ( in @ SV129 @ ( sK6_SY251 @ SV37 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1298]) ).
thf(1340,plain,
! [SV37: $i,SV119: $i] :
( ( ( ~ ( in @ SV119 @ ( sK6_SY251 @ SV37 ) ) )
= $false )
| ( ( subset @ SV119 @ ( sK6_SY251 @ SV37 ) )
= $false )
| ( ( are_equipotent @ SV119 @ ( sK6_SY251 @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1299]) ).
thf(1341,plain,
! [SV42: $i,SV108: $i,SV126: $i] :
( ( ( in @ ( ordered_pair @ SV126 @ ( sK31_SY417 @ SV108 @ SV42 @ SV126 ) ) @ SV42 )
= $true )
| ( ( in @ SV126 @ SV108 )
= $false )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $false )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1300]) ).
thf(1342,plain,
! [SV108: $i,SV42: $i,SV145: $i,SV126: $i] :
( ( ( in @ ( ordered_pair @ SV126 @ SV145 ) @ SV42 )
= $false )
| ( ( in @ SV126 @ SV108 )
= $true )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $false )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1301]) ).
thf(1343,plain,
! [SV108: $i,SV42: $i] :
( ( ( ~ ! [SY420: $i] :
~ ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ SY420 ) @ SV42 ) )
= $true )
| ( ( in @ ( sK21_SY394 @ SV42 @ SV108 ) @ SV108 )
= $true )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1302]) ).
thf(1344,plain,
! [SV143: $i,SV108: $i,SV42: $i] :
( ( ( ~ ~ ! [SY420: $i] :
~ ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ SY420 ) @ SV42 )
| ( in @ ( sK21_SY394 @ SV42 @ SV108 ) @ SV108 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ SV143 ) @ SV42 )
= $false )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1304]) ).
thf(1345,plain,
! [SV43: $i,SV101: $i,SV84: $i,SV124: $i] :
( ( ( in @ SV124 @ SV84 )
= $false )
| ( ( in @ SV124 @ SV101 )
= $false )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1306]) ).
thf(1346,plain,
! [SV101: $i,SV43: $i,SV84: $i,SV124: $i] :
( ( ( ~ ( in @ SV124 @ SV84 ) )
= $false )
| ( ( in @ SV124 @ SV43 )
= $false )
| ( ( in @ SV124 @ SV101 )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1307]) ).
thf(1347,plain,
! [SV101: $i,SV43: $i,SV84: $i] :
( ( ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
| ~ ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 ) )
= $false )
| ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV101 )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1308]) ).
thf(1348,plain,
! [SV101: $i,SV43: $i,SV84: $i] :
( ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 )
= $true )
| ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
| ~ ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 ) )
| ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV101 ) ) )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1309]) ).
thf(1349,plain,
! [SV137: $i,SV3: $i,SV133: $i] :
( ( ( ~ ( in @ SV133 @ ( sK5_SY160 @ SV3 ) ) )
= $true )
| ( ( ~ ( subset @ SV137 @ SV133 ) )
= $true )
| ( ( in @ SV137 @ ( sK5_SY160 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1310]) ).
thf(1350,plain,
! [SV3: $i,SV114: $i] :
( ( ( in @ SV114 @ ( sK5_SY160 @ SV3 ) )
= $true )
| ( ( subset @ SV114 @ ( sK5_SY160 @ SV3 ) )
= $false )
| ( ( are_equipotent @ SV114 @ ( sK5_SY160 @ SV3 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1311]) ).
thf(1351,plain,
! [SV4: $i,SV52: $i,SV115: $i] :
( ( ( in @ SV115 @ ( sK27_SY401 @ SV52 @ SV4 @ SV115 ) )
= $true )
| ( ( in @ SV115 @ SV52 )
= $false )
| ( ( SV52
= ( union @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1312]) ).
thf(1352,plain,
! [SV115: $i,SV4: $i,SV52: $i] :
( ( ( in @ ( sK27_SY401 @ SV52 @ SV4 @ SV115 ) @ SV4 )
= $true )
| ( ( in @ SV115 @ SV52 )
= $false )
| ( ( SV52
= ( union @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1313]) ).
thf(1353,plain,
! [SV52: $i,SV4: $i,SV138: $i,SV115: $i] :
( ( ( in @ SV115 @ SV138 )
= $false )
| ( ( ~ ( in @ SV138 @ SV4 ) )
= $true )
| ( ( in @ SV115 @ SV52 )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1314]) ).
thf(1354,plain,
! [SV52: $i,SV4: $i] :
( ( ( ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ ( sK32_SY404 @ SV52 @ SV4 ) )
| ~ ( in @ ( sK32_SY404 @ SV52 @ SV4 ) @ SV4 ) ) )
= $true )
| ( ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV52 )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1315]) ).
thf(1355,plain,
! [SV52: $i,SV4: $i,SV134: $i] :
( ( ( in @ SV134 @ SV4 )
= $false )
| ( ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV134 )
= $false )
| ( ( ~ ( ~ ~ ! [SY404: $i] :
~ ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SY404 )
| ~ ( in @ SY404 @ SV4 ) )
| ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV52 ) ) )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1316]) ).
thf(1356,plain,
! [SV105: $i,SV9: $i] :
( ( ( ! [SY416: $i] :
~ ( in @ ( ordered_pair @ SY416 @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 ) )
= $false )
| ( ( in @ ( sK20_SY388 @ SV9 @ SV105 ) @ SV105 )
= $true )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1319]) ).
thf(1357,plain,
! [SV141: $i,SV105: $i,SV9: $i] :
( ( ( ~ ~ ! [SY416: $i] :
~ ( in @ ( ordered_pair @ SY416 @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV141 @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 )
= $false )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1320]) ).
thf(1358,plain,
! [SV141: $i,SV105: $i,SV9: $i] :
( ( ( in @ ( sK20_SY388 @ SV9 @ SV105 ) @ SV105 )
= $false )
| ( ( in @ ( ordered_pair @ SV141 @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 )
= $false )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1320]) ).
thf(1359,plain,
! [SV93: $i,SV18: $i,SV63: $i] :
( ( ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 ) )
= $false )
| ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV93 )
= $true )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1322]) ).
thf(1360,plain,
! [SV93: $i,SV18: $i,SV63: $i] :
( ( ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 ) )
= $false )
| ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV93 )
= $true )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1322]) ).
thf(1361,plain,
! [SV93: $i,SV18: $i,SV63: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
| ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 ) ) )
= $false )
| ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
= $false )
| ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 )
= $false )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1323]) ).
thf(1362,plain,
! [SV93: $i,SV18: $i,SV63: $i] :
( ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV93 )
= $false )
| ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
= $false )
| ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 )
= $false )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1323]) ).
thf(1363,plain,
! [SV22: $i,SV67: $i,SV121: $i,SV95: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK28_SY405 @ SV95 @ SV121 @ SV67 @ SV22 ) @ SV22 )
| ~ ( in @ ( sK33_SY432 @ SV22 @ SV67 @ SV121 @ SV95 ) @ SV67 ) )
| ( SV121
!= ( ordered_pair @ ( sK28_SY405 @ SV95 @ SV121 @ SV67 @ SV22 ) @ ( sK33_SY432 @ SV22 @ SV67 @ SV121 @ SV95 ) ) ) ) )
= $false )
| ( ( in @ SV121 @ SV95 )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1324]) ).
thf(1364,plain,
! [SV95: $i,SV121: $i,SV67: $i,SV147: $i,SV22: $i,SV142: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV142 @ SV22 )
| ~ ( in @ SV147 @ SV67 ) )
| ( SV121
!= ( ordered_pair @ SV142 @ SV147 ) ) ) )
= $true )
| ( ( in @ SV121 @ SV95 )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1325]) ).
thf(1365,plain,
! [SV22: $i,SV67: $i,SV95: $i] :
( ( ( ~ ~ ! [SY435: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK34_SY411 @ SV95 @ SV67 @ SV22 ) @ SV22 )
| ~ ( in @ SY435 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ ( sK34_SY411 @ SV95 @ SV67 @ SV22 ) @ SY435 ) ) ) )
= $false )
| ( ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1326]) ).
thf(1366,plain,
! [SV95: $i,SV67: $i,SV146: $i,SV22: $i,SV139: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV139 @ SV22 )
| ~ ( in @ SV146 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SV139 @ SV146 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY411: $i] :
~ ~ ! [SY412: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY411 @ SV22 )
| ~ ( in @ SY412 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SY411 @ SY412 ) ) )
| ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 ) ) )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1327]) ).
thf(1367,plain,
! [SV27: $i,SV72: $i,SV135: $i] :
( ( ( in @ SV135 @ SV72 )
= $false )
| ( ( ! [SY426: $i] :
( ~ ( in @ SY426 @ SV27 )
| ( in @ SV135 @ SY426 ) ) )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $false )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1331]) ).
thf(1368,plain,
! [SV72: $i,SV135: $i,SV27: $i] :
( ( ( ! [SY427: $i] :
( ~ ( in @ SY427 @ SV27 )
| ( in @ SV135 @ SY427 ) ) )
= $false )
| ( ( in @ SV135 @ SV72 )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $false )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1332]) ).
thf(1369,plain,
! [SV72: $i,SV27: $i] :
( ( ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV72 )
= $true )
| ( ( ~ ( ~ ! [SY429: $i] :
( ~ ( in @ SY429 @ SV27 )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SY429 ) )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV72 ) ) )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1333]) ).
thf(1370,plain,
! [SV27: $i,SV72: $i] :
( ( ( ~ ( in @ ( sK35_SY428 @ SV72 @ SV27 ) @ SV27 )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ ( sK35_SY428 @ SV72 @ SV27 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY429: $i] :
( ~ ( in @ SY429 @ SV27 )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SY429 ) )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV72 ) ) )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1334]) ).
thf(1371,plain,
! [SV140: $i,SV37: $i,SV136: $i] :
( ( ( ~ ( in @ SV136 @ ( sK6_SY251 @ SV37 ) ) )
= $true )
| ( ( ~ ( subset @ SV140 @ SV136 ) )
= $true )
| ( ( in @ SV140 @ ( sK6_SY251 @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1338]) ).
thf(1372,plain,
! [SV37: $i,SV129: $i] :
( ( ( ~ ( in @ ( sK30_SY421 @ SV129 @ SV37 ) @ ( sK6_SY251 @ SV37 ) )
| ~ ! [SY434: $i] :
( ~ ( subset @ SY434 @ SV129 )
| ( in @ SY434 @ ( sK30_SY421 @ SV129 @ SV37 ) ) ) )
= $false )
| ( ( in @ SV129 @ ( sK6_SY251 @ SV37 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1339]) ).
thf(1373,plain,
! [SV37: $i,SV119: $i] :
( ( ( in @ SV119 @ ( sK6_SY251 @ SV37 ) )
= $true )
| ( ( subset @ SV119 @ ( sK6_SY251 @ SV37 ) )
= $false )
| ( ( are_equipotent @ SV119 @ ( sK6_SY251 @ SV37 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1340]) ).
thf(1374,plain,
! [SV108: $i,SV42: $i] :
( ( ( ! [SY420: $i] :
~ ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ SY420 ) @ SV42 ) )
= $false )
| ( ( in @ ( sK21_SY394 @ SV42 @ SV108 ) @ SV108 )
= $true )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1343]) ).
thf(1375,plain,
! [SV143: $i,SV108: $i,SV42: $i] :
( ( ( ~ ~ ! [SY420: $i] :
~ ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ SY420 ) @ SV42 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ SV143 ) @ SV42 )
= $false )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1344]) ).
thf(1376,plain,
! [SV143: $i,SV108: $i,SV42: $i] :
( ( ( in @ ( sK21_SY394 @ SV42 @ SV108 ) @ SV108 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ SV143 ) @ SV42 )
= $false )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1344]) ).
thf(1377,plain,
! [SV101: $i,SV43: $i,SV84: $i,SV124: $i] :
( ( ( in @ SV124 @ SV84 )
= $true )
| ( ( in @ SV124 @ SV43 )
= $false )
| ( ( in @ SV124 @ SV101 )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1346]) ).
thf(1378,plain,
! [SV101: $i,SV43: $i,SV84: $i] :
( ( ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 ) )
= $false )
| ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV101 )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1347]) ).
thf(1379,plain,
! [SV101: $i,SV43: $i,SV84: $i] :
( ( ( ~ ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 ) )
= $false )
| ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV101 )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1347]) ).
thf(1380,plain,
! [SV101: $i,SV43: $i,SV84: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
| ~ ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 ) )
| ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV101 ) )
= $false )
| ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
= $false )
| ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1348]) ).
thf(1381,plain,
! [SV137: $i,SV3: $i,SV133: $i] :
( ( ( in @ SV133 @ ( sK5_SY160 @ SV3 ) )
= $false )
| ( ( ~ ( subset @ SV137 @ SV133 ) )
= $true )
| ( ( in @ SV137 @ ( sK5_SY160 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1349]) ).
thf(1382,plain,
! [SV52: $i,SV115: $i,SV4: $i,SV138: $i] :
( ( ( in @ SV138 @ SV4 )
= $false )
| ( ( in @ SV115 @ SV138 )
= $false )
| ( ( in @ SV115 @ SV52 )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1353]) ).
thf(1383,plain,
! [SV52: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ ( sK32_SY404 @ SV52 @ SV4 ) )
| ~ ( in @ ( sK32_SY404 @ SV52 @ SV4 ) @ SV4 ) )
= $false )
| ( ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV52 )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1354]) ).
thf(1384,plain,
! [SV134: $i,SV52: $i,SV4: $i] :
( ( ( ~ ~ ! [SY404: $i] :
~ ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SY404 )
| ~ ( in @ SY404 @ SV4 ) )
| ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV52 ) )
= $false )
| ( ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV134 )
= $false )
| ( ( in @ SV134 @ SV4 )
= $false )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1355]) ).
thf(1385,plain,
! [SV9: $i,SV105: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK36_SY416 @ SV105 @ SV9 ) @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 ) )
= $false )
| ( ( in @ ( sK20_SY388 @ SV9 @ SV105 ) @ SV105 )
= $true )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1356]) ).
thf(1386,plain,
! [SV141: $i,SV105: $i,SV9: $i] :
( ( ( ~ ! [SY416: $i] :
~ ( in @ ( ordered_pair @ SY416 @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV141 @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 )
= $false )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1357]) ).
thf(1387,plain,
! [SV93: $i,SV18: $i,SV63: $i] :
( ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
= $true )
| ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV93 )
= $true )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1359]) ).
thf(1388,plain,
! [SV93: $i,SV18: $i,SV63: $i] :
( ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 )
= $true )
| ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV93 )
= $true )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1360]) ).
thf(1389,plain,
! [SV93: $i,SV18: $i,SV63: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
| ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 ) ) )
= $true )
| ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
= $false )
| ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 )
= $false )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1361]) ).
thf(1390,plain,
! [SV22: $i,SV67: $i,SV121: $i,SV95: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK28_SY405 @ SV95 @ SV121 @ SV67 @ SV22 ) @ SV22 )
| ~ ( in @ ( sK33_SY432 @ SV22 @ SV67 @ SV121 @ SV95 ) @ SV67 ) )
| ( SV121
!= ( ordered_pair @ ( sK28_SY405 @ SV95 @ SV121 @ SV67 @ SV22 ) @ ( sK33_SY432 @ SV22 @ SV67 @ SV121 @ SV95 ) ) ) ) )
= $true )
| ( ( in @ SV121 @ SV95 )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1363]) ).
thf(1391,plain,
! [SV95: $i,SV121: $i,SV67: $i,SV147: $i,SV22: $i,SV142: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV142 @ SV22 )
| ~ ( in @ SV147 @ SV67 ) )
| ( SV121
!= ( ordered_pair @ SV142 @ SV147 ) ) ) )
= $false )
| ( ( in @ SV121 @ SV95 )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1364]) ).
thf(1392,plain,
! [SV22: $i,SV67: $i,SV95: $i] :
( ( ( ~ ! [SY435: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK34_SY411 @ SV95 @ SV67 @ SV22 ) @ SV22 )
| ~ ( in @ SY435 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ ( sK34_SY411 @ SV95 @ SV67 @ SV22 ) @ SY435 ) ) ) )
= $true )
| ( ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1365]) ).
thf(1393,plain,
! [SV95: $i,SV67: $i,SV146: $i,SV22: $i,SV139: $i] :
( ( ( ~ ~ ( ~ ( in @ SV139 @ SV22 )
| ~ ( in @ SV146 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SV139 @ SV146 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY411: $i] :
~ ~ ! [SY412: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY411 @ SV22 )
| ~ ( in @ SY412 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SY411 @ SY412 ) ) )
| ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 ) ) )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1366]) ).
thf(1394,plain,
! [SV72: $i,SV135: $i,SV27: $i,SV148: $i] :
( ( ( ~ ( in @ SV148 @ SV27 )
| ( in @ SV135 @ SV148 ) )
= $true )
| ( ( in @ SV135 @ SV72 )
= $false )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $false )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1367]) ).
thf(1395,plain,
! [SV27: $i,SV135: $i,SV72: $i] :
( ( ( ~ ( in @ ( sK37_SY427 @ SV72 @ SV135 @ SV27 ) @ SV27 )
| ( in @ SV135 @ ( sK37_SY427 @ SV72 @ SV135 @ SV27 ) ) )
= $false )
| ( ( in @ SV135 @ SV72 )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $false )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1368]) ).
thf(1396,plain,
! [SV72: $i,SV27: $i] :
( ( ( ~ ! [SY429: $i] :
( ~ ( in @ SY429 @ SV27 )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SY429 ) )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV72 ) )
= $false )
| ( ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV72 )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1369]) ).
thf(1397,plain,
! [SV27: $i,SV72: $i] :
( ( ( ~ ( in @ ( sK35_SY428 @ SV72 @ SV27 ) @ SV27 ) )
= $false )
| ( ( ~ ( ~ ! [SY429: $i] :
( ~ ( in @ SY429 @ SV27 )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SY429 ) )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV72 ) ) )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1370]) ).
thf(1398,plain,
! [SV72: $i,SV27: $i] :
( ( ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ ( sK35_SY428 @ SV72 @ SV27 ) )
= $false )
| ( ( ~ ( ~ ! [SY429: $i] :
( ~ ( in @ SY429 @ SV27 )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SY429 ) )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV72 ) ) )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1370]) ).
thf(1399,plain,
! [SV140: $i,SV37: $i,SV136: $i] :
( ( ( in @ SV136 @ ( sK6_SY251 @ SV37 ) )
= $false )
| ( ( ~ ( subset @ SV140 @ SV136 ) )
= $true )
| ( ( in @ SV140 @ ( sK6_SY251 @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1371]) ).
thf(1400,plain,
! [SV37: $i,SV129: $i] :
( ( ( ~ ( in @ ( sK30_SY421 @ SV129 @ SV37 ) @ ( sK6_SY251 @ SV37 ) ) )
= $false )
| ( ( in @ SV129 @ ( sK6_SY251 @ SV37 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1372]) ).
thf(1401,plain,
! [SV37: $i,SV129: $i] :
( ( ( ~ ! [SY434: $i] :
( ~ ( subset @ SY434 @ SV129 )
| ( in @ SY434 @ ( sK30_SY421 @ SV129 @ SV37 ) ) ) )
= $false )
| ( ( in @ SV129 @ ( sK6_SY251 @ SV37 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1372]) ).
thf(1402,plain,
! [SV108: $i,SV42: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ ( sK38_SY420 @ SV108 @ SV42 ) ) @ SV42 ) )
= $false )
| ( ( in @ ( sK21_SY394 @ SV42 @ SV108 ) @ SV108 )
= $true )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1374]) ).
thf(1403,plain,
! [SV143: $i,SV108: $i,SV42: $i] :
( ( ( ~ ! [SY420: $i] :
~ ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ SY420 ) @ SV42 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ SV143 ) @ SV42 )
= $false )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1375]) ).
thf(1404,plain,
! [SV101: $i,SV43: $i,SV84: $i] :
( ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
= $true )
| ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV101 )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1378]) ).
thf(1405,plain,
! [SV101: $i,SV43: $i,SV84: $i] :
( ( ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 ) )
= $true )
| ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV101 )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1379]) ).
thf(1406,plain,
! [SV101: $i,SV43: $i,SV84: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
| ~ ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 ) ) )
= $false )
| ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
= $false )
| ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1380]) ).
thf(1407,plain,
! [SV101: $i,SV43: $i,SV84: $i] :
( ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV101 )
= $false )
| ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
= $false )
| ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1380]) ).
thf(1408,plain,
! [SV3: $i,SV133: $i,SV137: $i] :
( ( ( subset @ SV137 @ SV133 )
= $false )
| ( ( in @ SV133 @ ( sK5_SY160 @ SV3 ) )
= $false )
| ( ( in @ SV137 @ ( sK5_SY160 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1381]) ).
thf(1409,plain,
! [SV52: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ ( sK32_SY404 @ SV52 @ SV4 ) ) )
= $false )
| ( ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV52 )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1383]) ).
thf(1410,plain,
! [SV4: $i,SV52: $i] :
( ( ( ~ ( in @ ( sK32_SY404 @ SV52 @ SV4 ) @ SV4 ) )
= $false )
| ( ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV52 )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1383]) ).
thf(1411,plain,
! [SV134: $i,SV52: $i,SV4: $i] :
( ( ( ~ ~ ! [SY404: $i] :
~ ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SY404 )
| ~ ( in @ SY404 @ SV4 ) ) )
= $false )
| ( ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV134 )
= $false )
| ( ( in @ SV134 @ SV4 )
= $false )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1384]) ).
thf(1412,plain,
! [SV134: $i,SV52: $i,SV4: $i] :
( ( ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV52 )
= $false )
| ( ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV134 )
= $false )
| ( ( in @ SV134 @ SV4 )
= $false )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1384]) ).
thf(1413,plain,
! [SV9: $i,SV105: $i] :
( ( ( in @ ( ordered_pair @ ( sK36_SY416 @ SV105 @ SV9 ) @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 )
= $true )
| ( ( in @ ( sK20_SY388 @ SV9 @ SV105 ) @ SV105 )
= $true )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1385]) ).
thf(1414,plain,
! [SV141: $i,SV105: $i,SV9: $i] :
( ( ( ! [SY416: $i] :
~ ( in @ ( ordered_pair @ SY416 @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV141 @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 )
= $false )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1386]) ).
thf(1415,plain,
! [SV93: $i,SV18: $i,SV63: $i] :
( ( ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
| ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 ) )
= $false )
| ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
= $false )
| ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 )
= $false )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1389]) ).
thf(1416,plain,
! [SV22: $i,SV67: $i,SV121: $i,SV95: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK28_SY405 @ SV95 @ SV121 @ SV67 @ SV22 ) @ SV22 )
| ~ ( in @ ( sK33_SY432 @ SV22 @ SV67 @ SV121 @ SV95 ) @ SV67 ) )
| ( SV121
!= ( ordered_pair @ ( sK28_SY405 @ SV95 @ SV121 @ SV67 @ SV22 ) @ ( sK33_SY432 @ SV22 @ SV67 @ SV121 @ SV95 ) ) ) )
= $false )
| ( ( in @ SV121 @ SV95 )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1390]) ).
thf(1417,plain,
! [SV95: $i,SV121: $i,SV67: $i,SV147: $i,SV22: $i,SV142: $i] :
( ( ( ~ ~ ( ~ ( in @ SV142 @ SV22 )
| ~ ( in @ SV147 @ SV67 ) )
| ( SV121
!= ( ordered_pair @ SV142 @ SV147 ) ) )
= $true )
| ( ( in @ SV121 @ SV95 )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1391]) ).
thf(1418,plain,
! [SV22: $i,SV67: $i,SV95: $i] :
( ( ( ! [SY435: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK34_SY411 @ SV95 @ SV67 @ SV22 ) @ SV22 )
| ~ ( in @ SY435 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ ( sK34_SY411 @ SV95 @ SV67 @ SV22 ) @ SY435 ) ) ) )
= $false )
| ( ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1392]) ).
thf(1419,plain,
! [SV95: $i,SV67: $i,SV146: $i,SV22: $i,SV139: $i] :
( ( ( ~ ~ ( ~ ( in @ SV139 @ SV22 )
| ~ ( in @ SV146 @ SV67 ) ) )
= $true )
| ( ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SV139 @ SV146 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY411: $i] :
~ ~ ! [SY412: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY411 @ SV22 )
| ~ ( in @ SY412 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SY411 @ SY412 ) ) )
| ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 ) ) )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1393]) ).
thf(1420,plain,
! [SV72: $i,SV135: $i,SV27: $i,SV148: $i] :
( ( ( ~ ( in @ SV148 @ SV27 ) )
= $true )
| ( ( in @ SV135 @ SV148 )
= $true )
| ( ( in @ SV135 @ SV72 )
= $false )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $false )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1394]) ).
thf(1421,plain,
! [SV27: $i,SV135: $i,SV72: $i] :
( ( ( ~ ( in @ ( sK37_SY427 @ SV72 @ SV135 @ SV27 ) @ SV27 ) )
= $false )
| ( ( in @ SV135 @ SV72 )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $false )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1395]) ).
thf(1422,plain,
! [SV27: $i,SV72: $i,SV135: $i] :
( ( ( in @ SV135 @ ( sK37_SY427 @ SV72 @ SV135 @ SV27 ) )
= $false )
| ( ( in @ SV135 @ SV72 )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $false )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1395]) ).
thf(1423,plain,
! [SV72: $i,SV27: $i] :
( ( ( ~ ! [SY429: $i] :
( ~ ( in @ SY429 @ SV27 )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SY429 ) ) )
= $false )
| ( ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV72 )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1396]) ).
thf(1424,plain,
! [SV72: $i,SV27: $i] :
( ( ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV72 )
= $false )
| ( ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV72 )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1396]) ).
thf(1425,plain,
! [SV27: $i,SV72: $i] :
( ( ( in @ ( sK35_SY428 @ SV72 @ SV27 ) @ SV27 )
= $true )
| ( ( ~ ( ~ ! [SY429: $i] :
( ~ ( in @ SY429 @ SV27 )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SY429 ) )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV72 ) ) )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1397]) ).
thf(1426,plain,
! [SV72: $i,SV27: $i] :
( ( ( ~ ! [SY429: $i] :
( ~ ( in @ SY429 @ SV27 )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SY429 ) )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV72 ) )
= $false )
| ( ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ ( sK35_SY428 @ SV72 @ SV27 ) )
= $false )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1398]) ).
thf(1427,plain,
! [SV37: $i,SV136: $i,SV140: $i] :
( ( ( subset @ SV140 @ SV136 )
= $false )
| ( ( in @ SV136 @ ( sK6_SY251 @ SV37 ) )
= $false )
| ( ( in @ SV140 @ ( sK6_SY251 @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1399]) ).
thf(1428,plain,
! [SV37: $i,SV129: $i] :
( ( ( in @ ( sK30_SY421 @ SV129 @ SV37 ) @ ( sK6_SY251 @ SV37 ) )
= $true )
| ( ( in @ SV129 @ ( sK6_SY251 @ SV37 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1400]) ).
thf(1429,plain,
! [SV37: $i,SV129: $i] :
( ( ( ! [SY434: $i] :
( ~ ( subset @ SY434 @ SV129 )
| ( in @ SY434 @ ( sK30_SY421 @ SV129 @ SV37 ) ) ) )
= $true )
| ( ( in @ SV129 @ ( sK6_SY251 @ SV37 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1401]) ).
thf(1430,plain,
! [SV108: $i,SV42: $i] :
( ( ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ ( sK38_SY420 @ SV108 @ SV42 ) ) @ SV42 )
= $true )
| ( ( in @ ( sK21_SY394 @ SV42 @ SV108 ) @ SV108 )
= $true )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1402]) ).
thf(1431,plain,
! [SV143: $i,SV108: $i,SV42: $i] :
( ( ( ! [SY420: $i] :
~ ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ SY420 ) @ SV42 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ SV143 ) @ SV42 )
= $false )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1403]) ).
thf(1432,plain,
! [SV101: $i,SV43: $i,SV84: $i] :
( ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 )
= $false )
| ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV101 )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1405]) ).
thf(1433,plain,
! [SV101: $i,SV43: $i,SV84: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
| ~ ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 ) ) )
= $true )
| ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
= $false )
| ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1406]) ).
thf(1434,plain,
! [SV52: $i,SV4: $i] :
( ( ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ ( sK32_SY404 @ SV52 @ SV4 ) )
= $true )
| ( ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV52 )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1409]) ).
thf(1435,plain,
! [SV4: $i,SV52: $i] :
( ( ( in @ ( sK32_SY404 @ SV52 @ SV4 ) @ SV4 )
= $true )
| ( ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV52 )
= $true )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1410]) ).
thf(1436,plain,
! [SV134: $i,SV52: $i,SV4: $i] :
( ( ( ~ ! [SY404: $i] :
~ ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SY404 )
| ~ ( in @ SY404 @ SV4 ) ) )
= $true )
| ( ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV134 )
= $false )
| ( ( in @ SV134 @ SV4 )
= $false )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1411]) ).
thf(1437,plain,
! [SV9: $i,SV105: $i,SV141: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK39_SY416 @ SV141 @ SV105 @ SV9 ) @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV141 @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 )
= $false )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1414]) ).
thf(1438,plain,
! [SV93: $i,SV18: $i,SV63: $i] :
( ( ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 ) )
= $false )
| ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
= $false )
| ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 )
= $false )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1415]) ).
thf(1439,plain,
! [SV93: $i,SV18: $i,SV63: $i] :
( ( ( ~ ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 ) )
= $false )
| ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
= $false )
| ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 )
= $false )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1415]) ).
thf(1440,plain,
! [SV22: $i,SV67: $i,SV121: $i,SV95: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK28_SY405 @ SV95 @ SV121 @ SV67 @ SV22 ) @ SV22 )
| ~ ( in @ ( sK33_SY432 @ SV22 @ SV67 @ SV121 @ SV95 ) @ SV67 ) ) )
= $false )
| ( ( in @ SV121 @ SV95 )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1416]) ).
thf(1441,plain,
! [SV22: $i,SV67: $i,SV95: $i,SV121: $i] :
( ( ( SV121
!= ( ordered_pair @ ( sK28_SY405 @ SV95 @ SV121 @ SV67 @ SV22 ) @ ( sK33_SY432 @ SV22 @ SV67 @ SV121 @ SV95 ) ) )
= $false )
| ( ( in @ SV121 @ SV95 )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1416]) ).
thf(1442,plain,
! [SV95: $i,SV121: $i,SV67: $i,SV147: $i,SV22: $i,SV142: $i] :
( ( ( ~ ~ ( ~ ( in @ SV142 @ SV22 )
| ~ ( in @ SV147 @ SV67 ) ) )
= $true )
| ( ( SV121
!= ( ordered_pair @ SV142 @ SV147 ) )
= $true )
| ( ( in @ SV121 @ SV95 )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1417]) ).
thf(1443,plain,
! [SV22: $i,SV67: $i,SV95: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK34_SY411 @ SV95 @ SV67 @ SV22 ) @ SV22 )
| ~ ( in @ ( sK40_SY435 @ SV22 @ SV67 @ SV95 ) @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ ( sK34_SY411 @ SV95 @ SV67 @ SV22 ) @ ( sK40_SY435 @ SV22 @ SV67 @ SV95 ) ) ) ) )
= $false )
| ( ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1418]) ).
thf(1444,plain,
! [SV95: $i,SV67: $i,SV146: $i,SV22: $i,SV139: $i] :
( ( ( ~ ( ~ ( in @ SV139 @ SV22 )
| ~ ( in @ SV146 @ SV67 ) ) )
= $false )
| ( ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SV139 @ SV146 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY411: $i] :
~ ~ ! [SY412: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY411 @ SV22 )
| ~ ( in @ SY412 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SY411 @ SY412 ) ) )
| ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 ) ) )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1419]) ).
thf(1445,plain,
! [SV72: $i,SV135: $i,SV27: $i,SV148: $i] :
( ( ( in @ SV148 @ SV27 )
= $false )
| ( ( in @ SV135 @ SV148 )
= $true )
| ( ( in @ SV135 @ SV72 )
= $false )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $false )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1420]) ).
thf(1446,plain,
! [SV27: $i,SV135: $i,SV72: $i] :
( ( ( in @ ( sK37_SY427 @ SV72 @ SV135 @ SV27 ) @ SV27 )
= $true )
| ( ( in @ SV135 @ SV72 )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $false )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1421]) ).
thf(1447,plain,
! [SV72: $i,SV27: $i] :
( ( ( ! [SY429: $i] :
( ~ ( in @ SY429 @ SV27 )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SY429 ) ) )
= $true )
| ( ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV72 )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1423]) ).
thf(1448,plain,
! [SV72: $i,SV27: $i] :
( ( ( ~ ! [SY429: $i] :
( ~ ( in @ SY429 @ SV27 )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SY429 ) )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV72 ) )
= $false )
| ( ( in @ ( sK35_SY428 @ SV72 @ SV27 ) @ SV27 )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1425]) ).
thf(1449,plain,
! [SV72: $i,SV27: $i] :
( ( ( ~ ! [SY429: $i] :
( ~ ( in @ SY429 @ SV27 )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SY429 ) ) )
= $false )
| ( ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ ( sK35_SY428 @ SV72 @ SV27 ) )
= $false )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1426]) ).
thf(1450,plain,
! [SV72: $i,SV27: $i] :
( ( ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV72 )
= $false )
| ( ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ ( sK35_SY428 @ SV72 @ SV27 ) )
= $false )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1426]) ).
thf(1451,plain,
! [SV37: $i,SV129: $i,SV149: $i] :
( ( ( ~ ( subset @ SV149 @ SV129 )
| ( in @ SV149 @ ( sK30_SY421 @ SV129 @ SV37 ) ) )
= $true )
| ( ( in @ SV129 @ ( sK6_SY251 @ SV37 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1429]) ).
thf(1452,plain,
! [SV143: $i,SV108: $i,SV42: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ ( sK41_SY420 @ SV143 @ SV108 @ SV42 ) ) @ SV42 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ SV143 ) @ SV42 )
= $false )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1431]) ).
thf(1453,plain,
! [SV101: $i,SV43: $i,SV84: $i] :
( ( ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
| ~ ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 ) )
= $false )
| ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
= $false )
| ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1433]) ).
thf(1454,plain,
! [SV134: $i,SV52: $i,SV4: $i] :
( ( ( ! [SY404: $i] :
~ ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SY404 )
| ~ ( in @ SY404 @ SV4 ) ) )
= $false )
| ( ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV134 )
= $false )
| ( ( in @ SV134 @ SV4 )
= $false )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1436]) ).
thf(1455,plain,
! [SV9: $i,SV105: $i,SV141: $i] :
( ( ( in @ ( ordered_pair @ ( sK39_SY416 @ SV141 @ SV105 @ SV9 ) @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 )
= $true )
| ( ( in @ ( ordered_pair @ SV141 @ ( sK20_SY388 @ SV9 @ SV105 ) ) @ SV9 )
= $false )
| ( ( SV105
= ( relation_rng @ SV9 ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1437]) ).
thf(1456,plain,
! [SV93: $i,SV18: $i,SV63: $i] :
( ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
= $true )
| ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
= $false )
| ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 )
= $false )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1438]) ).
thf(1457,plain,
! [SV93: $i,SV18: $i,SV63: $i] :
( ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 )
= $true )
| ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV18 )
= $false )
| ( ( in @ ( sK15_SY359 @ SV63 @ SV18 @ SV93 ) @ SV63 )
= $false )
| ( ( SV93
= ( set_intersection2 @ SV18 @ SV63 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1439]) ).
thf(1458,plain,
! [SV22: $i,SV67: $i,SV121: $i,SV95: $i] :
( ( ( ~ ( ~ ( in @ ( sK28_SY405 @ SV95 @ SV121 @ SV67 @ SV22 ) @ SV22 )
| ~ ( in @ ( sK33_SY432 @ SV22 @ SV67 @ SV121 @ SV95 ) @ SV67 ) ) )
= $true )
| ( ( in @ SV121 @ SV95 )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1440]) ).
thf(1459,plain,
! [SV22: $i,SV67: $i,SV95: $i,SV121: $i] :
( ( ( SV121
= ( ordered_pair @ ( sK28_SY405 @ SV95 @ SV121 @ SV67 @ SV22 ) @ ( sK33_SY432 @ SV22 @ SV67 @ SV121 @ SV95 ) ) )
= $true )
| ( ( in @ SV121 @ SV95 )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1441]) ).
thf(1460,plain,
! [SV95: $i,SV121: $i,SV67: $i,SV147: $i,SV22: $i,SV142: $i] :
( ( ( ~ ( ~ ( in @ SV142 @ SV22 )
| ~ ( in @ SV147 @ SV67 ) ) )
= $false )
| ( ( SV121
!= ( ordered_pair @ SV142 @ SV147 ) )
= $true )
| ( ( in @ SV121 @ SV95 )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1442]) ).
thf(1461,plain,
! [SV22: $i,SV67: $i,SV95: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK34_SY411 @ SV95 @ SV67 @ SV22 ) @ SV22 )
| ~ ( in @ ( sK40_SY435 @ SV22 @ SV67 @ SV95 ) @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ ( sK34_SY411 @ SV95 @ SV67 @ SV22 ) @ ( sK40_SY435 @ SV22 @ SV67 @ SV95 ) ) ) ) )
= $true )
| ( ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1443]) ).
thf(1462,plain,
! [SV95: $i,SV67: $i,SV146: $i,SV22: $i,SV139: $i] :
( ( ( ~ ( in @ SV139 @ SV22 )
| ~ ( in @ SV146 @ SV67 ) )
= $true )
| ( ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SV139 @ SV146 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY411: $i] :
~ ~ ! [SY412: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY411 @ SV22 )
| ~ ( in @ SY412 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SY411 @ SY412 ) ) )
| ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 ) ) )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1444]) ).
thf(1463,plain,
! [SV72: $i,SV27: $i,SV150: $i] :
( ( ( ~ ( in @ SV150 @ SV27 )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV150 ) )
= $true )
| ( ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV72 )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1447]) ).
thf(1464,plain,
! [SV72: $i,SV27: $i] :
( ( ( ~ ! [SY429: $i] :
( ~ ( in @ SY429 @ SV27 )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SY429 ) ) )
= $false )
| ( ( in @ ( sK35_SY428 @ SV72 @ SV27 ) @ SV27 )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1448]) ).
thf(1465,plain,
! [SV72: $i,SV27: $i] :
( ( ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV72 )
= $false )
| ( ( in @ ( sK35_SY428 @ SV72 @ SV27 ) @ SV27 )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1448]) ).
thf(1466,plain,
! [SV72: $i,SV27: $i] :
( ( ( ! [SY429: $i] :
( ~ ( in @ SY429 @ SV27 )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SY429 ) ) )
= $true )
| ( ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ ( sK35_SY428 @ SV72 @ SV27 ) )
= $false )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1449]) ).
thf(1467,plain,
! [SV37: $i,SV129: $i,SV149: $i] :
( ( ( ~ ( subset @ SV149 @ SV129 ) )
= $true )
| ( ( in @ SV149 @ ( sK30_SY421 @ SV129 @ SV37 ) )
= $true )
| ( ( in @ SV129 @ ( sK6_SY251 @ SV37 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1451]) ).
thf(1468,plain,
! [SV143: $i,SV108: $i,SV42: $i] :
( ( ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ ( sK41_SY420 @ SV143 @ SV108 @ SV42 ) ) @ SV42 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK21_SY394 @ SV42 @ SV108 ) @ SV143 ) @ SV42 )
= $false )
| ( ( SV108
= ( relation_dom @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1452]) ).
thf(1469,plain,
! [SV101: $i,SV43: $i,SV84: $i] :
( ( ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 ) )
= $false )
| ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
= $false )
| ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1453]) ).
thf(1470,plain,
! [SV101: $i,SV43: $i,SV84: $i] :
( ( ( ~ ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 ) )
= $false )
| ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
= $false )
| ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1453]) ).
thf(1471,plain,
! [SV134: $i,SV52: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ ( sK42_SY404 @ SV134 @ SV52 @ SV4 ) )
| ~ ( in @ ( sK42_SY404 @ SV134 @ SV52 @ SV4 ) @ SV4 ) ) )
= $false )
| ( ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV134 )
= $false )
| ( ( in @ SV134 @ SV4 )
= $false )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1454]) ).
thf(1472,plain,
! [SV22: $i,SV67: $i,SV121: $i,SV95: $i] :
( ( ( ~ ( in @ ( sK28_SY405 @ SV95 @ SV121 @ SV67 @ SV22 ) @ SV22 )
| ~ ( in @ ( sK33_SY432 @ SV22 @ SV67 @ SV121 @ SV95 ) @ SV67 ) )
= $false )
| ( ( in @ SV121 @ SV95 )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1458]) ).
thf(1473,plain,
! [SV95: $i,SV121: $i,SV67: $i,SV147: $i,SV22: $i,SV142: $i] :
( ( ( ~ ( in @ SV142 @ SV22 )
| ~ ( in @ SV147 @ SV67 ) )
= $true )
| ( ( SV121
!= ( ordered_pair @ SV142 @ SV147 ) )
= $true )
| ( ( in @ SV121 @ SV95 )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1460]) ).
thf(1474,plain,
! [SV22: $i,SV67: $i,SV95: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK34_SY411 @ SV95 @ SV67 @ SV22 ) @ SV22 )
| ~ ( in @ ( sK40_SY435 @ SV22 @ SV67 @ SV95 ) @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ ( sK34_SY411 @ SV95 @ SV67 @ SV22 ) @ ( sK40_SY435 @ SV22 @ SV67 @ SV95 ) ) ) )
= $false )
| ( ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1461]) ).
thf(1475,plain,
! [SV95: $i,SV67: $i,SV146: $i,SV22: $i,SV139: $i] :
( ( ( ~ ( in @ SV139 @ SV22 ) )
= $true )
| ( ( ~ ( in @ SV146 @ SV67 ) )
= $true )
| ( ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SV139 @ SV146 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY411: $i] :
~ ~ ! [SY412: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY411 @ SV22 )
| ~ ( in @ SY412 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SY411 @ SY412 ) ) )
| ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 ) ) )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1462]) ).
thf(1476,plain,
! [SV72: $i,SV27: $i,SV150: $i] :
( ( ( ~ ( in @ SV150 @ SV27 ) )
= $true )
| ( ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV150 )
= $true )
| ( ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV72 )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1463]) ).
thf(1477,plain,
! [SV72: $i,SV27: $i] :
( ( ( ! [SY429: $i] :
( ~ ( in @ SY429 @ SV27 )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SY429 ) ) )
= $true )
| ( ( in @ ( sK35_SY428 @ SV72 @ SV27 ) @ SV27 )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1464]) ).
thf(1478,plain,
! [SV72: $i,SV27: $i,SV151: $i] :
( ( ( ~ ( in @ SV151 @ SV27 )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV151 ) )
= $true )
| ( ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ ( sK35_SY428 @ SV72 @ SV27 ) )
= $false )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1466]) ).
thf(1479,plain,
! [SV37: $i,SV129: $i,SV149: $i] :
( ( ( subset @ SV149 @ SV129 )
= $false )
| ( ( in @ SV149 @ ( sK30_SY421 @ SV129 @ SV37 ) )
= $true )
| ( ( in @ SV129 @ ( sK6_SY251 @ SV37 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1467]) ).
thf(1480,plain,
! [SV101: $i,SV43: $i,SV84: $i] :
( ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
= $true )
| ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
= $false )
| ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1469]) ).
thf(1481,plain,
! [SV101: $i,SV43: $i,SV84: $i] :
( ( ( ~ ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 ) )
= $true )
| ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
= $false )
| ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1470]) ).
thf(1482,plain,
! [SV134: $i,SV52: $i,SV4: $i] :
( ( ( ~ ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ ( sK42_SY404 @ SV134 @ SV52 @ SV4 ) )
| ~ ( in @ ( sK42_SY404 @ SV134 @ SV52 @ SV4 ) @ SV4 ) ) )
= $true )
| ( ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV134 )
= $false )
| ( ( in @ SV134 @ SV4 )
= $false )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1471]) ).
thf(1483,plain,
! [SV22: $i,SV67: $i,SV121: $i,SV95: $i] :
( ( ( ~ ( in @ ( sK28_SY405 @ SV95 @ SV121 @ SV67 @ SV22 ) @ SV22 ) )
= $false )
| ( ( in @ SV121 @ SV95 )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1472]) ).
thf(1484,plain,
! [SV95: $i,SV121: $i,SV67: $i,SV22: $i] :
( ( ( ~ ( in @ ( sK33_SY432 @ SV22 @ SV67 @ SV121 @ SV95 ) @ SV67 ) )
= $false )
| ( ( in @ SV121 @ SV95 )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1472]) ).
thf(1485,plain,
! [SV95: $i,SV121: $i,SV67: $i,SV147: $i,SV22: $i,SV142: $i] :
( ( ( ~ ( in @ SV142 @ SV22 ) )
= $true )
| ( ( ~ ( in @ SV147 @ SV67 ) )
= $true )
| ( ( SV121
!= ( ordered_pair @ SV142 @ SV147 ) )
= $true )
| ( ( in @ SV121 @ SV95 )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1473]) ).
thf(1486,plain,
! [SV22: $i,SV67: $i,SV95: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK34_SY411 @ SV95 @ SV67 @ SV22 ) @ SV22 )
| ~ ( in @ ( sK40_SY435 @ SV22 @ SV67 @ SV95 ) @ SV67 ) ) )
= $false )
| ( ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1474]) ).
thf(1487,plain,
! [SV95: $i,SV22: $i,SV67: $i] :
( ( ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ ( sK34_SY411 @ SV95 @ SV67 @ SV22 ) @ ( sK40_SY435 @ SV22 @ SV67 @ SV95 ) ) )
= $false )
| ( ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1474]) ).
thf(1488,plain,
! [SV95: $i,SV67: $i,SV146: $i,SV22: $i,SV139: $i] :
( ( ( in @ SV139 @ SV22 )
= $false )
| ( ( ~ ( in @ SV146 @ SV67 ) )
= $true )
| ( ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SV139 @ SV146 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY411: $i] :
~ ~ ! [SY412: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY411 @ SV22 )
| ~ ( in @ SY412 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SY411 @ SY412 ) ) )
| ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 ) ) )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1475]) ).
thf(1489,plain,
! [SV72: $i,SV27: $i,SV150: $i] :
( ( ( in @ SV150 @ SV27 )
= $false )
| ( ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV150 )
= $true )
| ( ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV72 )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1476]) ).
thf(1490,plain,
! [SV72: $i,SV27: $i,SV152: $i] :
( ( ( ~ ( in @ SV152 @ SV27 )
| ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV152 ) )
= $true )
| ( ( in @ ( sK35_SY428 @ SV72 @ SV27 ) @ SV27 )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1477]) ).
thf(1491,plain,
! [SV72: $i,SV27: $i,SV151: $i] :
( ( ( ~ ( in @ SV151 @ SV27 ) )
= $true )
| ( ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV151 )
= $true )
| ( ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ ( sK35_SY428 @ SV72 @ SV27 ) )
= $false )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1478]) ).
thf(1492,plain,
! [SV101: $i,SV43: $i,SV84: $i] :
( ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 )
= $false )
| ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV43 )
= $false )
| ( ( in @ ( sK19_SY382 @ SV84 @ SV43 @ SV101 ) @ SV84 )
= $true )
| ( ( SV101
= ( set_difference @ SV43 @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1481]) ).
thf(1493,plain,
! [SV134: $i,SV52: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ ( sK42_SY404 @ SV134 @ SV52 @ SV4 ) )
| ~ ( in @ ( sK42_SY404 @ SV134 @ SV52 @ SV4 ) @ SV4 ) )
= $false )
| ( ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV134 )
= $false )
| ( ( in @ SV134 @ SV4 )
= $false )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1482]) ).
thf(1494,plain,
! [SV22: $i,SV67: $i,SV121: $i,SV95: $i] :
( ( ( in @ ( sK28_SY405 @ SV95 @ SV121 @ SV67 @ SV22 ) @ SV22 )
= $true )
| ( ( in @ SV121 @ SV95 )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1483]) ).
thf(1495,plain,
! [SV95: $i,SV121: $i,SV67: $i,SV22: $i] :
( ( ( in @ ( sK33_SY432 @ SV22 @ SV67 @ SV121 @ SV95 ) @ SV67 )
= $true )
| ( ( in @ SV121 @ SV95 )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1484]) ).
thf(1496,plain,
! [SV95: $i,SV121: $i,SV67: $i,SV147: $i,SV22: $i,SV142: $i] :
( ( ( in @ SV142 @ SV22 )
= $false )
| ( ( ~ ( in @ SV147 @ SV67 ) )
= $true )
| ( ( SV121
!= ( ordered_pair @ SV142 @ SV147 ) )
= $true )
| ( ( in @ SV121 @ SV95 )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1485]) ).
thf(1497,plain,
! [SV22: $i,SV67: $i,SV95: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_SY411 @ SV95 @ SV67 @ SV22 ) @ SV22 )
| ~ ( in @ ( sK40_SY435 @ SV22 @ SV67 @ SV95 ) @ SV67 ) ) )
= $true )
| ( ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1486]) ).
thf(1498,plain,
! [SV95: $i,SV22: $i,SV67: $i] :
( ( ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
= ( ordered_pair @ ( sK34_SY411 @ SV95 @ SV67 @ SV22 ) @ ( sK40_SY435 @ SV22 @ SV67 @ SV95 ) ) )
= $true )
| ( ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1487]) ).
thf(1499,plain,
! [SV95: $i,SV22: $i,SV139: $i,SV67: $i,SV146: $i] :
( ( ( in @ SV146 @ SV67 )
= $false )
| ( ( in @ SV139 @ SV22 )
= $false )
| ( ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SV139 @ SV146 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY411: $i] :
~ ~ ! [SY412: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY411 @ SV22 )
| ~ ( in @ SY412 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SY411 @ SY412 ) ) )
| ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 ) ) )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1488]) ).
thf(1500,plain,
! [SV72: $i,SV27: $i,SV152: $i] :
( ( ( ~ ( in @ SV152 @ SV27 ) )
= $true )
| ( ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV152 )
= $true )
| ( ( in @ ( sK35_SY428 @ SV72 @ SV27 ) @ SV27 )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1490]) ).
thf(1501,plain,
! [SV72: $i,SV27: $i,SV151: $i] :
( ( ( in @ SV151 @ SV27 )
= $false )
| ( ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV151 )
= $true )
| ( ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ ( sK35_SY428 @ SV72 @ SV27 ) )
= $false )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1491]) ).
thf(1502,plain,
! [SV134: $i,SV52: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ ( sK42_SY404 @ SV134 @ SV52 @ SV4 ) ) )
= $false )
| ( ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV134 )
= $false )
| ( ( in @ SV134 @ SV4 )
= $false )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1493]) ).
thf(1503,plain,
! [SV4: $i,SV52: $i,SV134: $i] :
( ( ( ~ ( in @ ( sK42_SY404 @ SV134 @ SV52 @ SV4 ) @ SV4 ) )
= $false )
| ( ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV134 )
= $false )
| ( ( in @ SV134 @ SV4 )
= $false )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1493]) ).
thf(1504,plain,
! [SV95: $i,SV121: $i,SV22: $i,SV142: $i,SV67: $i,SV147: $i] :
( ( ( in @ SV147 @ SV67 )
= $false )
| ( ( in @ SV142 @ SV22 )
= $false )
| ( ( SV121
!= ( ordered_pair @ SV142 @ SV147 ) )
= $true )
| ( ( in @ SV121 @ SV95 )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1496]) ).
thf(1505,plain,
! [SV22: $i,SV67: $i,SV95: $i] :
( ( ( ~ ( in @ ( sK34_SY411 @ SV95 @ SV67 @ SV22 ) @ SV22 )
| ~ ( in @ ( sK40_SY435 @ SV22 @ SV67 @ SV95 ) @ SV67 ) )
= $false )
| ( ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1497]) ).
thf(1506,plain,
! [SV146: $i,SV139: $i,SV95: $i,SV22: $i,SV67: $i] :
( ( ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
= ( ordered_pair @ SV139 @ SV146 ) )
= $false )
| ( ( in @ SV139 @ SV22 )
= $false )
| ( ( in @ SV146 @ SV67 )
= $false )
| ( ( ~ ( ~ ~ ! [SY411: $i] :
~ ~ ! [SY412: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY411 @ SV22 )
| ~ ( in @ SY412 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SY411 @ SY412 ) ) )
| ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 ) ) )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1499]) ).
thf(1507,plain,
! [SV72: $i,SV27: $i,SV152: $i] :
( ( ( in @ SV152 @ SV27 )
= $false )
| ( ( in @ ( sK25_SY335 @ SV27 @ SV72 ) @ SV152 )
= $true )
| ( ( in @ ( sK35_SY428 @ SV72 @ SV27 ) @ SV27 )
= $true )
| ( ( SV72
= ( set_meet @ SV27 ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1500]) ).
thf(1508,plain,
! [SV134: $i,SV52: $i,SV4: $i] :
( ( ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ ( sK42_SY404 @ SV134 @ SV52 @ SV4 ) )
= $true )
| ( ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV134 )
= $false )
| ( ( in @ SV134 @ SV4 )
= $false )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1502]) ).
thf(1509,plain,
! [SV4: $i,SV52: $i,SV134: $i] :
( ( ( in @ ( sK42_SY404 @ SV134 @ SV52 @ SV4 ) @ SV4 )
= $true )
| ( ( in @ ( sK11_SY297 @ SV4 @ SV52 ) @ SV134 )
= $false )
| ( ( in @ SV134 @ SV4 )
= $false )
| ( ( SV52
= ( union @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1503]) ).
thf(1510,plain,
! [SV95: $i,SV67: $i,SV22: $i,SV147: $i,SV142: $i,SV121: $i] :
( ( ( SV121
= ( ordered_pair @ SV142 @ SV147 ) )
= $false )
| ( ( in @ SV142 @ SV22 )
= $false )
| ( ( in @ SV147 @ SV67 )
= $false )
| ( ( in @ SV121 @ SV95 )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1504]) ).
thf(1511,plain,
! [SV22: $i,SV67: $i,SV95: $i] :
( ( ( ~ ( in @ ( sK34_SY411 @ SV95 @ SV67 @ SV22 ) @ SV22 ) )
= $false )
| ( ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1505]) ).
thf(1512,plain,
! [SV95: $i,SV67: $i,SV22: $i] :
( ( ( ~ ( in @ ( sK40_SY435 @ SV22 @ SV67 @ SV95 ) @ SV67 ) )
= $false )
| ( ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1505]) ).
thf(1513,plain,
! [SV139: $i,SV146: $i,SV95: $i,SV67: $i,SV22: $i] :
( ( ( ~ ~ ! [SY411: $i] :
~ ~ ! [SY412: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY411 @ SV22 )
| ~ ( in @ SY412 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SY411 @ SY412 ) ) )
| ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 ) )
= $false )
| ( ( in @ SV146 @ SV67 )
= $false )
| ( ( in @ SV139 @ SV22 )
= $false )
| ( ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
= ( ordered_pair @ SV139 @ SV146 ) )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1506]) ).
thf(1514,plain,
! [SV22: $i,SV67: $i,SV95: $i] :
( ( ( in @ ( sK34_SY411 @ SV95 @ SV67 @ SV22 ) @ SV22 )
= $true )
| ( ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1511]) ).
thf(1515,plain,
! [SV95: $i,SV67: $i,SV22: $i] :
( ( ( in @ ( sK40_SY435 @ SV22 @ SV67 @ SV95 ) @ SV67 )
= $true )
| ( ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 )
= $true )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1512]) ).
thf(1516,plain,
! [SV139: $i,SV146: $i,SV95: $i,SV67: $i,SV22: $i] :
( ( ( ~ ~ ! [SY411: $i] :
~ ~ ! [SY412: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY411 @ SV22 )
| ~ ( in @ SY412 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SY411 @ SY412 ) ) ) )
= $false )
| ( ( in @ SV146 @ SV67 )
= $false )
| ( ( in @ SV139 @ SV22 )
= $false )
| ( ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
= ( ordered_pair @ SV139 @ SV146 ) )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1513]) ).
thf(1517,plain,
! [SV139: $i,SV146: $i,SV95: $i,SV22: $i,SV67: $i] :
( ( ( in @ ( sK16_SY365 @ SV67 @ SV22 @ SV95 ) @ SV95 )
= $false )
| ( ( in @ SV146 @ SV67 )
= $false )
| ( ( in @ SV139 @ SV22 )
= $false )
| ( ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
= ( ordered_pair @ SV139 @ SV146 ) )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1513]) ).
thf(1518,plain,
! [SV139: $i,SV146: $i,SV95: $i,SV67: $i,SV22: $i] :
( ( ( ~ ! [SY411: $i] :
~ ~ ! [SY412: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY411 @ SV22 )
| ~ ( in @ SY412 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SY411 @ SY412 ) ) ) )
= $true )
| ( ( in @ SV146 @ SV67 )
= $false )
| ( ( in @ SV139 @ SV22 )
= $false )
| ( ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
= ( ordered_pair @ SV139 @ SV146 ) )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1516]) ).
thf(1519,plain,
! [SV139: $i,SV146: $i,SV95: $i,SV67: $i,SV22: $i] :
( ( ( ! [SY411: $i] :
~ ~ ! [SY412: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY411 @ SV22 )
| ~ ( in @ SY412 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ SY411 @ SY412 ) ) ) )
= $false )
| ( ( in @ SV146 @ SV67 )
= $false )
| ( ( in @ SV139 @ SV22 )
= $false )
| ( ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
= ( ordered_pair @ SV139 @ SV146 ) )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1518]) ).
thf(1520,plain,
! [SV22: $i,SV67: $i,SV95: $i,SV146: $i,SV139: $i] :
( ( ( ~ ~ ! [SY436: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK43_SY411 @ SV139 @ SV146 @ SV95 @ SV67 @ SV22 ) @ SV22 )
| ~ ( in @ SY436 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ ( sK43_SY411 @ SV139 @ SV146 @ SV95 @ SV67 @ SV22 ) @ SY436 ) ) ) )
= $false )
| ( ( in @ SV146 @ SV67 )
= $false )
| ( ( in @ SV139 @ SV22 )
= $false )
| ( ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
= ( ordered_pair @ SV139 @ SV146 ) )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1519]) ).
thf(1521,plain,
! [SV22: $i,SV67: $i,SV95: $i,SV146: $i,SV139: $i] :
( ( ( ~ ! [SY436: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK43_SY411 @ SV139 @ SV146 @ SV95 @ SV67 @ SV22 ) @ SV22 )
| ~ ( in @ SY436 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ ( sK43_SY411 @ SV139 @ SV146 @ SV95 @ SV67 @ SV22 ) @ SY436 ) ) ) )
= $true )
| ( ( in @ SV146 @ SV67 )
= $false )
| ( ( in @ SV139 @ SV22 )
= $false )
| ( ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
= ( ordered_pair @ SV139 @ SV146 ) )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1520]) ).
thf(1522,plain,
! [SV22: $i,SV67: $i,SV95: $i,SV146: $i,SV139: $i] :
( ( ( ! [SY436: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK43_SY411 @ SV139 @ SV146 @ SV95 @ SV67 @ SV22 ) @ SV22 )
| ~ ( in @ SY436 @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ ( sK43_SY411 @ SV139 @ SV146 @ SV95 @ SV67 @ SV22 ) @ SY436 ) ) ) )
= $false )
| ( ( in @ SV146 @ SV67 )
= $false )
| ( ( in @ SV139 @ SV22 )
= $false )
| ( ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
= ( ordered_pair @ SV139 @ SV146 ) )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1521]) ).
thf(1523,plain,
! [SV22: $i,SV67: $i,SV95: $i,SV146: $i,SV139: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK43_SY411 @ SV139 @ SV146 @ SV95 @ SV67 @ SV22 ) @ SV22 )
| ~ ( in @ ( sK44_SY436 @ SV22 @ SV67 @ SV95 @ SV146 @ SV139 ) @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ ( sK43_SY411 @ SV139 @ SV146 @ SV95 @ SV67 @ SV22 ) @ ( sK44_SY436 @ SV22 @ SV67 @ SV95 @ SV146 @ SV139 ) ) ) ) )
= $false )
| ( ( in @ SV146 @ SV67 )
= $false )
| ( ( in @ SV139 @ SV22 )
= $false )
| ( ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
= ( ordered_pair @ SV139 @ SV146 ) )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1522]) ).
thf(1524,plain,
! [SV22: $i,SV67: $i,SV95: $i,SV146: $i,SV139: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK43_SY411 @ SV139 @ SV146 @ SV95 @ SV67 @ SV22 ) @ SV22 )
| ~ ( in @ ( sK44_SY436 @ SV22 @ SV67 @ SV95 @ SV146 @ SV139 ) @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ ( sK43_SY411 @ SV139 @ SV146 @ SV95 @ SV67 @ SV22 ) @ ( sK44_SY436 @ SV22 @ SV67 @ SV95 @ SV146 @ SV139 ) ) ) ) )
= $true )
| ( ( in @ SV146 @ SV67 )
= $false )
| ( ( in @ SV139 @ SV22 )
= $false )
| ( ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
= ( ordered_pair @ SV139 @ SV146 ) )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1523]) ).
thf(1525,plain,
! [SV22: $i,SV67: $i,SV95: $i,SV146: $i,SV139: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK43_SY411 @ SV139 @ SV146 @ SV95 @ SV67 @ SV22 ) @ SV22 )
| ~ ( in @ ( sK44_SY436 @ SV22 @ SV67 @ SV95 @ SV146 @ SV139 ) @ SV67 ) )
| ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ ( sK43_SY411 @ SV139 @ SV146 @ SV95 @ SV67 @ SV22 ) @ ( sK44_SY436 @ SV22 @ SV67 @ SV95 @ SV146 @ SV139 ) ) ) )
= $false )
| ( ( in @ SV146 @ SV67 )
= $false )
| ( ( in @ SV139 @ SV22 )
= $false )
| ( ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
= ( ordered_pair @ SV139 @ SV146 ) )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1524]) ).
thf(1526,plain,
! [SV22: $i,SV67: $i,SV95: $i,SV146: $i,SV139: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK43_SY411 @ SV139 @ SV146 @ SV95 @ SV67 @ SV22 ) @ SV22 )
| ~ ( in @ ( sK44_SY436 @ SV22 @ SV67 @ SV95 @ SV146 @ SV139 ) @ SV67 ) ) )
= $false )
| ( ( in @ SV146 @ SV67 )
= $false )
| ( ( in @ SV139 @ SV22 )
= $false )
| ( ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
= ( ordered_pair @ SV139 @ SV146 ) )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1525]) ).
thf(1527,plain,
! [SV146: $i,SV139: $i,SV95: $i,SV22: $i,SV67: $i] :
( ( ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
!= ( ordered_pair @ ( sK43_SY411 @ SV139 @ SV146 @ SV95 @ SV67 @ SV22 ) @ ( sK44_SY436 @ SV22 @ SV67 @ SV95 @ SV146 @ SV139 ) ) )
= $false )
| ( ( in @ SV146 @ SV67 )
= $false )
| ( ( in @ SV139 @ SV22 )
= $false )
| ( ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
= ( ordered_pair @ SV139 @ SV146 ) )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1525]) ).
thf(1528,plain,
! [SV22: $i,SV67: $i,SV95: $i,SV146: $i,SV139: $i] :
( ( ( ~ ( ~ ( in @ ( sK43_SY411 @ SV139 @ SV146 @ SV95 @ SV67 @ SV22 ) @ SV22 )
| ~ ( in @ ( sK44_SY436 @ SV22 @ SV67 @ SV95 @ SV146 @ SV139 ) @ SV67 ) ) )
= $true )
| ( ( in @ SV146 @ SV67 )
= $false )
| ( ( in @ SV139 @ SV22 )
= $false )
| ( ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
= ( ordered_pair @ SV139 @ SV146 ) )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1526]) ).
thf(1529,plain,
! [SV146: $i,SV139: $i,SV95: $i,SV22: $i,SV67: $i] :
( ( ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
= ( ordered_pair @ ( sK43_SY411 @ SV139 @ SV146 @ SV95 @ SV67 @ SV22 ) @ ( sK44_SY436 @ SV22 @ SV67 @ SV95 @ SV146 @ SV139 ) ) )
= $true )
| ( ( in @ SV146 @ SV67 )
= $false )
| ( ( in @ SV139 @ SV22 )
= $false )
| ( ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
= ( ordered_pair @ SV139 @ SV146 ) )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1527]) ).
thf(1530,plain,
! [SV22: $i,SV67: $i,SV95: $i,SV146: $i,SV139: $i] :
( ( ( ~ ( in @ ( sK43_SY411 @ SV139 @ SV146 @ SV95 @ SV67 @ SV22 ) @ SV22 )
| ~ ( in @ ( sK44_SY436 @ SV22 @ SV67 @ SV95 @ SV146 @ SV139 ) @ SV67 ) )
= $false )
| ( ( in @ SV146 @ SV67 )
= $false )
| ( ( in @ SV139 @ SV22 )
= $false )
| ( ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
= ( ordered_pair @ SV139 @ SV146 ) )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1528]) ).
thf(1531,plain,
! [SV22: $i,SV67: $i,SV95: $i,SV146: $i,SV139: $i] :
( ( ( ~ ( in @ ( sK43_SY411 @ SV139 @ SV146 @ SV95 @ SV67 @ SV22 ) @ SV22 ) )
= $false )
| ( ( in @ SV146 @ SV67 )
= $false )
| ( ( in @ SV139 @ SV22 )
= $false )
| ( ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
= ( ordered_pair @ SV139 @ SV146 ) )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1530]) ).
thf(1532,plain,
! [SV139: $i,SV146: $i,SV95: $i,SV67: $i,SV22: $i] :
( ( ( ~ ( in @ ( sK44_SY436 @ SV22 @ SV67 @ SV95 @ SV146 @ SV139 ) @ SV67 ) )
= $false )
| ( ( in @ SV146 @ SV67 )
= $false )
| ( ( in @ SV139 @ SV22 )
= $false )
| ( ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
= ( ordered_pair @ SV139 @ SV146 ) )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1530]) ).
thf(1533,plain,
! [SV22: $i,SV67: $i,SV95: $i,SV146: $i,SV139: $i] :
( ( ( in @ ( sK43_SY411 @ SV139 @ SV146 @ SV95 @ SV67 @ SV22 ) @ SV22 )
= $true )
| ( ( in @ SV146 @ SV67 )
= $false )
| ( ( in @ SV139 @ SV22 )
= $false )
| ( ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
= ( ordered_pair @ SV139 @ SV146 ) )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1531]) ).
thf(1534,plain,
! [SV139: $i,SV146: $i,SV95: $i,SV67: $i,SV22: $i] :
( ( ( in @ ( sK44_SY436 @ SV22 @ SV67 @ SV95 @ SV146 @ SV139 ) @ SV67 )
= $true )
| ( ( in @ SV146 @ SV67 )
= $false )
| ( ( in @ SV139 @ SV22 )
= $false )
| ( ( ( sK16_SY365 @ SV67 @ SV22 @ SV95 )
= ( ordered_pair @ SV139 @ SV146 ) )
= $false )
| ( ( SV95
= ( cartesian_product2 @ SV22 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1532]) ).
thf(1535,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[268,1534,1533,1529,1517,1515,1514,1510,1509,1508,1507,1501,1498,1495,1494,1492,1489,1480,1479,1468,1465,1459,1457,1456,1455,1450,1446,1445,1435,1434,1432,1430,1428,1427,1424,1422,1413,1412,1408,1407,1404,1388,1387,1382,1377,1376,1373,1362,1358,1352,1351,1350,1345,1342,1341,1337,1336,1335,1330,1329,1328,1321,1318,1317,1305,1303,1283,1279,1278,1276,1265,1253,1251,1249,1244,1243,1241,1239,1236,1231,1230,1228,1223,1204,1197,1196,1195,1192,1191,1186,1185,1184,1172,1171,1164,1150,1138,1120,1107,1106,1105,1104,1091,1086,1085,1080,1079,1064,1061,1060,1051,1049,1047,1046,1042,1041,1025,1024,1021,1020,1005,1001,1000,991,968,956,955,938,937,933,912,886,885,868,867,846,845,844,811,762,761,760,752,751,741,740,739,738,724,714,698,689,661,660,638,633,600,591,559,540,535,533,530,519,454,445,395,346,294,293,282,281,280,279,278,277,276,275,274,273,272,271,270,269]) ).
thf(1536,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(1537,plain,
( ( ! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(1538,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[215]) ).
thf(1539,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[214]) ).
thf(1540,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[213]) ).
thf(1541,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[212]) ).
thf(1542,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[211]) ).
thf(1543,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(1544,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(1545,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[208]) ).
thf(1546,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( powerset @ C ) @ B ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[207]) ).
thf(1547,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_dom @ C ) )
& ( in @ B @ ( relation_rng @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[206]) ).
thf(1548,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) )
& ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[205]) ).
thf(1549,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) )
= $true ),
inference(copy,[status(thm)],[204]) ).
thf(1550,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[203]) ).
thf(1551,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ C )
& ( in @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[202]) ).
thf(1552,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( in @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
& ( disjoint @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(1553,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[200]) ).
thf(1554,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[199]) ).
thf(1555,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ~ ( ( in @ B @ ( subset_complement @ A @ C ) )
& ( in @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[198]) ).
thf(1556,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
= A )
<=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[197]) ).
thf(1557,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[196]) ).
thf(1558,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(1559,plain,
( ( ! [A: $i] :
( ( relation @ A )
<=> ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[194]) ).
thf(1560,plain,
( ( ! [A: $i,B: $i] :
( ( ( A != empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ! [D: $i] :
( ( in @ D @ A )
=> ( in @ C @ D ) ) ) ) )
& ( ( A = empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ( B = empty_set ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[193]) ).
thf(1561,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(copy,[status(thm)],[192]) ).
thf(1562,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[191]) ).
thf(1563,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[190]) ).
thf(1564,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
=> ( ( element @ B @ A )
<=> ( in @ B @ A ) ) )
& ( ( empty @ A )
=> ( ( element @ B @ A )
<=> ( empty @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[189]) ).
thf(1565,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[188]) ).
thf(1566,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[187]) ).
thf(1567,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[186]) ).
thf(1568,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[185]) ).
thf(1569,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[184]) ).
thf(1570,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_dom @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[183]) ).
thf(1571,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[182]) ).
thf(1572,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[181]) ).
thf(1573,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[180]) ).
thf(1574,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[179]) ).
thf(1575,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[178]) ).
thf(1576,plain,
$true = $true,
inference(copy,[status(thm)],[177]) ).
thf(1577,plain,
$true = $true,
inference(copy,[status(thm)],[176]) ).
thf(1578,plain,
$true = $true,
inference(copy,[status(thm)],[175]) ).
thf(1579,plain,
$true = $true,
inference(copy,[status(thm)],[174]) ).
thf(1580,plain,
$true = $true,
inference(copy,[status(thm)],[173]) ).
thf(1581,plain,
$true = $true,
inference(copy,[status(thm)],[172]) ).
thf(1582,plain,
$true = $true,
inference(copy,[status(thm)],[171]) ).
thf(1583,plain,
$true = $true,
inference(copy,[status(thm)],[170]) ).
thf(1584,plain,
$true = $true,
inference(copy,[status(thm)],[169]) ).
thf(1585,plain,
$true = $true,
inference(copy,[status(thm)],[168]) ).
thf(1586,plain,
$true = $true,
inference(copy,[status(thm)],[167]) ).
thf(1587,plain,
$true = $true,
inference(copy,[status(thm)],[166]) ).
thf(1588,plain,
$true = $true,
inference(copy,[status(thm)],[165]) ).
thf(1589,plain,
$true = $true,
inference(copy,[status(thm)],[164]) ).
thf(1590,plain,
$true = $true,
inference(copy,[status(thm)],[163]) ).
thf(1591,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[162]) ).
thf(1592,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[161]) ).
thf(1593,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[160]) ).
thf(1594,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[159]) ).
thf(1595,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[158]) ).
thf(1596,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[157]) ).
thf(1597,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[156]) ).
thf(1598,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[155]) ).
thf(1599,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[154]) ).
thf(1600,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
( ( subset @ E @ C )
=> ( in @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[153]) ).
thf(1601,plain,
( ( in @ ( ordered_pair @ sK1_A @ sK2_SY155 ) @ sK3_SY157 )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(1602,plain,
( ( relation @ sK3_SY157 )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(1603,plain,
( ( ~ ( in @ sK2_SY155 @ ( relation_field @ sK3_SY157 ) ) )
= $true ),
inference(copy,[status(thm)],[227]) ).
thf(1604,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( set_union2 @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ( ~ ( ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ( ~ ( ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( set_union2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1566]) ).
thf(1605,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( set_union2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1592]) ).
thf(1606,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ( subset @ SX3 @ SX2 ) )
| ( in @ SX3 @ SX1 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SX1 )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) ) ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SX2 @ SX1 )
| ~ ~ ( are_equipotent @ SX2 @ SX1 ) )
| ~ ~ ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1600]) ).
thf(1607,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( in @ SX0 @ SX1 )
| ( disjoint @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1538]) ).
thf(1608,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( ordered_pair @ SX0 @ SX1 )
!= ( ordered_pair @ SX2 @ SX3 ) )
| ~ ( ( SX0 != SX2 )
| ( SX1 != SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1549]) ).
thf(1609,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ~ ( ~ ( in @ SX0 @ ( relation_dom @ SX2 ) )
| ~ ( in @ SX1 @ ( relation_rng @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1547]) ).
thf(1610,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1594]) ).
thf(1611,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_field @ SX0 )
= ( set_union2 @ ( relation_dom @ SX0 ) @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1575]) ).
thf(1612,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1599]) ).
thf(1613,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) )
| ~ ( ~ ~ ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1556]) ).
thf(1614,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ~ ( empty @ SX0 )
| ~ ( ~ ( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) )
| ~ ( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
| ~ ( ~ ( empty @ SX0 )
| ~ ( ~ ( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) )
| ~ ( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1564]) ).
thf(1615,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1568]) ).
thf(1616,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( ( set_union2 @ ( singleton @ SX0 ) @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1536]) ).
thf(1617,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ( SX0 != empty_set ) )
| ~ ( ~ ( ( SX1
!= ( set_meet @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
| ~ ( ( SX0 != empty_set )
| ~ ( ~ ( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) )
| ~ ( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1560]) ).
thf(1618,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX1
!= ( union @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1571]) ).
thf(1619,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( unordered_pair @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ( ~ ( ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ( ~ ( ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( unordered_pair @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1565]) ).
thf(1620,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ~ ( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 ) )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1545]) ).
thf(1621,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX1
!= ( singleton @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) )
| ~ ( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) )
| ~ ( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1561]) ).
thf(1622,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ SX0 @ ( union @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1542]) ).
thf(1623,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( relation @ SX0 )
| ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ! [SX2: $i,SX3: $i] :
( SX1
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
| ~ ( ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ! [SX2: $i,SX3: $i] :
( SX1
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1559]) ).
thf(1624,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) )
| ~ ( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1539]) ).
thf(1625,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( in @ SX2 @ SX0 )
| ( subset @ SX0 @ ( set_difference @ SX1 @ ( singleton @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1541]) ).
thf(1626,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ( subset @ SX3 @ SX2 ) )
| ( in @ SX3 @ SX1 ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ ( powerset @ SX2 ) @ SX1 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SX2 @ SX1 )
| ~ ~ ( are_equipotent @ SX2 @ SX1 ) )
| ~ ~ ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1546]) ).
thf(1627,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) )
| ~ ( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1550]) ).
thf(1628,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SX0 @ SX1 )
| ~ ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ~ ~ ( ~ ~ ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1554]) ).
thf(1629,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( set_intersection2 @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( set_intersection2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1569]) ).
thf(1630,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1540]) ).
thf(1631,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ SX1 )
| ( empty @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1595]) ).
thf(1632,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( disjoint @ ( singleton @ SX0 ) @ SX1 )
| ~ ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1537]) ).
thf(1633,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( set_difference @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( set_difference @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1572]) ).
thf(1634,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ SX2 ) ) )
| ~ ( empty @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1598]) ).
thf(1635,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1558]) ).
thf(1636,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ~ ( ~ ( subset @ ( relation_dom @ SX0 ) @ ( relation_dom @ SX1 ) )
| ~ ( subset @ ( relation_rng @ SX0 ) @ ( relation_rng @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1548]) ).
thf(1637,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ~ ( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 ) )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1543]) ).
thf(1638,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1596]) ).
thf(1639,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX1
!= ( powerset @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1563]) ).
thf(1640,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( element @ SX2 @ ( powerset @ SX0 ) )
| ~ ~ ( ~ ( in @ SX1 @ ( subset_complement @ SX0 @ SX2 ) )
| ~ ( in @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1555]) ).
thf(1641,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
~ ( ~ ( ( SX1
!= ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( relation_dom @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1570]) ).
thf(1642,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( cartesian_product2 @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 ) )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 ) )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 ) )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 ) )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( cartesian_product2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1567]) ).
thf(1643,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
~ ( ~ ( ( SX1
!= ( relation_rng @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( relation_rng @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1573]) ).
thf(1644,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ SX0 @ ( union @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1557]) ).
thf(1645,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SX0 @ SX1 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) ) )
| ~ ~ ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1552]) ).
thf(1646,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ SX2 ) ) )
| ( element @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1597]) ).
thf(1647,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( ( set_union2 @ ( singleton @ SX0 ) @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1553]) ).
thf(1648,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1593]) ).
thf(1649,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) )
| ~ ( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1562]) ).
thf(1650,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1544]) ).
thf(1651,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 )
| ~ ( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX2 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX2 ) )
| ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1551]) ).
thf(1652,plain,
! [SV153: $i] :
( ( ! [SY437: $i] :
( ( ordered_pair @ SV153 @ SY437 )
= ( unordered_pair @ ( unordered_pair @ SV153 @ SY437 ) @ ( singleton @ SV153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1574]) ).
thf(1653,plain,
! [SV154: $i] :
( ( ! [SY438: $i] :
~ ( empty @ ( ordered_pair @ SV154 @ SY438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1591]) ).
thf(1654,plain,
( ( in @ sK2_SY155 @ ( relation_field @ sK3_SY157 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1603]) ).
thf(1655,plain,
! [SV155: $i] :
( ( ! [SY439: $i,SY440: $i] :
~ ( ~ ( ( SY440
!= ( set_union2 @ SV155 @ SY439 ) )
| ! [SY441: $i] :
~ ( ~ ( ~ ( in @ SY441 @ SY440 )
| ( in @ SY441 @ SV155 )
| ( in @ SY441 @ SY439 ) )
| ~ ( ~ ( ( in @ SY441 @ SV155 )
| ( in @ SY441 @ SY439 ) )
| ( in @ SY441 @ SY440 ) ) ) )
| ~ ( ~ ! [SY442: $i] :
~ ( ~ ( ~ ( in @ SY442 @ SY440 )
| ( in @ SY442 @ SV155 )
| ( in @ SY442 @ SY439 ) )
| ~ ( ~ ( ( in @ SY442 @ SV155 )
| ( in @ SY442 @ SY439 ) )
| ( in @ SY442 @ SY440 ) ) )
| ( SY440
= ( set_union2 @ SV155 @ SY439 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1604]) ).
thf(1656,plain,
! [SV156: $i] :
( ( ! [SY443: $i] :
( ~ ~ ( ~ ( relation @ SV156 )
| ~ ( relation @ SY443 ) )
| ( relation @ ( set_union2 @ SV156 @ SY443 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1605]) ).
thf(1657,plain,
! [SV157: $i] :
( ( ~ ! [SY444: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV157 @ SY444 )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY444 )
| ~ ( subset @ SX3 @ SX2 ) )
| ( in @ SX3 @ SY444 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SY444 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SY444 )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) ) ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SX2 @ SY444 )
| ~ ~ ( are_equipotent @ SX2 @ SY444 ) )
| ~ ~ ( in @ SX2 @ SY444 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1606]) ).
thf(1658,plain,
! [SV158: $i] :
( ( ! [SY451: $i] :
( ~ ~ ( in @ SV158 @ SY451 )
| ( disjoint @ ( singleton @ SV158 ) @ SY451 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1607]) ).
thf(1659,plain,
! [SV159: $i] :
( ( ! [SY452: $i,SY453: $i,SY454: $i] :
( ( ( ordered_pair @ SV159 @ SY452 )
!= ( ordered_pair @ SY453 @ SY454 ) )
| ~ ( ( SV159 != SY453 )
| ( SY452 != SY454 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1608]) ).
thf(1660,plain,
! [SV160: $i] :
( ( ! [SY455: $i,SY456: $i] :
( ~ ( relation @ SY456 )
| ~ ( in @ ( ordered_pair @ SV160 @ SY455 ) @ SY456 )
| ~ ( ~ ( in @ SV160 @ ( relation_dom @ SY456 ) )
| ~ ( in @ SY455 @ ( relation_rng @ SY456 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1609]) ).
thf(1661,plain,
! [SV161: $i] :
( ( ! [SY457: $i] :
( ~ ( in @ SV161 @ SY457 )
| ( element @ SV161 @ SY457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1610]) ).
thf(1662,plain,
! [SV162: $i] :
( ( ~ ( relation @ SV162 )
| ( ( relation_field @ SV162 )
= ( set_union2 @ ( relation_dom @ SV162 ) @ ( relation_rng @ SV162 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1611]) ).
thf(1663,plain,
! [SV163: $i] :
( ( ! [SY458: $i] :
~ ~ ( ~ ( in @ SV163 @ SY458 )
| ~ ( empty @ SY458 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1612]) ).
thf(1664,plain,
! [SV164: $i] :
( ( ! [SY459: $i] :
~ ( ~ ( ( ( set_difference @ SV164 @ ( singleton @ SY459 ) )
!= SV164 )
| ~ ( in @ SY459 @ SV164 ) )
| ~ ( ~ ~ ( in @ SY459 @ SV164 )
| ( ( set_difference @ SV164 @ ( singleton @ SY459 ) )
= SV164 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1613]) ).
thf(1665,plain,
! [SV165: $i] :
( ( ! [SY460: $i] :
~ ( ~ ( ~ ~ ( empty @ SV165 )
| ~ ( ~ ( ~ ( element @ SY460 @ SV165 )
| ( in @ SY460 @ SV165 ) )
| ~ ( ~ ( in @ SY460 @ SV165 )
| ( element @ SY460 @ SV165 ) ) ) )
| ~ ( ~ ( empty @ SV165 )
| ~ ( ~ ( ~ ( element @ SY460 @ SV165 )
| ( empty @ SY460 ) )
| ~ ( ~ ( empty @ SY460 )
| ( element @ SY460 @ SV165 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1614]) ).
thf(1666,plain,
! [SV166: $i] :
( ( ! [SY461: $i] :
~ ( ~ ( ~ ( subset @ SV166 @ SY461 )
| ! [SY462: $i] :
( ~ ( in @ SY462 @ SV166 )
| ( in @ SY462 @ SY461 ) ) )
| ~ ( ~ ! [SY463: $i] :
( ~ ( in @ SY463 @ SV166 )
| ( in @ SY463 @ SY461 ) )
| ( subset @ SV166 @ SY461 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1615]) ).
thf(1667,plain,
! [SV167: $i] :
( ( ! [SY464: $i] :
( ~ ( in @ SV167 @ SY464 )
| ( ( set_union2 @ ( singleton @ SV167 ) @ SY464 )
= SY464 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1616]) ).
thf(1668,plain,
! [SV168: $i] :
( ( ! [SY465: $i] :
~ ( ~ ( ~ ( ( SV168 != empty_set ) )
| ~ ( ~ ( ( SY465
!= ( set_meet @ SV168 ) )
| ! [SY466: $i] :
~ ( ~ ( ~ ( in @ SY466 @ SY465 )
| ! [SY467: $i] :
( ~ ( in @ SY467 @ SV168 )
| ( in @ SY466 @ SY467 ) ) )
| ~ ( ~ ! [SY468: $i] :
( ~ ( in @ SY468 @ SV168 )
| ( in @ SY466 @ SY468 ) )
| ( in @ SY466 @ SY465 ) ) ) )
| ~ ( ~ ! [SY469: $i] :
~ ( ~ ( ~ ( in @ SY469 @ SY465 )
| ! [SY470: $i] :
( ~ ( in @ SY470 @ SV168 )
| ( in @ SY469 @ SY470 ) ) )
| ~ ( ~ ! [SY471: $i] :
( ~ ( in @ SY471 @ SV168 )
| ( in @ SY469 @ SY471 ) )
| ( in @ SY469 @ SY465 ) ) )
| ( SY465
= ( set_meet @ SV168 ) ) ) ) )
| ~ ( ( SV168 != empty_set )
| ~ ( ~ ( ( SY465
!= ( set_meet @ SV168 ) )
| ( SY465 = empty_set ) )
| ~ ( ( SY465 != empty_set )
| ( SY465
= ( set_meet @ SV168 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1617]) ).
thf(1669,plain,
! [SV169: $i] :
( ( ! [SY472: $i] :
~ ( ~ ( ( SY472
!= ( union @ SV169 ) )
| ! [SY473: $i] :
~ ( ~ ( ~ ( in @ SY473 @ SY472 )
| ~ ! [SY474: $i] :
~ ~ ( ~ ( in @ SY473 @ SY474 )
| ~ ( in @ SY474 @ SV169 ) ) )
| ~ ( ~ ~ ! [SY475: $i] :
~ ~ ( ~ ( in @ SY473 @ SY475 )
| ~ ( in @ SY475 @ SV169 ) )
| ( in @ SY473 @ SY472 ) ) ) )
| ~ ( ~ ! [SY476: $i] :
~ ( ~ ( ~ ( in @ SY476 @ SY472 )
| ~ ! [SY477: $i] :
~ ~ ( ~ ( in @ SY476 @ SY477 )
| ~ ( in @ SY477 @ SV169 ) ) )
| ~ ( ~ ~ ! [SY478: $i] :
~ ~ ( ~ ( in @ SY476 @ SY478 )
| ~ ( in @ SY478 @ SV169 ) )
| ( in @ SY476 @ SY472 ) ) )
| ( SY472
= ( union @ SV169 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1618]) ).
thf(1670,plain,
! [SV170: $i] :
( ( ! [SY479: $i,SY480: $i] :
~ ( ~ ( ( SY480
!= ( unordered_pair @ SV170 @ SY479 ) )
| ! [SY481: $i] :
~ ( ~ ( ~ ( in @ SY481 @ SY480 )
| ( SY481 = SV170 )
| ( SY481 = SY479 ) )
| ~ ( ~ ( ( SY481 = SV170 )
| ( SY481 = SY479 ) )
| ( in @ SY481 @ SY480 ) ) ) )
| ~ ( ~ ! [SY482: $i] :
~ ( ~ ( ~ ( in @ SY482 @ SY480 )
| ( SY482 = SV170 )
| ( SY482 = SY479 ) )
| ~ ( ~ ( ( SY482 = SV170 )
| ( SY482 = SY479 ) )
| ( in @ SY482 @ SY480 ) ) )
| ( SY480
= ( unordered_pair @ SV170 @ SY479 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1619]) ).
thf(1671,plain,
! [SV171: $i] :
( ( ! [SY483: $i,SY484: $i,SY485: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV171 @ SY483 ) @ ( cartesian_product2 @ SY484 @ SY485 ) )
| ~ ( ~ ( in @ SV171 @ SY484 )
| ~ ( in @ SY483 @ SY485 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV171 @ SY484 )
| ~ ( in @ SY483 @ SY485 ) )
| ( in @ ( ordered_pair @ SV171 @ SY483 ) @ ( cartesian_product2 @ SY484 @ SY485 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1620]) ).
thf(1672,plain,
! [SV172: $i] :
( ( ! [SY486: $i] :
~ ( ~ ( ( SY486
!= ( singleton @ SV172 ) )
| ! [SY487: $i] :
~ ( ~ ( ~ ( in @ SY487 @ SY486 )
| ( SY487 = SV172 ) )
| ~ ( ( SY487 != SV172 )
| ( in @ SY487 @ SY486 ) ) ) )
| ~ ( ~ ! [SY488: $i] :
~ ( ~ ( ~ ( in @ SY488 @ SY486 )
| ( SY488 = SV172 ) )
| ~ ( ( SY488 != SV172 )
| ( in @ SY488 @ SY486 ) ) )
| ( SY486
= ( singleton @ SV172 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1621]) ).
thf(1673,plain,
! [SV173: $i] :
( ( ! [SY489: $i] :
( ~ ( in @ SV173 @ SY489 )
| ( subset @ SV173 @ ( union @ SY489 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1622]) ).
thf(1674,plain,
! [SV174: $i] :
( ( ~ ( ~ ( ~ ( relation @ SV174 )
| ! [SY490: $i] :
~ ~ ( ~ ( in @ SY490 @ SV174 )
| ~ ! [SX2: $i,SX3: $i] :
( SY490
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
| ~ ( ~ ! [SY493: $i] :
~ ~ ( ~ ( in @ SY493 @ SV174 )
| ~ ! [SX2: $i,SX3: $i] :
( SY493
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SV174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1623]) ).
thf(1675,plain,
! [SV175: $i] :
( ( ! [SY496: $i] :
~ ( ~ ( ~ ( subset @ ( singleton @ SV175 ) @ SY496 )
| ( in @ SV175 @ SY496 ) )
| ~ ( ~ ( in @ SV175 @ SY496 )
| ( subset @ ( singleton @ SV175 ) @ SY496 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1624]) ).
thf(1676,plain,
! [SV176: $i] :
( ( ! [SY497: $i,SY498: $i] :
( ~ ( subset @ SV176 @ SY497 )
| ( in @ SY498 @ SV176 )
| ( subset @ SV176 @ ( set_difference @ SY497 @ ( singleton @ SY498 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1625]) ).
thf(1677,plain,
! [SV177: $i] :
( ( ~ ! [SY499: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV177 @ SY499 )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY499 )
| ~ ( subset @ SX3 @ SX2 ) )
| ( in @ SX3 @ SY499 ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY499 )
| ( in @ ( powerset @ SX2 ) @ SY499 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SX2 @ SY499 )
| ~ ~ ( are_equipotent @ SX2 @ SY499 ) )
| ~ ~ ( in @ SX2 @ SY499 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1626]) ).
thf(1678,plain,
! [SV178: $i] :
( ( ! [SY504: $i] :
~ ( ~ ( ~ ( subset @ ( singleton @ SV178 ) @ SY504 )
| ( in @ SV178 @ SY504 ) )
| ~ ( ~ ( in @ SV178 @ SY504 )
| ( subset @ ( singleton @ SV178 ) @ SY504 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1627]) ).
thf(1679,plain,
! [SV179: $i] :
( ( ! [SY505: $i] :
~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SV179 @ SY505 )
| ~ ! [SY506: $i] :
~ ( in @ SY506 @ ( set_intersection2 @ SV179 @ SY505 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY507: $i] :
~ ( in @ SY507 @ ( set_intersection2 @ SV179 @ SY505 ) )
| ~ ( disjoint @ SV179 @ SY505 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1628]) ).
thf(1680,plain,
! [SV180: $i] :
( ( ! [SY508: $i,SY509: $i] :
~ ( ~ ( ( SY509
!= ( set_intersection2 @ SV180 @ SY508 ) )
| ! [SY510: $i] :
~ ( ~ ( ~ ( in @ SY510 @ SY509 )
| ~ ( ~ ( in @ SY510 @ SV180 )
| ~ ( in @ SY510 @ SY508 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY510 @ SV180 )
| ~ ( in @ SY510 @ SY508 ) )
| ( in @ SY510 @ SY509 ) ) ) )
| ~ ( ~ ! [SY511: $i] :
~ ( ~ ( ~ ( in @ SY511 @ SY509 )
| ~ ( ~ ( in @ SY511 @ SV180 )
| ~ ( in @ SY511 @ SY508 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY511 @ SV180 )
| ~ ( in @ SY511 @ SY508 ) )
| ( in @ SY511 @ SY509 ) ) )
| ( SY509
= ( set_intersection2 @ SV180 @ SY508 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1629]) ).
thf(1681,plain,
! [SV181: $i] :
( ( ! [SY512: $i] :
( ~ ( element @ SY512 @ ( powerset @ SV181 ) )
| ! [SY513: $i] :
( ~ ( in @ SY513 @ SY512 )
| ( in @ SY513 @ SV181 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1630]) ).
thf(1682,plain,
! [SV182: $i] :
( ( ! [SY514: $i] :
( ~ ( element @ SV182 @ SY514 )
| ( empty @ SY514 )
| ( in @ SV182 @ SY514 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1631]) ).
thf(1683,plain,
! [SV183: $i] :
( ( ! [SY515: $i] :
~ ~ ( ~ ( disjoint @ ( singleton @ SV183 ) @ SY515 )
| ~ ( in @ SV183 @ SY515 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1632]) ).
thf(1684,plain,
! [SV184: $i] :
( ( ! [SY516: $i,SY517: $i] :
~ ( ~ ( ( SY517
!= ( set_difference @ SV184 @ SY516 ) )
| ! [SY518: $i] :
~ ( ~ ( ~ ( in @ SY518 @ SY517 )
| ~ ( ~ ( in @ SY518 @ SV184 )
| ~ ~ ( in @ SY518 @ SY516 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY518 @ SV184 )
| ~ ~ ( in @ SY518 @ SY516 ) )
| ( in @ SY518 @ SY517 ) ) ) )
| ~ ( ~ ! [SY519: $i] :
~ ( ~ ( ~ ( in @ SY519 @ SY517 )
| ~ ( ~ ( in @ SY519 @ SV184 )
| ~ ~ ( in @ SY519 @ SY516 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY519 @ SV184 )
| ~ ~ ( in @ SY519 @ SY516 ) )
| ( in @ SY519 @ SY517 ) ) )
| ( SY517
= ( set_difference @ SV184 @ SY516 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1633]) ).
thf(1685,plain,
! [SV185: $i] :
( ( ! [SY520: $i,SY521: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV185 @ SY520 )
| ~ ( element @ SY520 @ ( powerset @ SY521 ) ) )
| ~ ( empty @ SY521 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1634]) ).
thf(1686,plain,
! [SV186: $i] :
( ( ! [SY522: $i] :
( ~ ( in @ SV186 @ SY522 )
| ~ ( in @ SY522 @ SV186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1635]) ).
thf(1687,plain,
! [SV187: $i] :
( ( ~ ( relation @ SV187 )
| ! [SY523: $i] :
( ~ ( relation @ SY523 )
| ~ ( subset @ SV187 @ SY523 )
| ~ ( ~ ( subset @ ( relation_dom @ SV187 ) @ ( relation_dom @ SY523 ) )
| ~ ( subset @ ( relation_rng @ SV187 ) @ ( relation_rng @ SY523 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1636]) ).
thf(1688,plain,
! [SV188: $i] :
( ( ! [SY524: $i,SY525: $i,SY526: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV188 @ SY524 ) @ ( cartesian_product2 @ SY525 @ SY526 ) )
| ~ ( ~ ( in @ SV188 @ SY525 )
| ~ ( in @ SY524 @ SY526 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV188 @ SY525 )
| ~ ( in @ SY524 @ SY526 ) )
| ( in @ ( ordered_pair @ SV188 @ SY524 ) @ ( cartesian_product2 @ SY525 @ SY526 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1637]) ).
thf(1689,plain,
! [SV189: $i] :
( ( ! [SY527: $i] :
( ~ ! [SY528: $i] :
~ ( ~ ( ~ ( in @ SY528 @ SV189 )
| ( in @ SY528 @ SY527 ) )
| ~ ( ~ ( in @ SY528 @ SY527 )
| ( in @ SY528 @ SV189 ) ) )
| ( SV189 = SY527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(1690,plain,
! [SV190: $i] :
( ( ! [SY529: $i] :
~ ( ~ ( ( SY529
!= ( powerset @ SV190 ) )
| ! [SY530: $i] :
~ ( ~ ( ~ ( in @ SY530 @ SY529 )
| ( subset @ SY530 @ SV190 ) )
| ~ ( ~ ( subset @ SY530 @ SV190 )
| ( in @ SY530 @ SY529 ) ) ) )
| ~ ( ~ ! [SY531: $i] :
~ ( ~ ( ~ ( in @ SY531 @ SY529 )
| ( subset @ SY531 @ SV190 ) )
| ~ ( ~ ( subset @ SY531 @ SV190 )
| ( in @ SY531 @ SY529 ) ) )
| ( SY529
= ( powerset @ SV190 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1639]) ).
thf(1691,plain,
! [SV191: $i] :
( ( ! [SY532: $i,SY533: $i] :
( ~ ( element @ SY533 @ ( powerset @ SV191 ) )
| ~ ~ ( ~ ( in @ SY532 @ ( subset_complement @ SV191 @ SY533 ) )
| ~ ( in @ SY532 @ SY533 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(1692,plain,
! [SV192: $i] :
( ( ~ ( relation @ SV192 )
| ! [SY534: $i] :
~ ( ~ ( ( SY534
!= ( relation_dom @ SV192 ) )
| ! [SY535: $i] :
~ ( ~ ( ~ ( in @ SY535 @ SY534 )
| ~ ! [SY536: $i] :
~ ( in @ ( ordered_pair @ SY535 @ SY536 ) @ SV192 ) )
| ~ ( ~ ~ ! [SY537: $i] :
~ ( in @ ( ordered_pair @ SY535 @ SY537 ) @ SV192 )
| ( in @ SY535 @ SY534 ) ) ) )
| ~ ( ~ ! [SY538: $i] :
~ ( ~ ( ~ ( in @ SY538 @ SY534 )
| ~ ! [SY539: $i] :
~ ( in @ ( ordered_pair @ SY538 @ SY539 ) @ SV192 ) )
| ~ ( ~ ~ ! [SY540: $i] :
~ ( in @ ( ordered_pair @ SY538 @ SY540 ) @ SV192 )
| ( in @ SY538 @ SY534 ) ) )
| ( SY534
= ( relation_dom @ SV192 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1641]) ).
thf(1693,plain,
! [SV193: $i] :
( ( ! [SY541: $i,SY542: $i] :
~ ( ~ ( ( SY542
!= ( cartesian_product2 @ SV193 @ SY541 ) )
| ! [SY543: $i] :
~ ( ~ ( ~ ( in @ SY543 @ SY542 )
| ~ ! [SY544: $i] :
~ ~ ! [SY545: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY544 @ SV193 )
| ~ ( in @ SY545 @ SY541 ) )
| ( SY543
!= ( ordered_pair @ SY544 @ SY545 ) ) ) )
| ~ ( ~ ~ ! [SY546: $i] :
~ ~ ! [SY547: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY546 @ SV193 )
| ~ ( in @ SY547 @ SY541 ) )
| ( SY543
!= ( ordered_pair @ SY546 @ SY547 ) ) )
| ( in @ SY543 @ SY542 ) ) ) )
| ~ ( ~ ! [SY548: $i] :
~ ( ~ ( ~ ( in @ SY548 @ SY542 )
| ~ ! [SY549: $i] :
~ ~ ! [SY550: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY549 @ SV193 )
| ~ ( in @ SY550 @ SY541 ) )
| ( SY548
!= ( ordered_pair @ SY549 @ SY550 ) ) ) )
| ~ ( ~ ~ ! [SY551: $i] :
~ ~ ! [SY552: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY551 @ SV193 )
| ~ ( in @ SY552 @ SY541 ) )
| ( SY548
!= ( ordered_pair @ SY551 @ SY552 ) ) )
| ( in @ SY548 @ SY542 ) ) )
| ( SY542
= ( cartesian_product2 @ SV193 @ SY541 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1642]) ).
thf(1694,plain,
! [SV194: $i] :
( ( ~ ( relation @ SV194 )
| ! [SY553: $i] :
~ ( ~ ( ( SY553
!= ( relation_rng @ SV194 ) )
| ! [SY554: $i] :
~ ( ~ ( ~ ( in @ SY554 @ SY553 )
| ~ ! [SY555: $i] :
~ ( in @ ( ordered_pair @ SY555 @ SY554 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY556: $i] :
~ ( in @ ( ordered_pair @ SY556 @ SY554 ) @ SV194 )
| ( in @ SY554 @ SY553 ) ) ) )
| ~ ( ~ ! [SY557: $i] :
~ ( ~ ( ~ ( in @ SY557 @ SY553 )
| ~ ! [SY558: $i] :
~ ( in @ ( ordered_pair @ SY558 @ SY557 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY559: $i] :
~ ( in @ ( ordered_pair @ SY559 @ SY557 ) @ SV194 )
| ( in @ SY557 @ SY553 ) ) )
| ( SY553
= ( relation_rng @ SV194 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1643]) ).
thf(1695,plain,
! [SV195: $i] :
( ( ! [SY560: $i] :
( ~ ( in @ SV195 @ SY560 )
| ( subset @ SV195 @ ( union @ SY560 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1644]) ).
thf(1696,plain,
! [SV196: $i] :
( ( ! [SY561: $i] :
~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SV196 @ SY561 )
| ~ ! [SY562: $i] :
~ ~ ( ~ ( in @ SY562 @ SV196 )
| ~ ( in @ SY562 @ SY561 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY563: $i] :
~ ~ ( ~ ( in @ SY563 @ SV196 )
| ~ ( in @ SY563 @ SY561 ) )
| ~ ( disjoint @ SV196 @ SY561 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1645]) ).
thf(1697,plain,
! [SV197: $i] :
( ( ! [SY564: $i,SY565: $i] :
( ~ ~ ( ~ ( in @ SV197 @ SY564 )
| ~ ( element @ SY564 @ ( powerset @ SY565 ) ) )
| ( element @ SV197 @ SY565 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1646]) ).
thf(1698,plain,
! [SV198: $i] :
( ( ! [SY566: $i] :
( ~ ( in @ SV198 @ SY566 )
| ( ( set_union2 @ ( singleton @ SV198 ) @ SY566 )
= SY566 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1647]) ).
thf(1699,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1648]) ).
thf(1700,plain,
! [SV199: $i] :
( ( ~ ( ~ ( ( SV199 != empty_set )
| ! [SY567: $i] :
~ ( in @ SY567 @ SV199 ) )
| ~ ( ~ ! [SY568: $i] :
~ ( in @ SY568 @ SV199 )
| ( SV199 = empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1649]) ).
thf(1701,plain,
! [SV200: $i] :
( ( ! [SY569: $i] :
( ~ ! [SY570: $i] :
( ~ ( in @ SY570 @ SV200 )
| ( in @ SY570 @ SY569 ) )
| ( element @ SV200 @ ( powerset @ SY569 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1650]) ).
thf(1702,plain,
! [SV201: $i] :
( ( ! [SY571: $i,SY572: $i] :
~ ( ~ ( ~ ( subset @ ( unordered_pair @ SV201 @ SY571 ) @ SY572 )
| ~ ( ~ ( in @ SV201 @ SY572 )
| ~ ( in @ SY571 @ SY572 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV201 @ SY572 )
| ~ ( in @ SY571 @ SY572 ) )
| ( subset @ ( unordered_pair @ SV201 @ SY571 ) @ SY572 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1651]) ).
thf(1703,plain,
! [SV202: $i,SV153: $i] :
( ( ( ordered_pair @ SV153 @ SV202 )
= ( unordered_pair @ ( unordered_pair @ SV153 @ SV202 ) @ ( singleton @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1652]) ).
thf(1704,plain,
! [SV203: $i,SV154: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV154 @ SV203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1653]) ).
thf(1705,plain,
! [SV204: $i,SV155: $i] :
( ( ! [SY573: $i] :
~ ( ~ ( ( SY573
!= ( set_union2 @ SV155 @ SV204 ) )
| ! [SY574: $i] :
~ ( ~ ( ~ ( in @ SY574 @ SY573 )
| ( in @ SY574 @ SV155 )
| ( in @ SY574 @ SV204 ) )
| ~ ( ~ ( ( in @ SY574 @ SV155 )
| ( in @ SY574 @ SV204 ) )
| ( in @ SY574 @ SY573 ) ) ) )
| ~ ( ~ ! [SY575: $i] :
~ ( ~ ( ~ ( in @ SY575 @ SY573 )
| ( in @ SY575 @ SV155 )
| ( in @ SY575 @ SV204 ) )
| ~ ( ~ ( ( in @ SY575 @ SV155 )
| ( in @ SY575 @ SV204 ) )
| ( in @ SY575 @ SY573 ) ) )
| ( SY573
= ( set_union2 @ SV155 @ SV204 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1655]) ).
thf(1706,plain,
! [SV205: $i,SV156: $i] :
( ( ~ ~ ( ~ ( relation @ SV156 )
| ~ ( relation @ SV205 ) )
| ( relation @ ( set_union2 @ SV156 @ SV205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1656]) ).
thf(1707,plain,
! [SV157: $i] :
( ( ! [SY444: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV157 @ SY444 )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY444 )
| ~ ( subset @ SX3 @ SX2 ) )
| ( in @ SX3 @ SY444 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SY444 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SY444 )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) ) ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SX2 @ SY444 )
| ~ ~ ( are_equipotent @ SX2 @ SY444 ) )
| ~ ~ ( in @ SX2 @ SY444 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1657]) ).
thf(1708,plain,
! [SV206: $i,SV158: $i] :
( ( ~ ~ ( in @ SV158 @ SV206 )
| ( disjoint @ ( singleton @ SV158 ) @ SV206 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1658]) ).
thf(1709,plain,
! [SV207: $i,SV159: $i] :
( ( ! [SY576: $i,SY577: $i] :
( ( ( ordered_pair @ SV159 @ SV207 )
!= ( ordered_pair @ SY576 @ SY577 ) )
| ~ ( ( SV159 != SY576 )
| ( SV207 != SY577 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1659]) ).
thf(1710,plain,
! [SV208: $i,SV160: $i] :
( ( ! [SY578: $i] :
( ~ ( relation @ SY578 )
| ~ ( in @ ( ordered_pair @ SV160 @ SV208 ) @ SY578 )
| ~ ( ~ ( in @ SV160 @ ( relation_dom @ SY578 ) )
| ~ ( in @ SV208 @ ( relation_rng @ SY578 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1660]) ).
thf(1711,plain,
! [SV209: $i,SV161: $i] :
( ( ~ ( in @ SV161 @ SV209 )
| ( element @ SV161 @ SV209 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1661]) ).
thf(1712,plain,
! [SV162: $i] :
( ( ( ~ ( relation @ SV162 ) )
= $true )
| ( ( ( relation_field @ SV162 )
= ( set_union2 @ ( relation_dom @ SV162 ) @ ( relation_rng @ SV162 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1662]) ).
thf(1713,plain,
! [SV210: $i,SV163: $i] :
( ( ~ ~ ( ~ ( in @ SV163 @ SV210 )
| ~ ( empty @ SV210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1663]) ).
thf(1714,plain,
! [SV211: $i,SV164: $i] :
( ( ~ ( ~ ( ( ( set_difference @ SV164 @ ( singleton @ SV211 ) )
!= SV164 )
| ~ ( in @ SV211 @ SV164 ) )
| ~ ( ~ ~ ( in @ SV211 @ SV164 )
| ( ( set_difference @ SV164 @ ( singleton @ SV211 ) )
= SV164 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1664]) ).
thf(1715,plain,
! [SV212: $i,SV165: $i] :
( ( ~ ( ~ ( ~ ~ ( empty @ SV165 )
| ~ ( ~ ( ~ ( element @ SV212 @ SV165 )
| ( in @ SV212 @ SV165 ) )
| ~ ( ~ ( in @ SV212 @ SV165 )
| ( element @ SV212 @ SV165 ) ) ) )
| ~ ( ~ ( empty @ SV165 )
| ~ ( ~ ( ~ ( element @ SV212 @ SV165 )
| ( empty @ SV212 ) )
| ~ ( ~ ( empty @ SV212 )
| ( element @ SV212 @ SV165 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1665]) ).
thf(1716,plain,
! [SV213: $i,SV166: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV166 @ SV213 )
| ! [SY579: $i] :
( ~ ( in @ SY579 @ SV166 )
| ( in @ SY579 @ SV213 ) ) )
| ~ ( ~ ! [SY580: $i] :
( ~ ( in @ SY580 @ SV166 )
| ( in @ SY580 @ SV213 ) )
| ( subset @ SV166 @ SV213 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1666]) ).
thf(1717,plain,
! [SV214: $i,SV167: $i] :
( ( ~ ( in @ SV167 @ SV214 )
| ( ( set_union2 @ ( singleton @ SV167 ) @ SV214 )
= SV214 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1667]) ).
thf(1718,plain,
! [SV215: $i,SV168: $i] :
( ( ~ ( ~ ( ~ ( ( SV168 != empty_set ) )
| ~ ( ~ ( ( SV215
!= ( set_meet @ SV168 ) )
| ! [SY581: $i] :
~ ( ~ ( ~ ( in @ SY581 @ SV215 )
| ! [SY467: $i] :
( ~ ( in @ SY467 @ SV168 )
| ( in @ SY581 @ SY467 ) ) )
| ~ ( ~ ! [SY468: $i] :
( ~ ( in @ SY468 @ SV168 )
| ( in @ SY581 @ SY468 ) )
| ( in @ SY581 @ SV215 ) ) ) )
| ~ ( ~ ! [SY584: $i] :
~ ( ~ ( ~ ( in @ SY584 @ SV215 )
| ! [SY470: $i] :
( ~ ( in @ SY470 @ SV168 )
| ( in @ SY584 @ SY470 ) ) )
| ~ ( ~ ! [SY471: $i] :
( ~ ( in @ SY471 @ SV168 )
| ( in @ SY584 @ SY471 ) )
| ( in @ SY584 @ SV215 ) ) )
| ( SV215
= ( set_meet @ SV168 ) ) ) ) )
| ~ ( ( SV168 != empty_set )
| ~ ( ~ ( ( SV215
!= ( set_meet @ SV168 ) )
| ( SV215 = empty_set ) )
| ~ ( ( SV215 != empty_set )
| ( SV215
= ( set_meet @ SV168 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1668]) ).
thf(1719,plain,
! [SV169: $i,SV216: $i] :
( ( ~ ( ~ ( ( SV216
!= ( union @ SV169 ) )
| ! [SY587: $i] :
~ ( ~ ( ~ ( in @ SY587 @ SV216 )
| ~ ! [SY474: $i] :
~ ~ ( ~ ( in @ SY587 @ SY474 )
| ~ ( in @ SY474 @ SV169 ) ) )
| ~ ( ~ ~ ! [SY475: $i] :
~ ~ ( ~ ( in @ SY587 @ SY475 )
| ~ ( in @ SY475 @ SV169 ) )
| ( in @ SY587 @ SV216 ) ) ) )
| ~ ( ~ ! [SY590: $i] :
~ ( ~ ( ~ ( in @ SY590 @ SV216 )
| ~ ! [SY477: $i] :
~ ~ ( ~ ( in @ SY590 @ SY477 )
| ~ ( in @ SY477 @ SV169 ) ) )
| ~ ( ~ ~ ! [SY478: $i] :
~ ~ ( ~ ( in @ SY590 @ SY478 )
| ~ ( in @ SY478 @ SV169 ) )
| ( in @ SY590 @ SV216 ) ) )
| ( SV216
= ( union @ SV169 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1669]) ).
thf(1720,plain,
! [SV217: $i,SV170: $i] :
( ( ! [SY593: $i] :
~ ( ~ ( ( SY593
!= ( unordered_pair @ SV170 @ SV217 ) )
| ! [SY594: $i] :
~ ( ~ ( ~ ( in @ SY594 @ SY593 )
| ( SY594 = SV170 )
| ( SY594 = SV217 ) )
| ~ ( ~ ( ( SY594 = SV170 )
| ( SY594 = SV217 ) )
| ( in @ SY594 @ SY593 ) ) ) )
| ~ ( ~ ! [SY595: $i] :
~ ( ~ ( ~ ( in @ SY595 @ SY593 )
| ( SY595 = SV170 )
| ( SY595 = SV217 ) )
| ~ ( ~ ( ( SY595 = SV170 )
| ( SY595 = SV217 ) )
| ( in @ SY595 @ SY593 ) ) )
| ( SY593
= ( unordered_pair @ SV170 @ SV217 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1670]) ).
thf(1721,plain,
! [SV218: $i,SV171: $i] :
( ( ! [SY596: $i,SY597: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV171 @ SV218 ) @ ( cartesian_product2 @ SY596 @ SY597 ) )
| ~ ( ~ ( in @ SV171 @ SY596 )
| ~ ( in @ SV218 @ SY597 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV171 @ SY596 )
| ~ ( in @ SV218 @ SY597 ) )
| ( in @ ( ordered_pair @ SV171 @ SV218 ) @ ( cartesian_product2 @ SY596 @ SY597 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1671]) ).
thf(1722,plain,
! [SV172: $i,SV219: $i] :
( ( ~ ( ~ ( ( SV219
!= ( singleton @ SV172 ) )
| ! [SY598: $i] :
~ ( ~ ( ~ ( in @ SY598 @ SV219 )
| ( SY598 = SV172 ) )
| ~ ( ( SY598 != SV172 )
| ( in @ SY598 @ SV219 ) ) ) )
| ~ ( ~ ! [SY599: $i] :
~ ( ~ ( ~ ( in @ SY599 @ SV219 )
| ( SY599 = SV172 ) )
| ~ ( ( SY599 != SV172 )
| ( in @ SY599 @ SV219 ) ) )
| ( SV219
= ( singleton @ SV172 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1672]) ).
thf(1723,plain,
! [SV220: $i,SV173: $i] :
( ( ~ ( in @ SV173 @ SV220 )
| ( subset @ SV173 @ ( union @ SV220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1673]) ).
thf(1724,plain,
! [SV174: $i] :
( ( ~ ( ~ ( relation @ SV174 )
| ! [SY490: $i] :
~ ~ ( ~ ( in @ SY490 @ SV174 )
| ~ ! [SX2: $i,SX3: $i] :
( SY490
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
| ~ ( ~ ! [SY493: $i] :
~ ~ ( ~ ( in @ SY493 @ SV174 )
| ~ ! [SX2: $i,SX3: $i] :
( SY493
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SV174 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1674]) ).
thf(1725,plain,
! [SV221: $i,SV175: $i] :
( ( ~ ( ~ ( ~ ( subset @ ( singleton @ SV175 ) @ SV221 )
| ( in @ SV175 @ SV221 ) )
| ~ ( ~ ( in @ SV175 @ SV221 )
| ( subset @ ( singleton @ SV175 ) @ SV221 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1675]) ).
thf(1726,plain,
! [SV222: $i,SV176: $i] :
( ( ! [SY600: $i] :
( ~ ( subset @ SV176 @ SV222 )
| ( in @ SY600 @ SV176 )
| ( subset @ SV176 @ ( set_difference @ SV222 @ ( singleton @ SY600 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1676]) ).
thf(1727,plain,
! [SV177: $i] :
( ( ! [SY499: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV177 @ SY499 )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY499 )
| ~ ( subset @ SX3 @ SX2 ) )
| ( in @ SX3 @ SY499 ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY499 )
| ( in @ ( powerset @ SX2 ) @ SY499 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SX2 @ SY499 )
| ~ ~ ( are_equipotent @ SX2 @ SY499 ) )
| ~ ~ ( in @ SX2 @ SY499 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1677]) ).
thf(1728,plain,
! [SV223: $i,SV178: $i] :
( ( ~ ( ~ ( ~ ( subset @ ( singleton @ SV178 ) @ SV223 )
| ( in @ SV178 @ SV223 ) )
| ~ ( ~ ( in @ SV178 @ SV223 )
| ( subset @ ( singleton @ SV178 ) @ SV223 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1678]) ).
thf(1729,plain,
! [SV224: $i,SV179: $i] :
( ( ~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SV179 @ SV224 )
| ~ ! [SY601: $i] :
~ ( in @ SY601 @ ( set_intersection2 @ SV179 @ SV224 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY602: $i] :
~ ( in @ SY602 @ ( set_intersection2 @ SV179 @ SV224 ) )
| ~ ( disjoint @ SV179 @ SV224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1679]) ).
thf(1730,plain,
! [SV225: $i,SV180: $i] :
( ( ! [SY603: $i] :
~ ( ~ ( ( SY603
!= ( set_intersection2 @ SV180 @ SV225 ) )
| ! [SY604: $i] :
~ ( ~ ( ~ ( in @ SY604 @ SY603 )
| ~ ( ~ ( in @ SY604 @ SV180 )
| ~ ( in @ SY604 @ SV225 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY604 @ SV180 )
| ~ ( in @ SY604 @ SV225 ) )
| ( in @ SY604 @ SY603 ) ) ) )
| ~ ( ~ ! [SY605: $i] :
~ ( ~ ( ~ ( in @ SY605 @ SY603 )
| ~ ( ~ ( in @ SY605 @ SV180 )
| ~ ( in @ SY605 @ SV225 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY605 @ SV180 )
| ~ ( in @ SY605 @ SV225 ) )
| ( in @ SY605 @ SY603 ) ) )
| ( SY603
= ( set_intersection2 @ SV180 @ SV225 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1680]) ).
thf(1731,plain,
! [SV181: $i,SV226: $i] :
( ( ~ ( element @ SV226 @ ( powerset @ SV181 ) )
| ! [SY606: $i] :
( ~ ( in @ SY606 @ SV226 )
| ( in @ SY606 @ SV181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1681]) ).
thf(1732,plain,
! [SV227: $i,SV182: $i] :
( ( ~ ( element @ SV182 @ SV227 )
| ( empty @ SV227 )
| ( in @ SV182 @ SV227 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1682]) ).
thf(1733,plain,
! [SV228: $i,SV183: $i] :
( ( ~ ~ ( ~ ( disjoint @ ( singleton @ SV183 ) @ SV228 )
| ~ ( in @ SV183 @ SV228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1683]) ).
thf(1734,plain,
! [SV229: $i,SV184: $i] :
( ( ! [SY607: $i] :
~ ( ~ ( ( SY607
!= ( set_difference @ SV184 @ SV229 ) )
| ! [SY608: $i] :
~ ( ~ ( ~ ( in @ SY608 @ SY607 )
| ~ ( ~ ( in @ SY608 @ SV184 )
| ~ ~ ( in @ SY608 @ SV229 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY608 @ SV184 )
| ~ ~ ( in @ SY608 @ SV229 ) )
| ( in @ SY608 @ SY607 ) ) ) )
| ~ ( ~ ! [SY609: $i] :
~ ( ~ ( ~ ( in @ SY609 @ SY607 )
| ~ ( ~ ( in @ SY609 @ SV184 )
| ~ ~ ( in @ SY609 @ SV229 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY609 @ SV184 )
| ~ ~ ( in @ SY609 @ SV229 ) )
| ( in @ SY609 @ SY607 ) ) )
| ( SY607
= ( set_difference @ SV184 @ SV229 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1684]) ).
thf(1735,plain,
! [SV230: $i,SV185: $i] :
( ( ! [SY610: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV185 @ SV230 )
| ~ ( element @ SV230 @ ( powerset @ SY610 ) ) )
| ~ ( empty @ SY610 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1685]) ).
thf(1736,plain,
! [SV231: $i,SV186: $i] :
( ( ~ ( in @ SV186 @ SV231 )
| ~ ( in @ SV231 @ SV186 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1686]) ).
thf(1737,plain,
! [SV187: $i] :
( ( ( ~ ( relation @ SV187 ) )
= $true )
| ( ( ! [SY523: $i] :
( ~ ( relation @ SY523 )
| ~ ( subset @ SV187 @ SY523 )
| ~ ( ~ ( subset @ ( relation_dom @ SV187 ) @ ( relation_dom @ SY523 ) )
| ~ ( subset @ ( relation_rng @ SV187 ) @ ( relation_rng @ SY523 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1687]) ).
thf(1738,plain,
! [SV232: $i,SV188: $i] :
( ( ! [SY611: $i,SY612: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV188 @ SV232 ) @ ( cartesian_product2 @ SY611 @ SY612 ) )
| ~ ( ~ ( in @ SV188 @ SY611 )
| ~ ( in @ SV232 @ SY612 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV188 @ SY611 )
| ~ ( in @ SV232 @ SY612 ) )
| ( in @ ( ordered_pair @ SV188 @ SV232 ) @ ( cartesian_product2 @ SY611 @ SY612 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1688]) ).
thf(1739,plain,
! [SV233: $i,SV189: $i] :
( ( ~ ! [SY613: $i] :
~ ( ~ ( ~ ( in @ SY613 @ SV189 )
| ( in @ SY613 @ SV233 ) )
| ~ ( ~ ( in @ SY613 @ SV233 )
| ( in @ SY613 @ SV189 ) ) )
| ( SV189 = SV233 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1689]) ).
thf(1740,plain,
! [SV190: $i,SV234: $i] :
( ( ~ ( ~ ( ( SV234
!= ( powerset @ SV190 ) )
| ! [SY614: $i] :
~ ( ~ ( ~ ( in @ SY614 @ SV234 )
| ( subset @ SY614 @ SV190 ) )
| ~ ( ~ ( subset @ SY614 @ SV190 )
| ( in @ SY614 @ SV234 ) ) ) )
| ~ ( ~ ! [SY615: $i] :
~ ( ~ ( ~ ( in @ SY615 @ SV234 )
| ( subset @ SY615 @ SV190 ) )
| ~ ( ~ ( subset @ SY615 @ SV190 )
| ( in @ SY615 @ SV234 ) ) )
| ( SV234
= ( powerset @ SV190 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1690]) ).
thf(1741,plain,
! [SV235: $i,SV191: $i] :
( ( ! [SY616: $i] :
( ~ ( element @ SY616 @ ( powerset @ SV191 ) )
| ~ ~ ( ~ ( in @ SV235 @ ( subset_complement @ SV191 @ SY616 ) )
| ~ ( in @ SV235 @ SY616 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1691]) ).
thf(1742,plain,
! [SV192: $i] :
( ( ( ~ ( relation @ SV192 ) )
= $true )
| ( ( ! [SY534: $i] :
~ ( ~ ( ( SY534
!= ( relation_dom @ SV192 ) )
| ! [SY535: $i] :
~ ( ~ ( ~ ( in @ SY535 @ SY534 )
| ~ ! [SY536: $i] :
~ ( in @ ( ordered_pair @ SY535 @ SY536 ) @ SV192 ) )
| ~ ( ~ ~ ! [SY537: $i] :
~ ( in @ ( ordered_pair @ SY535 @ SY537 ) @ SV192 )
| ( in @ SY535 @ SY534 ) ) ) )
| ~ ( ~ ! [SY538: $i] :
~ ( ~ ( ~ ( in @ SY538 @ SY534 )
| ~ ! [SY539: $i] :
~ ( in @ ( ordered_pair @ SY538 @ SY539 ) @ SV192 ) )
| ~ ( ~ ~ ! [SY540: $i] :
~ ( in @ ( ordered_pair @ SY538 @ SY540 ) @ SV192 )
| ( in @ SY538 @ SY534 ) ) )
| ( SY534
= ( relation_dom @ SV192 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1692]) ).
thf(1743,plain,
! [SV236: $i,SV193: $i] :
( ( ! [SY617: $i] :
~ ( ~ ( ( SY617
!= ( cartesian_product2 @ SV193 @ SV236 ) )
| ! [SY618: $i] :
~ ( ~ ( ~ ( in @ SY618 @ SY617 )
| ~ ! [SY619: $i] :
~ ~ ! [SY620: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY619 @ SV193 )
| ~ ( in @ SY620 @ SV236 ) )
| ( SY618
!= ( ordered_pair @ SY619 @ SY620 ) ) ) )
| ~ ( ~ ~ ! [SY621: $i] :
~ ~ ! [SY622: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY621 @ SV193 )
| ~ ( in @ SY622 @ SV236 ) )
| ( SY618
!= ( ordered_pair @ SY621 @ SY622 ) ) )
| ( in @ SY618 @ SY617 ) ) ) )
| ~ ( ~ ! [SY623: $i] :
~ ( ~ ( ~ ( in @ SY623 @ SY617 )
| ~ ! [SY624: $i] :
~ ~ ! [SY625: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY624 @ SV193 )
| ~ ( in @ SY625 @ SV236 ) )
| ( SY623
!= ( ordered_pair @ SY624 @ SY625 ) ) ) )
| ~ ( ~ ~ ! [SY626: $i] :
~ ~ ! [SY627: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY626 @ SV193 )
| ~ ( in @ SY627 @ SV236 ) )
| ( SY623
!= ( ordered_pair @ SY626 @ SY627 ) ) )
| ( in @ SY623 @ SY617 ) ) )
| ( SY617
= ( cartesian_product2 @ SV193 @ SV236 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1693]) ).
thf(1744,plain,
! [SV194: $i] :
( ( ( ~ ( relation @ SV194 ) )
= $true )
| ( ( ! [SY553: $i] :
~ ( ~ ( ( SY553
!= ( relation_rng @ SV194 ) )
| ! [SY554: $i] :
~ ( ~ ( ~ ( in @ SY554 @ SY553 )
| ~ ! [SY555: $i] :
~ ( in @ ( ordered_pair @ SY555 @ SY554 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY556: $i] :
~ ( in @ ( ordered_pair @ SY556 @ SY554 ) @ SV194 )
| ( in @ SY554 @ SY553 ) ) ) )
| ~ ( ~ ! [SY557: $i] :
~ ( ~ ( ~ ( in @ SY557 @ SY553 )
| ~ ! [SY558: $i] :
~ ( in @ ( ordered_pair @ SY558 @ SY557 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY559: $i] :
~ ( in @ ( ordered_pair @ SY559 @ SY557 ) @ SV194 )
| ( in @ SY557 @ SY553 ) ) )
| ( SY553
= ( relation_rng @ SV194 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1694]) ).
thf(1745,plain,
! [SV237: $i,SV195: $i] :
( ( ~ ( in @ SV195 @ SV237 )
| ( subset @ SV195 @ ( union @ SV237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1695]) ).
thf(1746,plain,
! [SV238: $i,SV196: $i] :
( ( ~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SV196 @ SV238 )
| ~ ! [SY628: $i] :
~ ~ ( ~ ( in @ SY628 @ SV196 )
| ~ ( in @ SY628 @ SV238 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY629: $i] :
~ ~ ( ~ ( in @ SY629 @ SV196 )
| ~ ( in @ SY629 @ SV238 ) )
| ~ ( disjoint @ SV196 @ SV238 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1696]) ).
thf(1747,plain,
! [SV239: $i,SV197: $i] :
( ( ! [SY630: $i] :
( ~ ~ ( ~ ( in @ SV197 @ SV239 )
| ~ ( element @ SV239 @ ( powerset @ SY630 ) ) )
| ( element @ SV197 @ SY630 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1697]) ).
thf(1748,plain,
! [SV240: $i,SV198: $i] :
( ( ~ ( in @ SV198 @ SV240 )
| ( ( set_union2 @ ( singleton @ SV198 ) @ SV240 )
= SV240 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1698]) ).
thf(1749,plain,
( ( ~ ~ ( ~ ( empty @ sK45_SX0 )
| ~ ( relation @ sK45_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1699]) ).
thf(1750,plain,
! [SV199: $i] :
( ( ~ ( ( SV199 != empty_set )
| ! [SY567: $i] :
~ ( in @ SY567 @ SV199 ) )
| ~ ( ~ ! [SY568: $i] :
~ ( in @ SY568 @ SV199 )
| ( SV199 = empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1700]) ).
thf(1751,plain,
! [SV241: $i,SV200: $i] :
( ( ~ ! [SY631: $i] :
( ~ ( in @ SY631 @ SV200 )
| ( in @ SY631 @ SV241 ) )
| ( element @ SV200 @ ( powerset @ SV241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1701]) ).
thf(1752,plain,
! [SV242: $i,SV201: $i] :
( ( ! [SY632: $i] :
~ ( ~ ( ~ ( subset @ ( unordered_pair @ SV201 @ SV242 ) @ SY632 )
| ~ ( ~ ( in @ SV201 @ SY632 )
| ~ ( in @ SV242 @ SY632 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV201 @ SY632 )
| ~ ( in @ SV242 @ SY632 ) )
| ( subset @ ( unordered_pair @ SV201 @ SV242 ) @ SY632 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1702]) ).
thf(1753,plain,
! [SV203: $i,SV154: $i] :
( ( empty @ ( ordered_pair @ SV154 @ SV203 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1704]) ).
thf(1754,plain,
! [SV204: $i,SV155: $i,SV243: $i] :
( ( ~ ( ~ ( ( SV243
!= ( set_union2 @ SV155 @ SV204 ) )
| ! [SY633: $i] :
~ ( ~ ( ~ ( in @ SY633 @ SV243 )
| ( in @ SY633 @ SV155 )
| ( in @ SY633 @ SV204 ) )
| ~ ( ~ ( ( in @ SY633 @ SV155 )
| ( in @ SY633 @ SV204 ) )
| ( in @ SY633 @ SV243 ) ) ) )
| ~ ( ~ ! [SY634: $i] :
~ ( ~ ( ~ ( in @ SY634 @ SV243 )
| ( in @ SY634 @ SV155 )
| ( in @ SY634 @ SV204 ) )
| ~ ( ~ ( ( in @ SY634 @ SV155 )
| ( in @ SY634 @ SV204 ) )
| ( in @ SY634 @ SV243 ) ) )
| ( SV243
= ( set_union2 @ SV155 @ SV204 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1705]) ).
thf(1755,plain,
! [SV205: $i,SV156: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV156 )
| ~ ( relation @ SV205 ) ) )
= $true )
| ( ( relation @ ( set_union2 @ SV156 @ SV205 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1706]) ).
thf(1756,plain,
! [SV157: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV157 @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SY635: $i,SY636: $i] :
( ~ ~ ( ~ ( in @ SY635 @ ( sK46_SY444 @ SV157 ) )
| ~ ( subset @ SY636 @ SY635 ) )
| ( in @ SY636 @ ( sK46_SY444 @ SV157 ) ) ) )
| ~ ! [SY637: $i] :
~ ~ ( ~ ( in @ SY637 @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SY638: $i] :
~ ~ ( ~ ( in @ SY638 @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY637 )
| ( in @ SX4 @ SY638 ) ) ) ) )
| ~ ! [SY640: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY640 @ ( sK46_SY444 @ SV157 ) )
| ~ ~ ( are_equipotent @ SY640 @ ( sK46_SY444 @ SV157 ) ) )
| ~ ~ ( in @ SY640 @ ( sK46_SY444 @ SV157 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1707]) ).
thf(1757,plain,
! [SV206: $i,SV158: $i] :
( ( ( ~ ~ ( in @ SV158 @ SV206 ) )
= $true )
| ( ( disjoint @ ( singleton @ SV158 ) @ SV206 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1708]) ).
thf(1758,plain,
! [SV244: $i,SV207: $i,SV159: $i] :
( ( ! [SY641: $i] :
( ( ( ordered_pair @ SV159 @ SV207 )
!= ( ordered_pair @ SV244 @ SY641 ) )
| ~ ( ( SV159 != SV244 )
| ( SV207 != SY641 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1709]) ).
thf(1759,plain,
! [SV208: $i,SV160: $i,SV245: $i] :
( ( ~ ( relation @ SV245 )
| ~ ( in @ ( ordered_pair @ SV160 @ SV208 ) @ SV245 )
| ~ ( ~ ( in @ SV160 @ ( relation_dom @ SV245 ) )
| ~ ( in @ SV208 @ ( relation_rng @ SV245 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1710]) ).
thf(1760,plain,
! [SV209: $i,SV161: $i] :
( ( ( ~ ( in @ SV161 @ SV209 ) )
= $true )
| ( ( element @ SV161 @ SV209 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1711]) ).
thf(1761,plain,
! [SV162: $i] :
( ( ( relation @ SV162 )
= $false )
| ( ( ( relation_field @ SV162 )
= ( set_union2 @ ( relation_dom @ SV162 ) @ ( relation_rng @ SV162 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1712]) ).
thf(1762,plain,
! [SV210: $i,SV163: $i] :
( ( ~ ( ~ ( in @ SV163 @ SV210 )
| ~ ( empty @ SV210 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1713]) ).
thf(1763,plain,
! [SV211: $i,SV164: $i] :
( ( ~ ( ( ( set_difference @ SV164 @ ( singleton @ SV211 ) )
!= SV164 )
| ~ ( in @ SV211 @ SV164 ) )
| ~ ( ~ ~ ( in @ SV211 @ SV164 )
| ( ( set_difference @ SV164 @ ( singleton @ SV211 ) )
= SV164 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1714]) ).
thf(1764,plain,
! [SV212: $i,SV165: $i] :
( ( ~ ( ~ ~ ( empty @ SV165 )
| ~ ( ~ ( ~ ( element @ SV212 @ SV165 )
| ( in @ SV212 @ SV165 ) )
| ~ ( ~ ( in @ SV212 @ SV165 )
| ( element @ SV212 @ SV165 ) ) ) )
| ~ ( ~ ( empty @ SV165 )
| ~ ( ~ ( ~ ( element @ SV212 @ SV165 )
| ( empty @ SV212 ) )
| ~ ( ~ ( empty @ SV212 )
| ( element @ SV212 @ SV165 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1715]) ).
thf(1765,plain,
! [SV213: $i,SV166: $i] :
( ( ~ ( ~ ( subset @ SV166 @ SV213 )
| ! [SY579: $i] :
( ~ ( in @ SY579 @ SV166 )
| ( in @ SY579 @ SV213 ) ) )
| ~ ( ~ ! [SY580: $i] :
( ~ ( in @ SY580 @ SV166 )
| ( in @ SY580 @ SV213 ) )
| ( subset @ SV166 @ SV213 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1716]) ).
thf(1766,plain,
! [SV214: $i,SV167: $i] :
( ( ( ~ ( in @ SV167 @ SV214 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV167 ) @ SV214 )
= SV214 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1717]) ).
thf(1767,plain,
! [SV215: $i,SV168: $i] :
( ( ~ ( ~ ( ( SV168 != empty_set ) )
| ~ ( ~ ( ( SV215
!= ( set_meet @ SV168 ) )
| ! [SY581: $i] :
~ ( ~ ( ~ ( in @ SY581 @ SV215 )
| ! [SY467: $i] :
( ~ ( in @ SY467 @ SV168 )
| ( in @ SY581 @ SY467 ) ) )
| ~ ( ~ ! [SY468: $i] :
( ~ ( in @ SY468 @ SV168 )
| ( in @ SY581 @ SY468 ) )
| ( in @ SY581 @ SV215 ) ) ) )
| ~ ( ~ ! [SY584: $i] :
~ ( ~ ( ~ ( in @ SY584 @ SV215 )
| ! [SY470: $i] :
( ~ ( in @ SY470 @ SV168 )
| ( in @ SY584 @ SY470 ) ) )
| ~ ( ~ ! [SY471: $i] :
( ~ ( in @ SY471 @ SV168 )
| ( in @ SY584 @ SY471 ) )
| ( in @ SY584 @ SV215 ) ) )
| ( SV215
= ( set_meet @ SV168 ) ) ) ) )
| ~ ( ( SV168 != empty_set )
| ~ ( ~ ( ( SV215
!= ( set_meet @ SV168 ) )
| ( SV215 = empty_set ) )
| ~ ( ( SV215 != empty_set )
| ( SV215
= ( set_meet @ SV168 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1718]) ).
thf(1768,plain,
! [SV169: $i,SV216: $i] :
( ( ~ ( ( SV216
!= ( union @ SV169 ) )
| ! [SY587: $i] :
~ ( ~ ( ~ ( in @ SY587 @ SV216 )
| ~ ! [SY474: $i] :
~ ~ ( ~ ( in @ SY587 @ SY474 )
| ~ ( in @ SY474 @ SV169 ) ) )
| ~ ( ~ ~ ! [SY475: $i] :
~ ~ ( ~ ( in @ SY587 @ SY475 )
| ~ ( in @ SY475 @ SV169 ) )
| ( in @ SY587 @ SV216 ) ) ) )
| ~ ( ~ ! [SY590: $i] :
~ ( ~ ( ~ ( in @ SY590 @ SV216 )
| ~ ! [SY477: $i] :
~ ~ ( ~ ( in @ SY590 @ SY477 )
| ~ ( in @ SY477 @ SV169 ) ) )
| ~ ( ~ ~ ! [SY478: $i] :
~ ~ ( ~ ( in @ SY590 @ SY478 )
| ~ ( in @ SY478 @ SV169 ) )
| ( in @ SY590 @ SV216 ) ) )
| ( SV216
= ( union @ SV169 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1719]) ).
thf(1769,plain,
! [SV217: $i,SV170: $i,SV246: $i] :
( ( ~ ( ~ ( ( SV246
!= ( unordered_pair @ SV170 @ SV217 ) )
| ! [SY642: $i] :
~ ( ~ ( ~ ( in @ SY642 @ SV246 )
| ( SY642 = SV170 )
| ( SY642 = SV217 ) )
| ~ ( ~ ( ( SY642 = SV170 )
| ( SY642 = SV217 ) )
| ( in @ SY642 @ SV246 ) ) ) )
| ~ ( ~ ! [SY643: $i] :
~ ( ~ ( ~ ( in @ SY643 @ SV246 )
| ( SY643 = SV170 )
| ( SY643 = SV217 ) )
| ~ ( ~ ( ( SY643 = SV170 )
| ( SY643 = SV217 ) )
| ( in @ SY643 @ SV246 ) ) )
| ( SV246
= ( unordered_pair @ SV170 @ SV217 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1720]) ).
thf(1770,plain,
! [SV247: $i,SV218: $i,SV171: $i] :
( ( ! [SY644: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV171 @ SV218 ) @ ( cartesian_product2 @ SV247 @ SY644 ) )
| ~ ( ~ ( in @ SV171 @ SV247 )
| ~ ( in @ SV218 @ SY644 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV171 @ SV247 )
| ~ ( in @ SV218 @ SY644 ) )
| ( in @ ( ordered_pair @ SV171 @ SV218 ) @ ( cartesian_product2 @ SV247 @ SY644 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1721]) ).
thf(1771,plain,
! [SV172: $i,SV219: $i] :
( ( ~ ( ( SV219
!= ( singleton @ SV172 ) )
| ! [SY598: $i] :
~ ( ~ ( ~ ( in @ SY598 @ SV219 )
| ( SY598 = SV172 ) )
| ~ ( ( SY598 != SV172 )
| ( in @ SY598 @ SV219 ) ) ) )
| ~ ( ~ ! [SY599: $i] :
~ ( ~ ( ~ ( in @ SY599 @ SV219 )
| ( SY599 = SV172 ) )
| ~ ( ( SY599 != SV172 )
| ( in @ SY599 @ SV219 ) ) )
| ( SV219
= ( singleton @ SV172 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1722]) ).
thf(1772,plain,
! [SV220: $i,SV173: $i] :
( ( ( ~ ( in @ SV173 @ SV220 ) )
= $true )
| ( ( subset @ SV173 @ ( union @ SV220 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1723]) ).
thf(1773,plain,
! [SV174: $i] :
( ( ~ ( ~ ( relation @ SV174 )
| ! [SY490: $i] :
~ ~ ( ~ ( in @ SY490 @ SV174 )
| ~ ! [SX2: $i,SX3: $i] :
( SY490
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1724]) ).
thf(1774,plain,
! [SV174: $i] :
( ( ~ ( ~ ! [SY493: $i] :
~ ~ ( ~ ( in @ SY493 @ SV174 )
| ~ ! [SX2: $i,SX3: $i] :
( SY493
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SV174 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1724]) ).
thf(1775,plain,
! [SV221: $i,SV175: $i] :
( ( ~ ( ~ ( subset @ ( singleton @ SV175 ) @ SV221 )
| ( in @ SV175 @ SV221 ) )
| ~ ( ~ ( in @ SV175 @ SV221 )
| ( subset @ ( singleton @ SV175 ) @ SV221 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1725]) ).
thf(1776,plain,
! [SV248: $i,SV222: $i,SV176: $i] :
( ( ~ ( subset @ SV176 @ SV222 )
| ( in @ SV248 @ SV176 )
| ( subset @ SV176 @ ( set_difference @ SV222 @ ( singleton @ SV248 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1726]) ).
thf(1777,plain,
! [SV177: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV177 @ ( sK47_SY499 @ SV177 ) )
| ~ ! [SY645: $i,SY646: $i] :
( ~ ~ ( ~ ( in @ SY645 @ ( sK47_SY499 @ SV177 ) )
| ~ ( subset @ SY646 @ SY645 ) )
| ( in @ SY646 @ ( sK47_SY499 @ SV177 ) ) ) )
| ~ ! [SY647: $i] :
( ~ ( in @ SY647 @ ( sK47_SY499 @ SV177 ) )
| ( in @ ( powerset @ SY647 ) @ ( sK47_SY499 @ SV177 ) ) ) )
| ~ ! [SY648: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY648 @ ( sK47_SY499 @ SV177 ) )
| ~ ~ ( are_equipotent @ SY648 @ ( sK47_SY499 @ SV177 ) ) )
| ~ ~ ( in @ SY648 @ ( sK47_SY499 @ SV177 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1727]) ).
thf(1778,plain,
! [SV223: $i,SV178: $i] :
( ( ~ ( ~ ( subset @ ( singleton @ SV178 ) @ SV223 )
| ( in @ SV178 @ SV223 ) )
| ~ ( ~ ( in @ SV178 @ SV223 )
| ( subset @ ( singleton @ SV178 ) @ SV223 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1728]) ).
thf(1779,plain,
! [SV224: $i,SV179: $i] :
( ( ~ ~ ~ ( ~ ~ ( disjoint @ SV179 @ SV224 )
| ~ ! [SY601: $i] :
~ ( in @ SY601 @ ( set_intersection2 @ SV179 @ SV224 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY602: $i] :
~ ( in @ SY602 @ ( set_intersection2 @ SV179 @ SV224 ) )
| ~ ( disjoint @ SV179 @ SV224 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1729]) ).
thf(1780,plain,
! [SV225: $i,SV180: $i,SV249: $i] :
( ( ~ ( ~ ( ( SV249
!= ( set_intersection2 @ SV180 @ SV225 ) )
| ! [SY649: $i] :
~ ( ~ ( ~ ( in @ SY649 @ SV249 )
| ~ ( ~ ( in @ SY649 @ SV180 )
| ~ ( in @ SY649 @ SV225 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY649 @ SV180 )
| ~ ( in @ SY649 @ SV225 ) )
| ( in @ SY649 @ SV249 ) ) ) )
| ~ ( ~ ! [SY650: $i] :
~ ( ~ ( ~ ( in @ SY650 @ SV249 )
| ~ ( ~ ( in @ SY650 @ SV180 )
| ~ ( in @ SY650 @ SV225 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY650 @ SV180 )
| ~ ( in @ SY650 @ SV225 ) )
| ( in @ SY650 @ SV249 ) ) )
| ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1730]) ).
thf(1781,plain,
! [SV181: $i,SV226: $i] :
( ( ( ~ ( element @ SV226 @ ( powerset @ SV181 ) ) )
= $true )
| ( ( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV226 )
| ( in @ SY606 @ SV181 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1731]) ).
thf(1782,plain,
! [SV227: $i,SV182: $i] :
( ( ( ~ ( element @ SV182 @ SV227 ) )
= $true )
| ( ( ( empty @ SV227 )
| ( in @ SV182 @ SV227 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1732]) ).
thf(1783,plain,
! [SV228: $i,SV183: $i] :
( ( ~ ( ~ ( disjoint @ ( singleton @ SV183 ) @ SV228 )
| ~ ( in @ SV183 @ SV228 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1733]) ).
thf(1784,plain,
! [SV229: $i,SV184: $i,SV250: $i] :
( ( ~ ( ~ ( ( SV250
!= ( set_difference @ SV184 @ SV229 ) )
| ! [SY651: $i] :
~ ( ~ ( ~ ( in @ SY651 @ SV250 )
| ~ ( ~ ( in @ SY651 @ SV184 )
| ~ ~ ( in @ SY651 @ SV229 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY651 @ SV184 )
| ~ ~ ( in @ SY651 @ SV229 ) )
| ( in @ SY651 @ SV250 ) ) ) )
| ~ ( ~ ! [SY652: $i] :
~ ( ~ ( ~ ( in @ SY652 @ SV250 )
| ~ ( ~ ( in @ SY652 @ SV184 )
| ~ ~ ( in @ SY652 @ SV229 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY652 @ SV184 )
| ~ ~ ( in @ SY652 @ SV229 ) )
| ( in @ SY652 @ SV250 ) ) )
| ( SV250
= ( set_difference @ SV184 @ SV229 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1734]) ).
thf(1785,plain,
! [SV251: $i,SV230: $i,SV185: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( in @ SV185 @ SV230 )
| ~ ( element @ SV230 @ ( powerset @ SV251 ) ) )
| ~ ( empty @ SV251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1735]) ).
thf(1786,plain,
! [SV231: $i,SV186: $i] :
( ( ( ~ ( in @ SV186 @ SV231 ) )
= $true )
| ( ( ~ ( in @ SV231 @ SV186 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1736]) ).
thf(1787,plain,
! [SV187: $i] :
( ( ( relation @ SV187 )
= $false )
| ( ( ! [SY523: $i] :
( ~ ( relation @ SY523 )
| ~ ( subset @ SV187 @ SY523 )
| ~ ( ~ ( subset @ ( relation_dom @ SV187 ) @ ( relation_dom @ SY523 ) )
| ~ ( subset @ ( relation_rng @ SV187 ) @ ( relation_rng @ SY523 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1737]) ).
thf(1788,plain,
! [SV252: $i,SV232: $i,SV188: $i] :
( ( ! [SY653: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV188 @ SV232 ) @ ( cartesian_product2 @ SV252 @ SY653 ) )
| ~ ( ~ ( in @ SV188 @ SV252 )
| ~ ( in @ SV232 @ SY653 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV188 @ SV252 )
| ~ ( in @ SV232 @ SY653 ) )
| ( in @ ( ordered_pair @ SV188 @ SV232 ) @ ( cartesian_product2 @ SV252 @ SY653 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1738]) ).
thf(1789,plain,
! [SV233: $i,SV189: $i] :
( ( ( ~ ! [SY613: $i] :
~ ( ~ ( ~ ( in @ SY613 @ SV189 )
| ( in @ SY613 @ SV233 ) )
| ~ ( ~ ( in @ SY613 @ SV233 )
| ( in @ SY613 @ SV189 ) ) ) )
= $true )
| ( ( SV189 = SV233 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1739]) ).
thf(1790,plain,
! [SV190: $i,SV234: $i] :
( ( ~ ( ( SV234
!= ( powerset @ SV190 ) )
| ! [SY614: $i] :
~ ( ~ ( ~ ( in @ SY614 @ SV234 )
| ( subset @ SY614 @ SV190 ) )
| ~ ( ~ ( subset @ SY614 @ SV190 )
| ( in @ SY614 @ SV234 ) ) ) )
| ~ ( ~ ! [SY615: $i] :
~ ( ~ ( ~ ( in @ SY615 @ SV234 )
| ( subset @ SY615 @ SV190 ) )
| ~ ( ~ ( subset @ SY615 @ SV190 )
| ( in @ SY615 @ SV234 ) ) )
| ( SV234
= ( powerset @ SV190 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1740]) ).
thf(1791,plain,
! [SV235: $i,SV191: $i,SV253: $i] :
( ( ~ ( element @ SV253 @ ( powerset @ SV191 ) )
| ~ ~ ( ~ ( in @ SV235 @ ( subset_complement @ SV191 @ SV253 ) )
| ~ ( in @ SV235 @ SV253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1741]) ).
thf(1792,plain,
! [SV192: $i] :
( ( ( relation @ SV192 )
= $false )
| ( ( ! [SY534: $i] :
~ ( ~ ( ( SY534
!= ( relation_dom @ SV192 ) )
| ! [SY535: $i] :
~ ( ~ ( ~ ( in @ SY535 @ SY534 )
| ~ ! [SY536: $i] :
~ ( in @ ( ordered_pair @ SY535 @ SY536 ) @ SV192 ) )
| ~ ( ~ ~ ! [SY537: $i] :
~ ( in @ ( ordered_pair @ SY535 @ SY537 ) @ SV192 )
| ( in @ SY535 @ SY534 ) ) ) )
| ~ ( ~ ! [SY538: $i] :
~ ( ~ ( ~ ( in @ SY538 @ SY534 )
| ~ ! [SY539: $i] :
~ ( in @ ( ordered_pair @ SY538 @ SY539 ) @ SV192 ) )
| ~ ( ~ ~ ! [SY540: $i] :
~ ( in @ ( ordered_pair @ SY538 @ SY540 ) @ SV192 )
| ( in @ SY538 @ SY534 ) ) )
| ( SY534
= ( relation_dom @ SV192 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1742]) ).
thf(1793,plain,
! [SV236: $i,SV193: $i,SV254: $i] :
( ( ~ ( ~ ( ( SV254
!= ( cartesian_product2 @ SV193 @ SV236 ) )
| ! [SY654: $i] :
~ ( ~ ( ~ ( in @ SY654 @ SV254 )
| ~ ! [SY619: $i] :
~ ~ ! [SY620: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY619 @ SV193 )
| ~ ( in @ SY620 @ SV236 ) )
| ( SY654
!= ( ordered_pair @ SY619 @ SY620 ) ) ) )
| ~ ( ~ ~ ! [SY621: $i] :
~ ~ ! [SY622: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY621 @ SV193 )
| ~ ( in @ SY622 @ SV236 ) )
| ( SY654
!= ( ordered_pair @ SY621 @ SY622 ) ) )
| ( in @ SY654 @ SV254 ) ) ) )
| ~ ( ~ ! [SY659: $i] :
~ ( ~ ( ~ ( in @ SY659 @ SV254 )
| ~ ! [SY624: $i] :
~ ~ ! [SY625: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY624 @ SV193 )
| ~ ( in @ SY625 @ SV236 ) )
| ( SY659
!= ( ordered_pair @ SY624 @ SY625 ) ) ) )
| ~ ( ~ ~ ! [SY626: $i] :
~ ~ ! [SY627: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY626 @ SV193 )
| ~ ( in @ SY627 @ SV236 ) )
| ( SY659
!= ( ordered_pair @ SY626 @ SY627 ) ) )
| ( in @ SY659 @ SV254 ) ) )
| ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1743]) ).
thf(1794,plain,
! [SV194: $i] :
( ( ( relation @ SV194 )
= $false )
| ( ( ! [SY553: $i] :
~ ( ~ ( ( SY553
!= ( relation_rng @ SV194 ) )
| ! [SY554: $i] :
~ ( ~ ( ~ ( in @ SY554 @ SY553 )
| ~ ! [SY555: $i] :
~ ( in @ ( ordered_pair @ SY555 @ SY554 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY556: $i] :
~ ( in @ ( ordered_pair @ SY556 @ SY554 ) @ SV194 )
| ( in @ SY554 @ SY553 ) ) ) )
| ~ ( ~ ! [SY557: $i] :
~ ( ~ ( ~ ( in @ SY557 @ SY553 )
| ~ ! [SY558: $i] :
~ ( in @ ( ordered_pair @ SY558 @ SY557 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY559: $i] :
~ ( in @ ( ordered_pair @ SY559 @ SY557 ) @ SV194 )
| ( in @ SY557 @ SY553 ) ) )
| ( SY553
= ( relation_rng @ SV194 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1744]) ).
thf(1795,plain,
! [SV237: $i,SV195: $i] :
( ( ( ~ ( in @ SV195 @ SV237 ) )
= $true )
| ( ( subset @ SV195 @ ( union @ SV237 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1745]) ).
thf(1796,plain,
! [SV238: $i,SV196: $i] :
( ( ~ ~ ~ ( ~ ~ ( disjoint @ SV196 @ SV238 )
| ~ ! [SY628: $i] :
~ ~ ( ~ ( in @ SY628 @ SV196 )
| ~ ( in @ SY628 @ SV238 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY629: $i] :
~ ~ ( ~ ( in @ SY629 @ SV196 )
| ~ ( in @ SY629 @ SV238 ) )
| ~ ( disjoint @ SV196 @ SV238 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1746]) ).
thf(1797,plain,
! [SV255: $i,SV239: $i,SV197: $i] :
( ( ~ ~ ( ~ ( in @ SV197 @ SV239 )
| ~ ( element @ SV239 @ ( powerset @ SV255 ) ) )
| ( element @ SV197 @ SV255 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1747]) ).
thf(1798,plain,
! [SV240: $i,SV198: $i] :
( ( ( ~ ( in @ SV198 @ SV240 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV198 ) @ SV240 )
= SV240 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1748]) ).
thf(1799,plain,
( ( ~ ( ~ ( empty @ sK45_SX0 )
| ~ ( relation @ sK45_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1749]) ).
thf(1800,plain,
! [SV199: $i] :
( ( ~ ( ( SV199 != empty_set )
| ! [SY567: $i] :
~ ( in @ SY567 @ SV199 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1750]) ).
thf(1801,plain,
! [SV199: $i] :
( ( ~ ( ~ ! [SY568: $i] :
~ ( in @ SY568 @ SV199 )
| ( SV199 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1750]) ).
thf(1802,plain,
! [SV241: $i,SV200: $i] :
( ( ( ~ ! [SY631: $i] :
( ~ ( in @ SY631 @ SV200 )
| ( in @ SY631 @ SV241 ) ) )
= $true )
| ( ( element @ SV200 @ ( powerset @ SV241 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1751]) ).
thf(1803,plain,
! [SV256: $i,SV242: $i,SV201: $i] :
( ( ~ ( ~ ( ~ ( subset @ ( unordered_pair @ SV201 @ SV242 ) @ SV256 )
| ~ ( ~ ( in @ SV201 @ SV256 )
| ~ ( in @ SV242 @ SV256 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV201 @ SV256 )
| ~ ( in @ SV242 @ SV256 ) )
| ( subset @ ( unordered_pair @ SV201 @ SV242 ) @ SV256 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1752]) ).
thf(1804,plain,
! [SV204: $i,SV155: $i,SV243: $i] :
( ( ~ ( ( SV243
!= ( set_union2 @ SV155 @ SV204 ) )
| ! [SY633: $i] :
~ ( ~ ( ~ ( in @ SY633 @ SV243 )
| ( in @ SY633 @ SV155 )
| ( in @ SY633 @ SV204 ) )
| ~ ( ~ ( ( in @ SY633 @ SV155 )
| ( in @ SY633 @ SV204 ) )
| ( in @ SY633 @ SV243 ) ) ) )
| ~ ( ~ ! [SY634: $i] :
~ ( ~ ( ~ ( in @ SY634 @ SV243 )
| ( in @ SY634 @ SV155 )
| ( in @ SY634 @ SV204 ) )
| ~ ( ~ ( ( in @ SY634 @ SV155 )
| ( in @ SY634 @ SV204 ) )
| ( in @ SY634 @ SV243 ) ) )
| ( SV243
= ( set_union2 @ SV155 @ SV204 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1754]) ).
thf(1805,plain,
! [SV205: $i,SV156: $i] :
( ( ( ~ ( ~ ( relation @ SV156 )
| ~ ( relation @ SV205 ) ) )
= $false )
| ( ( relation @ ( set_union2 @ SV156 @ SV205 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1755]) ).
thf(1806,plain,
! [SV157: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV157 @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SY635: $i,SY636: $i] :
( ~ ~ ( ~ ( in @ SY635 @ ( sK46_SY444 @ SV157 ) )
| ~ ( subset @ SY636 @ SY635 ) )
| ( in @ SY636 @ ( sK46_SY444 @ SV157 ) ) ) )
| ~ ! [SY637: $i] :
~ ~ ( ~ ( in @ SY637 @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SY638: $i] :
~ ~ ( ~ ( in @ SY638 @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY637 )
| ( in @ SX4 @ SY638 ) ) ) ) )
| ~ ! [SY640: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY640 @ ( sK46_SY444 @ SV157 ) )
| ~ ~ ( are_equipotent @ SY640 @ ( sK46_SY444 @ SV157 ) ) )
| ~ ~ ( in @ SY640 @ ( sK46_SY444 @ SV157 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1756]) ).
thf(1807,plain,
! [SV206: $i,SV158: $i] :
( ( ( ~ ( in @ SV158 @ SV206 ) )
= $false )
| ( ( disjoint @ ( singleton @ SV158 ) @ SV206 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1757]) ).
thf(1808,plain,
! [SV257: $i,SV244: $i,SV207: $i,SV159: $i] :
( ( ( ( ordered_pair @ SV159 @ SV207 )
!= ( ordered_pair @ SV244 @ SV257 ) )
| ~ ( ( SV159 != SV244 )
| ( SV207 != SV257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1758]) ).
thf(1809,plain,
! [SV208: $i,SV160: $i,SV245: $i] :
( ( ( ~ ( relation @ SV245 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV160 @ SV208 ) @ SV245 )
| ~ ( ~ ( in @ SV160 @ ( relation_dom @ SV245 ) )
| ~ ( in @ SV208 @ ( relation_rng @ SV245 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1759]) ).
thf(1810,plain,
! [SV209: $i,SV161: $i] :
( ( ( in @ SV161 @ SV209 )
= $false )
| ( ( element @ SV161 @ SV209 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1760]) ).
thf(1811,plain,
! [SV210: $i,SV163: $i] :
( ( ~ ( in @ SV163 @ SV210 )
| ~ ( empty @ SV210 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1762]) ).
thf(1812,plain,
! [SV211: $i,SV164: $i] :
( ( ~ ( ( ( set_difference @ SV164 @ ( singleton @ SV211 ) )
!= SV164 )
| ~ ( in @ SV211 @ SV164 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1763]) ).
thf(1813,plain,
! [SV164: $i,SV211: $i] :
( ( ~ ( ~ ~ ( in @ SV211 @ SV164 )
| ( ( set_difference @ SV164 @ ( singleton @ SV211 ) )
= SV164 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1763]) ).
thf(1814,plain,
! [SV212: $i,SV165: $i] :
( ( ~ ( ~ ~ ( empty @ SV165 )
| ~ ( ~ ( ~ ( element @ SV212 @ SV165 )
| ( in @ SV212 @ SV165 ) )
| ~ ( ~ ( in @ SV212 @ SV165 )
| ( element @ SV212 @ SV165 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1764]) ).
thf(1815,plain,
! [SV212: $i,SV165: $i] :
( ( ~ ( ~ ( empty @ SV165 )
| ~ ( ~ ( ~ ( element @ SV212 @ SV165 )
| ( empty @ SV212 ) )
| ~ ( ~ ( empty @ SV212 )
| ( element @ SV212 @ SV165 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1764]) ).
thf(1816,plain,
! [SV213: $i,SV166: $i] :
( ( ~ ( ~ ( subset @ SV166 @ SV213 )
| ! [SY579: $i] :
( ~ ( in @ SY579 @ SV166 )
| ( in @ SY579 @ SV213 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1765]) ).
thf(1817,plain,
! [SV213: $i,SV166: $i] :
( ( ~ ( ~ ! [SY580: $i] :
( ~ ( in @ SY580 @ SV166 )
| ( in @ SY580 @ SV213 ) )
| ( subset @ SV166 @ SV213 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1765]) ).
thf(1818,plain,
! [SV214: $i,SV167: $i] :
( ( ( in @ SV167 @ SV214 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV167 ) @ SV214 )
= SV214 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1766]) ).
thf(1819,plain,
! [SV215: $i,SV168: $i] :
( ( ~ ( ~ ( ( SV168 != empty_set ) )
| ~ ( ~ ( ( SV215
!= ( set_meet @ SV168 ) )
| ! [SY581: $i] :
~ ( ~ ( ~ ( in @ SY581 @ SV215 )
| ! [SY467: $i] :
( ~ ( in @ SY467 @ SV168 )
| ( in @ SY581 @ SY467 ) ) )
| ~ ( ~ ! [SY468: $i] :
( ~ ( in @ SY468 @ SV168 )
| ( in @ SY581 @ SY468 ) )
| ( in @ SY581 @ SV215 ) ) ) )
| ~ ( ~ ! [SY584: $i] :
~ ( ~ ( ~ ( in @ SY584 @ SV215 )
| ! [SY470: $i] :
( ~ ( in @ SY470 @ SV168 )
| ( in @ SY584 @ SY470 ) ) )
| ~ ( ~ ! [SY471: $i] :
( ~ ( in @ SY471 @ SV168 )
| ( in @ SY584 @ SY471 ) )
| ( in @ SY584 @ SV215 ) ) )
| ( SV215
= ( set_meet @ SV168 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1767]) ).
thf(1820,plain,
! [SV215: $i,SV168: $i] :
( ( ~ ( ( SV168 != empty_set )
| ~ ( ~ ( ( SV215
!= ( set_meet @ SV168 ) )
| ( SV215 = empty_set ) )
| ~ ( ( SV215 != empty_set )
| ( SV215
= ( set_meet @ SV168 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1767]) ).
thf(1821,plain,
! [SV169: $i,SV216: $i] :
( ( ~ ( ( SV216
!= ( union @ SV169 ) )
| ! [SY587: $i] :
~ ( ~ ( ~ ( in @ SY587 @ SV216 )
| ~ ! [SY474: $i] :
~ ~ ( ~ ( in @ SY587 @ SY474 )
| ~ ( in @ SY474 @ SV169 ) ) )
| ~ ( ~ ~ ! [SY475: $i] :
~ ~ ( ~ ( in @ SY587 @ SY475 )
| ~ ( in @ SY475 @ SV169 ) )
| ( in @ SY587 @ SV216 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1768]) ).
thf(1822,plain,
! [SV169: $i,SV216: $i] :
( ( ~ ( ~ ! [SY590: $i] :
~ ( ~ ( ~ ( in @ SY590 @ SV216 )
| ~ ! [SY477: $i] :
~ ~ ( ~ ( in @ SY590 @ SY477 )
| ~ ( in @ SY477 @ SV169 ) ) )
| ~ ( ~ ~ ! [SY478: $i] :
~ ~ ( ~ ( in @ SY590 @ SY478 )
| ~ ( in @ SY478 @ SV169 ) )
| ( in @ SY590 @ SV216 ) ) )
| ( SV216
= ( union @ SV169 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1768]) ).
thf(1823,plain,
! [SV217: $i,SV170: $i,SV246: $i] :
( ( ~ ( ( SV246
!= ( unordered_pair @ SV170 @ SV217 ) )
| ! [SY642: $i] :
~ ( ~ ( ~ ( in @ SY642 @ SV246 )
| ( SY642 = SV170 )
| ( SY642 = SV217 ) )
| ~ ( ~ ( ( SY642 = SV170 )
| ( SY642 = SV217 ) )
| ( in @ SY642 @ SV246 ) ) ) )
| ~ ( ~ ! [SY643: $i] :
~ ( ~ ( ~ ( in @ SY643 @ SV246 )
| ( SY643 = SV170 )
| ( SY643 = SV217 ) )
| ~ ( ~ ( ( SY643 = SV170 )
| ( SY643 = SV217 ) )
| ( in @ SY643 @ SV246 ) ) )
| ( SV246
= ( unordered_pair @ SV170 @ SV217 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1769]) ).
thf(1824,plain,
! [SV258: $i,SV247: $i,SV218: $i,SV171: $i] :
( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV171 @ SV218 ) @ ( cartesian_product2 @ SV247 @ SV258 ) )
| ~ ( ~ ( in @ SV171 @ SV247 )
| ~ ( in @ SV218 @ SV258 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV171 @ SV247 )
| ~ ( in @ SV218 @ SV258 ) )
| ( in @ ( ordered_pair @ SV171 @ SV218 ) @ ( cartesian_product2 @ SV247 @ SV258 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1770]) ).
thf(1825,plain,
! [SV172: $i,SV219: $i] :
( ( ~ ( ( SV219
!= ( singleton @ SV172 ) )
| ! [SY598: $i] :
~ ( ~ ( ~ ( in @ SY598 @ SV219 )
| ( SY598 = SV172 ) )
| ~ ( ( SY598 != SV172 )
| ( in @ SY598 @ SV219 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1771]) ).
thf(1826,plain,
! [SV172: $i,SV219: $i] :
( ( ~ ( ~ ! [SY599: $i] :
~ ( ~ ( ~ ( in @ SY599 @ SV219 )
| ( SY599 = SV172 ) )
| ~ ( ( SY599 != SV172 )
| ( in @ SY599 @ SV219 ) ) )
| ( SV219
= ( singleton @ SV172 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1771]) ).
thf(1827,plain,
! [SV220: $i,SV173: $i] :
( ( ( in @ SV173 @ SV220 )
= $false )
| ( ( subset @ SV173 @ ( union @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1772]) ).
thf(1828,plain,
! [SV174: $i] :
( ( ~ ( relation @ SV174 )
| ! [SY490: $i] :
~ ~ ( ~ ( in @ SY490 @ SV174 )
| ~ ! [SX2: $i,SX3: $i] :
( SY490
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1773]) ).
thf(1829,plain,
! [SV174: $i] :
( ( ~ ! [SY493: $i] :
~ ~ ( ~ ( in @ SY493 @ SV174 )
| ~ ! [SX2: $i,SX3: $i] :
( SY493
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SV174 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1774]) ).
thf(1830,plain,
! [SV221: $i,SV175: $i] :
( ( ~ ( ~ ( subset @ ( singleton @ SV175 ) @ SV221 )
| ( in @ SV175 @ SV221 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1775]) ).
thf(1831,plain,
! [SV221: $i,SV175: $i] :
( ( ~ ( ~ ( in @ SV175 @ SV221 )
| ( subset @ ( singleton @ SV175 ) @ SV221 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1775]) ).
thf(1832,plain,
! [SV248: $i,SV222: $i,SV176: $i] :
( ( ( ~ ( subset @ SV176 @ SV222 ) )
= $true )
| ( ( ( in @ SV248 @ SV176 )
| ( subset @ SV176 @ ( set_difference @ SV222 @ ( singleton @ SV248 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1776]) ).
thf(1833,plain,
! [SV177: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV177 @ ( sK47_SY499 @ SV177 ) )
| ~ ! [SY645: $i,SY646: $i] :
( ~ ~ ( ~ ( in @ SY645 @ ( sK47_SY499 @ SV177 ) )
| ~ ( subset @ SY646 @ SY645 ) )
| ( in @ SY646 @ ( sK47_SY499 @ SV177 ) ) ) )
| ~ ! [SY647: $i] :
( ~ ( in @ SY647 @ ( sK47_SY499 @ SV177 ) )
| ( in @ ( powerset @ SY647 ) @ ( sK47_SY499 @ SV177 ) ) ) )
| ~ ! [SY648: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY648 @ ( sK47_SY499 @ SV177 ) )
| ~ ~ ( are_equipotent @ SY648 @ ( sK47_SY499 @ SV177 ) ) )
| ~ ~ ( in @ SY648 @ ( sK47_SY499 @ SV177 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1777]) ).
thf(1834,plain,
! [SV223: $i,SV178: $i] :
( ( ~ ( ~ ( subset @ ( singleton @ SV178 ) @ SV223 )
| ( in @ SV178 @ SV223 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1778]) ).
thf(1835,plain,
! [SV223: $i,SV178: $i] :
( ( ~ ( ~ ( in @ SV178 @ SV223 )
| ( subset @ ( singleton @ SV178 ) @ SV223 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1778]) ).
thf(1836,plain,
! [SV224: $i,SV179: $i] :
( ( ~ ~ ~ ( ~ ~ ( disjoint @ SV179 @ SV224 )
| ~ ! [SY601: $i] :
~ ( in @ SY601 @ ( set_intersection2 @ SV179 @ SV224 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1779]) ).
thf(1837,plain,
! [SV224: $i,SV179: $i] :
( ( ~ ~ ~ ( ~ ~ ! [SY602: $i] :
~ ( in @ SY602 @ ( set_intersection2 @ SV179 @ SV224 ) )
| ~ ( disjoint @ SV179 @ SV224 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1779]) ).
thf(1838,plain,
! [SV225: $i,SV180: $i,SV249: $i] :
( ( ~ ( ( SV249
!= ( set_intersection2 @ SV180 @ SV225 ) )
| ! [SY649: $i] :
~ ( ~ ( ~ ( in @ SY649 @ SV249 )
| ~ ( ~ ( in @ SY649 @ SV180 )
| ~ ( in @ SY649 @ SV225 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY649 @ SV180 )
| ~ ( in @ SY649 @ SV225 ) )
| ( in @ SY649 @ SV249 ) ) ) )
| ~ ( ~ ! [SY650: $i] :
~ ( ~ ( ~ ( in @ SY650 @ SV249 )
| ~ ( ~ ( in @ SY650 @ SV180 )
| ~ ( in @ SY650 @ SV225 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY650 @ SV180 )
| ~ ( in @ SY650 @ SV225 ) )
| ( in @ SY650 @ SV249 ) ) )
| ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1780]) ).
thf(1839,plain,
! [SV181: $i,SV226: $i] :
( ( ( element @ SV226 @ ( powerset @ SV181 ) )
= $false )
| ( ( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV226 )
| ( in @ SY606 @ SV181 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1781]) ).
thf(1840,plain,
! [SV227: $i,SV182: $i] :
( ( ( element @ SV182 @ SV227 )
= $false )
| ( ( ( empty @ SV227 )
| ( in @ SV182 @ SV227 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1782]) ).
thf(1841,plain,
! [SV228: $i,SV183: $i] :
( ( ~ ( disjoint @ ( singleton @ SV183 ) @ SV228 )
| ~ ( in @ SV183 @ SV228 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1783]) ).
thf(1842,plain,
! [SV229: $i,SV184: $i,SV250: $i] :
( ( ~ ( ( SV250
!= ( set_difference @ SV184 @ SV229 ) )
| ! [SY651: $i] :
~ ( ~ ( ~ ( in @ SY651 @ SV250 )
| ~ ( ~ ( in @ SY651 @ SV184 )
| ~ ~ ( in @ SY651 @ SV229 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY651 @ SV184 )
| ~ ~ ( in @ SY651 @ SV229 ) )
| ( in @ SY651 @ SV250 ) ) ) )
| ~ ( ~ ! [SY652: $i] :
~ ( ~ ( ~ ( in @ SY652 @ SV250 )
| ~ ( ~ ( in @ SY652 @ SV184 )
| ~ ~ ( in @ SY652 @ SV229 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY652 @ SV184 )
| ~ ~ ( in @ SY652 @ SV229 ) )
| ( in @ SY652 @ SV250 ) ) )
| ( SV250
= ( set_difference @ SV184 @ SV229 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1784]) ).
thf(1843,plain,
! [SV251: $i,SV230: $i,SV185: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV185 @ SV230 )
| ~ ( element @ SV230 @ ( powerset @ SV251 ) ) )
| ~ ( empty @ SV251 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1785]) ).
thf(1844,plain,
! [SV231: $i,SV186: $i] :
( ( ( in @ SV186 @ SV231 )
= $false )
| ( ( ~ ( in @ SV231 @ SV186 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1786]) ).
thf(1845,plain,
! [SV187: $i,SV259: $i] :
( ( ( ~ ( relation @ SV259 )
| ~ ( subset @ SV187 @ SV259 )
| ~ ( ~ ( subset @ ( relation_dom @ SV187 ) @ ( relation_dom @ SV259 ) )
| ~ ( subset @ ( relation_rng @ SV187 ) @ ( relation_rng @ SV259 ) ) ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1787]) ).
thf(1846,plain,
! [SV260: $i,SV252: $i,SV232: $i,SV188: $i] :
( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV188 @ SV232 ) @ ( cartesian_product2 @ SV252 @ SV260 ) )
| ~ ( ~ ( in @ SV188 @ SV252 )
| ~ ( in @ SV232 @ SV260 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV188 @ SV252 )
| ~ ( in @ SV232 @ SV260 ) )
| ( in @ ( ordered_pair @ SV188 @ SV232 ) @ ( cartesian_product2 @ SV252 @ SV260 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1788]) ).
thf(1847,plain,
! [SV233: $i,SV189: $i] :
( ( ( ! [SY613: $i] :
~ ( ~ ( ~ ( in @ SY613 @ SV189 )
| ( in @ SY613 @ SV233 ) )
| ~ ( ~ ( in @ SY613 @ SV233 )
| ( in @ SY613 @ SV189 ) ) ) )
= $false )
| ( ( SV189 = SV233 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1789]) ).
thf(1848,plain,
! [SV190: $i,SV234: $i] :
( ( ~ ( ( SV234
!= ( powerset @ SV190 ) )
| ! [SY614: $i] :
~ ( ~ ( ~ ( in @ SY614 @ SV234 )
| ( subset @ SY614 @ SV190 ) )
| ~ ( ~ ( subset @ SY614 @ SV190 )
| ( in @ SY614 @ SV234 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1790]) ).
thf(1849,plain,
! [SV190: $i,SV234: $i] :
( ( ~ ( ~ ! [SY615: $i] :
~ ( ~ ( ~ ( in @ SY615 @ SV234 )
| ( subset @ SY615 @ SV190 ) )
| ~ ( ~ ( subset @ SY615 @ SV190 )
| ( in @ SY615 @ SV234 ) ) )
| ( SV234
= ( powerset @ SV190 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1790]) ).
thf(1850,plain,
! [SV235: $i,SV191: $i,SV253: $i] :
( ( ( ~ ( element @ SV253 @ ( powerset @ SV191 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( in @ SV235 @ ( subset_complement @ SV191 @ SV253 ) )
| ~ ( in @ SV235 @ SV253 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1791]) ).
thf(1851,plain,
! [SV192: $i,SV261: $i] :
( ( ( ~ ( ~ ( ( SV261
!= ( relation_dom @ SV192 ) )
| ! [SY664: $i] :
~ ( ~ ( ~ ( in @ SY664 @ SV261 )
| ~ ! [SY536: $i] :
~ ( in @ ( ordered_pair @ SY664 @ SY536 ) @ SV192 ) )
| ~ ( ~ ~ ! [SY537: $i] :
~ ( in @ ( ordered_pair @ SY664 @ SY537 ) @ SV192 )
| ( in @ SY664 @ SV261 ) ) ) )
| ~ ( ~ ! [SY667: $i] :
~ ( ~ ( ~ ( in @ SY667 @ SV261 )
| ~ ! [SY539: $i] :
~ ( in @ ( ordered_pair @ SY667 @ SY539 ) @ SV192 ) )
| ~ ( ~ ~ ! [SY540: $i] :
~ ( in @ ( ordered_pair @ SY667 @ SY540 ) @ SV192 )
| ( in @ SY667 @ SV261 ) ) )
| ( SV261
= ( relation_dom @ SV192 ) ) ) ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1792]) ).
thf(1852,plain,
! [SV236: $i,SV193: $i,SV254: $i] :
( ( ~ ( ( SV254
!= ( cartesian_product2 @ SV193 @ SV236 ) )
| ! [SY654: $i] :
~ ( ~ ( ~ ( in @ SY654 @ SV254 )
| ~ ! [SY619: $i] :
~ ~ ! [SY620: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY619 @ SV193 )
| ~ ( in @ SY620 @ SV236 ) )
| ( SY654
!= ( ordered_pair @ SY619 @ SY620 ) ) ) )
| ~ ( ~ ~ ! [SY621: $i] :
~ ~ ! [SY622: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY621 @ SV193 )
| ~ ( in @ SY622 @ SV236 ) )
| ( SY654
!= ( ordered_pair @ SY621 @ SY622 ) ) )
| ( in @ SY654 @ SV254 ) ) ) )
| ~ ( ~ ! [SY659: $i] :
~ ( ~ ( ~ ( in @ SY659 @ SV254 )
| ~ ! [SY624: $i] :
~ ~ ! [SY625: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY624 @ SV193 )
| ~ ( in @ SY625 @ SV236 ) )
| ( SY659
!= ( ordered_pair @ SY624 @ SY625 ) ) ) )
| ~ ( ~ ~ ! [SY626: $i] :
~ ~ ! [SY627: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY626 @ SV193 )
| ~ ( in @ SY627 @ SV236 ) )
| ( SY659
!= ( ordered_pair @ SY626 @ SY627 ) ) )
| ( in @ SY659 @ SV254 ) ) )
| ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1793]) ).
thf(1853,plain,
! [SV194: $i,SV262: $i] :
( ( ( ~ ( ~ ( ( SV262
!= ( relation_rng @ SV194 ) )
| ! [SY670: $i] :
~ ( ~ ( ~ ( in @ SY670 @ SV262 )
| ~ ! [SY555: $i] :
~ ( in @ ( ordered_pair @ SY555 @ SY670 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY556: $i] :
~ ( in @ ( ordered_pair @ SY556 @ SY670 ) @ SV194 )
| ( in @ SY670 @ SV262 ) ) ) )
| ~ ( ~ ! [SY673: $i] :
~ ( ~ ( ~ ( in @ SY673 @ SV262 )
| ~ ! [SY558: $i] :
~ ( in @ ( ordered_pair @ SY558 @ SY673 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY559: $i] :
~ ( in @ ( ordered_pair @ SY559 @ SY673 ) @ SV194 )
| ( in @ SY673 @ SV262 ) ) )
| ( SV262
= ( relation_rng @ SV194 ) ) ) ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1794]) ).
thf(1854,plain,
! [SV237: $i,SV195: $i] :
( ( ( in @ SV195 @ SV237 )
= $false )
| ( ( subset @ SV195 @ ( union @ SV237 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1795]) ).
thf(1855,plain,
! [SV238: $i,SV196: $i] :
( ( ~ ~ ~ ( ~ ~ ( disjoint @ SV196 @ SV238 )
| ~ ! [SY628: $i] :
~ ~ ( ~ ( in @ SY628 @ SV196 )
| ~ ( in @ SY628 @ SV238 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1796]) ).
thf(1856,plain,
! [SV238: $i,SV196: $i] :
( ( ~ ~ ~ ( ~ ~ ! [SY629: $i] :
~ ~ ( ~ ( in @ SY629 @ SV196 )
| ~ ( in @ SY629 @ SV238 ) )
| ~ ( disjoint @ SV196 @ SV238 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1796]) ).
thf(1857,plain,
! [SV255: $i,SV239: $i,SV197: $i] :
( ( ( ~ ~ ( ~ ( in @ SV197 @ SV239 )
| ~ ( element @ SV239 @ ( powerset @ SV255 ) ) ) )
= $true )
| ( ( element @ SV197 @ SV255 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1797]) ).
thf(1858,plain,
! [SV240: $i,SV198: $i] :
( ( ( in @ SV198 @ SV240 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV198 ) @ SV240 )
= SV240 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1798]) ).
thf(1859,plain,
( ( ~ ( empty @ sK45_SX0 )
| ~ ( relation @ sK45_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1799]) ).
thf(1860,plain,
! [SV199: $i] :
( ( ( SV199 != empty_set )
| ! [SY567: $i] :
~ ( in @ SY567 @ SV199 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1800]) ).
thf(1861,plain,
! [SV199: $i] :
( ( ~ ! [SY568: $i] :
~ ( in @ SY568 @ SV199 )
| ( SV199 = empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1801]) ).
thf(1862,plain,
! [SV241: $i,SV200: $i] :
( ( ( ! [SY631: $i] :
( ~ ( in @ SY631 @ SV200 )
| ( in @ SY631 @ SV241 ) ) )
= $false )
| ( ( element @ SV200 @ ( powerset @ SV241 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1802]) ).
thf(1863,plain,
! [SV256: $i,SV242: $i,SV201: $i] :
( ( ~ ( ~ ( subset @ ( unordered_pair @ SV201 @ SV242 ) @ SV256 )
| ~ ( ~ ( in @ SV201 @ SV256 )
| ~ ( in @ SV242 @ SV256 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV201 @ SV256 )
| ~ ( in @ SV242 @ SV256 ) )
| ( subset @ ( unordered_pair @ SV201 @ SV242 ) @ SV256 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1803]) ).
thf(1864,plain,
! [SV204: $i,SV155: $i,SV243: $i] :
( ( ~ ( ( SV243
!= ( set_union2 @ SV155 @ SV204 ) )
| ! [SY633: $i] :
~ ( ~ ( ~ ( in @ SY633 @ SV243 )
| ( in @ SY633 @ SV155 )
| ( in @ SY633 @ SV204 ) )
| ~ ( ~ ( ( in @ SY633 @ SV155 )
| ( in @ SY633 @ SV204 ) )
| ( in @ SY633 @ SV243 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1804]) ).
thf(1865,plain,
! [SV204: $i,SV155: $i,SV243: $i] :
( ( ~ ( ~ ! [SY634: $i] :
~ ( ~ ( ~ ( in @ SY634 @ SV243 )
| ( in @ SY634 @ SV155 )
| ( in @ SY634 @ SV204 ) )
| ~ ( ~ ( ( in @ SY634 @ SV155 )
| ( in @ SY634 @ SV204 ) )
| ( in @ SY634 @ SV243 ) ) )
| ( SV243
= ( set_union2 @ SV155 @ SV204 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1804]) ).
thf(1866,plain,
! [SV205: $i,SV156: $i] :
( ( ( ~ ( relation @ SV156 )
| ~ ( relation @ SV205 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV156 @ SV205 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1805]) ).
thf(1867,plain,
! [SV157: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( in @ SV157 @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SY635: $i,SY636: $i] :
( ~ ~ ( ~ ( in @ SY635 @ ( sK46_SY444 @ SV157 ) )
| ~ ( subset @ SY636 @ SY635 ) )
| ( in @ SY636 @ ( sK46_SY444 @ SV157 ) ) ) )
| ~ ! [SY637: $i] :
~ ~ ( ~ ( in @ SY637 @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SY638: $i] :
~ ~ ( ~ ( in @ SY638 @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY637 )
| ( in @ SX4 @ SY638 ) ) ) ) )
| ~ ! [SY640: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY640 @ ( sK46_SY444 @ SV157 ) )
| ~ ~ ( are_equipotent @ SY640 @ ( sK46_SY444 @ SV157 ) ) )
| ~ ~ ( in @ SY640 @ ( sK46_SY444 @ SV157 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1806]) ).
thf(1868,plain,
! [SV206: $i,SV158: $i] :
( ( ( in @ SV158 @ SV206 )
= $true )
| ( ( disjoint @ ( singleton @ SV158 ) @ SV206 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1807]) ).
thf(1869,plain,
! [SV257: $i,SV244: $i,SV207: $i,SV159: $i] :
( ( ( ( ordered_pair @ SV159 @ SV207 )
!= ( ordered_pair @ SV244 @ SV257 ) )
= $true )
| ( ( ~ ( ( SV159 != SV244 )
| ( SV207 != SV257 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1808]) ).
thf(1870,plain,
! [SV208: $i,SV160: $i,SV245: $i] :
( ( ( relation @ SV245 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV160 @ SV208 ) @ SV245 )
| ~ ( ~ ( in @ SV160 @ ( relation_dom @ SV245 ) )
| ~ ( in @ SV208 @ ( relation_rng @ SV245 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1809]) ).
thf(1871,plain,
! [SV210: $i,SV163: $i] :
( ( ( ~ ( in @ SV163 @ SV210 ) )
= $true )
| ( ( ~ ( empty @ SV210 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1811]) ).
thf(1872,plain,
! [SV211: $i,SV164: $i] :
( ( ( ( set_difference @ SV164 @ ( singleton @ SV211 ) )
!= SV164 )
| ~ ( in @ SV211 @ SV164 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1812]) ).
thf(1873,plain,
! [SV164: $i,SV211: $i] :
( ( ~ ~ ( in @ SV211 @ SV164 )
| ( ( set_difference @ SV164 @ ( singleton @ SV211 ) )
= SV164 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1813]) ).
thf(1874,plain,
! [SV212: $i,SV165: $i] :
( ( ~ ~ ( empty @ SV165 )
| ~ ( ~ ( ~ ( element @ SV212 @ SV165 )
| ( in @ SV212 @ SV165 ) )
| ~ ( ~ ( in @ SV212 @ SV165 )
| ( element @ SV212 @ SV165 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1814]) ).
thf(1875,plain,
! [SV212: $i,SV165: $i] :
( ( ~ ( empty @ SV165 )
| ~ ( ~ ( ~ ( element @ SV212 @ SV165 )
| ( empty @ SV212 ) )
| ~ ( ~ ( empty @ SV212 )
| ( element @ SV212 @ SV165 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1815]) ).
thf(1876,plain,
! [SV213: $i,SV166: $i] :
( ( ~ ( subset @ SV166 @ SV213 )
| ! [SY579: $i] :
( ~ ( in @ SY579 @ SV166 )
| ( in @ SY579 @ SV213 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1816]) ).
thf(1877,plain,
! [SV213: $i,SV166: $i] :
( ( ~ ! [SY580: $i] :
( ~ ( in @ SY580 @ SV166 )
| ( in @ SY580 @ SV213 ) )
| ( subset @ SV166 @ SV213 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1817]) ).
thf(1878,plain,
! [SV215: $i,SV168: $i] :
( ( ~ ( ( SV168 != empty_set ) )
| ~ ( ~ ( ( SV215
!= ( set_meet @ SV168 ) )
| ! [SY581: $i] :
~ ( ~ ( ~ ( in @ SY581 @ SV215 )
| ! [SY467: $i] :
( ~ ( in @ SY467 @ SV168 )
| ( in @ SY581 @ SY467 ) ) )
| ~ ( ~ ! [SY468: $i] :
( ~ ( in @ SY468 @ SV168 )
| ( in @ SY581 @ SY468 ) )
| ( in @ SY581 @ SV215 ) ) ) )
| ~ ( ~ ! [SY584: $i] :
~ ( ~ ( ~ ( in @ SY584 @ SV215 )
| ! [SY470: $i] :
( ~ ( in @ SY470 @ SV168 )
| ( in @ SY584 @ SY470 ) ) )
| ~ ( ~ ! [SY471: $i] :
( ~ ( in @ SY471 @ SV168 )
| ( in @ SY584 @ SY471 ) )
| ( in @ SY584 @ SV215 ) ) )
| ( SV215
= ( set_meet @ SV168 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1819]) ).
thf(1879,plain,
! [SV215: $i,SV168: $i] :
( ( ( SV168 != empty_set )
| ~ ( ~ ( ( SV215
!= ( set_meet @ SV168 ) )
| ( SV215 = empty_set ) )
| ~ ( ( SV215 != empty_set )
| ( SV215
= ( set_meet @ SV168 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1820]) ).
thf(1880,plain,
! [SV169: $i,SV216: $i] :
( ( ( SV216
!= ( union @ SV169 ) )
| ! [SY587: $i] :
~ ( ~ ( ~ ( in @ SY587 @ SV216 )
| ~ ! [SY474: $i] :
~ ~ ( ~ ( in @ SY587 @ SY474 )
| ~ ( in @ SY474 @ SV169 ) ) )
| ~ ( ~ ~ ! [SY475: $i] :
~ ~ ( ~ ( in @ SY587 @ SY475 )
| ~ ( in @ SY475 @ SV169 ) )
| ( in @ SY587 @ SV216 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1821]) ).
thf(1881,plain,
! [SV169: $i,SV216: $i] :
( ( ~ ! [SY590: $i] :
~ ( ~ ( ~ ( in @ SY590 @ SV216 )
| ~ ! [SY477: $i] :
~ ~ ( ~ ( in @ SY590 @ SY477 )
| ~ ( in @ SY477 @ SV169 ) ) )
| ~ ( ~ ~ ! [SY478: $i] :
~ ~ ( ~ ( in @ SY590 @ SY478 )
| ~ ( in @ SY478 @ SV169 ) )
| ( in @ SY590 @ SV216 ) ) )
| ( SV216
= ( union @ SV169 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1822]) ).
thf(1882,plain,
! [SV217: $i,SV170: $i,SV246: $i] :
( ( ~ ( ( SV246
!= ( unordered_pair @ SV170 @ SV217 ) )
| ! [SY642: $i] :
~ ( ~ ( ~ ( in @ SY642 @ SV246 )
| ( SY642 = SV170 )
| ( SY642 = SV217 ) )
| ~ ( ~ ( ( SY642 = SV170 )
| ( SY642 = SV217 ) )
| ( in @ SY642 @ SV246 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1823]) ).
thf(1883,plain,
! [SV217: $i,SV170: $i,SV246: $i] :
( ( ~ ( ~ ! [SY643: $i] :
~ ( ~ ( ~ ( in @ SY643 @ SV246 )
| ( SY643 = SV170 )
| ( SY643 = SV217 ) )
| ~ ( ~ ( ( SY643 = SV170 )
| ( SY643 = SV217 ) )
| ( in @ SY643 @ SV246 ) ) )
| ( SV246
= ( unordered_pair @ SV170 @ SV217 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1823]) ).
thf(1884,plain,
! [SV258: $i,SV247: $i,SV218: $i,SV171: $i] :
( ( ~ ( ~ ( in @ ( ordered_pair @ SV171 @ SV218 ) @ ( cartesian_product2 @ SV247 @ SV258 ) )
| ~ ( ~ ( in @ SV171 @ SV247 )
| ~ ( in @ SV218 @ SV258 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV171 @ SV247 )
| ~ ( in @ SV218 @ SV258 ) )
| ( in @ ( ordered_pair @ SV171 @ SV218 ) @ ( cartesian_product2 @ SV247 @ SV258 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1824]) ).
thf(1885,plain,
! [SV172: $i,SV219: $i] :
( ( ( SV219
!= ( singleton @ SV172 ) )
| ! [SY598: $i] :
~ ( ~ ( ~ ( in @ SY598 @ SV219 )
| ( SY598 = SV172 ) )
| ~ ( ( SY598 != SV172 )
| ( in @ SY598 @ SV219 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1825]) ).
thf(1886,plain,
! [SV172: $i,SV219: $i] :
( ( ~ ! [SY599: $i] :
~ ( ~ ( ~ ( in @ SY599 @ SV219 )
| ( SY599 = SV172 ) )
| ~ ( ( SY599 != SV172 )
| ( in @ SY599 @ SV219 ) ) )
| ( SV219
= ( singleton @ SV172 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1826]) ).
thf(1887,plain,
! [SV174: $i] :
( ( ( ~ ( relation @ SV174 ) )
= $true )
| ( ( ! [SY490: $i] :
~ ~ ( ~ ( in @ SY490 @ SV174 )
| ~ ! [SX2: $i,SX3: $i] :
( SY490
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1828]) ).
thf(1888,plain,
! [SV174: $i] :
( ( ( ~ ! [SY493: $i] :
~ ~ ( ~ ( in @ SY493 @ SV174 )
| ~ ! [SX2: $i,SX3: $i] :
( SY493
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $true )
| ( ( relation @ SV174 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1829]) ).
thf(1889,plain,
! [SV221: $i,SV175: $i] :
( ( ~ ( subset @ ( singleton @ SV175 ) @ SV221 )
| ( in @ SV175 @ SV221 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1830]) ).
thf(1890,plain,
! [SV221: $i,SV175: $i] :
( ( ~ ( in @ SV175 @ SV221 )
| ( subset @ ( singleton @ SV175 ) @ SV221 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1831]) ).
thf(1891,plain,
! [SV248: $i,SV222: $i,SV176: $i] :
( ( ( subset @ SV176 @ SV222 )
= $false )
| ( ( ( in @ SV248 @ SV176 )
| ( subset @ SV176 @ ( set_difference @ SV222 @ ( singleton @ SV248 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1832]) ).
thf(1892,plain,
! [SV177: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( in @ SV177 @ ( sK47_SY499 @ SV177 ) )
| ~ ! [SY645: $i,SY646: $i] :
( ~ ~ ( ~ ( in @ SY645 @ ( sK47_SY499 @ SV177 ) )
| ~ ( subset @ SY646 @ SY645 ) )
| ( in @ SY646 @ ( sK47_SY499 @ SV177 ) ) ) )
| ~ ! [SY647: $i] :
( ~ ( in @ SY647 @ ( sK47_SY499 @ SV177 ) )
| ( in @ ( powerset @ SY647 ) @ ( sK47_SY499 @ SV177 ) ) ) )
| ~ ! [SY648: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY648 @ ( sK47_SY499 @ SV177 ) )
| ~ ~ ( are_equipotent @ SY648 @ ( sK47_SY499 @ SV177 ) ) )
| ~ ~ ( in @ SY648 @ ( sK47_SY499 @ SV177 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1833]) ).
thf(1893,plain,
! [SV223: $i,SV178: $i] :
( ( ~ ( subset @ ( singleton @ SV178 ) @ SV223 )
| ( in @ SV178 @ SV223 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1834]) ).
thf(1894,plain,
! [SV223: $i,SV178: $i] :
( ( ~ ( in @ SV178 @ SV223 )
| ( subset @ ( singleton @ SV178 ) @ SV223 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1835]) ).
thf(1895,plain,
! [SV224: $i,SV179: $i] :
( ( ~ ~ ( ~ ~ ( disjoint @ SV179 @ SV224 )
| ~ ! [SY601: $i] :
~ ( in @ SY601 @ ( set_intersection2 @ SV179 @ SV224 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1836]) ).
thf(1896,plain,
! [SV224: $i,SV179: $i] :
( ( ~ ~ ( ~ ~ ! [SY602: $i] :
~ ( in @ SY602 @ ( set_intersection2 @ SV179 @ SV224 ) )
| ~ ( disjoint @ SV179 @ SV224 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1837]) ).
thf(1897,plain,
! [SV225: $i,SV180: $i,SV249: $i] :
( ( ~ ( ( SV249
!= ( set_intersection2 @ SV180 @ SV225 ) )
| ! [SY649: $i] :
~ ( ~ ( ~ ( in @ SY649 @ SV249 )
| ~ ( ~ ( in @ SY649 @ SV180 )
| ~ ( in @ SY649 @ SV225 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY649 @ SV180 )
| ~ ( in @ SY649 @ SV225 ) )
| ( in @ SY649 @ SV249 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1838]) ).
thf(1898,plain,
! [SV225: $i,SV180: $i,SV249: $i] :
( ( ~ ( ~ ! [SY650: $i] :
~ ( ~ ( ~ ( in @ SY650 @ SV249 )
| ~ ( ~ ( in @ SY650 @ SV180 )
| ~ ( in @ SY650 @ SV225 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY650 @ SV180 )
| ~ ( in @ SY650 @ SV225 ) )
| ( in @ SY650 @ SV249 ) ) )
| ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1838]) ).
thf(1899,plain,
! [SV181: $i,SV226: $i,SV263: $i] :
( ( ( ~ ( in @ SV263 @ SV226 )
| ( in @ SV263 @ SV181 ) )
= $true )
| ( ( element @ SV226 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1839]) ).
thf(1900,plain,
! [SV182: $i,SV227: $i] :
( ( ( empty @ SV227 )
= $true )
| ( ( in @ SV182 @ SV227 )
= $true )
| ( ( element @ SV182 @ SV227 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1840]) ).
thf(1901,plain,
! [SV228: $i,SV183: $i] :
( ( ( ~ ( disjoint @ ( singleton @ SV183 ) @ SV228 ) )
= $true )
| ( ( ~ ( in @ SV183 @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1841]) ).
thf(1902,plain,
! [SV229: $i,SV184: $i,SV250: $i] :
( ( ~ ( ( SV250
!= ( set_difference @ SV184 @ SV229 ) )
| ! [SY651: $i] :
~ ( ~ ( ~ ( in @ SY651 @ SV250 )
| ~ ( ~ ( in @ SY651 @ SV184 )
| ~ ~ ( in @ SY651 @ SV229 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY651 @ SV184 )
| ~ ~ ( in @ SY651 @ SV229 ) )
| ( in @ SY651 @ SV250 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1842]) ).
thf(1903,plain,
! [SV229: $i,SV184: $i,SV250: $i] :
( ( ~ ( ~ ! [SY652: $i] :
~ ( ~ ( ~ ( in @ SY652 @ SV250 )
| ~ ( ~ ( in @ SY652 @ SV184 )
| ~ ~ ( in @ SY652 @ SV229 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY652 @ SV184 )
| ~ ~ ( in @ SY652 @ SV229 ) )
| ( in @ SY652 @ SV250 ) ) )
| ( SV250
= ( set_difference @ SV184 @ SV229 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1842]) ).
thf(1904,plain,
! [SV251: $i,SV230: $i,SV185: $i] :
( ( ~ ~ ( ~ ( in @ SV185 @ SV230 )
| ~ ( element @ SV230 @ ( powerset @ SV251 ) ) )
| ~ ( empty @ SV251 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1843]) ).
thf(1905,plain,
! [SV186: $i,SV231: $i] :
( ( ( in @ SV231 @ SV186 )
= $false )
| ( ( in @ SV186 @ SV231 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1844]) ).
thf(1906,plain,
! [SV187: $i,SV259: $i] :
( ( ( ~ ( relation @ SV259 ) )
= $true )
| ( ( ~ ( subset @ SV187 @ SV259 )
| ~ ( ~ ( subset @ ( relation_dom @ SV187 ) @ ( relation_dom @ SV259 ) )
| ~ ( subset @ ( relation_rng @ SV187 ) @ ( relation_rng @ SV259 ) ) ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1845]) ).
thf(1907,plain,
! [SV260: $i,SV252: $i,SV232: $i,SV188: $i] :
( ( ~ ( ~ ( in @ ( ordered_pair @ SV188 @ SV232 ) @ ( cartesian_product2 @ SV252 @ SV260 ) )
| ~ ( ~ ( in @ SV188 @ SV252 )
| ~ ( in @ SV232 @ SV260 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV188 @ SV252 )
| ~ ( in @ SV232 @ SV260 ) )
| ( in @ ( ordered_pair @ SV188 @ SV232 ) @ ( cartesian_product2 @ SV252 @ SV260 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1846]) ).
thf(1908,plain,
! [SV189: $i,SV233: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV189 )
| ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV233 ) )
| ~ ( ~ ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV233 )
| ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV189 ) ) ) )
= $false )
| ( ( SV189 = SV233 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1847]) ).
thf(1909,plain,
! [SV190: $i,SV234: $i] :
( ( ( SV234
!= ( powerset @ SV190 ) )
| ! [SY614: $i] :
~ ( ~ ( ~ ( in @ SY614 @ SV234 )
| ( subset @ SY614 @ SV190 ) )
| ~ ( ~ ( subset @ SY614 @ SV190 )
| ( in @ SY614 @ SV234 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1848]) ).
thf(1910,plain,
! [SV190: $i,SV234: $i] :
( ( ~ ! [SY615: $i] :
~ ( ~ ( ~ ( in @ SY615 @ SV234 )
| ( subset @ SY615 @ SV190 ) )
| ~ ( ~ ( subset @ SY615 @ SV190 )
| ( in @ SY615 @ SV234 ) ) )
| ( SV234
= ( powerset @ SV190 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1849]) ).
thf(1911,plain,
! [SV235: $i,SV191: $i,SV253: $i] :
( ( ( element @ SV253 @ ( powerset @ SV191 ) )
= $false )
| ( ( ~ ~ ( ~ ( in @ SV235 @ ( subset_complement @ SV191 @ SV253 ) )
| ~ ( in @ SV235 @ SV253 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1850]) ).
thf(1912,plain,
! [SV192: $i,SV261: $i] :
( ( ( ~ ( ( SV261
!= ( relation_dom @ SV192 ) )
| ! [SY664: $i] :
~ ( ~ ( ~ ( in @ SY664 @ SV261 )
| ~ ! [SY536: $i] :
~ ( in @ ( ordered_pair @ SY664 @ SY536 ) @ SV192 ) )
| ~ ( ~ ~ ! [SY537: $i] :
~ ( in @ ( ordered_pair @ SY664 @ SY537 ) @ SV192 )
| ( in @ SY664 @ SV261 ) ) ) )
| ~ ( ~ ! [SY667: $i] :
~ ( ~ ( ~ ( in @ SY667 @ SV261 )
| ~ ! [SY539: $i] :
~ ( in @ ( ordered_pair @ SY667 @ SY539 ) @ SV192 ) )
| ~ ( ~ ~ ! [SY540: $i] :
~ ( in @ ( ordered_pair @ SY667 @ SY540 ) @ SV192 )
| ( in @ SY667 @ SV261 ) ) )
| ( SV261
= ( relation_dom @ SV192 ) ) ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1851]) ).
thf(1913,plain,
! [SV236: $i,SV193: $i,SV254: $i] :
( ( ~ ( ( SV254
!= ( cartesian_product2 @ SV193 @ SV236 ) )
| ! [SY654: $i] :
~ ( ~ ( ~ ( in @ SY654 @ SV254 )
| ~ ! [SY619: $i] :
~ ~ ! [SY620: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY619 @ SV193 )
| ~ ( in @ SY620 @ SV236 ) )
| ( SY654
!= ( ordered_pair @ SY619 @ SY620 ) ) ) )
| ~ ( ~ ~ ! [SY621: $i] :
~ ~ ! [SY622: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY621 @ SV193 )
| ~ ( in @ SY622 @ SV236 ) )
| ( SY654
!= ( ordered_pair @ SY621 @ SY622 ) ) )
| ( in @ SY654 @ SV254 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1852]) ).
thf(1914,plain,
! [SV236: $i,SV193: $i,SV254: $i] :
( ( ~ ( ~ ! [SY659: $i] :
~ ( ~ ( ~ ( in @ SY659 @ SV254 )
| ~ ! [SY624: $i] :
~ ~ ! [SY625: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY624 @ SV193 )
| ~ ( in @ SY625 @ SV236 ) )
| ( SY659
!= ( ordered_pair @ SY624 @ SY625 ) ) ) )
| ~ ( ~ ~ ! [SY626: $i] :
~ ~ ! [SY627: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY626 @ SV193 )
| ~ ( in @ SY627 @ SV236 ) )
| ( SY659
!= ( ordered_pair @ SY626 @ SY627 ) ) )
| ( in @ SY659 @ SV254 ) ) )
| ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1852]) ).
thf(1915,plain,
! [SV194: $i,SV262: $i] :
( ( ( ~ ( ( SV262
!= ( relation_rng @ SV194 ) )
| ! [SY670: $i] :
~ ( ~ ( ~ ( in @ SY670 @ SV262 )
| ~ ! [SY555: $i] :
~ ( in @ ( ordered_pair @ SY555 @ SY670 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY556: $i] :
~ ( in @ ( ordered_pair @ SY556 @ SY670 ) @ SV194 )
| ( in @ SY670 @ SV262 ) ) ) )
| ~ ( ~ ! [SY673: $i] :
~ ( ~ ( ~ ( in @ SY673 @ SV262 )
| ~ ! [SY558: $i] :
~ ( in @ ( ordered_pair @ SY558 @ SY673 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY559: $i] :
~ ( in @ ( ordered_pair @ SY559 @ SY673 ) @ SV194 )
| ( in @ SY673 @ SV262 ) ) )
| ( SV262
= ( relation_rng @ SV194 ) ) ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1853]) ).
thf(1916,plain,
! [SV238: $i,SV196: $i] :
( ( ~ ~ ( ~ ~ ( disjoint @ SV196 @ SV238 )
| ~ ! [SY628: $i] :
~ ~ ( ~ ( in @ SY628 @ SV196 )
| ~ ( in @ SY628 @ SV238 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1855]) ).
thf(1917,plain,
! [SV238: $i,SV196: $i] :
( ( ~ ~ ( ~ ~ ! [SY629: $i] :
~ ~ ( ~ ( in @ SY629 @ SV196 )
| ~ ( in @ SY629 @ SV238 ) )
| ~ ( disjoint @ SV196 @ SV238 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1856]) ).
thf(1918,plain,
! [SV255: $i,SV239: $i,SV197: $i] :
( ( ( ~ ( ~ ( in @ SV197 @ SV239 )
| ~ ( element @ SV239 @ ( powerset @ SV255 ) ) ) )
= $false )
| ( ( element @ SV197 @ SV255 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1857]) ).
thf(1919,plain,
( ( ~ ( empty @ sK45_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1859]) ).
thf(1920,plain,
( ( ~ ( relation @ sK45_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1859]) ).
thf(1921,plain,
! [SV199: $i] :
( ( ( SV199 != empty_set )
= $true )
| ( ( ! [SY567: $i] :
~ ( in @ SY567 @ SV199 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1860]) ).
thf(1922,plain,
! [SV199: $i] :
( ( ( ~ ! [SY568: $i] :
~ ( in @ SY568 @ SV199 ) )
= $true )
| ( ( SV199 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1861]) ).
thf(1923,plain,
! [SV200: $i,SV241: $i] :
( ( ( ~ ( in @ ( sK49_SY631 @ SV241 @ SV200 ) @ SV200 )
| ( in @ ( sK49_SY631 @ SV241 @ SV200 ) @ SV241 ) )
= $false )
| ( ( element @ SV200 @ ( powerset @ SV241 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1862]) ).
thf(1924,plain,
! [SV256: $i,SV242: $i,SV201: $i] :
( ( ~ ( ~ ( subset @ ( unordered_pair @ SV201 @ SV242 ) @ SV256 )
| ~ ( ~ ( in @ SV201 @ SV256 )
| ~ ( in @ SV242 @ SV256 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1863]) ).
thf(1925,plain,
! [SV242: $i,SV256: $i,SV201: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV201 @ SV256 )
| ~ ( in @ SV242 @ SV256 ) )
| ( subset @ ( unordered_pair @ SV201 @ SV242 ) @ SV256 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1863]) ).
thf(1926,plain,
! [SV204: $i,SV155: $i,SV243: $i] :
( ( ( SV243
!= ( set_union2 @ SV155 @ SV204 ) )
| ! [SY633: $i] :
~ ( ~ ( ~ ( in @ SY633 @ SV243 )
| ( in @ SY633 @ SV155 )
| ( in @ SY633 @ SV204 ) )
| ~ ( ~ ( ( in @ SY633 @ SV155 )
| ( in @ SY633 @ SV204 ) )
| ( in @ SY633 @ SV243 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1864]) ).
thf(1927,plain,
! [SV204: $i,SV155: $i,SV243: $i] :
( ( ~ ! [SY634: $i] :
~ ( ~ ( ~ ( in @ SY634 @ SV243 )
| ( in @ SY634 @ SV155 )
| ( in @ SY634 @ SV204 ) )
| ~ ( ~ ( ( in @ SY634 @ SV155 )
| ( in @ SY634 @ SV204 ) )
| ( in @ SY634 @ SV243 ) ) )
| ( SV243
= ( set_union2 @ SV155 @ SV204 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1865]) ).
thf(1928,plain,
! [SV205: $i,SV156: $i] :
( ( ( ~ ( relation @ SV156 ) )
= $true )
| ( ( ~ ( relation @ SV205 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV156 @ SV205 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1866]) ).
thf(1929,plain,
! [SV157: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( in @ SV157 @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SY635: $i,SY636: $i] :
( ~ ~ ( ~ ( in @ SY635 @ ( sK46_SY444 @ SV157 ) )
| ~ ( subset @ SY636 @ SY635 ) )
| ( in @ SY636 @ ( sK46_SY444 @ SV157 ) ) ) )
| ~ ! [SY637: $i] :
~ ~ ( ~ ( in @ SY637 @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SY638: $i] :
~ ~ ( ~ ( in @ SY638 @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY637 )
| ( in @ SX4 @ SY638 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1867]) ).
thf(1930,plain,
! [SV157: $i] :
( ( ~ ! [SY640: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY640 @ ( sK46_SY444 @ SV157 ) )
| ~ ~ ( are_equipotent @ SY640 @ ( sK46_SY444 @ SV157 ) ) )
| ~ ~ ( in @ SY640 @ ( sK46_SY444 @ SV157 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1867]) ).
thf(1931,plain,
! [SV257: $i,SV244: $i,SV207: $i,SV159: $i] :
( ( ( ( ordered_pair @ SV159 @ SV207 )
= ( ordered_pair @ SV244 @ SV257 ) )
= $false )
| ( ( ~ ( ( SV159 != SV244 )
| ( SV207 != SV257 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1869]) ).
thf(1932,plain,
! [SV245: $i,SV208: $i,SV160: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV160 @ SV208 ) @ SV245 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV160 @ ( relation_dom @ SV245 ) )
| ~ ( in @ SV208 @ ( relation_rng @ SV245 ) ) ) )
= $true )
| ( ( relation @ SV245 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1870]) ).
thf(1933,plain,
! [SV210: $i,SV163: $i] :
( ( ( in @ SV163 @ SV210 )
= $false )
| ( ( ~ ( empty @ SV210 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1871]) ).
thf(1934,plain,
! [SV211: $i,SV164: $i] :
( ( ( ( set_difference @ SV164 @ ( singleton @ SV211 ) )
!= SV164 )
= $true )
| ( ( ~ ( in @ SV211 @ SV164 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1872]) ).
thf(1935,plain,
! [SV164: $i,SV211: $i] :
( ( ( ~ ~ ( in @ SV211 @ SV164 ) )
= $true )
| ( ( ( set_difference @ SV164 @ ( singleton @ SV211 ) )
= SV164 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1873]) ).
thf(1936,plain,
! [SV212: $i,SV165: $i] :
( ( ( ~ ~ ( empty @ SV165 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( element @ SV212 @ SV165 )
| ( in @ SV212 @ SV165 ) )
| ~ ( ~ ( in @ SV212 @ SV165 )
| ( element @ SV212 @ SV165 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1874]) ).
thf(1937,plain,
! [SV212: $i,SV165: $i] :
( ( ( ~ ( empty @ SV165 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( element @ SV212 @ SV165 )
| ( empty @ SV212 ) )
| ~ ( ~ ( empty @ SV212 )
| ( element @ SV212 @ SV165 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1875]) ).
thf(1938,plain,
! [SV213: $i,SV166: $i] :
( ( ( ~ ( subset @ SV166 @ SV213 ) )
= $true )
| ( ( ! [SY579: $i] :
( ~ ( in @ SY579 @ SV166 )
| ( in @ SY579 @ SV213 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1876]) ).
thf(1939,plain,
! [SV213: $i,SV166: $i] :
( ( ( ~ ! [SY580: $i] :
( ~ ( in @ SY580 @ SV166 )
| ( in @ SY580 @ SV213 ) ) )
= $true )
| ( ( subset @ SV166 @ SV213 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1877]) ).
thf(1940,plain,
! [SV215: $i,SV168: $i] :
( ( ( ~ ( ( SV168 != empty_set ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV215
!= ( set_meet @ SV168 ) )
| ! [SY581: $i] :
~ ( ~ ( ~ ( in @ SY581 @ SV215 )
| ! [SY467: $i] :
( ~ ( in @ SY467 @ SV168 )
| ( in @ SY581 @ SY467 ) ) )
| ~ ( ~ ! [SY468: $i] :
( ~ ( in @ SY468 @ SV168 )
| ( in @ SY581 @ SY468 ) )
| ( in @ SY581 @ SV215 ) ) ) )
| ~ ( ~ ! [SY584: $i] :
~ ( ~ ( ~ ( in @ SY584 @ SV215 )
| ! [SY470: $i] :
( ~ ( in @ SY470 @ SV168 )
| ( in @ SY584 @ SY470 ) ) )
| ~ ( ~ ! [SY471: $i] :
( ~ ( in @ SY471 @ SV168 )
| ( in @ SY584 @ SY471 ) )
| ( in @ SY584 @ SV215 ) ) )
| ( SV215
= ( set_meet @ SV168 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1878]) ).
thf(1941,plain,
! [SV215: $i,SV168: $i] :
( ( ( SV168 != empty_set )
= $true )
| ( ( ~ ( ~ ( ( SV215
!= ( set_meet @ SV168 ) )
| ( SV215 = empty_set ) )
| ~ ( ( SV215 != empty_set )
| ( SV215
= ( set_meet @ SV168 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1879]) ).
thf(1942,plain,
! [SV169: $i,SV216: $i] :
( ( ( SV216
!= ( union @ SV169 ) )
= $true )
| ( ( ! [SY587: $i] :
~ ( ~ ( ~ ( in @ SY587 @ SV216 )
| ~ ! [SY474: $i] :
~ ~ ( ~ ( in @ SY587 @ SY474 )
| ~ ( in @ SY474 @ SV169 ) ) )
| ~ ( ~ ~ ! [SY475: $i] :
~ ~ ( ~ ( in @ SY587 @ SY475 )
| ~ ( in @ SY475 @ SV169 ) )
| ( in @ SY587 @ SV216 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1880]) ).
thf(1943,plain,
! [SV169: $i,SV216: $i] :
( ( ( ~ ! [SY590: $i] :
~ ( ~ ( ~ ( in @ SY590 @ SV216 )
| ~ ! [SY477: $i] :
~ ~ ( ~ ( in @ SY590 @ SY477 )
| ~ ( in @ SY477 @ SV169 ) ) )
| ~ ( ~ ~ ! [SY478: $i] :
~ ~ ( ~ ( in @ SY590 @ SY478 )
| ~ ( in @ SY478 @ SV169 ) )
| ( in @ SY590 @ SV216 ) ) ) )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1881]) ).
thf(1944,plain,
! [SV217: $i,SV170: $i,SV246: $i] :
( ( ( SV246
!= ( unordered_pair @ SV170 @ SV217 ) )
| ! [SY642: $i] :
~ ( ~ ( ~ ( in @ SY642 @ SV246 )
| ( SY642 = SV170 )
| ( SY642 = SV217 ) )
| ~ ( ~ ( ( SY642 = SV170 )
| ( SY642 = SV217 ) )
| ( in @ SY642 @ SV246 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1882]) ).
thf(1945,plain,
! [SV217: $i,SV170: $i,SV246: $i] :
( ( ~ ! [SY643: $i] :
~ ( ~ ( ~ ( in @ SY643 @ SV246 )
| ( SY643 = SV170 )
| ( SY643 = SV217 ) )
| ~ ( ~ ( ( SY643 = SV170 )
| ( SY643 = SV217 ) )
| ( in @ SY643 @ SV246 ) ) )
| ( SV246
= ( unordered_pair @ SV170 @ SV217 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1883]) ).
thf(1946,plain,
! [SV258: $i,SV247: $i,SV218: $i,SV171: $i] :
( ( ~ ( ~ ( in @ ( ordered_pair @ SV171 @ SV218 ) @ ( cartesian_product2 @ SV247 @ SV258 ) )
| ~ ( ~ ( in @ SV171 @ SV247 )
| ~ ( in @ SV218 @ SV258 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1884]) ).
thf(1947,plain,
! [SV258: $i,SV218: $i,SV247: $i,SV171: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV171 @ SV247 )
| ~ ( in @ SV218 @ SV258 ) )
| ( in @ ( ordered_pair @ SV171 @ SV218 ) @ ( cartesian_product2 @ SV247 @ SV258 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1884]) ).
thf(1948,plain,
! [SV172: $i,SV219: $i] :
( ( ( SV219
!= ( singleton @ SV172 ) )
= $true )
| ( ( ! [SY598: $i] :
~ ( ~ ( ~ ( in @ SY598 @ SV219 )
| ( SY598 = SV172 ) )
| ~ ( ( SY598 != SV172 )
| ( in @ SY598 @ SV219 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1885]) ).
thf(1949,plain,
! [SV172: $i,SV219: $i] :
( ( ( ~ ! [SY599: $i] :
~ ( ~ ( ~ ( in @ SY599 @ SV219 )
| ( SY599 = SV172 ) )
| ~ ( ( SY599 != SV172 )
| ( in @ SY599 @ SV219 ) ) ) )
= $true )
| ( ( SV219
= ( singleton @ SV172 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1886]) ).
thf(1950,plain,
! [SV174: $i] :
( ( ( relation @ SV174 )
= $false )
| ( ( ! [SY490: $i] :
~ ~ ( ~ ( in @ SY490 @ SV174 )
| ~ ! [SX2: $i,SX3: $i] :
( SY490
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1887]) ).
thf(1951,plain,
! [SV174: $i] :
( ( ( ! [SY493: $i] :
~ ~ ( ~ ( in @ SY493 @ SV174 )
| ~ ! [SX2: $i,SX3: $i] :
( SY493
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $false )
| ( ( relation @ SV174 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1888]) ).
thf(1952,plain,
! [SV221: $i,SV175: $i] :
( ( ( ~ ( subset @ ( singleton @ SV175 ) @ SV221 ) )
= $true )
| ( ( in @ SV175 @ SV221 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1889]) ).
thf(1953,plain,
! [SV221: $i,SV175: $i] :
( ( ( ~ ( in @ SV175 @ SV221 ) )
= $true )
| ( ( subset @ ( singleton @ SV175 ) @ SV221 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1890]) ).
thf(1954,plain,
! [SV222: $i,SV176: $i,SV248: $i] :
( ( ( in @ SV248 @ SV176 )
= $true )
| ( ( subset @ SV176 @ ( set_difference @ SV222 @ ( singleton @ SV248 ) ) )
= $true )
| ( ( subset @ SV176 @ SV222 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1891]) ).
thf(1955,plain,
! [SV177: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( in @ SV177 @ ( sK47_SY499 @ SV177 ) )
| ~ ! [SY645: $i,SY646: $i] :
( ~ ~ ( ~ ( in @ SY645 @ ( sK47_SY499 @ SV177 ) )
| ~ ( subset @ SY646 @ SY645 ) )
| ( in @ SY646 @ ( sK47_SY499 @ SV177 ) ) ) )
| ~ ! [SY647: $i] :
( ~ ( in @ SY647 @ ( sK47_SY499 @ SV177 ) )
| ( in @ ( powerset @ SY647 ) @ ( sK47_SY499 @ SV177 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1892]) ).
thf(1956,plain,
! [SV177: $i] :
( ( ~ ! [SY648: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY648 @ ( sK47_SY499 @ SV177 ) )
| ~ ~ ( are_equipotent @ SY648 @ ( sK47_SY499 @ SV177 ) ) )
| ~ ~ ( in @ SY648 @ ( sK47_SY499 @ SV177 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1892]) ).
thf(1957,plain,
! [SV223: $i,SV178: $i] :
( ( ( ~ ( subset @ ( singleton @ SV178 ) @ SV223 ) )
= $true )
| ( ( in @ SV178 @ SV223 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1893]) ).
thf(1958,plain,
! [SV223: $i,SV178: $i] :
( ( ( ~ ( in @ SV178 @ SV223 ) )
= $true )
| ( ( subset @ ( singleton @ SV178 ) @ SV223 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1894]) ).
thf(1959,plain,
! [SV224: $i,SV179: $i] :
( ( ~ ( ~ ~ ( disjoint @ SV179 @ SV224 )
| ~ ! [SY601: $i] :
~ ( in @ SY601 @ ( set_intersection2 @ SV179 @ SV224 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1895]) ).
thf(1960,plain,
! [SV224: $i,SV179: $i] :
( ( ~ ( ~ ~ ! [SY602: $i] :
~ ( in @ SY602 @ ( set_intersection2 @ SV179 @ SV224 ) )
| ~ ( disjoint @ SV179 @ SV224 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1896]) ).
thf(1961,plain,
! [SV225: $i,SV180: $i,SV249: $i] :
( ( ( SV249
!= ( set_intersection2 @ SV180 @ SV225 ) )
| ! [SY649: $i] :
~ ( ~ ( ~ ( in @ SY649 @ SV249 )
| ~ ( ~ ( in @ SY649 @ SV180 )
| ~ ( in @ SY649 @ SV225 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY649 @ SV180 )
| ~ ( in @ SY649 @ SV225 ) )
| ( in @ SY649 @ SV249 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1897]) ).
thf(1962,plain,
! [SV225: $i,SV180: $i,SV249: $i] :
( ( ~ ! [SY650: $i] :
~ ( ~ ( ~ ( in @ SY650 @ SV249 )
| ~ ( ~ ( in @ SY650 @ SV180 )
| ~ ( in @ SY650 @ SV225 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY650 @ SV180 )
| ~ ( in @ SY650 @ SV225 ) )
| ( in @ SY650 @ SV249 ) ) )
| ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1898]) ).
thf(1963,plain,
! [SV181: $i,SV226: $i,SV263: $i] :
( ( ( ~ ( in @ SV263 @ SV226 ) )
= $true )
| ( ( in @ SV263 @ SV181 )
= $true )
| ( ( element @ SV226 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1899]) ).
thf(1964,plain,
! [SV228: $i,SV183: $i] :
( ( ( disjoint @ ( singleton @ SV183 ) @ SV228 )
= $false )
| ( ( ~ ( in @ SV183 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1901]) ).
thf(1965,plain,
! [SV229: $i,SV184: $i,SV250: $i] :
( ( ( SV250
!= ( set_difference @ SV184 @ SV229 ) )
| ! [SY651: $i] :
~ ( ~ ( ~ ( in @ SY651 @ SV250 )
| ~ ( ~ ( in @ SY651 @ SV184 )
| ~ ~ ( in @ SY651 @ SV229 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY651 @ SV184 )
| ~ ~ ( in @ SY651 @ SV229 ) )
| ( in @ SY651 @ SV250 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1902]) ).
thf(1966,plain,
! [SV229: $i,SV184: $i,SV250: $i] :
( ( ~ ! [SY652: $i] :
~ ( ~ ( ~ ( in @ SY652 @ SV250 )
| ~ ( ~ ( in @ SY652 @ SV184 )
| ~ ~ ( in @ SY652 @ SV229 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY652 @ SV184 )
| ~ ~ ( in @ SY652 @ SV229 ) )
| ( in @ SY652 @ SV250 ) ) )
| ( SV250
= ( set_difference @ SV184 @ SV229 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1903]) ).
thf(1967,plain,
! [SV251: $i,SV230: $i,SV185: $i] :
( ( ( ~ ~ ( ~ ( in @ SV185 @ SV230 )
| ~ ( element @ SV230 @ ( powerset @ SV251 ) ) ) )
= $true )
| ( ( ~ ( empty @ SV251 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1904]) ).
thf(1968,plain,
! [SV187: $i,SV259: $i] :
( ( ( relation @ SV259 )
= $false )
| ( ( ~ ( subset @ SV187 @ SV259 )
| ~ ( ~ ( subset @ ( relation_dom @ SV187 ) @ ( relation_dom @ SV259 ) )
| ~ ( subset @ ( relation_rng @ SV187 ) @ ( relation_rng @ SV259 ) ) ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1906]) ).
thf(1969,plain,
! [SV260: $i,SV252: $i,SV232: $i,SV188: $i] :
( ( ~ ( ~ ( in @ ( ordered_pair @ SV188 @ SV232 ) @ ( cartesian_product2 @ SV252 @ SV260 ) )
| ~ ( ~ ( in @ SV188 @ SV252 )
| ~ ( in @ SV232 @ SV260 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1907]) ).
thf(1970,plain,
! [SV260: $i,SV232: $i,SV252: $i,SV188: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV188 @ SV252 )
| ~ ( in @ SV232 @ SV260 ) )
| ( in @ ( ordered_pair @ SV188 @ SV232 ) @ ( cartesian_product2 @ SV252 @ SV260 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1907]) ).
thf(1971,plain,
! [SV189: $i,SV233: $i] :
( ( ( ~ ( ~ ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV189 )
| ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV233 ) )
| ~ ( ~ ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV233 )
| ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV189 ) ) )
= $true )
| ( ( SV189 = SV233 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1908]) ).
thf(1972,plain,
! [SV190: $i,SV234: $i] :
( ( ( SV234
!= ( powerset @ SV190 ) )
= $true )
| ( ( ! [SY614: $i] :
~ ( ~ ( ~ ( in @ SY614 @ SV234 )
| ( subset @ SY614 @ SV190 ) )
| ~ ( ~ ( subset @ SY614 @ SV190 )
| ( in @ SY614 @ SV234 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1909]) ).
thf(1973,plain,
! [SV190: $i,SV234: $i] :
( ( ( ~ ! [SY615: $i] :
~ ( ~ ( ~ ( in @ SY615 @ SV234 )
| ( subset @ SY615 @ SV190 ) )
| ~ ( ~ ( subset @ SY615 @ SV190 )
| ( in @ SY615 @ SV234 ) ) ) )
= $true )
| ( ( SV234
= ( powerset @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1910]) ).
thf(1974,plain,
! [SV253: $i,SV191: $i,SV235: $i] :
( ( ( ~ ( ~ ( in @ SV235 @ ( subset_complement @ SV191 @ SV253 ) )
| ~ ( in @ SV235 @ SV253 ) ) )
= $false )
| ( ( element @ SV253 @ ( powerset @ SV191 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1911]) ).
thf(1975,plain,
! [SV192: $i,SV261: $i] :
( ( ( ~ ( ( SV261
!= ( relation_dom @ SV192 ) )
| ! [SY664: $i] :
~ ( ~ ( ~ ( in @ SY664 @ SV261 )
| ~ ! [SY536: $i] :
~ ( in @ ( ordered_pair @ SY664 @ SY536 ) @ SV192 ) )
| ~ ( ~ ~ ! [SY537: $i] :
~ ( in @ ( ordered_pair @ SY664 @ SY537 ) @ SV192 )
| ( in @ SY664 @ SV261 ) ) ) ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1912]) ).
thf(1976,plain,
! [SV192: $i,SV261: $i] :
( ( ( ~ ( ~ ! [SY667: $i] :
~ ( ~ ( ~ ( in @ SY667 @ SV261 )
| ~ ! [SY539: $i] :
~ ( in @ ( ordered_pair @ SY667 @ SY539 ) @ SV192 ) )
| ~ ( ~ ~ ! [SY540: $i] :
~ ( in @ ( ordered_pair @ SY667 @ SY540 ) @ SV192 )
| ( in @ SY667 @ SV261 ) ) )
| ( SV261
= ( relation_dom @ SV192 ) ) ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1912]) ).
thf(1977,plain,
! [SV236: $i,SV193: $i,SV254: $i] :
( ( ( SV254
!= ( cartesian_product2 @ SV193 @ SV236 ) )
| ! [SY654: $i] :
~ ( ~ ( ~ ( in @ SY654 @ SV254 )
| ~ ! [SY619: $i] :
~ ~ ! [SY620: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY619 @ SV193 )
| ~ ( in @ SY620 @ SV236 ) )
| ( SY654
!= ( ordered_pair @ SY619 @ SY620 ) ) ) )
| ~ ( ~ ~ ! [SY621: $i] :
~ ~ ! [SY622: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY621 @ SV193 )
| ~ ( in @ SY622 @ SV236 ) )
| ( SY654
!= ( ordered_pair @ SY621 @ SY622 ) ) )
| ( in @ SY654 @ SV254 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1913]) ).
thf(1978,plain,
! [SV236: $i,SV193: $i,SV254: $i] :
( ( ~ ! [SY659: $i] :
~ ( ~ ( ~ ( in @ SY659 @ SV254 )
| ~ ! [SY624: $i] :
~ ~ ! [SY625: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY624 @ SV193 )
| ~ ( in @ SY625 @ SV236 ) )
| ( SY659
!= ( ordered_pair @ SY624 @ SY625 ) ) ) )
| ~ ( ~ ~ ! [SY626: $i] :
~ ~ ! [SY627: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY626 @ SV193 )
| ~ ( in @ SY627 @ SV236 ) )
| ( SY659
!= ( ordered_pair @ SY626 @ SY627 ) ) )
| ( in @ SY659 @ SV254 ) ) )
| ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1914]) ).
thf(1979,plain,
! [SV194: $i,SV262: $i] :
( ( ( ~ ( ( SV262
!= ( relation_rng @ SV194 ) )
| ! [SY670: $i] :
~ ( ~ ( ~ ( in @ SY670 @ SV262 )
| ~ ! [SY555: $i] :
~ ( in @ ( ordered_pair @ SY555 @ SY670 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY556: $i] :
~ ( in @ ( ordered_pair @ SY556 @ SY670 ) @ SV194 )
| ( in @ SY670 @ SV262 ) ) ) ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1915]) ).
thf(1980,plain,
! [SV194: $i,SV262: $i] :
( ( ( ~ ( ~ ! [SY673: $i] :
~ ( ~ ( ~ ( in @ SY673 @ SV262 )
| ~ ! [SY558: $i] :
~ ( in @ ( ordered_pair @ SY558 @ SY673 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY559: $i] :
~ ( in @ ( ordered_pair @ SY559 @ SY673 ) @ SV194 )
| ( in @ SY673 @ SV262 ) ) )
| ( SV262
= ( relation_rng @ SV194 ) ) ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1915]) ).
thf(1981,plain,
! [SV238: $i,SV196: $i] :
( ( ~ ( ~ ~ ( disjoint @ SV196 @ SV238 )
| ~ ! [SY628: $i] :
~ ~ ( ~ ( in @ SY628 @ SV196 )
| ~ ( in @ SY628 @ SV238 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1916]) ).
thf(1982,plain,
! [SV238: $i,SV196: $i] :
( ( ~ ( ~ ~ ! [SY629: $i] :
~ ~ ( ~ ( in @ SY629 @ SV196 )
| ~ ( in @ SY629 @ SV238 ) )
| ~ ( disjoint @ SV196 @ SV238 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1917]) ).
thf(1983,plain,
! [SV255: $i,SV239: $i,SV197: $i] :
( ( ( ~ ( in @ SV197 @ SV239 )
| ~ ( element @ SV239 @ ( powerset @ SV255 ) ) )
= $true )
| ( ( element @ SV197 @ SV255 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1918]) ).
thf(1984,plain,
( ( empty @ sK45_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1919]) ).
thf(1985,plain,
( ( relation @ sK45_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1920]) ).
thf(1986,plain,
! [SV199: $i] :
( ( ( SV199 = empty_set )
= $false )
| ( ( ! [SY567: $i] :
~ ( in @ SY567 @ SV199 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1921]) ).
thf(1987,plain,
! [SV199: $i] :
( ( ( ! [SY568: $i] :
~ ( in @ SY568 @ SV199 ) )
= $false )
| ( ( SV199 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1922]) ).
thf(1988,plain,
! [SV200: $i,SV241: $i] :
( ( ( ~ ( in @ ( sK49_SY631 @ SV241 @ SV200 ) @ SV200 ) )
= $false )
| ( ( element @ SV200 @ ( powerset @ SV241 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1923]) ).
thf(1989,plain,
! [SV200: $i,SV241: $i] :
( ( ( in @ ( sK49_SY631 @ SV241 @ SV200 ) @ SV241 )
= $false )
| ( ( element @ SV200 @ ( powerset @ SV241 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1923]) ).
thf(1990,plain,
! [SV256: $i,SV242: $i,SV201: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV201 @ SV242 ) @ SV256 )
| ~ ( ~ ( in @ SV201 @ SV256 )
| ~ ( in @ SV242 @ SV256 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1924]) ).
thf(1991,plain,
! [SV242: $i,SV256: $i,SV201: $i] :
( ( ~ ~ ( ~ ( in @ SV201 @ SV256 )
| ~ ( in @ SV242 @ SV256 ) )
| ( subset @ ( unordered_pair @ SV201 @ SV242 ) @ SV256 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1925]) ).
thf(1992,plain,
! [SV204: $i,SV155: $i,SV243: $i] :
( ( ( SV243
!= ( set_union2 @ SV155 @ SV204 ) )
= $true )
| ( ( ! [SY633: $i] :
~ ( ~ ( ~ ( in @ SY633 @ SV243 )
| ( in @ SY633 @ SV155 )
| ( in @ SY633 @ SV204 ) )
| ~ ( ~ ( ( in @ SY633 @ SV155 )
| ( in @ SY633 @ SV204 ) )
| ( in @ SY633 @ SV243 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1926]) ).
thf(1993,plain,
! [SV204: $i,SV155: $i,SV243: $i] :
( ( ( ~ ! [SY634: $i] :
~ ( ~ ( ~ ( in @ SY634 @ SV243 )
| ( in @ SY634 @ SV155 )
| ( in @ SY634 @ SV204 ) )
| ~ ( ~ ( ( in @ SY634 @ SV155 )
| ( in @ SY634 @ SV204 ) )
| ( in @ SY634 @ SV243 ) ) ) )
= $true )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1927]) ).
thf(1994,plain,
! [SV205: $i,SV156: $i] :
( ( ( relation @ SV156 )
= $false )
| ( ( ~ ( relation @ SV205 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV156 @ SV205 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1928]) ).
thf(1995,plain,
! [SV157: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV157 @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SY635: $i,SY636: $i] :
( ~ ~ ( ~ ( in @ SY635 @ ( sK46_SY444 @ SV157 ) )
| ~ ( subset @ SY636 @ SY635 ) )
| ( in @ SY636 @ ( sK46_SY444 @ SV157 ) ) ) )
| ~ ! [SY637: $i] :
~ ~ ( ~ ( in @ SY637 @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SY638: $i] :
~ ~ ( ~ ( in @ SY638 @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY637 )
| ( in @ SX4 @ SY638 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1929]) ).
thf(1996,plain,
! [SV157: $i] :
( ( ! [SY640: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY640 @ ( sK46_SY444 @ SV157 ) )
| ~ ~ ( are_equipotent @ SY640 @ ( sK46_SY444 @ SV157 ) ) )
| ~ ~ ( in @ SY640 @ ( sK46_SY444 @ SV157 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1930]) ).
thf(1997,plain,
! [SV257: $i,SV207: $i,SV244: $i,SV159: $i] :
( ( ( ( SV159 != SV244 )
| ( SV207 != SV257 ) )
= $false )
| ( ( ( ordered_pair @ SV159 @ SV207 )
= ( ordered_pair @ SV244 @ SV257 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1931]) ).
thf(1998,plain,
! [SV245: $i,SV208: $i,SV160: $i] :
( ( ( in @ ( ordered_pair @ SV160 @ SV208 ) @ SV245 )
= $false )
| ( ( ~ ( ~ ( in @ SV160 @ ( relation_dom @ SV245 ) )
| ~ ( in @ SV208 @ ( relation_rng @ SV245 ) ) ) )
= $true )
| ( ( relation @ SV245 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1932]) ).
thf(1999,plain,
! [SV163: $i,SV210: $i] :
( ( ( empty @ SV210 )
= $false )
| ( ( in @ SV163 @ SV210 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1933]) ).
thf(2000,plain,
! [SV211: $i,SV164: $i] :
( ( ( ( set_difference @ SV164 @ ( singleton @ SV211 ) )
= SV164 )
= $false )
| ( ( ~ ( in @ SV211 @ SV164 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1934]) ).
thf(2001,plain,
! [SV164: $i,SV211: $i] :
( ( ( ~ ( in @ SV211 @ SV164 ) )
= $false )
| ( ( ( set_difference @ SV164 @ ( singleton @ SV211 ) )
= SV164 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1935]) ).
thf(2002,plain,
! [SV212: $i,SV165: $i] :
( ( ( ~ ( empty @ SV165 ) )
= $false )
| ( ( ~ ( ~ ( ~ ( element @ SV212 @ SV165 )
| ( in @ SV212 @ SV165 ) )
| ~ ( ~ ( in @ SV212 @ SV165 )
| ( element @ SV212 @ SV165 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1936]) ).
thf(2003,plain,
! [SV212: $i,SV165: $i] :
( ( ( empty @ SV165 )
= $false )
| ( ( ~ ( ~ ( ~ ( element @ SV212 @ SV165 )
| ( empty @ SV212 ) )
| ~ ( ~ ( empty @ SV212 )
| ( element @ SV212 @ SV165 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1937]) ).
thf(2004,plain,
! [SV213: $i,SV166: $i] :
( ( ( subset @ SV166 @ SV213 )
= $false )
| ( ( ! [SY579: $i] :
( ~ ( in @ SY579 @ SV166 )
| ( in @ SY579 @ SV213 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1938]) ).
thf(2005,plain,
! [SV213: $i,SV166: $i] :
( ( ( ! [SY580: $i] :
( ~ ( in @ SY580 @ SV166 )
| ( in @ SY580 @ SV213 ) ) )
= $false )
| ( ( subset @ SV166 @ SV213 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1939]) ).
thf(2006,plain,
! [SV215: $i,SV168: $i] :
( ( ( SV168 != empty_set )
= $false )
| ( ( ~ ( ~ ( ( SV215
!= ( set_meet @ SV168 ) )
| ! [SY581: $i] :
~ ( ~ ( ~ ( in @ SY581 @ SV215 )
| ! [SY467: $i] :
( ~ ( in @ SY467 @ SV168 )
| ( in @ SY581 @ SY467 ) ) )
| ~ ( ~ ! [SY468: $i] :
( ~ ( in @ SY468 @ SV168 )
| ( in @ SY581 @ SY468 ) )
| ( in @ SY581 @ SV215 ) ) ) )
| ~ ( ~ ! [SY584: $i] :
~ ( ~ ( ~ ( in @ SY584 @ SV215 )
| ! [SY470: $i] :
( ~ ( in @ SY470 @ SV168 )
| ( in @ SY584 @ SY470 ) ) )
| ~ ( ~ ! [SY471: $i] :
( ~ ( in @ SY471 @ SV168 )
| ( in @ SY584 @ SY471 ) )
| ( in @ SY584 @ SV215 ) ) )
| ( SV215
= ( set_meet @ SV168 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1940]) ).
thf(2007,plain,
! [SV215: $i,SV168: $i] :
( ( ( SV168 = empty_set )
= $false )
| ( ( ~ ( ~ ( ( SV215
!= ( set_meet @ SV168 ) )
| ( SV215 = empty_set ) )
| ~ ( ( SV215 != empty_set )
| ( SV215
= ( set_meet @ SV168 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1941]) ).
thf(2008,plain,
! [SV169: $i,SV216: $i] :
( ( ( SV216
= ( union @ SV169 ) )
= $false )
| ( ( ! [SY587: $i] :
~ ( ~ ( ~ ( in @ SY587 @ SV216 )
| ~ ! [SY474: $i] :
~ ~ ( ~ ( in @ SY587 @ SY474 )
| ~ ( in @ SY474 @ SV169 ) ) )
| ~ ( ~ ~ ! [SY475: $i] :
~ ~ ( ~ ( in @ SY587 @ SY475 )
| ~ ( in @ SY475 @ SV169 ) )
| ( in @ SY587 @ SV216 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1942]) ).
thf(2009,plain,
! [SV169: $i,SV216: $i] :
( ( ( ! [SY590: $i] :
~ ( ~ ( ~ ( in @ SY590 @ SV216 )
| ~ ! [SY477: $i] :
~ ~ ( ~ ( in @ SY590 @ SY477 )
| ~ ( in @ SY477 @ SV169 ) ) )
| ~ ( ~ ~ ! [SY478: $i] :
~ ~ ( ~ ( in @ SY590 @ SY478 )
| ~ ( in @ SY478 @ SV169 ) )
| ( in @ SY590 @ SV216 ) ) ) )
= $false )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1943]) ).
thf(2010,plain,
! [SV217: $i,SV170: $i,SV246: $i] :
( ( ( SV246
!= ( unordered_pair @ SV170 @ SV217 ) )
= $true )
| ( ( ! [SY642: $i] :
~ ( ~ ( ~ ( in @ SY642 @ SV246 )
| ( SY642 = SV170 )
| ( SY642 = SV217 ) )
| ~ ( ~ ( ( SY642 = SV170 )
| ( SY642 = SV217 ) )
| ( in @ SY642 @ SV246 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1944]) ).
thf(2011,plain,
! [SV217: $i,SV170: $i,SV246: $i] :
( ( ( ~ ! [SY643: $i] :
~ ( ~ ( ~ ( in @ SY643 @ SV246 )
| ( SY643 = SV170 )
| ( SY643 = SV217 ) )
| ~ ( ~ ( ( SY643 = SV170 )
| ( SY643 = SV217 ) )
| ( in @ SY643 @ SV246 ) ) ) )
= $true )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1945]) ).
thf(2012,plain,
! [SV258: $i,SV247: $i,SV218: $i,SV171: $i] :
( ( ~ ( in @ ( ordered_pair @ SV171 @ SV218 ) @ ( cartesian_product2 @ SV247 @ SV258 ) )
| ~ ( ~ ( in @ SV171 @ SV247 )
| ~ ( in @ SV218 @ SV258 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1946]) ).
thf(2013,plain,
! [SV258: $i,SV218: $i,SV247: $i,SV171: $i] :
( ( ~ ~ ( ~ ( in @ SV171 @ SV247 )
| ~ ( in @ SV218 @ SV258 ) )
| ( in @ ( ordered_pair @ SV171 @ SV218 ) @ ( cartesian_product2 @ SV247 @ SV258 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1947]) ).
thf(2014,plain,
! [SV172: $i,SV219: $i] :
( ( ( SV219
= ( singleton @ SV172 ) )
= $false )
| ( ( ! [SY598: $i] :
~ ( ~ ( ~ ( in @ SY598 @ SV219 )
| ( SY598 = SV172 ) )
| ~ ( ( SY598 != SV172 )
| ( in @ SY598 @ SV219 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1948]) ).
thf(2015,plain,
! [SV172: $i,SV219: $i] :
( ( ( ! [SY599: $i] :
~ ( ~ ( ~ ( in @ SY599 @ SV219 )
| ( SY599 = SV172 ) )
| ~ ( ( SY599 != SV172 )
| ( in @ SY599 @ SV219 ) ) ) )
= $false )
| ( ( SV219
= ( singleton @ SV172 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1949]) ).
thf(2016,plain,
! [SV174: $i,SV264: $i] :
( ( ( ~ ~ ( ~ ( in @ SV264 @ SV174 )
| ~ ! [SY676: $i,SY677: $i] :
( SV264
!= ( ordered_pair @ SY676 @ SY677 ) ) ) )
= $true )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1950]) ).
thf(2017,plain,
! [SV174: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK50_SY493 @ SV174 ) @ SV174 )
| ~ ! [SY678: $i,SY679: $i] :
( ( sK50_SY493 @ SV174 )
!= ( ordered_pair @ SY678 @ SY679 ) ) ) )
= $false )
| ( ( relation @ SV174 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1951]) ).
thf(2018,plain,
! [SV221: $i,SV175: $i] :
( ( ( subset @ ( singleton @ SV175 ) @ SV221 )
= $false )
| ( ( in @ SV175 @ SV221 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1952]) ).
thf(2019,plain,
! [SV221: $i,SV175: $i] :
( ( ( in @ SV175 @ SV221 )
= $false )
| ( ( subset @ ( singleton @ SV175 ) @ SV221 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1953]) ).
thf(2020,plain,
! [SV177: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV177 @ ( sK47_SY499 @ SV177 ) )
| ~ ! [SY645: $i,SY646: $i] :
( ~ ~ ( ~ ( in @ SY645 @ ( sK47_SY499 @ SV177 ) )
| ~ ( subset @ SY646 @ SY645 ) )
| ( in @ SY646 @ ( sK47_SY499 @ SV177 ) ) ) )
| ~ ! [SY647: $i] :
( ~ ( in @ SY647 @ ( sK47_SY499 @ SV177 ) )
| ( in @ ( powerset @ SY647 ) @ ( sK47_SY499 @ SV177 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1955]) ).
thf(2021,plain,
! [SV177: $i] :
( ( ! [SY648: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY648 @ ( sK47_SY499 @ SV177 ) )
| ~ ~ ( are_equipotent @ SY648 @ ( sK47_SY499 @ SV177 ) ) )
| ~ ~ ( in @ SY648 @ ( sK47_SY499 @ SV177 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1956]) ).
thf(2022,plain,
! [SV223: $i,SV178: $i] :
( ( ( subset @ ( singleton @ SV178 ) @ SV223 )
= $false )
| ( ( in @ SV178 @ SV223 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1957]) ).
thf(2023,plain,
! [SV223: $i,SV178: $i] :
( ( ( in @ SV178 @ SV223 )
= $false )
| ( ( subset @ ( singleton @ SV178 ) @ SV223 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1958]) ).
thf(2024,plain,
! [SV224: $i,SV179: $i] :
( ( ~ ~ ( disjoint @ SV179 @ SV224 )
| ~ ! [SY601: $i] :
~ ( in @ SY601 @ ( set_intersection2 @ SV179 @ SV224 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1959]) ).
thf(2025,plain,
! [SV224: $i,SV179: $i] :
( ( ~ ~ ! [SY602: $i] :
~ ( in @ SY602 @ ( set_intersection2 @ SV179 @ SV224 ) )
| ~ ( disjoint @ SV179 @ SV224 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1960]) ).
thf(2026,plain,
! [SV225: $i,SV180: $i,SV249: $i] :
( ( ( SV249
!= ( set_intersection2 @ SV180 @ SV225 ) )
= $true )
| ( ( ! [SY649: $i] :
~ ( ~ ( ~ ( in @ SY649 @ SV249 )
| ~ ( ~ ( in @ SY649 @ SV180 )
| ~ ( in @ SY649 @ SV225 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY649 @ SV180 )
| ~ ( in @ SY649 @ SV225 ) )
| ( in @ SY649 @ SV249 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1961]) ).
thf(2027,plain,
! [SV225: $i,SV180: $i,SV249: $i] :
( ( ( ~ ! [SY650: $i] :
~ ( ~ ( ~ ( in @ SY650 @ SV249 )
| ~ ( ~ ( in @ SY650 @ SV180 )
| ~ ( in @ SY650 @ SV225 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY650 @ SV180 )
| ~ ( in @ SY650 @ SV225 ) )
| ( in @ SY650 @ SV249 ) ) ) )
= $true )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1962]) ).
thf(2028,plain,
! [SV181: $i,SV226: $i,SV263: $i] :
( ( ( in @ SV263 @ SV226 )
= $false )
| ( ( in @ SV263 @ SV181 )
= $true )
| ( ( element @ SV226 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1963]) ).
thf(2029,plain,
! [SV228: $i,SV183: $i] :
( ( ( in @ SV183 @ SV228 )
= $false )
| ( ( disjoint @ ( singleton @ SV183 ) @ SV228 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1964]) ).
thf(2030,plain,
! [SV229: $i,SV184: $i,SV250: $i] :
( ( ( SV250
!= ( set_difference @ SV184 @ SV229 ) )
= $true )
| ( ( ! [SY651: $i] :
~ ( ~ ( ~ ( in @ SY651 @ SV250 )
| ~ ( ~ ( in @ SY651 @ SV184 )
| ~ ~ ( in @ SY651 @ SV229 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY651 @ SV184 )
| ~ ~ ( in @ SY651 @ SV229 ) )
| ( in @ SY651 @ SV250 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1965]) ).
thf(2031,plain,
! [SV229: $i,SV184: $i,SV250: $i] :
( ( ( ~ ! [SY652: $i] :
~ ( ~ ( ~ ( in @ SY652 @ SV250 )
| ~ ( ~ ( in @ SY652 @ SV184 )
| ~ ~ ( in @ SY652 @ SV229 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY652 @ SV184 )
| ~ ~ ( in @ SY652 @ SV229 ) )
| ( in @ SY652 @ SV250 ) ) ) )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1966]) ).
thf(2032,plain,
! [SV251: $i,SV230: $i,SV185: $i] :
( ( ( ~ ( ~ ( in @ SV185 @ SV230 )
| ~ ( element @ SV230 @ ( powerset @ SV251 ) ) ) )
= $false )
| ( ( ~ ( empty @ SV251 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1967]) ).
thf(2033,plain,
! [SV259: $i,SV187: $i] :
( ( ( ~ ( subset @ SV187 @ SV259 ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( relation_dom @ SV187 ) @ ( relation_dom @ SV259 ) )
| ~ ( subset @ ( relation_rng @ SV187 ) @ ( relation_rng @ SV259 ) ) ) )
= $true )
| ( ( relation @ SV259 )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1968]) ).
thf(2034,plain,
! [SV260: $i,SV252: $i,SV232: $i,SV188: $i] :
( ( ~ ( in @ ( ordered_pair @ SV188 @ SV232 ) @ ( cartesian_product2 @ SV252 @ SV260 ) )
| ~ ( ~ ( in @ SV188 @ SV252 )
| ~ ( in @ SV232 @ SV260 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1969]) ).
thf(2035,plain,
! [SV260: $i,SV232: $i,SV252: $i,SV188: $i] :
( ( ~ ~ ( ~ ( in @ SV188 @ SV252 )
| ~ ( in @ SV232 @ SV260 ) )
| ( in @ ( ordered_pair @ SV188 @ SV232 ) @ ( cartesian_product2 @ SV252 @ SV260 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1970]) ).
thf(2036,plain,
! [SV189: $i,SV233: $i] :
( ( ( ~ ( ~ ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV189 )
| ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV233 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV233 )
| ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV189 ) ) )
= $true )
| ( ( SV189 = SV233 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1971]) ).
thf(2037,plain,
! [SV190: $i,SV234: $i] :
( ( ( SV234
= ( powerset @ SV190 ) )
= $false )
| ( ( ! [SY614: $i] :
~ ( ~ ( ~ ( in @ SY614 @ SV234 )
| ( subset @ SY614 @ SV190 ) )
| ~ ( ~ ( subset @ SY614 @ SV190 )
| ( in @ SY614 @ SV234 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1972]) ).
thf(2038,plain,
! [SV190: $i,SV234: $i] :
( ( ( ! [SY615: $i] :
~ ( ~ ( ~ ( in @ SY615 @ SV234 )
| ( subset @ SY615 @ SV190 ) )
| ~ ( ~ ( subset @ SY615 @ SV190 )
| ( in @ SY615 @ SV234 ) ) ) )
= $false )
| ( ( SV234
= ( powerset @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1973]) ).
thf(2039,plain,
! [SV253: $i,SV191: $i,SV235: $i] :
( ( ( ~ ( in @ SV235 @ ( subset_complement @ SV191 @ SV253 ) )
| ~ ( in @ SV235 @ SV253 ) )
= $true )
| ( ( element @ SV253 @ ( powerset @ SV191 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1974]) ).
thf(2040,plain,
! [SV192: $i,SV261: $i] :
( ( ( ( SV261
!= ( relation_dom @ SV192 ) )
| ! [SY664: $i] :
~ ( ~ ( ~ ( in @ SY664 @ SV261 )
| ~ ! [SY536: $i] :
~ ( in @ ( ordered_pair @ SY664 @ SY536 ) @ SV192 ) )
| ~ ( ~ ~ ! [SY537: $i] :
~ ( in @ ( ordered_pair @ SY664 @ SY537 ) @ SV192 )
| ( in @ SY664 @ SV261 ) ) ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1975]) ).
thf(2041,plain,
! [SV192: $i,SV261: $i] :
( ( ( ~ ! [SY667: $i] :
~ ( ~ ( ~ ( in @ SY667 @ SV261 )
| ~ ! [SY539: $i] :
~ ( in @ ( ordered_pair @ SY667 @ SY539 ) @ SV192 ) )
| ~ ( ~ ~ ! [SY540: $i] :
~ ( in @ ( ordered_pair @ SY667 @ SY540 ) @ SV192 )
| ( in @ SY667 @ SV261 ) ) )
| ( SV261
= ( relation_dom @ SV192 ) ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1976]) ).
thf(2042,plain,
! [SV236: $i,SV193: $i,SV254: $i] :
( ( ( SV254
!= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true )
| ( ( ! [SY654: $i] :
~ ( ~ ( ~ ( in @ SY654 @ SV254 )
| ~ ! [SY619: $i] :
~ ~ ! [SY620: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY619 @ SV193 )
| ~ ( in @ SY620 @ SV236 ) )
| ( SY654
!= ( ordered_pair @ SY619 @ SY620 ) ) ) )
| ~ ( ~ ~ ! [SY621: $i] :
~ ~ ! [SY622: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY621 @ SV193 )
| ~ ( in @ SY622 @ SV236 ) )
| ( SY654
!= ( ordered_pair @ SY621 @ SY622 ) ) )
| ( in @ SY654 @ SV254 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1977]) ).
thf(2043,plain,
! [SV236: $i,SV193: $i,SV254: $i] :
( ( ( ~ ! [SY659: $i] :
~ ( ~ ( ~ ( in @ SY659 @ SV254 )
| ~ ! [SY624: $i] :
~ ~ ! [SY625: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY624 @ SV193 )
| ~ ( in @ SY625 @ SV236 ) )
| ( SY659
!= ( ordered_pair @ SY624 @ SY625 ) ) ) )
| ~ ( ~ ~ ! [SY626: $i] :
~ ~ ! [SY627: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY626 @ SV193 )
| ~ ( in @ SY627 @ SV236 ) )
| ( SY659
!= ( ordered_pair @ SY626 @ SY627 ) ) )
| ( in @ SY659 @ SV254 ) ) ) )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1978]) ).
thf(2044,plain,
! [SV194: $i,SV262: $i] :
( ( ( ( SV262
!= ( relation_rng @ SV194 ) )
| ! [SY670: $i] :
~ ( ~ ( ~ ( in @ SY670 @ SV262 )
| ~ ! [SY555: $i] :
~ ( in @ ( ordered_pair @ SY555 @ SY670 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY556: $i] :
~ ( in @ ( ordered_pair @ SY556 @ SY670 ) @ SV194 )
| ( in @ SY670 @ SV262 ) ) ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1979]) ).
thf(2045,plain,
! [SV194: $i,SV262: $i] :
( ( ( ~ ! [SY673: $i] :
~ ( ~ ( ~ ( in @ SY673 @ SV262 )
| ~ ! [SY558: $i] :
~ ( in @ ( ordered_pair @ SY558 @ SY673 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY559: $i] :
~ ( in @ ( ordered_pair @ SY559 @ SY673 ) @ SV194 )
| ( in @ SY673 @ SV262 ) ) )
| ( SV262
= ( relation_rng @ SV194 ) ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1980]) ).
thf(2046,plain,
! [SV238: $i,SV196: $i] :
( ( ~ ~ ( disjoint @ SV196 @ SV238 )
| ~ ! [SY628: $i] :
~ ~ ( ~ ( in @ SY628 @ SV196 )
| ~ ( in @ SY628 @ SV238 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1981]) ).
thf(2047,plain,
! [SV238: $i,SV196: $i] :
( ( ~ ~ ! [SY629: $i] :
~ ~ ( ~ ( in @ SY629 @ SV196 )
| ~ ( in @ SY629 @ SV238 ) )
| ~ ( disjoint @ SV196 @ SV238 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1982]) ).
thf(2048,plain,
! [SV255: $i,SV239: $i,SV197: $i] :
( ( ( ~ ( in @ SV197 @ SV239 ) )
= $true )
| ( ( ~ ( element @ SV239 @ ( powerset @ SV255 ) ) )
= $true )
| ( ( element @ SV197 @ SV255 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1983]) ).
thf(2049,plain,
! [SV199: $i,SV265: $i] :
( ( ( ~ ( in @ SV265 @ SV199 ) )
= $true )
| ( ( SV199 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1986]) ).
thf(2050,plain,
! [SV199: $i] :
( ( ( ~ ( in @ ( sK51_SY568 @ SV199 ) @ SV199 ) )
= $false )
| ( ( SV199 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1987]) ).
thf(2051,plain,
! [SV200: $i,SV241: $i] :
( ( ( in @ ( sK49_SY631 @ SV241 @ SV200 ) @ SV200 )
= $true )
| ( ( element @ SV200 @ ( powerset @ SV241 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1988]) ).
thf(2052,plain,
! [SV256: $i,SV242: $i,SV201: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV201 @ SV242 ) @ SV256 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV201 @ SV256 )
| ~ ( in @ SV242 @ SV256 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1990]) ).
thf(2053,plain,
! [SV242: $i,SV256: $i,SV201: $i] :
( ( ( ~ ~ ( ~ ( in @ SV201 @ SV256 )
| ~ ( in @ SV242 @ SV256 ) ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV201 @ SV242 ) @ SV256 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1991]) ).
thf(2054,plain,
! [SV204: $i,SV155: $i,SV243: $i] :
( ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $false )
| ( ( ! [SY633: $i] :
~ ( ~ ( ~ ( in @ SY633 @ SV243 )
| ( in @ SY633 @ SV155 )
| ( in @ SY633 @ SV204 ) )
| ~ ( ~ ( ( in @ SY633 @ SV155 )
| ( in @ SY633 @ SV204 ) )
| ( in @ SY633 @ SV243 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1992]) ).
thf(2055,plain,
! [SV204: $i,SV155: $i,SV243: $i] :
( ( ( ! [SY634: $i] :
~ ( ~ ( ~ ( in @ SY634 @ SV243 )
| ( in @ SY634 @ SV155 )
| ( in @ SY634 @ SV204 ) )
| ~ ( ~ ( ( in @ SY634 @ SV155 )
| ( in @ SY634 @ SV204 ) )
| ( in @ SY634 @ SV243 ) ) ) )
= $false )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1993]) ).
thf(2056,plain,
! [SV156: $i,SV205: $i] :
( ( ( relation @ SV205 )
= $false )
| ( ( relation @ SV156 )
= $false )
| ( ( relation @ ( set_union2 @ SV156 @ SV205 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1994]) ).
thf(2057,plain,
! [SV157: $i] :
( ( ~ ~ ( ~ ( in @ SV157 @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SY635: $i,SY636: $i] :
( ~ ~ ( ~ ( in @ SY635 @ ( sK46_SY444 @ SV157 ) )
| ~ ( subset @ SY636 @ SY635 ) )
| ( in @ SY636 @ ( sK46_SY444 @ SV157 ) ) ) )
| ~ ! [SY637: $i] :
~ ~ ( ~ ( in @ SY637 @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SY638: $i] :
~ ~ ( ~ ( in @ SY638 @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY637 )
| ( in @ SX4 @ SY638 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1995]) ).
thf(2058,plain,
! [SV157: $i,SV266: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( subset @ SV266 @ ( sK46_SY444 @ SV157 ) )
| ~ ~ ( are_equipotent @ SV266 @ ( sK46_SY444 @ SV157 ) ) )
| ~ ~ ( in @ SV266 @ ( sK46_SY444 @ SV157 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1996]) ).
thf(2059,plain,
! [SV257: $i,SV207: $i,SV244: $i,SV159: $i] :
( ( ( SV159 != SV244 )
= $false )
| ( ( ( ordered_pair @ SV159 @ SV207 )
= ( ordered_pair @ SV244 @ SV257 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1997]) ).
thf(2060,plain,
! [SV244: $i,SV159: $i,SV257: $i,SV207: $i] :
( ( ( SV207 != SV257 )
= $false )
| ( ( ( ordered_pair @ SV159 @ SV207 )
= ( ordered_pair @ SV244 @ SV257 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1997]) ).
thf(2061,plain,
! [SV208: $i,SV245: $i,SV160: $i] :
( ( ( ~ ( in @ SV160 @ ( relation_dom @ SV245 ) )
| ~ ( in @ SV208 @ ( relation_rng @ SV245 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV160 @ SV208 ) @ SV245 )
= $false )
| ( ( relation @ SV245 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1998]) ).
thf(2062,plain,
! [SV164: $i,SV211: $i] :
( ( ( in @ SV211 @ SV164 )
= $false )
| ( ( ( set_difference @ SV164 @ ( singleton @ SV211 ) )
= SV164 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2000]) ).
thf(2063,plain,
! [SV164: $i,SV211: $i] :
( ( ( in @ SV211 @ SV164 )
= $true )
| ( ( ( set_difference @ SV164 @ ( singleton @ SV211 ) )
= SV164 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2001]) ).
thf(2064,plain,
! [SV212: $i,SV165: $i] :
( ( ( empty @ SV165 )
= $true )
| ( ( ~ ( ~ ( ~ ( element @ SV212 @ SV165 )
| ( in @ SV212 @ SV165 ) )
| ~ ( ~ ( in @ SV212 @ SV165 )
| ( element @ SV212 @ SV165 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2002]) ).
thf(2065,plain,
! [SV165: $i,SV212: $i] :
( ( ( ~ ( ~ ( element @ SV212 @ SV165 )
| ( empty @ SV212 ) )
| ~ ( ~ ( empty @ SV212 )
| ( element @ SV212 @ SV165 ) ) )
= $false )
| ( ( empty @ SV165 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2003]) ).
thf(2066,plain,
! [SV213: $i,SV166: $i,SV267: $i] :
( ( ( ~ ( in @ SV267 @ SV166 )
| ( in @ SV267 @ SV213 ) )
= $true )
| ( ( subset @ SV166 @ SV213 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2004]) ).
thf(2067,plain,
! [SV166: $i,SV213: $i] :
( ( ( ~ ( in @ ( sK52_SY580 @ SV213 @ SV166 ) @ SV166 )
| ( in @ ( sK52_SY580 @ SV213 @ SV166 ) @ SV213 ) )
= $false )
| ( ( subset @ SV166 @ SV213 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2005]) ).
thf(2068,plain,
! [SV215: $i,SV168: $i] :
( ( ( SV168 = empty_set )
= $true )
| ( ( ~ ( ~ ( ( SV215
!= ( set_meet @ SV168 ) )
| ! [SY581: $i] :
~ ( ~ ( ~ ( in @ SY581 @ SV215 )
| ! [SY467: $i] :
( ~ ( in @ SY467 @ SV168 )
| ( in @ SY581 @ SY467 ) ) )
| ~ ( ~ ! [SY468: $i] :
( ~ ( in @ SY468 @ SV168 )
| ( in @ SY581 @ SY468 ) )
| ( in @ SY581 @ SV215 ) ) ) )
| ~ ( ~ ! [SY584: $i] :
~ ( ~ ( ~ ( in @ SY584 @ SV215 )
| ! [SY470: $i] :
( ~ ( in @ SY470 @ SV168 )
| ( in @ SY584 @ SY470 ) ) )
| ~ ( ~ ! [SY471: $i] :
( ~ ( in @ SY471 @ SV168 )
| ( in @ SY584 @ SY471 ) )
| ( in @ SY584 @ SV215 ) ) )
| ( SV215
= ( set_meet @ SV168 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2006]) ).
thf(2069,plain,
! [SV168: $i,SV215: $i] :
( ( ( ~ ( ( SV215
!= ( set_meet @ SV168 ) )
| ( SV215 = empty_set ) )
| ~ ( ( SV215 != empty_set )
| ( SV215
= ( set_meet @ SV168 ) ) ) )
= $false )
| ( ( SV168 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2007]) ).
thf(2070,plain,
! [SV169: $i,SV216: $i,SV268: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV268 @ SV216 )
| ~ ! [SY680: $i] :
~ ~ ( ~ ( in @ SV268 @ SY680 )
| ~ ( in @ SY680 @ SV169 ) ) )
| ~ ( ~ ~ ! [SY681: $i] :
~ ~ ( ~ ( in @ SV268 @ SY681 )
| ~ ( in @ SY681 @ SV169 ) )
| ( in @ SV268 @ SV216 ) ) ) )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2008]) ).
thf(2071,plain,
! [SV216: $i,SV169: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV216 )
| ~ ! [SY682: $i] :
~ ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SY682 )
| ~ ( in @ SY682 @ SV169 ) ) )
| ~ ( ~ ~ ! [SY683: $i] :
~ ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SY683 )
| ~ ( in @ SY683 @ SV169 ) )
| ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV216 ) ) ) )
= $false )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2009]) ).
thf(2072,plain,
! [SV217: $i,SV170: $i,SV246: $i] :
( ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $false )
| ( ( ! [SY642: $i] :
~ ( ~ ( ~ ( in @ SY642 @ SV246 )
| ( SY642 = SV170 )
| ( SY642 = SV217 ) )
| ~ ( ~ ( ( SY642 = SV170 )
| ( SY642 = SV217 ) )
| ( in @ SY642 @ SV246 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2010]) ).
thf(2073,plain,
! [SV217: $i,SV170: $i,SV246: $i] :
( ( ( ! [SY643: $i] :
~ ( ~ ( ~ ( in @ SY643 @ SV246 )
| ( SY643 = SV170 )
| ( SY643 = SV217 ) )
| ~ ( ~ ( ( SY643 = SV170 )
| ( SY643 = SV217 ) )
| ( in @ SY643 @ SV246 ) ) ) )
= $false )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2011]) ).
thf(2074,plain,
! [SV258: $i,SV247: $i,SV218: $i,SV171: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV171 @ SV218 ) @ ( cartesian_product2 @ SV247 @ SV258 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV171 @ SV247 )
| ~ ( in @ SV218 @ SV258 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2012]) ).
thf(2075,plain,
! [SV258: $i,SV218: $i,SV247: $i,SV171: $i] :
( ( ( ~ ~ ( ~ ( in @ SV171 @ SV247 )
| ~ ( in @ SV218 @ SV258 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV171 @ SV218 ) @ ( cartesian_product2 @ SV247 @ SV258 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2013]) ).
thf(2076,plain,
! [SV172: $i,SV219: $i,SV269: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV269 @ SV219 )
| ( SV269 = SV172 ) )
| ~ ( ( SV269 != SV172 )
| ( in @ SV269 @ SV219 ) ) ) )
= $true )
| ( ( SV219
= ( singleton @ SV172 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2014]) ).
thf(2077,plain,
! [SV219: $i,SV172: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK54_SY599 @ SV172 @ SV219 ) @ SV219 )
| ( ( sK54_SY599 @ SV172 @ SV219 )
= SV172 ) )
| ~ ( ( ( sK54_SY599 @ SV172 @ SV219 )
!= SV172 )
| ( in @ ( sK54_SY599 @ SV172 @ SV219 ) @ SV219 ) ) ) )
= $false )
| ( ( SV219
= ( singleton @ SV172 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2015]) ).
thf(2078,plain,
! [SV174: $i,SV264: $i] :
( ( ( ~ ( ~ ( in @ SV264 @ SV174 )
| ~ ! [SY676: $i,SY677: $i] :
( SV264
!= ( ordered_pair @ SY676 @ SY677 ) ) ) )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2016]) ).
thf(2079,plain,
! [SV174: $i] :
( ( ( ~ ( ~ ( in @ ( sK50_SY493 @ SV174 ) @ SV174 )
| ~ ! [SY678: $i,SY679: $i] :
( ( sK50_SY493 @ SV174 )
!= ( ordered_pair @ SY678 @ SY679 ) ) ) )
= $true )
| ( ( relation @ SV174 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2017]) ).
thf(2080,plain,
! [SV177: $i] :
( ( ~ ~ ( ~ ( in @ SV177 @ ( sK47_SY499 @ SV177 ) )
| ~ ! [SY645: $i,SY646: $i] :
( ~ ~ ( ~ ( in @ SY645 @ ( sK47_SY499 @ SV177 ) )
| ~ ( subset @ SY646 @ SY645 ) )
| ( in @ SY646 @ ( sK47_SY499 @ SV177 ) ) ) )
| ~ ! [SY647: $i] :
( ~ ( in @ SY647 @ ( sK47_SY499 @ SV177 ) )
| ( in @ ( powerset @ SY647 ) @ ( sK47_SY499 @ SV177 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2020]) ).
thf(2081,plain,
! [SV177: $i,SV270: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( subset @ SV270 @ ( sK47_SY499 @ SV177 ) )
| ~ ~ ( are_equipotent @ SV270 @ ( sK47_SY499 @ SV177 ) ) )
| ~ ~ ( in @ SV270 @ ( sK47_SY499 @ SV177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2021]) ).
thf(2082,plain,
! [SV224: $i,SV179: $i] :
( ( ( ~ ~ ( disjoint @ SV179 @ SV224 ) )
= $true )
| ( ( ~ ! [SY601: $i] :
~ ( in @ SY601 @ ( set_intersection2 @ SV179 @ SV224 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2024]) ).
thf(2083,plain,
! [SV224: $i,SV179: $i] :
( ( ( ~ ~ ! [SY602: $i] :
~ ( in @ SY602 @ ( set_intersection2 @ SV179 @ SV224 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV179 @ SV224 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2025]) ).
thf(2084,plain,
! [SV225: $i,SV180: $i,SV249: $i] :
( ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $false )
| ( ( ! [SY649: $i] :
~ ( ~ ( ~ ( in @ SY649 @ SV249 )
| ~ ( ~ ( in @ SY649 @ SV180 )
| ~ ( in @ SY649 @ SV225 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY649 @ SV180 )
| ~ ( in @ SY649 @ SV225 ) )
| ( in @ SY649 @ SV249 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2026]) ).
thf(2085,plain,
! [SV225: $i,SV180: $i,SV249: $i] :
( ( ( ! [SY650: $i] :
~ ( ~ ( ~ ( in @ SY650 @ SV249 )
| ~ ( ~ ( in @ SY650 @ SV180 )
| ~ ( in @ SY650 @ SV225 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY650 @ SV180 )
| ~ ( in @ SY650 @ SV225 ) )
| ( in @ SY650 @ SV249 ) ) ) )
= $false )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2027]) ).
thf(2086,plain,
! [SV229: $i,SV184: $i,SV250: $i] :
( ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $false )
| ( ( ! [SY651: $i] :
~ ( ~ ( ~ ( in @ SY651 @ SV250 )
| ~ ( ~ ( in @ SY651 @ SV184 )
| ~ ~ ( in @ SY651 @ SV229 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY651 @ SV184 )
| ~ ~ ( in @ SY651 @ SV229 ) )
| ( in @ SY651 @ SV250 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2030]) ).
thf(2087,plain,
! [SV229: $i,SV184: $i,SV250: $i] :
( ( ( ! [SY652: $i] :
~ ( ~ ( ~ ( in @ SY652 @ SV250 )
| ~ ( ~ ( in @ SY652 @ SV184 )
| ~ ~ ( in @ SY652 @ SV229 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY652 @ SV184 )
| ~ ~ ( in @ SY652 @ SV229 ) )
| ( in @ SY652 @ SV250 ) ) ) )
= $false )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2031]) ).
thf(2088,plain,
! [SV251: $i,SV230: $i,SV185: $i] :
( ( ( ~ ( in @ SV185 @ SV230 )
| ~ ( element @ SV230 @ ( powerset @ SV251 ) ) )
= $true )
| ( ( ~ ( empty @ SV251 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2032]) ).
thf(2089,plain,
! [SV259: $i,SV187: $i] :
( ( ( subset @ SV187 @ SV259 )
= $false )
| ( ( ~ ( ~ ( subset @ ( relation_dom @ SV187 ) @ ( relation_dom @ SV259 ) )
| ~ ( subset @ ( relation_rng @ SV187 ) @ ( relation_rng @ SV259 ) ) ) )
= $true )
| ( ( relation @ SV259 )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2033]) ).
thf(2090,plain,
! [SV260: $i,SV252: $i,SV232: $i,SV188: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV188 @ SV232 ) @ ( cartesian_product2 @ SV252 @ SV260 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV188 @ SV252 )
| ~ ( in @ SV232 @ SV260 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2034]) ).
thf(2091,plain,
! [SV260: $i,SV232: $i,SV252: $i,SV188: $i] :
( ( ( ~ ~ ( ~ ( in @ SV188 @ SV252 )
| ~ ( in @ SV232 @ SV260 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV188 @ SV232 ) @ ( cartesian_product2 @ SV252 @ SV260 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2035]) ).
thf(2092,plain,
! [SV189: $i,SV233: $i] :
( ( ( ~ ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV189 )
| ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV233 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV233 )
| ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV189 ) ) )
= $true )
| ( ( SV189 = SV233 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2036]) ).
thf(2093,plain,
! [SV190: $i,SV234: $i,SV271: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV271 @ SV234 )
| ( subset @ SV271 @ SV190 ) )
| ~ ( ~ ( subset @ SV271 @ SV190 )
| ( in @ SV271 @ SV234 ) ) ) )
= $true )
| ( ( SV234
= ( powerset @ SV190 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2037]) ).
thf(2094,plain,
! [SV234: $i,SV190: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV234 )
| ( subset @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV190 ) )
| ~ ( ~ ( subset @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV190 )
| ( in @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV234 ) ) ) )
= $false )
| ( ( SV234
= ( powerset @ SV190 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2038]) ).
thf(2095,plain,
! [SV253: $i,SV191: $i,SV235: $i] :
( ( ( ~ ( in @ SV235 @ ( subset_complement @ SV191 @ SV253 ) ) )
= $true )
| ( ( ~ ( in @ SV235 @ SV253 ) )
= $true )
| ( ( element @ SV253 @ ( powerset @ SV191 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2039]) ).
thf(2096,plain,
! [SV192: $i,SV261: $i] :
( ( ( SV261
!= ( relation_dom @ SV192 ) )
= $true )
| ( ( ! [SY664: $i] :
~ ( ~ ( ~ ( in @ SY664 @ SV261 )
| ~ ! [SY536: $i] :
~ ( in @ ( ordered_pair @ SY664 @ SY536 ) @ SV192 ) )
| ~ ( ~ ~ ! [SY537: $i] :
~ ( in @ ( ordered_pair @ SY664 @ SY537 ) @ SV192 )
| ( in @ SY664 @ SV261 ) ) ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2040]) ).
thf(2097,plain,
! [SV192: $i,SV261: $i] :
( ( ( ~ ! [SY667: $i] :
~ ( ~ ( ~ ( in @ SY667 @ SV261 )
| ~ ! [SY539: $i] :
~ ( in @ ( ordered_pair @ SY667 @ SY539 ) @ SV192 ) )
| ~ ( ~ ~ ! [SY540: $i] :
~ ( in @ ( ordered_pair @ SY667 @ SY540 ) @ SV192 )
| ( in @ SY667 @ SV261 ) ) ) )
= $true )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2041]) ).
thf(2098,plain,
! [SV236: $i,SV193: $i,SV254: $i] :
( ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false )
| ( ( ! [SY654: $i] :
~ ( ~ ( ~ ( in @ SY654 @ SV254 )
| ~ ! [SY619: $i] :
~ ~ ! [SY620: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY619 @ SV193 )
| ~ ( in @ SY620 @ SV236 ) )
| ( SY654
!= ( ordered_pair @ SY619 @ SY620 ) ) ) )
| ~ ( ~ ~ ! [SY621: $i] :
~ ~ ! [SY622: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY621 @ SV193 )
| ~ ( in @ SY622 @ SV236 ) )
| ( SY654
!= ( ordered_pair @ SY621 @ SY622 ) ) )
| ( in @ SY654 @ SV254 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2042]) ).
thf(2099,plain,
! [SV236: $i,SV193: $i,SV254: $i] :
( ( ( ! [SY659: $i] :
~ ( ~ ( ~ ( in @ SY659 @ SV254 )
| ~ ! [SY624: $i] :
~ ~ ! [SY625: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY624 @ SV193 )
| ~ ( in @ SY625 @ SV236 ) )
| ( SY659
!= ( ordered_pair @ SY624 @ SY625 ) ) ) )
| ~ ( ~ ~ ! [SY626: $i] :
~ ~ ! [SY627: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY626 @ SV193 )
| ~ ( in @ SY627 @ SV236 ) )
| ( SY659
!= ( ordered_pair @ SY626 @ SY627 ) ) )
| ( in @ SY659 @ SV254 ) ) ) )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2043]) ).
thf(2100,plain,
! [SV194: $i,SV262: $i] :
( ( ( SV262
!= ( relation_rng @ SV194 ) )
= $true )
| ( ( ! [SY670: $i] :
~ ( ~ ( ~ ( in @ SY670 @ SV262 )
| ~ ! [SY555: $i] :
~ ( in @ ( ordered_pair @ SY555 @ SY670 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY556: $i] :
~ ( in @ ( ordered_pair @ SY556 @ SY670 ) @ SV194 )
| ( in @ SY670 @ SV262 ) ) ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2044]) ).
thf(2101,plain,
! [SV194: $i,SV262: $i] :
( ( ( ~ ! [SY673: $i] :
~ ( ~ ( ~ ( in @ SY673 @ SV262 )
| ~ ! [SY558: $i] :
~ ( in @ ( ordered_pair @ SY558 @ SY673 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY559: $i] :
~ ( in @ ( ordered_pair @ SY559 @ SY673 ) @ SV194 )
| ( in @ SY673 @ SV262 ) ) ) )
= $true )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2045]) ).
thf(2102,plain,
! [SV238: $i,SV196: $i] :
( ( ( ~ ~ ( disjoint @ SV196 @ SV238 ) )
= $true )
| ( ( ~ ! [SY628: $i] :
~ ~ ( ~ ( in @ SY628 @ SV196 )
| ~ ( in @ SY628 @ SV238 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2046]) ).
thf(2103,plain,
! [SV238: $i,SV196: $i] :
( ( ( ~ ~ ! [SY629: $i] :
~ ~ ( ~ ( in @ SY629 @ SV196 )
| ~ ( in @ SY629 @ SV238 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV196 @ SV238 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2047]) ).
thf(2104,plain,
! [SV255: $i,SV239: $i,SV197: $i] :
( ( ( in @ SV197 @ SV239 )
= $false )
| ( ( ~ ( element @ SV239 @ ( powerset @ SV255 ) ) )
= $true )
| ( ( element @ SV197 @ SV255 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2048]) ).
thf(2105,plain,
! [SV199: $i,SV265: $i] :
( ( ( in @ SV265 @ SV199 )
= $false )
| ( ( SV199 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2049]) ).
thf(2106,plain,
! [SV199: $i] :
( ( ( in @ ( sK51_SY568 @ SV199 ) @ SV199 )
= $true )
| ( ( SV199 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2050]) ).
thf(2107,plain,
! [SV256: $i,SV242: $i,SV201: $i] :
( ( ( subset @ ( unordered_pair @ SV201 @ SV242 ) @ SV256 )
= $false )
| ( ( ~ ( ~ ( in @ SV201 @ SV256 )
| ~ ( in @ SV242 @ SV256 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2052]) ).
thf(2108,plain,
! [SV242: $i,SV256: $i,SV201: $i] :
( ( ( ~ ( ~ ( in @ SV201 @ SV256 )
| ~ ( in @ SV242 @ SV256 ) ) )
= $false )
| ( ( subset @ ( unordered_pair @ SV201 @ SV242 ) @ SV256 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2053]) ).
thf(2109,plain,
! [SV204: $i,SV155: $i,SV243: $i,SV272: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV272 @ SV243 )
| ( in @ SV272 @ SV155 )
| ( in @ SV272 @ SV204 ) )
| ~ ( ~ ( ( in @ SV272 @ SV155 )
| ( in @ SV272 @ SV204 ) )
| ( in @ SV272 @ SV243 ) ) ) )
= $true )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2054]) ).
thf(2110,plain,
! [SV243: $i,SV155: $i,SV204: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV243 )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV155 )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV204 ) )
| ~ ( ~ ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV155 )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV204 ) )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV243 ) ) ) )
= $false )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2055]) ).
thf(2111,plain,
! [SV157: $i] :
( ( ~ ~ ( ~ ( in @ SV157 @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SY635: $i,SY636: $i] :
( ~ ~ ( ~ ( in @ SY635 @ ( sK46_SY444 @ SV157 ) )
| ~ ( subset @ SY636 @ SY635 ) )
| ( in @ SY636 @ ( sK46_SY444 @ SV157 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2057]) ).
thf(2112,plain,
! [SV157: $i] :
( ( ~ ! [SY637: $i] :
~ ~ ( ~ ( in @ SY637 @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SY638: $i] :
~ ~ ( ~ ( in @ SY638 @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY637 )
| ( in @ SX4 @ SY638 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2057]) ).
thf(2113,plain,
! [SV157: $i,SV266: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV266 @ ( sK46_SY444 @ SV157 ) )
| ~ ~ ( are_equipotent @ SV266 @ ( sK46_SY444 @ SV157 ) ) )
| ~ ~ ( in @ SV266 @ ( sK46_SY444 @ SV157 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2058]) ).
thf(2114,plain,
! [SV257: $i,SV207: $i,SV244: $i,SV159: $i] :
( ( ( SV159 = SV244 )
= $true )
| ( ( ( ordered_pair @ SV159 @ SV207 )
= ( ordered_pair @ SV244 @ SV257 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2059]) ).
thf(2115,plain,
! [SV244: $i,SV159: $i,SV257: $i,SV207: $i] :
( ( ( SV207 = SV257 )
= $true )
| ( ( ( ordered_pair @ SV159 @ SV207 )
= ( ordered_pair @ SV244 @ SV257 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2060]) ).
thf(2116,plain,
! [SV208: $i,SV245: $i,SV160: $i] :
( ( ( ~ ( in @ SV160 @ ( relation_dom @ SV245 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV160 @ SV208 ) @ SV245 )
= $false )
| ( ( relation @ SV245 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2061]) ).
thf(2117,plain,
! [SV160: $i,SV245: $i,SV208: $i] :
( ( ( ~ ( in @ SV208 @ ( relation_rng @ SV245 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV160 @ SV208 ) @ SV245 )
= $false )
| ( ( relation @ SV245 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2061]) ).
thf(2118,plain,
! [SV165: $i,SV212: $i] :
( ( ( ~ ( ~ ( element @ SV212 @ SV165 )
| ( in @ SV212 @ SV165 ) )
| ~ ( ~ ( in @ SV212 @ SV165 )
| ( element @ SV212 @ SV165 ) ) )
= $false )
| ( ( empty @ SV165 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2064]) ).
thf(2119,plain,
! [SV165: $i,SV212: $i] :
( ( ( ~ ( ~ ( element @ SV212 @ SV165 )
| ( empty @ SV212 ) ) )
= $false )
| ( ( empty @ SV165 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2065]) ).
thf(2120,plain,
! [SV165: $i,SV212: $i] :
( ( ( ~ ( ~ ( empty @ SV212 )
| ( element @ SV212 @ SV165 ) ) )
= $false )
| ( ( empty @ SV165 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2065]) ).
thf(2121,plain,
! [SV213: $i,SV166: $i,SV267: $i] :
( ( ( ~ ( in @ SV267 @ SV166 ) )
= $true )
| ( ( in @ SV267 @ SV213 )
= $true )
| ( ( subset @ SV166 @ SV213 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2066]) ).
thf(2122,plain,
! [SV166: $i,SV213: $i] :
( ( ( ~ ( in @ ( sK52_SY580 @ SV213 @ SV166 ) @ SV166 ) )
= $false )
| ( ( subset @ SV166 @ SV213 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2067]) ).
thf(2123,plain,
! [SV166: $i,SV213: $i] :
( ( ( in @ ( sK52_SY580 @ SV213 @ SV166 ) @ SV213 )
= $false )
| ( ( subset @ SV166 @ SV213 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2067]) ).
thf(2124,plain,
! [SV168: $i,SV215: $i] :
( ( ( ~ ( ( SV215
!= ( set_meet @ SV168 ) )
| ! [SY581: $i] :
~ ( ~ ( ~ ( in @ SY581 @ SV215 )
| ! [SY467: $i] :
( ~ ( in @ SY467 @ SV168 )
| ( in @ SY581 @ SY467 ) ) )
| ~ ( ~ ! [SY468: $i] :
( ~ ( in @ SY468 @ SV168 )
| ( in @ SY581 @ SY468 ) )
| ( in @ SY581 @ SV215 ) ) ) )
| ~ ( ~ ! [SY584: $i] :
~ ( ~ ( ~ ( in @ SY584 @ SV215 )
| ! [SY470: $i] :
( ~ ( in @ SY470 @ SV168 )
| ( in @ SY584 @ SY470 ) ) )
| ~ ( ~ ! [SY471: $i] :
( ~ ( in @ SY471 @ SV168 )
| ( in @ SY584 @ SY471 ) )
| ( in @ SY584 @ SV215 ) ) )
| ( SV215
= ( set_meet @ SV168 ) ) ) )
= $false )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2068]) ).
thf(2125,plain,
! [SV168: $i,SV215: $i] :
( ( ( ~ ( ( SV215
!= ( set_meet @ SV168 ) )
| ( SV215 = empty_set ) ) )
= $false )
| ( ( SV168 = empty_set )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2069]) ).
thf(2126,plain,
! [SV168: $i,SV215: $i] :
( ( ( ~ ( ( SV215 != empty_set )
| ( SV215
= ( set_meet @ SV168 ) ) ) )
= $false )
| ( ( SV168 = empty_set )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2069]) ).
thf(2127,plain,
! [SV169: $i,SV216: $i,SV268: $i] :
( ( ( ~ ( ~ ( in @ SV268 @ SV216 )
| ~ ! [SY680: $i] :
~ ~ ( ~ ( in @ SV268 @ SY680 )
| ~ ( in @ SY680 @ SV169 ) ) )
| ~ ( ~ ~ ! [SY681: $i] :
~ ~ ( ~ ( in @ SV268 @ SY681 )
| ~ ( in @ SY681 @ SV169 ) )
| ( in @ SV268 @ SV216 ) ) )
= $false )
| ( ( SV216
= ( union @ SV169 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2070]) ).
thf(2128,plain,
! [SV216: $i,SV169: $i] :
( ( ( ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV216 )
| ~ ! [SY682: $i] :
~ ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SY682 )
| ~ ( in @ SY682 @ SV169 ) ) )
| ~ ( ~ ~ ! [SY683: $i] :
~ ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SY683 )
| ~ ( in @ SY683 @ SV169 ) )
| ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV216 ) ) )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2071]) ).
thf(2129,plain,
! [SV217: $i,SV170: $i,SV246: $i,SV273: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV273 @ SV246 )
| ( SV273 = SV170 )
| ( SV273 = SV217 ) )
| ~ ( ~ ( ( SV273 = SV170 )
| ( SV273 = SV217 ) )
| ( in @ SV273 @ SV246 ) ) ) )
= $true )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2072]) ).
thf(2130,plain,
! [SV246: $i,SV170: $i,SV217: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK57_SY643 @ SV217 @ SV170 @ SV246 ) @ SV246 )
| ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV170 )
| ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV217 ) )
| ~ ( ~ ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV170 )
| ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV217 ) )
| ( in @ ( sK57_SY643 @ SV217 @ SV170 @ SV246 ) @ SV246 ) ) ) )
= $false )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2073]) ).
thf(2131,plain,
! [SV258: $i,SV247: $i,SV218: $i,SV171: $i] :
( ( ( in @ ( ordered_pair @ SV171 @ SV218 ) @ ( cartesian_product2 @ SV247 @ SV258 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV171 @ SV247 )
| ~ ( in @ SV218 @ SV258 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2074]) ).
thf(2132,plain,
! [SV258: $i,SV218: $i,SV247: $i,SV171: $i] :
( ( ( ~ ( ~ ( in @ SV171 @ SV247 )
| ~ ( in @ SV218 @ SV258 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV171 @ SV218 ) @ ( cartesian_product2 @ SV247 @ SV258 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2075]) ).
thf(2133,plain,
! [SV172: $i,SV219: $i,SV269: $i] :
( ( ( ~ ( ~ ( in @ SV269 @ SV219 )
| ( SV269 = SV172 ) )
| ~ ( ( SV269 != SV172 )
| ( in @ SV269 @ SV219 ) ) )
= $false )
| ( ( SV219
= ( singleton @ SV172 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2076]) ).
thf(2134,plain,
! [SV219: $i,SV172: $i] :
( ( ( ~ ( ~ ( in @ ( sK54_SY599 @ SV172 @ SV219 ) @ SV219 )
| ( ( sK54_SY599 @ SV172 @ SV219 )
= SV172 ) )
| ~ ( ( ( sK54_SY599 @ SV172 @ SV219 )
!= SV172 )
| ( in @ ( sK54_SY599 @ SV172 @ SV219 ) @ SV219 ) ) )
= $true )
| ( ( SV219
= ( singleton @ SV172 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2077]) ).
thf(2135,plain,
! [SV174: $i,SV264: $i] :
( ( ( ~ ( in @ SV264 @ SV174 )
| ~ ! [SY676: $i,SY677: $i] :
( SV264
!= ( ordered_pair @ SY676 @ SY677 ) ) )
= $true )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2078]) ).
thf(2136,plain,
! [SV174: $i] :
( ( ( ~ ( in @ ( sK50_SY493 @ SV174 ) @ SV174 )
| ~ ! [SY678: $i,SY679: $i] :
( ( sK50_SY493 @ SV174 )
!= ( ordered_pair @ SY678 @ SY679 ) ) )
= $false )
| ( ( relation @ SV174 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2079]) ).
thf(2137,plain,
! [SV177: $i] :
( ( ~ ~ ( ~ ( in @ SV177 @ ( sK47_SY499 @ SV177 ) )
| ~ ! [SY645: $i,SY646: $i] :
( ~ ~ ( ~ ( in @ SY645 @ ( sK47_SY499 @ SV177 ) )
| ~ ( subset @ SY646 @ SY645 ) )
| ( in @ SY646 @ ( sK47_SY499 @ SV177 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2080]) ).
thf(2138,plain,
! [SV177: $i] :
( ( ~ ! [SY647: $i] :
( ~ ( in @ SY647 @ ( sK47_SY499 @ SV177 ) )
| ( in @ ( powerset @ SY647 ) @ ( sK47_SY499 @ SV177 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2080]) ).
thf(2139,plain,
! [SV177: $i,SV270: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV270 @ ( sK47_SY499 @ SV177 ) )
| ~ ~ ( are_equipotent @ SV270 @ ( sK47_SY499 @ SV177 ) ) )
| ~ ~ ( in @ SV270 @ ( sK47_SY499 @ SV177 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2081]) ).
thf(2140,plain,
! [SV224: $i,SV179: $i] :
( ( ( ~ ( disjoint @ SV179 @ SV224 ) )
= $false )
| ( ( ~ ! [SY601: $i] :
~ ( in @ SY601 @ ( set_intersection2 @ SV179 @ SV224 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2082]) ).
thf(2141,plain,
! [SV224: $i,SV179: $i] :
( ( ( ~ ! [SY602: $i] :
~ ( in @ SY602 @ ( set_intersection2 @ SV179 @ SV224 ) ) )
= $false )
| ( ( ~ ( disjoint @ SV179 @ SV224 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2083]) ).
thf(2142,plain,
! [SV225: $i,SV180: $i,SV249: $i,SV274: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV274 @ SV249 )
| ~ ( ~ ( in @ SV274 @ SV180 )
| ~ ( in @ SV274 @ SV225 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV274 @ SV180 )
| ~ ( in @ SV274 @ SV225 ) )
| ( in @ SV274 @ SV249 ) ) ) )
= $true )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2084]) ).
thf(2143,plain,
! [SV249: $i,SV180: $i,SV225: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV249 )
| ~ ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
| ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
| ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 ) )
| ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV249 ) ) ) )
= $false )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2085]) ).
thf(2144,plain,
! [SV229: $i,SV184: $i,SV250: $i,SV275: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV275 @ SV250 )
| ~ ( ~ ( in @ SV275 @ SV184 )
| ~ ~ ( in @ SV275 @ SV229 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV275 @ SV184 )
| ~ ~ ( in @ SV275 @ SV229 ) )
| ( in @ SV275 @ SV250 ) ) ) )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2086]) ).
thf(2145,plain,
! [SV250: $i,SV184: $i,SV229: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV250 )
| ~ ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
| ~ ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
| ~ ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 ) )
| ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV250 ) ) ) )
= $false )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2087]) ).
thf(2146,plain,
! [SV251: $i,SV230: $i,SV185: $i] :
( ( ( ~ ( in @ SV185 @ SV230 ) )
= $true )
| ( ( ~ ( element @ SV230 @ ( powerset @ SV251 ) ) )
= $true )
| ( ( ~ ( empty @ SV251 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2088]) ).
thf(2147,plain,
! [SV259: $i,SV187: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV187 ) @ ( relation_dom @ SV259 ) )
| ~ ( subset @ ( relation_rng @ SV187 ) @ ( relation_rng @ SV259 ) ) )
= $false )
| ( ( subset @ SV187 @ SV259 )
= $false )
| ( ( relation @ SV259 )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2089]) ).
thf(2148,plain,
! [SV260: $i,SV252: $i,SV232: $i,SV188: $i] :
( ( ( in @ ( ordered_pair @ SV188 @ SV232 ) @ ( cartesian_product2 @ SV252 @ SV260 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV188 @ SV252 )
| ~ ( in @ SV232 @ SV260 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2090]) ).
thf(2149,plain,
! [SV260: $i,SV232: $i,SV252: $i,SV188: $i] :
( ( ( ~ ( ~ ( in @ SV188 @ SV252 )
| ~ ( in @ SV232 @ SV260 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV188 @ SV232 ) @ ( cartesian_product2 @ SV252 @ SV260 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2091]) ).
thf(2150,plain,
! [SV189: $i,SV233: $i] :
( ( ( ~ ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV189 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV233 )
| ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV189 ) ) )
= $true )
| ( ( SV189 = SV233 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2092]) ).
thf(2151,plain,
! [SV189: $i,SV233: $i] :
( ( ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV233 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV233 )
| ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV189 ) ) )
= $true )
| ( ( SV189 = SV233 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2092]) ).
thf(2152,plain,
! [SV190: $i,SV234: $i,SV271: $i] :
( ( ( ~ ( ~ ( in @ SV271 @ SV234 )
| ( subset @ SV271 @ SV190 ) )
| ~ ( ~ ( subset @ SV271 @ SV190 )
| ( in @ SV271 @ SV234 ) ) )
= $false )
| ( ( SV234
= ( powerset @ SV190 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2093]) ).
thf(2153,plain,
! [SV234: $i,SV190: $i] :
( ( ( ~ ( ~ ( in @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV234 )
| ( subset @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV190 ) )
| ~ ( ~ ( subset @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV190 )
| ( in @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV234 ) ) )
= $true )
| ( ( SV234
= ( powerset @ SV190 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2094]) ).
thf(2154,plain,
! [SV253: $i,SV191: $i,SV235: $i] :
( ( ( in @ SV235 @ ( subset_complement @ SV191 @ SV253 ) )
= $false )
| ( ( ~ ( in @ SV235 @ SV253 ) )
= $true )
| ( ( element @ SV253 @ ( powerset @ SV191 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2095]) ).
thf(2155,plain,
! [SV192: $i,SV261: $i] :
( ( ( SV261
= ( relation_dom @ SV192 ) )
= $false )
| ( ( ! [SY664: $i] :
~ ( ~ ( ~ ( in @ SY664 @ SV261 )
| ~ ! [SY536: $i] :
~ ( in @ ( ordered_pair @ SY664 @ SY536 ) @ SV192 ) )
| ~ ( ~ ~ ! [SY537: $i] :
~ ( in @ ( ordered_pair @ SY664 @ SY537 ) @ SV192 )
| ( in @ SY664 @ SV261 ) ) ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2096]) ).
thf(2156,plain,
! [SV192: $i,SV261: $i] :
( ( ( ! [SY667: $i] :
~ ( ~ ( ~ ( in @ SY667 @ SV261 )
| ~ ! [SY539: $i] :
~ ( in @ ( ordered_pair @ SY667 @ SY539 ) @ SV192 ) )
| ~ ( ~ ~ ! [SY540: $i] :
~ ( in @ ( ordered_pair @ SY667 @ SY540 ) @ SV192 )
| ( in @ SY667 @ SV261 ) ) ) )
= $false )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2097]) ).
thf(2157,plain,
! [SV236: $i,SV193: $i,SV254: $i,SV276: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV276 @ SV254 )
| ~ ! [SY684: $i] :
~ ~ ! [SY685: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY684 @ SV193 )
| ~ ( in @ SY685 @ SV236 ) )
| ( SV276
!= ( ordered_pair @ SY684 @ SY685 ) ) ) )
| ~ ( ~ ~ ! [SY686: $i] :
~ ~ ! [SY687: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY686 @ SV193 )
| ~ ( in @ SY687 @ SV236 ) )
| ( SV276
!= ( ordered_pair @ SY686 @ SY687 ) ) )
| ( in @ SV276 @ SV254 ) ) ) )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2098]) ).
thf(2158,plain,
! [SV254: $i,SV193: $i,SV236: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 )
| ~ ! [SY688: $i] :
~ ~ ! [SY689: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY688 @ SV193 )
| ~ ( in @ SY689 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SY688 @ SY689 ) ) ) )
| ~ ( ~ ~ ! [SY690: $i] :
~ ~ ! [SY691: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY690 @ SV193 )
| ~ ( in @ SY691 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SY690 @ SY691 ) ) )
| ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 ) ) ) )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2099]) ).
thf(2159,plain,
! [SV194: $i,SV262: $i] :
( ( ( SV262
= ( relation_rng @ SV194 ) )
= $false )
| ( ( ! [SY670: $i] :
~ ( ~ ( ~ ( in @ SY670 @ SV262 )
| ~ ! [SY555: $i] :
~ ( in @ ( ordered_pair @ SY555 @ SY670 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY556: $i] :
~ ( in @ ( ordered_pair @ SY556 @ SY670 ) @ SV194 )
| ( in @ SY670 @ SV262 ) ) ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2100]) ).
thf(2160,plain,
! [SV194: $i,SV262: $i] :
( ( ( ! [SY673: $i] :
~ ( ~ ( ~ ( in @ SY673 @ SV262 )
| ~ ! [SY558: $i] :
~ ( in @ ( ordered_pair @ SY558 @ SY673 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY559: $i] :
~ ( in @ ( ordered_pair @ SY559 @ SY673 ) @ SV194 )
| ( in @ SY673 @ SV262 ) ) ) )
= $false )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2101]) ).
thf(2161,plain,
! [SV238: $i,SV196: $i] :
( ( ( ~ ( disjoint @ SV196 @ SV238 ) )
= $false )
| ( ( ~ ! [SY628: $i] :
~ ~ ( ~ ( in @ SY628 @ SV196 )
| ~ ( in @ SY628 @ SV238 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2102]) ).
thf(2162,plain,
! [SV238: $i,SV196: $i] :
( ( ( ~ ! [SY629: $i] :
~ ~ ( ~ ( in @ SY629 @ SV196 )
| ~ ( in @ SY629 @ SV238 ) ) )
= $false )
| ( ( ~ ( disjoint @ SV196 @ SV238 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2103]) ).
thf(2163,plain,
! [SV197: $i,SV255: $i,SV239: $i] :
( ( ( element @ SV239 @ ( powerset @ SV255 ) )
= $false )
| ( ( in @ SV197 @ SV239 )
= $false )
| ( ( element @ SV197 @ SV255 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2104]) ).
thf(2164,plain,
! [SV242: $i,SV256: $i,SV201: $i] :
( ( ( ~ ( in @ SV201 @ SV256 )
| ~ ( in @ SV242 @ SV256 ) )
= $false )
| ( ( subset @ ( unordered_pair @ SV201 @ SV242 ) @ SV256 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2107]) ).
thf(2165,plain,
! [SV242: $i,SV256: $i,SV201: $i] :
( ( ( ~ ( in @ SV201 @ SV256 )
| ~ ( in @ SV242 @ SV256 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV201 @ SV242 ) @ SV256 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2108]) ).
thf(2166,plain,
! [SV204: $i,SV155: $i,SV243: $i,SV272: $i] :
( ( ( ~ ( ~ ( in @ SV272 @ SV243 )
| ( in @ SV272 @ SV155 )
| ( in @ SV272 @ SV204 ) )
| ~ ( ~ ( ( in @ SV272 @ SV155 )
| ( in @ SV272 @ SV204 ) )
| ( in @ SV272 @ SV243 ) ) )
= $false )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2109]) ).
thf(2167,plain,
! [SV243: $i,SV155: $i,SV204: $i] :
( ( ( ~ ( ~ ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV243 )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV155 )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV204 ) )
| ~ ( ~ ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV155 )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV204 ) )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV243 ) ) )
= $true )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2110]) ).
thf(2168,plain,
! [SV157: $i] :
( ( ~ ( ~ ( in @ SV157 @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SY635: $i,SY636: $i] :
( ~ ~ ( ~ ( in @ SY635 @ ( sK46_SY444 @ SV157 ) )
| ~ ( subset @ SY636 @ SY635 ) )
| ( in @ SY636 @ ( sK46_SY444 @ SV157 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2111]) ).
thf(2169,plain,
! [SV157: $i] :
( ( ! [SY637: $i] :
~ ~ ( ~ ( in @ SY637 @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SY638: $i] :
~ ~ ( ~ ( in @ SY638 @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY637 )
| ( in @ SX4 @ SY638 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2112]) ).
thf(2170,plain,
! [SV157: $i,SV266: $i] :
( ( ~ ~ ( ~ ( subset @ SV266 @ ( sK46_SY444 @ SV157 ) )
| ~ ~ ( are_equipotent @ SV266 @ ( sK46_SY444 @ SV157 ) ) )
| ~ ~ ( in @ SV266 @ ( sK46_SY444 @ SV157 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2113]) ).
thf(2171,plain,
! [SV208: $i,SV245: $i,SV160: $i] :
( ( ( in @ SV160 @ ( relation_dom @ SV245 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV160 @ SV208 ) @ SV245 )
= $false )
| ( ( relation @ SV245 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2116]) ).
thf(2172,plain,
! [SV160: $i,SV245: $i,SV208: $i] :
( ( ( in @ SV208 @ ( relation_rng @ SV245 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV160 @ SV208 ) @ SV245 )
= $false )
| ( ( relation @ SV245 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2117]) ).
thf(2173,plain,
! [SV165: $i,SV212: $i] :
( ( ( ~ ( ~ ( element @ SV212 @ SV165 )
| ( in @ SV212 @ SV165 ) ) )
= $false )
| ( ( empty @ SV165 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2118]) ).
thf(2174,plain,
! [SV165: $i,SV212: $i] :
( ( ( ~ ( ~ ( in @ SV212 @ SV165 )
| ( element @ SV212 @ SV165 ) ) )
= $false )
| ( ( empty @ SV165 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2118]) ).
thf(2175,plain,
! [SV165: $i,SV212: $i] :
( ( ( ~ ( element @ SV212 @ SV165 )
| ( empty @ SV212 ) )
= $true )
| ( ( empty @ SV165 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2119]) ).
thf(2176,plain,
! [SV165: $i,SV212: $i] :
( ( ( ~ ( empty @ SV212 )
| ( element @ SV212 @ SV165 ) )
= $true )
| ( ( empty @ SV165 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2120]) ).
thf(2177,plain,
! [SV213: $i,SV166: $i,SV267: $i] :
( ( ( in @ SV267 @ SV166 )
= $false )
| ( ( in @ SV267 @ SV213 )
= $true )
| ( ( subset @ SV166 @ SV213 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2121]) ).
thf(2178,plain,
! [SV166: $i,SV213: $i] :
( ( ( in @ ( sK52_SY580 @ SV213 @ SV166 ) @ SV166 )
= $true )
| ( ( subset @ SV166 @ SV213 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2122]) ).
thf(2179,plain,
! [SV168: $i,SV215: $i] :
( ( ( ~ ( ( SV215
!= ( set_meet @ SV168 ) )
| ! [SY581: $i] :
~ ( ~ ( ~ ( in @ SY581 @ SV215 )
| ! [SY467: $i] :
( ~ ( in @ SY467 @ SV168 )
| ( in @ SY581 @ SY467 ) ) )
| ~ ( ~ ! [SY468: $i] :
( ~ ( in @ SY468 @ SV168 )
| ( in @ SY581 @ SY468 ) )
| ( in @ SY581 @ SV215 ) ) ) ) )
= $false )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2124]) ).
thf(2180,plain,
! [SV168: $i,SV215: $i] :
( ( ( ~ ( ~ ! [SY584: $i] :
~ ( ~ ( ~ ( in @ SY584 @ SV215 )
| ! [SY470: $i] :
( ~ ( in @ SY470 @ SV168 )
| ( in @ SY584 @ SY470 ) ) )
| ~ ( ~ ! [SY471: $i] :
( ~ ( in @ SY471 @ SV168 )
| ( in @ SY584 @ SY471 ) )
| ( in @ SY584 @ SV215 ) ) )
| ( SV215
= ( set_meet @ SV168 ) ) ) )
= $false )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2124]) ).
thf(2181,plain,
! [SV168: $i,SV215: $i] :
( ( ( ( SV215
!= ( set_meet @ SV168 ) )
| ( SV215 = empty_set ) )
= $true )
| ( ( SV168 = empty_set )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2125]) ).
thf(2182,plain,
! [SV168: $i,SV215: $i] :
( ( ( ( SV215 != empty_set )
| ( SV215
= ( set_meet @ SV168 ) ) )
= $true )
| ( ( SV168 = empty_set )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2126]) ).
thf(2183,plain,
! [SV169: $i,SV216: $i,SV268: $i] :
( ( ( ~ ( ~ ( in @ SV268 @ SV216 )
| ~ ! [SY680: $i] :
~ ~ ( ~ ( in @ SV268 @ SY680 )
| ~ ( in @ SY680 @ SV169 ) ) ) )
= $false )
| ( ( SV216
= ( union @ SV169 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2127]) ).
thf(2184,plain,
! [SV216: $i,SV169: $i,SV268: $i] :
( ( ( ~ ( ~ ~ ! [SY681: $i] :
~ ~ ( ~ ( in @ SV268 @ SY681 )
| ~ ( in @ SY681 @ SV169 ) )
| ( in @ SV268 @ SV216 ) ) )
= $false )
| ( ( SV216
= ( union @ SV169 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2127]) ).
thf(2185,plain,
! [SV216: $i,SV169: $i] :
( ( ( ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV216 )
| ~ ! [SY682: $i] :
~ ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SY682 )
| ~ ( in @ SY682 @ SV169 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY683: $i] :
~ ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SY683 )
| ~ ( in @ SY683 @ SV169 ) )
| ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV216 ) ) )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2128]) ).
thf(2186,plain,
! [SV217: $i,SV170: $i,SV246: $i,SV273: $i] :
( ( ( ~ ( ~ ( in @ SV273 @ SV246 )
| ( SV273 = SV170 )
| ( SV273 = SV217 ) )
| ~ ( ~ ( ( SV273 = SV170 )
| ( SV273 = SV217 ) )
| ( in @ SV273 @ SV246 ) ) )
= $false )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2129]) ).
thf(2187,plain,
! [SV246: $i,SV170: $i,SV217: $i] :
( ( ( ~ ( ~ ( in @ ( sK57_SY643 @ SV217 @ SV170 @ SV246 ) @ SV246 )
| ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV170 )
| ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV217 ) )
| ~ ( ~ ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV170 )
| ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV217 ) )
| ( in @ ( sK57_SY643 @ SV217 @ SV170 @ SV246 ) @ SV246 ) ) )
= $true )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2130]) ).
thf(2188,plain,
! [SV258: $i,SV218: $i,SV247: $i,SV171: $i] :
( ( ( ~ ( in @ SV171 @ SV247 )
| ~ ( in @ SV218 @ SV258 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV171 @ SV218 ) @ ( cartesian_product2 @ SV247 @ SV258 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2131]) ).
thf(2189,plain,
! [SV258: $i,SV218: $i,SV247: $i,SV171: $i] :
( ( ( ~ ( in @ SV171 @ SV247 )
| ~ ( in @ SV218 @ SV258 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV171 @ SV218 ) @ ( cartesian_product2 @ SV247 @ SV258 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2132]) ).
thf(2190,plain,
! [SV172: $i,SV219: $i,SV269: $i] :
( ( ( ~ ( ~ ( in @ SV269 @ SV219 )
| ( SV269 = SV172 ) ) )
= $false )
| ( ( SV219
= ( singleton @ SV172 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2133]) ).
thf(2191,plain,
! [SV219: $i,SV172: $i,SV269: $i] :
( ( ( ~ ( ( SV269 != SV172 )
| ( in @ SV269 @ SV219 ) ) )
= $false )
| ( ( SV219
= ( singleton @ SV172 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2133]) ).
thf(2192,plain,
! [SV219: $i,SV172: $i] :
( ( ( ~ ( ~ ( in @ ( sK54_SY599 @ SV172 @ SV219 ) @ SV219 )
| ( ( sK54_SY599 @ SV172 @ SV219 )
= SV172 ) ) )
= $true )
| ( ( ~ ( ( ( sK54_SY599 @ SV172 @ SV219 )
!= SV172 )
| ( in @ ( sK54_SY599 @ SV172 @ SV219 ) @ SV219 ) ) )
= $true )
| ( ( SV219
= ( singleton @ SV172 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2134]) ).
thf(2193,plain,
! [SV174: $i,SV264: $i] :
( ( ( ~ ( in @ SV264 @ SV174 ) )
= $true )
| ( ( ~ ! [SY676: $i,SY677: $i] :
( SV264
!= ( ordered_pair @ SY676 @ SY677 ) ) )
= $true )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2135]) ).
thf(2194,plain,
! [SV174: $i] :
( ( ( ~ ( in @ ( sK50_SY493 @ SV174 ) @ SV174 ) )
= $false )
| ( ( relation @ SV174 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2136]) ).
thf(2195,plain,
! [SV174: $i] :
( ( ( ~ ! [SY678: $i,SY679: $i] :
( ( sK50_SY493 @ SV174 )
!= ( ordered_pair @ SY678 @ SY679 ) ) )
= $false )
| ( ( relation @ SV174 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2136]) ).
thf(2196,plain,
! [SV177: $i] :
( ( ~ ( ~ ( in @ SV177 @ ( sK47_SY499 @ SV177 ) )
| ~ ! [SY645: $i,SY646: $i] :
( ~ ~ ( ~ ( in @ SY645 @ ( sK47_SY499 @ SV177 ) )
| ~ ( subset @ SY646 @ SY645 ) )
| ( in @ SY646 @ ( sK47_SY499 @ SV177 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2137]) ).
thf(2197,plain,
! [SV177: $i] :
( ( ! [SY647: $i] :
( ~ ( in @ SY647 @ ( sK47_SY499 @ SV177 ) )
| ( in @ ( powerset @ SY647 ) @ ( sK47_SY499 @ SV177 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2138]) ).
thf(2198,plain,
! [SV177: $i,SV270: $i] :
( ( ~ ~ ( ~ ( subset @ SV270 @ ( sK47_SY499 @ SV177 ) )
| ~ ~ ( are_equipotent @ SV270 @ ( sK47_SY499 @ SV177 ) ) )
| ~ ~ ( in @ SV270 @ ( sK47_SY499 @ SV177 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2139]) ).
thf(2199,plain,
! [SV224: $i,SV179: $i] :
( ( ( disjoint @ SV179 @ SV224 )
= $true )
| ( ( ~ ! [SY601: $i] :
~ ( in @ SY601 @ ( set_intersection2 @ SV179 @ SV224 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2140]) ).
thf(2200,plain,
! [SV224: $i,SV179: $i] :
( ( ( ! [SY602: $i] :
~ ( in @ SY602 @ ( set_intersection2 @ SV179 @ SV224 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV179 @ SV224 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2141]) ).
thf(2201,plain,
! [SV225: $i,SV180: $i,SV249: $i,SV274: $i] :
( ( ( ~ ( ~ ( in @ SV274 @ SV249 )
| ~ ( ~ ( in @ SV274 @ SV180 )
| ~ ( in @ SV274 @ SV225 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV274 @ SV180 )
| ~ ( in @ SV274 @ SV225 ) )
| ( in @ SV274 @ SV249 ) ) )
= $false )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2142]) ).
thf(2202,plain,
! [SV249: $i,SV180: $i,SV225: $i] :
( ( ( ~ ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV249 )
| ~ ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
| ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
| ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 ) )
| ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV249 ) ) )
= $true )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2143]) ).
thf(2203,plain,
! [SV229: $i,SV184: $i,SV250: $i,SV275: $i] :
( ( ( ~ ( ~ ( in @ SV275 @ SV250 )
| ~ ( ~ ( in @ SV275 @ SV184 )
| ~ ~ ( in @ SV275 @ SV229 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV275 @ SV184 )
| ~ ~ ( in @ SV275 @ SV229 ) )
| ( in @ SV275 @ SV250 ) ) )
= $false )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2144]) ).
thf(2204,plain,
! [SV250: $i,SV184: $i,SV229: $i] :
( ( ( ~ ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV250 )
| ~ ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
| ~ ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
| ~ ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 ) )
| ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV250 ) ) )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2145]) ).
thf(2205,plain,
! [SV251: $i,SV230: $i,SV185: $i] :
( ( ( in @ SV185 @ SV230 )
= $false )
| ( ( ~ ( element @ SV230 @ ( powerset @ SV251 ) ) )
= $true )
| ( ( ~ ( empty @ SV251 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2146]) ).
thf(2206,plain,
! [SV259: $i,SV187: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV187 ) @ ( relation_dom @ SV259 ) ) )
= $false )
| ( ( subset @ SV187 @ SV259 )
= $false )
| ( ( relation @ SV259 )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2147]) ).
thf(2207,plain,
! [SV259: $i,SV187: $i] :
( ( ( ~ ( subset @ ( relation_rng @ SV187 ) @ ( relation_rng @ SV259 ) ) )
= $false )
| ( ( subset @ SV187 @ SV259 )
= $false )
| ( ( relation @ SV259 )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2147]) ).
thf(2208,plain,
! [SV260: $i,SV232: $i,SV252: $i,SV188: $i] :
( ( ( ~ ( in @ SV188 @ SV252 )
| ~ ( in @ SV232 @ SV260 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV188 @ SV232 ) @ ( cartesian_product2 @ SV252 @ SV260 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2148]) ).
thf(2209,plain,
! [SV260: $i,SV232: $i,SV252: $i,SV188: $i] :
( ( ( ~ ( in @ SV188 @ SV252 )
| ~ ( in @ SV232 @ SV260 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV188 @ SV232 ) @ ( cartesian_product2 @ SV252 @ SV260 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2149]) ).
thf(2210,plain,
! [SV189: $i,SV233: $i] :
( ( ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV189 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV233 )
| ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV189 ) ) )
= $true )
| ( ( SV189 = SV233 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2150]) ).
thf(2211,plain,
! [SV189: $i,SV233: $i] :
( ( ( ~ ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV233 )
| ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV189 ) )
= $false )
| ( ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV233 )
= $false )
| ( ( SV189 = SV233 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2151]) ).
thf(2212,plain,
! [SV190: $i,SV234: $i,SV271: $i] :
( ( ( ~ ( ~ ( in @ SV271 @ SV234 )
| ( subset @ SV271 @ SV190 ) ) )
= $false )
| ( ( SV234
= ( powerset @ SV190 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2152]) ).
thf(2213,plain,
! [SV234: $i,SV190: $i,SV271: $i] :
( ( ( ~ ( ~ ( subset @ SV271 @ SV190 )
| ( in @ SV271 @ SV234 ) ) )
= $false )
| ( ( SV234
= ( powerset @ SV190 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2152]) ).
thf(2214,plain,
! [SV234: $i,SV190: $i] :
( ( ( ~ ( ~ ( in @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV234 )
| ( subset @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV190 ) ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV190 )
| ( in @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV234 ) ) )
= $true )
| ( ( SV234
= ( powerset @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2153]) ).
thf(2215,plain,
! [SV191: $i,SV253: $i,SV235: $i] :
( ( ( in @ SV235 @ SV253 )
= $false )
| ( ( in @ SV235 @ ( subset_complement @ SV191 @ SV253 ) )
= $false )
| ( ( element @ SV253 @ ( powerset @ SV191 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2154]) ).
thf(2216,plain,
! [SV192: $i,SV261: $i,SV277: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV277 @ SV261 )
| ~ ! [SY692: $i] :
~ ( in @ ( ordered_pair @ SV277 @ SY692 ) @ SV192 ) )
| ~ ( ~ ~ ! [SY693: $i] :
~ ( in @ ( ordered_pair @ SV277 @ SY693 ) @ SV192 )
| ( in @ SV277 @ SV261 ) ) ) )
= $true )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2155]) ).
thf(2217,plain,
! [SV261: $i,SV192: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK61_SY667 @ SV192 @ SV261 ) @ SV261 )
| ~ ! [SY694: $i] :
~ ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ SY694 ) @ SV192 ) )
| ~ ( ~ ~ ! [SY695: $i] :
~ ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ SY695 ) @ SV192 )
| ( in @ ( sK61_SY667 @ SV192 @ SV261 ) @ SV261 ) ) ) )
= $false )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2156]) ).
thf(2218,plain,
! [SV236: $i,SV193: $i,SV254: $i,SV276: $i] :
( ( ( ~ ( ~ ( in @ SV276 @ SV254 )
| ~ ! [SY684: $i] :
~ ~ ! [SY685: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY684 @ SV193 )
| ~ ( in @ SY685 @ SV236 ) )
| ( SV276
!= ( ordered_pair @ SY684 @ SY685 ) ) ) )
| ~ ( ~ ~ ! [SY686: $i] :
~ ~ ! [SY687: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY686 @ SV193 )
| ~ ( in @ SY687 @ SV236 ) )
| ( SV276
!= ( ordered_pair @ SY686 @ SY687 ) ) )
| ( in @ SV276 @ SV254 ) ) )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2157]) ).
thf(2219,plain,
! [SV254: $i,SV193: $i,SV236: $i] :
( ( ( ~ ( ~ ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 )
| ~ ! [SY688: $i] :
~ ~ ! [SY689: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY688 @ SV193 )
| ~ ( in @ SY689 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SY688 @ SY689 ) ) ) )
| ~ ( ~ ~ ! [SY690: $i] :
~ ~ ! [SY691: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY690 @ SV193 )
| ~ ( in @ SY691 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SY690 @ SY691 ) ) )
| ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 ) ) )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2158]) ).
thf(2220,plain,
! [SV194: $i,SV262: $i,SV278: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV278 @ SV262 )
| ~ ! [SY696: $i] :
~ ( in @ ( ordered_pair @ SY696 @ SV278 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY697: $i] :
~ ( in @ ( ordered_pair @ SY697 @ SV278 ) @ SV194 )
| ( in @ SV278 @ SV262 ) ) ) )
= $true )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2159]) ).
thf(2221,plain,
! [SV262: $i,SV194: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK62_SY673 @ SV194 @ SV262 ) @ SV262 )
| ~ ! [SY698: $i] :
~ ( in @ ( ordered_pair @ SY698 @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 ) )
| ~ ( ~ ~ ! [SY699: $i] :
~ ( in @ ( ordered_pair @ SY699 @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 )
| ( in @ ( sK62_SY673 @ SV194 @ SV262 ) @ SV262 ) ) ) )
= $false )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2160]) ).
thf(2222,plain,
! [SV238: $i,SV196: $i] :
( ( ( disjoint @ SV196 @ SV238 )
= $true )
| ( ( ~ ! [SY628: $i] :
~ ~ ( ~ ( in @ SY628 @ SV196 )
| ~ ( in @ SY628 @ SV238 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2161]) ).
thf(2223,plain,
! [SV238: $i,SV196: $i] :
( ( ( ! [SY629: $i] :
~ ~ ( ~ ( in @ SY629 @ SV196 )
| ~ ( in @ SY629 @ SV238 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV196 @ SV238 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2162]) ).
thf(2224,plain,
! [SV242: $i,SV256: $i,SV201: $i] :
( ( ( ~ ( in @ SV201 @ SV256 ) )
= $false )
| ( ( subset @ ( unordered_pair @ SV201 @ SV242 ) @ SV256 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2164]) ).
thf(2225,plain,
! [SV201: $i,SV256: $i,SV242: $i] :
( ( ( ~ ( in @ SV242 @ SV256 ) )
= $false )
| ( ( subset @ ( unordered_pair @ SV201 @ SV242 ) @ SV256 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2164]) ).
thf(2226,plain,
! [SV242: $i,SV256: $i,SV201: $i] :
( ( ( ~ ( in @ SV201 @ SV256 ) )
= $true )
| ( ( ~ ( in @ SV242 @ SV256 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV201 @ SV242 ) @ SV256 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2165]) ).
thf(2227,plain,
! [SV204: $i,SV155: $i,SV243: $i,SV272: $i] :
( ( ( ~ ( ~ ( in @ SV272 @ SV243 )
| ( in @ SV272 @ SV155 )
| ( in @ SV272 @ SV204 ) ) )
= $false )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2166]) ).
thf(2228,plain,
! [SV243: $i,SV204: $i,SV155: $i,SV272: $i] :
( ( ( ~ ( ~ ( ( in @ SV272 @ SV155 )
| ( in @ SV272 @ SV204 ) )
| ( in @ SV272 @ SV243 ) ) )
= $false )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2166]) ).
thf(2229,plain,
! [SV243: $i,SV155: $i,SV204: $i] :
( ( ( ~ ( ~ ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV243 )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV155 )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV204 ) ) )
= $true )
| ( ( ~ ( ~ ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV155 )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV204 ) )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV243 ) ) )
= $true )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2167]) ).
thf(2230,plain,
! [SV157: $i] :
( ( ~ ( in @ SV157 @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SY635: $i,SY636: $i] :
( ~ ~ ( ~ ( in @ SY635 @ ( sK46_SY444 @ SV157 ) )
| ~ ( subset @ SY636 @ SY635 ) )
| ( in @ SY636 @ ( sK46_SY444 @ SV157 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2168]) ).
thf(2231,plain,
! [SV157: $i,SV279: $i] :
( ( ~ ~ ( ~ ( in @ SV279 @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SY700: $i] :
~ ~ ( ~ ( in @ SY700 @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SY701: $i] :
( ~ ( subset @ SY701 @ SV279 )
| ( in @ SY701 @ SY700 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2169]) ).
thf(2232,plain,
! [SV157: $i,SV266: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV266 @ ( sK46_SY444 @ SV157 ) )
| ~ ~ ( are_equipotent @ SV266 @ ( sK46_SY444 @ SV157 ) ) ) )
= $true )
| ( ( ~ ~ ( in @ SV266 @ ( sK46_SY444 @ SV157 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2170]) ).
thf(2233,plain,
! [SV165: $i,SV212: $i] :
( ( ( ~ ( element @ SV212 @ SV165 )
| ( in @ SV212 @ SV165 ) )
= $true )
| ( ( empty @ SV165 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2173]) ).
thf(2234,plain,
! [SV165: $i,SV212: $i] :
( ( ( ~ ( in @ SV212 @ SV165 )
| ( element @ SV212 @ SV165 ) )
= $true )
| ( ( empty @ SV165 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2174]) ).
thf(2235,plain,
! [SV165: $i,SV212: $i] :
( ( ( ~ ( element @ SV212 @ SV165 ) )
= $true )
| ( ( empty @ SV212 )
= $true )
| ( ( empty @ SV165 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2175]) ).
thf(2236,plain,
! [SV165: $i,SV212: $i] :
( ( ( ~ ( empty @ SV212 ) )
= $true )
| ( ( element @ SV212 @ SV165 )
= $true )
| ( ( empty @ SV165 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2176]) ).
thf(2237,plain,
! [SV168: $i,SV215: $i] :
( ( ( ( SV215
!= ( set_meet @ SV168 ) )
| ! [SY581: $i] :
~ ( ~ ( ~ ( in @ SY581 @ SV215 )
| ! [SY467: $i] :
( ~ ( in @ SY467 @ SV168 )
| ( in @ SY581 @ SY467 ) ) )
| ~ ( ~ ! [SY468: $i] :
( ~ ( in @ SY468 @ SV168 )
| ( in @ SY581 @ SY468 ) )
| ( in @ SY581 @ SV215 ) ) ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2179]) ).
thf(2238,plain,
! [SV168: $i,SV215: $i] :
( ( ( ~ ! [SY584: $i] :
~ ( ~ ( ~ ( in @ SY584 @ SV215 )
| ! [SY470: $i] :
( ~ ( in @ SY470 @ SV168 )
| ( in @ SY584 @ SY470 ) ) )
| ~ ( ~ ! [SY471: $i] :
( ~ ( in @ SY471 @ SV168 )
| ( in @ SY584 @ SY471 ) )
| ( in @ SY584 @ SV215 ) ) )
| ( SV215
= ( set_meet @ SV168 ) ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2180]) ).
thf(2239,plain,
! [SV168: $i,SV215: $i] :
( ( ( SV215
!= ( set_meet @ SV168 ) )
= $true )
| ( ( SV215 = empty_set )
= $true )
| ( ( SV168 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2181]) ).
thf(2240,plain,
! [SV168: $i,SV215: $i] :
( ( ( SV215 != empty_set )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $true )
| ( ( SV168 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2182]) ).
thf(2241,plain,
! [SV169: $i,SV216: $i,SV268: $i] :
( ( ( ~ ( in @ SV268 @ SV216 )
| ~ ! [SY680: $i] :
~ ~ ( ~ ( in @ SV268 @ SY680 )
| ~ ( in @ SY680 @ SV169 ) ) )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2183]) ).
thf(2242,plain,
! [SV216: $i,SV169: $i,SV268: $i] :
( ( ( ~ ~ ! [SY681: $i] :
~ ~ ( ~ ( in @ SV268 @ SY681 )
| ~ ( in @ SY681 @ SV169 ) )
| ( in @ SV268 @ SV216 ) )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2184]) ).
thf(2243,plain,
! [SV216: $i,SV169: $i] :
( ( ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV216 )
| ~ ! [SY682: $i] :
~ ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SY682 )
| ~ ( in @ SY682 @ SV169 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY683: $i] :
~ ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SY683 )
| ~ ( in @ SY683 @ SV169 ) )
| ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV216 ) ) )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2185]) ).
thf(2244,plain,
! [SV217: $i,SV170: $i,SV246: $i,SV273: $i] :
( ( ( ~ ( ~ ( in @ SV273 @ SV246 )
| ( SV273 = SV170 )
| ( SV273 = SV217 ) ) )
= $false )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2186]) ).
thf(2245,plain,
! [SV246: $i,SV217: $i,SV170: $i,SV273: $i] :
( ( ( ~ ( ~ ( ( SV273 = SV170 )
| ( SV273 = SV217 ) )
| ( in @ SV273 @ SV246 ) ) )
= $false )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2186]) ).
thf(2246,plain,
! [SV246: $i,SV170: $i,SV217: $i] :
( ( ( ~ ( ~ ( in @ ( sK57_SY643 @ SV217 @ SV170 @ SV246 ) @ SV246 )
| ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV170 )
| ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV217 ) ) )
= $true )
| ( ( ~ ( ~ ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV170 )
| ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV217 ) )
| ( in @ ( sK57_SY643 @ SV217 @ SV170 @ SV246 ) @ SV246 ) ) )
= $true )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2187]) ).
thf(2247,plain,
! [SV258: $i,SV218: $i,SV247: $i,SV171: $i] :
( ( ( ~ ( in @ SV171 @ SV247 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV171 @ SV218 ) @ ( cartesian_product2 @ SV247 @ SV258 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2188]) ).
thf(2248,plain,
! [SV247: $i,SV171: $i,SV258: $i,SV218: $i] :
( ( ( ~ ( in @ SV218 @ SV258 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV171 @ SV218 ) @ ( cartesian_product2 @ SV247 @ SV258 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2188]) ).
thf(2249,plain,
! [SV258: $i,SV218: $i,SV247: $i,SV171: $i] :
( ( ( ~ ( in @ SV171 @ SV247 ) )
= $true )
| ( ( ~ ( in @ SV218 @ SV258 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV171 @ SV218 ) @ ( cartesian_product2 @ SV247 @ SV258 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2189]) ).
thf(2250,plain,
! [SV172: $i,SV219: $i,SV269: $i] :
( ( ( ~ ( in @ SV269 @ SV219 )
| ( SV269 = SV172 ) )
= $true )
| ( ( SV219
= ( singleton @ SV172 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2190]) ).
thf(2251,plain,
! [SV219: $i,SV172: $i,SV269: $i] :
( ( ( ( SV269 != SV172 )
| ( in @ SV269 @ SV219 ) )
= $true )
| ( ( SV219
= ( singleton @ SV172 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2191]) ).
thf(2252,plain,
! [SV219: $i,SV172: $i] :
( ( ( ~ ( in @ ( sK54_SY599 @ SV172 @ SV219 ) @ SV219 )
| ( ( sK54_SY599 @ SV172 @ SV219 )
= SV172 ) )
= $false )
| ( ( ~ ( ( ( sK54_SY599 @ SV172 @ SV219 )
!= SV172 )
| ( in @ ( sK54_SY599 @ SV172 @ SV219 ) @ SV219 ) ) )
= $true )
| ( ( SV219
= ( singleton @ SV172 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2192]) ).
thf(2253,plain,
! [SV174: $i,SV264: $i] :
( ( ( in @ SV264 @ SV174 )
= $false )
| ( ( ~ ! [SY676: $i,SY677: $i] :
( SV264
!= ( ordered_pair @ SY676 @ SY677 ) ) )
= $true )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2193]) ).
thf(2254,plain,
! [SV174: $i] :
( ( ( in @ ( sK50_SY493 @ SV174 ) @ SV174 )
= $true )
| ( ( relation @ SV174 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2194]) ).
thf(2255,plain,
! [SV174: $i] :
( ( ( ! [SY678: $i,SY679: $i] :
( ( sK50_SY493 @ SV174 )
!= ( ordered_pair @ SY678 @ SY679 ) ) )
= $true )
| ( ( relation @ SV174 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2195]) ).
thf(2256,plain,
! [SV177: $i] :
( ( ~ ( in @ SV177 @ ( sK47_SY499 @ SV177 ) )
| ~ ! [SY645: $i,SY646: $i] :
( ~ ~ ( ~ ( in @ SY645 @ ( sK47_SY499 @ SV177 ) )
| ~ ( subset @ SY646 @ SY645 ) )
| ( in @ SY646 @ ( sK47_SY499 @ SV177 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2196]) ).
thf(2257,plain,
! [SV177: $i,SV280: $i] :
( ( ~ ( in @ SV280 @ ( sK47_SY499 @ SV177 ) )
| ( in @ ( powerset @ SV280 ) @ ( sK47_SY499 @ SV177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2197]) ).
thf(2258,plain,
! [SV177: $i,SV270: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV270 @ ( sK47_SY499 @ SV177 ) )
| ~ ~ ( are_equipotent @ SV270 @ ( sK47_SY499 @ SV177 ) ) ) )
= $true )
| ( ( ~ ~ ( in @ SV270 @ ( sK47_SY499 @ SV177 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2198]) ).
thf(2259,plain,
! [SV224: $i,SV179: $i] :
( ( ( ! [SY601: $i] :
~ ( in @ SY601 @ ( set_intersection2 @ SV179 @ SV224 ) ) )
= $false )
| ( ( disjoint @ SV179 @ SV224 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2199]) ).
thf(2260,plain,
! [SV224: $i,SV179: $i,SV281: $i] :
( ( ( ~ ( in @ SV281 @ ( set_intersection2 @ SV179 @ SV224 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV179 @ SV224 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2200]) ).
thf(2261,plain,
! [SV225: $i,SV180: $i,SV249: $i,SV274: $i] :
( ( ( ~ ( ~ ( in @ SV274 @ SV249 )
| ~ ( ~ ( in @ SV274 @ SV180 )
| ~ ( in @ SV274 @ SV225 ) ) ) )
= $false )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2201]) ).
thf(2262,plain,
! [SV249: $i,SV225: $i,SV180: $i,SV274: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV274 @ SV180 )
| ~ ( in @ SV274 @ SV225 ) )
| ( in @ SV274 @ SV249 ) ) )
= $false )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2201]) ).
thf(2263,plain,
! [SV249: $i,SV180: $i,SV225: $i] :
( ( ( ~ ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV249 )
| ~ ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
| ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
| ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 ) )
| ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV249 ) ) )
= $true )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2202]) ).
thf(2264,plain,
! [SV229: $i,SV184: $i,SV250: $i,SV275: $i] :
( ( ( ~ ( ~ ( in @ SV275 @ SV250 )
| ~ ( ~ ( in @ SV275 @ SV184 )
| ~ ~ ( in @ SV275 @ SV229 ) ) ) )
= $false )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2203]) ).
thf(2265,plain,
! [SV250: $i,SV229: $i,SV184: $i,SV275: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV275 @ SV184 )
| ~ ~ ( in @ SV275 @ SV229 ) )
| ( in @ SV275 @ SV250 ) ) )
= $false )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2203]) ).
thf(2266,plain,
! [SV250: $i,SV184: $i,SV229: $i] :
( ( ( ~ ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV250 )
| ~ ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
| ~ ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
| ~ ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 ) )
| ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV250 ) ) )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2204]) ).
thf(2267,plain,
! [SV185: $i,SV251: $i,SV230: $i] :
( ( ( element @ SV230 @ ( powerset @ SV251 ) )
= $false )
| ( ( in @ SV185 @ SV230 )
= $false )
| ( ( ~ ( empty @ SV251 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2205]) ).
thf(2268,plain,
! [SV259: $i,SV187: $i] :
( ( ( subset @ ( relation_dom @ SV187 ) @ ( relation_dom @ SV259 ) )
= $true )
| ( ( subset @ SV187 @ SV259 )
= $false )
| ( ( relation @ SV259 )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2206]) ).
thf(2269,plain,
! [SV259: $i,SV187: $i] :
( ( ( subset @ ( relation_rng @ SV187 ) @ ( relation_rng @ SV259 ) )
= $true )
| ( ( subset @ SV187 @ SV259 )
= $false )
| ( ( relation @ SV259 )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2207]) ).
thf(2270,plain,
! [SV260: $i,SV232: $i,SV252: $i,SV188: $i] :
( ( ( ~ ( in @ SV188 @ SV252 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV188 @ SV232 ) @ ( cartesian_product2 @ SV252 @ SV260 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2208]) ).
thf(2271,plain,
! [SV252: $i,SV188: $i,SV260: $i,SV232: $i] :
( ( ( ~ ( in @ SV232 @ SV260 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV188 @ SV232 ) @ ( cartesian_product2 @ SV252 @ SV260 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2208]) ).
thf(2272,plain,
! [SV260: $i,SV232: $i,SV252: $i,SV188: $i] :
( ( ( ~ ( in @ SV188 @ SV252 ) )
= $true )
| ( ( ~ ( in @ SV232 @ SV260 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV188 @ SV232 ) @ ( cartesian_product2 @ SV252 @ SV260 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2209]) ).
thf(2273,plain,
! [SV189: $i,SV233: $i] :
( ( ( ~ ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV233 )
| ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV189 ) )
= $false )
| ( ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV189 )
= $true )
| ( ( SV189 = SV233 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2210]) ).
thf(2274,plain,
! [SV189: $i,SV233: $i] :
( ( ( ~ ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV233 ) )
= $false )
| ( ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV233 )
= $false )
| ( ( SV189 = SV233 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2211]) ).
thf(2275,plain,
! [SV189: $i,SV233: $i] :
( ( ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV189 )
= $false )
| ( ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV233 )
= $false )
| ( ( SV189 = SV233 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2211]) ).
thf(2276,plain,
! [SV190: $i,SV234: $i,SV271: $i] :
( ( ( ~ ( in @ SV271 @ SV234 )
| ( subset @ SV271 @ SV190 ) )
= $true )
| ( ( SV234
= ( powerset @ SV190 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2212]) ).
thf(2277,plain,
! [SV234: $i,SV190: $i,SV271: $i] :
( ( ( ~ ( subset @ SV271 @ SV190 )
| ( in @ SV271 @ SV234 ) )
= $true )
| ( ( SV234
= ( powerset @ SV190 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2213]) ).
thf(2278,plain,
! [SV234: $i,SV190: $i] :
( ( ( ~ ( in @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV234 )
| ( subset @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV190 ) )
= $false )
| ( ( ~ ( ~ ( subset @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV190 )
| ( in @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV234 ) ) )
= $true )
| ( ( SV234
= ( powerset @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2214]) ).
thf(2279,plain,
! [SV192: $i,SV261: $i,SV277: $i] :
( ( ( ~ ( ~ ( in @ SV277 @ SV261 )
| ~ ! [SY692: $i] :
~ ( in @ ( ordered_pair @ SV277 @ SY692 ) @ SV192 ) )
| ~ ( ~ ~ ! [SY693: $i] :
~ ( in @ ( ordered_pair @ SV277 @ SY693 ) @ SV192 )
| ( in @ SV277 @ SV261 ) ) )
= $false )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2216]) ).
thf(2280,plain,
! [SV261: $i,SV192: $i] :
( ( ( ~ ( ~ ( in @ ( sK61_SY667 @ SV192 @ SV261 ) @ SV261 )
| ~ ! [SY694: $i] :
~ ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ SY694 ) @ SV192 ) )
| ~ ( ~ ~ ! [SY695: $i] :
~ ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ SY695 ) @ SV192 )
| ( in @ ( sK61_SY667 @ SV192 @ SV261 ) @ SV261 ) ) )
= $true )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2217]) ).
thf(2281,plain,
! [SV236: $i,SV193: $i,SV254: $i,SV276: $i] :
( ( ( ~ ( ~ ( in @ SV276 @ SV254 )
| ~ ! [SY684: $i] :
~ ~ ! [SY685: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY684 @ SV193 )
| ~ ( in @ SY685 @ SV236 ) )
| ( SV276
!= ( ordered_pair @ SY684 @ SY685 ) ) ) ) )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2218]) ).
thf(2282,plain,
! [SV254: $i,SV276: $i,SV236: $i,SV193: $i] :
( ( ( ~ ( ~ ~ ! [SY686: $i] :
~ ~ ! [SY687: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY686 @ SV193 )
| ~ ( in @ SY687 @ SV236 ) )
| ( SV276
!= ( ordered_pair @ SY686 @ SY687 ) ) )
| ( in @ SV276 @ SV254 ) ) )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2218]) ).
thf(2283,plain,
! [SV254: $i,SV193: $i,SV236: $i] :
( ( ( ~ ( ~ ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 )
| ~ ! [SY688: $i] :
~ ~ ! [SY689: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY688 @ SV193 )
| ~ ( in @ SY689 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SY688 @ SY689 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY690: $i] :
~ ~ ! [SY691: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY690 @ SV193 )
| ~ ( in @ SY691 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SY690 @ SY691 ) ) )
| ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 ) ) )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2219]) ).
thf(2284,plain,
! [SV194: $i,SV262: $i,SV278: $i] :
( ( ( ~ ( ~ ( in @ SV278 @ SV262 )
| ~ ! [SY696: $i] :
~ ( in @ ( ordered_pair @ SY696 @ SV278 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY697: $i] :
~ ( in @ ( ordered_pair @ SY697 @ SV278 ) @ SV194 )
| ( in @ SV278 @ SV262 ) ) )
= $false )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2220]) ).
thf(2285,plain,
! [SV262: $i,SV194: $i] :
( ( ( ~ ( ~ ( in @ ( sK62_SY673 @ SV194 @ SV262 ) @ SV262 )
| ~ ! [SY698: $i] :
~ ( in @ ( ordered_pair @ SY698 @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 ) )
| ~ ( ~ ~ ! [SY699: $i] :
~ ( in @ ( ordered_pair @ SY699 @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 )
| ( in @ ( sK62_SY673 @ SV194 @ SV262 ) @ SV262 ) ) )
= $true )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2221]) ).
thf(2286,plain,
! [SV238: $i,SV196: $i] :
( ( ( ! [SY628: $i] :
~ ~ ( ~ ( in @ SY628 @ SV196 )
| ~ ( in @ SY628 @ SV238 ) ) )
= $false )
| ( ( disjoint @ SV196 @ SV238 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2222]) ).
thf(2287,plain,
! [SV238: $i,SV196: $i,SV282: $i] :
( ( ( ~ ~ ( ~ ( in @ SV282 @ SV196 )
| ~ ( in @ SV282 @ SV238 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV196 @ SV238 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2223]) ).
thf(2288,plain,
! [SV242: $i,SV256: $i,SV201: $i] :
( ( ( in @ SV201 @ SV256 )
= $true )
| ( ( subset @ ( unordered_pair @ SV201 @ SV242 ) @ SV256 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2224]) ).
thf(2289,plain,
! [SV201: $i,SV256: $i,SV242: $i] :
( ( ( in @ SV242 @ SV256 )
= $true )
| ( ( subset @ ( unordered_pair @ SV201 @ SV242 ) @ SV256 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2225]) ).
thf(2290,plain,
! [SV242: $i,SV256: $i,SV201: $i] :
( ( ( in @ SV201 @ SV256 )
= $false )
| ( ( ~ ( in @ SV242 @ SV256 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV201 @ SV242 ) @ SV256 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2226]) ).
thf(2291,plain,
! [SV204: $i,SV155: $i,SV243: $i,SV272: $i] :
( ( ( ~ ( in @ SV272 @ SV243 )
| ( in @ SV272 @ SV155 )
| ( in @ SV272 @ SV204 ) )
= $true )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2227]) ).
thf(2292,plain,
! [SV243: $i,SV204: $i,SV155: $i,SV272: $i] :
( ( ( ~ ( ( in @ SV272 @ SV155 )
| ( in @ SV272 @ SV204 ) )
| ( in @ SV272 @ SV243 ) )
= $true )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2228]) ).
thf(2293,plain,
! [SV243: $i,SV155: $i,SV204: $i] :
( ( ( ~ ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV243 )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV155 )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV204 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV155 )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV204 ) )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV243 ) ) )
= $true )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2229]) ).
thf(2294,plain,
! [SV157: $i] :
( ( ~ ( in @ SV157 @ ( sK46_SY444 @ SV157 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2230]) ).
thf(2295,plain,
! [SV157: $i] :
( ( ~ ! [SY635: $i,SY636: $i] :
( ~ ~ ( ~ ( in @ SY635 @ ( sK46_SY444 @ SV157 ) )
| ~ ( subset @ SY636 @ SY635 ) )
| ( in @ SY636 @ ( sK46_SY444 @ SV157 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2230]) ).
thf(2296,plain,
! [SV157: $i,SV279: $i] :
( ( ~ ( ~ ( in @ SV279 @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SY700: $i] :
~ ~ ( ~ ( in @ SY700 @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SY701: $i] :
( ~ ( subset @ SY701 @ SV279 )
| ( in @ SY701 @ SY700 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2231]) ).
thf(2297,plain,
! [SV157: $i,SV266: $i] :
( ( ( ~ ( ~ ( subset @ SV266 @ ( sK46_SY444 @ SV157 ) )
| ~ ~ ( are_equipotent @ SV266 @ ( sK46_SY444 @ SV157 ) ) ) )
= $false )
| ( ( ~ ~ ( in @ SV266 @ ( sK46_SY444 @ SV157 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2232]) ).
thf(2298,plain,
! [SV165: $i,SV212: $i] :
( ( ( ~ ( element @ SV212 @ SV165 ) )
= $true )
| ( ( in @ SV212 @ SV165 )
= $true )
| ( ( empty @ SV165 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2233]) ).
thf(2299,plain,
! [SV165: $i,SV212: $i] :
( ( ( ~ ( in @ SV212 @ SV165 ) )
= $true )
| ( ( element @ SV212 @ SV165 )
= $true )
| ( ( empty @ SV165 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2234]) ).
thf(2300,plain,
! [SV165: $i,SV212: $i] :
( ( ( element @ SV212 @ SV165 )
= $false )
| ( ( empty @ SV212 )
= $true )
| ( ( empty @ SV165 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2235]) ).
thf(2301,plain,
! [SV165: $i,SV212: $i] :
( ( ( empty @ SV212 )
= $false )
| ( ( element @ SV212 @ SV165 )
= $true )
| ( ( empty @ SV165 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2236]) ).
thf(2302,plain,
! [SV168: $i,SV215: $i] :
( ( ( SV215
!= ( set_meet @ SV168 ) )
= $true )
| ( ( ! [SY581: $i] :
~ ( ~ ( ~ ( in @ SY581 @ SV215 )
| ! [SY467: $i] :
( ~ ( in @ SY467 @ SV168 )
| ( in @ SY581 @ SY467 ) ) )
| ~ ( ~ ! [SY468: $i] :
( ~ ( in @ SY468 @ SV168 )
| ( in @ SY581 @ SY468 ) )
| ( in @ SY581 @ SV215 ) ) ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2237]) ).
thf(2303,plain,
! [SV168: $i,SV215: $i] :
( ( ( ~ ! [SY584: $i] :
~ ( ~ ( ~ ( in @ SY584 @ SV215 )
| ! [SY470: $i] :
( ~ ( in @ SY470 @ SV168 )
| ( in @ SY584 @ SY470 ) ) )
| ~ ( ~ ! [SY471: $i] :
( ~ ( in @ SY471 @ SV168 )
| ( in @ SY584 @ SY471 ) )
| ( in @ SY584 @ SV215 ) ) ) )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2238]) ).
thf(2304,plain,
! [SV168: $i,SV215: $i] :
( ( ( SV215
= ( set_meet @ SV168 ) )
= $false )
| ( ( SV215 = empty_set )
= $true )
| ( ( SV168 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2239]) ).
thf(2305,plain,
! [SV168: $i,SV215: $i] :
( ( ( SV215 = empty_set )
= $false )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $true )
| ( ( SV168 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2240]) ).
thf(2306,plain,
! [SV169: $i,SV216: $i,SV268: $i] :
( ( ( ~ ( in @ SV268 @ SV216 ) )
= $true )
| ( ( ~ ! [SY680: $i] :
~ ~ ( ~ ( in @ SV268 @ SY680 )
| ~ ( in @ SY680 @ SV169 ) ) )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2241]) ).
thf(2307,plain,
! [SV216: $i,SV169: $i,SV268: $i] :
( ( ( ~ ~ ! [SY681: $i] :
~ ~ ( ~ ( in @ SV268 @ SY681 )
| ~ ( in @ SY681 @ SV169 ) ) )
= $true )
| ( ( in @ SV268 @ SV216 )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2242]) ).
thf(2308,plain,
! [SV216: $i,SV169: $i] :
( ( ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV216 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY683: $i] :
~ ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SY683 )
| ~ ( in @ SY683 @ SV169 ) )
| ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV216 ) ) )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2243]) ).
thf(2309,plain,
! [SV216: $i,SV169: $i] :
( ( ( ~ ! [SY682: $i] :
~ ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SY682 )
| ~ ( in @ SY682 @ SV169 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY683: $i] :
~ ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SY683 )
| ~ ( in @ SY683 @ SV169 ) )
| ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV216 ) ) )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2243]) ).
thf(2310,plain,
! [SV217: $i,SV170: $i,SV246: $i,SV273: $i] :
( ( ( ~ ( in @ SV273 @ SV246 )
| ( SV273 = SV170 )
| ( SV273 = SV217 ) )
= $true )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2244]) ).
thf(2311,plain,
! [SV246: $i,SV217: $i,SV170: $i,SV273: $i] :
( ( ( ~ ( ( SV273 = SV170 )
| ( SV273 = SV217 ) )
| ( in @ SV273 @ SV246 ) )
= $true )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2245]) ).
thf(2312,plain,
! [SV246: $i,SV170: $i,SV217: $i] :
( ( ( ~ ( in @ ( sK57_SY643 @ SV217 @ SV170 @ SV246 ) @ SV246 )
| ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV170 )
| ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV217 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV170 )
| ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV217 ) )
| ( in @ ( sK57_SY643 @ SV217 @ SV170 @ SV246 ) @ SV246 ) ) )
= $true )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2246]) ).
thf(2313,plain,
! [SV258: $i,SV218: $i,SV247: $i,SV171: $i] :
( ( ( in @ SV171 @ SV247 )
= $true )
| ( ( in @ ( ordered_pair @ SV171 @ SV218 ) @ ( cartesian_product2 @ SV247 @ SV258 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2247]) ).
thf(2314,plain,
! [SV247: $i,SV171: $i,SV258: $i,SV218: $i] :
( ( ( in @ SV218 @ SV258 )
= $true )
| ( ( in @ ( ordered_pair @ SV171 @ SV218 ) @ ( cartesian_product2 @ SV247 @ SV258 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2248]) ).
thf(2315,plain,
! [SV258: $i,SV218: $i,SV247: $i,SV171: $i] :
( ( ( in @ SV171 @ SV247 )
= $false )
| ( ( ~ ( in @ SV218 @ SV258 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV171 @ SV218 ) @ ( cartesian_product2 @ SV247 @ SV258 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2249]) ).
thf(2316,plain,
! [SV172: $i,SV219: $i,SV269: $i] :
( ( ( ~ ( in @ SV269 @ SV219 ) )
= $true )
| ( ( SV269 = SV172 )
= $true )
| ( ( SV219
= ( singleton @ SV172 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2250]) ).
thf(2317,plain,
! [SV219: $i,SV172: $i,SV269: $i] :
( ( ( SV269 != SV172 )
= $true )
| ( ( in @ SV269 @ SV219 )
= $true )
| ( ( SV219
= ( singleton @ SV172 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2251]) ).
thf(2318,plain,
! [SV219: $i,SV172: $i] :
( ( ( ~ ( in @ ( sK54_SY599 @ SV172 @ SV219 ) @ SV219 ) )
= $false )
| ( ( ~ ( ( ( sK54_SY599 @ SV172 @ SV219 )
!= SV172 )
| ( in @ ( sK54_SY599 @ SV172 @ SV219 ) @ SV219 ) ) )
= $true )
| ( ( SV219
= ( singleton @ SV172 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2252]) ).
thf(2319,plain,
! [SV219: $i,SV172: $i] :
( ( ( ( sK54_SY599 @ SV172 @ SV219 )
= SV172 )
= $false )
| ( ( ~ ( ( ( sK54_SY599 @ SV172 @ SV219 )
!= SV172 )
| ( in @ ( sK54_SY599 @ SV172 @ SV219 ) @ SV219 ) ) )
= $true )
| ( ( SV219
= ( singleton @ SV172 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2252]) ).
thf(2320,plain,
! [SV174: $i,SV264: $i] :
( ( ( ! [SY676: $i,SY677: $i] :
( SV264
!= ( ordered_pair @ SY676 @ SY677 ) ) )
= $false )
| ( ( in @ SV264 @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2253]) ).
thf(2321,plain,
! [SV283: $i,SV174: $i] :
( ( ( ! [SY702: $i] :
( ( sK50_SY493 @ SV174 )
!= ( ordered_pair @ SV283 @ SY702 ) ) )
= $true )
| ( ( relation @ SV174 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2255]) ).
thf(2322,plain,
! [SV177: $i] :
( ( ~ ( in @ SV177 @ ( sK47_SY499 @ SV177 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2256]) ).
thf(2323,plain,
! [SV177: $i] :
( ( ~ ! [SY645: $i,SY646: $i] :
( ~ ~ ( ~ ( in @ SY645 @ ( sK47_SY499 @ SV177 ) )
| ~ ( subset @ SY646 @ SY645 ) )
| ( in @ SY646 @ ( sK47_SY499 @ SV177 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2256]) ).
thf(2324,plain,
! [SV177: $i,SV280: $i] :
( ( ( ~ ( in @ SV280 @ ( sK47_SY499 @ SV177 ) ) )
= $true )
| ( ( in @ ( powerset @ SV280 ) @ ( sK47_SY499 @ SV177 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2257]) ).
thf(2325,plain,
! [SV177: $i,SV270: $i] :
( ( ( ~ ( ~ ( subset @ SV270 @ ( sK47_SY499 @ SV177 ) )
| ~ ~ ( are_equipotent @ SV270 @ ( sK47_SY499 @ SV177 ) ) ) )
= $false )
| ( ( ~ ~ ( in @ SV270 @ ( sK47_SY499 @ SV177 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2258]) ).
thf(2326,plain,
! [SV179: $i,SV224: $i] :
( ( ( ~ ( in @ ( sK63_SY601 @ SV224 @ SV179 ) @ ( set_intersection2 @ SV179 @ SV224 ) ) )
= $false )
| ( ( disjoint @ SV179 @ SV224 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2259]) ).
thf(2327,plain,
! [SV224: $i,SV179: $i,SV281: $i] :
( ( ( in @ SV281 @ ( set_intersection2 @ SV179 @ SV224 ) )
= $false )
| ( ( ~ ( disjoint @ SV179 @ SV224 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2260]) ).
thf(2328,plain,
! [SV225: $i,SV180: $i,SV249: $i,SV274: $i] :
( ( ( ~ ( in @ SV274 @ SV249 )
| ~ ( ~ ( in @ SV274 @ SV180 )
| ~ ( in @ SV274 @ SV225 ) ) )
= $true )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2261]) ).
thf(2329,plain,
! [SV249: $i,SV225: $i,SV180: $i,SV274: $i] :
( ( ( ~ ~ ( ~ ( in @ SV274 @ SV180 )
| ~ ( in @ SV274 @ SV225 ) )
| ( in @ SV274 @ SV249 ) )
= $true )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2262]) ).
thf(2330,plain,
! [SV249: $i,SV180: $i,SV225: $i] :
( ( ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV249 )
| ~ ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
| ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
| ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 ) )
| ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV249 ) ) )
= $true )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2263]) ).
thf(2331,plain,
! [SV229: $i,SV184: $i,SV250: $i,SV275: $i] :
( ( ( ~ ( in @ SV275 @ SV250 )
| ~ ( ~ ( in @ SV275 @ SV184 )
| ~ ~ ( in @ SV275 @ SV229 ) ) )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2264]) ).
thf(2332,plain,
! [SV250: $i,SV229: $i,SV184: $i,SV275: $i] :
( ( ( ~ ~ ( ~ ( in @ SV275 @ SV184 )
| ~ ~ ( in @ SV275 @ SV229 ) )
| ( in @ SV275 @ SV250 ) )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2265]) ).
thf(2333,plain,
! [SV250: $i,SV184: $i,SV229: $i] :
( ( ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV250 )
| ~ ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
| ~ ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
| ~ ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 ) )
| ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV250 ) ) )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2266]) ).
thf(2334,plain,
! [SV230: $i,SV185: $i,SV251: $i] :
( ( ( empty @ SV251 )
= $false )
| ( ( in @ SV185 @ SV230 )
= $false )
| ( ( element @ SV230 @ ( powerset @ SV251 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2267]) ).
thf(2335,plain,
! [SV260: $i,SV232: $i,SV252: $i,SV188: $i] :
( ( ( in @ SV188 @ SV252 )
= $true )
| ( ( in @ ( ordered_pair @ SV188 @ SV232 ) @ ( cartesian_product2 @ SV252 @ SV260 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2270]) ).
thf(2336,plain,
! [SV252: $i,SV188: $i,SV260: $i,SV232: $i] :
( ( ( in @ SV232 @ SV260 )
= $true )
| ( ( in @ ( ordered_pair @ SV188 @ SV232 ) @ ( cartesian_product2 @ SV252 @ SV260 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2271]) ).
thf(2337,plain,
! [SV260: $i,SV232: $i,SV252: $i,SV188: $i] :
( ( ( in @ SV188 @ SV252 )
= $false )
| ( ( ~ ( in @ SV232 @ SV260 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV188 @ SV232 ) @ ( cartesian_product2 @ SV252 @ SV260 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2272]) ).
thf(2338,plain,
! [SV189: $i,SV233: $i] :
( ( ( ~ ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV233 ) )
= $false )
| ( ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV189 )
= $true )
| ( ( SV189 = SV233 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2273]) ).
thf(2339,plain,
! [SV189: $i,SV233: $i] :
( ( ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV189 )
= $false )
| ( ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV189 )
= $true )
| ( ( SV189 = SV233 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2273]) ).
thf(2340,plain,
! [SV189: $i,SV233: $i] :
( ( ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV233 )
= $true )
| ( ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV233 )
= $false )
| ( ( SV189 = SV233 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2274]) ).
thf(2341,plain,
! [SV190: $i,SV234: $i,SV271: $i] :
( ( ( ~ ( in @ SV271 @ SV234 ) )
= $true )
| ( ( subset @ SV271 @ SV190 )
= $true )
| ( ( SV234
= ( powerset @ SV190 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2276]) ).
thf(2342,plain,
! [SV234: $i,SV190: $i,SV271: $i] :
( ( ( ~ ( subset @ SV271 @ SV190 ) )
= $true )
| ( ( in @ SV271 @ SV234 )
= $true )
| ( ( SV234
= ( powerset @ SV190 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2277]) ).
thf(2343,plain,
! [SV234: $i,SV190: $i] :
( ( ( ~ ( in @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV234 ) )
= $false )
| ( ( ~ ( ~ ( subset @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV190 )
| ( in @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV234 ) ) )
= $true )
| ( ( SV234
= ( powerset @ SV190 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2278]) ).
thf(2344,plain,
! [SV234: $i,SV190: $i] :
( ( ( subset @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV190 )
= $false )
| ( ( ~ ( ~ ( subset @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV190 )
| ( in @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV234 ) ) )
= $true )
| ( ( SV234
= ( powerset @ SV190 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2278]) ).
thf(2345,plain,
! [SV192: $i,SV261: $i,SV277: $i] :
( ( ( ~ ( ~ ( in @ SV277 @ SV261 )
| ~ ! [SY692: $i] :
~ ( in @ ( ordered_pair @ SV277 @ SY692 ) @ SV192 ) ) )
= $false )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2279]) ).
thf(2346,plain,
! [SV261: $i,SV192: $i,SV277: $i] :
( ( ( ~ ( ~ ~ ! [SY693: $i] :
~ ( in @ ( ordered_pair @ SV277 @ SY693 ) @ SV192 )
| ( in @ SV277 @ SV261 ) ) )
= $false )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2279]) ).
thf(2347,plain,
! [SV261: $i,SV192: $i] :
( ( ( ~ ( ~ ( in @ ( sK61_SY667 @ SV192 @ SV261 ) @ SV261 )
| ~ ! [SY694: $i] :
~ ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ SY694 ) @ SV192 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY695: $i] :
~ ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ SY695 ) @ SV192 )
| ( in @ ( sK61_SY667 @ SV192 @ SV261 ) @ SV261 ) ) )
= $true )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2280]) ).
thf(2348,plain,
! [SV236: $i,SV193: $i,SV254: $i,SV276: $i] :
( ( ( ~ ( in @ SV276 @ SV254 )
| ~ ! [SY684: $i] :
~ ~ ! [SY685: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY684 @ SV193 )
| ~ ( in @ SY685 @ SV236 ) )
| ( SV276
!= ( ordered_pair @ SY684 @ SY685 ) ) ) )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2281]) ).
thf(2349,plain,
! [SV254: $i,SV276: $i,SV236: $i,SV193: $i] :
( ( ( ~ ~ ! [SY686: $i] :
~ ~ ! [SY687: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY686 @ SV193 )
| ~ ( in @ SY687 @ SV236 ) )
| ( SV276
!= ( ordered_pair @ SY686 @ SY687 ) ) )
| ( in @ SV276 @ SV254 ) )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2282]) ).
thf(2350,plain,
! [SV254: $i,SV193: $i,SV236: $i] :
( ( ( ~ ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 )
| ~ ! [SY688: $i] :
~ ~ ! [SY689: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY688 @ SV193 )
| ~ ( in @ SY689 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SY688 @ SY689 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY690: $i] :
~ ~ ! [SY691: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY690 @ SV193 )
| ~ ( in @ SY691 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SY690 @ SY691 ) ) )
| ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 ) ) )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2283]) ).
thf(2351,plain,
! [SV194: $i,SV262: $i,SV278: $i] :
( ( ( ~ ( ~ ( in @ SV278 @ SV262 )
| ~ ! [SY696: $i] :
~ ( in @ ( ordered_pair @ SY696 @ SV278 ) @ SV194 ) ) )
= $false )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2284]) ).
thf(2352,plain,
! [SV262: $i,SV194: $i,SV278: $i] :
( ( ( ~ ( ~ ~ ! [SY697: $i] :
~ ( in @ ( ordered_pair @ SY697 @ SV278 ) @ SV194 )
| ( in @ SV278 @ SV262 ) ) )
= $false )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2284]) ).
thf(2353,plain,
! [SV262: $i,SV194: $i] :
( ( ( ~ ( ~ ( in @ ( sK62_SY673 @ SV194 @ SV262 ) @ SV262 )
| ~ ! [SY698: $i] :
~ ( in @ ( ordered_pair @ SY698 @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY699: $i] :
~ ( in @ ( ordered_pair @ SY699 @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 )
| ( in @ ( sK62_SY673 @ SV194 @ SV262 ) @ SV262 ) ) )
= $true )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2285]) ).
thf(2354,plain,
! [SV196: $i,SV238: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK64_SY628 @ SV238 @ SV196 ) @ SV196 )
| ~ ( in @ ( sK64_SY628 @ SV238 @ SV196 ) @ SV238 ) ) )
= $false )
| ( ( disjoint @ SV196 @ SV238 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2286]) ).
thf(2355,plain,
! [SV238: $i,SV196: $i,SV282: $i] :
( ( ( ~ ( ~ ( in @ SV282 @ SV196 )
| ~ ( in @ SV282 @ SV238 ) ) )
= $false )
| ( ( ~ ( disjoint @ SV196 @ SV238 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2287]) ).
thf(2356,plain,
! [SV201: $i,SV256: $i,SV242: $i] :
( ( ( in @ SV242 @ SV256 )
= $false )
| ( ( in @ SV201 @ SV256 )
= $false )
| ( ( subset @ ( unordered_pair @ SV201 @ SV242 ) @ SV256 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2290]) ).
thf(2357,plain,
! [SV204: $i,SV155: $i,SV243: $i,SV272: $i] :
( ( ( ~ ( in @ SV272 @ SV243 ) )
= $true )
| ( ( ( in @ SV272 @ SV155 )
| ( in @ SV272 @ SV204 ) )
= $true )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2291]) ).
thf(2358,plain,
! [SV243: $i,SV204: $i,SV155: $i,SV272: $i] :
( ( ( ~ ( ( in @ SV272 @ SV155 )
| ( in @ SV272 @ SV204 ) ) )
= $true )
| ( ( in @ SV272 @ SV243 )
= $true )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2292]) ).
thf(2359,plain,
! [SV243: $i,SV155: $i,SV204: $i] :
( ( ( ~ ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV243 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV155 )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV204 ) )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV243 ) ) )
= $true )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2293]) ).
thf(2360,plain,
! [SV243: $i,SV155: $i,SV204: $i] :
( ( ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV155 )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV204 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV155 )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV204 ) )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV243 ) ) )
= $true )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2293]) ).
thf(2361,plain,
! [SV157: $i] :
( ( in @ SV157 @ ( sK46_SY444 @ SV157 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2294]) ).
thf(2362,plain,
! [SV157: $i] :
( ( ! [SY635: $i,SY636: $i] :
( ~ ~ ( ~ ( in @ SY635 @ ( sK46_SY444 @ SV157 ) )
| ~ ( subset @ SY636 @ SY635 ) )
| ( in @ SY636 @ ( sK46_SY444 @ SV157 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2295]) ).
thf(2363,plain,
! [SV157: $i,SV279: $i] :
( ( ~ ( in @ SV279 @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SY700: $i] :
~ ~ ( ~ ( in @ SY700 @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SY701: $i] :
( ~ ( subset @ SY701 @ SV279 )
| ( in @ SY701 @ SY700 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2296]) ).
thf(2364,plain,
! [SV157: $i,SV266: $i] :
( ( ( ~ ( subset @ SV266 @ ( sK46_SY444 @ SV157 ) )
| ~ ~ ( are_equipotent @ SV266 @ ( sK46_SY444 @ SV157 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV266 @ ( sK46_SY444 @ SV157 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2297]) ).
thf(2365,plain,
! [SV165: $i,SV212: $i] :
( ( ( element @ SV212 @ SV165 )
= $false )
| ( ( in @ SV212 @ SV165 )
= $true )
| ( ( empty @ SV165 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2298]) ).
thf(2366,plain,
! [SV165: $i,SV212: $i] :
( ( ( in @ SV212 @ SV165 )
= $false )
| ( ( element @ SV212 @ SV165 )
= $true )
| ( ( empty @ SV165 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2299]) ).
thf(2367,plain,
! [SV168: $i,SV215: $i] :
( ( ( SV215
= ( set_meet @ SV168 ) )
= $false )
| ( ( ! [SY581: $i] :
~ ( ~ ( ~ ( in @ SY581 @ SV215 )
| ! [SY467: $i] :
( ~ ( in @ SY467 @ SV168 )
| ( in @ SY581 @ SY467 ) ) )
| ~ ( ~ ! [SY468: $i] :
( ~ ( in @ SY468 @ SV168 )
| ( in @ SY581 @ SY468 ) )
| ( in @ SY581 @ SV215 ) ) ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2302]) ).
thf(2368,plain,
! [SV168: $i,SV215: $i] :
( ( ( ! [SY584: $i] :
~ ( ~ ( ~ ( in @ SY584 @ SV215 )
| ! [SY470: $i] :
( ~ ( in @ SY470 @ SV168 )
| ( in @ SY584 @ SY470 ) ) )
| ~ ( ~ ! [SY471: $i] :
( ~ ( in @ SY471 @ SV168 )
| ( in @ SY584 @ SY471 ) )
| ( in @ SY584 @ SV215 ) ) ) )
= $false )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2303]) ).
thf(2369,plain,
! [SV169: $i,SV216: $i,SV268: $i] :
( ( ( in @ SV268 @ SV216 )
= $false )
| ( ( ~ ! [SY680: $i] :
~ ~ ( ~ ( in @ SV268 @ SY680 )
| ~ ( in @ SY680 @ SV169 ) ) )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2306]) ).
thf(2370,plain,
! [SV216: $i,SV169: $i,SV268: $i] :
( ( ( ~ ! [SY681: $i] :
~ ~ ( ~ ( in @ SV268 @ SY681 )
| ~ ( in @ SY681 @ SV169 ) ) )
= $false )
| ( ( in @ SV268 @ SV216 )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2307]) ).
thf(2371,plain,
! [SV216: $i,SV169: $i] :
( ( ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV216 )
= $true )
| ( ( ~ ( ~ ~ ! [SY683: $i] :
~ ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SY683 )
| ~ ( in @ SY683 @ SV169 ) )
| ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV216 ) ) )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2308]) ).
thf(2372,plain,
! [SV216: $i,SV169: $i] :
( ( ( ! [SY682: $i] :
~ ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SY682 )
| ~ ( in @ SY682 @ SV169 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY683: $i] :
~ ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SY683 )
| ~ ( in @ SY683 @ SV169 ) )
| ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV216 ) ) )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2309]) ).
thf(2373,plain,
! [SV217: $i,SV170: $i,SV246: $i,SV273: $i] :
( ( ( ~ ( in @ SV273 @ SV246 ) )
= $true )
| ( ( ( SV273 = SV170 )
| ( SV273 = SV217 ) )
= $true )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2310]) ).
thf(2374,plain,
! [SV246: $i,SV217: $i,SV170: $i,SV273: $i] :
( ( ( ~ ( ( SV273 = SV170 )
| ( SV273 = SV217 ) ) )
= $true )
| ( ( in @ SV273 @ SV246 )
= $true )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2311]) ).
thf(2375,plain,
! [SV246: $i,SV170: $i,SV217: $i] :
( ( ( ~ ( in @ ( sK57_SY643 @ SV217 @ SV170 @ SV246 ) @ SV246 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV170 )
| ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV217 ) )
| ( in @ ( sK57_SY643 @ SV217 @ SV170 @ SV246 ) @ SV246 ) ) )
= $true )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2312]) ).
thf(2376,plain,
! [SV246: $i,SV170: $i,SV217: $i] :
( ( ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV170 )
| ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV217 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV170 )
| ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV217 ) )
| ( in @ ( sK57_SY643 @ SV217 @ SV170 @ SV246 ) @ SV246 ) ) )
= $true )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2312]) ).
thf(2377,plain,
! [SV247: $i,SV171: $i,SV258: $i,SV218: $i] :
( ( ( in @ SV218 @ SV258 )
= $false )
| ( ( in @ SV171 @ SV247 )
= $false )
| ( ( in @ ( ordered_pair @ SV171 @ SV218 ) @ ( cartesian_product2 @ SV247 @ SV258 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2315]) ).
thf(2378,plain,
! [SV172: $i,SV219: $i,SV269: $i] :
( ( ( in @ SV269 @ SV219 )
= $false )
| ( ( SV269 = SV172 )
= $true )
| ( ( SV219
= ( singleton @ SV172 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2316]) ).
thf(2379,plain,
! [SV219: $i,SV172: $i,SV269: $i] :
( ( ( SV269 = SV172 )
= $false )
| ( ( in @ SV269 @ SV219 )
= $true )
| ( ( SV219
= ( singleton @ SV172 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2317]) ).
thf(2380,plain,
! [SV219: $i,SV172: $i] :
( ( ( in @ ( sK54_SY599 @ SV172 @ SV219 ) @ SV219 )
= $true )
| ( ( ~ ( ( ( sK54_SY599 @ SV172 @ SV219 )
!= SV172 )
| ( in @ ( sK54_SY599 @ SV172 @ SV219 ) @ SV219 ) ) )
= $true )
| ( ( SV219
= ( singleton @ SV172 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2318]) ).
thf(2381,plain,
! [SV219: $i,SV172: $i] :
( ( ( ( ( sK54_SY599 @ SV172 @ SV219 )
!= SV172 )
| ( in @ ( sK54_SY599 @ SV172 @ SV219 ) @ SV219 ) )
= $false )
| ( ( ( sK54_SY599 @ SV172 @ SV219 )
= SV172 )
= $false )
| ( ( SV219
= ( singleton @ SV172 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2319]) ).
thf(2382,plain,
! [SV174: $i,SV264: $i] :
( ( ( ! [SY703: $i] :
( SV264
!= ( ordered_pair @ ( sK65_SY676 @ SV174 @ SV264 ) @ SY703 ) ) )
= $false )
| ( ( in @ SV264 @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2320]) ).
thf(2383,plain,
! [SV284: $i,SV283: $i,SV174: $i] :
( ( ( ( sK50_SY493 @ SV174 )
!= ( ordered_pair @ SV283 @ SV284 ) )
= $true )
| ( ( relation @ SV174 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2321]) ).
thf(2384,plain,
! [SV177: $i] :
( ( in @ SV177 @ ( sK47_SY499 @ SV177 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2322]) ).
thf(2385,plain,
! [SV177: $i] :
( ( ! [SY645: $i,SY646: $i] :
( ~ ~ ( ~ ( in @ SY645 @ ( sK47_SY499 @ SV177 ) )
| ~ ( subset @ SY646 @ SY645 ) )
| ( in @ SY646 @ ( sK47_SY499 @ SV177 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2323]) ).
thf(2386,plain,
! [SV177: $i,SV280: $i] :
( ( ( in @ SV280 @ ( sK47_SY499 @ SV177 ) )
= $false )
| ( ( in @ ( powerset @ SV280 ) @ ( sK47_SY499 @ SV177 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2324]) ).
thf(2387,plain,
! [SV177: $i,SV270: $i] :
( ( ( ~ ( subset @ SV270 @ ( sK47_SY499 @ SV177 ) )
| ~ ~ ( are_equipotent @ SV270 @ ( sK47_SY499 @ SV177 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV270 @ ( sK47_SY499 @ SV177 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2325]) ).
thf(2388,plain,
! [SV179: $i,SV224: $i] :
( ( ( in @ ( sK63_SY601 @ SV224 @ SV179 ) @ ( set_intersection2 @ SV179 @ SV224 ) )
= $true )
| ( ( disjoint @ SV179 @ SV224 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2326]) ).
thf(2389,plain,
! [SV281: $i,SV224: $i,SV179: $i] :
( ( ( disjoint @ SV179 @ SV224 )
= $false )
| ( ( in @ SV281 @ ( set_intersection2 @ SV179 @ SV224 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2327]) ).
thf(2390,plain,
! [SV225: $i,SV180: $i,SV249: $i,SV274: $i] :
( ( ( ~ ( in @ SV274 @ SV249 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV274 @ SV180 )
| ~ ( in @ SV274 @ SV225 ) ) )
= $true )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2328]) ).
thf(2391,plain,
! [SV249: $i,SV225: $i,SV180: $i,SV274: $i] :
( ( ( ~ ~ ( ~ ( in @ SV274 @ SV180 )
| ~ ( in @ SV274 @ SV225 ) ) )
= $true )
| ( ( in @ SV274 @ SV249 )
= $true )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2329]) ).
thf(2392,plain,
! [SV249: $i,SV180: $i,SV225: $i] :
( ( ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV249 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
| ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 ) )
| ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV249 ) ) )
= $true )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2330]) ).
thf(2393,plain,
! [SV249: $i,SV180: $i,SV225: $i] :
( ( ( ~ ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
| ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
| ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 ) )
| ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV249 ) ) )
= $true )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2330]) ).
thf(2394,plain,
! [SV229: $i,SV184: $i,SV250: $i,SV275: $i] :
( ( ( ~ ( in @ SV275 @ SV250 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV275 @ SV184 )
| ~ ~ ( in @ SV275 @ SV229 ) ) )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2331]) ).
thf(2395,plain,
! [SV250: $i,SV229: $i,SV184: $i,SV275: $i] :
( ( ( ~ ~ ( ~ ( in @ SV275 @ SV184 )
| ~ ~ ( in @ SV275 @ SV229 ) ) )
= $true )
| ( ( in @ SV275 @ SV250 )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2332]) ).
thf(2396,plain,
! [SV250: $i,SV184: $i,SV229: $i] :
( ( ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV250 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
| ~ ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 ) )
| ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV250 ) ) )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2333]) ).
thf(2397,plain,
! [SV250: $i,SV184: $i,SV229: $i] :
( ( ( ~ ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
| ~ ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
| ~ ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 ) )
| ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV250 ) ) )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2333]) ).
thf(2398,plain,
! [SV252: $i,SV188: $i,SV260: $i,SV232: $i] :
( ( ( in @ SV232 @ SV260 )
= $false )
| ( ( in @ SV188 @ SV252 )
= $false )
| ( ( in @ ( ordered_pair @ SV188 @ SV232 ) @ ( cartesian_product2 @ SV252 @ SV260 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2337]) ).
thf(2399,plain,
! [SV189: $i,SV233: $i] :
( ( ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV233 )
= $true )
| ( ( in @ ( sK48_SY613 @ SV233 @ SV189 ) @ SV189 )
= $true )
| ( ( SV189 = SV233 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2338]) ).
thf(2400,plain,
! [SV190: $i,SV234: $i,SV271: $i] :
( ( ( in @ SV271 @ SV234 )
= $false )
| ( ( subset @ SV271 @ SV190 )
= $true )
| ( ( SV234
= ( powerset @ SV190 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2341]) ).
thf(2401,plain,
! [SV234: $i,SV190: $i,SV271: $i] :
( ( ( subset @ SV271 @ SV190 )
= $false )
| ( ( in @ SV271 @ SV234 )
= $true )
| ( ( SV234
= ( powerset @ SV190 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2342]) ).
thf(2402,plain,
! [SV234: $i,SV190: $i] :
( ( ( in @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV234 )
= $true )
| ( ( ~ ( ~ ( subset @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV190 )
| ( in @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV234 ) ) )
= $true )
| ( ( SV234
= ( powerset @ SV190 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2343]) ).
thf(2403,plain,
! [SV234: $i,SV190: $i] :
( ( ( ~ ( subset @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV190 )
| ( in @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV234 ) )
= $false )
| ( ( subset @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV190 )
= $false )
| ( ( SV234
= ( powerset @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2344]) ).
thf(2404,plain,
! [SV192: $i,SV261: $i,SV277: $i] :
( ( ( ~ ( in @ SV277 @ SV261 )
| ~ ! [SY692: $i] :
~ ( in @ ( ordered_pair @ SV277 @ SY692 ) @ SV192 ) )
= $true )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2345]) ).
thf(2405,plain,
! [SV261: $i,SV192: $i,SV277: $i] :
( ( ( ~ ~ ! [SY693: $i] :
~ ( in @ ( ordered_pair @ SV277 @ SY693 ) @ SV192 )
| ( in @ SV277 @ SV261 ) )
= $true )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2346]) ).
thf(2406,plain,
! [SV261: $i,SV192: $i] :
( ( ( ~ ( in @ ( sK61_SY667 @ SV192 @ SV261 ) @ SV261 )
| ~ ! [SY694: $i] :
~ ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ SY694 ) @ SV192 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY695: $i] :
~ ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ SY695 ) @ SV192 )
| ( in @ ( sK61_SY667 @ SV192 @ SV261 ) @ SV261 ) ) )
= $true )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2347]) ).
thf(2407,plain,
! [SV236: $i,SV193: $i,SV254: $i,SV276: $i] :
( ( ( ~ ( in @ SV276 @ SV254 ) )
= $true )
| ( ( ~ ! [SY684: $i] :
~ ~ ! [SY685: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY684 @ SV193 )
| ~ ( in @ SY685 @ SV236 ) )
| ( SV276
!= ( ordered_pair @ SY684 @ SY685 ) ) ) )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2348]) ).
thf(2408,plain,
! [SV254: $i,SV276: $i,SV236: $i,SV193: $i] :
( ( ( ~ ~ ! [SY686: $i] :
~ ~ ! [SY687: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY686 @ SV193 )
| ~ ( in @ SY687 @ SV236 ) )
| ( SV276
!= ( ordered_pair @ SY686 @ SY687 ) ) ) )
= $true )
| ( ( in @ SV276 @ SV254 )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2349]) ).
thf(2409,plain,
! [SV254: $i,SV193: $i,SV236: $i] :
( ( ( ~ ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY690: $i] :
~ ~ ! [SY691: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY690 @ SV193 )
| ~ ( in @ SY691 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SY690 @ SY691 ) ) )
| ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 ) ) )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2350]) ).
thf(2410,plain,
! [SV254: $i,SV236: $i,SV193: $i] :
( ( ( ~ ! [SY688: $i] :
~ ~ ! [SY689: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY688 @ SV193 )
| ~ ( in @ SY689 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SY688 @ SY689 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY690: $i] :
~ ~ ! [SY691: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY690 @ SV193 )
| ~ ( in @ SY691 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SY690 @ SY691 ) ) )
| ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 ) ) )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2350]) ).
thf(2411,plain,
! [SV194: $i,SV262: $i,SV278: $i] :
( ( ( ~ ( in @ SV278 @ SV262 )
| ~ ! [SY696: $i] :
~ ( in @ ( ordered_pair @ SY696 @ SV278 ) @ SV194 ) )
= $true )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2351]) ).
thf(2412,plain,
! [SV262: $i,SV194: $i,SV278: $i] :
( ( ( ~ ~ ! [SY697: $i] :
~ ( in @ ( ordered_pair @ SY697 @ SV278 ) @ SV194 )
| ( in @ SV278 @ SV262 ) )
= $true )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2352]) ).
thf(2413,plain,
! [SV262: $i,SV194: $i] :
( ( ( ~ ( in @ ( sK62_SY673 @ SV194 @ SV262 ) @ SV262 )
| ~ ! [SY698: $i] :
~ ( in @ ( ordered_pair @ SY698 @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY699: $i] :
~ ( in @ ( ordered_pair @ SY699 @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 )
| ( in @ ( sK62_SY673 @ SV194 @ SV262 ) @ SV262 ) ) )
= $true )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2353]) ).
thf(2414,plain,
! [SV196: $i,SV238: $i] :
( ( ( ~ ( ~ ( in @ ( sK64_SY628 @ SV238 @ SV196 ) @ SV196 )
| ~ ( in @ ( sK64_SY628 @ SV238 @ SV196 ) @ SV238 ) ) )
= $true )
| ( ( disjoint @ SV196 @ SV238 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2354]) ).
thf(2415,plain,
! [SV238: $i,SV196: $i,SV282: $i] :
( ( ( ~ ( in @ SV282 @ SV196 )
| ~ ( in @ SV282 @ SV238 ) )
= $true )
| ( ( ~ ( disjoint @ SV196 @ SV238 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2355]) ).
thf(2416,plain,
! [SV204: $i,SV155: $i,SV243: $i,SV272: $i] :
( ( ( in @ SV272 @ SV243 )
= $false )
| ( ( ( in @ SV272 @ SV155 )
| ( in @ SV272 @ SV204 ) )
= $true )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2357]) ).
thf(2417,plain,
! [SV243: $i,SV204: $i,SV155: $i,SV272: $i] :
( ( ( ( in @ SV272 @ SV155 )
| ( in @ SV272 @ SV204 ) )
= $false )
| ( ( in @ SV272 @ SV243 )
= $true )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2358]) ).
thf(2418,plain,
! [SV243: $i,SV155: $i,SV204: $i] :
( ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV243 )
= $true )
| ( ( ~ ( ~ ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV155 )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV204 ) )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV243 ) ) )
= $true )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2359]) ).
thf(2419,plain,
! [SV243: $i,SV155: $i,SV204: $i] :
( ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV155 )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV155 )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV204 ) )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV243 ) ) )
= $true )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2360]) ).
thf(2420,plain,
! [SV243: $i,SV155: $i,SV204: $i] :
( ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV204 )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV155 )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV204 ) )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV243 ) ) )
= $true )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2360]) ).
thf(2421,plain,
! [SV157: $i,SV285: $i] :
( ( ! [SY704: $i] :
( ~ ~ ( ~ ( in @ SV285 @ ( sK46_SY444 @ SV157 ) )
| ~ ( subset @ SY704 @ SV285 ) )
| ( in @ SY704 @ ( sK46_SY444 @ SV157 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2362]) ).
thf(2422,plain,
! [SV157: $i,SV279: $i] :
( ( ( ~ ( in @ SV279 @ ( sK46_SY444 @ SV157 ) ) )
= $true )
| ( ( ~ ! [SY700: $i] :
~ ~ ( ~ ( in @ SY700 @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SY701: $i] :
( ~ ( subset @ SY701 @ SV279 )
| ( in @ SY701 @ SY700 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2363]) ).
thf(2423,plain,
! [SV157: $i,SV266: $i] :
( ( ( ~ ( subset @ SV266 @ ( sK46_SY444 @ SV157 ) ) )
= $true )
| ( ( ~ ~ ( are_equipotent @ SV266 @ ( sK46_SY444 @ SV157 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV266 @ ( sK46_SY444 @ SV157 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2364]) ).
thf(2424,plain,
! [SV168: $i,SV215: $i,SV286: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV286 @ SV215 )
| ! [SY705: $i] :
( ~ ( in @ SY705 @ SV168 )
| ( in @ SV286 @ SY705 ) ) )
| ~ ( ~ ! [SY706: $i] :
( ~ ( in @ SY706 @ SV168 )
| ( in @ SV286 @ SY706 ) )
| ( in @ SV286 @ SV215 ) ) ) )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $false )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2367]) ).
thf(2425,plain,
! [SV215: $i,SV168: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV215 )
| ! [SY707: $i] :
( ~ ( in @ SY707 @ SV168 )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SY707 ) ) )
| ~ ( ~ ! [SY708: $i] :
( ~ ( in @ SY708 @ SV168 )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SY708 ) )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV215 ) ) ) )
= $false )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2368]) ).
thf(2426,plain,
! [SV216: $i,SV169: $i,SV268: $i] :
( ( ( ! [SY680: $i] :
~ ~ ( ~ ( in @ SV268 @ SY680 )
| ~ ( in @ SY680 @ SV169 ) ) )
= $false )
| ( ( in @ SV268 @ SV216 )
= $false )
| ( ( SV216
= ( union @ SV169 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2369]) ).
thf(2427,plain,
! [SV216: $i,SV169: $i,SV268: $i] :
( ( ( ! [SY681: $i] :
~ ~ ( ~ ( in @ SV268 @ SY681 )
| ~ ( in @ SY681 @ SV169 ) ) )
= $true )
| ( ( in @ SV268 @ SV216 )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2370]) ).
thf(2428,plain,
! [SV216: $i,SV169: $i] :
( ( ( ~ ~ ! [SY683: $i] :
~ ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SY683 )
| ~ ( in @ SY683 @ SV169 ) )
| ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV216 ) )
= $false )
| ( ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV216 )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2371]) ).
thf(2429,plain,
! [SV287: $i,SV216: $i,SV169: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV287 )
| ~ ( in @ SV287 @ SV169 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY683: $i] :
~ ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SY683 )
| ~ ( in @ SY683 @ SV169 ) )
| ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV216 ) ) )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2372]) ).
thf(2430,plain,
! [SV217: $i,SV170: $i,SV246: $i,SV273: $i] :
( ( ( in @ SV273 @ SV246 )
= $false )
| ( ( ( SV273 = SV170 )
| ( SV273 = SV217 ) )
= $true )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2373]) ).
thf(2431,plain,
! [SV246: $i,SV217: $i,SV170: $i,SV273: $i] :
( ( ( ( SV273 = SV170 )
| ( SV273 = SV217 ) )
= $false )
| ( ( in @ SV273 @ SV246 )
= $true )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2374]) ).
thf(2432,plain,
! [SV246: $i,SV170: $i,SV217: $i] :
( ( ( in @ ( sK57_SY643 @ SV217 @ SV170 @ SV246 ) @ SV246 )
= $true )
| ( ( ~ ( ~ ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV170 )
| ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV217 ) )
| ( in @ ( sK57_SY643 @ SV217 @ SV170 @ SV246 ) @ SV246 ) ) )
= $true )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2375]) ).
thf(2433,plain,
! [SV246: $i,SV170: $i,SV217: $i] :
( ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV170 )
= $false )
| ( ( ~ ( ~ ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV170 )
| ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV217 ) )
| ( in @ ( sK57_SY643 @ SV217 @ SV170 @ SV246 ) @ SV246 ) ) )
= $true )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2376]) ).
thf(2434,plain,
! [SV246: $i,SV170: $i,SV217: $i] :
( ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV217 )
= $false )
| ( ( ~ ( ~ ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV170 )
| ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV217 ) )
| ( in @ ( sK57_SY643 @ SV217 @ SV170 @ SV246 ) @ SV246 ) ) )
= $true )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2376]) ).
thf(2435,plain,
! [SV219: $i,SV172: $i] :
( ( ( ( ( sK54_SY599 @ SV172 @ SV219 )
!= SV172 )
| ( in @ ( sK54_SY599 @ SV172 @ SV219 ) @ SV219 ) )
= $false )
| ( ( in @ ( sK54_SY599 @ SV172 @ SV219 ) @ SV219 )
= $true )
| ( ( SV219
= ( singleton @ SV172 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2380]) ).
thf(2436,plain,
! [SV219: $i,SV172: $i] :
( ( ( ( sK54_SY599 @ SV172 @ SV219 )
!= SV172 )
= $false )
| ( ( ( sK54_SY599 @ SV172 @ SV219 )
= SV172 )
= $false )
| ( ( SV219
= ( singleton @ SV172 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2381]) ).
thf(2437,plain,
! [SV219: $i,SV172: $i] :
( ( ( in @ ( sK54_SY599 @ SV172 @ SV219 ) @ SV219 )
= $false )
| ( ( ( sK54_SY599 @ SV172 @ SV219 )
= SV172 )
= $false )
| ( ( SV219
= ( singleton @ SV172 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2381]) ).
thf(2438,plain,
! [SV174: $i,SV264: $i] :
( ( ( SV264
!= ( ordered_pair @ ( sK65_SY676 @ SV174 @ SV264 ) @ ( sK67_SY703 @ SV174 @ SV264 ) ) )
= $false )
| ( ( in @ SV264 @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2382]) ).
thf(2439,plain,
! [SV284: $i,SV283: $i,SV174: $i] :
( ( ( ( sK50_SY493 @ SV174 )
= ( ordered_pair @ SV283 @ SV284 ) )
= $false )
| ( ( relation @ SV174 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2383]) ).
thf(2440,plain,
! [SV177: $i,SV288: $i] :
( ( ! [SY709: $i] :
( ~ ~ ( ~ ( in @ SV288 @ ( sK47_SY499 @ SV177 ) )
| ~ ( subset @ SY709 @ SV288 ) )
| ( in @ SY709 @ ( sK47_SY499 @ SV177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2385]) ).
thf(2441,plain,
! [SV177: $i,SV270: $i] :
( ( ( ~ ( subset @ SV270 @ ( sK47_SY499 @ SV177 ) ) )
= $true )
| ( ( ~ ~ ( are_equipotent @ SV270 @ ( sK47_SY499 @ SV177 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV270 @ ( sK47_SY499 @ SV177 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2387]) ).
thf(2442,plain,
! [SV225: $i,SV180: $i,SV249: $i,SV274: $i] :
( ( ( in @ SV274 @ SV249 )
= $false )
| ( ( ~ ( ~ ( in @ SV274 @ SV180 )
| ~ ( in @ SV274 @ SV225 ) ) )
= $true )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2390]) ).
thf(2443,plain,
! [SV249: $i,SV225: $i,SV180: $i,SV274: $i] :
( ( ( ~ ( ~ ( in @ SV274 @ SV180 )
| ~ ( in @ SV274 @ SV225 ) ) )
= $false )
| ( ( in @ SV274 @ SV249 )
= $true )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2391]) ).
thf(2444,plain,
! [SV249: $i,SV180: $i,SV225: $i] :
( ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV249 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
| ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 ) )
| ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV249 ) ) )
= $true )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2392]) ).
thf(2445,plain,
! [SV249: $i,SV180: $i,SV225: $i] :
( ( ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
| ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
| ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 ) )
| ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV249 ) ) )
= $true )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2393]) ).
thf(2446,plain,
! [SV229: $i,SV184: $i,SV250: $i,SV275: $i] :
( ( ( in @ SV275 @ SV250 )
= $false )
| ( ( ~ ( ~ ( in @ SV275 @ SV184 )
| ~ ~ ( in @ SV275 @ SV229 ) ) )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2394]) ).
thf(2447,plain,
! [SV250: $i,SV229: $i,SV184: $i,SV275: $i] :
( ( ( ~ ( ~ ( in @ SV275 @ SV184 )
| ~ ~ ( in @ SV275 @ SV229 ) ) )
= $false )
| ( ( in @ SV275 @ SV250 )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2395]) ).
thf(2448,plain,
! [SV250: $i,SV184: $i,SV229: $i] :
( ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV250 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
| ~ ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 ) )
| ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV250 ) ) )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2396]) ).
thf(2449,plain,
! [SV250: $i,SV184: $i,SV229: $i] :
( ( ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
| ~ ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
| ~ ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 ) )
| ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV250 ) ) )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2397]) ).
thf(2450,plain,
! [SV234: $i,SV190: $i] :
( ( ( ~ ( subset @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV190 )
| ( in @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV234 ) )
= $false )
| ( ( in @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV234 )
= $true )
| ( ( SV234
= ( powerset @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2402]) ).
thf(2451,plain,
! [SV234: $i,SV190: $i] :
( ( ( ~ ( subset @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV190 ) )
= $false )
| ( ( subset @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV190 )
= $false )
| ( ( SV234
= ( powerset @ SV190 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2403]) ).
thf(2452,plain,
! [SV234: $i,SV190: $i] :
( ( ( in @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV234 )
= $false )
| ( ( subset @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV190 )
= $false )
| ( ( SV234
= ( powerset @ SV190 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2403]) ).
thf(2453,plain,
! [SV192: $i,SV261: $i,SV277: $i] :
( ( ( ~ ( in @ SV277 @ SV261 ) )
= $true )
| ( ( ~ ! [SY692: $i] :
~ ( in @ ( ordered_pair @ SV277 @ SY692 ) @ SV192 ) )
= $true )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2404]) ).
thf(2454,plain,
! [SV261: $i,SV192: $i,SV277: $i] :
( ( ( ~ ~ ! [SY693: $i] :
~ ( in @ ( ordered_pair @ SV277 @ SY693 ) @ SV192 ) )
= $true )
| ( ( in @ SV277 @ SV261 )
= $true )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2405]) ).
thf(2455,plain,
! [SV261: $i,SV192: $i] :
( ( ( ~ ( in @ ( sK61_SY667 @ SV192 @ SV261 ) @ SV261 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY695: $i] :
~ ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ SY695 ) @ SV192 )
| ( in @ ( sK61_SY667 @ SV192 @ SV261 ) @ SV261 ) ) )
= $true )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2406]) ).
thf(2456,plain,
! [SV261: $i,SV192: $i] :
( ( ( ~ ! [SY694: $i] :
~ ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ SY694 ) @ SV192 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY695: $i] :
~ ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ SY695 ) @ SV192 )
| ( in @ ( sK61_SY667 @ SV192 @ SV261 ) @ SV261 ) ) )
= $true )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2406]) ).
thf(2457,plain,
! [SV236: $i,SV193: $i,SV254: $i,SV276: $i] :
( ( ( in @ SV276 @ SV254 )
= $false )
| ( ( ~ ! [SY684: $i] :
~ ~ ! [SY685: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY684 @ SV193 )
| ~ ( in @ SY685 @ SV236 ) )
| ( SV276
!= ( ordered_pair @ SY684 @ SY685 ) ) ) )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2407]) ).
thf(2458,plain,
! [SV254: $i,SV276: $i,SV236: $i,SV193: $i] :
( ( ( ~ ! [SY686: $i] :
~ ~ ! [SY687: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY686 @ SV193 )
| ~ ( in @ SY687 @ SV236 ) )
| ( SV276
!= ( ordered_pair @ SY686 @ SY687 ) ) ) )
= $false )
| ( ( in @ SV276 @ SV254 )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2408]) ).
thf(2459,plain,
! [SV254: $i,SV193: $i,SV236: $i] :
( ( ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 )
= $true )
| ( ( ~ ( ~ ~ ! [SY690: $i] :
~ ~ ! [SY691: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY690 @ SV193 )
| ~ ( in @ SY691 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SY690 @ SY691 ) ) )
| ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 ) ) )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2409]) ).
thf(2460,plain,
! [SV254: $i,SV236: $i,SV193: $i] :
( ( ( ! [SY688: $i] :
~ ~ ! [SY689: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY688 @ SV193 )
| ~ ( in @ SY689 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SY688 @ SY689 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY690: $i] :
~ ~ ! [SY691: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY690 @ SV193 )
| ~ ( in @ SY691 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SY690 @ SY691 ) ) )
| ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 ) ) )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2410]) ).
thf(2461,plain,
! [SV194: $i,SV262: $i,SV278: $i] :
( ( ( ~ ( in @ SV278 @ SV262 ) )
= $true )
| ( ( ~ ! [SY696: $i] :
~ ( in @ ( ordered_pair @ SY696 @ SV278 ) @ SV194 ) )
= $true )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2411]) ).
thf(2462,plain,
! [SV262: $i,SV194: $i,SV278: $i] :
( ( ( ~ ~ ! [SY697: $i] :
~ ( in @ ( ordered_pair @ SY697 @ SV278 ) @ SV194 ) )
= $true )
| ( ( in @ SV278 @ SV262 )
= $true )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2412]) ).
thf(2463,plain,
! [SV262: $i,SV194: $i] :
( ( ( ~ ( in @ ( sK62_SY673 @ SV194 @ SV262 ) @ SV262 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY699: $i] :
~ ( in @ ( ordered_pair @ SY699 @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 )
| ( in @ ( sK62_SY673 @ SV194 @ SV262 ) @ SV262 ) ) )
= $true )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2413]) ).
thf(2464,plain,
! [SV262: $i,SV194: $i] :
( ( ( ~ ! [SY698: $i] :
~ ( in @ ( ordered_pair @ SY698 @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY699: $i] :
~ ( in @ ( ordered_pair @ SY699 @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 )
| ( in @ ( sK62_SY673 @ SV194 @ SV262 ) @ SV262 ) ) )
= $true )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2413]) ).
thf(2465,plain,
! [SV196: $i,SV238: $i] :
( ( ( ~ ( in @ ( sK64_SY628 @ SV238 @ SV196 ) @ SV196 )
| ~ ( in @ ( sK64_SY628 @ SV238 @ SV196 ) @ SV238 ) )
= $false )
| ( ( disjoint @ SV196 @ SV238 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2414]) ).
thf(2466,plain,
! [SV238: $i,SV196: $i,SV282: $i] :
( ( ( ~ ( in @ SV282 @ SV196 ) )
= $true )
| ( ( ~ ( in @ SV282 @ SV238 ) )
= $true )
| ( ( ~ ( disjoint @ SV196 @ SV238 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2415]) ).
thf(2467,plain,
! [SV243: $i,SV204: $i,SV155: $i,SV272: $i] :
( ( ( in @ SV272 @ SV155 )
= $true )
| ( ( in @ SV272 @ SV204 )
= $true )
| ( ( in @ SV272 @ SV243 )
= $false )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2416]) ).
thf(2468,plain,
! [SV204: $i,SV243: $i,SV155: $i,SV272: $i] :
( ( ( in @ SV272 @ SV155 )
= $false )
| ( ( in @ SV272 @ SV243 )
= $true )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2417]) ).
thf(2469,plain,
! [SV155: $i,SV243: $i,SV204: $i,SV272: $i] :
( ( ( in @ SV272 @ SV204 )
= $false )
| ( ( in @ SV272 @ SV243 )
= $true )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2417]) ).
thf(2470,plain,
! [SV243: $i,SV155: $i,SV204: $i] :
( ( ( ~ ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV155 )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV204 ) )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV243 ) )
= $false )
| ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV243 )
= $true )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2418]) ).
thf(2471,plain,
! [SV243: $i,SV155: $i,SV204: $i] :
( ( ( ~ ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV155 )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV204 ) )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV243 ) )
= $false )
| ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV155 )
= $false )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2419]) ).
thf(2472,plain,
! [SV243: $i,SV155: $i,SV204: $i] :
( ( ( ~ ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV155 )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV204 ) )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV243 ) )
= $false )
| ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV204 )
= $false )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2420]) ).
thf(2473,plain,
! [SV289: $i,SV157: $i,SV285: $i] :
( ( ~ ~ ( ~ ( in @ SV285 @ ( sK46_SY444 @ SV157 ) )
| ~ ( subset @ SV289 @ SV285 ) )
| ( in @ SV289 @ ( sK46_SY444 @ SV157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2421]) ).
thf(2474,plain,
! [SV157: $i,SV279: $i] :
( ( ( in @ SV279 @ ( sK46_SY444 @ SV157 ) )
= $false )
| ( ( ~ ! [SY700: $i] :
~ ~ ( ~ ( in @ SY700 @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SY701: $i] :
( ~ ( subset @ SY701 @ SV279 )
| ( in @ SY701 @ SY700 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2422]) ).
thf(2475,plain,
! [SV157: $i,SV266: $i] :
( ( ( subset @ SV266 @ ( sK46_SY444 @ SV157 ) )
= $false )
| ( ( ~ ~ ( are_equipotent @ SV266 @ ( sK46_SY444 @ SV157 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV266 @ ( sK46_SY444 @ SV157 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2423]) ).
thf(2476,plain,
! [SV168: $i,SV215: $i,SV286: $i] :
( ( ( ~ ( ~ ( in @ SV286 @ SV215 )
| ! [SY705: $i] :
( ~ ( in @ SY705 @ SV168 )
| ( in @ SV286 @ SY705 ) ) )
| ~ ( ~ ! [SY706: $i] :
( ~ ( in @ SY706 @ SV168 )
| ( in @ SV286 @ SY706 ) )
| ( in @ SV286 @ SV215 ) ) )
= $false )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $false )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2424]) ).
thf(2477,plain,
! [SV215: $i,SV168: $i] :
( ( ( ~ ( ~ ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV215 )
| ! [SY707: $i] :
( ~ ( in @ SY707 @ SV168 )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SY707 ) ) )
| ~ ( ~ ! [SY708: $i] :
( ~ ( in @ SY708 @ SV168 )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SY708 ) )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV215 ) ) )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2425]) ).
thf(2478,plain,
! [SV169: $i,SV216: $i,SV268: $i] :
( ( ( ~ ~ ( ~ ( in @ SV268 @ ( sK68_SY680 @ SV216 @ SV169 @ SV268 ) )
| ~ ( in @ ( sK68_SY680 @ SV216 @ SV169 @ SV268 ) @ SV169 ) ) )
= $false )
| ( ( in @ SV268 @ SV216 )
= $false )
| ( ( SV216
= ( union @ SV169 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2426]) ).
thf(2479,plain,
! [SV216: $i,SV169: $i,SV290: $i,SV268: $i] :
( ( ( ~ ~ ( ~ ( in @ SV268 @ SV290 )
| ~ ( in @ SV290 @ SV169 ) ) )
= $true )
| ( ( in @ SV268 @ SV216 )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2427]) ).
thf(2480,plain,
! [SV216: $i,SV169: $i] :
( ( ( ~ ~ ! [SY683: $i] :
~ ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SY683 )
| ~ ( in @ SY683 @ SV169 ) ) )
= $false )
| ( ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV216 )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2428]) ).
thf(2481,plain,
! [SV216: $i,SV169: $i] :
( ( ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV216 )
= $false )
| ( ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV216 )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2428]) ).
thf(2482,plain,
! [SV287: $i,SV216: $i,SV169: $i] :
( ( ( ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV287 )
| ~ ( in @ SV287 @ SV169 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY683: $i] :
~ ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SY683 )
| ~ ( in @ SY683 @ SV169 ) )
| ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV216 ) ) )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2429]) ).
thf(2483,plain,
! [SV246: $i,SV217: $i,SV170: $i,SV273: $i] :
( ( ( SV273 = SV170 )
= $true )
| ( ( SV273 = SV217 )
= $true )
| ( ( in @ SV273 @ SV246 )
= $false )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2430]) ).
thf(2484,plain,
! [SV217: $i,SV246: $i,SV170: $i,SV273: $i] :
( ( ( SV273 = SV170 )
= $false )
| ( ( in @ SV273 @ SV246 )
= $true )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2431]) ).
thf(2485,plain,
! [SV170: $i,SV246: $i,SV217: $i,SV273: $i] :
( ( ( SV273 = SV217 )
= $false )
| ( ( in @ SV273 @ SV246 )
= $true )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2431]) ).
thf(2486,plain,
! [SV246: $i,SV170: $i,SV217: $i] :
( ( ( ~ ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV170 )
| ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV217 ) )
| ( in @ ( sK57_SY643 @ SV217 @ SV170 @ SV246 ) @ SV246 ) )
= $false )
| ( ( in @ ( sK57_SY643 @ SV217 @ SV170 @ SV246 ) @ SV246 )
= $true )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2432]) ).
thf(2487,plain,
! [SV246: $i,SV170: $i,SV217: $i] :
( ( ( ~ ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV170 )
| ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV217 ) )
| ( in @ ( sK57_SY643 @ SV217 @ SV170 @ SV246 ) @ SV246 ) )
= $false )
| ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV170 )
= $false )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2433]) ).
thf(2488,plain,
! [SV246: $i,SV170: $i,SV217: $i] :
( ( ( ~ ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV170 )
| ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV217 ) )
| ( in @ ( sK57_SY643 @ SV217 @ SV170 @ SV246 ) @ SV246 ) )
= $false )
| ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV217 )
= $false )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2434]) ).
thf(2489,plain,
! [SV219: $i,SV172: $i] :
( ( ( ( sK54_SY599 @ SV172 @ SV219 )
!= SV172 )
= $false )
| ( ( in @ ( sK54_SY599 @ SV172 @ SV219 ) @ SV219 )
= $true )
| ( ( SV219
= ( singleton @ SV172 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2435]) ).
thf(2490,plain,
! [SV219: $i,SV172: $i] :
( ( ( in @ ( sK54_SY599 @ SV172 @ SV219 ) @ SV219 )
= $false )
| ( ( in @ ( sK54_SY599 @ SV172 @ SV219 ) @ SV219 )
= $true )
| ( ( SV219
= ( singleton @ SV172 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2435]) ).
thf(2491,plain,
! [SV219: $i,SV172: $i] :
( ( ( ( sK54_SY599 @ SV172 @ SV219 )
= SV172 )
= $true )
| ( ( ( sK54_SY599 @ SV172 @ SV219 )
= SV172 )
= $false )
| ( ( SV219
= ( singleton @ SV172 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2436]) ).
thf(2492,plain,
! [SV174: $i,SV264: $i] :
( ( ( SV264
= ( ordered_pair @ ( sK65_SY676 @ SV174 @ SV264 ) @ ( sK67_SY703 @ SV174 @ SV264 ) ) )
= $true )
| ( ( in @ SV264 @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2438]) ).
thf(2493,plain,
! [SV291: $i,SV177: $i,SV288: $i] :
( ( ~ ~ ( ~ ( in @ SV288 @ ( sK47_SY499 @ SV177 ) )
| ~ ( subset @ SV291 @ SV288 ) )
| ( in @ SV291 @ ( sK47_SY499 @ SV177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2440]) ).
thf(2494,plain,
! [SV177: $i,SV270: $i] :
( ( ( subset @ SV270 @ ( sK47_SY499 @ SV177 ) )
= $false )
| ( ( ~ ~ ( are_equipotent @ SV270 @ ( sK47_SY499 @ SV177 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV270 @ ( sK47_SY499 @ SV177 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2441]) ).
thf(2495,plain,
! [SV249: $i,SV225: $i,SV180: $i,SV274: $i] :
( ( ( ~ ( in @ SV274 @ SV180 )
| ~ ( in @ SV274 @ SV225 ) )
= $false )
| ( ( in @ SV274 @ SV249 )
= $false )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2442]) ).
thf(2496,plain,
! [SV249: $i,SV225: $i,SV180: $i,SV274: $i] :
( ( ( ~ ( in @ SV274 @ SV180 )
| ~ ( in @ SV274 @ SV225 ) )
= $true )
| ( ( in @ SV274 @ SV249 )
= $true )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2443]) ).
thf(2497,plain,
! [SV249: $i,SV180: $i,SV225: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
| ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 ) )
| ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV249 ) )
= $false )
| ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV249 )
= $true )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2444]) ).
thf(2498,plain,
! [SV249: $i,SV180: $i,SV225: $i] :
( ( ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 ) )
= $true )
| ( ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
| ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 ) )
| ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV249 ) ) )
= $true )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2445]) ).
thf(2499,plain,
! [SV250: $i,SV229: $i,SV184: $i,SV275: $i] :
( ( ( ~ ( in @ SV275 @ SV184 )
| ~ ~ ( in @ SV275 @ SV229 ) )
= $false )
| ( ( in @ SV275 @ SV250 )
= $false )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2446]) ).
thf(2500,plain,
! [SV250: $i,SV229: $i,SV184: $i,SV275: $i] :
( ( ( ~ ( in @ SV275 @ SV184 )
| ~ ~ ( in @ SV275 @ SV229 ) )
= $true )
| ( ( in @ SV275 @ SV250 )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2447]) ).
thf(2501,plain,
! [SV250: $i,SV184: $i,SV229: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
| ~ ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 ) )
| ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV250 ) )
= $false )
| ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV250 )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2448]) ).
thf(2502,plain,
! [SV250: $i,SV184: $i,SV229: $i] :
( ( ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 ) )
= $true )
| ( ( ~ ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
| ~ ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 ) )
| ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV250 ) ) )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2449]) ).
thf(2503,plain,
! [SV234: $i,SV190: $i] :
( ( ( ~ ( subset @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV190 ) )
= $false )
| ( ( in @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV234 )
= $true )
| ( ( SV234
= ( powerset @ SV190 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2450]) ).
thf(2504,plain,
! [SV234: $i,SV190: $i] :
( ( ( in @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV234 )
= $false )
| ( ( in @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV234 )
= $true )
| ( ( SV234
= ( powerset @ SV190 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2450]) ).
thf(2505,plain,
! [SV234: $i,SV190: $i] :
( ( ( subset @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV190 )
= $true )
| ( ( subset @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV190 )
= $false )
| ( ( SV234
= ( powerset @ SV190 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2451]) ).
thf(2506,plain,
! [SV192: $i,SV261: $i,SV277: $i] :
( ( ( in @ SV277 @ SV261 )
= $false )
| ( ( ~ ! [SY692: $i] :
~ ( in @ ( ordered_pair @ SV277 @ SY692 ) @ SV192 ) )
= $true )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2453]) ).
thf(2507,plain,
! [SV261: $i,SV192: $i,SV277: $i] :
( ( ( ~ ! [SY693: $i] :
~ ( in @ ( ordered_pair @ SV277 @ SY693 ) @ SV192 ) )
= $false )
| ( ( in @ SV277 @ SV261 )
= $true )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2454]) ).
thf(2508,plain,
! [SV261: $i,SV192: $i] :
( ( ( in @ ( sK61_SY667 @ SV192 @ SV261 ) @ SV261 )
= $true )
| ( ( ~ ( ~ ~ ! [SY695: $i] :
~ ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ SY695 ) @ SV192 )
| ( in @ ( sK61_SY667 @ SV192 @ SV261 ) @ SV261 ) ) )
= $true )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2455]) ).
thf(2509,plain,
! [SV261: $i,SV192: $i] :
( ( ( ! [SY694: $i] :
~ ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ SY694 ) @ SV192 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY695: $i] :
~ ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ SY695 ) @ SV192 )
| ( in @ ( sK61_SY667 @ SV192 @ SV261 ) @ SV261 ) ) )
= $true )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2456]) ).
thf(2510,plain,
! [SV254: $i,SV276: $i,SV236: $i,SV193: $i] :
( ( ( ! [SY684: $i] :
~ ~ ! [SY685: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY684 @ SV193 )
| ~ ( in @ SY685 @ SV236 ) )
| ( SV276
!= ( ordered_pair @ SY684 @ SY685 ) ) ) )
= $false )
| ( ( in @ SV276 @ SV254 )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2457]) ).
thf(2511,plain,
! [SV254: $i,SV276: $i,SV236: $i,SV193: $i] :
( ( ( ! [SY686: $i] :
~ ~ ! [SY687: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY686 @ SV193 )
| ~ ( in @ SY687 @ SV236 ) )
| ( SV276
!= ( ordered_pair @ SY686 @ SY687 ) ) ) )
= $true )
| ( ( in @ SV276 @ SV254 )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2458]) ).
thf(2512,plain,
! [SV254: $i,SV236: $i,SV193: $i] :
( ( ( ~ ~ ! [SY690: $i] :
~ ~ ! [SY691: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY690 @ SV193 )
| ~ ( in @ SY691 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SY690 @ SY691 ) ) )
| ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 ) )
= $false )
| ( ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2459]) ).
thf(2513,plain,
! [SV254: $i,SV236: $i,SV193: $i,SV292: $i] :
( ( ( ~ ~ ! [SY710: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV292 @ SV193 )
| ~ ( in @ SY710 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SV292 @ SY710 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY690: $i] :
~ ~ ! [SY691: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY690 @ SV193 )
| ~ ( in @ SY691 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SY690 @ SY691 ) ) )
| ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 ) ) )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2460]) ).
thf(2514,plain,
! [SV194: $i,SV262: $i,SV278: $i] :
( ( ( in @ SV278 @ SV262 )
= $false )
| ( ( ~ ! [SY696: $i] :
~ ( in @ ( ordered_pair @ SY696 @ SV278 ) @ SV194 ) )
= $true )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2461]) ).
thf(2515,plain,
! [SV262: $i,SV194: $i,SV278: $i] :
( ( ( ~ ! [SY697: $i] :
~ ( in @ ( ordered_pair @ SY697 @ SV278 ) @ SV194 ) )
= $false )
| ( ( in @ SV278 @ SV262 )
= $true )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2462]) ).
thf(2516,plain,
! [SV262: $i,SV194: $i] :
( ( ( in @ ( sK62_SY673 @ SV194 @ SV262 ) @ SV262 )
= $true )
| ( ( ~ ( ~ ~ ! [SY699: $i] :
~ ( in @ ( ordered_pair @ SY699 @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 )
| ( in @ ( sK62_SY673 @ SV194 @ SV262 ) @ SV262 ) ) )
= $true )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2463]) ).
thf(2517,plain,
! [SV262: $i,SV194: $i] :
( ( ( ! [SY698: $i] :
~ ( in @ ( ordered_pair @ SY698 @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY699: $i] :
~ ( in @ ( ordered_pair @ SY699 @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 )
| ( in @ ( sK62_SY673 @ SV194 @ SV262 ) @ SV262 ) ) )
= $true )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2464]) ).
thf(2518,plain,
! [SV196: $i,SV238: $i] :
( ( ( ~ ( in @ ( sK64_SY628 @ SV238 @ SV196 ) @ SV196 ) )
= $false )
| ( ( disjoint @ SV196 @ SV238 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2465]) ).
thf(2519,plain,
! [SV196: $i,SV238: $i] :
( ( ( ~ ( in @ ( sK64_SY628 @ SV238 @ SV196 ) @ SV238 ) )
= $false )
| ( ( disjoint @ SV196 @ SV238 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2465]) ).
thf(2520,plain,
! [SV238: $i,SV196: $i,SV282: $i] :
( ( ( in @ SV282 @ SV196 )
= $false )
| ( ( ~ ( in @ SV282 @ SV238 ) )
= $true )
| ( ( ~ ( disjoint @ SV196 @ SV238 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2466]) ).
thf(2521,plain,
! [SV243: $i,SV155: $i,SV204: $i] :
( ( ( ~ ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV155 )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV204 ) ) )
= $false )
| ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV243 )
= $true )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2470]) ).
thf(2522,plain,
! [SV243: $i,SV155: $i,SV204: $i] :
( ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV243 )
= $false )
| ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV243 )
= $true )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2470]) ).
thf(2523,plain,
! [SV243: $i,SV155: $i,SV204: $i] :
( ( ( ~ ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV155 )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV204 ) ) )
= $false )
| ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV155 )
= $false )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2471]) ).
thf(2524,plain,
! [SV243: $i,SV155: $i,SV204: $i] :
( ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV243 )
= $false )
| ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV155 )
= $false )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2471]) ).
thf(2525,plain,
! [SV243: $i,SV155: $i,SV204: $i] :
( ( ( ~ ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV155 )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV204 ) ) )
= $false )
| ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV204 )
= $false )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2472]) ).
thf(2526,plain,
! [SV243: $i,SV155: $i,SV204: $i] :
( ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV243 )
= $false )
| ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV204 )
= $false )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2472]) ).
thf(2527,plain,
! [SV289: $i,SV157: $i,SV285: $i] :
( ( ( ~ ~ ( ~ ( in @ SV285 @ ( sK46_SY444 @ SV157 ) )
| ~ ( subset @ SV289 @ SV285 ) ) )
= $true )
| ( ( in @ SV289 @ ( sK46_SY444 @ SV157 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2473]) ).
thf(2528,plain,
! [SV279: $i,SV157: $i] :
( ( ( ! [SY700: $i] :
~ ~ ( ~ ( in @ SY700 @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SY701: $i] :
( ~ ( subset @ SY701 @ SV279 )
| ( in @ SY701 @ SY700 ) ) ) )
= $false )
| ( ( in @ SV279 @ ( sK46_SY444 @ SV157 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2474]) ).
thf(2529,plain,
! [SV157: $i,SV266: $i] :
( ( ( ~ ( are_equipotent @ SV266 @ ( sK46_SY444 @ SV157 ) ) )
= $false )
| ( ( subset @ SV266 @ ( sK46_SY444 @ SV157 ) )
= $false )
| ( ( ~ ~ ( in @ SV266 @ ( sK46_SY444 @ SV157 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2475]) ).
thf(2530,plain,
! [SV168: $i,SV215: $i,SV286: $i] :
( ( ( ~ ( ~ ( in @ SV286 @ SV215 )
| ! [SY705: $i] :
( ~ ( in @ SY705 @ SV168 )
| ( in @ SV286 @ SY705 ) ) ) )
= $false )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $false )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2476]) ).
thf(2531,plain,
! [SV215: $i,SV286: $i,SV168: $i] :
( ( ( ~ ( ~ ! [SY706: $i] :
( ~ ( in @ SY706 @ SV168 )
| ( in @ SV286 @ SY706 ) )
| ( in @ SV286 @ SV215 ) ) )
= $false )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $false )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2476]) ).
thf(2532,plain,
! [SV215: $i,SV168: $i] :
( ( ( ~ ( ~ ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV215 )
| ! [SY707: $i] :
( ~ ( in @ SY707 @ SV168 )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SY707 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY708: $i] :
( ~ ( in @ SY708 @ SV168 )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SY708 ) )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV215 ) ) )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2477]) ).
thf(2533,plain,
! [SV169: $i,SV216: $i,SV268: $i] :
( ( ( ~ ( ~ ( in @ SV268 @ ( sK68_SY680 @ SV216 @ SV169 @ SV268 ) )
| ~ ( in @ ( sK68_SY680 @ SV216 @ SV169 @ SV268 ) @ SV169 ) ) )
= $true )
| ( ( in @ SV268 @ SV216 )
= $false )
| ( ( SV216
= ( union @ SV169 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2478]) ).
thf(2534,plain,
! [SV216: $i,SV169: $i,SV290: $i,SV268: $i] :
( ( ( ~ ( ~ ( in @ SV268 @ SV290 )
| ~ ( in @ SV290 @ SV169 ) ) )
= $false )
| ( ( in @ SV268 @ SV216 )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2479]) ).
thf(2535,plain,
! [SV216: $i,SV169: $i] :
( ( ( ~ ! [SY683: $i] :
~ ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SY683 )
| ~ ( in @ SY683 @ SV169 ) ) )
= $true )
| ( ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV216 )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2480]) ).
thf(2536,plain,
! [SV287: $i,SV216: $i,SV169: $i] :
( ( ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV287 )
| ~ ( in @ SV287 @ SV169 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY683: $i] :
~ ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SY683 )
| ~ ( in @ SY683 @ SV169 ) )
| ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV216 ) ) )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2482]) ).
thf(2537,plain,
! [SV246: $i,SV170: $i,SV217: $i] :
( ( ( ~ ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV170 )
| ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV217 ) ) )
= $false )
| ( ( in @ ( sK57_SY643 @ SV217 @ SV170 @ SV246 ) @ SV246 )
= $true )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2486]) ).
thf(2538,plain,
! [SV246: $i,SV170: $i,SV217: $i] :
( ( ( in @ ( sK57_SY643 @ SV217 @ SV170 @ SV246 ) @ SV246 )
= $false )
| ( ( in @ ( sK57_SY643 @ SV217 @ SV170 @ SV246 ) @ SV246 )
= $true )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2486]) ).
thf(2539,plain,
! [SV246: $i,SV170: $i,SV217: $i] :
( ( ( ~ ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV170 )
| ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV217 ) ) )
= $false )
| ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV170 )
= $false )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2487]) ).
thf(2540,plain,
! [SV246: $i,SV170: $i,SV217: $i] :
( ( ( in @ ( sK57_SY643 @ SV217 @ SV170 @ SV246 ) @ SV246 )
= $false )
| ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV170 )
= $false )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2487]) ).
thf(2541,plain,
! [SV246: $i,SV170: $i,SV217: $i] :
( ( ( ~ ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV170 )
| ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV217 ) ) )
= $false )
| ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV217 )
= $false )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2488]) ).
thf(2542,plain,
! [SV246: $i,SV170: $i,SV217: $i] :
( ( ( in @ ( sK57_SY643 @ SV217 @ SV170 @ SV246 ) @ SV246 )
= $false )
| ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV217 )
= $false )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2488]) ).
thf(2543,plain,
! [SV219: $i,SV172: $i] :
( ( ( ( sK54_SY599 @ SV172 @ SV219 )
= SV172 )
= $true )
| ( ( in @ ( sK54_SY599 @ SV172 @ SV219 ) @ SV219 )
= $true )
| ( ( SV219
= ( singleton @ SV172 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2489]) ).
thf(2544,plain,
! [SV291: $i,SV177: $i,SV288: $i] :
( ( ( ~ ~ ( ~ ( in @ SV288 @ ( sK47_SY499 @ SV177 ) )
| ~ ( subset @ SV291 @ SV288 ) ) )
= $true )
| ( ( in @ SV291 @ ( sK47_SY499 @ SV177 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2493]) ).
thf(2545,plain,
! [SV177: $i,SV270: $i] :
( ( ( ~ ( are_equipotent @ SV270 @ ( sK47_SY499 @ SV177 ) ) )
= $false )
| ( ( subset @ SV270 @ ( sK47_SY499 @ SV177 ) )
= $false )
| ( ( ~ ~ ( in @ SV270 @ ( sK47_SY499 @ SV177 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2494]) ).
thf(2546,plain,
! [SV225: $i,SV249: $i,SV180: $i,SV274: $i] :
( ( ( ~ ( in @ SV274 @ SV180 ) )
= $false )
| ( ( in @ SV274 @ SV249 )
= $false )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2495]) ).
thf(2547,plain,
! [SV180: $i,SV249: $i,SV225: $i,SV274: $i] :
( ( ( ~ ( in @ SV274 @ SV225 ) )
= $false )
| ( ( in @ SV274 @ SV249 )
= $false )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2495]) ).
thf(2548,plain,
! [SV249: $i,SV225: $i,SV180: $i,SV274: $i] :
( ( ( ~ ( in @ SV274 @ SV180 ) )
= $true )
| ( ( ~ ( in @ SV274 @ SV225 ) )
= $true )
| ( ( in @ SV274 @ SV249 )
= $true )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2496]) ).
thf(2549,plain,
! [SV249: $i,SV180: $i,SV225: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
| ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 ) ) )
= $false )
| ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV249 )
= $true )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2497]) ).
thf(2550,plain,
! [SV249: $i,SV180: $i,SV225: $i] :
( ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV249 )
= $false )
| ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV249 )
= $true )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2497]) ).
thf(2551,plain,
! [SV249: $i,SV180: $i,SV225: $i] :
( ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
= $false )
| ( ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
| ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 ) )
| ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV249 ) ) )
= $true )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2498]) ).
thf(2552,plain,
! [SV229: $i,SV250: $i,SV184: $i,SV275: $i] :
( ( ( ~ ( in @ SV275 @ SV184 ) )
= $false )
| ( ( in @ SV275 @ SV250 )
= $false )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2499]) ).
thf(2553,plain,
! [SV184: $i,SV250: $i,SV229: $i,SV275: $i] :
( ( ( ~ ~ ( in @ SV275 @ SV229 ) )
= $false )
| ( ( in @ SV275 @ SV250 )
= $false )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2499]) ).
thf(2554,plain,
! [SV250: $i,SV229: $i,SV184: $i,SV275: $i] :
( ( ( ~ ( in @ SV275 @ SV184 ) )
= $true )
| ( ( ~ ~ ( in @ SV275 @ SV229 ) )
= $true )
| ( ( in @ SV275 @ SV250 )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2500]) ).
thf(2555,plain,
! [SV250: $i,SV184: $i,SV229: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
| ~ ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 ) ) )
= $false )
| ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV250 )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2501]) ).
thf(2556,plain,
! [SV250: $i,SV184: $i,SV229: $i] :
( ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV250 )
= $false )
| ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV250 )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2501]) ).
thf(2557,plain,
! [SV250: $i,SV184: $i,SV229: $i] :
( ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
= $false )
| ( ( ~ ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
| ~ ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 ) )
| ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV250 ) ) )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2502]) ).
thf(2558,plain,
! [SV234: $i,SV190: $i] :
( ( ( subset @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV190 )
= $true )
| ( ( in @ ( sK55_SY615 @ SV190 @ SV234 ) @ SV234 )
= $true )
| ( ( SV234
= ( powerset @ SV190 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2503]) ).
thf(2559,plain,
! [SV261: $i,SV192: $i,SV277: $i] :
( ( ( ! [SY692: $i] :
~ ( in @ ( ordered_pair @ SV277 @ SY692 ) @ SV192 ) )
= $false )
| ( ( in @ SV277 @ SV261 )
= $false )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2506]) ).
thf(2560,plain,
! [SV261: $i,SV192: $i,SV277: $i] :
( ( ( ! [SY693: $i] :
~ ( in @ ( ordered_pair @ SV277 @ SY693 ) @ SV192 ) )
= $true )
| ( ( in @ SV277 @ SV261 )
= $true )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2507]) ).
thf(2561,plain,
! [SV261: $i,SV192: $i] :
( ( ( ~ ~ ! [SY695: $i] :
~ ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ SY695 ) @ SV192 )
| ( in @ ( sK61_SY667 @ SV192 @ SV261 ) @ SV261 ) )
= $false )
| ( ( in @ ( sK61_SY667 @ SV192 @ SV261 ) @ SV261 )
= $true )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2508]) ).
thf(2562,plain,
! [SV293: $i,SV261: $i,SV192: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ SV293 ) @ SV192 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY695: $i] :
~ ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ SY695 ) @ SV192 )
| ( in @ ( sK61_SY667 @ SV192 @ SV261 ) @ SV261 ) ) )
= $true )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2509]) ).
thf(2563,plain,
! [SV193: $i,SV236: $i,SV276: $i,SV254: $i] :
( ( ( ~ ~ ! [SY711: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK69_SY684 @ SV254 @ SV276 @ SV236 @ SV193 ) @ SV193 )
| ~ ( in @ SY711 @ SV236 ) )
| ( SV276
!= ( ordered_pair @ ( sK69_SY684 @ SV254 @ SV276 @ SV236 @ SV193 ) @ SY711 ) ) ) )
= $false )
| ( ( in @ SV276 @ SV254 )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2510]) ).
thf(2564,plain,
! [SV254: $i,SV276: $i,SV236: $i,SV193: $i,SV294: $i] :
( ( ( ~ ~ ! [SY712: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV294 @ SV193 )
| ~ ( in @ SY712 @ SV236 ) )
| ( SV276
!= ( ordered_pair @ SV294 @ SY712 ) ) ) )
= $true )
| ( ( in @ SV276 @ SV254 )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2511]) ).
thf(2565,plain,
! [SV254: $i,SV236: $i,SV193: $i] :
( ( ( ~ ~ ! [SY690: $i] :
~ ~ ! [SY691: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY690 @ SV193 )
| ~ ( in @ SY691 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SY690 @ SY691 ) ) ) )
= $false )
| ( ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2512]) ).
thf(2566,plain,
! [SV254: $i,SV193: $i,SV236: $i] :
( ( ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 )
= $false )
| ( ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2512]) ).
thf(2567,plain,
! [SV254: $i,SV236: $i,SV193: $i,SV292: $i] :
( ( ( ~ ! [SY710: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV292 @ SV193 )
| ~ ( in @ SY710 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SV292 @ SY710 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY690: $i] :
~ ~ ! [SY691: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY690 @ SV193 )
| ~ ( in @ SY691 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SY690 @ SY691 ) ) )
| ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 ) ) )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2513]) ).
thf(2568,plain,
! [SV262: $i,SV194: $i,SV278: $i] :
( ( ( ! [SY696: $i] :
~ ( in @ ( ordered_pair @ SY696 @ SV278 ) @ SV194 ) )
= $false )
| ( ( in @ SV278 @ SV262 )
= $false )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2514]) ).
thf(2569,plain,
! [SV262: $i,SV194: $i,SV278: $i] :
( ( ( ! [SY697: $i] :
~ ( in @ ( ordered_pair @ SY697 @ SV278 ) @ SV194 ) )
= $true )
| ( ( in @ SV278 @ SV262 )
= $true )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2515]) ).
thf(2570,plain,
! [SV262: $i,SV194: $i] :
( ( ( ~ ~ ! [SY699: $i] :
~ ( in @ ( ordered_pair @ SY699 @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 )
| ( in @ ( sK62_SY673 @ SV194 @ SV262 ) @ SV262 ) )
= $false )
| ( ( in @ ( sK62_SY673 @ SV194 @ SV262 ) @ SV262 )
= $true )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2516]) ).
thf(2571,plain,
! [SV262: $i,SV194: $i,SV295: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV295 @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY699: $i] :
~ ( in @ ( ordered_pair @ SY699 @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 )
| ( in @ ( sK62_SY673 @ SV194 @ SV262 ) @ SV262 ) ) )
= $true )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2517]) ).
thf(2572,plain,
! [SV196: $i,SV238: $i] :
( ( ( in @ ( sK64_SY628 @ SV238 @ SV196 ) @ SV196 )
= $true )
| ( ( disjoint @ SV196 @ SV238 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2518]) ).
thf(2573,plain,
! [SV196: $i,SV238: $i] :
( ( ( in @ ( sK64_SY628 @ SV238 @ SV196 ) @ SV238 )
= $true )
| ( ( disjoint @ SV196 @ SV238 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2519]) ).
thf(2574,plain,
! [SV196: $i,SV238: $i,SV282: $i] :
( ( ( in @ SV282 @ SV238 )
= $false )
| ( ( in @ SV282 @ SV196 )
= $false )
| ( ( ~ ( disjoint @ SV196 @ SV238 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2520]) ).
thf(2575,plain,
! [SV243: $i,SV155: $i,SV204: $i] :
( ( ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV155 )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV204 ) )
= $true )
| ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV243 )
= $true )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2521]) ).
thf(2576,plain,
! [SV243: $i,SV155: $i,SV204: $i] :
( ( ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV155 )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV204 ) )
= $true )
| ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV155 )
= $false )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2523]) ).
thf(2577,plain,
! [SV243: $i,SV155: $i,SV204: $i] :
( ( ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV155 )
| ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV204 ) )
= $true )
| ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV204 )
= $false )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2525]) ).
thf(2578,plain,
! [SV289: $i,SV157: $i,SV285: $i] :
( ( ( ~ ( ~ ( in @ SV285 @ ( sK46_SY444 @ SV157 ) )
| ~ ( subset @ SV289 @ SV285 ) ) )
= $false )
| ( ( in @ SV289 @ ( sK46_SY444 @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2527]) ).
thf(2579,plain,
! [SV157: $i,SV279: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK70_SY700 @ SV279 @ SV157 ) @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SY713: $i] :
( ~ ( subset @ SY713 @ SV279 )
| ( in @ SY713 @ ( sK70_SY700 @ SV279 @ SV157 ) ) ) ) )
= $false )
| ( ( in @ SV279 @ ( sK46_SY444 @ SV157 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2528]) ).
thf(2580,plain,
! [SV157: $i,SV266: $i] :
( ( ( are_equipotent @ SV266 @ ( sK46_SY444 @ SV157 ) )
= $true )
| ( ( subset @ SV266 @ ( sK46_SY444 @ SV157 ) )
= $false )
| ( ( ~ ~ ( in @ SV266 @ ( sK46_SY444 @ SV157 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2529]) ).
thf(2581,plain,
! [SV168: $i,SV215: $i,SV286: $i] :
( ( ( ~ ( in @ SV286 @ SV215 )
| ! [SY705: $i] :
( ~ ( in @ SY705 @ SV168 )
| ( in @ SV286 @ SY705 ) ) )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $false )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2530]) ).
thf(2582,plain,
! [SV215: $i,SV286: $i,SV168: $i] :
( ( ( ~ ! [SY706: $i] :
( ~ ( in @ SY706 @ SV168 )
| ( in @ SV286 @ SY706 ) )
| ( in @ SV286 @ SV215 ) )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $false )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2531]) ).
thf(2583,plain,
! [SV215: $i,SV168: $i] :
( ( ( ~ ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV215 )
| ! [SY707: $i] :
( ~ ( in @ SY707 @ SV168 )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SY707 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY708: $i] :
( ~ ( in @ SY708 @ SV168 )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SY708 ) )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV215 ) ) )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2532]) ).
thf(2584,plain,
! [SV169: $i,SV216: $i,SV268: $i] :
( ( ( ~ ( in @ SV268 @ ( sK68_SY680 @ SV216 @ SV169 @ SV268 ) )
| ~ ( in @ ( sK68_SY680 @ SV216 @ SV169 @ SV268 ) @ SV169 ) )
= $false )
| ( ( in @ SV268 @ SV216 )
= $false )
| ( ( SV216
= ( union @ SV169 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2533]) ).
thf(2585,plain,
! [SV216: $i,SV169: $i,SV290: $i,SV268: $i] :
( ( ( ~ ( in @ SV268 @ SV290 )
| ~ ( in @ SV290 @ SV169 ) )
= $true )
| ( ( in @ SV268 @ SV216 )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2534]) ).
thf(2586,plain,
! [SV216: $i,SV169: $i] :
( ( ( ! [SY683: $i] :
~ ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SY683 )
| ~ ( in @ SY683 @ SV169 ) ) )
= $false )
| ( ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV216 )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2535]) ).
thf(2587,plain,
! [SV287: $i,SV216: $i,SV169: $i] :
( ( ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV287 ) )
= $true )
| ( ( ~ ( in @ SV287 @ SV169 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY683: $i] :
~ ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SY683 )
| ~ ( in @ SY683 @ SV169 ) )
| ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV216 ) ) )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2536]) ).
thf(2588,plain,
! [SV246: $i,SV170: $i,SV217: $i] :
( ( ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV170 )
| ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV217 ) )
= $true )
| ( ( in @ ( sK57_SY643 @ SV217 @ SV170 @ SV246 ) @ SV246 )
= $true )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2537]) ).
thf(2589,plain,
! [SV246: $i,SV170: $i,SV217: $i] :
( ( ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV170 )
| ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV217 ) )
= $true )
| ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV170 )
= $false )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2539]) ).
thf(2590,plain,
! [SV246: $i,SV170: $i,SV217: $i] :
( ( ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV170 )
| ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV217 ) )
= $true )
| ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV217 )
= $false )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2541]) ).
thf(2591,plain,
! [SV291: $i,SV177: $i,SV288: $i] :
( ( ( ~ ( ~ ( in @ SV288 @ ( sK47_SY499 @ SV177 ) )
| ~ ( subset @ SV291 @ SV288 ) ) )
= $false )
| ( ( in @ SV291 @ ( sK47_SY499 @ SV177 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2544]) ).
thf(2592,plain,
! [SV177: $i,SV270: $i] :
( ( ( are_equipotent @ SV270 @ ( sK47_SY499 @ SV177 ) )
= $true )
| ( ( subset @ SV270 @ ( sK47_SY499 @ SV177 ) )
= $false )
| ( ( ~ ~ ( in @ SV270 @ ( sK47_SY499 @ SV177 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2545]) ).
thf(2593,plain,
! [SV225: $i,SV249: $i,SV180: $i,SV274: $i] :
( ( ( in @ SV274 @ SV180 )
= $true )
| ( ( in @ SV274 @ SV249 )
= $false )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2546]) ).
thf(2594,plain,
! [SV180: $i,SV249: $i,SV225: $i,SV274: $i] :
( ( ( in @ SV274 @ SV225 )
= $true )
| ( ( in @ SV274 @ SV249 )
= $false )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2547]) ).
thf(2595,plain,
! [SV249: $i,SV225: $i,SV180: $i,SV274: $i] :
( ( ( in @ SV274 @ SV180 )
= $false )
| ( ( ~ ( in @ SV274 @ SV225 ) )
= $true )
| ( ( in @ SV274 @ SV249 )
= $true )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2548]) ).
thf(2596,plain,
! [SV249: $i,SV180: $i,SV225: $i] :
( ( ( ~ ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
| ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 ) ) )
= $true )
| ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV249 )
= $true )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2549]) ).
thf(2597,plain,
! [SV249: $i,SV180: $i,SV225: $i] :
( ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 )
= $false )
| ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
| ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 ) )
| ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV249 ) ) )
= $true )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2551]) ).
thf(2598,plain,
! [SV229: $i,SV250: $i,SV184: $i,SV275: $i] :
( ( ( in @ SV275 @ SV184 )
= $true )
| ( ( in @ SV275 @ SV250 )
= $false )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2552]) ).
thf(2599,plain,
! [SV184: $i,SV250: $i,SV229: $i,SV275: $i] :
( ( ( ~ ( in @ SV275 @ SV229 ) )
= $true )
| ( ( in @ SV275 @ SV250 )
= $false )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2553]) ).
thf(2600,plain,
! [SV250: $i,SV229: $i,SV184: $i,SV275: $i] :
( ( ( in @ SV275 @ SV184 )
= $false )
| ( ( ~ ~ ( in @ SV275 @ SV229 ) )
= $true )
| ( ( in @ SV275 @ SV250 )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2554]) ).
thf(2601,plain,
! [SV250: $i,SV184: $i,SV229: $i] :
( ( ( ~ ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
| ~ ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 ) ) )
= $true )
| ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV250 )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2555]) ).
thf(2602,plain,
! [SV250: $i,SV184: $i,SV229: $i] :
( ( ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 ) )
= $false )
| ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
| ~ ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 ) )
| ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV250 ) ) )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2557]) ).
thf(2603,plain,
! [SV192: $i,SV261: $i,SV277: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV277 @ ( sK71_SY692 @ SV261 @ SV192 @ SV277 ) ) @ SV192 ) )
= $false )
| ( ( in @ SV277 @ SV261 )
= $false )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2559]) ).
thf(2604,plain,
! [SV261: $i,SV192: $i,SV296: $i,SV277: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV277 @ SV296 ) @ SV192 ) )
= $true )
| ( ( in @ SV277 @ SV261 )
= $true )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2560]) ).
thf(2605,plain,
! [SV261: $i,SV192: $i] :
( ( ( ~ ~ ! [SY695: $i] :
~ ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ SY695 ) @ SV192 ) )
= $false )
| ( ( in @ ( sK61_SY667 @ SV192 @ SV261 ) @ SV261 )
= $true )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2561]) ).
thf(2606,plain,
! [SV261: $i,SV192: $i] :
( ( ( in @ ( sK61_SY667 @ SV192 @ SV261 ) @ SV261 )
= $false )
| ( ( in @ ( sK61_SY667 @ SV192 @ SV261 ) @ SV261 )
= $true )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2561]) ).
thf(2607,plain,
! [SV293: $i,SV261: $i,SV192: $i] :
( ( ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ SV293 ) @ SV192 )
= $false )
| ( ( ~ ( ~ ~ ! [SY695: $i] :
~ ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ SY695 ) @ SV192 )
| ( in @ ( sK61_SY667 @ SV192 @ SV261 ) @ SV261 ) ) )
= $true )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2562]) ).
thf(2608,plain,
! [SV193: $i,SV236: $i,SV276: $i,SV254: $i] :
( ( ( ~ ! [SY711: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK69_SY684 @ SV254 @ SV276 @ SV236 @ SV193 ) @ SV193 )
| ~ ( in @ SY711 @ SV236 ) )
| ( SV276
!= ( ordered_pair @ ( sK69_SY684 @ SV254 @ SV276 @ SV236 @ SV193 ) @ SY711 ) ) ) )
= $true )
| ( ( in @ SV276 @ SV254 )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2563]) ).
thf(2609,plain,
! [SV254: $i,SV276: $i,SV236: $i,SV193: $i,SV294: $i] :
( ( ( ~ ! [SY712: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV294 @ SV193 )
| ~ ( in @ SY712 @ SV236 ) )
| ( SV276
!= ( ordered_pair @ SV294 @ SY712 ) ) ) )
= $false )
| ( ( in @ SV276 @ SV254 )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2564]) ).
thf(2610,plain,
! [SV254: $i,SV236: $i,SV193: $i] :
( ( ( ~ ! [SY690: $i] :
~ ~ ! [SY691: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY690 @ SV193 )
| ~ ( in @ SY691 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SY690 @ SY691 ) ) ) )
= $true )
| ( ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2565]) ).
thf(2611,plain,
! [SV254: $i,SV236: $i,SV193: $i,SV292: $i] :
( ( ( ! [SY710: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV292 @ SV193 )
| ~ ( in @ SY710 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SV292 @ SY710 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY690: $i] :
~ ~ ! [SY691: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY690 @ SV193 )
| ~ ( in @ SY691 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SY690 @ SY691 ) ) )
| ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 ) ) )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2567]) ).
thf(2612,plain,
! [SV278: $i,SV194: $i,SV262: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK72_SY696 @ SV262 @ SV194 @ SV278 ) @ SV278 ) @ SV194 ) )
= $false )
| ( ( in @ SV278 @ SV262 )
= $false )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2568]) ).
thf(2613,plain,
! [SV262: $i,SV194: $i,SV278: $i,SV297: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV297 @ SV278 ) @ SV194 ) )
= $true )
| ( ( in @ SV278 @ SV262 )
= $true )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2569]) ).
thf(2614,plain,
! [SV262: $i,SV194: $i] :
( ( ( ~ ~ ! [SY699: $i] :
~ ( in @ ( ordered_pair @ SY699 @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 ) )
= $false )
| ( ( in @ ( sK62_SY673 @ SV194 @ SV262 ) @ SV262 )
= $true )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2570]) ).
thf(2615,plain,
! [SV262: $i,SV194: $i] :
( ( ( in @ ( sK62_SY673 @ SV194 @ SV262 ) @ SV262 )
= $false )
| ( ( in @ ( sK62_SY673 @ SV194 @ SV262 ) @ SV262 )
= $true )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2570]) ).
thf(2616,plain,
! [SV262: $i,SV194: $i,SV295: $i] :
( ( ( in @ ( ordered_pair @ SV295 @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 )
= $false )
| ( ( ~ ( ~ ~ ! [SY699: $i] :
~ ( in @ ( ordered_pair @ SY699 @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 )
| ( in @ ( sK62_SY673 @ SV194 @ SV262 ) @ SV262 ) ) )
= $true )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2571]) ).
thf(2617,plain,
! [SV282: $i,SV238: $i,SV196: $i] :
( ( ( disjoint @ SV196 @ SV238 )
= $false )
| ( ( in @ SV282 @ SV196 )
= $false )
| ( ( in @ SV282 @ SV238 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2574]) ).
thf(2618,plain,
! [SV243: $i,SV155: $i,SV204: $i] :
( ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV155 )
= $true )
| ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV204 )
= $true )
| ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV243 )
= $true )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2575]) ).
thf(2619,plain,
! [SV243: $i,SV155: $i,SV204: $i] :
( ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV155 )
= $true )
| ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV204 )
= $true )
| ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV155 )
= $false )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2576]) ).
thf(2620,plain,
! [SV243: $i,SV155: $i,SV204: $i] :
( ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV155 )
= $true )
| ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV204 )
= $true )
| ( ( in @ ( sK56_SY634 @ SV204 @ SV155 @ SV243 ) @ SV204 )
= $false )
| ( ( SV243
= ( set_union2 @ SV155 @ SV204 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2577]) ).
thf(2621,plain,
! [SV289: $i,SV157: $i,SV285: $i] :
( ( ( ~ ( in @ SV285 @ ( sK46_SY444 @ SV157 ) )
| ~ ( subset @ SV289 @ SV285 ) )
= $true )
| ( ( in @ SV289 @ ( sK46_SY444 @ SV157 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2578]) ).
thf(2622,plain,
! [SV157: $i,SV279: $i] :
( ( ( ~ ( ~ ( in @ ( sK70_SY700 @ SV279 @ SV157 ) @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SY713: $i] :
( ~ ( subset @ SY713 @ SV279 )
| ( in @ SY713 @ ( sK70_SY700 @ SV279 @ SV157 ) ) ) ) )
= $true )
| ( ( in @ SV279 @ ( sK46_SY444 @ SV157 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2579]) ).
thf(2623,plain,
! [SV157: $i,SV266: $i] :
( ( ( ~ ( in @ SV266 @ ( sK46_SY444 @ SV157 ) ) )
= $false )
| ( ( subset @ SV266 @ ( sK46_SY444 @ SV157 ) )
= $false )
| ( ( are_equipotent @ SV266 @ ( sK46_SY444 @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2580]) ).
thf(2624,plain,
! [SV168: $i,SV215: $i,SV286: $i] :
( ( ( ~ ( in @ SV286 @ SV215 ) )
= $true )
| ( ( ! [SY705: $i] :
( ~ ( in @ SY705 @ SV168 )
| ( in @ SV286 @ SY705 ) ) )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $false )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2581]) ).
thf(2625,plain,
! [SV215: $i,SV286: $i,SV168: $i] :
( ( ( ~ ! [SY706: $i] :
( ~ ( in @ SY706 @ SV168 )
| ( in @ SV286 @ SY706 ) ) )
= $true )
| ( ( in @ SV286 @ SV215 )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $false )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2582]) ).
thf(2626,plain,
! [SV215: $i,SV168: $i] :
( ( ( ~ ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV215 ) )
= $false )
| ( ( ~ ( ~ ! [SY708: $i] :
( ~ ( in @ SY708 @ SV168 )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SY708 ) )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV215 ) ) )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2583]) ).
thf(2627,plain,
! [SV215: $i,SV168: $i] :
( ( ( ! [SY707: $i] :
( ~ ( in @ SY707 @ SV168 )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SY707 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY708: $i] :
( ~ ( in @ SY708 @ SV168 )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SY708 ) )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV215 ) ) )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2583]) ).
thf(2628,plain,
! [SV169: $i,SV216: $i,SV268: $i] :
( ( ( ~ ( in @ SV268 @ ( sK68_SY680 @ SV216 @ SV169 @ SV268 ) ) )
= $false )
| ( ( in @ SV268 @ SV216 )
= $false )
| ( ( SV216
= ( union @ SV169 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2584]) ).
thf(2629,plain,
! [SV268: $i,SV169: $i,SV216: $i] :
( ( ( ~ ( in @ ( sK68_SY680 @ SV216 @ SV169 @ SV268 ) @ SV169 ) )
= $false )
| ( ( in @ SV268 @ SV216 )
= $false )
| ( ( SV216
= ( union @ SV169 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2584]) ).
thf(2630,plain,
! [SV216: $i,SV169: $i,SV290: $i,SV268: $i] :
( ( ( ~ ( in @ SV268 @ SV290 ) )
= $true )
| ( ( ~ ( in @ SV290 @ SV169 ) )
= $true )
| ( ( in @ SV268 @ SV216 )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2585]) ).
thf(2631,plain,
! [SV216: $i,SV169: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ ( sK73_SY683 @ SV216 @ SV169 ) )
| ~ ( in @ ( sK73_SY683 @ SV216 @ SV169 ) @ SV169 ) ) )
= $false )
| ( ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV216 )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2586]) ).
thf(2632,plain,
! [SV287: $i,SV216: $i,SV169: $i] :
( ( ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV287 )
= $false )
| ( ( ~ ( in @ SV287 @ SV169 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY683: $i] :
~ ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SY683 )
| ~ ( in @ SY683 @ SV169 ) )
| ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV216 ) ) )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2587]) ).
thf(2633,plain,
! [SV246: $i,SV170: $i,SV217: $i] :
( ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV170 )
= $true )
| ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV217 )
= $true )
| ( ( in @ ( sK57_SY643 @ SV217 @ SV170 @ SV246 ) @ SV246 )
= $true )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2588]) ).
thf(2634,plain,
! [SV246: $i,SV170: $i,SV217: $i] :
( ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV170 )
= $true )
| ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV217 )
= $true )
| ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV170 )
= $false )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2589]) ).
thf(2635,plain,
! [SV246: $i,SV170: $i,SV217: $i] :
( ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV170 )
= $true )
| ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV217 )
= $true )
| ( ( ( sK57_SY643 @ SV217 @ SV170 @ SV246 )
= SV217 )
= $false )
| ( ( SV246
= ( unordered_pair @ SV170 @ SV217 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2590]) ).
thf(2636,plain,
! [SV291: $i,SV177: $i,SV288: $i] :
( ( ( ~ ( in @ SV288 @ ( sK47_SY499 @ SV177 ) )
| ~ ( subset @ SV291 @ SV288 ) )
= $true )
| ( ( in @ SV291 @ ( sK47_SY499 @ SV177 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2591]) ).
thf(2637,plain,
! [SV177: $i,SV270: $i] :
( ( ( ~ ( in @ SV270 @ ( sK47_SY499 @ SV177 ) ) )
= $false )
| ( ( subset @ SV270 @ ( sK47_SY499 @ SV177 ) )
= $false )
| ( ( are_equipotent @ SV270 @ ( sK47_SY499 @ SV177 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2592]) ).
thf(2638,plain,
! [SV249: $i,SV180: $i,SV225: $i,SV274: $i] :
( ( ( in @ SV274 @ SV225 )
= $false )
| ( ( in @ SV274 @ SV180 )
= $false )
| ( ( in @ SV274 @ SV249 )
= $true )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2595]) ).
thf(2639,plain,
! [SV249: $i,SV180: $i,SV225: $i] :
( ( ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
| ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 ) )
= $false )
| ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV249 )
= $true )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2596]) ).
thf(2640,plain,
! [SV249: $i,SV180: $i,SV225: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
| ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 ) )
| ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV249 ) )
= $false )
| ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
= $false )
| ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 )
= $false )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2597]) ).
thf(2641,plain,
! [SV184: $i,SV250: $i,SV229: $i,SV275: $i] :
( ( ( in @ SV275 @ SV229 )
= $false )
| ( ( in @ SV275 @ SV250 )
= $false )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2599]) ).
thf(2642,plain,
! [SV250: $i,SV184: $i,SV229: $i,SV275: $i] :
( ( ( ~ ( in @ SV275 @ SV229 ) )
= $false )
| ( ( in @ SV275 @ SV184 )
= $false )
| ( ( in @ SV275 @ SV250 )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2600]) ).
thf(2643,plain,
! [SV250: $i,SV184: $i,SV229: $i] :
( ( ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
| ~ ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 ) )
= $false )
| ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV250 )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2601]) ).
thf(2644,plain,
! [SV250: $i,SV184: $i,SV229: $i] :
( ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 )
= $true )
| ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
| ~ ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 ) )
| ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV250 ) ) )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2602]) ).
thf(2645,plain,
! [SV192: $i,SV261: $i,SV277: $i] :
( ( ( in @ ( ordered_pair @ SV277 @ ( sK71_SY692 @ SV261 @ SV192 @ SV277 ) ) @ SV192 )
= $true )
| ( ( in @ SV277 @ SV261 )
= $false )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2603]) ).
thf(2646,plain,
! [SV261: $i,SV192: $i,SV296: $i,SV277: $i] :
( ( ( in @ ( ordered_pair @ SV277 @ SV296 ) @ SV192 )
= $false )
| ( ( in @ SV277 @ SV261 )
= $true )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2604]) ).
thf(2647,plain,
! [SV261: $i,SV192: $i] :
( ( ( ~ ! [SY695: $i] :
~ ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ SY695 ) @ SV192 ) )
= $true )
| ( ( in @ ( sK61_SY667 @ SV192 @ SV261 ) @ SV261 )
= $true )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2605]) ).
thf(2648,plain,
! [SV293: $i,SV261: $i,SV192: $i] :
( ( ( ~ ~ ! [SY695: $i] :
~ ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ SY695 ) @ SV192 )
| ( in @ ( sK61_SY667 @ SV192 @ SV261 ) @ SV261 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ SV293 ) @ SV192 )
= $false )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2607]) ).
thf(2649,plain,
! [SV193: $i,SV236: $i,SV276: $i,SV254: $i] :
( ( ( ! [SY711: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK69_SY684 @ SV254 @ SV276 @ SV236 @ SV193 ) @ SV193 )
| ~ ( in @ SY711 @ SV236 ) )
| ( SV276
!= ( ordered_pair @ ( sK69_SY684 @ SV254 @ SV276 @ SV236 @ SV193 ) @ SY711 ) ) ) )
= $false )
| ( ( in @ SV276 @ SV254 )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2608]) ).
thf(2650,plain,
! [SV254: $i,SV276: $i,SV236: $i,SV193: $i,SV294: $i] :
( ( ( ! [SY712: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV294 @ SV193 )
| ~ ( in @ SY712 @ SV236 ) )
| ( SV276
!= ( ordered_pair @ SV294 @ SY712 ) ) ) )
= $true )
| ( ( in @ SV276 @ SV254 )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2609]) ).
thf(2651,plain,
! [SV254: $i,SV236: $i,SV193: $i] :
( ( ( ! [SY690: $i] :
~ ~ ! [SY691: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY690 @ SV193 )
| ~ ( in @ SY691 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SY690 @ SY691 ) ) ) )
= $false )
| ( ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2610]) ).
thf(2652,plain,
! [SV254: $i,SV236: $i,SV298: $i,SV193: $i,SV292: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV292 @ SV193 )
| ~ ( in @ SV298 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SV292 @ SV298 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY690: $i] :
~ ~ ! [SY691: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY690 @ SV193 )
| ~ ( in @ SY691 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SY690 @ SY691 ) ) )
| ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 ) ) )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2611]) ).
thf(2653,plain,
! [SV278: $i,SV194: $i,SV262: $i] :
( ( ( in @ ( ordered_pair @ ( sK72_SY696 @ SV262 @ SV194 @ SV278 ) @ SV278 ) @ SV194 )
= $true )
| ( ( in @ SV278 @ SV262 )
= $false )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2612]) ).
thf(2654,plain,
! [SV262: $i,SV194: $i,SV278: $i,SV297: $i] :
( ( ( in @ ( ordered_pair @ SV297 @ SV278 ) @ SV194 )
= $false )
| ( ( in @ SV278 @ SV262 )
= $true )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2613]) ).
thf(2655,plain,
! [SV262: $i,SV194: $i] :
( ( ( ~ ! [SY699: $i] :
~ ( in @ ( ordered_pair @ SY699 @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 ) )
= $true )
| ( ( in @ ( sK62_SY673 @ SV194 @ SV262 ) @ SV262 )
= $true )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2614]) ).
thf(2656,plain,
! [SV295: $i,SV262: $i,SV194: $i] :
( ( ( ~ ~ ! [SY699: $i] :
~ ( in @ ( ordered_pair @ SY699 @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 )
| ( in @ ( sK62_SY673 @ SV194 @ SV262 ) @ SV262 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV295 @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 )
= $false )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2616]) ).
thf(2657,plain,
! [SV289: $i,SV157: $i,SV285: $i] :
( ( ( ~ ( in @ SV285 @ ( sK46_SY444 @ SV157 ) ) )
= $true )
| ( ( ~ ( subset @ SV289 @ SV285 ) )
= $true )
| ( ( in @ SV289 @ ( sK46_SY444 @ SV157 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2621]) ).
thf(2658,plain,
! [SV157: $i,SV279: $i] :
( ( ( ~ ( in @ ( sK70_SY700 @ SV279 @ SV157 ) @ ( sK46_SY444 @ SV157 ) )
| ~ ! [SY713: $i] :
( ~ ( subset @ SY713 @ SV279 )
| ( in @ SY713 @ ( sK70_SY700 @ SV279 @ SV157 ) ) ) )
= $false )
| ( ( in @ SV279 @ ( sK46_SY444 @ SV157 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2622]) ).
thf(2659,plain,
! [SV157: $i,SV266: $i] :
( ( ( in @ SV266 @ ( sK46_SY444 @ SV157 ) )
= $true )
| ( ( subset @ SV266 @ ( sK46_SY444 @ SV157 ) )
= $false )
| ( ( are_equipotent @ SV266 @ ( sK46_SY444 @ SV157 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2623]) ).
thf(2660,plain,
! [SV168: $i,SV215: $i,SV286: $i] :
( ( ( in @ SV286 @ SV215 )
= $false )
| ( ( ! [SY705: $i] :
( ~ ( in @ SY705 @ SV168 )
| ( in @ SV286 @ SY705 ) ) )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $false )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2624]) ).
thf(2661,plain,
! [SV215: $i,SV286: $i,SV168: $i] :
( ( ( ! [SY706: $i] :
( ~ ( in @ SY706 @ SV168 )
| ( in @ SV286 @ SY706 ) ) )
= $false )
| ( ( in @ SV286 @ SV215 )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $false )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2625]) ).
thf(2662,plain,
! [SV215: $i,SV168: $i] :
( ( ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV215 )
= $true )
| ( ( ~ ( ~ ! [SY708: $i] :
( ~ ( in @ SY708 @ SV168 )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SY708 ) )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV215 ) ) )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2626]) ).
thf(2663,plain,
! [SV168: $i,SV215: $i] :
( ( ( ~ ( in @ ( sK74_SY707 @ SV215 @ SV168 ) @ SV168 )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ ( sK74_SY707 @ SV215 @ SV168 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY708: $i] :
( ~ ( in @ SY708 @ SV168 )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SY708 ) )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV215 ) ) )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2627]) ).
thf(2664,plain,
! [SV169: $i,SV216: $i,SV268: $i] :
( ( ( in @ SV268 @ ( sK68_SY680 @ SV216 @ SV169 @ SV268 ) )
= $true )
| ( ( in @ SV268 @ SV216 )
= $false )
| ( ( SV216
= ( union @ SV169 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2628]) ).
thf(2665,plain,
! [SV268: $i,SV169: $i,SV216: $i] :
( ( ( in @ ( sK68_SY680 @ SV216 @ SV169 @ SV268 ) @ SV169 )
= $true )
| ( ( in @ SV268 @ SV216 )
= $false )
| ( ( SV216
= ( union @ SV169 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2629]) ).
thf(2666,plain,
! [SV216: $i,SV169: $i,SV290: $i,SV268: $i] :
( ( ( in @ SV268 @ SV290 )
= $false )
| ( ( ~ ( in @ SV290 @ SV169 ) )
= $true )
| ( ( in @ SV268 @ SV216 )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2630]) ).
thf(2667,plain,
! [SV216: $i,SV169: $i] :
( ( ( ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ ( sK73_SY683 @ SV216 @ SV169 ) )
| ~ ( in @ ( sK73_SY683 @ SV216 @ SV169 ) @ SV169 ) ) )
= $true )
| ( ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV216 )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2631]) ).
thf(2668,plain,
! [SV216: $i,SV169: $i,SV287: $i] :
( ( ( in @ SV287 @ SV169 )
= $false )
| ( ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV287 )
= $false )
| ( ( ~ ( ~ ~ ! [SY683: $i] :
~ ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SY683 )
| ~ ( in @ SY683 @ SV169 ) )
| ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV216 ) ) )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2632]) ).
thf(2669,plain,
! [SV291: $i,SV177: $i,SV288: $i] :
( ( ( ~ ( in @ SV288 @ ( sK47_SY499 @ SV177 ) ) )
= $true )
| ( ( ~ ( subset @ SV291 @ SV288 ) )
= $true )
| ( ( in @ SV291 @ ( sK47_SY499 @ SV177 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2636]) ).
thf(2670,plain,
! [SV177: $i,SV270: $i] :
( ( ( in @ SV270 @ ( sK47_SY499 @ SV177 ) )
= $true )
| ( ( subset @ SV270 @ ( sK47_SY499 @ SV177 ) )
= $false )
| ( ( are_equipotent @ SV270 @ ( sK47_SY499 @ SV177 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2637]) ).
thf(2671,plain,
! [SV249: $i,SV180: $i,SV225: $i] :
( ( ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 ) )
= $false )
| ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV249 )
= $true )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2639]) ).
thf(2672,plain,
! [SV249: $i,SV180: $i,SV225: $i] :
( ( ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 ) )
= $false )
| ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV249 )
= $true )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2639]) ).
thf(2673,plain,
! [SV249: $i,SV180: $i,SV225: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
| ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 ) ) )
= $false )
| ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
= $false )
| ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 )
= $false )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2640]) ).
thf(2674,plain,
! [SV249: $i,SV180: $i,SV225: $i] :
( ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV249 )
= $false )
| ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
= $false )
| ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 )
= $false )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2640]) ).
thf(2675,plain,
! [SV250: $i,SV184: $i,SV229: $i,SV275: $i] :
( ( ( in @ SV275 @ SV229 )
= $true )
| ( ( in @ SV275 @ SV184 )
= $false )
| ( ( in @ SV275 @ SV250 )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2642]) ).
thf(2676,plain,
! [SV250: $i,SV184: $i,SV229: $i] :
( ( ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 ) )
= $false )
| ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV250 )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2643]) ).
thf(2677,plain,
! [SV250: $i,SV184: $i,SV229: $i] :
( ( ( ~ ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 ) )
= $false )
| ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV250 )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2643]) ).
thf(2678,plain,
! [SV250: $i,SV184: $i,SV229: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
| ~ ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 ) )
| ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV250 ) )
= $false )
| ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
= $false )
| ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2644]) ).
thf(2679,plain,
! [SV261: $i,SV192: $i] :
( ( ( ! [SY695: $i] :
~ ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ SY695 ) @ SV192 ) )
= $false )
| ( ( in @ ( sK61_SY667 @ SV192 @ SV261 ) @ SV261 )
= $true )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2647]) ).
thf(2680,plain,
! [SV293: $i,SV261: $i,SV192: $i] :
( ( ( ~ ~ ! [SY695: $i] :
~ ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ SY695 ) @ SV192 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ SV293 ) @ SV192 )
= $false )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2648]) ).
thf(2681,plain,
! [SV293: $i,SV261: $i,SV192: $i] :
( ( ( in @ ( sK61_SY667 @ SV192 @ SV261 ) @ SV261 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ SV293 ) @ SV192 )
= $false )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2648]) ).
thf(2682,plain,
! [SV193: $i,SV236: $i,SV276: $i,SV254: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK69_SY684 @ SV254 @ SV276 @ SV236 @ SV193 ) @ SV193 )
| ~ ( in @ ( sK75_SY711 @ SV193 @ SV236 @ SV276 @ SV254 ) @ SV236 ) )
| ( SV276
!= ( ordered_pair @ ( sK69_SY684 @ SV254 @ SV276 @ SV236 @ SV193 ) @ ( sK75_SY711 @ SV193 @ SV236 @ SV276 @ SV254 ) ) ) ) )
= $false )
| ( ( in @ SV276 @ SV254 )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2649]) ).
thf(2683,plain,
! [SV254: $i,SV276: $i,SV236: $i,SV299: $i,SV193: $i,SV294: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV294 @ SV193 )
| ~ ( in @ SV299 @ SV236 ) )
| ( SV276
!= ( ordered_pair @ SV294 @ SV299 ) ) ) )
= $true )
| ( ( in @ SV276 @ SV254 )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2650]) ).
thf(2684,plain,
! [SV193: $i,SV236: $i,SV254: $i] :
( ( ( ~ ~ ! [SY714: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK76_SY690 @ SV254 @ SV236 @ SV193 ) @ SV193 )
| ~ ( in @ SY714 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ ( sK76_SY690 @ SV254 @ SV236 @ SV193 ) @ SY714 ) ) ) )
= $false )
| ( ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2651]) ).
thf(2685,plain,
! [SV254: $i,SV236: $i,SV298: $i,SV193: $i,SV292: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV292 @ SV193 )
| ~ ( in @ SV298 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SV292 @ SV298 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY690: $i] :
~ ~ ! [SY691: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY690 @ SV193 )
| ~ ( in @ SY691 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SY690 @ SY691 ) ) )
| ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 ) ) )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2652]) ).
thf(2686,plain,
! [SV262: $i,SV194: $i] :
( ( ( ! [SY699: $i] :
~ ( in @ ( ordered_pair @ SY699 @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 ) )
= $false )
| ( ( in @ ( sK62_SY673 @ SV194 @ SV262 ) @ SV262 )
= $true )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2655]) ).
thf(2687,plain,
! [SV295: $i,SV262: $i,SV194: $i] :
( ( ( ~ ~ ! [SY699: $i] :
~ ( in @ ( ordered_pair @ SY699 @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV295 @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 )
= $false )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2656]) ).
thf(2688,plain,
! [SV295: $i,SV262: $i,SV194: $i] :
( ( ( in @ ( sK62_SY673 @ SV194 @ SV262 ) @ SV262 )
= $false )
| ( ( in @ ( ordered_pair @ SV295 @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 )
= $false )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2656]) ).
thf(2689,plain,
! [SV289: $i,SV157: $i,SV285: $i] :
( ( ( in @ SV285 @ ( sK46_SY444 @ SV157 ) )
= $false )
| ( ( ~ ( subset @ SV289 @ SV285 ) )
= $true )
| ( ( in @ SV289 @ ( sK46_SY444 @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2657]) ).
thf(2690,plain,
! [SV157: $i,SV279: $i] :
( ( ( ~ ( in @ ( sK70_SY700 @ SV279 @ SV157 ) @ ( sK46_SY444 @ SV157 ) ) )
= $false )
| ( ( in @ SV279 @ ( sK46_SY444 @ SV157 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2658]) ).
thf(2691,plain,
! [SV157: $i,SV279: $i] :
( ( ( ~ ! [SY713: $i] :
( ~ ( subset @ SY713 @ SV279 )
| ( in @ SY713 @ ( sK70_SY700 @ SV279 @ SV157 ) ) ) )
= $false )
| ( ( in @ SV279 @ ( sK46_SY444 @ SV157 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2658]) ).
thf(2692,plain,
! [SV215: $i,SV286: $i,SV168: $i,SV300: $i] :
( ( ( ~ ( in @ SV300 @ SV168 )
| ( in @ SV286 @ SV300 ) )
= $true )
| ( ( in @ SV286 @ SV215 )
= $false )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $false )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2660]) ).
thf(2693,plain,
! [SV168: $i,SV286: $i,SV215: $i] :
( ( ( ~ ( in @ ( sK77_SY706 @ SV215 @ SV286 @ SV168 ) @ SV168 )
| ( in @ SV286 @ ( sK77_SY706 @ SV215 @ SV286 @ SV168 ) ) )
= $false )
| ( ( in @ SV286 @ SV215 )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $false )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2661]) ).
thf(2694,plain,
! [SV215: $i,SV168: $i] :
( ( ( ~ ! [SY708: $i] :
( ~ ( in @ SY708 @ SV168 )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SY708 ) )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV215 ) )
= $false )
| ( ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV215 )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2662]) ).
thf(2695,plain,
! [SV168: $i,SV215: $i] :
( ( ( ~ ( in @ ( sK74_SY707 @ SV215 @ SV168 ) @ SV168 ) )
= $false )
| ( ( ~ ( ~ ! [SY708: $i] :
( ~ ( in @ SY708 @ SV168 )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SY708 ) )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV215 ) ) )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2663]) ).
thf(2696,plain,
! [SV215: $i,SV168: $i] :
( ( ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ ( sK74_SY707 @ SV215 @ SV168 ) )
= $false )
| ( ( ~ ( ~ ! [SY708: $i] :
( ~ ( in @ SY708 @ SV168 )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SY708 ) )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV215 ) ) )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2663]) ).
thf(2697,plain,
! [SV216: $i,SV268: $i,SV169: $i,SV290: $i] :
( ( ( in @ SV290 @ SV169 )
= $false )
| ( ( in @ SV268 @ SV290 )
= $false )
| ( ( in @ SV268 @ SV216 )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2666]) ).
thf(2698,plain,
! [SV216: $i,SV169: $i] :
( ( ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ ( sK73_SY683 @ SV216 @ SV169 ) )
| ~ ( in @ ( sK73_SY683 @ SV216 @ SV169 ) @ SV169 ) )
= $false )
| ( ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV216 )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2667]) ).
thf(2699,plain,
! [SV287: $i,SV216: $i,SV169: $i] :
( ( ( ~ ~ ! [SY683: $i] :
~ ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SY683 )
| ~ ( in @ SY683 @ SV169 ) )
| ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV216 ) )
= $false )
| ( ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV287 )
= $false )
| ( ( in @ SV287 @ SV169 )
= $false )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2668]) ).
thf(2700,plain,
! [SV291: $i,SV177: $i,SV288: $i] :
( ( ( in @ SV288 @ ( sK47_SY499 @ SV177 ) )
= $false )
| ( ( ~ ( subset @ SV291 @ SV288 ) )
= $true )
| ( ( in @ SV291 @ ( sK47_SY499 @ SV177 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2669]) ).
thf(2701,plain,
! [SV249: $i,SV180: $i,SV225: $i] :
( ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
= $true )
| ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV249 )
= $true )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2671]) ).
thf(2702,plain,
! [SV249: $i,SV180: $i,SV225: $i] :
( ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 )
= $true )
| ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV249 )
= $true )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2672]) ).
thf(2703,plain,
! [SV249: $i,SV180: $i,SV225: $i] :
( ( ( ~ ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
| ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 ) ) )
= $true )
| ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
= $false )
| ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 )
= $false )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2673]) ).
thf(2704,plain,
! [SV250: $i,SV184: $i,SV229: $i] :
( ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
= $true )
| ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV250 )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2676]) ).
thf(2705,plain,
! [SV250: $i,SV184: $i,SV229: $i] :
( ( ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 ) )
= $true )
| ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV250 )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2677]) ).
thf(2706,plain,
! [SV250: $i,SV184: $i,SV229: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
| ~ ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 ) ) )
= $false )
| ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
= $false )
| ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2678]) ).
thf(2707,plain,
! [SV250: $i,SV184: $i,SV229: $i] :
( ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV250 )
= $false )
| ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
= $false )
| ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2678]) ).
thf(2708,plain,
! [SV261: $i,SV192: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ ( sK78_SY695 @ SV261 @ SV192 ) ) @ SV192 ) )
= $false )
| ( ( in @ ( sK61_SY667 @ SV192 @ SV261 ) @ SV261 )
= $true )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2679]) ).
thf(2709,plain,
! [SV293: $i,SV261: $i,SV192: $i] :
( ( ( ~ ! [SY695: $i] :
~ ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ SY695 ) @ SV192 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ SV293 ) @ SV192 )
= $false )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2680]) ).
thf(2710,plain,
! [SV193: $i,SV236: $i,SV276: $i,SV254: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK69_SY684 @ SV254 @ SV276 @ SV236 @ SV193 ) @ SV193 )
| ~ ( in @ ( sK75_SY711 @ SV193 @ SV236 @ SV276 @ SV254 ) @ SV236 ) )
| ( SV276
!= ( ordered_pair @ ( sK69_SY684 @ SV254 @ SV276 @ SV236 @ SV193 ) @ ( sK75_SY711 @ SV193 @ SV236 @ SV276 @ SV254 ) ) ) ) )
= $true )
| ( ( in @ SV276 @ SV254 )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2682]) ).
thf(2711,plain,
! [SV254: $i,SV276: $i,SV236: $i,SV299: $i,SV193: $i,SV294: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV294 @ SV193 )
| ~ ( in @ SV299 @ SV236 ) )
| ( SV276
!= ( ordered_pair @ SV294 @ SV299 ) ) ) )
= $false )
| ( ( in @ SV276 @ SV254 )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2683]) ).
thf(2712,plain,
! [SV193: $i,SV236: $i,SV254: $i] :
( ( ( ~ ! [SY714: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK76_SY690 @ SV254 @ SV236 @ SV193 ) @ SV193 )
| ~ ( in @ SY714 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ ( sK76_SY690 @ SV254 @ SV236 @ SV193 ) @ SY714 ) ) ) )
= $true )
| ( ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2684]) ).
thf(2713,plain,
! [SV254: $i,SV236: $i,SV298: $i,SV193: $i,SV292: $i] :
( ( ( ~ ~ ( ~ ( in @ SV292 @ SV193 )
| ~ ( in @ SV298 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SV292 @ SV298 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY690: $i] :
~ ~ ! [SY691: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY690 @ SV193 )
| ~ ( in @ SY691 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SY690 @ SY691 ) ) )
| ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 ) ) )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2685]) ).
thf(2714,plain,
! [SV194: $i,SV262: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK79_SY699 @ SV262 @ SV194 ) @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 ) )
= $false )
| ( ( in @ ( sK62_SY673 @ SV194 @ SV262 ) @ SV262 )
= $true )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2686]) ).
thf(2715,plain,
! [SV295: $i,SV262: $i,SV194: $i] :
( ( ( ~ ! [SY699: $i] :
~ ( in @ ( ordered_pair @ SY699 @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV295 @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 )
= $false )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2687]) ).
thf(2716,plain,
! [SV157: $i,SV285: $i,SV289: $i] :
( ( ( subset @ SV289 @ SV285 )
= $false )
| ( ( in @ SV285 @ ( sK46_SY444 @ SV157 ) )
= $false )
| ( ( in @ SV289 @ ( sK46_SY444 @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2689]) ).
thf(2717,plain,
! [SV157: $i,SV279: $i] :
( ( ( in @ ( sK70_SY700 @ SV279 @ SV157 ) @ ( sK46_SY444 @ SV157 ) )
= $true )
| ( ( in @ SV279 @ ( sK46_SY444 @ SV157 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2690]) ).
thf(2718,plain,
! [SV157: $i,SV279: $i] :
( ( ( ! [SY713: $i] :
( ~ ( subset @ SY713 @ SV279 )
| ( in @ SY713 @ ( sK70_SY700 @ SV279 @ SV157 ) ) ) )
= $true )
| ( ( in @ SV279 @ ( sK46_SY444 @ SV157 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2691]) ).
thf(2719,plain,
! [SV215: $i,SV286: $i,SV168: $i,SV300: $i] :
( ( ( ~ ( in @ SV300 @ SV168 ) )
= $true )
| ( ( in @ SV286 @ SV300 )
= $true )
| ( ( in @ SV286 @ SV215 )
= $false )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $false )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2692]) ).
thf(2720,plain,
! [SV168: $i,SV286: $i,SV215: $i] :
( ( ( ~ ( in @ ( sK77_SY706 @ SV215 @ SV286 @ SV168 ) @ SV168 ) )
= $false )
| ( ( in @ SV286 @ SV215 )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $false )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2693]) ).
thf(2721,plain,
! [SV168: $i,SV215: $i,SV286: $i] :
( ( ( in @ SV286 @ ( sK77_SY706 @ SV215 @ SV286 @ SV168 ) )
= $false )
| ( ( in @ SV286 @ SV215 )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $false )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2693]) ).
thf(2722,plain,
! [SV215: $i,SV168: $i] :
( ( ( ~ ! [SY708: $i] :
( ~ ( in @ SY708 @ SV168 )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SY708 ) ) )
= $false )
| ( ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV215 )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2694]) ).
thf(2723,plain,
! [SV215: $i,SV168: $i] :
( ( ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV215 )
= $false )
| ( ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV215 )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2694]) ).
thf(2724,plain,
! [SV168: $i,SV215: $i] :
( ( ( in @ ( sK74_SY707 @ SV215 @ SV168 ) @ SV168 )
= $true )
| ( ( ~ ( ~ ! [SY708: $i] :
( ~ ( in @ SY708 @ SV168 )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SY708 ) )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV215 ) ) )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2695]) ).
thf(2725,plain,
! [SV215: $i,SV168: $i] :
( ( ( ~ ! [SY708: $i] :
( ~ ( in @ SY708 @ SV168 )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SY708 ) )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV215 ) )
= $false )
| ( ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ ( sK74_SY707 @ SV215 @ SV168 ) )
= $false )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2696]) ).
thf(2726,plain,
! [SV216: $i,SV169: $i] :
( ( ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ ( sK73_SY683 @ SV216 @ SV169 ) ) )
= $false )
| ( ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV216 )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2698]) ).
thf(2727,plain,
! [SV169: $i,SV216: $i] :
( ( ( ~ ( in @ ( sK73_SY683 @ SV216 @ SV169 ) @ SV169 ) )
= $false )
| ( ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV216 )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2698]) ).
thf(2728,plain,
! [SV287: $i,SV216: $i,SV169: $i] :
( ( ( ~ ~ ! [SY683: $i] :
~ ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SY683 )
| ~ ( in @ SY683 @ SV169 ) ) )
= $false )
| ( ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV287 )
= $false )
| ( ( in @ SV287 @ SV169 )
= $false )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2699]) ).
thf(2729,plain,
! [SV287: $i,SV216: $i,SV169: $i] :
( ( ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV216 )
= $false )
| ( ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV287 )
= $false )
| ( ( in @ SV287 @ SV169 )
= $false )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2699]) ).
thf(2730,plain,
! [SV177: $i,SV288: $i,SV291: $i] :
( ( ( subset @ SV291 @ SV288 )
= $false )
| ( ( in @ SV288 @ ( sK47_SY499 @ SV177 ) )
= $false )
| ( ( in @ SV291 @ ( sK47_SY499 @ SV177 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2700]) ).
thf(2731,plain,
! [SV249: $i,SV180: $i,SV225: $i] :
( ( ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
| ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 ) )
= $false )
| ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
= $false )
| ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 )
= $false )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2703]) ).
thf(2732,plain,
! [SV250: $i,SV184: $i,SV229: $i] :
( ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 )
= $false )
| ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV250 )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2705]) ).
thf(2733,plain,
! [SV250: $i,SV184: $i,SV229: $i] :
( ( ( ~ ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
| ~ ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 ) ) )
= $true )
| ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
= $false )
| ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2706]) ).
thf(2734,plain,
! [SV261: $i,SV192: $i] :
( ( ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ ( sK78_SY695 @ SV261 @ SV192 ) ) @ SV192 )
= $true )
| ( ( in @ ( sK61_SY667 @ SV192 @ SV261 ) @ SV261 )
= $true )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2708]) ).
thf(2735,plain,
! [SV293: $i,SV261: $i,SV192: $i] :
( ( ( ! [SY695: $i] :
~ ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ SY695 ) @ SV192 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ SV293 ) @ SV192 )
= $false )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2709]) ).
thf(2736,plain,
! [SV193: $i,SV236: $i,SV276: $i,SV254: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK69_SY684 @ SV254 @ SV276 @ SV236 @ SV193 ) @ SV193 )
| ~ ( in @ ( sK75_SY711 @ SV193 @ SV236 @ SV276 @ SV254 ) @ SV236 ) )
| ( SV276
!= ( ordered_pair @ ( sK69_SY684 @ SV254 @ SV276 @ SV236 @ SV193 ) @ ( sK75_SY711 @ SV193 @ SV236 @ SV276 @ SV254 ) ) ) )
= $false )
| ( ( in @ SV276 @ SV254 )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2710]) ).
thf(2737,plain,
! [SV254: $i,SV276: $i,SV236: $i,SV299: $i,SV193: $i,SV294: $i] :
( ( ( ~ ~ ( ~ ( in @ SV294 @ SV193 )
| ~ ( in @ SV299 @ SV236 ) )
| ( SV276
!= ( ordered_pair @ SV294 @ SV299 ) ) )
= $true )
| ( ( in @ SV276 @ SV254 )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2711]) ).
thf(2738,plain,
! [SV193: $i,SV236: $i,SV254: $i] :
( ( ( ! [SY714: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK76_SY690 @ SV254 @ SV236 @ SV193 ) @ SV193 )
| ~ ( in @ SY714 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ ( sK76_SY690 @ SV254 @ SV236 @ SV193 ) @ SY714 ) ) ) )
= $false )
| ( ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2712]) ).
thf(2739,plain,
! [SV254: $i,SV236: $i,SV298: $i,SV193: $i,SV292: $i] :
( ( ( ~ ~ ( ~ ( in @ SV292 @ SV193 )
| ~ ( in @ SV298 @ SV236 ) ) )
= $true )
| ( ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SV292 @ SV298 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY690: $i] :
~ ~ ! [SY691: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY690 @ SV193 )
| ~ ( in @ SY691 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SY690 @ SY691 ) ) )
| ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 ) ) )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2713]) ).
thf(2740,plain,
! [SV194: $i,SV262: $i] :
( ( ( in @ ( ordered_pair @ ( sK79_SY699 @ SV262 @ SV194 ) @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 )
= $true )
| ( ( in @ ( sK62_SY673 @ SV194 @ SV262 ) @ SV262 )
= $true )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2714]) ).
thf(2741,plain,
! [SV295: $i,SV262: $i,SV194: $i] :
( ( ( ! [SY699: $i] :
~ ( in @ ( ordered_pair @ SY699 @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV295 @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 )
= $false )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2715]) ).
thf(2742,plain,
! [SV157: $i,SV279: $i,SV301: $i] :
( ( ( ~ ( subset @ SV301 @ SV279 )
| ( in @ SV301 @ ( sK70_SY700 @ SV279 @ SV157 ) ) )
= $true )
| ( ( in @ SV279 @ ( sK46_SY444 @ SV157 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2718]) ).
thf(2743,plain,
! [SV215: $i,SV286: $i,SV168: $i,SV300: $i] :
( ( ( in @ SV300 @ SV168 )
= $false )
| ( ( in @ SV286 @ SV300 )
= $true )
| ( ( in @ SV286 @ SV215 )
= $false )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $false )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2719]) ).
thf(2744,plain,
! [SV168: $i,SV286: $i,SV215: $i] :
( ( ( in @ ( sK77_SY706 @ SV215 @ SV286 @ SV168 ) @ SV168 )
= $true )
| ( ( in @ SV286 @ SV215 )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $false )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2720]) ).
thf(2745,plain,
! [SV215: $i,SV168: $i] :
( ( ( ! [SY708: $i] :
( ~ ( in @ SY708 @ SV168 )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SY708 ) ) )
= $true )
| ( ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV215 )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2722]) ).
thf(2746,plain,
! [SV215: $i,SV168: $i] :
( ( ( ~ ! [SY708: $i] :
( ~ ( in @ SY708 @ SV168 )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SY708 ) )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV215 ) )
= $false )
| ( ( in @ ( sK74_SY707 @ SV215 @ SV168 ) @ SV168 )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2724]) ).
thf(2747,plain,
! [SV215: $i,SV168: $i] :
( ( ( ~ ! [SY708: $i] :
( ~ ( in @ SY708 @ SV168 )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SY708 ) ) )
= $false )
| ( ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ ( sK74_SY707 @ SV215 @ SV168 ) )
= $false )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2725]) ).
thf(2748,plain,
! [SV215: $i,SV168: $i] :
( ( ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV215 )
= $false )
| ( ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ ( sK74_SY707 @ SV215 @ SV168 ) )
= $false )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2725]) ).
thf(2749,plain,
! [SV216: $i,SV169: $i] :
( ( ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ ( sK73_SY683 @ SV216 @ SV169 ) )
= $true )
| ( ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV216 )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2726]) ).
thf(2750,plain,
! [SV169: $i,SV216: $i] :
( ( ( in @ ( sK73_SY683 @ SV216 @ SV169 ) @ SV169 )
= $true )
| ( ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV216 )
= $true )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2727]) ).
thf(2751,plain,
! [SV287: $i,SV216: $i,SV169: $i] :
( ( ( ~ ! [SY683: $i] :
~ ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SY683 )
| ~ ( in @ SY683 @ SV169 ) ) )
= $true )
| ( ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV287 )
= $false )
| ( ( in @ SV287 @ SV169 )
= $false )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2728]) ).
thf(2752,plain,
! [SV249: $i,SV180: $i,SV225: $i] :
( ( ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 ) )
= $false )
| ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
= $false )
| ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 )
= $false )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2731]) ).
thf(2753,plain,
! [SV249: $i,SV180: $i,SV225: $i] :
( ( ( ~ ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 ) )
= $false )
| ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
= $false )
| ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 )
= $false )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2731]) ).
thf(2754,plain,
! [SV250: $i,SV184: $i,SV229: $i] :
( ( ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
| ~ ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 ) )
= $false )
| ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
= $false )
| ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2733]) ).
thf(2755,plain,
! [SV293: $i,SV261: $i,SV192: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ ( sK80_SY695 @ SV293 @ SV261 @ SV192 ) ) @ SV192 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ SV293 ) @ SV192 )
= $false )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2735]) ).
thf(2756,plain,
! [SV193: $i,SV236: $i,SV276: $i,SV254: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK69_SY684 @ SV254 @ SV276 @ SV236 @ SV193 ) @ SV193 )
| ~ ( in @ ( sK75_SY711 @ SV193 @ SV236 @ SV276 @ SV254 ) @ SV236 ) ) )
= $false )
| ( ( in @ SV276 @ SV254 )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2736]) ).
thf(2757,plain,
! [SV193: $i,SV236: $i,SV254: $i,SV276: $i] :
( ( ( SV276
!= ( ordered_pair @ ( sK69_SY684 @ SV254 @ SV276 @ SV236 @ SV193 ) @ ( sK75_SY711 @ SV193 @ SV236 @ SV276 @ SV254 ) ) )
= $false )
| ( ( in @ SV276 @ SV254 )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2736]) ).
thf(2758,plain,
! [SV254: $i,SV276: $i,SV236: $i,SV299: $i,SV193: $i,SV294: $i] :
( ( ( ~ ~ ( ~ ( in @ SV294 @ SV193 )
| ~ ( in @ SV299 @ SV236 ) ) )
= $true )
| ( ( SV276
!= ( ordered_pair @ SV294 @ SV299 ) )
= $true )
| ( ( in @ SV276 @ SV254 )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2737]) ).
thf(2759,plain,
! [SV193: $i,SV236: $i,SV254: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK76_SY690 @ SV254 @ SV236 @ SV193 ) @ SV193 )
| ~ ( in @ ( sK81_SY714 @ SV193 @ SV236 @ SV254 ) @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ ( sK76_SY690 @ SV254 @ SV236 @ SV193 ) @ ( sK81_SY714 @ SV193 @ SV236 @ SV254 ) ) ) ) )
= $false )
| ( ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2738]) ).
thf(2760,plain,
! [SV254: $i,SV236: $i,SV298: $i,SV193: $i,SV292: $i] :
( ( ( ~ ( ~ ( in @ SV292 @ SV193 )
| ~ ( in @ SV298 @ SV236 ) ) )
= $false )
| ( ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SV292 @ SV298 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY690: $i] :
~ ~ ! [SY691: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY690 @ SV193 )
| ~ ( in @ SY691 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SY690 @ SY691 ) ) )
| ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 ) ) )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2739]) ).
thf(2761,plain,
! [SV194: $i,SV262: $i,SV295: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK82_SY699 @ SV295 @ SV262 @ SV194 ) @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV295 @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 )
= $false )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2741]) ).
thf(2762,plain,
! [SV157: $i,SV279: $i,SV301: $i] :
( ( ( ~ ( subset @ SV301 @ SV279 ) )
= $true )
| ( ( in @ SV301 @ ( sK70_SY700 @ SV279 @ SV157 ) )
= $true )
| ( ( in @ SV279 @ ( sK46_SY444 @ SV157 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2742]) ).
thf(2763,plain,
! [SV215: $i,SV168: $i,SV302: $i] :
( ( ( ~ ( in @ SV302 @ SV168 )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV302 ) )
= $true )
| ( ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV215 )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2745]) ).
thf(2764,plain,
! [SV215: $i,SV168: $i] :
( ( ( ~ ! [SY708: $i] :
( ~ ( in @ SY708 @ SV168 )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SY708 ) ) )
= $false )
| ( ( in @ ( sK74_SY707 @ SV215 @ SV168 ) @ SV168 )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2746]) ).
thf(2765,plain,
! [SV215: $i,SV168: $i] :
( ( ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV215 )
= $false )
| ( ( in @ ( sK74_SY707 @ SV215 @ SV168 ) @ SV168 )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2746]) ).
thf(2766,plain,
! [SV215: $i,SV168: $i] :
( ( ( ! [SY708: $i] :
( ~ ( in @ SY708 @ SV168 )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SY708 ) ) )
= $true )
| ( ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ ( sK74_SY707 @ SV215 @ SV168 ) )
= $false )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2747]) ).
thf(2767,plain,
! [SV287: $i,SV216: $i,SV169: $i] :
( ( ( ! [SY683: $i] :
~ ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SY683 )
| ~ ( in @ SY683 @ SV169 ) ) )
= $false )
| ( ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV287 )
= $false )
| ( ( in @ SV287 @ SV169 )
= $false )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2751]) ).
thf(2768,plain,
! [SV249: $i,SV180: $i,SV225: $i] :
( ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
= $true )
| ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
= $false )
| ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 )
= $false )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2752]) ).
thf(2769,plain,
! [SV249: $i,SV180: $i,SV225: $i] :
( ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 )
= $true )
| ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV180 )
= $false )
| ( ( in @ ( sK58_SY650 @ SV225 @ SV180 @ SV249 ) @ SV225 )
= $false )
| ( ( SV249
= ( set_intersection2 @ SV180 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2753]) ).
thf(2770,plain,
! [SV250: $i,SV184: $i,SV229: $i] :
( ( ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 ) )
= $false )
| ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
= $false )
| ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2754]) ).
thf(2771,plain,
! [SV250: $i,SV184: $i,SV229: $i] :
( ( ( ~ ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 ) )
= $false )
| ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
= $false )
| ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2754]) ).
thf(2772,plain,
! [SV293: $i,SV261: $i,SV192: $i] :
( ( ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ ( sK80_SY695 @ SV293 @ SV261 @ SV192 ) ) @ SV192 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK61_SY667 @ SV192 @ SV261 ) @ SV293 ) @ SV192 )
= $false )
| ( ( SV261
= ( relation_dom @ SV192 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2755]) ).
thf(2773,plain,
! [SV193: $i,SV236: $i,SV276: $i,SV254: $i] :
( ( ( ~ ( ~ ( in @ ( sK69_SY684 @ SV254 @ SV276 @ SV236 @ SV193 ) @ SV193 )
| ~ ( in @ ( sK75_SY711 @ SV193 @ SV236 @ SV276 @ SV254 ) @ SV236 ) ) )
= $true )
| ( ( in @ SV276 @ SV254 )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2756]) ).
thf(2774,plain,
! [SV193: $i,SV236: $i,SV254: $i,SV276: $i] :
( ( ( SV276
= ( ordered_pair @ ( sK69_SY684 @ SV254 @ SV276 @ SV236 @ SV193 ) @ ( sK75_SY711 @ SV193 @ SV236 @ SV276 @ SV254 ) ) )
= $true )
| ( ( in @ SV276 @ SV254 )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2757]) ).
thf(2775,plain,
! [SV254: $i,SV276: $i,SV236: $i,SV299: $i,SV193: $i,SV294: $i] :
( ( ( ~ ( ~ ( in @ SV294 @ SV193 )
| ~ ( in @ SV299 @ SV236 ) ) )
= $false )
| ( ( SV276
!= ( ordered_pair @ SV294 @ SV299 ) )
= $true )
| ( ( in @ SV276 @ SV254 )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2758]) ).
thf(2776,plain,
! [SV193: $i,SV236: $i,SV254: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK76_SY690 @ SV254 @ SV236 @ SV193 ) @ SV193 )
| ~ ( in @ ( sK81_SY714 @ SV193 @ SV236 @ SV254 ) @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ ( sK76_SY690 @ SV254 @ SV236 @ SV193 ) @ ( sK81_SY714 @ SV193 @ SV236 @ SV254 ) ) ) ) )
= $true )
| ( ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2759]) ).
thf(2777,plain,
! [SV254: $i,SV236: $i,SV298: $i,SV193: $i,SV292: $i] :
( ( ( ~ ( in @ SV292 @ SV193 )
| ~ ( in @ SV298 @ SV236 ) )
= $true )
| ( ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SV292 @ SV298 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY690: $i] :
~ ~ ! [SY691: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY690 @ SV193 )
| ~ ( in @ SY691 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SY690 @ SY691 ) ) )
| ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 ) ) )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2760]) ).
thf(2778,plain,
! [SV194: $i,SV262: $i,SV295: $i] :
( ( ( in @ ( ordered_pair @ ( sK82_SY699 @ SV295 @ SV262 @ SV194 ) @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 )
= $true )
| ( ( in @ ( ordered_pair @ SV295 @ ( sK62_SY673 @ SV194 @ SV262 ) ) @ SV194 )
= $false )
| ( ( SV262
= ( relation_rng @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2761]) ).
thf(2779,plain,
! [SV157: $i,SV279: $i,SV301: $i] :
( ( ( subset @ SV301 @ SV279 )
= $false )
| ( ( in @ SV301 @ ( sK70_SY700 @ SV279 @ SV157 ) )
= $true )
| ( ( in @ SV279 @ ( sK46_SY444 @ SV157 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2762]) ).
thf(2780,plain,
! [SV215: $i,SV168: $i,SV302: $i] :
( ( ( ~ ( in @ SV302 @ SV168 ) )
= $true )
| ( ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV302 )
= $true )
| ( ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV215 )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2763]) ).
thf(2781,plain,
! [SV215: $i,SV168: $i] :
( ( ( ! [SY708: $i] :
( ~ ( in @ SY708 @ SV168 )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SY708 ) ) )
= $true )
| ( ( in @ ( sK74_SY707 @ SV215 @ SV168 ) @ SV168 )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2764]) ).
thf(2782,plain,
! [SV215: $i,SV168: $i,SV303: $i] :
( ( ( ~ ( in @ SV303 @ SV168 )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV303 ) )
= $true )
| ( ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ ( sK74_SY707 @ SV215 @ SV168 ) )
= $false )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2766]) ).
thf(2783,plain,
! [SV287: $i,SV216: $i,SV169: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ ( sK83_SY683 @ SV287 @ SV216 @ SV169 ) )
| ~ ( in @ ( sK83_SY683 @ SV287 @ SV216 @ SV169 ) @ SV169 ) ) )
= $false )
| ( ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV287 )
= $false )
| ( ( in @ SV287 @ SV169 )
= $false )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2767]) ).
thf(2784,plain,
! [SV250: $i,SV184: $i,SV229: $i] :
( ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
= $true )
| ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
= $false )
| ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2770]) ).
thf(2785,plain,
! [SV250: $i,SV184: $i,SV229: $i] :
( ( ( ~ ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 ) )
= $true )
| ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
= $false )
| ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2771]) ).
thf(2786,plain,
! [SV193: $i,SV236: $i,SV276: $i,SV254: $i] :
( ( ( ~ ( in @ ( sK69_SY684 @ SV254 @ SV276 @ SV236 @ SV193 ) @ SV193 )
| ~ ( in @ ( sK75_SY711 @ SV193 @ SV236 @ SV276 @ SV254 ) @ SV236 ) )
= $false )
| ( ( in @ SV276 @ SV254 )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2773]) ).
thf(2787,plain,
! [SV254: $i,SV276: $i,SV236: $i,SV299: $i,SV193: $i,SV294: $i] :
( ( ( ~ ( in @ SV294 @ SV193 )
| ~ ( in @ SV299 @ SV236 ) )
= $true )
| ( ( SV276
!= ( ordered_pair @ SV294 @ SV299 ) )
= $true )
| ( ( in @ SV276 @ SV254 )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2775]) ).
thf(2788,plain,
! [SV193: $i,SV236: $i,SV254: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK76_SY690 @ SV254 @ SV236 @ SV193 ) @ SV193 )
| ~ ( in @ ( sK81_SY714 @ SV193 @ SV236 @ SV254 ) @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ ( sK76_SY690 @ SV254 @ SV236 @ SV193 ) @ ( sK81_SY714 @ SV193 @ SV236 @ SV254 ) ) ) )
= $false )
| ( ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2776]) ).
thf(2789,plain,
! [SV254: $i,SV236: $i,SV298: $i,SV193: $i,SV292: $i] :
( ( ( ~ ( in @ SV292 @ SV193 ) )
= $true )
| ( ( ~ ( in @ SV298 @ SV236 ) )
= $true )
| ( ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SV292 @ SV298 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY690: $i] :
~ ~ ! [SY691: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY690 @ SV193 )
| ~ ( in @ SY691 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SY690 @ SY691 ) ) )
| ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 ) ) )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2777]) ).
thf(2790,plain,
! [SV215: $i,SV168: $i,SV302: $i] :
( ( ( in @ SV302 @ SV168 )
= $false )
| ( ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV302 )
= $true )
| ( ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV215 )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2780]) ).
thf(2791,plain,
! [SV215: $i,SV168: $i,SV304: $i] :
( ( ( ~ ( in @ SV304 @ SV168 )
| ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV304 ) )
= $true )
| ( ( in @ ( sK74_SY707 @ SV215 @ SV168 ) @ SV168 )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2781]) ).
thf(2792,plain,
! [SV215: $i,SV168: $i,SV303: $i] :
( ( ( ~ ( in @ SV303 @ SV168 ) )
= $true )
| ( ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV303 )
= $true )
| ( ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ ( sK74_SY707 @ SV215 @ SV168 ) )
= $false )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2782]) ).
thf(2793,plain,
! [SV287: $i,SV216: $i,SV169: $i] :
( ( ( ~ ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ ( sK83_SY683 @ SV287 @ SV216 @ SV169 ) )
| ~ ( in @ ( sK83_SY683 @ SV287 @ SV216 @ SV169 ) @ SV169 ) ) )
= $true )
| ( ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV287 )
= $false )
| ( ( in @ SV287 @ SV169 )
= $false )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2783]) ).
thf(2794,plain,
! [SV250: $i,SV184: $i,SV229: $i] :
( ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 )
= $false )
| ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV184 )
= $false )
| ( ( in @ ( sK59_SY652 @ SV229 @ SV184 @ SV250 ) @ SV229 )
= $true )
| ( ( SV250
= ( set_difference @ SV184 @ SV229 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2785]) ).
thf(2795,plain,
! [SV193: $i,SV236: $i,SV276: $i,SV254: $i] :
( ( ( ~ ( in @ ( sK69_SY684 @ SV254 @ SV276 @ SV236 @ SV193 ) @ SV193 ) )
= $false )
| ( ( in @ SV276 @ SV254 )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2786]) ).
thf(2796,plain,
! [SV254: $i,SV276: $i,SV236: $i,SV193: $i] :
( ( ( ~ ( in @ ( sK75_SY711 @ SV193 @ SV236 @ SV276 @ SV254 ) @ SV236 ) )
= $false )
| ( ( in @ SV276 @ SV254 )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2786]) ).
thf(2797,plain,
! [SV254: $i,SV276: $i,SV236: $i,SV299: $i,SV193: $i,SV294: $i] :
( ( ( ~ ( in @ SV294 @ SV193 ) )
= $true )
| ( ( ~ ( in @ SV299 @ SV236 ) )
= $true )
| ( ( SV276
!= ( ordered_pair @ SV294 @ SV299 ) )
= $true )
| ( ( in @ SV276 @ SV254 )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2787]) ).
thf(2798,plain,
! [SV193: $i,SV236: $i,SV254: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK76_SY690 @ SV254 @ SV236 @ SV193 ) @ SV193 )
| ~ ( in @ ( sK81_SY714 @ SV193 @ SV236 @ SV254 ) @ SV236 ) ) )
= $false )
| ( ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2788]) ).
thf(2799,plain,
! [SV254: $i,SV193: $i,SV236: $i] :
( ( ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ ( sK76_SY690 @ SV254 @ SV236 @ SV193 ) @ ( sK81_SY714 @ SV193 @ SV236 @ SV254 ) ) )
= $false )
| ( ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2788]) ).
thf(2800,plain,
! [SV254: $i,SV236: $i,SV298: $i,SV193: $i,SV292: $i] :
( ( ( in @ SV292 @ SV193 )
= $false )
| ( ( ~ ( in @ SV298 @ SV236 ) )
= $true )
| ( ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SV292 @ SV298 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY690: $i] :
~ ~ ! [SY691: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY690 @ SV193 )
| ~ ( in @ SY691 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SY690 @ SY691 ) ) )
| ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 ) ) )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2789]) ).
thf(2801,plain,
! [SV215: $i,SV168: $i,SV304: $i] :
( ( ( ~ ( in @ SV304 @ SV168 ) )
= $true )
| ( ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV304 )
= $true )
| ( ( in @ ( sK74_SY707 @ SV215 @ SV168 ) @ SV168 )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2791]) ).
thf(2802,plain,
! [SV215: $i,SV168: $i,SV303: $i] :
( ( ( in @ SV303 @ SV168 )
= $false )
| ( ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV303 )
= $true )
| ( ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ ( sK74_SY707 @ SV215 @ SV168 ) )
= $false )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2792]) ).
thf(2803,plain,
! [SV287: $i,SV216: $i,SV169: $i] :
( ( ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ ( sK83_SY683 @ SV287 @ SV216 @ SV169 ) )
| ~ ( in @ ( sK83_SY683 @ SV287 @ SV216 @ SV169 ) @ SV169 ) )
= $false )
| ( ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV287 )
= $false )
| ( ( in @ SV287 @ SV169 )
= $false )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2793]) ).
thf(2804,plain,
! [SV193: $i,SV236: $i,SV276: $i,SV254: $i] :
( ( ( in @ ( sK69_SY684 @ SV254 @ SV276 @ SV236 @ SV193 ) @ SV193 )
= $true )
| ( ( in @ SV276 @ SV254 )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2795]) ).
thf(2805,plain,
! [SV254: $i,SV276: $i,SV236: $i,SV193: $i] :
( ( ( in @ ( sK75_SY711 @ SV193 @ SV236 @ SV276 @ SV254 ) @ SV236 )
= $true )
| ( ( in @ SV276 @ SV254 )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2796]) ).
thf(2806,plain,
! [SV254: $i,SV276: $i,SV236: $i,SV299: $i,SV193: $i,SV294: $i] :
( ( ( in @ SV294 @ SV193 )
= $false )
| ( ( ~ ( in @ SV299 @ SV236 ) )
= $true )
| ( ( SV276
!= ( ordered_pair @ SV294 @ SV299 ) )
= $true )
| ( ( in @ SV276 @ SV254 )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2797]) ).
thf(2807,plain,
! [SV193: $i,SV236: $i,SV254: $i] :
( ( ( ~ ( ~ ( in @ ( sK76_SY690 @ SV254 @ SV236 @ SV193 ) @ SV193 )
| ~ ( in @ ( sK81_SY714 @ SV193 @ SV236 @ SV254 ) @ SV236 ) ) )
= $true )
| ( ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2798]) ).
thf(2808,plain,
! [SV254: $i,SV193: $i,SV236: $i] :
( ( ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
= ( ordered_pair @ ( sK76_SY690 @ SV254 @ SV236 @ SV193 ) @ ( sK81_SY714 @ SV193 @ SV236 @ SV254 ) ) )
= $true )
| ( ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2799]) ).
thf(2809,plain,
! [SV254: $i,SV193: $i,SV292: $i,SV236: $i,SV298: $i] :
( ( ( in @ SV298 @ SV236 )
= $false )
| ( ( in @ SV292 @ SV193 )
= $false )
| ( ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SV292 @ SV298 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY690: $i] :
~ ~ ! [SY691: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY690 @ SV193 )
| ~ ( in @ SY691 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SY690 @ SY691 ) ) )
| ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 ) ) )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2800]) ).
thf(2810,plain,
! [SV215: $i,SV168: $i,SV304: $i] :
( ( ( in @ SV304 @ SV168 )
= $false )
| ( ( in @ ( sK66_SY584 @ SV168 @ SV215 ) @ SV304 )
= $true )
| ( ( in @ ( sK74_SY707 @ SV215 @ SV168 ) @ SV168 )
= $true )
| ( ( SV215
= ( set_meet @ SV168 ) )
= $true )
| ( ( SV168 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2801]) ).
thf(2811,plain,
! [SV287: $i,SV216: $i,SV169: $i] :
( ( ( ~ ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ ( sK83_SY683 @ SV287 @ SV216 @ SV169 ) ) )
= $false )
| ( ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV287 )
= $false )
| ( ( in @ SV287 @ SV169 )
= $false )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2803]) ).
thf(2812,plain,
! [SV169: $i,SV216: $i,SV287: $i] :
( ( ( ~ ( in @ ( sK83_SY683 @ SV287 @ SV216 @ SV169 ) @ SV169 ) )
= $false )
| ( ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV287 )
= $false )
| ( ( in @ SV287 @ SV169 )
= $false )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2803]) ).
thf(2813,plain,
! [SV254: $i,SV276: $i,SV193: $i,SV294: $i,SV236: $i,SV299: $i] :
( ( ( in @ SV299 @ SV236 )
= $false )
| ( ( in @ SV294 @ SV193 )
= $false )
| ( ( SV276
!= ( ordered_pair @ SV294 @ SV299 ) )
= $true )
| ( ( in @ SV276 @ SV254 )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2806]) ).
thf(2814,plain,
! [SV193: $i,SV236: $i,SV254: $i] :
( ( ( ~ ( in @ ( sK76_SY690 @ SV254 @ SV236 @ SV193 ) @ SV193 )
| ~ ( in @ ( sK81_SY714 @ SV193 @ SV236 @ SV254 ) @ SV236 ) )
= $false )
| ( ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2807]) ).
thf(2815,plain,
! [SV298: $i,SV292: $i,SV254: $i,SV193: $i,SV236: $i] :
( ( ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
= ( ordered_pair @ SV292 @ SV298 ) )
= $false )
| ( ( in @ SV292 @ SV193 )
= $false )
| ( ( in @ SV298 @ SV236 )
= $false )
| ( ( ~ ( ~ ~ ! [SY690: $i] :
~ ~ ! [SY691: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY690 @ SV193 )
| ~ ( in @ SY691 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SY690 @ SY691 ) ) )
| ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 ) ) )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2809]) ).
thf(2816,plain,
! [SV287: $i,SV216: $i,SV169: $i] :
( ( ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ ( sK83_SY683 @ SV287 @ SV216 @ SV169 ) )
= $true )
| ( ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV287 )
= $false )
| ( ( in @ SV287 @ SV169 )
= $false )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2811]) ).
thf(2817,plain,
! [SV169: $i,SV216: $i,SV287: $i] :
( ( ( in @ ( sK83_SY683 @ SV287 @ SV216 @ SV169 ) @ SV169 )
= $true )
| ( ( in @ ( sK53_SY590 @ SV169 @ SV216 ) @ SV287 )
= $false )
| ( ( in @ SV287 @ SV169 )
= $false )
| ( ( SV216
= ( union @ SV169 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2812]) ).
thf(2818,plain,
! [SV254: $i,SV236: $i,SV193: $i,SV299: $i,SV294: $i,SV276: $i] :
( ( ( SV276
= ( ordered_pair @ SV294 @ SV299 ) )
= $false )
| ( ( in @ SV294 @ SV193 )
= $false )
| ( ( in @ SV299 @ SV236 )
= $false )
| ( ( in @ SV276 @ SV254 )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2813]) ).
thf(2819,plain,
! [SV193: $i,SV236: $i,SV254: $i] :
( ( ( ~ ( in @ ( sK76_SY690 @ SV254 @ SV236 @ SV193 ) @ SV193 ) )
= $false )
| ( ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2814]) ).
thf(2820,plain,
! [SV254: $i,SV236: $i,SV193: $i] :
( ( ( ~ ( in @ ( sK81_SY714 @ SV193 @ SV236 @ SV254 ) @ SV236 ) )
= $false )
| ( ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2814]) ).
thf(2821,plain,
! [SV292: $i,SV298: $i,SV254: $i,SV236: $i,SV193: $i] :
( ( ( ~ ~ ! [SY690: $i] :
~ ~ ! [SY691: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY690 @ SV193 )
| ~ ( in @ SY691 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SY690 @ SY691 ) ) )
| ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 ) )
= $false )
| ( ( in @ SV298 @ SV236 )
= $false )
| ( ( in @ SV292 @ SV193 )
= $false )
| ( ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
= ( ordered_pair @ SV292 @ SV298 ) )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2815]) ).
thf(2822,plain,
! [SV193: $i,SV236: $i,SV254: $i] :
( ( ( in @ ( sK76_SY690 @ SV254 @ SV236 @ SV193 ) @ SV193 )
= $true )
| ( ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2819]) ).
thf(2823,plain,
! [SV254: $i,SV236: $i,SV193: $i] :
( ( ( in @ ( sK81_SY714 @ SV193 @ SV236 @ SV254 ) @ SV236 )
= $true )
| ( ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 )
= $true )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2820]) ).
thf(2824,plain,
! [SV292: $i,SV298: $i,SV254: $i,SV236: $i,SV193: $i] :
( ( ( ~ ~ ! [SY690: $i] :
~ ~ ! [SY691: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY690 @ SV193 )
| ~ ( in @ SY691 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SY690 @ SY691 ) ) ) )
= $false )
| ( ( in @ SV298 @ SV236 )
= $false )
| ( ( in @ SV292 @ SV193 )
= $false )
| ( ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
= ( ordered_pair @ SV292 @ SV298 ) )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2821]) ).
thf(2825,plain,
! [SV292: $i,SV298: $i,SV254: $i,SV193: $i,SV236: $i] :
( ( ( in @ ( sK60_SY659 @ SV236 @ SV193 @ SV254 ) @ SV254 )
= $false )
| ( ( in @ SV298 @ SV236 )
= $false )
| ( ( in @ SV292 @ SV193 )
= $false )
| ( ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
= ( ordered_pair @ SV292 @ SV298 ) )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2821]) ).
thf(2826,plain,
! [SV292: $i,SV298: $i,SV254: $i,SV236: $i,SV193: $i] :
( ( ( ~ ! [SY690: $i] :
~ ~ ! [SY691: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY690 @ SV193 )
| ~ ( in @ SY691 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SY690 @ SY691 ) ) ) )
= $true )
| ( ( in @ SV298 @ SV236 )
= $false )
| ( ( in @ SV292 @ SV193 )
= $false )
| ( ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
= ( ordered_pair @ SV292 @ SV298 ) )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2824]) ).
thf(2827,plain,
! [SV292: $i,SV298: $i,SV254: $i,SV236: $i,SV193: $i] :
( ( ( ! [SY690: $i] :
~ ~ ! [SY691: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY690 @ SV193 )
| ~ ( in @ SY691 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ SY690 @ SY691 ) ) ) )
= $false )
| ( ( in @ SV298 @ SV236 )
= $false )
| ( ( in @ SV292 @ SV193 )
= $false )
| ( ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
= ( ordered_pair @ SV292 @ SV298 ) )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2826]) ).
thf(2828,plain,
! [SV193: $i,SV236: $i,SV254: $i,SV298: $i,SV292: $i] :
( ( ( ~ ~ ! [SY715: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK84_SY690 @ SV292 @ SV298 @ SV254 @ SV236 @ SV193 ) @ SV193 )
| ~ ( in @ SY715 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ ( sK84_SY690 @ SV292 @ SV298 @ SV254 @ SV236 @ SV193 ) @ SY715 ) ) ) )
= $false )
| ( ( in @ SV298 @ SV236 )
= $false )
| ( ( in @ SV292 @ SV193 )
= $false )
| ( ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
= ( ordered_pair @ SV292 @ SV298 ) )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2827]) ).
thf(2829,plain,
! [SV193: $i,SV236: $i,SV254: $i,SV298: $i,SV292: $i] :
( ( ( ~ ! [SY715: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK84_SY690 @ SV292 @ SV298 @ SV254 @ SV236 @ SV193 ) @ SV193 )
| ~ ( in @ SY715 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ ( sK84_SY690 @ SV292 @ SV298 @ SV254 @ SV236 @ SV193 ) @ SY715 ) ) ) )
= $true )
| ( ( in @ SV298 @ SV236 )
= $false )
| ( ( in @ SV292 @ SV193 )
= $false )
| ( ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
= ( ordered_pair @ SV292 @ SV298 ) )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2828]) ).
thf(2830,plain,
! [SV193: $i,SV236: $i,SV254: $i,SV298: $i,SV292: $i] :
( ( ( ! [SY715: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK84_SY690 @ SV292 @ SV298 @ SV254 @ SV236 @ SV193 ) @ SV193 )
| ~ ( in @ SY715 @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ ( sK84_SY690 @ SV292 @ SV298 @ SV254 @ SV236 @ SV193 ) @ SY715 ) ) ) )
= $false )
| ( ( in @ SV298 @ SV236 )
= $false )
| ( ( in @ SV292 @ SV193 )
= $false )
| ( ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
= ( ordered_pair @ SV292 @ SV298 ) )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2829]) ).
thf(2831,plain,
! [SV193: $i,SV236: $i,SV254: $i,SV298: $i,SV292: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK84_SY690 @ SV292 @ SV298 @ SV254 @ SV236 @ SV193 ) @ SV193 )
| ~ ( in @ ( sK85_SY715 @ SV193 @ SV236 @ SV254 @ SV298 @ SV292 ) @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ ( sK84_SY690 @ SV292 @ SV298 @ SV254 @ SV236 @ SV193 ) @ ( sK85_SY715 @ SV193 @ SV236 @ SV254 @ SV298 @ SV292 ) ) ) ) )
= $false )
| ( ( in @ SV298 @ SV236 )
= $false )
| ( ( in @ SV292 @ SV193 )
= $false )
| ( ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
= ( ordered_pair @ SV292 @ SV298 ) )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2830]) ).
thf(2832,plain,
! [SV193: $i,SV236: $i,SV254: $i,SV298: $i,SV292: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK84_SY690 @ SV292 @ SV298 @ SV254 @ SV236 @ SV193 ) @ SV193 )
| ~ ( in @ ( sK85_SY715 @ SV193 @ SV236 @ SV254 @ SV298 @ SV292 ) @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ ( sK84_SY690 @ SV292 @ SV298 @ SV254 @ SV236 @ SV193 ) @ ( sK85_SY715 @ SV193 @ SV236 @ SV254 @ SV298 @ SV292 ) ) ) ) )
= $true )
| ( ( in @ SV298 @ SV236 )
= $false )
| ( ( in @ SV292 @ SV193 )
= $false )
| ( ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
= ( ordered_pair @ SV292 @ SV298 ) )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2831]) ).
thf(2833,plain,
! [SV193: $i,SV236: $i,SV254: $i,SV298: $i,SV292: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK84_SY690 @ SV292 @ SV298 @ SV254 @ SV236 @ SV193 ) @ SV193 )
| ~ ( in @ ( sK85_SY715 @ SV193 @ SV236 @ SV254 @ SV298 @ SV292 ) @ SV236 ) )
| ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ ( sK84_SY690 @ SV292 @ SV298 @ SV254 @ SV236 @ SV193 ) @ ( sK85_SY715 @ SV193 @ SV236 @ SV254 @ SV298 @ SV292 ) ) ) )
= $false )
| ( ( in @ SV298 @ SV236 )
= $false )
| ( ( in @ SV292 @ SV193 )
= $false )
| ( ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
= ( ordered_pair @ SV292 @ SV298 ) )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2832]) ).
thf(2834,plain,
! [SV193: $i,SV236: $i,SV254: $i,SV298: $i,SV292: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK84_SY690 @ SV292 @ SV298 @ SV254 @ SV236 @ SV193 ) @ SV193 )
| ~ ( in @ ( sK85_SY715 @ SV193 @ SV236 @ SV254 @ SV298 @ SV292 ) @ SV236 ) ) )
= $false )
| ( ( in @ SV298 @ SV236 )
= $false )
| ( ( in @ SV292 @ SV193 )
= $false )
| ( ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
= ( ordered_pair @ SV292 @ SV298 ) )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2833]) ).
thf(2835,plain,
! [SV298: $i,SV292: $i,SV254: $i,SV193: $i,SV236: $i] :
( ( ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
!= ( ordered_pair @ ( sK84_SY690 @ SV292 @ SV298 @ SV254 @ SV236 @ SV193 ) @ ( sK85_SY715 @ SV193 @ SV236 @ SV254 @ SV298 @ SV292 ) ) )
= $false )
| ( ( in @ SV298 @ SV236 )
= $false )
| ( ( in @ SV292 @ SV193 )
= $false )
| ( ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
= ( ordered_pair @ SV292 @ SV298 ) )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2833]) ).
thf(2836,plain,
! [SV193: $i,SV236: $i,SV254: $i,SV298: $i,SV292: $i] :
( ( ( ~ ( ~ ( in @ ( sK84_SY690 @ SV292 @ SV298 @ SV254 @ SV236 @ SV193 ) @ SV193 )
| ~ ( in @ ( sK85_SY715 @ SV193 @ SV236 @ SV254 @ SV298 @ SV292 ) @ SV236 ) ) )
= $true )
| ( ( in @ SV298 @ SV236 )
= $false )
| ( ( in @ SV292 @ SV193 )
= $false )
| ( ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
= ( ordered_pair @ SV292 @ SV298 ) )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2834]) ).
thf(2837,plain,
! [SV298: $i,SV292: $i,SV254: $i,SV193: $i,SV236: $i] :
( ( ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
= ( ordered_pair @ ( sK84_SY690 @ SV292 @ SV298 @ SV254 @ SV236 @ SV193 ) @ ( sK85_SY715 @ SV193 @ SV236 @ SV254 @ SV298 @ SV292 ) ) )
= $true )
| ( ( in @ SV298 @ SV236 )
= $false )
| ( ( in @ SV292 @ SV193 )
= $false )
| ( ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
= ( ordered_pair @ SV292 @ SV298 ) )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2835]) ).
thf(2838,plain,
! [SV193: $i,SV236: $i,SV254: $i,SV298: $i,SV292: $i] :
( ( ( ~ ( in @ ( sK84_SY690 @ SV292 @ SV298 @ SV254 @ SV236 @ SV193 ) @ SV193 )
| ~ ( in @ ( sK85_SY715 @ SV193 @ SV236 @ SV254 @ SV298 @ SV292 ) @ SV236 ) )
= $false )
| ( ( in @ SV298 @ SV236 )
= $false )
| ( ( in @ SV292 @ SV193 )
= $false )
| ( ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
= ( ordered_pair @ SV292 @ SV298 ) )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2836]) ).
thf(2839,plain,
! [SV193: $i,SV236: $i,SV254: $i,SV298: $i,SV292: $i] :
( ( ( ~ ( in @ ( sK84_SY690 @ SV292 @ SV298 @ SV254 @ SV236 @ SV193 ) @ SV193 ) )
= $false )
| ( ( in @ SV298 @ SV236 )
= $false )
| ( ( in @ SV292 @ SV193 )
= $false )
| ( ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
= ( ordered_pair @ SV292 @ SV298 ) )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2838]) ).
thf(2840,plain,
! [SV292: $i,SV298: $i,SV254: $i,SV236: $i,SV193: $i] :
( ( ( ~ ( in @ ( sK85_SY715 @ SV193 @ SV236 @ SV254 @ SV298 @ SV292 ) @ SV236 ) )
= $false )
| ( ( in @ SV298 @ SV236 )
= $false )
| ( ( in @ SV292 @ SV193 )
= $false )
| ( ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
= ( ordered_pair @ SV292 @ SV298 ) )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2838]) ).
thf(2841,plain,
! [SV193: $i,SV236: $i,SV254: $i,SV298: $i,SV292: $i] :
( ( ( in @ ( sK84_SY690 @ SV292 @ SV298 @ SV254 @ SV236 @ SV193 ) @ SV193 )
= $true )
| ( ( in @ SV298 @ SV236 )
= $false )
| ( ( in @ SV292 @ SV193 )
= $false )
| ( ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
= ( ordered_pair @ SV292 @ SV298 ) )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2839]) ).
thf(2842,plain,
! [SV292: $i,SV298: $i,SV254: $i,SV236: $i,SV193: $i] :
( ( ( in @ ( sK85_SY715 @ SV193 @ SV236 @ SV254 @ SV298 @ SV292 ) @ SV236 )
= $true )
| ( ( in @ SV298 @ SV236 )
= $false )
| ( ( in @ SV292 @ SV193 )
= $false )
| ( ( ( sK60_SY659 @ SV236 @ SV193 @ SV254 )
= ( ordered_pair @ SV292 @ SV298 ) )
= $false )
| ( ( SV254
= ( cartesian_product2 @ SV193 @ SV236 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2840]) ).
thf(2843,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[1576,2842,2841,2837,2825,2823,2822,2818,2817,2816,2810,2808,2805,2804,2802,2794,2790,2784,2779,2778,2774,2772,2769,2768,2765,2750,2749,2748,2744,2743,2740,2734,2732,2730,2729,2723,2721,2717,2716,2707,2704,2702,2701,2697,2688,2681,2675,2674,2670,2665,2664,2659,2654,2653,2646,2645,2641,2638,2635,2634,2633,2620,2619,2618,2617,2615,2606,2598,2594,2593,2573,2572,2566,2558,2556,2550,2543,2542,2540,2538,2526,2524,2522,2505,2504,2492,2491,2490,2485,2484,2483,2481,2469,2468,2467,2452,2439,2437,2401,2400,2399,2398,2389,2388,2386,2384,2379,2378,2377,2366,2365,2361,2356,2340,2339,2336,2335,2334,2314,2313,2305,2304,2301,2300,2289,2288,2275,2269,2268,2254,2215,2178,2177,2172,2171,2163,2123,2115,2114,2106,2105,2063,2062,2056,2051,2029,2028,2023,2022,2019,2018,1999,1989,1985,1984,1954,1905,1900,1868,1858,1854,1827,1818,1810,1761,1753,1703,1654,1602,1601,1590,1589,1588,1587,1586,1585,1584,1583,1582,1581,1580,1579,1578,1577]) ).
thf(2844,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[2843,1535]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU180+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.19 % Computer : n007.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 15:01:15 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 87.04/14.75 .
% 87.04/14.75
% 87.04/14.75 No.of.Axioms: 65
% 87.04/14.75
% 87.04/14.75 Length.of.Defs: 0
% 87.04/14.75
% 87.04/14.75 Contains.Choice.Funs: false
% 87.04/14.75 .....................................................................................................
% 87.04/14.75
% 87.04/14.75 ********************************
% 87.04/14.75 * All subproblems solved! *
% 87.04/14.75 ********************************
% 87.04/14.75 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:67,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:295,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2843,loop_count:0,foatp_calls:1,translation:fof_full)
% 87.04/14.75
% 87.04/14.75 %**** Beginning of derivation protocol ****
% 87.04/14.75 % SZS output start CNFRefutation
% See solution above
% 87.04/14.77
% 87.04/14.77 %**** End of derivation protocol ****
% 87.04/14.77 %**** no. of clauses in derivation: 2760 ****
% 87.04/14.77 %**** clause counter: 2843 ****
% 87.04/14.77
% 87.04/14.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:67,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:295,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2843,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------