%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU217+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 10:43:28 AM UTC 2026
% Result : Theorem 29.21s 5.09s
% Output : CNFRefutation 29.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 80
% Syntax : Number of formulae : 2120 ( 552 unt; 0 typ; 0 def)
% Number of atoms : 22441 (7990 equ; 0 cnn)
% Maximal formula atoms : 11 ( 10 avg)
% Number of connectives : 51437 (11883 ~;8472 |; 159 &;30585 @)
% ( 168 <=>; 170 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 111 ( 108 usr; 5 con; 0-5 aty)
% Number of variables : 7701 ( 0 ^;7665 !; 36 ?;7701 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_apply,type,
apply: $i > $i > $i ).
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_function,type,
function: $i > $o ).
thf(tp_identity_relation,type,
identity_relation: $i > $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_composition,type,
relation_composition: $i > $i > $i ).
thf(tp_relation_dom,type,
relation_dom: $i > $i ).
thf(tp_relation_dom_restriction,type,
relation_dom_restriction: $i > $i > $i ).
thf(tp_relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
thf(tp_relation_field,type,
relation_field: $i > $i ).
thf(tp_relation_image,type,
relation_image: $i > $i > $i ).
thf(tp_relation_inverse,type,
relation_inverse: $i > $i ).
thf(tp_relation_inverse_image,type,
relation_inverse_image: $i > $i > $i ).
thf(tp_relation_rng,type,
relation_rng: $i > $i ).
thf(tp_relation_rng_restriction,type,
relation_rng_restriction: $i > $i > $i ).
thf(tp_sK10_SY336,type,
sK10_SY336: $i > $i ).
thf(tp_sK11_SY427,type,
sK11_SY427: $i > $i > $i ).
thf(tp_sK12_SY454,type,
sK12_SY454: $i > $i > $i ).
thf(tp_sK13_SY458,type,
sK13_SY458: $i > $i > $i ).
thf(tp_sK14_SY464,type,
sK14_SY464: $i > $i > $i ).
thf(tp_sK15_SY483,type,
sK15_SY483: $i > $i > $i > $i ).
thf(tp_sK16_SY489,type,
sK16_SY489: $i > $i > $i > $i ).
thf(tp_sK17_SY503,type,
sK17_SY503: $i > $i > $i > $i ).
thf(tp_sK18_SY505,type,
sK18_SY505: $i > $i > $i > $i ).
thf(tp_sK19_SY507,type,
sK19_SY507: $i > $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_SY424,type,
sK20_SY424: $i > $i > $i ).
thf(tp_sK21_SY531,type,
sK21_SY531: $i > $i > $i ).
thf(tp_sK22_SY553,type,
sK22_SY553: $i > $i > $i ).
thf(tp_sK23_SY606,type,
sK23_SY606: $i > $i > $i ).
thf(tp_sK24_SY563,type,
sK24_SY563: $i > $i > $i > $i ).
thf(tp_sK25_SY573,type,
sK25_SY573: $i > $i > $i > $i ).
thf(tp_sK26_SY404,type,
sK26_SY404: $i > $i > $i ).
thf(tp_sK27_SY510,type,
sK27_SY510: $i > $i > $i ).
thf(tp_sK28_SY536,type,
sK28_SY536: $i > $i > $i ).
thf(tp_sK29_SY431,type,
sK29_SY431: $i > $i > $i ).
thf(tp_sK2_SY203,type,
sK2_SY203: $i ).
thf(tp_sK30_SY558,type,
sK30_SY558: $i > $i > $i ).
thf(tp_sK31_SY626,type,
sK31_SY626: $i > $i > $i ).
thf(tp_sK32_SY628,type,
sK32_SY628: $i > $i > $i ).
thf(tp_sK33_SY568,type,
sK33_SY568: $i > $i > $i > $i ).
thf(tp_sK34_SY589,type,
sK34_SY589: $i > $i > $i ).
thf(tp_sK35_SY578,type,
sK35_SY578: $i > $i > $i > $i ).
thf(tp_sK36_SY631,type,
sK36_SY631: $i > $i > $i ).
thf(tp_sK37_SY633,type,
sK37_SY633: $i > $i > $i > $i ).
thf(tp_sK38_SY437,type,
sK38_SY437: $i > $i > $i ).
thf(tp_sK39_SY634,type,
sK39_SY634: $i > $i > $i ).
thf(tp_sK3_SY291,type,
sK3_SY291: $i > $i ).
thf(tp_sK40_SY636,type,
sK40_SY636: $i > $i > $i > $i ).
thf(tp_sK41_SY585,type,
sK41_SY585: $i > $i > $i > $i ).
thf(tp_sK42_SY593,type,
sK42_SY593: $i > $i > $i > $i ).
thf(tp_sK43_SY646,type,
sK43_SY646: $i > $i > $i > $i ).
thf(tp_sK44_SY597,type,
sK44_SY597: $i > $i > $i > $i > $i ).
thf(tp_sK45_SY607,type,
sK45_SY607: $i > $i > $i > $i ).
thf(tp_sK46_SY623,type,
sK46_SY623: $i > $i > $i ).
thf(tp_sK47_SY611,type,
sK47_SY611: $i > $i > $i > $i ).
thf(tp_sK48_SY408,type,
sK48_SY408: $i > $i > $i ).
thf(tp_sK49_SY615,type,
sK49_SY615: $i > $i > $i > $i > $i ).
thf(tp_sK4_SY357,type,
sK4_SY357: $i > $i ).
thf(tp_sK50_SY619,type,
sK50_SY619: $i > $i > $i > $i > $i ).
thf(tp_sK51_SY596,type,
sK51_SY596: $i > $i > $i ).
thf(tp_sK52_SY654,type,
sK52_SY654: $i > $i > $i > $i > $i ).
thf(tp_sK53_SY603,type,
sK53_SY603: $i > $i > $i > $i ).
thf(tp_sK54_SY640,type,
sK54_SY640: $i > $i > $i ).
thf(tp_sK55_SY610,type,
sK55_SY610: $i > $i > $i ).
thf(tp_sK56_SY639,type,
sK56_SY639: $i > $i > $i > $i ).
thf(tp_sK57_SY614,type,
sK57_SY614: $i > $i > $i ).
thf(tp_sK58_SY618,type,
sK58_SY618: $i > $i > $i > $i ).
thf(tp_sK59_SY622,type,
sK59_SY622: $i > $i > $i > $i ).
thf(tp_sK5_SY406,type,
sK5_SY406: $i > $i > $i ).
thf(tp_sK60_SY657,type,
sK60_SY657: $i > $i > $i > $i ).
thf(tp_sK61_SY610,type,
sK61_SY610: $i > $i > $i > $i ).
thf(tp_sK62_SY614,type,
sK62_SY614: $i > $i > $i > $i ).
thf(tp_sK63_SY650,type,
sK63_SY650: $i > $i > $i > $i > $i > $i ).
thf(tp_sK64_SY596,type,
sK64_SY596: $i > $i > $i > $i ).
thf(tp_sK65_SY653,type,
sK65_SY653: $i > $i > $i > $i ).
thf(tp_sK66_SY618,type,
sK66_SY618: $i > $i > $i > $i > $i ).
thf(tp_sK67_SY622,type,
sK67_SY622: $i > $i > $i > $i > $i ).
thf(tp_sK68_SY653,type,
sK68_SY653: $i > $i > $i > $i > $i ).
thf(tp_sK69_SY603,type,
sK69_SY603: $i > $i > $i > $i > $i > $i ).
thf(tp_sK6_SY462,type,
sK6_SY462: $i > $i > $i ).
thf(tp_sK70_SY658,type,
sK70_SY658: $i > $i > $i > $i > $i > $i ).
thf(tp_sK7_SY277,type,
sK7_SY277: $i > $i ).
thf(tp_sK8_SY580,type,
sK8_SY580: $i > $i ).
thf(tp_sK9_SY328,type,
sK9_SY328: $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/sandbox/benchmark/theBenchmark.p',t9_tarski) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(46,axiom,
! [A: $i] :
( ( relation @ ( identity_relation @ A ) )
& ( function @ ( identity_relation @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
thf(55,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(56,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_relat_1) ).
thf(62,axiom,
! [A: $i] : ( relation @ ( identity_relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(65,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(66,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(68,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(69,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_tarski) ).
thf(71,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_relat_1) ).
thf(72,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(73,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(74,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(76,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(77,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(78,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(79,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(80,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_setfam_1) ).
thf(81,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(82,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_funct_1) ).
thf(83,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_relat_1) ).
thf(86,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_composition @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ? [F: $i] :
( ( in @ ( ordered_pair @ D @ F ) @ A )
& ( in @ ( ordered_pair @ F @ E ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_1) ).
thf(88,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( B
= ( relation_inverse @ A ) )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ B )
<=> ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_relat_1) ).
thf(92,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/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
thf(93,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/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(94,axiom,
! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
thf(96,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/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
thf(98,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/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(99,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(100,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ A )
=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_relat_1) ).
thf(101,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/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).
thf(102,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/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
thf(104,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
=> ( ( element @ B @ A )
<=> ( in @ B @ A ) ) )
& ( ( empty @ A )
=> ( ( element @ B @ A )
<=> ( empty @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
thf(105,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( A = B )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ A )
<=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_relat_1) ).
thf(106,axiom,
! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(107,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(108,axiom,
! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
thf(109,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/sandbox/benchmark/theBenchmark.p',d1_setfam_1) ).
thf(110,axiom,
! [A: $i] :
( ( relation @ A )
<=> ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_1) ).
thf(111,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_inverse_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ A )
& ( in @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_relat_1) ).
thf(112,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ ( ordered_pair @ E @ D ) @ A )
& ( in @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_relat_1) ).
thf(113,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_rng_restriction @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ( ( in @ E @ A )
& ( in @ ( ordered_pair @ D @ E ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_relat_1) ).
thf(114,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_dom_restriction @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ( ( in @ D @ B )
& ( in @ ( ordered_pair @ D @ E ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_relat_1) ).
thf(116,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( B
= ( identity_relation @ A ) )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ B )
<=> ( ( in @ C @ A )
& ( C = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_relat_1) ).
thf(123,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(127,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_dom_restriction @ B @ A )
= ( relation_composition @ ( identity_relation @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_relat_1) ).
thf(128,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_dom @ ( relation_dom_restriction @ C @ B ) ) )
<=> ( ( in @ A @ B )
& ( in @ A @ ( relation_dom @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_relat_1) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( relation @ D )
=> ( ( in @ ( ordered_pair @ A @ B ) @ ( relation_composition @ ( identity_relation @ C ) @ D ) )
<=> ( ( in @ A @ C )
& ( in @ ( ordered_pair @ A @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_relat_1) ).
thf(138,axiom,
! [A: $i] :
( ( ( relation_dom @ ( identity_relation @ A ) )
= A )
& ( ( relation_rng @ ( identity_relation @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_relat_1) ).
thf(141,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
= A )
<=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_zfmisc_1) ).
thf(147,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_relat_1) ).
thf(148,axiom,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ~ ( ( in @ B @ ( subset_complement @ A @ C ) )
& ( in @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_subset_1) ).
thf(150,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/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(155,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_zfmisc_1) ).
thf(164,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/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(167,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ C )
& ( in @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).
thf(168,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(172,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( B
= ( identity_relation @ A ) )
<=> ( ( ( relation_dom @ B )
= A )
& ! [C: $i] :
( ( in @ C @ A )
=> ( ( apply @ B @ C )
= C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
thf(175,axiom,
! [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/sandbox/benchmark/theBenchmark.p',t30_relat_1) ).
thf(199,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/sandbox/benchmark/theBenchmark.p',t136_zfmisc_1) ).
thf(207,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_rng @ ( relation_rng_restriction @ B @ C ) ) )
<=> ( ( in @ A @ B )
& ( in @ A @ ( relation_rng @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_relat_1) ).
thf(209,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/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
thf(210,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l71_subset_1) ).
thf(211,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/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).
thf(212,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l50_zfmisc_1) ).
thf(214,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_zfmisc_1) ).
thf(215,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_subset_1) ).
thf(217,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(218,axiom,
! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l28_zfmisc_1) ).
thf(219,axiom,
! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l25_zfmisc_1) ).
thf(220,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l23_zfmisc_1) ).
thf(222,conjecture,
! [A: $i,B: $i] :
( ( in @ B @ A )
=> ( ( apply @ ( identity_relation @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_funct_1) ).
thf(223,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( in @ B @ A )
=> ( ( apply @ ( identity_relation @ A ) @ B )
= B ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[222]) ).
thf(224,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ A )
=> ( ( apply @ ( identity_relation @ A ) @ B )
= B ) ) )
= $false ),
inference(unfold_def,[status(thm)],[223]) ).
thf(225,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(226,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(227,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(228,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(229,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(230,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(231,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(232,plain,
( ( ! [A: $i] :
( ( relation @ ( identity_relation @ A ) )
& ( function @ ( identity_relation @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(233,plain,
$true = $true,
inference(unfold_def,[status(thm)],[55]) ).
thf(234,plain,
$true = $true,
inference(unfold_def,[status(thm)],[56]) ).
thf(235,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(236,plain,
$true = $true,
inference(unfold_def,[status(thm)],[65]) ).
thf(237,plain,
$true = $true,
inference(unfold_def,[status(thm)],[66]) ).
thf(238,plain,
$true = $true,
inference(unfold_def,[status(thm)],[68]) ).
thf(239,plain,
$true = $true,
inference(unfold_def,[status(thm)],[69]) ).
thf(240,plain,
$true = $true,
inference(unfold_def,[status(thm)],[71]) ).
thf(241,plain,
$true = $true,
inference(unfold_def,[status(thm)],[72]) ).
thf(242,plain,
$true = $true,
inference(unfold_def,[status(thm)],[73]) ).
thf(243,plain,
$true = $true,
inference(unfold_def,[status(thm)],[74]) ).
thf(244,plain,
$true = $true,
inference(unfold_def,[status(thm)],[76]) ).
thf(245,plain,
$true = $true,
inference(unfold_def,[status(thm)],[77]) ).
thf(246,plain,
$true = $true,
inference(unfold_def,[status(thm)],[78]) ).
thf(247,plain,
$true = $true,
inference(unfold_def,[status(thm)],[79]) ).
thf(248,plain,
$true = $true,
inference(unfold_def,[status(thm)],[80]) ).
thf(249,plain,
$true = $true,
inference(unfold_def,[status(thm)],[81]) ).
thf(250,plain,
$true = $true,
inference(unfold_def,[status(thm)],[82]) ).
thf(251,plain,
$true = $true,
inference(unfold_def,[status(thm)],[83]) ).
thf(252,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_composition @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ? [F: $i] :
( ( in @ ( ordered_pair @ D @ F ) @ A )
& ( in @ ( ordered_pair @ F @ E ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(253,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( B
= ( relation_inverse @ A ) )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ B )
<=> ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(254,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)],[92]) ).
thf(255,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)],[93]) ).
thf(256,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)],[94]) ).
thf(257,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)],[96]) ).
thf(258,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)],[98]) ).
thf(259,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(260,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ A )
=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(261,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)],[101]) ).
thf(262,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)],[102]) ).
thf(263,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)],[103]) ).
thf(264,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)],[104]) ).
thf(265,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( A = B )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ A )
<=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(266,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(267,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(268,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(269,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)],[109]) ).
thf(270,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)],[110]) ).
thf(271,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_inverse_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ A )
& ( in @ E @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(272,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ ( ordered_pair @ E @ D ) @ A )
& ( in @ E @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(273,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_rng_restriction @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ( ( in @ E @ A )
& ( in @ ( ordered_pair @ D @ E ) @ B ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(274,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_dom_restriction @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ( ( in @ D @ B )
& ( in @ ( ordered_pair @ D @ E ) @ A ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(275,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( B
= ( identity_relation @ A ) )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ B )
<=> ( ( in @ C @ A )
& ( C = D ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(276,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(277,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_dom_restriction @ B @ A )
= ( relation_composition @ ( identity_relation @ A ) @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(278,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(279,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_dom @ ( relation_dom_restriction @ C @ B ) ) )
<=> ( ( in @ A @ B )
& ( in @ A @ ( relation_dom @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(280,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( relation @ D )
=> ( ( in @ ( ordered_pair @ A @ B ) @ ( relation_composition @ ( identity_relation @ C ) @ D ) )
<=> ( ( in @ A @ C )
& ( in @ ( ordered_pair @ A @ B ) @ D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(281,plain,
( ( ! [A: $i] :
( ( ( relation_dom @ ( identity_relation @ A ) )
= A )
& ( ( relation_rng @ ( identity_relation @ A ) )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(282,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
= A )
<=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(283,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(284,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)],[148]) ).
thf(285,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)],[150]) ).
thf(286,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(287,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)],[164]) ).
thf(288,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)],[167]) ).
thf(289,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(290,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( B
= ( identity_relation @ A ) )
<=> ( ( ( relation_dom @ B )
= A )
& ! [C: $i] :
( ( in @ C @ A )
=> ( ( apply @ B @ C )
= C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(291,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 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
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 )
=> ( in @ ( powerset @ C ) @ B ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(293,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_rng @ ( relation_rng_restriction @ B @ C ) ) )
<=> ( ( in @ A @ B )
& ( in @ A @ ( relation_rng @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(294,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)],[209]) ).
thf(295,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(296,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)],[211]) ).
thf(297,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(298,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)],[214]) ).
thf(299,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(300,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[217]) ).
thf(301,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(302,plain,
( ( ! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[219]) ).
thf(303,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[220]) ).
thf(304,plain,
( ( ! [SY203: $i] :
( ( in @ SY203 @ sK1_A )
=> ( ( apply @ ( identity_relation @ sK1_A ) @ SY203 )
= SY203 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[224]) ).
thf(305,plain,
( ( ( in @ sK2_SY203 @ sK1_A )
=> ( ( apply @ ( identity_relation @ sK1_A ) @ sK2_SY203 )
= sK2_SY203 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[304]) ).
thf(306,plain,
( ( in @ sK2_SY203 @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[305]) ).
thf(307,plain,
( ( ( apply @ ( identity_relation @ sK1_A ) @ sK2_SY203 )
= sK2_SY203 )
= $false ),
inference(standard_cnf,[status(thm)],[305]) ).
thf(308,plain,
( ( ( apply @ ( identity_relation @ sK1_A ) @ sK2_SY203 )
!= sK2_SY203 )
= $true ),
inference(polarity_switch,[status(thm)],[307]) ).
thf(309,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[303]) ).
thf(310,plain,
( ( ! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[302]) ).
thf(311,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[301]) ).
thf(312,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[300]) ).
thf(313,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[299]) ).
thf(314,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)],[298]) ).
thf(315,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[297]) ).
thf(316,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)],[296]) ).
thf(317,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[295]) ).
thf(318,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)],[294]) ).
thf(319,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_rng @ ( relation_rng_restriction @ B @ C ) ) )
<=> ( ( in @ A @ B )
& ( in @ A @ ( relation_rng @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[293]) ).
thf(320,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)],[292]) ).
thf(321,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 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[291]) ).
thf(322,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( B
= ( identity_relation @ A ) )
<=> ( ( ( relation_dom @ B )
= A )
& ! [C: $i] :
( ( in @ C @ A )
=> ( ( apply @ B @ C )
= C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[290]) ).
thf(323,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[289]) ).
thf(324,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ C )
& ( in @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[288]) ).
thf(325,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)],[287]) ).
thf(326,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[286]) ).
thf(327,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)],[285]) ).
thf(328,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)],[284]) ).
thf(329,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ) )
= $true ),
inference(copy,[status(thm)],[283]) ).
thf(330,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
= A )
<=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[282]) ).
thf(331,plain,
( ( ! [A: $i] :
( ( ( relation_dom @ ( identity_relation @ A ) )
= A )
& ( ( relation_rng @ ( identity_relation @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[281]) ).
thf(332,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( relation @ D )
=> ( ( in @ ( ordered_pair @ A @ B ) @ ( relation_composition @ ( identity_relation @ C ) @ D ) )
<=> ( ( in @ A @ C )
& ( in @ ( ordered_pair @ A @ B ) @ D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[280]) ).
thf(333,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_dom @ ( relation_dom_restriction @ C @ B ) ) )
<=> ( ( in @ A @ B )
& ( in @ A @ ( relation_dom @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[279]) ).
thf(334,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[278]) ).
thf(335,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_dom_restriction @ B @ A )
= ( relation_composition @ ( identity_relation @ A ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[277]) ).
thf(336,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[276]) ).
thf(337,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( B
= ( identity_relation @ A ) )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ B )
<=> ( ( in @ C @ A )
& ( C = D ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[275]) ).
thf(338,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_dom_restriction @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ( ( in @ D @ B )
& ( in @ ( ordered_pair @ D @ E ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[274]) ).
thf(339,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_rng_restriction @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ( ( in @ E @ A )
& ( in @ ( ordered_pair @ D @ E ) @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[273]) ).
thf(340,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ ( ordered_pair @ E @ D ) @ A )
& ( in @ E @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[272]) ).
thf(341,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_inverse_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ A )
& ( in @ E @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[271]) ).
thf(342,plain,
( ( ! [A: $i] :
( ( relation @ A )
<=> ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[270]) ).
thf(343,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)],[269]) ).
thf(344,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(copy,[status(thm)],[268]) ).
thf(345,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[267]) ).
thf(346,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[266]) ).
thf(347,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( A = B )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ A )
<=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[265]) ).
thf(348,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)],[264]) ).
thf(349,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)],[263]) ).
thf(350,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)],[262]) ).
thf(351,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)],[261]) ).
thf(352,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ A )
=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[260]) ).
thf(353,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[259]) ).
thf(354,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)],[258]) ).
thf(355,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)],[257]) ).
thf(356,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)],[256]) ).
thf(357,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)],[255]) ).
thf(358,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)],[254]) ).
thf(359,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( B
= ( relation_inverse @ A ) )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ B )
<=> ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[253]) ).
thf(360,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_composition @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ? [F: $i] :
( ( in @ ( ordered_pair @ D @ F ) @ A )
& ( in @ ( ordered_pair @ F @ E ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[252]) ).
thf(361,plain,
$true = $true,
inference(copy,[status(thm)],[251]) ).
thf(362,plain,
$true = $true,
inference(copy,[status(thm)],[250]) ).
thf(363,plain,
$true = $true,
inference(copy,[status(thm)],[249]) ).
thf(364,plain,
$true = $true,
inference(copy,[status(thm)],[248]) ).
thf(365,plain,
$true = $true,
inference(copy,[status(thm)],[247]) ).
thf(366,plain,
$true = $true,
inference(copy,[status(thm)],[246]) ).
thf(367,plain,
$true = $true,
inference(copy,[status(thm)],[245]) ).
thf(368,plain,
$true = $true,
inference(copy,[status(thm)],[244]) ).
thf(369,plain,
$true = $true,
inference(copy,[status(thm)],[243]) ).
thf(370,plain,
$true = $true,
inference(copy,[status(thm)],[242]) ).
thf(371,plain,
$true = $true,
inference(copy,[status(thm)],[241]) ).
thf(372,plain,
$true = $true,
inference(copy,[status(thm)],[240]) ).
thf(373,plain,
$true = $true,
inference(copy,[status(thm)],[239]) ).
thf(374,plain,
$true = $true,
inference(copy,[status(thm)],[238]) ).
thf(375,plain,
$true = $true,
inference(copy,[status(thm)],[237]) ).
thf(376,plain,
$true = $true,
inference(copy,[status(thm)],[236]) ).
thf(377,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[235]) ).
thf(378,plain,
$true = $true,
inference(copy,[status(thm)],[234]) ).
thf(379,plain,
$true = $true,
inference(copy,[status(thm)],[233]) ).
thf(380,plain,
( ( ! [A: $i] :
( ( relation @ ( identity_relation @ A ) )
& ( function @ ( identity_relation @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[232]) ).
thf(381,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[231]) ).
thf(382,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[230]) ).
thf(383,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[229]) ).
thf(384,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[228]) ).
thf(385,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[227]) ).
thf(386,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(387,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)],[225]) ).
thf(388,plain,
( ( in @ sK2_SY203 @ sK1_A )
= $true ),
inference(copy,[status(thm)],[306]) ).
thf(389,plain,
( ( ( apply @ ( identity_relation @ sK1_A ) @ sK2_SY203 )
!= sK2_SY203 )
= $true ),
inference(copy,[status(thm)],[308]) ).
thf(390,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[336]) ).
thf(391,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)],[327]) ).
thf(392,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( in @ SX0 @ SX1 )
| ( disjoint @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311]) ).
thf(393,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)],[383]) ).
thf(394,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX1 )
| ~ ( function @ SX1 ) )
| ~ ( ~ ( ( SX1
!= ( identity_relation @ SX0 ) )
| ~ ( ( ( relation_dom @ SX1 )
!= SX0 )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( ( apply @ SX1 @ SX2 )
= SX2 ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SX1 )
!= SX0 )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( ( apply @ SX1 @ SX2 )
= SX2 ) ) )
| ( SX1
= ( identity_relation @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[322]) ).
thf(395,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)],[316]) ).
thf(396,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( SX0 != SX1 )
| ! [SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 ) ) ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 ) ) )
| ( SX0 = SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[347]) ).
thf(397,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)],[312]) ).
thf(398,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ( SX2
!= ( relation_composition @ SX0 @ SX1 ) )
| ! [SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 )
| ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX5 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX5 @ SX4 ) @ SX1 ) ) )
| ~ ( ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX5 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX5 @ SX4 ) @ SX1 ) )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 )
| ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX5 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX5 @ SX4 ) @ SX1 ) ) )
| ~ ( ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX5 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX5 @ SX4 ) @ SX1 ) )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 ) ) )
| ( SX2
= ( relation_composition @ SX0 @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360]) ).
thf(399,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)],[351]) ).
thf(400,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( SX1
!= ( identity_relation @ SX0 ) )
| ! [SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ~ ( ~ ( in @ SX2 @ SX0 )
| ( SX2 != SX3 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX2 @ SX0 )
| ( SX2 != SX3 ) )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ~ ( ~ ( in @ SX2 @ SX0 )
| ( SX2 != SX3 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX2 @ SX0 )
| ( SX2 != SX3 ) )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) ) )
| ( SX1
= ( identity_relation @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[337]) ).
thf(401,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)],[346]) ).
thf(402,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( relation_inverse_image @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 )
| ~ ( in @ SX4 @ SX1 ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 )
| ~ ( in @ SX4 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 )
| ~ ( in @ SX4 @ SX1 ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 )
| ~ ( in @ SX4 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( relation_inverse_image @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[341]) ).
thf(403,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)],[358]) ).
thf(404,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(405,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)],[350]) ).
thf(406,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ! [SX1: $i,SX2: $i] :
~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(407,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( ( set_union2 @ ( singleton @ SX0 ) @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(408,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ( SX2
!= ( relation_dom_restriction @ SX0 @ SX1 ) )
| ! [SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX1 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX1 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 ) )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX1 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX1 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 ) )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 ) ) )
| ( SX2
= ( relation_dom_restriction @ SX0 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(409,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)],[325]) ).
thf(410,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ~ ( in @ SX0 @ ( relation_rng @ ( relation_rng_restriction @ SX1 @ SX2 ) ) )
| ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX0 @ ( relation_rng @ SX2 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX0 @ ( relation_rng @ SX2 ) ) )
| ( in @ SX0 @ ( relation_rng @ ( relation_rng_restriction @ SX1 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319]) ).
thf(411,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)],[320]) ).
thf(412,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ SX1 )
| ( empty @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[382]) ).
thf(413,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)],[323]) ).
thf(414,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)],[343]) ).
thf(415,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( relation @ SX3 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( relation_composition @ ( identity_relation @ SX2 ) @ SX3 ) )
| ~ ( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX3 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX3 ) )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( relation_composition @ ( identity_relation @ SX2 ) @ SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[332]) ).
thf(416,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( ( relation_dom_restriction @ SX1 @ SX0 )
= ( relation_composition @ ( identity_relation @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(417,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)],[318]) ).
thf(418,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( relation_image @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX4 @ SX3 ) @ SX0 )
| ~ ( in @ SX4 @ SX1 ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX4 @ SX3 ) @ SX0 )
| ~ ( in @ SX4 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX4 @ SX3 ) @ SX0 )
| ~ ( in @ SX4 @ SX1 ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX4 @ SX3 ) @ SX0 )
| ~ ( in @ SX4 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( relation_image @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(419,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)],[324]) ).
thf(420,plain,
( ( ! [SX0: $i] :
~ ( ~ ( relation @ ( identity_relation @ SX0 ) )
| ~ ( function @ ( identity_relation @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[380]) ).
thf(421,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ SX2 ) ) )
| ( element @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[384]) ).
thf(422,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)],[348]) ).
thf(423,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)],[342]) ).
thf(424,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)],[314]) ).
thf(425,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ~ ( ~ ( in @ SX0 @ ( relation_field @ SX2 ) )
| ~ ( in @ SX1 @ ( relation_field @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[321]) ).
thf(426,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)],[345]) ).
thf(427,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ( SX2
!= ( relation_rng_restriction @ SX0 @ SX1 ) )
| ! [SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 )
| ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX1 ) )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 )
| ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX1 ) )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 ) ) )
| ( SX2
= ( relation_rng_restriction @ SX0 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[339]) ).
thf(428,plain,
( ( ! [SX0: $i] :
~ ( ( ( relation_dom @ ( identity_relation @ SX0 ) )
!= SX0 )
| ( ( relation_rng @ ( identity_relation @ SX0 ) )
!= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(429,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)],[344]) ).
thf(430,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)],[356]) ).
thf(431,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ~ ( in @ SX0 @ ( relation_dom @ ( relation_dom_restriction @ SX2 @ SX1 ) ) )
| ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX0 @ ( relation_dom @ SX2 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX0 @ ( relation_dom @ SX2 ) ) )
| ( in @ SX0 @ ( relation_dom @ ( relation_dom_restriction @ SX2 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(432,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( disjoint @ ( singleton @ SX0 ) @ SX1 )
| ~ ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310]) ).
thf(433,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ SX0 @ ( union @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[315]) ).
thf(434,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)],[387]) ).
thf(435,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)],[355]) ).
thf(436,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317]) ).
thf(437,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( SX1
!= ( relation_inverse @ SX0 ) )
| ! [SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) ) )
| ( SX1
= ( relation_inverse @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359]) ).
thf(438,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)],[330]) ).
thf(439,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ SX0 @ ( union @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(440,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[381]) ).
thf(441,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)],[353]) ).
thf(442,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)],[328]) ).
thf(443,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[313]) ).
thf(444,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)],[349]) ).
thf(445,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( ( set_union2 @ ( singleton @ SX0 ) @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[326]) ).
thf(446,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)],[357]) ).
thf(447,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ SX2 ) ) )
| ~ ( empty @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[385]) ).
thf(448,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)],[354]) ).
thf(449,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[386]) ).
thf(450,plain,
! [SV1: $i] :
( ( relation @ ( identity_relation @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(451,plain,
( ( ( apply @ ( identity_relation @ sK1_A ) @ sK2_SY203 )
= sK2_SY203 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(452,plain,
! [SV2: $i] :
( ( ! [SY204: $i] :
( ~ ( in @ SV2 @ SY204 )
| ~ ( in @ SY204 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(453,plain,
! [SV3: $i] :
( ( ! [SY205: $i] :
~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SV3 @ SY205 )
| ~ ! [SY206: $i] :
~ ( in @ SY206 @ ( set_intersection2 @ SV3 @ SY205 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY207: $i] :
~ ( in @ SY207 @ ( set_intersection2 @ SV3 @ SY205 ) )
| ~ ( disjoint @ SV3 @ SY205 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(454,plain,
! [SV4: $i] :
( ( ! [SY208: $i] :
( ~ ~ ( in @ SV4 @ SY208 )
| ( disjoint @ ( singleton @ SV4 ) @ SY208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(455,plain,
! [SV5: $i] :
( ( ! [SY209: $i] :
( ~ ! [SY210: $i] :
~ ( ~ ( ~ ( in @ SY210 @ SV5 )
| ( in @ SY210 @ SY209 ) )
| ~ ( ~ ( in @ SY210 @ SY209 )
| ( in @ SY210 @ SV5 ) ) )
| ( SV5 = SY209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(456,plain,
! [SV6: $i] :
( ( ! [SY211: $i] :
( ~ ~ ( ~ ( relation @ SY211 )
| ~ ( function @ SY211 ) )
| ~ ( ~ ( ( SY211
!= ( identity_relation @ SV6 ) )
| ~ ( ( ( relation_dom @ SY211 )
!= SV6 )
| ~ ! [SY212: $i] :
( ~ ( in @ SY212 @ SV6 )
| ( ( apply @ SY211 @ SY212 )
= SY212 ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SY211 )
!= SV6 )
| ~ ! [SY213: $i] :
( ~ ( in @ SY213 @ SV6 )
| ( ( apply @ SY211 @ SY213 )
= SY213 ) ) )
| ( SY211
= ( identity_relation @ SV6 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(457,plain,
! [SV7: $i] :
( ( ! [SY214: $i,SY215: $i,SY216: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV7 @ SY214 ) @ ( cartesian_product2 @ SY215 @ SY216 ) )
| ~ ( ~ ( in @ SV7 @ SY215 )
| ~ ( in @ SY214 @ SY216 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV7 @ SY215 )
| ~ ( in @ SY214 @ SY216 ) )
| ( in @ ( ordered_pair @ SV7 @ SY214 ) @ ( cartesian_product2 @ SY215 @ SY216 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(458,plain,
! [SV8: $i] :
( ( ~ ( relation @ SV8 )
| ! [SY217: $i] :
( ~ ( relation @ SY217 )
| ~ ( ~ ( ( SV8 != SY217 )
| ! [SY218: $i,SY219: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY218 @ SY219 ) @ SV8 )
| ( in @ ( ordered_pair @ SY218 @ SY219 ) @ SY217 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY218 @ SY219 ) @ SY217 )
| ( in @ ( ordered_pair @ SY218 @ SY219 ) @ SV8 ) ) ) )
| ~ ( ~ ! [SY220: $i,SY221: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY220 @ SY221 ) @ SV8 )
| ( in @ ( ordered_pair @ SY220 @ SY221 ) @ SY217 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY220 @ SY221 ) @ SY217 )
| ( in @ ( ordered_pair @ SY220 @ SY221 ) @ SV8 ) ) )
| ( SV8 = SY217 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(459,plain,
! [SV9: $i] :
( ( ! [SY222: $i] :
~ ( ~ ( ~ ( subset @ ( singleton @ SV9 ) @ SY222 )
| ( in @ SV9 @ SY222 ) )
| ~ ( ~ ( in @ SV9 @ SY222 )
| ( subset @ ( singleton @ SV9 ) @ SY222 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(460,plain,
! [SV10: $i] :
( ( ~ ( relation @ SV10 )
| ! [SY223: $i] :
( ~ ( relation @ SY223 )
| ! [SY224: $i] :
( ~ ( relation @ SY224 )
| ~ ( ~ ( ( SY224
!= ( relation_composition @ SV10 @ SY223 ) )
| ! [SY225: $i,SY226: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY225 @ SY226 ) @ SY224 )
| ~ ! [SY227: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY225 @ SY227 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY227 @ SY226 ) @ SY223 ) ) )
| ~ ( ~ ~ ! [SY228: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY225 @ SY228 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY228 @ SY226 ) @ SY223 ) )
| ( in @ ( ordered_pair @ SY225 @ SY226 ) @ SY224 ) ) ) )
| ~ ( ~ ! [SY229: $i,SY230: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY229 @ SY230 ) @ SY224 )
| ~ ! [SY231: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY229 @ SY231 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY231 @ SY230 ) @ SY223 ) ) )
| ~ ( ~ ~ ! [SY232: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY229 @ SY232 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY232 @ SY230 ) @ SY223 ) )
| ( in @ ( ordered_pair @ SY229 @ SY230 ) @ SY224 ) ) )
| ( SY224
= ( relation_composition @ SV10 @ SY223 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(461,plain,
! [SV11: $i] :
( ( ! [SY233: $i,SY234: $i] :
~ ( ~ ( ( SY234
!= ( cartesian_product2 @ SV11 @ SY233 ) )
| ! [SY235: $i] :
~ ( ~ ( ~ ( in @ SY235 @ SY234 )
| ~ ! [SY236: $i] :
~ ~ ! [SY237: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY236 @ SV11 )
| ~ ( in @ SY237 @ SY233 ) )
| ( SY235
!= ( ordered_pair @ SY236 @ SY237 ) ) ) )
| ~ ( ~ ~ ! [SY238: $i] :
~ ~ ! [SY239: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY238 @ SV11 )
| ~ ( in @ SY239 @ SY233 ) )
| ( SY235
!= ( ordered_pair @ SY238 @ SY239 ) ) )
| ( in @ SY235 @ SY234 ) ) ) )
| ~ ( ~ ! [SY240: $i] :
~ ( ~ ( ~ ( in @ SY240 @ SY234 )
| ~ ! [SY241: $i] :
~ ~ ! [SY242: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY241 @ SV11 )
| ~ ( in @ SY242 @ SY233 ) )
| ( SY240
!= ( ordered_pair @ SY241 @ SY242 ) ) ) )
| ~ ( ~ ~ ! [SY243: $i] :
~ ~ ! [SY244: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY243 @ SV11 )
| ~ ( in @ SY244 @ SY233 ) )
| ( SY240
!= ( ordered_pair @ SY243 @ SY244 ) ) )
| ( in @ SY240 @ SY234 ) ) )
| ( SY234
= ( cartesian_product2 @ SV11 @ SY233 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(462,plain,
! [SV12: $i] :
( ( ! [SY245: $i] :
( ~ ( relation @ SY245 )
| ~ ( ~ ( ( SY245
!= ( identity_relation @ SV12 ) )
| ! [SY246: $i,SY247: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY246 @ SY247 ) @ SY245 )
| ~ ( ~ ( in @ SY246 @ SV12 )
| ( SY246 != SY247 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY246 @ SV12 )
| ( SY246 != SY247 ) )
| ( in @ ( ordered_pair @ SY246 @ SY247 ) @ SY245 ) ) ) )
| ~ ( ~ ! [SY248: $i,SY249: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY248 @ SY249 ) @ SY245 )
| ~ ( ~ ( in @ SY248 @ SV12 )
| ( SY248 != SY249 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY248 @ SV12 )
| ( SY248 != SY249 ) )
| ( in @ ( ordered_pair @ SY248 @ SY249 ) @ SY245 ) ) )
| ( SY245
= ( identity_relation @ SV12 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(463,plain,
! [SV13: $i] :
( ( ! [SY250: $i] :
~ ( ~ ( ( SY250
!= ( powerset @ SV13 ) )
| ! [SY251: $i] :
~ ( ~ ( ~ ( in @ SY251 @ SY250 )
| ( subset @ SY251 @ SV13 ) )
| ~ ( ~ ( subset @ SY251 @ SV13 )
| ( in @ SY251 @ SY250 ) ) ) )
| ~ ( ~ ! [SY252: $i] :
~ ( ~ ( ~ ( in @ SY252 @ SY250 )
| ( subset @ SY252 @ SV13 ) )
| ~ ( ~ ( subset @ SY252 @ SV13 )
| ( in @ SY252 @ SY250 ) ) )
| ( SY250
= ( powerset @ SV13 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(464,plain,
! [SV14: $i] :
( ( ~ ( relation @ SV14 )
| ! [SY253: $i,SY254: $i] :
~ ( ~ ( ( SY254
!= ( relation_inverse_image @ SV14 @ SY253 ) )
| ! [SY255: $i] :
~ ( ~ ( ~ ( in @ SY255 @ SY254 )
| ~ ! [SY256: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY255 @ SY256 ) @ SV14 )
| ~ ( in @ SY256 @ SY253 ) ) )
| ~ ( ~ ~ ! [SY257: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY255 @ SY257 ) @ SV14 )
| ~ ( in @ SY257 @ SY253 ) )
| ( in @ SY255 @ SY254 ) ) ) )
| ~ ( ~ ! [SY258: $i] :
~ ( ~ ( ~ ( in @ SY258 @ SY254 )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY258 @ SY259 ) @ SV14 )
| ~ ( in @ SY259 @ SY253 ) ) )
| ~ ( ~ ~ ! [SY260: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY258 @ SY260 ) @ SV14 )
| ~ ( in @ SY260 @ SY253 ) )
| ( in @ SY258 @ SY254 ) ) )
| ( SY254
= ( relation_inverse_image @ SV14 @ SY253 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(465,plain,
! [SV15: $i] :
( ( ~ ( relation @ SV15 )
| ! [SY261: $i] :
~ ( ~ ( ( SY261
!= ( relation_rng @ SV15 ) )
| ! [SY262: $i] :
~ ( ~ ( ~ ( in @ SY262 @ SY261 )
| ~ ! [SY263: $i] :
~ ( in @ ( ordered_pair @ SY263 @ SY262 ) @ SV15 ) )
| ~ ( ~ ~ ! [SY264: $i] :
~ ( in @ ( ordered_pair @ SY264 @ SY262 ) @ SV15 )
| ( in @ SY262 @ SY261 ) ) ) )
| ~ ( ~ ! [SY265: $i] :
~ ( ~ ( ~ ( in @ SY265 @ SY261 )
| ~ ! [SY266: $i] :
~ ( in @ ( ordered_pair @ SY266 @ SY265 ) @ SV15 ) )
| ~ ( ~ ~ ! [SY267: $i] :
~ ( in @ ( ordered_pair @ SY267 @ SY265 ) @ SV15 )
| ( in @ SY265 @ SY261 ) ) )
| ( SY261
= ( relation_rng @ SV15 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(466,plain,
! [SV16: $i] :
( ( ~ ( relation @ SV16 )
| ! [SY268: $i] :
( ~ ( relation @ SY268 )
| ~ ( ~ ( ~ ( subset @ SV16 @ SY268 )
| ! [SY269: $i,SY270: $i] :
( ~ ( in @ ( ordered_pair @ SY269 @ SY270 ) @ SV16 )
| ( in @ ( ordered_pair @ SY269 @ SY270 ) @ SY268 ) ) )
| ~ ( ~ ! [SY271: $i,SY272: $i] :
( ~ ( in @ ( ordered_pair @ SY271 @ SY272 ) @ SV16 )
| ( in @ ( ordered_pair @ SY271 @ SY272 ) @ SY268 ) )
| ( subset @ SV16 @ SY268 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(467,plain,
! [SV17: $i] :
( ( ! [SY273: $i,SY274: $i] :
~ ( ~ ( ( SY274
!= ( set_union2 @ SV17 @ SY273 ) )
| ! [SY275: $i] :
~ ( ~ ( ~ ( in @ SY275 @ SY274 )
| ( in @ SY275 @ SV17 )
| ( in @ SY275 @ SY273 ) )
| ~ ( ~ ( ( in @ SY275 @ SV17 )
| ( in @ SY275 @ SY273 ) )
| ( in @ SY275 @ SY274 ) ) ) )
| ~ ( ~ ! [SY276: $i] :
~ ( ~ ( ~ ( in @ SY276 @ SY274 )
| ( in @ SY276 @ SV17 )
| ( in @ SY276 @ SY273 ) )
| ~ ( ~ ( ( in @ SY276 @ SV17 )
| ( in @ SY276 @ SY273 ) )
| ( in @ SY276 @ SY274 ) ) )
| ( SY274
= ( set_union2 @ SV17 @ SY273 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(468,plain,
! [SV18: $i] :
( ( ~ ( relation @ SV18 )
| ~ ! [SY277: $i,SY278: $i] :
~ ( in @ ( ordered_pair @ SY277 @ SY278 ) @ SV18 )
| ( SV18 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(469,plain,
! [SV19: $i] :
( ( ! [SY279: $i] :
( ~ ( in @ SV19 @ SY279 )
| ( ( set_union2 @ ( singleton @ SV19 ) @ SY279 )
= SY279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(470,plain,
! [SV20: $i] :
( ( ~ ( relation @ SV20 )
| ! [SY280: $i,SY281: $i] :
( ~ ( relation @ SY281 )
| ~ ( ~ ( ( SY281
!= ( relation_dom_restriction @ SV20 @ SY280 ) )
| ! [SY282: $i,SY283: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY282 @ SY283 ) @ SY281 )
| ~ ( ~ ( in @ SY282 @ SY280 )
| ~ ( in @ ( ordered_pair @ SY282 @ SY283 ) @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY282 @ SY280 )
| ~ ( in @ ( ordered_pair @ SY282 @ SY283 ) @ SV20 ) )
| ( in @ ( ordered_pair @ SY282 @ SY283 ) @ SY281 ) ) ) )
| ~ ( ~ ! [SY284: $i,SY285: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY284 @ SY285 ) @ SY281 )
| ~ ( ~ ( in @ SY284 @ SY280 )
| ~ ( in @ ( ordered_pair @ SY284 @ SY285 ) @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY284 @ SY280 )
| ~ ( in @ ( ordered_pair @ SY284 @ SY285 ) @ SV20 ) )
| ( in @ ( ordered_pair @ SY284 @ SY285 ) @ SY281 ) ) )
| ( SY281
= ( relation_dom_restriction @ SV20 @ SY280 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(471,plain,
! [SV21: $i] :
( ( ! [SY286: $i] :
~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SV21 @ SY286 )
| ~ ! [SY287: $i] :
~ ~ ( ~ ( in @ SY287 @ SV21 )
| ~ ( in @ SY287 @ SY286 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY288: $i] :
~ ~ ( ~ ( in @ SY288 @ SV21 )
| ~ ( in @ SY288 @ SY286 ) )
| ~ ( disjoint @ SV21 @ SY286 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(472,plain,
! [SV22: $i] :
( ( ! [SY289: $i,SY290: $i] :
( ~ ( relation @ SY290 )
| ~ ( ~ ( ~ ( in @ SV22 @ ( relation_rng @ ( relation_rng_restriction @ SY289 @ SY290 ) ) )
| ~ ( ~ ( in @ SV22 @ SY289 )
| ~ ( in @ SV22 @ ( relation_rng @ SY290 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV22 @ SY289 )
| ~ ( in @ SV22 @ ( relation_rng @ SY290 ) ) )
| ( in @ SV22 @ ( relation_rng @ ( relation_rng_restriction @ SY289 @ SY290 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(473,plain,
! [SV23: $i] :
( ( ~ ! [SY291: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV23 @ SY291 )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY291 )
| ~ ( subset @ SX3 @ SX2 ) )
| ( in @ SX3 @ SY291 ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY291 )
| ( in @ ( powerset @ SX2 ) @ SY291 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SX2 @ SY291 )
| ~ ~ ( are_equipotent @ SX2 @ SY291 ) )
| ~ ~ ( in @ SX2 @ SY291 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(474,plain,
! [SV24: $i] :
( ( ! [SY296: $i] :
( ~ ( element @ SV24 @ SY296 )
| ( empty @ SY296 )
| ( in @ SV24 @ SY296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(475,plain,
! [SV25: $i] :
( ( ! [SY297: $i] :
~ ( ~ ( ~ ( subset @ ( singleton @ SV25 ) @ SY297 )
| ( in @ SV25 @ SY297 ) )
| ~ ( ~ ( in @ SV25 @ SY297 )
| ( subset @ ( singleton @ SV25 ) @ SY297 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(476,plain,
! [SV26: $i] :
( ( ! [SY298: $i] :
~ ( ~ ( ~ ( ( SV26 != empty_set ) )
| ~ ( ~ ( ( SY298
!= ( set_meet @ SV26 ) )
| ! [SY299: $i] :
~ ( ~ ( ~ ( in @ SY299 @ SY298 )
| ! [SY300: $i] :
( ~ ( in @ SY300 @ SV26 )
| ( in @ SY299 @ SY300 ) ) )
| ~ ( ~ ! [SY301: $i] :
( ~ ( in @ SY301 @ SV26 )
| ( in @ SY299 @ SY301 ) )
| ( in @ SY299 @ SY298 ) ) ) )
| ~ ( ~ ! [SY302: $i] :
~ ( ~ ( ~ ( in @ SY302 @ SY298 )
| ! [SY303: $i] :
( ~ ( in @ SY303 @ SV26 )
| ( in @ SY302 @ SY303 ) ) )
| ~ ( ~ ! [SY304: $i] :
( ~ ( in @ SY304 @ SV26 )
| ( in @ SY302 @ SY304 ) )
| ( in @ SY302 @ SY298 ) ) )
| ( SY298
= ( set_meet @ SV26 ) ) ) ) )
| ~ ( ( SV26 != empty_set )
| ~ ( ~ ( ( SY298
!= ( set_meet @ SV26 ) )
| ( SY298 = empty_set ) )
| ~ ( ( SY298 != empty_set )
| ( SY298
= ( set_meet @ SV26 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(477,plain,
! [SV27: $i] :
( ( ! [SY305: $i,SY306: $i,SY307: $i] :
( ~ ( relation @ SY307 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV27 @ SY305 ) @ ( relation_composition @ ( identity_relation @ SY306 ) @ SY307 ) )
| ~ ( ~ ( in @ SV27 @ SY306 )
| ~ ( in @ ( ordered_pair @ SV27 @ SY305 ) @ SY307 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV27 @ SY306 )
| ~ ( in @ ( ordered_pair @ SV27 @ SY305 ) @ SY307 ) )
| ( in @ ( ordered_pair @ SV27 @ SY305 ) @ ( relation_composition @ ( identity_relation @ SY306 ) @ SY307 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(478,plain,
! [SV28: $i] :
( ( ! [SY308: $i] :
( ~ ( relation @ SY308 )
| ( ( relation_dom_restriction @ SY308 @ SV28 )
= ( relation_composition @ ( identity_relation @ SV28 ) @ SY308 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(479,plain,
! [SV29: $i] :
( ( ! [SY309: $i,SY310: $i,SY311: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV29 @ SY309 ) @ ( cartesian_product2 @ SY310 @ SY311 ) )
| ~ ( ~ ( in @ SV29 @ SY310 )
| ~ ( in @ SY309 @ SY311 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV29 @ SY310 )
| ~ ( in @ SY309 @ SY311 ) )
| ( in @ ( ordered_pair @ SV29 @ SY309 ) @ ( cartesian_product2 @ SY310 @ SY311 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(480,plain,
! [SV30: $i] :
( ( ~ ( relation @ SV30 )
| ! [SY312: $i,SY313: $i] :
~ ( ~ ( ( SY313
!= ( relation_image @ SV30 @ SY312 ) )
| ! [SY314: $i] :
~ ( ~ ( ~ ( in @ SY314 @ SY313 )
| ~ ! [SY315: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY315 @ SY314 ) @ SV30 )
| ~ ( in @ SY315 @ SY312 ) ) )
| ~ ( ~ ~ ! [SY316: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY316 @ SY314 ) @ SV30 )
| ~ ( in @ SY316 @ SY312 ) )
| ( in @ SY314 @ SY313 ) ) ) )
| ~ ( ~ ! [SY317: $i] :
~ ( ~ ( ~ ( in @ SY317 @ SY313 )
| ~ ! [SY318: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY318 @ SY317 ) @ SV30 )
| ~ ( in @ SY318 @ SY312 ) ) )
| ~ ( ~ ~ ! [SY319: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY319 @ SY317 ) @ SV30 )
| ~ ( in @ SY319 @ SY312 ) )
| ( in @ SY317 @ SY313 ) ) )
| ( SY313
= ( relation_image @ SV30 @ SY312 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(481,plain,
! [SV31: $i] :
( ( ! [SY320: $i,SY321: $i] :
~ ( ~ ( ~ ( subset @ ( unordered_pair @ SV31 @ SY320 ) @ SY321 )
| ~ ( ~ ( in @ SV31 @ SY321 )
| ~ ( in @ SY320 @ SY321 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV31 @ SY321 )
| ~ ( in @ SY320 @ SY321 ) )
| ( subset @ ( unordered_pair @ SV31 @ SY320 ) @ SY321 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(482,plain,
! [SV32: $i] :
( ( ~ ( ~ ( relation @ ( identity_relation @ SV32 ) )
| ~ ( function @ ( identity_relation @ SV32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(483,plain,
! [SV33: $i] :
( ( ! [SY322: $i,SY323: $i] :
( ~ ~ ( ~ ( in @ SV33 @ SY322 )
| ~ ( element @ SY322 @ ( powerset @ SY323 ) ) )
| ( element @ SV33 @ SY323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(484,plain,
! [SV34: $i] :
( ( ! [SY324: $i] :
~ ( ~ ( ~ ~ ( empty @ SV34 )
| ~ ( ~ ( ~ ( element @ SY324 @ SV34 )
| ( in @ SY324 @ SV34 ) )
| ~ ( ~ ( in @ SY324 @ SV34 )
| ( element @ SY324 @ SV34 ) ) ) )
| ~ ( ~ ( empty @ SV34 )
| ~ ( ~ ( ~ ( element @ SY324 @ SV34 )
| ( empty @ SY324 ) )
| ~ ( ~ ( empty @ SY324 )
| ( element @ SY324 @ SV34 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(485,plain,
! [SV35: $i] :
( ( ~ ( ~ ( ~ ( relation @ SV35 )
| ! [SY325: $i] :
~ ~ ( ~ ( in @ SY325 @ SV35 )
| ~ ! [SX2: $i,SX3: $i] :
( SY325
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
| ~ ( ~ ! [SY328: $i] :
~ ~ ( ~ ( in @ SY328 @ SV35 )
| ~ ! [SX2: $i,SX3: $i] :
( SY328
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(486,plain,
! [SV36: $i] :
( ( ! [SY331: $i,SY332: $i] :
( ~ ( subset @ SV36 @ SY331 )
| ( in @ SY332 @ SV36 )
| ( subset @ SV36 @ ( set_difference @ SY331 @ ( singleton @ SY332 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(487,plain,
! [SV37: $i] :
( ( ! [SY333: $i,SY334: $i] :
( ~ ( relation @ SY334 )
| ~ ( in @ ( ordered_pair @ SV37 @ SY333 ) @ SY334 )
| ~ ( ~ ( in @ SV37 @ ( relation_field @ SY334 ) )
| ~ ( in @ SY333 @ ( relation_field @ SY334 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(488,plain,
! [SV38: $i] :
( ( ~ ( ~ ( ( SV38 != empty_set )
| ! [SY335: $i] :
~ ( in @ SY335 @ SV38 ) )
| ~ ( ~ ! [SY336: $i] :
~ ( in @ SY336 @ SV38 )
| ( SV38 = empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(489,plain,
! [SV39: $i] :
( ( ! [SY337: $i] :
( ~ ( relation @ SY337 )
| ! [SY338: $i] :
( ~ ( relation @ SY338 )
| ~ ( ~ ( ( SY338
!= ( relation_rng_restriction @ SV39 @ SY337 ) )
| ! [SY339: $i,SY340: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY339 @ SY340 ) @ SY338 )
| ~ ( ~ ( in @ SY340 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY339 @ SY340 ) @ SY337 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY340 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY339 @ SY340 ) @ SY337 ) )
| ( in @ ( ordered_pair @ SY339 @ SY340 ) @ SY338 ) ) ) )
| ~ ( ~ ! [SY341: $i,SY342: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY341 @ SY342 ) @ SY338 )
| ~ ( ~ ( in @ SY342 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY341 @ SY342 ) @ SY337 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY342 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY341 @ SY342 ) @ SY337 ) )
| ( in @ ( ordered_pair @ SY341 @ SY342 ) @ SY338 ) ) )
| ( SY338
= ( relation_rng_restriction @ SV39 @ SY337 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(490,plain,
! [SV40: $i] :
( ( ~ ( ( ( relation_dom @ ( identity_relation @ SV40 ) )
!= SV40 )
| ( ( relation_rng @ ( identity_relation @ SV40 ) )
!= SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(491,plain,
! [SV41: $i] :
( ( ! [SY343: $i] :
~ ( ~ ( ( SY343
!= ( singleton @ SV41 ) )
| ! [SY344: $i] :
~ ( ~ ( ~ ( in @ SY344 @ SY343 )
| ( SY344 = SV41 ) )
| ~ ( ( SY344 != SV41 )
| ( in @ SY344 @ SY343 ) ) ) )
| ~ ( ~ ! [SY345: $i] :
~ ( ~ ( ~ ( in @ SY345 @ SY343 )
| ( SY345 = SV41 ) )
| ~ ( ( SY345 != SV41 )
| ( in @ SY345 @ SY343 ) ) )
| ( SY343
= ( singleton @ SV41 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(492,plain,
! [SV42: $i] :
( ( ! [SY346: $i] :
~ ( ~ ( ( SY346
!= ( union @ SV42 ) )
| ! [SY347: $i] :
~ ( ~ ( ~ ( in @ SY347 @ SY346 )
| ~ ! [SY348: $i] :
~ ~ ( ~ ( in @ SY347 @ SY348 )
| ~ ( in @ SY348 @ SV42 ) ) )
| ~ ( ~ ~ ! [SY349: $i] :
~ ~ ( ~ ( in @ SY347 @ SY349 )
| ~ ( in @ SY349 @ SV42 ) )
| ( in @ SY347 @ SY346 ) ) ) )
| ~ ( ~ ! [SY350: $i] :
~ ( ~ ( ~ ( in @ SY350 @ SY346 )
| ~ ! [SY351: $i] :
~ ~ ( ~ ( in @ SY350 @ SY351 )
| ~ ( in @ SY351 @ SV42 ) ) )
| ~ ( ~ ~ ! [SY352: $i] :
~ ~ ( ~ ( in @ SY350 @ SY352 )
| ~ ( in @ SY352 @ SV42 ) )
| ( in @ SY350 @ SY346 ) ) )
| ( SY346
= ( union @ SV42 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(493,plain,
! [SV43: $i] :
( ( ! [SY353: $i,SY354: $i] :
( ~ ( relation @ SY354 )
| ~ ( ~ ( ~ ( in @ SV43 @ ( relation_dom @ ( relation_dom_restriction @ SY354 @ SY353 ) ) )
| ~ ( ~ ( in @ SV43 @ SY353 )
| ~ ( in @ SV43 @ ( relation_dom @ SY354 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV43 @ SY353 )
| ~ ( in @ SV43 @ ( relation_dom @ SY354 ) ) )
| ( in @ SV43 @ ( relation_dom @ ( relation_dom_restriction @ SY354 @ SY353 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(494,plain,
! [SV44: $i] :
( ( ! [SY355: $i] :
~ ~ ( ~ ( disjoint @ ( singleton @ SV44 ) @ SY355 )
| ~ ( in @ SV44 @ SY355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(495,plain,
! [SV45: $i] :
( ( ! [SY356: $i] :
( ~ ( in @ SV45 @ SY356 )
| ( subset @ SV45 @ ( union @ SY356 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(496,plain,
! [SV46: $i] :
( ( ~ ! [SY357: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV46 @ SY357 )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY357 )
| ~ ( subset @ SX3 @ SX2 ) )
| ( in @ SX3 @ SY357 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SY357 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SY357 )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) ) ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SX2 @ SY357 )
| ~ ~ ( are_equipotent @ SX2 @ SY357 ) )
| ~ ~ ( in @ SX2 @ SY357 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(497,plain,
! [SV47: $i] :
( ( ~ ( relation @ SV47 )
| ! [SY364: $i] :
~ ( ~ ( ( SY364
!= ( relation_dom @ SV47 ) )
| ! [SY365: $i] :
~ ( ~ ( ~ ( in @ SY365 @ SY364 )
| ~ ! [SY366: $i] :
~ ( in @ ( ordered_pair @ SY365 @ SY366 ) @ SV47 ) )
| ~ ( ~ ~ ! [SY367: $i] :
~ ( in @ ( ordered_pair @ SY365 @ SY367 ) @ SV47 )
| ( in @ SY365 @ SY364 ) ) ) )
| ~ ( ~ ! [SY368: $i] :
~ ( ~ ( ~ ( in @ SY368 @ SY364 )
| ~ ! [SY369: $i] :
~ ( in @ ( ordered_pair @ SY368 @ SY369 ) @ SV47 ) )
| ~ ( ~ ~ ! [SY370: $i] :
~ ( in @ ( ordered_pair @ SY368 @ SY370 ) @ SV47 )
| ( in @ SY368 @ SY364 ) ) )
| ( SY364
= ( relation_dom @ SV47 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(498,plain,
! [SV48: $i] :
( ( ! [SY371: $i] :
( ~ ! [SY372: $i] :
( ~ ( in @ SY372 @ SV48 )
| ( in @ SY372 @ SY371 ) )
| ( element @ SV48 @ ( powerset @ SY371 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(499,plain,
! [SV49: $i] :
( ( ~ ( relation @ SV49 )
| ! [SY373: $i] :
( ~ ( relation @ SY373 )
| ~ ( ~ ( ( SY373
!= ( relation_inverse @ SV49 ) )
| ! [SY374: $i,SY375: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY374 @ SY375 ) @ SY373 )
| ( in @ ( ordered_pair @ SY375 @ SY374 ) @ SV49 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY375 @ SY374 ) @ SV49 )
| ( in @ ( ordered_pair @ SY374 @ SY375 ) @ SY373 ) ) ) )
| ~ ( ~ ! [SY376: $i,SY377: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY376 @ SY377 ) @ SY373 )
| ( in @ ( ordered_pair @ SY377 @ SY376 ) @ SV49 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY377 @ SY376 ) @ SV49 )
| ( in @ ( ordered_pair @ SY376 @ SY377 ) @ SY373 ) ) )
| ( SY373
= ( relation_inverse @ SV49 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(500,plain,
! [SV50: $i] :
( ( ! [SY378: $i] :
~ ( ~ ( ( ( set_difference @ SV50 @ ( singleton @ SY378 ) )
!= SV50 )
| ~ ( in @ SY378 @ SV50 ) )
| ~ ( ~ ~ ( in @ SY378 @ SV50 )
| ( ( set_difference @ SV50 @ ( singleton @ SY378 ) )
= SV50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(501,plain,
! [SV51: $i] :
( ( ! [SY379: $i] :
( ~ ( in @ SV51 @ SY379 )
| ( subset @ SV51 @ ( union @ SY379 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(502,plain,
! [SV52: $i] :
( ( ! [SY380: $i] :
( ~ ( in @ SV52 @ SY380 )
| ( element @ SV52 @ SY380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(503,plain,
! [SV53: $i] :
( ( ! [SY381: $i] :
~ ( ~ ( ~ ( subset @ SV53 @ SY381 )
| ! [SY382: $i] :
( ~ ( in @ SY382 @ SV53 )
| ( in @ SY382 @ SY381 ) ) )
| ~ ( ~ ! [SY383: $i] :
( ~ ( in @ SY383 @ SV53 )
| ( in @ SY383 @ SY381 ) )
| ( subset @ SV53 @ SY381 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(504,plain,
! [SV54: $i] :
( ( ! [SY384: $i,SY385: $i] :
( ~ ( element @ SY385 @ ( powerset @ SV54 ) )
| ~ ~ ( ~ ( in @ SY384 @ ( subset_complement @ SV54 @ SY385 ) )
| ~ ( in @ SY384 @ SY385 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(505,plain,
! [SV55: $i] :
( ( ! [SY386: $i] :
( ~ ( element @ SY386 @ ( powerset @ SV55 ) )
| ! [SY387: $i] :
( ~ ( in @ SY387 @ SY386 )
| ( in @ SY387 @ SV55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(506,plain,
! [SV56: $i] :
( ( ! [SY388: $i,SY389: $i] :
~ ( ~ ( ( SY389
!= ( unordered_pair @ SV56 @ SY388 ) )
| ! [SY390: $i] :
~ ( ~ ( ~ ( in @ SY390 @ SY389 )
| ( SY390 = SV56 )
| ( SY390 = SY388 ) )
| ~ ( ~ ( ( SY390 = SV56 )
| ( SY390 = SY388 ) )
| ( in @ SY390 @ SY389 ) ) ) )
| ~ ( ~ ! [SY391: $i] :
~ ( ~ ( ~ ( in @ SY391 @ SY389 )
| ( SY391 = SV56 )
| ( SY391 = SY388 ) )
| ~ ( ~ ( ( SY391 = SV56 )
| ( SY391 = SY388 ) )
| ( in @ SY391 @ SY389 ) ) )
| ( SY389
= ( unordered_pair @ SV56 @ SY388 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(507,plain,
! [SV57: $i] :
( ( ! [SY392: $i] :
( ~ ( in @ SV57 @ SY392 )
| ( ( set_union2 @ ( singleton @ SV57 ) @ SY392 )
= SY392 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(508,plain,
! [SV58: $i] :
( ( ! [SY393: $i,SY394: $i] :
~ ( ~ ( ( SY394
!= ( set_difference @ SV58 @ SY393 ) )
| ! [SY395: $i] :
~ ( ~ ( ~ ( in @ SY395 @ SY394 )
| ~ ( ~ ( in @ SY395 @ SV58 )
| ~ ~ ( in @ SY395 @ SY393 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY395 @ SV58 )
| ~ ~ ( in @ SY395 @ SY393 ) )
| ( in @ SY395 @ SY394 ) ) ) )
| ~ ( ~ ! [SY396: $i] :
~ ( ~ ( ~ ( in @ SY396 @ SY394 )
| ~ ( ~ ( in @ SY396 @ SV58 )
| ~ ~ ( in @ SY396 @ SY393 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY396 @ SV58 )
| ~ ~ ( in @ SY396 @ SY393 ) )
| ( in @ SY396 @ SY394 ) ) )
| ( SY394
= ( set_difference @ SV58 @ SY393 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(509,plain,
! [SV59: $i] :
( ( ! [SY397: $i,SY398: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV59 @ SY397 )
| ~ ( element @ SY397 @ ( powerset @ SY398 ) ) )
| ~ ( empty @ SY398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(510,plain,
! [SV60: $i] :
( ( ! [SY399: $i,SY400: $i] :
~ ( ~ ( ( SY400
!= ( set_intersection2 @ SV60 @ SY399 ) )
| ! [SY401: $i] :
~ ( ~ ( ~ ( in @ SY401 @ SY400 )
| ~ ( ~ ( in @ SY401 @ SV60 )
| ~ ( in @ SY401 @ SY399 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY401 @ SV60 )
| ~ ( in @ SY401 @ SY399 ) )
| ( in @ SY401 @ SY400 ) ) ) )
| ~ ( ~ ! [SY402: $i] :
~ ( ~ ( ~ ( in @ SY402 @ SY400 )
| ~ ( ~ ( in @ SY402 @ SV60 )
| ~ ( in @ SY402 @ SY399 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY402 @ SV60 )
| ~ ( in @ SY402 @ SY399 ) )
| ( in @ SY402 @ SY400 ) ) )
| ( SY400
= ( set_intersection2 @ SV60 @ SY399 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(511,plain,
! [SV61: $i] :
( ( ! [SY403: $i] :
~ ~ ( ~ ( in @ SV61 @ SY403 )
| ~ ( empty @ SY403 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(512,plain,
! [SV62: $i,SV2: $i] :
( ( ~ ( in @ SV2 @ SV62 )
| ~ ( in @ SV62 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(513,plain,
! [SV63: $i,SV3: $i] :
( ( ~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SV3 @ SV63 )
| ~ ! [SY404: $i] :
~ ( in @ SY404 @ ( set_intersection2 @ SV3 @ SV63 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY405: $i] :
~ ( in @ SY405 @ ( set_intersection2 @ SV3 @ SV63 ) )
| ~ ( disjoint @ SV3 @ SV63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(514,plain,
! [SV64: $i,SV4: $i] :
( ( ~ ~ ( in @ SV4 @ SV64 )
| ( disjoint @ ( singleton @ SV4 ) @ SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(515,plain,
! [SV65: $i,SV5: $i] :
( ( ~ ! [SY406: $i] :
~ ( ~ ( ~ ( in @ SY406 @ SV5 )
| ( in @ SY406 @ SV65 ) )
| ~ ( ~ ( in @ SY406 @ SV65 )
| ( in @ SY406 @ SV5 ) ) )
| ( SV5 = SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(516,plain,
! [SV6: $i,SV66: $i] :
( ( ~ ~ ( ~ ( relation @ SV66 )
| ~ ( function @ SV66 ) )
| ~ ( ~ ( ( SV66
!= ( identity_relation @ SV6 ) )
| ~ ( ( ( relation_dom @ SV66 )
!= SV6 )
| ~ ! [SY407: $i] :
( ~ ( in @ SY407 @ SV6 )
| ( ( apply @ SV66 @ SY407 )
= SY407 ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV66 )
!= SV6 )
| ~ ! [SY408: $i] :
( ~ ( in @ SY408 @ SV6 )
| ( ( apply @ SV66 @ SY408 )
= SY408 ) ) )
| ( SV66
= ( identity_relation @ SV6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(517,plain,
! [SV67: $i,SV7: $i] :
( ( ! [SY409: $i,SY410: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV7 @ SV67 ) @ ( cartesian_product2 @ SY409 @ SY410 ) )
| ~ ( ~ ( in @ SV7 @ SY409 )
| ~ ( in @ SV67 @ SY410 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV7 @ SY409 )
| ~ ( in @ SV67 @ SY410 ) )
| ( in @ ( ordered_pair @ SV7 @ SV67 ) @ ( cartesian_product2 @ SY409 @ SY410 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(518,plain,
! [SV8: $i] :
( ( ( ~ ( relation @ SV8 ) )
= $true )
| ( ( ! [SY217: $i] :
( ~ ( relation @ SY217 )
| ~ ( ~ ( ( SV8 != SY217 )
| ! [SY218: $i,SY219: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY218 @ SY219 ) @ SV8 )
| ( in @ ( ordered_pair @ SY218 @ SY219 ) @ SY217 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY218 @ SY219 ) @ SY217 )
| ( in @ ( ordered_pair @ SY218 @ SY219 ) @ SV8 ) ) ) )
| ~ ( ~ ! [SY220: $i,SY221: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY220 @ SY221 ) @ SV8 )
| ( in @ ( ordered_pair @ SY220 @ SY221 ) @ SY217 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY220 @ SY221 ) @ SY217 )
| ( in @ ( ordered_pair @ SY220 @ SY221 ) @ SV8 ) ) )
| ( SV8 = SY217 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[458]) ).
thf(519,plain,
! [SV68: $i,SV9: $i] :
( ( ~ ( ~ ( ~ ( subset @ ( singleton @ SV9 ) @ SV68 )
| ( in @ SV9 @ SV68 ) )
| ~ ( ~ ( in @ SV9 @ SV68 )
| ( subset @ ( singleton @ SV9 ) @ SV68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(520,plain,
! [SV10: $i] :
( ( ( ~ ( relation @ SV10 ) )
= $true )
| ( ( ! [SY223: $i] :
( ~ ( relation @ SY223 )
| ! [SY224: $i] :
( ~ ( relation @ SY224 )
| ~ ( ~ ( ( SY224
!= ( relation_composition @ SV10 @ SY223 ) )
| ! [SY225: $i,SY226: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY225 @ SY226 ) @ SY224 )
| ~ ! [SY227: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY225 @ SY227 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY227 @ SY226 ) @ SY223 ) ) )
| ~ ( ~ ~ ! [SY228: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY225 @ SY228 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY228 @ SY226 ) @ SY223 ) )
| ( in @ ( ordered_pair @ SY225 @ SY226 ) @ SY224 ) ) ) )
| ~ ( ~ ! [SY229: $i,SY230: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY229 @ SY230 ) @ SY224 )
| ~ ! [SY231: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY229 @ SY231 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY231 @ SY230 ) @ SY223 ) ) )
| ~ ( ~ ~ ! [SY232: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY229 @ SY232 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY232 @ SY230 ) @ SY223 ) )
| ( in @ ( ordered_pair @ SY229 @ SY230 ) @ SY224 ) ) )
| ( SY224
= ( relation_composition @ SV10 @ SY223 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[460]) ).
thf(521,plain,
! [SV69: $i,SV11: $i] :
( ( ! [SY411: $i] :
~ ( ~ ( ( SY411
!= ( cartesian_product2 @ SV11 @ SV69 ) )
| ! [SY412: $i] :
~ ( ~ ( ~ ( in @ SY412 @ SY411 )
| ~ ! [SY413: $i] :
~ ~ ! [SY414: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY413 @ SV11 )
| ~ ( in @ SY414 @ SV69 ) )
| ( SY412
!= ( ordered_pair @ SY413 @ SY414 ) ) ) )
| ~ ( ~ ~ ! [SY415: $i] :
~ ~ ! [SY416: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY415 @ SV11 )
| ~ ( in @ SY416 @ SV69 ) )
| ( SY412
!= ( ordered_pair @ SY415 @ SY416 ) ) )
| ( in @ SY412 @ SY411 ) ) ) )
| ~ ( ~ ! [SY417: $i] :
~ ( ~ ( ~ ( in @ SY417 @ SY411 )
| ~ ! [SY418: $i] :
~ ~ ! [SY419: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY418 @ SV11 )
| ~ ( in @ SY419 @ SV69 ) )
| ( SY417
!= ( ordered_pair @ SY418 @ SY419 ) ) ) )
| ~ ( ~ ~ ! [SY420: $i] :
~ ~ ! [SY421: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY420 @ SV11 )
| ~ ( in @ SY421 @ SV69 ) )
| ( SY417
!= ( ordered_pair @ SY420 @ SY421 ) ) )
| ( in @ SY417 @ SY411 ) ) )
| ( SY411
= ( cartesian_product2 @ SV11 @ SV69 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(522,plain,
! [SV12: $i,SV70: $i] :
( ( ~ ( relation @ SV70 )
| ~ ( ~ ( ( SV70
!= ( identity_relation @ SV12 ) )
| ! [SY422: $i,SY423: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY422 @ SY423 ) @ SV70 )
| ~ ( ~ ( in @ SY422 @ SV12 )
| ( SY422 != SY423 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY422 @ SV12 )
| ( SY422 != SY423 ) )
| ( in @ ( ordered_pair @ SY422 @ SY423 ) @ SV70 ) ) ) )
| ~ ( ~ ! [SY424: $i,SY425: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY424 @ SY425 ) @ SV70 )
| ~ ( ~ ( in @ SY424 @ SV12 )
| ( SY424 != SY425 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY424 @ SV12 )
| ( SY424 != SY425 ) )
| ( in @ ( ordered_pair @ SY424 @ SY425 ) @ SV70 ) ) )
| ( SV70
= ( identity_relation @ SV12 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(523,plain,
! [SV13: $i,SV71: $i] :
( ( ~ ( ~ ( ( SV71
!= ( powerset @ SV13 ) )
| ! [SY426: $i] :
~ ( ~ ( ~ ( in @ SY426 @ SV71 )
| ( subset @ SY426 @ SV13 ) )
| ~ ( ~ ( subset @ SY426 @ SV13 )
| ( in @ SY426 @ SV71 ) ) ) )
| ~ ( ~ ! [SY427: $i] :
~ ( ~ ( ~ ( in @ SY427 @ SV71 )
| ( subset @ SY427 @ SV13 ) )
| ~ ( ~ ( subset @ SY427 @ SV13 )
| ( in @ SY427 @ SV71 ) ) )
| ( SV71
= ( powerset @ SV13 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(524,plain,
! [SV14: $i] :
( ( ( ~ ( relation @ SV14 ) )
= $true )
| ( ( ! [SY253: $i,SY254: $i] :
~ ( ~ ( ( SY254
!= ( relation_inverse_image @ SV14 @ SY253 ) )
| ! [SY255: $i] :
~ ( ~ ( ~ ( in @ SY255 @ SY254 )
| ~ ! [SY256: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY255 @ SY256 ) @ SV14 )
| ~ ( in @ SY256 @ SY253 ) ) )
| ~ ( ~ ~ ! [SY257: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY255 @ SY257 ) @ SV14 )
| ~ ( in @ SY257 @ SY253 ) )
| ( in @ SY255 @ SY254 ) ) ) )
| ~ ( ~ ! [SY258: $i] :
~ ( ~ ( ~ ( in @ SY258 @ SY254 )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY258 @ SY259 ) @ SV14 )
| ~ ( in @ SY259 @ SY253 ) ) )
| ~ ( ~ ~ ! [SY260: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY258 @ SY260 ) @ SV14 )
| ~ ( in @ SY260 @ SY253 ) )
| ( in @ SY258 @ SY254 ) ) )
| ( SY254
= ( relation_inverse_image @ SV14 @ SY253 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[464]) ).
thf(525,plain,
! [SV15: $i] :
( ( ( ~ ( relation @ SV15 ) )
= $true )
| ( ( ! [SY261: $i] :
~ ( ~ ( ( SY261
!= ( relation_rng @ SV15 ) )
| ! [SY262: $i] :
~ ( ~ ( ~ ( in @ SY262 @ SY261 )
| ~ ! [SY263: $i] :
~ ( in @ ( ordered_pair @ SY263 @ SY262 ) @ SV15 ) )
| ~ ( ~ ~ ! [SY264: $i] :
~ ( in @ ( ordered_pair @ SY264 @ SY262 ) @ SV15 )
| ( in @ SY262 @ SY261 ) ) ) )
| ~ ( ~ ! [SY265: $i] :
~ ( ~ ( ~ ( in @ SY265 @ SY261 )
| ~ ! [SY266: $i] :
~ ( in @ ( ordered_pair @ SY266 @ SY265 ) @ SV15 ) )
| ~ ( ~ ~ ! [SY267: $i] :
~ ( in @ ( ordered_pair @ SY267 @ SY265 ) @ SV15 )
| ( in @ SY265 @ SY261 ) ) )
| ( SY261
= ( relation_rng @ SV15 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[465]) ).
thf(526,plain,
! [SV16: $i] :
( ( ( ~ ( relation @ SV16 ) )
= $true )
| ( ( ! [SY268: $i] :
( ~ ( relation @ SY268 )
| ~ ( ~ ( ~ ( subset @ SV16 @ SY268 )
| ! [SY269: $i,SY270: $i] :
( ~ ( in @ ( ordered_pair @ SY269 @ SY270 ) @ SV16 )
| ( in @ ( ordered_pair @ SY269 @ SY270 ) @ SY268 ) ) )
| ~ ( ~ ! [SY271: $i,SY272: $i] :
( ~ ( in @ ( ordered_pair @ SY271 @ SY272 ) @ SV16 )
| ( in @ ( ordered_pair @ SY271 @ SY272 ) @ SY268 ) )
| ( subset @ SV16 @ SY268 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[466]) ).
thf(527,plain,
! [SV72: $i,SV17: $i] :
( ( ! [SY428: $i] :
~ ( ~ ( ( SY428
!= ( set_union2 @ SV17 @ SV72 ) )
| ! [SY429: $i] :
~ ( ~ ( ~ ( in @ SY429 @ SY428 )
| ( in @ SY429 @ SV17 )
| ( in @ SY429 @ SV72 ) )
| ~ ( ~ ( ( in @ SY429 @ SV17 )
| ( in @ SY429 @ SV72 ) )
| ( in @ SY429 @ SY428 ) ) ) )
| ~ ( ~ ! [SY430: $i] :
~ ( ~ ( ~ ( in @ SY430 @ SY428 )
| ( in @ SY430 @ SV17 )
| ( in @ SY430 @ SV72 ) )
| ~ ( ~ ( ( in @ SY430 @ SV17 )
| ( in @ SY430 @ SV72 ) )
| ( in @ SY430 @ SY428 ) ) )
| ( SY428
= ( set_union2 @ SV17 @ SV72 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(528,plain,
! [SV18: $i] :
( ( ( ~ ( relation @ SV18 ) )
= $true )
| ( ( ~ ! [SY277: $i,SY278: $i] :
~ ( in @ ( ordered_pair @ SY277 @ SY278 ) @ SV18 )
| ( SV18 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[468]) ).
thf(529,plain,
! [SV73: $i,SV19: $i] :
( ( ~ ( in @ SV19 @ SV73 )
| ( ( set_union2 @ ( singleton @ SV19 ) @ SV73 )
= SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(530,plain,
! [SV20: $i] :
( ( ( ~ ( relation @ SV20 ) )
= $true )
| ( ( ! [SY280: $i,SY281: $i] :
( ~ ( relation @ SY281 )
| ~ ( ~ ( ( SY281
!= ( relation_dom_restriction @ SV20 @ SY280 ) )
| ! [SY282: $i,SY283: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY282 @ SY283 ) @ SY281 )
| ~ ( ~ ( in @ SY282 @ SY280 )
| ~ ( in @ ( ordered_pair @ SY282 @ SY283 ) @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY282 @ SY280 )
| ~ ( in @ ( ordered_pair @ SY282 @ SY283 ) @ SV20 ) )
| ( in @ ( ordered_pair @ SY282 @ SY283 ) @ SY281 ) ) ) )
| ~ ( ~ ! [SY284: $i,SY285: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY284 @ SY285 ) @ SY281 )
| ~ ( ~ ( in @ SY284 @ SY280 )
| ~ ( in @ ( ordered_pair @ SY284 @ SY285 ) @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY284 @ SY280 )
| ~ ( in @ ( ordered_pair @ SY284 @ SY285 ) @ SV20 ) )
| ( in @ ( ordered_pair @ SY284 @ SY285 ) @ SY281 ) ) )
| ( SY281
= ( relation_dom_restriction @ SV20 @ SY280 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[470]) ).
thf(531,plain,
! [SV74: $i,SV21: $i] :
( ( ~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SV21 @ SV74 )
| ~ ! [SY431: $i] :
~ ~ ( ~ ( in @ SY431 @ SV21 )
| ~ ( in @ SY431 @ SV74 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY432: $i] :
~ ~ ( ~ ( in @ SY432 @ SV21 )
| ~ ( in @ SY432 @ SV74 ) )
| ~ ( disjoint @ SV21 @ SV74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(532,plain,
! [SV75: $i,SV22: $i] :
( ( ! [SY433: $i] :
( ~ ( relation @ SY433 )
| ~ ( ~ ( ~ ( in @ SV22 @ ( relation_rng @ ( relation_rng_restriction @ SV75 @ SY433 ) ) )
| ~ ( ~ ( in @ SV22 @ SV75 )
| ~ ( in @ SV22 @ ( relation_rng @ SY433 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV22 @ SV75 )
| ~ ( in @ SV22 @ ( relation_rng @ SY433 ) ) )
| ( in @ SV22 @ ( relation_rng @ ( relation_rng_restriction @ SV75 @ SY433 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(533,plain,
! [SV23: $i] :
( ( ! [SY291: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV23 @ SY291 )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY291 )
| ~ ( subset @ SX3 @ SX2 ) )
| ( in @ SX3 @ SY291 ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY291 )
| ( in @ ( powerset @ SX2 ) @ SY291 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SX2 @ SY291 )
| ~ ~ ( are_equipotent @ SX2 @ SY291 ) )
| ~ ~ ( in @ SX2 @ SY291 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[473]) ).
thf(534,plain,
! [SV76: $i,SV24: $i] :
( ( ~ ( element @ SV24 @ SV76 )
| ( empty @ SV76 )
| ( in @ SV24 @ SV76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(535,plain,
! [SV77: $i,SV25: $i] :
( ( ~ ( ~ ( ~ ( subset @ ( singleton @ SV25 ) @ SV77 )
| ( in @ SV25 @ SV77 ) )
| ~ ( ~ ( in @ SV25 @ SV77 )
| ( subset @ ( singleton @ SV25 ) @ SV77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(536,plain,
! [SV78: $i,SV26: $i] :
( ( ~ ( ~ ( ~ ( ( SV26 != empty_set ) )
| ~ ( ~ ( ( SV78
!= ( set_meet @ SV26 ) )
| ! [SY434: $i] :
~ ( ~ ( ~ ( in @ SY434 @ SV78 )
| ! [SY300: $i] :
( ~ ( in @ SY300 @ SV26 )
| ( in @ SY434 @ SY300 ) ) )
| ~ ( ~ ! [SY301: $i] :
( ~ ( in @ SY301 @ SV26 )
| ( in @ SY434 @ SY301 ) )
| ( in @ SY434 @ SV78 ) ) ) )
| ~ ( ~ ! [SY437: $i] :
~ ( ~ ( ~ ( in @ SY437 @ SV78 )
| ! [SY303: $i] :
( ~ ( in @ SY303 @ SV26 )
| ( in @ SY437 @ SY303 ) ) )
| ~ ( ~ ! [SY304: $i] :
( ~ ( in @ SY304 @ SV26 )
| ( in @ SY437 @ SY304 ) )
| ( in @ SY437 @ SV78 ) ) )
| ( SV78
= ( set_meet @ SV26 ) ) ) ) )
| ~ ( ( SV26 != empty_set )
| ~ ( ~ ( ( SV78
!= ( set_meet @ SV26 ) )
| ( SV78 = empty_set ) )
| ~ ( ( SV78 != empty_set )
| ( SV78
= ( set_meet @ SV26 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(537,plain,
! [SV79: $i,SV27: $i] :
( ( ! [SY440: $i,SY441: $i] :
( ~ ( relation @ SY441 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV27 @ SV79 ) @ ( relation_composition @ ( identity_relation @ SY440 ) @ SY441 ) )
| ~ ( ~ ( in @ SV27 @ SY440 )
| ~ ( in @ ( ordered_pair @ SV27 @ SV79 ) @ SY441 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV27 @ SY440 )
| ~ ( in @ ( ordered_pair @ SV27 @ SV79 ) @ SY441 ) )
| ( in @ ( ordered_pair @ SV27 @ SV79 ) @ ( relation_composition @ ( identity_relation @ SY440 ) @ SY441 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(538,plain,
! [SV28: $i,SV80: $i] :
( ( ~ ( relation @ SV80 )
| ( ( relation_dom_restriction @ SV80 @ SV28 )
= ( relation_composition @ ( identity_relation @ SV28 ) @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(539,plain,
! [SV81: $i,SV29: $i] :
( ( ! [SY442: $i,SY443: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV29 @ SV81 ) @ ( cartesian_product2 @ SY442 @ SY443 ) )
| ~ ( ~ ( in @ SV29 @ SY442 )
| ~ ( in @ SV81 @ SY443 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV29 @ SY442 )
| ~ ( in @ SV81 @ SY443 ) )
| ( in @ ( ordered_pair @ SV29 @ SV81 ) @ ( cartesian_product2 @ SY442 @ SY443 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(540,plain,
! [SV30: $i] :
( ( ( ~ ( relation @ SV30 ) )
= $true )
| ( ( ! [SY312: $i,SY313: $i] :
~ ( ~ ( ( SY313
!= ( relation_image @ SV30 @ SY312 ) )
| ! [SY314: $i] :
~ ( ~ ( ~ ( in @ SY314 @ SY313 )
| ~ ! [SY315: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY315 @ SY314 ) @ SV30 )
| ~ ( in @ SY315 @ SY312 ) ) )
| ~ ( ~ ~ ! [SY316: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY316 @ SY314 ) @ SV30 )
| ~ ( in @ SY316 @ SY312 ) )
| ( in @ SY314 @ SY313 ) ) ) )
| ~ ( ~ ! [SY317: $i] :
~ ( ~ ( ~ ( in @ SY317 @ SY313 )
| ~ ! [SY318: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY318 @ SY317 ) @ SV30 )
| ~ ( in @ SY318 @ SY312 ) ) )
| ~ ( ~ ~ ! [SY319: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY319 @ SY317 ) @ SV30 )
| ~ ( in @ SY319 @ SY312 ) )
| ( in @ SY317 @ SY313 ) ) )
| ( SY313
= ( relation_image @ SV30 @ SY312 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[480]) ).
thf(541,plain,
! [SV82: $i,SV31: $i] :
( ( ! [SY444: $i] :
~ ( ~ ( ~ ( subset @ ( unordered_pair @ SV31 @ SV82 ) @ SY444 )
| ~ ( ~ ( in @ SV31 @ SY444 )
| ~ ( in @ SV82 @ SY444 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV31 @ SY444 )
| ~ ( in @ SV82 @ SY444 ) )
| ( subset @ ( unordered_pair @ SV31 @ SV82 ) @ SY444 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(542,plain,
! [SV32: $i] :
( ( ~ ( relation @ ( identity_relation @ SV32 ) )
| ~ ( function @ ( identity_relation @ SV32 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[482]) ).
thf(543,plain,
! [SV83: $i,SV33: $i] :
( ( ! [SY445: $i] :
( ~ ~ ( ~ ( in @ SV33 @ SV83 )
| ~ ( element @ SV83 @ ( powerset @ SY445 ) ) )
| ( element @ SV33 @ SY445 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(544,plain,
! [SV84: $i,SV34: $i] :
( ( ~ ( ~ ( ~ ~ ( empty @ SV34 )
| ~ ( ~ ( ~ ( element @ SV84 @ SV34 )
| ( in @ SV84 @ SV34 ) )
| ~ ( ~ ( in @ SV84 @ SV34 )
| ( element @ SV84 @ SV34 ) ) ) )
| ~ ( ~ ( empty @ SV34 )
| ~ ( ~ ( ~ ( element @ SV84 @ SV34 )
| ( empty @ SV84 ) )
| ~ ( ~ ( empty @ SV84 )
| ( element @ SV84 @ SV34 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(545,plain,
! [SV35: $i] :
( ( ~ ( ~ ( relation @ SV35 )
| ! [SY325: $i] :
~ ~ ( ~ ( in @ SY325 @ SV35 )
| ~ ! [SX2: $i,SX3: $i] :
( SY325
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
| ~ ( ~ ! [SY328: $i] :
~ ~ ( ~ ( in @ SY328 @ SV35 )
| ~ ! [SX2: $i,SX3: $i] :
( SY328
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SV35 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[485]) ).
thf(546,plain,
! [SV85: $i,SV36: $i] :
( ( ! [SY446: $i] :
( ~ ( subset @ SV36 @ SV85 )
| ( in @ SY446 @ SV36 )
| ( subset @ SV36 @ ( set_difference @ SV85 @ ( singleton @ SY446 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(547,plain,
! [SV86: $i,SV37: $i] :
( ( ! [SY447: $i] :
( ~ ( relation @ SY447 )
| ~ ( in @ ( ordered_pair @ SV37 @ SV86 ) @ SY447 )
| ~ ( ~ ( in @ SV37 @ ( relation_field @ SY447 ) )
| ~ ( in @ SV86 @ ( relation_field @ SY447 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(548,plain,
! [SV38: $i] :
( ( ~ ( ( SV38 != empty_set )
| ! [SY335: $i] :
~ ( in @ SY335 @ SV38 ) )
| ~ ( ~ ! [SY336: $i] :
~ ( in @ SY336 @ SV38 )
| ( SV38 = empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[488]) ).
thf(549,plain,
! [SV39: $i,SV87: $i] :
( ( ~ ( relation @ SV87 )
| ! [SY448: $i] :
( ~ ( relation @ SY448 )
| ~ ( ~ ( ( SY448
!= ( relation_rng_restriction @ SV39 @ SV87 ) )
| ! [SY449: $i,SY450: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY449 @ SY450 ) @ SY448 )
| ~ ( ~ ( in @ SY450 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY449 @ SY450 ) @ SV87 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY450 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY449 @ SY450 ) @ SV87 ) )
| ( in @ ( ordered_pair @ SY449 @ SY450 ) @ SY448 ) ) ) )
| ~ ( ~ ! [SY451: $i,SY452: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SY448 )
| ~ ( ~ ( in @ SY452 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV87 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY452 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV87 ) )
| ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SY448 ) ) )
| ( SY448
= ( relation_rng_restriction @ SV39 @ SV87 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(550,plain,
! [SV40: $i] :
( ( ( ( relation_dom @ ( identity_relation @ SV40 ) )
!= SV40 )
| ( ( relation_rng @ ( identity_relation @ SV40 ) )
!= SV40 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[490]) ).
thf(551,plain,
! [SV41: $i,SV88: $i] :
( ( ~ ( ~ ( ( SV88
!= ( singleton @ SV41 ) )
| ! [SY453: $i] :
~ ( ~ ( ~ ( in @ SY453 @ SV88 )
| ( SY453 = SV41 ) )
| ~ ( ( SY453 != SV41 )
| ( in @ SY453 @ SV88 ) ) ) )
| ~ ( ~ ! [SY454: $i] :
~ ( ~ ( ~ ( in @ SY454 @ SV88 )
| ( SY454 = SV41 ) )
| ~ ( ( SY454 != SV41 )
| ( in @ SY454 @ SV88 ) ) )
| ( SV88
= ( singleton @ SV41 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(552,plain,
! [SV42: $i,SV89: $i] :
( ( ~ ( ~ ( ( SV89
!= ( union @ SV42 ) )
| ! [SY455: $i] :
~ ( ~ ( ~ ( in @ SY455 @ SV89 )
| ~ ! [SY348: $i] :
~ ~ ( ~ ( in @ SY455 @ SY348 )
| ~ ( in @ SY348 @ SV42 ) ) )
| ~ ( ~ ~ ! [SY349: $i] :
~ ~ ( ~ ( in @ SY455 @ SY349 )
| ~ ( in @ SY349 @ SV42 ) )
| ( in @ SY455 @ SV89 ) ) ) )
| ~ ( ~ ! [SY458: $i] :
~ ( ~ ( ~ ( in @ SY458 @ SV89 )
| ~ ! [SY351: $i] :
~ ~ ( ~ ( in @ SY458 @ SY351 )
| ~ ( in @ SY351 @ SV42 ) ) )
| ~ ( ~ ~ ! [SY352: $i] :
~ ~ ( ~ ( in @ SY458 @ SY352 )
| ~ ( in @ SY352 @ SV42 ) )
| ( in @ SY458 @ SV89 ) ) )
| ( SV89
= ( union @ SV42 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(553,plain,
! [SV90: $i,SV43: $i] :
( ( ! [SY461: $i] :
( ~ ( relation @ SY461 )
| ~ ( ~ ( ~ ( in @ SV43 @ ( relation_dom @ ( relation_dom_restriction @ SY461 @ SV90 ) ) )
| ~ ( ~ ( in @ SV43 @ SV90 )
| ~ ( in @ SV43 @ ( relation_dom @ SY461 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV43 @ SV90 )
| ~ ( in @ SV43 @ ( relation_dom @ SY461 ) ) )
| ( in @ SV43 @ ( relation_dom @ ( relation_dom_restriction @ SY461 @ SV90 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(554,plain,
! [SV91: $i,SV44: $i] :
( ( ~ ~ ( ~ ( disjoint @ ( singleton @ SV44 ) @ SV91 )
| ~ ( in @ SV44 @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(555,plain,
! [SV92: $i,SV45: $i] :
( ( ~ ( in @ SV45 @ SV92 )
| ( subset @ SV45 @ ( union @ SV92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(556,plain,
! [SV46: $i] :
( ( ! [SY357: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV46 @ SY357 )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY357 )
| ~ ( subset @ SX3 @ SX2 ) )
| ( in @ SX3 @ SY357 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SY357 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SY357 )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) ) ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SX2 @ SY357 )
| ~ ~ ( are_equipotent @ SX2 @ SY357 ) )
| ~ ~ ( in @ SX2 @ SY357 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(557,plain,
! [SV47: $i] :
( ( ( ~ ( relation @ SV47 ) )
= $true )
| ( ( ! [SY364: $i] :
~ ( ~ ( ( SY364
!= ( relation_dom @ SV47 ) )
| ! [SY365: $i] :
~ ( ~ ( ~ ( in @ SY365 @ SY364 )
| ~ ! [SY366: $i] :
~ ( in @ ( ordered_pair @ SY365 @ SY366 ) @ SV47 ) )
| ~ ( ~ ~ ! [SY367: $i] :
~ ( in @ ( ordered_pair @ SY365 @ SY367 ) @ SV47 )
| ( in @ SY365 @ SY364 ) ) ) )
| ~ ( ~ ! [SY368: $i] :
~ ( ~ ( ~ ( in @ SY368 @ SY364 )
| ~ ! [SY369: $i] :
~ ( in @ ( ordered_pair @ SY368 @ SY369 ) @ SV47 ) )
| ~ ( ~ ~ ! [SY370: $i] :
~ ( in @ ( ordered_pair @ SY368 @ SY370 ) @ SV47 )
| ( in @ SY368 @ SY364 ) ) )
| ( SY364
= ( relation_dom @ SV47 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[497]) ).
thf(558,plain,
! [SV93: $i,SV48: $i] :
( ( ~ ! [SY462: $i] :
( ~ ( in @ SY462 @ SV48 )
| ( in @ SY462 @ SV93 ) )
| ( element @ SV48 @ ( powerset @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(559,plain,
! [SV49: $i] :
( ( ( ~ ( relation @ SV49 ) )
= $true )
| ( ( ! [SY373: $i] :
( ~ ( relation @ SY373 )
| ~ ( ~ ( ( SY373
!= ( relation_inverse @ SV49 ) )
| ! [SY374: $i,SY375: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY374 @ SY375 ) @ SY373 )
| ( in @ ( ordered_pair @ SY375 @ SY374 ) @ SV49 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY375 @ SY374 ) @ SV49 )
| ( in @ ( ordered_pair @ SY374 @ SY375 ) @ SY373 ) ) ) )
| ~ ( ~ ! [SY376: $i,SY377: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY376 @ SY377 ) @ SY373 )
| ( in @ ( ordered_pair @ SY377 @ SY376 ) @ SV49 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY377 @ SY376 ) @ SV49 )
| ( in @ ( ordered_pair @ SY376 @ SY377 ) @ SY373 ) ) )
| ( SY373
= ( relation_inverse @ SV49 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[499]) ).
thf(560,plain,
! [SV94: $i,SV50: $i] :
( ( ~ ( ~ ( ( ( set_difference @ SV50 @ ( singleton @ SV94 ) )
!= SV50 )
| ~ ( in @ SV94 @ SV50 ) )
| ~ ( ~ ~ ( in @ SV94 @ SV50 )
| ( ( set_difference @ SV50 @ ( singleton @ SV94 ) )
= SV50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(561,plain,
! [SV95: $i,SV51: $i] :
( ( ~ ( in @ SV51 @ SV95 )
| ( subset @ SV51 @ ( union @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(562,plain,
! [SV96: $i,SV52: $i] :
( ( ~ ( in @ SV52 @ SV96 )
| ( element @ SV52 @ SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(563,plain,
! [SV97: $i,SV53: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV53 @ SV97 )
| ! [SY463: $i] :
( ~ ( in @ SY463 @ SV53 )
| ( in @ SY463 @ SV97 ) ) )
| ~ ( ~ ! [SY464: $i] :
( ~ ( in @ SY464 @ SV53 )
| ( in @ SY464 @ SV97 ) )
| ( subset @ SV53 @ SV97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(564,plain,
! [SV98: $i,SV54: $i] :
( ( ! [SY465: $i] :
( ~ ( element @ SY465 @ ( powerset @ SV54 ) )
| ~ ~ ( ~ ( in @ SV98 @ ( subset_complement @ SV54 @ SY465 ) )
| ~ ( in @ SV98 @ SY465 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(565,plain,
! [SV55: $i,SV99: $i] :
( ( ~ ( element @ SV99 @ ( powerset @ SV55 ) )
| ! [SY466: $i] :
( ~ ( in @ SY466 @ SV99 )
| ( in @ SY466 @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(566,plain,
! [SV100: $i,SV56: $i] :
( ( ! [SY467: $i] :
~ ( ~ ( ( SY467
!= ( unordered_pair @ SV56 @ SV100 ) )
| ! [SY468: $i] :
~ ( ~ ( ~ ( in @ SY468 @ SY467 )
| ( SY468 = SV56 )
| ( SY468 = SV100 ) )
| ~ ( ~ ( ( SY468 = SV56 )
| ( SY468 = SV100 ) )
| ( in @ SY468 @ SY467 ) ) ) )
| ~ ( ~ ! [SY469: $i] :
~ ( ~ ( ~ ( in @ SY469 @ SY467 )
| ( SY469 = SV56 )
| ( SY469 = SV100 ) )
| ~ ( ~ ( ( SY469 = SV56 )
| ( SY469 = SV100 ) )
| ( in @ SY469 @ SY467 ) ) )
| ( SY467
= ( unordered_pair @ SV56 @ SV100 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(567,plain,
! [SV101: $i,SV57: $i] :
( ( ~ ( in @ SV57 @ SV101 )
| ( ( set_union2 @ ( singleton @ SV57 ) @ SV101 )
= SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(568,plain,
! [SV102: $i,SV58: $i] :
( ( ! [SY470: $i] :
~ ( ~ ( ( SY470
!= ( set_difference @ SV58 @ SV102 ) )
| ! [SY471: $i] :
~ ( ~ ( ~ ( in @ SY471 @ SY470 )
| ~ ( ~ ( in @ SY471 @ SV58 )
| ~ ~ ( in @ SY471 @ SV102 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY471 @ SV58 )
| ~ ~ ( in @ SY471 @ SV102 ) )
| ( in @ SY471 @ SY470 ) ) ) )
| ~ ( ~ ! [SY472: $i] :
~ ( ~ ( ~ ( in @ SY472 @ SY470 )
| ~ ( ~ ( in @ SY472 @ SV58 )
| ~ ~ ( in @ SY472 @ SV102 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY472 @ SV58 )
| ~ ~ ( in @ SY472 @ SV102 ) )
| ( in @ SY472 @ SY470 ) ) )
| ( SY470
= ( set_difference @ SV58 @ SV102 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(569,plain,
! [SV103: $i,SV59: $i] :
( ( ! [SY473: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV59 @ SV103 )
| ~ ( element @ SV103 @ ( powerset @ SY473 ) ) )
| ~ ( empty @ SY473 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(570,plain,
! [SV104: $i,SV60: $i] :
( ( ! [SY474: $i] :
~ ( ~ ( ( SY474
!= ( set_intersection2 @ SV60 @ SV104 ) )
| ! [SY475: $i] :
~ ( ~ ( ~ ( in @ SY475 @ SY474 )
| ~ ( ~ ( in @ SY475 @ SV60 )
| ~ ( in @ SY475 @ SV104 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY475 @ SV60 )
| ~ ( in @ SY475 @ SV104 ) )
| ( in @ SY475 @ SY474 ) ) ) )
| ~ ( ~ ! [SY476: $i] :
~ ( ~ ( ~ ( in @ SY476 @ SY474 )
| ~ ( ~ ( in @ SY476 @ SV60 )
| ~ ( in @ SY476 @ SV104 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY476 @ SV60 )
| ~ ( in @ SY476 @ SV104 ) )
| ( in @ SY476 @ SY474 ) ) )
| ( SY474
= ( set_intersection2 @ SV60 @ SV104 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(571,plain,
! [SV105: $i,SV61: $i] :
( ( ~ ~ ( ~ ( in @ SV61 @ SV105 )
| ~ ( empty @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(572,plain,
! [SV62: $i,SV2: $i] :
( ( ( ~ ( in @ SV2 @ SV62 ) )
= $true )
| ( ( ~ ( in @ SV62 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[512]) ).
thf(573,plain,
! [SV63: $i,SV3: $i] :
( ( ~ ~ ~ ( ~ ~ ( disjoint @ SV3 @ SV63 )
| ~ ! [SY404: $i] :
~ ( in @ SY404 @ ( set_intersection2 @ SV3 @ SV63 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY405: $i] :
~ ( in @ SY405 @ ( set_intersection2 @ SV3 @ SV63 ) )
| ~ ( disjoint @ SV3 @ SV63 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[513]) ).
thf(574,plain,
! [SV64: $i,SV4: $i] :
( ( ( ~ ~ ( in @ SV4 @ SV64 ) )
= $true )
| ( ( disjoint @ ( singleton @ SV4 ) @ SV64 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[514]) ).
thf(575,plain,
! [SV65: $i,SV5: $i] :
( ( ( ~ ! [SY406: $i] :
~ ( ~ ( ~ ( in @ SY406 @ SV5 )
| ( in @ SY406 @ SV65 ) )
| ~ ( ~ ( in @ SY406 @ SV65 )
| ( in @ SY406 @ SV5 ) ) ) )
= $true )
| ( ( SV5 = SV65 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[515]) ).
thf(576,plain,
! [SV6: $i,SV66: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV66 )
| ~ ( function @ SV66 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV66
!= ( identity_relation @ SV6 ) )
| ~ ( ( ( relation_dom @ SV66 )
!= SV6 )
| ~ ! [SY407: $i] :
( ~ ( in @ SY407 @ SV6 )
| ( ( apply @ SV66 @ SY407 )
= SY407 ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV66 )
!= SV6 )
| ~ ! [SY408: $i] :
( ~ ( in @ SY408 @ SV6 )
| ( ( apply @ SV66 @ SY408 )
= SY408 ) ) )
| ( SV66
= ( identity_relation @ SV6 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[516]) ).
thf(577,plain,
! [SV106: $i,SV67: $i,SV7: $i] :
( ( ! [SY477: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV7 @ SV67 ) @ ( cartesian_product2 @ SV106 @ SY477 ) )
| ~ ( ~ ( in @ SV7 @ SV106 )
| ~ ( in @ SV67 @ SY477 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV7 @ SV106 )
| ~ ( in @ SV67 @ SY477 ) )
| ( in @ ( ordered_pair @ SV7 @ SV67 ) @ ( cartesian_product2 @ SV106 @ SY477 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(578,plain,
! [SV8: $i] :
( ( ( relation @ SV8 )
= $false )
| ( ( ! [SY217: $i] :
( ~ ( relation @ SY217 )
| ~ ( ~ ( ( SV8 != SY217 )
| ! [SY218: $i,SY219: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY218 @ SY219 ) @ SV8 )
| ( in @ ( ordered_pair @ SY218 @ SY219 ) @ SY217 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY218 @ SY219 ) @ SY217 )
| ( in @ ( ordered_pair @ SY218 @ SY219 ) @ SV8 ) ) ) )
| ~ ( ~ ! [SY220: $i,SY221: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY220 @ SY221 ) @ SV8 )
| ( in @ ( ordered_pair @ SY220 @ SY221 ) @ SY217 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY220 @ SY221 ) @ SY217 )
| ( in @ ( ordered_pair @ SY220 @ SY221 ) @ SV8 ) ) )
| ( SV8 = SY217 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(579,plain,
! [SV68: $i,SV9: $i] :
( ( ~ ( ~ ( subset @ ( singleton @ SV9 ) @ SV68 )
| ( in @ SV9 @ SV68 ) )
| ~ ( ~ ( in @ SV9 @ SV68 )
| ( subset @ ( singleton @ SV9 ) @ SV68 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[519]) ).
thf(580,plain,
! [SV10: $i] :
( ( ( relation @ SV10 )
= $false )
| ( ( ! [SY223: $i] :
( ~ ( relation @ SY223 )
| ! [SY224: $i] :
( ~ ( relation @ SY224 )
| ~ ( ~ ( ( SY224
!= ( relation_composition @ SV10 @ SY223 ) )
| ! [SY225: $i,SY226: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY225 @ SY226 ) @ SY224 )
| ~ ! [SY227: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY225 @ SY227 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY227 @ SY226 ) @ SY223 ) ) )
| ~ ( ~ ~ ! [SY228: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY225 @ SY228 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY228 @ SY226 ) @ SY223 ) )
| ( in @ ( ordered_pair @ SY225 @ SY226 ) @ SY224 ) ) ) )
| ~ ( ~ ! [SY229: $i,SY230: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY229 @ SY230 ) @ SY224 )
| ~ ! [SY231: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY229 @ SY231 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY231 @ SY230 ) @ SY223 ) ) )
| ~ ( ~ ~ ! [SY232: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY229 @ SY232 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY232 @ SY230 ) @ SY223 ) )
| ( in @ ( ordered_pair @ SY229 @ SY230 ) @ SY224 ) ) )
| ( SY224
= ( relation_composition @ SV10 @ SY223 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[520]) ).
thf(581,plain,
! [SV69: $i,SV11: $i,SV107: $i] :
( ( ~ ( ~ ( ( SV107
!= ( cartesian_product2 @ SV11 @ SV69 ) )
| ! [SY478: $i] :
~ ( ~ ( ~ ( in @ SY478 @ SV107 )
| ~ ! [SY413: $i] :
~ ~ ! [SY414: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY413 @ SV11 )
| ~ ( in @ SY414 @ SV69 ) )
| ( SY478
!= ( ordered_pair @ SY413 @ SY414 ) ) ) )
| ~ ( ~ ~ ! [SY415: $i] :
~ ~ ! [SY416: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY415 @ SV11 )
| ~ ( in @ SY416 @ SV69 ) )
| ( SY478
!= ( ordered_pair @ SY415 @ SY416 ) ) )
| ( in @ SY478 @ SV107 ) ) ) )
| ~ ( ~ ! [SY483: $i] :
~ ( ~ ( ~ ( in @ SY483 @ SV107 )
| ~ ! [SY418: $i] :
~ ~ ! [SY419: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY418 @ SV11 )
| ~ ( in @ SY419 @ SV69 ) )
| ( SY483
!= ( ordered_pair @ SY418 @ SY419 ) ) ) )
| ~ ( ~ ~ ! [SY420: $i] :
~ ~ ! [SY421: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY420 @ SV11 )
| ~ ( in @ SY421 @ SV69 ) )
| ( SY483
!= ( ordered_pair @ SY420 @ SY421 ) ) )
| ( in @ SY483 @ SV107 ) ) )
| ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(582,plain,
! [SV12: $i,SV70: $i] :
( ( ( ~ ( relation @ SV70 ) )
= $true )
| ( ( ~ ( ~ ( ( SV70
!= ( identity_relation @ SV12 ) )
| ! [SY422: $i,SY423: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY422 @ SY423 ) @ SV70 )
| ~ ( ~ ( in @ SY422 @ SV12 )
| ( SY422 != SY423 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY422 @ SV12 )
| ( SY422 != SY423 ) )
| ( in @ ( ordered_pair @ SY422 @ SY423 ) @ SV70 ) ) ) )
| ~ ( ~ ! [SY424: $i,SY425: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY424 @ SY425 ) @ SV70 )
| ~ ( ~ ( in @ SY424 @ SV12 )
| ( SY424 != SY425 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY424 @ SV12 )
| ( SY424 != SY425 ) )
| ( in @ ( ordered_pair @ SY424 @ SY425 ) @ SV70 ) ) )
| ( SV70
= ( identity_relation @ SV12 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[522]) ).
thf(583,plain,
! [SV13: $i,SV71: $i] :
( ( ~ ( ( SV71
!= ( powerset @ SV13 ) )
| ! [SY426: $i] :
~ ( ~ ( ~ ( in @ SY426 @ SV71 )
| ( subset @ SY426 @ SV13 ) )
| ~ ( ~ ( subset @ SY426 @ SV13 )
| ( in @ SY426 @ SV71 ) ) ) )
| ~ ( ~ ! [SY427: $i] :
~ ( ~ ( ~ ( in @ SY427 @ SV71 )
| ( subset @ SY427 @ SV13 ) )
| ~ ( ~ ( subset @ SY427 @ SV13 )
| ( in @ SY427 @ SV71 ) ) )
| ( SV71
= ( powerset @ SV13 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[523]) ).
thf(584,plain,
! [SV14: $i] :
( ( ( relation @ SV14 )
= $false )
| ( ( ! [SY253: $i,SY254: $i] :
~ ( ~ ( ( SY254
!= ( relation_inverse_image @ SV14 @ SY253 ) )
| ! [SY255: $i] :
~ ( ~ ( ~ ( in @ SY255 @ SY254 )
| ~ ! [SY256: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY255 @ SY256 ) @ SV14 )
| ~ ( in @ SY256 @ SY253 ) ) )
| ~ ( ~ ~ ! [SY257: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY255 @ SY257 ) @ SV14 )
| ~ ( in @ SY257 @ SY253 ) )
| ( in @ SY255 @ SY254 ) ) ) )
| ~ ( ~ ! [SY258: $i] :
~ ( ~ ( ~ ( in @ SY258 @ SY254 )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY258 @ SY259 ) @ SV14 )
| ~ ( in @ SY259 @ SY253 ) ) )
| ~ ( ~ ~ ! [SY260: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY258 @ SY260 ) @ SV14 )
| ~ ( in @ SY260 @ SY253 ) )
| ( in @ SY258 @ SY254 ) ) )
| ( SY254
= ( relation_inverse_image @ SV14 @ SY253 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(585,plain,
! [SV15: $i] :
( ( ( relation @ SV15 )
= $false )
| ( ( ! [SY261: $i] :
~ ( ~ ( ( SY261
!= ( relation_rng @ SV15 ) )
| ! [SY262: $i] :
~ ( ~ ( ~ ( in @ SY262 @ SY261 )
| ~ ! [SY263: $i] :
~ ( in @ ( ordered_pair @ SY263 @ SY262 ) @ SV15 ) )
| ~ ( ~ ~ ! [SY264: $i] :
~ ( in @ ( ordered_pair @ SY264 @ SY262 ) @ SV15 )
| ( in @ SY262 @ SY261 ) ) ) )
| ~ ( ~ ! [SY265: $i] :
~ ( ~ ( ~ ( in @ SY265 @ SY261 )
| ~ ! [SY266: $i] :
~ ( in @ ( ordered_pair @ SY266 @ SY265 ) @ SV15 ) )
| ~ ( ~ ~ ! [SY267: $i] :
~ ( in @ ( ordered_pair @ SY267 @ SY265 ) @ SV15 )
| ( in @ SY265 @ SY261 ) ) )
| ( SY261
= ( relation_rng @ SV15 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[525]) ).
thf(586,plain,
! [SV16: $i] :
( ( ( relation @ SV16 )
= $false )
| ( ( ! [SY268: $i] :
( ~ ( relation @ SY268 )
| ~ ( ~ ( ~ ( subset @ SV16 @ SY268 )
| ! [SY269: $i,SY270: $i] :
( ~ ( in @ ( ordered_pair @ SY269 @ SY270 ) @ SV16 )
| ( in @ ( ordered_pair @ SY269 @ SY270 ) @ SY268 ) ) )
| ~ ( ~ ! [SY271: $i,SY272: $i] :
( ~ ( in @ ( ordered_pair @ SY271 @ SY272 ) @ SV16 )
| ( in @ ( ordered_pair @ SY271 @ SY272 ) @ SY268 ) )
| ( subset @ SV16 @ SY268 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(587,plain,
! [SV72: $i,SV17: $i,SV108: $i] :
( ( ~ ( ~ ( ( SV108
!= ( set_union2 @ SV17 @ SV72 ) )
| ! [SY488: $i] :
~ ( ~ ( ~ ( in @ SY488 @ SV108 )
| ( in @ SY488 @ SV17 )
| ( in @ SY488 @ SV72 ) )
| ~ ( ~ ( ( in @ SY488 @ SV17 )
| ( in @ SY488 @ SV72 ) )
| ( in @ SY488 @ SV108 ) ) ) )
| ~ ( ~ ! [SY489: $i] :
~ ( ~ ( ~ ( in @ SY489 @ SV108 )
| ( in @ SY489 @ SV17 )
| ( in @ SY489 @ SV72 ) )
| ~ ( ~ ( ( in @ SY489 @ SV17 )
| ( in @ SY489 @ SV72 ) )
| ( in @ SY489 @ SV108 ) ) )
| ( SV108
= ( set_union2 @ SV17 @ SV72 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(588,plain,
! [SV18: $i] :
( ( ( relation @ SV18 )
= $false )
| ( ( ~ ! [SY277: $i,SY278: $i] :
~ ( in @ ( ordered_pair @ SY277 @ SY278 ) @ SV18 )
| ( SV18 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[528]) ).
thf(589,plain,
! [SV73: $i,SV19: $i] :
( ( ( ~ ( in @ SV19 @ SV73 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV19 ) @ SV73 )
= SV73 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[529]) ).
thf(590,plain,
! [SV20: $i] :
( ( ( relation @ SV20 )
= $false )
| ( ( ! [SY280: $i,SY281: $i] :
( ~ ( relation @ SY281 )
| ~ ( ~ ( ( SY281
!= ( relation_dom_restriction @ SV20 @ SY280 ) )
| ! [SY282: $i,SY283: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY282 @ SY283 ) @ SY281 )
| ~ ( ~ ( in @ SY282 @ SY280 )
| ~ ( in @ ( ordered_pair @ SY282 @ SY283 ) @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY282 @ SY280 )
| ~ ( in @ ( ordered_pair @ SY282 @ SY283 ) @ SV20 ) )
| ( in @ ( ordered_pair @ SY282 @ SY283 ) @ SY281 ) ) ) )
| ~ ( ~ ! [SY284: $i,SY285: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY284 @ SY285 ) @ SY281 )
| ~ ( ~ ( in @ SY284 @ SY280 )
| ~ ( in @ ( ordered_pair @ SY284 @ SY285 ) @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY284 @ SY280 )
| ~ ( in @ ( ordered_pair @ SY284 @ SY285 ) @ SV20 ) )
| ( in @ ( ordered_pair @ SY284 @ SY285 ) @ SY281 ) ) )
| ( SY281
= ( relation_dom_restriction @ SV20 @ SY280 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[530]) ).
thf(591,plain,
! [SV74: $i,SV21: $i] :
( ( ~ ~ ~ ( ~ ~ ( disjoint @ SV21 @ SV74 )
| ~ ! [SY431: $i] :
~ ~ ( ~ ( in @ SY431 @ SV21 )
| ~ ( in @ SY431 @ SV74 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY432: $i] :
~ ~ ( ~ ( in @ SY432 @ SV21 )
| ~ ( in @ SY432 @ SV74 ) )
| ~ ( disjoint @ SV21 @ SV74 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[531]) ).
thf(592,plain,
! [SV75: $i,SV22: $i,SV109: $i] :
( ( ~ ( relation @ SV109 )
| ~ ( ~ ( ~ ( in @ SV22 @ ( relation_rng @ ( relation_rng_restriction @ SV75 @ SV109 ) ) )
| ~ ( ~ ( in @ SV22 @ SV75 )
| ~ ( in @ SV22 @ ( relation_rng @ SV109 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV22 @ SV75 )
| ~ ( in @ SV22 @ ( relation_rng @ SV109 ) ) )
| ( in @ SV22 @ ( relation_rng @ ( relation_rng_restriction @ SV75 @ SV109 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(593,plain,
! [SV23: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV23 @ ( sK3_SY291 @ SV23 ) )
| ~ ! [SY490: $i,SY491: $i] :
( ~ ~ ( ~ ( in @ SY490 @ ( sK3_SY291 @ SV23 ) )
| ~ ( subset @ SY491 @ SY490 ) )
| ( in @ SY491 @ ( sK3_SY291 @ SV23 ) ) ) )
| ~ ! [SY492: $i] :
( ~ ( in @ SY492 @ ( sK3_SY291 @ SV23 ) )
| ( in @ ( powerset @ SY492 ) @ ( sK3_SY291 @ SV23 ) ) ) )
| ~ ! [SY493: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY493 @ ( sK3_SY291 @ SV23 ) )
| ~ ~ ( are_equipotent @ SY493 @ ( sK3_SY291 @ SV23 ) ) )
| ~ ~ ( in @ SY493 @ ( sK3_SY291 @ SV23 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[533]) ).
thf(594,plain,
! [SV76: $i,SV24: $i] :
( ( ( ~ ( element @ SV24 @ SV76 ) )
= $true )
| ( ( ( empty @ SV76 )
| ( in @ SV24 @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[534]) ).
thf(595,plain,
! [SV77: $i,SV25: $i] :
( ( ~ ( ~ ( subset @ ( singleton @ SV25 ) @ SV77 )
| ( in @ SV25 @ SV77 ) )
| ~ ( ~ ( in @ SV25 @ SV77 )
| ( subset @ ( singleton @ SV25 ) @ SV77 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[535]) ).
thf(596,plain,
! [SV78: $i,SV26: $i] :
( ( ~ ( ~ ( ( SV26 != empty_set ) )
| ~ ( ~ ( ( SV78
!= ( set_meet @ SV26 ) )
| ! [SY434: $i] :
~ ( ~ ( ~ ( in @ SY434 @ SV78 )
| ! [SY300: $i] :
( ~ ( in @ SY300 @ SV26 )
| ( in @ SY434 @ SY300 ) ) )
| ~ ( ~ ! [SY301: $i] :
( ~ ( in @ SY301 @ SV26 )
| ( in @ SY434 @ SY301 ) )
| ( in @ SY434 @ SV78 ) ) ) )
| ~ ( ~ ! [SY437: $i] :
~ ( ~ ( ~ ( in @ SY437 @ SV78 )
| ! [SY303: $i] :
( ~ ( in @ SY303 @ SV26 )
| ( in @ SY437 @ SY303 ) ) )
| ~ ( ~ ! [SY304: $i] :
( ~ ( in @ SY304 @ SV26 )
| ( in @ SY437 @ SY304 ) )
| ( in @ SY437 @ SV78 ) ) )
| ( SV78
= ( set_meet @ SV26 ) ) ) ) )
| ~ ( ( SV26 != empty_set )
| ~ ( ~ ( ( SV78
!= ( set_meet @ SV26 ) )
| ( SV78 = empty_set ) )
| ~ ( ( SV78 != empty_set )
| ( SV78
= ( set_meet @ SV26 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[536]) ).
thf(597,plain,
! [SV110: $i,SV79: $i,SV27: $i] :
( ( ! [SY494: $i] :
( ~ ( relation @ SY494 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV27 @ SV79 ) @ ( relation_composition @ ( identity_relation @ SV110 ) @ SY494 ) )
| ~ ( ~ ( in @ SV27 @ SV110 )
| ~ ( in @ ( ordered_pair @ SV27 @ SV79 ) @ SY494 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV27 @ SV110 )
| ~ ( in @ ( ordered_pair @ SV27 @ SV79 ) @ SY494 ) )
| ( in @ ( ordered_pair @ SV27 @ SV79 ) @ ( relation_composition @ ( identity_relation @ SV110 ) @ SY494 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(598,plain,
! [SV28: $i,SV80: $i] :
( ( ( ~ ( relation @ SV80 ) )
= $true )
| ( ( ( relation_dom_restriction @ SV80 @ SV28 )
= ( relation_composition @ ( identity_relation @ SV28 ) @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[538]) ).
thf(599,plain,
! [SV111: $i,SV81: $i,SV29: $i] :
( ( ! [SY495: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV29 @ SV81 ) @ ( cartesian_product2 @ SV111 @ SY495 ) )
| ~ ( ~ ( in @ SV29 @ SV111 )
| ~ ( in @ SV81 @ SY495 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV29 @ SV111 )
| ~ ( in @ SV81 @ SY495 ) )
| ( in @ ( ordered_pair @ SV29 @ SV81 ) @ ( cartesian_product2 @ SV111 @ SY495 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(600,plain,
! [SV30: $i] :
( ( ( relation @ SV30 )
= $false )
| ( ( ! [SY312: $i,SY313: $i] :
~ ( ~ ( ( SY313
!= ( relation_image @ SV30 @ SY312 ) )
| ! [SY314: $i] :
~ ( ~ ( ~ ( in @ SY314 @ SY313 )
| ~ ! [SY315: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY315 @ SY314 ) @ SV30 )
| ~ ( in @ SY315 @ SY312 ) ) )
| ~ ( ~ ~ ! [SY316: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY316 @ SY314 ) @ SV30 )
| ~ ( in @ SY316 @ SY312 ) )
| ( in @ SY314 @ SY313 ) ) ) )
| ~ ( ~ ! [SY317: $i] :
~ ( ~ ( ~ ( in @ SY317 @ SY313 )
| ~ ! [SY318: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY318 @ SY317 ) @ SV30 )
| ~ ( in @ SY318 @ SY312 ) ) )
| ~ ( ~ ~ ! [SY319: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY319 @ SY317 ) @ SV30 )
| ~ ( in @ SY319 @ SY312 ) )
| ( in @ SY317 @ SY313 ) ) )
| ( SY313
= ( relation_image @ SV30 @ SY312 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[540]) ).
thf(601,plain,
! [SV112: $i,SV82: $i,SV31: $i] :
( ( ~ ( ~ ( ~ ( subset @ ( unordered_pair @ SV31 @ SV82 ) @ SV112 )
| ~ ( ~ ( in @ SV31 @ SV112 )
| ~ ( in @ SV82 @ SV112 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV31 @ SV112 )
| ~ ( in @ SV82 @ SV112 ) )
| ( subset @ ( unordered_pair @ SV31 @ SV82 ) @ SV112 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(602,plain,
! [SV32: $i] :
( ( ~ ( relation @ ( identity_relation @ SV32 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[542]) ).
thf(603,plain,
! [SV32: $i] :
( ( ~ ( function @ ( identity_relation @ SV32 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[542]) ).
thf(604,plain,
! [SV113: $i,SV83: $i,SV33: $i] :
( ( ~ ~ ( ~ ( in @ SV33 @ SV83 )
| ~ ( element @ SV83 @ ( powerset @ SV113 ) ) )
| ( element @ SV33 @ SV113 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(605,plain,
! [SV84: $i,SV34: $i] :
( ( ~ ( ~ ~ ( empty @ SV34 )
| ~ ( ~ ( ~ ( element @ SV84 @ SV34 )
| ( in @ SV84 @ SV34 ) )
| ~ ( ~ ( in @ SV84 @ SV34 )
| ( element @ SV84 @ SV34 ) ) ) )
| ~ ( ~ ( empty @ SV34 )
| ~ ( ~ ( ~ ( element @ SV84 @ SV34 )
| ( empty @ SV84 ) )
| ~ ( ~ ( empty @ SV84 )
| ( element @ SV84 @ SV34 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[544]) ).
thf(606,plain,
! [SV35: $i] :
( ( ~ ( ~ ( relation @ SV35 )
| ! [SY325: $i] :
~ ~ ( ~ ( in @ SY325 @ SV35 )
| ~ ! [SX2: $i,SX3: $i] :
( SY325
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[545]) ).
thf(607,plain,
! [SV35: $i] :
( ( ~ ( ~ ! [SY328: $i] :
~ ~ ( ~ ( in @ SY328 @ SV35 )
| ~ ! [SX2: $i,SX3: $i] :
( SY328
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SV35 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[545]) ).
thf(608,plain,
! [SV114: $i,SV85: $i,SV36: $i] :
( ( ~ ( subset @ SV36 @ SV85 )
| ( in @ SV114 @ SV36 )
| ( subset @ SV36 @ ( set_difference @ SV85 @ ( singleton @ SV114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(609,plain,
! [SV86: $i,SV37: $i,SV115: $i] :
( ( ~ ( relation @ SV115 )
| ~ ( in @ ( ordered_pair @ SV37 @ SV86 ) @ SV115 )
| ~ ( ~ ( in @ SV37 @ ( relation_field @ SV115 ) )
| ~ ( in @ SV86 @ ( relation_field @ SV115 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(610,plain,
! [SV38: $i] :
( ( ~ ( ( SV38 != empty_set )
| ! [SY335: $i] :
~ ( in @ SY335 @ SV38 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[548]) ).
thf(611,plain,
! [SV38: $i] :
( ( ~ ( ~ ! [SY336: $i] :
~ ( in @ SY336 @ SV38 )
| ( SV38 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[548]) ).
thf(612,plain,
! [SV39: $i,SV87: $i] :
( ( ( ~ ( relation @ SV87 ) )
= $true )
| ( ( ! [SY448: $i] :
( ~ ( relation @ SY448 )
| ~ ( ~ ( ( SY448
!= ( relation_rng_restriction @ SV39 @ SV87 ) )
| ! [SY449: $i,SY450: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY449 @ SY450 ) @ SY448 )
| ~ ( ~ ( in @ SY450 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY449 @ SY450 ) @ SV87 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY450 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY449 @ SY450 ) @ SV87 ) )
| ( in @ ( ordered_pair @ SY449 @ SY450 ) @ SY448 ) ) ) )
| ~ ( ~ ! [SY451: $i,SY452: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SY448 )
| ~ ( ~ ( in @ SY452 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV87 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY452 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV87 ) )
| ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SY448 ) ) )
| ( SY448
= ( relation_rng_restriction @ SV39 @ SV87 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[549]) ).
thf(613,plain,
! [SV40: $i] :
( ( ( relation_dom @ ( identity_relation @ SV40 ) )
!= SV40 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[550]) ).
thf(614,plain,
! [SV40: $i] :
( ( ( relation_rng @ ( identity_relation @ SV40 ) )
!= SV40 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[550]) ).
thf(615,plain,
! [SV41: $i,SV88: $i] :
( ( ~ ( ( SV88
!= ( singleton @ SV41 ) )
| ! [SY453: $i] :
~ ( ~ ( ~ ( in @ SY453 @ SV88 )
| ( SY453 = SV41 ) )
| ~ ( ( SY453 != SV41 )
| ( in @ SY453 @ SV88 ) ) ) )
| ~ ( ~ ! [SY454: $i] :
~ ( ~ ( ~ ( in @ SY454 @ SV88 )
| ( SY454 = SV41 ) )
| ~ ( ( SY454 != SV41 )
| ( in @ SY454 @ SV88 ) ) )
| ( SV88
= ( singleton @ SV41 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[551]) ).
thf(616,plain,
! [SV42: $i,SV89: $i] :
( ( ~ ( ( SV89
!= ( union @ SV42 ) )
| ! [SY455: $i] :
~ ( ~ ( ~ ( in @ SY455 @ SV89 )
| ~ ! [SY348: $i] :
~ ~ ( ~ ( in @ SY455 @ SY348 )
| ~ ( in @ SY348 @ SV42 ) ) )
| ~ ( ~ ~ ! [SY349: $i] :
~ ~ ( ~ ( in @ SY455 @ SY349 )
| ~ ( in @ SY349 @ SV42 ) )
| ( in @ SY455 @ SV89 ) ) ) )
| ~ ( ~ ! [SY458: $i] :
~ ( ~ ( ~ ( in @ SY458 @ SV89 )
| ~ ! [SY351: $i] :
~ ~ ( ~ ( in @ SY458 @ SY351 )
| ~ ( in @ SY351 @ SV42 ) ) )
| ~ ( ~ ~ ! [SY352: $i] :
~ ~ ( ~ ( in @ SY458 @ SY352 )
| ~ ( in @ SY352 @ SV42 ) )
| ( in @ SY458 @ SV89 ) ) )
| ( SV89
= ( union @ SV42 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(617,plain,
! [SV90: $i,SV43: $i,SV116: $i] :
( ( ~ ( relation @ SV116 )
| ~ ( ~ ( ~ ( in @ SV43 @ ( relation_dom @ ( relation_dom_restriction @ SV116 @ SV90 ) ) )
| ~ ( ~ ( in @ SV43 @ SV90 )
| ~ ( in @ SV43 @ ( relation_dom @ SV116 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV43 @ SV90 )
| ~ ( in @ SV43 @ ( relation_dom @ SV116 ) ) )
| ( in @ SV43 @ ( relation_dom @ ( relation_dom_restriction @ SV116 @ SV90 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(618,plain,
! [SV91: $i,SV44: $i] :
( ( ~ ( ~ ( disjoint @ ( singleton @ SV44 ) @ SV91 )
| ~ ( in @ SV44 @ SV91 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[554]) ).
thf(619,plain,
! [SV92: $i,SV45: $i] :
( ( ( ~ ( in @ SV45 @ SV92 ) )
= $true )
| ( ( subset @ SV45 @ ( union @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[555]) ).
thf(620,plain,
! [SV46: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV46 @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SY496: $i,SY497: $i] :
( ~ ~ ( ~ ( in @ SY496 @ ( sK4_SY357 @ SV46 ) )
| ~ ( subset @ SY497 @ SY496 ) )
| ( in @ SY497 @ ( sK4_SY357 @ SV46 ) ) ) )
| ~ ! [SY498: $i] :
~ ~ ( ~ ( in @ SY498 @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SY499: $i] :
~ ~ ( ~ ( in @ SY499 @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY498 )
| ( in @ SX4 @ SY499 ) ) ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY501 @ ( sK4_SY357 @ SV46 ) )
| ~ ~ ( are_equipotent @ SY501 @ ( sK4_SY357 @ SV46 ) ) )
| ~ ~ ( in @ SY501 @ ( sK4_SY357 @ SV46 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[556]) ).
thf(621,plain,
! [SV47: $i] :
( ( ( relation @ SV47 )
= $false )
| ( ( ! [SY364: $i] :
~ ( ~ ( ( SY364
!= ( relation_dom @ SV47 ) )
| ! [SY365: $i] :
~ ( ~ ( ~ ( in @ SY365 @ SY364 )
| ~ ! [SY366: $i] :
~ ( in @ ( ordered_pair @ SY365 @ SY366 ) @ SV47 ) )
| ~ ( ~ ~ ! [SY367: $i] :
~ ( in @ ( ordered_pair @ SY365 @ SY367 ) @ SV47 )
| ( in @ SY365 @ SY364 ) ) ) )
| ~ ( ~ ! [SY368: $i] :
~ ( ~ ( ~ ( in @ SY368 @ SY364 )
| ~ ! [SY369: $i] :
~ ( in @ ( ordered_pair @ SY368 @ SY369 ) @ SV47 ) )
| ~ ( ~ ~ ! [SY370: $i] :
~ ( in @ ( ordered_pair @ SY368 @ SY370 ) @ SV47 )
| ( in @ SY368 @ SY364 ) ) )
| ( SY364
= ( relation_dom @ SV47 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[557]) ).
thf(622,plain,
! [SV93: $i,SV48: $i] :
( ( ( ~ ! [SY462: $i] :
( ~ ( in @ SY462 @ SV48 )
| ( in @ SY462 @ SV93 ) ) )
= $true )
| ( ( element @ SV48 @ ( powerset @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[558]) ).
thf(623,plain,
! [SV49: $i] :
( ( ( relation @ SV49 )
= $false )
| ( ( ! [SY373: $i] :
( ~ ( relation @ SY373 )
| ~ ( ~ ( ( SY373
!= ( relation_inverse @ SV49 ) )
| ! [SY374: $i,SY375: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY374 @ SY375 ) @ SY373 )
| ( in @ ( ordered_pair @ SY375 @ SY374 ) @ SV49 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY375 @ SY374 ) @ SV49 )
| ( in @ ( ordered_pair @ SY374 @ SY375 ) @ SY373 ) ) ) )
| ~ ( ~ ! [SY376: $i,SY377: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY376 @ SY377 ) @ SY373 )
| ( in @ ( ordered_pair @ SY377 @ SY376 ) @ SV49 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY377 @ SY376 ) @ SV49 )
| ( in @ ( ordered_pair @ SY376 @ SY377 ) @ SY373 ) ) )
| ( SY373
= ( relation_inverse @ SV49 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[559]) ).
thf(624,plain,
! [SV94: $i,SV50: $i] :
( ( ~ ( ( ( set_difference @ SV50 @ ( singleton @ SV94 ) )
!= SV50 )
| ~ ( in @ SV94 @ SV50 ) )
| ~ ( ~ ~ ( in @ SV94 @ SV50 )
| ( ( set_difference @ SV50 @ ( singleton @ SV94 ) )
= SV50 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[560]) ).
thf(625,plain,
! [SV95: $i,SV51: $i] :
( ( ( ~ ( in @ SV51 @ SV95 ) )
= $true )
| ( ( subset @ SV51 @ ( union @ SV95 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[561]) ).
thf(626,plain,
! [SV96: $i,SV52: $i] :
( ( ( ~ ( in @ SV52 @ SV96 ) )
= $true )
| ( ( element @ SV52 @ SV96 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[562]) ).
thf(627,plain,
! [SV97: $i,SV53: $i] :
( ( ~ ( ~ ( subset @ SV53 @ SV97 )
| ! [SY463: $i] :
( ~ ( in @ SY463 @ SV53 )
| ( in @ SY463 @ SV97 ) ) )
| ~ ( ~ ! [SY464: $i] :
( ~ ( in @ SY464 @ SV53 )
| ( in @ SY464 @ SV97 ) )
| ( subset @ SV53 @ SV97 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[563]) ).
thf(628,plain,
! [SV98: $i,SV54: $i,SV117: $i] :
( ( ~ ( element @ SV117 @ ( powerset @ SV54 ) )
| ~ ~ ( ~ ( in @ SV98 @ ( subset_complement @ SV54 @ SV117 ) )
| ~ ( in @ SV98 @ SV117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(629,plain,
! [SV55: $i,SV99: $i] :
( ( ( ~ ( element @ SV99 @ ( powerset @ SV55 ) ) )
= $true )
| ( ( ! [SY466: $i] :
( ~ ( in @ SY466 @ SV99 )
| ( in @ SY466 @ SV55 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[565]) ).
thf(630,plain,
! [SV100: $i,SV56: $i,SV118: $i] :
( ( ~ ( ~ ( ( SV118
!= ( unordered_pair @ SV56 @ SV100 ) )
| ! [SY502: $i] :
~ ( ~ ( ~ ( in @ SY502 @ SV118 )
| ( SY502 = SV56 )
| ( SY502 = SV100 ) )
| ~ ( ~ ( ( SY502 = SV56 )
| ( SY502 = SV100 ) )
| ( in @ SY502 @ SV118 ) ) ) )
| ~ ( ~ ! [SY503: $i] :
~ ( ~ ( ~ ( in @ SY503 @ SV118 )
| ( SY503 = SV56 )
| ( SY503 = SV100 ) )
| ~ ( ~ ( ( SY503 = SV56 )
| ( SY503 = SV100 ) )
| ( in @ SY503 @ SV118 ) ) )
| ( SV118
= ( unordered_pair @ SV56 @ SV100 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(631,plain,
! [SV101: $i,SV57: $i] :
( ( ( ~ ( in @ SV57 @ SV101 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV57 ) @ SV101 )
= SV101 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[567]) ).
thf(632,plain,
! [SV102: $i,SV58: $i,SV119: $i] :
( ( ~ ( ~ ( ( SV119
!= ( set_difference @ SV58 @ SV102 ) )
| ! [SY504: $i] :
~ ( ~ ( ~ ( in @ SY504 @ SV119 )
| ~ ( ~ ( in @ SY504 @ SV58 )
| ~ ~ ( in @ SY504 @ SV102 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY504 @ SV58 )
| ~ ~ ( in @ SY504 @ SV102 ) )
| ( in @ SY504 @ SV119 ) ) ) )
| ~ ( ~ ! [SY505: $i] :
~ ( ~ ( ~ ( in @ SY505 @ SV119 )
| ~ ( ~ ( in @ SY505 @ SV58 )
| ~ ~ ( in @ SY505 @ SV102 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY505 @ SV58 )
| ~ ~ ( in @ SY505 @ SV102 ) )
| ( in @ SY505 @ SV119 ) ) )
| ( SV119
= ( set_difference @ SV58 @ SV102 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(633,plain,
! [SV120: $i,SV103: $i,SV59: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( in @ SV59 @ SV103 )
| ~ ( element @ SV103 @ ( powerset @ SV120 ) ) )
| ~ ( empty @ SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(634,plain,
! [SV104: $i,SV60: $i,SV121: $i] :
( ( ~ ( ~ ( ( SV121
!= ( set_intersection2 @ SV60 @ SV104 ) )
| ! [SY506: $i] :
~ ( ~ ( ~ ( in @ SY506 @ SV121 )
| ~ ( ~ ( in @ SY506 @ SV60 )
| ~ ( in @ SY506 @ SV104 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY506 @ SV60 )
| ~ ( in @ SY506 @ SV104 ) )
| ( in @ SY506 @ SV121 ) ) ) )
| ~ ( ~ ! [SY507: $i] :
~ ( ~ ( ~ ( in @ SY507 @ SV121 )
| ~ ( ~ ( in @ SY507 @ SV60 )
| ~ ( in @ SY507 @ SV104 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY507 @ SV60 )
| ~ ( in @ SY507 @ SV104 ) )
| ( in @ SY507 @ SV121 ) ) )
| ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(635,plain,
! [SV105: $i,SV61: $i] :
( ( ~ ( ~ ( in @ SV61 @ SV105 )
| ~ ( empty @ SV105 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(636,plain,
! [SV62: $i,SV2: $i] :
( ( ( in @ SV2 @ SV62 )
= $false )
| ( ( ~ ( in @ SV62 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[572]) ).
thf(637,plain,
! [SV63: $i,SV3: $i] :
( ( ~ ~ ~ ( ~ ~ ( disjoint @ SV3 @ SV63 )
| ~ ! [SY404: $i] :
~ ( in @ SY404 @ ( set_intersection2 @ SV3 @ SV63 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[573]) ).
thf(638,plain,
! [SV63: $i,SV3: $i] :
( ( ~ ~ ~ ( ~ ~ ! [SY405: $i] :
~ ( in @ SY405 @ ( set_intersection2 @ SV3 @ SV63 ) )
| ~ ( disjoint @ SV3 @ SV63 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[573]) ).
thf(639,plain,
! [SV64: $i,SV4: $i] :
( ( ( ~ ( in @ SV4 @ SV64 ) )
= $false )
| ( ( disjoint @ ( singleton @ SV4 ) @ SV64 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[574]) ).
thf(640,plain,
! [SV65: $i,SV5: $i] :
( ( ( ! [SY406: $i] :
~ ( ~ ( ~ ( in @ SY406 @ SV5 )
| ( in @ SY406 @ SV65 ) )
| ~ ( ~ ( in @ SY406 @ SV65 )
| ( in @ SY406 @ SV5 ) ) ) )
= $false )
| ( ( SV5 = SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[575]) ).
thf(641,plain,
! [SV6: $i,SV66: $i] :
( ( ( ~ ( ~ ( relation @ SV66 )
| ~ ( function @ SV66 ) ) )
= $false )
| ( ( ~ ( ~ ( ( SV66
!= ( identity_relation @ SV6 ) )
| ~ ( ( ( relation_dom @ SV66 )
!= SV6 )
| ~ ! [SY407: $i] :
( ~ ( in @ SY407 @ SV6 )
| ( ( apply @ SV66 @ SY407 )
= SY407 ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV66 )
!= SV6 )
| ~ ! [SY408: $i] :
( ~ ( in @ SY408 @ SV6 )
| ( ( apply @ SV66 @ SY408 )
= SY408 ) ) )
| ( SV66
= ( identity_relation @ SV6 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(642,plain,
! [SV122: $i,SV106: $i,SV67: $i,SV7: $i] :
( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV7 @ SV67 ) @ ( cartesian_product2 @ SV106 @ SV122 ) )
| ~ ( ~ ( in @ SV7 @ SV106 )
| ~ ( in @ SV67 @ SV122 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV7 @ SV106 )
| ~ ( in @ SV67 @ SV122 ) )
| ( in @ ( ordered_pair @ SV7 @ SV67 ) @ ( cartesian_product2 @ SV106 @ SV122 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(643,plain,
! [SV8: $i,SV123: $i] :
( ( ( ~ ( relation @ SV123 )
| ~ ( ~ ( ( SV8 != SV123 )
| ! [SY508: $i,SY509: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY508 @ SY509 ) @ SV8 )
| ( in @ ( ordered_pair @ SY508 @ SY509 ) @ SV123 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY508 @ SY509 ) @ SV123 )
| ( in @ ( ordered_pair @ SY508 @ SY509 ) @ SV8 ) ) ) )
| ~ ( ~ ! [SY510: $i,SY511: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY510 @ SY511 ) @ SV8 )
| ( in @ ( ordered_pair @ SY510 @ SY511 ) @ SV123 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY510 @ SY511 ) @ SV123 )
| ( in @ ( ordered_pair @ SY510 @ SY511 ) @ SV8 ) ) )
| ( SV8 = SV123 ) ) ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(644,plain,
! [SV68: $i,SV9: $i] :
( ( ~ ( ~ ( subset @ ( singleton @ SV9 ) @ SV68 )
| ( in @ SV9 @ SV68 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[579]) ).
thf(645,plain,
! [SV68: $i,SV9: $i] :
( ( ~ ( ~ ( in @ SV9 @ SV68 )
| ( subset @ ( singleton @ SV9 ) @ SV68 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[579]) ).
thf(646,plain,
! [SV10: $i,SV124: $i] :
( ( ( ~ ( relation @ SV124 )
| ! [SY512: $i] :
( ~ ( relation @ SY512 )
| ~ ( ~ ( ( SY512
!= ( relation_composition @ SV10 @ SV124 ) )
| ! [SY513: $i,SY514: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY513 @ SY514 ) @ SY512 )
| ~ ! [SY515: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY513 @ SY515 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY515 @ SY514 ) @ SV124 ) ) )
| ~ ( ~ ~ ! [SY516: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY513 @ SY516 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY516 @ SY514 ) @ SV124 ) )
| ( in @ ( ordered_pair @ SY513 @ SY514 ) @ SY512 ) ) ) )
| ~ ( ~ ! [SY517: $i,SY518: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY517 @ SY518 ) @ SY512 )
| ~ ! [SY519: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY517 @ SY519 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY519 @ SY518 ) @ SV124 ) ) )
| ~ ( ~ ~ ! [SY520: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY517 @ SY520 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY520 @ SY518 ) @ SV124 ) )
| ( in @ ( ordered_pair @ SY517 @ SY518 ) @ SY512 ) ) )
| ( SY512
= ( relation_composition @ SV10 @ SV124 ) ) ) ) ) )
= $true )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(647,plain,
! [SV69: $i,SV11: $i,SV107: $i] :
( ( ~ ( ( SV107
!= ( cartesian_product2 @ SV11 @ SV69 ) )
| ! [SY478: $i] :
~ ( ~ ( ~ ( in @ SY478 @ SV107 )
| ~ ! [SY413: $i] :
~ ~ ! [SY414: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY413 @ SV11 )
| ~ ( in @ SY414 @ SV69 ) )
| ( SY478
!= ( ordered_pair @ SY413 @ SY414 ) ) ) )
| ~ ( ~ ~ ! [SY415: $i] :
~ ~ ! [SY416: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY415 @ SV11 )
| ~ ( in @ SY416 @ SV69 ) )
| ( SY478
!= ( ordered_pair @ SY415 @ SY416 ) ) )
| ( in @ SY478 @ SV107 ) ) ) )
| ~ ( ~ ! [SY483: $i] :
~ ( ~ ( ~ ( in @ SY483 @ SV107 )
| ~ ! [SY418: $i] :
~ ~ ! [SY419: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY418 @ SV11 )
| ~ ( in @ SY419 @ SV69 ) )
| ( SY483
!= ( ordered_pair @ SY418 @ SY419 ) ) ) )
| ~ ( ~ ~ ! [SY420: $i] :
~ ~ ! [SY421: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY420 @ SV11 )
| ~ ( in @ SY421 @ SV69 ) )
| ( SY483
!= ( ordered_pair @ SY420 @ SY421 ) ) )
| ( in @ SY483 @ SV107 ) ) )
| ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[581]) ).
thf(648,plain,
! [SV12: $i,SV70: $i] :
( ( ( relation @ SV70 )
= $false )
| ( ( ~ ( ~ ( ( SV70
!= ( identity_relation @ SV12 ) )
| ! [SY422: $i,SY423: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY422 @ SY423 ) @ SV70 )
| ~ ( ~ ( in @ SY422 @ SV12 )
| ( SY422 != SY423 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY422 @ SV12 )
| ( SY422 != SY423 ) )
| ( in @ ( ordered_pair @ SY422 @ SY423 ) @ SV70 ) ) ) )
| ~ ( ~ ! [SY424: $i,SY425: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY424 @ SY425 ) @ SV70 )
| ~ ( ~ ( in @ SY424 @ SV12 )
| ( SY424 != SY425 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY424 @ SV12 )
| ( SY424 != SY425 ) )
| ( in @ ( ordered_pair @ SY424 @ SY425 ) @ SV70 ) ) )
| ( SV70
= ( identity_relation @ SV12 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[582]) ).
thf(649,plain,
! [SV13: $i,SV71: $i] :
( ( ~ ( ( SV71
!= ( powerset @ SV13 ) )
| ! [SY426: $i] :
~ ( ~ ( ~ ( in @ SY426 @ SV71 )
| ( subset @ SY426 @ SV13 ) )
| ~ ( ~ ( subset @ SY426 @ SV13 )
| ( in @ SY426 @ SV71 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[583]) ).
thf(650,plain,
! [SV13: $i,SV71: $i] :
( ( ~ ( ~ ! [SY427: $i] :
~ ( ~ ( ~ ( in @ SY427 @ SV71 )
| ( subset @ SY427 @ SV13 ) )
| ~ ( ~ ( subset @ SY427 @ SV13 )
| ( in @ SY427 @ SV71 ) ) )
| ( SV71
= ( powerset @ SV13 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[583]) ).
thf(651,plain,
! [SV125: $i,SV14: $i] :
( ( ( ! [SY521: $i] :
~ ( ~ ( ( SY521
!= ( relation_inverse_image @ SV14 @ SV125 ) )
| ! [SY522: $i] :
~ ( ~ ( ~ ( in @ SY522 @ SY521 )
| ~ ! [SY523: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY522 @ SY523 ) @ SV14 )
| ~ ( in @ SY523 @ SV125 ) ) )
| ~ ( ~ ~ ! [SY524: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY522 @ SY524 ) @ SV14 )
| ~ ( in @ SY524 @ SV125 ) )
| ( in @ SY522 @ SY521 ) ) ) )
| ~ ( ~ ! [SY525: $i] :
~ ( ~ ( ~ ( in @ SY525 @ SY521 )
| ~ ! [SY526: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY525 @ SY526 ) @ SV14 )
| ~ ( in @ SY526 @ SV125 ) ) )
| ~ ( ~ ~ ! [SY527: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY525 @ SY527 ) @ SV14 )
| ~ ( in @ SY527 @ SV125 ) )
| ( in @ SY525 @ SY521 ) ) )
| ( SY521
= ( relation_inverse_image @ SV14 @ SV125 ) ) ) ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(652,plain,
! [SV15: $i,SV126: $i] :
( ( ( ~ ( ~ ( ( SV126
!= ( relation_rng @ SV15 ) )
| ! [SY528: $i] :
~ ( ~ ( ~ ( in @ SY528 @ SV126 )
| ~ ! [SY263: $i] :
~ ( in @ ( ordered_pair @ SY263 @ SY528 ) @ SV15 ) )
| ~ ( ~ ~ ! [SY264: $i] :
~ ( in @ ( ordered_pair @ SY264 @ SY528 ) @ SV15 )
| ( in @ SY528 @ SV126 ) ) ) )
| ~ ( ~ ! [SY531: $i] :
~ ( ~ ( ~ ( in @ SY531 @ SV126 )
| ~ ! [SY266: $i] :
~ ( in @ ( ordered_pair @ SY266 @ SY531 ) @ SV15 ) )
| ~ ( ~ ~ ! [SY267: $i] :
~ ( in @ ( ordered_pair @ SY267 @ SY531 ) @ SV15 )
| ( in @ SY531 @ SV126 ) ) )
| ( SV126
= ( relation_rng @ SV15 ) ) ) ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(653,plain,
! [SV16: $i,SV127: $i] :
( ( ( ~ ( relation @ SV127 )
| ~ ( ~ ( ~ ( subset @ SV16 @ SV127 )
| ! [SY534: $i,SY535: $i] :
( ~ ( in @ ( ordered_pair @ SY534 @ SY535 ) @ SV16 )
| ( in @ ( ordered_pair @ SY534 @ SY535 ) @ SV127 ) ) )
| ~ ( ~ ! [SY536: $i,SY537: $i] :
( ~ ( in @ ( ordered_pair @ SY536 @ SY537 ) @ SV16 )
| ( in @ ( ordered_pair @ SY536 @ SY537 ) @ SV127 ) )
| ( subset @ SV16 @ SV127 ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[586]) ).
thf(654,plain,
! [SV72: $i,SV17: $i,SV108: $i] :
( ( ~ ( ( SV108
!= ( set_union2 @ SV17 @ SV72 ) )
| ! [SY488: $i] :
~ ( ~ ( ~ ( in @ SY488 @ SV108 )
| ( in @ SY488 @ SV17 )
| ( in @ SY488 @ SV72 ) )
| ~ ( ~ ( ( in @ SY488 @ SV17 )
| ( in @ SY488 @ SV72 ) )
| ( in @ SY488 @ SV108 ) ) ) )
| ~ ( ~ ! [SY489: $i] :
~ ( ~ ( ~ ( in @ SY489 @ SV108 )
| ( in @ SY489 @ SV17 )
| ( in @ SY489 @ SV72 ) )
| ~ ( ~ ( ( in @ SY489 @ SV17 )
| ( in @ SY489 @ SV72 ) )
| ( in @ SY489 @ SV108 ) ) )
| ( SV108
= ( set_union2 @ SV17 @ SV72 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[587]) ).
thf(655,plain,
! [SV18: $i] :
( ( ( ~ ! [SY277: $i,SY278: $i] :
~ ( in @ ( ordered_pair @ SY277 @ SY278 ) @ SV18 ) )
= $true )
| ( ( SV18 = empty_set )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[588]) ).
thf(656,plain,
! [SV73: $i,SV19: $i] :
( ( ( in @ SV19 @ SV73 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV19 ) @ SV73 )
= SV73 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[589]) ).
thf(657,plain,
! [SV128: $i,SV20: $i] :
( ( ( ! [SY538: $i] :
( ~ ( relation @ SY538 )
| ~ ( ~ ( ( SY538
!= ( relation_dom_restriction @ SV20 @ SV128 ) )
| ! [SY539: $i,SY540: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY539 @ SY540 ) @ SY538 )
| ~ ( ~ ( in @ SY539 @ SV128 )
| ~ ( in @ ( ordered_pair @ SY539 @ SY540 ) @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY539 @ SV128 )
| ~ ( in @ ( ordered_pair @ SY539 @ SY540 ) @ SV20 ) )
| ( in @ ( ordered_pair @ SY539 @ SY540 ) @ SY538 ) ) ) )
| ~ ( ~ ! [SY541: $i,SY542: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY541 @ SY542 ) @ SY538 )
| ~ ( ~ ( in @ SY541 @ SV128 )
| ~ ( in @ ( ordered_pair @ SY541 @ SY542 ) @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY541 @ SV128 )
| ~ ( in @ ( ordered_pair @ SY541 @ SY542 ) @ SV20 ) )
| ( in @ ( ordered_pair @ SY541 @ SY542 ) @ SY538 ) ) )
| ( SY538
= ( relation_dom_restriction @ SV20 @ SV128 ) ) ) ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(658,plain,
! [SV74: $i,SV21: $i] :
( ( ~ ~ ~ ( ~ ~ ( disjoint @ SV21 @ SV74 )
| ~ ! [SY431: $i] :
~ ~ ( ~ ( in @ SY431 @ SV21 )
| ~ ( in @ SY431 @ SV74 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[591]) ).
thf(659,plain,
! [SV74: $i,SV21: $i] :
( ( ~ ~ ~ ( ~ ~ ! [SY432: $i] :
~ ~ ( ~ ( in @ SY432 @ SV21 )
| ~ ( in @ SY432 @ SV74 ) )
| ~ ( disjoint @ SV21 @ SV74 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[591]) ).
thf(660,plain,
! [SV75: $i,SV22: $i,SV109: $i] :
( ( ( ~ ( relation @ SV109 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV22 @ ( relation_rng @ ( relation_rng_restriction @ SV75 @ SV109 ) ) )
| ~ ( ~ ( in @ SV22 @ SV75 )
| ~ ( in @ SV22 @ ( relation_rng @ SV109 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV22 @ SV75 )
| ~ ( in @ SV22 @ ( relation_rng @ SV109 ) ) )
| ( in @ SV22 @ ( relation_rng @ ( relation_rng_restriction @ SV75 @ SV109 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[592]) ).
thf(661,plain,
! [SV23: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV23 @ ( sK3_SY291 @ SV23 ) )
| ~ ! [SY490: $i,SY491: $i] :
( ~ ~ ( ~ ( in @ SY490 @ ( sK3_SY291 @ SV23 ) )
| ~ ( subset @ SY491 @ SY490 ) )
| ( in @ SY491 @ ( sK3_SY291 @ SV23 ) ) ) )
| ~ ! [SY492: $i] :
( ~ ( in @ SY492 @ ( sK3_SY291 @ SV23 ) )
| ( in @ ( powerset @ SY492 ) @ ( sK3_SY291 @ SV23 ) ) ) )
| ~ ! [SY493: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY493 @ ( sK3_SY291 @ SV23 ) )
| ~ ~ ( are_equipotent @ SY493 @ ( sK3_SY291 @ SV23 ) ) )
| ~ ~ ( in @ SY493 @ ( sK3_SY291 @ SV23 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[593]) ).
thf(662,plain,
! [SV76: $i,SV24: $i] :
( ( ( element @ SV24 @ SV76 )
= $false )
| ( ( ( empty @ SV76 )
| ( in @ SV24 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[594]) ).
thf(663,plain,
! [SV77: $i,SV25: $i] :
( ( ~ ( ~ ( subset @ ( singleton @ SV25 ) @ SV77 )
| ( in @ SV25 @ SV77 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[595]) ).
thf(664,plain,
! [SV77: $i,SV25: $i] :
( ( ~ ( ~ ( in @ SV25 @ SV77 )
| ( subset @ ( singleton @ SV25 ) @ SV77 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[595]) ).
thf(665,plain,
! [SV78: $i,SV26: $i] :
( ( ~ ( ~ ( ( SV26 != empty_set ) )
| ~ ( ~ ( ( SV78
!= ( set_meet @ SV26 ) )
| ! [SY434: $i] :
~ ( ~ ( ~ ( in @ SY434 @ SV78 )
| ! [SY300: $i] :
( ~ ( in @ SY300 @ SV26 )
| ( in @ SY434 @ SY300 ) ) )
| ~ ( ~ ! [SY301: $i] :
( ~ ( in @ SY301 @ SV26 )
| ( in @ SY434 @ SY301 ) )
| ( in @ SY434 @ SV78 ) ) ) )
| ~ ( ~ ! [SY437: $i] :
~ ( ~ ( ~ ( in @ SY437 @ SV78 )
| ! [SY303: $i] :
( ~ ( in @ SY303 @ SV26 )
| ( in @ SY437 @ SY303 ) ) )
| ~ ( ~ ! [SY304: $i] :
( ~ ( in @ SY304 @ SV26 )
| ( in @ SY437 @ SY304 ) )
| ( in @ SY437 @ SV78 ) ) )
| ( SV78
= ( set_meet @ SV26 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[596]) ).
thf(666,plain,
! [SV78: $i,SV26: $i] :
( ( ~ ( ( SV26 != empty_set )
| ~ ( ~ ( ( SV78
!= ( set_meet @ SV26 ) )
| ( SV78 = empty_set ) )
| ~ ( ( SV78 != empty_set )
| ( SV78
= ( set_meet @ SV26 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[596]) ).
thf(667,plain,
! [SV110: $i,SV79: $i,SV27: $i,SV129: $i] :
( ( ~ ( relation @ SV129 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV27 @ SV79 ) @ ( relation_composition @ ( identity_relation @ SV110 ) @ SV129 ) )
| ~ ( ~ ( in @ SV27 @ SV110 )
| ~ ( in @ ( ordered_pair @ SV27 @ SV79 ) @ SV129 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV27 @ SV110 )
| ~ ( in @ ( ordered_pair @ SV27 @ SV79 ) @ SV129 ) )
| ( in @ ( ordered_pair @ SV27 @ SV79 ) @ ( relation_composition @ ( identity_relation @ SV110 ) @ SV129 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(668,plain,
! [SV28: $i,SV80: $i] :
( ( ( relation @ SV80 )
= $false )
| ( ( ( relation_dom_restriction @ SV80 @ SV28 )
= ( relation_composition @ ( identity_relation @ SV28 ) @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[598]) ).
thf(669,plain,
! [SV130: $i,SV111: $i,SV81: $i,SV29: $i] :
( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV29 @ SV81 ) @ ( cartesian_product2 @ SV111 @ SV130 ) )
| ~ ( ~ ( in @ SV29 @ SV111 )
| ~ ( in @ SV81 @ SV130 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV29 @ SV111 )
| ~ ( in @ SV81 @ SV130 ) )
| ( in @ ( ordered_pair @ SV29 @ SV81 ) @ ( cartesian_product2 @ SV111 @ SV130 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(670,plain,
! [SV131: $i,SV30: $i] :
( ( ( ! [SY543: $i] :
~ ( ~ ( ( SY543
!= ( relation_image @ SV30 @ SV131 ) )
| ! [SY544: $i] :
~ ( ~ ( ~ ( in @ SY544 @ SY543 )
| ~ ! [SY545: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY545 @ SY544 ) @ SV30 )
| ~ ( in @ SY545 @ SV131 ) ) )
| ~ ( ~ ~ ! [SY546: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY546 @ SY544 ) @ SV30 )
| ~ ( in @ SY546 @ SV131 ) )
| ( in @ SY544 @ SY543 ) ) ) )
| ~ ( ~ ! [SY547: $i] :
~ ( ~ ( ~ ( in @ SY547 @ SY543 )
| ~ ! [SY548: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY548 @ SY547 ) @ SV30 )
| ~ ( in @ SY548 @ SV131 ) ) )
| ~ ( ~ ~ ! [SY549: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY549 @ SY547 ) @ SV30 )
| ~ ( in @ SY549 @ SV131 ) )
| ( in @ SY547 @ SY543 ) ) )
| ( SY543
= ( relation_image @ SV30 @ SV131 ) ) ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(671,plain,
! [SV112: $i,SV82: $i,SV31: $i] :
( ( ~ ( ~ ( subset @ ( unordered_pair @ SV31 @ SV82 ) @ SV112 )
| ~ ( ~ ( in @ SV31 @ SV112 )
| ~ ( in @ SV82 @ SV112 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV31 @ SV112 )
| ~ ( in @ SV82 @ SV112 ) )
| ( subset @ ( unordered_pair @ SV31 @ SV82 ) @ SV112 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[601]) ).
thf(672,plain,
! [SV32: $i] :
( ( relation @ ( identity_relation @ SV32 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[602]) ).
thf(673,plain,
! [SV32: $i] :
( ( function @ ( identity_relation @ SV32 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[603]) ).
thf(674,plain,
! [SV113: $i,SV83: $i,SV33: $i] :
( ( ( ~ ~ ( ~ ( in @ SV33 @ SV83 )
| ~ ( element @ SV83 @ ( powerset @ SV113 ) ) ) )
= $true )
| ( ( element @ SV33 @ SV113 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[604]) ).
thf(675,plain,
! [SV84: $i,SV34: $i] :
( ( ~ ( ~ ~ ( empty @ SV34 )
| ~ ( ~ ( ~ ( element @ SV84 @ SV34 )
| ( in @ SV84 @ SV34 ) )
| ~ ( ~ ( in @ SV84 @ SV34 )
| ( element @ SV84 @ SV34 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[605]) ).
thf(676,plain,
! [SV84: $i,SV34: $i] :
( ( ~ ( ~ ( empty @ SV34 )
| ~ ( ~ ( ~ ( element @ SV84 @ SV34 )
| ( empty @ SV84 ) )
| ~ ( ~ ( empty @ SV84 )
| ( element @ SV84 @ SV34 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[605]) ).
thf(677,plain,
! [SV35: $i] :
( ( ~ ( relation @ SV35 )
| ! [SY325: $i] :
~ ~ ( ~ ( in @ SY325 @ SV35 )
| ~ ! [SX2: $i,SX3: $i] :
( SY325
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[606]) ).
thf(678,plain,
! [SV35: $i] :
( ( ~ ! [SY328: $i] :
~ ~ ( ~ ( in @ SY328 @ SV35 )
| ~ ! [SX2: $i,SX3: $i] :
( SY328
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SV35 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[607]) ).
thf(679,plain,
! [SV114: $i,SV85: $i,SV36: $i] :
( ( ( ~ ( subset @ SV36 @ SV85 ) )
= $true )
| ( ( ( in @ SV114 @ SV36 )
| ( subset @ SV36 @ ( set_difference @ SV85 @ ( singleton @ SV114 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[608]) ).
thf(680,plain,
! [SV86: $i,SV37: $i,SV115: $i] :
( ( ( ~ ( relation @ SV115 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV37 @ SV86 ) @ SV115 )
| ~ ( ~ ( in @ SV37 @ ( relation_field @ SV115 ) )
| ~ ( in @ SV86 @ ( relation_field @ SV115 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[609]) ).
thf(681,plain,
! [SV38: $i] :
( ( ( SV38 != empty_set )
| ! [SY335: $i] :
~ ( in @ SY335 @ SV38 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[610]) ).
thf(682,plain,
! [SV38: $i] :
( ( ~ ! [SY336: $i] :
~ ( in @ SY336 @ SV38 )
| ( SV38 = empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[611]) ).
thf(683,plain,
! [SV39: $i,SV87: $i] :
( ( ( relation @ SV87 )
= $false )
| ( ( ! [SY448: $i] :
( ~ ( relation @ SY448 )
| ~ ( ~ ( ( SY448
!= ( relation_rng_restriction @ SV39 @ SV87 ) )
| ! [SY449: $i,SY450: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY449 @ SY450 ) @ SY448 )
| ~ ( ~ ( in @ SY450 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY449 @ SY450 ) @ SV87 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY450 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY449 @ SY450 ) @ SV87 ) )
| ( in @ ( ordered_pair @ SY449 @ SY450 ) @ SY448 ) ) ) )
| ~ ( ~ ! [SY451: $i,SY452: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SY448 )
| ~ ( ~ ( in @ SY452 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV87 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY452 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV87 ) )
| ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SY448 ) ) )
| ( SY448
= ( relation_rng_restriction @ SV39 @ SV87 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[612]) ).
thf(684,plain,
! [SV40: $i] :
( ( ( relation_dom @ ( identity_relation @ SV40 ) )
= SV40 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[613]) ).
thf(685,plain,
! [SV40: $i] :
( ( ( relation_rng @ ( identity_relation @ SV40 ) )
= SV40 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[614]) ).
thf(686,plain,
! [SV41: $i,SV88: $i] :
( ( ~ ( ( SV88
!= ( singleton @ SV41 ) )
| ! [SY453: $i] :
~ ( ~ ( ~ ( in @ SY453 @ SV88 )
| ( SY453 = SV41 ) )
| ~ ( ( SY453 != SV41 )
| ( in @ SY453 @ SV88 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[615]) ).
thf(687,plain,
! [SV41: $i,SV88: $i] :
( ( ~ ( ~ ! [SY454: $i] :
~ ( ~ ( ~ ( in @ SY454 @ SV88 )
| ( SY454 = SV41 ) )
| ~ ( ( SY454 != SV41 )
| ( in @ SY454 @ SV88 ) ) )
| ( SV88
= ( singleton @ SV41 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[615]) ).
thf(688,plain,
! [SV42: $i,SV89: $i] :
( ( ~ ( ( SV89
!= ( union @ SV42 ) )
| ! [SY455: $i] :
~ ( ~ ( ~ ( in @ SY455 @ SV89 )
| ~ ! [SY348: $i] :
~ ~ ( ~ ( in @ SY455 @ SY348 )
| ~ ( in @ SY348 @ SV42 ) ) )
| ~ ( ~ ~ ! [SY349: $i] :
~ ~ ( ~ ( in @ SY455 @ SY349 )
| ~ ( in @ SY349 @ SV42 ) )
| ( in @ SY455 @ SV89 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[616]) ).
thf(689,plain,
! [SV42: $i,SV89: $i] :
( ( ~ ( ~ ! [SY458: $i] :
~ ( ~ ( ~ ( in @ SY458 @ SV89 )
| ~ ! [SY351: $i] :
~ ~ ( ~ ( in @ SY458 @ SY351 )
| ~ ( in @ SY351 @ SV42 ) ) )
| ~ ( ~ ~ ! [SY352: $i] :
~ ~ ( ~ ( in @ SY458 @ SY352 )
| ~ ( in @ SY352 @ SV42 ) )
| ( in @ SY458 @ SV89 ) ) )
| ( SV89
= ( union @ SV42 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[616]) ).
thf(690,plain,
! [SV90: $i,SV43: $i,SV116: $i] :
( ( ( ~ ( relation @ SV116 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV43 @ ( relation_dom @ ( relation_dom_restriction @ SV116 @ SV90 ) ) )
| ~ ( ~ ( in @ SV43 @ SV90 )
| ~ ( in @ SV43 @ ( relation_dom @ SV116 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV43 @ SV90 )
| ~ ( in @ SV43 @ ( relation_dom @ SV116 ) ) )
| ( in @ SV43 @ ( relation_dom @ ( relation_dom_restriction @ SV116 @ SV90 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[617]) ).
thf(691,plain,
! [SV91: $i,SV44: $i] :
( ( ~ ( disjoint @ ( singleton @ SV44 ) @ SV91 )
| ~ ( in @ SV44 @ SV91 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[618]) ).
thf(692,plain,
! [SV92: $i,SV45: $i] :
( ( ( in @ SV45 @ SV92 )
= $false )
| ( ( subset @ SV45 @ ( union @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[619]) ).
thf(693,plain,
! [SV46: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV46 @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SY496: $i,SY497: $i] :
( ~ ~ ( ~ ( in @ SY496 @ ( sK4_SY357 @ SV46 ) )
| ~ ( subset @ SY497 @ SY496 ) )
| ( in @ SY497 @ ( sK4_SY357 @ SV46 ) ) ) )
| ~ ! [SY498: $i] :
~ ~ ( ~ ( in @ SY498 @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SY499: $i] :
~ ~ ( ~ ( in @ SY499 @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY498 )
| ( in @ SX4 @ SY499 ) ) ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY501 @ ( sK4_SY357 @ SV46 ) )
| ~ ~ ( are_equipotent @ SY501 @ ( sK4_SY357 @ SV46 ) ) )
| ~ ~ ( in @ SY501 @ ( sK4_SY357 @ SV46 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[620]) ).
thf(694,plain,
! [SV47: $i,SV132: $i] :
( ( ( ~ ( ~ ( ( SV132
!= ( relation_dom @ SV47 ) )
| ! [SY550: $i] :
~ ( ~ ( ~ ( in @ SY550 @ SV132 )
| ~ ! [SY366: $i] :
~ ( in @ ( ordered_pair @ SY550 @ SY366 ) @ SV47 ) )
| ~ ( ~ ~ ! [SY367: $i] :
~ ( in @ ( ordered_pair @ SY550 @ SY367 ) @ SV47 )
| ( in @ SY550 @ SV132 ) ) ) )
| ~ ( ~ ! [SY553: $i] :
~ ( ~ ( ~ ( in @ SY553 @ SV132 )
| ~ ! [SY369: $i] :
~ ( in @ ( ordered_pair @ SY553 @ SY369 ) @ SV47 ) )
| ~ ( ~ ~ ! [SY370: $i] :
~ ( in @ ( ordered_pair @ SY553 @ SY370 ) @ SV47 )
| ( in @ SY553 @ SV132 ) ) )
| ( SV132
= ( relation_dom @ SV47 ) ) ) ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(695,plain,
! [SV93: $i,SV48: $i] :
( ( ( ! [SY462: $i] :
( ~ ( in @ SY462 @ SV48 )
| ( in @ SY462 @ SV93 ) ) )
= $false )
| ( ( element @ SV48 @ ( powerset @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[622]) ).
thf(696,plain,
! [SV49: $i,SV133: $i] :
( ( ( ~ ( relation @ SV133 )
| ~ ( ~ ( ( SV133
!= ( relation_inverse @ SV49 ) )
| ! [SY556: $i,SY557: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY556 @ SY557 ) @ SV133 )
| ( in @ ( ordered_pair @ SY557 @ SY556 ) @ SV49 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY557 @ SY556 ) @ SV49 )
| ( in @ ( ordered_pair @ SY556 @ SY557 ) @ SV133 ) ) ) )
| ~ ( ~ ! [SY558: $i,SY559: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY558 @ SY559 ) @ SV133 )
| ( in @ ( ordered_pair @ SY559 @ SY558 ) @ SV49 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY559 @ SY558 ) @ SV49 )
| ( in @ ( ordered_pair @ SY558 @ SY559 ) @ SV133 ) ) )
| ( SV133
= ( relation_inverse @ SV49 ) ) ) ) )
= $true )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(697,plain,
! [SV94: $i,SV50: $i] :
( ( ~ ( ( ( set_difference @ SV50 @ ( singleton @ SV94 ) )
!= SV50 )
| ~ ( in @ SV94 @ SV50 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[624]) ).
thf(698,plain,
! [SV50: $i,SV94: $i] :
( ( ~ ( ~ ~ ( in @ SV94 @ SV50 )
| ( ( set_difference @ SV50 @ ( singleton @ SV94 ) )
= SV50 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[624]) ).
thf(699,plain,
! [SV95: $i,SV51: $i] :
( ( ( in @ SV51 @ SV95 )
= $false )
| ( ( subset @ SV51 @ ( union @ SV95 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[625]) ).
thf(700,plain,
! [SV96: $i,SV52: $i] :
( ( ( in @ SV52 @ SV96 )
= $false )
| ( ( element @ SV52 @ SV96 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[626]) ).
thf(701,plain,
! [SV97: $i,SV53: $i] :
( ( ~ ( ~ ( subset @ SV53 @ SV97 )
| ! [SY463: $i] :
( ~ ( in @ SY463 @ SV53 )
| ( in @ SY463 @ SV97 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[627]) ).
thf(702,plain,
! [SV97: $i,SV53: $i] :
( ( ~ ( ~ ! [SY464: $i] :
( ~ ( in @ SY464 @ SV53 )
| ( in @ SY464 @ SV97 ) )
| ( subset @ SV53 @ SV97 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[627]) ).
thf(703,plain,
! [SV98: $i,SV54: $i,SV117: $i] :
( ( ( ~ ( element @ SV117 @ ( powerset @ SV54 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( in @ SV98 @ ( subset_complement @ SV54 @ SV117 ) )
| ~ ( in @ SV98 @ SV117 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[628]) ).
thf(704,plain,
! [SV55: $i,SV99: $i] :
( ( ( element @ SV99 @ ( powerset @ SV55 ) )
= $false )
| ( ( ! [SY466: $i] :
( ~ ( in @ SY466 @ SV99 )
| ( in @ SY466 @ SV55 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[629]) ).
thf(705,plain,
! [SV100: $i,SV56: $i,SV118: $i] :
( ( ~ ( ( SV118
!= ( unordered_pair @ SV56 @ SV100 ) )
| ! [SY502: $i] :
~ ( ~ ( ~ ( in @ SY502 @ SV118 )
| ( SY502 = SV56 )
| ( SY502 = SV100 ) )
| ~ ( ~ ( ( SY502 = SV56 )
| ( SY502 = SV100 ) )
| ( in @ SY502 @ SV118 ) ) ) )
| ~ ( ~ ! [SY503: $i] :
~ ( ~ ( ~ ( in @ SY503 @ SV118 )
| ( SY503 = SV56 )
| ( SY503 = SV100 ) )
| ~ ( ~ ( ( SY503 = SV56 )
| ( SY503 = SV100 ) )
| ( in @ SY503 @ SV118 ) ) )
| ( SV118
= ( unordered_pair @ SV56 @ SV100 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[630]) ).
thf(706,plain,
! [SV101: $i,SV57: $i] :
( ( ( in @ SV57 @ SV101 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV57 ) @ SV101 )
= SV101 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[631]) ).
thf(707,plain,
! [SV102: $i,SV58: $i,SV119: $i] :
( ( ~ ( ( SV119
!= ( set_difference @ SV58 @ SV102 ) )
| ! [SY504: $i] :
~ ( ~ ( ~ ( in @ SY504 @ SV119 )
| ~ ( ~ ( in @ SY504 @ SV58 )
| ~ ~ ( in @ SY504 @ SV102 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY504 @ SV58 )
| ~ ~ ( in @ SY504 @ SV102 ) )
| ( in @ SY504 @ SV119 ) ) ) )
| ~ ( ~ ! [SY505: $i] :
~ ( ~ ( ~ ( in @ SY505 @ SV119 )
| ~ ( ~ ( in @ SY505 @ SV58 )
| ~ ~ ( in @ SY505 @ SV102 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY505 @ SV58 )
| ~ ~ ( in @ SY505 @ SV102 ) )
| ( in @ SY505 @ SV119 ) ) )
| ( SV119
= ( set_difference @ SV58 @ SV102 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[632]) ).
thf(708,plain,
! [SV120: $i,SV103: $i,SV59: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV59 @ SV103 )
| ~ ( element @ SV103 @ ( powerset @ SV120 ) ) )
| ~ ( empty @ SV120 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[633]) ).
thf(709,plain,
! [SV104: $i,SV60: $i,SV121: $i] :
( ( ~ ( ( SV121
!= ( set_intersection2 @ SV60 @ SV104 ) )
| ! [SY506: $i] :
~ ( ~ ( ~ ( in @ SY506 @ SV121 )
| ~ ( ~ ( in @ SY506 @ SV60 )
| ~ ( in @ SY506 @ SV104 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY506 @ SV60 )
| ~ ( in @ SY506 @ SV104 ) )
| ( in @ SY506 @ SV121 ) ) ) )
| ~ ( ~ ! [SY507: $i] :
~ ( ~ ( ~ ( in @ SY507 @ SV121 )
| ~ ( ~ ( in @ SY507 @ SV60 )
| ~ ( in @ SY507 @ SV104 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY507 @ SV60 )
| ~ ( in @ SY507 @ SV104 ) )
| ( in @ SY507 @ SV121 ) ) )
| ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[634]) ).
thf(710,plain,
! [SV105: $i,SV61: $i] :
( ( ~ ( in @ SV61 @ SV105 )
| ~ ( empty @ SV105 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[635]) ).
thf(711,plain,
! [SV2: $i,SV62: $i] :
( ( ( in @ SV62 @ SV2 )
= $false )
| ( ( in @ SV2 @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[636]) ).
thf(712,plain,
! [SV63: $i,SV3: $i] :
( ( ~ ~ ( ~ ~ ( disjoint @ SV3 @ SV63 )
| ~ ! [SY404: $i] :
~ ( in @ SY404 @ ( set_intersection2 @ SV3 @ SV63 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[637]) ).
thf(713,plain,
! [SV63: $i,SV3: $i] :
( ( ~ ~ ( ~ ~ ! [SY405: $i] :
~ ( in @ SY405 @ ( set_intersection2 @ SV3 @ SV63 ) )
| ~ ( disjoint @ SV3 @ SV63 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[638]) ).
thf(714,plain,
! [SV64: $i,SV4: $i] :
( ( ( in @ SV4 @ SV64 )
= $true )
| ( ( disjoint @ ( singleton @ SV4 ) @ SV64 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[639]) ).
thf(715,plain,
! [SV5: $i,SV65: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV5 )
| ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV65 ) )
| ~ ( ~ ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV65 )
| ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV5 ) ) ) )
= $false )
| ( ( SV5 = SV65 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[640]) ).
thf(716,plain,
! [SV6: $i,SV66: $i] :
( ( ( ~ ( relation @ SV66 )
| ~ ( function @ SV66 ) )
= $true )
| ( ( ~ ( ~ ( ( SV66
!= ( identity_relation @ SV6 ) )
| ~ ( ( ( relation_dom @ SV66 )
!= SV6 )
| ~ ! [SY407: $i] :
( ~ ( in @ SY407 @ SV6 )
| ( ( apply @ SV66 @ SY407 )
= SY407 ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV66 )
!= SV6 )
| ~ ! [SY408: $i] :
( ~ ( in @ SY408 @ SV6 )
| ( ( apply @ SV66 @ SY408 )
= SY408 ) ) )
| ( SV66
= ( identity_relation @ SV6 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[641]) ).
thf(717,plain,
! [SV122: $i,SV106: $i,SV67: $i,SV7: $i] :
( ( ~ ( ~ ( in @ ( ordered_pair @ SV7 @ SV67 ) @ ( cartesian_product2 @ SV106 @ SV122 ) )
| ~ ( ~ ( in @ SV7 @ SV106 )
| ~ ( in @ SV67 @ SV122 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV7 @ SV106 )
| ~ ( in @ SV67 @ SV122 ) )
| ( in @ ( ordered_pair @ SV7 @ SV67 ) @ ( cartesian_product2 @ SV106 @ SV122 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[642]) ).
thf(718,plain,
! [SV8: $i,SV123: $i] :
( ( ( ~ ( relation @ SV123 ) )
= $true )
| ( ( ~ ( ~ ( ( SV8 != SV123 )
| ! [SY508: $i,SY509: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY508 @ SY509 ) @ SV8 )
| ( in @ ( ordered_pair @ SY508 @ SY509 ) @ SV123 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY508 @ SY509 ) @ SV123 )
| ( in @ ( ordered_pair @ SY508 @ SY509 ) @ SV8 ) ) ) )
| ~ ( ~ ! [SY510: $i,SY511: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY510 @ SY511 ) @ SV8 )
| ( in @ ( ordered_pair @ SY510 @ SY511 ) @ SV123 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY510 @ SY511 ) @ SV123 )
| ( in @ ( ordered_pair @ SY510 @ SY511 ) @ SV8 ) ) )
| ( SV8 = SV123 ) ) ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[643]) ).
thf(719,plain,
! [SV68: $i,SV9: $i] :
( ( ~ ( subset @ ( singleton @ SV9 ) @ SV68 )
| ( in @ SV9 @ SV68 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[644]) ).
thf(720,plain,
! [SV68: $i,SV9: $i] :
( ( ~ ( in @ SV9 @ SV68 )
| ( subset @ ( singleton @ SV9 ) @ SV68 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[645]) ).
thf(721,plain,
! [SV10: $i,SV124: $i] :
( ( ( ~ ( relation @ SV124 ) )
= $true )
| ( ( ! [SY512: $i] :
( ~ ( relation @ SY512 )
| ~ ( ~ ( ( SY512
!= ( relation_composition @ SV10 @ SV124 ) )
| ! [SY513: $i,SY514: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY513 @ SY514 ) @ SY512 )
| ~ ! [SY515: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY513 @ SY515 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY515 @ SY514 ) @ SV124 ) ) )
| ~ ( ~ ~ ! [SY516: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY513 @ SY516 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY516 @ SY514 ) @ SV124 ) )
| ( in @ ( ordered_pair @ SY513 @ SY514 ) @ SY512 ) ) ) )
| ~ ( ~ ! [SY517: $i,SY518: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY517 @ SY518 ) @ SY512 )
| ~ ! [SY519: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY517 @ SY519 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY519 @ SY518 ) @ SV124 ) ) )
| ~ ( ~ ~ ! [SY520: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY517 @ SY520 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY520 @ SY518 ) @ SV124 ) )
| ( in @ ( ordered_pair @ SY517 @ SY518 ) @ SY512 ) ) )
| ( SY512
= ( relation_composition @ SV10 @ SV124 ) ) ) ) ) )
= $true )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[646]) ).
thf(722,plain,
! [SV69: $i,SV11: $i,SV107: $i] :
( ( ~ ( ( SV107
!= ( cartesian_product2 @ SV11 @ SV69 ) )
| ! [SY478: $i] :
~ ( ~ ( ~ ( in @ SY478 @ SV107 )
| ~ ! [SY413: $i] :
~ ~ ! [SY414: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY413 @ SV11 )
| ~ ( in @ SY414 @ SV69 ) )
| ( SY478
!= ( ordered_pair @ SY413 @ SY414 ) ) ) )
| ~ ( ~ ~ ! [SY415: $i] :
~ ~ ! [SY416: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY415 @ SV11 )
| ~ ( in @ SY416 @ SV69 ) )
| ( SY478
!= ( ordered_pair @ SY415 @ SY416 ) ) )
| ( in @ SY478 @ SV107 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[647]) ).
thf(723,plain,
! [SV69: $i,SV11: $i,SV107: $i] :
( ( ~ ( ~ ! [SY483: $i] :
~ ( ~ ( ~ ( in @ SY483 @ SV107 )
| ~ ! [SY418: $i] :
~ ~ ! [SY419: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY418 @ SV11 )
| ~ ( in @ SY419 @ SV69 ) )
| ( SY483
!= ( ordered_pair @ SY418 @ SY419 ) ) ) )
| ~ ( ~ ~ ! [SY420: $i] :
~ ~ ! [SY421: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY420 @ SV11 )
| ~ ( in @ SY421 @ SV69 ) )
| ( SY483
!= ( ordered_pair @ SY420 @ SY421 ) ) )
| ( in @ SY483 @ SV107 ) ) )
| ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[647]) ).
thf(724,plain,
! [SV12: $i,SV70: $i] :
( ( ( ~ ( ( SV70
!= ( identity_relation @ SV12 ) )
| ! [SY422: $i,SY423: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY422 @ SY423 ) @ SV70 )
| ~ ( ~ ( in @ SY422 @ SV12 )
| ( SY422 != SY423 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY422 @ SV12 )
| ( SY422 != SY423 ) )
| ( in @ ( ordered_pair @ SY422 @ SY423 ) @ SV70 ) ) ) )
| ~ ( ~ ! [SY424: $i,SY425: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY424 @ SY425 ) @ SV70 )
| ~ ( ~ ( in @ SY424 @ SV12 )
| ( SY424 != SY425 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY424 @ SV12 )
| ( SY424 != SY425 ) )
| ( in @ ( ordered_pair @ SY424 @ SY425 ) @ SV70 ) ) )
| ( SV70
= ( identity_relation @ SV12 ) ) ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[648]) ).
thf(725,plain,
! [SV13: $i,SV71: $i] :
( ( ( SV71
!= ( powerset @ SV13 ) )
| ! [SY426: $i] :
~ ( ~ ( ~ ( in @ SY426 @ SV71 )
| ( subset @ SY426 @ SV13 ) )
| ~ ( ~ ( subset @ SY426 @ SV13 )
| ( in @ SY426 @ SV71 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[649]) ).
thf(726,plain,
! [SV13: $i,SV71: $i] :
( ( ~ ! [SY427: $i] :
~ ( ~ ( ~ ( in @ SY427 @ SV71 )
| ( subset @ SY427 @ SV13 ) )
| ~ ( ~ ( subset @ SY427 @ SV13 )
| ( in @ SY427 @ SV71 ) ) )
| ( SV71
= ( powerset @ SV13 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[650]) ).
thf(727,plain,
! [SV125: $i,SV14: $i,SV134: $i] :
( ( ( ~ ( ~ ( ( SV134
!= ( relation_inverse_image @ SV14 @ SV125 ) )
| ! [SY560: $i] :
~ ( ~ ( ~ ( in @ SY560 @ SV134 )
| ~ ! [SY523: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY560 @ SY523 ) @ SV14 )
| ~ ( in @ SY523 @ SV125 ) ) )
| ~ ( ~ ~ ! [SY524: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY560 @ SY524 ) @ SV14 )
| ~ ( in @ SY524 @ SV125 ) )
| ( in @ SY560 @ SV134 ) ) ) )
| ~ ( ~ ! [SY563: $i] :
~ ( ~ ( ~ ( in @ SY563 @ SV134 )
| ~ ! [SY526: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY563 @ SY526 ) @ SV14 )
| ~ ( in @ SY526 @ SV125 ) ) )
| ~ ( ~ ~ ! [SY527: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY563 @ SY527 ) @ SV14 )
| ~ ( in @ SY527 @ SV125 ) )
| ( in @ SY563 @ SV134 ) ) )
| ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) ) ) ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(728,plain,
! [SV15: $i,SV126: $i] :
( ( ( ~ ( ( SV126
!= ( relation_rng @ SV15 ) )
| ! [SY528: $i] :
~ ( ~ ( ~ ( in @ SY528 @ SV126 )
| ~ ! [SY263: $i] :
~ ( in @ ( ordered_pair @ SY263 @ SY528 ) @ SV15 ) )
| ~ ( ~ ~ ! [SY264: $i] :
~ ( in @ ( ordered_pair @ SY264 @ SY528 ) @ SV15 )
| ( in @ SY528 @ SV126 ) ) ) )
| ~ ( ~ ! [SY531: $i] :
~ ( ~ ( ~ ( in @ SY531 @ SV126 )
| ~ ! [SY266: $i] :
~ ( in @ ( ordered_pair @ SY266 @ SY531 ) @ SV15 ) )
| ~ ( ~ ~ ! [SY267: $i] :
~ ( in @ ( ordered_pair @ SY267 @ SY531 ) @ SV15 )
| ( in @ SY531 @ SV126 ) ) )
| ( SV126
= ( relation_rng @ SV15 ) ) ) )
= $false )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[652]) ).
thf(729,plain,
! [SV16: $i,SV127: $i] :
( ( ( ~ ( relation @ SV127 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( subset @ SV16 @ SV127 )
| ! [SY534: $i,SY535: $i] :
( ~ ( in @ ( ordered_pair @ SY534 @ SY535 ) @ SV16 )
| ( in @ ( ordered_pair @ SY534 @ SY535 ) @ SV127 ) ) )
| ~ ( ~ ! [SY536: $i,SY537: $i] :
( ~ ( in @ ( ordered_pair @ SY536 @ SY537 ) @ SV16 )
| ( in @ ( ordered_pair @ SY536 @ SY537 ) @ SV127 ) )
| ( subset @ SV16 @ SV127 ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[653]) ).
thf(730,plain,
! [SV72: $i,SV17: $i,SV108: $i] :
( ( ~ ( ( SV108
!= ( set_union2 @ SV17 @ SV72 ) )
| ! [SY488: $i] :
~ ( ~ ( ~ ( in @ SY488 @ SV108 )
| ( in @ SY488 @ SV17 )
| ( in @ SY488 @ SV72 ) )
| ~ ( ~ ( ( in @ SY488 @ SV17 )
| ( in @ SY488 @ SV72 ) )
| ( in @ SY488 @ SV108 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[654]) ).
thf(731,plain,
! [SV72: $i,SV17: $i,SV108: $i] :
( ( ~ ( ~ ! [SY489: $i] :
~ ( ~ ( ~ ( in @ SY489 @ SV108 )
| ( in @ SY489 @ SV17 )
| ( in @ SY489 @ SV72 ) )
| ~ ( ~ ( ( in @ SY489 @ SV17 )
| ( in @ SY489 @ SV72 ) )
| ( in @ SY489 @ SV108 ) ) )
| ( SV108
= ( set_union2 @ SV17 @ SV72 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[654]) ).
thf(732,plain,
! [SV18: $i] :
( ( ( ! [SY277: $i,SY278: $i] :
~ ( in @ ( ordered_pair @ SY277 @ SY278 ) @ SV18 ) )
= $false )
| ( ( SV18 = empty_set )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[655]) ).
thf(733,plain,
! [SV128: $i,SV20: $i,SV135: $i] :
( ( ( ~ ( relation @ SV135 )
| ~ ( ~ ( ( SV135
!= ( relation_dom_restriction @ SV20 @ SV128 ) )
| ! [SY566: $i,SY567: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV135 )
| ~ ( ~ ( in @ SY566 @ SV128 )
| ~ ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY566 @ SV128 )
| ~ ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV20 ) )
| ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV135 ) ) ) )
| ~ ( ~ ! [SY568: $i,SY569: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY568 @ SY569 ) @ SV135 )
| ~ ( ~ ( in @ SY568 @ SV128 )
| ~ ( in @ ( ordered_pair @ SY568 @ SY569 ) @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY568 @ SV128 )
| ~ ( in @ ( ordered_pair @ SY568 @ SY569 ) @ SV20 ) )
| ( in @ ( ordered_pair @ SY568 @ SY569 ) @ SV135 ) ) )
| ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) ) ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(734,plain,
! [SV74: $i,SV21: $i] :
( ( ~ ~ ( ~ ~ ( disjoint @ SV21 @ SV74 )
| ~ ! [SY431: $i] :
~ ~ ( ~ ( in @ SY431 @ SV21 )
| ~ ( in @ SY431 @ SV74 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[658]) ).
thf(735,plain,
! [SV74: $i,SV21: $i] :
( ( ~ ~ ( ~ ~ ! [SY432: $i] :
~ ~ ( ~ ( in @ SY432 @ SV21 )
| ~ ( in @ SY432 @ SV74 ) )
| ~ ( disjoint @ SV21 @ SV74 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[659]) ).
thf(736,plain,
! [SV75: $i,SV22: $i,SV109: $i] :
( ( ( relation @ SV109 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV22 @ ( relation_rng @ ( relation_rng_restriction @ SV75 @ SV109 ) ) )
| ~ ( ~ ( in @ SV22 @ SV75 )
| ~ ( in @ SV22 @ ( relation_rng @ SV109 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV22 @ SV75 )
| ~ ( in @ SV22 @ ( relation_rng @ SV109 ) ) )
| ( in @ SV22 @ ( relation_rng @ ( relation_rng_restriction @ SV75 @ SV109 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[660]) ).
thf(737,plain,
! [SV23: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( in @ SV23 @ ( sK3_SY291 @ SV23 ) )
| ~ ! [SY490: $i,SY491: $i] :
( ~ ~ ( ~ ( in @ SY490 @ ( sK3_SY291 @ SV23 ) )
| ~ ( subset @ SY491 @ SY490 ) )
| ( in @ SY491 @ ( sK3_SY291 @ SV23 ) ) ) )
| ~ ! [SY492: $i] :
( ~ ( in @ SY492 @ ( sK3_SY291 @ SV23 ) )
| ( in @ ( powerset @ SY492 ) @ ( sK3_SY291 @ SV23 ) ) ) )
| ~ ! [SY493: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY493 @ ( sK3_SY291 @ SV23 ) )
| ~ ~ ( are_equipotent @ SY493 @ ( sK3_SY291 @ SV23 ) ) )
| ~ ~ ( in @ SY493 @ ( sK3_SY291 @ SV23 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[661]) ).
thf(738,plain,
! [SV24: $i,SV76: $i] :
( ( ( empty @ SV76 )
= $true )
| ( ( in @ SV24 @ SV76 )
= $true )
| ( ( element @ SV24 @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[662]) ).
thf(739,plain,
! [SV77: $i,SV25: $i] :
( ( ~ ( subset @ ( singleton @ SV25 ) @ SV77 )
| ( in @ SV25 @ SV77 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[663]) ).
thf(740,plain,
! [SV77: $i,SV25: $i] :
( ( ~ ( in @ SV25 @ SV77 )
| ( subset @ ( singleton @ SV25 ) @ SV77 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[664]) ).
thf(741,plain,
! [SV78: $i,SV26: $i] :
( ( ~ ( ( SV26 != empty_set ) )
| ~ ( ~ ( ( SV78
!= ( set_meet @ SV26 ) )
| ! [SY434: $i] :
~ ( ~ ( ~ ( in @ SY434 @ SV78 )
| ! [SY300: $i] :
( ~ ( in @ SY300 @ SV26 )
| ( in @ SY434 @ SY300 ) ) )
| ~ ( ~ ! [SY301: $i] :
( ~ ( in @ SY301 @ SV26 )
| ( in @ SY434 @ SY301 ) )
| ( in @ SY434 @ SV78 ) ) ) )
| ~ ( ~ ! [SY437: $i] :
~ ( ~ ( ~ ( in @ SY437 @ SV78 )
| ! [SY303: $i] :
( ~ ( in @ SY303 @ SV26 )
| ( in @ SY437 @ SY303 ) ) )
| ~ ( ~ ! [SY304: $i] :
( ~ ( in @ SY304 @ SV26 )
| ( in @ SY437 @ SY304 ) )
| ( in @ SY437 @ SV78 ) ) )
| ( SV78
= ( set_meet @ SV26 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[665]) ).
thf(742,plain,
! [SV78: $i,SV26: $i] :
( ( ( SV26 != empty_set )
| ~ ( ~ ( ( SV78
!= ( set_meet @ SV26 ) )
| ( SV78 = empty_set ) )
| ~ ( ( SV78 != empty_set )
| ( SV78
= ( set_meet @ SV26 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[666]) ).
thf(743,plain,
! [SV110: $i,SV79: $i,SV27: $i,SV129: $i] :
( ( ( ~ ( relation @ SV129 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV27 @ SV79 ) @ ( relation_composition @ ( identity_relation @ SV110 ) @ SV129 ) )
| ~ ( ~ ( in @ SV27 @ SV110 )
| ~ ( in @ ( ordered_pair @ SV27 @ SV79 ) @ SV129 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV27 @ SV110 )
| ~ ( in @ ( ordered_pair @ SV27 @ SV79 ) @ SV129 ) )
| ( in @ ( ordered_pair @ SV27 @ SV79 ) @ ( relation_composition @ ( identity_relation @ SV110 ) @ SV129 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[667]) ).
thf(744,plain,
! [SV130: $i,SV111: $i,SV81: $i,SV29: $i] :
( ( ~ ( ~ ( in @ ( ordered_pair @ SV29 @ SV81 ) @ ( cartesian_product2 @ SV111 @ SV130 ) )
| ~ ( ~ ( in @ SV29 @ SV111 )
| ~ ( in @ SV81 @ SV130 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV29 @ SV111 )
| ~ ( in @ SV81 @ SV130 ) )
| ( in @ ( ordered_pair @ SV29 @ SV81 ) @ ( cartesian_product2 @ SV111 @ SV130 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[669]) ).
thf(745,plain,
! [SV131: $i,SV30: $i,SV136: $i] :
( ( ( ~ ( ~ ( ( SV136
!= ( relation_image @ SV30 @ SV131 ) )
| ! [SY570: $i] :
~ ( ~ ( ~ ( in @ SY570 @ SV136 )
| ~ ! [SY545: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY545 @ SY570 ) @ SV30 )
| ~ ( in @ SY545 @ SV131 ) ) )
| ~ ( ~ ~ ! [SY546: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY546 @ SY570 ) @ SV30 )
| ~ ( in @ SY546 @ SV131 ) )
| ( in @ SY570 @ SV136 ) ) ) )
| ~ ( ~ ! [SY573: $i] :
~ ( ~ ( ~ ( in @ SY573 @ SV136 )
| ~ ! [SY548: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY548 @ SY573 ) @ SV30 )
| ~ ( in @ SY548 @ SV131 ) ) )
| ~ ( ~ ~ ! [SY549: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY549 @ SY573 ) @ SV30 )
| ~ ( in @ SY549 @ SV131 ) )
| ( in @ SY573 @ SV136 ) ) )
| ( SV136
= ( relation_image @ SV30 @ SV131 ) ) ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(746,plain,
! [SV112: $i,SV82: $i,SV31: $i] :
( ( ~ ( ~ ( subset @ ( unordered_pair @ SV31 @ SV82 ) @ SV112 )
| ~ ( ~ ( in @ SV31 @ SV112 )
| ~ ( in @ SV82 @ SV112 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[671]) ).
thf(747,plain,
! [SV82: $i,SV112: $i,SV31: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV31 @ SV112 )
| ~ ( in @ SV82 @ SV112 ) )
| ( subset @ ( unordered_pair @ SV31 @ SV82 ) @ SV112 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[671]) ).
thf(748,plain,
! [SV113: $i,SV83: $i,SV33: $i] :
( ( ( ~ ( ~ ( in @ SV33 @ SV83 )
| ~ ( element @ SV83 @ ( powerset @ SV113 ) ) ) )
= $false )
| ( ( element @ SV33 @ SV113 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[674]) ).
thf(749,plain,
! [SV84: $i,SV34: $i] :
( ( ~ ~ ( empty @ SV34 )
| ~ ( ~ ( ~ ( element @ SV84 @ SV34 )
| ( in @ SV84 @ SV34 ) )
| ~ ( ~ ( in @ SV84 @ SV34 )
| ( element @ SV84 @ SV34 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[675]) ).
thf(750,plain,
! [SV84: $i,SV34: $i] :
( ( ~ ( empty @ SV34 )
| ~ ( ~ ( ~ ( element @ SV84 @ SV34 )
| ( empty @ SV84 ) )
| ~ ( ~ ( empty @ SV84 )
| ( element @ SV84 @ SV34 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[676]) ).
thf(751,plain,
! [SV35: $i] :
( ( ( ~ ( relation @ SV35 ) )
= $true )
| ( ( ! [SY325: $i] :
~ ~ ( ~ ( in @ SY325 @ SV35 )
| ~ ! [SX2: $i,SX3: $i] :
( SY325
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[677]) ).
thf(752,plain,
! [SV35: $i] :
( ( ( ~ ! [SY328: $i] :
~ ~ ( ~ ( in @ SY328 @ SV35 )
| ~ ! [SX2: $i,SX3: $i] :
( SY328
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $true )
| ( ( relation @ SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[678]) ).
thf(753,plain,
! [SV114: $i,SV85: $i,SV36: $i] :
( ( ( subset @ SV36 @ SV85 )
= $false )
| ( ( ( in @ SV114 @ SV36 )
| ( subset @ SV36 @ ( set_difference @ SV85 @ ( singleton @ SV114 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[679]) ).
thf(754,plain,
! [SV86: $i,SV37: $i,SV115: $i] :
( ( ( relation @ SV115 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV37 @ SV86 ) @ SV115 )
| ~ ( ~ ( in @ SV37 @ ( relation_field @ SV115 ) )
| ~ ( in @ SV86 @ ( relation_field @ SV115 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[680]) ).
thf(755,plain,
! [SV38: $i] :
( ( ( SV38 != empty_set )
= $true )
| ( ( ! [SY335: $i] :
~ ( in @ SY335 @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[681]) ).
thf(756,plain,
! [SV38: $i] :
( ( ( ~ ! [SY336: $i] :
~ ( in @ SY336 @ SV38 ) )
= $true )
| ( ( SV38 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[682]) ).
thf(757,plain,
! [SV87: $i,SV39: $i,SV137: $i] :
( ( ( ~ ( relation @ SV137 )
| ~ ( ~ ( ( SV137
!= ( relation_rng_restriction @ SV39 @ SV87 ) )
| ! [SY576: $i,SY577: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY576 @ SY577 ) @ SV137 )
| ~ ( ~ ( in @ SY577 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY576 @ SY577 ) @ SV87 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY577 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY576 @ SY577 ) @ SV87 ) )
| ( in @ ( ordered_pair @ SY576 @ SY577 ) @ SV137 ) ) ) )
| ~ ( ~ ! [SY578: $i,SY579: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY578 @ SY579 ) @ SV137 )
| ~ ( ~ ( in @ SY579 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY578 @ SY579 ) @ SV87 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY579 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY578 @ SY579 ) @ SV87 ) )
| ( in @ ( ordered_pair @ SY578 @ SY579 ) @ SV137 ) ) )
| ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) ) ) ) )
= $true )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(758,plain,
! [SV41: $i,SV88: $i] :
( ( ( SV88
!= ( singleton @ SV41 ) )
| ! [SY453: $i] :
~ ( ~ ( ~ ( in @ SY453 @ SV88 )
| ( SY453 = SV41 ) )
| ~ ( ( SY453 != SV41 )
| ( in @ SY453 @ SV88 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[686]) ).
thf(759,plain,
! [SV41: $i,SV88: $i] :
( ( ~ ! [SY454: $i] :
~ ( ~ ( ~ ( in @ SY454 @ SV88 )
| ( SY454 = SV41 ) )
| ~ ( ( SY454 != SV41 )
| ( in @ SY454 @ SV88 ) ) )
| ( SV88
= ( singleton @ SV41 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[687]) ).
thf(760,plain,
! [SV42: $i,SV89: $i] :
( ( ( SV89
!= ( union @ SV42 ) )
| ! [SY455: $i] :
~ ( ~ ( ~ ( in @ SY455 @ SV89 )
| ~ ! [SY348: $i] :
~ ~ ( ~ ( in @ SY455 @ SY348 )
| ~ ( in @ SY348 @ SV42 ) ) )
| ~ ( ~ ~ ! [SY349: $i] :
~ ~ ( ~ ( in @ SY455 @ SY349 )
| ~ ( in @ SY349 @ SV42 ) )
| ( in @ SY455 @ SV89 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[688]) ).
thf(761,plain,
! [SV42: $i,SV89: $i] :
( ( ~ ! [SY458: $i] :
~ ( ~ ( ~ ( in @ SY458 @ SV89 )
| ~ ! [SY351: $i] :
~ ~ ( ~ ( in @ SY458 @ SY351 )
| ~ ( in @ SY351 @ SV42 ) ) )
| ~ ( ~ ~ ! [SY352: $i] :
~ ~ ( ~ ( in @ SY458 @ SY352 )
| ~ ( in @ SY352 @ SV42 ) )
| ( in @ SY458 @ SV89 ) ) )
| ( SV89
= ( union @ SV42 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[689]) ).
thf(762,plain,
! [SV90: $i,SV43: $i,SV116: $i] :
( ( ( relation @ SV116 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV43 @ ( relation_dom @ ( relation_dom_restriction @ SV116 @ SV90 ) ) )
| ~ ( ~ ( in @ SV43 @ SV90 )
| ~ ( in @ SV43 @ ( relation_dom @ SV116 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV43 @ SV90 )
| ~ ( in @ SV43 @ ( relation_dom @ SV116 ) ) )
| ( in @ SV43 @ ( relation_dom @ ( relation_dom_restriction @ SV116 @ SV90 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[690]) ).
thf(763,plain,
! [SV91: $i,SV44: $i] :
( ( ( ~ ( disjoint @ ( singleton @ SV44 ) @ SV91 ) )
= $true )
| ( ( ~ ( in @ SV44 @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[691]) ).
thf(764,plain,
! [SV46: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( in @ SV46 @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SY496: $i,SY497: $i] :
( ~ ~ ( ~ ( in @ SY496 @ ( sK4_SY357 @ SV46 ) )
| ~ ( subset @ SY497 @ SY496 ) )
| ( in @ SY497 @ ( sK4_SY357 @ SV46 ) ) ) )
| ~ ! [SY498: $i] :
~ ~ ( ~ ( in @ SY498 @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SY499: $i] :
~ ~ ( ~ ( in @ SY499 @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY498 )
| ( in @ SX4 @ SY499 ) ) ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY501 @ ( sK4_SY357 @ SV46 ) )
| ~ ~ ( are_equipotent @ SY501 @ ( sK4_SY357 @ SV46 ) ) )
| ~ ~ ( in @ SY501 @ ( sK4_SY357 @ SV46 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[693]) ).
thf(765,plain,
! [SV47: $i,SV132: $i] :
( ( ( ~ ( ( SV132
!= ( relation_dom @ SV47 ) )
| ! [SY550: $i] :
~ ( ~ ( ~ ( in @ SY550 @ SV132 )
| ~ ! [SY366: $i] :
~ ( in @ ( ordered_pair @ SY550 @ SY366 ) @ SV47 ) )
| ~ ( ~ ~ ! [SY367: $i] :
~ ( in @ ( ordered_pair @ SY550 @ SY367 ) @ SV47 )
| ( in @ SY550 @ SV132 ) ) ) )
| ~ ( ~ ! [SY553: $i] :
~ ( ~ ( ~ ( in @ SY553 @ SV132 )
| ~ ! [SY369: $i] :
~ ( in @ ( ordered_pair @ SY553 @ SY369 ) @ SV47 ) )
| ~ ( ~ ~ ! [SY370: $i] :
~ ( in @ ( ordered_pair @ SY553 @ SY370 ) @ SV47 )
| ( in @ SY553 @ SV132 ) ) )
| ( SV132
= ( relation_dom @ SV47 ) ) ) )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[694]) ).
thf(766,plain,
! [SV48: $i,SV93: $i] :
( ( ( ~ ( in @ ( sK6_SY462 @ SV93 @ SV48 ) @ SV48 )
| ( in @ ( sK6_SY462 @ SV93 @ SV48 ) @ SV93 ) )
= $false )
| ( ( element @ SV48 @ ( powerset @ SV93 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[695]) ).
thf(767,plain,
! [SV49: $i,SV133: $i] :
( ( ( ~ ( relation @ SV133 ) )
= $true )
| ( ( ~ ( ~ ( ( SV133
!= ( relation_inverse @ SV49 ) )
| ! [SY556: $i,SY557: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY556 @ SY557 ) @ SV133 )
| ( in @ ( ordered_pair @ SY557 @ SY556 ) @ SV49 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY557 @ SY556 ) @ SV49 )
| ( in @ ( ordered_pair @ SY556 @ SY557 ) @ SV133 ) ) ) )
| ~ ( ~ ! [SY558: $i,SY559: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY558 @ SY559 ) @ SV133 )
| ( in @ ( ordered_pair @ SY559 @ SY558 ) @ SV49 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY559 @ SY558 ) @ SV49 )
| ( in @ ( ordered_pair @ SY558 @ SY559 ) @ SV133 ) ) )
| ( SV133
= ( relation_inverse @ SV49 ) ) ) ) )
= $true )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[696]) ).
thf(768,plain,
! [SV94: $i,SV50: $i] :
( ( ( ( set_difference @ SV50 @ ( singleton @ SV94 ) )
!= SV50 )
| ~ ( in @ SV94 @ SV50 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[697]) ).
thf(769,plain,
! [SV50: $i,SV94: $i] :
( ( ~ ~ ( in @ SV94 @ SV50 )
| ( ( set_difference @ SV50 @ ( singleton @ SV94 ) )
= SV50 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[698]) ).
thf(770,plain,
! [SV97: $i,SV53: $i] :
( ( ~ ( subset @ SV53 @ SV97 )
| ! [SY463: $i] :
( ~ ( in @ SY463 @ SV53 )
| ( in @ SY463 @ SV97 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[701]) ).
thf(771,plain,
! [SV97: $i,SV53: $i] :
( ( ~ ! [SY464: $i] :
( ~ ( in @ SY464 @ SV53 )
| ( in @ SY464 @ SV97 ) )
| ( subset @ SV53 @ SV97 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[702]) ).
thf(772,plain,
! [SV98: $i,SV54: $i,SV117: $i] :
( ( ( element @ SV117 @ ( powerset @ SV54 ) )
= $false )
| ( ( ~ ~ ( ~ ( in @ SV98 @ ( subset_complement @ SV54 @ SV117 ) )
| ~ ( in @ SV98 @ SV117 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[703]) ).
thf(773,plain,
! [SV55: $i,SV99: $i,SV138: $i] :
( ( ( ~ ( in @ SV138 @ SV99 )
| ( in @ SV138 @ SV55 ) )
= $true )
| ( ( element @ SV99 @ ( powerset @ SV55 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(774,plain,
! [SV100: $i,SV56: $i,SV118: $i] :
( ( ~ ( ( SV118
!= ( unordered_pair @ SV56 @ SV100 ) )
| ! [SY502: $i] :
~ ( ~ ( ~ ( in @ SY502 @ SV118 )
| ( SY502 = SV56 )
| ( SY502 = SV100 ) )
| ~ ( ~ ( ( SY502 = SV56 )
| ( SY502 = SV100 ) )
| ( in @ SY502 @ SV118 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[705]) ).
thf(775,plain,
! [SV100: $i,SV56: $i,SV118: $i] :
( ( ~ ( ~ ! [SY503: $i] :
~ ( ~ ( ~ ( in @ SY503 @ SV118 )
| ( SY503 = SV56 )
| ( SY503 = SV100 ) )
| ~ ( ~ ( ( SY503 = SV56 )
| ( SY503 = SV100 ) )
| ( in @ SY503 @ SV118 ) ) )
| ( SV118
= ( unordered_pair @ SV56 @ SV100 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[705]) ).
thf(776,plain,
! [SV102: $i,SV58: $i,SV119: $i] :
( ( ~ ( ( SV119
!= ( set_difference @ SV58 @ SV102 ) )
| ! [SY504: $i] :
~ ( ~ ( ~ ( in @ SY504 @ SV119 )
| ~ ( ~ ( in @ SY504 @ SV58 )
| ~ ~ ( in @ SY504 @ SV102 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY504 @ SV58 )
| ~ ~ ( in @ SY504 @ SV102 ) )
| ( in @ SY504 @ SV119 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[707]) ).
thf(777,plain,
! [SV102: $i,SV58: $i,SV119: $i] :
( ( ~ ( ~ ! [SY505: $i] :
~ ( ~ ( ~ ( in @ SY505 @ SV119 )
| ~ ( ~ ( in @ SY505 @ SV58 )
| ~ ~ ( in @ SY505 @ SV102 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY505 @ SV58 )
| ~ ~ ( in @ SY505 @ SV102 ) )
| ( in @ SY505 @ SV119 ) ) )
| ( SV119
= ( set_difference @ SV58 @ SV102 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[707]) ).
thf(778,plain,
! [SV120: $i,SV103: $i,SV59: $i] :
( ( ~ ~ ( ~ ( in @ SV59 @ SV103 )
| ~ ( element @ SV103 @ ( powerset @ SV120 ) ) )
| ~ ( empty @ SV120 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[708]) ).
thf(779,plain,
! [SV104: $i,SV60: $i,SV121: $i] :
( ( ~ ( ( SV121
!= ( set_intersection2 @ SV60 @ SV104 ) )
| ! [SY506: $i] :
~ ( ~ ( ~ ( in @ SY506 @ SV121 )
| ~ ( ~ ( in @ SY506 @ SV60 )
| ~ ( in @ SY506 @ SV104 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY506 @ SV60 )
| ~ ( in @ SY506 @ SV104 ) )
| ( in @ SY506 @ SV121 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[709]) ).
thf(780,plain,
! [SV104: $i,SV60: $i,SV121: $i] :
( ( ~ ( ~ ! [SY507: $i] :
~ ( ~ ( ~ ( in @ SY507 @ SV121 )
| ~ ( ~ ( in @ SY507 @ SV60 )
| ~ ( in @ SY507 @ SV104 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY507 @ SV60 )
| ~ ( in @ SY507 @ SV104 ) )
| ( in @ SY507 @ SV121 ) ) )
| ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[709]) ).
thf(781,plain,
! [SV105: $i,SV61: $i] :
( ( ( ~ ( in @ SV61 @ SV105 ) )
= $true )
| ( ( ~ ( empty @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[710]) ).
thf(782,plain,
! [SV63: $i,SV3: $i] :
( ( ~ ( ~ ~ ( disjoint @ SV3 @ SV63 )
| ~ ! [SY404: $i] :
~ ( in @ SY404 @ ( set_intersection2 @ SV3 @ SV63 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[712]) ).
thf(783,plain,
! [SV63: $i,SV3: $i] :
( ( ~ ( ~ ~ ! [SY405: $i] :
~ ( in @ SY405 @ ( set_intersection2 @ SV3 @ SV63 ) )
| ~ ( disjoint @ SV3 @ SV63 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[713]) ).
thf(784,plain,
! [SV5: $i,SV65: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV5 )
| ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV65 ) )
| ~ ( ~ ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV65 )
| ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( SV5 = SV65 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[715]) ).
thf(785,plain,
! [SV6: $i,SV66: $i] :
( ( ( ~ ( relation @ SV66 ) )
= $true )
| ( ( ~ ( function @ SV66 ) )
= $true )
| ( ( ~ ( ~ ( ( SV66
!= ( identity_relation @ SV6 ) )
| ~ ( ( ( relation_dom @ SV66 )
!= SV6 )
| ~ ! [SY407: $i] :
( ~ ( in @ SY407 @ SV6 )
| ( ( apply @ SV66 @ SY407 )
= SY407 ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV66 )
!= SV6 )
| ~ ! [SY408: $i] :
( ~ ( in @ SY408 @ SV6 )
| ( ( apply @ SV66 @ SY408 )
= SY408 ) ) )
| ( SV66
= ( identity_relation @ SV6 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[716]) ).
thf(786,plain,
! [SV122: $i,SV106: $i,SV67: $i,SV7: $i] :
( ( ~ ( ~ ( in @ ( ordered_pair @ SV7 @ SV67 ) @ ( cartesian_product2 @ SV106 @ SV122 ) )
| ~ ( ~ ( in @ SV7 @ SV106 )
| ~ ( in @ SV67 @ SV122 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[717]) ).
thf(787,plain,
! [SV122: $i,SV67: $i,SV106: $i,SV7: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV7 @ SV106 )
| ~ ( in @ SV67 @ SV122 ) )
| ( in @ ( ordered_pair @ SV7 @ SV67 ) @ ( cartesian_product2 @ SV106 @ SV122 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[717]) ).
thf(788,plain,
! [SV8: $i,SV123: $i] :
( ( ( relation @ SV123 )
= $false )
| ( ( ~ ( ~ ( ( SV8 != SV123 )
| ! [SY508: $i,SY509: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY508 @ SY509 ) @ SV8 )
| ( in @ ( ordered_pair @ SY508 @ SY509 ) @ SV123 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY508 @ SY509 ) @ SV123 )
| ( in @ ( ordered_pair @ SY508 @ SY509 ) @ SV8 ) ) ) )
| ~ ( ~ ! [SY510: $i,SY511: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY510 @ SY511 ) @ SV8 )
| ( in @ ( ordered_pair @ SY510 @ SY511 ) @ SV123 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY510 @ SY511 ) @ SV123 )
| ( in @ ( ordered_pair @ SY510 @ SY511 ) @ SV8 ) ) )
| ( SV8 = SV123 ) ) ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[718]) ).
thf(789,plain,
! [SV68: $i,SV9: $i] :
( ( ( ~ ( subset @ ( singleton @ SV9 ) @ SV68 ) )
= $true )
| ( ( in @ SV9 @ SV68 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[719]) ).
thf(790,plain,
! [SV68: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ SV68 ) )
= $true )
| ( ( subset @ ( singleton @ SV9 ) @ SV68 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[720]) ).
thf(791,plain,
! [SV10: $i,SV124: $i] :
( ( ( relation @ SV124 )
= $false )
| ( ( ! [SY512: $i] :
( ~ ( relation @ SY512 )
| ~ ( ~ ( ( SY512
!= ( relation_composition @ SV10 @ SV124 ) )
| ! [SY513: $i,SY514: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY513 @ SY514 ) @ SY512 )
| ~ ! [SY515: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY513 @ SY515 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY515 @ SY514 ) @ SV124 ) ) )
| ~ ( ~ ~ ! [SY516: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY513 @ SY516 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY516 @ SY514 ) @ SV124 ) )
| ( in @ ( ordered_pair @ SY513 @ SY514 ) @ SY512 ) ) ) )
| ~ ( ~ ! [SY517: $i,SY518: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY517 @ SY518 ) @ SY512 )
| ~ ! [SY519: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY517 @ SY519 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY519 @ SY518 ) @ SV124 ) ) )
| ~ ( ~ ~ ! [SY520: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY517 @ SY520 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY520 @ SY518 ) @ SV124 ) )
| ( in @ ( ordered_pair @ SY517 @ SY518 ) @ SY512 ) ) )
| ( SY512
= ( relation_composition @ SV10 @ SV124 ) ) ) ) ) )
= $true )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[721]) ).
thf(792,plain,
! [SV69: $i,SV11: $i,SV107: $i] :
( ( ( SV107
!= ( cartesian_product2 @ SV11 @ SV69 ) )
| ! [SY478: $i] :
~ ( ~ ( ~ ( in @ SY478 @ SV107 )
| ~ ! [SY413: $i] :
~ ~ ! [SY414: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY413 @ SV11 )
| ~ ( in @ SY414 @ SV69 ) )
| ( SY478
!= ( ordered_pair @ SY413 @ SY414 ) ) ) )
| ~ ( ~ ~ ! [SY415: $i] :
~ ~ ! [SY416: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY415 @ SV11 )
| ~ ( in @ SY416 @ SV69 ) )
| ( SY478
!= ( ordered_pair @ SY415 @ SY416 ) ) )
| ( in @ SY478 @ SV107 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[722]) ).
thf(793,plain,
! [SV69: $i,SV11: $i,SV107: $i] :
( ( ~ ! [SY483: $i] :
~ ( ~ ( ~ ( in @ SY483 @ SV107 )
| ~ ! [SY418: $i] :
~ ~ ! [SY419: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY418 @ SV11 )
| ~ ( in @ SY419 @ SV69 ) )
| ( SY483
!= ( ordered_pair @ SY418 @ SY419 ) ) ) )
| ~ ( ~ ~ ! [SY420: $i] :
~ ~ ! [SY421: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY420 @ SV11 )
| ~ ( in @ SY421 @ SV69 ) )
| ( SY483
!= ( ordered_pair @ SY420 @ SY421 ) ) )
| ( in @ SY483 @ SV107 ) ) )
| ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[723]) ).
thf(794,plain,
! [SV12: $i,SV70: $i] :
( ( ( ~ ( ( SV70
!= ( identity_relation @ SV12 ) )
| ! [SY422: $i,SY423: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY422 @ SY423 ) @ SV70 )
| ~ ( ~ ( in @ SY422 @ SV12 )
| ( SY422 != SY423 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY422 @ SV12 )
| ( SY422 != SY423 ) )
| ( in @ ( ordered_pair @ SY422 @ SY423 ) @ SV70 ) ) ) ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[724]) ).
thf(795,plain,
! [SV12: $i,SV70: $i] :
( ( ( ~ ( ~ ! [SY424: $i,SY425: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY424 @ SY425 ) @ SV70 )
| ~ ( ~ ( in @ SY424 @ SV12 )
| ( SY424 != SY425 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY424 @ SV12 )
| ( SY424 != SY425 ) )
| ( in @ ( ordered_pair @ SY424 @ SY425 ) @ SV70 ) ) )
| ( SV70
= ( identity_relation @ SV12 ) ) ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[724]) ).
thf(796,plain,
! [SV13: $i,SV71: $i] :
( ( ( SV71
!= ( powerset @ SV13 ) )
= $true )
| ( ( ! [SY426: $i] :
~ ( ~ ( ~ ( in @ SY426 @ SV71 )
| ( subset @ SY426 @ SV13 ) )
| ~ ( ~ ( subset @ SY426 @ SV13 )
| ( in @ SY426 @ SV71 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[725]) ).
thf(797,plain,
! [SV13: $i,SV71: $i] :
( ( ( ~ ! [SY427: $i] :
~ ( ~ ( ~ ( in @ SY427 @ SV71 )
| ( subset @ SY427 @ SV13 ) )
| ~ ( ~ ( subset @ SY427 @ SV13 )
| ( in @ SY427 @ SV71 ) ) ) )
= $true )
| ( ( SV71
= ( powerset @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[726]) ).
thf(798,plain,
! [SV125: $i,SV14: $i,SV134: $i] :
( ( ( ~ ( ( SV134
!= ( relation_inverse_image @ SV14 @ SV125 ) )
| ! [SY560: $i] :
~ ( ~ ( ~ ( in @ SY560 @ SV134 )
| ~ ! [SY523: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY560 @ SY523 ) @ SV14 )
| ~ ( in @ SY523 @ SV125 ) ) )
| ~ ( ~ ~ ! [SY524: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY560 @ SY524 ) @ SV14 )
| ~ ( in @ SY524 @ SV125 ) )
| ( in @ SY560 @ SV134 ) ) ) )
| ~ ( ~ ! [SY563: $i] :
~ ( ~ ( ~ ( in @ SY563 @ SV134 )
| ~ ! [SY526: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY563 @ SY526 ) @ SV14 )
| ~ ( in @ SY526 @ SV125 ) ) )
| ~ ( ~ ~ ! [SY527: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY563 @ SY527 ) @ SV14 )
| ~ ( in @ SY527 @ SV125 ) )
| ( in @ SY563 @ SV134 ) ) )
| ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) ) ) )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[727]) ).
thf(799,plain,
! [SV15: $i,SV126: $i] :
( ( ( ~ ( ( SV126
!= ( relation_rng @ SV15 ) )
| ! [SY528: $i] :
~ ( ~ ( ~ ( in @ SY528 @ SV126 )
| ~ ! [SY263: $i] :
~ ( in @ ( ordered_pair @ SY263 @ SY528 ) @ SV15 ) )
| ~ ( ~ ~ ! [SY264: $i] :
~ ( in @ ( ordered_pair @ SY264 @ SY528 ) @ SV15 )
| ( in @ SY528 @ SV126 ) ) ) ) )
= $false )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[728]) ).
thf(800,plain,
! [SV15: $i,SV126: $i] :
( ( ( ~ ( ~ ! [SY531: $i] :
~ ( ~ ( ~ ( in @ SY531 @ SV126 )
| ~ ! [SY266: $i] :
~ ( in @ ( ordered_pair @ SY266 @ SY531 ) @ SV15 ) )
| ~ ( ~ ~ ! [SY267: $i] :
~ ( in @ ( ordered_pair @ SY267 @ SY531 ) @ SV15 )
| ( in @ SY531 @ SV126 ) ) )
| ( SV126
= ( relation_rng @ SV15 ) ) ) )
= $false )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[728]) ).
thf(801,plain,
! [SV16: $i,SV127: $i] :
( ( ( relation @ SV127 )
= $false )
| ( ( ~ ( ~ ( ~ ( subset @ SV16 @ SV127 )
| ! [SY534: $i,SY535: $i] :
( ~ ( in @ ( ordered_pair @ SY534 @ SY535 ) @ SV16 )
| ( in @ ( ordered_pair @ SY534 @ SY535 ) @ SV127 ) ) )
| ~ ( ~ ! [SY536: $i,SY537: $i] :
( ~ ( in @ ( ordered_pair @ SY536 @ SY537 ) @ SV16 )
| ( in @ ( ordered_pair @ SY536 @ SY537 ) @ SV127 ) )
| ( subset @ SV16 @ SV127 ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[729]) ).
thf(802,plain,
! [SV72: $i,SV17: $i,SV108: $i] :
( ( ( SV108
!= ( set_union2 @ SV17 @ SV72 ) )
| ! [SY488: $i] :
~ ( ~ ( ~ ( in @ SY488 @ SV108 )
| ( in @ SY488 @ SV17 )
| ( in @ SY488 @ SV72 ) )
| ~ ( ~ ( ( in @ SY488 @ SV17 )
| ( in @ SY488 @ SV72 ) )
| ( in @ SY488 @ SV108 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[730]) ).
thf(803,plain,
! [SV72: $i,SV17: $i,SV108: $i] :
( ( ~ ! [SY489: $i] :
~ ( ~ ( ~ ( in @ SY489 @ SV108 )
| ( in @ SY489 @ SV17 )
| ( in @ SY489 @ SV72 ) )
| ~ ( ~ ( ( in @ SY489 @ SV17 )
| ( in @ SY489 @ SV72 ) )
| ( in @ SY489 @ SV108 ) ) )
| ( SV108
= ( set_union2 @ SV17 @ SV72 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[731]) ).
thf(804,plain,
! [SV18: $i] :
( ( ( ! [SY580: $i] :
~ ( in @ ( ordered_pair @ ( sK7_SY277 @ SV18 ) @ SY580 ) @ SV18 ) )
= $false )
| ( ( SV18 = empty_set )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[732]) ).
thf(805,plain,
! [SV128: $i,SV20: $i,SV135: $i] :
( ( ( ~ ( relation @ SV135 ) )
= $true )
| ( ( ~ ( ~ ( ( SV135
!= ( relation_dom_restriction @ SV20 @ SV128 ) )
| ! [SY566: $i,SY567: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV135 )
| ~ ( ~ ( in @ SY566 @ SV128 )
| ~ ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY566 @ SV128 )
| ~ ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV20 ) )
| ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV135 ) ) ) )
| ~ ( ~ ! [SY568: $i,SY569: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY568 @ SY569 ) @ SV135 )
| ~ ( ~ ( in @ SY568 @ SV128 )
| ~ ( in @ ( ordered_pair @ SY568 @ SY569 ) @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY568 @ SV128 )
| ~ ( in @ ( ordered_pair @ SY568 @ SY569 ) @ SV20 ) )
| ( in @ ( ordered_pair @ SY568 @ SY569 ) @ SV135 ) ) )
| ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) ) ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[733]) ).
thf(806,plain,
! [SV74: $i,SV21: $i] :
( ( ~ ( ~ ~ ( disjoint @ SV21 @ SV74 )
| ~ ! [SY431: $i] :
~ ~ ( ~ ( in @ SY431 @ SV21 )
| ~ ( in @ SY431 @ SV74 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[734]) ).
thf(807,plain,
! [SV74: $i,SV21: $i] :
( ( ~ ( ~ ~ ! [SY432: $i] :
~ ~ ( ~ ( in @ SY432 @ SV21 )
| ~ ( in @ SY432 @ SV74 ) )
| ~ ( disjoint @ SV21 @ SV74 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[735]) ).
thf(808,plain,
! [SV109: $i,SV75: $i,SV22: $i] :
( ( ( ~ ( ~ ( in @ SV22 @ ( relation_rng @ ( relation_rng_restriction @ SV75 @ SV109 ) ) )
| ~ ( ~ ( in @ SV22 @ SV75 )
| ~ ( in @ SV22 @ ( relation_rng @ SV109 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV22 @ SV75 )
| ~ ( in @ SV22 @ ( relation_rng @ SV109 ) ) )
| ( in @ SV22 @ ( relation_rng @ ( relation_rng_restriction @ SV75 @ SV109 ) ) ) ) )
= $false )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[736]) ).
thf(809,plain,
! [SV23: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( in @ SV23 @ ( sK3_SY291 @ SV23 ) )
| ~ ! [SY490: $i,SY491: $i] :
( ~ ~ ( ~ ( in @ SY490 @ ( sK3_SY291 @ SV23 ) )
| ~ ( subset @ SY491 @ SY490 ) )
| ( in @ SY491 @ ( sK3_SY291 @ SV23 ) ) ) )
| ~ ! [SY492: $i] :
( ~ ( in @ SY492 @ ( sK3_SY291 @ SV23 ) )
| ( in @ ( powerset @ SY492 ) @ ( sK3_SY291 @ SV23 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[737]) ).
thf(810,plain,
! [SV23: $i] :
( ( ~ ! [SY493: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY493 @ ( sK3_SY291 @ SV23 ) )
| ~ ~ ( are_equipotent @ SY493 @ ( sK3_SY291 @ SV23 ) ) )
| ~ ~ ( in @ SY493 @ ( sK3_SY291 @ SV23 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[737]) ).
thf(811,plain,
! [SV77: $i,SV25: $i] :
( ( ( ~ ( subset @ ( singleton @ SV25 ) @ SV77 ) )
= $true )
| ( ( in @ SV25 @ SV77 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[739]) ).
thf(812,plain,
! [SV77: $i,SV25: $i] :
( ( ( ~ ( in @ SV25 @ SV77 ) )
= $true )
| ( ( subset @ ( singleton @ SV25 ) @ SV77 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[740]) ).
thf(813,plain,
! [SV78: $i,SV26: $i] :
( ( ( ~ ( ( SV26 != empty_set ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV78
!= ( set_meet @ SV26 ) )
| ! [SY434: $i] :
~ ( ~ ( ~ ( in @ SY434 @ SV78 )
| ! [SY300: $i] :
( ~ ( in @ SY300 @ SV26 )
| ( in @ SY434 @ SY300 ) ) )
| ~ ( ~ ! [SY301: $i] :
( ~ ( in @ SY301 @ SV26 )
| ( in @ SY434 @ SY301 ) )
| ( in @ SY434 @ SV78 ) ) ) )
| ~ ( ~ ! [SY437: $i] :
~ ( ~ ( ~ ( in @ SY437 @ SV78 )
| ! [SY303: $i] :
( ~ ( in @ SY303 @ SV26 )
| ( in @ SY437 @ SY303 ) ) )
| ~ ( ~ ! [SY304: $i] :
( ~ ( in @ SY304 @ SV26 )
| ( in @ SY437 @ SY304 ) )
| ( in @ SY437 @ SV78 ) ) )
| ( SV78
= ( set_meet @ SV26 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[741]) ).
thf(814,plain,
! [SV78: $i,SV26: $i] :
( ( ( SV26 != empty_set )
= $true )
| ( ( ~ ( ~ ( ( SV78
!= ( set_meet @ SV26 ) )
| ( SV78 = empty_set ) )
| ~ ( ( SV78 != empty_set )
| ( SV78
= ( set_meet @ SV26 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[742]) ).
thf(815,plain,
! [SV110: $i,SV79: $i,SV27: $i,SV129: $i] :
( ( ( relation @ SV129 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV27 @ SV79 ) @ ( relation_composition @ ( identity_relation @ SV110 ) @ SV129 ) )
| ~ ( ~ ( in @ SV27 @ SV110 )
| ~ ( in @ ( ordered_pair @ SV27 @ SV79 ) @ SV129 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV27 @ SV110 )
| ~ ( in @ ( ordered_pair @ SV27 @ SV79 ) @ SV129 ) )
| ( in @ ( ordered_pair @ SV27 @ SV79 ) @ ( relation_composition @ ( identity_relation @ SV110 ) @ SV129 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[743]) ).
thf(816,plain,
! [SV130: $i,SV111: $i,SV81: $i,SV29: $i] :
( ( ~ ( ~ ( in @ ( ordered_pair @ SV29 @ SV81 ) @ ( cartesian_product2 @ SV111 @ SV130 ) )
| ~ ( ~ ( in @ SV29 @ SV111 )
| ~ ( in @ SV81 @ SV130 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[744]) ).
thf(817,plain,
! [SV130: $i,SV81: $i,SV111: $i,SV29: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV29 @ SV111 )
| ~ ( in @ SV81 @ SV130 ) )
| ( in @ ( ordered_pair @ SV29 @ SV81 ) @ ( cartesian_product2 @ SV111 @ SV130 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[744]) ).
thf(818,plain,
! [SV131: $i,SV30: $i,SV136: $i] :
( ( ( ~ ( ( SV136
!= ( relation_image @ SV30 @ SV131 ) )
| ! [SY570: $i] :
~ ( ~ ( ~ ( in @ SY570 @ SV136 )
| ~ ! [SY545: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY545 @ SY570 ) @ SV30 )
| ~ ( in @ SY545 @ SV131 ) ) )
| ~ ( ~ ~ ! [SY546: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY546 @ SY570 ) @ SV30 )
| ~ ( in @ SY546 @ SV131 ) )
| ( in @ SY570 @ SV136 ) ) ) )
| ~ ( ~ ! [SY573: $i] :
~ ( ~ ( ~ ( in @ SY573 @ SV136 )
| ~ ! [SY548: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY548 @ SY573 ) @ SV30 )
| ~ ( in @ SY548 @ SV131 ) ) )
| ~ ( ~ ~ ! [SY549: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY549 @ SY573 ) @ SV30 )
| ~ ( in @ SY549 @ SV131 ) )
| ( in @ SY573 @ SV136 ) ) )
| ( SV136
= ( relation_image @ SV30 @ SV131 ) ) ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[745]) ).
thf(819,plain,
! [SV112: $i,SV82: $i,SV31: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV31 @ SV82 ) @ SV112 )
| ~ ( ~ ( in @ SV31 @ SV112 )
| ~ ( in @ SV82 @ SV112 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[746]) ).
thf(820,plain,
! [SV82: $i,SV112: $i,SV31: $i] :
( ( ~ ~ ( ~ ( in @ SV31 @ SV112 )
| ~ ( in @ SV82 @ SV112 ) )
| ( subset @ ( unordered_pair @ SV31 @ SV82 ) @ SV112 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[747]) ).
thf(821,plain,
! [SV113: $i,SV83: $i,SV33: $i] :
( ( ( ~ ( in @ SV33 @ SV83 )
| ~ ( element @ SV83 @ ( powerset @ SV113 ) ) )
= $true )
| ( ( element @ SV33 @ SV113 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[748]) ).
thf(822,plain,
! [SV84: $i,SV34: $i] :
( ( ( ~ ~ ( empty @ SV34 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( element @ SV84 @ SV34 )
| ( in @ SV84 @ SV34 ) )
| ~ ( ~ ( in @ SV84 @ SV34 )
| ( element @ SV84 @ SV34 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[749]) ).
thf(823,plain,
! [SV84: $i,SV34: $i] :
( ( ( ~ ( empty @ SV34 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( element @ SV84 @ SV34 )
| ( empty @ SV84 ) )
| ~ ( ~ ( empty @ SV84 )
| ( element @ SV84 @ SV34 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[750]) ).
thf(824,plain,
! [SV35: $i] :
( ( ( relation @ SV35 )
= $false )
| ( ( ! [SY325: $i] :
~ ~ ( ~ ( in @ SY325 @ SV35 )
| ~ ! [SX2: $i,SX3: $i] :
( SY325
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[751]) ).
thf(825,plain,
! [SV35: $i] :
( ( ( ! [SY328: $i] :
~ ~ ( ~ ( in @ SY328 @ SV35 )
| ~ ! [SX2: $i,SX3: $i] :
( SY328
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $false )
| ( ( relation @ SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[752]) ).
thf(826,plain,
! [SV85: $i,SV36: $i,SV114: $i] :
( ( ( in @ SV114 @ SV36 )
= $true )
| ( ( subset @ SV36 @ ( set_difference @ SV85 @ ( singleton @ SV114 ) ) )
= $true )
| ( ( subset @ SV36 @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[753]) ).
thf(827,plain,
! [SV115: $i,SV86: $i,SV37: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV37 @ SV86 ) @ SV115 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV37 @ ( relation_field @ SV115 ) )
| ~ ( in @ SV86 @ ( relation_field @ SV115 ) ) ) )
= $true )
| ( ( relation @ SV115 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[754]) ).
thf(828,plain,
! [SV38: $i] :
( ( ( SV38 = empty_set )
= $false )
| ( ( ! [SY335: $i] :
~ ( in @ SY335 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[755]) ).
thf(829,plain,
! [SV38: $i] :
( ( ( ! [SY336: $i] :
~ ( in @ SY336 @ SV38 ) )
= $false )
| ( ( SV38 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[756]) ).
thf(830,plain,
! [SV87: $i,SV39: $i,SV137: $i] :
( ( ( ~ ( relation @ SV137 ) )
= $true )
| ( ( ~ ( ~ ( ( SV137
!= ( relation_rng_restriction @ SV39 @ SV87 ) )
| ! [SY576: $i,SY577: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY576 @ SY577 ) @ SV137 )
| ~ ( ~ ( in @ SY577 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY576 @ SY577 ) @ SV87 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY577 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY576 @ SY577 ) @ SV87 ) )
| ( in @ ( ordered_pair @ SY576 @ SY577 ) @ SV137 ) ) ) )
| ~ ( ~ ! [SY578: $i,SY579: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY578 @ SY579 ) @ SV137 )
| ~ ( ~ ( in @ SY579 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY578 @ SY579 ) @ SV87 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY579 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY578 @ SY579 ) @ SV87 ) )
| ( in @ ( ordered_pair @ SY578 @ SY579 ) @ SV137 ) ) )
| ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) ) ) ) )
= $true )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[757]) ).
thf(831,plain,
! [SV41: $i,SV88: $i] :
( ( ( SV88
!= ( singleton @ SV41 ) )
= $true )
| ( ( ! [SY453: $i] :
~ ( ~ ( ~ ( in @ SY453 @ SV88 )
| ( SY453 = SV41 ) )
| ~ ( ( SY453 != SV41 )
| ( in @ SY453 @ SV88 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[758]) ).
thf(832,plain,
! [SV41: $i,SV88: $i] :
( ( ( ~ ! [SY454: $i] :
~ ( ~ ( ~ ( in @ SY454 @ SV88 )
| ( SY454 = SV41 ) )
| ~ ( ( SY454 != SV41 )
| ( in @ SY454 @ SV88 ) ) ) )
= $true )
| ( ( SV88
= ( singleton @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[759]) ).
thf(833,plain,
! [SV42: $i,SV89: $i] :
( ( ( SV89
!= ( union @ SV42 ) )
= $true )
| ( ( ! [SY455: $i] :
~ ( ~ ( ~ ( in @ SY455 @ SV89 )
| ~ ! [SY348: $i] :
~ ~ ( ~ ( in @ SY455 @ SY348 )
| ~ ( in @ SY348 @ SV42 ) ) )
| ~ ( ~ ~ ! [SY349: $i] :
~ ~ ( ~ ( in @ SY455 @ SY349 )
| ~ ( in @ SY349 @ SV42 ) )
| ( in @ SY455 @ SV89 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[760]) ).
thf(834,plain,
! [SV42: $i,SV89: $i] :
( ( ( ~ ! [SY458: $i] :
~ ( ~ ( ~ ( in @ SY458 @ SV89 )
| ~ ! [SY351: $i] :
~ ~ ( ~ ( in @ SY458 @ SY351 )
| ~ ( in @ SY351 @ SV42 ) ) )
| ~ ( ~ ~ ! [SY352: $i] :
~ ~ ( ~ ( in @ SY458 @ SY352 )
| ~ ( in @ SY352 @ SV42 ) )
| ( in @ SY458 @ SV89 ) ) ) )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[761]) ).
thf(835,plain,
! [SV90: $i,SV116: $i,SV43: $i] :
( ( ( ~ ( ~ ( in @ SV43 @ ( relation_dom @ ( relation_dom_restriction @ SV116 @ SV90 ) ) )
| ~ ( ~ ( in @ SV43 @ SV90 )
| ~ ( in @ SV43 @ ( relation_dom @ SV116 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV43 @ SV90 )
| ~ ( in @ SV43 @ ( relation_dom @ SV116 ) ) )
| ( in @ SV43 @ ( relation_dom @ ( relation_dom_restriction @ SV116 @ SV90 ) ) ) ) )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[762]) ).
thf(836,plain,
! [SV91: $i,SV44: $i] :
( ( ( disjoint @ ( singleton @ SV44 ) @ SV91 )
= $false )
| ( ( ~ ( in @ SV44 @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[763]) ).
thf(837,plain,
! [SV46: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( in @ SV46 @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SY496: $i,SY497: $i] :
( ~ ~ ( ~ ( in @ SY496 @ ( sK4_SY357 @ SV46 ) )
| ~ ( subset @ SY497 @ SY496 ) )
| ( in @ SY497 @ ( sK4_SY357 @ SV46 ) ) ) )
| ~ ! [SY498: $i] :
~ ~ ( ~ ( in @ SY498 @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SY499: $i] :
~ ~ ( ~ ( in @ SY499 @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY498 )
| ( in @ SX4 @ SY499 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[764]) ).
thf(838,plain,
! [SV46: $i] :
( ( ~ ! [SY501: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY501 @ ( sK4_SY357 @ SV46 ) )
| ~ ~ ( are_equipotent @ SY501 @ ( sK4_SY357 @ SV46 ) ) )
| ~ ~ ( in @ SY501 @ ( sK4_SY357 @ SV46 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[764]) ).
thf(839,plain,
! [SV47: $i,SV132: $i] :
( ( ( ~ ( ( SV132
!= ( relation_dom @ SV47 ) )
| ! [SY550: $i] :
~ ( ~ ( ~ ( in @ SY550 @ SV132 )
| ~ ! [SY366: $i] :
~ ( in @ ( ordered_pair @ SY550 @ SY366 ) @ SV47 ) )
| ~ ( ~ ~ ! [SY367: $i] :
~ ( in @ ( ordered_pair @ SY550 @ SY367 ) @ SV47 )
| ( in @ SY550 @ SV132 ) ) ) ) )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[765]) ).
thf(840,plain,
! [SV47: $i,SV132: $i] :
( ( ( ~ ( ~ ! [SY553: $i] :
~ ( ~ ( ~ ( in @ SY553 @ SV132 )
| ~ ! [SY369: $i] :
~ ( in @ ( ordered_pair @ SY553 @ SY369 ) @ SV47 ) )
| ~ ( ~ ~ ! [SY370: $i] :
~ ( in @ ( ordered_pair @ SY553 @ SY370 ) @ SV47 )
| ( in @ SY553 @ SV132 ) ) )
| ( SV132
= ( relation_dom @ SV47 ) ) ) )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[765]) ).
thf(841,plain,
! [SV48: $i,SV93: $i] :
( ( ( ~ ( in @ ( sK6_SY462 @ SV93 @ SV48 ) @ SV48 ) )
= $false )
| ( ( element @ SV48 @ ( powerset @ SV93 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[766]) ).
thf(842,plain,
! [SV48: $i,SV93: $i] :
( ( ( in @ ( sK6_SY462 @ SV93 @ SV48 ) @ SV93 )
= $false )
| ( ( element @ SV48 @ ( powerset @ SV93 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[766]) ).
thf(843,plain,
! [SV49: $i,SV133: $i] :
( ( ( relation @ SV133 )
= $false )
| ( ( ~ ( ~ ( ( SV133
!= ( relation_inverse @ SV49 ) )
| ! [SY556: $i,SY557: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY556 @ SY557 ) @ SV133 )
| ( in @ ( ordered_pair @ SY557 @ SY556 ) @ SV49 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY557 @ SY556 ) @ SV49 )
| ( in @ ( ordered_pair @ SY556 @ SY557 ) @ SV133 ) ) ) )
| ~ ( ~ ! [SY558: $i,SY559: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY558 @ SY559 ) @ SV133 )
| ( in @ ( ordered_pair @ SY559 @ SY558 ) @ SV49 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY559 @ SY558 ) @ SV49 )
| ( in @ ( ordered_pair @ SY558 @ SY559 ) @ SV133 ) ) )
| ( SV133
= ( relation_inverse @ SV49 ) ) ) ) )
= $true )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[767]) ).
thf(844,plain,
! [SV94: $i,SV50: $i] :
( ( ( ( set_difference @ SV50 @ ( singleton @ SV94 ) )
!= SV50 )
= $true )
| ( ( ~ ( in @ SV94 @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[768]) ).
thf(845,plain,
! [SV50: $i,SV94: $i] :
( ( ( ~ ~ ( in @ SV94 @ SV50 ) )
= $true )
| ( ( ( set_difference @ SV50 @ ( singleton @ SV94 ) )
= SV50 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[769]) ).
thf(846,plain,
! [SV97: $i,SV53: $i] :
( ( ( ~ ( subset @ SV53 @ SV97 ) )
= $true )
| ( ( ! [SY463: $i] :
( ~ ( in @ SY463 @ SV53 )
| ( in @ SY463 @ SV97 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[770]) ).
thf(847,plain,
! [SV97: $i,SV53: $i] :
( ( ( ~ ! [SY464: $i] :
( ~ ( in @ SY464 @ SV53 )
| ( in @ SY464 @ SV97 ) ) )
= $true )
| ( ( subset @ SV53 @ SV97 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[771]) ).
thf(848,plain,
! [SV117: $i,SV54: $i,SV98: $i] :
( ( ( ~ ( ~ ( in @ SV98 @ ( subset_complement @ SV54 @ SV117 ) )
| ~ ( in @ SV98 @ SV117 ) ) )
= $false )
| ( ( element @ SV117 @ ( powerset @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[772]) ).
thf(849,plain,
! [SV55: $i,SV99: $i,SV138: $i] :
( ( ( ~ ( in @ SV138 @ SV99 ) )
= $true )
| ( ( in @ SV138 @ SV55 )
= $true )
| ( ( element @ SV99 @ ( powerset @ SV55 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[773]) ).
thf(850,plain,
! [SV100: $i,SV56: $i,SV118: $i] :
( ( ( SV118
!= ( unordered_pair @ SV56 @ SV100 ) )
| ! [SY502: $i] :
~ ( ~ ( ~ ( in @ SY502 @ SV118 )
| ( SY502 = SV56 )
| ( SY502 = SV100 ) )
| ~ ( ~ ( ( SY502 = SV56 )
| ( SY502 = SV100 ) )
| ( in @ SY502 @ SV118 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[774]) ).
thf(851,plain,
! [SV100: $i,SV56: $i,SV118: $i] :
( ( ~ ! [SY503: $i] :
~ ( ~ ( ~ ( in @ SY503 @ SV118 )
| ( SY503 = SV56 )
| ( SY503 = SV100 ) )
| ~ ( ~ ( ( SY503 = SV56 )
| ( SY503 = SV100 ) )
| ( in @ SY503 @ SV118 ) ) )
| ( SV118
= ( unordered_pair @ SV56 @ SV100 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[775]) ).
thf(852,plain,
! [SV102: $i,SV58: $i,SV119: $i] :
( ( ( SV119
!= ( set_difference @ SV58 @ SV102 ) )
| ! [SY504: $i] :
~ ( ~ ( ~ ( in @ SY504 @ SV119 )
| ~ ( ~ ( in @ SY504 @ SV58 )
| ~ ~ ( in @ SY504 @ SV102 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY504 @ SV58 )
| ~ ~ ( in @ SY504 @ SV102 ) )
| ( in @ SY504 @ SV119 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[776]) ).
thf(853,plain,
! [SV102: $i,SV58: $i,SV119: $i] :
( ( ~ ! [SY505: $i] :
~ ( ~ ( ~ ( in @ SY505 @ SV119 )
| ~ ( ~ ( in @ SY505 @ SV58 )
| ~ ~ ( in @ SY505 @ SV102 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY505 @ SV58 )
| ~ ~ ( in @ SY505 @ SV102 ) )
| ( in @ SY505 @ SV119 ) ) )
| ( SV119
= ( set_difference @ SV58 @ SV102 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[777]) ).
thf(854,plain,
! [SV120: $i,SV103: $i,SV59: $i] :
( ( ( ~ ~ ( ~ ( in @ SV59 @ SV103 )
| ~ ( element @ SV103 @ ( powerset @ SV120 ) ) ) )
= $true )
| ( ( ~ ( empty @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[778]) ).
thf(855,plain,
! [SV104: $i,SV60: $i,SV121: $i] :
( ( ( SV121
!= ( set_intersection2 @ SV60 @ SV104 ) )
| ! [SY506: $i] :
~ ( ~ ( ~ ( in @ SY506 @ SV121 )
| ~ ( ~ ( in @ SY506 @ SV60 )
| ~ ( in @ SY506 @ SV104 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY506 @ SV60 )
| ~ ( in @ SY506 @ SV104 ) )
| ( in @ SY506 @ SV121 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[779]) ).
thf(856,plain,
! [SV104: $i,SV60: $i,SV121: $i] :
( ( ~ ! [SY507: $i] :
~ ( ~ ( ~ ( in @ SY507 @ SV121 )
| ~ ( ~ ( in @ SY507 @ SV60 )
| ~ ( in @ SY507 @ SV104 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY507 @ SV60 )
| ~ ( in @ SY507 @ SV104 ) )
| ( in @ SY507 @ SV121 ) ) )
| ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[780]) ).
thf(857,plain,
! [SV105: $i,SV61: $i] :
( ( ( in @ SV61 @ SV105 )
= $false )
| ( ( ~ ( empty @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[781]) ).
thf(858,plain,
! [SV63: $i,SV3: $i] :
( ( ~ ~ ( disjoint @ SV3 @ SV63 )
| ~ ! [SY404: $i] :
~ ( in @ SY404 @ ( set_intersection2 @ SV3 @ SV63 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[782]) ).
thf(859,plain,
! [SV63: $i,SV3: $i] :
( ( ~ ~ ! [SY405: $i] :
~ ( in @ SY405 @ ( set_intersection2 @ SV3 @ SV63 ) )
| ~ ( disjoint @ SV3 @ SV63 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[783]) ).
thf(860,plain,
! [SV5: $i,SV65: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV5 )
| ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV65 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV65 )
| ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( SV5 = SV65 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[784]) ).
thf(861,plain,
! [SV6: $i,SV66: $i] :
( ( ( relation @ SV66 )
= $false )
| ( ( ~ ( function @ SV66 ) )
= $true )
| ( ( ~ ( ~ ( ( SV66
!= ( identity_relation @ SV6 ) )
| ~ ( ( ( relation_dom @ SV66 )
!= SV6 )
| ~ ! [SY407: $i] :
( ~ ( in @ SY407 @ SV6 )
| ( ( apply @ SV66 @ SY407 )
= SY407 ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV66 )
!= SV6 )
| ~ ! [SY408: $i] :
( ~ ( in @ SY408 @ SV6 )
| ( ( apply @ SV66 @ SY408 )
= SY408 ) ) )
| ( SV66
= ( identity_relation @ SV6 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[785]) ).
thf(862,plain,
! [SV122: $i,SV106: $i,SV67: $i,SV7: $i] :
( ( ~ ( in @ ( ordered_pair @ SV7 @ SV67 ) @ ( cartesian_product2 @ SV106 @ SV122 ) )
| ~ ( ~ ( in @ SV7 @ SV106 )
| ~ ( in @ SV67 @ SV122 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[786]) ).
thf(863,plain,
! [SV122: $i,SV67: $i,SV106: $i,SV7: $i] :
( ( ~ ~ ( ~ ( in @ SV7 @ SV106 )
| ~ ( in @ SV67 @ SV122 ) )
| ( in @ ( ordered_pair @ SV7 @ SV67 ) @ ( cartesian_product2 @ SV106 @ SV122 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[787]) ).
thf(864,plain,
! [SV123: $i,SV8: $i] :
( ( ( ~ ( ( SV8 != SV123 )
| ! [SY508: $i,SY509: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY508 @ SY509 ) @ SV8 )
| ( in @ ( ordered_pair @ SY508 @ SY509 ) @ SV123 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY508 @ SY509 ) @ SV123 )
| ( in @ ( ordered_pair @ SY508 @ SY509 ) @ SV8 ) ) ) )
| ~ ( ~ ! [SY510: $i,SY511: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY510 @ SY511 ) @ SV8 )
| ( in @ ( ordered_pair @ SY510 @ SY511 ) @ SV123 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY510 @ SY511 ) @ SV123 )
| ( in @ ( ordered_pair @ SY510 @ SY511 ) @ SV8 ) ) )
| ( SV8 = SV123 ) ) )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[788]) ).
thf(865,plain,
! [SV68: $i,SV9: $i] :
( ( ( subset @ ( singleton @ SV9 ) @ SV68 )
= $false )
| ( ( in @ SV9 @ SV68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[789]) ).
thf(866,plain,
! [SV68: $i,SV9: $i] :
( ( ( in @ SV9 @ SV68 )
= $false )
| ( ( subset @ ( singleton @ SV9 ) @ SV68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[790]) ).
thf(867,plain,
! [SV124: $i,SV10: $i,SV139: $i] :
( ( ( ~ ( relation @ SV139 )
| ~ ( ~ ( ( SV139
!= ( relation_composition @ SV10 @ SV124 ) )
| ! [SY581: $i,SY582: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY581 @ SY582 ) @ SV139 )
| ~ ! [SY515: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY581 @ SY515 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY515 @ SY582 ) @ SV124 ) ) )
| ~ ( ~ ~ ! [SY516: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY581 @ SY516 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY516 @ SY582 ) @ SV124 ) )
| ( in @ ( ordered_pair @ SY581 @ SY582 ) @ SV139 ) ) ) )
| ~ ( ~ ! [SY585: $i,SY586: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY585 @ SY586 ) @ SV139 )
| ~ ! [SY519: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY585 @ SY519 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY519 @ SY586 ) @ SV124 ) ) )
| ~ ( ~ ~ ! [SY520: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY585 @ SY520 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY520 @ SY586 ) @ SV124 ) )
| ( in @ ( ordered_pair @ SY585 @ SY586 ) @ SV139 ) ) )
| ( SV139
= ( relation_composition @ SV10 @ SV124 ) ) ) ) )
= $true )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(868,plain,
! [SV69: $i,SV11: $i,SV107: $i] :
( ( ( SV107
!= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true )
| ( ( ! [SY478: $i] :
~ ( ~ ( ~ ( in @ SY478 @ SV107 )
| ~ ! [SY413: $i] :
~ ~ ! [SY414: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY413 @ SV11 )
| ~ ( in @ SY414 @ SV69 ) )
| ( SY478
!= ( ordered_pair @ SY413 @ SY414 ) ) ) )
| ~ ( ~ ~ ! [SY415: $i] :
~ ~ ! [SY416: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY415 @ SV11 )
| ~ ( in @ SY416 @ SV69 ) )
| ( SY478
!= ( ordered_pair @ SY415 @ SY416 ) ) )
| ( in @ SY478 @ SV107 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[792]) ).
thf(869,plain,
! [SV69: $i,SV11: $i,SV107: $i] :
( ( ( ~ ! [SY483: $i] :
~ ( ~ ( ~ ( in @ SY483 @ SV107 )
| ~ ! [SY418: $i] :
~ ~ ! [SY419: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY418 @ SV11 )
| ~ ( in @ SY419 @ SV69 ) )
| ( SY483
!= ( ordered_pair @ SY418 @ SY419 ) ) ) )
| ~ ( ~ ~ ! [SY420: $i] :
~ ~ ! [SY421: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY420 @ SV11 )
| ~ ( in @ SY421 @ SV69 ) )
| ( SY483
!= ( ordered_pair @ SY420 @ SY421 ) ) )
| ( in @ SY483 @ SV107 ) ) ) )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[793]) ).
thf(870,plain,
! [SV12: $i,SV70: $i] :
( ( ( ( SV70
!= ( identity_relation @ SV12 ) )
| ! [SY422: $i,SY423: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY422 @ SY423 ) @ SV70 )
| ~ ( ~ ( in @ SY422 @ SV12 )
| ( SY422 != SY423 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY422 @ SV12 )
| ( SY422 != SY423 ) )
| ( in @ ( ordered_pair @ SY422 @ SY423 ) @ SV70 ) ) ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[794]) ).
thf(871,plain,
! [SV12: $i,SV70: $i] :
( ( ( ~ ! [SY424: $i,SY425: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY424 @ SY425 ) @ SV70 )
| ~ ( ~ ( in @ SY424 @ SV12 )
| ( SY424 != SY425 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY424 @ SV12 )
| ( SY424 != SY425 ) )
| ( in @ ( ordered_pair @ SY424 @ SY425 ) @ SV70 ) ) )
| ( SV70
= ( identity_relation @ SV12 ) ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[795]) ).
thf(872,plain,
! [SV13: $i,SV71: $i] :
( ( ( SV71
= ( powerset @ SV13 ) )
= $false )
| ( ( ! [SY426: $i] :
~ ( ~ ( ~ ( in @ SY426 @ SV71 )
| ( subset @ SY426 @ SV13 ) )
| ~ ( ~ ( subset @ SY426 @ SV13 )
| ( in @ SY426 @ SV71 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[796]) ).
thf(873,plain,
! [SV13: $i,SV71: $i] :
( ( ( ! [SY427: $i] :
~ ( ~ ( ~ ( in @ SY427 @ SV71 )
| ( subset @ SY427 @ SV13 ) )
| ~ ( ~ ( subset @ SY427 @ SV13 )
| ( in @ SY427 @ SV71 ) ) ) )
= $false )
| ( ( SV71
= ( powerset @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[797]) ).
thf(874,plain,
! [SV125: $i,SV14: $i,SV134: $i] :
( ( ( ~ ( ( SV134
!= ( relation_inverse_image @ SV14 @ SV125 ) )
| ! [SY560: $i] :
~ ( ~ ( ~ ( in @ SY560 @ SV134 )
| ~ ! [SY523: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY560 @ SY523 ) @ SV14 )
| ~ ( in @ SY523 @ SV125 ) ) )
| ~ ( ~ ~ ! [SY524: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY560 @ SY524 ) @ SV14 )
| ~ ( in @ SY524 @ SV125 ) )
| ( in @ SY560 @ SV134 ) ) ) ) )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[798]) ).
thf(875,plain,
! [SV125: $i,SV14: $i,SV134: $i] :
( ( ( ~ ( ~ ! [SY563: $i] :
~ ( ~ ( ~ ( in @ SY563 @ SV134 )
| ~ ! [SY526: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY563 @ SY526 ) @ SV14 )
| ~ ( in @ SY526 @ SV125 ) ) )
| ~ ( ~ ~ ! [SY527: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY563 @ SY527 ) @ SV14 )
| ~ ( in @ SY527 @ SV125 ) )
| ( in @ SY563 @ SV134 ) ) )
| ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) ) ) )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[798]) ).
thf(876,plain,
! [SV15: $i,SV126: $i] :
( ( ( ( SV126
!= ( relation_rng @ SV15 ) )
| ! [SY528: $i] :
~ ( ~ ( ~ ( in @ SY528 @ SV126 )
| ~ ! [SY263: $i] :
~ ( in @ ( ordered_pair @ SY263 @ SY528 ) @ SV15 ) )
| ~ ( ~ ~ ! [SY264: $i] :
~ ( in @ ( ordered_pair @ SY264 @ SY528 ) @ SV15 )
| ( in @ SY528 @ SV126 ) ) ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[799]) ).
thf(877,plain,
! [SV15: $i,SV126: $i] :
( ( ( ~ ! [SY531: $i] :
~ ( ~ ( ~ ( in @ SY531 @ SV126 )
| ~ ! [SY266: $i] :
~ ( in @ ( ordered_pair @ SY266 @ SY531 ) @ SV15 ) )
| ~ ( ~ ~ ! [SY267: $i] :
~ ( in @ ( ordered_pair @ SY267 @ SY531 ) @ SV15 )
| ( in @ SY531 @ SV126 ) ) )
| ( SV126
= ( relation_rng @ SV15 ) ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[800]) ).
thf(878,plain,
! [SV127: $i,SV16: $i] :
( ( ( ~ ( ~ ( subset @ SV16 @ SV127 )
| ! [SY534: $i,SY535: $i] :
( ~ ( in @ ( ordered_pair @ SY534 @ SY535 ) @ SV16 )
| ( in @ ( ordered_pair @ SY534 @ SY535 ) @ SV127 ) ) )
| ~ ( ~ ! [SY536: $i,SY537: $i] :
( ~ ( in @ ( ordered_pair @ SY536 @ SY537 ) @ SV16 )
| ( in @ ( ordered_pair @ SY536 @ SY537 ) @ SV127 ) )
| ( subset @ SV16 @ SV127 ) ) )
= $false )
| ( ( relation @ SV127 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[801]) ).
thf(879,plain,
! [SV72: $i,SV17: $i,SV108: $i] :
( ( ( SV108
!= ( set_union2 @ SV17 @ SV72 ) )
= $true )
| ( ( ! [SY488: $i] :
~ ( ~ ( ~ ( in @ SY488 @ SV108 )
| ( in @ SY488 @ SV17 )
| ( in @ SY488 @ SV72 ) )
| ~ ( ~ ( ( in @ SY488 @ SV17 )
| ( in @ SY488 @ SV72 ) )
| ( in @ SY488 @ SV108 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[802]) ).
thf(880,plain,
! [SV72: $i,SV17: $i,SV108: $i] :
( ( ( ~ ! [SY489: $i] :
~ ( ~ ( ~ ( in @ SY489 @ SV108 )
| ( in @ SY489 @ SV17 )
| ( in @ SY489 @ SV72 ) )
| ~ ( ~ ( ( in @ SY489 @ SV17 )
| ( in @ SY489 @ SV72 ) )
| ( in @ SY489 @ SV108 ) ) ) )
= $true )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[803]) ).
thf(881,plain,
! [SV18: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK7_SY277 @ SV18 ) @ ( sK8_SY580 @ SV18 ) ) @ SV18 ) )
= $false )
| ( ( SV18 = empty_set )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[804]) ).
thf(882,plain,
! [SV128: $i,SV20: $i,SV135: $i] :
( ( ( relation @ SV135 )
= $false )
| ( ( ~ ( ~ ( ( SV135
!= ( relation_dom_restriction @ SV20 @ SV128 ) )
| ! [SY566: $i,SY567: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV135 )
| ~ ( ~ ( in @ SY566 @ SV128 )
| ~ ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY566 @ SV128 )
| ~ ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV20 ) )
| ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV135 ) ) ) )
| ~ ( ~ ! [SY568: $i,SY569: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY568 @ SY569 ) @ SV135 )
| ~ ( ~ ( in @ SY568 @ SV128 )
| ~ ( in @ ( ordered_pair @ SY568 @ SY569 ) @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY568 @ SV128 )
| ~ ( in @ ( ordered_pair @ SY568 @ SY569 ) @ SV20 ) )
| ( in @ ( ordered_pair @ SY568 @ SY569 ) @ SV135 ) ) )
| ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) ) ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[805]) ).
thf(883,plain,
! [SV74: $i,SV21: $i] :
( ( ~ ~ ( disjoint @ SV21 @ SV74 )
| ~ ! [SY431: $i] :
~ ~ ( ~ ( in @ SY431 @ SV21 )
| ~ ( in @ SY431 @ SV74 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[806]) ).
thf(884,plain,
! [SV74: $i,SV21: $i] :
( ( ~ ~ ! [SY432: $i] :
~ ~ ( ~ ( in @ SY432 @ SV21 )
| ~ ( in @ SY432 @ SV74 ) )
| ~ ( disjoint @ SV21 @ SV74 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[807]) ).
thf(885,plain,
! [SV109: $i,SV75: $i,SV22: $i] :
( ( ( ~ ( ~ ( in @ SV22 @ ( relation_rng @ ( relation_rng_restriction @ SV75 @ SV109 ) ) )
| ~ ( ~ ( in @ SV22 @ SV75 )
| ~ ( in @ SV22 @ ( relation_rng @ SV109 ) ) ) ) )
= $false )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[808]) ).
thf(886,plain,
! [SV109: $i,SV75: $i,SV22: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV22 @ SV75 )
| ~ ( in @ SV22 @ ( relation_rng @ SV109 ) ) )
| ( in @ SV22 @ ( relation_rng @ ( relation_rng_restriction @ SV75 @ SV109 ) ) ) ) )
= $false )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[808]) ).
thf(887,plain,
! [SV23: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV23 @ ( sK3_SY291 @ SV23 ) )
| ~ ! [SY490: $i,SY491: $i] :
( ~ ~ ( ~ ( in @ SY490 @ ( sK3_SY291 @ SV23 ) )
| ~ ( subset @ SY491 @ SY490 ) )
| ( in @ SY491 @ ( sK3_SY291 @ SV23 ) ) ) )
| ~ ! [SY492: $i] :
( ~ ( in @ SY492 @ ( sK3_SY291 @ SV23 ) )
| ( in @ ( powerset @ SY492 ) @ ( sK3_SY291 @ SV23 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[809]) ).
thf(888,plain,
! [SV23: $i] :
( ( ! [SY493: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY493 @ ( sK3_SY291 @ SV23 ) )
| ~ ~ ( are_equipotent @ SY493 @ ( sK3_SY291 @ SV23 ) ) )
| ~ ~ ( in @ SY493 @ ( sK3_SY291 @ SV23 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[810]) ).
thf(889,plain,
! [SV77: $i,SV25: $i] :
( ( ( subset @ ( singleton @ SV25 ) @ SV77 )
= $false )
| ( ( in @ SV25 @ SV77 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[811]) ).
thf(890,plain,
! [SV77: $i,SV25: $i] :
( ( ( in @ SV25 @ SV77 )
= $false )
| ( ( subset @ ( singleton @ SV25 ) @ SV77 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[812]) ).
thf(891,plain,
! [SV78: $i,SV26: $i] :
( ( ( SV26 != empty_set )
= $false )
| ( ( ~ ( ~ ( ( SV78
!= ( set_meet @ SV26 ) )
| ! [SY434: $i] :
~ ( ~ ( ~ ( in @ SY434 @ SV78 )
| ! [SY300: $i] :
( ~ ( in @ SY300 @ SV26 )
| ( in @ SY434 @ SY300 ) ) )
| ~ ( ~ ! [SY301: $i] :
( ~ ( in @ SY301 @ SV26 )
| ( in @ SY434 @ SY301 ) )
| ( in @ SY434 @ SV78 ) ) ) )
| ~ ( ~ ! [SY437: $i] :
~ ( ~ ( ~ ( in @ SY437 @ SV78 )
| ! [SY303: $i] :
( ~ ( in @ SY303 @ SV26 )
| ( in @ SY437 @ SY303 ) ) )
| ~ ( ~ ! [SY304: $i] :
( ~ ( in @ SY304 @ SV26 )
| ( in @ SY437 @ SY304 ) )
| ( in @ SY437 @ SV78 ) ) )
| ( SV78
= ( set_meet @ SV26 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[813]) ).
thf(892,plain,
! [SV78: $i,SV26: $i] :
( ( ( SV26 = empty_set )
= $false )
| ( ( ~ ( ~ ( ( SV78
!= ( set_meet @ SV26 ) )
| ( SV78 = empty_set ) )
| ~ ( ( SV78 != empty_set )
| ( SV78
= ( set_meet @ SV26 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[814]) ).
thf(893,plain,
! [SV129: $i,SV110: $i,SV79: $i,SV27: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV27 @ SV79 ) @ ( relation_composition @ ( identity_relation @ SV110 ) @ SV129 ) )
| ~ ( ~ ( in @ SV27 @ SV110 )
| ~ ( in @ ( ordered_pair @ SV27 @ SV79 ) @ SV129 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV27 @ SV110 )
| ~ ( in @ ( ordered_pair @ SV27 @ SV79 ) @ SV129 ) )
| ( in @ ( ordered_pair @ SV27 @ SV79 ) @ ( relation_composition @ ( identity_relation @ SV110 ) @ SV129 ) ) ) )
= $false )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[815]) ).
thf(894,plain,
! [SV130: $i,SV111: $i,SV81: $i,SV29: $i] :
( ( ~ ( in @ ( ordered_pair @ SV29 @ SV81 ) @ ( cartesian_product2 @ SV111 @ SV130 ) )
| ~ ( ~ ( in @ SV29 @ SV111 )
| ~ ( in @ SV81 @ SV130 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[816]) ).
thf(895,plain,
! [SV130: $i,SV81: $i,SV111: $i,SV29: $i] :
( ( ~ ~ ( ~ ( in @ SV29 @ SV111 )
| ~ ( in @ SV81 @ SV130 ) )
| ( in @ ( ordered_pair @ SV29 @ SV81 ) @ ( cartesian_product2 @ SV111 @ SV130 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[817]) ).
thf(896,plain,
! [SV131: $i,SV30: $i,SV136: $i] :
( ( ( ~ ( ( SV136
!= ( relation_image @ SV30 @ SV131 ) )
| ! [SY570: $i] :
~ ( ~ ( ~ ( in @ SY570 @ SV136 )
| ~ ! [SY545: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY545 @ SY570 ) @ SV30 )
| ~ ( in @ SY545 @ SV131 ) ) )
| ~ ( ~ ~ ! [SY546: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY546 @ SY570 ) @ SV30 )
| ~ ( in @ SY546 @ SV131 ) )
| ( in @ SY570 @ SV136 ) ) ) ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[818]) ).
thf(897,plain,
! [SV131: $i,SV30: $i,SV136: $i] :
( ( ( ~ ( ~ ! [SY573: $i] :
~ ( ~ ( ~ ( in @ SY573 @ SV136 )
| ~ ! [SY548: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY548 @ SY573 ) @ SV30 )
| ~ ( in @ SY548 @ SV131 ) ) )
| ~ ( ~ ~ ! [SY549: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY549 @ SY573 ) @ SV30 )
| ~ ( in @ SY549 @ SV131 ) )
| ( in @ SY573 @ SV136 ) ) )
| ( SV136
= ( relation_image @ SV30 @ SV131 ) ) ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[818]) ).
thf(898,plain,
! [SV112: $i,SV82: $i,SV31: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV31 @ SV82 ) @ SV112 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV31 @ SV112 )
| ~ ( in @ SV82 @ SV112 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[819]) ).
thf(899,plain,
! [SV82: $i,SV112: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ( in @ SV31 @ SV112 )
| ~ ( in @ SV82 @ SV112 ) ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV31 @ SV82 ) @ SV112 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[820]) ).
thf(900,plain,
! [SV113: $i,SV83: $i,SV33: $i] :
( ( ( ~ ( in @ SV33 @ SV83 ) )
= $true )
| ( ( ~ ( element @ SV83 @ ( powerset @ SV113 ) ) )
= $true )
| ( ( element @ SV33 @ SV113 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[821]) ).
thf(901,plain,
! [SV84: $i,SV34: $i] :
( ( ( ~ ( empty @ SV34 ) )
= $false )
| ( ( ~ ( ~ ( ~ ( element @ SV84 @ SV34 )
| ( in @ SV84 @ SV34 ) )
| ~ ( ~ ( in @ SV84 @ SV34 )
| ( element @ SV84 @ SV34 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[822]) ).
thf(902,plain,
! [SV84: $i,SV34: $i] :
( ( ( empty @ SV34 )
= $false )
| ( ( ~ ( ~ ( ~ ( element @ SV84 @ SV34 )
| ( empty @ SV84 ) )
| ~ ( ~ ( empty @ SV84 )
| ( element @ SV84 @ SV34 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[823]) ).
thf(903,plain,
! [SV35: $i,SV140: $i] :
( ( ( ~ ~ ( ~ ( in @ SV140 @ SV35 )
| ~ ! [SY589: $i,SY590: $i] :
( SV140
!= ( ordered_pair @ SY589 @ SY590 ) ) ) )
= $true )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(904,plain,
! [SV35: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK9_SY328 @ SV35 ) @ SV35 )
| ~ ! [SY591: $i,SY592: $i] :
( ( sK9_SY328 @ SV35 )
!= ( ordered_pair @ SY591 @ SY592 ) ) ) )
= $false )
| ( ( relation @ SV35 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[825]) ).
thf(905,plain,
! [SV115: $i,SV86: $i,SV37: $i] :
( ( ( in @ ( ordered_pair @ SV37 @ SV86 ) @ SV115 )
= $false )
| ( ( ~ ( ~ ( in @ SV37 @ ( relation_field @ SV115 ) )
| ~ ( in @ SV86 @ ( relation_field @ SV115 ) ) ) )
= $true )
| ( ( relation @ SV115 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[827]) ).
thf(906,plain,
! [SV38: $i,SV141: $i] :
( ( ( ~ ( in @ SV141 @ SV38 ) )
= $true )
| ( ( SV38 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(907,plain,
! [SV38: $i] :
( ( ( ~ ( in @ ( sK10_SY336 @ SV38 ) @ SV38 ) )
= $false )
| ( ( SV38 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[829]) ).
thf(908,plain,
! [SV87: $i,SV39: $i,SV137: $i] :
( ( ( relation @ SV137 )
= $false )
| ( ( ~ ( ~ ( ( SV137
!= ( relation_rng_restriction @ SV39 @ SV87 ) )
| ! [SY576: $i,SY577: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY576 @ SY577 ) @ SV137 )
| ~ ( ~ ( in @ SY577 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY576 @ SY577 ) @ SV87 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY577 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY576 @ SY577 ) @ SV87 ) )
| ( in @ ( ordered_pair @ SY576 @ SY577 ) @ SV137 ) ) ) )
| ~ ( ~ ! [SY578: $i,SY579: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY578 @ SY579 ) @ SV137 )
| ~ ( ~ ( in @ SY579 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY578 @ SY579 ) @ SV87 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY579 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY578 @ SY579 ) @ SV87 ) )
| ( in @ ( ordered_pair @ SY578 @ SY579 ) @ SV137 ) ) )
| ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) ) ) ) )
= $true )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[830]) ).
thf(909,plain,
! [SV41: $i,SV88: $i] :
( ( ( SV88
= ( singleton @ SV41 ) )
= $false )
| ( ( ! [SY453: $i] :
~ ( ~ ( ~ ( in @ SY453 @ SV88 )
| ( SY453 = SV41 ) )
| ~ ( ( SY453 != SV41 )
| ( in @ SY453 @ SV88 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[831]) ).
thf(910,plain,
! [SV41: $i,SV88: $i] :
( ( ( ! [SY454: $i] :
~ ( ~ ( ~ ( in @ SY454 @ SV88 )
| ( SY454 = SV41 ) )
| ~ ( ( SY454 != SV41 )
| ( in @ SY454 @ SV88 ) ) ) )
= $false )
| ( ( SV88
= ( singleton @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[832]) ).
thf(911,plain,
! [SV42: $i,SV89: $i] :
( ( ( SV89
= ( union @ SV42 ) )
= $false )
| ( ( ! [SY455: $i] :
~ ( ~ ( ~ ( in @ SY455 @ SV89 )
| ~ ! [SY348: $i] :
~ ~ ( ~ ( in @ SY455 @ SY348 )
| ~ ( in @ SY348 @ SV42 ) ) )
| ~ ( ~ ~ ! [SY349: $i] :
~ ~ ( ~ ( in @ SY455 @ SY349 )
| ~ ( in @ SY349 @ SV42 ) )
| ( in @ SY455 @ SV89 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[833]) ).
thf(912,plain,
! [SV42: $i,SV89: $i] :
( ( ( ! [SY458: $i] :
~ ( ~ ( ~ ( in @ SY458 @ SV89 )
| ~ ! [SY351: $i] :
~ ~ ( ~ ( in @ SY458 @ SY351 )
| ~ ( in @ SY351 @ SV42 ) ) )
| ~ ( ~ ~ ! [SY352: $i] :
~ ~ ( ~ ( in @ SY458 @ SY352 )
| ~ ( in @ SY352 @ SV42 ) )
| ( in @ SY458 @ SV89 ) ) ) )
= $false )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[834]) ).
thf(913,plain,
! [SV90: $i,SV116: $i,SV43: $i] :
( ( ( ~ ( ~ ( in @ SV43 @ ( relation_dom @ ( relation_dom_restriction @ SV116 @ SV90 ) ) )
| ~ ( ~ ( in @ SV43 @ SV90 )
| ~ ( in @ SV43 @ ( relation_dom @ SV116 ) ) ) ) )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[835]) ).
thf(914,plain,
! [SV116: $i,SV90: $i,SV43: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV43 @ SV90 )
| ~ ( in @ SV43 @ ( relation_dom @ SV116 ) ) )
| ( in @ SV43 @ ( relation_dom @ ( relation_dom_restriction @ SV116 @ SV90 ) ) ) ) )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[835]) ).
thf(915,plain,
! [SV91: $i,SV44: $i] :
( ( ( in @ SV44 @ SV91 )
= $false )
| ( ( disjoint @ ( singleton @ SV44 ) @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[836]) ).
thf(916,plain,
! [SV46: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV46 @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SY496: $i,SY497: $i] :
( ~ ~ ( ~ ( in @ SY496 @ ( sK4_SY357 @ SV46 ) )
| ~ ( subset @ SY497 @ SY496 ) )
| ( in @ SY497 @ ( sK4_SY357 @ SV46 ) ) ) )
| ~ ! [SY498: $i] :
~ ~ ( ~ ( in @ SY498 @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SY499: $i] :
~ ~ ( ~ ( in @ SY499 @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY498 )
| ( in @ SX4 @ SY499 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[837]) ).
thf(917,plain,
! [SV46: $i] :
( ( ! [SY501: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY501 @ ( sK4_SY357 @ SV46 ) )
| ~ ~ ( are_equipotent @ SY501 @ ( sK4_SY357 @ SV46 ) ) )
| ~ ~ ( in @ SY501 @ ( sK4_SY357 @ SV46 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[838]) ).
thf(918,plain,
! [SV47: $i,SV132: $i] :
( ( ( ( SV132
!= ( relation_dom @ SV47 ) )
| ! [SY550: $i] :
~ ( ~ ( ~ ( in @ SY550 @ SV132 )
| ~ ! [SY366: $i] :
~ ( in @ ( ordered_pair @ SY550 @ SY366 ) @ SV47 ) )
| ~ ( ~ ~ ! [SY367: $i] :
~ ( in @ ( ordered_pair @ SY550 @ SY367 ) @ SV47 )
| ( in @ SY550 @ SV132 ) ) ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[839]) ).
thf(919,plain,
! [SV47: $i,SV132: $i] :
( ( ( ~ ! [SY553: $i] :
~ ( ~ ( ~ ( in @ SY553 @ SV132 )
| ~ ! [SY369: $i] :
~ ( in @ ( ordered_pair @ SY553 @ SY369 ) @ SV47 ) )
| ~ ( ~ ~ ! [SY370: $i] :
~ ( in @ ( ordered_pair @ SY553 @ SY370 ) @ SV47 )
| ( in @ SY553 @ SV132 ) ) )
| ( SV132
= ( relation_dom @ SV47 ) ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[840]) ).
thf(920,plain,
! [SV48: $i,SV93: $i] :
( ( ( in @ ( sK6_SY462 @ SV93 @ SV48 ) @ SV48 )
= $true )
| ( ( element @ SV48 @ ( powerset @ SV93 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[841]) ).
thf(921,plain,
! [SV49: $i,SV133: $i] :
( ( ( ~ ( ( SV133
!= ( relation_inverse @ SV49 ) )
| ! [SY556: $i,SY557: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY556 @ SY557 ) @ SV133 )
| ( in @ ( ordered_pair @ SY557 @ SY556 ) @ SV49 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY557 @ SY556 ) @ SV49 )
| ( in @ ( ordered_pair @ SY556 @ SY557 ) @ SV133 ) ) ) )
| ~ ( ~ ! [SY558: $i,SY559: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY558 @ SY559 ) @ SV133 )
| ( in @ ( ordered_pair @ SY559 @ SY558 ) @ SV49 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY559 @ SY558 ) @ SV49 )
| ( in @ ( ordered_pair @ SY558 @ SY559 ) @ SV133 ) ) )
| ( SV133
= ( relation_inverse @ SV49 ) ) ) )
= $false )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[843]) ).
thf(922,plain,
! [SV94: $i,SV50: $i] :
( ( ( ( set_difference @ SV50 @ ( singleton @ SV94 ) )
= SV50 )
= $false )
| ( ( ~ ( in @ SV94 @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[844]) ).
thf(923,plain,
! [SV50: $i,SV94: $i] :
( ( ( ~ ( in @ SV94 @ SV50 ) )
= $false )
| ( ( ( set_difference @ SV50 @ ( singleton @ SV94 ) )
= SV50 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[845]) ).
thf(924,plain,
! [SV97: $i,SV53: $i] :
( ( ( subset @ SV53 @ SV97 )
= $false )
| ( ( ! [SY463: $i] :
( ~ ( in @ SY463 @ SV53 )
| ( in @ SY463 @ SV97 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[846]) ).
thf(925,plain,
! [SV97: $i,SV53: $i] :
( ( ( ! [SY464: $i] :
( ~ ( in @ SY464 @ SV53 )
| ( in @ SY464 @ SV97 ) ) )
= $false )
| ( ( subset @ SV53 @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[847]) ).
thf(926,plain,
! [SV117: $i,SV54: $i,SV98: $i] :
( ( ( ~ ( in @ SV98 @ ( subset_complement @ SV54 @ SV117 ) )
| ~ ( in @ SV98 @ SV117 ) )
= $true )
| ( ( element @ SV117 @ ( powerset @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[848]) ).
thf(927,plain,
! [SV55: $i,SV99: $i,SV138: $i] :
( ( ( in @ SV138 @ SV99 )
= $false )
| ( ( in @ SV138 @ SV55 )
= $true )
| ( ( element @ SV99 @ ( powerset @ SV55 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[849]) ).
thf(928,plain,
! [SV100: $i,SV56: $i,SV118: $i] :
( ( ( SV118
!= ( unordered_pair @ SV56 @ SV100 ) )
= $true )
| ( ( ! [SY502: $i] :
~ ( ~ ( ~ ( in @ SY502 @ SV118 )
| ( SY502 = SV56 )
| ( SY502 = SV100 ) )
| ~ ( ~ ( ( SY502 = SV56 )
| ( SY502 = SV100 ) )
| ( in @ SY502 @ SV118 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[850]) ).
thf(929,plain,
! [SV100: $i,SV56: $i,SV118: $i] :
( ( ( ~ ! [SY503: $i] :
~ ( ~ ( ~ ( in @ SY503 @ SV118 )
| ( SY503 = SV56 )
| ( SY503 = SV100 ) )
| ~ ( ~ ( ( SY503 = SV56 )
| ( SY503 = SV100 ) )
| ( in @ SY503 @ SV118 ) ) ) )
= $true )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[851]) ).
thf(930,plain,
! [SV102: $i,SV58: $i,SV119: $i] :
( ( ( SV119
!= ( set_difference @ SV58 @ SV102 ) )
= $true )
| ( ( ! [SY504: $i] :
~ ( ~ ( ~ ( in @ SY504 @ SV119 )
| ~ ( ~ ( in @ SY504 @ SV58 )
| ~ ~ ( in @ SY504 @ SV102 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY504 @ SV58 )
| ~ ~ ( in @ SY504 @ SV102 ) )
| ( in @ SY504 @ SV119 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[852]) ).
thf(931,plain,
! [SV102: $i,SV58: $i,SV119: $i] :
( ( ( ~ ! [SY505: $i] :
~ ( ~ ( ~ ( in @ SY505 @ SV119 )
| ~ ( ~ ( in @ SY505 @ SV58 )
| ~ ~ ( in @ SY505 @ SV102 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY505 @ SV58 )
| ~ ~ ( in @ SY505 @ SV102 ) )
| ( in @ SY505 @ SV119 ) ) ) )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[853]) ).
thf(932,plain,
! [SV120: $i,SV103: $i,SV59: $i] :
( ( ( ~ ( ~ ( in @ SV59 @ SV103 )
| ~ ( element @ SV103 @ ( powerset @ SV120 ) ) ) )
= $false )
| ( ( ~ ( empty @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[854]) ).
thf(933,plain,
! [SV104: $i,SV60: $i,SV121: $i] :
( ( ( SV121
!= ( set_intersection2 @ SV60 @ SV104 ) )
= $true )
| ( ( ! [SY506: $i] :
~ ( ~ ( ~ ( in @ SY506 @ SV121 )
| ~ ( ~ ( in @ SY506 @ SV60 )
| ~ ( in @ SY506 @ SV104 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY506 @ SV60 )
| ~ ( in @ SY506 @ SV104 ) )
| ( in @ SY506 @ SV121 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[855]) ).
thf(934,plain,
! [SV104: $i,SV60: $i,SV121: $i] :
( ( ( ~ ! [SY507: $i] :
~ ( ~ ( ~ ( in @ SY507 @ SV121 )
| ~ ( ~ ( in @ SY507 @ SV60 )
| ~ ( in @ SY507 @ SV104 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY507 @ SV60 )
| ~ ( in @ SY507 @ SV104 ) )
| ( in @ SY507 @ SV121 ) ) ) )
= $true )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[856]) ).
thf(935,plain,
! [SV61: $i,SV105: $i] :
( ( ( empty @ SV105 )
= $false )
| ( ( in @ SV61 @ SV105 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[857]) ).
thf(936,plain,
! [SV63: $i,SV3: $i] :
( ( ( ~ ~ ( disjoint @ SV3 @ SV63 ) )
= $true )
| ( ( ~ ! [SY404: $i] :
~ ( in @ SY404 @ ( set_intersection2 @ SV3 @ SV63 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[858]) ).
thf(937,plain,
! [SV63: $i,SV3: $i] :
( ( ( ~ ~ ! [SY405: $i] :
~ ( in @ SY405 @ ( set_intersection2 @ SV3 @ SV63 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV3 @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[859]) ).
thf(938,plain,
! [SV5: $i,SV65: $i] :
( ( ( ~ ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV5 )
| ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV65 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV65 )
| ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( SV5 = SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[860]) ).
thf(939,plain,
! [SV6: $i,SV66: $i] :
( ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false )
| ( ( ~ ( ~ ( ( SV66
!= ( identity_relation @ SV6 ) )
| ~ ( ( ( relation_dom @ SV66 )
!= SV6 )
| ~ ! [SY407: $i] :
( ~ ( in @ SY407 @ SV6 )
| ( ( apply @ SV66 @ SY407 )
= SY407 ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV66 )
!= SV6 )
| ~ ! [SY408: $i] :
( ~ ( in @ SY408 @ SV6 )
| ( ( apply @ SV66 @ SY408 )
= SY408 ) ) )
| ( SV66
= ( identity_relation @ SV6 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[861]) ).
thf(940,plain,
! [SV122: $i,SV106: $i,SV67: $i,SV7: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV7 @ SV67 ) @ ( cartesian_product2 @ SV106 @ SV122 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV7 @ SV106 )
| ~ ( in @ SV67 @ SV122 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[862]) ).
thf(941,plain,
! [SV122: $i,SV67: $i,SV106: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( in @ SV7 @ SV106 )
| ~ ( in @ SV67 @ SV122 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV7 @ SV67 ) @ ( cartesian_product2 @ SV106 @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[863]) ).
thf(942,plain,
! [SV123: $i,SV8: $i] :
( ( ( ~ ( ( SV8 != SV123 )
| ! [SY508: $i,SY509: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY508 @ SY509 ) @ SV8 )
| ( in @ ( ordered_pair @ SY508 @ SY509 ) @ SV123 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY508 @ SY509 ) @ SV123 )
| ( in @ ( ordered_pair @ SY508 @ SY509 ) @ SV8 ) ) ) ) )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[864]) ).
thf(943,plain,
! [SV123: $i,SV8: $i] :
( ( ( ~ ( ~ ! [SY510: $i,SY511: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY510 @ SY511 ) @ SV8 )
| ( in @ ( ordered_pair @ SY510 @ SY511 ) @ SV123 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY510 @ SY511 ) @ SV123 )
| ( in @ ( ordered_pair @ SY510 @ SY511 ) @ SV8 ) ) )
| ( SV8 = SV123 ) ) )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[864]) ).
thf(944,plain,
! [SV124: $i,SV10: $i,SV139: $i] :
( ( ( ~ ( relation @ SV139 ) )
= $true )
| ( ( ~ ( ~ ( ( SV139
!= ( relation_composition @ SV10 @ SV124 ) )
| ! [SY581: $i,SY582: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY581 @ SY582 ) @ SV139 )
| ~ ! [SY515: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY581 @ SY515 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY515 @ SY582 ) @ SV124 ) ) )
| ~ ( ~ ~ ! [SY516: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY581 @ SY516 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY516 @ SY582 ) @ SV124 ) )
| ( in @ ( ordered_pair @ SY581 @ SY582 ) @ SV139 ) ) ) )
| ~ ( ~ ! [SY585: $i,SY586: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY585 @ SY586 ) @ SV139 )
| ~ ! [SY519: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY585 @ SY519 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY519 @ SY586 ) @ SV124 ) ) )
| ~ ( ~ ~ ! [SY520: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY585 @ SY520 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY520 @ SY586 ) @ SV124 ) )
| ( in @ ( ordered_pair @ SY585 @ SY586 ) @ SV139 ) ) )
| ( SV139
= ( relation_composition @ SV10 @ SV124 ) ) ) ) )
= $true )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[867]) ).
thf(945,plain,
! [SV69: $i,SV11: $i,SV107: $i] :
( ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false )
| ( ( ! [SY478: $i] :
~ ( ~ ( ~ ( in @ SY478 @ SV107 )
| ~ ! [SY413: $i] :
~ ~ ! [SY414: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY413 @ SV11 )
| ~ ( in @ SY414 @ SV69 ) )
| ( SY478
!= ( ordered_pair @ SY413 @ SY414 ) ) ) )
| ~ ( ~ ~ ! [SY415: $i] :
~ ~ ! [SY416: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY415 @ SV11 )
| ~ ( in @ SY416 @ SV69 ) )
| ( SY478
!= ( ordered_pair @ SY415 @ SY416 ) ) )
| ( in @ SY478 @ SV107 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[868]) ).
thf(946,plain,
! [SV69: $i,SV11: $i,SV107: $i] :
( ( ( ! [SY483: $i] :
~ ( ~ ( ~ ( in @ SY483 @ SV107 )
| ~ ! [SY418: $i] :
~ ~ ! [SY419: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY418 @ SV11 )
| ~ ( in @ SY419 @ SV69 ) )
| ( SY483
!= ( ordered_pair @ SY418 @ SY419 ) ) ) )
| ~ ( ~ ~ ! [SY420: $i] :
~ ~ ! [SY421: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY420 @ SV11 )
| ~ ( in @ SY421 @ SV69 ) )
| ( SY483
!= ( ordered_pair @ SY420 @ SY421 ) ) )
| ( in @ SY483 @ SV107 ) ) ) )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[869]) ).
thf(947,plain,
! [SV12: $i,SV70: $i] :
( ( ( SV70
!= ( identity_relation @ SV12 ) )
= $true )
| ( ( ! [SY422: $i,SY423: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY422 @ SY423 ) @ SV70 )
| ~ ( ~ ( in @ SY422 @ SV12 )
| ( SY422 != SY423 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY422 @ SV12 )
| ( SY422 != SY423 ) )
| ( in @ ( ordered_pair @ SY422 @ SY423 ) @ SV70 ) ) ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[870]) ).
thf(948,plain,
! [SV12: $i,SV70: $i] :
( ( ( ~ ! [SY424: $i,SY425: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY424 @ SY425 ) @ SV70 )
| ~ ( ~ ( in @ SY424 @ SV12 )
| ( SY424 != SY425 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY424 @ SV12 )
| ( SY424 != SY425 ) )
| ( in @ ( ordered_pair @ SY424 @ SY425 ) @ SV70 ) ) ) )
= $true )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[871]) ).
thf(949,plain,
! [SV13: $i,SV71: $i,SV142: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV142 @ SV71 )
| ( subset @ SV142 @ SV13 ) )
| ~ ( ~ ( subset @ SV142 @ SV13 )
| ( in @ SV142 @ SV71 ) ) ) )
= $true )
| ( ( SV71
= ( powerset @ SV13 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[872]) ).
thf(950,plain,
! [SV71: $i,SV13: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV71 )
| ( subset @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV13 ) )
| ~ ( ~ ( subset @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV13 )
| ( in @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV71 ) ) ) )
= $false )
| ( ( SV71
= ( powerset @ SV13 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[873]) ).
thf(951,plain,
! [SV125: $i,SV14: $i,SV134: $i] :
( ( ( ( SV134
!= ( relation_inverse_image @ SV14 @ SV125 ) )
| ! [SY560: $i] :
~ ( ~ ( ~ ( in @ SY560 @ SV134 )
| ~ ! [SY523: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY560 @ SY523 ) @ SV14 )
| ~ ( in @ SY523 @ SV125 ) ) )
| ~ ( ~ ~ ! [SY524: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY560 @ SY524 ) @ SV14 )
| ~ ( in @ SY524 @ SV125 ) )
| ( in @ SY560 @ SV134 ) ) ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[874]) ).
thf(952,plain,
! [SV125: $i,SV14: $i,SV134: $i] :
( ( ( ~ ! [SY563: $i] :
~ ( ~ ( ~ ( in @ SY563 @ SV134 )
| ~ ! [SY526: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY563 @ SY526 ) @ SV14 )
| ~ ( in @ SY526 @ SV125 ) ) )
| ~ ( ~ ~ ! [SY527: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY563 @ SY527 ) @ SV14 )
| ~ ( in @ SY527 @ SV125 ) )
| ( in @ SY563 @ SV134 ) ) )
| ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[875]) ).
thf(953,plain,
! [SV15: $i,SV126: $i] :
( ( ( SV126
!= ( relation_rng @ SV15 ) )
= $true )
| ( ( ! [SY528: $i] :
~ ( ~ ( ~ ( in @ SY528 @ SV126 )
| ~ ! [SY263: $i] :
~ ( in @ ( ordered_pair @ SY263 @ SY528 ) @ SV15 ) )
| ~ ( ~ ~ ! [SY264: $i] :
~ ( in @ ( ordered_pair @ SY264 @ SY528 ) @ SV15 )
| ( in @ SY528 @ SV126 ) ) ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[876]) ).
thf(954,plain,
! [SV15: $i,SV126: $i] :
( ( ( ~ ! [SY531: $i] :
~ ( ~ ( ~ ( in @ SY531 @ SV126 )
| ~ ! [SY266: $i] :
~ ( in @ ( ordered_pair @ SY266 @ SY531 ) @ SV15 ) )
| ~ ( ~ ~ ! [SY267: $i] :
~ ( in @ ( ordered_pair @ SY267 @ SY531 ) @ SV15 )
| ( in @ SY531 @ SV126 ) ) ) )
= $true )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[877]) ).
thf(955,plain,
! [SV127: $i,SV16: $i] :
( ( ( ~ ( ~ ( subset @ SV16 @ SV127 )
| ! [SY534: $i,SY535: $i] :
( ~ ( in @ ( ordered_pair @ SY534 @ SY535 ) @ SV16 )
| ( in @ ( ordered_pair @ SY534 @ SY535 ) @ SV127 ) ) ) )
= $false )
| ( ( relation @ SV127 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[878]) ).
thf(956,plain,
! [SV127: $i,SV16: $i] :
( ( ( ~ ( ~ ! [SY536: $i,SY537: $i] :
( ~ ( in @ ( ordered_pair @ SY536 @ SY537 ) @ SV16 )
| ( in @ ( ordered_pair @ SY536 @ SY537 ) @ SV127 ) )
| ( subset @ SV16 @ SV127 ) ) )
= $false )
| ( ( relation @ SV127 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[878]) ).
thf(957,plain,
! [SV72: $i,SV17: $i,SV108: $i] :
( ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $false )
| ( ( ! [SY488: $i] :
~ ( ~ ( ~ ( in @ SY488 @ SV108 )
| ( in @ SY488 @ SV17 )
| ( in @ SY488 @ SV72 ) )
| ~ ( ~ ( ( in @ SY488 @ SV17 )
| ( in @ SY488 @ SV72 ) )
| ( in @ SY488 @ SV108 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[879]) ).
thf(958,plain,
! [SV72: $i,SV17: $i,SV108: $i] :
( ( ( ! [SY489: $i] :
~ ( ~ ( ~ ( in @ SY489 @ SV108 )
| ( in @ SY489 @ SV17 )
| ( in @ SY489 @ SV72 ) )
| ~ ( ~ ( ( in @ SY489 @ SV17 )
| ( in @ SY489 @ SV72 ) )
| ( in @ SY489 @ SV108 ) ) ) )
= $false )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[880]) ).
thf(959,plain,
! [SV18: $i] :
( ( ( in @ ( ordered_pair @ ( sK7_SY277 @ SV18 ) @ ( sK8_SY580 @ SV18 ) ) @ SV18 )
= $true )
| ( ( SV18 = empty_set )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[881]) ).
thf(960,plain,
! [SV128: $i,SV20: $i,SV135: $i] :
( ( ( ~ ( ( SV135
!= ( relation_dom_restriction @ SV20 @ SV128 ) )
| ! [SY566: $i,SY567: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV135 )
| ~ ( ~ ( in @ SY566 @ SV128 )
| ~ ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY566 @ SV128 )
| ~ ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV20 ) )
| ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV135 ) ) ) )
| ~ ( ~ ! [SY568: $i,SY569: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY568 @ SY569 ) @ SV135 )
| ~ ( ~ ( in @ SY568 @ SV128 )
| ~ ( in @ ( ordered_pair @ SY568 @ SY569 ) @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY568 @ SV128 )
| ~ ( in @ ( ordered_pair @ SY568 @ SY569 ) @ SV20 ) )
| ( in @ ( ordered_pair @ SY568 @ SY569 ) @ SV135 ) ) )
| ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) ) ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[882]) ).
thf(961,plain,
! [SV74: $i,SV21: $i] :
( ( ( ~ ~ ( disjoint @ SV21 @ SV74 ) )
= $true )
| ( ( ~ ! [SY431: $i] :
~ ~ ( ~ ( in @ SY431 @ SV21 )
| ~ ( in @ SY431 @ SV74 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[883]) ).
thf(962,plain,
! [SV74: $i,SV21: $i] :
( ( ( ~ ~ ! [SY432: $i] :
~ ~ ( ~ ( in @ SY432 @ SV21 )
| ~ ( in @ SY432 @ SV74 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV21 @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[884]) ).
thf(963,plain,
! [SV109: $i,SV75: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ ( relation_rng @ ( relation_rng_restriction @ SV75 @ SV109 ) ) )
| ~ ( ~ ( in @ SV22 @ SV75 )
| ~ ( in @ SV22 @ ( relation_rng @ SV109 ) ) ) )
= $true )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[885]) ).
thf(964,plain,
! [SV109: $i,SV75: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ( in @ SV22 @ SV75 )
| ~ ( in @ SV22 @ ( relation_rng @ SV109 ) ) )
| ( in @ SV22 @ ( relation_rng @ ( relation_rng_restriction @ SV75 @ SV109 ) ) ) )
= $true )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[886]) ).
thf(965,plain,
! [SV23: $i] :
( ( ~ ~ ( ~ ( in @ SV23 @ ( sK3_SY291 @ SV23 ) )
| ~ ! [SY490: $i,SY491: $i] :
( ~ ~ ( ~ ( in @ SY490 @ ( sK3_SY291 @ SV23 ) )
| ~ ( subset @ SY491 @ SY490 ) )
| ( in @ SY491 @ ( sK3_SY291 @ SV23 ) ) ) )
| ~ ! [SY492: $i] :
( ~ ( in @ SY492 @ ( sK3_SY291 @ SV23 ) )
| ( in @ ( powerset @ SY492 ) @ ( sK3_SY291 @ SV23 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[887]) ).
thf(966,plain,
! [SV23: $i,SV143: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( subset @ SV143 @ ( sK3_SY291 @ SV23 ) )
| ~ ~ ( are_equipotent @ SV143 @ ( sK3_SY291 @ SV23 ) ) )
| ~ ~ ( in @ SV143 @ ( sK3_SY291 @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[888]) ).
thf(967,plain,
! [SV78: $i,SV26: $i] :
( ( ( SV26 = empty_set )
= $true )
| ( ( ~ ( ~ ( ( SV78
!= ( set_meet @ SV26 ) )
| ! [SY434: $i] :
~ ( ~ ( ~ ( in @ SY434 @ SV78 )
| ! [SY300: $i] :
( ~ ( in @ SY300 @ SV26 )
| ( in @ SY434 @ SY300 ) ) )
| ~ ( ~ ! [SY301: $i] :
( ~ ( in @ SY301 @ SV26 )
| ( in @ SY434 @ SY301 ) )
| ( in @ SY434 @ SV78 ) ) ) )
| ~ ( ~ ! [SY437: $i] :
~ ( ~ ( ~ ( in @ SY437 @ SV78 )
| ! [SY303: $i] :
( ~ ( in @ SY303 @ SV26 )
| ( in @ SY437 @ SY303 ) ) )
| ~ ( ~ ! [SY304: $i] :
( ~ ( in @ SY304 @ SV26 )
| ( in @ SY437 @ SY304 ) )
| ( in @ SY437 @ SV78 ) ) )
| ( SV78
= ( set_meet @ SV26 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[891]) ).
thf(968,plain,
! [SV26: $i,SV78: $i] :
( ( ( ~ ( ( SV78
!= ( set_meet @ SV26 ) )
| ( SV78 = empty_set ) )
| ~ ( ( SV78 != empty_set )
| ( SV78
= ( set_meet @ SV26 ) ) ) )
= $false )
| ( ( SV26 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[892]) ).
thf(969,plain,
! [SV129: $i,SV110: $i,SV79: $i,SV27: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV27 @ SV79 ) @ ( relation_composition @ ( identity_relation @ SV110 ) @ SV129 ) )
| ~ ( ~ ( in @ SV27 @ SV110 )
| ~ ( in @ ( ordered_pair @ SV27 @ SV79 ) @ SV129 ) ) ) )
= $false )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[893]) ).
thf(970,plain,
! [SV129: $i,SV79: $i,SV110: $i,SV27: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV27 @ SV110 )
| ~ ( in @ ( ordered_pair @ SV27 @ SV79 ) @ SV129 ) )
| ( in @ ( ordered_pair @ SV27 @ SV79 ) @ ( relation_composition @ ( identity_relation @ SV110 ) @ SV129 ) ) ) )
= $false )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[893]) ).
thf(971,plain,
! [SV130: $i,SV111: $i,SV81: $i,SV29: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV29 @ SV81 ) @ ( cartesian_product2 @ SV111 @ SV130 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV29 @ SV111 )
| ~ ( in @ SV81 @ SV130 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[894]) ).
thf(972,plain,
! [SV130: $i,SV81: $i,SV111: $i,SV29: $i] :
( ( ( ~ ~ ( ~ ( in @ SV29 @ SV111 )
| ~ ( in @ SV81 @ SV130 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV29 @ SV81 ) @ ( cartesian_product2 @ SV111 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[895]) ).
thf(973,plain,
! [SV131: $i,SV30: $i,SV136: $i] :
( ( ( ( SV136
!= ( relation_image @ SV30 @ SV131 ) )
| ! [SY570: $i] :
~ ( ~ ( ~ ( in @ SY570 @ SV136 )
| ~ ! [SY545: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY545 @ SY570 ) @ SV30 )
| ~ ( in @ SY545 @ SV131 ) ) )
| ~ ( ~ ~ ! [SY546: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY546 @ SY570 ) @ SV30 )
| ~ ( in @ SY546 @ SV131 ) )
| ( in @ SY570 @ SV136 ) ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[896]) ).
thf(974,plain,
! [SV131: $i,SV30: $i,SV136: $i] :
( ( ( ~ ! [SY573: $i] :
~ ( ~ ( ~ ( in @ SY573 @ SV136 )
| ~ ! [SY548: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY548 @ SY573 ) @ SV30 )
| ~ ( in @ SY548 @ SV131 ) ) )
| ~ ( ~ ~ ! [SY549: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY549 @ SY573 ) @ SV30 )
| ~ ( in @ SY549 @ SV131 ) )
| ( in @ SY573 @ SV136 ) ) )
| ( SV136
= ( relation_image @ SV30 @ SV131 ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[897]) ).
thf(975,plain,
! [SV112: $i,SV82: $i,SV31: $i] :
( ( ( subset @ ( unordered_pair @ SV31 @ SV82 ) @ SV112 )
= $false )
| ( ( ~ ( ~ ( in @ SV31 @ SV112 )
| ~ ( in @ SV82 @ SV112 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[898]) ).
thf(976,plain,
! [SV82: $i,SV112: $i,SV31: $i] :
( ( ( ~ ( ~ ( in @ SV31 @ SV112 )
| ~ ( in @ SV82 @ SV112 ) ) )
= $false )
| ( ( subset @ ( unordered_pair @ SV31 @ SV82 ) @ SV112 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[899]) ).
thf(977,plain,
! [SV113: $i,SV83: $i,SV33: $i] :
( ( ( in @ SV33 @ SV83 )
= $false )
| ( ( ~ ( element @ SV83 @ ( powerset @ SV113 ) ) )
= $true )
| ( ( element @ SV33 @ SV113 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[900]) ).
thf(978,plain,
! [SV84: $i,SV34: $i] :
( ( ( empty @ SV34 )
= $true )
| ( ( ~ ( ~ ( ~ ( element @ SV84 @ SV34 )
| ( in @ SV84 @ SV34 ) )
| ~ ( ~ ( in @ SV84 @ SV34 )
| ( element @ SV84 @ SV34 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[901]) ).
thf(979,plain,
! [SV34: $i,SV84: $i] :
( ( ( ~ ( ~ ( element @ SV84 @ SV34 )
| ( empty @ SV84 ) )
| ~ ( ~ ( empty @ SV84 )
| ( element @ SV84 @ SV34 ) ) )
= $false )
| ( ( empty @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(980,plain,
! [SV35: $i,SV140: $i] :
( ( ( ~ ( ~ ( in @ SV140 @ SV35 )
| ~ ! [SY589: $i,SY590: $i] :
( SV140
!= ( ordered_pair @ SY589 @ SY590 ) ) ) )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[903]) ).
thf(981,plain,
! [SV35: $i] :
( ( ( ~ ( ~ ( in @ ( sK9_SY328 @ SV35 ) @ SV35 )
| ~ ! [SY591: $i,SY592: $i] :
( ( sK9_SY328 @ SV35 )
!= ( ordered_pair @ SY591 @ SY592 ) ) ) )
= $true )
| ( ( relation @ SV35 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[904]) ).
thf(982,plain,
! [SV86: $i,SV115: $i,SV37: $i] :
( ( ( ~ ( in @ SV37 @ ( relation_field @ SV115 ) )
| ~ ( in @ SV86 @ ( relation_field @ SV115 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV37 @ SV86 ) @ SV115 )
= $false )
| ( ( relation @ SV115 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[905]) ).
thf(983,plain,
! [SV38: $i,SV141: $i] :
( ( ( in @ SV141 @ SV38 )
= $false )
| ( ( SV38 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[906]) ).
thf(984,plain,
! [SV38: $i] :
( ( ( in @ ( sK10_SY336 @ SV38 ) @ SV38 )
= $true )
| ( ( SV38 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[907]) ).
thf(985,plain,
! [SV87: $i,SV39: $i,SV137: $i] :
( ( ( ~ ( ( SV137
!= ( relation_rng_restriction @ SV39 @ SV87 ) )
| ! [SY576: $i,SY577: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY576 @ SY577 ) @ SV137 )
| ~ ( ~ ( in @ SY577 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY576 @ SY577 ) @ SV87 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY577 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY576 @ SY577 ) @ SV87 ) )
| ( in @ ( ordered_pair @ SY576 @ SY577 ) @ SV137 ) ) ) )
| ~ ( ~ ! [SY578: $i,SY579: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY578 @ SY579 ) @ SV137 )
| ~ ( ~ ( in @ SY579 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY578 @ SY579 ) @ SV87 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY579 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY578 @ SY579 ) @ SV87 ) )
| ( in @ ( ordered_pair @ SY578 @ SY579 ) @ SV137 ) ) )
| ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) ) ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[908]) ).
thf(986,plain,
! [SV41: $i,SV88: $i,SV144: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV144 @ SV88 )
| ( SV144 = SV41 ) )
| ~ ( ( SV144 != SV41 )
| ( in @ SV144 @ SV88 ) ) ) )
= $true )
| ( ( SV88
= ( singleton @ SV41 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[909]) ).
thf(987,plain,
! [SV88: $i,SV41: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK12_SY454 @ SV41 @ SV88 ) @ SV88 )
| ( ( sK12_SY454 @ SV41 @ SV88 )
= SV41 ) )
| ~ ( ( ( sK12_SY454 @ SV41 @ SV88 )
!= SV41 )
| ( in @ ( sK12_SY454 @ SV41 @ SV88 ) @ SV88 ) ) ) )
= $false )
| ( ( SV88
= ( singleton @ SV41 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[910]) ).
thf(988,plain,
! [SV42: $i,SV89: $i,SV145: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV145 @ SV89 )
| ~ ! [SY593: $i] :
~ ~ ( ~ ( in @ SV145 @ SY593 )
| ~ ( in @ SY593 @ SV42 ) ) )
| ~ ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( in @ SV145 @ SY594 )
| ~ ( in @ SY594 @ SV42 ) )
| ( in @ SV145 @ SV89 ) ) ) )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(989,plain,
! [SV89: $i,SV42: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV89 )
| ~ ! [SY595: $i] :
~ ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SY595 )
| ~ ( in @ SY595 @ SV42 ) ) )
| ~ ( ~ ~ ! [SY596: $i] :
~ ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SY596 )
| ~ ( in @ SY596 @ SV42 ) )
| ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV89 ) ) ) )
= $false )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[912]) ).
thf(990,plain,
! [SV90: $i,SV116: $i,SV43: $i] :
( ( ( ~ ( in @ SV43 @ ( relation_dom @ ( relation_dom_restriction @ SV116 @ SV90 ) ) )
| ~ ( ~ ( in @ SV43 @ SV90 )
| ~ ( in @ SV43 @ ( relation_dom @ SV116 ) ) ) )
= $true )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[913]) ).
thf(991,plain,
! [SV116: $i,SV90: $i,SV43: $i] :
( ( ( ~ ~ ( ~ ( in @ SV43 @ SV90 )
| ~ ( in @ SV43 @ ( relation_dom @ SV116 ) ) )
| ( in @ SV43 @ ( relation_dom @ ( relation_dom_restriction @ SV116 @ SV90 ) ) ) )
= $true )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[914]) ).
thf(992,plain,
! [SV46: $i] :
( ( ~ ~ ( ~ ( in @ SV46 @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SY496: $i,SY497: $i] :
( ~ ~ ( ~ ( in @ SY496 @ ( sK4_SY357 @ SV46 ) )
| ~ ( subset @ SY497 @ SY496 ) )
| ( in @ SY497 @ ( sK4_SY357 @ SV46 ) ) ) )
| ~ ! [SY498: $i] :
~ ~ ( ~ ( in @ SY498 @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SY499: $i] :
~ ~ ( ~ ( in @ SY499 @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY498 )
| ( in @ SX4 @ SY499 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[916]) ).
thf(993,plain,
! [SV46: $i,SV146: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( subset @ SV146 @ ( sK4_SY357 @ SV46 ) )
| ~ ~ ( are_equipotent @ SV146 @ ( sK4_SY357 @ SV46 ) ) )
| ~ ~ ( in @ SV146 @ ( sK4_SY357 @ SV46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[917]) ).
thf(994,plain,
! [SV47: $i,SV132: $i] :
( ( ( SV132
!= ( relation_dom @ SV47 ) )
= $true )
| ( ( ! [SY550: $i] :
~ ( ~ ( ~ ( in @ SY550 @ SV132 )
| ~ ! [SY366: $i] :
~ ( in @ ( ordered_pair @ SY550 @ SY366 ) @ SV47 ) )
| ~ ( ~ ~ ! [SY367: $i] :
~ ( in @ ( ordered_pair @ SY550 @ SY367 ) @ SV47 )
| ( in @ SY550 @ SV132 ) ) ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[918]) ).
thf(995,plain,
! [SV47: $i,SV132: $i] :
( ( ( ~ ! [SY553: $i] :
~ ( ~ ( ~ ( in @ SY553 @ SV132 )
| ~ ! [SY369: $i] :
~ ( in @ ( ordered_pair @ SY553 @ SY369 ) @ SV47 ) )
| ~ ( ~ ~ ! [SY370: $i] :
~ ( in @ ( ordered_pair @ SY553 @ SY370 ) @ SV47 )
| ( in @ SY553 @ SV132 ) ) ) )
= $true )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[919]) ).
thf(996,plain,
! [SV49: $i,SV133: $i] :
( ( ( ~ ( ( SV133
!= ( relation_inverse @ SV49 ) )
| ! [SY556: $i,SY557: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY556 @ SY557 ) @ SV133 )
| ( in @ ( ordered_pair @ SY557 @ SY556 ) @ SV49 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY557 @ SY556 ) @ SV49 )
| ( in @ ( ordered_pair @ SY556 @ SY557 ) @ SV133 ) ) ) ) )
= $false )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[921]) ).
thf(997,plain,
! [SV49: $i,SV133: $i] :
( ( ( ~ ( ~ ! [SY558: $i,SY559: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY558 @ SY559 ) @ SV133 )
| ( in @ ( ordered_pair @ SY559 @ SY558 ) @ SV49 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY559 @ SY558 ) @ SV49 )
| ( in @ ( ordered_pair @ SY558 @ SY559 ) @ SV133 ) ) )
| ( SV133
= ( relation_inverse @ SV49 ) ) ) )
= $false )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[921]) ).
thf(998,plain,
! [SV50: $i,SV94: $i] :
( ( ( in @ SV94 @ SV50 )
= $false )
| ( ( ( set_difference @ SV50 @ ( singleton @ SV94 ) )
= SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[922]) ).
thf(999,plain,
! [SV50: $i,SV94: $i] :
( ( ( in @ SV94 @ SV50 )
= $true )
| ( ( ( set_difference @ SV50 @ ( singleton @ SV94 ) )
= SV50 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[923]) ).
thf(1000,plain,
! [SV97: $i,SV53: $i,SV147: $i] :
( ( ( ~ ( in @ SV147 @ SV53 )
| ( in @ SV147 @ SV97 ) )
= $true )
| ( ( subset @ SV53 @ SV97 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(1001,plain,
! [SV53: $i,SV97: $i] :
( ( ( ~ ( in @ ( sK14_SY464 @ SV97 @ SV53 ) @ SV53 )
| ( in @ ( sK14_SY464 @ SV97 @ SV53 ) @ SV97 ) )
= $false )
| ( ( subset @ SV53 @ SV97 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[925]) ).
thf(1002,plain,
! [SV117: $i,SV54: $i,SV98: $i] :
( ( ( ~ ( in @ SV98 @ ( subset_complement @ SV54 @ SV117 ) ) )
= $true )
| ( ( ~ ( in @ SV98 @ SV117 ) )
= $true )
| ( ( element @ SV117 @ ( powerset @ SV54 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[926]) ).
thf(1003,plain,
! [SV100: $i,SV56: $i,SV118: $i] :
( ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $false )
| ( ( ! [SY502: $i] :
~ ( ~ ( ~ ( in @ SY502 @ SV118 )
| ( SY502 = SV56 )
| ( SY502 = SV100 ) )
| ~ ( ~ ( ( SY502 = SV56 )
| ( SY502 = SV100 ) )
| ( in @ SY502 @ SV118 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[928]) ).
thf(1004,plain,
! [SV100: $i,SV56: $i,SV118: $i] :
( ( ( ! [SY503: $i] :
~ ( ~ ( ~ ( in @ SY503 @ SV118 )
| ( SY503 = SV56 )
| ( SY503 = SV100 ) )
| ~ ( ~ ( ( SY503 = SV56 )
| ( SY503 = SV100 ) )
| ( in @ SY503 @ SV118 ) ) ) )
= $false )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[929]) ).
thf(1005,plain,
! [SV102: $i,SV58: $i,SV119: $i] :
( ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $false )
| ( ( ! [SY504: $i] :
~ ( ~ ( ~ ( in @ SY504 @ SV119 )
| ~ ( ~ ( in @ SY504 @ SV58 )
| ~ ~ ( in @ SY504 @ SV102 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY504 @ SV58 )
| ~ ~ ( in @ SY504 @ SV102 ) )
| ( in @ SY504 @ SV119 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[930]) ).
thf(1006,plain,
! [SV102: $i,SV58: $i,SV119: $i] :
( ( ( ! [SY505: $i] :
~ ( ~ ( ~ ( in @ SY505 @ SV119 )
| ~ ( ~ ( in @ SY505 @ SV58 )
| ~ ~ ( in @ SY505 @ SV102 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY505 @ SV58 )
| ~ ~ ( in @ SY505 @ SV102 ) )
| ( in @ SY505 @ SV119 ) ) ) )
= $false )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[931]) ).
thf(1007,plain,
! [SV120: $i,SV103: $i,SV59: $i] :
( ( ( ~ ( in @ SV59 @ SV103 )
| ~ ( element @ SV103 @ ( powerset @ SV120 ) ) )
= $true )
| ( ( ~ ( empty @ SV120 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[932]) ).
thf(1008,plain,
! [SV104: $i,SV60: $i,SV121: $i] :
( ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $false )
| ( ( ! [SY506: $i] :
~ ( ~ ( ~ ( in @ SY506 @ SV121 )
| ~ ( ~ ( in @ SY506 @ SV60 )
| ~ ( in @ SY506 @ SV104 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY506 @ SV60 )
| ~ ( in @ SY506 @ SV104 ) )
| ( in @ SY506 @ SV121 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[933]) ).
thf(1009,plain,
! [SV104: $i,SV60: $i,SV121: $i] :
( ( ( ! [SY507: $i] :
~ ( ~ ( ~ ( in @ SY507 @ SV121 )
| ~ ( ~ ( in @ SY507 @ SV60 )
| ~ ( in @ SY507 @ SV104 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY507 @ SV60 )
| ~ ( in @ SY507 @ SV104 ) )
| ( in @ SY507 @ SV121 ) ) ) )
= $false )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[934]) ).
thf(1010,plain,
! [SV63: $i,SV3: $i] :
( ( ( ~ ( disjoint @ SV3 @ SV63 ) )
= $false )
| ( ( ~ ! [SY404: $i] :
~ ( in @ SY404 @ ( set_intersection2 @ SV3 @ SV63 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[936]) ).
thf(1011,plain,
! [SV63: $i,SV3: $i] :
( ( ( ~ ! [SY405: $i] :
~ ( in @ SY405 @ ( set_intersection2 @ SV3 @ SV63 ) ) )
= $false )
| ( ( ~ ( disjoint @ SV3 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[937]) ).
thf(1012,plain,
! [SV5: $i,SV65: $i] :
( ( ( ~ ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV5 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV65 )
| ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( SV5 = SV65 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[938]) ).
thf(1013,plain,
! [SV5: $i,SV65: $i] :
( ( ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV65 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV65 )
| ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( SV5 = SV65 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[938]) ).
thf(1014,plain,
! [SV6: $i,SV66: $i] :
( ( ( ~ ( ( SV66
!= ( identity_relation @ SV6 ) )
| ~ ( ( ( relation_dom @ SV66 )
!= SV6 )
| ~ ! [SY407: $i] :
( ~ ( in @ SY407 @ SV6 )
| ( ( apply @ SV66 @ SY407 )
= SY407 ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV66 )
!= SV6 )
| ~ ! [SY408: $i] :
( ~ ( in @ SY408 @ SV6 )
| ( ( apply @ SV66 @ SY408 )
= SY408 ) ) )
| ( SV66
= ( identity_relation @ SV6 ) ) ) )
= $false )
| ( ( relation @ SV66 )
= $false )
| ( ( function @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[939]) ).
thf(1015,plain,
! [SV122: $i,SV106: $i,SV67: $i,SV7: $i] :
( ( ( in @ ( ordered_pair @ SV7 @ SV67 ) @ ( cartesian_product2 @ SV106 @ SV122 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV7 @ SV106 )
| ~ ( in @ SV67 @ SV122 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[940]) ).
thf(1016,plain,
! [SV122: $i,SV67: $i,SV106: $i,SV7: $i] :
( ( ( ~ ( ~ ( in @ SV7 @ SV106 )
| ~ ( in @ SV67 @ SV122 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV7 @ SV67 ) @ ( cartesian_product2 @ SV106 @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[941]) ).
thf(1017,plain,
! [SV123: $i,SV8: $i] :
( ( ( ( SV8 != SV123 )
| ! [SY508: $i,SY509: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY508 @ SY509 ) @ SV8 )
| ( in @ ( ordered_pair @ SY508 @ SY509 ) @ SV123 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY508 @ SY509 ) @ SV123 )
| ( in @ ( ordered_pair @ SY508 @ SY509 ) @ SV8 ) ) ) )
= $true )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[942]) ).
thf(1018,plain,
! [SV123: $i,SV8: $i] :
( ( ( ~ ! [SY510: $i,SY511: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY510 @ SY511 ) @ SV8 )
| ( in @ ( ordered_pair @ SY510 @ SY511 ) @ SV123 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY510 @ SY511 ) @ SV123 )
| ( in @ ( ordered_pair @ SY510 @ SY511 ) @ SV8 ) ) )
| ( SV8 = SV123 ) )
= $true )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[943]) ).
thf(1019,plain,
! [SV124: $i,SV10: $i,SV139: $i] :
( ( ( relation @ SV139 )
= $false )
| ( ( ~ ( ~ ( ( SV139
!= ( relation_composition @ SV10 @ SV124 ) )
| ! [SY581: $i,SY582: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY581 @ SY582 ) @ SV139 )
| ~ ! [SY515: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY581 @ SY515 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY515 @ SY582 ) @ SV124 ) ) )
| ~ ( ~ ~ ! [SY516: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY581 @ SY516 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY516 @ SY582 ) @ SV124 ) )
| ( in @ ( ordered_pair @ SY581 @ SY582 ) @ SV139 ) ) ) )
| ~ ( ~ ! [SY585: $i,SY586: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY585 @ SY586 ) @ SV139 )
| ~ ! [SY519: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY585 @ SY519 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY519 @ SY586 ) @ SV124 ) ) )
| ~ ( ~ ~ ! [SY520: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY585 @ SY520 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY520 @ SY586 ) @ SV124 ) )
| ( in @ ( ordered_pair @ SY585 @ SY586 ) @ SV139 ) ) )
| ( SV139
= ( relation_composition @ SV10 @ SV124 ) ) ) ) )
= $true )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[944]) ).
thf(1020,plain,
! [SV69: $i,SV11: $i,SV107: $i,SV148: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV148 @ SV107 )
| ~ ! [SY597: $i] :
~ ~ ! [SY598: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY597 @ SV11 )
| ~ ( in @ SY598 @ SV69 ) )
| ( SV148
!= ( ordered_pair @ SY597 @ SY598 ) ) ) )
| ~ ( ~ ~ ! [SY599: $i] :
~ ~ ! [SY600: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY599 @ SV11 )
| ~ ( in @ SY600 @ SV69 ) )
| ( SV148
!= ( ordered_pair @ SY599 @ SY600 ) ) )
| ( in @ SV148 @ SV107 ) ) ) )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(1021,plain,
! [SV107: $i,SV11: $i,SV69: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 )
| ~ ! [SY601: $i] :
~ ~ ! [SY602: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY601 @ SV11 )
| ~ ( in @ SY602 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SY601 @ SY602 ) ) ) )
| ~ ( ~ ~ ! [SY603: $i] :
~ ~ ! [SY604: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY603 @ SV11 )
| ~ ( in @ SY604 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SY603 @ SY604 ) ) )
| ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 ) ) ) )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[946]) ).
thf(1022,plain,
! [SV12: $i,SV70: $i] :
( ( ( SV70
= ( identity_relation @ SV12 ) )
= $false )
| ( ( ! [SY422: $i,SY423: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY422 @ SY423 ) @ SV70 )
| ~ ( ~ ( in @ SY422 @ SV12 )
| ( SY422 != SY423 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY422 @ SV12 )
| ( SY422 != SY423 ) )
| ( in @ ( ordered_pair @ SY422 @ SY423 ) @ SV70 ) ) ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[947]) ).
thf(1023,plain,
! [SV12: $i,SV70: $i] :
( ( ( ! [SY424: $i,SY425: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY424 @ SY425 ) @ SV70 )
| ~ ( ~ ( in @ SY424 @ SV12 )
| ( SY424 != SY425 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY424 @ SV12 )
| ( SY424 != SY425 ) )
| ( in @ ( ordered_pair @ SY424 @ SY425 ) @ SV70 ) ) ) )
= $false )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[948]) ).
thf(1024,plain,
! [SV13: $i,SV71: $i,SV142: $i] :
( ( ( ~ ( ~ ( in @ SV142 @ SV71 )
| ( subset @ SV142 @ SV13 ) )
| ~ ( ~ ( subset @ SV142 @ SV13 )
| ( in @ SV142 @ SV71 ) ) )
= $false )
| ( ( SV71
= ( powerset @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[949]) ).
thf(1025,plain,
! [SV71: $i,SV13: $i] :
( ( ( ~ ( ~ ( in @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV71 )
| ( subset @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV13 ) )
| ~ ( ~ ( subset @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV13 )
| ( in @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV71 ) ) )
= $true )
| ( ( SV71
= ( powerset @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[950]) ).
thf(1026,plain,
! [SV125: $i,SV14: $i,SV134: $i] :
( ( ( SV134
!= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( ! [SY560: $i] :
~ ( ~ ( ~ ( in @ SY560 @ SV134 )
| ~ ! [SY523: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY560 @ SY523 ) @ SV14 )
| ~ ( in @ SY523 @ SV125 ) ) )
| ~ ( ~ ~ ! [SY524: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY560 @ SY524 ) @ SV14 )
| ~ ( in @ SY524 @ SV125 ) )
| ( in @ SY560 @ SV134 ) ) ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[951]) ).
thf(1027,plain,
! [SV125: $i,SV14: $i,SV134: $i] :
( ( ( ~ ! [SY563: $i] :
~ ( ~ ( ~ ( in @ SY563 @ SV134 )
| ~ ! [SY526: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY563 @ SY526 ) @ SV14 )
| ~ ( in @ SY526 @ SV125 ) ) )
| ~ ( ~ ~ ! [SY527: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY563 @ SY527 ) @ SV14 )
| ~ ( in @ SY527 @ SV125 ) )
| ( in @ SY563 @ SV134 ) ) ) )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[952]) ).
thf(1028,plain,
! [SV15: $i,SV126: $i] :
( ( ( SV126
= ( relation_rng @ SV15 ) )
= $false )
| ( ( ! [SY528: $i] :
~ ( ~ ( ~ ( in @ SY528 @ SV126 )
| ~ ! [SY263: $i] :
~ ( in @ ( ordered_pair @ SY263 @ SY528 ) @ SV15 ) )
| ~ ( ~ ~ ! [SY264: $i] :
~ ( in @ ( ordered_pair @ SY264 @ SY528 ) @ SV15 )
| ( in @ SY528 @ SV126 ) ) ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[953]) ).
thf(1029,plain,
! [SV15: $i,SV126: $i] :
( ( ( ! [SY531: $i] :
~ ( ~ ( ~ ( in @ SY531 @ SV126 )
| ~ ! [SY266: $i] :
~ ( in @ ( ordered_pair @ SY266 @ SY531 ) @ SV15 ) )
| ~ ( ~ ~ ! [SY267: $i] :
~ ( in @ ( ordered_pair @ SY267 @ SY531 ) @ SV15 )
| ( in @ SY531 @ SV126 ) ) ) )
= $false )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[954]) ).
thf(1030,plain,
! [SV127: $i,SV16: $i] :
( ( ( ~ ( subset @ SV16 @ SV127 )
| ! [SY534: $i,SY535: $i] :
( ~ ( in @ ( ordered_pair @ SY534 @ SY535 ) @ SV16 )
| ( in @ ( ordered_pair @ SY534 @ SY535 ) @ SV127 ) ) )
= $true )
| ( ( relation @ SV127 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[955]) ).
thf(1031,plain,
! [SV127: $i,SV16: $i] :
( ( ( ~ ! [SY536: $i,SY537: $i] :
( ~ ( in @ ( ordered_pair @ SY536 @ SY537 ) @ SV16 )
| ( in @ ( ordered_pair @ SY536 @ SY537 ) @ SV127 ) )
| ( subset @ SV16 @ SV127 ) )
= $true )
| ( ( relation @ SV127 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[956]) ).
thf(1032,plain,
! [SV72: $i,SV17: $i,SV108: $i,SV149: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV149 @ SV108 )
| ( in @ SV149 @ SV17 )
| ( in @ SV149 @ SV72 ) )
| ~ ( ~ ( ( in @ SV149 @ SV17 )
| ( in @ SV149 @ SV72 ) )
| ( in @ SV149 @ SV108 ) ) ) )
= $true )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(1033,plain,
! [SV108: $i,SV17: $i,SV72: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV108 )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV17 )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV72 ) )
| ~ ( ~ ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV17 )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV72 ) )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV108 ) ) ) )
= $false )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[958]) ).
thf(1034,plain,
! [SV128: $i,SV20: $i,SV135: $i] :
( ( ( ~ ( ( SV135
!= ( relation_dom_restriction @ SV20 @ SV128 ) )
| ! [SY566: $i,SY567: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV135 )
| ~ ( ~ ( in @ SY566 @ SV128 )
| ~ ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY566 @ SV128 )
| ~ ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV20 ) )
| ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV135 ) ) ) ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[960]) ).
thf(1035,plain,
! [SV20: $i,SV128: $i,SV135: $i] :
( ( ( ~ ( ~ ! [SY568: $i,SY569: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY568 @ SY569 ) @ SV135 )
| ~ ( ~ ( in @ SY568 @ SV128 )
| ~ ( in @ ( ordered_pair @ SY568 @ SY569 ) @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY568 @ SV128 )
| ~ ( in @ ( ordered_pair @ SY568 @ SY569 ) @ SV20 ) )
| ( in @ ( ordered_pair @ SY568 @ SY569 ) @ SV135 ) ) )
| ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) ) ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[960]) ).
thf(1036,plain,
! [SV74: $i,SV21: $i] :
( ( ( ~ ( disjoint @ SV21 @ SV74 ) )
= $false )
| ( ( ~ ! [SY431: $i] :
~ ~ ( ~ ( in @ SY431 @ SV21 )
| ~ ( in @ SY431 @ SV74 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[961]) ).
thf(1037,plain,
! [SV74: $i,SV21: $i] :
( ( ( ~ ! [SY432: $i] :
~ ~ ( ~ ( in @ SY432 @ SV21 )
| ~ ( in @ SY432 @ SV74 ) ) )
= $false )
| ( ( ~ ( disjoint @ SV21 @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[962]) ).
thf(1038,plain,
! [SV109: $i,SV75: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ ( relation_rng @ ( relation_rng_restriction @ SV75 @ SV109 ) ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV22 @ SV75 )
| ~ ( in @ SV22 @ ( relation_rng @ SV109 ) ) ) )
= $true )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[963]) ).
thf(1039,plain,
! [SV109: $i,SV75: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ( in @ SV22 @ SV75 )
| ~ ( in @ SV22 @ ( relation_rng @ SV109 ) ) ) )
= $true )
| ( ( in @ SV22 @ ( relation_rng @ ( relation_rng_restriction @ SV75 @ SV109 ) ) )
= $true )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[964]) ).
thf(1040,plain,
! [SV23: $i] :
( ( ~ ~ ( ~ ( in @ SV23 @ ( sK3_SY291 @ SV23 ) )
| ~ ! [SY490: $i,SY491: $i] :
( ~ ~ ( ~ ( in @ SY490 @ ( sK3_SY291 @ SV23 ) )
| ~ ( subset @ SY491 @ SY490 ) )
| ( in @ SY491 @ ( sK3_SY291 @ SV23 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[965]) ).
thf(1041,plain,
! [SV23: $i] :
( ( ~ ! [SY492: $i] :
( ~ ( in @ SY492 @ ( sK3_SY291 @ SV23 ) )
| ( in @ ( powerset @ SY492 ) @ ( sK3_SY291 @ SV23 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[965]) ).
thf(1042,plain,
! [SV23: $i,SV143: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV143 @ ( sK3_SY291 @ SV23 ) )
| ~ ~ ( are_equipotent @ SV143 @ ( sK3_SY291 @ SV23 ) ) )
| ~ ~ ( in @ SV143 @ ( sK3_SY291 @ SV23 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[966]) ).
thf(1043,plain,
! [SV26: $i,SV78: $i] :
( ( ( ~ ( ( SV78
!= ( set_meet @ SV26 ) )
| ! [SY434: $i] :
~ ( ~ ( ~ ( in @ SY434 @ SV78 )
| ! [SY300: $i] :
( ~ ( in @ SY300 @ SV26 )
| ( in @ SY434 @ SY300 ) ) )
| ~ ( ~ ! [SY301: $i] :
( ~ ( in @ SY301 @ SV26 )
| ( in @ SY434 @ SY301 ) )
| ( in @ SY434 @ SV78 ) ) ) )
| ~ ( ~ ! [SY437: $i] :
~ ( ~ ( ~ ( in @ SY437 @ SV78 )
| ! [SY303: $i] :
( ~ ( in @ SY303 @ SV26 )
| ( in @ SY437 @ SY303 ) ) )
| ~ ( ~ ! [SY304: $i] :
( ~ ( in @ SY304 @ SV26 )
| ( in @ SY437 @ SY304 ) )
| ( in @ SY437 @ SV78 ) ) )
| ( SV78
= ( set_meet @ SV26 ) ) ) )
= $false )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[967]) ).
thf(1044,plain,
! [SV26: $i,SV78: $i] :
( ( ( ~ ( ( SV78
!= ( set_meet @ SV26 ) )
| ( SV78 = empty_set ) ) )
= $false )
| ( ( SV26 = empty_set )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[968]) ).
thf(1045,plain,
! [SV26: $i,SV78: $i] :
( ( ( ~ ( ( SV78 != empty_set )
| ( SV78
= ( set_meet @ SV26 ) ) ) )
= $false )
| ( ( SV26 = empty_set )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[968]) ).
thf(1046,plain,
! [SV129: $i,SV110: $i,SV79: $i,SV27: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV27 @ SV79 ) @ ( relation_composition @ ( identity_relation @ SV110 ) @ SV129 ) )
| ~ ( ~ ( in @ SV27 @ SV110 )
| ~ ( in @ ( ordered_pair @ SV27 @ SV79 ) @ SV129 ) ) )
= $true )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[969]) ).
thf(1047,plain,
! [SV129: $i,SV79: $i,SV110: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( in @ SV27 @ SV110 )
| ~ ( in @ ( ordered_pair @ SV27 @ SV79 ) @ SV129 ) )
| ( in @ ( ordered_pair @ SV27 @ SV79 ) @ ( relation_composition @ ( identity_relation @ SV110 ) @ SV129 ) ) )
= $true )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[970]) ).
thf(1048,plain,
! [SV130: $i,SV111: $i,SV81: $i,SV29: $i] :
( ( ( in @ ( ordered_pair @ SV29 @ SV81 ) @ ( cartesian_product2 @ SV111 @ SV130 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV29 @ SV111 )
| ~ ( in @ SV81 @ SV130 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[971]) ).
thf(1049,plain,
! [SV130: $i,SV81: $i,SV111: $i,SV29: $i] :
( ( ( ~ ( ~ ( in @ SV29 @ SV111 )
| ~ ( in @ SV81 @ SV130 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV29 @ SV81 ) @ ( cartesian_product2 @ SV111 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[972]) ).
thf(1050,plain,
! [SV131: $i,SV30: $i,SV136: $i] :
( ( ( SV136
!= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( ! [SY570: $i] :
~ ( ~ ( ~ ( in @ SY570 @ SV136 )
| ~ ! [SY545: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY545 @ SY570 ) @ SV30 )
| ~ ( in @ SY545 @ SV131 ) ) )
| ~ ( ~ ~ ! [SY546: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY546 @ SY570 ) @ SV30 )
| ~ ( in @ SY546 @ SV131 ) )
| ( in @ SY570 @ SV136 ) ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[973]) ).
thf(1051,plain,
! [SV131: $i,SV30: $i,SV136: $i] :
( ( ( ~ ! [SY573: $i] :
~ ( ~ ( ~ ( in @ SY573 @ SV136 )
| ~ ! [SY548: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY548 @ SY573 ) @ SV30 )
| ~ ( in @ SY548 @ SV131 ) ) )
| ~ ( ~ ~ ! [SY549: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY549 @ SY573 ) @ SV30 )
| ~ ( in @ SY549 @ SV131 ) )
| ( in @ SY573 @ SV136 ) ) ) )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[974]) ).
thf(1052,plain,
! [SV82: $i,SV112: $i,SV31: $i] :
( ( ( ~ ( in @ SV31 @ SV112 )
| ~ ( in @ SV82 @ SV112 ) )
= $false )
| ( ( subset @ ( unordered_pair @ SV31 @ SV82 ) @ SV112 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[975]) ).
thf(1053,plain,
! [SV82: $i,SV112: $i,SV31: $i] :
( ( ( ~ ( in @ SV31 @ SV112 )
| ~ ( in @ SV82 @ SV112 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV31 @ SV82 ) @ SV112 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[976]) ).
thf(1054,plain,
! [SV33: $i,SV113: $i,SV83: $i] :
( ( ( element @ SV83 @ ( powerset @ SV113 ) )
= $false )
| ( ( in @ SV33 @ SV83 )
= $false )
| ( ( element @ SV33 @ SV113 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[977]) ).
thf(1055,plain,
! [SV34: $i,SV84: $i] :
( ( ( ~ ( ~ ( element @ SV84 @ SV34 )
| ( in @ SV84 @ SV34 ) )
| ~ ( ~ ( in @ SV84 @ SV34 )
| ( element @ SV84 @ SV34 ) ) )
= $false )
| ( ( empty @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[978]) ).
thf(1056,plain,
! [SV34: $i,SV84: $i] :
( ( ( ~ ( ~ ( element @ SV84 @ SV34 )
| ( empty @ SV84 ) ) )
= $false )
| ( ( empty @ SV34 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[979]) ).
thf(1057,plain,
! [SV34: $i,SV84: $i] :
( ( ( ~ ( ~ ( empty @ SV84 )
| ( element @ SV84 @ SV34 ) ) )
= $false )
| ( ( empty @ SV34 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[979]) ).
thf(1058,plain,
! [SV35: $i,SV140: $i] :
( ( ( ~ ( in @ SV140 @ SV35 )
| ~ ! [SY589: $i,SY590: $i] :
( SV140
!= ( ordered_pair @ SY589 @ SY590 ) ) )
= $true )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[980]) ).
thf(1059,plain,
! [SV35: $i] :
( ( ( ~ ( in @ ( sK9_SY328 @ SV35 ) @ SV35 )
| ~ ! [SY591: $i,SY592: $i] :
( ( sK9_SY328 @ SV35 )
!= ( ordered_pair @ SY591 @ SY592 ) ) )
= $false )
| ( ( relation @ SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[981]) ).
thf(1060,plain,
! [SV86: $i,SV115: $i,SV37: $i] :
( ( ( ~ ( in @ SV37 @ ( relation_field @ SV115 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV37 @ SV86 ) @ SV115 )
= $false )
| ( ( relation @ SV115 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[982]) ).
thf(1061,plain,
! [SV37: $i,SV115: $i,SV86: $i] :
( ( ( ~ ( in @ SV86 @ ( relation_field @ SV115 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV37 @ SV86 ) @ SV115 )
= $false )
| ( ( relation @ SV115 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[982]) ).
thf(1062,plain,
! [SV87: $i,SV39: $i,SV137: $i] :
( ( ( ~ ( ( SV137
!= ( relation_rng_restriction @ SV39 @ SV87 ) )
| ! [SY576: $i,SY577: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY576 @ SY577 ) @ SV137 )
| ~ ( ~ ( in @ SY577 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY576 @ SY577 ) @ SV87 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY577 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY576 @ SY577 ) @ SV87 ) )
| ( in @ ( ordered_pair @ SY576 @ SY577 ) @ SV137 ) ) ) ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[985]) ).
thf(1063,plain,
! [SV87: $i,SV39: $i,SV137: $i] :
( ( ( ~ ( ~ ! [SY578: $i,SY579: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY578 @ SY579 ) @ SV137 )
| ~ ( ~ ( in @ SY579 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY578 @ SY579 ) @ SV87 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY579 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY578 @ SY579 ) @ SV87 ) )
| ( in @ ( ordered_pair @ SY578 @ SY579 ) @ SV137 ) ) )
| ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) ) ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[985]) ).
thf(1064,plain,
! [SV41: $i,SV88: $i,SV144: $i] :
( ( ( ~ ( ~ ( in @ SV144 @ SV88 )
| ( SV144 = SV41 ) )
| ~ ( ( SV144 != SV41 )
| ( in @ SV144 @ SV88 ) ) )
= $false )
| ( ( SV88
= ( singleton @ SV41 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[986]) ).
thf(1065,plain,
! [SV88: $i,SV41: $i] :
( ( ( ~ ( ~ ( in @ ( sK12_SY454 @ SV41 @ SV88 ) @ SV88 )
| ( ( sK12_SY454 @ SV41 @ SV88 )
= SV41 ) )
| ~ ( ( ( sK12_SY454 @ SV41 @ SV88 )
!= SV41 )
| ( in @ ( sK12_SY454 @ SV41 @ SV88 ) @ SV88 ) ) )
= $true )
| ( ( SV88
= ( singleton @ SV41 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[987]) ).
thf(1066,plain,
! [SV42: $i,SV89: $i,SV145: $i] :
( ( ( ~ ( ~ ( in @ SV145 @ SV89 )
| ~ ! [SY593: $i] :
~ ~ ( ~ ( in @ SV145 @ SY593 )
| ~ ( in @ SY593 @ SV42 ) ) )
| ~ ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( in @ SV145 @ SY594 )
| ~ ( in @ SY594 @ SV42 ) )
| ( in @ SV145 @ SV89 ) ) )
= $false )
| ( ( SV89
= ( union @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[988]) ).
thf(1067,plain,
! [SV89: $i,SV42: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV89 )
| ~ ! [SY595: $i] :
~ ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SY595 )
| ~ ( in @ SY595 @ SV42 ) ) )
| ~ ( ~ ~ ! [SY596: $i] :
~ ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SY596 )
| ~ ( in @ SY596 @ SV42 ) )
| ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[989]) ).
thf(1068,plain,
! [SV90: $i,SV116: $i,SV43: $i] :
( ( ( ~ ( in @ SV43 @ ( relation_dom @ ( relation_dom_restriction @ SV116 @ SV90 ) ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV43 @ SV90 )
| ~ ( in @ SV43 @ ( relation_dom @ SV116 ) ) ) )
= $true )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[990]) ).
thf(1069,plain,
! [SV116: $i,SV90: $i,SV43: $i] :
( ( ( ~ ~ ( ~ ( in @ SV43 @ SV90 )
| ~ ( in @ SV43 @ ( relation_dom @ SV116 ) ) ) )
= $true )
| ( ( in @ SV43 @ ( relation_dom @ ( relation_dom_restriction @ SV116 @ SV90 ) ) )
= $true )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[991]) ).
thf(1070,plain,
! [SV46: $i] :
( ( ~ ~ ( ~ ( in @ SV46 @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SY496: $i,SY497: $i] :
( ~ ~ ( ~ ( in @ SY496 @ ( sK4_SY357 @ SV46 ) )
| ~ ( subset @ SY497 @ SY496 ) )
| ( in @ SY497 @ ( sK4_SY357 @ SV46 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[992]) ).
thf(1071,plain,
! [SV46: $i] :
( ( ~ ! [SY498: $i] :
~ ~ ( ~ ( in @ SY498 @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SY499: $i] :
~ ~ ( ~ ( in @ SY499 @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY498 )
| ( in @ SX4 @ SY499 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[992]) ).
thf(1072,plain,
! [SV46: $i,SV146: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV146 @ ( sK4_SY357 @ SV46 ) )
| ~ ~ ( are_equipotent @ SV146 @ ( sK4_SY357 @ SV46 ) ) )
| ~ ~ ( in @ SV146 @ ( sK4_SY357 @ SV46 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[993]) ).
thf(1073,plain,
! [SV47: $i,SV132: $i] :
( ( ( SV132
= ( relation_dom @ SV47 ) )
= $false )
| ( ( ! [SY550: $i] :
~ ( ~ ( ~ ( in @ SY550 @ SV132 )
| ~ ! [SY366: $i] :
~ ( in @ ( ordered_pair @ SY550 @ SY366 ) @ SV47 ) )
| ~ ( ~ ~ ! [SY367: $i] :
~ ( in @ ( ordered_pair @ SY550 @ SY367 ) @ SV47 )
| ( in @ SY550 @ SV132 ) ) ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[994]) ).
thf(1074,plain,
! [SV47: $i,SV132: $i] :
( ( ( ! [SY553: $i] :
~ ( ~ ( ~ ( in @ SY553 @ SV132 )
| ~ ! [SY369: $i] :
~ ( in @ ( ordered_pair @ SY553 @ SY369 ) @ SV47 ) )
| ~ ( ~ ~ ! [SY370: $i] :
~ ( in @ ( ordered_pair @ SY553 @ SY370 ) @ SV47 )
| ( in @ SY553 @ SV132 ) ) ) )
= $false )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[995]) ).
thf(1075,plain,
! [SV49: $i,SV133: $i] :
( ( ( ( SV133
!= ( relation_inverse @ SV49 ) )
| ! [SY556: $i,SY557: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY556 @ SY557 ) @ SV133 )
| ( in @ ( ordered_pair @ SY557 @ SY556 ) @ SV49 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY557 @ SY556 ) @ SV49 )
| ( in @ ( ordered_pair @ SY556 @ SY557 ) @ SV133 ) ) ) )
= $true )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[996]) ).
thf(1076,plain,
! [SV49: $i,SV133: $i] :
( ( ( ~ ! [SY558: $i,SY559: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY558 @ SY559 ) @ SV133 )
| ( in @ ( ordered_pair @ SY559 @ SY558 ) @ SV49 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY559 @ SY558 ) @ SV49 )
| ( in @ ( ordered_pair @ SY558 @ SY559 ) @ SV133 ) ) )
| ( SV133
= ( relation_inverse @ SV49 ) ) )
= $true )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[997]) ).
thf(1077,plain,
! [SV97: $i,SV53: $i,SV147: $i] :
( ( ( ~ ( in @ SV147 @ SV53 ) )
= $true )
| ( ( in @ SV147 @ SV97 )
= $true )
| ( ( subset @ SV53 @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1000]) ).
thf(1078,plain,
! [SV53: $i,SV97: $i] :
( ( ( ~ ( in @ ( sK14_SY464 @ SV97 @ SV53 ) @ SV53 ) )
= $false )
| ( ( subset @ SV53 @ SV97 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1001]) ).
thf(1079,plain,
! [SV53: $i,SV97: $i] :
( ( ( in @ ( sK14_SY464 @ SV97 @ SV53 ) @ SV97 )
= $false )
| ( ( subset @ SV53 @ SV97 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1001]) ).
thf(1080,plain,
! [SV117: $i,SV54: $i,SV98: $i] :
( ( ( in @ SV98 @ ( subset_complement @ SV54 @ SV117 ) )
= $false )
| ( ( ~ ( in @ SV98 @ SV117 ) )
= $true )
| ( ( element @ SV117 @ ( powerset @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1002]) ).
thf(1081,plain,
! [SV100: $i,SV56: $i,SV118: $i,SV150: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV150 @ SV118 )
| ( SV150 = SV56 )
| ( SV150 = SV100 ) )
| ~ ( ~ ( ( SV150 = SV56 )
| ( SV150 = SV100 ) )
| ( in @ SV150 @ SV118 ) ) ) )
= $true )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1082,plain,
! [SV118: $i,SV56: $i,SV100: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK17_SY503 @ SV100 @ SV56 @ SV118 ) @ SV118 )
| ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV56 )
| ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV100 ) )
| ~ ( ~ ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV56 )
| ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV100 ) )
| ( in @ ( sK17_SY503 @ SV100 @ SV56 @ SV118 ) @ SV118 ) ) ) )
= $false )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1004]) ).
thf(1083,plain,
! [SV102: $i,SV58: $i,SV119: $i,SV151: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV151 @ SV119 )
| ~ ( ~ ( in @ SV151 @ SV58 )
| ~ ~ ( in @ SV151 @ SV102 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV151 @ SV58 )
| ~ ~ ( in @ SV151 @ SV102 ) )
| ( in @ SV151 @ SV119 ) ) ) )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1084,plain,
! [SV119: $i,SV58: $i,SV102: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV119 )
| ~ ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
| ~ ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
| ~ ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 ) )
| ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV119 ) ) ) )
= $false )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1006]) ).
thf(1085,plain,
! [SV120: $i,SV103: $i,SV59: $i] :
( ( ( ~ ( in @ SV59 @ SV103 ) )
= $true )
| ( ( ~ ( element @ SV103 @ ( powerset @ SV120 ) ) )
= $true )
| ( ( ~ ( empty @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1007]) ).
thf(1086,plain,
! [SV104: $i,SV60: $i,SV121: $i,SV152: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV152 @ SV121 )
| ~ ( ~ ( in @ SV152 @ SV60 )
| ~ ( in @ SV152 @ SV104 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV152 @ SV60 )
| ~ ( in @ SV152 @ SV104 ) )
| ( in @ SV152 @ SV121 ) ) ) )
= $true )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1087,plain,
! [SV121: $i,SV60: $i,SV104: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV121 )
| ~ ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
| ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
| ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 ) )
| ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV121 ) ) ) )
= $false )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1009]) ).
thf(1088,plain,
! [SV63: $i,SV3: $i] :
( ( ( disjoint @ SV3 @ SV63 )
= $true )
| ( ( ~ ! [SY404: $i] :
~ ( in @ SY404 @ ( set_intersection2 @ SV3 @ SV63 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1010]) ).
thf(1089,plain,
! [SV63: $i,SV3: $i] :
( ( ( ! [SY405: $i] :
~ ( in @ SY405 @ ( set_intersection2 @ SV3 @ SV63 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV3 @ SV63 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1011]) ).
thf(1090,plain,
! [SV5: $i,SV65: $i] :
( ( ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV5 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV65 )
| ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( SV5 = SV65 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1012]) ).
thf(1091,plain,
! [SV5: $i,SV65: $i] :
( ( ( ~ ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV65 )
| ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV5 ) )
= $false )
| ( ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV65 )
= $false )
| ( ( SV5 = SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1013]) ).
thf(1092,plain,
! [SV6: $i,SV66: $i] :
( ( ( ~ ( ( SV66
!= ( identity_relation @ SV6 ) )
| ~ ( ( ( relation_dom @ SV66 )
!= SV6 )
| ~ ! [SY407: $i] :
( ~ ( in @ SY407 @ SV6 )
| ( ( apply @ SV66 @ SY407 )
= SY407 ) ) ) ) )
= $false )
| ( ( relation @ SV66 )
= $false )
| ( ( function @ SV66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1014]) ).
thf(1093,plain,
! [SV6: $i,SV66: $i] :
( ( ( ~ ( ~ ~ ( ( ( relation_dom @ SV66 )
!= SV6 )
| ~ ! [SY408: $i] :
( ~ ( in @ SY408 @ SV6 )
| ( ( apply @ SV66 @ SY408 )
= SY408 ) ) )
| ( SV66
= ( identity_relation @ SV6 ) ) ) )
= $false )
| ( ( relation @ SV66 )
= $false )
| ( ( function @ SV66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1014]) ).
thf(1094,plain,
! [SV122: $i,SV67: $i,SV106: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV106 )
| ~ ( in @ SV67 @ SV122 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV7 @ SV67 ) @ ( cartesian_product2 @ SV106 @ SV122 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1015]) ).
thf(1095,plain,
! [SV122: $i,SV67: $i,SV106: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV106 )
| ~ ( in @ SV67 @ SV122 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV7 @ SV67 ) @ ( cartesian_product2 @ SV106 @ SV122 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1016]) ).
thf(1096,plain,
! [SV123: $i,SV8: $i] :
( ( ( SV8 != SV123 )
= $true )
| ( ( ! [SY508: $i,SY509: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY508 @ SY509 ) @ SV8 )
| ( in @ ( ordered_pair @ SY508 @ SY509 ) @ SV123 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY508 @ SY509 ) @ SV123 )
| ( in @ ( ordered_pair @ SY508 @ SY509 ) @ SV8 ) ) ) )
= $true )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1017]) ).
thf(1097,plain,
! [SV123: $i,SV8: $i] :
( ( ( ~ ! [SY510: $i,SY511: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY510 @ SY511 ) @ SV8 )
| ( in @ ( ordered_pair @ SY510 @ SY511 ) @ SV123 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY510 @ SY511 ) @ SV123 )
| ( in @ ( ordered_pair @ SY510 @ SY511 ) @ SV8 ) ) ) )
= $true )
| ( ( SV8 = SV123 )
= $true )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1018]) ).
thf(1098,plain,
! [SV124: $i,SV10: $i,SV139: $i] :
( ( ( ~ ( ( SV139
!= ( relation_composition @ SV10 @ SV124 ) )
| ! [SY581: $i,SY582: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY581 @ SY582 ) @ SV139 )
| ~ ! [SY515: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY581 @ SY515 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY515 @ SY582 ) @ SV124 ) ) )
| ~ ( ~ ~ ! [SY516: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY581 @ SY516 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY516 @ SY582 ) @ SV124 ) )
| ( in @ ( ordered_pair @ SY581 @ SY582 ) @ SV139 ) ) ) )
| ~ ( ~ ! [SY585: $i,SY586: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY585 @ SY586 ) @ SV139 )
| ~ ! [SY519: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY585 @ SY519 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY519 @ SY586 ) @ SV124 ) ) )
| ~ ( ~ ~ ! [SY520: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY585 @ SY520 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY520 @ SY586 ) @ SV124 ) )
| ( in @ ( ordered_pair @ SY585 @ SY586 ) @ SV139 ) ) )
| ( SV139
= ( relation_composition @ SV10 @ SV124 ) ) ) )
= $false )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1019]) ).
thf(1099,plain,
! [SV69: $i,SV11: $i,SV107: $i,SV148: $i] :
( ( ( ~ ( ~ ( in @ SV148 @ SV107 )
| ~ ! [SY597: $i] :
~ ~ ! [SY598: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY597 @ SV11 )
| ~ ( in @ SY598 @ SV69 ) )
| ( SV148
!= ( ordered_pair @ SY597 @ SY598 ) ) ) )
| ~ ( ~ ~ ! [SY599: $i] :
~ ~ ! [SY600: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY599 @ SV11 )
| ~ ( in @ SY600 @ SV69 ) )
| ( SV148
!= ( ordered_pair @ SY599 @ SY600 ) ) )
| ( in @ SV148 @ SV107 ) ) )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1020]) ).
thf(1100,plain,
! [SV107: $i,SV11: $i,SV69: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 )
| ~ ! [SY601: $i] :
~ ~ ! [SY602: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY601 @ SV11 )
| ~ ( in @ SY602 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SY601 @ SY602 ) ) ) )
| ~ ( ~ ~ ! [SY603: $i] :
~ ~ ! [SY604: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY603 @ SV11 )
| ~ ( in @ SY604 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SY603 @ SY604 ) ) )
| ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 ) ) )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1021]) ).
thf(1101,plain,
! [SV12: $i,SV70: $i,SV153: $i] :
( ( ( ! [SY605: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV153 @ SY605 ) @ SV70 )
| ~ ( ~ ( in @ SV153 @ SV12 )
| ( SV153 != SY605 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV153 @ SV12 )
| ( SV153 != SY605 ) )
| ( in @ ( ordered_pair @ SV153 @ SY605 ) @ SV70 ) ) ) )
= $true )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1102,plain,
! [SV70: $i,SV12: $i] :
( ( ( ! [SY606: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK20_SY424 @ SV12 @ SV70 ) @ SY606 ) @ SV70 )
| ~ ( ~ ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
| ( ( sK20_SY424 @ SV12 @ SV70 )
!= SY606 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
| ( ( sK20_SY424 @ SV12 @ SV70 )
!= SY606 ) )
| ( in @ ( ordered_pair @ ( sK20_SY424 @ SV12 @ SV70 ) @ SY606 ) @ SV70 ) ) ) )
= $false )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1023]) ).
thf(1103,plain,
! [SV13: $i,SV71: $i,SV142: $i] :
( ( ( ~ ( ~ ( in @ SV142 @ SV71 )
| ( subset @ SV142 @ SV13 ) ) )
= $false )
| ( ( SV71
= ( powerset @ SV13 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1024]) ).
thf(1104,plain,
! [SV71: $i,SV13: $i,SV142: $i] :
( ( ( ~ ( ~ ( subset @ SV142 @ SV13 )
| ( in @ SV142 @ SV71 ) ) )
= $false )
| ( ( SV71
= ( powerset @ SV13 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1024]) ).
thf(1105,plain,
! [SV71: $i,SV13: $i] :
( ( ( ~ ( ~ ( in @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV71 )
| ( subset @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV13 ) ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV13 )
| ( in @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV71 ) ) )
= $true )
| ( ( SV71
= ( powerset @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1025]) ).
thf(1106,plain,
! [SV125: $i,SV14: $i,SV134: $i] :
( ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $false )
| ( ( ! [SY560: $i] :
~ ( ~ ( ~ ( in @ SY560 @ SV134 )
| ~ ! [SY523: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY560 @ SY523 ) @ SV14 )
| ~ ( in @ SY523 @ SV125 ) ) )
| ~ ( ~ ~ ! [SY524: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY560 @ SY524 ) @ SV14 )
| ~ ( in @ SY524 @ SV125 ) )
| ( in @ SY560 @ SV134 ) ) ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1026]) ).
thf(1107,plain,
! [SV125: $i,SV14: $i,SV134: $i] :
( ( ( ! [SY563: $i] :
~ ( ~ ( ~ ( in @ SY563 @ SV134 )
| ~ ! [SY526: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY563 @ SY526 ) @ SV14 )
| ~ ( in @ SY526 @ SV125 ) ) )
| ~ ( ~ ~ ! [SY527: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY563 @ SY527 ) @ SV14 )
| ~ ( in @ SY527 @ SV125 ) )
| ( in @ SY563 @ SV134 ) ) ) )
= $false )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1027]) ).
thf(1108,plain,
! [SV15: $i,SV126: $i,SV154: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV154 @ SV126 )
| ~ ! [SY607: $i] :
~ ( in @ ( ordered_pair @ SY607 @ SV154 ) @ SV15 ) )
| ~ ( ~ ~ ! [SY608: $i] :
~ ( in @ ( ordered_pair @ SY608 @ SV154 ) @ SV15 )
| ( in @ SV154 @ SV126 ) ) ) )
= $true )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $false )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1109,plain,
! [SV126: $i,SV15: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK21_SY531 @ SV15 @ SV126 ) @ SV126 )
| ~ ! [SY609: $i] :
~ ( in @ ( ordered_pair @ SY609 @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 ) )
| ~ ( ~ ~ ! [SY610: $i] :
~ ( in @ ( ordered_pair @ SY610 @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 )
| ( in @ ( sK21_SY531 @ SV15 @ SV126 ) @ SV126 ) ) ) )
= $false )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1029]) ).
thf(1110,plain,
! [SV127: $i,SV16: $i] :
( ( ( ~ ( subset @ SV16 @ SV127 ) )
= $true )
| ( ( ! [SY534: $i,SY535: $i] :
( ~ ( in @ ( ordered_pair @ SY534 @ SY535 ) @ SV16 )
| ( in @ ( ordered_pair @ SY534 @ SY535 ) @ SV127 ) ) )
= $true )
| ( ( relation @ SV127 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1030]) ).
thf(1111,plain,
! [SV127: $i,SV16: $i] :
( ( ( ~ ! [SY536: $i,SY537: $i] :
( ~ ( in @ ( ordered_pair @ SY536 @ SY537 ) @ SV16 )
| ( in @ ( ordered_pair @ SY536 @ SY537 ) @ SV127 ) ) )
= $true )
| ( ( subset @ SV16 @ SV127 )
= $true )
| ( ( relation @ SV127 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1031]) ).
thf(1112,plain,
! [SV72: $i,SV17: $i,SV108: $i,SV149: $i] :
( ( ( ~ ( ~ ( in @ SV149 @ SV108 )
| ( in @ SV149 @ SV17 )
| ( in @ SV149 @ SV72 ) )
| ~ ( ~ ( ( in @ SV149 @ SV17 )
| ( in @ SV149 @ SV72 ) )
| ( in @ SV149 @ SV108 ) ) )
= $false )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1032]) ).
thf(1113,plain,
! [SV108: $i,SV17: $i,SV72: $i] :
( ( ( ~ ( ~ ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV108 )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV17 )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV72 ) )
| ~ ( ~ ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV17 )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV72 ) )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV108 ) ) )
= $true )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1033]) ).
thf(1114,plain,
! [SV128: $i,SV20: $i,SV135: $i] :
( ( ( ( SV135
!= ( relation_dom_restriction @ SV20 @ SV128 ) )
| ! [SY566: $i,SY567: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV135 )
| ~ ( ~ ( in @ SY566 @ SV128 )
| ~ ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY566 @ SV128 )
| ~ ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV20 ) )
| ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV135 ) ) ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1034]) ).
thf(1115,plain,
! [SV20: $i,SV128: $i,SV135: $i] :
( ( ( ~ ! [SY568: $i,SY569: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY568 @ SY569 ) @ SV135 )
| ~ ( ~ ( in @ SY568 @ SV128 )
| ~ ( in @ ( ordered_pair @ SY568 @ SY569 ) @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY568 @ SV128 )
| ~ ( in @ ( ordered_pair @ SY568 @ SY569 ) @ SV20 ) )
| ( in @ ( ordered_pair @ SY568 @ SY569 ) @ SV135 ) ) )
| ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1035]) ).
thf(1116,plain,
! [SV74: $i,SV21: $i] :
( ( ( disjoint @ SV21 @ SV74 )
= $true )
| ( ( ~ ! [SY431: $i] :
~ ~ ( ~ ( in @ SY431 @ SV21 )
| ~ ( in @ SY431 @ SV74 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1036]) ).
thf(1117,plain,
! [SV74: $i,SV21: $i] :
( ( ( ! [SY432: $i] :
~ ~ ( ~ ( in @ SY432 @ SV21 )
| ~ ( in @ SY432 @ SV74 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV21 @ SV74 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1037]) ).
thf(1118,plain,
! [SV109: $i,SV75: $i,SV22: $i] :
( ( ( in @ SV22 @ ( relation_rng @ ( relation_rng_restriction @ SV75 @ SV109 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV22 @ SV75 )
| ~ ( in @ SV22 @ ( relation_rng @ SV109 ) ) ) )
= $true )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1038]) ).
thf(1119,plain,
! [SV109: $i,SV75: $i,SV22: $i] :
( ( ( ~ ( ~ ( in @ SV22 @ SV75 )
| ~ ( in @ SV22 @ ( relation_rng @ SV109 ) ) ) )
= $false )
| ( ( in @ SV22 @ ( relation_rng @ ( relation_rng_restriction @ SV75 @ SV109 ) ) )
= $true )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1039]) ).
thf(1120,plain,
! [SV23: $i] :
( ( ~ ( ~ ( in @ SV23 @ ( sK3_SY291 @ SV23 ) )
| ~ ! [SY490: $i,SY491: $i] :
( ~ ~ ( ~ ( in @ SY490 @ ( sK3_SY291 @ SV23 ) )
| ~ ( subset @ SY491 @ SY490 ) )
| ( in @ SY491 @ ( sK3_SY291 @ SV23 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1040]) ).
thf(1121,plain,
! [SV23: $i] :
( ( ! [SY492: $i] :
( ~ ( in @ SY492 @ ( sK3_SY291 @ SV23 ) )
| ( in @ ( powerset @ SY492 ) @ ( sK3_SY291 @ SV23 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1041]) ).
thf(1122,plain,
! [SV23: $i,SV143: $i] :
( ( ~ ~ ( ~ ( subset @ SV143 @ ( sK3_SY291 @ SV23 ) )
| ~ ~ ( are_equipotent @ SV143 @ ( sK3_SY291 @ SV23 ) ) )
| ~ ~ ( in @ SV143 @ ( sK3_SY291 @ SV23 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1042]) ).
thf(1123,plain,
! [SV26: $i,SV78: $i] :
( ( ( ~ ( ( SV78
!= ( set_meet @ SV26 ) )
| ! [SY434: $i] :
~ ( ~ ( ~ ( in @ SY434 @ SV78 )
| ! [SY300: $i] :
( ~ ( in @ SY300 @ SV26 )
| ( in @ SY434 @ SY300 ) ) )
| ~ ( ~ ! [SY301: $i] :
( ~ ( in @ SY301 @ SV26 )
| ( in @ SY434 @ SY301 ) )
| ( in @ SY434 @ SV78 ) ) ) ) )
= $false )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1043]) ).
thf(1124,plain,
! [SV26: $i,SV78: $i] :
( ( ( ~ ( ~ ! [SY437: $i] :
~ ( ~ ( ~ ( in @ SY437 @ SV78 )
| ! [SY303: $i] :
( ~ ( in @ SY303 @ SV26 )
| ( in @ SY437 @ SY303 ) ) )
| ~ ( ~ ! [SY304: $i] :
( ~ ( in @ SY304 @ SV26 )
| ( in @ SY437 @ SY304 ) )
| ( in @ SY437 @ SV78 ) ) )
| ( SV78
= ( set_meet @ SV26 ) ) ) )
= $false )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1043]) ).
thf(1125,plain,
! [SV26: $i,SV78: $i] :
( ( ( ( SV78
!= ( set_meet @ SV26 ) )
| ( SV78 = empty_set ) )
= $true )
| ( ( SV26 = empty_set )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1044]) ).
thf(1126,plain,
! [SV26: $i,SV78: $i] :
( ( ( ( SV78 != empty_set )
| ( SV78
= ( set_meet @ SV26 ) ) )
= $true )
| ( ( SV26 = empty_set )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1045]) ).
thf(1127,plain,
! [SV129: $i,SV110: $i,SV79: $i,SV27: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV27 @ SV79 ) @ ( relation_composition @ ( identity_relation @ SV110 ) @ SV129 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV27 @ SV110 )
| ~ ( in @ ( ordered_pair @ SV27 @ SV79 ) @ SV129 ) ) )
= $true )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1046]) ).
thf(1128,plain,
! [SV129: $i,SV79: $i,SV110: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( in @ SV27 @ SV110 )
| ~ ( in @ ( ordered_pair @ SV27 @ SV79 ) @ SV129 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV27 @ SV79 ) @ ( relation_composition @ ( identity_relation @ SV110 ) @ SV129 ) )
= $true )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1047]) ).
thf(1129,plain,
! [SV130: $i,SV81: $i,SV111: $i,SV29: $i] :
( ( ( ~ ( in @ SV29 @ SV111 )
| ~ ( in @ SV81 @ SV130 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV29 @ SV81 ) @ ( cartesian_product2 @ SV111 @ SV130 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1048]) ).
thf(1130,plain,
! [SV130: $i,SV81: $i,SV111: $i,SV29: $i] :
( ( ( ~ ( in @ SV29 @ SV111 )
| ~ ( in @ SV81 @ SV130 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV29 @ SV81 ) @ ( cartesian_product2 @ SV111 @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1049]) ).
thf(1131,plain,
! [SV131: $i,SV30: $i,SV136: $i] :
( ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $false )
| ( ( ! [SY570: $i] :
~ ( ~ ( ~ ( in @ SY570 @ SV136 )
| ~ ! [SY545: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY545 @ SY570 ) @ SV30 )
| ~ ( in @ SY545 @ SV131 ) ) )
| ~ ( ~ ~ ! [SY546: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY546 @ SY570 ) @ SV30 )
| ~ ( in @ SY546 @ SV131 ) )
| ( in @ SY570 @ SV136 ) ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1050]) ).
thf(1132,plain,
! [SV131: $i,SV30: $i,SV136: $i] :
( ( ( ! [SY573: $i] :
~ ( ~ ( ~ ( in @ SY573 @ SV136 )
| ~ ! [SY548: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY548 @ SY573 ) @ SV30 )
| ~ ( in @ SY548 @ SV131 ) ) )
| ~ ( ~ ~ ! [SY549: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY549 @ SY573 ) @ SV30 )
| ~ ( in @ SY549 @ SV131 ) )
| ( in @ SY573 @ SV136 ) ) ) )
= $false )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1051]) ).
thf(1133,plain,
! [SV82: $i,SV112: $i,SV31: $i] :
( ( ( ~ ( in @ SV31 @ SV112 ) )
= $false )
| ( ( subset @ ( unordered_pair @ SV31 @ SV82 ) @ SV112 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1052]) ).
thf(1134,plain,
! [SV31: $i,SV112: $i,SV82: $i] :
( ( ( ~ ( in @ SV82 @ SV112 ) )
= $false )
| ( ( subset @ ( unordered_pair @ SV31 @ SV82 ) @ SV112 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1052]) ).
thf(1135,plain,
! [SV82: $i,SV112: $i,SV31: $i] :
( ( ( ~ ( in @ SV31 @ SV112 ) )
= $true )
| ( ( ~ ( in @ SV82 @ SV112 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV31 @ SV82 ) @ SV112 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1053]) ).
thf(1136,plain,
! [SV34: $i,SV84: $i] :
( ( ( ~ ( ~ ( element @ SV84 @ SV34 )
| ( in @ SV84 @ SV34 ) ) )
= $false )
| ( ( empty @ SV34 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1055]) ).
thf(1137,plain,
! [SV34: $i,SV84: $i] :
( ( ( ~ ( ~ ( in @ SV84 @ SV34 )
| ( element @ SV84 @ SV34 ) ) )
= $false )
| ( ( empty @ SV34 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1055]) ).
thf(1138,plain,
! [SV34: $i,SV84: $i] :
( ( ( ~ ( element @ SV84 @ SV34 )
| ( empty @ SV84 ) )
= $true )
| ( ( empty @ SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1056]) ).
thf(1139,plain,
! [SV34: $i,SV84: $i] :
( ( ( ~ ( empty @ SV84 )
| ( element @ SV84 @ SV34 ) )
= $true )
| ( ( empty @ SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1057]) ).
thf(1140,plain,
! [SV35: $i,SV140: $i] :
( ( ( ~ ( in @ SV140 @ SV35 ) )
= $true )
| ( ( ~ ! [SY589: $i,SY590: $i] :
( SV140
!= ( ordered_pair @ SY589 @ SY590 ) ) )
= $true )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1058]) ).
thf(1141,plain,
! [SV35: $i] :
( ( ( ~ ( in @ ( sK9_SY328 @ SV35 ) @ SV35 ) )
= $false )
| ( ( relation @ SV35 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1059]) ).
thf(1142,plain,
! [SV35: $i] :
( ( ( ~ ! [SY591: $i,SY592: $i] :
( ( sK9_SY328 @ SV35 )
!= ( ordered_pair @ SY591 @ SY592 ) ) )
= $false )
| ( ( relation @ SV35 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1059]) ).
thf(1143,plain,
! [SV86: $i,SV115: $i,SV37: $i] :
( ( ( in @ SV37 @ ( relation_field @ SV115 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV37 @ SV86 ) @ SV115 )
= $false )
| ( ( relation @ SV115 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1060]) ).
thf(1144,plain,
! [SV37: $i,SV115: $i,SV86: $i] :
( ( ( in @ SV86 @ ( relation_field @ SV115 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV37 @ SV86 ) @ SV115 )
= $false )
| ( ( relation @ SV115 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1061]) ).
thf(1145,plain,
! [SV87: $i,SV39: $i,SV137: $i] :
( ( ( ( SV137
!= ( relation_rng_restriction @ SV39 @ SV87 ) )
| ! [SY576: $i,SY577: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY576 @ SY577 ) @ SV137 )
| ~ ( ~ ( in @ SY577 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY576 @ SY577 ) @ SV87 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY577 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY576 @ SY577 ) @ SV87 ) )
| ( in @ ( ordered_pair @ SY576 @ SY577 ) @ SV137 ) ) ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1062]) ).
thf(1146,plain,
! [SV87: $i,SV39: $i,SV137: $i] :
( ( ( ~ ! [SY578: $i,SY579: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY578 @ SY579 ) @ SV137 )
| ~ ( ~ ( in @ SY579 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY578 @ SY579 ) @ SV87 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY579 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY578 @ SY579 ) @ SV87 ) )
| ( in @ ( ordered_pair @ SY578 @ SY579 ) @ SV137 ) ) )
| ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1063]) ).
thf(1147,plain,
! [SV41: $i,SV88: $i,SV144: $i] :
( ( ( ~ ( ~ ( in @ SV144 @ SV88 )
| ( SV144 = SV41 ) ) )
= $false )
| ( ( SV88
= ( singleton @ SV41 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1064]) ).
thf(1148,plain,
! [SV88: $i,SV41: $i,SV144: $i] :
( ( ( ~ ( ( SV144 != SV41 )
| ( in @ SV144 @ SV88 ) ) )
= $false )
| ( ( SV88
= ( singleton @ SV41 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1064]) ).
thf(1149,plain,
! [SV88: $i,SV41: $i] :
( ( ( ~ ( ~ ( in @ ( sK12_SY454 @ SV41 @ SV88 ) @ SV88 )
| ( ( sK12_SY454 @ SV41 @ SV88 )
= SV41 ) ) )
= $true )
| ( ( ~ ( ( ( sK12_SY454 @ SV41 @ SV88 )
!= SV41 )
| ( in @ ( sK12_SY454 @ SV41 @ SV88 ) @ SV88 ) ) )
= $true )
| ( ( SV88
= ( singleton @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1065]) ).
thf(1150,plain,
! [SV42: $i,SV89: $i,SV145: $i] :
( ( ( ~ ( ~ ( in @ SV145 @ SV89 )
| ~ ! [SY593: $i] :
~ ~ ( ~ ( in @ SV145 @ SY593 )
| ~ ( in @ SY593 @ SV42 ) ) ) )
= $false )
| ( ( SV89
= ( union @ SV42 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1066]) ).
thf(1151,plain,
! [SV89: $i,SV42: $i,SV145: $i] :
( ( ( ~ ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( in @ SV145 @ SY594 )
| ~ ( in @ SY594 @ SV42 ) )
| ( in @ SV145 @ SV89 ) ) )
= $false )
| ( ( SV89
= ( union @ SV42 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1066]) ).
thf(1152,plain,
! [SV89: $i,SV42: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV89 )
| ~ ! [SY595: $i] :
~ ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SY595 )
| ~ ( in @ SY595 @ SV42 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY596: $i] :
~ ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SY596 )
| ~ ( in @ SY596 @ SV42 ) )
| ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1067]) ).
thf(1153,plain,
! [SV90: $i,SV116: $i,SV43: $i] :
( ( ( in @ SV43 @ ( relation_dom @ ( relation_dom_restriction @ SV116 @ SV90 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV43 @ SV90 )
| ~ ( in @ SV43 @ ( relation_dom @ SV116 ) ) ) )
= $true )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1068]) ).
thf(1154,plain,
! [SV116: $i,SV90: $i,SV43: $i] :
( ( ( ~ ( ~ ( in @ SV43 @ SV90 )
| ~ ( in @ SV43 @ ( relation_dom @ SV116 ) ) ) )
= $false )
| ( ( in @ SV43 @ ( relation_dom @ ( relation_dom_restriction @ SV116 @ SV90 ) ) )
= $true )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1069]) ).
thf(1155,plain,
! [SV46: $i] :
( ( ~ ( ~ ( in @ SV46 @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SY496: $i,SY497: $i] :
( ~ ~ ( ~ ( in @ SY496 @ ( sK4_SY357 @ SV46 ) )
| ~ ( subset @ SY497 @ SY496 ) )
| ( in @ SY497 @ ( sK4_SY357 @ SV46 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1070]) ).
thf(1156,plain,
! [SV46: $i] :
( ( ! [SY498: $i] :
~ ~ ( ~ ( in @ SY498 @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SY499: $i] :
~ ~ ( ~ ( in @ SY499 @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY498 )
| ( in @ SX4 @ SY499 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1071]) ).
thf(1157,plain,
! [SV46: $i,SV146: $i] :
( ( ~ ~ ( ~ ( subset @ SV146 @ ( sK4_SY357 @ SV46 ) )
| ~ ~ ( are_equipotent @ SV146 @ ( sK4_SY357 @ SV46 ) ) )
| ~ ~ ( in @ SV146 @ ( sK4_SY357 @ SV46 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1072]) ).
thf(1158,plain,
! [SV47: $i,SV132: $i,SV155: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV155 @ SV132 )
| ~ ! [SY611: $i] :
~ ( in @ ( ordered_pair @ SV155 @ SY611 ) @ SV47 ) )
| ~ ( ~ ~ ! [SY612: $i] :
~ ( in @ ( ordered_pair @ SV155 @ SY612 ) @ SV47 )
| ( in @ SV155 @ SV132 ) ) ) )
= $true )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1073]) ).
thf(1159,plain,
! [SV132: $i,SV47: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK22_SY553 @ SV47 @ SV132 ) @ SV132 )
| ~ ! [SY613: $i] :
~ ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ SY613 ) @ SV47 ) )
| ~ ( ~ ~ ! [SY614: $i] :
~ ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ SY614 ) @ SV47 )
| ( in @ ( sK22_SY553 @ SV47 @ SV132 ) @ SV132 ) ) ) )
= $false )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1074]) ).
thf(1160,plain,
! [SV49: $i,SV133: $i] :
( ( ( SV133
!= ( relation_inverse @ SV49 ) )
= $true )
| ( ( ! [SY556: $i,SY557: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY556 @ SY557 ) @ SV133 )
| ( in @ ( ordered_pair @ SY557 @ SY556 ) @ SV49 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY557 @ SY556 ) @ SV49 )
| ( in @ ( ordered_pair @ SY556 @ SY557 ) @ SV133 ) ) ) )
= $true )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1075]) ).
thf(1161,plain,
! [SV49: $i,SV133: $i] :
( ( ( ~ ! [SY558: $i,SY559: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY558 @ SY559 ) @ SV133 )
| ( in @ ( ordered_pair @ SY559 @ SY558 ) @ SV49 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY559 @ SY558 ) @ SV49 )
| ( in @ ( ordered_pair @ SY558 @ SY559 ) @ SV133 ) ) ) )
= $true )
| ( ( SV133
= ( relation_inverse @ SV49 ) )
= $true )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1076]) ).
thf(1162,plain,
! [SV97: $i,SV53: $i,SV147: $i] :
( ( ( in @ SV147 @ SV53 )
= $false )
| ( ( in @ SV147 @ SV97 )
= $true )
| ( ( subset @ SV53 @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1077]) ).
thf(1163,plain,
! [SV53: $i,SV97: $i] :
( ( ( in @ ( sK14_SY464 @ SV97 @ SV53 ) @ SV53 )
= $true )
| ( ( subset @ SV53 @ SV97 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1078]) ).
thf(1164,plain,
! [SV54: $i,SV117: $i,SV98: $i] :
( ( ( in @ SV98 @ SV117 )
= $false )
| ( ( in @ SV98 @ ( subset_complement @ SV54 @ SV117 ) )
= $false )
| ( ( element @ SV117 @ ( powerset @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1080]) ).
thf(1165,plain,
! [SV100: $i,SV56: $i,SV118: $i,SV150: $i] :
( ( ( ~ ( ~ ( in @ SV150 @ SV118 )
| ( SV150 = SV56 )
| ( SV150 = SV100 ) )
| ~ ( ~ ( ( SV150 = SV56 )
| ( SV150 = SV100 ) )
| ( in @ SV150 @ SV118 ) ) )
= $false )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1081]) ).
thf(1166,plain,
! [SV118: $i,SV56: $i,SV100: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_SY503 @ SV100 @ SV56 @ SV118 ) @ SV118 )
| ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV56 )
| ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV100 ) )
| ~ ( ~ ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV56 )
| ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV100 ) )
| ( in @ ( sK17_SY503 @ SV100 @ SV56 @ SV118 ) @ SV118 ) ) )
= $true )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1082]) ).
thf(1167,plain,
! [SV102: $i,SV58: $i,SV119: $i,SV151: $i] :
( ( ( ~ ( ~ ( in @ SV151 @ SV119 )
| ~ ( ~ ( in @ SV151 @ SV58 )
| ~ ~ ( in @ SV151 @ SV102 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV151 @ SV58 )
| ~ ~ ( in @ SV151 @ SV102 ) )
| ( in @ SV151 @ SV119 ) ) )
= $false )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1083]) ).
thf(1168,plain,
! [SV119: $i,SV58: $i,SV102: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV119 )
| ~ ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
| ~ ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
| ~ ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 ) )
| ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV119 ) ) )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1084]) ).
thf(1169,plain,
! [SV120: $i,SV103: $i,SV59: $i] :
( ( ( in @ SV59 @ SV103 )
= $false )
| ( ( ~ ( element @ SV103 @ ( powerset @ SV120 ) ) )
= $true )
| ( ( ~ ( empty @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1085]) ).
thf(1170,plain,
! [SV104: $i,SV60: $i,SV121: $i,SV152: $i] :
( ( ( ~ ( ~ ( in @ SV152 @ SV121 )
| ~ ( ~ ( in @ SV152 @ SV60 )
| ~ ( in @ SV152 @ SV104 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV152 @ SV60 )
| ~ ( in @ SV152 @ SV104 ) )
| ( in @ SV152 @ SV121 ) ) )
= $false )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1086]) ).
thf(1171,plain,
! [SV121: $i,SV60: $i,SV104: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV121 )
| ~ ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
| ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
| ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 ) )
| ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV121 ) ) )
= $true )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1087]) ).
thf(1172,plain,
! [SV63: $i,SV3: $i] :
( ( ( ! [SY404: $i] :
~ ( in @ SY404 @ ( set_intersection2 @ SV3 @ SV63 ) ) )
= $false )
| ( ( disjoint @ SV3 @ SV63 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1088]) ).
thf(1173,plain,
! [SV63: $i,SV3: $i,SV156: $i] :
( ( ( ~ ( in @ SV156 @ ( set_intersection2 @ SV3 @ SV63 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV3 @ SV63 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1089]) ).
thf(1174,plain,
! [SV5: $i,SV65: $i] :
( ( ( ~ ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV65 )
| ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV5 ) )
= $false )
| ( ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV5 )
= $true )
| ( ( SV5 = SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1090]) ).
thf(1175,plain,
! [SV5: $i,SV65: $i] :
( ( ( ~ ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV65 ) )
= $false )
| ( ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV65 )
= $false )
| ( ( SV5 = SV65 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1091]) ).
thf(1176,plain,
! [SV5: $i,SV65: $i] :
( ( ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV5 )
= $false )
| ( ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV65 )
= $false )
| ( ( SV5 = SV65 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1091]) ).
thf(1177,plain,
! [SV6: $i,SV66: $i] :
( ( ( ( SV66
!= ( identity_relation @ SV6 ) )
| ~ ( ( ( relation_dom @ SV66 )
!= SV6 )
| ~ ! [SY407: $i] :
( ~ ( in @ SY407 @ SV6 )
| ( ( apply @ SV66 @ SY407 )
= SY407 ) ) ) )
= $true )
| ( ( relation @ SV66 )
= $false )
| ( ( function @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1092]) ).
thf(1178,plain,
! [SV6: $i,SV66: $i] :
( ( ( ~ ~ ( ( ( relation_dom @ SV66 )
!= SV6 )
| ~ ! [SY408: $i] :
( ~ ( in @ SY408 @ SV6 )
| ( ( apply @ SV66 @ SY408 )
= SY408 ) ) )
| ( SV66
= ( identity_relation @ SV6 ) ) )
= $true )
| ( ( relation @ SV66 )
= $false )
| ( ( function @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1093]) ).
thf(1179,plain,
! [SV122: $i,SV67: $i,SV106: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV106 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV7 @ SV67 ) @ ( cartesian_product2 @ SV106 @ SV122 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1094]) ).
thf(1180,plain,
! [SV106: $i,SV7: $i,SV122: $i,SV67: $i] :
( ( ( ~ ( in @ SV67 @ SV122 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV7 @ SV67 ) @ ( cartesian_product2 @ SV106 @ SV122 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1094]) ).
thf(1181,plain,
! [SV122: $i,SV67: $i,SV106: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV106 ) )
= $true )
| ( ( ~ ( in @ SV67 @ SV122 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV7 @ SV67 ) @ ( cartesian_product2 @ SV106 @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1095]) ).
thf(1182,plain,
! [SV123: $i,SV8: $i] :
( ( ( SV8 = SV123 )
= $false )
| ( ( ! [SY508: $i,SY509: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY508 @ SY509 ) @ SV8 )
| ( in @ ( ordered_pair @ SY508 @ SY509 ) @ SV123 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY508 @ SY509 ) @ SV123 )
| ( in @ ( ordered_pair @ SY508 @ SY509 ) @ SV8 ) ) ) )
= $true )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1096]) ).
thf(1183,plain,
! [SV123: $i,SV8: $i] :
( ( ( ! [SY510: $i,SY511: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY510 @ SY511 ) @ SV8 )
| ( in @ ( ordered_pair @ SY510 @ SY511 ) @ SV123 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY510 @ SY511 ) @ SV123 )
| ( in @ ( ordered_pair @ SY510 @ SY511 ) @ SV8 ) ) ) )
= $false )
| ( ( SV8 = SV123 )
= $true )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1097]) ).
thf(1184,plain,
! [SV124: $i,SV10: $i,SV139: $i] :
( ( ( ~ ( ( SV139
!= ( relation_composition @ SV10 @ SV124 ) )
| ! [SY581: $i,SY582: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY581 @ SY582 ) @ SV139 )
| ~ ! [SY515: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY581 @ SY515 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY515 @ SY582 ) @ SV124 ) ) )
| ~ ( ~ ~ ! [SY516: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY581 @ SY516 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY516 @ SY582 ) @ SV124 ) )
| ( in @ ( ordered_pair @ SY581 @ SY582 ) @ SV139 ) ) ) ) )
= $false )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1098]) ).
thf(1185,plain,
! [SV124: $i,SV10: $i,SV139: $i] :
( ( ( ~ ( ~ ! [SY585: $i,SY586: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY585 @ SY586 ) @ SV139 )
| ~ ! [SY519: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY585 @ SY519 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY519 @ SY586 ) @ SV124 ) ) )
| ~ ( ~ ~ ! [SY520: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY585 @ SY520 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY520 @ SY586 ) @ SV124 ) )
| ( in @ ( ordered_pair @ SY585 @ SY586 ) @ SV139 ) ) )
| ( SV139
= ( relation_composition @ SV10 @ SV124 ) ) ) )
= $false )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1098]) ).
thf(1186,plain,
! [SV69: $i,SV11: $i,SV107: $i,SV148: $i] :
( ( ( ~ ( ~ ( in @ SV148 @ SV107 )
| ~ ! [SY597: $i] :
~ ~ ! [SY598: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY597 @ SV11 )
| ~ ( in @ SY598 @ SV69 ) )
| ( SV148
!= ( ordered_pair @ SY597 @ SY598 ) ) ) ) )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1099]) ).
thf(1187,plain,
! [SV107: $i,SV148: $i,SV69: $i,SV11: $i] :
( ( ( ~ ( ~ ~ ! [SY599: $i] :
~ ~ ! [SY600: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY599 @ SV11 )
| ~ ( in @ SY600 @ SV69 ) )
| ( SV148
!= ( ordered_pair @ SY599 @ SY600 ) ) )
| ( in @ SV148 @ SV107 ) ) )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1099]) ).
thf(1188,plain,
! [SV107: $i,SV11: $i,SV69: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 )
| ~ ! [SY601: $i] :
~ ~ ! [SY602: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY601 @ SV11 )
| ~ ( in @ SY602 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SY601 @ SY602 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY603: $i] :
~ ~ ! [SY604: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY603 @ SV11 )
| ~ ( in @ SY604 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SY603 @ SY604 ) ) )
| ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 ) ) )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1100]) ).
thf(1189,plain,
! [SV12: $i,SV70: $i,SV157: $i,SV153: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV153 @ SV157 ) @ SV70 )
| ~ ( ~ ( in @ SV153 @ SV12 )
| ( SV153 != SV157 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV153 @ SV12 )
| ( SV153 != SV157 ) )
| ( in @ ( ordered_pair @ SV153 @ SV157 ) @ SV70 ) ) ) )
= $true )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1190,plain,
! [SV70: $i,SV12: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK20_SY424 @ SV12 @ SV70 ) @ ( sK23_SY606 @ SV70 @ SV12 ) ) @ SV70 )
| ~ ( ~ ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
| ( ( sK20_SY424 @ SV12 @ SV70 )
!= ( sK23_SY606 @ SV70 @ SV12 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
| ( ( sK20_SY424 @ SV12 @ SV70 )
!= ( sK23_SY606 @ SV70 @ SV12 ) ) )
| ( in @ ( ordered_pair @ ( sK20_SY424 @ SV12 @ SV70 ) @ ( sK23_SY606 @ SV70 @ SV12 ) ) @ SV70 ) ) ) )
= $false )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1102]) ).
thf(1191,plain,
! [SV13: $i,SV71: $i,SV142: $i] :
( ( ( ~ ( in @ SV142 @ SV71 )
| ( subset @ SV142 @ SV13 ) )
= $true )
| ( ( SV71
= ( powerset @ SV13 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1103]) ).
thf(1192,plain,
! [SV71: $i,SV13: $i,SV142: $i] :
( ( ( ~ ( subset @ SV142 @ SV13 )
| ( in @ SV142 @ SV71 ) )
= $true )
| ( ( SV71
= ( powerset @ SV13 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1104]) ).
thf(1193,plain,
! [SV71: $i,SV13: $i] :
( ( ( ~ ( in @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV71 )
| ( subset @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV13 ) )
= $false )
| ( ( ~ ( ~ ( subset @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV13 )
| ( in @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV71 ) ) )
= $true )
| ( ( SV71
= ( powerset @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1105]) ).
thf(1194,plain,
! [SV125: $i,SV14: $i,SV134: $i,SV158: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV158 @ SV134 )
| ~ ! [SY615: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV158 @ SY615 ) @ SV14 )
| ~ ( in @ SY615 @ SV125 ) ) )
| ~ ( ~ ~ ! [SY616: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV158 @ SY616 ) @ SV14 )
| ~ ( in @ SY616 @ SV125 ) )
| ( in @ SV158 @ SV134 ) ) ) )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1106]) ).
thf(1195,plain,
! [SV134: $i,SV14: $i,SV125: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV134 )
| ~ ! [SY617: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SY617 ) @ SV14 )
| ~ ( in @ SY617 @ SV125 ) ) )
| ~ ( ~ ~ ! [SY618: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SY618 ) @ SV14 )
| ~ ( in @ SY618 @ SV125 ) )
| ( in @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV134 ) ) ) )
= $false )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1107]) ).
thf(1196,plain,
! [SV15: $i,SV126: $i,SV154: $i] :
( ( ( ~ ( ~ ( in @ SV154 @ SV126 )
| ~ ! [SY607: $i] :
~ ( in @ ( ordered_pair @ SY607 @ SV154 ) @ SV15 ) )
| ~ ( ~ ~ ! [SY608: $i] :
~ ( in @ ( ordered_pair @ SY608 @ SV154 ) @ SV15 )
| ( in @ SV154 @ SV126 ) ) )
= $false )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $false )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1108]) ).
thf(1197,plain,
! [SV126: $i,SV15: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_SY531 @ SV15 @ SV126 ) @ SV126 )
| ~ ! [SY609: $i] :
~ ( in @ ( ordered_pair @ SY609 @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 ) )
| ~ ( ~ ~ ! [SY610: $i] :
~ ( in @ ( ordered_pair @ SY610 @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 )
| ( in @ ( sK21_SY531 @ SV15 @ SV126 ) @ SV126 ) ) )
= $true )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1109]) ).
thf(1198,plain,
! [SV127: $i,SV16: $i] :
( ( ( subset @ SV16 @ SV127 )
= $false )
| ( ( ! [SY534: $i,SY535: $i] :
( ~ ( in @ ( ordered_pair @ SY534 @ SY535 ) @ SV16 )
| ( in @ ( ordered_pair @ SY534 @ SY535 ) @ SV127 ) ) )
= $true )
| ( ( relation @ SV127 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1110]) ).
thf(1199,plain,
! [SV127: $i,SV16: $i] :
( ( ( ! [SY536: $i,SY537: $i] :
( ~ ( in @ ( ordered_pair @ SY536 @ SY537 ) @ SV16 )
| ( in @ ( ordered_pair @ SY536 @ SY537 ) @ SV127 ) ) )
= $false )
| ( ( subset @ SV16 @ SV127 )
= $true )
| ( ( relation @ SV127 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1111]) ).
thf(1200,plain,
! [SV72: $i,SV17: $i,SV108: $i,SV149: $i] :
( ( ( ~ ( ~ ( in @ SV149 @ SV108 )
| ( in @ SV149 @ SV17 )
| ( in @ SV149 @ SV72 ) ) )
= $false )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1112]) ).
thf(1201,plain,
! [SV108: $i,SV72: $i,SV17: $i,SV149: $i] :
( ( ( ~ ( ~ ( ( in @ SV149 @ SV17 )
| ( in @ SV149 @ SV72 ) )
| ( in @ SV149 @ SV108 ) ) )
= $false )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1112]) ).
thf(1202,plain,
! [SV108: $i,SV17: $i,SV72: $i] :
( ( ( ~ ( ~ ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV108 )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV17 )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV72 ) ) )
= $true )
| ( ( ~ ( ~ ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV17 )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV72 ) )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV108 ) ) )
= $true )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1113]) ).
thf(1203,plain,
! [SV128: $i,SV20: $i,SV135: $i] :
( ( ( SV135
!= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $true )
| ( ( ! [SY566: $i,SY567: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV135 )
| ~ ( ~ ( in @ SY566 @ SV128 )
| ~ ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY566 @ SV128 )
| ~ ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV20 ) )
| ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV135 ) ) ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1114]) ).
thf(1204,plain,
! [SV20: $i,SV128: $i,SV135: $i] :
( ( ( ~ ! [SY568: $i,SY569: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY568 @ SY569 ) @ SV135 )
| ~ ( ~ ( in @ SY568 @ SV128 )
| ~ ( in @ ( ordered_pair @ SY568 @ SY569 ) @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY568 @ SV128 )
| ~ ( in @ ( ordered_pair @ SY568 @ SY569 ) @ SV20 ) )
| ( in @ ( ordered_pair @ SY568 @ SY569 ) @ SV135 ) ) ) )
= $true )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1115]) ).
thf(1205,plain,
! [SV74: $i,SV21: $i] :
( ( ( ! [SY431: $i] :
~ ~ ( ~ ( in @ SY431 @ SV21 )
| ~ ( in @ SY431 @ SV74 ) ) )
= $false )
| ( ( disjoint @ SV21 @ SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1116]) ).
thf(1206,plain,
! [SV74: $i,SV21: $i,SV159: $i] :
( ( ( ~ ~ ( ~ ( in @ SV159 @ SV21 )
| ~ ( in @ SV159 @ SV74 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV21 @ SV74 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1207,plain,
! [SV109: $i,SV75: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ SV75 )
| ~ ( in @ SV22 @ ( relation_rng @ SV109 ) ) )
= $false )
| ( ( in @ SV22 @ ( relation_rng @ ( relation_rng_restriction @ SV75 @ SV109 ) ) )
= $false )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1118]) ).
thf(1208,plain,
! [SV109: $i,SV75: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ SV75 )
| ~ ( in @ SV22 @ ( relation_rng @ SV109 ) ) )
= $true )
| ( ( in @ SV22 @ ( relation_rng @ ( relation_rng_restriction @ SV75 @ SV109 ) ) )
= $true )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1119]) ).
thf(1209,plain,
! [SV23: $i] :
( ( ~ ( in @ SV23 @ ( sK3_SY291 @ SV23 ) )
| ~ ! [SY490: $i,SY491: $i] :
( ~ ~ ( ~ ( in @ SY490 @ ( sK3_SY291 @ SV23 ) )
| ~ ( subset @ SY491 @ SY490 ) )
| ( in @ SY491 @ ( sK3_SY291 @ SV23 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1120]) ).
thf(1210,plain,
! [SV23: $i,SV160: $i] :
( ( ~ ( in @ SV160 @ ( sK3_SY291 @ SV23 ) )
| ( in @ ( powerset @ SV160 ) @ ( sK3_SY291 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1211,plain,
! [SV23: $i,SV143: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV143 @ ( sK3_SY291 @ SV23 ) )
| ~ ~ ( are_equipotent @ SV143 @ ( sK3_SY291 @ SV23 ) ) ) )
= $true )
| ( ( ~ ~ ( in @ SV143 @ ( sK3_SY291 @ SV23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1122]) ).
thf(1212,plain,
! [SV26: $i,SV78: $i] :
( ( ( ( SV78
!= ( set_meet @ SV26 ) )
| ! [SY434: $i] :
~ ( ~ ( ~ ( in @ SY434 @ SV78 )
| ! [SY300: $i] :
( ~ ( in @ SY300 @ SV26 )
| ( in @ SY434 @ SY300 ) ) )
| ~ ( ~ ! [SY301: $i] :
( ~ ( in @ SY301 @ SV26 )
| ( in @ SY434 @ SY301 ) )
| ( in @ SY434 @ SV78 ) ) ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1123]) ).
thf(1213,plain,
! [SV26: $i,SV78: $i] :
( ( ( ~ ! [SY437: $i] :
~ ( ~ ( ~ ( in @ SY437 @ SV78 )
| ! [SY303: $i] :
( ~ ( in @ SY303 @ SV26 )
| ( in @ SY437 @ SY303 ) ) )
| ~ ( ~ ! [SY304: $i] :
( ~ ( in @ SY304 @ SV26 )
| ( in @ SY437 @ SY304 ) )
| ( in @ SY437 @ SV78 ) ) )
| ( SV78
= ( set_meet @ SV26 ) ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1124]) ).
thf(1214,plain,
! [SV26: $i,SV78: $i] :
( ( ( SV78
!= ( set_meet @ SV26 ) )
= $true )
| ( ( SV78 = empty_set )
= $true )
| ( ( SV26 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1125]) ).
thf(1215,plain,
! [SV26: $i,SV78: $i] :
( ( ( SV78 != empty_set )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1126]) ).
thf(1216,plain,
! [SV129: $i,SV110: $i,SV79: $i,SV27: $i] :
( ( ( in @ ( ordered_pair @ SV27 @ SV79 ) @ ( relation_composition @ ( identity_relation @ SV110 ) @ SV129 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV27 @ SV110 )
| ~ ( in @ ( ordered_pair @ SV27 @ SV79 ) @ SV129 ) ) )
= $true )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1127]) ).
thf(1217,plain,
! [SV129: $i,SV79: $i,SV110: $i,SV27: $i] :
( ( ( ~ ( ~ ( in @ SV27 @ SV110 )
| ~ ( in @ ( ordered_pair @ SV27 @ SV79 ) @ SV129 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV27 @ SV79 ) @ ( relation_composition @ ( identity_relation @ SV110 ) @ SV129 ) )
= $true )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1128]) ).
thf(1218,plain,
! [SV130: $i,SV81: $i,SV111: $i,SV29: $i] :
( ( ( ~ ( in @ SV29 @ SV111 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV29 @ SV81 ) @ ( cartesian_product2 @ SV111 @ SV130 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1129]) ).
thf(1219,plain,
! [SV111: $i,SV29: $i,SV130: $i,SV81: $i] :
( ( ( ~ ( in @ SV81 @ SV130 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV29 @ SV81 ) @ ( cartesian_product2 @ SV111 @ SV130 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1129]) ).
thf(1220,plain,
! [SV130: $i,SV81: $i,SV111: $i,SV29: $i] :
( ( ( ~ ( in @ SV29 @ SV111 ) )
= $true )
| ( ( ~ ( in @ SV81 @ SV130 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV29 @ SV81 ) @ ( cartesian_product2 @ SV111 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1130]) ).
thf(1221,plain,
! [SV131: $i,SV30: $i,SV136: $i,SV161: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV161 @ SV136 )
| ~ ! [SY619: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY619 @ SV161 ) @ SV30 )
| ~ ( in @ SY619 @ SV131 ) ) )
| ~ ( ~ ~ ! [SY620: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY620 @ SV161 ) @ SV30 )
| ~ ( in @ SY620 @ SV131 ) )
| ( in @ SV161 @ SV136 ) ) ) )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1131]) ).
thf(1222,plain,
! [SV136: $i,SV30: $i,SV131: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) @ SV136 )
| ~ ! [SY621: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY621 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ SY621 @ SV131 ) ) )
| ~ ( ~ ~ ! [SY622: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY622 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ SY622 @ SV131 ) )
| ( in @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) @ SV136 ) ) ) )
= $false )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1132]) ).
thf(1223,plain,
! [SV82: $i,SV112: $i,SV31: $i] :
( ( ( in @ SV31 @ SV112 )
= $true )
| ( ( subset @ ( unordered_pair @ SV31 @ SV82 ) @ SV112 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1133]) ).
thf(1224,plain,
! [SV31: $i,SV112: $i,SV82: $i] :
( ( ( in @ SV82 @ SV112 )
= $true )
| ( ( subset @ ( unordered_pair @ SV31 @ SV82 ) @ SV112 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1134]) ).
thf(1225,plain,
! [SV82: $i,SV112: $i,SV31: $i] :
( ( ( in @ SV31 @ SV112 )
= $false )
| ( ( ~ ( in @ SV82 @ SV112 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV31 @ SV82 ) @ SV112 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1135]) ).
thf(1226,plain,
! [SV34: $i,SV84: $i] :
( ( ( ~ ( element @ SV84 @ SV34 )
| ( in @ SV84 @ SV34 ) )
= $true )
| ( ( empty @ SV34 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1136]) ).
thf(1227,plain,
! [SV34: $i,SV84: $i] :
( ( ( ~ ( in @ SV84 @ SV34 )
| ( element @ SV84 @ SV34 ) )
= $true )
| ( ( empty @ SV34 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1137]) ).
thf(1228,plain,
! [SV34: $i,SV84: $i] :
( ( ( ~ ( element @ SV84 @ SV34 ) )
= $true )
| ( ( empty @ SV84 )
= $true )
| ( ( empty @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1138]) ).
thf(1229,plain,
! [SV34: $i,SV84: $i] :
( ( ( ~ ( empty @ SV84 ) )
= $true )
| ( ( element @ SV84 @ SV34 )
= $true )
| ( ( empty @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1139]) ).
thf(1230,plain,
! [SV35: $i,SV140: $i] :
( ( ( in @ SV140 @ SV35 )
= $false )
| ( ( ~ ! [SY589: $i,SY590: $i] :
( SV140
!= ( ordered_pair @ SY589 @ SY590 ) ) )
= $true )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1140]) ).
thf(1231,plain,
! [SV35: $i] :
( ( ( in @ ( sK9_SY328 @ SV35 ) @ SV35 )
= $true )
| ( ( relation @ SV35 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1141]) ).
thf(1232,plain,
! [SV35: $i] :
( ( ( ! [SY591: $i,SY592: $i] :
( ( sK9_SY328 @ SV35 )
!= ( ordered_pair @ SY591 @ SY592 ) ) )
= $true )
| ( ( relation @ SV35 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1142]) ).
thf(1233,plain,
! [SV87: $i,SV39: $i,SV137: $i] :
( ( ( SV137
!= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $true )
| ( ( ! [SY576: $i,SY577: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY576 @ SY577 ) @ SV137 )
| ~ ( ~ ( in @ SY577 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY576 @ SY577 ) @ SV87 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY577 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY576 @ SY577 ) @ SV87 ) )
| ( in @ ( ordered_pair @ SY576 @ SY577 ) @ SV137 ) ) ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1145]) ).
thf(1234,plain,
! [SV87: $i,SV39: $i,SV137: $i] :
( ( ( ~ ! [SY578: $i,SY579: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY578 @ SY579 ) @ SV137 )
| ~ ( ~ ( in @ SY579 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY578 @ SY579 ) @ SV87 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY579 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY578 @ SY579 ) @ SV87 ) )
| ( in @ ( ordered_pair @ SY578 @ SY579 ) @ SV137 ) ) ) )
= $true )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1146]) ).
thf(1235,plain,
! [SV41: $i,SV88: $i,SV144: $i] :
( ( ( ~ ( in @ SV144 @ SV88 )
| ( SV144 = SV41 ) )
= $true )
| ( ( SV88
= ( singleton @ SV41 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1147]) ).
thf(1236,plain,
! [SV88: $i,SV41: $i,SV144: $i] :
( ( ( ( SV144 != SV41 )
| ( in @ SV144 @ SV88 ) )
= $true )
| ( ( SV88
= ( singleton @ SV41 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1148]) ).
thf(1237,plain,
! [SV88: $i,SV41: $i] :
( ( ( ~ ( in @ ( sK12_SY454 @ SV41 @ SV88 ) @ SV88 )
| ( ( sK12_SY454 @ SV41 @ SV88 )
= SV41 ) )
= $false )
| ( ( ~ ( ( ( sK12_SY454 @ SV41 @ SV88 )
!= SV41 )
| ( in @ ( sK12_SY454 @ SV41 @ SV88 ) @ SV88 ) ) )
= $true )
| ( ( SV88
= ( singleton @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1149]) ).
thf(1238,plain,
! [SV42: $i,SV89: $i,SV145: $i] :
( ( ( ~ ( in @ SV145 @ SV89 )
| ~ ! [SY593: $i] :
~ ~ ( ~ ( in @ SV145 @ SY593 )
| ~ ( in @ SY593 @ SV42 ) ) )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1150]) ).
thf(1239,plain,
! [SV89: $i,SV42: $i,SV145: $i] :
( ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( in @ SV145 @ SY594 )
| ~ ( in @ SY594 @ SV42 ) )
| ( in @ SV145 @ SV89 ) )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1151]) ).
thf(1240,plain,
! [SV89: $i,SV42: $i] :
( ( ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV89 )
| ~ ! [SY595: $i] :
~ ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SY595 )
| ~ ( in @ SY595 @ SV42 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY596: $i] :
~ ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SY596 )
| ~ ( in @ SY596 @ SV42 ) )
| ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1152]) ).
thf(1241,plain,
! [SV116: $i,SV90: $i,SV43: $i] :
( ( ( ~ ( in @ SV43 @ SV90 )
| ~ ( in @ SV43 @ ( relation_dom @ SV116 ) ) )
= $false )
| ( ( in @ SV43 @ ( relation_dom @ ( relation_dom_restriction @ SV116 @ SV90 ) ) )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1153]) ).
thf(1242,plain,
! [SV116: $i,SV90: $i,SV43: $i] :
( ( ( ~ ( in @ SV43 @ SV90 )
| ~ ( in @ SV43 @ ( relation_dom @ SV116 ) ) )
= $true )
| ( ( in @ SV43 @ ( relation_dom @ ( relation_dom_restriction @ SV116 @ SV90 ) ) )
= $true )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1154]) ).
thf(1243,plain,
! [SV46: $i] :
( ( ~ ( in @ SV46 @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SY496: $i,SY497: $i] :
( ~ ~ ( ~ ( in @ SY496 @ ( sK4_SY357 @ SV46 ) )
| ~ ( subset @ SY497 @ SY496 ) )
| ( in @ SY497 @ ( sK4_SY357 @ SV46 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1155]) ).
thf(1244,plain,
! [SV46: $i,SV162: $i] :
( ( ~ ~ ( ~ ( in @ SV162 @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SY623: $i] :
~ ~ ( ~ ( in @ SY623 @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SY624: $i] :
( ~ ( subset @ SY624 @ SV162 )
| ( in @ SY624 @ SY623 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1156]) ).
thf(1245,plain,
! [SV46: $i,SV146: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV146 @ ( sK4_SY357 @ SV46 ) )
| ~ ~ ( are_equipotent @ SV146 @ ( sK4_SY357 @ SV46 ) ) ) )
= $true )
| ( ( ~ ~ ( in @ SV146 @ ( sK4_SY357 @ SV46 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1157]) ).
thf(1246,plain,
! [SV47: $i,SV132: $i,SV155: $i] :
( ( ( ~ ( ~ ( in @ SV155 @ SV132 )
| ~ ! [SY611: $i] :
~ ( in @ ( ordered_pair @ SV155 @ SY611 ) @ SV47 ) )
| ~ ( ~ ~ ! [SY612: $i] :
~ ( in @ ( ordered_pair @ SV155 @ SY612 ) @ SV47 )
| ( in @ SV155 @ SV132 ) ) )
= $false )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1158]) ).
thf(1247,plain,
! [SV132: $i,SV47: $i] :
( ( ( ~ ( ~ ( in @ ( sK22_SY553 @ SV47 @ SV132 ) @ SV132 )
| ~ ! [SY613: $i] :
~ ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ SY613 ) @ SV47 ) )
| ~ ( ~ ~ ! [SY614: $i] :
~ ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ SY614 ) @ SV47 )
| ( in @ ( sK22_SY553 @ SV47 @ SV132 ) @ SV132 ) ) )
= $true )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1159]) ).
thf(1248,plain,
! [SV49: $i,SV133: $i] :
( ( ( SV133
= ( relation_inverse @ SV49 ) )
= $false )
| ( ( ! [SY556: $i,SY557: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY556 @ SY557 ) @ SV133 )
| ( in @ ( ordered_pair @ SY557 @ SY556 ) @ SV49 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY557 @ SY556 ) @ SV49 )
| ( in @ ( ordered_pair @ SY556 @ SY557 ) @ SV133 ) ) ) )
= $true )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1160]) ).
thf(1249,plain,
! [SV49: $i,SV133: $i] :
( ( ( ! [SY558: $i,SY559: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY558 @ SY559 ) @ SV133 )
| ( in @ ( ordered_pair @ SY559 @ SY558 ) @ SV49 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY559 @ SY558 ) @ SV49 )
| ( in @ ( ordered_pair @ SY558 @ SY559 ) @ SV133 ) ) ) )
= $false )
| ( ( SV133
= ( relation_inverse @ SV49 ) )
= $true )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1161]) ).
thf(1250,plain,
! [SV100: $i,SV56: $i,SV118: $i,SV150: $i] :
( ( ( ~ ( ~ ( in @ SV150 @ SV118 )
| ( SV150 = SV56 )
| ( SV150 = SV100 ) ) )
= $false )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1165]) ).
thf(1251,plain,
! [SV118: $i,SV100: $i,SV56: $i,SV150: $i] :
( ( ( ~ ( ~ ( ( SV150 = SV56 )
| ( SV150 = SV100 ) )
| ( in @ SV150 @ SV118 ) ) )
= $false )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1165]) ).
thf(1252,plain,
! [SV118: $i,SV56: $i,SV100: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_SY503 @ SV100 @ SV56 @ SV118 ) @ SV118 )
| ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV56 )
| ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV100 ) ) )
= $true )
| ( ( ~ ( ~ ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV56 )
| ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV100 ) )
| ( in @ ( sK17_SY503 @ SV100 @ SV56 @ SV118 ) @ SV118 ) ) )
= $true )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1166]) ).
thf(1253,plain,
! [SV102: $i,SV58: $i,SV119: $i,SV151: $i] :
( ( ( ~ ( ~ ( in @ SV151 @ SV119 )
| ~ ( ~ ( in @ SV151 @ SV58 )
| ~ ~ ( in @ SV151 @ SV102 ) ) ) )
= $false )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1167]) ).
thf(1254,plain,
! [SV119: $i,SV102: $i,SV58: $i,SV151: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV151 @ SV58 )
| ~ ~ ( in @ SV151 @ SV102 ) )
| ( in @ SV151 @ SV119 ) ) )
= $false )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1167]) ).
thf(1255,plain,
! [SV119: $i,SV58: $i,SV102: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV119 )
| ~ ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
| ~ ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
| ~ ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 ) )
| ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV119 ) ) )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1168]) ).
thf(1256,plain,
! [SV59: $i,SV120: $i,SV103: $i] :
( ( ( element @ SV103 @ ( powerset @ SV120 ) )
= $false )
| ( ( in @ SV59 @ SV103 )
= $false )
| ( ( ~ ( empty @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1169]) ).
thf(1257,plain,
! [SV104: $i,SV60: $i,SV121: $i,SV152: $i] :
( ( ( ~ ( ~ ( in @ SV152 @ SV121 )
| ~ ( ~ ( in @ SV152 @ SV60 )
| ~ ( in @ SV152 @ SV104 ) ) ) )
= $false )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1170]) ).
thf(1258,plain,
! [SV121: $i,SV104: $i,SV60: $i,SV152: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV152 @ SV60 )
| ~ ( in @ SV152 @ SV104 ) )
| ( in @ SV152 @ SV121 ) ) )
= $false )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1170]) ).
thf(1259,plain,
! [SV121: $i,SV60: $i,SV104: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV121 )
| ~ ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
| ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
| ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 ) )
| ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV121 ) ) )
= $true )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1171]) ).
thf(1260,plain,
! [SV3: $i,SV63: $i] :
( ( ( ~ ( in @ ( sK26_SY404 @ SV63 @ SV3 ) @ ( set_intersection2 @ SV3 @ SV63 ) ) )
= $false )
| ( ( disjoint @ SV3 @ SV63 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1172]) ).
thf(1261,plain,
! [SV63: $i,SV3: $i,SV156: $i] :
( ( ( in @ SV156 @ ( set_intersection2 @ SV3 @ SV63 ) )
= $false )
| ( ( ~ ( disjoint @ SV3 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1173]) ).
thf(1262,plain,
! [SV5: $i,SV65: $i] :
( ( ( ~ ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV65 ) )
= $false )
| ( ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV5 )
= $true )
| ( ( SV5 = SV65 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1174]) ).
thf(1263,plain,
! [SV5: $i,SV65: $i] :
( ( ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV5 )
= $false )
| ( ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV5 )
= $true )
| ( ( SV5 = SV65 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1174]) ).
thf(1264,plain,
! [SV5: $i,SV65: $i] :
( ( ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV65 )
= $true )
| ( ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV65 )
= $false )
| ( ( SV5 = SV65 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1175]) ).
thf(1265,plain,
! [SV6: $i,SV66: $i] :
( ( ( SV66
!= ( identity_relation @ SV6 ) )
= $true )
| ( ( ~ ( ( ( relation_dom @ SV66 )
!= SV6 )
| ~ ! [SY407: $i] :
( ~ ( in @ SY407 @ SV6 )
| ( ( apply @ SV66 @ SY407 )
= SY407 ) ) ) )
= $true )
| ( ( relation @ SV66 )
= $false )
| ( ( function @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1177]) ).
thf(1266,plain,
! [SV6: $i,SV66: $i] :
( ( ( ~ ~ ( ( ( relation_dom @ SV66 )
!= SV6 )
| ~ ! [SY408: $i] :
( ~ ( in @ SY408 @ SV6 )
| ( ( apply @ SV66 @ SY408 )
= SY408 ) ) ) )
= $true )
| ( ( SV66
= ( identity_relation @ SV6 ) )
= $true )
| ( ( relation @ SV66 )
= $false )
| ( ( function @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1178]) ).
thf(1267,plain,
! [SV122: $i,SV67: $i,SV106: $i,SV7: $i] :
( ( ( in @ SV7 @ SV106 )
= $true )
| ( ( in @ ( ordered_pair @ SV7 @ SV67 ) @ ( cartesian_product2 @ SV106 @ SV122 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1179]) ).
thf(1268,plain,
! [SV106: $i,SV7: $i,SV122: $i,SV67: $i] :
( ( ( in @ SV67 @ SV122 )
= $true )
| ( ( in @ ( ordered_pair @ SV7 @ SV67 ) @ ( cartesian_product2 @ SV106 @ SV122 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1180]) ).
thf(1269,plain,
! [SV122: $i,SV67: $i,SV106: $i,SV7: $i] :
( ( ( in @ SV7 @ SV106 )
= $false )
| ( ( ~ ( in @ SV67 @ SV122 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV7 @ SV67 ) @ ( cartesian_product2 @ SV106 @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1181]) ).
thf(1270,plain,
! [SV123: $i,SV8: $i,SV163: $i] :
( ( ( ! [SY625: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV163 @ SY625 ) @ SV8 )
| ( in @ ( ordered_pair @ SV163 @ SY625 ) @ SV123 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV163 @ SY625 ) @ SV123 )
| ( in @ ( ordered_pair @ SV163 @ SY625 ) @ SV8 ) ) ) )
= $true )
| ( ( SV8 = SV123 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1182]) ).
thf(1271,plain,
! [SV8: $i,SV123: $i] :
( ( ( ! [SY626: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ SY626 ) @ SV8 )
| ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ SY626 ) @ SV123 ) )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ SY626 ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ SY626 ) @ SV8 ) ) ) )
= $false )
| ( ( SV8 = SV123 )
= $true )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1183]) ).
thf(1272,plain,
! [SV124: $i,SV10: $i,SV139: $i] :
( ( ( ( SV139
!= ( relation_composition @ SV10 @ SV124 ) )
| ! [SY581: $i,SY582: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY581 @ SY582 ) @ SV139 )
| ~ ! [SY515: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY581 @ SY515 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY515 @ SY582 ) @ SV124 ) ) )
| ~ ( ~ ~ ! [SY516: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY581 @ SY516 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY516 @ SY582 ) @ SV124 ) )
| ( in @ ( ordered_pair @ SY581 @ SY582 ) @ SV139 ) ) ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1184]) ).
thf(1273,plain,
! [SV124: $i,SV10: $i,SV139: $i] :
( ( ( ~ ! [SY585: $i,SY586: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY585 @ SY586 ) @ SV139 )
| ~ ! [SY519: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY585 @ SY519 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY519 @ SY586 ) @ SV124 ) ) )
| ~ ( ~ ~ ! [SY520: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY585 @ SY520 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY520 @ SY586 ) @ SV124 ) )
| ( in @ ( ordered_pair @ SY585 @ SY586 ) @ SV139 ) ) )
| ( SV139
= ( relation_composition @ SV10 @ SV124 ) ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1185]) ).
thf(1274,plain,
! [SV69: $i,SV11: $i,SV107: $i,SV148: $i] :
( ( ( ~ ( in @ SV148 @ SV107 )
| ~ ! [SY597: $i] :
~ ~ ! [SY598: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY597 @ SV11 )
| ~ ( in @ SY598 @ SV69 ) )
| ( SV148
!= ( ordered_pair @ SY597 @ SY598 ) ) ) )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1186]) ).
thf(1275,plain,
! [SV107: $i,SV148: $i,SV69: $i,SV11: $i] :
( ( ( ~ ~ ! [SY599: $i] :
~ ~ ! [SY600: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY599 @ SV11 )
| ~ ( in @ SY600 @ SV69 ) )
| ( SV148
!= ( ordered_pair @ SY599 @ SY600 ) ) )
| ( in @ SV148 @ SV107 ) )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1187]) ).
thf(1276,plain,
! [SV107: $i,SV11: $i,SV69: $i] :
( ( ( ~ ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 )
| ~ ! [SY601: $i] :
~ ~ ! [SY602: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY601 @ SV11 )
| ~ ( in @ SY602 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SY601 @ SY602 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY603: $i] :
~ ~ ! [SY604: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY603 @ SV11 )
| ~ ( in @ SY604 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SY603 @ SY604 ) ) )
| ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 ) ) )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1188]) ).
thf(1277,plain,
! [SV12: $i,SV70: $i,SV157: $i,SV153: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV153 @ SV157 ) @ SV70 )
| ~ ( ~ ( in @ SV153 @ SV12 )
| ( SV153 != SV157 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV153 @ SV12 )
| ( SV153 != SV157 ) )
| ( in @ ( ordered_pair @ SV153 @ SV157 ) @ SV70 ) ) )
= $false )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1189]) ).
thf(1278,plain,
! [SV70: $i,SV12: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK20_SY424 @ SV12 @ SV70 ) @ ( sK23_SY606 @ SV70 @ SV12 ) ) @ SV70 )
| ~ ( ~ ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
| ( ( sK20_SY424 @ SV12 @ SV70 )
!= ( sK23_SY606 @ SV70 @ SV12 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
| ( ( sK20_SY424 @ SV12 @ SV70 )
!= ( sK23_SY606 @ SV70 @ SV12 ) ) )
| ( in @ ( ordered_pair @ ( sK20_SY424 @ SV12 @ SV70 ) @ ( sK23_SY606 @ SV70 @ SV12 ) ) @ SV70 ) ) )
= $true )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1190]) ).
thf(1279,plain,
! [SV13: $i,SV71: $i,SV142: $i] :
( ( ( ~ ( in @ SV142 @ SV71 ) )
= $true )
| ( ( subset @ SV142 @ SV13 )
= $true )
| ( ( SV71
= ( powerset @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1191]) ).
thf(1280,plain,
! [SV71: $i,SV13: $i,SV142: $i] :
( ( ( ~ ( subset @ SV142 @ SV13 ) )
= $true )
| ( ( in @ SV142 @ SV71 )
= $true )
| ( ( SV71
= ( powerset @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1192]) ).
thf(1281,plain,
! [SV71: $i,SV13: $i] :
( ( ( ~ ( in @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV71 ) )
= $false )
| ( ( ~ ( ~ ( subset @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV13 )
| ( in @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV71 ) ) )
= $true )
| ( ( SV71
= ( powerset @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1193]) ).
thf(1282,plain,
! [SV71: $i,SV13: $i] :
( ( ( subset @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV13 )
= $false )
| ( ( ~ ( ~ ( subset @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV13 )
| ( in @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV71 ) ) )
= $true )
| ( ( SV71
= ( powerset @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1193]) ).
thf(1283,plain,
! [SV125: $i,SV14: $i,SV134: $i,SV158: $i] :
( ( ( ~ ( ~ ( in @ SV158 @ SV134 )
| ~ ! [SY615: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV158 @ SY615 ) @ SV14 )
| ~ ( in @ SY615 @ SV125 ) ) )
| ~ ( ~ ~ ! [SY616: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV158 @ SY616 ) @ SV14 )
| ~ ( in @ SY616 @ SV125 ) )
| ( in @ SV158 @ SV134 ) ) )
= $false )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1194]) ).
thf(1284,plain,
! [SV134: $i,SV14: $i,SV125: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV134 )
| ~ ! [SY617: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SY617 ) @ SV14 )
| ~ ( in @ SY617 @ SV125 ) ) )
| ~ ( ~ ~ ! [SY618: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SY618 ) @ SV14 )
| ~ ( in @ SY618 @ SV125 ) )
| ( in @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV134 ) ) )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1195]) ).
thf(1285,plain,
! [SV15: $i,SV126: $i,SV154: $i] :
( ( ( ~ ( ~ ( in @ SV154 @ SV126 )
| ~ ! [SY607: $i] :
~ ( in @ ( ordered_pair @ SY607 @ SV154 ) @ SV15 ) ) )
= $false )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $false )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1196]) ).
thf(1286,plain,
! [SV126: $i,SV15: $i,SV154: $i] :
( ( ( ~ ( ~ ~ ! [SY608: $i] :
~ ( in @ ( ordered_pair @ SY608 @ SV154 ) @ SV15 )
| ( in @ SV154 @ SV126 ) ) )
= $false )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $false )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1196]) ).
thf(1287,plain,
! [SV126: $i,SV15: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_SY531 @ SV15 @ SV126 ) @ SV126 )
| ~ ! [SY609: $i] :
~ ( in @ ( ordered_pair @ SY609 @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY610: $i] :
~ ( in @ ( ordered_pair @ SY610 @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 )
| ( in @ ( sK21_SY531 @ SV15 @ SV126 ) @ SV126 ) ) )
= $true )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1197]) ).
thf(1288,plain,
! [SV127: $i,SV16: $i,SV164: $i] :
( ( ( ! [SY627: $i] :
( ~ ( in @ ( ordered_pair @ SV164 @ SY627 ) @ SV16 )
| ( in @ ( ordered_pair @ SV164 @ SY627 ) @ SV127 ) ) )
= $true )
| ( ( subset @ SV16 @ SV127 )
= $false )
| ( ( relation @ SV127 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(1289,plain,
! [SV16: $i,SV127: $i] :
( ( ( ! [SY628: $i] :
( ~ ( in @ ( ordered_pair @ ( sK28_SY536 @ SV127 @ SV16 ) @ SY628 ) @ SV16 )
| ( in @ ( ordered_pair @ ( sK28_SY536 @ SV127 @ SV16 ) @ SY628 ) @ SV127 ) ) )
= $false )
| ( ( subset @ SV16 @ SV127 )
= $true )
| ( ( relation @ SV127 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1199]) ).
thf(1290,plain,
! [SV72: $i,SV17: $i,SV108: $i,SV149: $i] :
( ( ( ~ ( in @ SV149 @ SV108 )
| ( in @ SV149 @ SV17 )
| ( in @ SV149 @ SV72 ) )
= $true )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1200]) ).
thf(1291,plain,
! [SV108: $i,SV72: $i,SV17: $i,SV149: $i] :
( ( ( ~ ( ( in @ SV149 @ SV17 )
| ( in @ SV149 @ SV72 ) )
| ( in @ SV149 @ SV108 ) )
= $true )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1201]) ).
thf(1292,plain,
! [SV108: $i,SV17: $i,SV72: $i] :
( ( ( ~ ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV108 )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV17 )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV72 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV17 )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV72 ) )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV108 ) ) )
= $true )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1202]) ).
thf(1293,plain,
! [SV128: $i,SV20: $i,SV135: $i] :
( ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $false )
| ( ( ! [SY566: $i,SY567: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV135 )
| ~ ( ~ ( in @ SY566 @ SV128 )
| ~ ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY566 @ SV128 )
| ~ ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV20 ) )
| ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV135 ) ) ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1203]) ).
thf(1294,plain,
! [SV20: $i,SV128: $i,SV135: $i] :
( ( ( ! [SY568: $i,SY569: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY568 @ SY569 ) @ SV135 )
| ~ ( ~ ( in @ SY568 @ SV128 )
| ~ ( in @ ( ordered_pair @ SY568 @ SY569 ) @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY568 @ SV128 )
| ~ ( in @ ( ordered_pair @ SY568 @ SY569 ) @ SV20 ) )
| ( in @ ( ordered_pair @ SY568 @ SY569 ) @ SV135 ) ) ) )
= $false )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1204]) ).
thf(1295,plain,
! [SV21: $i,SV74: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK29_SY431 @ SV74 @ SV21 ) @ SV21 )
| ~ ( in @ ( sK29_SY431 @ SV74 @ SV21 ) @ SV74 ) ) )
= $false )
| ( ( disjoint @ SV21 @ SV74 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1205]) ).
thf(1296,plain,
! [SV74: $i,SV21: $i,SV159: $i] :
( ( ( ~ ( ~ ( in @ SV159 @ SV21 )
| ~ ( in @ SV159 @ SV74 ) ) )
= $false )
| ( ( ~ ( disjoint @ SV21 @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1206]) ).
thf(1297,plain,
! [SV109: $i,SV75: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ SV75 ) )
= $false )
| ( ( in @ SV22 @ ( relation_rng @ ( relation_rng_restriction @ SV75 @ SV109 ) ) )
= $false )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1207]) ).
thf(1298,plain,
! [SV75: $i,SV109: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ ( relation_rng @ SV109 ) ) )
= $false )
| ( ( in @ SV22 @ ( relation_rng @ ( relation_rng_restriction @ SV75 @ SV109 ) ) )
= $false )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1207]) ).
thf(1299,plain,
! [SV109: $i,SV75: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ SV75 ) )
= $true )
| ( ( ~ ( in @ SV22 @ ( relation_rng @ SV109 ) ) )
= $true )
| ( ( in @ SV22 @ ( relation_rng @ ( relation_rng_restriction @ SV75 @ SV109 ) ) )
= $true )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1208]) ).
thf(1300,plain,
! [SV23: $i] :
( ( ~ ( in @ SV23 @ ( sK3_SY291 @ SV23 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1209]) ).
thf(1301,plain,
! [SV23: $i] :
( ( ~ ! [SY490: $i,SY491: $i] :
( ~ ~ ( ~ ( in @ SY490 @ ( sK3_SY291 @ SV23 ) )
| ~ ( subset @ SY491 @ SY490 ) )
| ( in @ SY491 @ ( sK3_SY291 @ SV23 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1209]) ).
thf(1302,plain,
! [SV23: $i,SV160: $i] :
( ( ( ~ ( in @ SV160 @ ( sK3_SY291 @ SV23 ) ) )
= $true )
| ( ( in @ ( powerset @ SV160 ) @ ( sK3_SY291 @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1210]) ).
thf(1303,plain,
! [SV23: $i,SV143: $i] :
( ( ( ~ ( ~ ( subset @ SV143 @ ( sK3_SY291 @ SV23 ) )
| ~ ~ ( are_equipotent @ SV143 @ ( sK3_SY291 @ SV23 ) ) ) )
= $false )
| ( ( ~ ~ ( in @ SV143 @ ( sK3_SY291 @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1211]) ).
thf(1304,plain,
! [SV26: $i,SV78: $i] :
( ( ( SV78
!= ( set_meet @ SV26 ) )
= $true )
| ( ( ! [SY434: $i] :
~ ( ~ ( ~ ( in @ SY434 @ SV78 )
| ! [SY300: $i] :
( ~ ( in @ SY300 @ SV26 )
| ( in @ SY434 @ SY300 ) ) )
| ~ ( ~ ! [SY301: $i] :
( ~ ( in @ SY301 @ SV26 )
| ( in @ SY434 @ SY301 ) )
| ( in @ SY434 @ SV78 ) ) ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1212]) ).
thf(1305,plain,
! [SV26: $i,SV78: $i] :
( ( ( ~ ! [SY437: $i] :
~ ( ~ ( ~ ( in @ SY437 @ SV78 )
| ! [SY303: $i] :
( ~ ( in @ SY303 @ SV26 )
| ( in @ SY437 @ SY303 ) ) )
| ~ ( ~ ! [SY304: $i] :
( ~ ( in @ SY304 @ SV26 )
| ( in @ SY437 @ SY304 ) )
| ( in @ SY437 @ SV78 ) ) ) )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1213]) ).
thf(1306,plain,
! [SV26: $i,SV78: $i] :
( ( ( SV78
= ( set_meet @ SV26 ) )
= $false )
| ( ( SV78 = empty_set )
= $true )
| ( ( SV26 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1214]) ).
thf(1307,plain,
! [SV26: $i,SV78: $i] :
( ( ( SV78 = empty_set )
= $false )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1215]) ).
thf(1308,plain,
! [SV129: $i,SV79: $i,SV110: $i,SV27: $i] :
( ( ( ~ ( in @ SV27 @ SV110 )
| ~ ( in @ ( ordered_pair @ SV27 @ SV79 ) @ SV129 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV27 @ SV79 ) @ ( relation_composition @ ( identity_relation @ SV110 ) @ SV129 ) )
= $false )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1216]) ).
thf(1309,plain,
! [SV129: $i,SV79: $i,SV110: $i,SV27: $i] :
( ( ( ~ ( in @ SV27 @ SV110 )
| ~ ( in @ ( ordered_pair @ SV27 @ SV79 ) @ SV129 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV27 @ SV79 ) @ ( relation_composition @ ( identity_relation @ SV110 ) @ SV129 ) )
= $true )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1217]) ).
thf(1310,plain,
! [SV130: $i,SV81: $i,SV111: $i,SV29: $i] :
( ( ( in @ SV29 @ SV111 )
= $true )
| ( ( in @ ( ordered_pair @ SV29 @ SV81 ) @ ( cartesian_product2 @ SV111 @ SV130 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1218]) ).
thf(1311,plain,
! [SV111: $i,SV29: $i,SV130: $i,SV81: $i] :
( ( ( in @ SV81 @ SV130 )
= $true )
| ( ( in @ ( ordered_pair @ SV29 @ SV81 ) @ ( cartesian_product2 @ SV111 @ SV130 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1219]) ).
thf(1312,plain,
! [SV130: $i,SV81: $i,SV111: $i,SV29: $i] :
( ( ( in @ SV29 @ SV111 )
= $false )
| ( ( ~ ( in @ SV81 @ SV130 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV29 @ SV81 ) @ ( cartesian_product2 @ SV111 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1220]) ).
thf(1313,plain,
! [SV131: $i,SV30: $i,SV136: $i,SV161: $i] :
( ( ( ~ ( ~ ( in @ SV161 @ SV136 )
| ~ ! [SY619: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY619 @ SV161 ) @ SV30 )
| ~ ( in @ SY619 @ SV131 ) ) )
| ~ ( ~ ~ ! [SY620: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY620 @ SV161 ) @ SV30 )
| ~ ( in @ SY620 @ SV131 ) )
| ( in @ SV161 @ SV136 ) ) )
= $false )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1221]) ).
thf(1314,plain,
! [SV136: $i,SV30: $i,SV131: $i] :
( ( ( ~ ( ~ ( in @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) @ SV136 )
| ~ ! [SY621: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY621 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ SY621 @ SV131 ) ) )
| ~ ( ~ ~ ! [SY622: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY622 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ SY622 @ SV131 ) )
| ( in @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) @ SV136 ) ) )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1222]) ).
thf(1315,plain,
! [SV31: $i,SV112: $i,SV82: $i] :
( ( ( in @ SV82 @ SV112 )
= $false )
| ( ( in @ SV31 @ SV112 )
= $false )
| ( ( subset @ ( unordered_pair @ SV31 @ SV82 ) @ SV112 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1225]) ).
thf(1316,plain,
! [SV34: $i,SV84: $i] :
( ( ( ~ ( element @ SV84 @ SV34 ) )
= $true )
| ( ( in @ SV84 @ SV34 )
= $true )
| ( ( empty @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1226]) ).
thf(1317,plain,
! [SV34: $i,SV84: $i] :
( ( ( ~ ( in @ SV84 @ SV34 ) )
= $true )
| ( ( element @ SV84 @ SV34 )
= $true )
| ( ( empty @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1227]) ).
thf(1318,plain,
! [SV34: $i,SV84: $i] :
( ( ( element @ SV84 @ SV34 )
= $false )
| ( ( empty @ SV84 )
= $true )
| ( ( empty @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1228]) ).
thf(1319,plain,
! [SV34: $i,SV84: $i] :
( ( ( empty @ SV84 )
= $false )
| ( ( element @ SV84 @ SV34 )
= $true )
| ( ( empty @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1229]) ).
thf(1320,plain,
! [SV35: $i,SV140: $i] :
( ( ( ! [SY589: $i,SY590: $i] :
( SV140
!= ( ordered_pair @ SY589 @ SY590 ) ) )
= $false )
| ( ( in @ SV140 @ SV35 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1230]) ).
thf(1321,plain,
! [SV165: $i,SV35: $i] :
( ( ( ! [SY629: $i] :
( ( sK9_SY328 @ SV35 )
!= ( ordered_pair @ SV165 @ SY629 ) ) )
= $true )
| ( ( relation @ SV35 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1232]) ).
thf(1322,plain,
! [SV87: $i,SV39: $i,SV137: $i] :
( ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $false )
| ( ( ! [SY576: $i,SY577: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY576 @ SY577 ) @ SV137 )
| ~ ( ~ ( in @ SY577 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY576 @ SY577 ) @ SV87 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY577 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY576 @ SY577 ) @ SV87 ) )
| ( in @ ( ordered_pair @ SY576 @ SY577 ) @ SV137 ) ) ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1233]) ).
thf(1323,plain,
! [SV87: $i,SV39: $i,SV137: $i] :
( ( ( ! [SY578: $i,SY579: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY578 @ SY579 ) @ SV137 )
| ~ ( ~ ( in @ SY579 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY578 @ SY579 ) @ SV87 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY579 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY578 @ SY579 ) @ SV87 ) )
| ( in @ ( ordered_pair @ SY578 @ SY579 ) @ SV137 ) ) ) )
= $false )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1234]) ).
thf(1324,plain,
! [SV41: $i,SV88: $i,SV144: $i] :
( ( ( ~ ( in @ SV144 @ SV88 ) )
= $true )
| ( ( SV144 = SV41 )
= $true )
| ( ( SV88
= ( singleton @ SV41 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1235]) ).
thf(1325,plain,
! [SV88: $i,SV41: $i,SV144: $i] :
( ( ( SV144 != SV41 )
= $true )
| ( ( in @ SV144 @ SV88 )
= $true )
| ( ( SV88
= ( singleton @ SV41 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1236]) ).
thf(1326,plain,
! [SV88: $i,SV41: $i] :
( ( ( ~ ( in @ ( sK12_SY454 @ SV41 @ SV88 ) @ SV88 ) )
= $false )
| ( ( ~ ( ( ( sK12_SY454 @ SV41 @ SV88 )
!= SV41 )
| ( in @ ( sK12_SY454 @ SV41 @ SV88 ) @ SV88 ) ) )
= $true )
| ( ( SV88
= ( singleton @ SV41 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1237]) ).
thf(1327,plain,
! [SV88: $i,SV41: $i] :
( ( ( ( sK12_SY454 @ SV41 @ SV88 )
= SV41 )
= $false )
| ( ( ~ ( ( ( sK12_SY454 @ SV41 @ SV88 )
!= SV41 )
| ( in @ ( sK12_SY454 @ SV41 @ SV88 ) @ SV88 ) ) )
= $true )
| ( ( SV88
= ( singleton @ SV41 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1237]) ).
thf(1328,plain,
! [SV42: $i,SV89: $i,SV145: $i] :
( ( ( ~ ( in @ SV145 @ SV89 ) )
= $true )
| ( ( ~ ! [SY593: $i] :
~ ~ ( ~ ( in @ SV145 @ SY593 )
| ~ ( in @ SY593 @ SV42 ) ) )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1238]) ).
thf(1329,plain,
! [SV89: $i,SV42: $i,SV145: $i] :
( ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( in @ SV145 @ SY594 )
| ~ ( in @ SY594 @ SV42 ) ) )
= $true )
| ( ( in @ SV145 @ SV89 )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1239]) ).
thf(1330,plain,
! [SV89: $i,SV42: $i] :
( ( ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV89 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY596: $i] :
~ ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SY596 )
| ~ ( in @ SY596 @ SV42 ) )
| ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1240]) ).
thf(1331,plain,
! [SV89: $i,SV42: $i] :
( ( ( ~ ! [SY595: $i] :
~ ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SY595 )
| ~ ( in @ SY595 @ SV42 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY596: $i] :
~ ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SY596 )
| ~ ( in @ SY596 @ SV42 ) )
| ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1240]) ).
thf(1332,plain,
! [SV116: $i,SV90: $i,SV43: $i] :
( ( ( ~ ( in @ SV43 @ SV90 ) )
= $false )
| ( ( in @ SV43 @ ( relation_dom @ ( relation_dom_restriction @ SV116 @ SV90 ) ) )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1241]) ).
thf(1333,plain,
! [SV90: $i,SV116: $i,SV43: $i] :
( ( ( ~ ( in @ SV43 @ ( relation_dom @ SV116 ) ) )
= $false )
| ( ( in @ SV43 @ ( relation_dom @ ( relation_dom_restriction @ SV116 @ SV90 ) ) )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1241]) ).
thf(1334,plain,
! [SV116: $i,SV90: $i,SV43: $i] :
( ( ( ~ ( in @ SV43 @ SV90 ) )
= $true )
| ( ( ~ ( in @ SV43 @ ( relation_dom @ SV116 ) ) )
= $true )
| ( ( in @ SV43 @ ( relation_dom @ ( relation_dom_restriction @ SV116 @ SV90 ) ) )
= $true )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1242]) ).
thf(1335,plain,
! [SV46: $i] :
( ( ~ ( in @ SV46 @ ( sK4_SY357 @ SV46 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1243]) ).
thf(1336,plain,
! [SV46: $i] :
( ( ~ ! [SY496: $i,SY497: $i] :
( ~ ~ ( ~ ( in @ SY496 @ ( sK4_SY357 @ SV46 ) )
| ~ ( subset @ SY497 @ SY496 ) )
| ( in @ SY497 @ ( sK4_SY357 @ SV46 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1243]) ).
thf(1337,plain,
! [SV46: $i,SV162: $i] :
( ( ~ ( ~ ( in @ SV162 @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SY623: $i] :
~ ~ ( ~ ( in @ SY623 @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SY624: $i] :
( ~ ( subset @ SY624 @ SV162 )
| ( in @ SY624 @ SY623 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1244]) ).
thf(1338,plain,
! [SV46: $i,SV146: $i] :
( ( ( ~ ( ~ ( subset @ SV146 @ ( sK4_SY357 @ SV46 ) )
| ~ ~ ( are_equipotent @ SV146 @ ( sK4_SY357 @ SV46 ) ) ) )
= $false )
| ( ( ~ ~ ( in @ SV146 @ ( sK4_SY357 @ SV46 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1245]) ).
thf(1339,plain,
! [SV47: $i,SV132: $i,SV155: $i] :
( ( ( ~ ( ~ ( in @ SV155 @ SV132 )
| ~ ! [SY611: $i] :
~ ( in @ ( ordered_pair @ SV155 @ SY611 ) @ SV47 ) ) )
= $false )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1246]) ).
thf(1340,plain,
! [SV132: $i,SV47: $i,SV155: $i] :
( ( ( ~ ( ~ ~ ! [SY612: $i] :
~ ( in @ ( ordered_pair @ SV155 @ SY612 ) @ SV47 )
| ( in @ SV155 @ SV132 ) ) )
= $false )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1246]) ).
thf(1341,plain,
! [SV132: $i,SV47: $i] :
( ( ( ~ ( ~ ( in @ ( sK22_SY553 @ SV47 @ SV132 ) @ SV132 )
| ~ ! [SY613: $i] :
~ ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ SY613 ) @ SV47 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY614: $i] :
~ ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ SY614 ) @ SV47 )
| ( in @ ( sK22_SY553 @ SV47 @ SV132 ) @ SV132 ) ) )
= $true )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1247]) ).
thf(1342,plain,
! [SV49: $i,SV133: $i,SV166: $i] :
( ( ( ! [SY630: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV166 @ SY630 ) @ SV133 )
| ( in @ ( ordered_pair @ SY630 @ SV166 ) @ SV49 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY630 @ SV166 ) @ SV49 )
| ( in @ ( ordered_pair @ SV166 @ SY630 ) @ SV133 ) ) ) )
= $true )
| ( ( SV133
= ( relation_inverse @ SV49 ) )
= $false )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1248]) ).
thf(1343,plain,
! [SV133: $i,SV49: $i] :
( ( ( ! [SY631: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK30_SY558 @ SV49 @ SV133 ) @ SY631 ) @ SV133 )
| ( in @ ( ordered_pair @ SY631 @ ( sK30_SY558 @ SV49 @ SV133 ) ) @ SV49 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY631 @ ( sK30_SY558 @ SV49 @ SV133 ) ) @ SV49 )
| ( in @ ( ordered_pair @ ( sK30_SY558 @ SV49 @ SV133 ) @ SY631 ) @ SV133 ) ) ) )
= $false )
| ( ( SV133
= ( relation_inverse @ SV49 ) )
= $true )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1249]) ).
thf(1344,plain,
! [SV100: $i,SV56: $i,SV118: $i,SV150: $i] :
( ( ( ~ ( in @ SV150 @ SV118 )
| ( SV150 = SV56 )
| ( SV150 = SV100 ) )
= $true )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1250]) ).
thf(1345,plain,
! [SV118: $i,SV100: $i,SV56: $i,SV150: $i] :
( ( ( ~ ( ( SV150 = SV56 )
| ( SV150 = SV100 ) )
| ( in @ SV150 @ SV118 ) )
= $true )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1251]) ).
thf(1346,plain,
! [SV118: $i,SV56: $i,SV100: $i] :
( ( ( ~ ( in @ ( sK17_SY503 @ SV100 @ SV56 @ SV118 ) @ SV118 )
| ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV56 )
| ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV100 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV56 )
| ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV100 ) )
| ( in @ ( sK17_SY503 @ SV100 @ SV56 @ SV118 ) @ SV118 ) ) )
= $true )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1252]) ).
thf(1347,plain,
! [SV102: $i,SV58: $i,SV119: $i,SV151: $i] :
( ( ( ~ ( in @ SV151 @ SV119 )
| ~ ( ~ ( in @ SV151 @ SV58 )
| ~ ~ ( in @ SV151 @ SV102 ) ) )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1253]) ).
thf(1348,plain,
! [SV119: $i,SV102: $i,SV58: $i,SV151: $i] :
( ( ( ~ ~ ( ~ ( in @ SV151 @ SV58 )
| ~ ~ ( in @ SV151 @ SV102 ) )
| ( in @ SV151 @ SV119 ) )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1254]) ).
thf(1349,plain,
! [SV119: $i,SV58: $i,SV102: $i] :
( ( ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV119 )
| ~ ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
| ~ ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
| ~ ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 ) )
| ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV119 ) ) )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1255]) ).
thf(1350,plain,
! [SV103: $i,SV59: $i,SV120: $i] :
( ( ( empty @ SV120 )
= $false )
| ( ( in @ SV59 @ SV103 )
= $false )
| ( ( element @ SV103 @ ( powerset @ SV120 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1256]) ).
thf(1351,plain,
! [SV104: $i,SV60: $i,SV121: $i,SV152: $i] :
( ( ( ~ ( in @ SV152 @ SV121 )
| ~ ( ~ ( in @ SV152 @ SV60 )
| ~ ( in @ SV152 @ SV104 ) ) )
= $true )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1257]) ).
thf(1352,plain,
! [SV121: $i,SV104: $i,SV60: $i,SV152: $i] :
( ( ( ~ ~ ( ~ ( in @ SV152 @ SV60 )
| ~ ( in @ SV152 @ SV104 ) )
| ( in @ SV152 @ SV121 ) )
= $true )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1258]) ).
thf(1353,plain,
! [SV121: $i,SV60: $i,SV104: $i] :
( ( ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV121 )
| ~ ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
| ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
| ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 ) )
| ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV121 ) ) )
= $true )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1259]) ).
thf(1354,plain,
! [SV3: $i,SV63: $i] :
( ( ( in @ ( sK26_SY404 @ SV63 @ SV3 ) @ ( set_intersection2 @ SV3 @ SV63 ) )
= $true )
| ( ( disjoint @ SV3 @ SV63 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1260]) ).
thf(1355,plain,
! [SV156: $i,SV63: $i,SV3: $i] :
( ( ( disjoint @ SV3 @ SV63 )
= $false )
| ( ( in @ SV156 @ ( set_intersection2 @ SV3 @ SV63 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1261]) ).
thf(1356,plain,
! [SV5: $i,SV65: $i] :
( ( ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV65 )
= $true )
| ( ( in @ ( sK5_SY406 @ SV65 @ SV5 ) @ SV5 )
= $true )
| ( ( SV5 = SV65 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1262]) ).
thf(1357,plain,
! [SV6: $i,SV66: $i] :
( ( ( SV66
= ( identity_relation @ SV6 ) )
= $false )
| ( ( ~ ( ( ( relation_dom @ SV66 )
!= SV6 )
| ~ ! [SY407: $i] :
( ~ ( in @ SY407 @ SV6 )
| ( ( apply @ SV66 @ SY407 )
= SY407 ) ) ) )
= $true )
| ( ( relation @ SV66 )
= $false )
| ( ( function @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1265]) ).
thf(1358,plain,
! [SV6: $i,SV66: $i] :
( ( ( ~ ( ( ( relation_dom @ SV66 )
!= SV6 )
| ~ ! [SY408: $i] :
( ~ ( in @ SY408 @ SV6 )
| ( ( apply @ SV66 @ SY408 )
= SY408 ) ) ) )
= $false )
| ( ( SV66
= ( identity_relation @ SV6 ) )
= $true )
| ( ( relation @ SV66 )
= $false )
| ( ( function @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1266]) ).
thf(1359,plain,
! [SV106: $i,SV7: $i,SV122: $i,SV67: $i] :
( ( ( in @ SV67 @ SV122 )
= $false )
| ( ( in @ SV7 @ SV106 )
= $false )
| ( ( in @ ( ordered_pair @ SV7 @ SV67 ) @ ( cartesian_product2 @ SV106 @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1269]) ).
thf(1360,plain,
! [SV123: $i,SV8: $i,SV167: $i,SV163: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV163 @ SV167 ) @ SV8 )
| ( in @ ( ordered_pair @ SV163 @ SV167 ) @ SV123 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV163 @ SV167 ) @ SV123 )
| ( in @ ( ordered_pair @ SV163 @ SV167 ) @ SV8 ) ) ) )
= $true )
| ( ( SV8 = SV123 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1270]) ).
thf(1361,plain,
! [SV8: $i,SV123: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV8 )
| ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV123 ) )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV8 ) ) ) )
= $false )
| ( ( SV8 = SV123 )
= $true )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1271]) ).
thf(1362,plain,
! [SV124: $i,SV10: $i,SV139: $i] :
( ( ( SV139
!= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( ! [SY581: $i,SY582: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY581 @ SY582 ) @ SV139 )
| ~ ! [SY515: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY581 @ SY515 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY515 @ SY582 ) @ SV124 ) ) )
| ~ ( ~ ~ ! [SY516: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY581 @ SY516 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY516 @ SY582 ) @ SV124 ) )
| ( in @ ( ordered_pair @ SY581 @ SY582 ) @ SV139 ) ) ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1272]) ).
thf(1363,plain,
! [SV124: $i,SV10: $i,SV139: $i] :
( ( ( ~ ! [SY585: $i,SY586: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY585 @ SY586 ) @ SV139 )
| ~ ! [SY519: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY585 @ SY519 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY519 @ SY586 ) @ SV124 ) ) )
| ~ ( ~ ~ ! [SY520: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY585 @ SY520 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY520 @ SY586 ) @ SV124 ) )
| ( in @ ( ordered_pair @ SY585 @ SY586 ) @ SV139 ) ) ) )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1273]) ).
thf(1364,plain,
! [SV69: $i,SV11: $i,SV107: $i,SV148: $i] :
( ( ( ~ ( in @ SV148 @ SV107 ) )
= $true )
| ( ( ~ ! [SY597: $i] :
~ ~ ! [SY598: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY597 @ SV11 )
| ~ ( in @ SY598 @ SV69 ) )
| ( SV148
!= ( ordered_pair @ SY597 @ SY598 ) ) ) )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1274]) ).
thf(1365,plain,
! [SV107: $i,SV148: $i,SV69: $i,SV11: $i] :
( ( ( ~ ~ ! [SY599: $i] :
~ ~ ! [SY600: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY599 @ SV11 )
| ~ ( in @ SY600 @ SV69 ) )
| ( SV148
!= ( ordered_pair @ SY599 @ SY600 ) ) ) )
= $true )
| ( ( in @ SV148 @ SV107 )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1275]) ).
thf(1366,plain,
! [SV107: $i,SV11: $i,SV69: $i] :
( ( ( ~ ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY603: $i] :
~ ~ ! [SY604: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY603 @ SV11 )
| ~ ( in @ SY604 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SY603 @ SY604 ) ) )
| ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 ) ) )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1276]) ).
thf(1367,plain,
! [SV107: $i,SV69: $i,SV11: $i] :
( ( ( ~ ! [SY601: $i] :
~ ~ ! [SY602: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY601 @ SV11 )
| ~ ( in @ SY602 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SY601 @ SY602 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY603: $i] :
~ ~ ! [SY604: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY603 @ SV11 )
| ~ ( in @ SY604 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SY603 @ SY604 ) ) )
| ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 ) ) )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1276]) ).
thf(1368,plain,
! [SV12: $i,SV70: $i,SV157: $i,SV153: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV153 @ SV157 ) @ SV70 )
| ~ ( ~ ( in @ SV153 @ SV12 )
| ( SV153 != SV157 ) ) ) )
= $false )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1277]) ).
thf(1369,plain,
! [SV70: $i,SV157: $i,SV12: $i,SV153: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV153 @ SV12 )
| ( SV153 != SV157 ) )
| ( in @ ( ordered_pair @ SV153 @ SV157 ) @ SV70 ) ) )
= $false )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1277]) ).
thf(1370,plain,
! [SV70: $i,SV12: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK20_SY424 @ SV12 @ SV70 ) @ ( sK23_SY606 @ SV70 @ SV12 ) ) @ SV70 )
| ~ ( ~ ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
| ( ( sK20_SY424 @ SV12 @ SV70 )
!= ( sK23_SY606 @ SV70 @ SV12 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
| ( ( sK20_SY424 @ SV12 @ SV70 )
!= ( sK23_SY606 @ SV70 @ SV12 ) ) )
| ( in @ ( ordered_pair @ ( sK20_SY424 @ SV12 @ SV70 ) @ ( sK23_SY606 @ SV70 @ SV12 ) ) @ SV70 ) ) )
= $true )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1278]) ).
thf(1371,plain,
! [SV13: $i,SV71: $i,SV142: $i] :
( ( ( in @ SV142 @ SV71 )
= $false )
| ( ( subset @ SV142 @ SV13 )
= $true )
| ( ( SV71
= ( powerset @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1279]) ).
thf(1372,plain,
! [SV71: $i,SV13: $i,SV142: $i] :
( ( ( subset @ SV142 @ SV13 )
= $false )
| ( ( in @ SV142 @ SV71 )
= $true )
| ( ( SV71
= ( powerset @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1280]) ).
thf(1373,plain,
! [SV71: $i,SV13: $i] :
( ( ( in @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV71 )
= $true )
| ( ( ~ ( ~ ( subset @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV13 )
| ( in @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV71 ) ) )
= $true )
| ( ( SV71
= ( powerset @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1281]) ).
thf(1374,plain,
! [SV71: $i,SV13: $i] :
( ( ( ~ ( subset @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV13 )
| ( in @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV71 ) )
= $false )
| ( ( subset @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV13 )
= $false )
| ( ( SV71
= ( powerset @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1282]) ).
thf(1375,plain,
! [SV125: $i,SV14: $i,SV134: $i,SV158: $i] :
( ( ( ~ ( ~ ( in @ SV158 @ SV134 )
| ~ ! [SY615: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV158 @ SY615 ) @ SV14 )
| ~ ( in @ SY615 @ SV125 ) ) ) )
= $false )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1283]) ).
thf(1376,plain,
! [SV134: $i,SV125: $i,SV14: $i,SV158: $i] :
( ( ( ~ ( ~ ~ ! [SY616: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV158 @ SY616 ) @ SV14 )
| ~ ( in @ SY616 @ SV125 ) )
| ( in @ SV158 @ SV134 ) ) )
= $false )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1283]) ).
thf(1377,plain,
! [SV134: $i,SV14: $i,SV125: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV134 )
| ~ ! [SY617: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SY617 ) @ SV14 )
| ~ ( in @ SY617 @ SV125 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY618: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SY618 ) @ SV14 )
| ~ ( in @ SY618 @ SV125 ) )
| ( in @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV134 ) ) )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1284]) ).
thf(1378,plain,
! [SV15: $i,SV126: $i,SV154: $i] :
( ( ( ~ ( in @ SV154 @ SV126 )
| ~ ! [SY607: $i] :
~ ( in @ ( ordered_pair @ SY607 @ SV154 ) @ SV15 ) )
= $true )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $false )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1285]) ).
thf(1379,plain,
! [SV126: $i,SV15: $i,SV154: $i] :
( ( ( ~ ~ ! [SY608: $i] :
~ ( in @ ( ordered_pair @ SY608 @ SV154 ) @ SV15 )
| ( in @ SV154 @ SV126 ) )
= $true )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $false )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1286]) ).
thf(1380,plain,
! [SV126: $i,SV15: $i] :
( ( ( ~ ( in @ ( sK21_SY531 @ SV15 @ SV126 ) @ SV126 )
| ~ ! [SY609: $i] :
~ ( in @ ( ordered_pair @ SY609 @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY610: $i] :
~ ( in @ ( ordered_pair @ SY610 @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 )
| ( in @ ( sK21_SY531 @ SV15 @ SV126 ) @ SV126 ) ) )
= $true )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1287]) ).
thf(1381,plain,
! [SV127: $i,SV16: $i,SV168: $i,SV164: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV164 @ SV168 ) @ SV16 )
| ( in @ ( ordered_pair @ SV164 @ SV168 ) @ SV127 ) )
= $true )
| ( ( subset @ SV16 @ SV127 )
= $false )
| ( ( relation @ SV127 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1382,plain,
! [SV16: $i,SV127: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK28_SY536 @ SV127 @ SV16 ) @ ( sK32_SY628 @ SV16 @ SV127 ) ) @ SV16 )
| ( in @ ( ordered_pair @ ( sK28_SY536 @ SV127 @ SV16 ) @ ( sK32_SY628 @ SV16 @ SV127 ) ) @ SV127 ) )
= $false )
| ( ( subset @ SV16 @ SV127 )
= $true )
| ( ( relation @ SV127 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1289]) ).
thf(1383,plain,
! [SV72: $i,SV17: $i,SV108: $i,SV149: $i] :
( ( ( ~ ( in @ SV149 @ SV108 ) )
= $true )
| ( ( ( in @ SV149 @ SV17 )
| ( in @ SV149 @ SV72 ) )
= $true )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1290]) ).
thf(1384,plain,
! [SV108: $i,SV72: $i,SV17: $i,SV149: $i] :
( ( ( ~ ( ( in @ SV149 @ SV17 )
| ( in @ SV149 @ SV72 ) ) )
= $true )
| ( ( in @ SV149 @ SV108 )
= $true )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1291]) ).
thf(1385,plain,
! [SV108: $i,SV17: $i,SV72: $i] :
( ( ( ~ ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV108 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV17 )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV72 ) )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV108 ) ) )
= $true )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1292]) ).
thf(1386,plain,
! [SV108: $i,SV17: $i,SV72: $i] :
( ( ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV17 )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV72 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV17 )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV72 ) )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV108 ) ) )
= $true )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1292]) ).
thf(1387,plain,
! [SV20: $i,SV128: $i,SV135: $i,SV169: $i] :
( ( ( ! [SY632: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV169 @ SY632 ) @ SV135 )
| ~ ( ~ ( in @ SV169 @ SV128 )
| ~ ( in @ ( ordered_pair @ SV169 @ SY632 ) @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV169 @ SV128 )
| ~ ( in @ ( ordered_pair @ SV169 @ SY632 ) @ SV20 ) )
| ( in @ ( ordered_pair @ SV169 @ SY632 ) @ SV135 ) ) ) )
= $true )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1293]) ).
thf(1388,plain,
! [SV135: $i,SV128: $i,SV20: $i] :
( ( ( ! [SY633: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SY633 ) @ SV135 )
| ~ ( ~ ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
| ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SY633 ) @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
| ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SY633 ) @ SV20 ) )
| ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SY633 ) @ SV135 ) ) ) )
= $false )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1294]) ).
thf(1389,plain,
! [SV21: $i,SV74: $i] :
( ( ( ~ ( ~ ( in @ ( sK29_SY431 @ SV74 @ SV21 ) @ SV21 )
| ~ ( in @ ( sK29_SY431 @ SV74 @ SV21 ) @ SV74 ) ) )
= $true )
| ( ( disjoint @ SV21 @ SV74 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1295]) ).
thf(1390,plain,
! [SV74: $i,SV21: $i,SV159: $i] :
( ( ( ~ ( in @ SV159 @ SV21 )
| ~ ( in @ SV159 @ SV74 ) )
= $true )
| ( ( ~ ( disjoint @ SV21 @ SV74 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1296]) ).
thf(1391,plain,
! [SV109: $i,SV75: $i,SV22: $i] :
( ( ( in @ SV22 @ SV75 )
= $true )
| ( ( in @ SV22 @ ( relation_rng @ ( relation_rng_restriction @ SV75 @ SV109 ) ) )
= $false )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1297]) ).
thf(1392,plain,
! [SV75: $i,SV109: $i,SV22: $i] :
( ( ( in @ SV22 @ ( relation_rng @ SV109 ) )
= $true )
| ( ( in @ SV22 @ ( relation_rng @ ( relation_rng_restriction @ SV75 @ SV109 ) ) )
= $false )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1298]) ).
thf(1393,plain,
! [SV109: $i,SV75: $i,SV22: $i] :
( ( ( in @ SV22 @ SV75 )
= $false )
| ( ( ~ ( in @ SV22 @ ( relation_rng @ SV109 ) ) )
= $true )
| ( ( in @ SV22 @ ( relation_rng @ ( relation_rng_restriction @ SV75 @ SV109 ) ) )
= $true )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1299]) ).
thf(1394,plain,
! [SV23: $i] :
( ( in @ SV23 @ ( sK3_SY291 @ SV23 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1300]) ).
thf(1395,plain,
! [SV23: $i] :
( ( ! [SY490: $i,SY491: $i] :
( ~ ~ ( ~ ( in @ SY490 @ ( sK3_SY291 @ SV23 ) )
| ~ ( subset @ SY491 @ SY490 ) )
| ( in @ SY491 @ ( sK3_SY291 @ SV23 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1301]) ).
thf(1396,plain,
! [SV23: $i,SV160: $i] :
( ( ( in @ SV160 @ ( sK3_SY291 @ SV23 ) )
= $false )
| ( ( in @ ( powerset @ SV160 ) @ ( sK3_SY291 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1302]) ).
thf(1397,plain,
! [SV23: $i,SV143: $i] :
( ( ( ~ ( subset @ SV143 @ ( sK3_SY291 @ SV23 ) )
| ~ ~ ( are_equipotent @ SV143 @ ( sK3_SY291 @ SV23 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV143 @ ( sK3_SY291 @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1303]) ).
thf(1398,plain,
! [SV26: $i,SV78: $i] :
( ( ( SV78
= ( set_meet @ SV26 ) )
= $false )
| ( ( ! [SY434: $i] :
~ ( ~ ( ~ ( in @ SY434 @ SV78 )
| ! [SY300: $i] :
( ~ ( in @ SY300 @ SV26 )
| ( in @ SY434 @ SY300 ) ) )
| ~ ( ~ ! [SY301: $i] :
( ~ ( in @ SY301 @ SV26 )
| ( in @ SY434 @ SY301 ) )
| ( in @ SY434 @ SV78 ) ) ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1304]) ).
thf(1399,plain,
! [SV26: $i,SV78: $i] :
( ( ( ! [SY437: $i] :
~ ( ~ ( ~ ( in @ SY437 @ SV78 )
| ! [SY303: $i] :
( ~ ( in @ SY303 @ SV26 )
| ( in @ SY437 @ SY303 ) ) )
| ~ ( ~ ! [SY304: $i] :
( ~ ( in @ SY304 @ SV26 )
| ( in @ SY437 @ SY304 ) )
| ( in @ SY437 @ SV78 ) ) ) )
= $false )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1305]) ).
thf(1400,plain,
! [SV129: $i,SV79: $i,SV110: $i,SV27: $i] :
( ( ( ~ ( in @ SV27 @ SV110 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV27 @ SV79 ) @ ( relation_composition @ ( identity_relation @ SV110 ) @ SV129 ) )
= $false )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1308]) ).
thf(1401,plain,
! [SV110: $i,SV129: $i,SV79: $i,SV27: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV27 @ SV79 ) @ SV129 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV27 @ SV79 ) @ ( relation_composition @ ( identity_relation @ SV110 ) @ SV129 ) )
= $false )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1308]) ).
thf(1402,plain,
! [SV129: $i,SV79: $i,SV110: $i,SV27: $i] :
( ( ( ~ ( in @ SV27 @ SV110 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV27 @ SV79 ) @ SV129 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV27 @ SV79 ) @ ( relation_composition @ ( identity_relation @ SV110 ) @ SV129 ) )
= $true )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1309]) ).
thf(1403,plain,
! [SV111: $i,SV29: $i,SV130: $i,SV81: $i] :
( ( ( in @ SV81 @ SV130 )
= $false )
| ( ( in @ SV29 @ SV111 )
= $false )
| ( ( in @ ( ordered_pair @ SV29 @ SV81 ) @ ( cartesian_product2 @ SV111 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1312]) ).
thf(1404,plain,
! [SV131: $i,SV30: $i,SV136: $i,SV161: $i] :
( ( ( ~ ( ~ ( in @ SV161 @ SV136 )
| ~ ! [SY619: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY619 @ SV161 ) @ SV30 )
| ~ ( in @ SY619 @ SV131 ) ) ) )
= $false )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1313]) ).
thf(1405,plain,
! [SV136: $i,SV131: $i,SV30: $i,SV161: $i] :
( ( ( ~ ( ~ ~ ! [SY620: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY620 @ SV161 ) @ SV30 )
| ~ ( in @ SY620 @ SV131 ) )
| ( in @ SV161 @ SV136 ) ) )
= $false )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1313]) ).
thf(1406,plain,
! [SV136: $i,SV30: $i,SV131: $i] :
( ( ( ~ ( ~ ( in @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) @ SV136 )
| ~ ! [SY621: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY621 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ SY621 @ SV131 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY622: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY622 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ SY622 @ SV131 ) )
| ( in @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) @ SV136 ) ) )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1314]) ).
thf(1407,plain,
! [SV34: $i,SV84: $i] :
( ( ( element @ SV84 @ SV34 )
= $false )
| ( ( in @ SV84 @ SV34 )
= $true )
| ( ( empty @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1316]) ).
thf(1408,plain,
! [SV34: $i,SV84: $i] :
( ( ( in @ SV84 @ SV34 )
= $false )
| ( ( element @ SV84 @ SV34 )
= $true )
| ( ( empty @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1317]) ).
thf(1409,plain,
! [SV35: $i,SV140: $i] :
( ( ( ! [SY634: $i] :
( SV140
!= ( ordered_pair @ ( sK34_SY589 @ SV35 @ SV140 ) @ SY634 ) ) )
= $false )
| ( ( in @ SV140 @ SV35 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1320]) ).
thf(1410,plain,
! [SV170: $i,SV165: $i,SV35: $i] :
( ( ( ( sK9_SY328 @ SV35 )
!= ( ordered_pair @ SV165 @ SV170 ) )
= $true )
| ( ( relation @ SV35 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1321]) ).
thf(1411,plain,
! [SV87: $i,SV39: $i,SV137: $i,SV171: $i] :
( ( ( ! [SY635: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV171 @ SY635 ) @ SV137 )
| ~ ( ~ ( in @ SY635 @ SV39 )
| ~ ( in @ ( ordered_pair @ SV171 @ SY635 ) @ SV87 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY635 @ SV39 )
| ~ ( in @ ( ordered_pair @ SV171 @ SY635 ) @ SV87 ) )
| ( in @ ( ordered_pair @ SV171 @ SY635 ) @ SV137 ) ) ) )
= $true )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1322]) ).
thf(1412,plain,
! [SV137: $i,SV39: $i,SV87: $i] :
( ( ( ! [SY636: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ SY636 ) @ SV137 )
| ~ ( ~ ( in @ SY636 @ SV39 )
| ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ SY636 ) @ SV87 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY636 @ SV39 )
| ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ SY636 ) @ SV87 ) )
| ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ SY636 ) @ SV137 ) ) ) )
= $false )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1323]) ).
thf(1413,plain,
! [SV41: $i,SV88: $i,SV144: $i] :
( ( ( in @ SV144 @ SV88 )
= $false )
| ( ( SV144 = SV41 )
= $true )
| ( ( SV88
= ( singleton @ SV41 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1324]) ).
thf(1414,plain,
! [SV88: $i,SV41: $i,SV144: $i] :
( ( ( SV144 = SV41 )
= $false )
| ( ( in @ SV144 @ SV88 )
= $true )
| ( ( SV88
= ( singleton @ SV41 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1325]) ).
thf(1415,plain,
! [SV88: $i,SV41: $i] :
( ( ( in @ ( sK12_SY454 @ SV41 @ SV88 ) @ SV88 )
= $true )
| ( ( ~ ( ( ( sK12_SY454 @ SV41 @ SV88 )
!= SV41 )
| ( in @ ( sK12_SY454 @ SV41 @ SV88 ) @ SV88 ) ) )
= $true )
| ( ( SV88
= ( singleton @ SV41 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1326]) ).
thf(1416,plain,
! [SV88: $i,SV41: $i] :
( ( ( ( ( sK12_SY454 @ SV41 @ SV88 )
!= SV41 )
| ( in @ ( sK12_SY454 @ SV41 @ SV88 ) @ SV88 ) )
= $false )
| ( ( ( sK12_SY454 @ SV41 @ SV88 )
= SV41 )
= $false )
| ( ( SV88
= ( singleton @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1327]) ).
thf(1417,plain,
! [SV42: $i,SV89: $i,SV145: $i] :
( ( ( in @ SV145 @ SV89 )
= $false )
| ( ( ~ ! [SY593: $i] :
~ ~ ( ~ ( in @ SV145 @ SY593 )
| ~ ( in @ SY593 @ SV42 ) ) )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1328]) ).
thf(1418,plain,
! [SV89: $i,SV42: $i,SV145: $i] :
( ( ( ~ ! [SY594: $i] :
~ ~ ( ~ ( in @ SV145 @ SY594 )
| ~ ( in @ SY594 @ SV42 ) ) )
= $false )
| ( ( in @ SV145 @ SV89 )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1329]) ).
thf(1419,plain,
! [SV89: $i,SV42: $i] :
( ( ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV89 )
= $true )
| ( ( ~ ( ~ ~ ! [SY596: $i] :
~ ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SY596 )
| ~ ( in @ SY596 @ SV42 ) )
| ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1330]) ).
thf(1420,plain,
! [SV89: $i,SV42: $i] :
( ( ( ! [SY595: $i] :
~ ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SY595 )
| ~ ( in @ SY595 @ SV42 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY596: $i] :
~ ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SY596 )
| ~ ( in @ SY596 @ SV42 ) )
| ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1331]) ).
thf(1421,plain,
! [SV116: $i,SV90: $i,SV43: $i] :
( ( ( in @ SV43 @ SV90 )
= $true )
| ( ( in @ SV43 @ ( relation_dom @ ( relation_dom_restriction @ SV116 @ SV90 ) ) )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1332]) ).
thf(1422,plain,
! [SV90: $i,SV116: $i,SV43: $i] :
( ( ( in @ SV43 @ ( relation_dom @ SV116 ) )
= $true )
| ( ( in @ SV43 @ ( relation_dom @ ( relation_dom_restriction @ SV116 @ SV90 ) ) )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1333]) ).
thf(1423,plain,
! [SV116: $i,SV90: $i,SV43: $i] :
( ( ( in @ SV43 @ SV90 )
= $false )
| ( ( ~ ( in @ SV43 @ ( relation_dom @ SV116 ) ) )
= $true )
| ( ( in @ SV43 @ ( relation_dom @ ( relation_dom_restriction @ SV116 @ SV90 ) ) )
= $true )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1334]) ).
thf(1424,plain,
! [SV46: $i] :
( ( in @ SV46 @ ( sK4_SY357 @ SV46 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1335]) ).
thf(1425,plain,
! [SV46: $i] :
( ( ! [SY496: $i,SY497: $i] :
( ~ ~ ( ~ ( in @ SY496 @ ( sK4_SY357 @ SV46 ) )
| ~ ( subset @ SY497 @ SY496 ) )
| ( in @ SY497 @ ( sK4_SY357 @ SV46 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1336]) ).
thf(1426,plain,
! [SV46: $i,SV162: $i] :
( ( ~ ( in @ SV162 @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SY623: $i] :
~ ~ ( ~ ( in @ SY623 @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SY624: $i] :
( ~ ( subset @ SY624 @ SV162 )
| ( in @ SY624 @ SY623 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1337]) ).
thf(1427,plain,
! [SV46: $i,SV146: $i] :
( ( ( ~ ( subset @ SV146 @ ( sK4_SY357 @ SV46 ) )
| ~ ~ ( are_equipotent @ SV146 @ ( sK4_SY357 @ SV46 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV146 @ ( sK4_SY357 @ SV46 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1338]) ).
thf(1428,plain,
! [SV47: $i,SV132: $i,SV155: $i] :
( ( ( ~ ( in @ SV155 @ SV132 )
| ~ ! [SY611: $i] :
~ ( in @ ( ordered_pair @ SV155 @ SY611 ) @ SV47 ) )
= $true )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1339]) ).
thf(1429,plain,
! [SV132: $i,SV47: $i,SV155: $i] :
( ( ( ~ ~ ! [SY612: $i] :
~ ( in @ ( ordered_pair @ SV155 @ SY612 ) @ SV47 )
| ( in @ SV155 @ SV132 ) )
= $true )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1340]) ).
thf(1430,plain,
! [SV132: $i,SV47: $i] :
( ( ( ~ ( in @ ( sK22_SY553 @ SV47 @ SV132 ) @ SV132 )
| ~ ! [SY613: $i] :
~ ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ SY613 ) @ SV47 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY614: $i] :
~ ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ SY614 ) @ SV47 )
| ( in @ ( sK22_SY553 @ SV47 @ SV132 ) @ SV132 ) ) )
= $true )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1341]) ).
thf(1431,plain,
! [SV49: $i,SV133: $i,SV172: $i,SV166: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV166 @ SV172 ) @ SV133 )
| ( in @ ( ordered_pair @ SV172 @ SV166 ) @ SV49 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV172 @ SV166 ) @ SV49 )
| ( in @ ( ordered_pair @ SV166 @ SV172 ) @ SV133 ) ) ) )
= $true )
| ( ( SV133
= ( relation_inverse @ SV49 ) )
= $false )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1342]) ).
thf(1432,plain,
! [SV133: $i,SV49: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK30_SY558 @ SV49 @ SV133 ) @ ( sK36_SY631 @ SV133 @ SV49 ) ) @ SV133 )
| ( in @ ( ordered_pair @ ( sK36_SY631 @ SV133 @ SV49 ) @ ( sK30_SY558 @ SV49 @ SV133 ) ) @ SV49 ) )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK36_SY631 @ SV133 @ SV49 ) @ ( sK30_SY558 @ SV49 @ SV133 ) ) @ SV49 )
| ( in @ ( ordered_pair @ ( sK30_SY558 @ SV49 @ SV133 ) @ ( sK36_SY631 @ SV133 @ SV49 ) ) @ SV133 ) ) ) )
= $false )
| ( ( SV133
= ( relation_inverse @ SV49 ) )
= $true )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1343]) ).
thf(1433,plain,
! [SV100: $i,SV56: $i,SV118: $i,SV150: $i] :
( ( ( ~ ( in @ SV150 @ SV118 ) )
= $true )
| ( ( ( SV150 = SV56 )
| ( SV150 = SV100 ) )
= $true )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1344]) ).
thf(1434,plain,
! [SV118: $i,SV100: $i,SV56: $i,SV150: $i] :
( ( ( ~ ( ( SV150 = SV56 )
| ( SV150 = SV100 ) ) )
= $true )
| ( ( in @ SV150 @ SV118 )
= $true )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1345]) ).
thf(1435,plain,
! [SV118: $i,SV56: $i,SV100: $i] :
( ( ( ~ ( in @ ( sK17_SY503 @ SV100 @ SV56 @ SV118 ) @ SV118 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV56 )
| ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV100 ) )
| ( in @ ( sK17_SY503 @ SV100 @ SV56 @ SV118 ) @ SV118 ) ) )
= $true )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1346]) ).
thf(1436,plain,
! [SV118: $i,SV56: $i,SV100: $i] :
( ( ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV56 )
| ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV100 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV56 )
| ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV100 ) )
| ( in @ ( sK17_SY503 @ SV100 @ SV56 @ SV118 ) @ SV118 ) ) )
= $true )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1346]) ).
thf(1437,plain,
! [SV102: $i,SV58: $i,SV119: $i,SV151: $i] :
( ( ( ~ ( in @ SV151 @ SV119 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV151 @ SV58 )
| ~ ~ ( in @ SV151 @ SV102 ) ) )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1347]) ).
thf(1438,plain,
! [SV119: $i,SV102: $i,SV58: $i,SV151: $i] :
( ( ( ~ ~ ( ~ ( in @ SV151 @ SV58 )
| ~ ~ ( in @ SV151 @ SV102 ) ) )
= $true )
| ( ( in @ SV151 @ SV119 )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1348]) ).
thf(1439,plain,
! [SV119: $i,SV58: $i,SV102: $i] :
( ( ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV119 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
| ~ ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 ) )
| ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV119 ) ) )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1349]) ).
thf(1440,plain,
! [SV119: $i,SV58: $i,SV102: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
| ~ ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
| ~ ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 ) )
| ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV119 ) ) )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1349]) ).
thf(1441,plain,
! [SV104: $i,SV60: $i,SV121: $i,SV152: $i] :
( ( ( ~ ( in @ SV152 @ SV121 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV152 @ SV60 )
| ~ ( in @ SV152 @ SV104 ) ) )
= $true )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1351]) ).
thf(1442,plain,
! [SV121: $i,SV104: $i,SV60: $i,SV152: $i] :
( ( ( ~ ~ ( ~ ( in @ SV152 @ SV60 )
| ~ ( in @ SV152 @ SV104 ) ) )
= $true )
| ( ( in @ SV152 @ SV121 )
= $true )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1352]) ).
thf(1443,plain,
! [SV121: $i,SV60: $i,SV104: $i] :
( ( ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV121 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
| ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 ) )
| ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV121 ) ) )
= $true )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1353]) ).
thf(1444,plain,
! [SV121: $i,SV60: $i,SV104: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
| ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
| ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 ) )
| ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV121 ) ) )
= $true )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1353]) ).
thf(1445,plain,
! [SV6: $i,SV66: $i] :
( ( ( ( ( relation_dom @ SV66 )
!= SV6 )
| ~ ! [SY407: $i] :
( ~ ( in @ SY407 @ SV6 )
| ( ( apply @ SV66 @ SY407 )
= SY407 ) ) )
= $false )
| ( ( SV66
= ( identity_relation @ SV6 ) )
= $false )
| ( ( relation @ SV66 )
= $false )
| ( ( function @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1357]) ).
thf(1446,plain,
! [SV6: $i,SV66: $i] :
( ( ( ( ( relation_dom @ SV66 )
!= SV6 )
| ~ ! [SY408: $i] :
( ~ ( in @ SY408 @ SV6 )
| ( ( apply @ SV66 @ SY408 )
= SY408 ) ) )
= $true )
| ( ( SV66
= ( identity_relation @ SV6 ) )
= $true )
| ( ( relation @ SV66 )
= $false )
| ( ( function @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1358]) ).
thf(1447,plain,
! [SV123: $i,SV8: $i,SV167: $i,SV163: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV163 @ SV167 ) @ SV8 )
| ( in @ ( ordered_pair @ SV163 @ SV167 ) @ SV123 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV163 @ SV167 ) @ SV123 )
| ( in @ ( ordered_pair @ SV163 @ SV167 ) @ SV8 ) ) )
= $false )
| ( ( SV8 = SV123 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1360]) ).
thf(1448,plain,
! [SV8: $i,SV123: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV8 )
| ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV123 ) )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV8 ) ) )
= $true )
| ( ( SV8 = SV123 )
= $true )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1361]) ).
thf(1449,plain,
! [SV124: $i,SV10: $i,SV139: $i] :
( ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $false )
| ( ( ! [SY581: $i,SY582: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY581 @ SY582 ) @ SV139 )
| ~ ! [SY515: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY581 @ SY515 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY515 @ SY582 ) @ SV124 ) ) )
| ~ ( ~ ~ ! [SY516: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY581 @ SY516 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY516 @ SY582 ) @ SV124 ) )
| ( in @ ( ordered_pair @ SY581 @ SY582 ) @ SV139 ) ) ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1362]) ).
thf(1450,plain,
! [SV124: $i,SV10: $i,SV139: $i] :
( ( ( ! [SY585: $i,SY586: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY585 @ SY586 ) @ SV139 )
| ~ ! [SY519: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY585 @ SY519 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY519 @ SY586 ) @ SV124 ) ) )
| ~ ( ~ ~ ! [SY520: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY585 @ SY520 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY520 @ SY586 ) @ SV124 ) )
| ( in @ ( ordered_pair @ SY585 @ SY586 ) @ SV139 ) ) ) )
= $false )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1363]) ).
thf(1451,plain,
! [SV69: $i,SV11: $i,SV107: $i,SV148: $i] :
( ( ( in @ SV148 @ SV107 )
= $false )
| ( ( ~ ! [SY597: $i] :
~ ~ ! [SY598: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY597 @ SV11 )
| ~ ( in @ SY598 @ SV69 ) )
| ( SV148
!= ( ordered_pair @ SY597 @ SY598 ) ) ) )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1364]) ).
thf(1452,plain,
! [SV107: $i,SV148: $i,SV69: $i,SV11: $i] :
( ( ( ~ ! [SY599: $i] :
~ ~ ! [SY600: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY599 @ SV11 )
| ~ ( in @ SY600 @ SV69 ) )
| ( SV148
!= ( ordered_pair @ SY599 @ SY600 ) ) ) )
= $false )
| ( ( in @ SV148 @ SV107 )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1365]) ).
thf(1453,plain,
! [SV107: $i,SV11: $i,SV69: $i] :
( ( ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 )
= $true )
| ( ( ~ ( ~ ~ ! [SY603: $i] :
~ ~ ! [SY604: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY603 @ SV11 )
| ~ ( in @ SY604 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SY603 @ SY604 ) ) )
| ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 ) ) )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1366]) ).
thf(1454,plain,
! [SV107: $i,SV69: $i,SV11: $i] :
( ( ( ! [SY601: $i] :
~ ~ ! [SY602: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY601 @ SV11 )
| ~ ( in @ SY602 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SY601 @ SY602 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY603: $i] :
~ ~ ! [SY604: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY603 @ SV11 )
| ~ ( in @ SY604 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SY603 @ SY604 ) ) )
| ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 ) ) )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1367]) ).
thf(1455,plain,
! [SV12: $i,SV70: $i,SV157: $i,SV153: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV153 @ SV157 ) @ SV70 )
| ~ ( ~ ( in @ SV153 @ SV12 )
| ( SV153 != SV157 ) ) )
= $true )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1368]) ).
thf(1456,plain,
! [SV70: $i,SV157: $i,SV12: $i,SV153: $i] :
( ( ( ~ ~ ( ~ ( in @ SV153 @ SV12 )
| ( SV153 != SV157 ) )
| ( in @ ( ordered_pair @ SV153 @ SV157 ) @ SV70 ) )
= $true )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1369]) ).
thf(1457,plain,
! [SV70: $i,SV12: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK20_SY424 @ SV12 @ SV70 ) @ ( sK23_SY606 @ SV70 @ SV12 ) ) @ SV70 )
| ~ ( ~ ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
| ( ( sK20_SY424 @ SV12 @ SV70 )
!= ( sK23_SY606 @ SV70 @ SV12 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
| ( ( sK20_SY424 @ SV12 @ SV70 )
!= ( sK23_SY606 @ SV70 @ SV12 ) ) )
| ( in @ ( ordered_pair @ ( sK20_SY424 @ SV12 @ SV70 ) @ ( sK23_SY606 @ SV70 @ SV12 ) ) @ SV70 ) ) )
= $true )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1370]) ).
thf(1458,plain,
! [SV71: $i,SV13: $i] :
( ( ( ~ ( subset @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV13 )
| ( in @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV71 ) )
= $false )
| ( ( in @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV71 )
= $true )
| ( ( SV71
= ( powerset @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1373]) ).
thf(1459,plain,
! [SV71: $i,SV13: $i] :
( ( ( ~ ( subset @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV13 ) )
= $false )
| ( ( subset @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV13 )
= $false )
| ( ( SV71
= ( powerset @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1374]) ).
thf(1460,plain,
! [SV71: $i,SV13: $i] :
( ( ( in @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV71 )
= $false )
| ( ( subset @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV13 )
= $false )
| ( ( SV71
= ( powerset @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1374]) ).
thf(1461,plain,
! [SV125: $i,SV14: $i,SV134: $i,SV158: $i] :
( ( ( ~ ( in @ SV158 @ SV134 )
| ~ ! [SY615: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV158 @ SY615 ) @ SV14 )
| ~ ( in @ SY615 @ SV125 ) ) )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1375]) ).
thf(1462,plain,
! [SV134: $i,SV125: $i,SV14: $i,SV158: $i] :
( ( ( ~ ~ ! [SY616: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV158 @ SY616 ) @ SV14 )
| ~ ( in @ SY616 @ SV125 ) )
| ( in @ SV158 @ SV134 ) )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1376]) ).
thf(1463,plain,
! [SV134: $i,SV14: $i,SV125: $i] :
( ( ( ~ ( in @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV134 )
| ~ ! [SY617: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SY617 ) @ SV14 )
| ~ ( in @ SY617 @ SV125 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY618: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SY618 ) @ SV14 )
| ~ ( in @ SY618 @ SV125 ) )
| ( in @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV134 ) ) )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1377]) ).
thf(1464,plain,
! [SV15: $i,SV126: $i,SV154: $i] :
( ( ( ~ ( in @ SV154 @ SV126 ) )
= $true )
| ( ( ~ ! [SY607: $i] :
~ ( in @ ( ordered_pair @ SY607 @ SV154 ) @ SV15 ) )
= $true )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $false )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1378]) ).
thf(1465,plain,
! [SV126: $i,SV15: $i,SV154: $i] :
( ( ( ~ ~ ! [SY608: $i] :
~ ( in @ ( ordered_pair @ SY608 @ SV154 ) @ SV15 ) )
= $true )
| ( ( in @ SV154 @ SV126 )
= $true )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $false )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1379]) ).
thf(1466,plain,
! [SV126: $i,SV15: $i] :
( ( ( ~ ( in @ ( sK21_SY531 @ SV15 @ SV126 ) @ SV126 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY610: $i] :
~ ( in @ ( ordered_pair @ SY610 @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 )
| ( in @ ( sK21_SY531 @ SV15 @ SV126 ) @ SV126 ) ) )
= $true )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1380]) ).
thf(1467,plain,
! [SV126: $i,SV15: $i] :
( ( ( ~ ! [SY609: $i] :
~ ( in @ ( ordered_pair @ SY609 @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY610: $i] :
~ ( in @ ( ordered_pair @ SY610 @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 )
| ( in @ ( sK21_SY531 @ SV15 @ SV126 ) @ SV126 ) ) )
= $true )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1380]) ).
thf(1468,plain,
! [SV127: $i,SV16: $i,SV168: $i,SV164: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV164 @ SV168 ) @ SV16 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV164 @ SV168 ) @ SV127 )
= $true )
| ( ( subset @ SV16 @ SV127 )
= $false )
| ( ( relation @ SV127 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1381]) ).
thf(1469,plain,
! [SV16: $i,SV127: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK28_SY536 @ SV127 @ SV16 ) @ ( sK32_SY628 @ SV16 @ SV127 ) ) @ SV16 ) )
= $false )
| ( ( subset @ SV16 @ SV127 )
= $true )
| ( ( relation @ SV127 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1382]) ).
thf(1470,plain,
! [SV16: $i,SV127: $i] :
( ( ( in @ ( ordered_pair @ ( sK28_SY536 @ SV127 @ SV16 ) @ ( sK32_SY628 @ SV16 @ SV127 ) ) @ SV127 )
= $false )
| ( ( subset @ SV16 @ SV127 )
= $true )
| ( ( relation @ SV127 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1382]) ).
thf(1471,plain,
! [SV72: $i,SV17: $i,SV108: $i,SV149: $i] :
( ( ( in @ SV149 @ SV108 )
= $false )
| ( ( ( in @ SV149 @ SV17 )
| ( in @ SV149 @ SV72 ) )
= $true )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1383]) ).
thf(1472,plain,
! [SV108: $i,SV72: $i,SV17: $i,SV149: $i] :
( ( ( ( in @ SV149 @ SV17 )
| ( in @ SV149 @ SV72 ) )
= $false )
| ( ( in @ SV149 @ SV108 )
= $true )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1384]) ).
thf(1473,plain,
! [SV108: $i,SV17: $i,SV72: $i] :
( ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV108 )
= $true )
| ( ( ~ ( ~ ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV17 )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV72 ) )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV108 ) ) )
= $true )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1385]) ).
thf(1474,plain,
! [SV108: $i,SV17: $i,SV72: $i] :
( ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV17 )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV17 )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV72 ) )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV108 ) ) )
= $true )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1386]) ).
thf(1475,plain,
! [SV108: $i,SV17: $i,SV72: $i] :
( ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV72 )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV17 )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV72 ) )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV108 ) ) )
= $true )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1386]) ).
thf(1476,plain,
! [SV20: $i,SV128: $i,SV135: $i,SV173: $i,SV169: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV135 )
| ~ ( ~ ( in @ SV169 @ SV128 )
| ~ ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV169 @ SV128 )
| ~ ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV20 ) )
| ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV135 ) ) ) )
= $true )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1387]) ).
thf(1477,plain,
! [SV135: $i,SV128: $i,SV20: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV135 )
| ~ ( ~ ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
| ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
| ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 ) )
| ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV135 ) ) ) )
= $false )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1388]) ).
thf(1478,plain,
! [SV21: $i,SV74: $i] :
( ( ( ~ ( in @ ( sK29_SY431 @ SV74 @ SV21 ) @ SV21 )
| ~ ( in @ ( sK29_SY431 @ SV74 @ SV21 ) @ SV74 ) )
= $false )
| ( ( disjoint @ SV21 @ SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1389]) ).
thf(1479,plain,
! [SV74: $i,SV21: $i,SV159: $i] :
( ( ( ~ ( in @ SV159 @ SV21 ) )
= $true )
| ( ( ~ ( in @ SV159 @ SV74 ) )
= $true )
| ( ( ~ ( disjoint @ SV21 @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1390]) ).
thf(1480,plain,
! [SV75: $i,SV109: $i,SV22: $i] :
( ( ( in @ SV22 @ ( relation_rng @ SV109 ) )
= $false )
| ( ( in @ SV22 @ SV75 )
= $false )
| ( ( in @ SV22 @ ( relation_rng @ ( relation_rng_restriction @ SV75 @ SV109 ) ) )
= $true )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1393]) ).
thf(1481,plain,
! [SV23: $i,SV174: $i] :
( ( ! [SY637: $i] :
( ~ ~ ( ~ ( in @ SV174 @ ( sK3_SY291 @ SV23 ) )
| ~ ( subset @ SY637 @ SV174 ) )
| ( in @ SY637 @ ( sK3_SY291 @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1395]) ).
thf(1482,plain,
! [SV23: $i,SV143: $i] :
( ( ( ~ ( subset @ SV143 @ ( sK3_SY291 @ SV23 ) ) )
= $true )
| ( ( ~ ~ ( are_equipotent @ SV143 @ ( sK3_SY291 @ SV23 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV143 @ ( sK3_SY291 @ SV23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1397]) ).
thf(1483,plain,
! [SV26: $i,SV78: $i,SV175: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV175 @ SV78 )
| ! [SY638: $i] :
( ~ ( in @ SY638 @ SV26 )
| ( in @ SV175 @ SY638 ) ) )
| ~ ( ~ ! [SY639: $i] :
( ~ ( in @ SY639 @ SV26 )
| ( in @ SV175 @ SY639 ) )
| ( in @ SV175 @ SV78 ) ) ) )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $false )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1398]) ).
thf(1484,plain,
! [SV78: $i,SV26: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV78 )
| ! [SY640: $i] :
( ~ ( in @ SY640 @ SV26 )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SY640 ) ) )
| ~ ( ~ ! [SY641: $i] :
( ~ ( in @ SY641 @ SV26 )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SY641 ) )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV78 ) ) ) )
= $false )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1399]) ).
thf(1485,plain,
! [SV129: $i,SV79: $i,SV110: $i,SV27: $i] :
( ( ( in @ SV27 @ SV110 )
= $true )
| ( ( in @ ( ordered_pair @ SV27 @ SV79 ) @ ( relation_composition @ ( identity_relation @ SV110 ) @ SV129 ) )
= $false )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1400]) ).
thf(1486,plain,
! [SV110: $i,SV129: $i,SV79: $i,SV27: $i] :
( ( ( in @ ( ordered_pair @ SV27 @ SV79 ) @ SV129 )
= $true )
| ( ( in @ ( ordered_pair @ SV27 @ SV79 ) @ ( relation_composition @ ( identity_relation @ SV110 ) @ SV129 ) )
= $false )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1401]) ).
thf(1487,plain,
! [SV129: $i,SV79: $i,SV110: $i,SV27: $i] :
( ( ( in @ SV27 @ SV110 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV27 @ SV79 ) @ SV129 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV27 @ SV79 ) @ ( relation_composition @ ( identity_relation @ SV110 ) @ SV129 ) )
= $true )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1402]) ).
thf(1488,plain,
! [SV131: $i,SV30: $i,SV136: $i,SV161: $i] :
( ( ( ~ ( in @ SV161 @ SV136 )
| ~ ! [SY619: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY619 @ SV161 ) @ SV30 )
| ~ ( in @ SY619 @ SV131 ) ) )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1404]) ).
thf(1489,plain,
! [SV136: $i,SV131: $i,SV30: $i,SV161: $i] :
( ( ( ~ ~ ! [SY620: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY620 @ SV161 ) @ SV30 )
| ~ ( in @ SY620 @ SV131 ) )
| ( in @ SV161 @ SV136 ) )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1405]) ).
thf(1490,plain,
! [SV136: $i,SV30: $i,SV131: $i] :
( ( ( ~ ( in @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) @ SV136 )
| ~ ! [SY621: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY621 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ SY621 @ SV131 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY622: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY622 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ SY622 @ SV131 ) )
| ( in @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) @ SV136 ) ) )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1406]) ).
thf(1491,plain,
! [SV35: $i,SV140: $i] :
( ( ( SV140
!= ( ordered_pair @ ( sK34_SY589 @ SV35 @ SV140 ) @ ( sK39_SY634 @ SV35 @ SV140 ) ) )
= $false )
| ( ( in @ SV140 @ SV35 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1409]) ).
thf(1492,plain,
! [SV170: $i,SV165: $i,SV35: $i] :
( ( ( ( sK9_SY328 @ SV35 )
= ( ordered_pair @ SV165 @ SV170 ) )
= $false )
| ( ( relation @ SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1410]) ).
thf(1493,plain,
! [SV87: $i,SV39: $i,SV137: $i,SV176: $i,SV171: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV137 )
| ~ ( ~ ( in @ SV176 @ SV39 )
| ~ ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV87 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV176 @ SV39 )
| ~ ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV87 ) )
| ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV137 ) ) ) )
= $true )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1411]) ).
thf(1494,plain,
! [SV137: $i,SV39: $i,SV87: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV137 )
| ~ ( ~ ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
| ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
| ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 ) )
| ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV137 ) ) ) )
= $false )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1412]) ).
thf(1495,plain,
! [SV88: $i,SV41: $i] :
( ( ( ( ( sK12_SY454 @ SV41 @ SV88 )
!= SV41 )
| ( in @ ( sK12_SY454 @ SV41 @ SV88 ) @ SV88 ) )
= $false )
| ( ( in @ ( sK12_SY454 @ SV41 @ SV88 ) @ SV88 )
= $true )
| ( ( SV88
= ( singleton @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1415]) ).
thf(1496,plain,
! [SV88: $i,SV41: $i] :
( ( ( ( sK12_SY454 @ SV41 @ SV88 )
!= SV41 )
= $false )
| ( ( ( sK12_SY454 @ SV41 @ SV88 )
= SV41 )
= $false )
| ( ( SV88
= ( singleton @ SV41 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1416]) ).
thf(1497,plain,
! [SV88: $i,SV41: $i] :
( ( ( in @ ( sK12_SY454 @ SV41 @ SV88 ) @ SV88 )
= $false )
| ( ( ( sK12_SY454 @ SV41 @ SV88 )
= SV41 )
= $false )
| ( ( SV88
= ( singleton @ SV41 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1416]) ).
thf(1498,plain,
! [SV89: $i,SV42: $i,SV145: $i] :
( ( ( ! [SY593: $i] :
~ ~ ( ~ ( in @ SV145 @ SY593 )
| ~ ( in @ SY593 @ SV42 ) ) )
= $false )
| ( ( in @ SV145 @ SV89 )
= $false )
| ( ( SV89
= ( union @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1417]) ).
thf(1499,plain,
! [SV89: $i,SV42: $i,SV145: $i] :
( ( ( ! [SY594: $i] :
~ ~ ( ~ ( in @ SV145 @ SY594 )
| ~ ( in @ SY594 @ SV42 ) ) )
= $true )
| ( ( in @ SV145 @ SV89 )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1418]) ).
thf(1500,plain,
! [SV89: $i,SV42: $i] :
( ( ( ~ ~ ! [SY596: $i] :
~ ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SY596 )
| ~ ( in @ SY596 @ SV42 ) )
| ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV89 ) )
= $false )
| ( ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1419]) ).
thf(1501,plain,
! [SV177: $i,SV89: $i,SV42: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV177 )
| ~ ( in @ SV177 @ SV42 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY596: $i] :
~ ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SY596 )
| ~ ( in @ SY596 @ SV42 ) )
| ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1420]) ).
thf(1502,plain,
! [SV90: $i,SV116: $i,SV43: $i] :
( ( ( in @ SV43 @ ( relation_dom @ SV116 ) )
= $false )
| ( ( in @ SV43 @ SV90 )
= $false )
| ( ( in @ SV43 @ ( relation_dom @ ( relation_dom_restriction @ SV116 @ SV90 ) ) )
= $true )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1423]) ).
thf(1503,plain,
! [SV46: $i,SV178: $i] :
( ( ! [SY642: $i] :
( ~ ~ ( ~ ( in @ SV178 @ ( sK4_SY357 @ SV46 ) )
| ~ ( subset @ SY642 @ SV178 ) )
| ( in @ SY642 @ ( sK4_SY357 @ SV46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1425]) ).
thf(1504,plain,
! [SV46: $i,SV162: $i] :
( ( ( ~ ( in @ SV162 @ ( sK4_SY357 @ SV46 ) ) )
= $true )
| ( ( ~ ! [SY623: $i] :
~ ~ ( ~ ( in @ SY623 @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SY624: $i] :
( ~ ( subset @ SY624 @ SV162 )
| ( in @ SY624 @ SY623 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1426]) ).
thf(1505,plain,
! [SV46: $i,SV146: $i] :
( ( ( ~ ( subset @ SV146 @ ( sK4_SY357 @ SV46 ) ) )
= $true )
| ( ( ~ ~ ( are_equipotent @ SV146 @ ( sK4_SY357 @ SV46 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV146 @ ( sK4_SY357 @ SV46 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1427]) ).
thf(1506,plain,
! [SV47: $i,SV132: $i,SV155: $i] :
( ( ( ~ ( in @ SV155 @ SV132 ) )
= $true )
| ( ( ~ ! [SY611: $i] :
~ ( in @ ( ordered_pair @ SV155 @ SY611 ) @ SV47 ) )
= $true )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1428]) ).
thf(1507,plain,
! [SV132: $i,SV47: $i,SV155: $i] :
( ( ( ~ ~ ! [SY612: $i] :
~ ( in @ ( ordered_pair @ SV155 @ SY612 ) @ SV47 ) )
= $true )
| ( ( in @ SV155 @ SV132 )
= $true )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1429]) ).
thf(1508,plain,
! [SV132: $i,SV47: $i] :
( ( ( ~ ( in @ ( sK22_SY553 @ SV47 @ SV132 ) @ SV132 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY614: $i] :
~ ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ SY614 ) @ SV47 )
| ( in @ ( sK22_SY553 @ SV47 @ SV132 ) @ SV132 ) ) )
= $true )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1430]) ).
thf(1509,plain,
! [SV132: $i,SV47: $i] :
( ( ( ~ ! [SY613: $i] :
~ ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ SY613 ) @ SV47 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY614: $i] :
~ ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ SY614 ) @ SV47 )
| ( in @ ( sK22_SY553 @ SV47 @ SV132 ) @ SV132 ) ) )
= $true )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1430]) ).
thf(1510,plain,
! [SV49: $i,SV133: $i,SV172: $i,SV166: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV166 @ SV172 ) @ SV133 )
| ( in @ ( ordered_pair @ SV172 @ SV166 ) @ SV49 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV172 @ SV166 ) @ SV49 )
| ( in @ ( ordered_pair @ SV166 @ SV172 ) @ SV133 ) ) )
= $false )
| ( ( SV133
= ( relation_inverse @ SV49 ) )
= $false )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1431]) ).
thf(1511,plain,
! [SV133: $i,SV49: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK30_SY558 @ SV49 @ SV133 ) @ ( sK36_SY631 @ SV133 @ SV49 ) ) @ SV133 )
| ( in @ ( ordered_pair @ ( sK36_SY631 @ SV133 @ SV49 ) @ ( sK30_SY558 @ SV49 @ SV133 ) ) @ SV49 ) )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK36_SY631 @ SV133 @ SV49 ) @ ( sK30_SY558 @ SV49 @ SV133 ) ) @ SV49 )
| ( in @ ( ordered_pair @ ( sK30_SY558 @ SV49 @ SV133 ) @ ( sK36_SY631 @ SV133 @ SV49 ) ) @ SV133 ) ) )
= $true )
| ( ( SV133
= ( relation_inverse @ SV49 ) )
= $true )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1432]) ).
thf(1512,plain,
! [SV100: $i,SV56: $i,SV118: $i,SV150: $i] :
( ( ( in @ SV150 @ SV118 )
= $false )
| ( ( ( SV150 = SV56 )
| ( SV150 = SV100 ) )
= $true )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1433]) ).
thf(1513,plain,
! [SV118: $i,SV100: $i,SV56: $i,SV150: $i] :
( ( ( ( SV150 = SV56 )
| ( SV150 = SV100 ) )
= $false )
| ( ( in @ SV150 @ SV118 )
= $true )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1434]) ).
thf(1514,plain,
! [SV118: $i,SV56: $i,SV100: $i] :
( ( ( in @ ( sK17_SY503 @ SV100 @ SV56 @ SV118 ) @ SV118 )
= $true )
| ( ( ~ ( ~ ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV56 )
| ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV100 ) )
| ( in @ ( sK17_SY503 @ SV100 @ SV56 @ SV118 ) @ SV118 ) ) )
= $true )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1435]) ).
thf(1515,plain,
! [SV118: $i,SV56: $i,SV100: $i] :
( ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV56 )
= $false )
| ( ( ~ ( ~ ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV56 )
| ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV100 ) )
| ( in @ ( sK17_SY503 @ SV100 @ SV56 @ SV118 ) @ SV118 ) ) )
= $true )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1436]) ).
thf(1516,plain,
! [SV118: $i,SV56: $i,SV100: $i] :
( ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV100 )
= $false )
| ( ( ~ ( ~ ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV56 )
| ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV100 ) )
| ( in @ ( sK17_SY503 @ SV100 @ SV56 @ SV118 ) @ SV118 ) ) )
= $true )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1436]) ).
thf(1517,plain,
! [SV102: $i,SV58: $i,SV119: $i,SV151: $i] :
( ( ( in @ SV151 @ SV119 )
= $false )
| ( ( ~ ( ~ ( in @ SV151 @ SV58 )
| ~ ~ ( in @ SV151 @ SV102 ) ) )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1437]) ).
thf(1518,plain,
! [SV119: $i,SV102: $i,SV58: $i,SV151: $i] :
( ( ( ~ ( ~ ( in @ SV151 @ SV58 )
| ~ ~ ( in @ SV151 @ SV102 ) ) )
= $false )
| ( ( in @ SV151 @ SV119 )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1438]) ).
thf(1519,plain,
! [SV119: $i,SV58: $i,SV102: $i] :
( ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV119 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
| ~ ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 ) )
| ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV119 ) ) )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1439]) ).
thf(1520,plain,
! [SV119: $i,SV58: $i,SV102: $i] :
( ( ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
| ~ ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
| ~ ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 ) )
| ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV119 ) ) )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1440]) ).
thf(1521,plain,
! [SV104: $i,SV60: $i,SV121: $i,SV152: $i] :
( ( ( in @ SV152 @ SV121 )
= $false )
| ( ( ~ ( ~ ( in @ SV152 @ SV60 )
| ~ ( in @ SV152 @ SV104 ) ) )
= $true )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1441]) ).
thf(1522,plain,
! [SV121: $i,SV104: $i,SV60: $i,SV152: $i] :
( ( ( ~ ( ~ ( in @ SV152 @ SV60 )
| ~ ( in @ SV152 @ SV104 ) ) )
= $false )
| ( ( in @ SV152 @ SV121 )
= $true )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1442]) ).
thf(1523,plain,
! [SV121: $i,SV60: $i,SV104: $i] :
( ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV121 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
| ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 ) )
| ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV121 ) ) )
= $true )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1443]) ).
thf(1524,plain,
! [SV121: $i,SV60: $i,SV104: $i] :
( ( ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
| ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
| ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 ) )
| ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV121 ) ) )
= $true )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1444]) ).
thf(1525,plain,
! [SV6: $i,SV66: $i] :
( ( ( ( relation_dom @ SV66 )
!= SV6 )
= $false )
| ( ( SV66
= ( identity_relation @ SV6 ) )
= $false )
| ( ( relation @ SV66 )
= $false )
| ( ( function @ SV66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1445]) ).
thf(1526,plain,
! [SV66: $i,SV6: $i] :
( ( ( ~ ! [SY407: $i] :
( ~ ( in @ SY407 @ SV6 )
| ( ( apply @ SV66 @ SY407 )
= SY407 ) ) )
= $false )
| ( ( SV66
= ( identity_relation @ SV6 ) )
= $false )
| ( ( relation @ SV66 )
= $false )
| ( ( function @ SV66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1445]) ).
thf(1527,plain,
! [SV6: $i,SV66: $i] :
( ( ( ( relation_dom @ SV66 )
!= SV6 )
= $true )
| ( ( ~ ! [SY408: $i] :
( ~ ( in @ SY408 @ SV6 )
| ( ( apply @ SV66 @ SY408 )
= SY408 ) ) )
= $true )
| ( ( SV66
= ( identity_relation @ SV6 ) )
= $true )
| ( ( relation @ SV66 )
= $false )
| ( ( function @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1446]) ).
thf(1528,plain,
! [SV123: $i,SV8: $i,SV167: $i,SV163: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV163 @ SV167 ) @ SV8 )
| ( in @ ( ordered_pair @ SV163 @ SV167 ) @ SV123 ) ) )
= $false )
| ( ( SV8 = SV123 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1447]) ).
thf(1529,plain,
! [SV8: $i,SV123: $i,SV167: $i,SV163: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV163 @ SV167 ) @ SV123 )
| ( in @ ( ordered_pair @ SV163 @ SV167 ) @ SV8 ) ) )
= $false )
| ( ( SV8 = SV123 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1447]) ).
thf(1530,plain,
! [SV8: $i,SV123: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV8 )
| ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV123 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV8 ) ) )
= $true )
| ( ( SV8 = SV123 )
= $true )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1448]) ).
thf(1531,plain,
! [SV124: $i,SV10: $i,SV139: $i,SV179: $i] :
( ( ( ! [SY643: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV179 @ SY643 ) @ SV139 )
| ~ ! [SY644: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV179 @ SY644 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY644 @ SY643 ) @ SV124 ) ) )
| ~ ( ~ ~ ! [SY645: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV179 @ SY645 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY645 @ SY643 ) @ SV124 ) )
| ( in @ ( ordered_pair @ SV179 @ SY643 ) @ SV139 ) ) ) )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $false )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1449]) ).
thf(1532,plain,
! [SV139: $i,SV10: $i,SV124: $i] :
( ( ( ! [SY646: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SY646 ) @ SV139 )
| ~ ! [SY647: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SY647 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY647 @ SY646 ) @ SV124 ) ) )
| ~ ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SY648 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY648 @ SY646 ) @ SV124 ) )
| ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SY646 ) @ SV139 ) ) ) )
= $false )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1450]) ).
thf(1533,plain,
! [SV107: $i,SV148: $i,SV69: $i,SV11: $i] :
( ( ( ! [SY597: $i] :
~ ~ ! [SY598: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY597 @ SV11 )
| ~ ( in @ SY598 @ SV69 ) )
| ( SV148
!= ( ordered_pair @ SY597 @ SY598 ) ) ) )
= $false )
| ( ( in @ SV148 @ SV107 )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1451]) ).
thf(1534,plain,
! [SV107: $i,SV148: $i,SV69: $i,SV11: $i] :
( ( ( ! [SY599: $i] :
~ ~ ! [SY600: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY599 @ SV11 )
| ~ ( in @ SY600 @ SV69 ) )
| ( SV148
!= ( ordered_pair @ SY599 @ SY600 ) ) ) )
= $true )
| ( ( in @ SV148 @ SV107 )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1452]) ).
thf(1535,plain,
! [SV107: $i,SV69: $i,SV11: $i] :
( ( ( ~ ~ ! [SY603: $i] :
~ ~ ! [SY604: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY603 @ SV11 )
| ~ ( in @ SY604 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SY603 @ SY604 ) ) )
| ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 ) )
= $false )
| ( ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1453]) ).
thf(1536,plain,
! [SV107: $i,SV69: $i,SV11: $i,SV180: $i] :
( ( ( ~ ~ ! [SY649: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV180 @ SV11 )
| ~ ( in @ SY649 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SV180 @ SY649 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY603: $i] :
~ ~ ! [SY604: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY603 @ SV11 )
| ~ ( in @ SY604 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SY603 @ SY604 ) ) )
| ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 ) ) )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1454]) ).
thf(1537,plain,
! [SV12: $i,SV70: $i,SV157: $i,SV153: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV153 @ SV157 ) @ SV70 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV153 @ SV12 )
| ( SV153 != SV157 ) ) )
= $true )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1455]) ).
thf(1538,plain,
! [SV70: $i,SV157: $i,SV12: $i,SV153: $i] :
( ( ( ~ ~ ( ~ ( in @ SV153 @ SV12 )
| ( SV153 != SV157 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV153 @ SV157 ) @ SV70 )
= $true )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1456]) ).
thf(1539,plain,
! [SV70: $i,SV12: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK20_SY424 @ SV12 @ SV70 ) @ ( sK23_SY606 @ SV70 @ SV12 ) ) @ SV70 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
| ( ( sK20_SY424 @ SV12 @ SV70 )
!= ( sK23_SY606 @ SV70 @ SV12 ) ) )
| ( in @ ( ordered_pair @ ( sK20_SY424 @ SV12 @ SV70 ) @ ( sK23_SY606 @ SV70 @ SV12 ) ) @ SV70 ) ) )
= $true )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1457]) ).
thf(1540,plain,
! [SV70: $i,SV12: $i] :
( ( ( ~ ( ~ ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
| ( ( sK20_SY424 @ SV12 @ SV70 )
!= ( sK23_SY606 @ SV70 @ SV12 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
| ( ( sK20_SY424 @ SV12 @ SV70 )
!= ( sK23_SY606 @ SV70 @ SV12 ) ) )
| ( in @ ( ordered_pair @ ( sK20_SY424 @ SV12 @ SV70 ) @ ( sK23_SY606 @ SV70 @ SV12 ) ) @ SV70 ) ) )
= $true )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1457]) ).
thf(1541,plain,
! [SV71: $i,SV13: $i] :
( ( ( ~ ( subset @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV13 ) )
= $false )
| ( ( in @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV71 )
= $true )
| ( ( SV71
= ( powerset @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1458]) ).
thf(1542,plain,
! [SV71: $i,SV13: $i] :
( ( ( in @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV71 )
= $false )
| ( ( in @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV71 )
= $true )
| ( ( SV71
= ( powerset @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1458]) ).
thf(1543,plain,
! [SV71: $i,SV13: $i] :
( ( ( subset @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV13 )
= $true )
| ( ( subset @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV13 )
= $false )
| ( ( SV71
= ( powerset @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1459]) ).
thf(1544,plain,
! [SV125: $i,SV14: $i,SV134: $i,SV158: $i] :
( ( ( ~ ( in @ SV158 @ SV134 ) )
= $true )
| ( ( ~ ! [SY615: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV158 @ SY615 ) @ SV14 )
| ~ ( in @ SY615 @ SV125 ) ) )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1461]) ).
thf(1545,plain,
! [SV134: $i,SV125: $i,SV14: $i,SV158: $i] :
( ( ( ~ ~ ! [SY616: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV158 @ SY616 ) @ SV14 )
| ~ ( in @ SY616 @ SV125 ) ) )
= $true )
| ( ( in @ SV158 @ SV134 )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1462]) ).
thf(1546,plain,
! [SV134: $i,SV14: $i,SV125: $i] :
( ( ( ~ ( in @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV134 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY618: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SY618 ) @ SV14 )
| ~ ( in @ SY618 @ SV125 ) )
| ( in @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV134 ) ) )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1463]) ).
thf(1547,plain,
! [SV134: $i,SV14: $i,SV125: $i] :
( ( ( ~ ! [SY617: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SY617 ) @ SV14 )
| ~ ( in @ SY617 @ SV125 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY618: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SY618 ) @ SV14 )
| ~ ( in @ SY618 @ SV125 ) )
| ( in @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV134 ) ) )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1463]) ).
thf(1548,plain,
! [SV15: $i,SV126: $i,SV154: $i] :
( ( ( in @ SV154 @ SV126 )
= $false )
| ( ( ~ ! [SY607: $i] :
~ ( in @ ( ordered_pair @ SY607 @ SV154 ) @ SV15 ) )
= $true )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $false )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1464]) ).
thf(1549,plain,
! [SV126: $i,SV15: $i,SV154: $i] :
( ( ( ~ ! [SY608: $i] :
~ ( in @ ( ordered_pair @ SY608 @ SV154 ) @ SV15 ) )
= $false )
| ( ( in @ SV154 @ SV126 )
= $true )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $false )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1465]) ).
thf(1550,plain,
! [SV126: $i,SV15: $i] :
( ( ( in @ ( sK21_SY531 @ SV15 @ SV126 ) @ SV126 )
= $true )
| ( ( ~ ( ~ ~ ! [SY610: $i] :
~ ( in @ ( ordered_pair @ SY610 @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 )
| ( in @ ( sK21_SY531 @ SV15 @ SV126 ) @ SV126 ) ) )
= $true )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1466]) ).
thf(1551,plain,
! [SV126: $i,SV15: $i] :
( ( ( ! [SY609: $i] :
~ ( in @ ( ordered_pair @ SY609 @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY610: $i] :
~ ( in @ ( ordered_pair @ SY610 @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 )
| ( in @ ( sK21_SY531 @ SV15 @ SV126 ) @ SV126 ) ) )
= $true )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1467]) ).
thf(1552,plain,
! [SV127: $i,SV16: $i,SV168: $i,SV164: $i] :
( ( ( in @ ( ordered_pair @ SV164 @ SV168 ) @ SV16 )
= $false )
| ( ( in @ ( ordered_pair @ SV164 @ SV168 ) @ SV127 )
= $true )
| ( ( subset @ SV16 @ SV127 )
= $false )
| ( ( relation @ SV127 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1468]) ).
thf(1553,plain,
! [SV16: $i,SV127: $i] :
( ( ( in @ ( ordered_pair @ ( sK28_SY536 @ SV127 @ SV16 ) @ ( sK32_SY628 @ SV16 @ SV127 ) ) @ SV16 )
= $true )
| ( ( subset @ SV16 @ SV127 )
= $true )
| ( ( relation @ SV127 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1469]) ).
thf(1554,plain,
! [SV108: $i,SV72: $i,SV17: $i,SV149: $i] :
( ( ( in @ SV149 @ SV17 )
= $true )
| ( ( in @ SV149 @ SV72 )
= $true )
| ( ( in @ SV149 @ SV108 )
= $false )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1471]) ).
thf(1555,plain,
! [SV72: $i,SV108: $i,SV17: $i,SV149: $i] :
( ( ( in @ SV149 @ SV17 )
= $false )
| ( ( in @ SV149 @ SV108 )
= $true )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1472]) ).
thf(1556,plain,
! [SV17: $i,SV108: $i,SV72: $i,SV149: $i] :
( ( ( in @ SV149 @ SV72 )
= $false )
| ( ( in @ SV149 @ SV108 )
= $true )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1472]) ).
thf(1557,plain,
! [SV108: $i,SV17: $i,SV72: $i] :
( ( ( ~ ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV17 )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV72 ) )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV108 ) )
= $false )
| ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV108 )
= $true )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1473]) ).
thf(1558,plain,
! [SV108: $i,SV17: $i,SV72: $i] :
( ( ( ~ ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV17 )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV72 ) )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV108 ) )
= $false )
| ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV17 )
= $false )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1474]) ).
thf(1559,plain,
! [SV108: $i,SV17: $i,SV72: $i] :
( ( ( ~ ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV17 )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV72 ) )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV108 ) )
= $false )
| ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV72 )
= $false )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1475]) ).
thf(1560,plain,
! [SV20: $i,SV128: $i,SV135: $i,SV173: $i,SV169: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV135 )
| ~ ( ~ ( in @ SV169 @ SV128 )
| ~ ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV169 @ SV128 )
| ~ ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV20 ) )
| ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV135 ) ) )
= $false )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1476]) ).
thf(1561,plain,
! [SV135: $i,SV128: $i,SV20: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV135 )
| ~ ( ~ ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
| ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
| ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 ) )
| ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV135 ) ) )
= $true )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1477]) ).
thf(1562,plain,
! [SV21: $i,SV74: $i] :
( ( ( ~ ( in @ ( sK29_SY431 @ SV74 @ SV21 ) @ SV21 ) )
= $false )
| ( ( disjoint @ SV21 @ SV74 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1478]) ).
thf(1563,plain,
! [SV21: $i,SV74: $i] :
( ( ( ~ ( in @ ( sK29_SY431 @ SV74 @ SV21 ) @ SV74 ) )
= $false )
| ( ( disjoint @ SV21 @ SV74 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1478]) ).
thf(1564,plain,
! [SV74: $i,SV21: $i,SV159: $i] :
( ( ( in @ SV159 @ SV21 )
= $false )
| ( ( ~ ( in @ SV159 @ SV74 ) )
= $true )
| ( ( ~ ( disjoint @ SV21 @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1479]) ).
thf(1565,plain,
! [SV181: $i,SV23: $i,SV174: $i] :
( ( ~ ~ ( ~ ( in @ SV174 @ ( sK3_SY291 @ SV23 ) )
| ~ ( subset @ SV181 @ SV174 ) )
| ( in @ SV181 @ ( sK3_SY291 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1481]) ).
thf(1566,plain,
! [SV23: $i,SV143: $i] :
( ( ( subset @ SV143 @ ( sK3_SY291 @ SV23 ) )
= $false )
| ( ( ~ ~ ( are_equipotent @ SV143 @ ( sK3_SY291 @ SV23 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV143 @ ( sK3_SY291 @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1482]) ).
thf(1567,plain,
! [SV26: $i,SV78: $i,SV175: $i] :
( ( ( ~ ( ~ ( in @ SV175 @ SV78 )
| ! [SY638: $i] :
( ~ ( in @ SY638 @ SV26 )
| ( in @ SV175 @ SY638 ) ) )
| ~ ( ~ ! [SY639: $i] :
( ~ ( in @ SY639 @ SV26 )
| ( in @ SV175 @ SY639 ) )
| ( in @ SV175 @ SV78 ) ) )
= $false )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $false )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1483]) ).
thf(1568,plain,
! [SV78: $i,SV26: $i] :
( ( ( ~ ( ~ ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV78 )
| ! [SY640: $i] :
( ~ ( in @ SY640 @ SV26 )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SY640 ) ) )
| ~ ( ~ ! [SY641: $i] :
( ~ ( in @ SY641 @ SV26 )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SY641 ) )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV78 ) ) )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1484]) ).
thf(1569,plain,
! [SV110: $i,SV129: $i,SV79: $i,SV27: $i] :
( ( ( in @ ( ordered_pair @ SV27 @ SV79 ) @ SV129 )
= $false )
| ( ( in @ SV27 @ SV110 )
= $false )
| ( ( in @ ( ordered_pair @ SV27 @ SV79 ) @ ( relation_composition @ ( identity_relation @ SV110 ) @ SV129 ) )
= $true )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1487]) ).
thf(1570,plain,
! [SV131: $i,SV30: $i,SV136: $i,SV161: $i] :
( ( ( ~ ( in @ SV161 @ SV136 ) )
= $true )
| ( ( ~ ! [SY619: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY619 @ SV161 ) @ SV30 )
| ~ ( in @ SY619 @ SV131 ) ) )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1488]) ).
thf(1571,plain,
! [SV136: $i,SV131: $i,SV30: $i,SV161: $i] :
( ( ( ~ ~ ! [SY620: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY620 @ SV161 ) @ SV30 )
| ~ ( in @ SY620 @ SV131 ) ) )
= $true )
| ( ( in @ SV161 @ SV136 )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1489]) ).
thf(1572,plain,
! [SV136: $i,SV30: $i,SV131: $i] :
( ( ( ~ ( in @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) @ SV136 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY622: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY622 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ SY622 @ SV131 ) )
| ( in @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) @ SV136 ) ) )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1490]) ).
thf(1573,plain,
! [SV136: $i,SV30: $i,SV131: $i] :
( ( ( ~ ! [SY621: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY621 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ SY621 @ SV131 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY622: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY622 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ SY622 @ SV131 ) )
| ( in @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) @ SV136 ) ) )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1490]) ).
thf(1574,plain,
! [SV35: $i,SV140: $i] :
( ( ( SV140
= ( ordered_pair @ ( sK34_SY589 @ SV35 @ SV140 ) @ ( sK39_SY634 @ SV35 @ SV140 ) ) )
= $true )
| ( ( in @ SV140 @ SV35 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1491]) ).
thf(1575,plain,
! [SV87: $i,SV39: $i,SV137: $i,SV176: $i,SV171: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV137 )
| ~ ( ~ ( in @ SV176 @ SV39 )
| ~ ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV87 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV176 @ SV39 )
| ~ ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV87 ) )
| ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV137 ) ) )
= $false )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1493]) ).
thf(1576,plain,
! [SV137: $i,SV39: $i,SV87: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV137 )
| ~ ( ~ ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
| ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
| ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 ) )
| ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV137 ) ) )
= $true )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1494]) ).
thf(1577,plain,
! [SV88: $i,SV41: $i] :
( ( ( ( sK12_SY454 @ SV41 @ SV88 )
!= SV41 )
= $false )
| ( ( in @ ( sK12_SY454 @ SV41 @ SV88 ) @ SV88 )
= $true )
| ( ( SV88
= ( singleton @ SV41 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1495]) ).
thf(1578,plain,
! [SV88: $i,SV41: $i] :
( ( ( in @ ( sK12_SY454 @ SV41 @ SV88 ) @ SV88 )
= $false )
| ( ( in @ ( sK12_SY454 @ SV41 @ SV88 ) @ SV88 )
= $true )
| ( ( SV88
= ( singleton @ SV41 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1495]) ).
thf(1579,plain,
! [SV88: $i,SV41: $i] :
( ( ( ( sK12_SY454 @ SV41 @ SV88 )
= SV41 )
= $true )
| ( ( ( sK12_SY454 @ SV41 @ SV88 )
= SV41 )
= $false )
| ( ( SV88
= ( singleton @ SV41 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1496]) ).
thf(1580,plain,
! [SV42: $i,SV89: $i,SV145: $i] :
( ( ( ~ ~ ( ~ ( in @ SV145 @ ( sK42_SY593 @ SV89 @ SV42 @ SV145 ) )
| ~ ( in @ ( sK42_SY593 @ SV89 @ SV42 @ SV145 ) @ SV42 ) ) )
= $false )
| ( ( in @ SV145 @ SV89 )
= $false )
| ( ( SV89
= ( union @ SV42 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1498]) ).
thf(1581,plain,
! [SV89: $i,SV42: $i,SV182: $i,SV145: $i] :
( ( ( ~ ~ ( ~ ( in @ SV145 @ SV182 )
| ~ ( in @ SV182 @ SV42 ) ) )
= $true )
| ( ( in @ SV145 @ SV89 )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1499]) ).
thf(1582,plain,
! [SV89: $i,SV42: $i] :
( ( ( ~ ~ ! [SY596: $i] :
~ ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SY596 )
| ~ ( in @ SY596 @ SV42 ) ) )
= $false )
| ( ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1500]) ).
thf(1583,plain,
! [SV89: $i,SV42: $i] :
( ( ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV89 )
= $false )
| ( ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1500]) ).
thf(1584,plain,
! [SV177: $i,SV89: $i,SV42: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV177 )
| ~ ( in @ SV177 @ SV42 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY596: $i] :
~ ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SY596 )
| ~ ( in @ SY596 @ SV42 ) )
| ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1501]) ).
thf(1585,plain,
! [SV183: $i,SV46: $i,SV178: $i] :
( ( ~ ~ ( ~ ( in @ SV178 @ ( sK4_SY357 @ SV46 ) )
| ~ ( subset @ SV183 @ SV178 ) )
| ( in @ SV183 @ ( sK4_SY357 @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1503]) ).
thf(1586,plain,
! [SV46: $i,SV162: $i] :
( ( ( in @ SV162 @ ( sK4_SY357 @ SV46 ) )
= $false )
| ( ( ~ ! [SY623: $i] :
~ ~ ( ~ ( in @ SY623 @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SY624: $i] :
( ~ ( subset @ SY624 @ SV162 )
| ( in @ SY624 @ SY623 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1504]) ).
thf(1587,plain,
! [SV46: $i,SV146: $i] :
( ( ( subset @ SV146 @ ( sK4_SY357 @ SV46 ) )
= $false )
| ( ( ~ ~ ( are_equipotent @ SV146 @ ( sK4_SY357 @ SV46 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV146 @ ( sK4_SY357 @ SV46 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1505]) ).
thf(1588,plain,
! [SV47: $i,SV132: $i,SV155: $i] :
( ( ( in @ SV155 @ SV132 )
= $false )
| ( ( ~ ! [SY611: $i] :
~ ( in @ ( ordered_pair @ SV155 @ SY611 ) @ SV47 ) )
= $true )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1506]) ).
thf(1589,plain,
! [SV132: $i,SV47: $i,SV155: $i] :
( ( ( ~ ! [SY612: $i] :
~ ( in @ ( ordered_pair @ SV155 @ SY612 ) @ SV47 ) )
= $false )
| ( ( in @ SV155 @ SV132 )
= $true )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1507]) ).
thf(1590,plain,
! [SV132: $i,SV47: $i] :
( ( ( in @ ( sK22_SY553 @ SV47 @ SV132 ) @ SV132 )
= $true )
| ( ( ~ ( ~ ~ ! [SY614: $i] :
~ ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ SY614 ) @ SV47 )
| ( in @ ( sK22_SY553 @ SV47 @ SV132 ) @ SV132 ) ) )
= $true )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1508]) ).
thf(1591,plain,
! [SV132: $i,SV47: $i] :
( ( ( ! [SY613: $i] :
~ ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ SY613 ) @ SV47 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY614: $i] :
~ ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ SY614 ) @ SV47 )
| ( in @ ( sK22_SY553 @ SV47 @ SV132 ) @ SV132 ) ) )
= $true )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1509]) ).
thf(1592,plain,
! [SV49: $i,SV133: $i,SV172: $i,SV166: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV166 @ SV172 ) @ SV133 )
| ( in @ ( ordered_pair @ SV172 @ SV166 ) @ SV49 ) ) )
= $false )
| ( ( SV133
= ( relation_inverse @ SV49 ) )
= $false )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1510]) ).
thf(1593,plain,
! [SV133: $i,SV49: $i,SV166: $i,SV172: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV172 @ SV166 ) @ SV49 )
| ( in @ ( ordered_pair @ SV166 @ SV172 ) @ SV133 ) ) )
= $false )
| ( ( SV133
= ( relation_inverse @ SV49 ) )
= $false )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1510]) ).
thf(1594,plain,
! [SV133: $i,SV49: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK30_SY558 @ SV49 @ SV133 ) @ ( sK36_SY631 @ SV133 @ SV49 ) ) @ SV133 )
| ( in @ ( ordered_pair @ ( sK36_SY631 @ SV133 @ SV49 ) @ ( sK30_SY558 @ SV49 @ SV133 ) ) @ SV49 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK36_SY631 @ SV133 @ SV49 ) @ ( sK30_SY558 @ SV49 @ SV133 ) ) @ SV49 )
| ( in @ ( ordered_pair @ ( sK30_SY558 @ SV49 @ SV133 ) @ ( sK36_SY631 @ SV133 @ SV49 ) ) @ SV133 ) ) )
= $true )
| ( ( SV133
= ( relation_inverse @ SV49 ) )
= $true )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1511]) ).
thf(1595,plain,
! [SV118: $i,SV100: $i,SV56: $i,SV150: $i] :
( ( ( SV150 = SV56 )
= $true )
| ( ( SV150 = SV100 )
= $true )
| ( ( in @ SV150 @ SV118 )
= $false )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1512]) ).
thf(1596,plain,
! [SV100: $i,SV118: $i,SV56: $i,SV150: $i] :
( ( ( SV150 = SV56 )
= $false )
| ( ( in @ SV150 @ SV118 )
= $true )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1513]) ).
thf(1597,plain,
! [SV56: $i,SV118: $i,SV100: $i,SV150: $i] :
( ( ( SV150 = SV100 )
= $false )
| ( ( in @ SV150 @ SV118 )
= $true )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1513]) ).
thf(1598,plain,
! [SV118: $i,SV56: $i,SV100: $i] :
( ( ( ~ ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV56 )
| ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV100 ) )
| ( in @ ( sK17_SY503 @ SV100 @ SV56 @ SV118 ) @ SV118 ) )
= $false )
| ( ( in @ ( sK17_SY503 @ SV100 @ SV56 @ SV118 ) @ SV118 )
= $true )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1514]) ).
thf(1599,plain,
! [SV118: $i,SV56: $i,SV100: $i] :
( ( ( ~ ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV56 )
| ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV100 ) )
| ( in @ ( sK17_SY503 @ SV100 @ SV56 @ SV118 ) @ SV118 ) )
= $false )
| ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV56 )
= $false )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1515]) ).
thf(1600,plain,
! [SV118: $i,SV56: $i,SV100: $i] :
( ( ( ~ ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV56 )
| ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV100 ) )
| ( in @ ( sK17_SY503 @ SV100 @ SV56 @ SV118 ) @ SV118 ) )
= $false )
| ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV100 )
= $false )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1516]) ).
thf(1601,plain,
! [SV119: $i,SV102: $i,SV58: $i,SV151: $i] :
( ( ( ~ ( in @ SV151 @ SV58 )
| ~ ~ ( in @ SV151 @ SV102 ) )
= $false )
| ( ( in @ SV151 @ SV119 )
= $false )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1517]) ).
thf(1602,plain,
! [SV119: $i,SV102: $i,SV58: $i,SV151: $i] :
( ( ( ~ ( in @ SV151 @ SV58 )
| ~ ~ ( in @ SV151 @ SV102 ) )
= $true )
| ( ( in @ SV151 @ SV119 )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1518]) ).
thf(1603,plain,
! [SV119: $i,SV58: $i,SV102: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
| ~ ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 ) )
| ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV119 ) )
= $false )
| ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV119 )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1519]) ).
thf(1604,plain,
! [SV119: $i,SV58: $i,SV102: $i] :
( ( ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 ) )
= $true )
| ( ( ~ ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
| ~ ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 ) )
| ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV119 ) ) )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1520]) ).
thf(1605,plain,
! [SV121: $i,SV104: $i,SV60: $i,SV152: $i] :
( ( ( ~ ( in @ SV152 @ SV60 )
| ~ ( in @ SV152 @ SV104 ) )
= $false )
| ( ( in @ SV152 @ SV121 )
= $false )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1521]) ).
thf(1606,plain,
! [SV121: $i,SV104: $i,SV60: $i,SV152: $i] :
( ( ( ~ ( in @ SV152 @ SV60 )
| ~ ( in @ SV152 @ SV104 ) )
= $true )
| ( ( in @ SV152 @ SV121 )
= $true )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1522]) ).
thf(1607,plain,
! [SV121: $i,SV60: $i,SV104: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
| ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 ) )
| ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV121 ) )
= $false )
| ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV121 )
= $true )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1523]) ).
thf(1608,plain,
! [SV121: $i,SV60: $i,SV104: $i] :
( ( ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 ) )
= $true )
| ( ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
| ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 ) )
| ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV121 ) ) )
= $true )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1524]) ).
thf(1609,plain,
! [SV6: $i,SV66: $i] :
( ( ( ( relation_dom @ SV66 )
= SV6 )
= $true )
| ( ( SV66
= ( identity_relation @ SV6 ) )
= $false )
| ( ( relation @ SV66 )
= $false )
| ( ( function @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1525]) ).
thf(1610,plain,
! [SV66: $i,SV6: $i] :
( ( ( ! [SY407: $i] :
( ~ ( in @ SY407 @ SV6 )
| ( ( apply @ SV66 @ SY407 )
= SY407 ) ) )
= $true )
| ( ( SV66
= ( identity_relation @ SV6 ) )
= $false )
| ( ( relation @ SV66 )
= $false )
| ( ( function @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1526]) ).
thf(1611,plain,
! [SV6: $i,SV66: $i] :
( ( ( ( relation_dom @ SV66 )
= SV6 )
= $false )
| ( ( ~ ! [SY408: $i] :
( ~ ( in @ SY408 @ SV6 )
| ( ( apply @ SV66 @ SY408 )
= SY408 ) ) )
= $true )
| ( ( SV66
= ( identity_relation @ SV6 ) )
= $true )
| ( ( relation @ SV66 )
= $false )
| ( ( function @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1527]) ).
thf(1612,plain,
! [SV123: $i,SV8: $i,SV167: $i,SV163: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV163 @ SV167 ) @ SV8 )
| ( in @ ( ordered_pair @ SV163 @ SV167 ) @ SV123 ) )
= $true )
| ( ( SV8 = SV123 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1528]) ).
thf(1613,plain,
! [SV8: $i,SV123: $i,SV167: $i,SV163: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV163 @ SV167 ) @ SV123 )
| ( in @ ( ordered_pair @ SV163 @ SV167 ) @ SV8 ) )
= $true )
| ( ( SV8 = SV123 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1529]) ).
thf(1614,plain,
! [SV8: $i,SV123: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV8 )
| ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV123 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV8 ) ) )
= $true )
| ( ( SV8 = SV123 )
= $true )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1530]) ).
thf(1615,plain,
! [SV124: $i,SV10: $i,SV139: $i,SV184: $i,SV179: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV179 @ SV184 ) @ SV139 )
| ~ ! [SY650: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV179 @ SY650 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY650 @ SV184 ) @ SV124 ) ) )
| ~ ( ~ ~ ! [SY651: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV179 @ SY651 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY651 @ SV184 ) @ SV124 ) )
| ( in @ ( ordered_pair @ SV179 @ SV184 ) @ SV139 ) ) ) )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $false )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1531]) ).
thf(1616,plain,
! [SV139: $i,SV10: $i,SV124: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV139 )
| ~ ! [SY652: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SY652 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY652 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) ) )
| ~ ( ~ ~ ! [SY653: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SY653 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY653 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) )
| ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV139 ) ) ) )
= $false )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1532]) ).
thf(1617,plain,
! [SV11: $i,SV69: $i,SV148: $i,SV107: $i] :
( ( ( ~ ~ ! [SY654: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK44_SY597 @ SV107 @ SV148 @ SV69 @ SV11 ) @ SV11 )
| ~ ( in @ SY654 @ SV69 ) )
| ( SV148
!= ( ordered_pair @ ( sK44_SY597 @ SV107 @ SV148 @ SV69 @ SV11 ) @ SY654 ) ) ) )
= $false )
| ( ( in @ SV148 @ SV107 )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1533]) ).
thf(1618,plain,
! [SV107: $i,SV148: $i,SV69: $i,SV11: $i,SV185: $i] :
( ( ( ~ ~ ! [SY655: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV185 @ SV11 )
| ~ ( in @ SY655 @ SV69 ) )
| ( SV148
!= ( ordered_pair @ SV185 @ SY655 ) ) ) )
= $true )
| ( ( in @ SV148 @ SV107 )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1534]) ).
thf(1619,plain,
! [SV107: $i,SV69: $i,SV11: $i] :
( ( ( ~ ~ ! [SY603: $i] :
~ ~ ! [SY604: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY603 @ SV11 )
| ~ ( in @ SY604 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SY603 @ SY604 ) ) ) )
= $false )
| ( ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1535]) ).
thf(1620,plain,
! [SV107: $i,SV11: $i,SV69: $i] :
( ( ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 )
= $false )
| ( ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1535]) ).
thf(1621,plain,
! [SV107: $i,SV69: $i,SV11: $i,SV180: $i] :
( ( ( ~ ! [SY649: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV180 @ SV11 )
| ~ ( in @ SY649 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SV180 @ SY649 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY603: $i] :
~ ~ ! [SY604: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY603 @ SV11 )
| ~ ( in @ SY604 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SY603 @ SY604 ) ) )
| ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 ) ) )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1536]) ).
thf(1622,plain,
! [SV12: $i,SV70: $i,SV157: $i,SV153: $i] :
( ( ( in @ ( ordered_pair @ SV153 @ SV157 ) @ SV70 )
= $false )
| ( ( ~ ( ~ ( in @ SV153 @ SV12 )
| ( SV153 != SV157 ) ) )
= $true )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1537]) ).
thf(1623,plain,
! [SV70: $i,SV157: $i,SV12: $i,SV153: $i] :
( ( ( ~ ( ~ ( in @ SV153 @ SV12 )
| ( SV153 != SV157 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV153 @ SV157 ) @ SV70 )
= $true )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1538]) ).
thf(1624,plain,
! [SV70: $i,SV12: $i] :
( ( ( in @ ( ordered_pair @ ( sK20_SY424 @ SV12 @ SV70 ) @ ( sK23_SY606 @ SV70 @ SV12 ) ) @ SV70 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
| ( ( sK20_SY424 @ SV12 @ SV70 )
!= ( sK23_SY606 @ SV70 @ SV12 ) ) )
| ( in @ ( ordered_pair @ ( sK20_SY424 @ SV12 @ SV70 ) @ ( sK23_SY606 @ SV70 @ SV12 ) ) @ SV70 ) ) )
= $true )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1539]) ).
thf(1625,plain,
! [SV70: $i,SV12: $i] :
( ( ( ~ ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
| ( ( sK20_SY424 @ SV12 @ SV70 )
!= ( sK23_SY606 @ SV70 @ SV12 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
| ( ( sK20_SY424 @ SV12 @ SV70 )
!= ( sK23_SY606 @ SV70 @ SV12 ) ) )
| ( in @ ( ordered_pair @ ( sK20_SY424 @ SV12 @ SV70 ) @ ( sK23_SY606 @ SV70 @ SV12 ) ) @ SV70 ) ) )
= $true )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1540]) ).
thf(1626,plain,
! [SV71: $i,SV13: $i] :
( ( ( subset @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV13 )
= $true )
| ( ( in @ ( sK11_SY427 @ SV13 @ SV71 ) @ SV71 )
= $true )
| ( ( SV71
= ( powerset @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1541]) ).
thf(1627,plain,
! [SV125: $i,SV14: $i,SV134: $i,SV158: $i] :
( ( ( in @ SV158 @ SV134 )
= $false )
| ( ( ~ ! [SY615: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV158 @ SY615 ) @ SV14 )
| ~ ( in @ SY615 @ SV125 ) ) )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1544]) ).
thf(1628,plain,
! [SV134: $i,SV125: $i,SV14: $i,SV158: $i] :
( ( ( ~ ! [SY616: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV158 @ SY616 ) @ SV14 )
| ~ ( in @ SY616 @ SV125 ) ) )
= $false )
| ( ( in @ SV158 @ SV134 )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1545]) ).
thf(1629,plain,
! [SV134: $i,SV14: $i,SV125: $i] :
( ( ( in @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV134 )
= $true )
| ( ( ~ ( ~ ~ ! [SY618: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SY618 ) @ SV14 )
| ~ ( in @ SY618 @ SV125 ) )
| ( in @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV134 ) ) )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1546]) ).
thf(1630,plain,
! [SV134: $i,SV14: $i,SV125: $i] :
( ( ( ! [SY617: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SY617 ) @ SV14 )
| ~ ( in @ SY617 @ SV125 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY618: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SY618 ) @ SV14 )
| ~ ( in @ SY618 @ SV125 ) )
| ( in @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV134 ) ) )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1547]) ).
thf(1631,plain,
! [SV126: $i,SV15: $i,SV154: $i] :
( ( ( ! [SY607: $i] :
~ ( in @ ( ordered_pair @ SY607 @ SV154 ) @ SV15 ) )
= $false )
| ( ( in @ SV154 @ SV126 )
= $false )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $false )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1548]) ).
thf(1632,plain,
! [SV126: $i,SV15: $i,SV154: $i] :
( ( ( ! [SY608: $i] :
~ ( in @ ( ordered_pair @ SY608 @ SV154 ) @ SV15 ) )
= $true )
| ( ( in @ SV154 @ SV126 )
= $true )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $false )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1549]) ).
thf(1633,plain,
! [SV126: $i,SV15: $i] :
( ( ( ~ ~ ! [SY610: $i] :
~ ( in @ ( ordered_pair @ SY610 @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 )
| ( in @ ( sK21_SY531 @ SV15 @ SV126 ) @ SV126 ) )
= $false )
| ( ( in @ ( sK21_SY531 @ SV15 @ SV126 ) @ SV126 )
= $true )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1550]) ).
thf(1634,plain,
! [SV126: $i,SV15: $i,SV186: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV186 @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY610: $i] :
~ ( in @ ( ordered_pair @ SY610 @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 )
| ( in @ ( sK21_SY531 @ SV15 @ SV126 ) @ SV126 ) ) )
= $true )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1551]) ).
thf(1635,plain,
! [SV108: $i,SV17: $i,SV72: $i] :
( ( ( ~ ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV17 )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV72 ) ) )
= $false )
| ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV108 )
= $true )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1557]) ).
thf(1636,plain,
! [SV108: $i,SV17: $i,SV72: $i] :
( ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV108 )
= $false )
| ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV108 )
= $true )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1557]) ).
thf(1637,plain,
! [SV108: $i,SV17: $i,SV72: $i] :
( ( ( ~ ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV17 )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV72 ) ) )
= $false )
| ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV17 )
= $false )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1558]) ).
thf(1638,plain,
! [SV108: $i,SV17: $i,SV72: $i] :
( ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV108 )
= $false )
| ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV17 )
= $false )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1558]) ).
thf(1639,plain,
! [SV108: $i,SV17: $i,SV72: $i] :
( ( ( ~ ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV17 )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV72 ) ) )
= $false )
| ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV72 )
= $false )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1559]) ).
thf(1640,plain,
! [SV108: $i,SV17: $i,SV72: $i] :
( ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV108 )
= $false )
| ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV72 )
= $false )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1559]) ).
thf(1641,plain,
! [SV20: $i,SV128: $i,SV135: $i,SV173: $i,SV169: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV135 )
| ~ ( ~ ( in @ SV169 @ SV128 )
| ~ ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV20 ) ) ) )
= $false )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1560]) ).
thf(1642,plain,
! [SV135: $i,SV20: $i,SV173: $i,SV128: $i,SV169: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV169 @ SV128 )
| ~ ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV20 ) )
| ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV135 ) ) )
= $false )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1560]) ).
thf(1643,plain,
! [SV135: $i,SV128: $i,SV20: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV135 )
| ~ ( ~ ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
| ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
| ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 ) )
| ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV135 ) ) )
= $true )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1561]) ).
thf(1644,plain,
! [SV21: $i,SV74: $i] :
( ( ( in @ ( sK29_SY431 @ SV74 @ SV21 ) @ SV21 )
= $true )
| ( ( disjoint @ SV21 @ SV74 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1562]) ).
thf(1645,plain,
! [SV21: $i,SV74: $i] :
( ( ( in @ ( sK29_SY431 @ SV74 @ SV21 ) @ SV74 )
= $true )
| ( ( disjoint @ SV21 @ SV74 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1563]) ).
thf(1646,plain,
! [SV21: $i,SV74: $i,SV159: $i] :
( ( ( in @ SV159 @ SV74 )
= $false )
| ( ( in @ SV159 @ SV21 )
= $false )
| ( ( ~ ( disjoint @ SV21 @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1564]) ).
thf(1647,plain,
! [SV181: $i,SV23: $i,SV174: $i] :
( ( ( ~ ~ ( ~ ( in @ SV174 @ ( sK3_SY291 @ SV23 ) )
| ~ ( subset @ SV181 @ SV174 ) ) )
= $true )
| ( ( in @ SV181 @ ( sK3_SY291 @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1565]) ).
thf(1648,plain,
! [SV23: $i,SV143: $i] :
( ( ( ~ ( are_equipotent @ SV143 @ ( sK3_SY291 @ SV23 ) ) )
= $false )
| ( ( subset @ SV143 @ ( sK3_SY291 @ SV23 ) )
= $false )
| ( ( ~ ~ ( in @ SV143 @ ( sK3_SY291 @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1566]) ).
thf(1649,plain,
! [SV26: $i,SV78: $i,SV175: $i] :
( ( ( ~ ( ~ ( in @ SV175 @ SV78 )
| ! [SY638: $i] :
( ~ ( in @ SY638 @ SV26 )
| ( in @ SV175 @ SY638 ) ) ) )
= $false )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $false )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1567]) ).
thf(1650,plain,
! [SV78: $i,SV175: $i,SV26: $i] :
( ( ( ~ ( ~ ! [SY639: $i] :
( ~ ( in @ SY639 @ SV26 )
| ( in @ SV175 @ SY639 ) )
| ( in @ SV175 @ SV78 ) ) )
= $false )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $false )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1567]) ).
thf(1651,plain,
! [SV78: $i,SV26: $i] :
( ( ( ~ ( ~ ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV78 )
| ! [SY640: $i] :
( ~ ( in @ SY640 @ SV26 )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SY640 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY641: $i] :
( ~ ( in @ SY641 @ SV26 )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SY641 ) )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV78 ) ) )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1568]) ).
thf(1652,plain,
! [SV131: $i,SV30: $i,SV136: $i,SV161: $i] :
( ( ( in @ SV161 @ SV136 )
= $false )
| ( ( ~ ! [SY619: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY619 @ SV161 ) @ SV30 )
| ~ ( in @ SY619 @ SV131 ) ) )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1570]) ).
thf(1653,plain,
! [SV136: $i,SV131: $i,SV30: $i,SV161: $i] :
( ( ( ~ ! [SY620: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY620 @ SV161 ) @ SV30 )
| ~ ( in @ SY620 @ SV131 ) ) )
= $false )
| ( ( in @ SV161 @ SV136 )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1571]) ).
thf(1654,plain,
! [SV136: $i,SV30: $i,SV131: $i] :
( ( ( in @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) @ SV136 )
= $true )
| ( ( ~ ( ~ ~ ! [SY622: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY622 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ SY622 @ SV131 ) )
| ( in @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) @ SV136 ) ) )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1572]) ).
thf(1655,plain,
! [SV136: $i,SV30: $i,SV131: $i] :
( ( ( ! [SY621: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY621 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ SY621 @ SV131 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY622: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY622 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ SY622 @ SV131 ) )
| ( in @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) @ SV136 ) ) )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1573]) ).
thf(1656,plain,
! [SV87: $i,SV39: $i,SV137: $i,SV176: $i,SV171: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV137 )
| ~ ( ~ ( in @ SV176 @ SV39 )
| ~ ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV87 ) ) ) )
= $false )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1575]) ).
thf(1657,plain,
! [SV137: $i,SV87: $i,SV171: $i,SV39: $i,SV176: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV176 @ SV39 )
| ~ ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV87 ) )
| ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV137 ) ) )
= $false )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1575]) ).
thf(1658,plain,
! [SV137: $i,SV39: $i,SV87: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV137 )
| ~ ( ~ ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
| ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
| ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 ) )
| ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV137 ) ) )
= $true )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1576]) ).
thf(1659,plain,
! [SV88: $i,SV41: $i] :
( ( ( ( sK12_SY454 @ SV41 @ SV88 )
= SV41 )
= $true )
| ( ( in @ ( sK12_SY454 @ SV41 @ SV88 ) @ SV88 )
= $true )
| ( ( SV88
= ( singleton @ SV41 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1577]) ).
thf(1660,plain,
! [SV42: $i,SV89: $i,SV145: $i] :
( ( ( ~ ( ~ ( in @ SV145 @ ( sK42_SY593 @ SV89 @ SV42 @ SV145 ) )
| ~ ( in @ ( sK42_SY593 @ SV89 @ SV42 @ SV145 ) @ SV42 ) ) )
= $true )
| ( ( in @ SV145 @ SV89 )
= $false )
| ( ( SV89
= ( union @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1580]) ).
thf(1661,plain,
! [SV89: $i,SV42: $i,SV182: $i,SV145: $i] :
( ( ( ~ ( ~ ( in @ SV145 @ SV182 )
| ~ ( in @ SV182 @ SV42 ) ) )
= $false )
| ( ( in @ SV145 @ SV89 )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1581]) ).
thf(1662,plain,
! [SV89: $i,SV42: $i] :
( ( ( ~ ! [SY596: $i] :
~ ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SY596 )
| ~ ( in @ SY596 @ SV42 ) ) )
= $true )
| ( ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1582]) ).
thf(1663,plain,
! [SV177: $i,SV89: $i,SV42: $i] :
( ( ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV177 )
| ~ ( in @ SV177 @ SV42 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY596: $i] :
~ ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SY596 )
| ~ ( in @ SY596 @ SV42 ) )
| ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1584]) ).
thf(1664,plain,
! [SV183: $i,SV46: $i,SV178: $i] :
( ( ( ~ ~ ( ~ ( in @ SV178 @ ( sK4_SY357 @ SV46 ) )
| ~ ( subset @ SV183 @ SV178 ) ) )
= $true )
| ( ( in @ SV183 @ ( sK4_SY357 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1585]) ).
thf(1665,plain,
! [SV162: $i,SV46: $i] :
( ( ( ! [SY623: $i] :
~ ~ ( ~ ( in @ SY623 @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SY624: $i] :
( ~ ( subset @ SY624 @ SV162 )
| ( in @ SY624 @ SY623 ) ) ) )
= $false )
| ( ( in @ SV162 @ ( sK4_SY357 @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1586]) ).
thf(1666,plain,
! [SV46: $i,SV146: $i] :
( ( ( ~ ( are_equipotent @ SV146 @ ( sK4_SY357 @ SV46 ) ) )
= $false )
| ( ( subset @ SV146 @ ( sK4_SY357 @ SV46 ) )
= $false )
| ( ( ~ ~ ( in @ SV146 @ ( sK4_SY357 @ SV46 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1587]) ).
thf(1667,plain,
! [SV132: $i,SV47: $i,SV155: $i] :
( ( ( ! [SY611: $i] :
~ ( in @ ( ordered_pair @ SV155 @ SY611 ) @ SV47 ) )
= $false )
| ( ( in @ SV155 @ SV132 )
= $false )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1588]) ).
thf(1668,plain,
! [SV132: $i,SV47: $i,SV155: $i] :
( ( ( ! [SY612: $i] :
~ ( in @ ( ordered_pair @ SV155 @ SY612 ) @ SV47 ) )
= $true )
| ( ( in @ SV155 @ SV132 )
= $true )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1589]) ).
thf(1669,plain,
! [SV132: $i,SV47: $i] :
( ( ( ~ ~ ! [SY614: $i] :
~ ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ SY614 ) @ SV47 )
| ( in @ ( sK22_SY553 @ SV47 @ SV132 ) @ SV132 ) )
= $false )
| ( ( in @ ( sK22_SY553 @ SV47 @ SV132 ) @ SV132 )
= $true )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1590]) ).
thf(1670,plain,
! [SV187: $i,SV132: $i,SV47: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ SV187 ) @ SV47 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY614: $i] :
~ ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ SY614 ) @ SV47 )
| ( in @ ( sK22_SY553 @ SV47 @ SV132 ) @ SV132 ) ) )
= $true )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1591]) ).
thf(1671,plain,
! [SV49: $i,SV133: $i,SV172: $i,SV166: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV166 @ SV172 ) @ SV133 )
| ( in @ ( ordered_pair @ SV172 @ SV166 ) @ SV49 ) )
= $true )
| ( ( SV133
= ( relation_inverse @ SV49 ) )
= $false )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1592]) ).
thf(1672,plain,
! [SV133: $i,SV49: $i,SV166: $i,SV172: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV172 @ SV166 ) @ SV49 )
| ( in @ ( ordered_pair @ SV166 @ SV172 ) @ SV133 ) )
= $true )
| ( ( SV133
= ( relation_inverse @ SV49 ) )
= $false )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1593]) ).
thf(1673,plain,
! [SV133: $i,SV49: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK30_SY558 @ SV49 @ SV133 ) @ ( sK36_SY631 @ SV133 @ SV49 ) ) @ SV133 )
| ( in @ ( ordered_pair @ ( sK36_SY631 @ SV133 @ SV49 ) @ ( sK30_SY558 @ SV49 @ SV133 ) ) @ SV49 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK36_SY631 @ SV133 @ SV49 ) @ ( sK30_SY558 @ SV49 @ SV133 ) ) @ SV49 )
| ( in @ ( ordered_pair @ ( sK30_SY558 @ SV49 @ SV133 ) @ ( sK36_SY631 @ SV133 @ SV49 ) ) @ SV133 ) ) )
= $true )
| ( ( SV133
= ( relation_inverse @ SV49 ) )
= $true )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1594]) ).
thf(1674,plain,
! [SV118: $i,SV56: $i,SV100: $i] :
( ( ( ~ ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV56 )
| ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV100 ) ) )
= $false )
| ( ( in @ ( sK17_SY503 @ SV100 @ SV56 @ SV118 ) @ SV118 )
= $true )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1598]) ).
thf(1675,plain,
! [SV118: $i,SV56: $i,SV100: $i] :
( ( ( in @ ( sK17_SY503 @ SV100 @ SV56 @ SV118 ) @ SV118 )
= $false )
| ( ( in @ ( sK17_SY503 @ SV100 @ SV56 @ SV118 ) @ SV118 )
= $true )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1598]) ).
thf(1676,plain,
! [SV118: $i,SV56: $i,SV100: $i] :
( ( ( ~ ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV56 )
| ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV100 ) ) )
= $false )
| ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV56 )
= $false )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1599]) ).
thf(1677,plain,
! [SV118: $i,SV56: $i,SV100: $i] :
( ( ( in @ ( sK17_SY503 @ SV100 @ SV56 @ SV118 ) @ SV118 )
= $false )
| ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV56 )
= $false )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1599]) ).
thf(1678,plain,
! [SV118: $i,SV56: $i,SV100: $i] :
( ( ( ~ ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV56 )
| ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV100 ) ) )
= $false )
| ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV100 )
= $false )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1600]) ).
thf(1679,plain,
! [SV118: $i,SV56: $i,SV100: $i] :
( ( ( in @ ( sK17_SY503 @ SV100 @ SV56 @ SV118 ) @ SV118 )
= $false )
| ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV100 )
= $false )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1600]) ).
thf(1680,plain,
! [SV102: $i,SV119: $i,SV58: $i,SV151: $i] :
( ( ( ~ ( in @ SV151 @ SV58 ) )
= $false )
| ( ( in @ SV151 @ SV119 )
= $false )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1601]) ).
thf(1681,plain,
! [SV58: $i,SV119: $i,SV102: $i,SV151: $i] :
( ( ( ~ ~ ( in @ SV151 @ SV102 ) )
= $false )
| ( ( in @ SV151 @ SV119 )
= $false )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1601]) ).
thf(1682,plain,
! [SV119: $i,SV102: $i,SV58: $i,SV151: $i] :
( ( ( ~ ( in @ SV151 @ SV58 ) )
= $true )
| ( ( ~ ~ ( in @ SV151 @ SV102 ) )
= $true )
| ( ( in @ SV151 @ SV119 )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1602]) ).
thf(1683,plain,
! [SV119: $i,SV58: $i,SV102: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
| ~ ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 ) ) )
= $false )
| ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV119 )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1603]) ).
thf(1684,plain,
! [SV119: $i,SV58: $i,SV102: $i] :
( ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV119 )
= $false )
| ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV119 )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1603]) ).
thf(1685,plain,
! [SV119: $i,SV58: $i,SV102: $i] :
( ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
= $false )
| ( ( ~ ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
| ~ ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 ) )
| ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV119 ) ) )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1604]) ).
thf(1686,plain,
! [SV104: $i,SV121: $i,SV60: $i,SV152: $i] :
( ( ( ~ ( in @ SV152 @ SV60 ) )
= $false )
| ( ( in @ SV152 @ SV121 )
= $false )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1605]) ).
thf(1687,plain,
! [SV60: $i,SV121: $i,SV104: $i,SV152: $i] :
( ( ( ~ ( in @ SV152 @ SV104 ) )
= $false )
| ( ( in @ SV152 @ SV121 )
= $false )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1605]) ).
thf(1688,plain,
! [SV121: $i,SV104: $i,SV60: $i,SV152: $i] :
( ( ( ~ ( in @ SV152 @ SV60 ) )
= $true )
| ( ( ~ ( in @ SV152 @ SV104 ) )
= $true )
| ( ( in @ SV152 @ SV121 )
= $true )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1606]) ).
thf(1689,plain,
! [SV121: $i,SV60: $i,SV104: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
| ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 ) ) )
= $false )
| ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV121 )
= $true )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1607]) ).
thf(1690,plain,
! [SV121: $i,SV60: $i,SV104: $i] :
( ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV121 )
= $false )
| ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV121 )
= $true )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1607]) ).
thf(1691,plain,
! [SV121: $i,SV60: $i,SV104: $i] :
( ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
= $false )
| ( ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
| ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 ) )
| ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV121 ) ) )
= $true )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1608]) ).
thf(1692,plain,
! [SV66: $i,SV6: $i,SV188: $i] :
( ( ( ~ ( in @ SV188 @ SV6 )
| ( ( apply @ SV66 @ SV188 )
= SV188 ) )
= $true )
| ( ( SV66
= ( identity_relation @ SV6 ) )
= $false )
| ( ( relation @ SV66 )
= $false )
| ( ( function @ SV66 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1610]) ).
thf(1693,plain,
! [SV66: $i,SV6: $i] :
( ( ( ! [SY408: $i] :
( ~ ( in @ SY408 @ SV6 )
| ( ( apply @ SV66 @ SY408 )
= SY408 ) ) )
= $false )
| ( ( ( relation_dom @ SV66 )
= SV6 )
= $false )
| ( ( SV66
= ( identity_relation @ SV6 ) )
= $true )
| ( ( relation @ SV66 )
= $false )
| ( ( function @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1611]) ).
thf(1694,plain,
! [SV123: $i,SV8: $i,SV167: $i,SV163: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV163 @ SV167 ) @ SV8 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV163 @ SV167 ) @ SV123 )
= $true )
| ( ( SV8 = SV123 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1612]) ).
thf(1695,plain,
! [SV8: $i,SV123: $i,SV167: $i,SV163: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV163 @ SV167 ) @ SV123 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV163 @ SV167 ) @ SV8 )
= $true )
| ( ( SV8 = SV123 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1613]) ).
thf(1696,plain,
! [SV8: $i,SV123: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV8 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV8 ) ) )
= $true )
| ( ( SV8 = SV123 )
= $true )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1614]) ).
thf(1697,plain,
! [SV8: $i,SV123: $i] :
( ( ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV123 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV8 ) ) )
= $true )
| ( ( SV8 = SV123 )
= $true )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1614]) ).
thf(1698,plain,
! [SV124: $i,SV10: $i,SV139: $i,SV184: $i,SV179: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV179 @ SV184 ) @ SV139 )
| ~ ! [SY650: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV179 @ SY650 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY650 @ SV184 ) @ SV124 ) ) )
| ~ ( ~ ~ ! [SY651: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV179 @ SY651 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY651 @ SV184 ) @ SV124 ) )
| ( in @ ( ordered_pair @ SV179 @ SV184 ) @ SV139 ) ) )
= $false )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $false )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1615]) ).
thf(1699,plain,
! [SV139: $i,SV10: $i,SV124: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV139 )
| ~ ! [SY652: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SY652 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY652 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) ) )
| ~ ( ~ ~ ! [SY653: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SY653 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY653 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) )
| ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV139 ) ) )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1616]) ).
thf(1700,plain,
! [SV11: $i,SV69: $i,SV148: $i,SV107: $i] :
( ( ( ~ ! [SY654: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK44_SY597 @ SV107 @ SV148 @ SV69 @ SV11 ) @ SV11 )
| ~ ( in @ SY654 @ SV69 ) )
| ( SV148
!= ( ordered_pair @ ( sK44_SY597 @ SV107 @ SV148 @ SV69 @ SV11 ) @ SY654 ) ) ) )
= $true )
| ( ( in @ SV148 @ SV107 )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1617]) ).
thf(1701,plain,
! [SV107: $i,SV148: $i,SV69: $i,SV11: $i,SV185: $i] :
( ( ( ~ ! [SY655: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV185 @ SV11 )
| ~ ( in @ SY655 @ SV69 ) )
| ( SV148
!= ( ordered_pair @ SV185 @ SY655 ) ) ) )
= $false )
| ( ( in @ SV148 @ SV107 )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1618]) ).
thf(1702,plain,
! [SV107: $i,SV69: $i,SV11: $i] :
( ( ( ~ ! [SY603: $i] :
~ ~ ! [SY604: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY603 @ SV11 )
| ~ ( in @ SY604 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SY603 @ SY604 ) ) ) )
= $true )
| ( ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1619]) ).
thf(1703,plain,
! [SV107: $i,SV69: $i,SV11: $i,SV180: $i] :
( ( ( ! [SY649: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV180 @ SV11 )
| ~ ( in @ SY649 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SV180 @ SY649 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY603: $i] :
~ ~ ! [SY604: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY603 @ SV11 )
| ~ ( in @ SY604 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SY603 @ SY604 ) ) )
| ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 ) ) )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1621]) ).
thf(1704,plain,
! [SV70: $i,SV157: $i,SV12: $i,SV153: $i] :
( ( ( ~ ( in @ SV153 @ SV12 )
| ( SV153 != SV157 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV153 @ SV157 ) @ SV70 )
= $false )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1622]) ).
thf(1705,plain,
! [SV70: $i,SV157: $i,SV12: $i,SV153: $i] :
( ( ( ~ ( in @ SV153 @ SV12 )
| ( SV153 != SV157 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV153 @ SV157 ) @ SV70 )
= $true )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1623]) ).
thf(1706,plain,
! [SV70: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
| ( ( sK20_SY424 @ SV12 @ SV70 )
!= ( sK23_SY606 @ SV70 @ SV12 ) ) )
| ( in @ ( ordered_pair @ ( sK20_SY424 @ SV12 @ SV70 ) @ ( sK23_SY606 @ SV70 @ SV12 ) ) @ SV70 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK20_SY424 @ SV12 @ SV70 ) @ ( sK23_SY606 @ SV70 @ SV12 ) ) @ SV70 )
= $true )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1624]) ).
thf(1707,plain,
! [SV70: $i,SV12: $i] :
( ( ( ~ ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 ) )
= $true )
| ( ( ( sK20_SY424 @ SV12 @ SV70 )
!= ( sK23_SY606 @ SV70 @ SV12 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
| ( ( sK20_SY424 @ SV12 @ SV70 )
!= ( sK23_SY606 @ SV70 @ SV12 ) ) )
| ( in @ ( ordered_pair @ ( sK20_SY424 @ SV12 @ SV70 ) @ ( sK23_SY606 @ SV70 @ SV12 ) ) @ SV70 ) ) )
= $true )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1625]) ).
thf(1708,plain,
! [SV134: $i,SV125: $i,SV14: $i,SV158: $i] :
( ( ( ! [SY615: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV158 @ SY615 ) @ SV14 )
| ~ ( in @ SY615 @ SV125 ) ) )
= $false )
| ( ( in @ SV158 @ SV134 )
= $false )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1627]) ).
thf(1709,plain,
! [SV134: $i,SV125: $i,SV14: $i,SV158: $i] :
( ( ( ! [SY616: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV158 @ SY616 ) @ SV14 )
| ~ ( in @ SY616 @ SV125 ) ) )
= $true )
| ( ( in @ SV158 @ SV134 )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1628]) ).
thf(1710,plain,
! [SV134: $i,SV14: $i,SV125: $i] :
( ( ( ~ ~ ! [SY618: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SY618 ) @ SV14 )
| ~ ( in @ SY618 @ SV125 ) )
| ( in @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV134 ) )
= $false )
| ( ( in @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV134 )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1629]) ).
thf(1711,plain,
! [SV189: $i,SV134: $i,SV14: $i,SV125: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV189 ) @ SV14 )
| ~ ( in @ SV189 @ SV125 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY618: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SY618 ) @ SV14 )
| ~ ( in @ SY618 @ SV125 ) )
| ( in @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV134 ) ) )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1630]) ).
thf(1712,plain,
! [SV154: $i,SV15: $i,SV126: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK45_SY607 @ SV126 @ SV15 @ SV154 ) @ SV154 ) @ SV15 ) )
= $false )
| ( ( in @ SV154 @ SV126 )
= $false )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $false )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1631]) ).
thf(1713,plain,
! [SV126: $i,SV15: $i,SV154: $i,SV190: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV190 @ SV154 ) @ SV15 ) )
= $true )
| ( ( in @ SV154 @ SV126 )
= $true )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $false )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1632]) ).
thf(1714,plain,
! [SV126: $i,SV15: $i] :
( ( ( ~ ~ ! [SY610: $i] :
~ ( in @ ( ordered_pair @ SY610 @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 ) )
= $false )
| ( ( in @ ( sK21_SY531 @ SV15 @ SV126 ) @ SV126 )
= $true )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1633]) ).
thf(1715,plain,
! [SV126: $i,SV15: $i] :
( ( ( in @ ( sK21_SY531 @ SV15 @ SV126 ) @ SV126 )
= $false )
| ( ( in @ ( sK21_SY531 @ SV15 @ SV126 ) @ SV126 )
= $true )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1633]) ).
thf(1716,plain,
! [SV126: $i,SV15: $i,SV186: $i] :
( ( ( in @ ( ordered_pair @ SV186 @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 )
= $false )
| ( ( ~ ( ~ ~ ! [SY610: $i] :
~ ( in @ ( ordered_pair @ SY610 @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 )
| ( in @ ( sK21_SY531 @ SV15 @ SV126 ) @ SV126 ) ) )
= $true )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1634]) ).
thf(1717,plain,
! [SV108: $i,SV17: $i,SV72: $i] :
( ( ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV17 )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV72 ) )
= $true )
| ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV108 )
= $true )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1635]) ).
thf(1718,plain,
! [SV108: $i,SV17: $i,SV72: $i] :
( ( ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV17 )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV72 ) )
= $true )
| ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV17 )
= $false )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1637]) ).
thf(1719,plain,
! [SV108: $i,SV17: $i,SV72: $i] :
( ( ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV17 )
| ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV72 ) )
= $true )
| ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV72 )
= $false )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1639]) ).
thf(1720,plain,
! [SV20: $i,SV128: $i,SV135: $i,SV173: $i,SV169: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV135 )
| ~ ( ~ ( in @ SV169 @ SV128 )
| ~ ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV20 ) ) )
= $true )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1641]) ).
thf(1721,plain,
! [SV135: $i,SV20: $i,SV173: $i,SV128: $i,SV169: $i] :
( ( ( ~ ~ ( ~ ( in @ SV169 @ SV128 )
| ~ ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV20 ) )
| ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV135 ) )
= $true )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1642]) ).
thf(1722,plain,
! [SV135: $i,SV128: $i,SV20: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV135 )
| ~ ( ~ ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
| ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
| ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 ) )
| ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV135 ) ) )
= $true )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1643]) ).
thf(1723,plain,
! [SV159: $i,SV74: $i,SV21: $i] :
( ( ( disjoint @ SV21 @ SV74 )
= $false )
| ( ( in @ SV159 @ SV21 )
= $false )
| ( ( in @ SV159 @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1646]) ).
thf(1724,plain,
! [SV181: $i,SV23: $i,SV174: $i] :
( ( ( ~ ( ~ ( in @ SV174 @ ( sK3_SY291 @ SV23 ) )
| ~ ( subset @ SV181 @ SV174 ) ) )
= $false )
| ( ( in @ SV181 @ ( sK3_SY291 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1647]) ).
thf(1725,plain,
! [SV23: $i,SV143: $i] :
( ( ( are_equipotent @ SV143 @ ( sK3_SY291 @ SV23 ) )
= $true )
| ( ( subset @ SV143 @ ( sK3_SY291 @ SV23 ) )
= $false )
| ( ( ~ ~ ( in @ SV143 @ ( sK3_SY291 @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1648]) ).
thf(1726,plain,
! [SV26: $i,SV78: $i,SV175: $i] :
( ( ( ~ ( in @ SV175 @ SV78 )
| ! [SY638: $i] :
( ~ ( in @ SY638 @ SV26 )
| ( in @ SV175 @ SY638 ) ) )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $false )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1649]) ).
thf(1727,plain,
! [SV78: $i,SV175: $i,SV26: $i] :
( ( ( ~ ! [SY639: $i] :
( ~ ( in @ SY639 @ SV26 )
| ( in @ SV175 @ SY639 ) )
| ( in @ SV175 @ SV78 ) )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $false )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1650]) ).
thf(1728,plain,
! [SV78: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV78 )
| ! [SY640: $i] :
( ~ ( in @ SY640 @ SV26 )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SY640 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY641: $i] :
( ~ ( in @ SY641 @ SV26 )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SY641 ) )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV78 ) ) )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1651]) ).
thf(1729,plain,
! [SV136: $i,SV131: $i,SV30: $i,SV161: $i] :
( ( ( ! [SY619: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY619 @ SV161 ) @ SV30 )
| ~ ( in @ SY619 @ SV131 ) ) )
= $false )
| ( ( in @ SV161 @ SV136 )
= $false )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1652]) ).
thf(1730,plain,
! [SV136: $i,SV131: $i,SV30: $i,SV161: $i] :
( ( ( ! [SY620: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY620 @ SV161 ) @ SV30 )
| ~ ( in @ SY620 @ SV131 ) ) )
= $true )
| ( ( in @ SV161 @ SV136 )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1653]) ).
thf(1731,plain,
! [SV136: $i,SV30: $i,SV131: $i] :
( ( ( ~ ~ ! [SY622: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY622 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ SY622 @ SV131 ) )
| ( in @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) @ SV136 ) )
= $false )
| ( ( in @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) @ SV136 )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1654]) ).
thf(1732,plain,
! [SV136: $i,SV30: $i,SV131: $i,SV191: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ SV191 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ SV191 @ SV131 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY622: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY622 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ SY622 @ SV131 ) )
| ( in @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) @ SV136 ) ) )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1655]) ).
thf(1733,plain,
! [SV87: $i,SV39: $i,SV137: $i,SV176: $i,SV171: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV137 )
| ~ ( ~ ( in @ SV176 @ SV39 )
| ~ ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV87 ) ) )
= $true )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1656]) ).
thf(1734,plain,
! [SV137: $i,SV87: $i,SV171: $i,SV39: $i,SV176: $i] :
( ( ( ~ ~ ( ~ ( in @ SV176 @ SV39 )
| ~ ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV87 ) )
| ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV137 ) )
= $true )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1657]) ).
thf(1735,plain,
! [SV137: $i,SV39: $i,SV87: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV137 )
| ~ ( ~ ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
| ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
| ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 ) )
| ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV137 ) ) )
= $true )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1658]) ).
thf(1736,plain,
! [SV42: $i,SV89: $i,SV145: $i] :
( ( ( ~ ( in @ SV145 @ ( sK42_SY593 @ SV89 @ SV42 @ SV145 ) )
| ~ ( in @ ( sK42_SY593 @ SV89 @ SV42 @ SV145 ) @ SV42 ) )
= $false )
| ( ( in @ SV145 @ SV89 )
= $false )
| ( ( SV89
= ( union @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1660]) ).
thf(1737,plain,
! [SV89: $i,SV42: $i,SV182: $i,SV145: $i] :
( ( ( ~ ( in @ SV145 @ SV182 )
| ~ ( in @ SV182 @ SV42 ) )
= $true )
| ( ( in @ SV145 @ SV89 )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1661]) ).
thf(1738,plain,
! [SV89: $i,SV42: $i] :
( ( ( ! [SY596: $i] :
~ ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SY596 )
| ~ ( in @ SY596 @ SV42 ) ) )
= $false )
| ( ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1662]) ).
thf(1739,plain,
! [SV177: $i,SV89: $i,SV42: $i] :
( ( ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV177 ) )
= $true )
| ( ( ~ ( in @ SV177 @ SV42 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY596: $i] :
~ ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SY596 )
| ~ ( in @ SY596 @ SV42 ) )
| ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1663]) ).
thf(1740,plain,
! [SV183: $i,SV46: $i,SV178: $i] :
( ( ( ~ ( ~ ( in @ SV178 @ ( sK4_SY357 @ SV46 ) )
| ~ ( subset @ SV183 @ SV178 ) ) )
= $false )
| ( ( in @ SV183 @ ( sK4_SY357 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1664]) ).
thf(1741,plain,
! [SV46: $i,SV162: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK46_SY623 @ SV162 @ SV46 ) @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SY656: $i] :
( ~ ( subset @ SY656 @ SV162 )
| ( in @ SY656 @ ( sK46_SY623 @ SV162 @ SV46 ) ) ) ) )
= $false )
| ( ( in @ SV162 @ ( sK4_SY357 @ SV46 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1665]) ).
thf(1742,plain,
! [SV46: $i,SV146: $i] :
( ( ( are_equipotent @ SV146 @ ( sK4_SY357 @ SV46 ) )
= $true )
| ( ( subset @ SV146 @ ( sK4_SY357 @ SV46 ) )
= $false )
| ( ( ~ ~ ( in @ SV146 @ ( sK4_SY357 @ SV46 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1666]) ).
thf(1743,plain,
! [SV47: $i,SV132: $i,SV155: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV155 @ ( sK47_SY611 @ SV132 @ SV47 @ SV155 ) ) @ SV47 ) )
= $false )
| ( ( in @ SV155 @ SV132 )
= $false )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1667]) ).
thf(1744,plain,
! [SV132: $i,SV47: $i,SV192: $i,SV155: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV155 @ SV192 ) @ SV47 ) )
= $true )
| ( ( in @ SV155 @ SV132 )
= $true )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1668]) ).
thf(1745,plain,
! [SV132: $i,SV47: $i] :
( ( ( ~ ~ ! [SY614: $i] :
~ ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ SY614 ) @ SV47 ) )
= $false )
| ( ( in @ ( sK22_SY553 @ SV47 @ SV132 ) @ SV132 )
= $true )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1669]) ).
thf(1746,plain,
! [SV132: $i,SV47: $i] :
( ( ( in @ ( sK22_SY553 @ SV47 @ SV132 ) @ SV132 )
= $false )
| ( ( in @ ( sK22_SY553 @ SV47 @ SV132 ) @ SV132 )
= $true )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1669]) ).
thf(1747,plain,
! [SV187: $i,SV132: $i,SV47: $i] :
( ( ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ SV187 ) @ SV47 )
= $false )
| ( ( ~ ( ~ ~ ! [SY614: $i] :
~ ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ SY614 ) @ SV47 )
| ( in @ ( sK22_SY553 @ SV47 @ SV132 ) @ SV132 ) ) )
= $true )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1670]) ).
thf(1748,plain,
! [SV49: $i,SV133: $i,SV172: $i,SV166: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV166 @ SV172 ) @ SV133 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV172 @ SV166 ) @ SV49 )
= $true )
| ( ( SV133
= ( relation_inverse @ SV49 ) )
= $false )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1671]) ).
thf(1749,plain,
! [SV133: $i,SV49: $i,SV166: $i,SV172: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV172 @ SV166 ) @ SV49 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV166 @ SV172 ) @ SV133 )
= $true )
| ( ( SV133
= ( relation_inverse @ SV49 ) )
= $false )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1672]) ).
thf(1750,plain,
! [SV133: $i,SV49: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK30_SY558 @ SV49 @ SV133 ) @ ( sK36_SY631 @ SV133 @ SV49 ) ) @ SV133 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK36_SY631 @ SV133 @ SV49 ) @ ( sK30_SY558 @ SV49 @ SV133 ) ) @ SV49 )
| ( in @ ( ordered_pair @ ( sK30_SY558 @ SV49 @ SV133 ) @ ( sK36_SY631 @ SV133 @ SV49 ) ) @ SV133 ) ) )
= $true )
| ( ( SV133
= ( relation_inverse @ SV49 ) )
= $true )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1673]) ).
thf(1751,plain,
! [SV49: $i,SV133: $i] :
( ( ( in @ ( ordered_pair @ ( sK36_SY631 @ SV133 @ SV49 ) @ ( sK30_SY558 @ SV49 @ SV133 ) ) @ SV49 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK36_SY631 @ SV133 @ SV49 ) @ ( sK30_SY558 @ SV49 @ SV133 ) ) @ SV49 )
| ( in @ ( ordered_pair @ ( sK30_SY558 @ SV49 @ SV133 ) @ ( sK36_SY631 @ SV133 @ SV49 ) ) @ SV133 ) ) )
= $true )
| ( ( SV133
= ( relation_inverse @ SV49 ) )
= $true )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1673]) ).
thf(1752,plain,
! [SV118: $i,SV56: $i,SV100: $i] :
( ( ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV56 )
| ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV100 ) )
= $true )
| ( ( in @ ( sK17_SY503 @ SV100 @ SV56 @ SV118 ) @ SV118 )
= $true )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1674]) ).
thf(1753,plain,
! [SV118: $i,SV56: $i,SV100: $i] :
( ( ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV56 )
| ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV100 ) )
= $true )
| ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV56 )
= $false )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1676]) ).
thf(1754,plain,
! [SV118: $i,SV56: $i,SV100: $i] :
( ( ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV56 )
| ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV100 ) )
= $true )
| ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV100 )
= $false )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1678]) ).
thf(1755,plain,
! [SV102: $i,SV119: $i,SV58: $i,SV151: $i] :
( ( ( in @ SV151 @ SV58 )
= $true )
| ( ( in @ SV151 @ SV119 )
= $false )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1680]) ).
thf(1756,plain,
! [SV58: $i,SV119: $i,SV102: $i,SV151: $i] :
( ( ( ~ ( in @ SV151 @ SV102 ) )
= $true )
| ( ( in @ SV151 @ SV119 )
= $false )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1681]) ).
thf(1757,plain,
! [SV119: $i,SV102: $i,SV58: $i,SV151: $i] :
( ( ( in @ SV151 @ SV58 )
= $false )
| ( ( ~ ~ ( in @ SV151 @ SV102 ) )
= $true )
| ( ( in @ SV151 @ SV119 )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1682]) ).
thf(1758,plain,
! [SV119: $i,SV58: $i,SV102: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
| ~ ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 ) ) )
= $true )
| ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV119 )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1683]) ).
thf(1759,plain,
! [SV119: $i,SV58: $i,SV102: $i] :
( ( ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 ) )
= $false )
| ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
| ~ ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 ) )
| ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV119 ) ) )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1685]) ).
thf(1760,plain,
! [SV104: $i,SV121: $i,SV60: $i,SV152: $i] :
( ( ( in @ SV152 @ SV60 )
= $true )
| ( ( in @ SV152 @ SV121 )
= $false )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1686]) ).
thf(1761,plain,
! [SV60: $i,SV121: $i,SV104: $i,SV152: $i] :
( ( ( in @ SV152 @ SV104 )
= $true )
| ( ( in @ SV152 @ SV121 )
= $false )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1687]) ).
thf(1762,plain,
! [SV121: $i,SV104: $i,SV60: $i,SV152: $i] :
( ( ( in @ SV152 @ SV60 )
= $false )
| ( ( ~ ( in @ SV152 @ SV104 ) )
= $true )
| ( ( in @ SV152 @ SV121 )
= $true )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1688]) ).
thf(1763,plain,
! [SV121: $i,SV60: $i,SV104: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
| ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 ) ) )
= $true )
| ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV121 )
= $true )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1689]) ).
thf(1764,plain,
! [SV121: $i,SV60: $i,SV104: $i] :
( ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 )
= $false )
| ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
| ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 ) )
| ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV121 ) ) )
= $true )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1691]) ).
thf(1765,plain,
! [SV66: $i,SV6: $i,SV188: $i] :
( ( ( ~ ( in @ SV188 @ SV6 ) )
= $true )
| ( ( ( apply @ SV66 @ SV188 )
= SV188 )
= $true )
| ( ( SV66
= ( identity_relation @ SV6 ) )
= $false )
| ( ( relation @ SV66 )
= $false )
| ( ( function @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1692]) ).
thf(1766,plain,
! [SV6: $i,SV66: $i] :
( ( ( ~ ( in @ ( sK48_SY408 @ SV66 @ SV6 ) @ SV6 )
| ( ( apply @ SV66 @ ( sK48_SY408 @ SV66 @ SV6 ) )
= ( sK48_SY408 @ SV66 @ SV6 ) ) )
= $false )
| ( ( ( relation_dom @ SV66 )
= SV6 )
= $false )
| ( ( SV66
= ( identity_relation @ SV6 ) )
= $true )
| ( ( relation @ SV66 )
= $false )
| ( ( function @ SV66 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1693]) ).
thf(1767,plain,
! [SV123: $i,SV8: $i,SV167: $i,SV163: $i] :
( ( ( in @ ( ordered_pair @ SV163 @ SV167 ) @ SV8 )
= $false )
| ( ( in @ ( ordered_pair @ SV163 @ SV167 ) @ SV123 )
= $true )
| ( ( SV8 = SV123 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1694]) ).
thf(1768,plain,
! [SV8: $i,SV123: $i,SV167: $i,SV163: $i] :
( ( ( in @ ( ordered_pair @ SV163 @ SV167 ) @ SV123 )
= $false )
| ( ( in @ ( ordered_pair @ SV163 @ SV167 ) @ SV8 )
= $true )
| ( ( SV8 = SV123 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1695]) ).
thf(1769,plain,
! [SV8: $i,SV123: $i] :
( ( ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV8 )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV8 ) ) )
= $true )
| ( ( SV8 = SV123 )
= $true )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1696]) ).
thf(1770,plain,
! [SV8: $i,SV123: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV8 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV123 )
= $false )
| ( ( SV8 = SV123 )
= $true )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1697]) ).
thf(1771,plain,
! [SV124: $i,SV10: $i,SV139: $i,SV184: $i,SV179: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV179 @ SV184 ) @ SV139 )
| ~ ! [SY650: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV179 @ SY650 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY650 @ SV184 ) @ SV124 ) ) ) )
= $false )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $false )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1698]) ).
thf(1772,plain,
! [SV139: $i,SV124: $i,SV184: $i,SV10: $i,SV179: $i] :
( ( ( ~ ( ~ ~ ! [SY651: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV179 @ SY651 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY651 @ SV184 ) @ SV124 ) )
| ( in @ ( ordered_pair @ SV179 @ SV184 ) @ SV139 ) ) )
= $false )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $false )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1698]) ).
thf(1773,plain,
! [SV139: $i,SV10: $i,SV124: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV139 )
| ~ ! [SY652: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SY652 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY652 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY653: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SY653 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY653 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) )
| ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV139 ) ) )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1699]) ).
thf(1774,plain,
! [SV11: $i,SV69: $i,SV148: $i,SV107: $i] :
( ( ( ! [SY654: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK44_SY597 @ SV107 @ SV148 @ SV69 @ SV11 ) @ SV11 )
| ~ ( in @ SY654 @ SV69 ) )
| ( SV148
!= ( ordered_pair @ ( sK44_SY597 @ SV107 @ SV148 @ SV69 @ SV11 ) @ SY654 ) ) ) )
= $false )
| ( ( in @ SV148 @ SV107 )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1700]) ).
thf(1775,plain,
! [SV107: $i,SV148: $i,SV69: $i,SV11: $i,SV185: $i] :
( ( ( ! [SY655: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV185 @ SV11 )
| ~ ( in @ SY655 @ SV69 ) )
| ( SV148
!= ( ordered_pair @ SV185 @ SY655 ) ) ) )
= $true )
| ( ( in @ SV148 @ SV107 )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1701]) ).
thf(1776,plain,
! [SV107: $i,SV69: $i,SV11: $i] :
( ( ( ! [SY603: $i] :
~ ~ ! [SY604: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY603 @ SV11 )
| ~ ( in @ SY604 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SY603 @ SY604 ) ) ) )
= $false )
| ( ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1702]) ).
thf(1777,plain,
! [SV107: $i,SV69: $i,SV193: $i,SV11: $i,SV180: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV180 @ SV11 )
| ~ ( in @ SV193 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SV180 @ SV193 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY603: $i] :
~ ~ ! [SY604: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY603 @ SV11 )
| ~ ( in @ SY604 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SY603 @ SY604 ) ) )
| ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 ) ) )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1703]) ).
thf(1778,plain,
! [SV70: $i,SV157: $i,SV12: $i,SV153: $i] :
( ( ( ~ ( in @ SV153 @ SV12 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV153 @ SV157 ) @ SV70 )
= $false )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1704]) ).
thf(1779,plain,
! [SV12: $i,SV70: $i,SV157: $i,SV153: $i] :
( ( ( SV153 != SV157 )
= $false )
| ( ( in @ ( ordered_pair @ SV153 @ SV157 ) @ SV70 )
= $false )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1704]) ).
thf(1780,plain,
! [SV70: $i,SV157: $i,SV12: $i,SV153: $i] :
( ( ( ~ ( in @ SV153 @ SV12 ) )
= $true )
| ( ( SV153 != SV157 )
= $true )
| ( ( in @ ( ordered_pair @ SV153 @ SV157 ) @ SV70 )
= $true )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1705]) ).
thf(1781,plain,
! [SV70: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
| ( ( sK20_SY424 @ SV12 @ SV70 )
!= ( sK23_SY606 @ SV70 @ SV12 ) ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK20_SY424 @ SV12 @ SV70 ) @ ( sK23_SY606 @ SV70 @ SV12 ) ) @ SV70 )
= $true )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1706]) ).
thf(1782,plain,
! [SV70: $i,SV12: $i] :
( ( ( in @ ( ordered_pair @ ( sK20_SY424 @ SV12 @ SV70 ) @ ( sK23_SY606 @ SV70 @ SV12 ) ) @ SV70 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK20_SY424 @ SV12 @ SV70 ) @ ( sK23_SY606 @ SV70 @ SV12 ) ) @ SV70 )
= $true )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1706]) ).
thf(1783,plain,
! [SV70: $i,SV12: $i] :
( ( ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
= $false )
| ( ( ( sK20_SY424 @ SV12 @ SV70 )
!= ( sK23_SY606 @ SV70 @ SV12 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
| ( ( sK20_SY424 @ SV12 @ SV70 )
!= ( sK23_SY606 @ SV70 @ SV12 ) ) )
| ( in @ ( ordered_pair @ ( sK20_SY424 @ SV12 @ SV70 ) @ ( sK23_SY606 @ SV70 @ SV12 ) ) @ SV70 ) ) )
= $true )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1707]) ).
thf(1784,plain,
! [SV14: $i,SV125: $i,SV134: $i,SV158: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ SV158 @ ( sK49_SY615 @ SV134 @ SV125 @ SV14 @ SV158 ) ) @ SV14 )
| ~ ( in @ ( sK49_SY615 @ SV134 @ SV125 @ SV14 @ SV158 ) @ SV125 ) ) )
= $false )
| ( ( in @ SV158 @ SV134 )
= $false )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1708]) ).
thf(1785,plain,
! [SV134: $i,SV125: $i,SV14: $i,SV194: $i,SV158: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ SV158 @ SV194 ) @ SV14 )
| ~ ( in @ SV194 @ SV125 ) ) )
= $true )
| ( ( in @ SV158 @ SV134 )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1709]) ).
thf(1786,plain,
! [SV134: $i,SV14: $i,SV125: $i] :
( ( ( ~ ~ ! [SY618: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SY618 ) @ SV14 )
| ~ ( in @ SY618 @ SV125 ) ) )
= $false )
| ( ( in @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV134 )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1710]) ).
thf(1787,plain,
! [SV134: $i,SV14: $i,SV125: $i] :
( ( ( in @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV134 )
= $false )
| ( ( in @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV134 )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1710]) ).
thf(1788,plain,
! [SV189: $i,SV134: $i,SV14: $i,SV125: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV189 ) @ SV14 )
| ~ ( in @ SV189 @ SV125 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY618: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SY618 ) @ SV14 )
| ~ ( in @ SY618 @ SV125 ) )
| ( in @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV134 ) ) )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1711]) ).
thf(1789,plain,
! [SV154: $i,SV15: $i,SV126: $i] :
( ( ( in @ ( ordered_pair @ ( sK45_SY607 @ SV126 @ SV15 @ SV154 ) @ SV154 ) @ SV15 )
= $true )
| ( ( in @ SV154 @ SV126 )
= $false )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $false )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1712]) ).
thf(1790,plain,
! [SV126: $i,SV15: $i,SV154: $i,SV190: $i] :
( ( ( in @ ( ordered_pair @ SV190 @ SV154 ) @ SV15 )
= $false )
| ( ( in @ SV154 @ SV126 )
= $true )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $false )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1713]) ).
thf(1791,plain,
! [SV126: $i,SV15: $i] :
( ( ( ~ ! [SY610: $i] :
~ ( in @ ( ordered_pair @ SY610 @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 ) )
= $true )
| ( ( in @ ( sK21_SY531 @ SV15 @ SV126 ) @ SV126 )
= $true )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1714]) ).
thf(1792,plain,
! [SV186: $i,SV126: $i,SV15: $i] :
( ( ( ~ ~ ! [SY610: $i] :
~ ( in @ ( ordered_pair @ SY610 @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 )
| ( in @ ( sK21_SY531 @ SV15 @ SV126 ) @ SV126 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV186 @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 )
= $false )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1716]) ).
thf(1793,plain,
! [SV108: $i,SV17: $i,SV72: $i] :
( ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV17 )
= $true )
| ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV72 )
= $true )
| ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV108 )
= $true )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1717]) ).
thf(1794,plain,
! [SV108: $i,SV17: $i,SV72: $i] :
( ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV17 )
= $true )
| ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV72 )
= $true )
| ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV17 )
= $false )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1718]) ).
thf(1795,plain,
! [SV108: $i,SV17: $i,SV72: $i] :
( ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV17 )
= $true )
| ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV72 )
= $true )
| ( ( in @ ( sK16_SY489 @ SV72 @ SV17 @ SV108 ) @ SV72 )
= $false )
| ( ( SV108
= ( set_union2 @ SV17 @ SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1719]) ).
thf(1796,plain,
! [SV20: $i,SV128: $i,SV135: $i,SV173: $i,SV169: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV135 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV169 @ SV128 )
| ~ ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV20 ) ) )
= $true )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1720]) ).
thf(1797,plain,
! [SV135: $i,SV20: $i,SV173: $i,SV128: $i,SV169: $i] :
( ( ( ~ ~ ( ~ ( in @ SV169 @ SV128 )
| ~ ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV20 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV135 )
= $true )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1721]) ).
thf(1798,plain,
! [SV135: $i,SV128: $i,SV20: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV135 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
| ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 ) )
| ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV135 ) ) )
= $true )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1722]) ).
thf(1799,plain,
! [SV135: $i,SV128: $i,SV20: $i] :
( ( ( ~ ( ~ ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
| ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
| ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 ) )
| ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV135 ) ) )
= $true )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1722]) ).
thf(1800,plain,
! [SV181: $i,SV23: $i,SV174: $i] :
( ( ( ~ ( in @ SV174 @ ( sK3_SY291 @ SV23 ) )
| ~ ( subset @ SV181 @ SV174 ) )
= $true )
| ( ( in @ SV181 @ ( sK3_SY291 @ SV23 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1724]) ).
thf(1801,plain,
! [SV23: $i,SV143: $i] :
( ( ( ~ ( in @ SV143 @ ( sK3_SY291 @ SV23 ) ) )
= $false )
| ( ( subset @ SV143 @ ( sK3_SY291 @ SV23 ) )
= $false )
| ( ( are_equipotent @ SV143 @ ( sK3_SY291 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1725]) ).
thf(1802,plain,
! [SV26: $i,SV78: $i,SV175: $i] :
( ( ( ~ ( in @ SV175 @ SV78 ) )
= $true )
| ( ( ! [SY638: $i] :
( ~ ( in @ SY638 @ SV26 )
| ( in @ SV175 @ SY638 ) ) )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $false )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1726]) ).
thf(1803,plain,
! [SV78: $i,SV175: $i,SV26: $i] :
( ( ( ~ ! [SY639: $i] :
( ~ ( in @ SY639 @ SV26 )
| ( in @ SV175 @ SY639 ) ) )
= $true )
| ( ( in @ SV175 @ SV78 )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $false )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1727]) ).
thf(1804,plain,
! [SV78: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV78 ) )
= $false )
| ( ( ~ ( ~ ! [SY641: $i] :
( ~ ( in @ SY641 @ SV26 )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SY641 ) )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV78 ) ) )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1728]) ).
thf(1805,plain,
! [SV78: $i,SV26: $i] :
( ( ( ! [SY640: $i] :
( ~ ( in @ SY640 @ SV26 )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SY640 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY641: $i] :
( ~ ( in @ SY641 @ SV26 )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SY641 ) )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV78 ) ) )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1728]) ).
thf(1806,plain,
! [SV161: $i,SV30: $i,SV131: $i,SV136: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK50_SY619 @ SV136 @ SV131 @ SV30 @ SV161 ) @ SV161 ) @ SV30 )
| ~ ( in @ ( sK50_SY619 @ SV136 @ SV131 @ SV30 @ SV161 ) @ SV131 ) ) )
= $false )
| ( ( in @ SV161 @ SV136 )
= $false )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1729]) ).
thf(1807,plain,
! [SV136: $i,SV131: $i,SV30: $i,SV161: $i,SV195: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ SV195 @ SV161 ) @ SV30 )
| ~ ( in @ SV195 @ SV131 ) ) )
= $true )
| ( ( in @ SV161 @ SV136 )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1730]) ).
thf(1808,plain,
! [SV136: $i,SV30: $i,SV131: $i] :
( ( ( ~ ~ ! [SY622: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY622 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ SY622 @ SV131 ) ) )
= $false )
| ( ( in @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) @ SV136 )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1731]) ).
thf(1809,plain,
! [SV136: $i,SV30: $i,SV131: $i] :
( ( ( in @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) @ SV136 )
= $false )
| ( ( in @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) @ SV136 )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1731]) ).
thf(1810,plain,
! [SV136: $i,SV30: $i,SV131: $i,SV191: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV191 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ SV191 @ SV131 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY622: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY622 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ SY622 @ SV131 ) )
| ( in @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) @ SV136 ) ) )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1732]) ).
thf(1811,plain,
! [SV87: $i,SV39: $i,SV137: $i,SV176: $i,SV171: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV137 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV176 @ SV39 )
| ~ ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV87 ) ) )
= $true )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1733]) ).
thf(1812,plain,
! [SV137: $i,SV87: $i,SV171: $i,SV39: $i,SV176: $i] :
( ( ( ~ ~ ( ~ ( in @ SV176 @ SV39 )
| ~ ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV87 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV137 )
= $true )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1734]) ).
thf(1813,plain,
! [SV137: $i,SV39: $i,SV87: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV137 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
| ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 ) )
| ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV137 ) ) )
= $true )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1735]) ).
thf(1814,plain,
! [SV87: $i,SV39: $i,SV137: $i] :
( ( ( ~ ( ~ ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
| ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
| ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 ) )
| ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV137 ) ) )
= $true )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1735]) ).
thf(1815,plain,
! [SV42: $i,SV89: $i,SV145: $i] :
( ( ( ~ ( in @ SV145 @ ( sK42_SY593 @ SV89 @ SV42 @ SV145 ) ) )
= $false )
| ( ( in @ SV145 @ SV89 )
= $false )
| ( ( SV89
= ( union @ SV42 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1736]) ).
thf(1816,plain,
! [SV145: $i,SV42: $i,SV89: $i] :
( ( ( ~ ( in @ ( sK42_SY593 @ SV89 @ SV42 @ SV145 ) @ SV42 ) )
= $false )
| ( ( in @ SV145 @ SV89 )
= $false )
| ( ( SV89
= ( union @ SV42 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1736]) ).
thf(1817,plain,
! [SV89: $i,SV42: $i,SV182: $i,SV145: $i] :
( ( ( ~ ( in @ SV145 @ SV182 ) )
= $true )
| ( ( ~ ( in @ SV182 @ SV42 ) )
= $true )
| ( ( in @ SV145 @ SV89 )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1737]) ).
thf(1818,plain,
! [SV89: $i,SV42: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ ( sK51_SY596 @ SV89 @ SV42 ) )
| ~ ( in @ ( sK51_SY596 @ SV89 @ SV42 ) @ SV42 ) ) )
= $false )
| ( ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1738]) ).
thf(1819,plain,
! [SV177: $i,SV89: $i,SV42: $i] :
( ( ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV177 )
= $false )
| ( ( ~ ( in @ SV177 @ SV42 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY596: $i] :
~ ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SY596 )
| ~ ( in @ SY596 @ SV42 ) )
| ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1739]) ).
thf(1820,plain,
! [SV183: $i,SV46: $i,SV178: $i] :
( ( ( ~ ( in @ SV178 @ ( sK4_SY357 @ SV46 ) )
| ~ ( subset @ SV183 @ SV178 ) )
= $true )
| ( ( in @ SV183 @ ( sK4_SY357 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1740]) ).
thf(1821,plain,
! [SV46: $i,SV162: $i] :
( ( ( ~ ( ~ ( in @ ( sK46_SY623 @ SV162 @ SV46 ) @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SY656: $i] :
( ~ ( subset @ SY656 @ SV162 )
| ( in @ SY656 @ ( sK46_SY623 @ SV162 @ SV46 ) ) ) ) )
= $true )
| ( ( in @ SV162 @ ( sK4_SY357 @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1741]) ).
thf(1822,plain,
! [SV46: $i,SV146: $i] :
( ( ( ~ ( in @ SV146 @ ( sK4_SY357 @ SV46 ) ) )
= $false )
| ( ( subset @ SV146 @ ( sK4_SY357 @ SV46 ) )
= $false )
| ( ( are_equipotent @ SV146 @ ( sK4_SY357 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1742]) ).
thf(1823,plain,
! [SV47: $i,SV132: $i,SV155: $i] :
( ( ( in @ ( ordered_pair @ SV155 @ ( sK47_SY611 @ SV132 @ SV47 @ SV155 ) ) @ SV47 )
= $true )
| ( ( in @ SV155 @ SV132 )
= $false )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1743]) ).
thf(1824,plain,
! [SV132: $i,SV47: $i,SV192: $i,SV155: $i] :
( ( ( in @ ( ordered_pair @ SV155 @ SV192 ) @ SV47 )
= $false )
| ( ( in @ SV155 @ SV132 )
= $true )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1744]) ).
thf(1825,plain,
! [SV132: $i,SV47: $i] :
( ( ( ~ ! [SY614: $i] :
~ ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ SY614 ) @ SV47 ) )
= $true )
| ( ( in @ ( sK22_SY553 @ SV47 @ SV132 ) @ SV132 )
= $true )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1745]) ).
thf(1826,plain,
! [SV187: $i,SV132: $i,SV47: $i] :
( ( ( ~ ~ ! [SY614: $i] :
~ ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ SY614 ) @ SV47 )
| ( in @ ( sK22_SY553 @ SV47 @ SV132 ) @ SV132 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ SV187 ) @ SV47 )
= $false )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1747]) ).
thf(1827,plain,
! [SV49: $i,SV133: $i,SV172: $i,SV166: $i] :
( ( ( in @ ( ordered_pair @ SV166 @ SV172 ) @ SV133 )
= $false )
| ( ( in @ ( ordered_pair @ SV172 @ SV166 ) @ SV49 )
= $true )
| ( ( SV133
= ( relation_inverse @ SV49 ) )
= $false )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1748]) ).
thf(1828,plain,
! [SV133: $i,SV49: $i,SV166: $i,SV172: $i] :
( ( ( in @ ( ordered_pair @ SV172 @ SV166 ) @ SV49 )
= $false )
| ( ( in @ ( ordered_pair @ SV166 @ SV172 ) @ SV133 )
= $true )
| ( ( SV133
= ( relation_inverse @ SV49 ) )
= $false )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1749]) ).
thf(1829,plain,
! [SV133: $i,SV49: $i] :
( ( ( in @ ( ordered_pair @ ( sK30_SY558 @ SV49 @ SV133 ) @ ( sK36_SY631 @ SV133 @ SV49 ) ) @ SV133 )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK36_SY631 @ SV133 @ SV49 ) @ ( sK30_SY558 @ SV49 @ SV133 ) ) @ SV49 )
| ( in @ ( ordered_pair @ ( sK30_SY558 @ SV49 @ SV133 ) @ ( sK36_SY631 @ SV133 @ SV49 ) ) @ SV133 ) ) )
= $true )
| ( ( SV133
= ( relation_inverse @ SV49 ) )
= $true )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1750]) ).
thf(1830,plain,
! [SV49: $i,SV133: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK36_SY631 @ SV133 @ SV49 ) @ ( sK30_SY558 @ SV49 @ SV133 ) ) @ SV49 )
| ( in @ ( ordered_pair @ ( sK30_SY558 @ SV49 @ SV133 ) @ ( sK36_SY631 @ SV133 @ SV49 ) ) @ SV133 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK36_SY631 @ SV133 @ SV49 ) @ ( sK30_SY558 @ SV49 @ SV133 ) ) @ SV49 )
= $false )
| ( ( SV133
= ( relation_inverse @ SV49 ) )
= $true )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1751]) ).
thf(1831,plain,
! [SV118: $i,SV56: $i,SV100: $i] :
( ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV56 )
= $true )
| ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV100 )
= $true )
| ( ( in @ ( sK17_SY503 @ SV100 @ SV56 @ SV118 ) @ SV118 )
= $true )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1752]) ).
thf(1832,plain,
! [SV118: $i,SV56: $i,SV100: $i] :
( ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV56 )
= $true )
| ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV100 )
= $true )
| ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV56 )
= $false )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1753]) ).
thf(1833,plain,
! [SV118: $i,SV56: $i,SV100: $i] :
( ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV56 )
= $true )
| ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV100 )
= $true )
| ( ( ( sK17_SY503 @ SV100 @ SV56 @ SV118 )
= SV100 )
= $false )
| ( ( SV118
= ( unordered_pair @ SV56 @ SV100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1754]) ).
thf(1834,plain,
! [SV58: $i,SV119: $i,SV102: $i,SV151: $i] :
( ( ( in @ SV151 @ SV102 )
= $false )
| ( ( in @ SV151 @ SV119 )
= $false )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1756]) ).
thf(1835,plain,
! [SV119: $i,SV58: $i,SV102: $i,SV151: $i] :
( ( ( ~ ( in @ SV151 @ SV102 ) )
= $false )
| ( ( in @ SV151 @ SV58 )
= $false )
| ( ( in @ SV151 @ SV119 )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1757]) ).
thf(1836,plain,
! [SV119: $i,SV58: $i,SV102: $i] :
( ( ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
| ~ ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 ) )
= $false )
| ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV119 )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1758]) ).
thf(1837,plain,
! [SV119: $i,SV58: $i,SV102: $i] :
( ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 )
= $true )
| ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
| ~ ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 ) )
| ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV119 ) ) )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1759]) ).
thf(1838,plain,
! [SV121: $i,SV60: $i,SV104: $i,SV152: $i] :
( ( ( in @ SV152 @ SV104 )
= $false )
| ( ( in @ SV152 @ SV60 )
= $false )
| ( ( in @ SV152 @ SV121 )
= $true )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1762]) ).
thf(1839,plain,
! [SV121: $i,SV60: $i,SV104: $i] :
( ( ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
| ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 ) )
= $false )
| ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV121 )
= $true )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1763]) ).
thf(1840,plain,
! [SV121: $i,SV60: $i,SV104: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
| ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 ) )
| ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV121 ) )
= $false )
| ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
= $false )
| ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 )
= $false )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1764]) ).
thf(1841,plain,
! [SV66: $i,SV6: $i,SV188: $i] :
( ( ( in @ SV188 @ SV6 )
= $false )
| ( ( ( apply @ SV66 @ SV188 )
= SV188 )
= $true )
| ( ( SV66
= ( identity_relation @ SV6 ) )
= $false )
| ( ( relation @ SV66 )
= $false )
| ( ( function @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1765]) ).
thf(1842,plain,
! [SV6: $i,SV66: $i] :
( ( ( ~ ( in @ ( sK48_SY408 @ SV66 @ SV6 ) @ SV6 ) )
= $false )
| ( ( ( relation_dom @ SV66 )
= SV6 )
= $false )
| ( ( SV66
= ( identity_relation @ SV6 ) )
= $true )
| ( ( relation @ SV66 )
= $false )
| ( ( function @ SV66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1766]) ).
thf(1843,plain,
! [SV6: $i,SV66: $i] :
( ( ( ( apply @ SV66 @ ( sK48_SY408 @ SV66 @ SV6 ) )
= ( sK48_SY408 @ SV66 @ SV6 ) )
= $false )
| ( ( ( relation_dom @ SV66 )
= SV6 )
= $false )
| ( ( SV66
= ( identity_relation @ SV6 ) )
= $true )
| ( ( relation @ SV66 )
= $false )
| ( ( function @ SV66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1766]) ).
thf(1844,plain,
! [SV8: $i,SV123: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV8 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV8 )
= $true )
| ( ( SV8 = SV123 )
= $true )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1769]) ).
thf(1845,plain,
! [SV8: $i,SV123: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV123 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV123 )
= $false )
| ( ( SV8 = SV123 )
= $true )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1770]) ).
thf(1846,plain,
! [SV8: $i,SV123: $i] :
( ( ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV8 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV123 )
= $false )
| ( ( SV8 = SV123 )
= $true )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1770]) ).
thf(1847,plain,
! [SV124: $i,SV10: $i,SV139: $i,SV184: $i,SV179: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV179 @ SV184 ) @ SV139 )
| ~ ! [SY650: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV179 @ SY650 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY650 @ SV184 ) @ SV124 ) ) )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $false )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1771]) ).
thf(1848,plain,
! [SV139: $i,SV124: $i,SV184: $i,SV10: $i,SV179: $i] :
( ( ( ~ ~ ! [SY651: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV179 @ SY651 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY651 @ SV184 ) @ SV124 ) )
| ( in @ ( ordered_pair @ SV179 @ SV184 ) @ SV139 ) )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $false )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1772]) ).
thf(1849,plain,
! [SV139: $i,SV10: $i,SV124: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV139 )
| ~ ! [SY652: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SY652 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY652 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY653: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SY653 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY653 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) )
| ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV139 ) ) )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1773]) ).
thf(1850,plain,
! [SV11: $i,SV69: $i,SV148: $i,SV107: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK44_SY597 @ SV107 @ SV148 @ SV69 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK52_SY654 @ SV11 @ SV69 @ SV148 @ SV107 ) @ SV69 ) )
| ( SV148
!= ( ordered_pair @ ( sK44_SY597 @ SV107 @ SV148 @ SV69 @ SV11 ) @ ( sK52_SY654 @ SV11 @ SV69 @ SV148 @ SV107 ) ) ) ) )
= $false )
| ( ( in @ SV148 @ SV107 )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1774]) ).
thf(1851,plain,
! [SV107: $i,SV148: $i,SV69: $i,SV196: $i,SV11: $i,SV185: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV185 @ SV11 )
| ~ ( in @ SV196 @ SV69 ) )
| ( SV148
!= ( ordered_pair @ SV185 @ SV196 ) ) ) )
= $true )
| ( ( in @ SV148 @ SV107 )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1775]) ).
thf(1852,plain,
! [SV11: $i,SV69: $i,SV107: $i] :
( ( ( ~ ~ ! [SY657: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK53_SY603 @ SV107 @ SV69 @ SV11 ) @ SV11 )
| ~ ( in @ SY657 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ ( sK53_SY603 @ SV107 @ SV69 @ SV11 ) @ SY657 ) ) ) )
= $false )
| ( ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1776]) ).
thf(1853,plain,
! [SV107: $i,SV69: $i,SV193: $i,SV11: $i,SV180: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV180 @ SV11 )
| ~ ( in @ SV193 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SV180 @ SV193 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY603: $i] :
~ ~ ! [SY604: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY603 @ SV11 )
| ~ ( in @ SY604 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SY603 @ SY604 ) ) )
| ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 ) ) )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1777]) ).
thf(1854,plain,
! [SV70: $i,SV157: $i,SV12: $i,SV153: $i] :
( ( ( in @ SV153 @ SV12 )
= $true )
| ( ( in @ ( ordered_pair @ SV153 @ SV157 ) @ SV70 )
= $false )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1778]) ).
thf(1855,plain,
! [SV12: $i,SV70: $i,SV157: $i,SV153: $i] :
( ( ( SV153 = SV157 )
= $true )
| ( ( in @ ( ordered_pair @ SV153 @ SV157 ) @ SV70 )
= $false )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1779]) ).
thf(1856,plain,
! [SV70: $i,SV157: $i,SV12: $i,SV153: $i] :
( ( ( in @ SV153 @ SV12 )
= $false )
| ( ( SV153 != SV157 )
= $true )
| ( ( in @ ( ordered_pair @ SV153 @ SV157 ) @ SV70 )
= $true )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1780]) ).
thf(1857,plain,
! [SV70: $i,SV12: $i] :
( ( ( ~ ( ~ ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
| ( ( sK20_SY424 @ SV12 @ SV70 )
!= ( sK23_SY606 @ SV70 @ SV12 ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK20_SY424 @ SV12 @ SV70 ) @ ( sK23_SY606 @ SV70 @ SV12 ) ) @ SV70 )
= $true )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1781]) ).
thf(1858,plain,
! [SV70: $i,SV12: $i] :
( ( ( ( sK20_SY424 @ SV12 @ SV70 )
= ( sK23_SY606 @ SV70 @ SV12 ) )
= $false )
| ( ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
| ( ( sK20_SY424 @ SV12 @ SV70 )
!= ( sK23_SY606 @ SV70 @ SV12 ) ) )
| ( in @ ( ordered_pair @ ( sK20_SY424 @ SV12 @ SV70 ) @ ( sK23_SY606 @ SV70 @ SV12 ) ) @ SV70 ) ) )
= $true )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1783]) ).
thf(1859,plain,
! [SV14: $i,SV125: $i,SV134: $i,SV158: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV158 @ ( sK49_SY615 @ SV134 @ SV125 @ SV14 @ SV158 ) ) @ SV14 )
| ~ ( in @ ( sK49_SY615 @ SV134 @ SV125 @ SV14 @ SV158 ) @ SV125 ) ) )
= $true )
| ( ( in @ SV158 @ SV134 )
= $false )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1784]) ).
thf(1860,plain,
! [SV134: $i,SV125: $i,SV14: $i,SV194: $i,SV158: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV158 @ SV194 ) @ SV14 )
| ~ ( in @ SV194 @ SV125 ) ) )
= $false )
| ( ( in @ SV158 @ SV134 )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1785]) ).
thf(1861,plain,
! [SV134: $i,SV14: $i,SV125: $i] :
( ( ( ~ ! [SY618: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SY618 ) @ SV14 )
| ~ ( in @ SY618 @ SV125 ) ) )
= $true )
| ( ( in @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV134 )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1786]) ).
thf(1862,plain,
! [SV189: $i,SV134: $i,SV14: $i,SV125: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV189 ) @ SV14 )
| ~ ( in @ SV189 @ SV125 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY618: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SY618 ) @ SV14 )
| ~ ( in @ SY618 @ SV125 ) )
| ( in @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV134 ) ) )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1788]) ).
thf(1863,plain,
! [SV126: $i,SV15: $i] :
( ( ( ! [SY610: $i] :
~ ( in @ ( ordered_pair @ SY610 @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 ) )
= $false )
| ( ( in @ ( sK21_SY531 @ SV15 @ SV126 ) @ SV126 )
= $true )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1791]) ).
thf(1864,plain,
! [SV186: $i,SV126: $i,SV15: $i] :
( ( ( ~ ~ ! [SY610: $i] :
~ ( in @ ( ordered_pair @ SY610 @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV186 @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 )
= $false )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1792]) ).
thf(1865,plain,
! [SV186: $i,SV126: $i,SV15: $i] :
( ( ( in @ ( sK21_SY531 @ SV15 @ SV126 ) @ SV126 )
= $false )
| ( ( in @ ( ordered_pair @ SV186 @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 )
= $false )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1792]) ).
thf(1866,plain,
! [SV20: $i,SV128: $i,SV135: $i,SV173: $i,SV169: $i] :
( ( ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV135 )
= $false )
| ( ( ~ ( ~ ( in @ SV169 @ SV128 )
| ~ ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV20 ) ) )
= $true )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1796]) ).
thf(1867,plain,
! [SV135: $i,SV20: $i,SV173: $i,SV128: $i,SV169: $i] :
( ( ( ~ ( ~ ( in @ SV169 @ SV128 )
| ~ ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV20 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV135 )
= $true )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1797]) ).
thf(1868,plain,
! [SV135: $i,SV128: $i,SV20: $i] :
( ( ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV135 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
| ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 ) )
| ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV135 ) ) )
= $true )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1798]) ).
thf(1869,plain,
! [SV135: $i,SV128: $i,SV20: $i] :
( ( ( ~ ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
| ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
| ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 ) )
| ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV135 ) ) )
= $true )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1799]) ).
thf(1870,plain,
! [SV181: $i,SV23: $i,SV174: $i] :
( ( ( ~ ( in @ SV174 @ ( sK3_SY291 @ SV23 ) ) )
= $true )
| ( ( ~ ( subset @ SV181 @ SV174 ) )
= $true )
| ( ( in @ SV181 @ ( sK3_SY291 @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1800]) ).
thf(1871,plain,
! [SV23: $i,SV143: $i] :
( ( ( in @ SV143 @ ( sK3_SY291 @ SV23 ) )
= $true )
| ( ( subset @ SV143 @ ( sK3_SY291 @ SV23 ) )
= $false )
| ( ( are_equipotent @ SV143 @ ( sK3_SY291 @ SV23 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1801]) ).
thf(1872,plain,
! [SV26: $i,SV78: $i,SV175: $i] :
( ( ( in @ SV175 @ SV78 )
= $false )
| ( ( ! [SY638: $i] :
( ~ ( in @ SY638 @ SV26 )
| ( in @ SV175 @ SY638 ) ) )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $false )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1802]) ).
thf(1873,plain,
! [SV78: $i,SV175: $i,SV26: $i] :
( ( ( ! [SY639: $i] :
( ~ ( in @ SY639 @ SV26 )
| ( in @ SV175 @ SY639 ) ) )
= $false )
| ( ( in @ SV175 @ SV78 )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $false )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1803]) ).
thf(1874,plain,
! [SV78: $i,SV26: $i] :
( ( ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV78 )
= $true )
| ( ( ~ ( ~ ! [SY641: $i] :
( ~ ( in @ SY641 @ SV26 )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SY641 ) )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV78 ) ) )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1804]) ).
thf(1875,plain,
! [SV26: $i,SV78: $i] :
( ( ( ~ ( in @ ( sK54_SY640 @ SV78 @ SV26 ) @ SV26 )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ ( sK54_SY640 @ SV78 @ SV26 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY641: $i] :
( ~ ( in @ SY641 @ SV26 )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SY641 ) )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV78 ) ) )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1805]) ).
thf(1876,plain,
! [SV161: $i,SV30: $i,SV131: $i,SV136: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK50_SY619 @ SV136 @ SV131 @ SV30 @ SV161 ) @ SV161 ) @ SV30 )
| ~ ( in @ ( sK50_SY619 @ SV136 @ SV131 @ SV30 @ SV161 ) @ SV131 ) ) )
= $true )
| ( ( in @ SV161 @ SV136 )
= $false )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1806]) ).
thf(1877,plain,
! [SV136: $i,SV131: $i,SV30: $i,SV161: $i,SV195: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV195 @ SV161 ) @ SV30 )
| ~ ( in @ SV195 @ SV131 ) ) )
= $false )
| ( ( in @ SV161 @ SV136 )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1807]) ).
thf(1878,plain,
! [SV136: $i,SV30: $i,SV131: $i] :
( ( ( ~ ! [SY622: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY622 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ SY622 @ SV131 ) ) )
= $true )
| ( ( in @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) @ SV136 )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1808]) ).
thf(1879,plain,
! [SV136: $i,SV30: $i,SV131: $i,SV191: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV191 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ SV191 @ SV131 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY622: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY622 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ SY622 @ SV131 ) )
| ( in @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) @ SV136 ) ) )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1810]) ).
thf(1880,plain,
! [SV87: $i,SV39: $i,SV137: $i,SV176: $i,SV171: $i] :
( ( ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV137 )
= $false )
| ( ( ~ ( ~ ( in @ SV176 @ SV39 )
| ~ ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV87 ) ) )
= $true )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1811]) ).
thf(1881,plain,
! [SV137: $i,SV87: $i,SV171: $i,SV39: $i,SV176: $i] :
( ( ( ~ ( ~ ( in @ SV176 @ SV39 )
| ~ ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV87 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV137 )
= $true )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1812]) ).
thf(1882,plain,
! [SV137: $i,SV39: $i,SV87: $i] :
( ( ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV137 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
| ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 ) )
| ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV137 ) ) )
= $true )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1813]) ).
thf(1883,plain,
! [SV87: $i,SV39: $i,SV137: $i] :
( ( ( ~ ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
| ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
| ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 ) )
| ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV137 ) ) )
= $true )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1814]) ).
thf(1884,plain,
! [SV42: $i,SV89: $i,SV145: $i] :
( ( ( in @ SV145 @ ( sK42_SY593 @ SV89 @ SV42 @ SV145 ) )
= $true )
| ( ( in @ SV145 @ SV89 )
= $false )
| ( ( SV89
= ( union @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1815]) ).
thf(1885,plain,
! [SV145: $i,SV42: $i,SV89: $i] :
( ( ( in @ ( sK42_SY593 @ SV89 @ SV42 @ SV145 ) @ SV42 )
= $true )
| ( ( in @ SV145 @ SV89 )
= $false )
| ( ( SV89
= ( union @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1816]) ).
thf(1886,plain,
! [SV89: $i,SV42: $i,SV182: $i,SV145: $i] :
( ( ( in @ SV145 @ SV182 )
= $false )
| ( ( ~ ( in @ SV182 @ SV42 ) )
= $true )
| ( ( in @ SV145 @ SV89 )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1817]) ).
thf(1887,plain,
! [SV89: $i,SV42: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ ( sK51_SY596 @ SV89 @ SV42 ) )
| ~ ( in @ ( sK51_SY596 @ SV89 @ SV42 ) @ SV42 ) ) )
= $true )
| ( ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1818]) ).
thf(1888,plain,
! [SV89: $i,SV42: $i,SV177: $i] :
( ( ( in @ SV177 @ SV42 )
= $false )
| ( ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV177 )
= $false )
| ( ( ~ ( ~ ~ ! [SY596: $i] :
~ ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SY596 )
| ~ ( in @ SY596 @ SV42 ) )
| ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1819]) ).
thf(1889,plain,
! [SV183: $i,SV46: $i,SV178: $i] :
( ( ( ~ ( in @ SV178 @ ( sK4_SY357 @ SV46 ) ) )
= $true )
| ( ( ~ ( subset @ SV183 @ SV178 ) )
= $true )
| ( ( in @ SV183 @ ( sK4_SY357 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1820]) ).
thf(1890,plain,
! [SV46: $i,SV162: $i] :
( ( ( ~ ( in @ ( sK46_SY623 @ SV162 @ SV46 ) @ ( sK4_SY357 @ SV46 ) )
| ~ ! [SY656: $i] :
( ~ ( subset @ SY656 @ SV162 )
| ( in @ SY656 @ ( sK46_SY623 @ SV162 @ SV46 ) ) ) )
= $false )
| ( ( in @ SV162 @ ( sK4_SY357 @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1821]) ).
thf(1891,plain,
! [SV46: $i,SV146: $i] :
( ( ( in @ SV146 @ ( sK4_SY357 @ SV46 ) )
= $true )
| ( ( subset @ SV146 @ ( sK4_SY357 @ SV46 ) )
= $false )
| ( ( are_equipotent @ SV146 @ ( sK4_SY357 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1822]) ).
thf(1892,plain,
! [SV132: $i,SV47: $i] :
( ( ( ! [SY614: $i] :
~ ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ SY614 ) @ SV47 ) )
= $false )
| ( ( in @ ( sK22_SY553 @ SV47 @ SV132 ) @ SV132 )
= $true )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1825]) ).
thf(1893,plain,
! [SV187: $i,SV132: $i,SV47: $i] :
( ( ( ~ ~ ! [SY614: $i] :
~ ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ SY614 ) @ SV47 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ SV187 ) @ SV47 )
= $false )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1826]) ).
thf(1894,plain,
! [SV187: $i,SV132: $i,SV47: $i] :
( ( ( in @ ( sK22_SY553 @ SV47 @ SV132 ) @ SV132 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ SV187 ) @ SV47 )
= $false )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1826]) ).
thf(1895,plain,
! [SV49: $i,SV133: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK36_SY631 @ SV133 @ SV49 ) @ ( sK30_SY558 @ SV49 @ SV133 ) ) @ SV49 )
| ( in @ ( ordered_pair @ ( sK30_SY558 @ SV49 @ SV133 ) @ ( sK36_SY631 @ SV133 @ SV49 ) ) @ SV133 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK30_SY558 @ SV49 @ SV133 ) @ ( sK36_SY631 @ SV133 @ SV49 ) ) @ SV133 )
= $true )
| ( ( SV133
= ( relation_inverse @ SV49 ) )
= $true )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1829]) ).
thf(1896,plain,
! [SV49: $i,SV133: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK36_SY631 @ SV133 @ SV49 ) @ ( sK30_SY558 @ SV49 @ SV133 ) ) @ SV49 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK36_SY631 @ SV133 @ SV49 ) @ ( sK30_SY558 @ SV49 @ SV133 ) ) @ SV49 )
= $false )
| ( ( SV133
= ( relation_inverse @ SV49 ) )
= $true )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1830]) ).
thf(1897,plain,
! [SV133: $i,SV49: $i] :
( ( ( in @ ( ordered_pair @ ( sK30_SY558 @ SV49 @ SV133 ) @ ( sK36_SY631 @ SV133 @ SV49 ) ) @ SV133 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK36_SY631 @ SV133 @ SV49 ) @ ( sK30_SY558 @ SV49 @ SV133 ) ) @ SV49 )
= $false )
| ( ( SV133
= ( relation_inverse @ SV49 ) )
= $true )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1830]) ).
thf(1898,plain,
! [SV119: $i,SV58: $i,SV102: $i,SV151: $i] :
( ( ( in @ SV151 @ SV102 )
= $true )
| ( ( in @ SV151 @ SV58 )
= $false )
| ( ( in @ SV151 @ SV119 )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1835]) ).
thf(1899,plain,
! [SV119: $i,SV58: $i,SV102: $i] :
( ( ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 ) )
= $false )
| ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV119 )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1836]) ).
thf(1900,plain,
! [SV119: $i,SV58: $i,SV102: $i] :
( ( ( ~ ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 ) )
= $false )
| ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV119 )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1836]) ).
thf(1901,plain,
! [SV119: $i,SV58: $i,SV102: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
| ~ ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 ) )
| ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV119 ) )
= $false )
| ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
= $false )
| ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1837]) ).
thf(1902,plain,
! [SV121: $i,SV60: $i,SV104: $i] :
( ( ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 ) )
= $false )
| ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV121 )
= $true )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1839]) ).
thf(1903,plain,
! [SV121: $i,SV60: $i,SV104: $i] :
( ( ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 ) )
= $false )
| ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV121 )
= $true )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1839]) ).
thf(1904,plain,
! [SV121: $i,SV60: $i,SV104: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
| ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 ) ) )
= $false )
| ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
= $false )
| ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 )
= $false )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1840]) ).
thf(1905,plain,
! [SV121: $i,SV60: $i,SV104: $i] :
( ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV121 )
= $false )
| ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
= $false )
| ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 )
= $false )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1840]) ).
thf(1906,plain,
! [SV6: $i,SV66: $i] :
( ( ( in @ ( sK48_SY408 @ SV66 @ SV6 ) @ SV6 )
= $true )
| ( ( ( relation_dom @ SV66 )
= SV6 )
= $false )
| ( ( SV66
= ( identity_relation @ SV6 ) )
= $true )
| ( ( relation @ SV66 )
= $false )
| ( ( function @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1842]) ).
thf(1907,plain,
! [SV8: $i,SV123: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV123 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV8 )
= $true )
| ( ( SV8 = SV123 )
= $true )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1844]) ).
thf(1908,plain,
! [SV8: $i,SV123: $i] :
( ( ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV8 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV8 )
= $true )
| ( ( SV8 = SV123 )
= $true )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1844]) ).
thf(1909,plain,
! [SV8: $i,SV123: $i] :
( ( ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV123 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV123 )
= $false )
| ( ( SV8 = SV123 )
= $true )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1845]) ).
thf(1910,plain,
! [SV124: $i,SV10: $i,SV139: $i,SV184: $i,SV179: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV179 @ SV184 ) @ SV139 ) )
= $true )
| ( ( ~ ! [SY650: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV179 @ SY650 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY650 @ SV184 ) @ SV124 ) ) )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $false )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1847]) ).
thf(1911,plain,
! [SV139: $i,SV124: $i,SV184: $i,SV10: $i,SV179: $i] :
( ( ( ~ ~ ! [SY651: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV179 @ SY651 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY651 @ SV184 ) @ SV124 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV179 @ SV184 ) @ SV139 )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $false )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1848]) ).
thf(1912,plain,
! [SV139: $i,SV10: $i,SV124: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV139 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY653: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SY653 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY653 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) )
| ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV139 ) ) )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1849]) ).
thf(1913,plain,
! [SV139: $i,SV10: $i,SV124: $i] :
( ( ( ~ ! [SY652: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SY652 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY652 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY653: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SY653 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY653 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) )
| ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV139 ) ) )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1849]) ).
thf(1914,plain,
! [SV11: $i,SV69: $i,SV148: $i,SV107: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK44_SY597 @ SV107 @ SV148 @ SV69 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK52_SY654 @ SV11 @ SV69 @ SV148 @ SV107 ) @ SV69 ) )
| ( SV148
!= ( ordered_pair @ ( sK44_SY597 @ SV107 @ SV148 @ SV69 @ SV11 ) @ ( sK52_SY654 @ SV11 @ SV69 @ SV148 @ SV107 ) ) ) ) )
= $true )
| ( ( in @ SV148 @ SV107 )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1850]) ).
thf(1915,plain,
! [SV107: $i,SV148: $i,SV69: $i,SV196: $i,SV11: $i,SV185: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV185 @ SV11 )
| ~ ( in @ SV196 @ SV69 ) )
| ( SV148
!= ( ordered_pair @ SV185 @ SV196 ) ) ) )
= $false )
| ( ( in @ SV148 @ SV107 )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1851]) ).
thf(1916,plain,
! [SV11: $i,SV69: $i,SV107: $i] :
( ( ( ~ ! [SY657: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK53_SY603 @ SV107 @ SV69 @ SV11 ) @ SV11 )
| ~ ( in @ SY657 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ ( sK53_SY603 @ SV107 @ SV69 @ SV11 ) @ SY657 ) ) ) )
= $true )
| ( ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1852]) ).
thf(1917,plain,
! [SV107: $i,SV69: $i,SV193: $i,SV11: $i,SV180: $i] :
( ( ( ~ ~ ( ~ ( in @ SV180 @ SV11 )
| ~ ( in @ SV193 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SV180 @ SV193 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY603: $i] :
~ ~ ! [SY604: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY603 @ SV11 )
| ~ ( in @ SY604 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SY603 @ SY604 ) ) )
| ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 ) ) )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1853]) ).
thf(1918,plain,
! [SV70: $i,SV12: $i,SV157: $i,SV153: $i] :
( ( ( SV153 = SV157 )
= $false )
| ( ( in @ SV153 @ SV12 )
= $false )
| ( ( in @ ( ordered_pair @ SV153 @ SV157 ) @ SV70 )
= $true )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1856]) ).
thf(1919,plain,
! [SV70: $i,SV12: $i] :
( ( ( ~ ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
| ( ( sK20_SY424 @ SV12 @ SV70 )
!= ( sK23_SY606 @ SV70 @ SV12 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK20_SY424 @ SV12 @ SV70 ) @ ( sK23_SY606 @ SV70 @ SV12 ) ) @ SV70 )
= $true )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1857]) ).
thf(1920,plain,
! [SV70: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
| ( ( sK20_SY424 @ SV12 @ SV70 )
!= ( sK23_SY606 @ SV70 @ SV12 ) ) )
| ( in @ ( ordered_pair @ ( sK20_SY424 @ SV12 @ SV70 ) @ ( sK23_SY606 @ SV70 @ SV12 ) ) @ SV70 ) )
= $false )
| ( ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
= $false )
| ( ( ( sK20_SY424 @ SV12 @ SV70 )
= ( sK23_SY606 @ SV70 @ SV12 ) )
= $false )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1858]) ).
thf(1921,plain,
! [SV14: $i,SV125: $i,SV134: $i,SV158: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV158 @ ( sK49_SY615 @ SV134 @ SV125 @ SV14 @ SV158 ) ) @ SV14 )
| ~ ( in @ ( sK49_SY615 @ SV134 @ SV125 @ SV14 @ SV158 ) @ SV125 ) )
= $false )
| ( ( in @ SV158 @ SV134 )
= $false )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1859]) ).
thf(1922,plain,
! [SV134: $i,SV125: $i,SV14: $i,SV194: $i,SV158: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV158 @ SV194 ) @ SV14 )
| ~ ( in @ SV194 @ SV125 ) )
= $true )
| ( ( in @ SV158 @ SV134 )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1860]) ).
thf(1923,plain,
! [SV134: $i,SV14: $i,SV125: $i] :
( ( ( ! [SY618: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SY618 ) @ SV14 )
| ~ ( in @ SY618 @ SV125 ) ) )
= $false )
| ( ( in @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV134 )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1861]) ).
thf(1924,plain,
! [SV189: $i,SV134: $i,SV14: $i,SV125: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV189 ) @ SV14 ) )
= $true )
| ( ( ~ ( in @ SV189 @ SV125 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY618: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SY618 ) @ SV14 )
| ~ ( in @ SY618 @ SV125 ) )
| ( in @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV134 ) ) )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1862]) ).
thf(1925,plain,
! [SV15: $i,SV126: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK55_SY610 @ SV126 @ SV15 ) @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 ) )
= $false )
| ( ( in @ ( sK21_SY531 @ SV15 @ SV126 ) @ SV126 )
= $true )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1863]) ).
thf(1926,plain,
! [SV186: $i,SV126: $i,SV15: $i] :
( ( ( ~ ! [SY610: $i] :
~ ( in @ ( ordered_pair @ SY610 @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV186 @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 )
= $false )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1864]) ).
thf(1927,plain,
! [SV135: $i,SV20: $i,SV173: $i,SV128: $i,SV169: $i] :
( ( ( ~ ( in @ SV169 @ SV128 )
| ~ ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV20 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV135 )
= $false )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1866]) ).
thf(1928,plain,
! [SV135: $i,SV20: $i,SV173: $i,SV128: $i,SV169: $i] :
( ( ( ~ ( in @ SV169 @ SV128 )
| ~ ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV20 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV135 )
= $true )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1867]) ).
thf(1929,plain,
! [SV135: $i,SV128: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
| ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 ) )
| ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV135 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV135 )
= $true )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1868]) ).
thf(1930,plain,
! [SV135: $i,SV128: $i,SV20: $i] :
( ( ( ~ ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
| ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 ) )
| ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV135 ) ) )
= $true )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1869]) ).
thf(1931,plain,
! [SV181: $i,SV23: $i,SV174: $i] :
( ( ( in @ SV174 @ ( sK3_SY291 @ SV23 ) )
= $false )
| ( ( ~ ( subset @ SV181 @ SV174 ) )
= $true )
| ( ( in @ SV181 @ ( sK3_SY291 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1870]) ).
thf(1932,plain,
! [SV78: $i,SV175: $i,SV26: $i,SV197: $i] :
( ( ( ~ ( in @ SV197 @ SV26 )
| ( in @ SV175 @ SV197 ) )
= $true )
| ( ( in @ SV175 @ SV78 )
= $false )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $false )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1872]) ).
thf(1933,plain,
! [SV26: $i,SV175: $i,SV78: $i] :
( ( ( ~ ( in @ ( sK56_SY639 @ SV78 @ SV175 @ SV26 ) @ SV26 )
| ( in @ SV175 @ ( sK56_SY639 @ SV78 @ SV175 @ SV26 ) ) )
= $false )
| ( ( in @ SV175 @ SV78 )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $false )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1873]) ).
thf(1934,plain,
! [SV78: $i,SV26: $i] :
( ( ( ~ ! [SY641: $i] :
( ~ ( in @ SY641 @ SV26 )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SY641 ) )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV78 ) )
= $false )
| ( ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV78 )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1874]) ).
thf(1935,plain,
! [SV26: $i,SV78: $i] :
( ( ( ~ ( in @ ( sK54_SY640 @ SV78 @ SV26 ) @ SV26 ) )
= $false )
| ( ( ~ ( ~ ! [SY641: $i] :
( ~ ( in @ SY641 @ SV26 )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SY641 ) )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV78 ) ) )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1875]) ).
thf(1936,plain,
! [SV78: $i,SV26: $i] :
( ( ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ ( sK54_SY640 @ SV78 @ SV26 ) )
= $false )
| ( ( ~ ( ~ ! [SY641: $i] :
( ~ ( in @ SY641 @ SV26 )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SY641 ) )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV78 ) ) )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1875]) ).
thf(1937,plain,
! [SV161: $i,SV30: $i,SV131: $i,SV136: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK50_SY619 @ SV136 @ SV131 @ SV30 @ SV161 ) @ SV161 ) @ SV30 )
| ~ ( in @ ( sK50_SY619 @ SV136 @ SV131 @ SV30 @ SV161 ) @ SV131 ) )
= $false )
| ( ( in @ SV161 @ SV136 )
= $false )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1876]) ).
thf(1938,plain,
! [SV136: $i,SV131: $i,SV30: $i,SV161: $i,SV195: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV195 @ SV161 ) @ SV30 )
| ~ ( in @ SV195 @ SV131 ) )
= $true )
| ( ( in @ SV161 @ SV136 )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1877]) ).
thf(1939,plain,
! [SV136: $i,SV30: $i,SV131: $i] :
( ( ( ! [SY622: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY622 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ SY622 @ SV131 ) ) )
= $false )
| ( ( in @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) @ SV136 )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1878]) ).
thf(1940,plain,
! [SV136: $i,SV30: $i,SV131: $i,SV191: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV191 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 ) )
= $true )
| ( ( ~ ( in @ SV191 @ SV131 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY622: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY622 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ SY622 @ SV131 ) )
| ( in @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) @ SV136 ) ) )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1879]) ).
thf(1941,plain,
! [SV137: $i,SV87: $i,SV171: $i,SV39: $i,SV176: $i] :
( ( ( ~ ( in @ SV176 @ SV39 )
| ~ ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV87 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV137 )
= $false )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1880]) ).
thf(1942,plain,
! [SV137: $i,SV87: $i,SV171: $i,SV39: $i,SV176: $i] :
( ( ( ~ ( in @ SV176 @ SV39 )
| ~ ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV87 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV137 )
= $true )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1881]) ).
thf(1943,plain,
! [SV87: $i,SV39: $i,SV137: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
| ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 ) )
| ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV137 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV137 )
= $true )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1882]) ).
thf(1944,plain,
! [SV87: $i,SV39: $i,SV137: $i] :
( ( ( ~ ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
| ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 ) )
| ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV137 ) ) )
= $true )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1883]) ).
thf(1945,plain,
! [SV89: $i,SV145: $i,SV42: $i,SV182: $i] :
( ( ( in @ SV182 @ SV42 )
= $false )
| ( ( in @ SV145 @ SV182 )
= $false )
| ( ( in @ SV145 @ SV89 )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1886]) ).
thf(1946,plain,
! [SV89: $i,SV42: $i] :
( ( ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ ( sK51_SY596 @ SV89 @ SV42 ) )
| ~ ( in @ ( sK51_SY596 @ SV89 @ SV42 ) @ SV42 ) )
= $false )
| ( ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1887]) ).
thf(1947,plain,
! [SV177: $i,SV89: $i,SV42: $i] :
( ( ( ~ ~ ! [SY596: $i] :
~ ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SY596 )
| ~ ( in @ SY596 @ SV42 ) )
| ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV89 ) )
= $false )
| ( ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV177 )
= $false )
| ( ( in @ SV177 @ SV42 )
= $false )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1888]) ).
thf(1948,plain,
! [SV183: $i,SV46: $i,SV178: $i] :
( ( ( in @ SV178 @ ( sK4_SY357 @ SV46 ) )
= $false )
| ( ( ~ ( subset @ SV183 @ SV178 ) )
= $true )
| ( ( in @ SV183 @ ( sK4_SY357 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1889]) ).
thf(1949,plain,
! [SV46: $i,SV162: $i] :
( ( ( ~ ( in @ ( sK46_SY623 @ SV162 @ SV46 ) @ ( sK4_SY357 @ SV46 ) ) )
= $false )
| ( ( in @ SV162 @ ( sK4_SY357 @ SV46 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1890]) ).
thf(1950,plain,
! [SV46: $i,SV162: $i] :
( ( ( ~ ! [SY656: $i] :
( ~ ( subset @ SY656 @ SV162 )
| ( in @ SY656 @ ( sK46_SY623 @ SV162 @ SV46 ) ) ) )
= $false )
| ( ( in @ SV162 @ ( sK4_SY357 @ SV46 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1890]) ).
thf(1951,plain,
! [SV132: $i,SV47: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ ( sK57_SY614 @ SV132 @ SV47 ) ) @ SV47 ) )
= $false )
| ( ( in @ ( sK22_SY553 @ SV47 @ SV132 ) @ SV132 )
= $true )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1892]) ).
thf(1952,plain,
! [SV187: $i,SV132: $i,SV47: $i] :
( ( ( ~ ! [SY614: $i] :
~ ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ SY614 ) @ SV47 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ SV187 ) @ SV47 )
= $false )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1893]) ).
thf(1953,plain,
! [SV49: $i,SV133: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK36_SY631 @ SV133 @ SV49 ) @ ( sK30_SY558 @ SV49 @ SV133 ) ) @ SV49 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK30_SY558 @ SV49 @ SV133 ) @ ( sK36_SY631 @ SV133 @ SV49 ) ) @ SV133 )
= $true )
| ( ( SV133
= ( relation_inverse @ SV49 ) )
= $true )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1895]) ).
thf(1954,plain,
! [SV133: $i,SV49: $i] :
( ( ( in @ ( ordered_pair @ ( sK30_SY558 @ SV49 @ SV133 ) @ ( sK36_SY631 @ SV133 @ SV49 ) ) @ SV133 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK30_SY558 @ SV49 @ SV133 ) @ ( sK36_SY631 @ SV133 @ SV49 ) ) @ SV133 )
= $true )
| ( ( SV133
= ( relation_inverse @ SV49 ) )
= $true )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1895]) ).
thf(1955,plain,
! [SV49: $i,SV133: $i] :
( ( ( in @ ( ordered_pair @ ( sK36_SY631 @ SV133 @ SV49 ) @ ( sK30_SY558 @ SV49 @ SV133 ) ) @ SV49 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK36_SY631 @ SV133 @ SV49 ) @ ( sK30_SY558 @ SV49 @ SV133 ) ) @ SV49 )
= $false )
| ( ( SV133
= ( relation_inverse @ SV49 ) )
= $true )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1896]) ).
thf(1956,plain,
! [SV119: $i,SV58: $i,SV102: $i] :
( ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
= $true )
| ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV119 )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1899]) ).
thf(1957,plain,
! [SV119: $i,SV58: $i,SV102: $i] :
( ( ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 ) )
= $true )
| ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV119 )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1900]) ).
thf(1958,plain,
! [SV119: $i,SV58: $i,SV102: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
| ~ ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 ) ) )
= $false )
| ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
= $false )
| ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1901]) ).
thf(1959,plain,
! [SV119: $i,SV58: $i,SV102: $i] :
( ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV119 )
= $false )
| ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
= $false )
| ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1901]) ).
thf(1960,plain,
! [SV121: $i,SV60: $i,SV104: $i] :
( ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
= $true )
| ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV121 )
= $true )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1902]) ).
thf(1961,plain,
! [SV121: $i,SV60: $i,SV104: $i] :
( ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 )
= $true )
| ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV121 )
= $true )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1903]) ).
thf(1962,plain,
! [SV121: $i,SV60: $i,SV104: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
| ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 ) ) )
= $true )
| ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
= $false )
| ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 )
= $false )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1904]) ).
thf(1963,plain,
! [SV8: $i,SV123: $i] :
( ( ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV123 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK27_SY510 @ SV123 @ SV8 ) @ ( sK31_SY626 @ SV8 @ SV123 ) ) @ SV8 )
= $true )
| ( ( SV8 = SV123 )
= $true )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1907]) ).
thf(1964,plain,
! [SV124: $i,SV10: $i,SV139: $i,SV184: $i,SV179: $i] :
( ( ( in @ ( ordered_pair @ SV179 @ SV184 ) @ SV139 )
= $false )
| ( ( ~ ! [SY650: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV179 @ SY650 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY650 @ SV184 ) @ SV124 ) ) )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $false )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1910]) ).
thf(1965,plain,
! [SV139: $i,SV124: $i,SV184: $i,SV10: $i,SV179: $i] :
( ( ( ~ ! [SY651: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV179 @ SY651 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY651 @ SV184 ) @ SV124 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV179 @ SV184 ) @ SV139 )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $false )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1911]) ).
thf(1966,plain,
! [SV139: $i,SV10: $i,SV124: $i] :
( ( ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV139 )
= $true )
| ( ( ~ ( ~ ~ ! [SY653: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SY653 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY653 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) )
| ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV139 ) ) )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1912]) ).
thf(1967,plain,
! [SV139: $i,SV10: $i,SV124: $i] :
( ( ( ! [SY652: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SY652 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY652 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY653: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SY653 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY653 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) )
| ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV139 ) ) )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1913]) ).
thf(1968,plain,
! [SV11: $i,SV69: $i,SV148: $i,SV107: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK44_SY597 @ SV107 @ SV148 @ SV69 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK52_SY654 @ SV11 @ SV69 @ SV148 @ SV107 ) @ SV69 ) )
| ( SV148
!= ( ordered_pair @ ( sK44_SY597 @ SV107 @ SV148 @ SV69 @ SV11 ) @ ( sK52_SY654 @ SV11 @ SV69 @ SV148 @ SV107 ) ) ) )
= $false )
| ( ( in @ SV148 @ SV107 )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1914]) ).
thf(1969,plain,
! [SV107: $i,SV148: $i,SV69: $i,SV196: $i,SV11: $i,SV185: $i] :
( ( ( ~ ~ ( ~ ( in @ SV185 @ SV11 )
| ~ ( in @ SV196 @ SV69 ) )
| ( SV148
!= ( ordered_pair @ SV185 @ SV196 ) ) )
= $true )
| ( ( in @ SV148 @ SV107 )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1915]) ).
thf(1970,plain,
! [SV11: $i,SV69: $i,SV107: $i] :
( ( ( ! [SY657: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK53_SY603 @ SV107 @ SV69 @ SV11 ) @ SV11 )
| ~ ( in @ SY657 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ ( sK53_SY603 @ SV107 @ SV69 @ SV11 ) @ SY657 ) ) ) )
= $false )
| ( ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1916]) ).
thf(1971,plain,
! [SV107: $i,SV69: $i,SV193: $i,SV11: $i,SV180: $i] :
( ( ( ~ ~ ( ~ ( in @ SV180 @ SV11 )
| ~ ( in @ SV193 @ SV69 ) ) )
= $true )
| ( ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SV180 @ SV193 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY603: $i] :
~ ~ ! [SY604: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY603 @ SV11 )
| ~ ( in @ SY604 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SY603 @ SY604 ) ) )
| ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 ) ) )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1917]) ).
thf(1972,plain,
! [SV70: $i,SV12: $i] :
( ( ( ~ ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK20_SY424 @ SV12 @ SV70 ) @ ( sK23_SY606 @ SV70 @ SV12 ) ) @ SV70 )
= $true )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1919]) ).
thf(1973,plain,
! [SV70: $i,SV12: $i] :
( ( ( ( sK20_SY424 @ SV12 @ SV70 )
!= ( sK23_SY606 @ SV70 @ SV12 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK20_SY424 @ SV12 @ SV70 ) @ ( sK23_SY606 @ SV70 @ SV12 ) ) @ SV70 )
= $true )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1919]) ).
thf(1974,plain,
! [SV70: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
| ( ( sK20_SY424 @ SV12 @ SV70 )
!= ( sK23_SY606 @ SV70 @ SV12 ) ) ) )
= $false )
| ( ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
= $false )
| ( ( ( sK20_SY424 @ SV12 @ SV70 )
= ( sK23_SY606 @ SV70 @ SV12 ) )
= $false )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1920]) ).
thf(1975,plain,
! [SV70: $i,SV12: $i] :
( ( ( in @ ( ordered_pair @ ( sK20_SY424 @ SV12 @ SV70 ) @ ( sK23_SY606 @ SV70 @ SV12 ) ) @ SV70 )
= $false )
| ( ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
= $false )
| ( ( ( sK20_SY424 @ SV12 @ SV70 )
= ( sK23_SY606 @ SV70 @ SV12 ) )
= $false )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1920]) ).
thf(1976,plain,
! [SV14: $i,SV125: $i,SV134: $i,SV158: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV158 @ ( sK49_SY615 @ SV134 @ SV125 @ SV14 @ SV158 ) ) @ SV14 ) )
= $false )
| ( ( in @ SV158 @ SV134 )
= $false )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1921]) ).
thf(1977,plain,
! [SV158: $i,SV14: $i,SV125: $i,SV134: $i] :
( ( ( ~ ( in @ ( sK49_SY615 @ SV134 @ SV125 @ SV14 @ SV158 ) @ SV125 ) )
= $false )
| ( ( in @ SV158 @ SV134 )
= $false )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1921]) ).
thf(1978,plain,
! [SV134: $i,SV125: $i,SV14: $i,SV194: $i,SV158: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV158 @ SV194 ) @ SV14 ) )
= $true )
| ( ( ~ ( in @ SV194 @ SV125 ) )
= $true )
| ( ( in @ SV158 @ SV134 )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1922]) ).
thf(1979,plain,
! [SV134: $i,SV14: $i,SV125: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ ( sK58_SY618 @ SV134 @ SV14 @ SV125 ) ) @ SV14 )
| ~ ( in @ ( sK58_SY618 @ SV134 @ SV14 @ SV125 ) @ SV125 ) ) )
= $false )
| ( ( in @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV134 )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1923]) ).
thf(1980,plain,
! [SV189: $i,SV134: $i,SV14: $i,SV125: $i] :
( ( ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV189 ) @ SV14 )
= $false )
| ( ( ~ ( in @ SV189 @ SV125 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY618: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SY618 ) @ SV14 )
| ~ ( in @ SY618 @ SV125 ) )
| ( in @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV134 ) ) )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1924]) ).
thf(1981,plain,
! [SV15: $i,SV126: $i] :
( ( ( in @ ( ordered_pair @ ( sK55_SY610 @ SV126 @ SV15 ) @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 )
= $true )
| ( ( in @ ( sK21_SY531 @ SV15 @ SV126 ) @ SV126 )
= $true )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1925]) ).
thf(1982,plain,
! [SV186: $i,SV126: $i,SV15: $i] :
( ( ( ! [SY610: $i] :
~ ( in @ ( ordered_pair @ SY610 @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV186 @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 )
= $false )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1926]) ).
thf(1983,plain,
! [SV20: $i,SV135: $i,SV173: $i,SV128: $i,SV169: $i] :
( ( ( ~ ( in @ SV169 @ SV128 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV135 )
= $false )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1927]) ).
thf(1984,plain,
! [SV128: $i,SV135: $i,SV20: $i,SV173: $i,SV169: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV20 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV135 )
= $false )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1927]) ).
thf(1985,plain,
! [SV135: $i,SV20: $i,SV173: $i,SV128: $i,SV169: $i] :
( ( ( ~ ( in @ SV169 @ SV128 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV20 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV135 )
= $true )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1928]) ).
thf(1986,plain,
! [SV135: $i,SV128: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
| ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV135 )
= $true )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1929]) ).
thf(1987,plain,
! [SV135: $i,SV128: $i,SV20: $i] :
( ( ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV135 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV135 )
= $true )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1929]) ).
thf(1988,plain,
! [SV135: $i,SV128: $i,SV20: $i] :
( ( ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
| ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 ) )
| ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV135 ) ) )
= $true )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1930]) ).
thf(1989,plain,
! [SV23: $i,SV174: $i,SV181: $i] :
( ( ( subset @ SV181 @ SV174 )
= $false )
| ( ( in @ SV174 @ ( sK3_SY291 @ SV23 ) )
= $false )
| ( ( in @ SV181 @ ( sK3_SY291 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1931]) ).
thf(1990,plain,
! [SV78: $i,SV175: $i,SV26: $i,SV197: $i] :
( ( ( ~ ( in @ SV197 @ SV26 ) )
= $true )
| ( ( in @ SV175 @ SV197 )
= $true )
| ( ( in @ SV175 @ SV78 )
= $false )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $false )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1932]) ).
thf(1991,plain,
! [SV26: $i,SV175: $i,SV78: $i] :
( ( ( ~ ( in @ ( sK56_SY639 @ SV78 @ SV175 @ SV26 ) @ SV26 ) )
= $false )
| ( ( in @ SV175 @ SV78 )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $false )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1933]) ).
thf(1992,plain,
! [SV26: $i,SV78: $i,SV175: $i] :
( ( ( in @ SV175 @ ( sK56_SY639 @ SV78 @ SV175 @ SV26 ) )
= $false )
| ( ( in @ SV175 @ SV78 )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $false )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1933]) ).
thf(1993,plain,
! [SV78: $i,SV26: $i] :
( ( ( ~ ! [SY641: $i] :
( ~ ( in @ SY641 @ SV26 )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SY641 ) ) )
= $false )
| ( ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV78 )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1934]) ).
thf(1994,plain,
! [SV78: $i,SV26: $i] :
( ( ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV78 )
= $false )
| ( ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV78 )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1934]) ).
thf(1995,plain,
! [SV26: $i,SV78: $i] :
( ( ( in @ ( sK54_SY640 @ SV78 @ SV26 ) @ SV26 )
= $true )
| ( ( ~ ( ~ ! [SY641: $i] :
( ~ ( in @ SY641 @ SV26 )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SY641 ) )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV78 ) ) )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1935]) ).
thf(1996,plain,
! [SV78: $i,SV26: $i] :
( ( ( ~ ! [SY641: $i] :
( ~ ( in @ SY641 @ SV26 )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SY641 ) )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV78 ) )
= $false )
| ( ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ ( sK54_SY640 @ SV78 @ SV26 ) )
= $false )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1936]) ).
thf(1997,plain,
! [SV161: $i,SV30: $i,SV131: $i,SV136: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK50_SY619 @ SV136 @ SV131 @ SV30 @ SV161 ) @ SV161 ) @ SV30 ) )
= $false )
| ( ( in @ SV161 @ SV136 )
= $false )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1937]) ).
thf(1998,plain,
! [SV161: $i,SV30: $i,SV131: $i,SV136: $i] :
( ( ( ~ ( in @ ( sK50_SY619 @ SV136 @ SV131 @ SV30 @ SV161 ) @ SV131 ) )
= $false )
| ( ( in @ SV161 @ SV136 )
= $false )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1937]) ).
thf(1999,plain,
! [SV136: $i,SV131: $i,SV30: $i,SV161: $i,SV195: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV195 @ SV161 ) @ SV30 ) )
= $true )
| ( ( ~ ( in @ SV195 @ SV131 ) )
= $true )
| ( ( in @ SV161 @ SV136 )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1938]) ).
thf(2000,plain,
! [SV131: $i,SV30: $i,SV136: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK59_SY622 @ SV136 @ SV30 @ SV131 ) @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ ( sK59_SY622 @ SV136 @ SV30 @ SV131 ) @ SV131 ) ) )
= $false )
| ( ( in @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) @ SV136 )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1939]) ).
thf(2001,plain,
! [SV136: $i,SV30: $i,SV131: $i,SV191: $i] :
( ( ( in @ ( ordered_pair @ SV191 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
= $false )
| ( ( ~ ( in @ SV191 @ SV131 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY622: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY622 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ SY622 @ SV131 ) )
| ( in @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) @ SV136 ) ) )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1940]) ).
thf(2002,plain,
! [SV87: $i,SV137: $i,SV171: $i,SV39: $i,SV176: $i] :
( ( ( ~ ( in @ SV176 @ SV39 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV137 )
= $false )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1941]) ).
thf(2003,plain,
! [SV39: $i,SV137: $i,SV87: $i,SV176: $i,SV171: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV87 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV137 )
= $false )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1941]) ).
thf(2004,plain,
! [SV137: $i,SV87: $i,SV171: $i,SV39: $i,SV176: $i] :
( ( ( ~ ( in @ SV176 @ SV39 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV87 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV137 )
= $true )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1942]) ).
thf(2005,plain,
! [SV87: $i,SV39: $i,SV137: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
| ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV137 )
= $true )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1943]) ).
thf(2006,plain,
! [SV137: $i,SV39: $i,SV87: $i] :
( ( ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV137 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV137 )
= $true )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1943]) ).
thf(2007,plain,
! [SV87: $i,SV39: $i,SV137: $i] :
( ( ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
| ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 ) )
| ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV137 ) ) )
= $true )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1944]) ).
thf(2008,plain,
! [SV89: $i,SV42: $i] :
( ( ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ ( sK51_SY596 @ SV89 @ SV42 ) ) )
= $false )
| ( ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1946]) ).
thf(2009,plain,
! [SV42: $i,SV89: $i] :
( ( ( ~ ( in @ ( sK51_SY596 @ SV89 @ SV42 ) @ SV42 ) )
= $false )
| ( ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1946]) ).
thf(2010,plain,
! [SV177: $i,SV89: $i,SV42: $i] :
( ( ( ~ ~ ! [SY596: $i] :
~ ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SY596 )
| ~ ( in @ SY596 @ SV42 ) ) )
= $false )
| ( ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV177 )
= $false )
| ( ( in @ SV177 @ SV42 )
= $false )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1947]) ).
thf(2011,plain,
! [SV177: $i,SV89: $i,SV42: $i] :
( ( ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV89 )
= $false )
| ( ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV177 )
= $false )
| ( ( in @ SV177 @ SV42 )
= $false )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1947]) ).
thf(2012,plain,
! [SV46: $i,SV178: $i,SV183: $i] :
( ( ( subset @ SV183 @ SV178 )
= $false )
| ( ( in @ SV178 @ ( sK4_SY357 @ SV46 ) )
= $false )
| ( ( in @ SV183 @ ( sK4_SY357 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1948]) ).
thf(2013,plain,
! [SV46: $i,SV162: $i] :
( ( ( in @ ( sK46_SY623 @ SV162 @ SV46 ) @ ( sK4_SY357 @ SV46 ) )
= $true )
| ( ( in @ SV162 @ ( sK4_SY357 @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1949]) ).
thf(2014,plain,
! [SV46: $i,SV162: $i] :
( ( ( ! [SY656: $i] :
( ~ ( subset @ SY656 @ SV162 )
| ( in @ SY656 @ ( sK46_SY623 @ SV162 @ SV46 ) ) ) )
= $true )
| ( ( in @ SV162 @ ( sK4_SY357 @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1950]) ).
thf(2015,plain,
! [SV132: $i,SV47: $i] :
( ( ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ ( sK57_SY614 @ SV132 @ SV47 ) ) @ SV47 )
= $true )
| ( ( in @ ( sK22_SY553 @ SV47 @ SV132 ) @ SV132 )
= $true )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1951]) ).
thf(2016,plain,
! [SV187: $i,SV132: $i,SV47: $i] :
( ( ( ! [SY614: $i] :
~ ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ SY614 ) @ SV47 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ SV187 ) @ SV47 )
= $false )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1952]) ).
thf(2017,plain,
! [SV49: $i,SV133: $i] :
( ( ( in @ ( ordered_pair @ ( sK36_SY631 @ SV133 @ SV49 ) @ ( sK30_SY558 @ SV49 @ SV133 ) ) @ SV49 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK30_SY558 @ SV49 @ SV133 ) @ ( sK36_SY631 @ SV133 @ SV49 ) ) @ SV133 )
= $true )
| ( ( SV133
= ( relation_inverse @ SV49 ) )
= $true )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1953]) ).
thf(2018,plain,
! [SV119: $i,SV58: $i,SV102: $i] :
( ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 )
= $false )
| ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV119 )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1957]) ).
thf(2019,plain,
! [SV119: $i,SV58: $i,SV102: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
| ~ ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 ) ) )
= $true )
| ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
= $false )
| ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1958]) ).
thf(2020,plain,
! [SV121: $i,SV60: $i,SV104: $i] :
( ( ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
| ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 ) )
= $false )
| ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
= $false )
| ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 )
= $false )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1962]) ).
thf(2021,plain,
! [SV139: $i,SV124: $i,SV184: $i,SV10: $i,SV179: $i] :
( ( ( ! [SY650: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV179 @ SY650 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY650 @ SV184 ) @ SV124 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV179 @ SV184 ) @ SV139 )
= $false )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $false )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1964]) ).
thf(2022,plain,
! [SV139: $i,SV124: $i,SV184: $i,SV10: $i,SV179: $i] :
( ( ( ! [SY651: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV179 @ SY651 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY651 @ SV184 ) @ SV124 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV179 @ SV184 ) @ SV139 )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $false )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1965]) ).
thf(2023,plain,
! [SV139: $i,SV10: $i,SV124: $i] :
( ( ( ~ ~ ! [SY653: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SY653 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY653 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) )
| ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV139 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV139 )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1966]) ).
thf(2024,plain,
! [SV198: $i,SV139: $i,SV10: $i,SV124: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SV198 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SV198 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY653: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SY653 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY653 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) )
| ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV139 ) ) )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1967]) ).
thf(2025,plain,
! [SV11: $i,SV69: $i,SV148: $i,SV107: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK44_SY597 @ SV107 @ SV148 @ SV69 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK52_SY654 @ SV11 @ SV69 @ SV148 @ SV107 ) @ SV69 ) ) )
= $false )
| ( ( in @ SV148 @ SV107 )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1968]) ).
thf(2026,plain,
! [SV11: $i,SV69: $i,SV107: $i,SV148: $i] :
( ( ( SV148
!= ( ordered_pair @ ( sK44_SY597 @ SV107 @ SV148 @ SV69 @ SV11 ) @ ( sK52_SY654 @ SV11 @ SV69 @ SV148 @ SV107 ) ) )
= $false )
| ( ( in @ SV148 @ SV107 )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1968]) ).
thf(2027,plain,
! [SV107: $i,SV148: $i,SV69: $i,SV196: $i,SV11: $i,SV185: $i] :
( ( ( ~ ~ ( ~ ( in @ SV185 @ SV11 )
| ~ ( in @ SV196 @ SV69 ) ) )
= $true )
| ( ( SV148
!= ( ordered_pair @ SV185 @ SV196 ) )
= $true )
| ( ( in @ SV148 @ SV107 )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1969]) ).
thf(2028,plain,
! [SV11: $i,SV69: $i,SV107: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK53_SY603 @ SV107 @ SV69 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK60_SY657 @ SV11 @ SV69 @ SV107 ) @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ ( sK53_SY603 @ SV107 @ SV69 @ SV11 ) @ ( sK60_SY657 @ SV11 @ SV69 @ SV107 ) ) ) ) )
= $false )
| ( ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1970]) ).
thf(2029,plain,
! [SV107: $i,SV69: $i,SV193: $i,SV11: $i,SV180: $i] :
( ( ( ~ ( ~ ( in @ SV180 @ SV11 )
| ~ ( in @ SV193 @ SV69 ) ) )
= $false )
| ( ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SV180 @ SV193 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY603: $i] :
~ ~ ! [SY604: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY603 @ SV11 )
| ~ ( in @ SY604 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SY603 @ SY604 ) ) )
| ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 ) ) )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1971]) ).
thf(2030,plain,
! [SV70: $i,SV12: $i] :
( ( ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK20_SY424 @ SV12 @ SV70 ) @ ( sK23_SY606 @ SV70 @ SV12 ) ) @ SV70 )
= $true )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1972]) ).
thf(2031,plain,
! [SV70: $i,SV12: $i] :
( ( ( ( sK20_SY424 @ SV12 @ SV70 )
= ( sK23_SY606 @ SV70 @ SV12 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK20_SY424 @ SV12 @ SV70 ) @ ( sK23_SY606 @ SV70 @ SV12 ) ) @ SV70 )
= $true )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1973]) ).
thf(2032,plain,
! [SV70: $i,SV12: $i] :
( ( ( ~ ( ~ ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
| ( ( sK20_SY424 @ SV12 @ SV70 )
!= ( sK23_SY606 @ SV70 @ SV12 ) ) ) )
= $true )
| ( ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
= $false )
| ( ( ( sK20_SY424 @ SV12 @ SV70 )
= ( sK23_SY606 @ SV70 @ SV12 ) )
= $false )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1974]) ).
thf(2033,plain,
! [SV14: $i,SV125: $i,SV134: $i,SV158: $i] :
( ( ( in @ ( ordered_pair @ SV158 @ ( sK49_SY615 @ SV134 @ SV125 @ SV14 @ SV158 ) ) @ SV14 )
= $true )
| ( ( in @ SV158 @ SV134 )
= $false )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1976]) ).
thf(2034,plain,
! [SV158: $i,SV14: $i,SV125: $i,SV134: $i] :
( ( ( in @ ( sK49_SY615 @ SV134 @ SV125 @ SV14 @ SV158 ) @ SV125 )
= $true )
| ( ( in @ SV158 @ SV134 )
= $false )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1977]) ).
thf(2035,plain,
! [SV134: $i,SV125: $i,SV14: $i,SV194: $i,SV158: $i] :
( ( ( in @ ( ordered_pair @ SV158 @ SV194 ) @ SV14 )
= $false )
| ( ( ~ ( in @ SV194 @ SV125 ) )
= $true )
| ( ( in @ SV158 @ SV134 )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1978]) ).
thf(2036,plain,
! [SV134: $i,SV14: $i,SV125: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ ( sK58_SY618 @ SV134 @ SV14 @ SV125 ) ) @ SV14 )
| ~ ( in @ ( sK58_SY618 @ SV134 @ SV14 @ SV125 ) @ SV125 ) ) )
= $true )
| ( ( in @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV134 )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1979]) ).
thf(2037,plain,
! [SV134: $i,SV14: $i,SV125: $i,SV189: $i] :
( ( ( in @ SV189 @ SV125 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV189 ) @ SV14 )
= $false )
| ( ( ~ ( ~ ~ ! [SY618: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SY618 ) @ SV14 )
| ~ ( in @ SY618 @ SV125 ) )
| ( in @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV134 ) ) )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1980]) ).
thf(2038,plain,
! [SV15: $i,SV126: $i,SV186: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK61_SY610 @ SV186 @ SV126 @ SV15 ) @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV186 @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 )
= $false )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1982]) ).
thf(2039,plain,
! [SV20: $i,SV135: $i,SV173: $i,SV128: $i,SV169: $i] :
( ( ( in @ SV169 @ SV128 )
= $true )
| ( ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV135 )
= $false )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1983]) ).
thf(2040,plain,
! [SV128: $i,SV135: $i,SV20: $i,SV173: $i,SV169: $i] :
( ( ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV20 )
= $true )
| ( ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV135 )
= $false )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1984]) ).
thf(2041,plain,
! [SV135: $i,SV20: $i,SV173: $i,SV128: $i,SV169: $i] :
( ( ( in @ SV169 @ SV128 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV20 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV135 )
= $true )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1985]) ).
thf(2042,plain,
! [SV135: $i,SV128: $i,SV20: $i] :
( ( ( ~ ( ~ ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
| ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV135 )
= $true )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1986]) ).
thf(2043,plain,
! [SV135: $i,SV128: $i,SV20: $i] :
( ( ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 )
= $false )
| ( ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
| ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 ) )
| ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV135 ) ) )
= $true )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1988]) ).
thf(2044,plain,
! [SV78: $i,SV175: $i,SV26: $i,SV197: $i] :
( ( ( in @ SV197 @ SV26 )
= $false )
| ( ( in @ SV175 @ SV197 )
= $true )
| ( ( in @ SV175 @ SV78 )
= $false )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $false )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1990]) ).
thf(2045,plain,
! [SV26: $i,SV175: $i,SV78: $i] :
( ( ( in @ ( sK56_SY639 @ SV78 @ SV175 @ SV26 ) @ SV26 )
= $true )
| ( ( in @ SV175 @ SV78 )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $false )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1991]) ).
thf(2046,plain,
! [SV78: $i,SV26: $i] :
( ( ( ! [SY641: $i] :
( ~ ( in @ SY641 @ SV26 )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SY641 ) ) )
= $true )
| ( ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV78 )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1993]) ).
thf(2047,plain,
! [SV78: $i,SV26: $i] :
( ( ( ~ ! [SY641: $i] :
( ~ ( in @ SY641 @ SV26 )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SY641 ) )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV78 ) )
= $false )
| ( ( in @ ( sK54_SY640 @ SV78 @ SV26 ) @ SV26 )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1995]) ).
thf(2048,plain,
! [SV78: $i,SV26: $i] :
( ( ( ~ ! [SY641: $i] :
( ~ ( in @ SY641 @ SV26 )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SY641 ) ) )
= $false )
| ( ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ ( sK54_SY640 @ SV78 @ SV26 ) )
= $false )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1996]) ).
thf(2049,plain,
! [SV78: $i,SV26: $i] :
( ( ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV78 )
= $false )
| ( ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ ( sK54_SY640 @ SV78 @ SV26 ) )
= $false )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1996]) ).
thf(2050,plain,
! [SV161: $i,SV30: $i,SV131: $i,SV136: $i] :
( ( ( in @ ( ordered_pair @ ( sK50_SY619 @ SV136 @ SV131 @ SV30 @ SV161 ) @ SV161 ) @ SV30 )
= $true )
| ( ( in @ SV161 @ SV136 )
= $false )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1997]) ).
thf(2051,plain,
! [SV161: $i,SV30: $i,SV131: $i,SV136: $i] :
( ( ( in @ ( sK50_SY619 @ SV136 @ SV131 @ SV30 @ SV161 ) @ SV131 )
= $true )
| ( ( in @ SV161 @ SV136 )
= $false )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1998]) ).
thf(2052,plain,
! [SV136: $i,SV131: $i,SV30: $i,SV161: $i,SV195: $i] :
( ( ( in @ ( ordered_pair @ SV195 @ SV161 ) @ SV30 )
= $false )
| ( ( ~ ( in @ SV195 @ SV131 ) )
= $true )
| ( ( in @ SV161 @ SV136 )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1999]) ).
thf(2053,plain,
! [SV131: $i,SV30: $i,SV136: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK59_SY622 @ SV136 @ SV30 @ SV131 ) @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ ( sK59_SY622 @ SV136 @ SV30 @ SV131 ) @ SV131 ) ) )
= $true )
| ( ( in @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) @ SV136 )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2000]) ).
thf(2054,plain,
! [SV136: $i,SV30: $i,SV131: $i,SV191: $i] :
( ( ( in @ SV191 @ SV131 )
= $false )
| ( ( in @ ( ordered_pair @ SV191 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
= $false )
| ( ( ~ ( ~ ~ ! [SY622: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY622 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ SY622 @ SV131 ) )
| ( in @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) @ SV136 ) ) )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2001]) ).
thf(2055,plain,
! [SV87: $i,SV137: $i,SV171: $i,SV39: $i,SV176: $i] :
( ( ( in @ SV176 @ SV39 )
= $true )
| ( ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV137 )
= $false )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2002]) ).
thf(2056,plain,
! [SV39: $i,SV137: $i,SV87: $i,SV176: $i,SV171: $i] :
( ( ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV87 )
= $true )
| ( ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV137 )
= $false )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2003]) ).
thf(2057,plain,
! [SV137: $i,SV87: $i,SV171: $i,SV39: $i,SV176: $i] :
( ( ( in @ SV176 @ SV39 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV87 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV137 )
= $true )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2004]) ).
thf(2058,plain,
! [SV87: $i,SV39: $i,SV137: $i] :
( ( ( ~ ( ~ ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
| ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV137 )
= $true )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2005]) ).
thf(2059,plain,
! [SV137: $i,SV39: $i,SV87: $i] :
( ( ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 )
= $false )
| ( ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
| ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 ) )
| ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV137 ) ) )
= $true )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2007]) ).
thf(2060,plain,
! [SV89: $i,SV42: $i] :
( ( ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ ( sK51_SY596 @ SV89 @ SV42 ) )
= $true )
| ( ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2008]) ).
thf(2061,plain,
! [SV42: $i,SV89: $i] :
( ( ( in @ ( sK51_SY596 @ SV89 @ SV42 ) @ SV42 )
= $true )
| ( ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2009]) ).
thf(2062,plain,
! [SV177: $i,SV89: $i,SV42: $i] :
( ( ( ~ ! [SY596: $i] :
~ ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SY596 )
| ~ ( in @ SY596 @ SV42 ) ) )
= $true )
| ( ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV177 )
= $false )
| ( ( in @ SV177 @ SV42 )
= $false )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2010]) ).
thf(2063,plain,
! [SV46: $i,SV162: $i,SV199: $i] :
( ( ( ~ ( subset @ SV199 @ SV162 )
| ( in @ SV199 @ ( sK46_SY623 @ SV162 @ SV46 ) ) )
= $true )
| ( ( in @ SV162 @ ( sK4_SY357 @ SV46 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2014]) ).
thf(2064,plain,
! [SV187: $i,SV132: $i,SV47: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ ( sK62_SY614 @ SV187 @ SV132 @ SV47 ) ) @ SV47 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ SV187 ) @ SV47 )
= $false )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2016]) ).
thf(2065,plain,
! [SV119: $i,SV58: $i,SV102: $i] :
( ( ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
| ~ ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 ) )
= $false )
| ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
= $false )
| ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2019]) ).
thf(2066,plain,
! [SV121: $i,SV60: $i,SV104: $i] :
( ( ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 ) )
= $false )
| ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
= $false )
| ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 )
= $false )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2020]) ).
thf(2067,plain,
! [SV121: $i,SV60: $i,SV104: $i] :
( ( ( ~ ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 ) )
= $false )
| ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
= $false )
| ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 )
= $false )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2020]) ).
thf(2068,plain,
! [SV10: $i,SV184: $i,SV124: $i,SV139: $i,SV179: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ SV179 @ ( sK63_SY650 @ SV139 @ SV124 @ SV184 @ SV10 @ SV179 ) ) @ SV10 )
| ~ ( in @ ( ordered_pair @ ( sK63_SY650 @ SV139 @ SV124 @ SV184 @ SV10 @ SV179 ) @ SV184 ) @ SV124 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV179 @ SV184 ) @ SV139 )
= $false )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $false )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2021]) ).
thf(2069,plain,
! [SV139: $i,SV124: $i,SV184: $i,SV10: $i,SV200: $i,SV179: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ SV179 @ SV200 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SV200 @ SV184 ) @ SV124 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV179 @ SV184 ) @ SV139 )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $false )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2022]) ).
thf(2070,plain,
! [SV139: $i,SV10: $i,SV124: $i] :
( ( ( ~ ~ ! [SY653: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SY653 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY653 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV139 )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2023]) ).
thf(2071,plain,
! [SV139: $i,SV10: $i,SV124: $i] :
( ( ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV139 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV139 )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2023]) ).
thf(2072,plain,
! [SV198: $i,SV139: $i,SV10: $i,SV124: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SV198 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SV198 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY653: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SY653 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY653 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) )
| ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV139 ) ) )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2024]) ).
thf(2073,plain,
! [SV11: $i,SV69: $i,SV148: $i,SV107: $i] :
( ( ( ~ ( ~ ( in @ ( sK44_SY597 @ SV107 @ SV148 @ SV69 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK52_SY654 @ SV11 @ SV69 @ SV148 @ SV107 ) @ SV69 ) ) )
= $true )
| ( ( in @ SV148 @ SV107 )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2025]) ).
thf(2074,plain,
! [SV11: $i,SV69: $i,SV107: $i,SV148: $i] :
( ( ( SV148
= ( ordered_pair @ ( sK44_SY597 @ SV107 @ SV148 @ SV69 @ SV11 ) @ ( sK52_SY654 @ SV11 @ SV69 @ SV148 @ SV107 ) ) )
= $true )
| ( ( in @ SV148 @ SV107 )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2026]) ).
thf(2075,plain,
! [SV107: $i,SV148: $i,SV69: $i,SV196: $i,SV11: $i,SV185: $i] :
( ( ( ~ ( ~ ( in @ SV185 @ SV11 )
| ~ ( in @ SV196 @ SV69 ) ) )
= $false )
| ( ( SV148
!= ( ordered_pair @ SV185 @ SV196 ) )
= $true )
| ( ( in @ SV148 @ SV107 )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2027]) ).
thf(2076,plain,
! [SV11: $i,SV69: $i,SV107: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK53_SY603 @ SV107 @ SV69 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK60_SY657 @ SV11 @ SV69 @ SV107 ) @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ ( sK53_SY603 @ SV107 @ SV69 @ SV11 ) @ ( sK60_SY657 @ SV11 @ SV69 @ SV107 ) ) ) ) )
= $true )
| ( ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2028]) ).
thf(2077,plain,
! [SV107: $i,SV69: $i,SV193: $i,SV11: $i,SV180: $i] :
( ( ( ~ ( in @ SV180 @ SV11 )
| ~ ( in @ SV193 @ SV69 ) )
= $true )
| ( ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SV180 @ SV193 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY603: $i] :
~ ~ ! [SY604: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY603 @ SV11 )
| ~ ( in @ SY604 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SY603 @ SY604 ) ) )
| ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 ) ) )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2029]) ).
thf(2078,plain,
! [SV70: $i,SV12: $i] :
( ( ( ~ ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
| ( ( sK20_SY424 @ SV12 @ SV70 )
!= ( sK23_SY606 @ SV70 @ SV12 ) ) )
= $false )
| ( ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
= $false )
| ( ( ( sK20_SY424 @ SV12 @ SV70 )
= ( sK23_SY606 @ SV70 @ SV12 ) )
= $false )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2032]) ).
thf(2079,plain,
! [SV134: $i,SV14: $i,SV158: $i,SV125: $i,SV194: $i] :
( ( ( in @ SV194 @ SV125 )
= $false )
| ( ( in @ ( ordered_pair @ SV158 @ SV194 ) @ SV14 )
= $false )
| ( ( in @ SV158 @ SV134 )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2035]) ).
thf(2080,plain,
! [SV134: $i,SV14: $i,SV125: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ ( sK58_SY618 @ SV134 @ SV14 @ SV125 ) ) @ SV14 )
| ~ ( in @ ( sK58_SY618 @ SV134 @ SV14 @ SV125 ) @ SV125 ) )
= $false )
| ( ( in @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV134 )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2036]) ).
thf(2081,plain,
! [SV189: $i,SV134: $i,SV14: $i,SV125: $i] :
( ( ( ~ ~ ! [SY618: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SY618 ) @ SV14 )
| ~ ( in @ SY618 @ SV125 ) )
| ( in @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV134 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV189 ) @ SV14 )
= $false )
| ( ( in @ SV189 @ SV125 )
= $false )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2037]) ).
thf(2082,plain,
! [SV15: $i,SV126: $i,SV186: $i] :
( ( ( in @ ( ordered_pair @ ( sK61_SY610 @ SV186 @ SV126 @ SV15 ) @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 )
= $true )
| ( ( in @ ( ordered_pair @ SV186 @ ( sK21_SY531 @ SV15 @ SV126 ) ) @ SV15 )
= $false )
| ( ( SV126
= ( relation_rng @ SV15 ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2038]) ).
thf(2083,plain,
! [SV135: $i,SV128: $i,SV20: $i,SV173: $i,SV169: $i] :
( ( ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV20 )
= $false )
| ( ( in @ SV169 @ SV128 )
= $false )
| ( ( in @ ( ordered_pair @ SV169 @ SV173 ) @ SV135 )
= $true )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2041]) ).
thf(2084,plain,
! [SV135: $i,SV128: $i,SV20: $i] :
( ( ( ~ ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
| ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV135 )
= $true )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2042]) ).
thf(2085,plain,
! [SV135: $i,SV128: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
| ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 ) )
| ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV135 ) )
= $false )
| ( ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 )
= $false )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2043]) ).
thf(2086,plain,
! [SV78: $i,SV26: $i,SV201: $i] :
( ( ( ~ ( in @ SV201 @ SV26 )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV201 ) )
= $true )
| ( ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV78 )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2046]) ).
thf(2087,plain,
! [SV78: $i,SV26: $i] :
( ( ( ~ ! [SY641: $i] :
( ~ ( in @ SY641 @ SV26 )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SY641 ) ) )
= $false )
| ( ( in @ ( sK54_SY640 @ SV78 @ SV26 ) @ SV26 )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2047]) ).
thf(2088,plain,
! [SV78: $i,SV26: $i] :
( ( ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV78 )
= $false )
| ( ( in @ ( sK54_SY640 @ SV78 @ SV26 ) @ SV26 )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2047]) ).
thf(2089,plain,
! [SV78: $i,SV26: $i] :
( ( ( ! [SY641: $i] :
( ~ ( in @ SY641 @ SV26 )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SY641 ) ) )
= $true )
| ( ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ ( sK54_SY640 @ SV78 @ SV26 ) )
= $false )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2048]) ).
thf(2090,plain,
! [SV136: $i,SV30: $i,SV161: $i,SV131: $i,SV195: $i] :
( ( ( in @ SV195 @ SV131 )
= $false )
| ( ( in @ ( ordered_pair @ SV195 @ SV161 ) @ SV30 )
= $false )
| ( ( in @ SV161 @ SV136 )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2052]) ).
thf(2091,plain,
! [SV131: $i,SV30: $i,SV136: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK59_SY622 @ SV136 @ SV30 @ SV131 ) @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ ( sK59_SY622 @ SV136 @ SV30 @ SV131 ) @ SV131 ) )
= $false )
| ( ( in @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) @ SV136 )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2053]) ).
thf(2092,plain,
! [SV191: $i,SV136: $i,SV30: $i,SV131: $i] :
( ( ( ~ ~ ! [SY622: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY622 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ SY622 @ SV131 ) )
| ( in @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) @ SV136 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV191 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
= $false )
| ( ( in @ SV191 @ SV131 )
= $false )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2054]) ).
thf(2093,plain,
! [SV137: $i,SV39: $i,SV87: $i,SV176: $i,SV171: $i] :
( ( ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV87 )
= $false )
| ( ( in @ SV176 @ SV39 )
= $false )
| ( ( in @ ( ordered_pair @ SV171 @ SV176 ) @ SV137 )
= $true )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2057]) ).
thf(2094,plain,
! [SV87: $i,SV39: $i,SV137: $i] :
( ( ( ~ ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
| ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV137 )
= $true )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2058]) ).
thf(2095,plain,
! [SV87: $i,SV39: $i,SV137: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
| ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 ) )
| ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV137 ) )
= $false )
| ( ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 )
= $false )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2059]) ).
thf(2096,plain,
! [SV177: $i,SV89: $i,SV42: $i] :
( ( ( ! [SY596: $i] :
~ ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SY596 )
| ~ ( in @ SY596 @ SV42 ) ) )
= $false )
| ( ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV177 )
= $false )
| ( ( in @ SV177 @ SV42 )
= $false )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2062]) ).
thf(2097,plain,
! [SV46: $i,SV162: $i,SV199: $i] :
( ( ( ~ ( subset @ SV199 @ SV162 ) )
= $true )
| ( ( in @ SV199 @ ( sK46_SY623 @ SV162 @ SV46 ) )
= $true )
| ( ( in @ SV162 @ ( sK4_SY357 @ SV46 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2063]) ).
thf(2098,plain,
! [SV187: $i,SV132: $i,SV47: $i] :
( ( ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ ( sK62_SY614 @ SV187 @ SV132 @ SV47 ) ) @ SV47 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK22_SY553 @ SV47 @ SV132 ) @ SV187 ) @ SV47 )
= $false )
| ( ( SV132
= ( relation_dom @ SV47 ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2064]) ).
thf(2099,plain,
! [SV119: $i,SV58: $i,SV102: $i] :
( ( ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 ) )
= $false )
| ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
= $false )
| ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2065]) ).
thf(2100,plain,
! [SV119: $i,SV58: $i,SV102: $i] :
( ( ( ~ ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 ) )
= $false )
| ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
= $false )
| ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2065]) ).
thf(2101,plain,
! [SV121: $i,SV60: $i,SV104: $i] :
( ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
= $true )
| ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
= $false )
| ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 )
= $false )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2066]) ).
thf(2102,plain,
! [SV121: $i,SV60: $i,SV104: $i] :
( ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 )
= $true )
| ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV60 )
= $false )
| ( ( in @ ( sK19_SY507 @ SV104 @ SV60 @ SV121 ) @ SV104 )
= $false )
| ( ( SV121
= ( set_intersection2 @ SV60 @ SV104 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2067]) ).
thf(2103,plain,
! [SV10: $i,SV184: $i,SV124: $i,SV139: $i,SV179: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV179 @ ( sK63_SY650 @ SV139 @ SV124 @ SV184 @ SV10 @ SV179 ) ) @ SV10 )
| ~ ( in @ ( ordered_pair @ ( sK63_SY650 @ SV139 @ SV124 @ SV184 @ SV10 @ SV179 ) @ SV184 ) @ SV124 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV179 @ SV184 ) @ SV139 )
= $false )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $false )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2068]) ).
thf(2104,plain,
! [SV139: $i,SV124: $i,SV184: $i,SV10: $i,SV200: $i,SV179: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV179 @ SV200 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SV200 @ SV184 ) @ SV124 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV179 @ SV184 ) @ SV139 )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $false )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2069]) ).
thf(2105,plain,
! [SV139: $i,SV10: $i,SV124: $i] :
( ( ( ~ ! [SY653: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SY653 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY653 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV139 )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2070]) ).
thf(2106,plain,
! [SV198: $i,SV139: $i,SV10: $i,SV124: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SV198 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SV198 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY653: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SY653 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY653 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) )
| ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV139 ) ) )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2072]) ).
thf(2107,plain,
! [SV11: $i,SV69: $i,SV148: $i,SV107: $i] :
( ( ( ~ ( in @ ( sK44_SY597 @ SV107 @ SV148 @ SV69 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK52_SY654 @ SV11 @ SV69 @ SV148 @ SV107 ) @ SV69 ) )
= $false )
| ( ( in @ SV148 @ SV107 )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2073]) ).
thf(2108,plain,
! [SV107: $i,SV148: $i,SV69: $i,SV196: $i,SV11: $i,SV185: $i] :
( ( ( ~ ( in @ SV185 @ SV11 )
| ~ ( in @ SV196 @ SV69 ) )
= $true )
| ( ( SV148
!= ( ordered_pair @ SV185 @ SV196 ) )
= $true )
| ( ( in @ SV148 @ SV107 )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2075]) ).
thf(2109,plain,
! [SV11: $i,SV69: $i,SV107: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK53_SY603 @ SV107 @ SV69 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK60_SY657 @ SV11 @ SV69 @ SV107 ) @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ ( sK53_SY603 @ SV107 @ SV69 @ SV11 ) @ ( sK60_SY657 @ SV11 @ SV69 @ SV107 ) ) ) )
= $false )
| ( ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2076]) ).
thf(2110,plain,
! [SV107: $i,SV69: $i,SV193: $i,SV11: $i,SV180: $i] :
( ( ( ~ ( in @ SV180 @ SV11 ) )
= $true )
| ( ( ~ ( in @ SV193 @ SV69 ) )
= $true )
| ( ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SV180 @ SV193 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY603: $i] :
~ ~ ! [SY604: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY603 @ SV11 )
| ~ ( in @ SY604 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SY603 @ SY604 ) ) )
| ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 ) ) )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2077]) ).
thf(2111,plain,
! [SV70: $i,SV12: $i] :
( ( ( ~ ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 ) )
= $false )
| ( ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
= $false )
| ( ( ( sK20_SY424 @ SV12 @ SV70 )
= ( sK23_SY606 @ SV70 @ SV12 ) )
= $false )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2078]) ).
thf(2112,plain,
! [SV70: $i,SV12: $i] :
( ( ( ( sK20_SY424 @ SV12 @ SV70 )
!= ( sK23_SY606 @ SV70 @ SV12 ) )
= $false )
| ( ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
= $false )
| ( ( ( sK20_SY424 @ SV12 @ SV70 )
= ( sK23_SY606 @ SV70 @ SV12 ) )
= $false )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2078]) ).
thf(2113,plain,
! [SV134: $i,SV14: $i,SV125: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ ( sK58_SY618 @ SV134 @ SV14 @ SV125 ) ) @ SV14 ) )
= $false )
| ( ( in @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV134 )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2080]) ).
thf(2114,plain,
! [SV125: $i,SV14: $i,SV134: $i] :
( ( ( ~ ( in @ ( sK58_SY618 @ SV134 @ SV14 @ SV125 ) @ SV125 ) )
= $false )
| ( ( in @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV134 )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2080]) ).
thf(2115,plain,
! [SV189: $i,SV134: $i,SV14: $i,SV125: $i] :
( ( ( ~ ~ ! [SY618: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SY618 ) @ SV14 )
| ~ ( in @ SY618 @ SV125 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV189 ) @ SV14 )
= $false )
| ( ( in @ SV189 @ SV125 )
= $false )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2081]) ).
thf(2116,plain,
! [SV189: $i,SV134: $i,SV14: $i,SV125: $i] :
( ( ( in @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV134 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV189 ) @ SV14 )
= $false )
| ( ( in @ SV189 @ SV125 )
= $false )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2081]) ).
thf(2117,plain,
! [SV135: $i,SV128: $i,SV20: $i] :
( ( ( ~ ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV135 )
= $true )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2084]) ).
thf(2118,plain,
! [SV135: $i,SV128: $i,SV20: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV135 )
= $true )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2084]) ).
thf(2119,plain,
! [SV135: $i,SV128: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
| ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 ) ) )
= $false )
| ( ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 )
= $false )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2085]) ).
thf(2120,plain,
! [SV135: $i,SV128: $i,SV20: $i] :
( ( ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV135 )
= $false )
| ( ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 )
= $false )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2085]) ).
thf(2121,plain,
! [SV78: $i,SV26: $i,SV201: $i] :
( ( ( ~ ( in @ SV201 @ SV26 ) )
= $true )
| ( ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV201 )
= $true )
| ( ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV78 )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2086]) ).
thf(2122,plain,
! [SV78: $i,SV26: $i] :
( ( ( ! [SY641: $i] :
( ~ ( in @ SY641 @ SV26 )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SY641 ) ) )
= $true )
| ( ( in @ ( sK54_SY640 @ SV78 @ SV26 ) @ SV26 )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2087]) ).
thf(2123,plain,
! [SV78: $i,SV26: $i,SV202: $i] :
( ( ( ~ ( in @ SV202 @ SV26 )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV202 ) )
= $true )
| ( ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ ( sK54_SY640 @ SV78 @ SV26 ) )
= $false )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2089]) ).
thf(2124,plain,
! [SV131: $i,SV30: $i,SV136: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK59_SY622 @ SV136 @ SV30 @ SV131 ) @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 ) )
= $false )
| ( ( in @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) @ SV136 )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2091]) ).
thf(2125,plain,
! [SV131: $i,SV30: $i,SV136: $i] :
( ( ( ~ ( in @ ( sK59_SY622 @ SV136 @ SV30 @ SV131 ) @ SV131 ) )
= $false )
| ( ( in @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) @ SV136 )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2091]) ).
thf(2126,plain,
! [SV191: $i,SV136: $i,SV30: $i,SV131: $i] :
( ( ( ~ ~ ! [SY622: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY622 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ SY622 @ SV131 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV191 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
= $false )
| ( ( in @ SV191 @ SV131 )
= $false )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2092]) ).
thf(2127,plain,
! [SV191: $i,SV136: $i,SV30: $i,SV131: $i] :
( ( ( in @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) @ SV136 )
= $false )
| ( ( in @ ( ordered_pair @ SV191 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
= $false )
| ( ( in @ SV191 @ SV131 )
= $false )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2092]) ).
thf(2128,plain,
! [SV87: $i,SV39: $i,SV137: $i] :
( ( ( ~ ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV137 )
= $true )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2094]) ).
thf(2129,plain,
! [SV137: $i,SV39: $i,SV87: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV137 )
= $true )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2094]) ).
thf(2130,plain,
! [SV87: $i,SV39: $i,SV137: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
| ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 ) ) )
= $false )
| ( ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 )
= $false )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2095]) ).
thf(2131,plain,
! [SV137: $i,SV39: $i,SV87: $i] :
( ( ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV137 )
= $false )
| ( ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 )
= $false )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2095]) ).
thf(2132,plain,
! [SV177: $i,SV89: $i,SV42: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ ( sK64_SY596 @ SV177 @ SV89 @ SV42 ) )
| ~ ( in @ ( sK64_SY596 @ SV177 @ SV89 @ SV42 ) @ SV42 ) ) )
= $false )
| ( ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV177 )
= $false )
| ( ( in @ SV177 @ SV42 )
= $false )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2096]) ).
thf(2133,plain,
! [SV46: $i,SV162: $i,SV199: $i] :
( ( ( subset @ SV199 @ SV162 )
= $false )
| ( ( in @ SV199 @ ( sK46_SY623 @ SV162 @ SV46 ) )
= $true )
| ( ( in @ SV162 @ ( sK4_SY357 @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2097]) ).
thf(2134,plain,
! [SV119: $i,SV58: $i,SV102: $i] :
( ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
= $true )
| ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
= $false )
| ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2099]) ).
thf(2135,plain,
! [SV119: $i,SV58: $i,SV102: $i] :
( ( ( ~ ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 ) )
= $true )
| ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
= $false )
| ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2100]) ).
thf(2136,plain,
! [SV10: $i,SV184: $i,SV124: $i,SV139: $i,SV179: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV179 @ ( sK63_SY650 @ SV139 @ SV124 @ SV184 @ SV10 @ SV179 ) ) @ SV10 )
| ~ ( in @ ( ordered_pair @ ( sK63_SY650 @ SV139 @ SV124 @ SV184 @ SV10 @ SV179 ) @ SV184 ) @ SV124 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV179 @ SV184 ) @ SV139 )
= $false )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $false )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2103]) ).
thf(2137,plain,
! [SV139: $i,SV124: $i,SV184: $i,SV10: $i,SV200: $i,SV179: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV179 @ SV200 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SV200 @ SV184 ) @ SV124 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV179 @ SV184 ) @ SV139 )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $false )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2104]) ).
thf(2138,plain,
! [SV139: $i,SV10: $i,SV124: $i] :
( ( ( ! [SY653: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SY653 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY653 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV139 )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2105]) ).
thf(2139,plain,
! [SV198: $i,SV139: $i,SV10: $i,SV124: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SV198 ) @ SV10 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV198 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY653: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SY653 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY653 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) )
| ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV139 ) ) )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2106]) ).
thf(2140,plain,
! [SV11: $i,SV69: $i,SV148: $i,SV107: $i] :
( ( ( ~ ( in @ ( sK44_SY597 @ SV107 @ SV148 @ SV69 @ SV11 ) @ SV11 ) )
= $false )
| ( ( in @ SV148 @ SV107 )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2107]) ).
thf(2141,plain,
! [SV107: $i,SV148: $i,SV69: $i,SV11: $i] :
( ( ( ~ ( in @ ( sK52_SY654 @ SV11 @ SV69 @ SV148 @ SV107 ) @ SV69 ) )
= $false )
| ( ( in @ SV148 @ SV107 )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2107]) ).
thf(2142,plain,
! [SV107: $i,SV148: $i,SV69: $i,SV196: $i,SV11: $i,SV185: $i] :
( ( ( ~ ( in @ SV185 @ SV11 ) )
= $true )
| ( ( ~ ( in @ SV196 @ SV69 ) )
= $true )
| ( ( SV148
!= ( ordered_pair @ SV185 @ SV196 ) )
= $true )
| ( ( in @ SV148 @ SV107 )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2108]) ).
thf(2143,plain,
! [SV11: $i,SV69: $i,SV107: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK53_SY603 @ SV107 @ SV69 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK60_SY657 @ SV11 @ SV69 @ SV107 ) @ SV69 ) ) )
= $false )
| ( ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2109]) ).
thf(2144,plain,
! [SV107: $i,SV11: $i,SV69: $i] :
( ( ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ ( sK53_SY603 @ SV107 @ SV69 @ SV11 ) @ ( sK60_SY657 @ SV11 @ SV69 @ SV107 ) ) )
= $false )
| ( ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2109]) ).
thf(2145,plain,
! [SV107: $i,SV69: $i,SV193: $i,SV11: $i,SV180: $i] :
( ( ( in @ SV180 @ SV11 )
= $false )
| ( ( ~ ( in @ SV193 @ SV69 ) )
= $true )
| ( ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SV180 @ SV193 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY603: $i] :
~ ~ ! [SY604: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY603 @ SV11 )
| ~ ( in @ SY604 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SY603 @ SY604 ) ) )
| ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 ) ) )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2110]) ).
thf(2146,plain,
! [SV70: $i,SV12: $i] :
( ( ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
= $true )
| ( ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
= $false )
| ( ( ( sK20_SY424 @ SV12 @ SV70 )
= ( sK23_SY606 @ SV70 @ SV12 ) )
= $false )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2111]) ).
thf(2147,plain,
! [SV70: $i,SV12: $i] :
( ( ( ( sK20_SY424 @ SV12 @ SV70 )
= ( sK23_SY606 @ SV70 @ SV12 ) )
= $true )
| ( ( in @ ( sK20_SY424 @ SV12 @ SV70 ) @ SV12 )
= $false )
| ( ( ( sK20_SY424 @ SV12 @ SV70 )
= ( sK23_SY606 @ SV70 @ SV12 ) )
= $false )
| ( ( SV70
= ( identity_relation @ SV12 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2112]) ).
thf(2148,plain,
! [SV134: $i,SV14: $i,SV125: $i] :
( ( ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ ( sK58_SY618 @ SV134 @ SV14 @ SV125 ) ) @ SV14 )
= $true )
| ( ( in @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV134 )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2113]) ).
thf(2149,plain,
! [SV125: $i,SV14: $i,SV134: $i] :
( ( ( in @ ( sK58_SY618 @ SV134 @ SV14 @ SV125 ) @ SV125 )
= $true )
| ( ( in @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV134 )
= $true )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2114]) ).
thf(2150,plain,
! [SV189: $i,SV134: $i,SV14: $i,SV125: $i] :
( ( ( ~ ! [SY618: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SY618 ) @ SV14 )
| ~ ( in @ SY618 @ SV125 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV189 ) @ SV14 )
= $false )
| ( ( in @ SV189 @ SV125 )
= $false )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2115]) ).
thf(2151,plain,
! [SV135: $i,SV128: $i,SV20: $i] :
( ( ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV135 )
= $true )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2117]) ).
thf(2152,plain,
! [SV135: $i,SV128: $i,SV20: $i] :
( ( ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV135 )
= $true )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2118]) ).
thf(2153,plain,
! [SV135: $i,SV128: $i,SV20: $i] :
( ( ( ~ ( ~ ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
| ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 ) ) )
= $true )
| ( ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 )
= $false )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2119]) ).
thf(2154,plain,
! [SV78: $i,SV26: $i,SV201: $i] :
( ( ( in @ SV201 @ SV26 )
= $false )
| ( ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV201 )
= $true )
| ( ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV78 )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2121]) ).
thf(2155,plain,
! [SV78: $i,SV26: $i,SV203: $i] :
( ( ( ~ ( in @ SV203 @ SV26 )
| ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV203 ) )
= $true )
| ( ( in @ ( sK54_SY640 @ SV78 @ SV26 ) @ SV26 )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2122]) ).
thf(2156,plain,
! [SV78: $i,SV26: $i,SV202: $i] :
( ( ( ~ ( in @ SV202 @ SV26 ) )
= $true )
| ( ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV202 )
= $true )
| ( ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ ( sK54_SY640 @ SV78 @ SV26 ) )
= $false )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2123]) ).
thf(2157,plain,
! [SV131: $i,SV30: $i,SV136: $i] :
( ( ( in @ ( ordered_pair @ ( sK59_SY622 @ SV136 @ SV30 @ SV131 ) @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
= $true )
| ( ( in @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) @ SV136 )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2124]) ).
thf(2158,plain,
! [SV131: $i,SV30: $i,SV136: $i] :
( ( ( in @ ( sK59_SY622 @ SV136 @ SV30 @ SV131 ) @ SV131 )
= $true )
| ( ( in @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) @ SV136 )
= $true )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2125]) ).
thf(2159,plain,
! [SV191: $i,SV136: $i,SV30: $i,SV131: $i] :
( ( ( ~ ! [SY622: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY622 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ SY622 @ SV131 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV191 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
= $false )
| ( ( in @ SV191 @ SV131 )
= $false )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2126]) ).
thf(2160,plain,
! [SV87: $i,SV39: $i,SV137: $i] :
( ( ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV137 )
= $true )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2128]) ).
thf(2161,plain,
! [SV137: $i,SV39: $i,SV87: $i] :
( ( ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV137 )
= $true )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2129]) ).
thf(2162,plain,
! [SV87: $i,SV39: $i,SV137: $i] :
( ( ( ~ ( ~ ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
| ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 ) ) )
= $true )
| ( ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 )
= $false )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2130]) ).
thf(2163,plain,
! [SV177: $i,SV89: $i,SV42: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ ( sK64_SY596 @ SV177 @ SV89 @ SV42 ) )
| ~ ( in @ ( sK64_SY596 @ SV177 @ SV89 @ SV42 ) @ SV42 ) ) )
= $true )
| ( ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV177 )
= $false )
| ( ( in @ SV177 @ SV42 )
= $false )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2132]) ).
thf(2164,plain,
! [SV119: $i,SV58: $i,SV102: $i] :
( ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 )
= $false )
| ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV58 )
= $false )
| ( ( in @ ( sK18_SY505 @ SV102 @ SV58 @ SV119 ) @ SV102 )
= $true )
| ( ( SV119
= ( set_difference @ SV58 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2135]) ).
thf(2165,plain,
! [SV10: $i,SV184: $i,SV124: $i,SV139: $i,SV179: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV179 @ ( sK63_SY650 @ SV139 @ SV124 @ SV184 @ SV10 @ SV179 ) ) @ SV10 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV179 @ SV184 ) @ SV139 )
= $false )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $false )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2136]) ).
thf(2166,plain,
! [SV179: $i,SV10: $i,SV184: $i,SV124: $i,SV139: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK63_SY650 @ SV139 @ SV124 @ SV184 @ SV10 @ SV179 ) @ SV184 ) @ SV124 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV179 @ SV184 ) @ SV139 )
= $false )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $false )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2136]) ).
thf(2167,plain,
! [SV139: $i,SV124: $i,SV184: $i,SV10: $i,SV200: $i,SV179: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV179 @ SV200 ) @ SV10 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV200 @ SV184 ) @ SV124 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV179 @ SV184 ) @ SV139 )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $false )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2137]) ).
thf(2168,plain,
! [SV139: $i,SV10: $i,SV124: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK65_SY653 @ SV139 @ SV10 @ SV124 ) ) @ SV10 )
| ~ ( in @ ( ordered_pair @ ( sK65_SY653 @ SV139 @ SV10 @ SV124 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV139 )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2138]) ).
thf(2169,plain,
! [SV198: $i,SV139: $i,SV10: $i,SV124: $i] :
( ( ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SV198 ) @ SV10 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV198 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY653: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SY653 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY653 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) )
| ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV139 ) ) )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2139]) ).
thf(2170,plain,
! [SV11: $i,SV69: $i,SV148: $i,SV107: $i] :
( ( ( in @ ( sK44_SY597 @ SV107 @ SV148 @ SV69 @ SV11 ) @ SV11 )
= $true )
| ( ( in @ SV148 @ SV107 )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2140]) ).
thf(2171,plain,
! [SV107: $i,SV148: $i,SV69: $i,SV11: $i] :
( ( ( in @ ( sK52_SY654 @ SV11 @ SV69 @ SV148 @ SV107 ) @ SV69 )
= $true )
| ( ( in @ SV148 @ SV107 )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2141]) ).
thf(2172,plain,
! [SV107: $i,SV148: $i,SV69: $i,SV196: $i,SV11: $i,SV185: $i] :
( ( ( in @ SV185 @ SV11 )
= $false )
| ( ( ~ ( in @ SV196 @ SV69 ) )
= $true )
| ( ( SV148
!= ( ordered_pair @ SV185 @ SV196 ) )
= $true )
| ( ( in @ SV148 @ SV107 )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2142]) ).
thf(2173,plain,
! [SV11: $i,SV69: $i,SV107: $i] :
( ( ( ~ ( ~ ( in @ ( sK53_SY603 @ SV107 @ SV69 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK60_SY657 @ SV11 @ SV69 @ SV107 ) @ SV69 ) ) )
= $true )
| ( ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2143]) ).
thf(2174,plain,
! [SV107: $i,SV11: $i,SV69: $i] :
( ( ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
= ( ordered_pair @ ( sK53_SY603 @ SV107 @ SV69 @ SV11 ) @ ( sK60_SY657 @ SV11 @ SV69 @ SV107 ) ) )
= $true )
| ( ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2144]) ).
thf(2175,plain,
! [SV107: $i,SV11: $i,SV180: $i,SV69: $i,SV193: $i] :
( ( ( in @ SV193 @ SV69 )
= $false )
| ( ( in @ SV180 @ SV11 )
= $false )
| ( ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SV180 @ SV193 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY603: $i] :
~ ~ ! [SY604: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY603 @ SV11 )
| ~ ( in @ SY604 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SY603 @ SY604 ) ) )
| ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 ) ) )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2145]) ).
thf(2176,plain,
! [SV189: $i,SV134: $i,SV14: $i,SV125: $i] :
( ( ( ! [SY618: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SY618 ) @ SV14 )
| ~ ( in @ SY618 @ SV125 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV189 ) @ SV14 )
= $false )
| ( ( in @ SV189 @ SV125 )
= $false )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2150]) ).
thf(2177,plain,
! [SV135: $i,SV128: $i,SV20: $i] :
( ( ( ~ ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
| ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 ) )
= $false )
| ( ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 )
= $false )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2153]) ).
thf(2178,plain,
! [SV78: $i,SV26: $i,SV203: $i] :
( ( ( ~ ( in @ SV203 @ SV26 ) )
= $true )
| ( ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV203 )
= $true )
| ( ( in @ ( sK54_SY640 @ SV78 @ SV26 ) @ SV26 )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2155]) ).
thf(2179,plain,
! [SV78: $i,SV26: $i,SV202: $i] :
( ( ( in @ SV202 @ SV26 )
= $false )
| ( ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV202 )
= $true )
| ( ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ ( sK54_SY640 @ SV78 @ SV26 ) )
= $false )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2156]) ).
thf(2180,plain,
! [SV191: $i,SV136: $i,SV30: $i,SV131: $i] :
( ( ( ! [SY622: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY622 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ SY622 @ SV131 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV191 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
= $false )
| ( ( in @ SV191 @ SV131 )
= $false )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2159]) ).
thf(2181,plain,
! [SV87: $i,SV39: $i,SV137: $i] :
( ( ( ~ ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
| ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 ) )
= $false )
| ( ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 )
= $false )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2162]) ).
thf(2182,plain,
! [SV177: $i,SV89: $i,SV42: $i] :
( ( ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ ( sK64_SY596 @ SV177 @ SV89 @ SV42 ) )
| ~ ( in @ ( sK64_SY596 @ SV177 @ SV89 @ SV42 ) @ SV42 ) )
= $false )
| ( ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV177 )
= $false )
| ( ( in @ SV177 @ SV42 )
= $false )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2163]) ).
thf(2183,plain,
! [SV10: $i,SV184: $i,SV124: $i,SV139: $i,SV179: $i] :
( ( ( in @ ( ordered_pair @ SV179 @ ( sK63_SY650 @ SV139 @ SV124 @ SV184 @ SV10 @ SV179 ) ) @ SV10 )
= $true )
| ( ( in @ ( ordered_pair @ SV179 @ SV184 ) @ SV139 )
= $false )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $false )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2165]) ).
thf(2184,plain,
! [SV179: $i,SV10: $i,SV184: $i,SV124: $i,SV139: $i] :
( ( ( in @ ( ordered_pair @ ( sK63_SY650 @ SV139 @ SV124 @ SV184 @ SV10 @ SV179 ) @ SV184 ) @ SV124 )
= $true )
| ( ( in @ ( ordered_pair @ SV179 @ SV184 ) @ SV139 )
= $false )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $false )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2166]) ).
thf(2185,plain,
! [SV139: $i,SV124: $i,SV184: $i,SV10: $i,SV200: $i,SV179: $i] :
( ( ( in @ ( ordered_pair @ SV179 @ SV200 ) @ SV10 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV200 @ SV184 ) @ SV124 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV179 @ SV184 ) @ SV139 )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $false )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2167]) ).
thf(2186,plain,
! [SV139: $i,SV10: $i,SV124: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK65_SY653 @ SV139 @ SV10 @ SV124 ) ) @ SV10 )
| ~ ( in @ ( ordered_pair @ ( sK65_SY653 @ SV139 @ SV10 @ SV124 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV139 )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2168]) ).
thf(2187,plain,
! [SV124: $i,SV10: $i,SV139: $i,SV198: $i] :
( ( ( in @ ( ordered_pair @ SV198 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SV198 ) @ SV10 )
= $false )
| ( ( ~ ( ~ ~ ! [SY653: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SY653 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY653 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) )
| ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV139 ) ) )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2169]) ).
thf(2188,plain,
! [SV107: $i,SV148: $i,SV11: $i,SV185: $i,SV69: $i,SV196: $i] :
( ( ( in @ SV196 @ SV69 )
= $false )
| ( ( in @ SV185 @ SV11 )
= $false )
| ( ( SV148
!= ( ordered_pair @ SV185 @ SV196 ) )
= $true )
| ( ( in @ SV148 @ SV107 )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2172]) ).
thf(2189,plain,
! [SV11: $i,SV69: $i,SV107: $i] :
( ( ( ~ ( in @ ( sK53_SY603 @ SV107 @ SV69 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK60_SY657 @ SV11 @ SV69 @ SV107 ) @ SV69 ) )
= $false )
| ( ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2173]) ).
thf(2190,plain,
! [SV193: $i,SV180: $i,SV107: $i,SV11: $i,SV69: $i] :
( ( ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
= ( ordered_pair @ SV180 @ SV193 ) )
= $false )
| ( ( in @ SV180 @ SV11 )
= $false )
| ( ( in @ SV193 @ SV69 )
= $false )
| ( ( ~ ( ~ ~ ! [SY603: $i] :
~ ~ ! [SY604: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY603 @ SV11 )
| ~ ( in @ SY604 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SY603 @ SY604 ) ) )
| ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 ) ) )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2175]) ).
thf(2191,plain,
! [SV189: $i,SV134: $i,SV14: $i,SV125: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ ( sK66_SY618 @ SV189 @ SV134 @ SV14 @ SV125 ) ) @ SV14 )
| ~ ( in @ ( sK66_SY618 @ SV189 @ SV134 @ SV14 @ SV125 ) @ SV125 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV189 ) @ SV14 )
= $false )
| ( ( in @ SV189 @ SV125 )
= $false )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2176]) ).
thf(2192,plain,
! [SV135: $i,SV128: $i,SV20: $i] :
( ( ( ~ ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 ) )
= $false )
| ( ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 )
= $false )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2177]) ).
thf(2193,plain,
! [SV135: $i,SV128: $i,SV20: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 ) )
= $false )
| ( ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 )
= $false )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2177]) ).
thf(2194,plain,
! [SV78: $i,SV26: $i,SV203: $i] :
( ( ( in @ SV203 @ SV26 )
= $false )
| ( ( in @ ( sK38_SY437 @ SV26 @ SV78 ) @ SV203 )
= $true )
| ( ( in @ ( sK54_SY640 @ SV78 @ SV26 ) @ SV26 )
= $true )
| ( ( SV78
= ( set_meet @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2178]) ).
thf(2195,plain,
! [SV131: $i,SV30: $i,SV136: $i,SV191: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK67_SY622 @ SV191 @ SV136 @ SV30 @ SV131 ) @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ ( sK67_SY622 @ SV191 @ SV136 @ SV30 @ SV131 ) @ SV131 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV191 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
= $false )
| ( ( in @ SV191 @ SV131 )
= $false )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2180]) ).
thf(2196,plain,
! [SV87: $i,SV39: $i,SV137: $i] :
( ( ( ~ ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 ) )
= $false )
| ( ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 )
= $false )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2181]) ).
thf(2197,plain,
! [SV137: $i,SV39: $i,SV87: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 ) )
= $false )
| ( ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 )
= $false )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2181]) ).
thf(2198,plain,
! [SV177: $i,SV89: $i,SV42: $i] :
( ( ( ~ ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ ( sK64_SY596 @ SV177 @ SV89 @ SV42 ) ) )
= $false )
| ( ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV177 )
= $false )
| ( ( in @ SV177 @ SV42 )
= $false )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2182]) ).
thf(2199,plain,
! [SV42: $i,SV89: $i,SV177: $i] :
( ( ( ~ ( in @ ( sK64_SY596 @ SV177 @ SV89 @ SV42 ) @ SV42 ) )
= $false )
| ( ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV177 )
= $false )
| ( ( in @ SV177 @ SV42 )
= $false )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2182]) ).
thf(2200,plain,
! [SV139: $i,SV10: $i,SV179: $i,SV124: $i,SV184: $i,SV200: $i] :
( ( ( in @ ( ordered_pair @ SV200 @ SV184 ) @ SV124 )
= $false )
| ( ( in @ ( ordered_pair @ SV179 @ SV200 ) @ SV10 )
= $false )
| ( ( in @ ( ordered_pair @ SV179 @ SV184 ) @ SV139 )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $false )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2185]) ).
thf(2201,plain,
! [SV139: $i,SV10: $i,SV124: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK65_SY653 @ SV139 @ SV10 @ SV124 ) ) @ SV10 )
| ~ ( in @ ( ordered_pair @ ( sK65_SY653 @ SV139 @ SV10 @ SV124 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV139 )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2186]) ).
thf(2202,plain,
! [SV198: $i,SV139: $i,SV10: $i,SV124: $i] :
( ( ( ~ ~ ! [SY653: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SY653 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY653 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) )
| ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV139 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SV198 ) @ SV10 )
= $false )
| ( ( in @ ( ordered_pair @ SV198 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 )
= $false )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2187]) ).
thf(2203,plain,
! [SV107: $i,SV69: $i,SV11: $i,SV196: $i,SV185: $i,SV148: $i] :
( ( ( SV148
= ( ordered_pair @ SV185 @ SV196 ) )
= $false )
| ( ( in @ SV185 @ SV11 )
= $false )
| ( ( in @ SV196 @ SV69 )
= $false )
| ( ( in @ SV148 @ SV107 )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2188]) ).
thf(2204,plain,
! [SV11: $i,SV69: $i,SV107: $i] :
( ( ( ~ ( in @ ( sK53_SY603 @ SV107 @ SV69 @ SV11 ) @ SV11 ) )
= $false )
| ( ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2189]) ).
thf(2205,plain,
! [SV107: $i,SV69: $i,SV11: $i] :
( ( ( ~ ( in @ ( sK60_SY657 @ SV11 @ SV69 @ SV107 ) @ SV69 ) )
= $false )
| ( ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2189]) ).
thf(2206,plain,
! [SV180: $i,SV193: $i,SV107: $i,SV69: $i,SV11: $i] :
( ( ( ~ ~ ! [SY603: $i] :
~ ~ ! [SY604: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY603 @ SV11 )
| ~ ( in @ SY604 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SY603 @ SY604 ) ) )
| ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 ) )
= $false )
| ( ( in @ SV193 @ SV69 )
= $false )
| ( ( in @ SV180 @ SV11 )
= $false )
| ( ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
= ( ordered_pair @ SV180 @ SV193 ) )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2190]) ).
thf(2207,plain,
! [SV189: $i,SV134: $i,SV14: $i,SV125: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ ( sK66_SY618 @ SV189 @ SV134 @ SV14 @ SV125 ) ) @ SV14 )
| ~ ( in @ ( sK66_SY618 @ SV189 @ SV134 @ SV14 @ SV125 ) @ SV125 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV189 ) @ SV14 )
= $false )
| ( ( in @ SV189 @ SV125 )
= $false )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2191]) ).
thf(2208,plain,
! [SV135: $i,SV128: $i,SV20: $i] :
( ( ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
= $true )
| ( ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 )
= $false )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2192]) ).
thf(2209,plain,
! [SV135: $i,SV128: $i,SV20: $i] :
( ( ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 )
= $true )
| ( ( in @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ SV128 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK33_SY568 @ SV20 @ SV128 @ SV135 ) @ ( sK37_SY633 @ SV135 @ SV128 @ SV20 ) ) @ SV20 )
= $false )
| ( ( SV135
= ( relation_dom_restriction @ SV20 @ SV128 ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2193]) ).
thf(2210,plain,
! [SV131: $i,SV30: $i,SV136: $i,SV191: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK67_SY622 @ SV191 @ SV136 @ SV30 @ SV131 ) @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ ( sK67_SY622 @ SV191 @ SV136 @ SV30 @ SV131 ) @ SV131 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV191 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
= $false )
| ( ( in @ SV191 @ SV131 )
= $false )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2195]) ).
thf(2211,plain,
! [SV87: $i,SV39: $i,SV137: $i] :
( ( ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
= $true )
| ( ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 )
= $false )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2196]) ).
thf(2212,plain,
! [SV137: $i,SV39: $i,SV87: $i] :
( ( ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 )
= $true )
| ( ( in @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) @ SV39 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK35_SY578 @ SV87 @ SV39 @ SV137 ) @ ( sK40_SY636 @ SV137 @ SV39 @ SV87 ) ) @ SV87 )
= $false )
| ( ( SV137
= ( relation_rng_restriction @ SV39 @ SV87 ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2197]) ).
thf(2213,plain,
! [SV177: $i,SV89: $i,SV42: $i] :
( ( ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ ( sK64_SY596 @ SV177 @ SV89 @ SV42 ) )
= $true )
| ( ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV177 )
= $false )
| ( ( in @ SV177 @ SV42 )
= $false )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2198]) ).
thf(2214,plain,
! [SV42: $i,SV89: $i,SV177: $i] :
( ( ( in @ ( sK64_SY596 @ SV177 @ SV89 @ SV42 ) @ SV42 )
= $true )
| ( ( in @ ( sK13_SY458 @ SV42 @ SV89 ) @ SV177 )
= $false )
| ( ( in @ SV177 @ SV42 )
= $false )
| ( ( SV89
= ( union @ SV42 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2199]) ).
thf(2215,plain,
! [SV139: $i,SV10: $i,SV124: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK65_SY653 @ SV139 @ SV10 @ SV124 ) ) @ SV10 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV139 )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2201]) ).
thf(2216,plain,
! [SV124: $i,SV10: $i,SV139: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK65_SY653 @ SV139 @ SV10 @ SV124 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV139 )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2201]) ).
thf(2217,plain,
! [SV198: $i,SV139: $i,SV10: $i,SV124: $i] :
( ( ( ~ ~ ! [SY653: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SY653 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY653 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SV198 ) @ SV10 )
= $false )
| ( ( in @ ( ordered_pair @ SV198 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 )
= $false )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2202]) ).
thf(2218,plain,
! [SV198: $i,SV139: $i,SV10: $i,SV124: $i] :
( ( ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV139 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SV198 ) @ SV10 )
= $false )
| ( ( in @ ( ordered_pair @ SV198 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 )
= $false )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2202]) ).
thf(2219,plain,
! [SV11: $i,SV69: $i,SV107: $i] :
( ( ( in @ ( sK53_SY603 @ SV107 @ SV69 @ SV11 ) @ SV11 )
= $true )
| ( ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2204]) ).
thf(2220,plain,
! [SV107: $i,SV69: $i,SV11: $i] :
( ( ( in @ ( sK60_SY657 @ SV11 @ SV69 @ SV107 ) @ SV69 )
= $true )
| ( ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 )
= $true )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2205]) ).
thf(2221,plain,
! [SV180: $i,SV193: $i,SV107: $i,SV69: $i,SV11: $i] :
( ( ( ~ ~ ! [SY603: $i] :
~ ~ ! [SY604: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY603 @ SV11 )
| ~ ( in @ SY604 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SY603 @ SY604 ) ) ) )
= $false )
| ( ( in @ SV193 @ SV69 )
= $false )
| ( ( in @ SV180 @ SV11 )
= $false )
| ( ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
= ( ordered_pair @ SV180 @ SV193 ) )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2206]) ).
thf(2222,plain,
! [SV180: $i,SV193: $i,SV107: $i,SV11: $i,SV69: $i] :
( ( ( in @ ( sK15_SY483 @ SV69 @ SV11 @ SV107 ) @ SV107 )
= $false )
| ( ( in @ SV193 @ SV69 )
= $false )
| ( ( in @ SV180 @ SV11 )
= $false )
| ( ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
= ( ordered_pair @ SV180 @ SV193 ) )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2206]) ).
thf(2223,plain,
! [SV189: $i,SV134: $i,SV14: $i,SV125: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ ( sK66_SY618 @ SV189 @ SV134 @ SV14 @ SV125 ) ) @ SV14 )
| ~ ( in @ ( sK66_SY618 @ SV189 @ SV134 @ SV14 @ SV125 ) @ SV125 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV189 ) @ SV14 )
= $false )
| ( ( in @ SV189 @ SV125 )
= $false )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2207]) ).
thf(2224,plain,
! [SV131: $i,SV30: $i,SV136: $i,SV191: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK67_SY622 @ SV191 @ SV136 @ SV30 @ SV131 ) @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
| ~ ( in @ ( sK67_SY622 @ SV191 @ SV136 @ SV30 @ SV131 ) @ SV131 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV191 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
= $false )
| ( ( in @ SV191 @ SV131 )
= $false )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2210]) ).
thf(2225,plain,
! [SV139: $i,SV10: $i,SV124: $i] :
( ( ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK65_SY653 @ SV139 @ SV10 @ SV124 ) ) @ SV10 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV139 )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2215]) ).
thf(2226,plain,
! [SV124: $i,SV10: $i,SV139: $i] :
( ( ( in @ ( ordered_pair @ ( sK65_SY653 @ SV139 @ SV10 @ SV124 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV139 )
= $true )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2216]) ).
thf(2227,plain,
! [SV198: $i,SV139: $i,SV10: $i,SV124: $i] :
( ( ( ~ ! [SY653: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SY653 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY653 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SV198 ) @ SV10 )
= $false )
| ( ( in @ ( ordered_pair @ SV198 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 )
= $false )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2217]) ).
thf(2228,plain,
! [SV180: $i,SV193: $i,SV107: $i,SV69: $i,SV11: $i] :
( ( ( ~ ! [SY603: $i] :
~ ~ ! [SY604: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY603 @ SV11 )
| ~ ( in @ SY604 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SY603 @ SY604 ) ) ) )
= $true )
| ( ( in @ SV193 @ SV69 )
= $false )
| ( ( in @ SV180 @ SV11 )
= $false )
| ( ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
= ( ordered_pair @ SV180 @ SV193 ) )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2221]) ).
thf(2229,plain,
! [SV189: $i,SV134: $i,SV14: $i,SV125: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ ( sK66_SY618 @ SV189 @ SV134 @ SV14 @ SV125 ) ) @ SV14 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV189 ) @ SV14 )
= $false )
| ( ( in @ SV189 @ SV125 )
= $false )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2223]) ).
thf(2230,plain,
! [SV125: $i,SV14: $i,SV134: $i,SV189: $i] :
( ( ( ~ ( in @ ( sK66_SY618 @ SV189 @ SV134 @ SV14 @ SV125 ) @ SV125 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV189 ) @ SV14 )
= $false )
| ( ( in @ SV189 @ SV125 )
= $false )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2223]) ).
thf(2231,plain,
! [SV131: $i,SV30: $i,SV136: $i,SV191: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK67_SY622 @ SV191 @ SV136 @ SV30 @ SV131 ) @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV191 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
= $false )
| ( ( in @ SV191 @ SV131 )
= $false )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2224]) ).
thf(2232,plain,
! [SV131: $i,SV30: $i,SV136: $i,SV191: $i] :
( ( ( ~ ( in @ ( sK67_SY622 @ SV191 @ SV136 @ SV30 @ SV131 ) @ SV131 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV191 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
= $false )
| ( ( in @ SV191 @ SV131 )
= $false )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2224]) ).
thf(2233,plain,
! [SV198: $i,SV139: $i,SV10: $i,SV124: $i] :
( ( ( ! [SY653: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SY653 ) @ SV10 )
| ~ ( in @ ( ordered_pair @ SY653 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SV198 ) @ SV10 )
= $false )
| ( ( in @ ( ordered_pair @ SV198 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 )
= $false )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2227]) ).
thf(2234,plain,
! [SV180: $i,SV193: $i,SV107: $i,SV69: $i,SV11: $i] :
( ( ( ! [SY603: $i] :
~ ~ ! [SY604: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY603 @ SV11 )
| ~ ( in @ SY604 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ SY603 @ SY604 ) ) ) )
= $false )
| ( ( in @ SV193 @ SV69 )
= $false )
| ( ( in @ SV180 @ SV11 )
= $false )
| ( ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
= ( ordered_pair @ SV180 @ SV193 ) )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2228]) ).
thf(2235,plain,
! [SV189: $i,SV134: $i,SV14: $i,SV125: $i] :
( ( ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ ( sK66_SY618 @ SV189 @ SV134 @ SV14 @ SV125 ) ) @ SV14 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV189 ) @ SV14 )
= $false )
| ( ( in @ SV189 @ SV125 )
= $false )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2229]) ).
thf(2236,plain,
! [SV125: $i,SV14: $i,SV134: $i,SV189: $i] :
( ( ( in @ ( sK66_SY618 @ SV189 @ SV134 @ SV14 @ SV125 ) @ SV125 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK24_SY563 @ SV125 @ SV14 @ SV134 ) @ SV189 ) @ SV14 )
= $false )
| ( ( in @ SV189 @ SV125 )
= $false )
| ( ( SV134
= ( relation_inverse_image @ SV14 @ SV125 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2230]) ).
thf(2237,plain,
! [SV131: $i,SV30: $i,SV136: $i,SV191: $i] :
( ( ( in @ ( ordered_pair @ ( sK67_SY622 @ SV191 @ SV136 @ SV30 @ SV131 ) @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
= $true )
| ( ( in @ ( ordered_pair @ SV191 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
= $false )
| ( ( in @ SV191 @ SV131 )
= $false )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2231]) ).
thf(2238,plain,
! [SV131: $i,SV30: $i,SV136: $i,SV191: $i] :
( ( ( in @ ( sK67_SY622 @ SV191 @ SV136 @ SV30 @ SV131 ) @ SV131 )
= $true )
| ( ( in @ ( ordered_pair @ SV191 @ ( sK25_SY573 @ SV131 @ SV30 @ SV136 ) ) @ SV30 )
= $false )
| ( ( in @ SV191 @ SV131 )
= $false )
| ( ( SV136
= ( relation_image @ SV30 @ SV131 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2232]) ).
thf(2239,plain,
! [SV198: $i,SV139: $i,SV10: $i,SV124: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK68_SY653 @ SV198 @ SV139 @ SV10 @ SV124 ) ) @ SV10 )
| ~ ( in @ ( ordered_pair @ ( sK68_SY653 @ SV198 @ SV139 @ SV10 @ SV124 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SV198 ) @ SV10 )
= $false )
| ( ( in @ ( ordered_pair @ SV198 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 )
= $false )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2233]) ).
thf(2240,plain,
! [SV11: $i,SV69: $i,SV107: $i,SV193: $i,SV180: $i] :
( ( ( ~ ~ ! [SY658: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK69_SY603 @ SV180 @ SV193 @ SV107 @ SV69 @ SV11 ) @ SV11 )
| ~ ( in @ SY658 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ ( sK69_SY603 @ SV180 @ SV193 @ SV107 @ SV69 @ SV11 ) @ SY658 ) ) ) )
= $false )
| ( ( in @ SV193 @ SV69 )
= $false )
| ( ( in @ SV180 @ SV11 )
= $false )
| ( ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
= ( ordered_pair @ SV180 @ SV193 ) )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2234]) ).
thf(2241,plain,
! [SV198: $i,SV139: $i,SV10: $i,SV124: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK68_SY653 @ SV198 @ SV139 @ SV10 @ SV124 ) ) @ SV10 )
| ~ ( in @ ( ordered_pair @ ( sK68_SY653 @ SV198 @ SV139 @ SV10 @ SV124 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SV198 ) @ SV10 )
= $false )
| ( ( in @ ( ordered_pair @ SV198 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 )
= $false )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2239]) ).
thf(2242,plain,
! [SV11: $i,SV69: $i,SV107: $i,SV193: $i,SV180: $i] :
( ( ( ~ ! [SY658: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK69_SY603 @ SV180 @ SV193 @ SV107 @ SV69 @ SV11 ) @ SV11 )
| ~ ( in @ SY658 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ ( sK69_SY603 @ SV180 @ SV193 @ SV107 @ SV69 @ SV11 ) @ SY658 ) ) ) )
= $true )
| ( ( in @ SV193 @ SV69 )
= $false )
| ( ( in @ SV180 @ SV11 )
= $false )
| ( ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
= ( ordered_pair @ SV180 @ SV193 ) )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2240]) ).
thf(2243,plain,
! [SV198: $i,SV139: $i,SV10: $i,SV124: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK68_SY653 @ SV198 @ SV139 @ SV10 @ SV124 ) ) @ SV10 )
| ~ ( in @ ( ordered_pair @ ( sK68_SY653 @ SV198 @ SV139 @ SV10 @ SV124 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SV198 ) @ SV10 )
= $false )
| ( ( in @ ( ordered_pair @ SV198 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 )
= $false )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2241]) ).
thf(2244,plain,
! [SV11: $i,SV69: $i,SV107: $i,SV193: $i,SV180: $i] :
( ( ( ! [SY658: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK69_SY603 @ SV180 @ SV193 @ SV107 @ SV69 @ SV11 ) @ SV11 )
| ~ ( in @ SY658 @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ ( sK69_SY603 @ SV180 @ SV193 @ SV107 @ SV69 @ SV11 ) @ SY658 ) ) ) )
= $false )
| ( ( in @ SV193 @ SV69 )
= $false )
| ( ( in @ SV180 @ SV11 )
= $false )
| ( ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
= ( ordered_pair @ SV180 @ SV193 ) )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2242]) ).
thf(2245,plain,
! [SV198: $i,SV139: $i,SV10: $i,SV124: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK68_SY653 @ SV198 @ SV139 @ SV10 @ SV124 ) ) @ SV10 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SV198 ) @ SV10 )
= $false )
| ( ( in @ ( ordered_pair @ SV198 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 )
= $false )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2243]) ).
thf(2246,plain,
! [SV124: $i,SV10: $i,SV139: $i,SV198: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK68_SY653 @ SV198 @ SV139 @ SV10 @ SV124 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SV198 ) @ SV10 )
= $false )
| ( ( in @ ( ordered_pair @ SV198 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 )
= $false )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2243]) ).
thf(2247,plain,
! [SV11: $i,SV69: $i,SV107: $i,SV193: $i,SV180: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK69_SY603 @ SV180 @ SV193 @ SV107 @ SV69 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK70_SY658 @ SV11 @ SV69 @ SV107 @ SV193 @ SV180 ) @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ ( sK69_SY603 @ SV180 @ SV193 @ SV107 @ SV69 @ SV11 ) @ ( sK70_SY658 @ SV11 @ SV69 @ SV107 @ SV193 @ SV180 ) ) ) ) )
= $false )
| ( ( in @ SV193 @ SV69 )
= $false )
| ( ( in @ SV180 @ SV11 )
= $false )
| ( ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
= ( ordered_pair @ SV180 @ SV193 ) )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2244]) ).
thf(2248,plain,
! [SV198: $i,SV139: $i,SV10: $i,SV124: $i] :
( ( ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ ( sK68_SY653 @ SV198 @ SV139 @ SV10 @ SV124 ) ) @ SV10 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SV198 ) @ SV10 )
= $false )
| ( ( in @ ( ordered_pair @ SV198 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 )
= $false )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2245]) ).
thf(2249,plain,
! [SV124: $i,SV10: $i,SV139: $i,SV198: $i] :
( ( ( in @ ( ordered_pair @ ( sK68_SY653 @ SV198 @ SV139 @ SV10 @ SV124 ) @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK41_SY585 @ SV124 @ SV10 @ SV139 ) @ SV198 ) @ SV10 )
= $false )
| ( ( in @ ( ordered_pair @ SV198 @ ( sK43_SY646 @ SV139 @ SV10 @ SV124 ) ) @ SV124 )
= $false )
| ( ( SV139
= ( relation_composition @ SV10 @ SV124 ) )
= $true )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ SV124 )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2246]) ).
thf(2250,plain,
! [SV11: $i,SV69: $i,SV107: $i,SV193: $i,SV180: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK69_SY603 @ SV180 @ SV193 @ SV107 @ SV69 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK70_SY658 @ SV11 @ SV69 @ SV107 @ SV193 @ SV180 ) @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ ( sK69_SY603 @ SV180 @ SV193 @ SV107 @ SV69 @ SV11 ) @ ( sK70_SY658 @ SV11 @ SV69 @ SV107 @ SV193 @ SV180 ) ) ) ) )
= $true )
| ( ( in @ SV193 @ SV69 )
= $false )
| ( ( in @ SV180 @ SV11 )
= $false )
| ( ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
= ( ordered_pair @ SV180 @ SV193 ) )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2247]) ).
thf(2251,plain,
! [SV11: $i,SV69: $i,SV107: $i,SV193: $i,SV180: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK69_SY603 @ SV180 @ SV193 @ SV107 @ SV69 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK70_SY658 @ SV11 @ SV69 @ SV107 @ SV193 @ SV180 ) @ SV69 ) )
| ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ ( sK69_SY603 @ SV180 @ SV193 @ SV107 @ SV69 @ SV11 ) @ ( sK70_SY658 @ SV11 @ SV69 @ SV107 @ SV193 @ SV180 ) ) ) )
= $false )
| ( ( in @ SV193 @ SV69 )
= $false )
| ( ( in @ SV180 @ SV11 )
= $false )
| ( ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
= ( ordered_pair @ SV180 @ SV193 ) )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2250]) ).
thf(2252,plain,
! [SV11: $i,SV69: $i,SV107: $i,SV193: $i,SV180: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK69_SY603 @ SV180 @ SV193 @ SV107 @ SV69 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK70_SY658 @ SV11 @ SV69 @ SV107 @ SV193 @ SV180 ) @ SV69 ) ) )
= $false )
| ( ( in @ SV193 @ SV69 )
= $false )
| ( ( in @ SV180 @ SV11 )
= $false )
| ( ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
= ( ordered_pair @ SV180 @ SV193 ) )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2251]) ).
thf(2253,plain,
! [SV193: $i,SV180: $i,SV107: $i,SV11: $i,SV69: $i] :
( ( ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
!= ( ordered_pair @ ( sK69_SY603 @ SV180 @ SV193 @ SV107 @ SV69 @ SV11 ) @ ( sK70_SY658 @ SV11 @ SV69 @ SV107 @ SV193 @ SV180 ) ) )
= $false )
| ( ( in @ SV193 @ SV69 )
= $false )
| ( ( in @ SV180 @ SV11 )
= $false )
| ( ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
= ( ordered_pair @ SV180 @ SV193 ) )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2251]) ).
thf(2254,plain,
! [SV11: $i,SV69: $i,SV107: $i,SV193: $i,SV180: $i] :
( ( ( ~ ( ~ ( in @ ( sK69_SY603 @ SV180 @ SV193 @ SV107 @ SV69 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK70_SY658 @ SV11 @ SV69 @ SV107 @ SV193 @ SV180 ) @ SV69 ) ) )
= $true )
| ( ( in @ SV193 @ SV69 )
= $false )
| ( ( in @ SV180 @ SV11 )
= $false )
| ( ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
= ( ordered_pair @ SV180 @ SV193 ) )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2252]) ).
thf(2255,plain,
! [SV193: $i,SV180: $i,SV107: $i,SV11: $i,SV69: $i] :
( ( ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
= ( ordered_pair @ ( sK69_SY603 @ SV180 @ SV193 @ SV107 @ SV69 @ SV11 ) @ ( sK70_SY658 @ SV11 @ SV69 @ SV107 @ SV193 @ SV180 ) ) )
= $true )
| ( ( in @ SV193 @ SV69 )
= $false )
| ( ( in @ SV180 @ SV11 )
= $false )
| ( ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
= ( ordered_pair @ SV180 @ SV193 ) )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2253]) ).
thf(2256,plain,
! [SV11: $i,SV69: $i,SV107: $i,SV193: $i,SV180: $i] :
( ( ( ~ ( in @ ( sK69_SY603 @ SV180 @ SV193 @ SV107 @ SV69 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK70_SY658 @ SV11 @ SV69 @ SV107 @ SV193 @ SV180 ) @ SV69 ) )
= $false )
| ( ( in @ SV193 @ SV69 )
= $false )
| ( ( in @ SV180 @ SV11 )
= $false )
| ( ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
= ( ordered_pair @ SV180 @ SV193 ) )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2254]) ).
thf(2257,plain,
! [SV11: $i,SV69: $i,SV107: $i,SV193: $i,SV180: $i] :
( ( ( ~ ( in @ ( sK69_SY603 @ SV180 @ SV193 @ SV107 @ SV69 @ SV11 ) @ SV11 ) )
= $false )
| ( ( in @ SV193 @ SV69 )
= $false )
| ( ( in @ SV180 @ SV11 )
= $false )
| ( ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
= ( ordered_pair @ SV180 @ SV193 ) )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2256]) ).
thf(2258,plain,
! [SV180: $i,SV193: $i,SV107: $i,SV69: $i,SV11: $i] :
( ( ( ~ ( in @ ( sK70_SY658 @ SV11 @ SV69 @ SV107 @ SV193 @ SV180 ) @ SV69 ) )
= $false )
| ( ( in @ SV193 @ SV69 )
= $false )
| ( ( in @ SV180 @ SV11 )
= $false )
| ( ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
= ( ordered_pair @ SV180 @ SV193 ) )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2256]) ).
thf(2259,plain,
! [SV11: $i,SV69: $i,SV107: $i,SV193: $i,SV180: $i] :
( ( ( in @ ( sK69_SY603 @ SV180 @ SV193 @ SV107 @ SV69 @ SV11 ) @ SV11 )
= $true )
| ( ( in @ SV193 @ SV69 )
= $false )
| ( ( in @ SV180 @ SV11 )
= $false )
| ( ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
= ( ordered_pair @ SV180 @ SV193 ) )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2257]) ).
thf(2260,plain,
! [SV180: $i,SV193: $i,SV107: $i,SV69: $i,SV11: $i] :
( ( ( in @ ( sK70_SY658 @ SV11 @ SV69 @ SV107 @ SV193 @ SV180 ) @ SV69 )
= $true )
| ( ( in @ SV193 @ SV69 )
= $false )
| ( ( in @ SV180 @ SV11 )
= $false )
| ( ( ( sK15_SY483 @ SV69 @ SV11 @ SV107 )
= ( ordered_pair @ SV180 @ SV193 ) )
= $false )
| ( ( SV107
= ( cartesian_product2 @ SV11 @ SV69 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2258]) ).
thf(2261,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[361,2260,2259,2255,2249,2248,2238,2237,2236,2235,2226,2225,2222,2220,2219,2218,2214,2213,2212,2211,2209,2208,2203,2200,2194,2184,2183,2179,2174,2171,2170,2164,2161,2160,2158,2157,2154,2152,2151,2149,2148,2147,2146,2134,2133,2131,2127,2120,2116,2102,2101,2098,2093,2090,2088,2083,2082,2079,2074,2071,2061,2060,2056,2055,2051,2050,2049,2045,2044,2040,2039,2034,2033,2031,2030,2018,2017,2015,2013,2012,2011,2006,1994,1992,1989,1987,1981,1975,1963,1961,1960,1959,1956,1955,1954,1945,1918,1909,1908,1906,1905,1898,1897,1894,1891,1885,1884,1871,1865,1855,1854,1846,1843,1841,1838,1834,1833,1832,1831,1828,1827,1824,1823,1809,1795,1794,1793,1790,1789,1787,1782,1768,1767,1761,1760,1755,1746,1723,1715,1690,1684,1679,1677,1675,1659,1645,1644,1640,1638,1636,1626,1620,1609,1597,1596,1595,1583,1579,1578,1574,1569,1556,1555,1554,1553,1552,1543,1542,1502,1497,1492,1486,1485,1480,1470,1460,1424,1422,1421,1414,1413,1408,1407,1403,1396,1394,1392,1391,1372,1371,1359,1356,1355,1354,1350,1319,1318,1315,1311,1310,1307,1306,1268,1267,1264,1263,1231,1224,1223,1176,1164,1163,1162,1144,1143,1079,1054,999,998,984,983,959,935,927,920,915,890,889,866,865,842,826,738,714,711,706,700,699,692,685,684,673,672,668,656,451,450,388,379,378,376,375,374,373,372,371,370,369,368,367,366,365,364,363,362]) ).
thf(2262,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[2261]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU217+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.16 % Computer : n019.cluster.edu
% 0.07/0.16 % Model : x86_64 x86_64
% 0.07/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.16 % Memory : 8046.5625MB
% 0.07/0.16 % OS : Linux 6.8.0-71-generic
% 0.07/0.16 % CPULimit : 300
% 0.07/0.16 % WCLimit : 300
% 0.07/0.16 % DateTime : Tue Oct 6 15:06:58 UTC 2026
% 0.07/0.16 % CPUTime :
% 0.07/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 29.21/5.09 .
% 29.21/5.09
% 29.21/5.09 No.of.Axioms: 79
% 29.21/5.09
% 29.21/5.09 Length.of.Defs: 0
% 29.21/5.09
% 29.21/5.09 Contains.Choice.Funs: false
% 29.21/5.09 ..................................................................................
% 29.21/5.09
% 29.21/5.09 ********************************
% 29.21/5.09 * All subproblems solved! *
% 29.21/5.09 ********************************
% 29.21/5.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:80,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2261,loop_count:0,foatp_calls:1,translation:fof_full)
% 29.21/5.09
% 29.21/5.09 %**** Beginning of derivation protocol ****
% 29.21/5.09 % SZS output start CNFRefutation
% See solution above
% 29.21/5.11
% 29.21/5.11 %**** End of derivation protocol ****
% 29.21/5.11 %**** no. of clauses in derivation: 2120 ****
% 29.21/5.11 %**** clause counter: 2261 ****
% 29.21/5.11
% 29.21/5.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:80,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2261,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------