%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU275+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 10:43:45 AM UTC 2026
% Result : Theorem 21.37s 3.95s
% Output : CNFRefutation 21.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 137
% Syntax : Number of formulae : 2560 (1040 unt; 0 typ; 0 def)
% Number of atoms : 22791 (7901 equ; 0 cnn)
% Maximal formula atoms : 16 ( 8 avg)
% Number of connectives : 47081 (9373 ~;8475 |; 476 &;28465 @)
% ( 82 <=>; 210 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 126 ( 123 usr; 10 con; 0-4 aty)
% Number of variables : 7270 ( 0 ^;7232 !; 38 ?;7270 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_antisymmetric,type,
antisymmetric: $i > $o ).
thf(tp_apply,type,
apply: $i > $i > $i ).
thf(tp_are_equipotent,type,
are_equipotent: $i > $i > $o ).
thf(tp_being_limit_ordinal,type,
being_limit_ordinal: $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_connected,type,
connected: $i > $o ).
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_epsilon_connected,type,
epsilon_connected: $i > $o ).
thf(tp_epsilon_transitive,type,
epsilon_transitive: $i > $o ).
thf(tp_fiber,type,
fiber: $i > $i > $i ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_function_inverse,type,
function_inverse: $i > $i ).
thf(tp_identity_relation,type,
identity_relation: $i > $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_inclusion_relation,type,
inclusion_relation: $i > $i ).
thf(tp_is_antisymmetric_in,type,
is_antisymmetric_in: $i > $i > $o ).
thf(tp_is_connected_in,type,
is_connected_in: $i > $i > $o ).
thf(tp_is_reflexive_in,type,
is_reflexive_in: $i > $i > $o ).
thf(tp_is_transitive_in,type,
is_transitive_in: $i > $i > $o ).
thf(tp_is_well_founded_in,type,
is_well_founded_in: $i > $i > $o ).
thf(tp_meet_of_subsets,type,
meet_of_subsets: $i > $i > $i ).
thf(tp_one_to_one,type,
one_to_one: $i > $o ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_ordinal,type,
ordinal: $i > $o ).
thf(tp_ordinal_subset,type,
ordinal_subset: $i > $i > $o ).
thf(tp_pair_first,type,
pair_first: $i > $i ).
thf(tp_pair_second,type,
pair_second: $i > $i ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_proper_subset,type,
proper_subset: $i > $i > $o ).
thf(tp_reflexive,type,
reflexive: $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_as_subset,type,
relation_dom_as_subset: $i > $i > $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_isomorphism,type,
relation_isomorphism: $i > $i > $i > $o ).
thf(tp_relation_of2,type,
relation_of2: $i > $i > $i > $o ).
thf(tp_relation_of2_as_subset,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(tp_relation_restriction,type,
relation_restriction: $i > $i > $i ).
thf(tp_relation_rng,type,
relation_rng: $i > $i ).
thf(tp_relation_rng_as_subset,type,
relation_rng_as_subset: $i > $i > $i > $i ).
thf(tp_relation_rng_restriction,type,
relation_rng_restriction: $i > $i > $i ).
thf(tp_sK10_A,type,
sK10_A: $i ).
thf(tp_sK11_D,type,
sK11_D: $i > $i > $i > $i ).
thf(tp_sK12_D,type,
sK12_D: $i > $i > $i > $i ).
thf(tp_sK13_C,type,
sK13_C: $i > $i > $i ).
thf(tp_sK14_SY277,type,
sK14_SY277: $i > $i > $i ).
thf(tp_sK15_D,type,
sK15_D: $i > $i > $i > $i ).
thf(tp_sK16_C,type,
sK16_C: $i > $i > $i ).
thf(tp_sK17_C,type,
sK17_C: $i > $i > $i ).
thf(tp_sK18_SY278,type,
sK18_SY278: $i > $i > $i ).
thf(tp_sK19_B,type,
sK19_B: $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_SY279,type,
sK20_SY279: $i > $i ).
thf(tp_sK21_D,type,
sK21_D: $i > $i > $i > $i ).
thf(tp_sK22_D,type,
sK22_D: $i > $i > $i > $i ).
thf(tp_sK23_C,type,
sK23_C: $i > $i > $i ).
thf(tp_sK24_SY280,type,
sK24_SY280: $i > $i > $i ).
thf(tp_sK25_B,type,
sK25_B: $i > $i ).
thf(tp_sK26_C,type,
sK26_C: $i > $i > $i ).
thf(tp_sK27_B,type,
sK27_B: $i > $i ).
thf(tp_sK28_C,type,
sK28_C: $i > $i > $i ).
thf(tp_sK29_C,type,
sK29_C: $i > $i > $i ).
thf(tp_sK2_B,type,
sK2_B: $i > $i ).
thf(tp_sK30_SY281,type,
sK30_SY281: $i > $i > $i ).
thf(tp_sK31_B,type,
sK31_B: $i > $i ).
thf(tp_sK32_E,type,
sK32_E: $i > $i > $i > $i > $i ).
thf(tp_sK33_B,type,
sK33_B: $i > $i ).
thf(tp_sK34_C,type,
sK34_C: $i > $i > $i ).
thf(tp_sK35_C,type,
sK35_C: $i > $i > $i ).
thf(tp_sK36_B,type,
sK36_B: $i > $i ).
thf(tp_sK37_SY285,type,
sK37_SY285: $i > $i ).
thf(tp_sK38_B,type,
sK38_B: $i > $i ).
thf(tp_sK39_SY286,type,
sK39_SY286: $i > $i ).
thf(tp_sK3_SY270,type,
sK3_SY270: $i > $i > $i ).
thf(tp_sK40_SY288,type,
sK40_SY288: $i > $i ).
thf(tp_sK41_C,type,
sK41_C: $i > $i > $i ).
thf(tp_sK42_H,type,
sK42_H: $i > $i > $i > $i ).
thf(tp_sK43_E,type,
sK43_E: $i > $i > $i > $i ).
thf(tp_sK44_C,type,
sK44_C: $i > $i > $i ).
thf(tp_sK45_SY295,type,
sK45_SY295: $i > $i > $i ).
thf(tp_sK46_SY299,type,
sK46_SY299: $i > $i > $i ).
thf(tp_sK47_SY303,type,
sK47_SY303: $i > $i > $i ).
thf(tp_sK48_SY300,type,
sK48_SY300: $i > $i > $i ).
thf(tp_sK49_A,type,
sK49_A: $i ).
thf(tp_sK4_C,type,
sK4_C: $i > $i > $i ).
thf(tp_sK50_B,type,
sK50_B: $i > $i ).
thf(tp_sK51_B,type,
sK51_B: $i > $i ).
thf(tp_sK52_C,type,
sK52_C: $i > $i > $i ).
thf(tp_sK53_E,type,
sK53_E: $i > $i > $i > $i ).
thf(tp_sK54_B,type,
sK54_B: $i > $i ).
thf(tp_sK5_C,type,
sK5_C: $i > $i > $i ).
thf(tp_sK6_A,type,
sK6_A: $i ).
thf(tp_sK7_A,type,
sK7_A: $i ).
thf(tp_sK8_A,type,
sK8_A: $i ).
thf(tp_sK9_A,type,
sK9_A: $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_succ,type,
succ: $i > $i ).
thf(tp_transitive,type,
transitive: $i > $o ).
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(tp_unordered_triple,type,
unordered_triple: $i > $i > $i > $i ).
thf(tp_well_founded_relation,type,
well_founded_relation: $i > $o ).
thf(tp_well_ordering,type,
well_ordering: $i > $o ).
thf(tp_well_orders,type,
well_orders: $i > $i > $o ).
thf(1,axiom,
! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
( ( subset @ E @ C )
=> ( in @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_tarski) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ( in @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_tarski) ).
thf(4,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ordinal @ B )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ( C = D )
& ? [F: $i] :
( ( ordinal @ F )
& ( D = F )
& ( in @ F @ A ) )
& ( C = E )
& ? [G: $i] :
( ( ordinal @ G )
& ( E = G )
& ( in @ G @ A ) ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ E @ ( succ @ B ) )
& ( E = D )
& ? [H: $i] :
( ( ordinal @ H )
& ( D = H )
& ( in @ H @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e8_6__wellord2__1) ).
thf(18,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ordinal_subset @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_ordinal1) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ( ordinal_subset @ A @ B )
<=> ( subset @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
thf(28,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(29,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_ordinal1) ).
thf(33,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(38,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(39,axiom,
? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_ordinal1) ).
thf(40,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(43,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
thf(55,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ ( union @ A ) )
& ( epsilon_connected @ ( union @ A ) )
& ( ordinal @ ( union @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_ordinal1) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_difference @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_relat_1) ).
thf(60,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ( ~ ( empty @ ( succ @ A ) )
& ( epsilon_transitive @ ( succ @ A ) )
& ( epsilon_connected @ ( succ @ A ) )
& ( ordinal @ ( succ @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_ordinal1) ).
thf(64,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_relat_1) ).
thf(70,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_relat_1) ).
thf(71,axiom,
! [A: $i] :
~ ( empty @ ( succ @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_ordinal1) ).
thf(81,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(82,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_relset_1) ).
thf(83,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_relat_1) ).
thf(84,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relat_1) ).
thf(86,axiom,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).
thf(89,axiom,
! [A: $i] : ( relation @ ( identity_relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(92,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(93,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(94,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(96,axiom,
! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relat_1) ).
thf(97,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(98,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_tarski) ).
thf(100,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_relat_1) ).
thf(101,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(102,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(103,axiom,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_wellord1) ).
thf(104,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(106,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(107,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_mcart_1) ).
thf(109,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(110,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(111,axiom,
! [A: $i] : ( relation @ ( inclusion_relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_wellord2) ).
thf(112,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_wellord1) ).
thf(113,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(114,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_setfam_1) ).
thf(115,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(116,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_ordinal1) ).
thf(117,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_mcart_1) ).
thf(118,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_funct_1) ).
thf(119,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_enumset1) ).
thf(120,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_relat_1) ).
thf(123,axiom,
! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_xboole_0) ).
thf(134,axiom,
! [A: $i] :
( ( being_limit_ordinal @ A )
<=> ( A
= ( union @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_ordinal1) ).
thf(140,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(141,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( well_ordering @ A )
<=> ( ( reflexive @ A )
& ( transitive @ A )
& ( antisymmetric @ A )
& ( connected @ A )
& ( well_founded_relation @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_wellord1) ).
thf(142,axiom,
! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
thf(146,axiom,
! [A: $i] :
( ( ordinal @ A )
<=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_ordinal1) ).
thf(148,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(150,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(151,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/sandbox2/benchmark/theBenchmark.p',d3_relat_1) ).
thf(152,axiom,
! [A: $i] :
( ( epsilon_connected @ A )
<=> ! [B: $i,C: $i] :
~ ( ( in @ B @ A )
& ( in @ C @ A )
& ~ ( in @ B @ C )
& ( B != C )
& ~ ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_ordinal1) ).
thf(154,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
thf(158,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/sandbox2/benchmark/theBenchmark.p',d2_relat_1) ).
thf(159,axiom,
! [A: $i] :
( ( epsilon_transitive @ A )
<=> ! [B: $i] :
( ( in @ B @ A )
=> ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
thf(161,axiom,
! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(162,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(165,axiom,
! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(169,axiom,
! [A: $i] :
( ( relation @ A )
<=> ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
thf(172,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( unordered_triple @ A @ B @ C ) )
<=> ! [E: $i] :
( ( in @ E @ D )
<=> ~ ( ( E != A )
& ( E != B )
& ( E != C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_enumset1) ).
thf(182,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(184,axiom,
! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ( ordinal_subset @ A @ B )
| ( ordinal_subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
thf(188,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_ordinal1) ).
thf(189,axiom,
! [A: $i] :
( ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) )
=> ( ordinal @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_ordinal1) ).
thf(192,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(193,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).
thf(196,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(201,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(204,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(207,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_relat_1) ).
thf(210,axiom,
! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(216,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(217,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ( well_founded_relation @ ( inclusion_relation @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_wellord2) ).
thf(223,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(225,axiom,
! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_xboole_1) ).
thf(227,axiom,
! [A: $i] : ( antisymmetric @ ( inclusion_relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_wellord2) ).
thf(238,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ( connected @ ( inclusion_relation @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_wellord2) ).
thf(251,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ( ~ ( ~ ( being_limit_ordinal @ A )
& ! [B: $i] :
( ( ordinal @ B )
=> ( A
!= ( succ @ B ) ) ) )
& ~ ( ? [B: $i] :
( ( ordinal @ B )
& ( A
= ( succ @ B ) ) )
& ( being_limit_ordinal @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_ordinal1) ).
thf(252,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ( ( being_limit_ordinal @ A )
<=> ! [B: $i] :
( ( ordinal @ B )
=> ( ( in @ B @ A )
=> ( in @ ( succ @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_ordinal1) ).
thf(254,axiom,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(255,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( in @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
& ( disjoint @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(256,axiom,
! [A: $i] : ( transitive @ ( inclusion_relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_wellord2) ).
thf(257,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( in @ B @ C )
& ( in @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_ordinal1) ).
thf(260,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( ( well_ordering @ B )
& ( subset @ A @ ( relation_field @ B ) ) )
=> ( ( relation_field @ ( relation_restriction @ B @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_wellord1) ).
thf(261,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ C )
& ( in @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).
thf(262,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(265,axiom,
! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(269,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(270,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ( ( in @ A @ B )
<=> ( ordinal_subset @ ( succ @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_ordinal1) ).
thf(271,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( well_ordering @ B )
=> ( well_ordering @ ( relation_restriction @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_wellord1) ).
thf(272,axiom,
! [A: $i,B: $i] :
( ( ordinal @ B )
=> ~ ( ( subset @ A @ B )
& ( A != empty_set )
& ! [C: $i] :
( ( ordinal @ C )
=> ~ ( ( in @ C @ A )
& ! [D: $i] :
( ( ordinal @ D )
=> ( ( in @ D @ A )
=> ( ordinal_subset @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_ordinal1) ).
thf(273,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( well_founded_relation @ B )
=> ( well_founded_relation @ ( relation_restriction @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_wellord1) ).
thf(274,axiom,
! [A: $i] :
( ! [B: $i] :
( ( in @ B @ A )
=> ( ( ordinal @ B )
& ( subset @ B @ A ) ) )
=> ( ordinal @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_ordinal1) ).
thf(276,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(277,axiom,
! [A: $i] : ( reflexive @ ( inclusion_relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_wellord2) ).
thf(278,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(279,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(280,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( antisymmetric @ B )
=> ( antisymmetric @ ( relation_restriction @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_wellord1) ).
thf(282,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( transitive @ B )
=> ( transitive @ ( relation_restriction @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_wellord1) ).
thf(283,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ~ ( ~ ( in @ A @ B )
& ( A != B )
& ~ ( in @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_ordinal1) ).
thf(284,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( connected @ B )
=> ( connected @ ( relation_restriction @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_wellord1) ).
thf(286,axiom,
! [A: $i,B: $i] :
( ( ordinal @ B )
=> ( ( in @ A @ B )
=> ( ordinal @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_ordinal1) ).
thf(288,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( reflexive @ B )
=> ( reflexive @ ( relation_restriction @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_wellord1) ).
thf(291,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( subset @ ( fiber @ ( relation_restriction @ C @ A ) @ B ) @ ( fiber @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_wellord1) ).
thf(293,axiom,
! [A: $i] :
( ( epsilon_transitive @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ( ( proper_subset @ A @ B )
=> ( in @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_ordinal1) ).
thf(295,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( subset @ ( relation_field @ ( relation_restriction @ B @ A ) ) @ ( relation_field @ B ) )
& ( subset @ ( relation_field @ ( relation_restriction @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_wellord1) ).
thf(298,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(299,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(300,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_field @ ( relation_restriction @ C @ B ) ) )
=> ( ( in @ A @ ( relation_field @ C ) )
& ( in @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_wellord1) ).
thf(302,axiom,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(304,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( subset @ A @ B )
=> ( subset @ ( relation_inverse_image @ C @ A ) @ ( relation_inverse_image @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t178_relat_1) ).
thf(306,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_restriction @ C @ B ) )
<=> ( ( in @ A @ C )
& ( in @ A @ ( cartesian_product2 @ B @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_wellord1) ).
thf(307,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( relation_of2_as_subset @ D @ C @ A )
=> ( ( subset @ A @ B )
=> ( relation_of2_as_subset @ D @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_relset_1) ).
thf(321,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(323,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(325,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(327,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_relat_1) ).
thf(331,axiom,
! [A: $i] : ( in @ A @ ( succ @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_ordinal1) ).
thf(333,axiom,
! [A: $i,B: $i] :
( ( ordinal @ B )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ ( succ @ B ) )
& ? [E: $i] :
( ( ordinal @ E )
& ( D = E )
& ( in @ E @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e8_6__wellord2__1) ).
thf(334,axiom,
! [A: $i] :
( ? [B: $i] :
( ( ordinal @ B )
& ( in @ B @ A ) )
=> ? [B: $i] :
( ( ordinal @ B )
& ( in @ B @ A )
& ! [C: $i] :
( ( ordinal @ C )
=> ( ( in @ C @ A )
=> ( ordinal_subset @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_ordinal1__e8_6__wellord2) ).
thf(338,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l50_zfmisc_1) ).
thf(342,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( antisymmetric @ A )
<=> ! [B: $i,C: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ C @ B ) @ A ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_wellord1) ).
thf(345,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(346,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( transitive @ A )
<=> ! [B: $i,C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ C @ D ) @ A ) )
=> ( in @ ( ordered_pair @ B @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_wellord1) ).
thf(353,conjecture,
! [A: $i] :
( ( ordinal @ A )
=> ( well_ordering @ ( inclusion_relation @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_wellord2) ).
thf(354,negated_conjecture,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ( well_ordering @ ( inclusion_relation @ A ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[353]) ).
thf(355,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ( well_ordering @ ( inclusion_relation @ A ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[354]) ).
thf(356,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(357,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ( in @ D @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(358,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(359,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(360,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(361,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(362,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(363,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(364,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(365,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(366,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(367,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(368,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ ( union @ A ) )
& ( epsilon_connected @ ( union @ A ) )
& ( ordinal @ ( union @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(369,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(370,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ( ~ ( empty @ ( succ @ A ) )
& ( epsilon_transitive @ ( succ @ A ) )
& ( epsilon_connected @ ( succ @ A ) )
& ( ordinal @ ( succ @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(371,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(372,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(373,plain,
( ( ! [A: $i] :
~ ( empty @ ( succ @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(374,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(375,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(376,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(377,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(378,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(379,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(380,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(381,plain,
( ( ! [A: $i] :
( ( being_limit_ordinal @ A )
<=> ( A
= ( union @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(382,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)],[140]) ).
thf(383,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( well_ordering @ A )
<=> ( ( reflexive @ A )
& ( transitive @ A )
& ( antisymmetric @ A )
& ( connected @ A )
& ( well_founded_relation @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(384,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)],[142]) ).
thf(385,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)],[148]) ).
thf(386,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(387,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)],[151]) ).
thf(388,plain,
( ( ! [A: $i] :
( ( epsilon_connected @ A )
<=> ! [B: $i,C: $i] :
~ ( ( in @ B @ A )
& ( in @ C @ A )
& ~ ( in @ B @ C )
& ( B != C )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(389,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)],[154]) ).
thf(390,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)],[156]) ).
thf(391,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)],[158]) ).
thf(392,plain,
( ( ! [A: $i] :
( ( epsilon_transitive @ A )
<=> ! [B: $i] :
( ( in @ B @ A )
=> ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(393,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(394,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(395,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(396,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)],[169]) ).
thf(397,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( unordered_triple @ A @ B @ C ) )
<=> ! [E: $i] :
( ( in @ E @ D )
<=> ~ ( ( E != A )
& ( E != B )
& ( E != C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(398,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(399,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(400,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(401,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(402,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(403,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[204]) ).
thf(404,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(405,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(406,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[216]) ).
thf(407,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(408,plain,
( ( ! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(409,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ( ( being_limit_ordinal @ A )
<=> ! [B: $i] :
( ( ordinal @ B )
=> ( ( in @ B @ A )
=> ( in @ ( succ @ B ) @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[252]) ).
thf(410,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(411,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)],[255]) ).
thf(412,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( in @ B @ C )
& ( in @ C @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(413,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( ( well_ordering @ B )
& ( subset @ A @ ( relation_field @ B ) ) )
=> ( ( relation_field @ ( relation_restriction @ B @ A ) )
= A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(414,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)],[261]) ).
thf(415,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(416,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(417,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[269]) ).
thf(418,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ( ( in @ A @ B )
<=> ( ordinal_subset @ ( succ @ A ) @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[270]) ).
thf(419,plain,
( ( ! [A: $i,B: $i] :
( ( ordinal @ B )
=> ~ ( ( subset @ A @ B )
& ( A != empty_set )
& ! [C: $i] :
( ( ordinal @ C )
=> ~ ( ( in @ C @ A )
& ! [D: $i] :
( ( ordinal @ D )
=> ( ( in @ D @ A )
=> ( ordinal_subset @ C @ D ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[272]) ).
thf(420,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( well_founded_relation @ B )
=> ( well_founded_relation @ ( relation_restriction @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[273]) ).
thf(421,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[276]) ).
thf(422,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[278]) ).
thf(423,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[279]) ).
thf(424,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( antisymmetric @ B )
=> ( antisymmetric @ ( relation_restriction @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[280]) ).
thf(425,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( transitive @ B )
=> ( transitive @ ( relation_restriction @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(426,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( connected @ B )
=> ( connected @ ( relation_restriction @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(427,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( reflexive @ B )
=> ( reflexive @ ( relation_restriction @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(428,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( subset @ ( fiber @ ( relation_restriction @ C @ A ) @ B ) @ ( fiber @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(429,plain,
( ( ! [A: $i] :
( ( epsilon_transitive @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ( ( proper_subset @ A @ B )
=> ( in @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(430,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( subset @ ( relation_field @ ( relation_restriction @ B @ A ) ) @ ( relation_field @ B ) )
& ( subset @ ( relation_field @ ( relation_restriction @ B @ A ) ) @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(431,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(432,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(433,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_field @ ( relation_restriction @ C @ B ) ) )
=> ( ( in @ A @ ( relation_field @ C ) )
& ( in @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(434,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(435,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( subset @ A @ B )
=> ( subset @ ( relation_inverse_image @ C @ A ) @ ( relation_inverse_image @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[304]) ).
thf(436,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_restriction @ C @ B ) )
<=> ( ( in @ A @ C )
& ( in @ A @ ( cartesian_product2 @ B @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(437,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( relation_of2_as_subset @ D @ C @ A )
=> ( ( subset @ A @ B )
=> ( relation_of2_as_subset @ D @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(438,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[321]) ).
thf(439,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[323]) ).
thf(440,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[325]) ).
thf(441,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[327]) ).
thf(442,plain,
( ( ! [A: $i] : ( in @ A @ ( succ @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(443,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(444,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( antisymmetric @ A )
<=> ! [B: $i,C: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ C @ B ) @ A ) )
=> ( B = C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(445,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(446,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( transitive @ A )
<=> ! [B: $i,C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ C @ D ) @ A ) )
=> ( in @ ( ordered_pair @ B @ D ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[346]) ).
thf(447,plain,
( ( ! [A: $i,B: $i] :
( ( ordinal @ B )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ( C = D )
& ? [F: $i] :
( ( ordinal @ F )
& ( D = F )
& ( in @ F @ A ) )
& ( C = E )
& ? [G: $i] :
( ( ordinal @ G )
& ( E = G )
& ( in @ G @ A ) ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ E @ ( succ @ B ) )
& ( E = D )
& ? [H: $i] :
( ( ordinal @ H )
& ( D = H )
& ( in @ H @ A ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(448,plain,
( ( ! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ordinal_subset @ A @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(449,plain,
( ( ! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ( ordinal_subset @ A @ B )
<=> ( subset @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(450,plain,
( ( ? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(451,plain,
$true = $true,
inference(unfold_def,[status(thm)],[81]) ).
thf(452,plain,
$true = $true,
inference(unfold_def,[status(thm)],[82]) ).
thf(453,plain,
$true = $true,
inference(unfold_def,[status(thm)],[83]) ).
thf(454,plain,
$true = $true,
inference(unfold_def,[status(thm)],[93]) ).
thf(455,plain,
$true = $true,
inference(unfold_def,[status(thm)],[94]) ).
thf(456,plain,
$true = $true,
inference(unfold_def,[status(thm)],[97]) ).
thf(457,plain,
$true = $true,
inference(unfold_def,[status(thm)],[98]) ).
thf(458,plain,
$true = $true,
inference(unfold_def,[status(thm)],[100]) ).
thf(459,plain,
$true = $true,
inference(unfold_def,[status(thm)],[101]) ).
thf(460,plain,
$true = $true,
inference(unfold_def,[status(thm)],[102]) ).
thf(461,plain,
$true = $true,
inference(unfold_def,[status(thm)],[104]) ).
thf(462,plain,
$true = $true,
inference(unfold_def,[status(thm)],[106]) ).
thf(463,plain,
$true = $true,
inference(unfold_def,[status(thm)],[107]) ).
thf(464,plain,
$true = $true,
inference(unfold_def,[status(thm)],[109]) ).
thf(465,plain,
$true = $true,
inference(unfold_def,[status(thm)],[110]) ).
thf(466,plain,
( ( ! [A: $i] : ( relation @ ( inclusion_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(467,plain,
$true = $true,
inference(unfold_def,[status(thm)],[112]) ).
thf(468,plain,
$true = $true,
inference(unfold_def,[status(thm)],[113]) ).
thf(469,plain,
$true = $true,
inference(unfold_def,[status(thm)],[114]) ).
thf(470,plain,
$true = $true,
inference(unfold_def,[status(thm)],[115]) ).
thf(471,plain,
$true = $true,
inference(unfold_def,[status(thm)],[116]) ).
thf(472,plain,
$true = $true,
inference(unfold_def,[status(thm)],[117]) ).
thf(473,plain,
$true = $true,
inference(unfold_def,[status(thm)],[118]) ).
thf(474,plain,
$true = $true,
inference(unfold_def,[status(thm)],[119]) ).
thf(475,plain,
$true = $true,
inference(unfold_def,[status(thm)],[120]) ).
thf(476,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
<=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(477,plain,
( ( ! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ( ordinal_subset @ A @ B )
| ( ordinal_subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(478,plain,
( ( ! [A: $i] :
( ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) )
=> ( ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[189]) ).
thf(479,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(480,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ( well_founded_relation @ ( inclusion_relation @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[217]) ).
thf(481,plain,
( ( ! [A: $i] : ( antisymmetric @ ( inclusion_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[227]) ).
thf(482,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ( connected @ ( inclusion_relation @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(483,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ( ~ ( ~ ( being_limit_ordinal @ A )
& ! [B: $i] :
( ( ordinal @ B )
=> ( A
!= ( succ @ B ) ) ) )
& ~ ( ? [B: $i] :
( ( ordinal @ B )
& ( A
= ( succ @ B ) ) )
& ( being_limit_ordinal @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(484,plain,
( ( ! [A: $i] : ( transitive @ ( inclusion_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[256]) ).
thf(485,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( well_ordering @ B )
=> ( well_ordering @ ( relation_restriction @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[271]) ).
thf(486,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ( in @ B @ A )
=> ( ( ordinal @ B )
& ( subset @ B @ A ) ) )
=> ( ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[274]) ).
thf(487,plain,
( ( ! [A: $i] : ( reflexive @ ( inclusion_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[277]) ).
thf(488,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ~ ( ~ ( in @ A @ B )
& ( A != B )
& ~ ( in @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(489,plain,
( ( ! [A: $i,B: $i] :
( ( ordinal @ B )
=> ( ( in @ A @ B )
=> ( ordinal @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286]) ).
thf(490,plain,
( ( ! [A: $i,B: $i] :
( ( ordinal @ B )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ ( succ @ B ) )
& ? [E: $i] :
( ( ordinal @ E )
& ( D = E )
& ( in @ E @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(491,plain,
( ( ! [A: $i] :
( ? [B: $i] :
( ( ordinal @ B )
& ( in @ B @ A ) )
=> ? [B: $i] :
( ( ordinal @ B )
& ( in @ B @ A )
& ! [C: $i] :
( ( ordinal @ C )
=> ( ( in @ C @ A )
=> ( ordinal_subset @ B @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(492,plain,
( ( ( ordinal @ sK1_A )
=> ( well_ordering @ ( inclusion_relation @ sK1_A ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[355]) ).
thf(493,plain,
( ( ordinal @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[492]) ).
thf(494,plain,
( ( well_ordering @ ( inclusion_relation @ sK1_A ) )
= $false ),
inference(standard_cnf,[status(thm)],[492]) ).
thf(495,plain,
( ( ~ ( well_ordering @ ( inclusion_relation @ sK1_A ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[494]) ).
thf(496,plain,
( ( ! [A: $i] :
( ! [SY268: $i] :
( ~ ( subset @ SY268 @ ( sK2_B @ A ) )
| ( are_equipotent @ SY268 @ ( sK2_B @ A ) )
| ( in @ SY268 @ ( sK2_B @ A ) ) )
& ! [SY269: $i] :
( ( ! [SY274: $i] :
( ~ ( subset @ SY274 @ SY269 )
| ( in @ SY274 @ ( sK3_SY270 @ SY269 @ A ) ) )
& ( in @ ( sK3_SY270 @ SY269 @ A ) @ ( sK2_B @ A ) ) )
| ~ ( in @ SY269 @ ( sK2_B @ A ) ) )
& ! [SY272: $i,SY273: $i] :
( ~ ( in @ SY272 @ ( sK2_B @ A ) )
| ~ ( subset @ SY273 @ SY272 )
| ( in @ SY273 @ ( sK2_B @ A ) ) )
& ( in @ A @ ( sK2_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[356]) ).
thf(497,plain,
( ( ! [A: $i,B: $i] :
( ( ! [SY275: $i] :
( ~ ( in @ SY275 @ B )
| ~ ( in @ SY275 @ ( sK4_C @ B @ A ) ) )
& ( in @ ( sK4_C @ B @ A ) @ B ) )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[357]) ).
thf(498,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[358]) ).
thf(499,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK5_C @ B @ A ) @ A )
| ~ ( in @ ( sK5_C @ B @ A ) @ B ) )
& ( ( in @ ( sK5_C @ B @ A ) @ A )
| ( in @ ( sK5_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[359]) ).
thf(500,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[360]) ).
thf(501,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[361]) ).
thf(502,plain,
( ( ( relation @ sK6_A )
& ( relation_empty_yielding @ sK6_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[362]) ).
thf(503,plain,
( ( ~ ( empty @ sK7_A )
& ( epsilon_transitive @ sK7_A )
& ( epsilon_connected @ sK7_A )
& ( ordinal @ sK7_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[363]) ).
thf(504,plain,
( ( ~ ( empty @ sK8_A )
& ( relation @ sK8_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[364]) ).
thf(505,plain,
( ( ( empty @ sK9_A )
& ( relation @ sK9_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[365]) ).
thf(506,plain,
( ( ( function @ sK10_A )
& ( relation @ sK10_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[366]) ).
thf(507,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[367]) ).
thf(508,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_connected @ ( union @ A ) ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_transitive @ ( union @ A ) ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ( ordinal @ ( union @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[368]) ).
thf(509,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[369]) ).
thf(510,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ~ ( empty @ ( succ @ A ) ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_transitive @ ( succ @ A ) ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_connected @ ( succ @ A ) ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ( ordinal @ ( succ @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[370]) ).
thf(511,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[371]) ).
thf(512,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[372]) ).
thf(513,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[374]) ).
thf(514,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] : ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[375]) ).
thf(515,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[377]) ).
thf(516,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[378]) ).
thf(517,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] : ( relation @ ( relation_restriction @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[379]) ).
thf(518,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ( proper_subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( A != B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[380]) ).
thf(519,plain,
( ( ! [A: $i] :
( ( A
!= ( union @ A ) )
| ( being_limit_ordinal @ A ) )
& ! [A: $i] :
( ~ ( being_limit_ordinal @ A )
| ( A
= ( union @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[381]) ).
thf(520,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK11_D @ C @ B @ A ) @ A )
| ( in @ ( sK11_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK11_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK11_D @ C @ B @ A ) @ A )
| ( in @ ( sK11_D @ C @ B @ A ) @ C ) )
& ( ~ ( in @ ( sK11_D @ C @ B @ A ) @ B )
| ( in @ ( sK11_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_difference @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_difference @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ~ ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[382]) ).
thf(521,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ~ ( reflexive @ A )
| ~ ( transitive @ A )
| ~ ( antisymmetric @ A )
| ~ ( connected @ A )
| ~ ( well_founded_relation @ A )
| ( well_ordering @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( reflexive @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( transitive @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( antisymmetric @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( connected @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( well_founded_relation @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[383]) ).
thf(522,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY276: $i] :
( ~ ( in @ ( sK13_C @ B @ A ) @ SY276 )
| ~ ( in @ SY276 @ A ) )
| ~ ( in @ ( sK13_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK13_C @ B @ A ) @ ( sK14_SY277 @ B @ A ) )
& ( in @ ( sK14_SY277 @ B @ A ) @ A ) )
| ( in @ ( sK13_C @ B @ A ) @ B ) ) )
| ( B
= ( union @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( union @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
( ~ ( in @ C @ D )
| ~ ( in @ D @ A ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( ( in @ C @ ( sK12_D @ C @ B @ A ) )
& ( in @ ( sK12_D @ C @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[384]) ).
thf(523,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK15_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK15_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK15_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK15_D @ C @ B @ A ) @ A )
| ( in @ ( sK15_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK15_D @ C @ B @ A ) @ B )
| ( in @ ( sK15_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_intersection2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_intersection2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ~ ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[385]) ).
thf(524,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK16_C @ B @ A ) @ A )
& ~ ( in @ ( sK16_C @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[386]) ).
thf(525,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( in @ ( ordered_pair @ ( sK17_C @ B @ A ) @ ( sK18_SY278 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK17_C @ B @ A ) @ ( sK18_SY278 @ B @ A ) ) @ B ) )
| ( subset @ A @ B ) )
& ! [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(extcnf_combined,[status(esa)],[387]) ).
thf(526,plain,
( ( ! [A: $i] :
( ( ( ( sK19_B @ A )
!= ( sK20_SY279 @ A ) )
& ( in @ ( sK19_B @ A ) @ A )
& ( in @ ( sK20_SY279 @ A ) @ A )
& ~ ( in @ ( sK19_B @ A ) @ ( sK20_SY279 @ A ) )
& ~ ( in @ ( sK20_SY279 @ A ) @ ( sK19_B @ A ) ) )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( epsilon_connected @ A )
| ! [B: $i,C: $i] :
( ( B = C )
| ~ ( in @ B @ A )
| ~ ( in @ C @ A )
| ( in @ B @ C )
| ( in @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[388]) ).
thf(527,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK21_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK21_D @ C @ B @ A ) @ A ) )
& ( ~ ( in @ ( sK21_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK21_D @ C @ B @ A ) @ B ) )
& ( ( in @ ( sK21_D @ C @ B @ A ) @ C )
| ( in @ ( sK21_D @ C @ B @ A ) @ A )
| ( in @ ( sK21_D @ C @ B @ A ) @ B ) ) )
| ( C
= ( set_union2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_union2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A )
| ( in @ D @ B ) )
& ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[389]) ).
thf(528,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK22_D @ C @ B @ A ) @ C )
| ( ( sK22_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK22_D @ C @ B @ A ) @ C )
| ( ( sK22_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK22_D @ C @ B @ A ) @ C )
| ( ( sK22_D @ C @ B @ A )
= A )
| ( ( sK22_D @ C @ B @ A )
= B ) ) )
| ( C
= ( unordered_pair @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( unordered_pair @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( D = A )
| ( D = B ) )
& ! [D: $i] :
( ( D != A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ( D != B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[390]) ).
thf(529,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK23_C @ B @ A ) @ ( sK24_SY280 @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK23_C @ B @ A ) @ ( sK24_SY280 @ B @ A ) ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK23_C @ B @ A ) @ ( sK24_SY280 @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK23_C @ B @ A ) @ ( sK24_SY280 @ B @ A ) ) @ B ) ) )
| ( A = B ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ( A != B )
| ( ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ ( ordered_pair @ C @ D ) @ B ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ B )
| ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[391]) ).
thf(530,plain,
( ( ! [A: $i] :
( ( ( in @ ( sK25_B @ A ) @ A )
& ~ ( subset @ ( sK25_B @ A ) @ A ) )
| ( epsilon_transitive @ A ) )
& ! [A: $i] :
( ~ ( epsilon_transitive @ A )
| ! [B: $i] :
( ~ ( in @ B @ A )
| ( subset @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[392]) ).
thf(531,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK26_C @ B @ A ) @ B )
| ~ ( subset @ ( sK26_C @ B @ A ) @ A ) )
& ( ( in @ ( sK26_C @ B @ A ) @ B )
| ( subset @ ( sK26_C @ B @ A ) @ A ) ) )
| ( B
= ( powerset @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( powerset @ A ) )
| ( ! [C: $i] :
( ~ ( in @ C @ B )
| ( subset @ C @ A ) )
& ! [C: $i] :
( ~ ( subset @ C @ A )
| ( in @ C @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[393]) ).
thf(532,plain,
( ( ! [A: $i] :
( ( in @ ( sK27_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[394]) ).
thf(533,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK28_C @ B @ A )
!= A )
| ~ ( in @ ( sK28_C @ B @ A ) @ B ) )
& ( ( ( sK28_C @ B @ A )
= A )
| ( in @ ( sK28_C @ B @ A ) @ B ) ) )
| ( B
= ( singleton @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( singleton @ A ) )
| ( ! [C: $i] :
( ( C != A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( C = A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[395]) ).
thf(534,plain,
( ( ! [A: $i] :
( ( ! [SY282: $i,SY283: $i] :
( ( sK31_B @ A )
!= ( ordered_pair @ SY282 @ SY283 ) )
& ( in @ ( sK31_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK29_C @ B @ A ) @ ( sK30_SY281 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[396]) ).
thf(535,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( ~ ( in @ ( sK32_E @ D @ C @ B @ A ) @ D )
| ( ( sK32_E @ D @ C @ B @ A )
!= C ) )
& ( ~ ( in @ ( sK32_E @ D @ C @ B @ A ) @ D )
| ( ( sK32_E @ D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK32_E @ D @ C @ B @ A ) @ D )
| ( ( sK32_E @ D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK32_E @ D @ C @ B @ A ) @ D )
| ( ( sK32_E @ D @ C @ B @ A )
= C )
| ( ( sK32_E @ D @ C @ B @ A )
= A )
| ( ( sK32_E @ D @ C @ B @ A )
= B ) ) )
| ( D
= ( unordered_triple @ A @ B @ C ) ) )
& ! [C: $i,D: $i] :
( ( D
!= ( unordered_triple @ A @ B @ C ) )
| ( ! [E: $i] :
( ~ ( in @ E @ D )
| ( E = C )
| ( E = A )
| ( E = B ) )
& ! [E: $i] :
( ( E != C )
| ( in @ E @ D ) )
& ! [E: $i] :
( ( E != A )
| ( in @ E @ D ) )
& ! [E: $i] :
( ( E != B )
| ( in @ E @ D ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[397]) ).
thf(536,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[398]) ).
thf(537,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( epsilon_transitive @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( ordinal @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[399]) ).
thf(538,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[400]) ).
thf(539,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[401]) ).
thf(540,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[402]) ).
thf(541,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ B )
| ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[403]) ).
thf(542,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[404]) ).
thf(543,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[406]) ).
thf(544,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[407]) ).
thf(545,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[408]) ).
thf(546,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ( ( ordinal @ ( sK33_B @ A ) )
& ( in @ ( sK33_B @ A ) @ A )
& ~ ( in @ ( succ @ ( sK33_B @ A ) ) @ A ) )
| ( being_limit_ordinal @ A ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ~ ( being_limit_ordinal @ A )
| ! [B: $i] :
( ~ ( ordinal @ B )
| ~ ( in @ B @ A )
| ( in @ ( succ @ B ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[409]) ).
thf(547,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[410]) ).
thf(548,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK34_C @ B @ A ) @ A )
& ( in @ ( sK34_C @ B @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ C @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[411]) ).
thf(549,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ C )
| ~ ( in @ C @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[412]) ).
thf(550,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ ( relation_field @ B ) )
| ~ ( well_ordering @ B )
| ( ( relation_field @ ( relation_restriction @ B @ A ) )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[413]) ).
thf(551,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ C )
| ( subset @ ( unordered_pair @ A @ B ) @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ A @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[414]) ).
thf(552,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[415]) ).
thf(553,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[417]) ).
thf(554,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ( ! [B: $i] :
( ~ ( ordinal @ B )
| ~ ( in @ A @ B )
| ( ordinal_subset @ ( succ @ A ) @ B ) )
& ! [B: $i] :
( ~ ( ordinal @ B )
| ~ ( ordinal_subset @ ( succ @ A ) @ B )
| ( in @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[418]) ).
thf(555,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ordinal @ B )
| ( ( ordinal @ ( sK35_C @ B @ A ) )
& ! [SY284: $i] :
( ~ ( ordinal @ SY284 )
| ~ ( in @ SY284 @ A )
| ( ordinal_subset @ ( sK35_C @ B @ A ) @ SY284 ) )
& ( in @ ( sK35_C @ B @ A ) @ A ) )
| ( A = empty_set )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[419]) ).
thf(556,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ~ ( well_founded_relation @ B )
| ( well_founded_relation @ ( relation_restriction @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[420]) ).
thf(557,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[422]) ).
thf(558,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[423]) ).
thf(559,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ~ ( antisymmetric @ B )
| ( antisymmetric @ ( relation_restriction @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[424]) ).
thf(560,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ~ ( transitive @ B )
| ( transitive @ ( relation_restriction @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[425]) ).
thf(561,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ~ ( connected @ B )
| ( connected @ ( relation_restriction @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[426]) ).
thf(562,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ~ ( reflexive @ B )
| ( reflexive @ ( relation_restriction @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[427]) ).
thf(563,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation @ C )
| ( subset @ ( fiber @ ( relation_restriction @ C @ A ) @ B ) @ ( fiber @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[428]) ).
thf(564,plain,
( ( ! [A: $i] :
( ~ ( epsilon_transitive @ A )
| ! [B: $i] :
( ~ ( ordinal @ B )
| ~ ( proper_subset @ A @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[429]) ).
thf(565,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_field @ ( relation_restriction @ B @ A ) ) @ ( relation_field @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_field @ ( relation_restriction @ B @ A ) ) @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[430]) ).
thf(566,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[431]) ).
thf(567,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ A @ C )
| ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[432]) ).
thf(568,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_field @ ( relation_restriction @ C @ B ) ) )
| ( in @ A @ ( relation_field @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_field @ ( relation_restriction @ C @ B ) ) )
| ( in @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[433]) ).
thf(569,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_inverse_image @ C @ A ) @ ( relation_inverse_image @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[435]) ).
thf(570,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ C )
| ~ ( in @ A @ ( cartesian_product2 @ B @ B ) )
| ( in @ A @ ( relation_restriction @ C @ B ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_restriction @ C @ B ) )
| ( in @ A @ C ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_restriction @ C @ B ) )
| ( in @ A @ ( cartesian_product2 @ B @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[436]) ).
thf(571,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( relation_of2_as_subset @ D @ C @ A )
| ~ ( subset @ A @ B )
| ( relation_of2_as_subset @ D @ C @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[437]) ).
thf(572,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[438]) ).
thf(573,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ D )
| ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[439]) ).
thf(574,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) ) )
& ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[440]) ).
thf(575,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[441]) ).
thf(576,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[443]) ).
thf(577,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( in @ ( ordered_pair @ ( sK36_B @ A ) @ ( sK37_SY285 @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK37_SY285 @ A ) @ ( sK36_B @ A ) ) @ A )
& ( ( sK36_B @ A )
!= ( sK37_SY285 @ A ) ) )
| ( antisymmetric @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( antisymmetric @ A )
| ! [B: $i,C: $i] :
( ~ ( in @ ( ordered_pair @ B @ C ) @ A )
| ~ ( in @ ( ordered_pair @ C @ B ) @ A )
| ( B = C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[444]) ).
thf(578,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[445]) ).
thf(579,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( in @ ( ordered_pair @ ( sK38_B @ A ) @ ( sK39_SY286 @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK39_SY286 @ A ) @ ( sK40_SY288 @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK38_B @ A ) @ ( sK40_SY288 @ A ) ) @ A ) )
| ( transitive @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( transitive @ A )
| ! [B: $i,C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ B @ C ) @ A )
| ~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ ( ordered_pair @ B @ D ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[446]) ).
thf(580,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ordinal @ B )
| ( ( ( sK44_C @ B @ A )
= ( sK45_SY295 @ B @ A ) )
& ( ( sK45_SY295 @ B @ A )
= ( sK48_SY300 @ B @ A ) )
& ( ordinal @ ( sK48_SY300 @ B @ A ) )
& ( in @ ( sK48_SY300 @ B @ A ) @ A )
& ( ( sK44_C @ B @ A )
= ( sK46_SY299 @ B @ A ) )
& ( ( sK46_SY299 @ B @ A )
= ( sK47_SY303 @ B @ A ) )
& ( ordinal @ ( sK47_SY303 @ B @ A ) )
& ( in @ ( sK47_SY303 @ B @ A ) @ A )
& ( ( sK45_SY295 @ B @ A )
!= ( sK46_SY299 @ B @ A ) ) )
| ( ! [SY289: $i] :
( ! [E: $i] :
( ( E != SY289 )
| ~ ( in @ E @ ( succ @ B ) ) )
| ! [H: $i] :
( ( SY289 != H )
| ~ ( ordinal @ H )
| ~ ( in @ H @ A ) )
| ( in @ SY289 @ ( sK41_C @ B @ A ) ) )
& ! [SY292: $i] :
( ~ ( in @ SY292 @ ( sK41_C @ B @ A ) )
| ( ( ( sK43_E @ SY292 @ B @ A )
= SY292 )
& ( in @ ( sK43_E @ SY292 @ B @ A ) @ ( succ @ B ) )
& ( SY292
= ( sK42_H @ SY292 @ B @ A ) )
& ( ordinal @ ( sK42_H @ SY292 @ B @ A ) )
& ( in @ ( sK42_H @ SY292 @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[447]) ).
thf(581,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ! [B: $i] :
~ ( ordinal @ B )
| ( ordinal_subset @ A @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[448]) ).
thf(582,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ordinal @ A )
| ~ ( ordinal @ B )
| ~ ( ordinal_subset @ A @ B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( ordinal @ A )
| ~ ( ordinal @ B )
| ~ ( subset @ A @ B )
| ( ordinal_subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[449]) ).
thf(583,plain,
( ( ( epsilon_connected @ sK49_A )
& ( epsilon_transitive @ sK49_A )
& ( ordinal @ sK49_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[450]) ).
thf(584,plain,
( ( ! [A: $i] :
( ~ ( epsilon_connected @ A )
| ~ ( epsilon_transitive @ A )
| ( ordinal @ A ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_transitive @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[476]) ).
thf(585,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ordinal @ A )
| ~ ( ordinal @ B )
| ( ordinal_subset @ A @ B )
| ( ordinal_subset @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[477]) ).
thf(586,plain,
( ( ! [A: $i] :
( ~ ( epsilon_connected @ A )
| ~ ( epsilon_transitive @ A )
| ( ordinal @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[478]) ).
thf(587,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_transitive @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[479]) ).
thf(588,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ( well_founded_relation @ ( inclusion_relation @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[480]) ).
thf(589,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ( connected @ ( inclusion_relation @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[482]) ).
thf(590,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ( being_limit_ordinal @ A )
| ( ( ordinal @ ( sK50_B @ A ) )
& ( A
= ( succ @ ( sK50_B @ A ) ) ) ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ! [B: $i] :
( ( A
!= ( succ @ B ) )
| ~ ( ordinal @ B ) )
| ~ ( being_limit_ordinal @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[483]) ).
thf(591,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ~ ( well_ordering @ B )
| ( well_ordering @ ( relation_restriction @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[485]) ).
thf(592,plain,
( ( ! [A: $i] :
( ( ( in @ ( sK51_B @ A ) @ A )
& ( ~ ( ordinal @ ( sK51_B @ A ) )
| ~ ( subset @ ( sK51_B @ A ) @ A ) ) )
| ( ordinal @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[486]) ).
thf(593,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ! [B: $i] :
( ~ ( ordinal @ B )
| ( in @ A @ B )
| ( A = B )
| ( in @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[488]) ).
thf(594,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ordinal @ B )
| ~ ( in @ A @ B )
| ( ordinal @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[489]) ).
thf(595,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ordinal @ B )
| ( ! [SY304: $i] :
( ! [E: $i] :
( ( SY304 != E )
| ~ ( ordinal @ E )
| ~ ( in @ E @ A ) )
| ~ ( in @ SY304 @ ( succ @ B ) )
| ( in @ SY304 @ ( sK52_C @ B @ A ) ) )
& ! [SY306: $i] :
( ~ ( in @ SY306 @ ( sK52_C @ B @ A ) )
| ( ( SY306
= ( sK53_E @ SY306 @ B @ A ) )
& ( ordinal @ ( sK53_E @ SY306 @ B @ A ) )
& ( in @ ( sK53_E @ SY306 @ B @ A ) @ A ) ) )
& ! [SY308: $i] :
( ~ ( in @ SY308 @ ( sK52_C @ B @ A ) )
| ( in @ SY308 @ ( succ @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[490]) ).
thf(596,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ~ ( in @ B @ A )
| ~ ( ordinal @ B ) )
| ( ! [SY309: $i] :
( ~ ( ordinal @ SY309 )
| ~ ( in @ SY309 @ A )
| ( ordinal_subset @ ( sK54_B @ A ) @ SY309 ) )
& ( in @ ( sK54_B @ A ) @ A )
& ( ordinal @ ( sK54_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[491]) ).
thf(597,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ~ ( in @ B @ A )
| ~ ( ordinal @ B ) )
| ( ! [SY309: $i] :
( ~ ( ordinal @ SY309 )
| ~ ( in @ SY309 @ A )
| ( ordinal_subset @ ( sK54_B @ A ) @ SY309 ) )
& ( in @ ( sK54_B @ A ) @ A )
& ( ordinal @ ( sK54_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[596]) ).
thf(598,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ordinal @ B )
| ( ! [SY304: $i] :
( ! [E: $i] :
( ( SY304 != E )
| ~ ( ordinal @ E )
| ~ ( in @ E @ A ) )
| ~ ( in @ SY304 @ ( succ @ B ) )
| ( in @ SY304 @ ( sK52_C @ B @ A ) ) )
& ! [SY306: $i] :
( ~ ( in @ SY306 @ ( sK52_C @ B @ A ) )
| ( ( SY306
= ( sK53_E @ SY306 @ B @ A ) )
& ( ordinal @ ( sK53_E @ SY306 @ B @ A ) )
& ( in @ ( sK53_E @ SY306 @ B @ A ) @ A ) ) )
& ! [SY308: $i] :
( ~ ( in @ SY308 @ ( sK52_C @ B @ A ) )
| ( in @ SY308 @ ( succ @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[595]) ).
thf(599,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ordinal @ B )
| ~ ( in @ A @ B )
| ( ordinal @ A ) ) )
= $true ),
inference(copy,[status(thm)],[594]) ).
thf(600,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ! [B: $i] :
( ~ ( ordinal @ B )
| ( in @ A @ B )
| ( A = B )
| ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[593]) ).
thf(601,plain,
( ( ! [A: $i] : ( reflexive @ ( inclusion_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[487]) ).
thf(602,plain,
( ( ! [A: $i] :
( ( ( in @ ( sK51_B @ A ) @ A )
& ( ~ ( ordinal @ ( sK51_B @ A ) )
| ~ ( subset @ ( sK51_B @ A ) @ A ) ) )
| ( ordinal @ A ) ) )
= $true ),
inference(copy,[status(thm)],[592]) ).
thf(603,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ~ ( well_ordering @ B )
| ( well_ordering @ ( relation_restriction @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[591]) ).
thf(604,plain,
( ( ! [A: $i] : ( transitive @ ( inclusion_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[484]) ).
thf(605,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ( being_limit_ordinal @ A )
| ( ( ordinal @ ( sK50_B @ A ) )
& ( A
= ( succ @ ( sK50_B @ A ) ) ) ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ! [B: $i] :
( ( A
!= ( succ @ B ) )
| ~ ( ordinal @ B ) )
| ~ ( being_limit_ordinal @ A ) ) )
= $true ),
inference(copy,[status(thm)],[590]) ).
thf(606,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ( connected @ ( inclusion_relation @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[589]) ).
thf(607,plain,
( ( ! [A: $i] : ( antisymmetric @ ( inclusion_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[481]) ).
thf(608,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ( well_founded_relation @ ( inclusion_relation @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[588]) ).
thf(609,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_transitive @ A ) ) )
= $true ),
inference(copy,[status(thm)],[587]) ).
thf(610,plain,
( ( ! [A: $i] :
( ~ ( epsilon_connected @ A )
| ~ ( epsilon_transitive @ A )
| ( ordinal @ A ) ) )
= $true ),
inference(copy,[status(thm)],[586]) ).
thf(611,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ordinal @ A )
| ~ ( ordinal @ B )
| ( ordinal_subset @ A @ B )
| ( ordinal_subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[585]) ).
thf(612,plain,
( ( ! [A: $i] :
( ~ ( epsilon_connected @ A )
| ~ ( epsilon_transitive @ A )
| ( ordinal @ A ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_transitive @ A ) ) )
= $true ),
inference(copy,[status(thm)],[584]) ).
thf(613,plain,
$true = $true,
inference(copy,[status(thm)],[475]) ).
thf(614,plain,
$true = $true,
inference(copy,[status(thm)],[474]) ).
thf(615,plain,
$true = $true,
inference(copy,[status(thm)],[473]) ).
thf(616,plain,
$true = $true,
inference(copy,[status(thm)],[472]) ).
thf(617,plain,
$true = $true,
inference(copy,[status(thm)],[471]) ).
thf(618,plain,
$true = $true,
inference(copy,[status(thm)],[470]) ).
thf(619,plain,
$true = $true,
inference(copy,[status(thm)],[469]) ).
thf(620,plain,
$true = $true,
inference(copy,[status(thm)],[468]) ).
thf(621,plain,
$true = $true,
inference(copy,[status(thm)],[467]) ).
thf(622,plain,
( ( ! [A: $i] : ( relation @ ( inclusion_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[466]) ).
thf(623,plain,
$true = $true,
inference(copy,[status(thm)],[465]) ).
thf(624,plain,
$true = $true,
inference(copy,[status(thm)],[464]) ).
thf(625,plain,
$true = $true,
inference(copy,[status(thm)],[463]) ).
thf(626,plain,
$true = $true,
inference(copy,[status(thm)],[462]) ).
thf(627,plain,
$true = $true,
inference(copy,[status(thm)],[461]) ).
thf(628,plain,
$true = $true,
inference(copy,[status(thm)],[460]) ).
thf(629,plain,
$true = $true,
inference(copy,[status(thm)],[459]) ).
thf(630,plain,
$true = $true,
inference(copy,[status(thm)],[458]) ).
thf(631,plain,
$true = $true,
inference(copy,[status(thm)],[457]) ).
thf(632,plain,
$true = $true,
inference(copy,[status(thm)],[456]) ).
thf(633,plain,
$true = $true,
inference(copy,[status(thm)],[455]) ).
thf(634,plain,
$true = $true,
inference(copy,[status(thm)],[454]) ).
thf(635,plain,
$true = $true,
inference(copy,[status(thm)],[453]) ).
thf(636,plain,
$true = $true,
inference(copy,[status(thm)],[452]) ).
thf(637,plain,
$true = $true,
inference(copy,[status(thm)],[451]) ).
thf(638,plain,
( ( ( epsilon_connected @ sK49_A )
& ( epsilon_transitive @ sK49_A )
& ( ordinal @ sK49_A ) )
= $true ),
inference(copy,[status(thm)],[583]) ).
thf(639,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ordinal @ A )
| ~ ( ordinal @ B )
| ~ ( ordinal_subset @ A @ B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( ordinal @ A )
| ~ ( ordinal @ B )
| ~ ( subset @ A @ B )
| ( ordinal_subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[582]) ).
thf(640,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ! [B: $i] :
~ ( ordinal @ B )
| ( ordinal_subset @ A @ A ) ) )
= $true ),
inference(copy,[status(thm)],[581]) ).
thf(641,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ordinal @ B )
| ( ( ( sK44_C @ B @ A )
= ( sK45_SY295 @ B @ A ) )
& ( ( sK45_SY295 @ B @ A )
= ( sK48_SY300 @ B @ A ) )
& ( ordinal @ ( sK48_SY300 @ B @ A ) )
& ( in @ ( sK48_SY300 @ B @ A ) @ A )
& ( ( sK44_C @ B @ A )
= ( sK46_SY299 @ B @ A ) )
& ( ( sK46_SY299 @ B @ A )
= ( sK47_SY303 @ B @ A ) )
& ( ordinal @ ( sK47_SY303 @ B @ A ) )
& ( in @ ( sK47_SY303 @ B @ A ) @ A )
& ( ( sK45_SY295 @ B @ A )
!= ( sK46_SY299 @ B @ A ) ) )
| ( ! [SY289: $i] :
( ! [E: $i] :
( ( E != SY289 )
| ~ ( in @ E @ ( succ @ B ) ) )
| ! [H: $i] :
( ( SY289 != H )
| ~ ( ordinal @ H )
| ~ ( in @ H @ A ) )
| ( in @ SY289 @ ( sK41_C @ B @ A ) ) )
& ! [SY292: $i] :
( ~ ( in @ SY292 @ ( sK41_C @ B @ A ) )
| ( ( ( sK43_E @ SY292 @ B @ A )
= SY292 )
& ( in @ ( sK43_E @ SY292 @ B @ A ) @ ( succ @ B ) )
& ( SY292
= ( sK42_H @ SY292 @ B @ A ) )
& ( ordinal @ ( sK42_H @ SY292 @ B @ A ) )
& ( in @ ( sK42_H @ SY292 @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[580]) ).
thf(642,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( in @ ( ordered_pair @ ( sK38_B @ A ) @ ( sK39_SY286 @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK39_SY286 @ A ) @ ( sK40_SY288 @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK38_B @ A ) @ ( sK40_SY288 @ A ) ) @ A ) )
| ( transitive @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( transitive @ A )
| ! [B: $i,C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ B @ C ) @ A )
| ~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ ( ordered_pair @ B @ D ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[579]) ).
thf(643,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[578]) ).
thf(644,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( in @ ( ordered_pair @ ( sK36_B @ A ) @ ( sK37_SY285 @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK37_SY285 @ A ) @ ( sK36_B @ A ) ) @ A )
& ( ( sK36_B @ A )
!= ( sK37_SY285 @ A ) ) )
| ( antisymmetric @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( antisymmetric @ A )
| ! [B: $i,C: $i] :
( ~ ( in @ ( ordered_pair @ B @ C ) @ A )
| ~ ( in @ ( ordered_pair @ C @ B ) @ A )
| ( B = C ) ) ) )
= $true ),
inference(copy,[status(thm)],[577]) ).
thf(645,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[576]) ).
thf(646,plain,
( ( ! [A: $i] : ( in @ A @ ( succ @ A ) ) )
= $true ),
inference(copy,[status(thm)],[442]) ).
thf(647,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[575]) ).
thf(648,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) ) )
& ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[574]) ).
thf(649,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ D )
| ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[573]) ).
thf(650,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[572]) ).
thf(651,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( relation_of2_as_subset @ D @ C @ A )
| ~ ( subset @ A @ B )
| ( relation_of2_as_subset @ D @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[571]) ).
thf(652,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ C )
| ~ ( in @ A @ ( cartesian_product2 @ B @ B ) )
| ( in @ A @ ( relation_restriction @ C @ B ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_restriction @ C @ B ) )
| ( in @ A @ C ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_restriction @ C @ B ) )
| ( in @ A @ ( cartesian_product2 @ B @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[570]) ).
thf(653,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_inverse_image @ C @ A ) @ ( relation_inverse_image @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[569]) ).
thf(654,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[434]) ).
thf(655,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_field @ ( relation_restriction @ C @ B ) ) )
| ( in @ A @ ( relation_field @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_field @ ( relation_restriction @ C @ B ) ) )
| ( in @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[568]) ).
thf(656,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ A @ C )
| ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[567]) ).
thf(657,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[566]) ).
thf(658,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_field @ ( relation_restriction @ B @ A ) ) @ ( relation_field @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_field @ ( relation_restriction @ B @ A ) ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[565]) ).
thf(659,plain,
( ( ! [A: $i] :
( ~ ( epsilon_transitive @ A )
| ! [B: $i] :
( ~ ( ordinal @ B )
| ~ ( proper_subset @ A @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[564]) ).
thf(660,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation @ C )
| ( subset @ ( fiber @ ( relation_restriction @ C @ A ) @ B ) @ ( fiber @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[563]) ).
thf(661,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ~ ( reflexive @ B )
| ( reflexive @ ( relation_restriction @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[562]) ).
thf(662,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ~ ( connected @ B )
| ( connected @ ( relation_restriction @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[561]) ).
thf(663,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ~ ( transitive @ B )
| ( transitive @ ( relation_restriction @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[560]) ).
thf(664,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ~ ( antisymmetric @ B )
| ( antisymmetric @ ( relation_restriction @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[559]) ).
thf(665,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[558]) ).
thf(666,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[557]) ).
thf(667,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[421]) ).
thf(668,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ~ ( well_founded_relation @ B )
| ( well_founded_relation @ ( relation_restriction @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[556]) ).
thf(669,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ordinal @ B )
| ( ( ordinal @ ( sK35_C @ B @ A ) )
& ! [SY284: $i] :
( ~ ( ordinal @ SY284 )
| ~ ( in @ SY284 @ A )
| ( ordinal_subset @ ( sK35_C @ B @ A ) @ SY284 ) )
& ( in @ ( sK35_C @ B @ A ) @ A ) )
| ( A = empty_set )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[555]) ).
thf(670,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ( ! [B: $i] :
( ~ ( ordinal @ B )
| ~ ( in @ A @ B )
| ( ordinal_subset @ ( succ @ A ) @ B ) )
& ! [B: $i] :
( ~ ( ordinal @ B )
| ~ ( ordinal_subset @ ( succ @ A ) @ B )
| ( in @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[554]) ).
thf(671,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[553]) ).
thf(672,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[416]) ).
thf(673,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[552]) ).
thf(674,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ C )
| ( subset @ ( unordered_pair @ A @ B ) @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ A @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[551]) ).
thf(675,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ ( relation_field @ B ) )
| ~ ( well_ordering @ B )
| ( ( relation_field @ ( relation_restriction @ B @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[550]) ).
thf(676,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ C )
| ~ ( in @ C @ A ) ) )
= $true ),
inference(copy,[status(thm)],[549]) ).
thf(677,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK34_C @ B @ A ) @ A )
& ( in @ ( sK34_C @ B @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ C @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[548]) ).
thf(678,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[547]) ).
thf(679,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ( ( ordinal @ ( sK33_B @ A ) )
& ( in @ ( sK33_B @ A ) @ A )
& ~ ( in @ ( succ @ ( sK33_B @ A ) ) @ A ) )
| ( being_limit_ordinal @ A ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ~ ( being_limit_ordinal @ A )
| ! [B: $i] :
( ~ ( ordinal @ B )
| ~ ( in @ B @ A )
| ( in @ ( succ @ B ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[546]) ).
thf(680,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[545]) ).
thf(681,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[544]) ).
thf(682,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[543]) ).
thf(683,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[405]) ).
thf(684,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[542]) ).
thf(685,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ B )
| ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[541]) ).
thf(686,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[540]) ).
thf(687,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[539]) ).
thf(688,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[538]) ).
thf(689,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( epsilon_transitive @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( ordinal @ A ) ) )
= $true ),
inference(copy,[status(thm)],[537]) ).
thf(690,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[536]) ).
thf(691,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( ~ ( in @ ( sK32_E @ D @ C @ B @ A ) @ D )
| ( ( sK32_E @ D @ C @ B @ A )
!= C ) )
& ( ~ ( in @ ( sK32_E @ D @ C @ B @ A ) @ D )
| ( ( sK32_E @ D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK32_E @ D @ C @ B @ A ) @ D )
| ( ( sK32_E @ D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK32_E @ D @ C @ B @ A ) @ D )
| ( ( sK32_E @ D @ C @ B @ A )
= C )
| ( ( sK32_E @ D @ C @ B @ A )
= A )
| ( ( sK32_E @ D @ C @ B @ A )
= B ) ) )
| ( D
= ( unordered_triple @ A @ B @ C ) ) )
& ! [C: $i,D: $i] :
( ( D
!= ( unordered_triple @ A @ B @ C ) )
| ( ! [E: $i] :
( ~ ( in @ E @ D )
| ( E = C )
| ( E = A )
| ( E = B ) )
& ! [E: $i] :
( ( E != C )
| ( in @ E @ D ) )
& ! [E: $i] :
( ( E != A )
| ( in @ E @ D ) )
& ! [E: $i] :
( ( E != B )
| ( in @ E @ D ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[535]) ).
thf(692,plain,
( ( ! [A: $i] :
( ( ! [SY282: $i,SY283: $i] :
( ( sK31_B @ A )
!= ( ordered_pair @ SY282 @ SY283 ) )
& ( in @ ( sK31_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK29_C @ B @ A ) @ ( sK30_SY281 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[534]) ).
thf(693,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK28_C @ B @ A )
!= A )
| ~ ( in @ ( sK28_C @ B @ A ) @ B ) )
& ( ( ( sK28_C @ B @ A )
= A )
| ( in @ ( sK28_C @ B @ A ) @ B ) ) )
| ( B
= ( singleton @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( singleton @ A ) )
| ( ! [C: $i] :
( ( C != A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( C = A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[533]) ).
thf(694,plain,
( ( ! [A: $i] :
( ( in @ ( sK27_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[532]) ).
thf(695,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK26_C @ B @ A ) @ B )
| ~ ( subset @ ( sK26_C @ B @ A ) @ A ) )
& ( ( in @ ( sK26_C @ B @ A ) @ B )
| ( subset @ ( sK26_C @ B @ A ) @ A ) ) )
| ( B
= ( powerset @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( powerset @ A ) )
| ( ! [C: $i] :
( ~ ( in @ C @ B )
| ( subset @ C @ A ) )
& ! [C: $i] :
( ~ ( subset @ C @ A )
| ( in @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[531]) ).
thf(696,plain,
( ( ! [A: $i] :
( ( ( in @ ( sK25_B @ A ) @ A )
& ~ ( subset @ ( sK25_B @ A ) @ A ) )
| ( epsilon_transitive @ A ) )
& ! [A: $i] :
( ~ ( epsilon_transitive @ A )
| ! [B: $i] :
( ~ ( in @ B @ A )
| ( subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[530]) ).
thf(697,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK23_C @ B @ A ) @ ( sK24_SY280 @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK23_C @ B @ A ) @ ( sK24_SY280 @ B @ A ) ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK23_C @ B @ A ) @ ( sK24_SY280 @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK23_C @ B @ A ) @ ( sK24_SY280 @ B @ A ) ) @ B ) ) )
| ( A = B ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ( A != B )
| ( ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ ( ordered_pair @ C @ D ) @ B ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ B )
| ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[529]) ).
thf(698,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK22_D @ C @ B @ A ) @ C )
| ( ( sK22_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK22_D @ C @ B @ A ) @ C )
| ( ( sK22_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK22_D @ C @ B @ A ) @ C )
| ( ( sK22_D @ C @ B @ A )
= A )
| ( ( sK22_D @ C @ B @ A )
= B ) ) )
| ( C
= ( unordered_pair @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( unordered_pair @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( D = A )
| ( D = B ) )
& ! [D: $i] :
( ( D != A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ( D != B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[528]) ).
thf(699,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK21_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK21_D @ C @ B @ A ) @ A ) )
& ( ~ ( in @ ( sK21_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK21_D @ C @ B @ A ) @ B ) )
& ( ( in @ ( sK21_D @ C @ B @ A ) @ C )
| ( in @ ( sK21_D @ C @ B @ A ) @ A )
| ( in @ ( sK21_D @ C @ B @ A ) @ B ) ) )
| ( C
= ( set_union2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_union2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A )
| ( in @ D @ B ) )
& ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[527]) ).
thf(700,plain,
( ( ! [A: $i] :
( ( ( ( sK19_B @ A )
!= ( sK20_SY279 @ A ) )
& ( in @ ( sK19_B @ A ) @ A )
& ( in @ ( sK20_SY279 @ A ) @ A )
& ~ ( in @ ( sK19_B @ A ) @ ( sK20_SY279 @ A ) )
& ~ ( in @ ( sK20_SY279 @ A ) @ ( sK19_B @ A ) ) )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( epsilon_connected @ A )
| ! [B: $i,C: $i] :
( ( B = C )
| ~ ( in @ B @ A )
| ~ ( in @ C @ A )
| ( in @ B @ C )
| ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[526]) ).
thf(701,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( in @ ( ordered_pair @ ( sK17_C @ B @ A ) @ ( sK18_SY278 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK17_C @ B @ A ) @ ( sK18_SY278 @ B @ A ) ) @ B ) )
| ( subset @ A @ B ) )
& ! [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)],[525]) ).
thf(702,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK16_C @ B @ A ) @ A )
& ~ ( in @ ( sK16_C @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[524]) ).
thf(703,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK15_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK15_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK15_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK15_D @ C @ B @ A ) @ A )
| ( in @ ( sK15_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK15_D @ C @ B @ A ) @ B )
| ( in @ ( sK15_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_intersection2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_intersection2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ~ ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[523]) ).
thf(704,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY276: $i] :
( ~ ( in @ ( sK13_C @ B @ A ) @ SY276 )
| ~ ( in @ SY276 @ A ) )
| ~ ( in @ ( sK13_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK13_C @ B @ A ) @ ( sK14_SY277 @ B @ A ) )
& ( in @ ( sK14_SY277 @ B @ A ) @ A ) )
| ( in @ ( sK13_C @ B @ A ) @ B ) ) )
| ( B
= ( union @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( union @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
( ~ ( in @ C @ D )
| ~ ( in @ D @ A ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( ( in @ C @ ( sK12_D @ C @ B @ A ) )
& ( in @ ( sK12_D @ C @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[522]) ).
thf(705,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ~ ( reflexive @ A )
| ~ ( transitive @ A )
| ~ ( antisymmetric @ A )
| ~ ( connected @ A )
| ~ ( well_founded_relation @ A )
| ( well_ordering @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( reflexive @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( transitive @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( antisymmetric @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( connected @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( well_founded_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[521]) ).
thf(706,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK11_D @ C @ B @ A ) @ A )
| ( in @ ( sK11_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK11_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK11_D @ C @ B @ A ) @ A )
| ( in @ ( sK11_D @ C @ B @ A ) @ C ) )
& ( ~ ( in @ ( sK11_D @ C @ B @ A ) @ B )
| ( in @ ( sK11_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_difference @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_difference @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ~ ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[520]) ).
thf(707,plain,
( ( ! [A: $i] :
( ( A
!= ( union @ A ) )
| ( being_limit_ordinal @ A ) )
& ! [A: $i] :
( ~ ( being_limit_ordinal @ A )
| ( A
= ( union @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[519]) ).
thf(708,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ( proper_subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( A != B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[518]) ).
thf(709,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] : ( relation @ ( relation_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[517]) ).
thf(710,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[516]) ).
thf(711,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[515]) ).
thf(712,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[376]) ).
thf(713,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] : ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[514]) ).
thf(714,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[513]) ).
thf(715,plain,
( ( ! [A: $i] :
~ ( empty @ ( succ @ A ) ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(716,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[512]) ).
thf(717,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[511]) ).
thf(718,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ~ ( empty @ ( succ @ A ) ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_transitive @ ( succ @ A ) ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_connected @ ( succ @ A ) ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ( ordinal @ ( succ @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[510]) ).
thf(719,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[509]) ).
thf(720,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_connected @ ( union @ A ) ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_transitive @ ( union @ A ) ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ( ordinal @ ( union @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[508]) ).
thf(721,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[507]) ).
thf(722,plain,
( ( ( function @ sK10_A )
& ( relation @ sK10_A ) )
= $true ),
inference(copy,[status(thm)],[506]) ).
thf(723,plain,
( ( ( empty @ sK9_A )
& ( relation @ sK9_A ) )
= $true ),
inference(copy,[status(thm)],[505]) ).
thf(724,plain,
( ( ~ ( empty @ sK8_A )
& ( relation @ sK8_A ) )
= $true ),
inference(copy,[status(thm)],[504]) ).
thf(725,plain,
( ( ~ ( empty @ sK7_A )
& ( epsilon_transitive @ sK7_A )
& ( epsilon_connected @ sK7_A )
& ( ordinal @ sK7_A ) )
= $true ),
inference(copy,[status(thm)],[503]) ).
thf(726,plain,
( ( ( relation @ sK6_A )
& ( relation_empty_yielding @ sK6_A ) )
= $true ),
inference(copy,[status(thm)],[502]) ).
thf(727,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[501]) ).
thf(728,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[500]) ).
thf(729,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK5_C @ B @ A ) @ A )
| ~ ( in @ ( sK5_C @ B @ A ) @ B ) )
& ( ( in @ ( sK5_C @ B @ A ) @ A )
| ( in @ ( sK5_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[499]) ).
thf(730,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[498]) ).
thf(731,plain,
( ( ! [A: $i,B: $i] :
( ( ! [SY275: $i] :
( ~ ( in @ SY275 @ B )
| ~ ( in @ SY275 @ ( sK4_C @ B @ A ) ) )
& ( in @ ( sK4_C @ B @ A ) @ B ) )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[497]) ).
thf(732,plain,
( ( ! [A: $i] :
( ! [SY268: $i] :
( ~ ( subset @ SY268 @ ( sK2_B @ A ) )
| ( are_equipotent @ SY268 @ ( sK2_B @ A ) )
| ( in @ SY268 @ ( sK2_B @ A ) ) )
& ! [SY269: $i] :
( ( ! [SY274: $i] :
( ~ ( subset @ SY274 @ SY269 )
| ( in @ SY274 @ ( sK3_SY270 @ SY269 @ A ) ) )
& ( in @ ( sK3_SY270 @ SY269 @ A ) @ ( sK2_B @ A ) ) )
| ~ ( in @ SY269 @ ( sK2_B @ A ) ) )
& ! [SY272: $i,SY273: $i] :
( ~ ( in @ SY272 @ ( sK2_B @ A ) )
| ~ ( subset @ SY273 @ SY272 )
| ( in @ SY273 @ ( sK2_B @ A ) ) )
& ( in @ A @ ( sK2_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[496]) ).
thf(733,plain,
( ( ordinal @ sK1_A )
= $true ),
inference(copy,[status(thm)],[493]) ).
thf(734,plain,
( ( ~ ( well_ordering @ ( inclusion_relation @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[495]) ).
thf(735,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[643]) ).
thf(736,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX0 @ ( cartesian_product2 @ SX1 @ SX1 ) )
| ( in @ SX0 @ ( relation_restriction @ SX2 @ SX1 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_restriction @ SX2 @ SX1 ) )
| ( in @ SX0 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_restriction @ SX2 @ SX1 ) )
| ( in @ SX0 @ ( cartesian_product2 @ SX1 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[652]) ).
thf(737,plain,
( ( ~ ( ~ ( function @ sK10_A )
| ~ ( relation @ sK10_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[722]) ).
thf(738,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ~ ( ordinal @ ( sK33_B @ SX0 ) )
| ~ ~ ( ~ ( in @ ( sK33_B @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( succ @ ( sK33_B @ SX0 ) ) @ SX0 ) ) )
| ( being_limit_ordinal @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( being_limit_ordinal @ SX0 )
| ! [SX1: $i] :
( ~ ( ordinal @ SX1 )
| ~ ( in @ SX1 @ SX0 )
| ( in @ ( succ @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[679]) ).
thf(739,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ordinal @ SX1 )
| ~ ( in @ SX0 @ SX1 )
| ( ordinal_subset @ ( succ @ SX0 ) @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( ordinal @ SX1 )
| ~ ( ordinal_subset @ ( succ @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[670]) ).
thf(740,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ordinal @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ( SX2 != SX3 )
| ~ ( ordinal @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ~ ( in @ SX2 @ ( succ @ SX1 ) )
| ( in @ SX2 @ ( sK52_C @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( sK52_C @ SX1 @ SX0 ) )
| ~ ( ~ ~ ( ( SX2
!= ( sK53_E @ SX2 @ SX1 @ SX0 ) )
| ~ ( ordinal @ ( sK53_E @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK53_E @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( sK52_C @ SX1 @ SX0 ) )
| ( in @ SX2 @ ( succ @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[598]) ).
thf(741,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] : ( subset @ ( cartesian_product2 @ SX0 @ SX2 ) @ ( cartesian_product2 @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] : ( subset @ ( cartesian_product2 @ SX2 @ SX0 ) @ ( cartesian_product2 @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[648]) ).
thf(742,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( epsilon_connected @ SX0 )
| ~ ( epsilon_transitive @ SX0 )
| ( ordinal @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[612]) ).
thf(743,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX2 )
| ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX0 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[674]) ).
thf(744,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( empty @ ( succ @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ ( succ @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ ( succ @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( ordinal @ ( succ @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[718]) ).
thf(745,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ ( sK14_SY277 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK14_SY277 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK12_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[704]) ).
thf(746,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK31_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK31_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK29_C @ SX1 @ SX0 ) @ ( sK30_SY281 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[692]) ).
thf(747,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( ( ( sK19_B @ SX0 )
!= ( sK20_SY279 @ SX0 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_B @ SX0 ) @ SX0 )
| ~ ( in @ ( sK20_SY279 @ SX0 ) @ SX0 ) )
| ~ ~ ( in @ ( sK19_B @ SX0 ) @ ( sK20_SY279 @ SX0 ) ) ) )
| ~ ~ ( in @ ( sK20_SY279 @ SX0 ) @ ( sK19_B @ SX0 ) ) )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( epsilon_connected @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( SX1 = SX2 )
| ~ ( in @ SX1 @ SX0 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX1 @ SX2 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[700]) ).
thf(748,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[708]) ).
thf(749,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( reflexive @ SX0 )
| ~ ( transitive @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ~ ( connected @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ( well_ordering @ SX0 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( well_founded_relation @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[705]) ).
thf(750,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ( in @ ( sK51_B @ SX0 ) @ SX0 )
| ~ ( ~ ( ordinal @ ( sK51_B @ SX0 ) )
| ~ ( subset @ ( sK51_B @ SX0 ) @ SX0 ) ) )
| ( ordinal @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[602]) ).
thf(751,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( sK4_C @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK4_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[731]) ).
thf(752,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( in @ ( sK27_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[694]) ).
thf(753,plain,
( ( ~ ( ~ ( relation @ sK6_A )
| ~ ( relation_empty_yielding @ sK6_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[726]) ).
thf(754,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK34_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK34_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[677]) ).
thf(755,plain,
( ( ~ ( ~ ( empty @ sK9_A )
| ~ ( relation @ sK9_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[723]) ).
thf(756,plain,
( ( ~ ( ~ ~ ( empty @ sK8_A )
| ~ ( relation @ sK8_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[724]) ).
thf(757,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK28_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK28_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[693]) ).
thf(758,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK7_A )
| ~ ( epsilon_transitive @ sK7_A ) )
| ~ ( epsilon_connected @ sK7_A ) )
| ~ ( ordinal @ sK7_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[725]) ).
thf(759,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ordinal @ SX1 )
| ~ ( ~ ( ordinal @ ( sK35_C @ SX1 @ SX0 ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ~ ( ordinal @ SX2 )
| ~ ( in @ SX2 @ SX0 )
| ( ordinal_subset @ ( sK35_C @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( in @ ( sK35_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX0 = empty_set )
| ~ ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[669]) ).
thf(760,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK21_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK21_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ~ ( in @ ( sK21_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK21_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ( ( in @ ( sK21_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( in @ ( sK21_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK21_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX2
= ( set_union2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_union2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[699]) ).
thf(761,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK26_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK26_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK26_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK26_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[695]) ).
thf(762,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK15_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK15_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK15_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ( in @ ( sK15_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK15_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) )
| ( SX2
= ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[703]) ).
thf(763,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ ( union @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ ( union @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( ordinal @ ( union @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[720]) ).
thf(764,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ordinal @ SX1 )
| ~ ( ordinal_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ordinal @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( ordinal_subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[639]) ).
thf(765,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ~ ( ordinal @ SX1 ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ordinal @ SX1 )
| ~ ( in @ SX1 @ SX0 )
| ( ordinal_subset @ ( sK54_B @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ( in @ ( sK54_B @ SX0 ) @ SX0 )
| ~ ( ordinal @ ( sK54_B @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[597]) ).
thf(766,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ordinal @ SX1 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK44_C @ SX1 @ SX0 )
!= ( sK45_SY295 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ~ ( ( ( sK45_SY295 @ SX1 @ SX0 )
!= ( sK48_SY300 @ SX1 @ SX0 ) )
| ~ ( ordinal @ ( sK48_SY300 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK48_SY300 @ SX1 @ SX0 ) @ SX0 ) ) )
| ( ( sK44_C @ SX1 @ SX0 )
!= ( sK46_SY299 @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ~ ( ( ( sK46_SY299 @ SX1 @ SX0 )
!= ( sK47_SY303 @ SX1 @ SX0 ) )
| ~ ( ordinal @ ( sK47_SY303 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK47_SY303 @ SX1 @ SX0 ) @ SX0 ) ) )
| ~ ( ( ( sK45_SY295 @ SX1 @ SX0 )
!= ( sK46_SY299 @ SX1 @ SX0 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ( SX3 != SX2 )
| ~ ( in @ SX3 @ ( succ @ SX1 ) ) )
| ! [SX3: $i] :
( ( SX2 != SX3 )
| ~ ( ordinal @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ ( sK41_C @ SX1 @ SX0 ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( sK41_C @ SX1 @ SX0 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SX2 @ SX1 @ SX0 )
!= SX2 )
| ~ ( in @ ( sK43_E @ SX2 @ SX1 @ SX0 ) @ ( succ @ SX1 ) ) )
| ~ ~ ( ~ ~ ( ( SX2
!= ( sK42_H @ SX2 @ SX1 @ SX0 ) )
| ~ ( ordinal @ ( sK42_H @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK42_H @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[641]) ).
thf(767,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK23_C @ SX1 @ SX0 ) @ ( sK24_SY280 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK23_C @ SX1 @ SX0 ) @ ( sK24_SY280 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK23_C @ SX1 @ SX0 ) @ ( sK24_SY280 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK23_C @ SX1 @ SX0 ) @ ( sK24_SY280 @ SX1 @ SX0 ) ) @ SX1 ) ) )
| ( SX0 = SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ( 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 ) @ SX1 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[697]) ).
thf(768,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[609]) ).
thf(769,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK22_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK22_D @ SX2 @ SX1 @ SX0 )
!= SX0 ) )
| ~ ( ~ ( in @ ( sK22_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK22_D @ SX2 @ SX1 @ SX0 )
!= SX1 ) ) )
| ~ ( ( in @ ( sK22_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK22_D @ SX2 @ SX1 @ SX0 )
= SX0 )
| ( ( sK22_D @ SX2 @ SX1 @ SX0 )
= SX1 ) ) )
| ( SX2
= ( unordered_pair @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( unordered_pair @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ( SX3 != SX0 )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SX1 )
| ( in @ SX3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[698]) ).
thf(770,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ( in @ ( sK25_B @ SX0 ) @ SX0 )
| ~ ~ ( subset @ ( sK25_B @ SX0 ) @ SX0 ) )
| ( epsilon_transitive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( epsilon_transitive @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[696]) ).
thf(771,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX1 @ ( sK2_B @ SX0 ) )
| ( are_equipotent @ SX1 @ ( sK2_B @ SX0 ) )
| ( in @ SX1 @ ( sK2_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK3_SY270 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK3_SY270 @ SX1 @ SX0 ) @ ( sK2_B @ SX0 ) ) )
| ~ ( in @ SX1 @ ( sK2_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( sK2_B @ SX0 ) )
| ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK2_B @ SX0 ) ) )
| ~ ( in @ SX0 @ ( sK2_B @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[732]) ).
thf(772,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_field @ ( relation_restriction @ SX2 @ SX1 ) ) )
| ( in @ SX0 @ ( relation_field @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_field @ ( relation_restriction @ SX2 @ SX1 ) ) )
| ( in @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[655]) ).
thf(773,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK17_C @ SX1 @ SX0 ) @ ( sK18_SY278 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( in @ ( ordered_pair @ ( sK17_C @ SX1 @ SX0 ) @ ( sK18_SY278 @ SX1 @ SX0 ) ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[701]) ).
thf(774,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK16_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK16_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[702]) ).
thf(775,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK11_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK11_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK11_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK11_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK11_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( in @ ( sK11_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK11_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) )
| ( SX2
= ( set_difference @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_difference @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ~ ( in @ SX3 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[706]) ).
thf(776,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_field @ ( relation_restriction @ SX1 @ SX0 ) ) @ ( relation_field @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_field @ ( relation_restriction @ SX1 @ SX0 ) ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[658]) ).
thf(777,plain,
( ( ~ ( ~ ~ ( ~ ( epsilon_connected @ sK49_A )
| ~ ( epsilon_transitive @ sK49_A ) )
| ~ ( ordinal @ sK49_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[638]) ).
thf(778,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK36_B @ SX0 ) @ ( sK37_SY285 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK37_SY285 @ SX0 ) @ ( sK36_B @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK36_B @ SX0 )
!= ( sK37_SY285 @ SX0 ) ) ) )
| ( antisymmetric @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX2 @ SX1 ) @ SX0 )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[644]) ).
thf(779,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[690]) ).
thf(780,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK38_B @ SX0 ) @ ( sK39_SY286 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK39_SY286 @ SX0 ) @ ( sK40_SY288 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK38_B @ SX0 ) @ ( sK40_SY288 @ SX0 ) ) @ SX0 ) )
| ( transitive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( transitive @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ ( ordered_pair @ SX1 @ SX3 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[642]) ).
thf(781,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[729]) ).
thf(782,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0
!= ( union @ SX0 ) )
| ( being_limit_ordinal @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( being_limit_ordinal @ SX0 )
| ( SX0
= ( union @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[707]) ).
thf(783,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( ordinal @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[689]) ).
thf(784,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( being_limit_ordinal @ SX0 )
| ~ ( ~ ( ordinal @ ( sK50_B @ SX0 ) )
| ( SX0
!= ( succ @ ( sK50_B @ SX0 ) ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ! [SX1: $i] :
( ( SX0
!= ( succ @ SX1 ) )
| ~ ( ordinal @ SX1 ) )
| ~ ( being_limit_ordinal @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[605]) ).
thf(785,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[673]) ).
thf(786,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK32_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 )
| ( ( sK32_E @ SX3 @ SX2 @ SX1 @ SX0 )
!= SX2 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK32_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 )
| ( ( sK32_E @ SX3 @ SX2 @ SX1 @ SX0 )
!= SX0 ) )
| ~ ( ~ ( in @ ( sK32_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 )
| ( ( sK32_E @ SX3 @ SX2 @ SX1 @ SX0 )
!= SX1 ) ) ) )
| ~ ( ( in @ ( sK32_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 )
| ( ( sK32_E @ SX3 @ SX2 @ SX1 @ SX0 )
= SX2 )
| ( ( sK32_E @ SX3 @ SX2 @ SX1 @ SX0 )
= SX0 )
| ( ( sK32_E @ SX3 @ SX2 @ SX1 @ SX0 )
= SX1 ) ) )
| ( SX3
= ( unordered_triple @ SX0 @ SX1 @ SX2 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( SX3
!= ( unordered_triple @ SX0 @ SX1 @ SX2 ) )
| ~ ( ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( SX4 = SX2 )
| ( SX4 = SX0 )
| ( SX4 = SX1 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ( SX4 != SX2 )
| ( in @ SX4 @ SX3 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ( SX4 != SX0 )
| ( in @ SX4 @ SX3 ) )
| ~ ! [SX4: $i] :
( ( SX4 != SX1 )
| ( in @ SX4 @ SX3 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[691]) ).
thf(787,plain,
! [SV1: $i] :
( ( ! [SY310: $i] :
( ~ ( ordinal @ SY310 )
| ~ ( in @ SV1 @ SY310 )
| ( ordinal @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(788,plain,
! [SV2: $i] :
( ( ~ ( ordinal @ SV2 )
| ! [SY311: $i] :
( ~ ( ordinal @ SY311 )
| ( in @ SV2 @ SY311 )
| ( SV2 = SY311 )
| ( in @ SY311 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(789,plain,
! [SV3: $i] :
( ( reflexive @ ( inclusion_relation @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(790,plain,
! [SV4: $i] :
( ( ! [SY312: $i] :
( ~ ( relation @ SY312 )
| ~ ( well_ordering @ SY312 )
| ( well_ordering @ ( relation_restriction @ SY312 @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(791,plain,
! [SV5: $i] :
( ( transitive @ ( inclusion_relation @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(792,plain,
! [SV6: $i] :
( ( ~ ( ordinal @ SV6 )
| ( connected @ ( inclusion_relation @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(793,plain,
! [SV7: $i] :
( ( antisymmetric @ ( inclusion_relation @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(794,plain,
! [SV8: $i] :
( ( ~ ( ordinal @ SV8 )
| ( well_founded_relation @ ( inclusion_relation @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(795,plain,
! [SV9: $i] :
( ( ~ ( epsilon_connected @ SV9 )
| ~ ( epsilon_transitive @ SV9 )
| ( ordinal @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(796,plain,
! [SV10: $i] :
( ( ! [SY313: $i] :
( ~ ( ordinal @ SV10 )
| ~ ( ordinal @ SY313 )
| ( ordinal_subset @ SV10 @ SY313 )
| ( ordinal_subset @ SY313 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(797,plain,
! [SV11: $i] :
( ( relation @ ( inclusion_relation @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(798,plain,
! [SV12: $i] :
( ( ~ ( ordinal @ SV12 )
| ! [B: $i] :
~ ( ordinal @ B )
| ( ordinal_subset @ SV12 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(799,plain,
! [SV13: $i] :
( ( ! [SY315: $i] :
( ~ ( in @ SV13 @ SY315 )
| ( subset @ SV13 @ ( union @ SY315 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(800,plain,
! [SV14: $i] :
( ( in @ SV14 @ ( succ @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(801,plain,
! [SV15: $i] :
( ( ! [SY316: $i] :
( ~ ( relation @ SY316 )
| ( subset @ ( relation_rng_restriction @ SV15 @ SY316 ) @ SY316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(802,plain,
! [SV16: $i] :
( ( ! [SY317: $i,SY318: $i,SY319: $i] :
( ~ ( subset @ SV16 @ SY317 )
| ~ ( subset @ SY318 @ SY319 )
| ( subset @ ( cartesian_product2 @ SV16 @ SY318 ) @ ( cartesian_product2 @ SY317 @ SY319 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(803,plain,
! [SV17: $i] :
( ( ! [SY320: $i] :
( ~ ( subset @ SV17 @ SY320 )
| ( ( set_union2 @ SV17 @ SY320 )
= SY320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(804,plain,
! [SV18: $i] :
( ( ! [SY321: $i,SY322: $i,SY323: $i] :
( ~ ( relation_of2_as_subset @ SY323 @ SY322 @ SV18 )
| ~ ( subset @ SV18 @ SY321 )
| ( relation_of2_as_subset @ SY323 @ SY322 @ SY321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(805,plain,
! [SV19: $i] :
( ( ! [SY324: $i,SY325: $i] :
( ~ ( relation @ SY325 )
| ~ ( subset @ SV19 @ SY324 )
| ( subset @ ( relation_inverse_image @ SY325 @ SV19 ) @ ( relation_inverse_image @ SY325 @ SY324 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(806,plain,
! [SV20: $i] :
( ( ! [SY326: $i] : ( subset @ ( set_intersection2 @ SV20 @ SY326 ) @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(807,plain,
! [SV21: $i] :
( ( ! [SY327: $i,SY328: $i] :
( ~ ( subset @ SV21 @ SY327 )
| ~ ( subset @ SV21 @ SY328 )
| ( subset @ SV21 @ ( set_intersection2 @ SY327 @ SY328 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(808,plain,
! [SV22: $i] :
( ( ! [SY329: $i,SY330: $i] :
( ~ ( subset @ SV22 @ SY329 )
| ~ ( subset @ SY329 @ SY330 )
| ( subset @ SV22 @ SY330 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(809,plain,
! [SV23: $i] :
( ( ~ ( epsilon_transitive @ SV23 )
| ! [SY331: $i] :
( ~ ( ordinal @ SY331 )
| ~ ( proper_subset @ SV23 @ SY331 )
| ( in @ SV23 @ SY331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(810,plain,
! [SV24: $i] :
( ( ! [SY332: $i,SY333: $i] :
( ~ ( relation @ SY333 )
| ( subset @ ( fiber @ ( relation_restriction @ SY333 @ SV24 ) @ SY332 ) @ ( fiber @ SY333 @ SY332 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(811,plain,
! [SV25: $i] :
( ( ! [SY334: $i] :
( ~ ( relation @ SY334 )
| ~ ( reflexive @ SY334 )
| ( reflexive @ ( relation_restriction @ SY334 @ SV25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(812,plain,
! [SV26: $i] :
( ( ! [SY335: $i] :
( ~ ( relation @ SY335 )
| ~ ( connected @ SY335 )
| ( connected @ ( relation_restriction @ SY335 @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(813,plain,
! [SV27: $i] :
( ( ! [SY336: $i] :
( ~ ( relation @ SY336 )
| ~ ( transitive @ SY336 )
| ( transitive @ ( relation_restriction @ SY336 @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(814,plain,
! [SV28: $i] :
( ( ! [SY337: $i] :
( ~ ( relation @ SY337 )
| ~ ( antisymmetric @ SY337 )
| ( antisymmetric @ ( relation_restriction @ SY337 @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(815,plain,
! [SV29: $i] :
( ( ! [SY338: $i] :
( ~ ( subset @ SV29 @ SY338 )
| ! [SY339: $i] : ( subset @ ( set_intersection2 @ SV29 @ SY339 ) @ ( set_intersection2 @ SY338 @ SY339 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(816,plain,
! [SV30: $i] :
( ( ! [SY340: $i] :
( ~ ( subset @ SV30 @ SY340 )
| ( ( set_intersection2 @ SV30 @ SY340 )
= SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(817,plain,
! [SV31: $i] :
( ( subset @ empty_set @ SV31 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(818,plain,
! [SV32: $i] :
( ( ! [SY341: $i] :
( ~ ( relation @ SY341 )
| ~ ( well_founded_relation @ SY341 )
| ( well_founded_relation @ ( relation_restriction @ SY341 @ SV32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(819,plain,
! [SV33: $i] :
( ( ! [SY342: $i] :
( ~ ( subset @ SV33 @ SY342 )
| ! [SY343: $i] : ( subset @ ( set_difference @ SV33 @ SY343 ) @ ( set_difference @ SY342 @ SY343 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(820,plain,
! [SV34: $i] :
( ( ! [SY344: $i] : ( subset @ ( set_difference @ SV34 @ SY344 ) @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(821,plain,
! [SV35: $i] :
( ( ! [SY345: $i] :
( ~ ( relation @ SY345 )
| ~ ( subset @ SV35 @ ( relation_field @ SY345 ) )
| ~ ( well_ordering @ SY345 )
| ( ( relation_field @ ( relation_restriction @ SY345 @ SV35 ) )
= SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(822,plain,
! [SV36: $i] :
( ( ! [SY346: $i,SY347: $i] :
( ~ ( in @ SV36 @ SY346 )
| ~ ( in @ SY346 @ SY347 )
| ~ ( in @ SY347 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(823,plain,
! [SV37: $i] :
( ( ~ ( subset @ SV37 @ empty_set )
| ( SV37 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(824,plain,
! [SV38: $i] :
( ( ! [SY348: $i] :
( ~ ( proper_subset @ SY348 @ SV38 )
| ~ ( subset @ SV38 @ SY348 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(825,plain,
! [SV39: $i] :
( ( ! [SY349: $i,SY350: $i] :
( ~ ( disjoint @ SY349 @ SY350 )
| ~ ( subset @ SV39 @ SY349 )
| ( disjoint @ SV39 @ SY350 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(826,plain,
! [SV40: $i] :
( ( ! [SY351: $i] :
( ~ ( subset @ ( singleton @ SV40 ) @ ( singleton @ SY351 ) )
| ( SV40 = SY351 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(827,plain,
! [SV41: $i] :
( ( ! [SY352: $i] : ( subset @ SV41 @ ( set_union2 @ SV41 @ SY352 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(828,plain,
! [SV42: $i] :
( ( ! [SY353: $i] :
( ~ ( relation @ SY353 )
| ( subset @ ( relation_dom_restriction @ SY353 @ SV42 ) @ SY353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(829,plain,
! [SV43: $i] :
( ( ! [SY354: $i,SY355: $i] :
( ~ ( subset @ SV43 @ SY354 )
| ~ ( subset @ SY355 @ SY354 )
| ( subset @ ( set_union2 @ SV43 @ SY355 ) @ SY354 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(830,plain,
! [SV44: $i] :
( ( ! [SY356: $i] :
( ~ ( in @ SV44 @ SY356 )
| ( subset @ SV44 @ ( union @ SY356 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(831,plain,
! [SV45: $i] :
( ( ! [SY357: $i] :
( ~ ( in @ SV45 @ SY357 )
| ~ ( in @ SY357 @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(832,plain,
! [SV46: $i] :
( ( ~ ( empty @ SV46 )
| ( relation @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(833,plain,
! [SV47: $i] :
( ( ~ ( relation @ SV47 )
| ! [SY358: $i] : ( relation @ ( relation_restriction @ SV47 @ SY358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(834,plain,
! [SV48: $i] :
( ( ~ ( relation @ SV48 )
| ( relation @ ( relation_inverse @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(835,plain,
! [SV49: $i] :
( ( ! [SY359: $i] :
( ~ ( relation @ SV49 )
| ~ ( relation @ SY359 )
| ( relation @ ( relation_composition @ SV49 @ SY359 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(836,plain,
! [SV50: $i] :
( ( relation @ ( identity_relation @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(837,plain,
! [SV51: $i] :
( ( ~ ( relation @ SV51 )
| ! [SY360: $i] : ( relation @ ( relation_dom_restriction @ SV51 @ SY360 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(838,plain,
! [SV52: $i] :
( ( ! [SY361: $i] :
( ~ ( relation @ SY361 )
| ( relation @ ( relation_rng_restriction @ SV52 @ SY361 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(839,plain,
! [SV53: $i] :
( ( ~ ( empty @ ( succ @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(840,plain,
! [SV54: $i] :
( ( ! [SY362: $i] :
( ~ ( relation @ SV54 )
| ~ ( relation @ SY362 )
| ( relation @ ( set_intersection2 @ SV54 @ SY362 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(841,plain,
! [SV55: $i] :
( ( ! [SY363: $i] :
( ~ ( relation @ SV55 )
| ~ ( relation @ SY363 )
| ( relation @ ( set_union2 @ SV55 @ SY363 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(842,plain,
! [SV56: $i] :
( ( ! [SY364: $i] :
( ~ ( relation @ SV56 )
| ~ ( relation @ SY364 )
| ( relation @ ( set_difference @ SV56 @ SY364 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(843,plain,
! [SV57: $i] :
( ( ~ ( relation @ SV57 )
| ( ( relation_inverse @ ( relation_inverse @ SV57 ) )
= SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(844,plain,
! [SV58: $i] :
( ( subset @ SV58 @ SV58 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(845,plain,
! [SV59: $i] :
( ( ! [SY365: $i] :
( ~ ( in @ SV59 @ SY365 )
| ( element @ SV59 @ SY365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(846,plain,
! [SV60: $i] :
( ( ! [SY366: $i] :
( ~ ( empty @ SY366 )
| ~ ( in @ SV60 @ SY366 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(847,plain,
( ( well_ordering @ ( inclusion_relation @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[734]) ).
thf(848,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[735]) ).
thf(849,plain,
! [SV61: $i] :
( ( ~ ( ~ ! [SY367: $i,SY368: $i] :
( ~ ( relation @ SY368 )
| ~ ( in @ SV61 @ SY368 )
| ~ ( in @ SV61 @ ( cartesian_product2 @ SY367 @ SY367 ) )
| ( in @ SV61 @ ( relation_restriction @ SY368 @ SY367 ) ) )
| ~ ~ ( ~ ! [SY369: $i,SY370: $i] :
( ~ ( relation @ SY370 )
| ~ ( in @ SV61 @ ( relation_restriction @ SY370 @ SY369 ) )
| ( in @ SV61 @ SY370 ) )
| ~ ! [SY371: $i,SY372: $i] :
( ~ ( relation @ SY372 )
| ~ ( in @ SV61 @ ( relation_restriction @ SY372 @ SY371 ) )
| ( in @ SV61 @ ( cartesian_product2 @ SY371 @ SY371 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(850,plain,
( ( ~ ( function @ sK10_A )
| ~ ( relation @ sK10_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[737]) ).
thf(851,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ~ ( ordinal @ ( sK33_B @ SX0 ) )
| ~ ~ ( ~ ( in @ ( sK33_B @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( succ @ ( sK33_B @ SX0 ) ) @ SX0 ) ) )
| ( being_limit_ordinal @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( being_limit_ordinal @ SX0 )
| ! [SX1: $i] :
( ~ ( ordinal @ SX1 )
| ~ ( in @ SX1 @ SX0 )
| ( in @ ( succ @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[738]) ).
thf(852,plain,
! [SV62: $i] :
( ( ~ ( ordinal @ SV62 )
| ~ ( ~ ! [SY373: $i] :
( ~ ( ordinal @ SY373 )
| ~ ( in @ SV62 @ SY373 )
| ( ordinal_subset @ ( succ @ SV62 ) @ SY373 ) )
| ~ ! [SY374: $i] :
( ~ ( ordinal @ SY374 )
| ~ ( ordinal_subset @ ( succ @ SV62 ) @ SY374 )
| ( in @ SV62 @ SY374 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(853,plain,
! [SV63: $i] :
( ( ! [SY375: $i] :
( ~ ( ordinal @ SY375 )
| ~ ( ~ ! [SY376: $i] :
( ! [SY377: $i] :
( ( SY376 != SY377 )
| ~ ( ordinal @ SY377 )
| ~ ( in @ SY377 @ SV63 ) )
| ~ ( in @ SY376 @ ( succ @ SY375 ) )
| ( in @ SY376 @ ( sK52_C @ SY375 @ SV63 ) ) )
| ~ ~ ( ~ ! [SY378: $i] :
( ~ ( in @ SY378 @ ( sK52_C @ SY375 @ SV63 ) )
| ~ ( ~ ~ ( ( SY378
!= ( sK53_E @ SY378 @ SY375 @ SV63 ) )
| ~ ( ordinal @ ( sK53_E @ SY378 @ SY375 @ SV63 ) ) )
| ~ ( in @ ( sK53_E @ SY378 @ SY375 @ SV63 ) @ SV63 ) ) )
| ~ ! [SY379: $i] :
( ~ ( in @ SY379 @ ( sK52_C @ SY375 @ SV63 ) )
| ( in @ SY379 @ ( succ @ SY375 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(854,plain,
! [SV64: $i] :
( ( ~ ( ~ ! [SY380: $i] :
( ~ ( subset @ SV64 @ SY380 )
| ! [SY381: $i] : ( subset @ ( cartesian_product2 @ SV64 @ SY381 ) @ ( cartesian_product2 @ SY380 @ SY381 ) ) )
| ~ ! [SY382: $i] :
( ~ ( subset @ SV64 @ SY382 )
| ! [SY383: $i] : ( subset @ ( cartesian_product2 @ SY383 @ SV64 ) @ ( cartesian_product2 @ SY383 @ SY382 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(855,plain,
( ( ~ ! [SX0: $i] :
( ~ ( epsilon_connected @ SX0 )
| ~ ( epsilon_transitive @ SX0 )
| ( ordinal @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[742]) ).
thf(856,plain,
! [SV65: $i] :
( ( ~ ( ~ ! [SY384: $i,SY385: $i] :
( ~ ( in @ SV65 @ SY385 )
| ~ ( in @ SY384 @ SY385 )
| ( subset @ ( unordered_pair @ SV65 @ SY384 ) @ SY385 ) )
| ~ ~ ( ~ ! [SY386: $i,SY387: $i] :
( ~ ( subset @ ( unordered_pair @ SV65 @ SY386 ) @ SY387 )
| ( in @ SV65 @ SY387 ) )
| ~ ! [SY388: $i,SY389: $i] :
( ~ ( subset @ ( unordered_pair @ SV65 @ SY388 ) @ SY389 )
| ( in @ SY388 @ SY389 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(857,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( empty @ ( succ @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ ( succ @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ ( succ @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( ordinal @ ( succ @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[744]) ).
thf(858,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ ( sK14_SY277 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK14_SY277 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK12_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[745]) ).
thf(859,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK31_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK31_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK29_C @ SX1 @ SX0 ) @ ( sK30_SY281 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[746]) ).
thf(860,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( ( ( sK19_B @ SX0 )
!= ( sK20_SY279 @ SX0 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_B @ SX0 ) @ SX0 )
| ~ ( in @ ( sK20_SY279 @ SX0 ) @ SX0 ) )
| ~ ~ ( in @ ( sK19_B @ SX0 ) @ ( sK20_SY279 @ SX0 ) ) ) )
| ~ ~ ( in @ ( sK20_SY279 @ SX0 ) @ ( sK19_B @ SX0 ) ) )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( epsilon_connected @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( SX1 = SX2 )
| ~ ( in @ SX1 @ SX0 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX1 @ SX2 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[747]) ).
thf(861,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[748]) ).
thf(862,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( reflexive @ SX0 )
| ~ ( transitive @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ~ ( connected @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ( well_ordering @ SX0 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( well_founded_relation @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[749]) ).
thf(863,plain,
! [SV66: $i] :
( ( ~ ( ~ ( in @ ( sK51_B @ SV66 ) @ SV66 )
| ~ ( ~ ( ordinal @ ( sK51_B @ SV66 ) )
| ~ ( subset @ ( sK51_B @ SV66 ) @ SV66 ) ) )
| ( ordinal @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(864,plain,
! [SV67: $i] :
( ( ! [SY390: $i] :
( ~ ( ~ ! [SY391: $i] :
( ~ ( in @ SY391 @ SY390 )
| ~ ( in @ SY391 @ ( sK4_C @ SY390 @ SV67 ) ) )
| ~ ( in @ ( sK4_C @ SY390 @ SV67 ) @ SY390 ) )
| ~ ( in @ SV67 @ SY390 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(865,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK27_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[752]) ).
thf(866,plain,
( ( ~ ( relation @ sK6_A )
| ~ ( relation_empty_yielding @ sK6_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[753]) ).
thf(867,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK34_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK34_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[754]) ).
thf(868,plain,
( ( ~ ( empty @ sK9_A )
| ~ ( relation @ sK9_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[755]) ).
thf(869,plain,
( ( ~ ~ ( empty @ sK8_A )
| ~ ( relation @ sK8_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[756]) ).
thf(870,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK28_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK28_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[757]) ).
thf(871,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK7_A )
| ~ ( epsilon_transitive @ sK7_A ) )
| ~ ( epsilon_connected @ sK7_A ) )
| ~ ( ordinal @ sK7_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[758]) ).
thf(872,plain,
! [SV68: $i] :
( ( ! [SY392: $i] :
( ~ ( ordinal @ SY392 )
| ~ ( ~ ( ordinal @ ( sK35_C @ SY392 @ SV68 ) )
| ~ ~ ( ~ ! [SY393: $i] :
( ~ ( ordinal @ SY393 )
| ~ ( in @ SY393 @ SV68 )
| ( ordinal_subset @ ( sK35_C @ SY392 @ SV68 ) @ SY393 ) )
| ~ ( in @ ( sK35_C @ SY392 @ SV68 ) @ SV68 ) ) )
| ( SV68 = empty_set )
| ~ ( subset @ SV68 @ SY392 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(873,plain,
! [SV69: $i] :
( ( ~ ( ~ ! [SY394: $i,SY395: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK21_D @ SY395 @ SY394 @ SV69 ) @ SY395 )
| ~ ( in @ ( sK21_D @ SY395 @ SY394 @ SV69 ) @ SV69 ) )
| ~ ( ~ ( in @ ( sK21_D @ SY395 @ SY394 @ SV69 ) @ SY395 )
| ~ ( in @ ( sK21_D @ SY395 @ SY394 @ SV69 ) @ SY394 ) ) )
| ~ ( ( in @ ( sK21_D @ SY395 @ SY394 @ SV69 ) @ SY395 )
| ( in @ ( sK21_D @ SY395 @ SY394 @ SV69 ) @ SV69 )
| ( in @ ( sK21_D @ SY395 @ SY394 @ SV69 ) @ SY394 ) ) )
| ( SY395
= ( set_union2 @ SV69 @ SY394 ) ) )
| ~ ! [SY396: $i,SY397: $i] :
( ( SY397
!= ( set_union2 @ SV69 @ SY396 ) )
| ~ ( ~ ! [SY398: $i] :
( ~ ( in @ SY398 @ SY397 )
| ( in @ SY398 @ SV69 )
| ( in @ SY398 @ SY396 ) )
| ~ ~ ( ~ ! [SY399: $i] :
( ~ ( in @ SY399 @ SV69 )
| ( in @ SY399 @ SY397 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY396 )
| ( in @ SX3 @ SY397 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(874,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK26_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK26_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK26_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK26_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[761]) ).
thf(875,plain,
! [SV70: $i] :
( ( ~ ( ~ ! [SY401: $i,SY402: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SY402 @ SY401 @ SV70 ) @ SV70 )
| ~ ( in @ ( sK15_D @ SY402 @ SY401 @ SV70 ) @ SY401 )
| ~ ( in @ ( sK15_D @ SY402 @ SY401 @ SV70 ) @ SY402 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SY402 @ SY401 @ SV70 ) @ SV70 )
| ( in @ ( sK15_D @ SY402 @ SY401 @ SV70 ) @ SY402 ) )
| ~ ( ( in @ ( sK15_D @ SY402 @ SY401 @ SV70 ) @ SY401 )
| ( in @ ( sK15_D @ SY402 @ SY401 @ SV70 ) @ SY402 ) ) ) )
| ( SY402
= ( set_intersection2 @ SV70 @ SY401 ) ) )
| ~ ! [SY403: $i,SY404: $i] :
( ( SY404
!= ( set_intersection2 @ SV70 @ SY403 ) )
| ~ ( ~ ! [SY405: $i] :
( ~ ( in @ SY405 @ SV70 )
| ~ ( in @ SY405 @ SY403 )
| ( in @ SY405 @ SY404 ) )
| ~ ~ ( ~ ! [SY406: $i] :
( ~ ( in @ SY406 @ SY404 )
| ( in @ SY406 @ SV70 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY404 )
| ( in @ SX3 @ SY403 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(876,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ ( union @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ ( union @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( ordinal @ ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[763]) ).
thf(877,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ordinal @ SX1 )
| ~ ( ordinal_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ordinal @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( ordinal_subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[764]) ).
thf(878,plain,
! [SV71: $i] :
( ( ! [SY408: $i] :
( ~ ( in @ SY408 @ SV71 )
| ~ ( ordinal @ SY408 ) )
| ~ ( ~ ! [SY409: $i] :
( ~ ( ordinal @ SY409 )
| ~ ( in @ SY409 @ SV71 )
| ( ordinal_subset @ ( sK54_B @ SV71 ) @ SY409 ) )
| ~ ~ ( ~ ( in @ ( sK54_B @ SV71 ) @ SV71 )
| ~ ( ordinal @ ( sK54_B @ SV71 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(879,plain,
! [SV72: $i] :
( ( ! [SY410: $i] :
( ~ ( ordinal @ SY410 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK44_C @ SY410 @ SV72 )
!= ( sK45_SY295 @ SY410 @ SV72 ) )
| ~ ~ ( ~ ~ ( ( ( sK45_SY295 @ SY410 @ SV72 )
!= ( sK48_SY300 @ SY410 @ SV72 ) )
| ~ ( ordinal @ ( sK48_SY300 @ SY410 @ SV72 ) ) )
| ~ ( in @ ( sK48_SY300 @ SY410 @ SV72 ) @ SV72 ) ) )
| ( ( sK44_C @ SY410 @ SV72 )
!= ( sK46_SY299 @ SY410 @ SV72 ) ) )
| ~ ~ ( ~ ~ ( ( ( sK46_SY299 @ SY410 @ SV72 )
!= ( sK47_SY303 @ SY410 @ SV72 ) )
| ~ ( ordinal @ ( sK47_SY303 @ SY410 @ SV72 ) ) )
| ~ ( in @ ( sK47_SY303 @ SY410 @ SV72 ) @ SV72 ) ) )
| ~ ( ( ( sK45_SY295 @ SY410 @ SV72 )
!= ( sK46_SY299 @ SY410 @ SV72 ) ) ) )
| ~ ( ~ ! [SY411: $i] :
( ! [SX3: $i] :
( ( SX3 != SY411 )
| ~ ( in @ SX3 @ ( succ @ SY410 ) ) )
| ! [SY413: $i] :
( ( SY411 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY411 @ ( sK41_C @ SY410 @ SV72 ) ) )
| ~ ! [SY414: $i] :
( ~ ( in @ SY414 @ ( sK41_C @ SY410 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY414 @ SY410 @ SV72 )
!= SY414 )
| ~ ( in @ ( sK43_E @ SY414 @ SY410 @ SV72 ) @ ( succ @ SY410 ) ) )
| ~ ~ ( ~ ~ ( ( SY414
!= ( sK42_H @ SY414 @ SY410 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY414 @ SY410 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY414 @ SY410 @ SV72 ) @ SV72 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(880,plain,
! [SV73: $i] :
( ( ~ ( relation @ SV73 )
| ~ ( ~ ! [SY415: $i] :
( ~ ( relation @ SY415 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK23_C @ SY415 @ SV73 ) @ ( sK24_SY280 @ SY415 @ SV73 ) ) @ SV73 )
| ~ ( in @ ( ordered_pair @ ( sK23_C @ SY415 @ SV73 ) @ ( sK24_SY280 @ SY415 @ SV73 ) ) @ SY415 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK23_C @ SY415 @ SV73 ) @ ( sK24_SY280 @ SY415 @ SV73 ) ) @ SV73 )
| ( in @ ( ordered_pair @ ( sK23_C @ SY415 @ SV73 ) @ ( sK24_SY280 @ SY415 @ SV73 ) ) @ SY415 ) ) )
| ( SV73 = SY415 ) )
| ~ ! [SY416: $i] :
( ~ ( relation @ SY416 )
| ( SV73 != SY416 )
| ~ ( ~ ! [SY417: $i,SY418: $i] :
( ~ ( in @ ( ordered_pair @ SY417 @ SY418 ) @ SV73 )
| ( in @ ( ordered_pair @ SY417 @ SY418 ) @ SY416 ) )
| ~ ! [SY419: $i,SY420: $i] :
( ~ ( in @ ( ordered_pair @ SY419 @ SY420 ) @ SY416 )
| ( in @ ( ordered_pair @ SY419 @ SY420 ) @ SV73 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(881,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[768]) ).
thf(882,plain,
! [SV74: $i] :
( ( ~ ( ~ ! [SY421: $i,SY422: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK22_D @ SY422 @ SY421 @ SV74 ) @ SY422 )
| ( ( sK22_D @ SY422 @ SY421 @ SV74 )
!= SV74 ) )
| ~ ( ~ ( in @ ( sK22_D @ SY422 @ SY421 @ SV74 ) @ SY422 )
| ( ( sK22_D @ SY422 @ SY421 @ SV74 )
!= SY421 ) ) )
| ~ ( ( in @ ( sK22_D @ SY422 @ SY421 @ SV74 ) @ SY422 )
| ( ( sK22_D @ SY422 @ SY421 @ SV74 )
= SV74 )
| ( ( sK22_D @ SY422 @ SY421 @ SV74 )
= SY421 ) ) )
| ( SY422
= ( unordered_pair @ SV74 @ SY421 ) ) )
| ~ ! [SY423: $i,SY424: $i] :
( ( SY424
!= ( unordered_pair @ SV74 @ SY423 ) )
| ~ ( ~ ! [SY425: $i] :
( ~ ( in @ SY425 @ SY424 )
| ( SY425 = SV74 )
| ( SY425 = SY423 ) )
| ~ ~ ( ~ ! [SY426: $i] :
( ( SY426 != SV74 )
| ( in @ SY426 @ SY424 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY423 )
| ( in @ SX3 @ SY424 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(883,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ( in @ ( sK25_B @ SX0 ) @ SX0 )
| ~ ~ ( subset @ ( sK25_B @ SX0 ) @ SX0 ) )
| ( epsilon_transitive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( epsilon_transitive @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[770]) ).
thf(884,plain,
! [SV75: $i] :
( ( ~ ( ~ ! [SY428: $i] :
( ~ ( subset @ SY428 @ ( sK2_B @ SV75 ) )
| ( are_equipotent @ SY428 @ ( sK2_B @ SV75 ) )
| ( in @ SY428 @ ( sK2_B @ SV75 ) ) )
| ~ ~ ( ~ ! [SY429: $i] :
( ~ ( ~ ! [SY430: $i] :
( ~ ( subset @ SY430 @ SY429 )
| ( in @ SY430 @ ( sK3_SY270 @ SY429 @ SV75 ) ) )
| ~ ( in @ ( sK3_SY270 @ SY429 @ SV75 ) @ ( sK2_B @ SV75 ) ) )
| ~ ( in @ SY429 @ ( sK2_B @ SV75 ) ) )
| ~ ~ ( ~ ! [SY431: $i,SY432: $i] :
( ~ ( in @ SY431 @ ( sK2_B @ SV75 ) )
| ~ ( subset @ SY432 @ SY431 )
| ( in @ SY432 @ ( sK2_B @ SV75 ) ) )
| ~ ( in @ SV75 @ ( sK2_B @ SV75 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(885,plain,
! [SV76: $i] :
( ( ~ ( ~ ! [SY433: $i,SY434: $i] :
( ~ ( relation @ SY434 )
| ~ ( in @ SV76 @ ( relation_field @ ( relation_restriction @ SY434 @ SY433 ) ) )
| ( in @ SV76 @ ( relation_field @ SY434 ) ) )
| ~ ! [SY435: $i,SY436: $i] :
( ~ ( relation @ SY436 )
| ~ ( in @ SV76 @ ( relation_field @ ( relation_restriction @ SY436 @ SY435 ) ) )
| ( in @ SV76 @ SY435 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(886,plain,
! [SV77: $i] :
( ( ~ ( relation @ SV77 )
| ~ ( ~ ! [SY437: $i] :
( ~ ( relation @ SY437 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK17_C @ SY437 @ SV77 ) @ ( sK18_SY278 @ SY437 @ SV77 ) ) @ SV77 )
| ~ ~ ( in @ ( ordered_pair @ ( sK17_C @ SY437 @ SV77 ) @ ( sK18_SY278 @ SY437 @ SV77 ) ) @ SY437 ) )
| ( subset @ SV77 @ SY437 ) )
| ~ ! [SY438: $i] :
( ~ ( relation @ SY438 )
| ~ ( subset @ SV77 @ SY438 )
| ! [SY439: $i,SY440: $i] :
( ~ ( in @ ( ordered_pair @ SY439 @ SY440 ) @ SV77 )
| ( in @ ( ordered_pair @ SY439 @ SY440 ) @ SY438 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(887,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK16_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK16_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[774]) ).
thf(888,plain,
! [SV78: $i] :
( ( ~ ( ~ ! [SY441: $i,SY442: $i] :
( ~ ( ~ ( ~ ( in @ ( sK11_D @ SY442 @ SY441 @ SV78 ) @ SV78 )
| ( in @ ( sK11_D @ SY442 @ SY441 @ SV78 ) @ SY441 )
| ~ ( in @ ( sK11_D @ SY442 @ SY441 @ SV78 ) @ SY442 ) )
| ~ ~ ( ~ ( ( in @ ( sK11_D @ SY442 @ SY441 @ SV78 ) @ SV78 )
| ( in @ ( sK11_D @ SY442 @ SY441 @ SV78 ) @ SY442 ) )
| ~ ( ~ ( in @ ( sK11_D @ SY442 @ SY441 @ SV78 ) @ SY441 )
| ( in @ ( sK11_D @ SY442 @ SY441 @ SV78 ) @ SY442 ) ) ) )
| ( SY442
= ( set_difference @ SV78 @ SY441 ) ) )
| ~ ! [SY443: $i,SY444: $i] :
( ( SY444
!= ( set_difference @ SV78 @ SY443 ) )
| ~ ( ~ ! [SY445: $i] :
( ~ ( in @ SY445 @ SV78 )
| ( in @ SY445 @ SY443 )
| ( in @ SY445 @ SY444 ) )
| ~ ~ ( ~ ! [SY446: $i] :
( ~ ( in @ SY446 @ SY444 )
| ( in @ SY446 @ SV78 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY444 )
| ~ ( in @ SX3 @ SY443 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(889,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_field @ ( relation_restriction @ SX1 @ SX0 ) ) @ ( relation_field @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_field @ ( relation_restriction @ SX1 @ SX0 ) ) @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[776]) ).
thf(890,plain,
( ( ~ ~ ( ~ ( epsilon_connected @ sK49_A )
| ~ ( epsilon_transitive @ sK49_A ) )
| ~ ( ordinal @ sK49_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[777]) ).
thf(891,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK36_B @ SX0 ) @ ( sK37_SY285 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK37_SY285 @ SX0 ) @ ( sK36_B @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK36_B @ SX0 )
!= ( sK37_SY285 @ SX0 ) ) ) )
| ( antisymmetric @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX2 @ SX1 ) @ SX0 )
| ( SX1 = SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[778]) ).
thf(892,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[779]) ).
thf(893,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK38_B @ SX0 ) @ ( sK39_SY286 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK39_SY286 @ SX0 ) @ ( sK40_SY288 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK38_B @ SX0 ) @ ( sK40_SY288 @ SX0 ) ) @ SX0 ) )
| ( transitive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( transitive @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ ( ordered_pair @ SX1 @ SX3 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[780]) ).
thf(894,plain,
! [SV79: $i] :
( ( ! [SY448: $i] :
( ~ ( ~ ( ~ ( in @ ( sK5_C @ SY448 @ SV79 ) @ SV79 )
| ~ ( in @ ( sK5_C @ SY448 @ SV79 ) @ SY448 ) )
| ~ ( ( in @ ( sK5_C @ SY448 @ SV79 ) @ SV79 )
| ( in @ ( sK5_C @ SY448 @ SV79 ) @ SY448 ) ) )
| ( SV79 = SY448 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(895,plain,
( ( ~ ! [SX0: $i] :
( ( SX0
!= ( union @ SX0 ) )
| ( being_limit_ordinal @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( being_limit_ordinal @ SX0 )
| ( SX0
= ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[782]) ).
thf(896,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( ordinal @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[783]) ).
thf(897,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( being_limit_ordinal @ SX0 )
| ~ ( ~ ( ordinal @ ( sK50_B @ SX0 ) )
| ( SX0
!= ( succ @ ( sK50_B @ SX0 ) ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ! [SX1: $i] :
( ( SX0
!= ( succ @ SX1 ) )
| ~ ( ordinal @ SX1 ) )
| ~ ( being_limit_ordinal @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[784]) ).
thf(898,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[785]) ).
thf(899,plain,
! [SV80: $i] :
( ( ! [SY449: $i] :
~ ( ~ ! [SY450: $i,SY451: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK32_E @ SY451 @ SY450 @ SY449 @ SV80 ) @ SY451 )
| ( ( sK32_E @ SY451 @ SY450 @ SY449 @ SV80 )
!= SY450 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK32_E @ SY451 @ SY450 @ SY449 @ SV80 ) @ SY451 )
| ( ( sK32_E @ SY451 @ SY450 @ SY449 @ SV80 )
!= SV80 ) )
| ~ ( ~ ( in @ ( sK32_E @ SY451 @ SY450 @ SY449 @ SV80 ) @ SY451 )
| ( ( sK32_E @ SY451 @ SY450 @ SY449 @ SV80 )
!= SY449 ) ) ) )
| ~ ( ( in @ ( sK32_E @ SY451 @ SY450 @ SY449 @ SV80 ) @ SY451 )
| ( ( sK32_E @ SY451 @ SY450 @ SY449 @ SV80 )
= SY450 )
| ( ( sK32_E @ SY451 @ SY450 @ SY449 @ SV80 )
= SV80 )
| ( ( sK32_E @ SY451 @ SY450 @ SY449 @ SV80 )
= SY449 ) ) )
| ( SY451
= ( unordered_triple @ SV80 @ SY449 @ SY450 ) ) )
| ~ ! [SY452: $i,SY453: $i] :
( ( SY453
!= ( unordered_triple @ SV80 @ SY449 @ SY452 ) )
| ~ ( ~ ! [SY454: $i] :
( ~ ( in @ SY454 @ SY453 )
| ( SY454 = SY452 )
| ( SY454 = SV80 )
| ( SY454 = SY449 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ( SX4 != SY452 )
| ( in @ SX4 @ SY453 ) )
| ~ ~ ( ~ ! [SY456: $i] :
( ( SY456 != SV80 )
| ( in @ SY456 @ SY453 ) )
| ~ ! [SX4: $i] :
( ( SX4 != SY449 )
| ( in @ SX4 @ SY453 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(900,plain,
! [SV1: $i,SV81: $i] :
( ( ~ ( ordinal @ SV81 )
| ~ ( in @ SV1 @ SV81 )
| ( ordinal @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(901,plain,
! [SV2: $i] :
( ( ( ~ ( ordinal @ SV2 ) )
= $true )
| ( ( ! [SY311: $i] :
( ~ ( ordinal @ SY311 )
| ( in @ SV2 @ SY311 )
| ( SV2 = SY311 )
| ( in @ SY311 @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[788]) ).
thf(902,plain,
! [SV4: $i,SV82: $i] :
( ( ~ ( relation @ SV82 )
| ~ ( well_ordering @ SV82 )
| ( well_ordering @ ( relation_restriction @ SV82 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(903,plain,
! [SV6: $i] :
( ( ( ~ ( ordinal @ SV6 ) )
= $true )
| ( ( connected @ ( inclusion_relation @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[792]) ).
thf(904,plain,
! [SV8: $i] :
( ( ( ~ ( ordinal @ SV8 ) )
= $true )
| ( ( well_founded_relation @ ( inclusion_relation @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[794]) ).
thf(905,plain,
! [SV9: $i] :
( ( ( ~ ( epsilon_connected @ SV9 )
| ~ ( epsilon_transitive @ SV9 ) )
= $true )
| ( ( ordinal @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[795]) ).
thf(906,plain,
! [SV83: $i,SV10: $i] :
( ( ~ ( ordinal @ SV10 )
| ~ ( ordinal @ SV83 )
| ( ordinal_subset @ SV10 @ SV83 )
| ( ordinal_subset @ SV83 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(907,plain,
! [SV12: $i] :
( ( ( ~ ( ordinal @ SV12 )
| ! [B: $i] :
~ ( ordinal @ B ) )
= $true )
| ( ( ordinal_subset @ SV12 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[798]) ).
thf(908,plain,
! [SV84: $i,SV13: $i] :
( ( ~ ( in @ SV13 @ SV84 )
| ( subset @ SV13 @ ( union @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(909,plain,
! [SV15: $i,SV85: $i] :
( ( ~ ( relation @ SV85 )
| ( subset @ ( relation_rng_restriction @ SV15 @ SV85 ) @ SV85 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(910,plain,
! [SV86: $i,SV16: $i] :
( ( ! [SY458: $i,SY459: $i] :
( ~ ( subset @ SV16 @ SV86 )
| ~ ( subset @ SY458 @ SY459 )
| ( subset @ ( cartesian_product2 @ SV16 @ SY458 ) @ ( cartesian_product2 @ SV86 @ SY459 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(911,plain,
! [SV87: $i,SV17: $i] :
( ( ~ ( subset @ SV17 @ SV87 )
| ( ( set_union2 @ SV17 @ SV87 )
= SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(912,plain,
! [SV88: $i,SV18: $i] :
( ( ! [SY460: $i,SY461: $i] :
( ~ ( relation_of2_as_subset @ SY461 @ SY460 @ SV18 )
| ~ ( subset @ SV18 @ SV88 )
| ( relation_of2_as_subset @ SY461 @ SY460 @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(913,plain,
! [SV89: $i,SV19: $i] :
( ( ! [SY462: $i] :
( ~ ( relation @ SY462 )
| ~ ( subset @ SV19 @ SV89 )
| ( subset @ ( relation_inverse_image @ SY462 @ SV19 ) @ ( relation_inverse_image @ SY462 @ SV89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(914,plain,
! [SV90: $i,SV20: $i] :
( ( subset @ ( set_intersection2 @ SV20 @ SV90 ) @ SV20 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(915,plain,
! [SV91: $i,SV21: $i] :
( ( ! [SY463: $i] :
( ~ ( subset @ SV21 @ SV91 )
| ~ ( subset @ SV21 @ SY463 )
| ( subset @ SV21 @ ( set_intersection2 @ SV91 @ SY463 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(916,plain,
! [SV92: $i,SV22: $i] :
( ( ! [SY464: $i] :
( ~ ( subset @ SV22 @ SV92 )
| ~ ( subset @ SV92 @ SY464 )
| ( subset @ SV22 @ SY464 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(917,plain,
! [SV23: $i] :
( ( ( ~ ( epsilon_transitive @ SV23 ) )
= $true )
| ( ( ! [SY331: $i] :
( ~ ( ordinal @ SY331 )
| ~ ( proper_subset @ SV23 @ SY331 )
| ( in @ SV23 @ SY331 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[809]) ).
thf(918,plain,
! [SV93: $i,SV24: $i] :
( ( ! [SY465: $i] :
( ~ ( relation @ SY465 )
| ( subset @ ( fiber @ ( relation_restriction @ SY465 @ SV24 ) @ SV93 ) @ ( fiber @ SY465 @ SV93 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(919,plain,
! [SV25: $i,SV94: $i] :
( ( ~ ( relation @ SV94 )
| ~ ( reflexive @ SV94 )
| ( reflexive @ ( relation_restriction @ SV94 @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(920,plain,
! [SV26: $i,SV95: $i] :
( ( ~ ( relation @ SV95 )
| ~ ( connected @ SV95 )
| ( connected @ ( relation_restriction @ SV95 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(921,plain,
! [SV27: $i,SV96: $i] :
( ( ~ ( relation @ SV96 )
| ~ ( transitive @ SV96 )
| ( transitive @ ( relation_restriction @ SV96 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(922,plain,
! [SV28: $i,SV97: $i] :
( ( ~ ( relation @ SV97 )
| ~ ( antisymmetric @ SV97 )
| ( antisymmetric @ ( relation_restriction @ SV97 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(923,plain,
! [SV98: $i,SV29: $i] :
( ( ~ ( subset @ SV29 @ SV98 )
| ! [SY466: $i] : ( subset @ ( set_intersection2 @ SV29 @ SY466 ) @ ( set_intersection2 @ SV98 @ SY466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(924,plain,
! [SV99: $i,SV30: $i] :
( ( ~ ( subset @ SV30 @ SV99 )
| ( ( set_intersection2 @ SV30 @ SV99 )
= SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(925,plain,
! [SV32: $i,SV100: $i] :
( ( ~ ( relation @ SV100 )
| ~ ( well_founded_relation @ SV100 )
| ( well_founded_relation @ ( relation_restriction @ SV100 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(926,plain,
! [SV101: $i,SV33: $i] :
( ( ~ ( subset @ SV33 @ SV101 )
| ! [SY467: $i] : ( subset @ ( set_difference @ SV33 @ SY467 ) @ ( set_difference @ SV101 @ SY467 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(927,plain,
! [SV102: $i,SV34: $i] :
( ( subset @ ( set_difference @ SV34 @ SV102 ) @ SV34 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(928,plain,
! [SV35: $i,SV103: $i] :
( ( ~ ( relation @ SV103 )
| ~ ( subset @ SV35 @ ( relation_field @ SV103 ) )
| ~ ( well_ordering @ SV103 )
| ( ( relation_field @ ( relation_restriction @ SV103 @ SV35 ) )
= SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(929,plain,
! [SV104: $i,SV36: $i] :
( ( ! [SY468: $i] :
( ~ ( in @ SV36 @ SV104 )
| ~ ( in @ SV104 @ SY468 )
| ~ ( in @ SY468 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(930,plain,
! [SV37: $i] :
( ( ( ~ ( subset @ SV37 @ empty_set ) )
= $true )
| ( ( SV37 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[823]) ).
thf(931,plain,
! [SV38: $i,SV105: $i] :
( ( ~ ( proper_subset @ SV105 @ SV38 )
| ~ ( subset @ SV38 @ SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(932,plain,
! [SV39: $i,SV106: $i] :
( ( ! [SY469: $i] :
( ~ ( disjoint @ SV106 @ SY469 )
| ~ ( subset @ SV39 @ SV106 )
| ( disjoint @ SV39 @ SY469 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(933,plain,
! [SV107: $i,SV40: $i] :
( ( ~ ( subset @ ( singleton @ SV40 ) @ ( singleton @ SV107 ) )
| ( SV40 = SV107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(934,plain,
! [SV108: $i,SV41: $i] :
( ( subset @ SV41 @ ( set_union2 @ SV41 @ SV108 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(935,plain,
! [SV42: $i,SV109: $i] :
( ( ~ ( relation @ SV109 )
| ( subset @ ( relation_dom_restriction @ SV109 @ SV42 ) @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(936,plain,
! [SV110: $i,SV43: $i] :
( ( ! [SY470: $i] :
( ~ ( subset @ SV43 @ SV110 )
| ~ ( subset @ SY470 @ SV110 )
| ( subset @ ( set_union2 @ SV43 @ SY470 ) @ SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(937,plain,
! [SV111: $i,SV44: $i] :
( ( ~ ( in @ SV44 @ SV111 )
| ( subset @ SV44 @ ( union @ SV111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(938,plain,
! [SV112: $i,SV45: $i] :
( ( ~ ( in @ SV45 @ SV112 )
| ~ ( in @ SV112 @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(939,plain,
! [SV46: $i] :
( ( ( ~ ( empty @ SV46 ) )
= $true )
| ( ( relation @ SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[832]) ).
thf(940,plain,
! [SV47: $i] :
( ( ( ~ ( relation @ SV47 ) )
= $true )
| ( ( ! [SY358: $i] : ( relation @ ( relation_restriction @ SV47 @ SY358 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[833]) ).
thf(941,plain,
! [SV48: $i] :
( ( ( ~ ( relation @ SV48 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[834]) ).
thf(942,plain,
! [SV113: $i,SV49: $i] :
( ( ~ ( relation @ SV49 )
| ~ ( relation @ SV113 )
| ( relation @ ( relation_composition @ SV49 @ SV113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(943,plain,
! [SV51: $i] :
( ( ( ~ ( relation @ SV51 ) )
= $true )
| ( ( ! [SY360: $i] : ( relation @ ( relation_dom_restriction @ SV51 @ SY360 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[837]) ).
thf(944,plain,
! [SV52: $i,SV114: $i] :
( ( ~ ( relation @ SV114 )
| ( relation @ ( relation_rng_restriction @ SV52 @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(945,plain,
! [SV53: $i] :
( ( empty @ ( succ @ SV53 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[839]) ).
thf(946,plain,
! [SV115: $i,SV54: $i] :
( ( ~ ( relation @ SV54 )
| ~ ( relation @ SV115 )
| ( relation @ ( set_intersection2 @ SV54 @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(947,plain,
! [SV116: $i,SV55: $i] :
( ( ~ ( relation @ SV55 )
| ~ ( relation @ SV116 )
| ( relation @ ( set_union2 @ SV55 @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(948,plain,
! [SV117: $i,SV56: $i] :
( ( ~ ( relation @ SV56 )
| ~ ( relation @ SV117 )
| ( relation @ ( set_difference @ SV56 @ SV117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(949,plain,
! [SV57: $i] :
( ( ( ~ ( relation @ SV57 ) )
= $true )
| ( ( ( relation_inverse @ ( relation_inverse @ SV57 ) )
= SV57 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[843]) ).
thf(950,plain,
! [SV118: $i,SV59: $i] :
( ( ~ ( in @ SV59 @ SV118 )
| ( element @ SV59 @ SV118 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(951,plain,
! [SV60: $i,SV119: $i] :
( ( ~ ( empty @ SV119 )
| ~ ( in @ SV60 @ SV119 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(952,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[848]) ).
thf(953,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[848]) ).
thf(954,plain,
! [SV61: $i] :
( ( ~ ! [SY367: $i,SY368: $i] :
( ~ ( relation @ SY368 )
| ~ ( in @ SV61 @ SY368 )
| ~ ( in @ SV61 @ ( cartesian_product2 @ SY367 @ SY367 ) )
| ( in @ SV61 @ ( relation_restriction @ SY368 @ SY367 ) ) )
| ~ ~ ( ~ ! [SY369: $i,SY370: $i] :
( ~ ( relation @ SY370 )
| ~ ( in @ SV61 @ ( relation_restriction @ SY370 @ SY369 ) )
| ( in @ SV61 @ SY370 ) )
| ~ ! [SY371: $i,SY372: $i] :
( ~ ( relation @ SY372 )
| ~ ( in @ SV61 @ ( relation_restriction @ SY372 @ SY371 ) )
| ( in @ SV61 @ ( cartesian_product2 @ SY371 @ SY371 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[849]) ).
thf(955,plain,
( ( ~ ( function @ sK10_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[850]) ).
thf(956,plain,
( ( ~ ( relation @ sK10_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[850]) ).
thf(957,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ~ ( ordinal @ ( sK33_B @ SX0 ) )
| ~ ~ ( ~ ( in @ ( sK33_B @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( succ @ ( sK33_B @ SX0 ) ) @ SX0 ) ) )
| ( being_limit_ordinal @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[851]) ).
thf(958,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( being_limit_ordinal @ SX0 )
| ! [SX1: $i] :
( ~ ( ordinal @ SX1 )
| ~ ( in @ SX1 @ SX0 )
| ( in @ ( succ @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[851]) ).
thf(959,plain,
! [SV62: $i] :
( ( ( ~ ( ordinal @ SV62 ) )
= $true )
| ( ( ~ ( ~ ! [SY373: $i] :
( ~ ( ordinal @ SY373 )
| ~ ( in @ SV62 @ SY373 )
| ( ordinal_subset @ ( succ @ SV62 ) @ SY373 ) )
| ~ ! [SY374: $i] :
( ~ ( ordinal @ SY374 )
| ~ ( ordinal_subset @ ( succ @ SV62 ) @ SY374 )
| ( in @ SV62 @ SY374 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[852]) ).
thf(960,plain,
! [SV63: $i,SV120: $i] :
( ( ~ ( ordinal @ SV120 )
| ~ ( ~ ! [SY471: $i] :
( ! [SY377: $i] :
( ( SY471 != SY377 )
| ~ ( ordinal @ SY377 )
| ~ ( in @ SY377 @ SV63 ) )
| ~ ( in @ SY471 @ ( succ @ SV120 ) )
| ( in @ SY471 @ ( sK52_C @ SV120 @ SV63 ) ) )
| ~ ~ ( ~ ! [SY473: $i] :
( ~ ( in @ SY473 @ ( sK52_C @ SV120 @ SV63 ) )
| ~ ( ~ ~ ( ( SY473
!= ( sK53_E @ SY473 @ SV120 @ SV63 ) )
| ~ ( ordinal @ ( sK53_E @ SY473 @ SV120 @ SV63 ) ) )
| ~ ( in @ ( sK53_E @ SY473 @ SV120 @ SV63 ) @ SV63 ) ) )
| ~ ! [SY474: $i] :
( ~ ( in @ SY474 @ ( sK52_C @ SV120 @ SV63 ) )
| ( in @ SY474 @ ( succ @ SV120 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(961,plain,
! [SV64: $i] :
( ( ~ ! [SY380: $i] :
( ~ ( subset @ SV64 @ SY380 )
| ! [SY381: $i] : ( subset @ ( cartesian_product2 @ SV64 @ SY381 ) @ ( cartesian_product2 @ SY380 @ SY381 ) ) )
| ~ ! [SY382: $i] :
( ~ ( subset @ SV64 @ SY382 )
| ! [SY383: $i] : ( subset @ ( cartesian_product2 @ SY383 @ SV64 ) @ ( cartesian_product2 @ SY383 @ SY382 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[854]) ).
thf(962,plain,
( ( ~ ! [SX0: $i] :
( ~ ( epsilon_connected @ SX0 )
| ~ ( epsilon_transitive @ SX0 )
| ( ordinal @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[855]) ).
thf(963,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[855]) ).
thf(964,plain,
! [SV65: $i] :
( ( ~ ! [SY384: $i,SY385: $i] :
( ~ ( in @ SV65 @ SY385 )
| ~ ( in @ SY384 @ SY385 )
| ( subset @ ( unordered_pair @ SV65 @ SY384 ) @ SY385 ) )
| ~ ~ ( ~ ! [SY386: $i,SY387: $i] :
( ~ ( subset @ ( unordered_pair @ SV65 @ SY386 ) @ SY387 )
| ( in @ SV65 @ SY387 ) )
| ~ ! [SY388: $i,SY389: $i] :
( ~ ( subset @ ( unordered_pair @ SV65 @ SY388 ) @ SY389 )
| ( in @ SY388 @ SY389 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[856]) ).
thf(965,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( empty @ ( succ @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ ( succ @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ ( succ @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[857]) ).
thf(966,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( ordinal @ ( succ @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[857]) ).
thf(967,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ ( sK14_SY277 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK14_SY277 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[858]) ).
thf(968,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK12_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[858]) ).
thf(969,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK31_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK31_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[859]) ).
thf(970,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK29_C @ SX1 @ SX0 ) @ ( sK30_SY281 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[859]) ).
thf(971,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( ( ( sK19_B @ SX0 )
!= ( sK20_SY279 @ SX0 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_B @ SX0 ) @ SX0 )
| ~ ( in @ ( sK20_SY279 @ SX0 ) @ SX0 ) )
| ~ ~ ( in @ ( sK19_B @ SX0 ) @ ( sK20_SY279 @ SX0 ) ) ) )
| ~ ~ ( in @ ( sK20_SY279 @ SX0 ) @ ( sK19_B @ SX0 ) ) )
| ( epsilon_connected @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[860]) ).
thf(972,plain,
( ( ~ ! [SX0: $i] :
( ~ ( epsilon_connected @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( SX1 = SX2 )
| ~ ( in @ SX1 @ SX0 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX1 @ SX2 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[860]) ).
thf(973,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[861]) ).
thf(974,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[861]) ).
thf(975,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( reflexive @ SX0 )
| ~ ( transitive @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ~ ( connected @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ( well_ordering @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[862]) ).
thf(976,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( well_founded_relation @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[862]) ).
thf(977,plain,
! [SV66: $i] :
( ( ( ~ ( ~ ( in @ ( sK51_B @ SV66 ) @ SV66 )
| ~ ( ~ ( ordinal @ ( sK51_B @ SV66 ) )
| ~ ( subset @ ( sK51_B @ SV66 ) @ SV66 ) ) ) )
= $true )
| ( ( ordinal @ SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[863]) ).
thf(978,plain,
! [SV67: $i,SV121: $i] :
( ( ~ ( ~ ! [SY475: $i] :
( ~ ( in @ SY475 @ SV121 )
| ~ ( in @ SY475 @ ( sK4_C @ SV121 @ SV67 ) ) )
| ~ ( in @ ( sK4_C @ SV121 @ SV67 ) @ SV121 ) )
| ~ ( in @ SV67 @ SV121 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(979,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK27_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[865]) ).
thf(980,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[865]) ).
thf(981,plain,
( ( ~ ( relation @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[866]) ).
thf(982,plain,
( ( ~ ( relation_empty_yielding @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[866]) ).
thf(983,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK34_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK34_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[867]) ).
thf(984,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[867]) ).
thf(985,plain,
( ( ~ ( empty @ sK9_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[868]) ).
thf(986,plain,
( ( ~ ( relation @ sK9_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[868]) ).
thf(987,plain,
( ( ~ ~ ( empty @ sK8_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[869]) ).
thf(988,plain,
( ( ~ ( relation @ sK8_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[869]) ).
thf(989,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK28_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK28_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[870]) ).
thf(990,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[870]) ).
thf(991,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK7_A )
| ~ ( epsilon_transitive @ sK7_A ) )
| ~ ( epsilon_connected @ sK7_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[871]) ).
thf(992,plain,
( ( ~ ( ordinal @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[871]) ).
thf(993,plain,
! [SV68: $i,SV122: $i] :
( ( ~ ( ordinal @ SV122 )
| ~ ( ~ ( ordinal @ ( sK35_C @ SV122 @ SV68 ) )
| ~ ~ ( ~ ! [SY476: $i] :
( ~ ( ordinal @ SY476 )
| ~ ( in @ SY476 @ SV68 )
| ( ordinal_subset @ ( sK35_C @ SV122 @ SV68 ) @ SY476 ) )
| ~ ( in @ ( sK35_C @ SV122 @ SV68 ) @ SV68 ) ) )
| ( SV68 = empty_set )
| ~ ( subset @ SV68 @ SV122 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[872]) ).
thf(994,plain,
! [SV69: $i] :
( ( ~ ! [SY394: $i,SY395: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK21_D @ SY395 @ SY394 @ SV69 ) @ SY395 )
| ~ ( in @ ( sK21_D @ SY395 @ SY394 @ SV69 ) @ SV69 ) )
| ~ ( ~ ( in @ ( sK21_D @ SY395 @ SY394 @ SV69 ) @ SY395 )
| ~ ( in @ ( sK21_D @ SY395 @ SY394 @ SV69 ) @ SY394 ) ) )
| ~ ( ( in @ ( sK21_D @ SY395 @ SY394 @ SV69 ) @ SY395 )
| ( in @ ( sK21_D @ SY395 @ SY394 @ SV69 ) @ SV69 )
| ( in @ ( sK21_D @ SY395 @ SY394 @ SV69 ) @ SY394 ) ) )
| ( SY395
= ( set_union2 @ SV69 @ SY394 ) ) )
| ~ ! [SY396: $i,SY397: $i] :
( ( SY397
!= ( set_union2 @ SV69 @ SY396 ) )
| ~ ( ~ ! [SY398: $i] :
( ~ ( in @ SY398 @ SY397 )
| ( in @ SY398 @ SV69 )
| ( in @ SY398 @ SY396 ) )
| ~ ~ ( ~ ! [SY399: $i] :
( ~ ( in @ SY399 @ SV69 )
| ( in @ SY399 @ SY397 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY396 )
| ( in @ SX3 @ SY397 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[873]) ).
thf(995,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK26_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK26_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK26_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK26_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[874]) ).
thf(996,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[874]) ).
thf(997,plain,
! [SV70: $i] :
( ( ~ ! [SY401: $i,SY402: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SY402 @ SY401 @ SV70 ) @ SV70 )
| ~ ( in @ ( sK15_D @ SY402 @ SY401 @ SV70 ) @ SY401 )
| ~ ( in @ ( sK15_D @ SY402 @ SY401 @ SV70 ) @ SY402 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SY402 @ SY401 @ SV70 ) @ SV70 )
| ( in @ ( sK15_D @ SY402 @ SY401 @ SV70 ) @ SY402 ) )
| ~ ( ( in @ ( sK15_D @ SY402 @ SY401 @ SV70 ) @ SY401 )
| ( in @ ( sK15_D @ SY402 @ SY401 @ SV70 ) @ SY402 ) ) ) )
| ( SY402
= ( set_intersection2 @ SV70 @ SY401 ) ) )
| ~ ! [SY403: $i,SY404: $i] :
( ( SY404
!= ( set_intersection2 @ SV70 @ SY403 ) )
| ~ ( ~ ! [SY405: $i] :
( ~ ( in @ SY405 @ SV70 )
| ~ ( in @ SY405 @ SY403 )
| ( in @ SY405 @ SY404 ) )
| ~ ~ ( ~ ! [SY406: $i] :
( ~ ( in @ SY406 @ SY404 )
| ( in @ SY406 @ SV70 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY404 )
| ( in @ SX3 @ SY403 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[875]) ).
thf(998,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ ( union @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ ( union @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[876]) ).
thf(999,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( ordinal @ ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[876]) ).
thf(1000,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ordinal @ SX1 )
| ~ ( ordinal_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[877]) ).
thf(1001,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ordinal @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( ordinal_subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[877]) ).
thf(1002,plain,
! [SV71: $i] :
( ( ( ! [SY408: $i] :
( ~ ( in @ SY408 @ SV71 )
| ~ ( ordinal @ SY408 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY409: $i] :
( ~ ( ordinal @ SY409 )
| ~ ( in @ SY409 @ SV71 )
| ( ordinal_subset @ ( sK54_B @ SV71 ) @ SY409 ) )
| ~ ~ ( ~ ( in @ ( sK54_B @ SV71 ) @ SV71 )
| ~ ( ordinal @ ( sK54_B @ SV71 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[878]) ).
thf(1003,plain,
! [SV72: $i,SV123: $i] :
( ( ~ ( ordinal @ SV123 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK44_C @ SV123 @ SV72 )
!= ( sK45_SY295 @ SV123 @ SV72 ) )
| ~ ~ ( ~ ~ ( ( ( sK45_SY295 @ SV123 @ SV72 )
!= ( sK48_SY300 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 ) ) )
| ( ( sK44_C @ SV123 @ SV72 )
!= ( sK46_SY299 @ SV123 @ SV72 ) ) )
| ~ ~ ( ~ ~ ( ( ( sK46_SY299 @ SV123 @ SV72 )
!= ( sK47_SY303 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 ) ) )
| ~ ( ( ( sK45_SY295 @ SV123 @ SV72 )
!= ( sK46_SY299 @ SV123 @ SV72 ) ) ) )
| ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[879]) ).
thf(1004,plain,
! [SV73: $i] :
( ( ( ~ ( relation @ SV73 ) )
= $true )
| ( ( ~ ( ~ ! [SY415: $i] :
( ~ ( relation @ SY415 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK23_C @ SY415 @ SV73 ) @ ( sK24_SY280 @ SY415 @ SV73 ) ) @ SV73 )
| ~ ( in @ ( ordered_pair @ ( sK23_C @ SY415 @ SV73 ) @ ( sK24_SY280 @ SY415 @ SV73 ) ) @ SY415 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK23_C @ SY415 @ SV73 ) @ ( sK24_SY280 @ SY415 @ SV73 ) ) @ SV73 )
| ( in @ ( ordered_pair @ ( sK23_C @ SY415 @ SV73 ) @ ( sK24_SY280 @ SY415 @ SV73 ) ) @ SY415 ) ) )
| ( SV73 = SY415 ) )
| ~ ! [SY416: $i] :
( ~ ( relation @ SY416 )
| ( SV73 != SY416 )
| ~ ( ~ ! [SY417: $i,SY418: $i] :
( ~ ( in @ ( ordered_pair @ SY417 @ SY418 ) @ SV73 )
| ( in @ ( ordered_pair @ SY417 @ SY418 ) @ SY416 ) )
| ~ ! [SY419: $i,SY420: $i] :
( ~ ( in @ ( ordered_pair @ SY419 @ SY420 ) @ SY416 )
| ( in @ ( ordered_pair @ SY419 @ SY420 ) @ SV73 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[880]) ).
thf(1005,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[881]) ).
thf(1006,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[881]) ).
thf(1007,plain,
! [SV74: $i] :
( ( ~ ! [SY421: $i,SY422: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK22_D @ SY422 @ SY421 @ SV74 ) @ SY422 )
| ( ( sK22_D @ SY422 @ SY421 @ SV74 )
!= SV74 ) )
| ~ ( ~ ( in @ ( sK22_D @ SY422 @ SY421 @ SV74 ) @ SY422 )
| ( ( sK22_D @ SY422 @ SY421 @ SV74 )
!= SY421 ) ) )
| ~ ( ( in @ ( sK22_D @ SY422 @ SY421 @ SV74 ) @ SY422 )
| ( ( sK22_D @ SY422 @ SY421 @ SV74 )
= SV74 )
| ( ( sK22_D @ SY422 @ SY421 @ SV74 )
= SY421 ) ) )
| ( SY422
= ( unordered_pair @ SV74 @ SY421 ) ) )
| ~ ! [SY423: $i,SY424: $i] :
( ( SY424
!= ( unordered_pair @ SV74 @ SY423 ) )
| ~ ( ~ ! [SY425: $i] :
( ~ ( in @ SY425 @ SY424 )
| ( SY425 = SV74 )
| ( SY425 = SY423 ) )
| ~ ~ ( ~ ! [SY426: $i] :
( ( SY426 != SV74 )
| ( in @ SY426 @ SY424 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY423 )
| ( in @ SX3 @ SY424 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[882]) ).
thf(1008,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ( in @ ( sK25_B @ SX0 ) @ SX0 )
| ~ ~ ( subset @ ( sK25_B @ SX0 ) @ SX0 ) )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[883]) ).
thf(1009,plain,
( ( ~ ! [SX0: $i] :
( ~ ( epsilon_transitive @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[883]) ).
thf(1010,plain,
! [SV75: $i] :
( ( ~ ! [SY428: $i] :
( ~ ( subset @ SY428 @ ( sK2_B @ SV75 ) )
| ( are_equipotent @ SY428 @ ( sK2_B @ SV75 ) )
| ( in @ SY428 @ ( sK2_B @ SV75 ) ) )
| ~ ~ ( ~ ! [SY429: $i] :
( ~ ( ~ ! [SY430: $i] :
( ~ ( subset @ SY430 @ SY429 )
| ( in @ SY430 @ ( sK3_SY270 @ SY429 @ SV75 ) ) )
| ~ ( in @ ( sK3_SY270 @ SY429 @ SV75 ) @ ( sK2_B @ SV75 ) ) )
| ~ ( in @ SY429 @ ( sK2_B @ SV75 ) ) )
| ~ ~ ( ~ ! [SY431: $i,SY432: $i] :
( ~ ( in @ SY431 @ ( sK2_B @ SV75 ) )
| ~ ( subset @ SY432 @ SY431 )
| ( in @ SY432 @ ( sK2_B @ SV75 ) ) )
| ~ ( in @ SV75 @ ( sK2_B @ SV75 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[884]) ).
thf(1011,plain,
! [SV76: $i] :
( ( ~ ! [SY433: $i,SY434: $i] :
( ~ ( relation @ SY434 )
| ~ ( in @ SV76 @ ( relation_field @ ( relation_restriction @ SY434 @ SY433 ) ) )
| ( in @ SV76 @ ( relation_field @ SY434 ) ) )
| ~ ! [SY435: $i,SY436: $i] :
( ~ ( relation @ SY436 )
| ~ ( in @ SV76 @ ( relation_field @ ( relation_restriction @ SY436 @ SY435 ) ) )
| ( in @ SV76 @ SY435 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[885]) ).
thf(1012,plain,
! [SV77: $i] :
( ( ( ~ ( relation @ SV77 ) )
= $true )
| ( ( ~ ( ~ ! [SY437: $i] :
( ~ ( relation @ SY437 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK17_C @ SY437 @ SV77 ) @ ( sK18_SY278 @ SY437 @ SV77 ) ) @ SV77 )
| ~ ~ ( in @ ( ordered_pair @ ( sK17_C @ SY437 @ SV77 ) @ ( sK18_SY278 @ SY437 @ SV77 ) ) @ SY437 ) )
| ( subset @ SV77 @ SY437 ) )
| ~ ! [SY438: $i] :
( ~ ( relation @ SY438 )
| ~ ( subset @ SV77 @ SY438 )
| ! [SY439: $i,SY440: $i] :
( ~ ( in @ ( ordered_pair @ SY439 @ SY440 ) @ SV77 )
| ( in @ ( ordered_pair @ SY439 @ SY440 ) @ SY438 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[886]) ).
thf(1013,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK16_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK16_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[887]) ).
thf(1014,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[887]) ).
thf(1015,plain,
! [SV78: $i] :
( ( ~ ! [SY441: $i,SY442: $i] :
( ~ ( ~ ( ~ ( in @ ( sK11_D @ SY442 @ SY441 @ SV78 ) @ SV78 )
| ( in @ ( sK11_D @ SY442 @ SY441 @ SV78 ) @ SY441 )
| ~ ( in @ ( sK11_D @ SY442 @ SY441 @ SV78 ) @ SY442 ) )
| ~ ~ ( ~ ( ( in @ ( sK11_D @ SY442 @ SY441 @ SV78 ) @ SV78 )
| ( in @ ( sK11_D @ SY442 @ SY441 @ SV78 ) @ SY442 ) )
| ~ ( ~ ( in @ ( sK11_D @ SY442 @ SY441 @ SV78 ) @ SY441 )
| ( in @ ( sK11_D @ SY442 @ SY441 @ SV78 ) @ SY442 ) ) ) )
| ( SY442
= ( set_difference @ SV78 @ SY441 ) ) )
| ~ ! [SY443: $i,SY444: $i] :
( ( SY444
!= ( set_difference @ SV78 @ SY443 ) )
| ~ ( ~ ! [SY445: $i] :
( ~ ( in @ SY445 @ SV78 )
| ( in @ SY445 @ SY443 )
| ( in @ SY445 @ SY444 ) )
| ~ ~ ( ~ ! [SY446: $i] :
( ~ ( in @ SY446 @ SY444 )
| ( in @ SY446 @ SV78 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY444 )
| ~ ( in @ SX3 @ SY443 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[888]) ).
thf(1016,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_field @ ( relation_restriction @ SX1 @ SX0 ) ) @ ( relation_field @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[889]) ).
thf(1017,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_field @ ( relation_restriction @ SX1 @ SX0 ) ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[889]) ).
thf(1018,plain,
( ( ~ ~ ( ~ ( epsilon_connected @ sK49_A )
| ~ ( epsilon_transitive @ sK49_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[890]) ).
thf(1019,plain,
( ( ~ ( ordinal @ sK49_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[890]) ).
thf(1020,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK36_B @ SX0 ) @ ( sK37_SY285 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK37_SY285 @ SX0 ) @ ( sK36_B @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK36_B @ SX0 )
!= ( sK37_SY285 @ SX0 ) ) ) )
| ( antisymmetric @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[891]) ).
thf(1021,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX2 @ SX1 ) @ SX0 )
| ( SX1 = SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[891]) ).
thf(1022,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[892]) ).
thf(1023,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[892]) ).
thf(1024,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK38_B @ SX0 ) @ ( sK39_SY286 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK39_SY286 @ SX0 ) @ ( sK40_SY288 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK38_B @ SX0 ) @ ( sK40_SY288 @ SX0 ) ) @ SX0 ) )
| ( transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[893]) ).
thf(1025,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( transitive @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ ( ordered_pair @ SX1 @ SX3 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[893]) ).
thf(1026,plain,
! [SV79: $i,SV124: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK5_C @ SV124 @ SV79 ) @ SV79 )
| ~ ( in @ ( sK5_C @ SV124 @ SV79 ) @ SV124 ) )
| ~ ( ( in @ ( sK5_C @ SV124 @ SV79 ) @ SV79 )
| ( in @ ( sK5_C @ SV124 @ SV79 ) @ SV124 ) ) )
| ( SV79 = SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(1027,plain,
( ( ~ ! [SX0: $i] :
( ( SX0
!= ( union @ SX0 ) )
| ( being_limit_ordinal @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[895]) ).
thf(1028,plain,
( ( ~ ! [SX0: $i] :
( ~ ( being_limit_ordinal @ SX0 )
| ( SX0
= ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[895]) ).
thf(1029,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_transitive @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[896]) ).
thf(1030,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( ordinal @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[896]) ).
thf(1031,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( being_limit_ordinal @ SX0 )
| ~ ( ~ ( ordinal @ ( sK50_B @ SX0 ) )
| ( SX0
!= ( succ @ ( sK50_B @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[897]) ).
thf(1032,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ! [SX1: $i] :
( ( SX0
!= ( succ @ SX1 ) )
| ~ ( ordinal @ SX1 ) )
| ~ ( being_limit_ordinal @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[897]) ).
thf(1033,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[898]) ).
thf(1034,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[898]) ).
thf(1035,plain,
! [SV80: $i,SV125: $i] :
( ( ~ ( ~ ! [SY481: $i,SY482: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 ) @ SY482 )
| ( ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 )
!= SY481 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 ) @ SY482 )
| ( ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 )
!= SV80 ) )
| ~ ( ~ ( in @ ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 ) @ SY482 )
| ( ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 )
!= SV125 ) ) ) )
| ~ ( ( in @ ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 ) @ SY482 )
| ( ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 )
= SY481 )
| ( ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 )
= SV80 )
| ( ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 )
= SV125 ) ) )
| ( SY482
= ( unordered_triple @ SV80 @ SV125 @ SY481 ) ) )
| ~ ! [SY483: $i,SY484: $i] :
( ( SY484
!= ( unordered_triple @ SV80 @ SV125 @ SY483 ) )
| ~ ( ~ ! [SY485: $i] :
( ~ ( in @ SY485 @ SY484 )
| ( SY485 = SY483 )
| ( SY485 = SV80 )
| ( SY485 = SV125 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ( SX4 != SY483 )
| ( in @ SX4 @ SY484 ) )
| ~ ~ ( ~ ! [SY456: $i] :
( ( SY456 != SV80 )
| ( in @ SY456 @ SY484 ) )
| ~ ! [SY488: $i] :
( ( SY488 != SV125 )
| ( in @ SY488 @ SY484 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(1036,plain,
! [SV1: $i,SV81: $i] :
( ( ( ~ ( ordinal @ SV81 ) )
= $true )
| ( ( ~ ( in @ SV1 @ SV81 )
| ( ordinal @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[900]) ).
thf(1037,plain,
! [SV2: $i] :
( ( ( ordinal @ SV2 )
= $false )
| ( ( ! [SY311: $i] :
( ~ ( ordinal @ SY311 )
| ( in @ SV2 @ SY311 )
| ( SV2 = SY311 )
| ( in @ SY311 @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[901]) ).
thf(1038,plain,
! [SV4: $i,SV82: $i] :
( ( ( ~ ( relation @ SV82 ) )
= $true )
| ( ( ~ ( well_ordering @ SV82 )
| ( well_ordering @ ( relation_restriction @ SV82 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[902]) ).
thf(1039,plain,
! [SV6: $i] :
( ( ( ordinal @ SV6 )
= $false )
| ( ( connected @ ( inclusion_relation @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[903]) ).
thf(1040,plain,
! [SV8: $i] :
( ( ( ordinal @ SV8 )
= $false )
| ( ( well_founded_relation @ ( inclusion_relation @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[904]) ).
thf(1041,plain,
! [SV9: $i] :
( ( ( ~ ( epsilon_connected @ SV9 ) )
= $true )
| ( ( ~ ( epsilon_transitive @ SV9 ) )
= $true )
| ( ( ordinal @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[905]) ).
thf(1042,plain,
! [SV83: $i,SV10: $i] :
( ( ( ~ ( ordinal @ SV10 )
| ~ ( ordinal @ SV83 ) )
= $true )
| ( ( ( ordinal_subset @ SV10 @ SV83 )
| ( ordinal_subset @ SV83 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[906]) ).
thf(1043,plain,
! [SV12: $i] :
( ( ( ~ ( ordinal @ SV12 ) )
= $true )
| ( ( ! [B: $i] :
~ ( ordinal @ B ) )
= $true )
| ( ( ordinal_subset @ SV12 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[907]) ).
thf(1044,plain,
! [SV84: $i,SV13: $i] :
( ( ( ~ ( in @ SV13 @ SV84 ) )
= $true )
| ( ( subset @ SV13 @ ( union @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[908]) ).
thf(1045,plain,
! [SV15: $i,SV85: $i] :
( ( ( ~ ( relation @ SV85 ) )
= $true )
| ( ( subset @ ( relation_rng_restriction @ SV15 @ SV85 ) @ SV85 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[909]) ).
thf(1046,plain,
! [SV126: $i,SV86: $i,SV16: $i] :
( ( ! [SY489: $i] :
( ~ ( subset @ SV16 @ SV86 )
| ~ ( subset @ SV126 @ SY489 )
| ( subset @ ( cartesian_product2 @ SV16 @ SV126 ) @ ( cartesian_product2 @ SV86 @ SY489 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(1047,plain,
! [SV87: $i,SV17: $i] :
( ( ( ~ ( subset @ SV17 @ SV87 ) )
= $true )
| ( ( ( set_union2 @ SV17 @ SV87 )
= SV87 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[911]) ).
thf(1048,plain,
! [SV88: $i,SV18: $i,SV127: $i] :
( ( ! [SY490: $i] :
( ~ ( relation_of2_as_subset @ SY490 @ SV127 @ SV18 )
| ~ ( subset @ SV18 @ SV88 )
| ( relation_of2_as_subset @ SY490 @ SV127 @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[912]) ).
thf(1049,plain,
! [SV89: $i,SV19: $i,SV128: $i] :
( ( ~ ( relation @ SV128 )
| ~ ( subset @ SV19 @ SV89 )
| ( subset @ ( relation_inverse_image @ SV128 @ SV19 ) @ ( relation_inverse_image @ SV128 @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[913]) ).
thf(1050,plain,
! [SV129: $i,SV91: $i,SV21: $i] :
( ( ~ ( subset @ SV21 @ SV91 )
| ~ ( subset @ SV21 @ SV129 )
| ( subset @ SV21 @ ( set_intersection2 @ SV91 @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(1051,plain,
! [SV130: $i,SV92: $i,SV22: $i] :
( ( ~ ( subset @ SV22 @ SV92 )
| ~ ( subset @ SV92 @ SV130 )
| ( subset @ SV22 @ SV130 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(1052,plain,
! [SV23: $i] :
( ( ( epsilon_transitive @ SV23 )
= $false )
| ( ( ! [SY331: $i] :
( ~ ( ordinal @ SY331 )
| ~ ( proper_subset @ SV23 @ SY331 )
| ( in @ SV23 @ SY331 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[917]) ).
thf(1053,plain,
! [SV93: $i,SV24: $i,SV131: $i] :
( ( ~ ( relation @ SV131 )
| ( subset @ ( fiber @ ( relation_restriction @ SV131 @ SV24 ) @ SV93 ) @ ( fiber @ SV131 @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[918]) ).
thf(1054,plain,
! [SV25: $i,SV94: $i] :
( ( ( ~ ( relation @ SV94 ) )
= $true )
| ( ( ~ ( reflexive @ SV94 )
| ( reflexive @ ( relation_restriction @ SV94 @ SV25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[919]) ).
thf(1055,plain,
! [SV26: $i,SV95: $i] :
( ( ( ~ ( relation @ SV95 ) )
= $true )
| ( ( ~ ( connected @ SV95 )
| ( connected @ ( relation_restriction @ SV95 @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[920]) ).
thf(1056,plain,
! [SV27: $i,SV96: $i] :
( ( ( ~ ( relation @ SV96 ) )
= $true )
| ( ( ~ ( transitive @ SV96 )
| ( transitive @ ( relation_restriction @ SV96 @ SV27 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[921]) ).
thf(1057,plain,
! [SV28: $i,SV97: $i] :
( ( ( ~ ( relation @ SV97 ) )
= $true )
| ( ( ~ ( antisymmetric @ SV97 )
| ( antisymmetric @ ( relation_restriction @ SV97 @ SV28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[922]) ).
thf(1058,plain,
! [SV98: $i,SV29: $i] :
( ( ( ~ ( subset @ SV29 @ SV98 ) )
= $true )
| ( ( ! [SY466: $i] : ( subset @ ( set_intersection2 @ SV29 @ SY466 ) @ ( set_intersection2 @ SV98 @ SY466 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[923]) ).
thf(1059,plain,
! [SV99: $i,SV30: $i] :
( ( ( ~ ( subset @ SV30 @ SV99 ) )
= $true )
| ( ( ( set_intersection2 @ SV30 @ SV99 )
= SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[924]) ).
thf(1060,plain,
! [SV32: $i,SV100: $i] :
( ( ( ~ ( relation @ SV100 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV100 )
| ( well_founded_relation @ ( relation_restriction @ SV100 @ SV32 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[925]) ).
thf(1061,plain,
! [SV101: $i,SV33: $i] :
( ( ( ~ ( subset @ SV33 @ SV101 ) )
= $true )
| ( ( ! [SY467: $i] : ( subset @ ( set_difference @ SV33 @ SY467 ) @ ( set_difference @ SV101 @ SY467 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[926]) ).
thf(1062,plain,
! [SV35: $i,SV103: $i] :
( ( ( ~ ( relation @ SV103 ) )
= $true )
| ( ( ~ ( subset @ SV35 @ ( relation_field @ SV103 ) )
| ~ ( well_ordering @ SV103 )
| ( ( relation_field @ ( relation_restriction @ SV103 @ SV35 ) )
= SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[928]) ).
thf(1063,plain,
! [SV132: $i,SV104: $i,SV36: $i] :
( ( ~ ( in @ SV36 @ SV104 )
| ~ ( in @ SV104 @ SV132 )
| ~ ( in @ SV132 @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(1064,plain,
! [SV37: $i] :
( ( ( subset @ SV37 @ empty_set )
= $false )
| ( ( SV37 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[930]) ).
thf(1065,plain,
! [SV38: $i,SV105: $i] :
( ( ( ~ ( proper_subset @ SV105 @ SV38 ) )
= $true )
| ( ( ~ ( subset @ SV38 @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[931]) ).
thf(1066,plain,
! [SV39: $i,SV133: $i,SV106: $i] :
( ( ~ ( disjoint @ SV106 @ SV133 )
| ~ ( subset @ SV39 @ SV106 )
| ( disjoint @ SV39 @ SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(1067,plain,
! [SV107: $i,SV40: $i] :
( ( ( ~ ( subset @ ( singleton @ SV40 ) @ ( singleton @ SV107 ) ) )
= $true )
| ( ( SV40 = SV107 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[933]) ).
thf(1068,plain,
! [SV42: $i,SV109: $i] :
( ( ( ~ ( relation @ SV109 ) )
= $true )
| ( ( subset @ ( relation_dom_restriction @ SV109 @ SV42 ) @ SV109 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[935]) ).
thf(1069,plain,
! [SV134: $i,SV110: $i,SV43: $i] :
( ( ~ ( subset @ SV43 @ SV110 )
| ~ ( subset @ SV134 @ SV110 )
| ( subset @ ( set_union2 @ SV43 @ SV134 ) @ SV110 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1070,plain,
! [SV111: $i,SV44: $i] :
( ( ( ~ ( in @ SV44 @ SV111 ) )
= $true )
| ( ( subset @ SV44 @ ( union @ SV111 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[937]) ).
thf(1071,plain,
! [SV112: $i,SV45: $i] :
( ( ( ~ ( in @ SV45 @ SV112 ) )
= $true )
| ( ( ~ ( in @ SV112 @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[938]) ).
thf(1072,plain,
! [SV46: $i] :
( ( ( empty @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[939]) ).
thf(1073,plain,
! [SV47: $i] :
( ( ( relation @ SV47 )
= $false )
| ( ( ! [SY358: $i] : ( relation @ ( relation_restriction @ SV47 @ SY358 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[940]) ).
thf(1074,plain,
! [SV48: $i] :
( ( ( relation @ SV48 )
= $false )
| ( ( relation @ ( relation_inverse @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[941]) ).
thf(1075,plain,
! [SV113: $i,SV49: $i] :
( ( ( ~ ( relation @ SV49 )
| ~ ( relation @ SV113 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV49 @ SV113 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[942]) ).
thf(1076,plain,
! [SV51: $i] :
( ( ( relation @ SV51 )
= $false )
| ( ( ! [SY360: $i] : ( relation @ ( relation_dom_restriction @ SV51 @ SY360 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[943]) ).
thf(1077,plain,
! [SV52: $i,SV114: $i] :
( ( ( ~ ( relation @ SV114 ) )
= $true )
| ( ( relation @ ( relation_rng_restriction @ SV52 @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[944]) ).
thf(1078,plain,
! [SV115: $i,SV54: $i] :
( ( ( ~ ( relation @ SV54 )
| ~ ( relation @ SV115 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV54 @ SV115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[946]) ).
thf(1079,plain,
! [SV116: $i,SV55: $i] :
( ( ( ~ ( relation @ SV55 )
| ~ ( relation @ SV116 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV55 @ SV116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[947]) ).
thf(1080,plain,
! [SV117: $i,SV56: $i] :
( ( ( ~ ( relation @ SV56 )
| ~ ( relation @ SV117 ) )
= $true )
| ( ( relation @ ( set_difference @ SV56 @ SV117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[948]) ).
thf(1081,plain,
! [SV57: $i] :
( ( ( relation @ SV57 )
= $false )
| ( ( ( relation_inverse @ ( relation_inverse @ SV57 ) )
= SV57 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[949]) ).
thf(1082,plain,
! [SV118: $i,SV59: $i] :
( ( ( ~ ( in @ SV59 @ SV118 ) )
= $true )
| ( ( element @ SV59 @ SV118 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[950]) ).
thf(1083,plain,
! [SV60: $i,SV119: $i] :
( ( ( ~ ( empty @ SV119 ) )
= $true )
| ( ( ~ ( in @ SV60 @ SV119 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[951]) ).
thf(1084,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[952]) ).
thf(1085,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[953]) ).
thf(1086,plain,
! [SV61: $i] :
( ( ~ ! [SY367: $i,SY368: $i] :
( ~ ( relation @ SY368 )
| ~ ( in @ SV61 @ SY368 )
| ~ ( in @ SV61 @ ( cartesian_product2 @ SY367 @ SY367 ) )
| ( in @ SV61 @ ( relation_restriction @ SY368 @ SY367 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[954]) ).
thf(1087,plain,
! [SV61: $i] :
( ( ~ ~ ( ~ ! [SY369: $i,SY370: $i] :
( ~ ( relation @ SY370 )
| ~ ( in @ SV61 @ ( relation_restriction @ SY370 @ SY369 ) )
| ( in @ SV61 @ SY370 ) )
| ~ ! [SY371: $i,SY372: $i] :
( ~ ( relation @ SY372 )
| ~ ( in @ SV61 @ ( relation_restriction @ SY372 @ SY371 ) )
| ( in @ SV61 @ ( cartesian_product2 @ SY371 @ SY371 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[954]) ).
thf(1088,plain,
( ( function @ sK10_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[955]) ).
thf(1089,plain,
( ( relation @ sK10_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[956]) ).
thf(1090,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ~ ( ordinal @ ( sK33_B @ SX0 ) )
| ~ ~ ( ~ ( in @ ( sK33_B @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( succ @ ( sK33_B @ SX0 ) ) @ SX0 ) ) )
| ( being_limit_ordinal @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[957]) ).
thf(1091,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( being_limit_ordinal @ SX0 )
| ! [SX1: $i] :
( ~ ( ordinal @ SX1 )
| ~ ( in @ SX1 @ SX0 )
| ( in @ ( succ @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[958]) ).
thf(1092,plain,
! [SV62: $i] :
( ( ( ordinal @ SV62 )
= $false )
| ( ( ~ ( ~ ! [SY373: $i] :
( ~ ( ordinal @ SY373 )
| ~ ( in @ SV62 @ SY373 )
| ( ordinal_subset @ ( succ @ SV62 ) @ SY373 ) )
| ~ ! [SY374: $i] :
( ~ ( ordinal @ SY374 )
| ~ ( ordinal_subset @ ( succ @ SV62 ) @ SY374 )
| ( in @ SV62 @ SY374 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[959]) ).
thf(1093,plain,
! [SV63: $i,SV120: $i] :
( ( ( ~ ( ordinal @ SV120 ) )
= $true )
| ( ( ~ ( ~ ! [SY471: $i] :
( ! [SY377: $i] :
( ( SY471 != SY377 )
| ~ ( ordinal @ SY377 )
| ~ ( in @ SY377 @ SV63 ) )
| ~ ( in @ SY471 @ ( succ @ SV120 ) )
| ( in @ SY471 @ ( sK52_C @ SV120 @ SV63 ) ) )
| ~ ~ ( ~ ! [SY473: $i] :
( ~ ( in @ SY473 @ ( sK52_C @ SV120 @ SV63 ) )
| ~ ( ~ ~ ( ( SY473
!= ( sK53_E @ SY473 @ SV120 @ SV63 ) )
| ~ ( ordinal @ ( sK53_E @ SY473 @ SV120 @ SV63 ) ) )
| ~ ( in @ ( sK53_E @ SY473 @ SV120 @ SV63 ) @ SV63 ) ) )
| ~ ! [SY474: $i] :
( ~ ( in @ SY474 @ ( sK52_C @ SV120 @ SV63 ) )
| ( in @ SY474 @ ( succ @ SV120 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[960]) ).
thf(1094,plain,
! [SV64: $i] :
( ( ~ ! [SY380: $i] :
( ~ ( subset @ SV64 @ SY380 )
| ! [SY381: $i] : ( subset @ ( cartesian_product2 @ SV64 @ SY381 ) @ ( cartesian_product2 @ SY380 @ SY381 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[961]) ).
thf(1095,plain,
! [SV64: $i] :
( ( ~ ! [SY382: $i] :
( ~ ( subset @ SV64 @ SY382 )
| ! [SY383: $i] : ( subset @ ( cartesian_product2 @ SY383 @ SV64 ) @ ( cartesian_product2 @ SY383 @ SY382 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[961]) ).
thf(1096,plain,
( ( ! [SX0: $i] :
( ~ ( epsilon_connected @ SX0 )
| ~ ( epsilon_transitive @ SX0 )
| ( ordinal @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[962]) ).
thf(1097,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[963]) ).
thf(1098,plain,
! [SV65: $i] :
( ( ~ ! [SY384: $i,SY385: $i] :
( ~ ( in @ SV65 @ SY385 )
| ~ ( in @ SY384 @ SY385 )
| ( subset @ ( unordered_pair @ SV65 @ SY384 ) @ SY385 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[964]) ).
thf(1099,plain,
! [SV65: $i] :
( ( ~ ~ ( ~ ! [SY386: $i,SY387: $i] :
( ~ ( subset @ ( unordered_pair @ SV65 @ SY386 ) @ SY387 )
| ( in @ SV65 @ SY387 ) )
| ~ ! [SY388: $i,SY389: $i] :
( ~ ( subset @ ( unordered_pair @ SV65 @ SY388 ) @ SY389 )
| ( in @ SY388 @ SY389 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[964]) ).
thf(1100,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( empty @ ( succ @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ ( succ @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ ( succ @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[965]) ).
thf(1101,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( ordinal @ ( succ @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[966]) ).
thf(1102,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ ( sK14_SY277 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK14_SY277 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[967]) ).
thf(1103,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK12_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[968]) ).
thf(1104,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK31_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK31_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[969]) ).
thf(1105,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK29_C @ SX1 @ SX0 ) @ ( sK30_SY281 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[970]) ).
thf(1106,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( ( ( sK19_B @ SX0 )
!= ( sK20_SY279 @ SX0 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_B @ SX0 ) @ SX0 )
| ~ ( in @ ( sK20_SY279 @ SX0 ) @ SX0 ) )
| ~ ~ ( in @ ( sK19_B @ SX0 ) @ ( sK20_SY279 @ SX0 ) ) ) )
| ~ ~ ( in @ ( sK20_SY279 @ SX0 ) @ ( sK19_B @ SX0 ) ) )
| ( epsilon_connected @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[971]) ).
thf(1107,plain,
( ( ! [SX0: $i] :
( ~ ( epsilon_connected @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( SX1 = SX2 )
| ~ ( in @ SX1 @ SX0 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX1 @ SX2 )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[972]) ).
thf(1108,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[973]) ).
thf(1109,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[974]) ).
thf(1110,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( reflexive @ SX0 )
| ~ ( transitive @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ~ ( connected @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ( well_ordering @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[975]) ).
thf(1111,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( well_founded_relation @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[976]) ).
thf(1112,plain,
! [SV66: $i] :
( ( ( ~ ( in @ ( sK51_B @ SV66 ) @ SV66 )
| ~ ( ~ ( ordinal @ ( sK51_B @ SV66 ) )
| ~ ( subset @ ( sK51_B @ SV66 ) @ SV66 ) ) )
= $false )
| ( ( ordinal @ SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[977]) ).
thf(1113,plain,
! [SV67: $i,SV121: $i] :
( ( ( ~ ( ~ ! [SY475: $i] :
( ~ ( in @ SY475 @ SV121 )
| ~ ( in @ SY475 @ ( sK4_C @ SV121 @ SV67 ) ) )
| ~ ( in @ ( sK4_C @ SV121 @ SV67 ) @ SV121 ) ) )
= $true )
| ( ( ~ ( in @ SV67 @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[978]) ).
thf(1114,plain,
( ( ! [SX0: $i] :
( ( in @ ( sK27_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[979]) ).
thf(1115,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[980]) ).
thf(1116,plain,
( ( relation @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[981]) ).
thf(1117,plain,
( ( relation_empty_yielding @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[982]) ).
thf(1118,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK34_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK34_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[983]) ).
thf(1119,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[984]) ).
thf(1120,plain,
( ( empty @ sK9_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[985]) ).
thf(1121,plain,
( ( relation @ sK9_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[986]) ).
thf(1122,plain,
( ( ~ ( empty @ sK8_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[987]) ).
thf(1123,plain,
( ( relation @ sK8_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[988]) ).
thf(1124,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK28_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK28_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[989]) ).
thf(1125,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[990]) ).
thf(1126,plain,
( ( ~ ( ~ ~ ( ~ ~ ( empty @ sK7_A )
| ~ ( epsilon_transitive @ sK7_A ) )
| ~ ( epsilon_connected @ sK7_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[991]) ).
thf(1127,plain,
( ( ordinal @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[992]) ).
thf(1128,plain,
! [SV68: $i,SV122: $i] :
( ( ( ~ ( ordinal @ SV122 ) )
= $true )
| ( ( ~ ( ~ ( ordinal @ ( sK35_C @ SV122 @ SV68 ) )
| ~ ~ ( ~ ! [SY476: $i] :
( ~ ( ordinal @ SY476 )
| ~ ( in @ SY476 @ SV68 )
| ( ordinal_subset @ ( sK35_C @ SV122 @ SV68 ) @ SY476 ) )
| ~ ( in @ ( sK35_C @ SV122 @ SV68 ) @ SV68 ) ) )
| ( SV68 = empty_set )
| ~ ( subset @ SV68 @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[993]) ).
thf(1129,plain,
! [SV69: $i] :
( ( ~ ! [SY394: $i,SY395: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK21_D @ SY395 @ SY394 @ SV69 ) @ SY395 )
| ~ ( in @ ( sK21_D @ SY395 @ SY394 @ SV69 ) @ SV69 ) )
| ~ ( ~ ( in @ ( sK21_D @ SY395 @ SY394 @ SV69 ) @ SY395 )
| ~ ( in @ ( sK21_D @ SY395 @ SY394 @ SV69 ) @ SY394 ) ) )
| ~ ( ( in @ ( sK21_D @ SY395 @ SY394 @ SV69 ) @ SY395 )
| ( in @ ( sK21_D @ SY395 @ SY394 @ SV69 ) @ SV69 )
| ( in @ ( sK21_D @ SY395 @ SY394 @ SV69 ) @ SY394 ) ) )
| ( SY395
= ( set_union2 @ SV69 @ SY394 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[994]) ).
thf(1130,plain,
! [SV69: $i] :
( ( ~ ! [SY396: $i,SY397: $i] :
( ( SY397
!= ( set_union2 @ SV69 @ SY396 ) )
| ~ ( ~ ! [SY398: $i] :
( ~ ( in @ SY398 @ SY397 )
| ( in @ SY398 @ SV69 )
| ( in @ SY398 @ SY396 ) )
| ~ ~ ( ~ ! [SY399: $i] :
( ~ ( in @ SY399 @ SV69 )
| ( in @ SY399 @ SY397 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY396 )
| ( in @ SX3 @ SY397 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[994]) ).
thf(1131,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK26_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK26_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK26_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK26_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[995]) ).
thf(1132,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[996]) ).
thf(1133,plain,
! [SV70: $i] :
( ( ~ ! [SY401: $i,SY402: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SY402 @ SY401 @ SV70 ) @ SV70 )
| ~ ( in @ ( sK15_D @ SY402 @ SY401 @ SV70 ) @ SY401 )
| ~ ( in @ ( sK15_D @ SY402 @ SY401 @ SV70 ) @ SY402 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SY402 @ SY401 @ SV70 ) @ SV70 )
| ( in @ ( sK15_D @ SY402 @ SY401 @ SV70 ) @ SY402 ) )
| ~ ( ( in @ ( sK15_D @ SY402 @ SY401 @ SV70 ) @ SY401 )
| ( in @ ( sK15_D @ SY402 @ SY401 @ SV70 ) @ SY402 ) ) ) )
| ( SY402
= ( set_intersection2 @ SV70 @ SY401 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[997]) ).
thf(1134,plain,
! [SV70: $i] :
( ( ~ ! [SY403: $i,SY404: $i] :
( ( SY404
!= ( set_intersection2 @ SV70 @ SY403 ) )
| ~ ( ~ ! [SY405: $i] :
( ~ ( in @ SY405 @ SV70 )
| ~ ( in @ SY405 @ SY403 )
| ( in @ SY405 @ SY404 ) )
| ~ ~ ( ~ ! [SY406: $i] :
( ~ ( in @ SY406 @ SY404 )
| ( in @ SY406 @ SV70 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY404 )
| ( in @ SX3 @ SY403 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[997]) ).
thf(1135,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ ( union @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ ( union @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[998]) ).
thf(1136,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( ordinal @ ( union @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[999]) ).
thf(1137,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ordinal @ SX1 )
| ~ ( ordinal_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1000]) ).
thf(1138,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ordinal @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( ordinal_subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1001]) ).
thf(1139,plain,
! [SV71: $i,SV135: $i] :
( ( ( ~ ( in @ SV135 @ SV71 )
| ~ ( ordinal @ SV135 ) )
= $true )
| ( ( ~ ( ~ ! [SY409: $i] :
( ~ ( ordinal @ SY409 )
| ~ ( in @ SY409 @ SV71 )
| ( ordinal_subset @ ( sK54_B @ SV71 ) @ SY409 ) )
| ~ ~ ( ~ ( in @ ( sK54_B @ SV71 ) @ SV71 )
| ~ ( ordinal @ ( sK54_B @ SV71 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1140,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ( ordinal @ SV123 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK44_C @ SV123 @ SV72 )
!= ( sK45_SY295 @ SV123 @ SV72 ) )
| ~ ~ ( ~ ~ ( ( ( sK45_SY295 @ SV123 @ SV72 )
!= ( sK48_SY300 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 ) ) )
| ( ( sK44_C @ SV123 @ SV72 )
!= ( sK46_SY299 @ SV123 @ SV72 ) ) )
| ~ ~ ( ~ ~ ( ( ( sK46_SY299 @ SV123 @ SV72 )
!= ( sK47_SY303 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 ) ) )
| ~ ( ( ( sK45_SY295 @ SV123 @ SV72 )
!= ( sK46_SY299 @ SV123 @ SV72 ) ) ) )
| ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1003]) ).
thf(1141,plain,
! [SV73: $i] :
( ( ( relation @ SV73 )
= $false )
| ( ( ~ ( ~ ! [SY415: $i] :
( ~ ( relation @ SY415 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK23_C @ SY415 @ SV73 ) @ ( sK24_SY280 @ SY415 @ SV73 ) ) @ SV73 )
| ~ ( in @ ( ordered_pair @ ( sK23_C @ SY415 @ SV73 ) @ ( sK24_SY280 @ SY415 @ SV73 ) ) @ SY415 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK23_C @ SY415 @ SV73 ) @ ( sK24_SY280 @ SY415 @ SV73 ) ) @ SV73 )
| ( in @ ( ordered_pair @ ( sK23_C @ SY415 @ SV73 ) @ ( sK24_SY280 @ SY415 @ SV73 ) ) @ SY415 ) ) )
| ( SV73 = SY415 ) )
| ~ ! [SY416: $i] :
( ~ ( relation @ SY416 )
| ( SV73 != SY416 )
| ~ ( ~ ! [SY417: $i,SY418: $i] :
( ~ ( in @ ( ordered_pair @ SY417 @ SY418 ) @ SV73 )
| ( in @ ( ordered_pair @ SY417 @ SY418 ) @ SY416 ) )
| ~ ! [SY419: $i,SY420: $i] :
( ~ ( in @ ( ordered_pair @ SY419 @ SY420 ) @ SY416 )
| ( in @ ( ordered_pair @ SY419 @ SY420 ) @ SV73 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1004]) ).
thf(1142,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1005]) ).
thf(1143,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1006]) ).
thf(1144,plain,
! [SV74: $i] :
( ( ~ ! [SY421: $i,SY422: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK22_D @ SY422 @ SY421 @ SV74 ) @ SY422 )
| ( ( sK22_D @ SY422 @ SY421 @ SV74 )
!= SV74 ) )
| ~ ( ~ ( in @ ( sK22_D @ SY422 @ SY421 @ SV74 ) @ SY422 )
| ( ( sK22_D @ SY422 @ SY421 @ SV74 )
!= SY421 ) ) )
| ~ ( ( in @ ( sK22_D @ SY422 @ SY421 @ SV74 ) @ SY422 )
| ( ( sK22_D @ SY422 @ SY421 @ SV74 )
= SV74 )
| ( ( sK22_D @ SY422 @ SY421 @ SV74 )
= SY421 ) ) )
| ( SY422
= ( unordered_pair @ SV74 @ SY421 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1007]) ).
thf(1145,plain,
! [SV74: $i] :
( ( ~ ! [SY423: $i,SY424: $i] :
( ( SY424
!= ( unordered_pair @ SV74 @ SY423 ) )
| ~ ( ~ ! [SY425: $i] :
( ~ ( in @ SY425 @ SY424 )
| ( SY425 = SV74 )
| ( SY425 = SY423 ) )
| ~ ~ ( ~ ! [SY426: $i] :
( ( SY426 != SV74 )
| ( in @ SY426 @ SY424 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY423 )
| ( in @ SX3 @ SY424 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1007]) ).
thf(1146,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ( in @ ( sK25_B @ SX0 ) @ SX0 )
| ~ ~ ( subset @ ( sK25_B @ SX0 ) @ SX0 ) )
| ( epsilon_transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1008]) ).
thf(1147,plain,
( ( ! [SX0: $i] :
( ~ ( epsilon_transitive @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1009]) ).
thf(1148,plain,
! [SV75: $i] :
( ( ~ ! [SY428: $i] :
( ~ ( subset @ SY428 @ ( sK2_B @ SV75 ) )
| ( are_equipotent @ SY428 @ ( sK2_B @ SV75 ) )
| ( in @ SY428 @ ( sK2_B @ SV75 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1010]) ).
thf(1149,plain,
! [SV75: $i] :
( ( ~ ~ ( ~ ! [SY429: $i] :
( ~ ( ~ ! [SY430: $i] :
( ~ ( subset @ SY430 @ SY429 )
| ( in @ SY430 @ ( sK3_SY270 @ SY429 @ SV75 ) ) )
| ~ ( in @ ( sK3_SY270 @ SY429 @ SV75 ) @ ( sK2_B @ SV75 ) ) )
| ~ ( in @ SY429 @ ( sK2_B @ SV75 ) ) )
| ~ ~ ( ~ ! [SY431: $i,SY432: $i] :
( ~ ( in @ SY431 @ ( sK2_B @ SV75 ) )
| ~ ( subset @ SY432 @ SY431 )
| ( in @ SY432 @ ( sK2_B @ SV75 ) ) )
| ~ ( in @ SV75 @ ( sK2_B @ SV75 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1010]) ).
thf(1150,plain,
! [SV76: $i] :
( ( ~ ! [SY433: $i,SY434: $i] :
( ~ ( relation @ SY434 )
| ~ ( in @ SV76 @ ( relation_field @ ( relation_restriction @ SY434 @ SY433 ) ) )
| ( in @ SV76 @ ( relation_field @ SY434 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1011]) ).
thf(1151,plain,
! [SV76: $i] :
( ( ~ ! [SY435: $i,SY436: $i] :
( ~ ( relation @ SY436 )
| ~ ( in @ SV76 @ ( relation_field @ ( relation_restriction @ SY436 @ SY435 ) ) )
| ( in @ SV76 @ SY435 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1011]) ).
thf(1152,plain,
! [SV77: $i] :
( ( ( relation @ SV77 )
= $false )
| ( ( ~ ( ~ ! [SY437: $i] :
( ~ ( relation @ SY437 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK17_C @ SY437 @ SV77 ) @ ( sK18_SY278 @ SY437 @ SV77 ) ) @ SV77 )
| ~ ~ ( in @ ( ordered_pair @ ( sK17_C @ SY437 @ SV77 ) @ ( sK18_SY278 @ SY437 @ SV77 ) ) @ SY437 ) )
| ( subset @ SV77 @ SY437 ) )
| ~ ! [SY438: $i] :
( ~ ( relation @ SY438 )
| ~ ( subset @ SV77 @ SY438 )
| ! [SY439: $i,SY440: $i] :
( ~ ( in @ ( ordered_pair @ SY439 @ SY440 ) @ SV77 )
| ( in @ ( ordered_pair @ SY439 @ SY440 ) @ SY438 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1012]) ).
thf(1153,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK16_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK16_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1013]) ).
thf(1154,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1014]) ).
thf(1155,plain,
! [SV78: $i] :
( ( ~ ! [SY441: $i,SY442: $i] :
( ~ ( ~ ( ~ ( in @ ( sK11_D @ SY442 @ SY441 @ SV78 ) @ SV78 )
| ( in @ ( sK11_D @ SY442 @ SY441 @ SV78 ) @ SY441 )
| ~ ( in @ ( sK11_D @ SY442 @ SY441 @ SV78 ) @ SY442 ) )
| ~ ~ ( ~ ( ( in @ ( sK11_D @ SY442 @ SY441 @ SV78 ) @ SV78 )
| ( in @ ( sK11_D @ SY442 @ SY441 @ SV78 ) @ SY442 ) )
| ~ ( ~ ( in @ ( sK11_D @ SY442 @ SY441 @ SV78 ) @ SY441 )
| ( in @ ( sK11_D @ SY442 @ SY441 @ SV78 ) @ SY442 ) ) ) )
| ( SY442
= ( set_difference @ SV78 @ SY441 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1015]) ).
thf(1156,plain,
! [SV78: $i] :
( ( ~ ! [SY443: $i,SY444: $i] :
( ( SY444
!= ( set_difference @ SV78 @ SY443 ) )
| ~ ( ~ ! [SY445: $i] :
( ~ ( in @ SY445 @ SV78 )
| ( in @ SY445 @ SY443 )
| ( in @ SY445 @ SY444 ) )
| ~ ~ ( ~ ! [SY446: $i] :
( ~ ( in @ SY446 @ SY444 )
| ( in @ SY446 @ SV78 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY444 )
| ~ ( in @ SX3 @ SY443 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1015]) ).
thf(1157,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_field @ ( relation_restriction @ SX1 @ SX0 ) ) @ ( relation_field @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1016]) ).
thf(1158,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_field @ ( relation_restriction @ SX1 @ SX0 ) ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1017]) ).
thf(1159,plain,
( ( ~ ( ~ ( epsilon_connected @ sK49_A )
| ~ ( epsilon_transitive @ sK49_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1018]) ).
thf(1160,plain,
( ( ordinal @ sK49_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1019]) ).
thf(1161,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK36_B @ SX0 ) @ ( sK37_SY285 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK37_SY285 @ SX0 ) @ ( sK36_B @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK36_B @ SX0 )
!= ( sK37_SY285 @ SX0 ) ) ) )
| ( antisymmetric @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1020]) ).
thf(1162,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX2 @ SX1 ) @ SX0 )
| ( SX1 = SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1021]) ).
thf(1163,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1022]) ).
thf(1164,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1023]) ).
thf(1165,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK38_B @ SX0 ) @ ( sK39_SY286 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK39_SY286 @ SX0 ) @ ( sK40_SY288 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK38_B @ SX0 ) @ ( sK40_SY288 @ SX0 ) ) @ SX0 ) )
| ( transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1024]) ).
thf(1166,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( transitive @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ ( ordered_pair @ SX1 @ SX3 ) @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1025]) ).
thf(1167,plain,
! [SV79: $i,SV124: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK5_C @ SV124 @ SV79 ) @ SV79 )
| ~ ( in @ ( sK5_C @ SV124 @ SV79 ) @ SV124 ) )
| ~ ( ( in @ ( sK5_C @ SV124 @ SV79 ) @ SV79 )
| ( in @ ( sK5_C @ SV124 @ SV79 ) @ SV124 ) ) ) )
= $true )
| ( ( SV79 = SV124 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1026]) ).
thf(1168,plain,
( ( ! [SX0: $i] :
( ( SX0
!= ( union @ SX0 ) )
| ( being_limit_ordinal @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1027]) ).
thf(1169,plain,
( ( ! [SX0: $i] :
( ~ ( being_limit_ordinal @ SX0 )
| ( SX0
= ( union @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1028]) ).
thf(1170,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_transitive @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1029]) ).
thf(1171,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( ordinal @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1030]) ).
thf(1172,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( being_limit_ordinal @ SX0 )
| ~ ( ~ ( ordinal @ ( sK50_B @ SX0 ) )
| ( SX0
!= ( succ @ ( sK50_B @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1031]) ).
thf(1173,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ! [SX1: $i] :
( ( SX0
!= ( succ @ SX1 ) )
| ~ ( ordinal @ SX1 ) )
| ~ ( being_limit_ordinal @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1032]) ).
thf(1174,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1033]) ).
thf(1175,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1034]) ).
thf(1176,plain,
! [SV80: $i,SV125: $i] :
( ( ~ ! [SY481: $i,SY482: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 ) @ SY482 )
| ( ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 )
!= SY481 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 ) @ SY482 )
| ( ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 )
!= SV80 ) )
| ~ ( ~ ( in @ ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 ) @ SY482 )
| ( ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 )
!= SV125 ) ) ) )
| ~ ( ( in @ ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 ) @ SY482 )
| ( ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 )
= SY481 )
| ( ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 )
= SV80 )
| ( ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 )
= SV125 ) ) )
| ( SY482
= ( unordered_triple @ SV80 @ SV125 @ SY481 ) ) )
| ~ ! [SY483: $i,SY484: $i] :
( ( SY484
!= ( unordered_triple @ SV80 @ SV125 @ SY483 ) )
| ~ ( ~ ! [SY485: $i] :
( ~ ( in @ SY485 @ SY484 )
| ( SY485 = SY483 )
| ( SY485 = SV80 )
| ( SY485 = SV125 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ( SX4 != SY483 )
| ( in @ SX4 @ SY484 ) )
| ~ ~ ( ~ ! [SY456: $i] :
( ( SY456 != SV80 )
| ( in @ SY456 @ SY484 ) )
| ~ ! [SY488: $i] :
( ( SY488 != SV125 )
| ( in @ SY488 @ SY484 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1035]) ).
thf(1177,plain,
! [SV1: $i,SV81: $i] :
( ( ( ordinal @ SV81 )
= $false )
| ( ( ~ ( in @ SV1 @ SV81 )
| ( ordinal @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1036]) ).
thf(1178,plain,
! [SV2: $i,SV136: $i] :
( ( ( ~ ( ordinal @ SV136 )
| ( in @ SV2 @ SV136 )
| ( SV2 = SV136 )
| ( in @ SV136 @ SV2 ) )
= $true )
| ( ( ordinal @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1037]) ).
thf(1179,plain,
! [SV4: $i,SV82: $i] :
( ( ( relation @ SV82 )
= $false )
| ( ( ~ ( well_ordering @ SV82 )
| ( well_ordering @ ( relation_restriction @ SV82 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1038]) ).
thf(1180,plain,
! [SV9: $i] :
( ( ( epsilon_connected @ SV9 )
= $false )
| ( ( ~ ( epsilon_transitive @ SV9 ) )
= $true )
| ( ( ordinal @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1041]) ).
thf(1181,plain,
! [SV83: $i,SV10: $i] :
( ( ( ~ ( ordinal @ SV10 ) )
= $true )
| ( ( ~ ( ordinal @ SV83 ) )
= $true )
| ( ( ( ordinal_subset @ SV10 @ SV83 )
| ( ordinal_subset @ SV83 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1042]) ).
thf(1182,plain,
! [SV12: $i] :
( ( ( ordinal @ SV12 )
= $false )
| ( ( ! [B: $i] :
~ ( ordinal @ B ) )
= $true )
| ( ( ordinal_subset @ SV12 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1043]) ).
thf(1183,plain,
! [SV84: $i,SV13: $i] :
( ( ( in @ SV13 @ SV84 )
= $false )
| ( ( subset @ SV13 @ ( union @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1044]) ).
thf(1184,plain,
! [SV15: $i,SV85: $i] :
( ( ( relation @ SV85 )
= $false )
| ( ( subset @ ( relation_rng_restriction @ SV15 @ SV85 ) @ SV85 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1045]) ).
thf(1185,plain,
! [SV137: $i,SV126: $i,SV86: $i,SV16: $i] :
( ( ~ ( subset @ SV16 @ SV86 )
| ~ ( subset @ SV126 @ SV137 )
| ( subset @ ( cartesian_product2 @ SV16 @ SV126 ) @ ( cartesian_product2 @ SV86 @ SV137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1186,plain,
! [SV87: $i,SV17: $i] :
( ( ( subset @ SV17 @ SV87 )
= $false )
| ( ( ( set_union2 @ SV17 @ SV87 )
= SV87 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1047]) ).
thf(1187,plain,
! [SV88: $i,SV18: $i,SV127: $i,SV138: $i] :
( ( ~ ( relation_of2_as_subset @ SV138 @ SV127 @ SV18 )
| ~ ( subset @ SV18 @ SV88 )
| ( relation_of2_as_subset @ SV138 @ SV127 @ SV88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1048]) ).
thf(1188,plain,
! [SV89: $i,SV19: $i,SV128: $i] :
( ( ( ~ ( relation @ SV128 ) )
= $true )
| ( ( ~ ( subset @ SV19 @ SV89 )
| ( subset @ ( relation_inverse_image @ SV128 @ SV19 ) @ ( relation_inverse_image @ SV128 @ SV89 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1049]) ).
thf(1189,plain,
! [SV129: $i,SV91: $i,SV21: $i] :
( ( ( ~ ( subset @ SV21 @ SV91 )
| ~ ( subset @ SV21 @ SV129 ) )
= $true )
| ( ( subset @ SV21 @ ( set_intersection2 @ SV91 @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1050]) ).
thf(1190,plain,
! [SV130: $i,SV92: $i,SV22: $i] :
( ( ( ~ ( subset @ SV22 @ SV92 )
| ~ ( subset @ SV92 @ SV130 ) )
= $true )
| ( ( subset @ SV22 @ SV130 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1051]) ).
thf(1191,plain,
! [SV23: $i,SV139: $i] :
( ( ( ~ ( ordinal @ SV139 )
| ~ ( proper_subset @ SV23 @ SV139 )
| ( in @ SV23 @ SV139 ) )
= $true )
| ( ( epsilon_transitive @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1052]) ).
thf(1192,plain,
! [SV93: $i,SV24: $i,SV131: $i] :
( ( ( ~ ( relation @ SV131 ) )
= $true )
| ( ( subset @ ( fiber @ ( relation_restriction @ SV131 @ SV24 ) @ SV93 ) @ ( fiber @ SV131 @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1053]) ).
thf(1193,plain,
! [SV25: $i,SV94: $i] :
( ( ( relation @ SV94 )
= $false )
| ( ( ~ ( reflexive @ SV94 )
| ( reflexive @ ( relation_restriction @ SV94 @ SV25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1054]) ).
thf(1194,plain,
! [SV26: $i,SV95: $i] :
( ( ( relation @ SV95 )
= $false )
| ( ( ~ ( connected @ SV95 )
| ( connected @ ( relation_restriction @ SV95 @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1055]) ).
thf(1195,plain,
! [SV27: $i,SV96: $i] :
( ( ( relation @ SV96 )
= $false )
| ( ( ~ ( transitive @ SV96 )
| ( transitive @ ( relation_restriction @ SV96 @ SV27 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1056]) ).
thf(1196,plain,
! [SV28: $i,SV97: $i] :
( ( ( relation @ SV97 )
= $false )
| ( ( ~ ( antisymmetric @ SV97 )
| ( antisymmetric @ ( relation_restriction @ SV97 @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1057]) ).
thf(1197,plain,
! [SV98: $i,SV29: $i] :
( ( ( subset @ SV29 @ SV98 )
= $false )
| ( ( ! [SY466: $i] : ( subset @ ( set_intersection2 @ SV29 @ SY466 ) @ ( set_intersection2 @ SV98 @ SY466 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1058]) ).
thf(1198,plain,
! [SV99: $i,SV30: $i] :
( ( ( subset @ SV30 @ SV99 )
= $false )
| ( ( ( set_intersection2 @ SV30 @ SV99 )
= SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1059]) ).
thf(1199,plain,
! [SV32: $i,SV100: $i] :
( ( ( relation @ SV100 )
= $false )
| ( ( ~ ( well_founded_relation @ SV100 )
| ( well_founded_relation @ ( relation_restriction @ SV100 @ SV32 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1060]) ).
thf(1200,plain,
! [SV101: $i,SV33: $i] :
( ( ( subset @ SV33 @ SV101 )
= $false )
| ( ( ! [SY467: $i] : ( subset @ ( set_difference @ SV33 @ SY467 ) @ ( set_difference @ SV101 @ SY467 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1061]) ).
thf(1201,plain,
! [SV35: $i,SV103: $i] :
( ( ( relation @ SV103 )
= $false )
| ( ( ~ ( subset @ SV35 @ ( relation_field @ SV103 ) )
| ~ ( well_ordering @ SV103 )
| ( ( relation_field @ ( relation_restriction @ SV103 @ SV35 ) )
= SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1062]) ).
thf(1202,plain,
! [SV132: $i,SV104: $i,SV36: $i] :
( ( ( ~ ( in @ SV36 @ SV104 )
| ~ ( in @ SV104 @ SV132 ) )
= $true )
| ( ( ~ ( in @ SV132 @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1063]) ).
thf(1203,plain,
! [SV38: $i,SV105: $i] :
( ( ( proper_subset @ SV105 @ SV38 )
= $false )
| ( ( ~ ( subset @ SV38 @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1065]) ).
thf(1204,plain,
! [SV39: $i,SV133: $i,SV106: $i] :
( ( ( ~ ( disjoint @ SV106 @ SV133 )
| ~ ( subset @ SV39 @ SV106 ) )
= $true )
| ( ( disjoint @ SV39 @ SV133 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1066]) ).
thf(1205,plain,
! [SV107: $i,SV40: $i] :
( ( ( subset @ ( singleton @ SV40 ) @ ( singleton @ SV107 ) )
= $false )
| ( ( SV40 = SV107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1067]) ).
thf(1206,plain,
! [SV42: $i,SV109: $i] :
( ( ( relation @ SV109 )
= $false )
| ( ( subset @ ( relation_dom_restriction @ SV109 @ SV42 ) @ SV109 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1068]) ).
thf(1207,plain,
! [SV134: $i,SV110: $i,SV43: $i] :
( ( ( ~ ( subset @ SV43 @ SV110 )
| ~ ( subset @ SV134 @ SV110 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV43 @ SV134 ) @ SV110 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1069]) ).
thf(1208,plain,
! [SV111: $i,SV44: $i] :
( ( ( in @ SV44 @ SV111 )
= $false )
| ( ( subset @ SV44 @ ( union @ SV111 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1070]) ).
thf(1209,plain,
! [SV112: $i,SV45: $i] :
( ( ( in @ SV45 @ SV112 )
= $false )
| ( ( ~ ( in @ SV112 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1071]) ).
thf(1210,plain,
! [SV140: $i,SV47: $i] :
( ( ( relation @ ( relation_restriction @ SV47 @ SV140 ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1073]) ).
thf(1211,plain,
! [SV113: $i,SV49: $i] :
( ( ( ~ ( relation @ SV49 ) )
= $true )
| ( ( ~ ( relation @ SV113 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV49 @ SV113 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1075]) ).
thf(1212,plain,
! [SV141: $i,SV51: $i] :
( ( ( relation @ ( relation_dom_restriction @ SV51 @ SV141 ) )
= $true )
| ( ( relation @ SV51 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1076]) ).
thf(1213,plain,
! [SV52: $i,SV114: $i] :
( ( ( relation @ SV114 )
= $false )
| ( ( relation @ ( relation_rng_restriction @ SV52 @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1077]) ).
thf(1214,plain,
! [SV115: $i,SV54: $i] :
( ( ( ~ ( relation @ SV54 ) )
= $true )
| ( ( ~ ( relation @ SV115 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV54 @ SV115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1078]) ).
thf(1215,plain,
! [SV116: $i,SV55: $i] :
( ( ( ~ ( relation @ SV55 ) )
= $true )
| ( ( ~ ( relation @ SV116 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV55 @ SV116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1079]) ).
thf(1216,plain,
! [SV117: $i,SV56: $i] :
( ( ( ~ ( relation @ SV56 ) )
= $true )
| ( ( ~ ( relation @ SV117 ) )
= $true )
| ( ( relation @ ( set_difference @ SV56 @ SV117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1080]) ).
thf(1217,plain,
! [SV118: $i,SV59: $i] :
( ( ( in @ SV59 @ SV118 )
= $false )
| ( ( element @ SV59 @ SV118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1082]) ).
thf(1218,plain,
! [SV60: $i,SV119: $i] :
( ( ( empty @ SV119 )
= $false )
| ( ( ~ ( in @ SV60 @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1083]) ).
thf(1219,plain,
! [SV142: $i] :
( ( ! [SY491: $i] :
( ~ ( in @ SV142 @ SY491 )
| ( subset @ ( singleton @ SV142 ) @ SY491 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1084]) ).
thf(1220,plain,
! [SV143: $i] :
( ( ! [SY492: $i] :
( ~ ( subset @ ( singleton @ SV143 ) @ SY492 )
| ( in @ SV143 @ SY492 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1221,plain,
! [SV61: $i] :
( ( ! [SY367: $i,SY368: $i] :
( ~ ( relation @ SY368 )
| ~ ( in @ SV61 @ SY368 )
| ~ ( in @ SV61 @ ( cartesian_product2 @ SY367 @ SY367 ) )
| ( in @ SV61 @ ( relation_restriction @ SY368 @ SY367 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1086]) ).
thf(1222,plain,
! [SV61: $i] :
( ( ~ ( ~ ! [SY369: $i,SY370: $i] :
( ~ ( relation @ SY370 )
| ~ ( in @ SV61 @ ( relation_restriction @ SY370 @ SY369 ) )
| ( in @ SV61 @ SY370 ) )
| ~ ! [SY371: $i,SY372: $i] :
( ~ ( relation @ SY372 )
| ~ ( in @ SV61 @ ( relation_restriction @ SY372 @ SY371 ) )
| ( in @ SV61 @ ( cartesian_product2 @ SY371 @ SY371 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1087]) ).
thf(1223,plain,
! [SV144: $i] :
( ( ~ ( ordinal @ SV144 )
| ~ ( ~ ( ordinal @ ( sK33_B @ SV144 ) )
| ~ ~ ( ~ ( in @ ( sK33_B @ SV144 ) @ SV144 )
| ~ ~ ( in @ ( succ @ ( sK33_B @ SV144 ) ) @ SV144 ) ) )
| ( being_limit_ordinal @ SV144 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1090]) ).
thf(1224,plain,
! [SV145: $i] :
( ( ~ ( ordinal @ SV145 )
| ~ ( being_limit_ordinal @ SV145 )
| ! [SY493: $i] :
( ~ ( ordinal @ SY493 )
| ~ ( in @ SY493 @ SV145 )
| ( in @ ( succ @ SY493 ) @ SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1225,plain,
! [SV62: $i] :
( ( ( ~ ! [SY373: $i] :
( ~ ( ordinal @ SY373 )
| ~ ( in @ SV62 @ SY373 )
| ( ordinal_subset @ ( succ @ SV62 ) @ SY373 ) )
| ~ ! [SY374: $i] :
( ~ ( ordinal @ SY374 )
| ~ ( ordinal_subset @ ( succ @ SV62 ) @ SY374 )
| ( in @ SV62 @ SY374 ) ) )
= $false )
| ( ( ordinal @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1092]) ).
thf(1226,plain,
! [SV63: $i,SV120: $i] :
( ( ( ordinal @ SV120 )
= $false )
| ( ( ~ ( ~ ! [SY471: $i] :
( ! [SY377: $i] :
( ( SY471 != SY377 )
| ~ ( ordinal @ SY377 )
| ~ ( in @ SY377 @ SV63 ) )
| ~ ( in @ SY471 @ ( succ @ SV120 ) )
| ( in @ SY471 @ ( sK52_C @ SV120 @ SV63 ) ) )
| ~ ~ ( ~ ! [SY473: $i] :
( ~ ( in @ SY473 @ ( sK52_C @ SV120 @ SV63 ) )
| ~ ( ~ ~ ( ( SY473
!= ( sK53_E @ SY473 @ SV120 @ SV63 ) )
| ~ ( ordinal @ ( sK53_E @ SY473 @ SV120 @ SV63 ) ) )
| ~ ( in @ ( sK53_E @ SY473 @ SV120 @ SV63 ) @ SV63 ) ) )
| ~ ! [SY474: $i] :
( ~ ( in @ SY474 @ ( sK52_C @ SV120 @ SV63 ) )
| ( in @ SY474 @ ( succ @ SV120 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1093]) ).
thf(1227,plain,
! [SV64: $i] :
( ( ! [SY380: $i] :
( ~ ( subset @ SV64 @ SY380 )
| ! [SY381: $i] : ( subset @ ( cartesian_product2 @ SV64 @ SY381 ) @ ( cartesian_product2 @ SY380 @ SY381 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1094]) ).
thf(1228,plain,
! [SV64: $i] :
( ( ! [SY382: $i] :
( ~ ( subset @ SV64 @ SY382 )
| ! [SY383: $i] : ( subset @ ( cartesian_product2 @ SY383 @ SV64 ) @ ( cartesian_product2 @ SY383 @ SY382 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1095]) ).
thf(1229,plain,
! [SV146: $i] :
( ( ~ ( epsilon_connected @ SV146 )
| ~ ( epsilon_transitive @ SV146 )
| ( ordinal @ SV146 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1096]) ).
thf(1230,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1097]) ).
thf(1231,plain,
! [SV65: $i] :
( ( ! [SY384: $i,SY385: $i] :
( ~ ( in @ SV65 @ SY385 )
| ~ ( in @ SY384 @ SY385 )
| ( subset @ ( unordered_pair @ SV65 @ SY384 ) @ SY385 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1098]) ).
thf(1232,plain,
! [SV65: $i] :
( ( ~ ( ~ ! [SY386: $i,SY387: $i] :
( ~ ( subset @ ( unordered_pair @ SV65 @ SY386 ) @ SY387 )
| ( in @ SV65 @ SY387 ) )
| ~ ! [SY388: $i,SY389: $i] :
( ~ ( subset @ ( unordered_pair @ SV65 @ SY388 ) @ SY389 )
| ( in @ SY388 @ SY389 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1099]) ).
thf(1233,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( empty @ ( succ @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ ( succ @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ ( succ @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1100]) ).
thf(1234,plain,
! [SV147: $i] :
( ( ~ ( ordinal @ SV147 )
| ( ordinal @ ( succ @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1235,plain,
! [SV148: $i] :
( ( ! [SY494: $i] :
( ~ ( ~ ( ! [SY495: $i] :
( ~ ( in @ ( sK13_C @ SY494 @ SV148 ) @ SY495 )
| ~ ( in @ SY495 @ SV148 ) )
| ~ ( in @ ( sK13_C @ SY494 @ SV148 ) @ SY494 ) )
| ~ ( ~ ( ~ ( in @ ( sK13_C @ SY494 @ SV148 ) @ ( sK14_SY277 @ SY494 @ SV148 ) )
| ~ ( in @ ( sK14_SY277 @ SY494 @ SV148 ) @ SV148 ) )
| ( in @ ( sK13_C @ SY494 @ SV148 ) @ SY494 ) ) )
| ( SY494
= ( union @ SV148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1102]) ).
thf(1236,plain,
! [SV149: $i] :
( ( ! [SY496: $i] :
( ( SY496
!= ( union @ SV149 ) )
| ~ ( ~ ! [SY497: $i] :
( ! [SY498: $i] :
( ~ ( in @ SY497 @ SY498 )
| ~ ( in @ SY498 @ SV149 ) )
| ( in @ SY497 @ SY496 ) )
| ~ ! [SY499: $i] :
( ~ ( in @ SY499 @ SY496 )
| ~ ( ~ ( in @ SY499 @ ( sK12_D @ SY499 @ SY496 @ SV149 ) )
| ~ ( in @ ( sK12_D @ SY499 @ SY496 @ SV149 ) @ SV149 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1103]) ).
thf(1237,plain,
! [SV150: $i] :
( ( ~ ( ~ ! [SY500: $i,SY501: $i] :
( ( sK31_B @ SV150 )
!= ( ordered_pair @ SY500 @ SY501 ) )
| ~ ( in @ ( sK31_B @ SV150 ) @ SV150 ) )
| ( relation @ SV150 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1238,plain,
! [SV151: $i] :
( ( ~ ( relation @ SV151 )
| ! [SY502: $i] :
( ( SY502
= ( ordered_pair @ ( sK29_C @ SY502 @ SV151 ) @ ( sK30_SY281 @ SY502 @ SV151 ) ) )
| ~ ( in @ SY502 @ SV151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1105]) ).
thf(1239,plain,
! [SV152: $i] :
( ( ~ ( ~ ~ ( ~ ( ( ( sK19_B @ SV152 )
!= ( sK20_SY279 @ SV152 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_B @ SV152 ) @ SV152 )
| ~ ( in @ ( sK20_SY279 @ SV152 ) @ SV152 ) )
| ~ ~ ( in @ ( sK19_B @ SV152 ) @ ( sK20_SY279 @ SV152 ) ) ) )
| ~ ~ ( in @ ( sK20_SY279 @ SV152 ) @ ( sK19_B @ SV152 ) ) )
| ( epsilon_connected @ SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1106]) ).
thf(1240,plain,
! [SV153: $i] :
( ( ~ ( epsilon_connected @ SV153 )
| ! [SY503: $i,SY504: $i] :
( ( SY503 = SY504 )
| ~ ( in @ SY503 @ SV153 )
| ~ ( in @ SY504 @ SV153 )
| ( in @ SY503 @ SY504 )
| ( in @ SY504 @ SY503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1107]) ).
thf(1241,plain,
! [SV154: $i] :
( ( ! [SY505: $i] :
( ( SV154 = SY505 )
| ~ ( subset @ SV154 @ SY505 )
| ( proper_subset @ SV154 @ SY505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1242,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1109]) ).
thf(1243,plain,
! [SV155: $i] :
( ( ~ ( relation @ SV155 )
| ~ ( reflexive @ SV155 )
| ~ ( transitive @ SV155 )
| ~ ( antisymmetric @ SV155 )
| ~ ( connected @ SV155 )
| ~ ( well_founded_relation @ SV155 )
| ( well_ordering @ SV155 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1110]) ).
thf(1244,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( well_founded_relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1111]) ).
thf(1245,plain,
! [SV66: $i] :
( ( ( ~ ( in @ ( sK51_B @ SV66 ) @ SV66 ) )
= $false )
| ( ( ordinal @ SV66 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1112]) ).
thf(1246,plain,
! [SV66: $i] :
( ( ( ~ ( ~ ( ordinal @ ( sK51_B @ SV66 ) )
| ~ ( subset @ ( sK51_B @ SV66 ) @ SV66 ) ) )
= $false )
| ( ( ordinal @ SV66 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1112]) ).
thf(1247,plain,
! [SV67: $i,SV121: $i] :
( ( ( ~ ! [SY475: $i] :
( ~ ( in @ SY475 @ SV121 )
| ~ ( in @ SY475 @ ( sK4_C @ SV121 @ SV67 ) ) )
| ~ ( in @ ( sK4_C @ SV121 @ SV67 ) @ SV121 ) )
= $false )
| ( ( ~ ( in @ SV67 @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1113]) ).
thf(1248,plain,
! [SV156: $i] :
( ( ( in @ ( sK27_B @ SV156 ) @ SV156 )
| ( SV156 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1114]) ).
thf(1249,plain,
! [SV157: $i] :
( ( ( SV157 != empty_set )
| ! [SY506: $i] :
~ ( in @ SY506 @ SV157 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1250,plain,
! [SV158: $i] :
( ( ! [SY507: $i] :
( ( disjoint @ SV158 @ SY507 )
| ~ ( ~ ( in @ ( sK34_C @ SY507 @ SV158 ) @ SV158 )
| ~ ( in @ ( sK34_C @ SY507 @ SV158 ) @ SY507 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1118]) ).
thf(1251,plain,
! [SV159: $i] :
( ( ! [SY508: $i] :
( ! [SY509: $i] :
( ~ ( in @ SY509 @ SV159 )
| ~ ( in @ SY509 @ SY508 ) )
| ~ ( disjoint @ SV159 @ SY508 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1119]) ).
thf(1252,plain,
( ( empty @ sK8_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1122]) ).
thf(1253,plain,
! [SV160: $i] :
( ( ! [SY510: $i] :
( ~ ( ~ ( ( ( sK28_C @ SY510 @ SV160 )
!= SV160 )
| ~ ( in @ ( sK28_C @ SY510 @ SV160 ) @ SY510 ) )
| ~ ( ( ( sK28_C @ SY510 @ SV160 )
= SV160 )
| ( in @ ( sK28_C @ SY510 @ SV160 ) @ SY510 ) ) )
| ( SY510
= ( singleton @ SV160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1124]) ).
thf(1254,plain,
! [SV161: $i] :
( ( ! [SY511: $i] :
( ( SY511
!= ( singleton @ SV161 ) )
| ~ ( ~ ! [SY512: $i] :
( ( SY512 != SV161 )
| ( in @ SY512 @ SY511 ) )
| ~ ! [SY513: $i] :
( ~ ( in @ SY513 @ SY511 )
| ( SY513 = SV161 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1125]) ).
thf(1255,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK7_A )
| ~ ( epsilon_transitive @ sK7_A ) )
| ~ ( epsilon_connected @ sK7_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1126]) ).
thf(1256,plain,
! [SV68: $i,SV122: $i] :
( ( ( ordinal @ SV122 )
= $false )
| ( ( ~ ( ~ ( ordinal @ ( sK35_C @ SV122 @ SV68 ) )
| ~ ~ ( ~ ! [SY476: $i] :
( ~ ( ordinal @ SY476 )
| ~ ( in @ SY476 @ SV68 )
| ( ordinal_subset @ ( sK35_C @ SV122 @ SV68 ) @ SY476 ) )
| ~ ( in @ ( sK35_C @ SV122 @ SV68 ) @ SV68 ) ) )
| ( SV68 = empty_set )
| ~ ( subset @ SV68 @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1128]) ).
thf(1257,plain,
! [SV69: $i] :
( ( ! [SY394: $i,SY395: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK21_D @ SY395 @ SY394 @ SV69 ) @ SY395 )
| ~ ( in @ ( sK21_D @ SY395 @ SY394 @ SV69 ) @ SV69 ) )
| ~ ( ~ ( in @ ( sK21_D @ SY395 @ SY394 @ SV69 ) @ SY395 )
| ~ ( in @ ( sK21_D @ SY395 @ SY394 @ SV69 ) @ SY394 ) ) )
| ~ ( ( in @ ( sK21_D @ SY395 @ SY394 @ SV69 ) @ SY395 )
| ( in @ ( sK21_D @ SY395 @ SY394 @ SV69 ) @ SV69 )
| ( in @ ( sK21_D @ SY395 @ SY394 @ SV69 ) @ SY394 ) ) )
| ( SY395
= ( set_union2 @ SV69 @ SY394 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1129]) ).
thf(1258,plain,
! [SV69: $i] :
( ( ! [SY396: $i,SY397: $i] :
( ( SY397
!= ( set_union2 @ SV69 @ SY396 ) )
| ~ ( ~ ! [SY398: $i] :
( ~ ( in @ SY398 @ SY397 )
| ( in @ SY398 @ SV69 )
| ( in @ SY398 @ SY396 ) )
| ~ ~ ( ~ ! [SY399: $i] :
( ~ ( in @ SY399 @ SV69 )
| ( in @ SY399 @ SY397 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY396 )
| ( in @ SX3 @ SY397 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1130]) ).
thf(1259,plain,
! [SV162: $i] :
( ( ! [SY514: $i] :
( ~ ( ~ ( ~ ( in @ ( sK26_C @ SY514 @ SV162 ) @ SY514 )
| ~ ( subset @ ( sK26_C @ SY514 @ SV162 ) @ SV162 ) )
| ~ ( ( in @ ( sK26_C @ SY514 @ SV162 ) @ SY514 )
| ( subset @ ( sK26_C @ SY514 @ SV162 ) @ SV162 ) ) )
| ( SY514
= ( powerset @ SV162 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1131]) ).
thf(1260,plain,
! [SV163: $i] :
( ( ! [SY515: $i] :
( ( SY515
!= ( powerset @ SV163 ) )
| ~ ( ~ ! [SY516: $i] :
( ~ ( in @ SY516 @ SY515 )
| ( subset @ SY516 @ SV163 ) )
| ~ ! [SY517: $i] :
( ~ ( subset @ SY517 @ SV163 )
| ( in @ SY517 @ SY515 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1261,plain,
! [SV70: $i] :
( ( ! [SY401: $i,SY402: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SY402 @ SY401 @ SV70 ) @ SV70 )
| ~ ( in @ ( sK15_D @ SY402 @ SY401 @ SV70 ) @ SY401 )
| ~ ( in @ ( sK15_D @ SY402 @ SY401 @ SV70 ) @ SY402 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SY402 @ SY401 @ SV70 ) @ SV70 )
| ( in @ ( sK15_D @ SY402 @ SY401 @ SV70 ) @ SY402 ) )
| ~ ( ( in @ ( sK15_D @ SY402 @ SY401 @ SV70 ) @ SY401 )
| ( in @ ( sK15_D @ SY402 @ SY401 @ SV70 ) @ SY402 ) ) ) )
| ( SY402
= ( set_intersection2 @ SV70 @ SY401 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1133]) ).
thf(1262,plain,
! [SV70: $i] :
( ( ! [SY403: $i,SY404: $i] :
( ( SY404
!= ( set_intersection2 @ SV70 @ SY403 ) )
| ~ ( ~ ! [SY405: $i] :
( ~ ( in @ SY405 @ SV70 )
| ~ ( in @ SY405 @ SY403 )
| ( in @ SY405 @ SY404 ) )
| ~ ~ ( ~ ! [SY406: $i] :
( ~ ( in @ SY406 @ SY404 )
| ( in @ SY406 @ SV70 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY404 )
| ( in @ SX3 @ SY403 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1134]) ).
thf(1263,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ ( union @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1135]) ).
thf(1264,plain,
! [SV164: $i] :
( ( ~ ( ordinal @ SV164 )
| ( ordinal @ ( union @ SV164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1136]) ).
thf(1265,plain,
! [SV165: $i] :
( ( ! [SY518: $i] :
( ~ ( ordinal @ SV165 )
| ~ ( ordinal @ SY518 )
| ~ ( ordinal_subset @ SV165 @ SY518 )
| ( subset @ SV165 @ SY518 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1137]) ).
thf(1266,plain,
! [SV166: $i] :
( ( ! [SY519: $i] :
( ~ ( ordinal @ SV166 )
| ~ ( ordinal @ SY519 )
| ~ ( subset @ SV166 @ SY519 )
| ( ordinal_subset @ SV166 @ SY519 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1138]) ).
thf(1267,plain,
! [SV71: $i,SV135: $i] :
( ( ( ~ ( in @ SV135 @ SV71 ) )
= $true )
| ( ( ~ ( ordinal @ SV135 ) )
= $true )
| ( ( ~ ( ~ ! [SY409: $i] :
( ~ ( ordinal @ SY409 )
| ~ ( in @ SY409 @ SV71 )
| ( ordinal_subset @ ( sK54_B @ SV71 ) @ SY409 ) )
| ~ ~ ( ~ ( in @ ( sK54_B @ SV71 ) @ SV71 )
| ~ ( ordinal @ ( sK54_B @ SV71 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1139]) ).
thf(1268,plain,
! [SV72: $i,SV123: $i] :
( ( ( ordinal @ SV123 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK44_C @ SV123 @ SV72 )
!= ( sK45_SY295 @ SV123 @ SV72 ) )
| ~ ~ ( ~ ~ ( ( ( sK45_SY295 @ SV123 @ SV72 )
!= ( sK48_SY300 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 ) ) )
| ( ( sK44_C @ SV123 @ SV72 )
!= ( sK46_SY299 @ SV123 @ SV72 ) ) )
| ~ ~ ( ~ ~ ( ( ( sK46_SY299 @ SV123 @ SV72 )
!= ( sK47_SY303 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 ) ) )
| ~ ( ( ( sK45_SY295 @ SV123 @ SV72 )
!= ( sK46_SY299 @ SV123 @ SV72 ) ) ) )
| ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1140]) ).
thf(1269,plain,
! [SV73: $i] :
( ( ( ~ ! [SY415: $i] :
( ~ ( relation @ SY415 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK23_C @ SY415 @ SV73 ) @ ( sK24_SY280 @ SY415 @ SV73 ) ) @ SV73 )
| ~ ( in @ ( ordered_pair @ ( sK23_C @ SY415 @ SV73 ) @ ( sK24_SY280 @ SY415 @ SV73 ) ) @ SY415 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK23_C @ SY415 @ SV73 ) @ ( sK24_SY280 @ SY415 @ SV73 ) ) @ SV73 )
| ( in @ ( ordered_pair @ ( sK23_C @ SY415 @ SV73 ) @ ( sK24_SY280 @ SY415 @ SV73 ) ) @ SY415 ) ) )
| ( SV73 = SY415 ) )
| ~ ! [SY416: $i] :
( ~ ( relation @ SY416 )
| ( SV73 != SY416 )
| ~ ( ~ ! [SY417: $i,SY418: $i] :
( ~ ( in @ ( ordered_pair @ SY417 @ SY418 ) @ SV73 )
| ( in @ ( ordered_pair @ SY417 @ SY418 ) @ SY416 ) )
| ~ ! [SY419: $i,SY420: $i] :
( ~ ( in @ ( ordered_pair @ SY419 @ SY420 ) @ SY416 )
| ( in @ ( ordered_pair @ SY419 @ SY420 ) @ SV73 ) ) ) ) )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1141]) ).
thf(1270,plain,
! [SV167: $i] :
( ( ~ ( ordinal @ SV167 )
| ( epsilon_connected @ SV167 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1142]) ).
thf(1271,plain,
! [SV168: $i] :
( ( ~ ( ordinal @ SV168 )
| ( epsilon_transitive @ SV168 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1143]) ).
thf(1272,plain,
! [SV74: $i] :
( ( ! [SY421: $i,SY422: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK22_D @ SY422 @ SY421 @ SV74 ) @ SY422 )
| ( ( sK22_D @ SY422 @ SY421 @ SV74 )
!= SV74 ) )
| ~ ( ~ ( in @ ( sK22_D @ SY422 @ SY421 @ SV74 ) @ SY422 )
| ( ( sK22_D @ SY422 @ SY421 @ SV74 )
!= SY421 ) ) )
| ~ ( ( in @ ( sK22_D @ SY422 @ SY421 @ SV74 ) @ SY422 )
| ( ( sK22_D @ SY422 @ SY421 @ SV74 )
= SV74 )
| ( ( sK22_D @ SY422 @ SY421 @ SV74 )
= SY421 ) ) )
| ( SY422
= ( unordered_pair @ SV74 @ SY421 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1144]) ).
thf(1273,plain,
! [SV74: $i] :
( ( ! [SY423: $i,SY424: $i] :
( ( SY424
!= ( unordered_pair @ SV74 @ SY423 ) )
| ~ ( ~ ! [SY425: $i] :
( ~ ( in @ SY425 @ SY424 )
| ( SY425 = SV74 )
| ( SY425 = SY423 ) )
| ~ ~ ( ~ ! [SY426: $i] :
( ( SY426 != SV74 )
| ( in @ SY426 @ SY424 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY423 )
| ( in @ SX3 @ SY424 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1145]) ).
thf(1274,plain,
! [SV169: $i] :
( ( ~ ( ~ ( in @ ( sK25_B @ SV169 ) @ SV169 )
| ~ ~ ( subset @ ( sK25_B @ SV169 ) @ SV169 ) )
| ( epsilon_transitive @ SV169 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1275,plain,
! [SV170: $i] :
( ( ~ ( epsilon_transitive @ SV170 )
| ! [SY520: $i] :
( ~ ( in @ SY520 @ SV170 )
| ( subset @ SY520 @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1147]) ).
thf(1276,plain,
! [SV75: $i] :
( ( ! [SY428: $i] :
( ~ ( subset @ SY428 @ ( sK2_B @ SV75 ) )
| ( are_equipotent @ SY428 @ ( sK2_B @ SV75 ) )
| ( in @ SY428 @ ( sK2_B @ SV75 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1148]) ).
thf(1277,plain,
! [SV75: $i] :
( ( ~ ( ~ ! [SY429: $i] :
( ~ ( ~ ! [SY430: $i] :
( ~ ( subset @ SY430 @ SY429 )
| ( in @ SY430 @ ( sK3_SY270 @ SY429 @ SV75 ) ) )
| ~ ( in @ ( sK3_SY270 @ SY429 @ SV75 ) @ ( sK2_B @ SV75 ) ) )
| ~ ( in @ SY429 @ ( sK2_B @ SV75 ) ) )
| ~ ~ ( ~ ! [SY431: $i,SY432: $i] :
( ~ ( in @ SY431 @ ( sK2_B @ SV75 ) )
| ~ ( subset @ SY432 @ SY431 )
| ( in @ SY432 @ ( sK2_B @ SV75 ) ) )
| ~ ( in @ SV75 @ ( sK2_B @ SV75 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1149]) ).
thf(1278,plain,
! [SV76: $i] :
( ( ! [SY433: $i,SY434: $i] :
( ~ ( relation @ SY434 )
| ~ ( in @ SV76 @ ( relation_field @ ( relation_restriction @ SY434 @ SY433 ) ) )
| ( in @ SV76 @ ( relation_field @ SY434 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1150]) ).
thf(1279,plain,
! [SV76: $i] :
( ( ! [SY435: $i,SY436: $i] :
( ~ ( relation @ SY436 )
| ~ ( in @ SV76 @ ( relation_field @ ( relation_restriction @ SY436 @ SY435 ) ) )
| ( in @ SV76 @ SY435 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1151]) ).
thf(1280,plain,
! [SV77: $i] :
( ( ( ~ ! [SY437: $i] :
( ~ ( relation @ SY437 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK17_C @ SY437 @ SV77 ) @ ( sK18_SY278 @ SY437 @ SV77 ) ) @ SV77 )
| ~ ~ ( in @ ( ordered_pair @ ( sK17_C @ SY437 @ SV77 ) @ ( sK18_SY278 @ SY437 @ SV77 ) ) @ SY437 ) )
| ( subset @ SV77 @ SY437 ) )
| ~ ! [SY438: $i] :
( ~ ( relation @ SY438 )
| ~ ( subset @ SV77 @ SY438 )
| ! [SY439: $i,SY440: $i] :
( ~ ( in @ ( ordered_pair @ SY439 @ SY440 ) @ SV77 )
| ( in @ ( ordered_pair @ SY439 @ SY440 ) @ SY438 ) ) ) )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1152]) ).
thf(1281,plain,
! [SV171: $i] :
( ( ! [SY521: $i] :
( ~ ( ~ ( in @ ( sK16_C @ SY521 @ SV171 ) @ SV171 )
| ~ ~ ( in @ ( sK16_C @ SY521 @ SV171 ) @ SY521 ) )
| ( subset @ SV171 @ SY521 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1153]) ).
thf(1282,plain,
! [SV172: $i] :
( ( ! [SY522: $i] :
( ~ ( subset @ SV172 @ SY522 )
| ! [SY523: $i] :
( ~ ( in @ SY523 @ SV172 )
| ( in @ SY523 @ SY522 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1154]) ).
thf(1283,plain,
! [SV78: $i] :
( ( ! [SY441: $i,SY442: $i] :
( ~ ( ~ ( ~ ( in @ ( sK11_D @ SY442 @ SY441 @ SV78 ) @ SV78 )
| ( in @ ( sK11_D @ SY442 @ SY441 @ SV78 ) @ SY441 )
| ~ ( in @ ( sK11_D @ SY442 @ SY441 @ SV78 ) @ SY442 ) )
| ~ ~ ( ~ ( ( in @ ( sK11_D @ SY442 @ SY441 @ SV78 ) @ SV78 )
| ( in @ ( sK11_D @ SY442 @ SY441 @ SV78 ) @ SY442 ) )
| ~ ( ~ ( in @ ( sK11_D @ SY442 @ SY441 @ SV78 ) @ SY441 )
| ( in @ ( sK11_D @ SY442 @ SY441 @ SV78 ) @ SY442 ) ) ) )
| ( SY442
= ( set_difference @ SV78 @ SY441 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1155]) ).
thf(1284,plain,
! [SV78: $i] :
( ( ! [SY443: $i,SY444: $i] :
( ( SY444
!= ( set_difference @ SV78 @ SY443 ) )
| ~ ( ~ ! [SY445: $i] :
( ~ ( in @ SY445 @ SV78 )
| ( in @ SY445 @ SY443 )
| ( in @ SY445 @ SY444 ) )
| ~ ~ ( ~ ! [SY446: $i] :
( ~ ( in @ SY446 @ SY444 )
| ( in @ SY446 @ SV78 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY444 )
| ~ ( in @ SX3 @ SY443 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1156]) ).
thf(1285,plain,
! [SV173: $i] :
( ( ! [SY524: $i] :
( ~ ( relation @ SY524 )
| ( subset @ ( relation_field @ ( relation_restriction @ SY524 @ SV173 ) ) @ ( relation_field @ SY524 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1157]) ).
thf(1286,plain,
! [SV174: $i] :
( ( ! [SY525: $i] :
( ~ ( relation @ SY525 )
| ( subset @ ( relation_field @ ( relation_restriction @ SY525 @ SV174 ) ) @ SV174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1158]) ).
thf(1287,plain,
( ( ~ ( epsilon_connected @ sK49_A )
| ~ ( epsilon_transitive @ sK49_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1159]) ).
thf(1288,plain,
! [SV175: $i] :
( ( ~ ( relation @ SV175 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK36_B @ SV175 ) @ ( sK37_SY285 @ SV175 ) ) @ SV175 )
| ~ ( in @ ( ordered_pair @ ( sK37_SY285 @ SV175 ) @ ( sK36_B @ SV175 ) ) @ SV175 ) )
| ~ ( ( ( sK36_B @ SV175 )
!= ( sK37_SY285 @ SV175 ) ) ) )
| ( antisymmetric @ SV175 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1289,plain,
! [SV176: $i] :
( ( ~ ( relation @ SV176 )
| ~ ( antisymmetric @ SV176 )
| ! [SY526: $i,SY527: $i] :
( ~ ( in @ ( ordered_pair @ SY526 @ SY527 ) @ SV176 )
| ~ ( in @ ( ordered_pair @ SY527 @ SY526 ) @ SV176 )
| ( SY526 = SY527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1162]) ).
thf(1290,plain,
! [SV177: $i] :
( ( ! [SY528: $i] :
( ~ ( subset @ SV177 @ SY528 )
| ~ ( subset @ SY528 @ SV177 )
| ( SV177 = SY528 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1163]) ).
thf(1291,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1164]) ).
thf(1292,plain,
! [SV178: $i] :
( ( ~ ( relation @ SV178 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK38_B @ SV178 ) @ ( sK39_SY286 @ SV178 ) ) @ SV178 )
| ~ ( in @ ( ordered_pair @ ( sK39_SY286 @ SV178 ) @ ( sK40_SY288 @ SV178 ) ) @ SV178 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK38_B @ SV178 ) @ ( sK40_SY288 @ SV178 ) ) @ SV178 ) )
| ( transitive @ SV178 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1165]) ).
thf(1293,plain,
! [SV179: $i] :
( ( ~ ( relation @ SV179 )
| ~ ( transitive @ SV179 )
| ! [SY529: $i,SY530: $i,SY531: $i] :
( ~ ( in @ ( ordered_pair @ SY529 @ SY530 ) @ SV179 )
| ~ ( in @ ( ordered_pair @ SY530 @ SY531 ) @ SV179 )
| ( in @ ( ordered_pair @ SY529 @ SY531 ) @ SV179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1294,plain,
! [SV79: $i,SV124: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_C @ SV124 @ SV79 ) @ SV79 )
| ~ ( in @ ( sK5_C @ SV124 @ SV79 ) @ SV124 ) )
| ~ ( ( in @ ( sK5_C @ SV124 @ SV79 ) @ SV79 )
| ( in @ ( sK5_C @ SV124 @ SV79 ) @ SV124 ) ) )
= $false )
| ( ( SV79 = SV124 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1167]) ).
thf(1295,plain,
! [SV180: $i] :
( ( ( SV180
!= ( union @ SV180 ) )
| ( being_limit_ordinal @ SV180 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1168]) ).
thf(1296,plain,
! [SV181: $i] :
( ( ~ ( being_limit_ordinal @ SV181 )
| ( SV181
= ( union @ SV181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1169]) ).
thf(1297,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1170]) ).
thf(1298,plain,
! [SV182: $i] :
( ( ~ ( empty @ SV182 )
| ( ordinal @ SV182 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1171]) ).
thf(1299,plain,
! [SV183: $i] :
( ( ~ ( ordinal @ SV183 )
| ( being_limit_ordinal @ SV183 )
| ~ ( ~ ( ordinal @ ( sK50_B @ SV183 ) )
| ( SV183
!= ( succ @ ( sK50_B @ SV183 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1172]) ).
thf(1300,plain,
! [SV184: $i] :
( ( ~ ( ordinal @ SV184 )
| ! [SY532: $i] :
( ( SV184
!= ( succ @ SY532 ) )
| ~ ( ordinal @ SY532 ) )
| ~ ( being_limit_ordinal @ SV184 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1173]) ).
thf(1301,plain,
! [SV185: $i] :
( ( ! [SY533: $i] :
( ~ ( in @ SV185 @ SY533 )
| ( subset @ ( singleton @ SV185 ) @ SY533 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1302,plain,
! [SV186: $i] :
( ( ! [SY534: $i] :
( ~ ( subset @ ( singleton @ SV186 ) @ SY534 )
| ( in @ SV186 @ SY534 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1175]) ).
thf(1303,plain,
! [SV80: $i,SV125: $i] :
( ( ~ ! [SY481: $i,SY482: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 ) @ SY482 )
| ( ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 )
!= SY481 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 ) @ SY482 )
| ( ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 )
!= SV80 ) )
| ~ ( ~ ( in @ ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 ) @ SY482 )
| ( ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 )
!= SV125 ) ) ) )
| ~ ( ( in @ ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 ) @ SY482 )
| ( ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 )
= SY481 )
| ( ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 )
= SV80 )
| ( ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 )
= SV125 ) ) )
| ( SY482
= ( unordered_triple @ SV80 @ SV125 @ SY481 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1176]) ).
thf(1304,plain,
! [SV125: $i,SV80: $i] :
( ( ~ ! [SY483: $i,SY484: $i] :
( ( SY484
!= ( unordered_triple @ SV80 @ SV125 @ SY483 ) )
| ~ ( ~ ! [SY485: $i] :
( ~ ( in @ SY485 @ SY484 )
| ( SY485 = SY483 )
| ( SY485 = SV80 )
| ( SY485 = SV125 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ( SX4 != SY483 )
| ( in @ SX4 @ SY484 ) )
| ~ ~ ( ~ ! [SY456: $i] :
( ( SY456 != SV80 )
| ( in @ SY456 @ SY484 ) )
| ~ ! [SY488: $i] :
( ( SY488 != SV125 )
| ( in @ SY488 @ SY484 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1176]) ).
thf(1305,plain,
! [SV81: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV81 ) )
= $true )
| ( ( ordinal @ SV1 )
= $true )
| ( ( ordinal @ SV81 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1177]) ).
thf(1306,plain,
! [SV2: $i,SV136: $i] :
( ( ( ~ ( ordinal @ SV136 ) )
= $true )
| ( ( ( in @ SV2 @ SV136 )
| ( SV2 = SV136 )
| ( in @ SV136 @ SV2 ) )
= $true )
| ( ( ordinal @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1178]) ).
thf(1307,plain,
! [SV4: $i,SV82: $i] :
( ( ( ~ ( well_ordering @ SV82 ) )
= $true )
| ( ( well_ordering @ ( relation_restriction @ SV82 @ SV4 ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1179]) ).
thf(1308,plain,
! [SV9: $i] :
( ( ( epsilon_transitive @ SV9 )
= $false )
| ( ( epsilon_connected @ SV9 )
= $false )
| ( ( ordinal @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1180]) ).
thf(1309,plain,
! [SV83: $i,SV10: $i] :
( ( ( ordinal @ SV10 )
= $false )
| ( ( ~ ( ordinal @ SV83 ) )
= $true )
| ( ( ( ordinal_subset @ SV10 @ SV83 )
| ( ordinal_subset @ SV83 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1181]) ).
thf(1310,plain,
! [SV12: $i,SV187: $i] :
( ( ( ~ ( ordinal @ SV187 ) )
= $true )
| ( ( ordinal @ SV12 )
= $false )
| ( ( ordinal_subset @ SV12 @ SV12 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1182]) ).
thf(1311,plain,
! [SV137: $i,SV126: $i,SV86: $i,SV16: $i] :
( ( ( ~ ( subset @ SV16 @ SV86 )
| ~ ( subset @ SV126 @ SV137 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV16 @ SV126 ) @ ( cartesian_product2 @ SV86 @ SV137 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1185]) ).
thf(1312,plain,
! [SV88: $i,SV18: $i,SV127: $i,SV138: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV138 @ SV127 @ SV18 ) )
= $true )
| ( ( ~ ( subset @ SV18 @ SV88 )
| ( relation_of2_as_subset @ SV138 @ SV127 @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1187]) ).
thf(1313,plain,
! [SV89: $i,SV19: $i,SV128: $i] :
( ( ( relation @ SV128 )
= $false )
| ( ( ~ ( subset @ SV19 @ SV89 )
| ( subset @ ( relation_inverse_image @ SV128 @ SV19 ) @ ( relation_inverse_image @ SV128 @ SV89 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1188]) ).
thf(1314,plain,
! [SV129: $i,SV91: $i,SV21: $i] :
( ( ( ~ ( subset @ SV21 @ SV91 ) )
= $true )
| ( ( ~ ( subset @ SV21 @ SV129 ) )
= $true )
| ( ( subset @ SV21 @ ( set_intersection2 @ SV91 @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1189]) ).
thf(1315,plain,
! [SV130: $i,SV92: $i,SV22: $i] :
( ( ( ~ ( subset @ SV22 @ SV92 ) )
= $true )
| ( ( ~ ( subset @ SV92 @ SV130 ) )
= $true )
| ( ( subset @ SV22 @ SV130 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1190]) ).
thf(1316,plain,
! [SV23: $i,SV139: $i] :
( ( ( ~ ( ordinal @ SV139 ) )
= $true )
| ( ( ~ ( proper_subset @ SV23 @ SV139 )
| ( in @ SV23 @ SV139 ) )
= $true )
| ( ( epsilon_transitive @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1191]) ).
thf(1317,plain,
! [SV93: $i,SV24: $i,SV131: $i] :
( ( ( relation @ SV131 )
= $false )
| ( ( subset @ ( fiber @ ( relation_restriction @ SV131 @ SV24 ) @ SV93 ) @ ( fiber @ SV131 @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1192]) ).
thf(1318,plain,
! [SV25: $i,SV94: $i] :
( ( ( ~ ( reflexive @ SV94 ) )
= $true )
| ( ( reflexive @ ( relation_restriction @ SV94 @ SV25 ) )
= $true )
| ( ( relation @ SV94 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1193]) ).
thf(1319,plain,
! [SV26: $i,SV95: $i] :
( ( ( ~ ( connected @ SV95 ) )
= $true )
| ( ( connected @ ( relation_restriction @ SV95 @ SV26 ) )
= $true )
| ( ( relation @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1194]) ).
thf(1320,plain,
! [SV27: $i,SV96: $i] :
( ( ( ~ ( transitive @ SV96 ) )
= $true )
| ( ( transitive @ ( relation_restriction @ SV96 @ SV27 ) )
= $true )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1195]) ).
thf(1321,plain,
! [SV28: $i,SV97: $i] :
( ( ( ~ ( antisymmetric @ SV97 ) )
= $true )
| ( ( antisymmetric @ ( relation_restriction @ SV97 @ SV28 ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1196]) ).
thf(1322,plain,
! [SV98: $i,SV188: $i,SV29: $i] :
( ( ( subset @ ( set_intersection2 @ SV29 @ SV188 ) @ ( set_intersection2 @ SV98 @ SV188 ) )
= $true )
| ( ( subset @ SV29 @ SV98 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1197]) ).
thf(1323,plain,
! [SV32: $i,SV100: $i] :
( ( ( ~ ( well_founded_relation @ SV100 ) )
= $true )
| ( ( well_founded_relation @ ( relation_restriction @ SV100 @ SV32 ) )
= $true )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1199]) ).
thf(1324,plain,
! [SV101: $i,SV189: $i,SV33: $i] :
( ( ( subset @ ( set_difference @ SV33 @ SV189 ) @ ( set_difference @ SV101 @ SV189 ) )
= $true )
| ( ( subset @ SV33 @ SV101 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1200]) ).
thf(1325,plain,
! [SV103: $i,SV35: $i] :
( ( ( ~ ( subset @ SV35 @ ( relation_field @ SV103 ) )
| ~ ( well_ordering @ SV103 ) )
= $true )
| ( ( ( relation_field @ ( relation_restriction @ SV103 @ SV35 ) )
= SV35 )
= $true )
| ( ( relation @ SV103 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1201]) ).
thf(1326,plain,
! [SV132: $i,SV104: $i,SV36: $i] :
( ( ( ~ ( in @ SV36 @ SV104 ) )
= $true )
| ( ( ~ ( in @ SV104 @ SV132 ) )
= $true )
| ( ( ~ ( in @ SV132 @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1202]) ).
thf(1327,plain,
! [SV105: $i,SV38: $i] :
( ( ( subset @ SV38 @ SV105 )
= $false )
| ( ( proper_subset @ SV105 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1203]) ).
thf(1328,plain,
! [SV39: $i,SV133: $i,SV106: $i] :
( ( ( ~ ( disjoint @ SV106 @ SV133 ) )
= $true )
| ( ( ~ ( subset @ SV39 @ SV106 ) )
= $true )
| ( ( disjoint @ SV39 @ SV133 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1204]) ).
thf(1329,plain,
! [SV134: $i,SV110: $i,SV43: $i] :
( ( ( ~ ( subset @ SV43 @ SV110 ) )
= $true )
| ( ( ~ ( subset @ SV134 @ SV110 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV43 @ SV134 ) @ SV110 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1207]) ).
thf(1330,plain,
! [SV45: $i,SV112: $i] :
( ( ( in @ SV112 @ SV45 )
= $false )
| ( ( in @ SV45 @ SV112 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1209]) ).
thf(1331,plain,
! [SV113: $i,SV49: $i] :
( ( ( relation @ SV49 )
= $false )
| ( ( ~ ( relation @ SV113 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV49 @ SV113 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1211]) ).
thf(1332,plain,
! [SV115: $i,SV54: $i] :
( ( ( relation @ SV54 )
= $false )
| ( ( ~ ( relation @ SV115 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV54 @ SV115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1214]) ).
thf(1333,plain,
! [SV116: $i,SV55: $i] :
( ( ( relation @ SV55 )
= $false )
| ( ( ~ ( relation @ SV116 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV55 @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1215]) ).
thf(1334,plain,
! [SV117: $i,SV56: $i] :
( ( ( relation @ SV56 )
= $false )
| ( ( ~ ( relation @ SV117 ) )
= $true )
| ( ( relation @ ( set_difference @ SV56 @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1216]) ).
thf(1335,plain,
! [SV119: $i,SV60: $i] :
( ( ( in @ SV60 @ SV119 )
= $false )
| ( ( empty @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1218]) ).
thf(1336,plain,
! [SV190: $i,SV142: $i] :
( ( ~ ( in @ SV142 @ SV190 )
| ( subset @ ( singleton @ SV142 ) @ SV190 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1219]) ).
thf(1337,plain,
! [SV191: $i,SV143: $i] :
( ( ~ ( subset @ ( singleton @ SV143 ) @ SV191 )
| ( in @ SV143 @ SV191 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1220]) ).
thf(1338,plain,
! [SV192: $i,SV61: $i] :
( ( ! [SY535: $i] :
( ~ ( relation @ SY535 )
| ~ ( in @ SV61 @ SY535 )
| ~ ( in @ SV61 @ ( cartesian_product2 @ SV192 @ SV192 ) )
| ( in @ SV61 @ ( relation_restriction @ SY535 @ SV192 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1221]) ).
thf(1339,plain,
! [SV61: $i] :
( ( ~ ! [SY369: $i,SY370: $i] :
( ~ ( relation @ SY370 )
| ~ ( in @ SV61 @ ( relation_restriction @ SY370 @ SY369 ) )
| ( in @ SV61 @ SY370 ) )
| ~ ! [SY371: $i,SY372: $i] :
( ~ ( relation @ SY372 )
| ~ ( in @ SV61 @ ( relation_restriction @ SY372 @ SY371 ) )
| ( in @ SV61 @ ( cartesian_product2 @ SY371 @ SY371 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1222]) ).
thf(1340,plain,
! [SV144: $i] :
( ( ( ~ ( ordinal @ SV144 ) )
= $true )
| ( ( ~ ( ~ ( ordinal @ ( sK33_B @ SV144 ) )
| ~ ~ ( ~ ( in @ ( sK33_B @ SV144 ) @ SV144 )
| ~ ~ ( in @ ( succ @ ( sK33_B @ SV144 ) ) @ SV144 ) ) )
| ( being_limit_ordinal @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1223]) ).
thf(1341,plain,
! [SV145: $i] :
( ( ( ~ ( ordinal @ SV145 ) )
= $true )
| ( ( ~ ( being_limit_ordinal @ SV145 )
| ! [SY493: $i] :
( ~ ( ordinal @ SY493 )
| ~ ( in @ SY493 @ SV145 )
| ( in @ ( succ @ SY493 ) @ SV145 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1224]) ).
thf(1342,plain,
! [SV62: $i] :
( ( ( ~ ! [SY373: $i] :
( ~ ( ordinal @ SY373 )
| ~ ( in @ SV62 @ SY373 )
| ( ordinal_subset @ ( succ @ SV62 ) @ SY373 ) ) )
= $false )
| ( ( ordinal @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1225]) ).
thf(1343,plain,
! [SV62: $i] :
( ( ( ~ ! [SY374: $i] :
( ~ ( ordinal @ SY374 )
| ~ ( ordinal_subset @ ( succ @ SV62 ) @ SY374 )
| ( in @ SV62 @ SY374 ) ) )
= $false )
| ( ( ordinal @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1225]) ).
thf(1344,plain,
! [SV120: $i,SV63: $i] :
( ( ( ~ ! [SY471: $i] :
( ! [SY377: $i] :
( ( SY471 != SY377 )
| ~ ( ordinal @ SY377 )
| ~ ( in @ SY377 @ SV63 ) )
| ~ ( in @ SY471 @ ( succ @ SV120 ) )
| ( in @ SY471 @ ( sK52_C @ SV120 @ SV63 ) ) )
| ~ ~ ( ~ ! [SY473: $i] :
( ~ ( in @ SY473 @ ( sK52_C @ SV120 @ SV63 ) )
| ~ ( ~ ~ ( ( SY473
!= ( sK53_E @ SY473 @ SV120 @ SV63 ) )
| ~ ( ordinal @ ( sK53_E @ SY473 @ SV120 @ SV63 ) ) )
| ~ ( in @ ( sK53_E @ SY473 @ SV120 @ SV63 ) @ SV63 ) ) )
| ~ ! [SY474: $i] :
( ~ ( in @ SY474 @ ( sK52_C @ SV120 @ SV63 ) )
| ( in @ SY474 @ ( succ @ SV120 ) ) ) ) )
= $false )
| ( ( ordinal @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1226]) ).
thf(1345,plain,
! [SV193: $i,SV64: $i] :
( ( ~ ( subset @ SV64 @ SV193 )
| ! [SY536: $i] : ( subset @ ( cartesian_product2 @ SV64 @ SY536 ) @ ( cartesian_product2 @ SV193 @ SY536 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1227]) ).
thf(1346,plain,
! [SV194: $i,SV64: $i] :
( ( ~ ( subset @ SV64 @ SV194 )
| ! [SY537: $i] : ( subset @ ( cartesian_product2 @ SY537 @ SV64 ) @ ( cartesian_product2 @ SY537 @ SV194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1228]) ).
thf(1347,plain,
! [SV146: $i] :
( ( ( ~ ( epsilon_connected @ SV146 )
| ~ ( epsilon_transitive @ SV146 ) )
= $true )
| ( ( ordinal @ SV146 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1229]) ).
thf(1348,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1230]) ).
thf(1349,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1230]) ).
thf(1350,plain,
! [SV195: $i,SV65: $i] :
( ( ! [SY538: $i] :
( ~ ( in @ SV65 @ SY538 )
| ~ ( in @ SV195 @ SY538 )
| ( subset @ ( unordered_pair @ SV65 @ SV195 ) @ SY538 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1231]) ).
thf(1351,plain,
! [SV65: $i] :
( ( ~ ! [SY386: $i,SY387: $i] :
( ~ ( subset @ ( unordered_pair @ SV65 @ SY386 ) @ SY387 )
| ( in @ SV65 @ SY387 ) )
| ~ ! [SY388: $i,SY389: $i] :
( ~ ( subset @ ( unordered_pair @ SV65 @ SY388 ) @ SY389 )
| ( in @ SY388 @ SY389 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1232]) ).
thf(1352,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( empty @ ( succ @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ ( succ @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1233]) ).
thf(1353,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ ( succ @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1233]) ).
thf(1354,plain,
! [SV147: $i] :
( ( ( ~ ( ordinal @ SV147 ) )
= $true )
| ( ( ordinal @ ( succ @ SV147 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1234]) ).
thf(1355,plain,
! [SV148: $i,SV196: $i] :
( ( ~ ( ~ ( ! [SY539: $i] :
( ~ ( in @ ( sK13_C @ SV196 @ SV148 ) @ SY539 )
| ~ ( in @ SY539 @ SV148 ) )
| ~ ( in @ ( sK13_C @ SV196 @ SV148 ) @ SV196 ) )
| ~ ( ~ ( ~ ( in @ ( sK13_C @ SV196 @ SV148 ) @ ( sK14_SY277 @ SV196 @ SV148 ) )
| ~ ( in @ ( sK14_SY277 @ SV196 @ SV148 ) @ SV148 ) )
| ( in @ ( sK13_C @ SV196 @ SV148 ) @ SV196 ) ) )
| ( SV196
= ( union @ SV148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1235]) ).
thf(1356,plain,
! [SV149: $i,SV197: $i] :
( ( ( SV197
!= ( union @ SV149 ) )
| ~ ( ~ ! [SY540: $i] :
( ! [SY498: $i] :
( ~ ( in @ SY540 @ SY498 )
| ~ ( in @ SY498 @ SV149 ) )
| ( in @ SY540 @ SV197 ) )
| ~ ! [SY542: $i] :
( ~ ( in @ SY542 @ SV197 )
| ~ ( ~ ( in @ SY542 @ ( sK12_D @ SY542 @ SV197 @ SV149 ) )
| ~ ( in @ ( sK12_D @ SY542 @ SV197 @ SV149 ) @ SV149 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1236]) ).
thf(1357,plain,
! [SV150: $i] :
( ( ( ~ ( ~ ! [SY500: $i,SY501: $i] :
( ( sK31_B @ SV150 )
!= ( ordered_pair @ SY500 @ SY501 ) )
| ~ ( in @ ( sK31_B @ SV150 ) @ SV150 ) ) )
= $true )
| ( ( relation @ SV150 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1237]) ).
thf(1358,plain,
! [SV151: $i] :
( ( ( ~ ( relation @ SV151 ) )
= $true )
| ( ( ! [SY502: $i] :
( ( SY502
= ( ordered_pair @ ( sK29_C @ SY502 @ SV151 ) @ ( sK30_SY281 @ SY502 @ SV151 ) ) )
| ~ ( in @ SY502 @ SV151 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1238]) ).
thf(1359,plain,
! [SV152: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK19_B @ SV152 )
!= ( sK20_SY279 @ SV152 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_B @ SV152 ) @ SV152 )
| ~ ( in @ ( sK20_SY279 @ SV152 ) @ SV152 ) )
| ~ ~ ( in @ ( sK19_B @ SV152 ) @ ( sK20_SY279 @ SV152 ) ) ) )
| ~ ~ ( in @ ( sK20_SY279 @ SV152 ) @ ( sK19_B @ SV152 ) ) ) )
= $true )
| ( ( epsilon_connected @ SV152 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1239]) ).
thf(1360,plain,
! [SV153: $i] :
( ( ( ~ ( epsilon_connected @ SV153 ) )
= $true )
| ( ( ! [SY503: $i,SY504: $i] :
( ( SY503 = SY504 )
| ~ ( in @ SY503 @ SV153 )
| ~ ( in @ SY504 @ SV153 )
| ( in @ SY503 @ SY504 )
| ( in @ SY504 @ SY503 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1240]) ).
thf(1361,plain,
! [SV198: $i,SV154: $i] :
( ( ( SV154 = SV198 )
| ~ ( subset @ SV154 @ SV198 )
| ( proper_subset @ SV154 @ SV198 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1241]) ).
thf(1362,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1242]) ).
thf(1363,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1242]) ).
thf(1364,plain,
! [SV155: $i] :
( ( ( ~ ( relation @ SV155 ) )
= $true )
| ( ( ~ ( reflexive @ SV155 )
| ~ ( transitive @ SV155 )
| ~ ( antisymmetric @ SV155 )
| ~ ( connected @ SV155 )
| ~ ( well_founded_relation @ SV155 )
| ( well_ordering @ SV155 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1243]) ).
thf(1365,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1244]) ).
thf(1366,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( well_founded_relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1244]) ).
thf(1367,plain,
! [SV66: $i] :
( ( ( in @ ( sK51_B @ SV66 ) @ SV66 )
= $true )
| ( ( ordinal @ SV66 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1245]) ).
thf(1368,plain,
! [SV66: $i] :
( ( ( ~ ( ordinal @ ( sK51_B @ SV66 ) )
| ~ ( subset @ ( sK51_B @ SV66 ) @ SV66 ) )
= $true )
| ( ( ordinal @ SV66 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1246]) ).
thf(1369,plain,
! [SV67: $i,SV121: $i] :
( ( ( ~ ! [SY475: $i] :
( ~ ( in @ SY475 @ SV121 )
| ~ ( in @ SY475 @ ( sK4_C @ SV121 @ SV67 ) ) ) )
= $false )
| ( ( ~ ( in @ SV67 @ SV121 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1247]) ).
thf(1370,plain,
! [SV67: $i,SV121: $i] :
( ( ( ~ ( in @ ( sK4_C @ SV121 @ SV67 ) @ SV121 ) )
= $false )
| ( ( ~ ( in @ SV67 @ SV121 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1247]) ).
thf(1371,plain,
! [SV156: $i] :
( ( ( in @ ( sK27_B @ SV156 ) @ SV156 )
= $true )
| ( ( SV156 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1248]) ).
thf(1372,plain,
! [SV157: $i] :
( ( ( SV157 != empty_set )
= $true )
| ( ( ! [SY506: $i] :
~ ( in @ SY506 @ SV157 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1249]) ).
thf(1373,plain,
! [SV199: $i,SV158: $i] :
( ( ( disjoint @ SV158 @ SV199 )
| ~ ( ~ ( in @ ( sK34_C @ SV199 @ SV158 ) @ SV158 )
| ~ ( in @ ( sK34_C @ SV199 @ SV158 ) @ SV199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1250]) ).
thf(1374,plain,
! [SV200: $i,SV159: $i] :
( ( ! [SY543: $i] :
( ~ ( in @ SY543 @ SV159 )
| ~ ( in @ SY543 @ SV200 ) )
| ~ ( disjoint @ SV159 @ SV200 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1251]) ).
thf(1375,plain,
! [SV160: $i,SV201: $i] :
( ( ~ ( ~ ( ( ( sK28_C @ SV201 @ SV160 )
!= SV160 )
| ~ ( in @ ( sK28_C @ SV201 @ SV160 ) @ SV201 ) )
| ~ ( ( ( sK28_C @ SV201 @ SV160 )
= SV160 )
| ( in @ ( sK28_C @ SV201 @ SV160 ) @ SV201 ) ) )
| ( SV201
= ( singleton @ SV160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1253]) ).
thf(1376,plain,
! [SV161: $i,SV202: $i] :
( ( ( SV202
!= ( singleton @ SV161 ) )
| ~ ( ~ ! [SY544: $i] :
( ( SY544 != SV161 )
| ( in @ SY544 @ SV202 ) )
| ~ ! [SY545: $i] :
( ~ ( in @ SY545 @ SV202 )
| ( SY545 = SV161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1254]) ).
thf(1377,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK7_A )
| ~ ( epsilon_transitive @ sK7_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1255]) ).
thf(1378,plain,
( ( ~ ( epsilon_connected @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1255]) ).
thf(1379,plain,
! [SV68: $i,SV122: $i] :
( ( ( ~ ( ~ ( ordinal @ ( sK35_C @ SV122 @ SV68 ) )
| ~ ~ ( ~ ! [SY476: $i] :
( ~ ( ordinal @ SY476 )
| ~ ( in @ SY476 @ SV68 )
| ( ordinal_subset @ ( sK35_C @ SV122 @ SV68 ) @ SY476 ) )
| ~ ( in @ ( sK35_C @ SV122 @ SV68 ) @ SV68 ) ) ) )
= $true )
| ( ( ( SV68 = empty_set )
| ~ ( subset @ SV68 @ SV122 ) )
= $true )
| ( ( ordinal @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1256]) ).
thf(1380,plain,
! [SV69: $i,SV203: $i] :
( ( ! [SY546: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK21_D @ SY546 @ SV203 @ SV69 ) @ SY546 )
| ~ ( in @ ( sK21_D @ SY546 @ SV203 @ SV69 ) @ SV69 ) )
| ~ ( ~ ( in @ ( sK21_D @ SY546 @ SV203 @ SV69 ) @ SY546 )
| ~ ( in @ ( sK21_D @ SY546 @ SV203 @ SV69 ) @ SV203 ) ) )
| ~ ( ( in @ ( sK21_D @ SY546 @ SV203 @ SV69 ) @ SY546 )
| ( in @ ( sK21_D @ SY546 @ SV203 @ SV69 ) @ SV69 )
| ( in @ ( sK21_D @ SY546 @ SV203 @ SV69 ) @ SV203 ) ) )
| ( SY546
= ( set_union2 @ SV69 @ SV203 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1257]) ).
thf(1381,plain,
! [SV204: $i,SV69: $i] :
( ( ! [SY547: $i] :
( ( SY547
!= ( set_union2 @ SV69 @ SV204 ) )
| ~ ( ~ ! [SY548: $i] :
( ~ ( in @ SY548 @ SY547 )
| ( in @ SY548 @ SV69 )
| ( in @ SY548 @ SV204 ) )
| ~ ~ ( ~ ! [SY399: $i] :
( ~ ( in @ SY399 @ SV69 )
| ( in @ SY399 @ SY547 ) )
| ~ ! [SY550: $i] :
( ~ ( in @ SY550 @ SV204 )
| ( in @ SY550 @ SY547 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1258]) ).
thf(1382,plain,
! [SV162: $i,SV205: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK26_C @ SV205 @ SV162 ) @ SV205 )
| ~ ( subset @ ( sK26_C @ SV205 @ SV162 ) @ SV162 ) )
| ~ ( ( in @ ( sK26_C @ SV205 @ SV162 ) @ SV205 )
| ( subset @ ( sK26_C @ SV205 @ SV162 ) @ SV162 ) ) )
| ( SV205
= ( powerset @ SV162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1259]) ).
thf(1383,plain,
! [SV163: $i,SV206: $i] :
( ( ( SV206
!= ( powerset @ SV163 ) )
| ~ ( ~ ! [SY551: $i] :
( ~ ( in @ SY551 @ SV206 )
| ( subset @ SY551 @ SV163 ) )
| ~ ! [SY552: $i] :
( ~ ( subset @ SY552 @ SV163 )
| ( in @ SY552 @ SV206 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1260]) ).
thf(1384,plain,
! [SV70: $i,SV207: $i] :
( ( ! [SY553: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SY553 @ SV207 @ SV70 ) @ SV70 )
| ~ ( in @ ( sK15_D @ SY553 @ SV207 @ SV70 ) @ SV207 )
| ~ ( in @ ( sK15_D @ SY553 @ SV207 @ SV70 ) @ SY553 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SY553 @ SV207 @ SV70 ) @ SV70 )
| ( in @ ( sK15_D @ SY553 @ SV207 @ SV70 ) @ SY553 ) )
| ~ ( ( in @ ( sK15_D @ SY553 @ SV207 @ SV70 ) @ SV207 )
| ( in @ ( sK15_D @ SY553 @ SV207 @ SV70 ) @ SY553 ) ) ) )
| ( SY553
= ( set_intersection2 @ SV70 @ SV207 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(1385,plain,
! [SV208: $i,SV70: $i] :
( ( ! [SY554: $i] :
( ( SY554
!= ( set_intersection2 @ SV70 @ SV208 ) )
| ~ ( ~ ! [SY555: $i] :
( ~ ( in @ SY555 @ SV70 )
| ~ ( in @ SY555 @ SV208 )
| ( in @ SY555 @ SY554 ) )
| ~ ~ ( ~ ! [SY406: $i] :
( ~ ( in @ SY406 @ SY554 )
| ( in @ SY406 @ SV70 ) )
| ~ ! [SY557: $i] :
( ~ ( in @ SY557 @ SY554 )
| ( in @ SY557 @ SV208 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1262]) ).
thf(1386,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1263]) ).
thf(1387,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1263]) ).
thf(1388,plain,
! [SV164: $i] :
( ( ( ~ ( ordinal @ SV164 ) )
= $true )
| ( ( ordinal @ ( union @ SV164 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1264]) ).
thf(1389,plain,
! [SV209: $i,SV165: $i] :
( ( ~ ( ordinal @ SV165 )
| ~ ( ordinal @ SV209 )
| ~ ( ordinal_subset @ SV165 @ SV209 )
| ( subset @ SV165 @ SV209 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1265]) ).
thf(1390,plain,
! [SV210: $i,SV166: $i] :
( ( ~ ( ordinal @ SV166 )
| ~ ( ordinal @ SV210 )
| ~ ( subset @ SV166 @ SV210 )
| ( ordinal_subset @ SV166 @ SV210 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1266]) ).
thf(1391,plain,
! [SV71: $i,SV135: $i] :
( ( ( in @ SV135 @ SV71 )
= $false )
| ( ( ~ ( ordinal @ SV135 ) )
= $true )
| ( ( ~ ( ~ ! [SY409: $i] :
( ~ ( ordinal @ SY409 )
| ~ ( in @ SY409 @ SV71 )
| ( ordinal_subset @ ( sK54_B @ SV71 ) @ SY409 ) )
| ~ ~ ( ~ ( in @ ( sK54_B @ SV71 ) @ SV71 )
| ~ ( ordinal @ ( sK54_B @ SV71 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1267]) ).
thf(1392,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK44_C @ SV123 @ SV72 )
!= ( sK45_SY295 @ SV123 @ SV72 ) )
| ~ ~ ( ~ ~ ( ( ( sK45_SY295 @ SV123 @ SV72 )
!= ( sK48_SY300 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 ) ) )
| ( ( sK44_C @ SV123 @ SV72 )
!= ( sK46_SY299 @ SV123 @ SV72 ) ) )
| ~ ~ ( ~ ~ ( ( ( sK46_SY299 @ SV123 @ SV72 )
!= ( sK47_SY303 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 ) ) )
| ~ ( ( ( sK45_SY295 @ SV123 @ SV72 )
!= ( sK46_SY299 @ SV123 @ SV72 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1268]) ).
thf(1393,plain,
! [SV73: $i] :
( ( ( ~ ! [SY415: $i] :
( ~ ( relation @ SY415 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK23_C @ SY415 @ SV73 ) @ ( sK24_SY280 @ SY415 @ SV73 ) ) @ SV73 )
| ~ ( in @ ( ordered_pair @ ( sK23_C @ SY415 @ SV73 ) @ ( sK24_SY280 @ SY415 @ SV73 ) ) @ SY415 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK23_C @ SY415 @ SV73 ) @ ( sK24_SY280 @ SY415 @ SV73 ) ) @ SV73 )
| ( in @ ( ordered_pair @ ( sK23_C @ SY415 @ SV73 ) @ ( sK24_SY280 @ SY415 @ SV73 ) ) @ SY415 ) ) )
| ( SV73 = SY415 ) ) )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1269]) ).
thf(1394,plain,
! [SV73: $i] :
( ( ( ~ ! [SY416: $i] :
( ~ ( relation @ SY416 )
| ( SV73 != SY416 )
| ~ ( ~ ! [SY417: $i,SY418: $i] :
( ~ ( in @ ( ordered_pair @ SY417 @ SY418 ) @ SV73 )
| ( in @ ( ordered_pair @ SY417 @ SY418 ) @ SY416 ) )
| ~ ! [SY419: $i,SY420: $i] :
( ~ ( in @ ( ordered_pair @ SY419 @ SY420 ) @ SY416 )
| ( in @ ( ordered_pair @ SY419 @ SY420 ) @ SV73 ) ) ) ) )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1269]) ).
thf(1395,plain,
! [SV167: $i] :
( ( ( ~ ( ordinal @ SV167 ) )
= $true )
| ( ( epsilon_connected @ SV167 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1270]) ).
thf(1396,plain,
! [SV168: $i] :
( ( ( ~ ( ordinal @ SV168 ) )
= $true )
| ( ( epsilon_transitive @ SV168 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1271]) ).
thf(1397,plain,
! [SV74: $i,SV211: $i] :
( ( ! [SY558: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK22_D @ SY558 @ SV211 @ SV74 ) @ SY558 )
| ( ( sK22_D @ SY558 @ SV211 @ SV74 )
!= SV74 ) )
| ~ ( ~ ( in @ ( sK22_D @ SY558 @ SV211 @ SV74 ) @ SY558 )
| ( ( sK22_D @ SY558 @ SV211 @ SV74 )
!= SV211 ) ) )
| ~ ( ( in @ ( sK22_D @ SY558 @ SV211 @ SV74 ) @ SY558 )
| ( ( sK22_D @ SY558 @ SV211 @ SV74 )
= SV74 )
| ( ( sK22_D @ SY558 @ SV211 @ SV74 )
= SV211 ) ) )
| ( SY558
= ( unordered_pair @ SV74 @ SV211 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1272]) ).
thf(1398,plain,
! [SV212: $i,SV74: $i] :
( ( ! [SY559: $i] :
( ( SY559
!= ( unordered_pair @ SV74 @ SV212 ) )
| ~ ( ~ ! [SY560: $i] :
( ~ ( in @ SY560 @ SY559 )
| ( SY560 = SV74 )
| ( SY560 = SV212 ) )
| ~ ~ ( ~ ! [SY426: $i] :
( ( SY426 != SV74 )
| ( in @ SY426 @ SY559 ) )
| ~ ! [SY562: $i] :
( ( SY562 != SV212 )
| ( in @ SY562 @ SY559 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1273]) ).
thf(1399,plain,
! [SV169: $i] :
( ( ( ~ ( ~ ( in @ ( sK25_B @ SV169 ) @ SV169 )
| ~ ~ ( subset @ ( sK25_B @ SV169 ) @ SV169 ) ) )
= $true )
| ( ( epsilon_transitive @ SV169 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1274]) ).
thf(1400,plain,
! [SV170: $i] :
( ( ( ~ ( epsilon_transitive @ SV170 ) )
= $true )
| ( ( ! [SY520: $i] :
( ~ ( in @ SY520 @ SV170 )
| ( subset @ SY520 @ SV170 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1275]) ).
thf(1401,plain,
! [SV75: $i,SV213: $i] :
( ( ~ ( subset @ SV213 @ ( sK2_B @ SV75 ) )
| ( are_equipotent @ SV213 @ ( sK2_B @ SV75 ) )
| ( in @ SV213 @ ( sK2_B @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1276]) ).
thf(1402,plain,
! [SV75: $i] :
( ( ~ ! [SY429: $i] :
( ~ ( ~ ! [SY430: $i] :
( ~ ( subset @ SY430 @ SY429 )
| ( in @ SY430 @ ( sK3_SY270 @ SY429 @ SV75 ) ) )
| ~ ( in @ ( sK3_SY270 @ SY429 @ SV75 ) @ ( sK2_B @ SV75 ) ) )
| ~ ( in @ SY429 @ ( sK2_B @ SV75 ) ) )
| ~ ~ ( ~ ! [SY431: $i,SY432: $i] :
( ~ ( in @ SY431 @ ( sK2_B @ SV75 ) )
| ~ ( subset @ SY432 @ SY431 )
| ( in @ SY432 @ ( sK2_B @ SV75 ) ) )
| ~ ( in @ SV75 @ ( sK2_B @ SV75 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1277]) ).
thf(1403,plain,
! [SV214: $i,SV76: $i] :
( ( ! [SY563: $i] :
( ~ ( relation @ SY563 )
| ~ ( in @ SV76 @ ( relation_field @ ( relation_restriction @ SY563 @ SV214 ) ) )
| ( in @ SV76 @ ( relation_field @ SY563 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1278]) ).
thf(1404,plain,
! [SV215: $i,SV76: $i] :
( ( ! [SY564: $i] :
( ~ ( relation @ SY564 )
| ~ ( in @ SV76 @ ( relation_field @ ( relation_restriction @ SY564 @ SV215 ) ) )
| ( in @ SV76 @ SV215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1279]) ).
thf(1405,plain,
! [SV77: $i] :
( ( ( ~ ! [SY437: $i] :
( ~ ( relation @ SY437 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK17_C @ SY437 @ SV77 ) @ ( sK18_SY278 @ SY437 @ SV77 ) ) @ SV77 )
| ~ ~ ( in @ ( ordered_pair @ ( sK17_C @ SY437 @ SV77 ) @ ( sK18_SY278 @ SY437 @ SV77 ) ) @ SY437 ) )
| ( subset @ SV77 @ SY437 ) ) )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1280]) ).
thf(1406,plain,
! [SV77: $i] :
( ( ( ~ ! [SY438: $i] :
( ~ ( relation @ SY438 )
| ~ ( subset @ SV77 @ SY438 )
| ! [SY439: $i,SY440: $i] :
( ~ ( in @ ( ordered_pair @ SY439 @ SY440 ) @ SV77 )
| ( in @ ( ordered_pair @ SY439 @ SY440 ) @ SY438 ) ) ) )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1280]) ).
thf(1407,plain,
! [SV171: $i,SV216: $i] :
( ( ~ ( ~ ( in @ ( sK16_C @ SV216 @ SV171 ) @ SV171 )
| ~ ~ ( in @ ( sK16_C @ SV216 @ SV171 ) @ SV216 ) )
| ( subset @ SV171 @ SV216 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1281]) ).
thf(1408,plain,
! [SV217: $i,SV172: $i] :
( ( ~ ( subset @ SV172 @ SV217 )
| ! [SY565: $i] :
( ~ ( in @ SY565 @ SV172 )
| ( in @ SY565 @ SV217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1282]) ).
thf(1409,plain,
! [SV78: $i,SV218: $i] :
( ( ! [SY566: $i] :
( ~ ( ~ ( ~ ( in @ ( sK11_D @ SY566 @ SV218 @ SV78 ) @ SV78 )
| ( in @ ( sK11_D @ SY566 @ SV218 @ SV78 ) @ SV218 )
| ~ ( in @ ( sK11_D @ SY566 @ SV218 @ SV78 ) @ SY566 ) )
| ~ ~ ( ~ ( ( in @ ( sK11_D @ SY566 @ SV218 @ SV78 ) @ SV78 )
| ( in @ ( sK11_D @ SY566 @ SV218 @ SV78 ) @ SY566 ) )
| ~ ( ~ ( in @ ( sK11_D @ SY566 @ SV218 @ SV78 ) @ SV218 )
| ( in @ ( sK11_D @ SY566 @ SV218 @ SV78 ) @ SY566 ) ) ) )
| ( SY566
= ( set_difference @ SV78 @ SV218 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1283]) ).
thf(1410,plain,
! [SV219: $i,SV78: $i] :
( ( ! [SY567: $i] :
( ( SY567
!= ( set_difference @ SV78 @ SV219 ) )
| ~ ( ~ ! [SY568: $i] :
( ~ ( in @ SY568 @ SV78 )
| ( in @ SY568 @ SV219 )
| ( in @ SY568 @ SY567 ) )
| ~ ~ ( ~ ! [SY446: $i] :
( ~ ( in @ SY446 @ SY567 )
| ( in @ SY446 @ SV78 ) )
| ~ ! [SY570: $i] :
( ~ ( in @ SY570 @ SY567 )
| ~ ( in @ SY570 @ SV219 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1284]) ).
thf(1411,plain,
! [SV173: $i,SV220: $i] :
( ( ~ ( relation @ SV220 )
| ( subset @ ( relation_field @ ( relation_restriction @ SV220 @ SV173 ) ) @ ( relation_field @ SV220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1285]) ).
thf(1412,plain,
! [SV174: $i,SV221: $i] :
( ( ~ ( relation @ SV221 )
| ( subset @ ( relation_field @ ( relation_restriction @ SV221 @ SV174 ) ) @ SV174 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1286]) ).
thf(1413,plain,
( ( ~ ( epsilon_connected @ sK49_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1287]) ).
thf(1414,plain,
( ( ~ ( epsilon_transitive @ sK49_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1287]) ).
thf(1415,plain,
! [SV175: $i] :
( ( ( ~ ( relation @ SV175 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK36_B @ SV175 ) @ ( sK37_SY285 @ SV175 ) ) @ SV175 )
| ~ ( in @ ( ordered_pair @ ( sK37_SY285 @ SV175 ) @ ( sK36_B @ SV175 ) ) @ SV175 ) )
| ~ ( ( ( sK36_B @ SV175 )
!= ( sK37_SY285 @ SV175 ) ) ) )
| ( antisymmetric @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1288]) ).
thf(1416,plain,
! [SV176: $i] :
( ( ( ~ ( relation @ SV176 ) )
= $true )
| ( ( ~ ( antisymmetric @ SV176 )
| ! [SY526: $i,SY527: $i] :
( ~ ( in @ ( ordered_pair @ SY526 @ SY527 ) @ SV176 )
| ~ ( in @ ( ordered_pair @ SY527 @ SY526 ) @ SV176 )
| ( SY526 = SY527 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1289]) ).
thf(1417,plain,
! [SV222: $i,SV177: $i] :
( ( ~ ( subset @ SV177 @ SV222 )
| ~ ( subset @ SV222 @ SV177 )
| ( SV177 = SV222 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1290]) ).
thf(1418,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1291]) ).
thf(1419,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1291]) ).
thf(1420,plain,
! [SV178: $i] :
( ( ( ~ ( relation @ SV178 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK38_B @ SV178 ) @ ( sK39_SY286 @ SV178 ) ) @ SV178 )
| ~ ( in @ ( ordered_pair @ ( sK39_SY286 @ SV178 ) @ ( sK40_SY288 @ SV178 ) ) @ SV178 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK38_B @ SV178 ) @ ( sK40_SY288 @ SV178 ) ) @ SV178 ) )
| ( transitive @ SV178 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1292]) ).
thf(1421,plain,
! [SV179: $i] :
( ( ( ~ ( relation @ SV179 ) )
= $true )
| ( ( ~ ( transitive @ SV179 )
| ! [SY529: $i,SY530: $i,SY531: $i] :
( ~ ( in @ ( ordered_pair @ SY529 @ SY530 ) @ SV179 )
| ~ ( in @ ( ordered_pair @ SY530 @ SY531 ) @ SV179 )
| ( in @ ( ordered_pair @ SY529 @ SY531 ) @ SV179 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1293]) ).
thf(1422,plain,
! [SV79: $i,SV124: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_C @ SV124 @ SV79 ) @ SV79 )
| ~ ( in @ ( sK5_C @ SV124 @ SV79 ) @ SV124 ) ) )
= $false )
| ( ( SV79 = SV124 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1294]) ).
thf(1423,plain,
! [SV79: $i,SV124: $i] :
( ( ( ~ ( ( in @ ( sK5_C @ SV124 @ SV79 ) @ SV79 )
| ( in @ ( sK5_C @ SV124 @ SV79 ) @ SV124 ) ) )
= $false )
| ( ( SV79 = SV124 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1294]) ).
thf(1424,plain,
! [SV180: $i] :
( ( ( SV180
!= ( union @ SV180 ) )
= $true )
| ( ( being_limit_ordinal @ SV180 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1295]) ).
thf(1425,plain,
! [SV181: $i] :
( ( ( ~ ( being_limit_ordinal @ SV181 ) )
= $true )
| ( ( SV181
= ( union @ SV181 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1296]) ).
thf(1426,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_connected @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1297]) ).
thf(1427,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1297]) ).
thf(1428,plain,
! [SV182: $i] :
( ( ( ~ ( empty @ SV182 ) )
= $true )
| ( ( ordinal @ SV182 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1298]) ).
thf(1429,plain,
! [SV183: $i] :
( ( ( ~ ( ordinal @ SV183 ) )
= $true )
| ( ( ( being_limit_ordinal @ SV183 )
| ~ ( ~ ( ordinal @ ( sK50_B @ SV183 ) )
| ( SV183
!= ( succ @ ( sK50_B @ SV183 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1299]) ).
thf(1430,plain,
! [SV184: $i] :
( ( ( ~ ( ordinal @ SV184 ) )
= $true )
| ( ( ! [SY532: $i] :
( ( SV184
!= ( succ @ SY532 ) )
| ~ ( ordinal @ SY532 ) )
| ~ ( being_limit_ordinal @ SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1300]) ).
thf(1431,plain,
! [SV223: $i,SV185: $i] :
( ( ~ ( in @ SV185 @ SV223 )
| ( subset @ ( singleton @ SV185 ) @ SV223 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1301]) ).
thf(1432,plain,
! [SV224: $i,SV186: $i] :
( ( ~ ( subset @ ( singleton @ SV186 ) @ SV224 )
| ( in @ SV186 @ SV224 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1302]) ).
thf(1433,plain,
! [SV80: $i,SV125: $i] :
( ( ! [SY481: $i,SY482: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 ) @ SY482 )
| ( ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 )
!= SY481 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 ) @ SY482 )
| ( ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 )
!= SV80 ) )
| ~ ( ~ ( in @ ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 ) @ SY482 )
| ( ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 )
!= SV125 ) ) ) )
| ~ ( ( in @ ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 ) @ SY482 )
| ( ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 )
= SY481 )
| ( ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 )
= SV80 )
| ( ( sK32_E @ SY482 @ SY481 @ SV125 @ SV80 )
= SV125 ) ) )
| ( SY482
= ( unordered_triple @ SV80 @ SV125 @ SY481 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1303]) ).
thf(1434,plain,
! [SV125: $i,SV80: $i] :
( ( ! [SY483: $i,SY484: $i] :
( ( SY484
!= ( unordered_triple @ SV80 @ SV125 @ SY483 ) )
| ~ ( ~ ! [SY485: $i] :
( ~ ( in @ SY485 @ SY484 )
| ( SY485 = SY483 )
| ( SY485 = SV80 )
| ( SY485 = SV125 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ( SX4 != SY483 )
| ( in @ SX4 @ SY484 ) )
| ~ ~ ( ~ ! [SY456: $i] :
( ( SY456 != SV80 )
| ( in @ SY456 @ SY484 ) )
| ~ ! [SY488: $i] :
( ( SY488 != SV125 )
| ( in @ SY488 @ SY484 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1304]) ).
thf(1435,plain,
! [SV81: $i,SV1: $i] :
( ( ( in @ SV1 @ SV81 )
= $false )
| ( ( ordinal @ SV1 )
= $true )
| ( ( ordinal @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1305]) ).
thf(1436,plain,
! [SV2: $i,SV136: $i] :
( ( ( ordinal @ SV136 )
= $false )
| ( ( ( in @ SV2 @ SV136 )
| ( SV2 = SV136 )
| ( in @ SV136 @ SV2 ) )
= $true )
| ( ( ordinal @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1306]) ).
thf(1437,plain,
! [SV4: $i,SV82: $i] :
( ( ( well_ordering @ SV82 )
= $false )
| ( ( well_ordering @ ( relation_restriction @ SV82 @ SV4 ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1307]) ).
thf(1438,plain,
! [SV10: $i,SV83: $i] :
( ( ( ordinal @ SV83 )
= $false )
| ( ( ordinal @ SV10 )
= $false )
| ( ( ( ordinal_subset @ SV10 @ SV83 )
| ( ordinal_subset @ SV83 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1309]) ).
thf(1439,plain,
! [SV12: $i,SV187: $i] :
( ( ( ordinal @ SV187 )
= $false )
| ( ( ordinal @ SV12 )
= $false )
| ( ( ordinal_subset @ SV12 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1310]) ).
thf(1440,plain,
! [SV137: $i,SV126: $i,SV86: $i,SV16: $i] :
( ( ( ~ ( subset @ SV16 @ SV86 ) )
= $true )
| ( ( ~ ( subset @ SV126 @ SV137 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV16 @ SV126 ) @ ( cartesian_product2 @ SV86 @ SV137 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1311]) ).
thf(1441,plain,
! [SV88: $i,SV18: $i,SV127: $i,SV138: $i] :
( ( ( relation_of2_as_subset @ SV138 @ SV127 @ SV18 )
= $false )
| ( ( ~ ( subset @ SV18 @ SV88 )
| ( relation_of2_as_subset @ SV138 @ SV127 @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1312]) ).
thf(1442,plain,
! [SV128: $i,SV89: $i,SV19: $i] :
( ( ( ~ ( subset @ SV19 @ SV89 ) )
= $true )
| ( ( subset @ ( relation_inverse_image @ SV128 @ SV19 ) @ ( relation_inverse_image @ SV128 @ SV89 ) )
= $true )
| ( ( relation @ SV128 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1313]) ).
thf(1443,plain,
! [SV129: $i,SV91: $i,SV21: $i] :
( ( ( subset @ SV21 @ SV91 )
= $false )
| ( ( ~ ( subset @ SV21 @ SV129 ) )
= $true )
| ( ( subset @ SV21 @ ( set_intersection2 @ SV91 @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1314]) ).
thf(1444,plain,
! [SV130: $i,SV92: $i,SV22: $i] :
( ( ( subset @ SV22 @ SV92 )
= $false )
| ( ( ~ ( subset @ SV92 @ SV130 ) )
= $true )
| ( ( subset @ SV22 @ SV130 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1315]) ).
thf(1445,plain,
! [SV23: $i,SV139: $i] :
( ( ( ordinal @ SV139 )
= $false )
| ( ( ~ ( proper_subset @ SV23 @ SV139 )
| ( in @ SV23 @ SV139 ) )
= $true )
| ( ( epsilon_transitive @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1316]) ).
thf(1446,plain,
! [SV25: $i,SV94: $i] :
( ( ( reflexive @ SV94 )
= $false )
| ( ( reflexive @ ( relation_restriction @ SV94 @ SV25 ) )
= $true )
| ( ( relation @ SV94 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1318]) ).
thf(1447,plain,
! [SV26: $i,SV95: $i] :
( ( ( connected @ SV95 )
= $false )
| ( ( connected @ ( relation_restriction @ SV95 @ SV26 ) )
= $true )
| ( ( relation @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1319]) ).
thf(1448,plain,
! [SV27: $i,SV96: $i] :
( ( ( transitive @ SV96 )
= $false )
| ( ( transitive @ ( relation_restriction @ SV96 @ SV27 ) )
= $true )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1320]) ).
thf(1449,plain,
! [SV28: $i,SV97: $i] :
( ( ( antisymmetric @ SV97 )
= $false )
| ( ( antisymmetric @ ( relation_restriction @ SV97 @ SV28 ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1321]) ).
thf(1450,plain,
! [SV32: $i,SV100: $i] :
( ( ( well_founded_relation @ SV100 )
= $false )
| ( ( well_founded_relation @ ( relation_restriction @ SV100 @ SV32 ) )
= $true )
| ( ( relation @ SV100 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1323]) ).
thf(1451,plain,
! [SV103: $i,SV35: $i] :
( ( ( ~ ( subset @ SV35 @ ( relation_field @ SV103 ) ) )
= $true )
| ( ( ~ ( well_ordering @ SV103 ) )
= $true )
| ( ( ( relation_field @ ( relation_restriction @ SV103 @ SV35 ) )
= SV35 )
= $true )
| ( ( relation @ SV103 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1325]) ).
thf(1452,plain,
! [SV132: $i,SV104: $i,SV36: $i] :
( ( ( in @ SV36 @ SV104 )
= $false )
| ( ( ~ ( in @ SV104 @ SV132 ) )
= $true )
| ( ( ~ ( in @ SV132 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1326]) ).
thf(1453,plain,
! [SV39: $i,SV133: $i,SV106: $i] :
( ( ( disjoint @ SV106 @ SV133 )
= $false )
| ( ( ~ ( subset @ SV39 @ SV106 ) )
= $true )
| ( ( disjoint @ SV39 @ SV133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1328]) ).
thf(1454,plain,
! [SV134: $i,SV110: $i,SV43: $i] :
( ( ( subset @ SV43 @ SV110 )
= $false )
| ( ( ~ ( subset @ SV134 @ SV110 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV43 @ SV134 ) @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1329]) ).
thf(1455,plain,
! [SV49: $i,SV113: $i] :
( ( ( relation @ SV113 )
= $false )
| ( ( relation @ SV49 )
= $false )
| ( ( relation @ ( relation_composition @ SV49 @ SV113 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1331]) ).
thf(1456,plain,
! [SV54: $i,SV115: $i] :
( ( ( relation @ SV115 )
= $false )
| ( ( relation @ SV54 )
= $false )
| ( ( relation @ ( set_intersection2 @ SV54 @ SV115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1332]) ).
thf(1457,plain,
! [SV55: $i,SV116: $i] :
( ( ( relation @ SV116 )
= $false )
| ( ( relation @ SV55 )
= $false )
| ( ( relation @ ( set_union2 @ SV55 @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1333]) ).
thf(1458,plain,
! [SV56: $i,SV117: $i] :
( ( ( relation @ SV117 )
= $false )
| ( ( relation @ SV56 )
= $false )
| ( ( relation @ ( set_difference @ SV56 @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1334]) ).
thf(1459,plain,
! [SV190: $i,SV142: $i] :
( ( ( ~ ( in @ SV142 @ SV190 ) )
= $true )
| ( ( subset @ ( singleton @ SV142 ) @ SV190 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1336]) ).
thf(1460,plain,
! [SV191: $i,SV143: $i] :
( ( ( ~ ( subset @ ( singleton @ SV143 ) @ SV191 ) )
= $true )
| ( ( in @ SV143 @ SV191 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1337]) ).
thf(1461,plain,
! [SV192: $i,SV61: $i,SV225: $i] :
( ( ~ ( relation @ SV225 )
| ~ ( in @ SV61 @ SV225 )
| ~ ( in @ SV61 @ ( cartesian_product2 @ SV192 @ SV192 ) )
| ( in @ SV61 @ ( relation_restriction @ SV225 @ SV192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1338]) ).
thf(1462,plain,
! [SV61: $i] :
( ( ~ ! [SY369: $i,SY370: $i] :
( ~ ( relation @ SY370 )
| ~ ( in @ SV61 @ ( relation_restriction @ SY370 @ SY369 ) )
| ( in @ SV61 @ SY370 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1339]) ).
thf(1463,plain,
! [SV61: $i] :
( ( ~ ! [SY371: $i,SY372: $i] :
( ~ ( relation @ SY372 )
| ~ ( in @ SV61 @ ( relation_restriction @ SY372 @ SY371 ) )
| ( in @ SV61 @ ( cartesian_product2 @ SY371 @ SY371 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1339]) ).
thf(1464,plain,
! [SV144: $i] :
( ( ( ordinal @ SV144 )
= $false )
| ( ( ~ ( ~ ( ordinal @ ( sK33_B @ SV144 ) )
| ~ ~ ( ~ ( in @ ( sK33_B @ SV144 ) @ SV144 )
| ~ ~ ( in @ ( succ @ ( sK33_B @ SV144 ) ) @ SV144 ) ) )
| ( being_limit_ordinal @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1340]) ).
thf(1465,plain,
! [SV145: $i] :
( ( ( ordinal @ SV145 )
= $false )
| ( ( ~ ( being_limit_ordinal @ SV145 )
| ! [SY493: $i] :
( ~ ( ordinal @ SY493 )
| ~ ( in @ SY493 @ SV145 )
| ( in @ ( succ @ SY493 ) @ SV145 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1341]) ).
thf(1466,plain,
! [SV62: $i] :
( ( ( ! [SY373: $i] :
( ~ ( ordinal @ SY373 )
| ~ ( in @ SV62 @ SY373 )
| ( ordinal_subset @ ( succ @ SV62 ) @ SY373 ) ) )
= $true )
| ( ( ordinal @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1342]) ).
thf(1467,plain,
! [SV62: $i] :
( ( ( ! [SY374: $i] :
( ~ ( ordinal @ SY374 )
| ~ ( ordinal_subset @ ( succ @ SV62 ) @ SY374 )
| ( in @ SV62 @ SY374 ) ) )
= $true )
| ( ( ordinal @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1343]) ).
thf(1468,plain,
! [SV120: $i,SV63: $i] :
( ( ( ~ ! [SY471: $i] :
( ! [SY377: $i] :
( ( SY471 != SY377 )
| ~ ( ordinal @ SY377 )
| ~ ( in @ SY377 @ SV63 ) )
| ~ ( in @ SY471 @ ( succ @ SV120 ) )
| ( in @ SY471 @ ( sK52_C @ SV120 @ SV63 ) ) ) )
= $false )
| ( ( ordinal @ SV120 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1344]) ).
thf(1469,plain,
! [SV63: $i,SV120: $i] :
( ( ( ~ ~ ( ~ ! [SY473: $i] :
( ~ ( in @ SY473 @ ( sK52_C @ SV120 @ SV63 ) )
| ~ ( ~ ~ ( ( SY473
!= ( sK53_E @ SY473 @ SV120 @ SV63 ) )
| ~ ( ordinal @ ( sK53_E @ SY473 @ SV120 @ SV63 ) ) )
| ~ ( in @ ( sK53_E @ SY473 @ SV120 @ SV63 ) @ SV63 ) ) )
| ~ ! [SY474: $i] :
( ~ ( in @ SY474 @ ( sK52_C @ SV120 @ SV63 ) )
| ( in @ SY474 @ ( succ @ SV120 ) ) ) ) )
= $false )
| ( ( ordinal @ SV120 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1344]) ).
thf(1470,plain,
! [SV193: $i,SV64: $i] :
( ( ( ~ ( subset @ SV64 @ SV193 ) )
= $true )
| ( ( ! [SY536: $i] : ( subset @ ( cartesian_product2 @ SV64 @ SY536 ) @ ( cartesian_product2 @ SV193 @ SY536 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1345]) ).
thf(1471,plain,
! [SV194: $i,SV64: $i] :
( ( ( ~ ( subset @ SV64 @ SV194 ) )
= $true )
| ( ( ! [SY537: $i] : ( subset @ ( cartesian_product2 @ SY537 @ SV64 ) @ ( cartesian_product2 @ SY537 @ SV194 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1346]) ).
thf(1472,plain,
! [SV146: $i] :
( ( ( ~ ( epsilon_connected @ SV146 ) )
= $true )
| ( ( ~ ( epsilon_transitive @ SV146 ) )
= $true )
| ( ( ordinal @ SV146 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1347]) ).
thf(1473,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1348]) ).
thf(1474,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1349]) ).
thf(1475,plain,
! [SV195: $i,SV226: $i,SV65: $i] :
( ( ~ ( in @ SV65 @ SV226 )
| ~ ( in @ SV195 @ SV226 )
| ( subset @ ( unordered_pair @ SV65 @ SV195 ) @ SV226 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1350]) ).
thf(1476,plain,
! [SV65: $i] :
( ( ~ ! [SY386: $i,SY387: $i] :
( ~ ( subset @ ( unordered_pair @ SV65 @ SY386 ) @ SY387 )
| ( in @ SV65 @ SY387 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1351]) ).
thf(1477,plain,
! [SV65: $i] :
( ( ~ ! [SY388: $i,SY389: $i] :
( ~ ( subset @ ( unordered_pair @ SV65 @ SY388 ) @ SY389 )
| ( in @ SY388 @ SY389 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1351]) ).
thf(1478,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( empty @ ( succ @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ ( succ @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1352]) ).
thf(1479,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ ( succ @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1353]) ).
thf(1480,plain,
! [SV147: $i] :
( ( ( ordinal @ SV147 )
= $false )
| ( ( ordinal @ ( succ @ SV147 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1354]) ).
thf(1481,plain,
! [SV148: $i,SV196: $i] :
( ( ( ~ ( ~ ( ! [SY539: $i] :
( ~ ( in @ ( sK13_C @ SV196 @ SV148 ) @ SY539 )
| ~ ( in @ SY539 @ SV148 ) )
| ~ ( in @ ( sK13_C @ SV196 @ SV148 ) @ SV196 ) )
| ~ ( ~ ( ~ ( in @ ( sK13_C @ SV196 @ SV148 ) @ ( sK14_SY277 @ SV196 @ SV148 ) )
| ~ ( in @ ( sK14_SY277 @ SV196 @ SV148 ) @ SV148 ) )
| ( in @ ( sK13_C @ SV196 @ SV148 ) @ SV196 ) ) ) )
= $true )
| ( ( SV196
= ( union @ SV148 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1355]) ).
thf(1482,plain,
! [SV149: $i,SV197: $i] :
( ( ( SV197
!= ( union @ SV149 ) )
= $true )
| ( ( ~ ( ~ ! [SY540: $i] :
( ! [SY498: $i] :
( ~ ( in @ SY540 @ SY498 )
| ~ ( in @ SY498 @ SV149 ) )
| ( in @ SY540 @ SV197 ) )
| ~ ! [SY542: $i] :
( ~ ( in @ SY542 @ SV197 )
| ~ ( ~ ( in @ SY542 @ ( sK12_D @ SY542 @ SV197 @ SV149 ) )
| ~ ( in @ ( sK12_D @ SY542 @ SV197 @ SV149 ) @ SV149 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1356]) ).
thf(1483,plain,
! [SV150: $i] :
( ( ( ~ ! [SY500: $i,SY501: $i] :
( ( sK31_B @ SV150 )
!= ( ordered_pair @ SY500 @ SY501 ) )
| ~ ( in @ ( sK31_B @ SV150 ) @ SV150 ) )
= $false )
| ( ( relation @ SV150 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1357]) ).
thf(1484,plain,
! [SV151: $i] :
( ( ( relation @ SV151 )
= $false )
| ( ( ! [SY502: $i] :
( ( SY502
= ( ordered_pair @ ( sK29_C @ SY502 @ SV151 ) @ ( sK30_SY281 @ SY502 @ SV151 ) ) )
| ~ ( in @ SY502 @ SV151 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1358]) ).
thf(1485,plain,
! [SV152: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK19_B @ SV152 )
!= ( sK20_SY279 @ SV152 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_B @ SV152 ) @ SV152 )
| ~ ( in @ ( sK20_SY279 @ SV152 ) @ SV152 ) )
| ~ ~ ( in @ ( sK19_B @ SV152 ) @ ( sK20_SY279 @ SV152 ) ) ) )
| ~ ~ ( in @ ( sK20_SY279 @ SV152 ) @ ( sK19_B @ SV152 ) ) )
= $false )
| ( ( epsilon_connected @ SV152 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1359]) ).
thf(1486,plain,
! [SV153: $i] :
( ( ( epsilon_connected @ SV153 )
= $false )
| ( ( ! [SY503: $i,SY504: $i] :
( ( SY503 = SY504 )
| ~ ( in @ SY503 @ SV153 )
| ~ ( in @ SY504 @ SV153 )
| ( in @ SY503 @ SY504 )
| ( in @ SY504 @ SY503 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1360]) ).
thf(1487,plain,
! [SV198: $i,SV154: $i] :
( ( ( ( SV154 = SV198 )
| ~ ( subset @ SV154 @ SV198 ) )
= $true )
| ( ( proper_subset @ SV154 @ SV198 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1361]) ).
thf(1488,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1362]) ).
thf(1489,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1363]) ).
thf(1490,plain,
! [SV155: $i] :
( ( ( relation @ SV155 )
= $false )
| ( ( ~ ( reflexive @ SV155 )
| ~ ( transitive @ SV155 )
| ~ ( antisymmetric @ SV155 )
| ~ ( connected @ SV155 )
| ~ ( well_founded_relation @ SV155 )
| ( well_ordering @ SV155 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1364]) ).
thf(1491,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1365]) ).
thf(1492,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( well_founded_relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1366]) ).
thf(1493,plain,
! [SV66: $i] :
( ( ( ~ ( ordinal @ ( sK51_B @ SV66 ) ) )
= $true )
| ( ( ~ ( subset @ ( sK51_B @ SV66 ) @ SV66 ) )
= $true )
| ( ( ordinal @ SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1368]) ).
thf(1494,plain,
! [SV67: $i,SV121: $i] :
( ( ( ! [SY475: $i] :
( ~ ( in @ SY475 @ SV121 )
| ~ ( in @ SY475 @ ( sK4_C @ SV121 @ SV67 ) ) ) )
= $true )
| ( ( ~ ( in @ SV67 @ SV121 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1369]) ).
thf(1495,plain,
! [SV67: $i,SV121: $i] :
( ( ( in @ ( sK4_C @ SV121 @ SV67 ) @ SV121 )
= $true )
| ( ( ~ ( in @ SV67 @ SV121 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1370]) ).
thf(1496,plain,
! [SV157: $i] :
( ( ( SV157 = empty_set )
= $false )
| ( ( ! [SY506: $i] :
~ ( in @ SY506 @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1372]) ).
thf(1497,plain,
! [SV199: $i,SV158: $i] :
( ( ( disjoint @ SV158 @ SV199 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK34_C @ SV199 @ SV158 ) @ SV158 )
| ~ ( in @ ( sK34_C @ SV199 @ SV158 ) @ SV199 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1373]) ).
thf(1498,plain,
! [SV200: $i,SV159: $i] :
( ( ( ! [SY543: $i] :
( ~ ( in @ SY543 @ SV159 )
| ~ ( in @ SY543 @ SV200 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV159 @ SV200 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1374]) ).
thf(1499,plain,
! [SV160: $i,SV201: $i] :
( ( ( ~ ( ~ ( ( ( sK28_C @ SV201 @ SV160 )
!= SV160 )
| ~ ( in @ ( sK28_C @ SV201 @ SV160 ) @ SV201 ) )
| ~ ( ( ( sK28_C @ SV201 @ SV160 )
= SV160 )
| ( in @ ( sK28_C @ SV201 @ SV160 ) @ SV201 ) ) ) )
= $true )
| ( ( SV201
= ( singleton @ SV160 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1375]) ).
thf(1500,plain,
! [SV161: $i,SV202: $i] :
( ( ( SV202
!= ( singleton @ SV161 ) )
= $true )
| ( ( ~ ( ~ ! [SY544: $i] :
( ( SY544 != SV161 )
| ( in @ SY544 @ SV202 ) )
| ~ ! [SY545: $i] :
( ~ ( in @ SY545 @ SV202 )
| ( SY545 = SV161 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1376]) ).
thf(1501,plain,
( ( ~ ( ~ ~ ( empty @ sK7_A )
| ~ ( epsilon_transitive @ sK7_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1377]) ).
thf(1502,plain,
( ( epsilon_connected @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1378]) ).
thf(1503,plain,
! [SV68: $i,SV122: $i] :
( ( ( ~ ( ordinal @ ( sK35_C @ SV122 @ SV68 ) )
| ~ ~ ( ~ ! [SY476: $i] :
( ~ ( ordinal @ SY476 )
| ~ ( in @ SY476 @ SV68 )
| ( ordinal_subset @ ( sK35_C @ SV122 @ SV68 ) @ SY476 ) )
| ~ ( in @ ( sK35_C @ SV122 @ SV68 ) @ SV68 ) ) )
= $false )
| ( ( ( SV68 = empty_set )
| ~ ( subset @ SV68 @ SV122 ) )
= $true )
| ( ( ordinal @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1379]) ).
thf(1504,plain,
! [SV69: $i,SV203: $i,SV227: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV227 )
| ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV69 ) )
| ~ ( ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV227 )
| ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV203 ) ) )
| ~ ( ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV227 )
| ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV69 )
| ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV203 ) ) )
| ( SV227
= ( set_union2 @ SV69 @ SV203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1380]) ).
thf(1505,plain,
! [SV204: $i,SV69: $i,SV228: $i] :
( ( ( SV228
!= ( set_union2 @ SV69 @ SV204 ) )
| ~ ( ~ ! [SY571: $i] :
( ~ ( in @ SY571 @ SV228 )
| ( in @ SY571 @ SV69 )
| ( in @ SY571 @ SV204 ) )
| ~ ~ ( ~ ! [SY572: $i] :
( ~ ( in @ SY572 @ SV69 )
| ( in @ SY572 @ SV228 ) )
| ~ ! [SY573: $i] :
( ~ ( in @ SY573 @ SV204 )
| ( in @ SY573 @ SV228 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1381]) ).
thf(1506,plain,
! [SV162: $i,SV205: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK26_C @ SV205 @ SV162 ) @ SV205 )
| ~ ( subset @ ( sK26_C @ SV205 @ SV162 ) @ SV162 ) )
| ~ ( ( in @ ( sK26_C @ SV205 @ SV162 ) @ SV205 )
| ( subset @ ( sK26_C @ SV205 @ SV162 ) @ SV162 ) ) ) )
= $true )
| ( ( SV205
= ( powerset @ SV162 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1382]) ).
thf(1507,plain,
! [SV163: $i,SV206: $i] :
( ( ( SV206
!= ( powerset @ SV163 ) )
= $true )
| ( ( ~ ( ~ ! [SY551: $i] :
( ~ ( in @ SY551 @ SV206 )
| ( subset @ SY551 @ SV163 ) )
| ~ ! [SY552: $i] :
( ~ ( subset @ SY552 @ SV163 )
| ( in @ SY552 @ SV206 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1383]) ).
thf(1508,plain,
! [SV70: $i,SV207: $i,SV229: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV70 )
| ~ ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV207 )
| ~ ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV229 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV70 )
| ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV229 ) )
| ~ ( ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV207 )
| ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV229 ) ) ) )
| ( SV229
= ( set_intersection2 @ SV70 @ SV207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1384]) ).
thf(1509,plain,
! [SV208: $i,SV70: $i,SV230: $i] :
( ( ( SV230
!= ( set_intersection2 @ SV70 @ SV208 ) )
| ~ ( ~ ! [SY574: $i] :
( ~ ( in @ SY574 @ SV70 )
| ~ ( in @ SY574 @ SV208 )
| ( in @ SY574 @ SV230 ) )
| ~ ~ ( ~ ! [SY575: $i] :
( ~ ( in @ SY575 @ SV230 )
| ( in @ SY575 @ SV70 ) )
| ~ ! [SY576: $i] :
( ~ ( in @ SY576 @ SV230 )
| ( in @ SY576 @ SV208 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1385]) ).
thf(1510,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ ( union @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1386]) ).
thf(1511,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ ( union @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1387]) ).
thf(1512,plain,
! [SV164: $i] :
( ( ( ordinal @ SV164 )
= $false )
| ( ( ordinal @ ( union @ SV164 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1388]) ).
thf(1513,plain,
! [SV209: $i,SV165: $i] :
( ( ( ~ ( ordinal @ SV165 )
| ~ ( ordinal @ SV209 ) )
= $true )
| ( ( ~ ( ordinal_subset @ SV165 @ SV209 )
| ( subset @ SV165 @ SV209 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1389]) ).
thf(1514,plain,
! [SV210: $i,SV166: $i] :
( ( ( ~ ( ordinal @ SV166 )
| ~ ( ordinal @ SV210 ) )
= $true )
| ( ( ~ ( subset @ SV166 @ SV210 )
| ( ordinal_subset @ SV166 @ SV210 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1390]) ).
thf(1515,plain,
! [SV71: $i,SV135: $i] :
( ( ( ordinal @ SV135 )
= $false )
| ( ( in @ SV135 @ SV71 )
= $false )
| ( ( ~ ( ~ ! [SY409: $i] :
( ~ ( ordinal @ SY409 )
| ~ ( in @ SY409 @ SV71 )
| ( ordinal_subset @ ( sK54_B @ SV71 ) @ SY409 ) )
| ~ ~ ( ~ ( in @ ( sK54_B @ SV71 ) @ SV71 )
| ~ ( ordinal @ ( sK54_B @ SV71 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1391]) ).
thf(1516,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK44_C @ SV123 @ SV72 )
!= ( sK45_SY295 @ SV123 @ SV72 ) )
| ~ ~ ( ~ ~ ( ( ( sK45_SY295 @ SV123 @ SV72 )
!= ( sK48_SY300 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 ) ) )
| ( ( sK44_C @ SV123 @ SV72 )
!= ( sK46_SY299 @ SV123 @ SV72 ) ) )
| ~ ~ ( ~ ~ ( ( ( sK46_SY299 @ SV123 @ SV72 )
!= ( sK47_SY303 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 ) ) )
| ~ ( ( ( sK45_SY295 @ SV123 @ SV72 )
!= ( sK46_SY299 @ SV123 @ SV72 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1392]) ).
thf(1517,plain,
! [SV73: $i] :
( ( ( ! [SY415: $i] :
( ~ ( relation @ SY415 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK23_C @ SY415 @ SV73 ) @ ( sK24_SY280 @ SY415 @ SV73 ) ) @ SV73 )
| ~ ( in @ ( ordered_pair @ ( sK23_C @ SY415 @ SV73 ) @ ( sK24_SY280 @ SY415 @ SV73 ) ) @ SY415 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK23_C @ SY415 @ SV73 ) @ ( sK24_SY280 @ SY415 @ SV73 ) ) @ SV73 )
| ( in @ ( ordered_pair @ ( sK23_C @ SY415 @ SV73 ) @ ( sK24_SY280 @ SY415 @ SV73 ) ) @ SY415 ) ) )
| ( SV73 = SY415 ) ) )
= $true )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1393]) ).
thf(1518,plain,
! [SV73: $i] :
( ( ( ! [SY416: $i] :
( ~ ( relation @ SY416 )
| ( SV73 != SY416 )
| ~ ( ~ ! [SY417: $i,SY418: $i] :
( ~ ( in @ ( ordered_pair @ SY417 @ SY418 ) @ SV73 )
| ( in @ ( ordered_pair @ SY417 @ SY418 ) @ SY416 ) )
| ~ ! [SY419: $i,SY420: $i] :
( ~ ( in @ ( ordered_pair @ SY419 @ SY420 ) @ SY416 )
| ( in @ ( ordered_pair @ SY419 @ SY420 ) @ SV73 ) ) ) ) )
= $true )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1394]) ).
thf(1519,plain,
! [SV167: $i] :
( ( ( ordinal @ SV167 )
= $false )
| ( ( epsilon_connected @ SV167 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1395]) ).
thf(1520,plain,
! [SV168: $i] :
( ( ( ordinal @ SV168 )
= $false )
| ( ( epsilon_transitive @ SV168 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1396]) ).
thf(1521,plain,
! [SV74: $i,SV211: $i,SV231: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK22_D @ SV231 @ SV211 @ SV74 ) @ SV231 )
| ( ( sK22_D @ SV231 @ SV211 @ SV74 )
!= SV74 ) )
| ~ ( ~ ( in @ ( sK22_D @ SV231 @ SV211 @ SV74 ) @ SV231 )
| ( ( sK22_D @ SV231 @ SV211 @ SV74 )
!= SV211 ) ) )
| ~ ( ( in @ ( sK22_D @ SV231 @ SV211 @ SV74 ) @ SV231 )
| ( ( sK22_D @ SV231 @ SV211 @ SV74 )
= SV74 )
| ( ( sK22_D @ SV231 @ SV211 @ SV74 )
= SV211 ) ) )
| ( SV231
= ( unordered_pair @ SV74 @ SV211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1397]) ).
thf(1522,plain,
! [SV212: $i,SV74: $i,SV232: $i] :
( ( ( SV232
!= ( unordered_pair @ SV74 @ SV212 ) )
| ~ ( ~ ! [SY577: $i] :
( ~ ( in @ SY577 @ SV232 )
| ( SY577 = SV74 )
| ( SY577 = SV212 ) )
| ~ ~ ( ~ ! [SY578: $i] :
( ( SY578 != SV74 )
| ( in @ SY578 @ SV232 ) )
| ~ ! [SY579: $i] :
( ( SY579 != SV212 )
| ( in @ SY579 @ SV232 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1398]) ).
thf(1523,plain,
! [SV169: $i] :
( ( ( ~ ( in @ ( sK25_B @ SV169 ) @ SV169 )
| ~ ~ ( subset @ ( sK25_B @ SV169 ) @ SV169 ) )
= $false )
| ( ( epsilon_transitive @ SV169 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1399]) ).
thf(1524,plain,
! [SV170: $i] :
( ( ( epsilon_transitive @ SV170 )
= $false )
| ( ( ! [SY520: $i] :
( ~ ( in @ SY520 @ SV170 )
| ( subset @ SY520 @ SV170 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1400]) ).
thf(1525,plain,
! [SV75: $i,SV213: $i] :
( ( ( ~ ( subset @ SV213 @ ( sK2_B @ SV75 ) )
| ( are_equipotent @ SV213 @ ( sK2_B @ SV75 ) ) )
= $true )
| ( ( in @ SV213 @ ( sK2_B @ SV75 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1401]) ).
thf(1526,plain,
! [SV75: $i] :
( ( ~ ! [SY429: $i] :
( ~ ( ~ ! [SY430: $i] :
( ~ ( subset @ SY430 @ SY429 )
| ( in @ SY430 @ ( sK3_SY270 @ SY429 @ SV75 ) ) )
| ~ ( in @ ( sK3_SY270 @ SY429 @ SV75 ) @ ( sK2_B @ SV75 ) ) )
| ~ ( in @ SY429 @ ( sK2_B @ SV75 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1402]) ).
thf(1527,plain,
! [SV75: $i] :
( ( ~ ~ ( ~ ! [SY431: $i,SY432: $i] :
( ~ ( in @ SY431 @ ( sK2_B @ SV75 ) )
| ~ ( subset @ SY432 @ SY431 )
| ( in @ SY432 @ ( sK2_B @ SV75 ) ) )
| ~ ( in @ SV75 @ ( sK2_B @ SV75 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1402]) ).
thf(1528,plain,
! [SV214: $i,SV76: $i,SV233: $i] :
( ( ~ ( relation @ SV233 )
| ~ ( in @ SV76 @ ( relation_field @ ( relation_restriction @ SV233 @ SV214 ) ) )
| ( in @ SV76 @ ( relation_field @ SV233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1403]) ).
thf(1529,plain,
! [SV215: $i,SV76: $i,SV234: $i] :
( ( ~ ( relation @ SV234 )
| ~ ( in @ SV76 @ ( relation_field @ ( relation_restriction @ SV234 @ SV215 ) ) )
| ( in @ SV76 @ SV215 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1404]) ).
thf(1530,plain,
! [SV77: $i] :
( ( ( ! [SY437: $i] :
( ~ ( relation @ SY437 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK17_C @ SY437 @ SV77 ) @ ( sK18_SY278 @ SY437 @ SV77 ) ) @ SV77 )
| ~ ~ ( in @ ( ordered_pair @ ( sK17_C @ SY437 @ SV77 ) @ ( sK18_SY278 @ SY437 @ SV77 ) ) @ SY437 ) )
| ( subset @ SV77 @ SY437 ) ) )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1405]) ).
thf(1531,plain,
! [SV77: $i] :
( ( ( ! [SY438: $i] :
( ~ ( relation @ SY438 )
| ~ ( subset @ SV77 @ SY438 )
| ! [SY439: $i,SY440: $i] :
( ~ ( in @ ( ordered_pair @ SY439 @ SY440 ) @ SV77 )
| ( in @ ( ordered_pair @ SY439 @ SY440 ) @ SY438 ) ) ) )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1406]) ).
thf(1532,plain,
! [SV171: $i,SV216: $i] :
( ( ( ~ ( ~ ( in @ ( sK16_C @ SV216 @ SV171 ) @ SV171 )
| ~ ~ ( in @ ( sK16_C @ SV216 @ SV171 ) @ SV216 ) ) )
= $true )
| ( ( subset @ SV171 @ SV216 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1407]) ).
thf(1533,plain,
! [SV217: $i,SV172: $i] :
( ( ( ~ ( subset @ SV172 @ SV217 ) )
= $true )
| ( ( ! [SY565: $i] :
( ~ ( in @ SY565 @ SV172 )
| ( in @ SY565 @ SV217 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1408]) ).
thf(1534,plain,
! [SV78: $i,SV218: $i,SV235: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV78 )
| ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV218 )
| ~ ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV235 ) )
| ~ ~ ( ~ ( ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV78 )
| ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV235 ) )
| ~ ( ~ ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV218 )
| ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV235 ) ) ) )
| ( SV235
= ( set_difference @ SV78 @ SV218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1409]) ).
thf(1535,plain,
! [SV219: $i,SV78: $i,SV236: $i] :
( ( ( SV236
!= ( set_difference @ SV78 @ SV219 ) )
| ~ ( ~ ! [SY580: $i] :
( ~ ( in @ SY580 @ SV78 )
| ( in @ SY580 @ SV219 )
| ( in @ SY580 @ SV236 ) )
| ~ ~ ( ~ ! [SY581: $i] :
( ~ ( in @ SY581 @ SV236 )
| ( in @ SY581 @ SV78 ) )
| ~ ! [SY582: $i] :
( ~ ( in @ SY582 @ SV236 )
| ~ ( in @ SY582 @ SV219 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1410]) ).
thf(1536,plain,
! [SV173: $i,SV220: $i] :
( ( ( ~ ( relation @ SV220 ) )
= $true )
| ( ( subset @ ( relation_field @ ( relation_restriction @ SV220 @ SV173 ) ) @ ( relation_field @ SV220 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1411]) ).
thf(1537,plain,
! [SV174: $i,SV221: $i] :
( ( ( ~ ( relation @ SV221 ) )
= $true )
| ( ( subset @ ( relation_field @ ( relation_restriction @ SV221 @ SV174 ) ) @ SV174 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1412]) ).
thf(1538,plain,
( ( epsilon_connected @ sK49_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1413]) ).
thf(1539,plain,
( ( epsilon_transitive @ sK49_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1414]) ).
thf(1540,plain,
! [SV175: $i] :
( ( ( relation @ SV175 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK36_B @ SV175 ) @ ( sK37_SY285 @ SV175 ) ) @ SV175 )
| ~ ( in @ ( ordered_pair @ ( sK37_SY285 @ SV175 ) @ ( sK36_B @ SV175 ) ) @ SV175 ) )
| ~ ( ( ( sK36_B @ SV175 )
!= ( sK37_SY285 @ SV175 ) ) ) )
| ( antisymmetric @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1415]) ).
thf(1541,plain,
! [SV176: $i] :
( ( ( relation @ SV176 )
= $false )
| ( ( ~ ( antisymmetric @ SV176 )
| ! [SY526: $i,SY527: $i] :
( ~ ( in @ ( ordered_pair @ SY526 @ SY527 ) @ SV176 )
| ~ ( in @ ( ordered_pair @ SY527 @ SY526 ) @ SV176 )
| ( SY526 = SY527 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1416]) ).
thf(1542,plain,
! [SV222: $i,SV177: $i] :
( ( ( ~ ( subset @ SV177 @ SV222 )
| ~ ( subset @ SV222 @ SV177 ) )
= $true )
| ( ( SV177 = SV222 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1417]) ).
thf(1543,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1418]) ).
thf(1544,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1419]) ).
thf(1545,plain,
! [SV178: $i] :
( ( ( relation @ SV178 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK38_B @ SV178 ) @ ( sK39_SY286 @ SV178 ) ) @ SV178 )
| ~ ( in @ ( ordered_pair @ ( sK39_SY286 @ SV178 ) @ ( sK40_SY288 @ SV178 ) ) @ SV178 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK38_B @ SV178 ) @ ( sK40_SY288 @ SV178 ) ) @ SV178 ) )
| ( transitive @ SV178 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1420]) ).
thf(1546,plain,
! [SV179: $i] :
( ( ( relation @ SV179 )
= $false )
| ( ( ~ ( transitive @ SV179 )
| ! [SY529: $i,SY530: $i,SY531: $i] :
( ~ ( in @ ( ordered_pair @ SY529 @ SY530 ) @ SV179 )
| ~ ( in @ ( ordered_pair @ SY530 @ SY531 ) @ SV179 )
| ( in @ ( ordered_pair @ SY529 @ SY531 ) @ SV179 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1421]) ).
thf(1547,plain,
! [SV79: $i,SV124: $i] :
( ( ( ~ ( in @ ( sK5_C @ SV124 @ SV79 ) @ SV79 )
| ~ ( in @ ( sK5_C @ SV124 @ SV79 ) @ SV124 ) )
= $true )
| ( ( SV79 = SV124 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1422]) ).
thf(1548,plain,
! [SV79: $i,SV124: $i] :
( ( ( ( in @ ( sK5_C @ SV124 @ SV79 ) @ SV79 )
| ( in @ ( sK5_C @ SV124 @ SV79 ) @ SV124 ) )
= $true )
| ( ( SV79 = SV124 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1423]) ).
thf(1549,plain,
! [SV180: $i] :
( ( ( SV180
= ( union @ SV180 ) )
= $false )
| ( ( being_limit_ordinal @ SV180 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1424]) ).
thf(1550,plain,
! [SV181: $i] :
( ( ( being_limit_ordinal @ SV181 )
= $false )
| ( ( SV181
= ( union @ SV181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1425]) ).
thf(1551,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_connected @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1426]) ).
thf(1552,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1427]) ).
thf(1553,plain,
! [SV182: $i] :
( ( ( empty @ SV182 )
= $false )
| ( ( ordinal @ SV182 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1428]) ).
thf(1554,plain,
! [SV183: $i] :
( ( ( ordinal @ SV183 )
= $false )
| ( ( ( being_limit_ordinal @ SV183 )
| ~ ( ~ ( ordinal @ ( sK50_B @ SV183 ) )
| ( SV183
!= ( succ @ ( sK50_B @ SV183 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1429]) ).
thf(1555,plain,
! [SV184: $i] :
( ( ( ordinal @ SV184 )
= $false )
| ( ( ! [SY532: $i] :
( ( SV184
!= ( succ @ SY532 ) )
| ~ ( ordinal @ SY532 ) )
| ~ ( being_limit_ordinal @ SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1430]) ).
thf(1556,plain,
! [SV223: $i,SV185: $i] :
( ( ( ~ ( in @ SV185 @ SV223 ) )
= $true )
| ( ( subset @ ( singleton @ SV185 ) @ SV223 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1431]) ).
thf(1557,plain,
! [SV224: $i,SV186: $i] :
( ( ( ~ ( subset @ ( singleton @ SV186 ) @ SV224 ) )
= $true )
| ( ( in @ SV186 @ SV224 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1432]) ).
thf(1558,plain,
! [SV80: $i,SV125: $i,SV237: $i] :
( ( ! [SY583: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK32_E @ SY583 @ SV237 @ SV125 @ SV80 ) @ SY583 )
| ( ( sK32_E @ SY583 @ SV237 @ SV125 @ SV80 )
!= SV237 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK32_E @ SY583 @ SV237 @ SV125 @ SV80 ) @ SY583 )
| ( ( sK32_E @ SY583 @ SV237 @ SV125 @ SV80 )
!= SV80 ) )
| ~ ( ~ ( in @ ( sK32_E @ SY583 @ SV237 @ SV125 @ SV80 ) @ SY583 )
| ( ( sK32_E @ SY583 @ SV237 @ SV125 @ SV80 )
!= SV125 ) ) ) )
| ~ ( ( in @ ( sK32_E @ SY583 @ SV237 @ SV125 @ SV80 ) @ SY583 )
| ( ( sK32_E @ SY583 @ SV237 @ SV125 @ SV80 )
= SV237 )
| ( ( sK32_E @ SY583 @ SV237 @ SV125 @ SV80 )
= SV80 )
| ( ( sK32_E @ SY583 @ SV237 @ SV125 @ SV80 )
= SV125 ) ) )
| ( SY583
= ( unordered_triple @ SV80 @ SV125 @ SV237 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1433]) ).
thf(1559,plain,
! [SV238: $i,SV125: $i,SV80: $i] :
( ( ! [SY584: $i] :
( ( SY584
!= ( unordered_triple @ SV80 @ SV125 @ SV238 ) )
| ~ ( ~ ! [SY585: $i] :
( ~ ( in @ SY585 @ SY584 )
| ( SY585 = SV238 )
| ( SY585 = SV80 )
| ( SY585 = SV125 ) )
| ~ ~ ( ~ ! [SY586: $i] :
( ( SY586 != SV238 )
| ( in @ SY586 @ SY584 ) )
| ~ ~ ( ~ ! [SY456: $i] :
( ( SY456 != SV80 )
| ( in @ SY456 @ SY584 ) )
| ~ ! [SY488: $i] :
( ( SY488 != SV125 )
| ( in @ SY488 @ SY584 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1434]) ).
thf(1560,plain,
! [SV136: $i,SV2: $i] :
( ( ( ( in @ SV2 @ SV136 )
| ( SV2 = SV136 ) )
= $true )
| ( ( in @ SV136 @ SV2 )
= $true )
| ( ( ordinal @ SV136 )
= $false )
| ( ( ordinal @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1436]) ).
thf(1561,plain,
! [SV83: $i,SV10: $i] :
( ( ( ordinal_subset @ SV10 @ SV83 )
= $true )
| ( ( ordinal_subset @ SV83 @ SV10 )
= $true )
| ( ( ordinal @ SV10 )
= $false )
| ( ( ordinal @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1438]) ).
thf(1562,plain,
! [SV137: $i,SV126: $i,SV86: $i,SV16: $i] :
( ( ( subset @ SV16 @ SV86 )
= $false )
| ( ( ~ ( subset @ SV126 @ SV137 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV16 @ SV126 ) @ ( cartesian_product2 @ SV86 @ SV137 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1440]) ).
thf(1563,plain,
! [SV127: $i,SV138: $i,SV88: $i,SV18: $i] :
( ( ( ~ ( subset @ SV18 @ SV88 ) )
= $true )
| ( ( relation_of2_as_subset @ SV138 @ SV127 @ SV88 )
= $true )
| ( ( relation_of2_as_subset @ SV138 @ SV127 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1441]) ).
thf(1564,plain,
! [SV128: $i,SV89: $i,SV19: $i] :
( ( ( subset @ SV19 @ SV89 )
= $false )
| ( ( subset @ ( relation_inverse_image @ SV128 @ SV19 ) @ ( relation_inverse_image @ SV128 @ SV89 ) )
= $true )
| ( ( relation @ SV128 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1442]) ).
thf(1565,plain,
! [SV91: $i,SV129: $i,SV21: $i] :
( ( ( subset @ SV21 @ SV129 )
= $false )
| ( ( subset @ SV21 @ SV91 )
= $false )
| ( ( subset @ SV21 @ ( set_intersection2 @ SV91 @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1443]) ).
thf(1566,plain,
! [SV22: $i,SV130: $i,SV92: $i] :
( ( ( subset @ SV92 @ SV130 )
= $false )
| ( ( subset @ SV22 @ SV92 )
= $false )
| ( ( subset @ SV22 @ SV130 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1444]) ).
thf(1567,plain,
! [SV139: $i,SV23: $i] :
( ( ( ~ ( proper_subset @ SV23 @ SV139 ) )
= $true )
| ( ( in @ SV23 @ SV139 )
= $true )
| ( ( ordinal @ SV139 )
= $false )
| ( ( epsilon_transitive @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1445]) ).
thf(1568,plain,
! [SV103: $i,SV35: $i] :
( ( ( subset @ SV35 @ ( relation_field @ SV103 ) )
= $false )
| ( ( ~ ( well_ordering @ SV103 ) )
= $true )
| ( ( ( relation_field @ ( relation_restriction @ SV103 @ SV35 ) )
= SV35 )
= $true )
| ( ( relation @ SV103 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1451]) ).
thf(1569,plain,
! [SV36: $i,SV132: $i,SV104: $i] :
( ( ( in @ SV104 @ SV132 )
= $false )
| ( ( in @ SV36 @ SV104 )
= $false )
| ( ( ~ ( in @ SV132 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1452]) ).
thf(1570,plain,
! [SV133: $i,SV106: $i,SV39: $i] :
( ( ( subset @ SV39 @ SV106 )
= $false )
| ( ( disjoint @ SV106 @ SV133 )
= $false )
| ( ( disjoint @ SV39 @ SV133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1453]) ).
thf(1571,plain,
! [SV43: $i,SV110: $i,SV134: $i] :
( ( ( subset @ SV134 @ SV110 )
= $false )
| ( ( subset @ SV43 @ SV110 )
= $false )
| ( ( subset @ ( set_union2 @ SV43 @ SV134 ) @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1454]) ).
thf(1572,plain,
! [SV190: $i,SV142: $i] :
( ( ( in @ SV142 @ SV190 )
= $false )
| ( ( subset @ ( singleton @ SV142 ) @ SV190 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1459]) ).
thf(1573,plain,
! [SV191: $i,SV143: $i] :
( ( ( subset @ ( singleton @ SV143 ) @ SV191 )
= $false )
| ( ( in @ SV143 @ SV191 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1460]) ).
thf(1574,plain,
! [SV192: $i,SV61: $i,SV225: $i] :
( ( ( ~ ( relation @ SV225 ) )
= $true )
| ( ( ~ ( in @ SV61 @ SV225 )
| ~ ( in @ SV61 @ ( cartesian_product2 @ SV192 @ SV192 ) )
| ( in @ SV61 @ ( relation_restriction @ SV225 @ SV192 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1461]) ).
thf(1575,plain,
! [SV61: $i] :
( ( ! [SY369: $i,SY370: $i] :
( ~ ( relation @ SY370 )
| ~ ( in @ SV61 @ ( relation_restriction @ SY370 @ SY369 ) )
| ( in @ SV61 @ SY370 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1462]) ).
thf(1576,plain,
! [SV61: $i] :
( ( ! [SY371: $i,SY372: $i] :
( ~ ( relation @ SY372 )
| ~ ( in @ SV61 @ ( relation_restriction @ SY372 @ SY371 ) )
| ( in @ SV61 @ ( cartesian_product2 @ SY371 @ SY371 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1463]) ).
thf(1577,plain,
! [SV144: $i] :
( ( ( ~ ( ~ ( ordinal @ ( sK33_B @ SV144 ) )
| ~ ~ ( ~ ( in @ ( sK33_B @ SV144 ) @ SV144 )
| ~ ~ ( in @ ( succ @ ( sK33_B @ SV144 ) ) @ SV144 ) ) ) )
= $true )
| ( ( being_limit_ordinal @ SV144 )
= $true )
| ( ( ordinal @ SV144 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1464]) ).
thf(1578,plain,
! [SV145: $i] :
( ( ( ~ ( being_limit_ordinal @ SV145 ) )
= $true )
| ( ( ! [SY493: $i] :
( ~ ( ordinal @ SY493 )
| ~ ( in @ SY493 @ SV145 )
| ( in @ ( succ @ SY493 ) @ SV145 ) ) )
= $true )
| ( ( ordinal @ SV145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1465]) ).
thf(1579,plain,
! [SV62: $i,SV239: $i] :
( ( ( ~ ( ordinal @ SV239 )
| ~ ( in @ SV62 @ SV239 )
| ( ordinal_subset @ ( succ @ SV62 ) @ SV239 ) )
= $true )
| ( ( ordinal @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1466]) ).
thf(1580,plain,
! [SV62: $i,SV240: $i] :
( ( ( ~ ( ordinal @ SV240 )
| ~ ( ordinal_subset @ ( succ @ SV62 ) @ SV240 )
| ( in @ SV62 @ SV240 ) )
= $true )
| ( ( ordinal @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1467]) ).
thf(1581,plain,
! [SV120: $i,SV63: $i] :
( ( ( ! [SY471: $i] :
( ! [SY377: $i] :
( ( SY471 != SY377 )
| ~ ( ordinal @ SY377 )
| ~ ( in @ SY377 @ SV63 ) )
| ~ ( in @ SY471 @ ( succ @ SV120 ) )
| ( in @ SY471 @ ( sK52_C @ SV120 @ SV63 ) ) ) )
= $true )
| ( ( ordinal @ SV120 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1468]) ).
thf(1582,plain,
! [SV63: $i,SV120: $i] :
( ( ( ~ ( ~ ! [SY473: $i] :
( ~ ( in @ SY473 @ ( sK52_C @ SV120 @ SV63 ) )
| ~ ( ~ ~ ( ( SY473
!= ( sK53_E @ SY473 @ SV120 @ SV63 ) )
| ~ ( ordinal @ ( sK53_E @ SY473 @ SV120 @ SV63 ) ) )
| ~ ( in @ ( sK53_E @ SY473 @ SV120 @ SV63 ) @ SV63 ) ) )
| ~ ! [SY474: $i] :
( ~ ( in @ SY474 @ ( sK52_C @ SV120 @ SV63 ) )
| ( in @ SY474 @ ( succ @ SV120 ) ) ) ) )
= $true )
| ( ( ordinal @ SV120 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1469]) ).
thf(1583,plain,
! [SV193: $i,SV64: $i] :
( ( ( subset @ SV64 @ SV193 )
= $false )
| ( ( ! [SY536: $i] : ( subset @ ( cartesian_product2 @ SV64 @ SY536 ) @ ( cartesian_product2 @ SV193 @ SY536 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1470]) ).
thf(1584,plain,
! [SV194: $i,SV64: $i] :
( ( ( subset @ SV64 @ SV194 )
= $false )
| ( ( ! [SY537: $i] : ( subset @ ( cartesian_product2 @ SY537 @ SV64 ) @ ( cartesian_product2 @ SY537 @ SV194 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1471]) ).
thf(1585,plain,
! [SV146: $i] :
( ( ( epsilon_connected @ SV146 )
= $false )
| ( ( ~ ( epsilon_transitive @ SV146 ) )
= $true )
| ( ( ordinal @ SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1472]) ).
thf(1586,plain,
! [SV241: $i] :
( ( ~ ( ordinal @ SV241 )
| ( epsilon_connected @ SV241 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1473]) ).
thf(1587,plain,
! [SV242: $i] :
( ( ~ ( ordinal @ SV242 )
| ( epsilon_transitive @ SV242 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1474]) ).
thf(1588,plain,
! [SV195: $i,SV226: $i,SV65: $i] :
( ( ( ~ ( in @ SV65 @ SV226 )
| ~ ( in @ SV195 @ SV226 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV65 @ SV195 ) @ SV226 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1475]) ).
thf(1589,plain,
! [SV65: $i] :
( ( ! [SY386: $i,SY387: $i] :
( ~ ( subset @ ( unordered_pair @ SV65 @ SY386 ) @ SY387 )
| ( in @ SV65 @ SY387 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1476]) ).
thf(1590,plain,
! [SV65: $i] :
( ( ! [SY388: $i,SY389: $i] :
( ~ ( subset @ ( unordered_pair @ SV65 @ SY388 ) @ SY389 )
| ( in @ SY388 @ SY389 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1477]) ).
thf(1591,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( empty @ ( succ @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ ( succ @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1478]) ).
thf(1592,plain,
! [SV243: $i] :
( ( ~ ( ordinal @ SV243 )
| ( epsilon_connected @ ( succ @ SV243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1479]) ).
thf(1593,plain,
! [SV148: $i,SV196: $i] :
( ( ( ~ ( ! [SY539: $i] :
( ~ ( in @ ( sK13_C @ SV196 @ SV148 ) @ SY539 )
| ~ ( in @ SY539 @ SV148 ) )
| ~ ( in @ ( sK13_C @ SV196 @ SV148 ) @ SV196 ) )
| ~ ( ~ ( ~ ( in @ ( sK13_C @ SV196 @ SV148 ) @ ( sK14_SY277 @ SV196 @ SV148 ) )
| ~ ( in @ ( sK14_SY277 @ SV196 @ SV148 ) @ SV148 ) )
| ( in @ ( sK13_C @ SV196 @ SV148 ) @ SV196 ) ) )
= $false )
| ( ( SV196
= ( union @ SV148 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1481]) ).
thf(1594,plain,
! [SV149: $i,SV197: $i] :
( ( ( SV197
= ( union @ SV149 ) )
= $false )
| ( ( ~ ( ~ ! [SY540: $i] :
( ! [SY498: $i] :
( ~ ( in @ SY540 @ SY498 )
| ~ ( in @ SY498 @ SV149 ) )
| ( in @ SY540 @ SV197 ) )
| ~ ! [SY542: $i] :
( ~ ( in @ SY542 @ SV197 )
| ~ ( ~ ( in @ SY542 @ ( sK12_D @ SY542 @ SV197 @ SV149 ) )
| ~ ( in @ ( sK12_D @ SY542 @ SV197 @ SV149 ) @ SV149 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1482]) ).
thf(1595,plain,
! [SV150: $i] :
( ( ( ~ ! [SY500: $i,SY501: $i] :
( ( sK31_B @ SV150 )
!= ( ordered_pair @ SY500 @ SY501 ) ) )
= $false )
| ( ( relation @ SV150 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1483]) ).
thf(1596,plain,
! [SV150: $i] :
( ( ( ~ ( in @ ( sK31_B @ SV150 ) @ SV150 ) )
= $false )
| ( ( relation @ SV150 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1483]) ).
thf(1597,plain,
! [SV151: $i,SV244: $i] :
( ( ( ( SV244
= ( ordered_pair @ ( sK29_C @ SV244 @ SV151 ) @ ( sK30_SY281 @ SV244 @ SV151 ) ) )
| ~ ( in @ SV244 @ SV151 ) )
= $true )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1484]) ).
thf(1598,plain,
! [SV152: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK19_B @ SV152 )
!= ( sK20_SY279 @ SV152 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_B @ SV152 ) @ SV152 )
| ~ ( in @ ( sK20_SY279 @ SV152 ) @ SV152 ) )
| ~ ~ ( in @ ( sK19_B @ SV152 ) @ ( sK20_SY279 @ SV152 ) ) ) ) )
= $false )
| ( ( epsilon_connected @ SV152 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1485]) ).
thf(1599,plain,
! [SV152: $i] :
( ( ( ~ ~ ( in @ ( sK20_SY279 @ SV152 ) @ ( sK19_B @ SV152 ) ) )
= $false )
| ( ( epsilon_connected @ SV152 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1485]) ).
thf(1600,plain,
! [SV153: $i,SV245: $i] :
( ( ( ! [SY589: $i] :
( ( SV245 = SY589 )
| ~ ( in @ SV245 @ SV153 )
| ~ ( in @ SY589 @ SV153 )
| ( in @ SV245 @ SY589 )
| ( in @ SY589 @ SV245 ) ) )
= $true )
| ( ( epsilon_connected @ SV153 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1486]) ).
thf(1601,plain,
! [SV198: $i,SV154: $i] :
( ( ( SV154 = SV198 )
= $true )
| ( ( ~ ( subset @ SV154 @ SV198 ) )
= $true )
| ( ( proper_subset @ SV154 @ SV198 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1487]) ).
thf(1602,plain,
! [SV246: $i] :
( ( ! [SY590: $i] :
( ~ ( proper_subset @ SV246 @ SY590 )
| ( SV246 != SY590 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1488]) ).
thf(1603,plain,
! [SV247: $i] :
( ( ! [SY591: $i] :
( ~ ( proper_subset @ SV247 @ SY591 )
| ( subset @ SV247 @ SY591 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1489]) ).
thf(1604,plain,
! [SV155: $i] :
( ( ( ~ ( reflexive @ SV155 )
| ~ ( transitive @ SV155 )
| ~ ( antisymmetric @ SV155 )
| ~ ( connected @ SV155 )
| ~ ( well_founded_relation @ SV155 ) )
= $true )
| ( ( well_ordering @ SV155 )
= $true )
| ( ( relation @ SV155 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1490]) ).
thf(1605,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1491]) ).
thf(1606,plain,
! [SV248: $i] :
( ( ~ ( relation @ SV248 )
| ~ ( well_ordering @ SV248 )
| ( well_founded_relation @ SV248 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1492]) ).
thf(1607,plain,
! [SV66: $i] :
( ( ( ordinal @ ( sK51_B @ SV66 ) )
= $false )
| ( ( ~ ( subset @ ( sK51_B @ SV66 ) @ SV66 ) )
= $true )
| ( ( ordinal @ SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1493]) ).
thf(1608,plain,
! [SV67: $i,SV121: $i,SV249: $i] :
( ( ( ~ ( in @ SV249 @ SV121 )
| ~ ( in @ SV249 @ ( sK4_C @ SV121 @ SV67 ) ) )
= $true )
| ( ( ~ ( in @ SV67 @ SV121 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1494]) ).
thf(1609,plain,
! [SV121: $i,SV67: $i] :
( ( ( in @ SV67 @ SV121 )
= $false )
| ( ( in @ ( sK4_C @ SV121 @ SV67 ) @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1495]) ).
thf(1610,plain,
! [SV157: $i,SV250: $i] :
( ( ( ~ ( in @ SV250 @ SV157 ) )
= $true )
| ( ( SV157 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1496]) ).
thf(1611,plain,
! [SV158: $i,SV199: $i] :
( ( ( ~ ( in @ ( sK34_C @ SV199 @ SV158 ) @ SV158 )
| ~ ( in @ ( sK34_C @ SV199 @ SV158 ) @ SV199 ) )
= $false )
| ( ( disjoint @ SV158 @ SV199 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1497]) ).
thf(1612,plain,
! [SV200: $i,SV159: $i,SV251: $i] :
( ( ( ~ ( in @ SV251 @ SV159 )
| ~ ( in @ SV251 @ SV200 ) )
= $true )
| ( ( ~ ( disjoint @ SV159 @ SV200 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1498]) ).
thf(1613,plain,
! [SV160: $i,SV201: $i] :
( ( ( ~ ( ( ( sK28_C @ SV201 @ SV160 )
!= SV160 )
| ~ ( in @ ( sK28_C @ SV201 @ SV160 ) @ SV201 ) )
| ~ ( ( ( sK28_C @ SV201 @ SV160 )
= SV160 )
| ( in @ ( sK28_C @ SV201 @ SV160 ) @ SV201 ) ) )
= $false )
| ( ( SV201
= ( singleton @ SV160 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1499]) ).
thf(1614,plain,
! [SV161: $i,SV202: $i] :
( ( ( SV202
= ( singleton @ SV161 ) )
= $false )
| ( ( ~ ( ~ ! [SY544: $i] :
( ( SY544 != SV161 )
| ( in @ SY544 @ SV202 ) )
| ~ ! [SY545: $i] :
( ~ ( in @ SY545 @ SV202 )
| ( SY545 = SV161 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1500]) ).
thf(1615,plain,
( ( ~ ~ ( empty @ sK7_A )
| ~ ( epsilon_transitive @ sK7_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1501]) ).
thf(1616,plain,
! [SV68: $i,SV122: $i] :
( ( ( ~ ( ordinal @ ( sK35_C @ SV122 @ SV68 ) ) )
= $false )
| ( ( ( SV68 = empty_set )
| ~ ( subset @ SV68 @ SV122 ) )
= $true )
| ( ( ordinal @ SV122 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1503]) ).
thf(1617,plain,
! [SV122: $i,SV68: $i] :
( ( ( ~ ~ ( ~ ! [SY476: $i] :
( ~ ( ordinal @ SY476 )
| ~ ( in @ SY476 @ SV68 )
| ( ordinal_subset @ ( sK35_C @ SV122 @ SV68 ) @ SY476 ) )
| ~ ( in @ ( sK35_C @ SV122 @ SV68 ) @ SV68 ) ) )
= $false )
| ( ( ( SV68 = empty_set )
| ~ ( subset @ SV68 @ SV122 ) )
= $true )
| ( ( ordinal @ SV122 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1503]) ).
thf(1618,plain,
! [SV69: $i,SV203: $i,SV227: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV227 )
| ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV69 ) )
| ~ ( ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV227 )
| ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV203 ) ) )
| ~ ( ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV227 )
| ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV69 )
| ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV203 ) ) ) )
= $true )
| ( ( SV227
= ( set_union2 @ SV69 @ SV203 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1504]) ).
thf(1619,plain,
! [SV204: $i,SV69: $i,SV228: $i] :
( ( ( SV228
!= ( set_union2 @ SV69 @ SV204 ) )
= $true )
| ( ( ~ ( ~ ! [SY571: $i] :
( ~ ( in @ SY571 @ SV228 )
| ( in @ SY571 @ SV69 )
| ( in @ SY571 @ SV204 ) )
| ~ ~ ( ~ ! [SY572: $i] :
( ~ ( in @ SY572 @ SV69 )
| ( in @ SY572 @ SV228 ) )
| ~ ! [SY573: $i] :
( ~ ( in @ SY573 @ SV204 )
| ( in @ SY573 @ SV228 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1505]) ).
thf(1620,plain,
! [SV162: $i,SV205: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_C @ SV205 @ SV162 ) @ SV205 )
| ~ ( subset @ ( sK26_C @ SV205 @ SV162 ) @ SV162 ) )
| ~ ( ( in @ ( sK26_C @ SV205 @ SV162 ) @ SV205 )
| ( subset @ ( sK26_C @ SV205 @ SV162 ) @ SV162 ) ) )
= $false )
| ( ( SV205
= ( powerset @ SV162 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1506]) ).
thf(1621,plain,
! [SV163: $i,SV206: $i] :
( ( ( SV206
= ( powerset @ SV163 ) )
= $false )
| ( ( ~ ( ~ ! [SY551: $i] :
( ~ ( in @ SY551 @ SV206 )
| ( subset @ SY551 @ SV163 ) )
| ~ ! [SY552: $i] :
( ~ ( subset @ SY552 @ SV163 )
| ( in @ SY552 @ SV206 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1507]) ).
thf(1622,plain,
! [SV70: $i,SV207: $i,SV229: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV70 )
| ~ ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV207 )
| ~ ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV229 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV70 )
| ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV229 ) )
| ~ ( ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV207 )
| ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV229 ) ) ) ) )
= $true )
| ( ( SV229
= ( set_intersection2 @ SV70 @ SV207 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1508]) ).
thf(1623,plain,
! [SV208: $i,SV70: $i,SV230: $i] :
( ( ( SV230
!= ( set_intersection2 @ SV70 @ SV208 ) )
= $true )
| ( ( ~ ( ~ ! [SY574: $i] :
( ~ ( in @ SY574 @ SV70 )
| ~ ( in @ SY574 @ SV208 )
| ( in @ SY574 @ SV230 ) )
| ~ ~ ( ~ ! [SY575: $i] :
( ~ ( in @ SY575 @ SV230 )
| ( in @ SY575 @ SV70 ) )
| ~ ! [SY576: $i] :
( ~ ( in @ SY576 @ SV230 )
| ( in @ SY576 @ SV208 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1509]) ).
thf(1624,plain,
! [SV252: $i] :
( ( ~ ( ordinal @ SV252 )
| ( epsilon_connected @ ( union @ SV252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1510]) ).
thf(1625,plain,
! [SV253: $i] :
( ( ~ ( ordinal @ SV253 )
| ( epsilon_transitive @ ( union @ SV253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1511]) ).
thf(1626,plain,
! [SV209: $i,SV165: $i] :
( ( ( ~ ( ordinal @ SV165 ) )
= $true )
| ( ( ~ ( ordinal @ SV209 ) )
= $true )
| ( ( ~ ( ordinal_subset @ SV165 @ SV209 )
| ( subset @ SV165 @ SV209 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1513]) ).
thf(1627,plain,
! [SV210: $i,SV166: $i] :
( ( ( ~ ( ordinal @ SV166 ) )
= $true )
| ( ( ~ ( ordinal @ SV210 ) )
= $true )
| ( ( ~ ( subset @ SV166 @ SV210 )
| ( ordinal_subset @ SV166 @ SV210 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1514]) ).
thf(1628,plain,
! [SV135: $i,SV71: $i] :
( ( ( ~ ! [SY409: $i] :
( ~ ( ordinal @ SY409 )
| ~ ( in @ SY409 @ SV71 )
| ( ordinal_subset @ ( sK54_B @ SV71 ) @ SY409 ) )
| ~ ~ ( ~ ( in @ ( sK54_B @ SV71 ) @ SV71 )
| ~ ( ordinal @ ( sK54_B @ SV71 ) ) ) )
= $false )
| ( ( in @ SV135 @ SV71 )
= $false )
| ( ( ordinal @ SV135 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1515]) ).
thf(1629,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK44_C @ SV123 @ SV72 )
!= ( sK45_SY295 @ SV123 @ SV72 ) )
| ~ ~ ( ~ ~ ( ( ( sK45_SY295 @ SV123 @ SV72 )
!= ( sK48_SY300 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 ) ) )
| ( ( sK44_C @ SV123 @ SV72 )
!= ( sK46_SY299 @ SV123 @ SV72 ) ) )
| ~ ~ ( ~ ~ ( ( ( sK46_SY299 @ SV123 @ SV72 )
!= ( sK47_SY303 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1516]) ).
thf(1630,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ( ( ( sK45_SY295 @ SV123 @ SV72 )
!= ( sK46_SY299 @ SV123 @ SV72 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1516]) ).
thf(1631,plain,
! [SV73: $i,SV254: $i] :
( ( ( ~ ( relation @ SV254 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK23_C @ SV254 @ SV73 ) @ ( sK24_SY280 @ SV254 @ SV73 ) ) @ SV73 )
| ~ ( in @ ( ordered_pair @ ( sK23_C @ SV254 @ SV73 ) @ ( sK24_SY280 @ SV254 @ SV73 ) ) @ SV254 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK23_C @ SV254 @ SV73 ) @ ( sK24_SY280 @ SV254 @ SV73 ) ) @ SV73 )
| ( in @ ( ordered_pair @ ( sK23_C @ SV254 @ SV73 ) @ ( sK24_SY280 @ SV254 @ SV73 ) ) @ SV254 ) ) )
| ( SV73 = SV254 ) )
= $true )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1517]) ).
thf(1632,plain,
! [SV73: $i,SV255: $i] :
( ( ( ~ ( relation @ SV255 )
| ( SV73 != SV255 )
| ~ ( ~ ! [SY592: $i,SY593: $i] :
( ~ ( in @ ( ordered_pair @ SY592 @ SY593 ) @ SV73 )
| ( in @ ( ordered_pair @ SY592 @ SY593 ) @ SV255 ) )
| ~ ! [SY594: $i,SY595: $i] :
( ~ ( in @ ( ordered_pair @ SY594 @ SY595 ) @ SV255 )
| ( in @ ( ordered_pair @ SY594 @ SY595 ) @ SV73 ) ) ) )
= $true )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1518]) ).
thf(1633,plain,
! [SV74: $i,SV211: $i,SV231: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK22_D @ SV231 @ SV211 @ SV74 ) @ SV231 )
| ( ( sK22_D @ SV231 @ SV211 @ SV74 )
!= SV74 ) )
| ~ ( ~ ( in @ ( sK22_D @ SV231 @ SV211 @ SV74 ) @ SV231 )
| ( ( sK22_D @ SV231 @ SV211 @ SV74 )
!= SV211 ) ) )
| ~ ( ( in @ ( sK22_D @ SV231 @ SV211 @ SV74 ) @ SV231 )
| ( ( sK22_D @ SV231 @ SV211 @ SV74 )
= SV74 )
| ( ( sK22_D @ SV231 @ SV211 @ SV74 )
= SV211 ) ) ) )
= $true )
| ( ( SV231
= ( unordered_pair @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1521]) ).
thf(1634,plain,
! [SV212: $i,SV74: $i,SV232: $i] :
( ( ( SV232
!= ( unordered_pair @ SV74 @ SV212 ) )
= $true )
| ( ( ~ ( ~ ! [SY577: $i] :
( ~ ( in @ SY577 @ SV232 )
| ( SY577 = SV74 )
| ( SY577 = SV212 ) )
| ~ ~ ( ~ ! [SY578: $i] :
( ( SY578 != SV74 )
| ( in @ SY578 @ SV232 ) )
| ~ ! [SY579: $i] :
( ( SY579 != SV212 )
| ( in @ SY579 @ SV232 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1522]) ).
thf(1635,plain,
! [SV169: $i] :
( ( ( ~ ( in @ ( sK25_B @ SV169 ) @ SV169 ) )
= $false )
| ( ( epsilon_transitive @ SV169 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1523]) ).
thf(1636,plain,
! [SV169: $i] :
( ( ( ~ ~ ( subset @ ( sK25_B @ SV169 ) @ SV169 ) )
= $false )
| ( ( epsilon_transitive @ SV169 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1523]) ).
thf(1637,plain,
! [SV170: $i,SV256: $i] :
( ( ( ~ ( in @ SV256 @ SV170 )
| ( subset @ SV256 @ SV170 ) )
= $true )
| ( ( epsilon_transitive @ SV170 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1524]) ).
thf(1638,plain,
! [SV75: $i,SV213: $i] :
( ( ( ~ ( subset @ SV213 @ ( sK2_B @ SV75 ) ) )
= $true )
| ( ( are_equipotent @ SV213 @ ( sK2_B @ SV75 ) )
= $true )
| ( ( in @ SV213 @ ( sK2_B @ SV75 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1525]) ).
thf(1639,plain,
! [SV75: $i] :
( ( ! [SY429: $i] :
( ~ ( ~ ! [SY430: $i] :
( ~ ( subset @ SY430 @ SY429 )
| ( in @ SY430 @ ( sK3_SY270 @ SY429 @ SV75 ) ) )
| ~ ( in @ ( sK3_SY270 @ SY429 @ SV75 ) @ ( sK2_B @ SV75 ) ) )
| ~ ( in @ SY429 @ ( sK2_B @ SV75 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1526]) ).
thf(1640,plain,
! [SV75: $i] :
( ( ~ ( ~ ! [SY431: $i,SY432: $i] :
( ~ ( in @ SY431 @ ( sK2_B @ SV75 ) )
| ~ ( subset @ SY432 @ SY431 )
| ( in @ SY432 @ ( sK2_B @ SV75 ) ) )
| ~ ( in @ SV75 @ ( sK2_B @ SV75 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1527]) ).
thf(1641,plain,
! [SV214: $i,SV76: $i,SV233: $i] :
( ( ( ~ ( relation @ SV233 ) )
= $true )
| ( ( ~ ( in @ SV76 @ ( relation_field @ ( relation_restriction @ SV233 @ SV214 ) ) )
| ( in @ SV76 @ ( relation_field @ SV233 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1528]) ).
thf(1642,plain,
! [SV215: $i,SV76: $i,SV234: $i] :
( ( ( ~ ( relation @ SV234 ) )
= $true )
| ( ( ~ ( in @ SV76 @ ( relation_field @ ( relation_restriction @ SV234 @ SV215 ) ) )
| ( in @ SV76 @ SV215 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1529]) ).
thf(1643,plain,
! [SV77: $i,SV257: $i] :
( ( ( ~ ( relation @ SV257 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK17_C @ SV257 @ SV77 ) @ ( sK18_SY278 @ SV257 @ SV77 ) ) @ SV77 )
| ~ ~ ( in @ ( ordered_pair @ ( sK17_C @ SV257 @ SV77 ) @ ( sK18_SY278 @ SV257 @ SV77 ) ) @ SV257 ) )
| ( subset @ SV77 @ SV257 ) )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1530]) ).
thf(1644,plain,
! [SV77: $i,SV258: $i] :
( ( ( ~ ( relation @ SV258 )
| ~ ( subset @ SV77 @ SV258 )
| ! [SY596: $i,SY597: $i] :
( ~ ( in @ ( ordered_pair @ SY596 @ SY597 ) @ SV77 )
| ( in @ ( ordered_pair @ SY596 @ SY597 ) @ SV258 ) ) )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1531]) ).
thf(1645,plain,
! [SV171: $i,SV216: $i] :
( ( ( ~ ( in @ ( sK16_C @ SV216 @ SV171 ) @ SV171 )
| ~ ~ ( in @ ( sK16_C @ SV216 @ SV171 ) @ SV216 ) )
= $false )
| ( ( subset @ SV171 @ SV216 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1532]) ).
thf(1646,plain,
! [SV217: $i,SV172: $i] :
( ( ( subset @ SV172 @ SV217 )
= $false )
| ( ( ! [SY565: $i] :
( ~ ( in @ SY565 @ SV172 )
| ( in @ SY565 @ SV217 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1533]) ).
thf(1647,plain,
! [SV78: $i,SV218: $i,SV235: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV78 )
| ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV218 )
| ~ ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV235 ) )
| ~ ~ ( ~ ( ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV78 )
| ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV235 ) )
| ~ ( ~ ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV218 )
| ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV235 ) ) ) ) )
= $true )
| ( ( SV235
= ( set_difference @ SV78 @ SV218 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1534]) ).
thf(1648,plain,
! [SV219: $i,SV78: $i,SV236: $i] :
( ( ( SV236
!= ( set_difference @ SV78 @ SV219 ) )
= $true )
| ( ( ~ ( ~ ! [SY580: $i] :
( ~ ( in @ SY580 @ SV78 )
| ( in @ SY580 @ SV219 )
| ( in @ SY580 @ SV236 ) )
| ~ ~ ( ~ ! [SY581: $i] :
( ~ ( in @ SY581 @ SV236 )
| ( in @ SY581 @ SV78 ) )
| ~ ! [SY582: $i] :
( ~ ( in @ SY582 @ SV236 )
| ~ ( in @ SY582 @ SV219 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1535]) ).
thf(1649,plain,
! [SV173: $i,SV220: $i] :
( ( ( relation @ SV220 )
= $false )
| ( ( subset @ ( relation_field @ ( relation_restriction @ SV220 @ SV173 ) ) @ ( relation_field @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1536]) ).
thf(1650,plain,
! [SV174: $i,SV221: $i] :
( ( ( relation @ SV221 )
= $false )
| ( ( subset @ ( relation_field @ ( relation_restriction @ SV221 @ SV174 ) ) @ SV174 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1537]) ).
thf(1651,plain,
! [SV175: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK36_B @ SV175 ) @ ( sK37_SY285 @ SV175 ) ) @ SV175 )
| ~ ( in @ ( ordered_pair @ ( sK37_SY285 @ SV175 ) @ ( sK36_B @ SV175 ) ) @ SV175 ) )
| ~ ( ( ( sK36_B @ SV175 )
!= ( sK37_SY285 @ SV175 ) ) ) ) )
= $true )
| ( ( antisymmetric @ SV175 )
= $true )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1540]) ).
thf(1652,plain,
! [SV176: $i] :
( ( ( ~ ( antisymmetric @ SV176 ) )
= $true )
| ( ( ! [SY526: $i,SY527: $i] :
( ~ ( in @ ( ordered_pair @ SY526 @ SY527 ) @ SV176 )
| ~ ( in @ ( ordered_pair @ SY527 @ SY526 ) @ SV176 )
| ( SY526 = SY527 ) ) )
= $true )
| ( ( relation @ SV176 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1541]) ).
thf(1653,plain,
! [SV222: $i,SV177: $i] :
( ( ( ~ ( subset @ SV177 @ SV222 ) )
= $true )
| ( ( ~ ( subset @ SV222 @ SV177 ) )
= $true )
| ( ( SV177 = SV222 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1542]) ).
thf(1654,plain,
! [SV259: $i] :
( ( ! [SY598: $i] :
( ( SV259 != SY598 )
| ( subset @ SV259 @ SY598 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1543]) ).
thf(1655,plain,
! [SV260: $i] :
( ( ! [SY599: $i] :
( ( SV260 != SY599 )
| ( subset @ SY599 @ SV260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1544]) ).
thf(1656,plain,
! [SV178: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK38_B @ SV178 ) @ ( sK39_SY286 @ SV178 ) ) @ SV178 )
| ~ ( in @ ( ordered_pair @ ( sK39_SY286 @ SV178 ) @ ( sK40_SY288 @ SV178 ) ) @ SV178 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK38_B @ SV178 ) @ ( sK40_SY288 @ SV178 ) ) @ SV178 ) ) )
= $true )
| ( ( transitive @ SV178 )
= $true )
| ( ( relation @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1545]) ).
thf(1657,plain,
! [SV179: $i] :
( ( ( ~ ( transitive @ SV179 ) )
= $true )
| ( ( ! [SY529: $i,SY530: $i,SY531: $i] :
( ~ ( in @ ( ordered_pair @ SY529 @ SY530 ) @ SV179 )
| ~ ( in @ ( ordered_pair @ SY530 @ SY531 ) @ SV179 )
| ( in @ ( ordered_pair @ SY529 @ SY531 ) @ SV179 ) ) )
= $true )
| ( ( relation @ SV179 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1546]) ).
thf(1658,plain,
! [SV79: $i,SV124: $i] :
( ( ( ~ ( in @ ( sK5_C @ SV124 @ SV79 ) @ SV79 ) )
= $true )
| ( ( ~ ( in @ ( sK5_C @ SV124 @ SV79 ) @ SV124 ) )
= $true )
| ( ( SV79 = SV124 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1547]) ).
thf(1659,plain,
! [SV79: $i,SV124: $i] :
( ( ( in @ ( sK5_C @ SV124 @ SV79 ) @ SV79 )
= $true )
| ( ( in @ ( sK5_C @ SV124 @ SV79 ) @ SV124 )
= $true )
| ( ( SV79 = SV124 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1548]) ).
thf(1660,plain,
! [SV261: $i] :
( ( ~ ( empty @ SV261 )
| ( epsilon_connected @ SV261 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1551]) ).
thf(1661,plain,
! [SV262: $i] :
( ( ~ ( empty @ SV262 )
| ( epsilon_transitive @ SV262 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1552]) ).
thf(1662,plain,
! [SV183: $i] :
( ( ( being_limit_ordinal @ SV183 )
= $true )
| ( ( ~ ( ~ ( ordinal @ ( sK50_B @ SV183 ) )
| ( SV183
!= ( succ @ ( sK50_B @ SV183 ) ) ) ) )
= $true )
| ( ( ordinal @ SV183 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1554]) ).
thf(1663,plain,
! [SV184: $i] :
( ( ( ! [SY532: $i] :
( ( SV184
!= ( succ @ SY532 ) )
| ~ ( ordinal @ SY532 ) ) )
= $true )
| ( ( ~ ( being_limit_ordinal @ SV184 ) )
= $true )
| ( ( ordinal @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1555]) ).
thf(1664,plain,
! [SV223: $i,SV185: $i] :
( ( ( in @ SV185 @ SV223 )
= $false )
| ( ( subset @ ( singleton @ SV185 ) @ SV223 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1556]) ).
thf(1665,plain,
! [SV224: $i,SV186: $i] :
( ( ( subset @ ( singleton @ SV186 ) @ SV224 )
= $false )
| ( ( in @ SV186 @ SV224 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1557]) ).
thf(1666,plain,
! [SV80: $i,SV125: $i,SV237: $i,SV263: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
!= SV237 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
!= SV80 ) )
| ~ ( ~ ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
!= SV125 ) ) ) )
| ~ ( ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
= SV237 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
= SV80 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
= SV125 ) ) )
| ( SV263
= ( unordered_triple @ SV80 @ SV125 @ SV237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1558]) ).
thf(1667,plain,
! [SV238: $i,SV125: $i,SV80: $i,SV264: $i] :
( ( ( SV264
!= ( unordered_triple @ SV80 @ SV125 @ SV238 ) )
| ~ ( ~ ! [SY600: $i] :
( ~ ( in @ SY600 @ SV264 )
| ( SY600 = SV238 )
| ( SY600 = SV80 )
| ( SY600 = SV125 ) )
| ~ ~ ( ~ ! [SY601: $i] :
( ( SY601 != SV238 )
| ( in @ SY601 @ SV264 ) )
| ~ ~ ( ~ ! [SY602: $i] :
( ( SY602 != SV80 )
| ( in @ SY602 @ SV264 ) )
| ~ ! [SY603: $i] :
( ( SY603 != SV125 )
| ( in @ SY603 @ SV264 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1559]) ).
thf(1668,plain,
! [SV136: $i,SV2: $i] :
( ( ( in @ SV2 @ SV136 )
= $true )
| ( ( SV2 = SV136 )
= $true )
| ( ( in @ SV136 @ SV2 )
= $true )
| ( ( ordinal @ SV136 )
= $false )
| ( ( ordinal @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1560]) ).
thf(1669,plain,
! [SV86: $i,SV16: $i,SV137: $i,SV126: $i] :
( ( ( subset @ SV126 @ SV137 )
= $false )
| ( ( subset @ SV16 @ SV86 )
= $false )
| ( ( subset @ ( cartesian_product2 @ SV16 @ SV126 ) @ ( cartesian_product2 @ SV86 @ SV137 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1562]) ).
thf(1670,plain,
! [SV127: $i,SV138: $i,SV88: $i,SV18: $i] :
( ( ( subset @ SV18 @ SV88 )
= $false )
| ( ( relation_of2_as_subset @ SV138 @ SV127 @ SV88 )
= $true )
| ( ( relation_of2_as_subset @ SV138 @ SV127 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1563]) ).
thf(1671,plain,
! [SV139: $i,SV23: $i] :
( ( ( proper_subset @ SV23 @ SV139 )
= $false )
| ( ( in @ SV23 @ SV139 )
= $true )
| ( ( ordinal @ SV139 )
= $false )
| ( ( epsilon_transitive @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1567]) ).
thf(1672,plain,
! [SV35: $i,SV103: $i] :
( ( ( well_ordering @ SV103 )
= $false )
| ( ( subset @ SV35 @ ( relation_field @ SV103 ) )
= $false )
| ( ( ( relation_field @ ( relation_restriction @ SV103 @ SV35 ) )
= SV35 )
= $true )
| ( ( relation @ SV103 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1568]) ).
thf(1673,plain,
! [SV104: $i,SV36: $i,SV132: $i] :
( ( ( in @ SV132 @ SV36 )
= $false )
| ( ( in @ SV36 @ SV104 )
= $false )
| ( ( in @ SV104 @ SV132 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1569]) ).
thf(1674,plain,
! [SV192: $i,SV61: $i,SV225: $i] :
( ( ( relation @ SV225 )
= $false )
| ( ( ~ ( in @ SV61 @ SV225 )
| ~ ( in @ SV61 @ ( cartesian_product2 @ SV192 @ SV192 ) )
| ( in @ SV61 @ ( relation_restriction @ SV225 @ SV192 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1574]) ).
thf(1675,plain,
! [SV265: $i,SV61: $i] :
( ( ! [SY604: $i] :
( ~ ( relation @ SY604 )
| ~ ( in @ SV61 @ ( relation_restriction @ SY604 @ SV265 ) )
| ( in @ SV61 @ SY604 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1575]) ).
thf(1676,plain,
! [SV266: $i,SV61: $i] :
( ( ! [SY605: $i] :
( ~ ( relation @ SY605 )
| ~ ( in @ SV61 @ ( relation_restriction @ SY605 @ SV266 ) )
| ( in @ SV61 @ ( cartesian_product2 @ SV266 @ SV266 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1576]) ).
thf(1677,plain,
! [SV144: $i] :
( ( ( ~ ( ordinal @ ( sK33_B @ SV144 ) )
| ~ ~ ( ~ ( in @ ( sK33_B @ SV144 ) @ SV144 )
| ~ ~ ( in @ ( succ @ ( sK33_B @ SV144 ) ) @ SV144 ) ) )
= $false )
| ( ( being_limit_ordinal @ SV144 )
= $true )
| ( ( ordinal @ SV144 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1577]) ).
thf(1678,plain,
! [SV145: $i] :
( ( ( being_limit_ordinal @ SV145 )
= $false )
| ( ( ! [SY493: $i] :
( ~ ( ordinal @ SY493 )
| ~ ( in @ SY493 @ SV145 )
| ( in @ ( succ @ SY493 ) @ SV145 ) ) )
= $true )
| ( ( ordinal @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1578]) ).
thf(1679,plain,
! [SV62: $i,SV239: $i] :
( ( ( ~ ( ordinal @ SV239 ) )
= $true )
| ( ( ~ ( in @ SV62 @ SV239 )
| ( ordinal_subset @ ( succ @ SV62 ) @ SV239 ) )
= $true )
| ( ( ordinal @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1579]) ).
thf(1680,plain,
! [SV62: $i,SV240: $i] :
( ( ( ~ ( ordinal @ SV240 ) )
= $true )
| ( ( ~ ( ordinal_subset @ ( succ @ SV62 ) @ SV240 )
| ( in @ SV62 @ SV240 ) )
= $true )
| ( ( ordinal @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1580]) ).
thf(1681,plain,
! [SV120: $i,SV63: $i,SV267: $i] :
( ( ( ! [SY606: $i] :
( ( SV267 != SY606 )
| ~ ( ordinal @ SY606 )
| ~ ( in @ SY606 @ SV63 ) )
| ~ ( in @ SV267 @ ( succ @ SV120 ) )
| ( in @ SV267 @ ( sK52_C @ SV120 @ SV63 ) ) )
= $true )
| ( ( ordinal @ SV120 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1581]) ).
thf(1682,plain,
! [SV63: $i,SV120: $i] :
( ( ( ~ ! [SY473: $i] :
( ~ ( in @ SY473 @ ( sK52_C @ SV120 @ SV63 ) )
| ~ ( ~ ~ ( ( SY473
!= ( sK53_E @ SY473 @ SV120 @ SV63 ) )
| ~ ( ordinal @ ( sK53_E @ SY473 @ SV120 @ SV63 ) ) )
| ~ ( in @ ( sK53_E @ SY473 @ SV120 @ SV63 ) @ SV63 ) ) )
| ~ ! [SY474: $i] :
( ~ ( in @ SY474 @ ( sK52_C @ SV120 @ SV63 ) )
| ( in @ SY474 @ ( succ @ SV120 ) ) ) )
= $false )
| ( ( ordinal @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1582]) ).
thf(1683,plain,
! [SV193: $i,SV268: $i,SV64: $i] :
( ( ( subset @ ( cartesian_product2 @ SV64 @ SV268 ) @ ( cartesian_product2 @ SV193 @ SV268 ) )
= $true )
| ( ( subset @ SV64 @ SV193 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1583]) ).
thf(1684,plain,
! [SV194: $i,SV64: $i,SV269: $i] :
( ( ( subset @ ( cartesian_product2 @ SV269 @ SV64 ) @ ( cartesian_product2 @ SV269 @ SV194 ) )
= $true )
| ( ( subset @ SV64 @ SV194 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1584]) ).
thf(1685,plain,
! [SV146: $i] :
( ( ( epsilon_transitive @ SV146 )
= $false )
| ( ( epsilon_connected @ SV146 )
= $false )
| ( ( ordinal @ SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1585]) ).
thf(1686,plain,
! [SV241: $i] :
( ( ( ~ ( ordinal @ SV241 ) )
= $true )
| ( ( epsilon_connected @ SV241 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1586]) ).
thf(1687,plain,
! [SV242: $i] :
( ( ( ~ ( ordinal @ SV242 ) )
= $true )
| ( ( epsilon_transitive @ SV242 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1587]) ).
thf(1688,plain,
! [SV195: $i,SV226: $i,SV65: $i] :
( ( ( ~ ( in @ SV65 @ SV226 ) )
= $true )
| ( ( ~ ( in @ SV195 @ SV226 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV65 @ SV195 ) @ SV226 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1588]) ).
thf(1689,plain,
! [SV270: $i,SV65: $i] :
( ( ! [SY607: $i] :
( ~ ( subset @ ( unordered_pair @ SV65 @ SV270 ) @ SY607 )
| ( in @ SV65 @ SY607 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1589]) ).
thf(1690,plain,
! [SV271: $i,SV65: $i] :
( ( ! [SY608: $i] :
( ~ ( subset @ ( unordered_pair @ SV65 @ SV271 ) @ SY608 )
| ( in @ SV271 @ SY608 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1590]) ).
thf(1691,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( empty @ ( succ @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1591]) ).
thf(1692,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ ( succ @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1591]) ).
thf(1693,plain,
! [SV243: $i] :
( ( ( ~ ( ordinal @ SV243 ) )
= $true )
| ( ( epsilon_connected @ ( succ @ SV243 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1592]) ).
thf(1694,plain,
! [SV148: $i,SV196: $i] :
( ( ( ~ ( ! [SY539: $i] :
( ~ ( in @ ( sK13_C @ SV196 @ SV148 ) @ SY539 )
| ~ ( in @ SY539 @ SV148 ) )
| ~ ( in @ ( sK13_C @ SV196 @ SV148 ) @ SV196 ) ) )
= $false )
| ( ( SV196
= ( union @ SV148 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1593]) ).
thf(1695,plain,
! [SV148: $i,SV196: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK13_C @ SV196 @ SV148 ) @ ( sK14_SY277 @ SV196 @ SV148 ) )
| ~ ( in @ ( sK14_SY277 @ SV196 @ SV148 ) @ SV148 ) )
| ( in @ ( sK13_C @ SV196 @ SV148 ) @ SV196 ) ) )
= $false )
| ( ( SV196
= ( union @ SV148 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1593]) ).
thf(1696,plain,
! [SV197: $i,SV149: $i] :
( ( ( ~ ! [SY540: $i] :
( ! [SY498: $i] :
( ~ ( in @ SY540 @ SY498 )
| ~ ( in @ SY498 @ SV149 ) )
| ( in @ SY540 @ SV197 ) )
| ~ ! [SY542: $i] :
( ~ ( in @ SY542 @ SV197 )
| ~ ( ~ ( in @ SY542 @ ( sK12_D @ SY542 @ SV197 @ SV149 ) )
| ~ ( in @ ( sK12_D @ SY542 @ SV197 @ SV149 ) @ SV149 ) ) ) )
= $false )
| ( ( SV197
= ( union @ SV149 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1594]) ).
thf(1697,plain,
! [SV150: $i] :
( ( ( ! [SY500: $i,SY501: $i] :
( ( sK31_B @ SV150 )
!= ( ordered_pair @ SY500 @ SY501 ) ) )
= $true )
| ( ( relation @ SV150 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1595]) ).
thf(1698,plain,
! [SV150: $i] :
( ( ( in @ ( sK31_B @ SV150 ) @ SV150 )
= $true )
| ( ( relation @ SV150 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1596]) ).
thf(1699,plain,
! [SV151: $i,SV244: $i] :
( ( ( SV244
= ( ordered_pair @ ( sK29_C @ SV244 @ SV151 ) @ ( sK30_SY281 @ SV244 @ SV151 ) ) )
= $true )
| ( ( ~ ( in @ SV244 @ SV151 ) )
= $true )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1597]) ).
thf(1700,plain,
! [SV152: $i] :
( ( ( ~ ( ~ ( ( ( sK19_B @ SV152 )
!= ( sK20_SY279 @ SV152 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_B @ SV152 ) @ SV152 )
| ~ ( in @ ( sK20_SY279 @ SV152 ) @ SV152 ) )
| ~ ~ ( in @ ( sK19_B @ SV152 ) @ ( sK20_SY279 @ SV152 ) ) ) ) )
= $true )
| ( ( epsilon_connected @ SV152 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1598]) ).
thf(1701,plain,
! [SV152: $i] :
( ( ( ~ ( in @ ( sK20_SY279 @ SV152 ) @ ( sK19_B @ SV152 ) ) )
= $true )
| ( ( epsilon_connected @ SV152 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1599]) ).
thf(1702,plain,
! [SV153: $i,SV272: $i,SV245: $i] :
( ( ( ( SV245 = SV272 )
| ~ ( in @ SV245 @ SV153 )
| ~ ( in @ SV272 @ SV153 )
| ( in @ SV245 @ SV272 )
| ( in @ SV272 @ SV245 ) )
= $true )
| ( ( epsilon_connected @ SV153 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1600]) ).
thf(1703,plain,
! [SV198: $i,SV154: $i] :
( ( ( subset @ SV154 @ SV198 )
= $false )
| ( ( SV154 = SV198 )
= $true )
| ( ( proper_subset @ SV154 @ SV198 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1601]) ).
thf(1704,plain,
! [SV273: $i,SV246: $i] :
( ( ~ ( proper_subset @ SV246 @ SV273 )
| ( SV246 != SV273 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1602]) ).
thf(1705,plain,
! [SV274: $i,SV247: $i] :
( ( ~ ( proper_subset @ SV247 @ SV274 )
| ( subset @ SV247 @ SV274 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1603]) ).
thf(1706,plain,
! [SV155: $i] :
( ( ( ~ ( reflexive @ SV155 )
| ~ ( transitive @ SV155 )
| ~ ( antisymmetric @ SV155 )
| ~ ( connected @ SV155 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV155 ) )
= $true )
| ( ( well_ordering @ SV155 )
= $true )
| ( ( relation @ SV155 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1604]) ).
thf(1707,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1605]) ).
thf(1708,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1605]) ).
thf(1709,plain,
! [SV248: $i] :
( ( ( ~ ( relation @ SV248 ) )
= $true )
| ( ( ~ ( well_ordering @ SV248 )
| ( well_founded_relation @ SV248 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1606]) ).
thf(1710,plain,
! [SV66: $i] :
( ( ( subset @ ( sK51_B @ SV66 ) @ SV66 )
= $false )
| ( ( ordinal @ ( sK51_B @ SV66 ) )
= $false )
| ( ( ordinal @ SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1607]) ).
thf(1711,plain,
! [SV67: $i,SV121: $i,SV249: $i] :
( ( ( ~ ( in @ SV249 @ SV121 ) )
= $true )
| ( ( ~ ( in @ SV249 @ ( sK4_C @ SV121 @ SV67 ) ) )
= $true )
| ( ( ~ ( in @ SV67 @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1608]) ).
thf(1712,plain,
! [SV157: $i,SV250: $i] :
( ( ( in @ SV250 @ SV157 )
= $false )
| ( ( SV157 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1610]) ).
thf(1713,plain,
! [SV158: $i,SV199: $i] :
( ( ( ~ ( in @ ( sK34_C @ SV199 @ SV158 ) @ SV158 ) )
= $false )
| ( ( disjoint @ SV158 @ SV199 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1611]) ).
thf(1714,plain,
! [SV158: $i,SV199: $i] :
( ( ( ~ ( in @ ( sK34_C @ SV199 @ SV158 ) @ SV199 ) )
= $false )
| ( ( disjoint @ SV158 @ SV199 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1611]) ).
thf(1715,plain,
! [SV200: $i,SV159: $i,SV251: $i] :
( ( ( ~ ( in @ SV251 @ SV159 ) )
= $true )
| ( ( ~ ( in @ SV251 @ SV200 ) )
= $true )
| ( ( ~ ( disjoint @ SV159 @ SV200 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1612]) ).
thf(1716,plain,
! [SV160: $i,SV201: $i] :
( ( ( ~ ( ( ( sK28_C @ SV201 @ SV160 )
!= SV160 )
| ~ ( in @ ( sK28_C @ SV201 @ SV160 ) @ SV201 ) ) )
= $false )
| ( ( SV201
= ( singleton @ SV160 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1613]) ).
thf(1717,plain,
! [SV160: $i,SV201: $i] :
( ( ( ~ ( ( ( sK28_C @ SV201 @ SV160 )
= SV160 )
| ( in @ ( sK28_C @ SV201 @ SV160 ) @ SV201 ) ) )
= $false )
| ( ( SV201
= ( singleton @ SV160 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1613]) ).
thf(1718,plain,
! [SV202: $i,SV161: $i] :
( ( ( ~ ! [SY544: $i] :
( ( SY544 != SV161 )
| ( in @ SY544 @ SV202 ) )
| ~ ! [SY545: $i] :
( ~ ( in @ SY545 @ SV202 )
| ( SY545 = SV161 ) ) )
= $false )
| ( ( SV202
= ( singleton @ SV161 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1614]) ).
thf(1719,plain,
( ( ~ ~ ( empty @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1615]) ).
thf(1720,plain,
( ( ~ ( epsilon_transitive @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1615]) ).
thf(1721,plain,
! [SV68: $i,SV122: $i] :
( ( ( ordinal @ ( sK35_C @ SV122 @ SV68 ) )
= $true )
| ( ( ( SV68 = empty_set )
| ~ ( subset @ SV68 @ SV122 ) )
= $true )
| ( ( ordinal @ SV122 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1616]) ).
thf(1722,plain,
! [SV122: $i,SV68: $i] :
( ( ( ~ ( ~ ! [SY476: $i] :
( ~ ( ordinal @ SY476 )
| ~ ( in @ SY476 @ SV68 )
| ( ordinal_subset @ ( sK35_C @ SV122 @ SV68 ) @ SY476 ) )
| ~ ( in @ ( sK35_C @ SV122 @ SV68 ) @ SV68 ) ) )
= $true )
| ( ( ( SV68 = empty_set )
| ~ ( subset @ SV68 @ SV122 ) )
= $true )
| ( ( ordinal @ SV122 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1617]) ).
thf(1723,plain,
! [SV69: $i,SV203: $i,SV227: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV227 )
| ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV69 ) )
| ~ ( ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV227 )
| ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV203 ) ) )
| ~ ( ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV227 )
| ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV69 )
| ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV203 ) ) )
= $false )
| ( ( SV227
= ( set_union2 @ SV69 @ SV203 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1618]) ).
thf(1724,plain,
! [SV204: $i,SV69: $i,SV228: $i] :
( ( ( SV228
= ( set_union2 @ SV69 @ SV204 ) )
= $false )
| ( ( ~ ( ~ ! [SY571: $i] :
( ~ ( in @ SY571 @ SV228 )
| ( in @ SY571 @ SV69 )
| ( in @ SY571 @ SV204 ) )
| ~ ~ ( ~ ! [SY572: $i] :
( ~ ( in @ SY572 @ SV69 )
| ( in @ SY572 @ SV228 ) )
| ~ ! [SY573: $i] :
( ~ ( in @ SY573 @ SV204 )
| ( in @ SY573 @ SV228 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1619]) ).
thf(1725,plain,
! [SV162: $i,SV205: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_C @ SV205 @ SV162 ) @ SV205 )
| ~ ( subset @ ( sK26_C @ SV205 @ SV162 ) @ SV162 ) ) )
= $false )
| ( ( SV205
= ( powerset @ SV162 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1620]) ).
thf(1726,plain,
! [SV162: $i,SV205: $i] :
( ( ( ~ ( ( in @ ( sK26_C @ SV205 @ SV162 ) @ SV205 )
| ( subset @ ( sK26_C @ SV205 @ SV162 ) @ SV162 ) ) )
= $false )
| ( ( SV205
= ( powerset @ SV162 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1620]) ).
thf(1727,plain,
! [SV163: $i,SV206: $i] :
( ( ( ~ ! [SY551: $i] :
( ~ ( in @ SY551 @ SV206 )
| ( subset @ SY551 @ SV163 ) )
| ~ ! [SY552: $i] :
( ~ ( subset @ SY552 @ SV163 )
| ( in @ SY552 @ SV206 ) ) )
= $false )
| ( ( SV206
= ( powerset @ SV163 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1621]) ).
thf(1728,plain,
! [SV70: $i,SV207: $i,SV229: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV70 )
| ~ ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV207 )
| ~ ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV229 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV70 )
| ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV229 ) )
| ~ ( ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV207 )
| ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV229 ) ) ) )
= $false )
| ( ( SV229
= ( set_intersection2 @ SV70 @ SV207 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1622]) ).
thf(1729,plain,
! [SV208: $i,SV70: $i,SV230: $i] :
( ( ( SV230
= ( set_intersection2 @ SV70 @ SV208 ) )
= $false )
| ( ( ~ ( ~ ! [SY574: $i] :
( ~ ( in @ SY574 @ SV70 )
| ~ ( in @ SY574 @ SV208 )
| ( in @ SY574 @ SV230 ) )
| ~ ~ ( ~ ! [SY575: $i] :
( ~ ( in @ SY575 @ SV230 )
| ( in @ SY575 @ SV70 ) )
| ~ ! [SY576: $i] :
( ~ ( in @ SY576 @ SV230 )
| ( in @ SY576 @ SV208 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1623]) ).
thf(1730,plain,
! [SV252: $i] :
( ( ( ~ ( ordinal @ SV252 ) )
= $true )
| ( ( epsilon_connected @ ( union @ SV252 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1624]) ).
thf(1731,plain,
! [SV253: $i] :
( ( ( ~ ( ordinal @ SV253 ) )
= $true )
| ( ( epsilon_transitive @ ( union @ SV253 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1625]) ).
thf(1732,plain,
! [SV209: $i,SV165: $i] :
( ( ( ordinal @ SV165 )
= $false )
| ( ( ~ ( ordinal @ SV209 ) )
= $true )
| ( ( ~ ( ordinal_subset @ SV165 @ SV209 )
| ( subset @ SV165 @ SV209 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1626]) ).
thf(1733,plain,
! [SV210: $i,SV166: $i] :
( ( ( ordinal @ SV166 )
= $false )
| ( ( ~ ( ordinal @ SV210 ) )
= $true )
| ( ( ~ ( subset @ SV166 @ SV210 )
| ( ordinal_subset @ SV166 @ SV210 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1627]) ).
thf(1734,plain,
! [SV135: $i,SV71: $i] :
( ( ( ~ ! [SY409: $i] :
( ~ ( ordinal @ SY409 )
| ~ ( in @ SY409 @ SV71 )
| ( ordinal_subset @ ( sK54_B @ SV71 ) @ SY409 ) ) )
= $false )
| ( ( in @ SV135 @ SV71 )
= $false )
| ( ( ordinal @ SV135 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1628]) ).
thf(1735,plain,
! [SV135: $i,SV71: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK54_B @ SV71 ) @ SV71 )
| ~ ( ordinal @ ( sK54_B @ SV71 ) ) ) )
= $false )
| ( ( in @ SV135 @ SV71 )
= $false )
| ( ( ordinal @ SV135 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1628]) ).
thf(1736,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ( ( sK44_C @ SV123 @ SV72 )
!= ( sK45_SY295 @ SV123 @ SV72 ) )
| ~ ~ ( ~ ~ ( ( ( sK45_SY295 @ SV123 @ SV72 )
!= ( sK48_SY300 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 ) ) )
| ( ( sK44_C @ SV123 @ SV72 )
!= ( sK46_SY299 @ SV123 @ SV72 ) ) )
| ~ ~ ( ~ ~ ( ( ( sK46_SY299 @ SV123 @ SV72 )
!= ( sK47_SY303 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1629]) ).
thf(1737,plain,
! [SV72: $i,SV123: $i] :
( ( ( ( sK45_SY295 @ SV123 @ SV72 )
!= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1630]) ).
thf(1738,plain,
! [SV73: $i,SV254: $i] :
( ( ( ~ ( relation @ SV254 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK23_C @ SV254 @ SV73 ) @ ( sK24_SY280 @ SV254 @ SV73 ) ) @ SV73 )
| ~ ( in @ ( ordered_pair @ ( sK23_C @ SV254 @ SV73 ) @ ( sK24_SY280 @ SV254 @ SV73 ) ) @ SV254 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK23_C @ SV254 @ SV73 ) @ ( sK24_SY280 @ SV254 @ SV73 ) ) @ SV73 )
| ( in @ ( ordered_pair @ ( sK23_C @ SV254 @ SV73 ) @ ( sK24_SY280 @ SV254 @ SV73 ) ) @ SV254 ) ) )
| ( SV73 = SV254 ) )
= $true )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1631]) ).
thf(1739,plain,
! [SV73: $i,SV255: $i] :
( ( ( ~ ( relation @ SV255 ) )
= $true )
| ( ( ( SV73 != SV255 )
| ~ ( ~ ! [SY592: $i,SY593: $i] :
( ~ ( in @ ( ordered_pair @ SY592 @ SY593 ) @ SV73 )
| ( in @ ( ordered_pair @ SY592 @ SY593 ) @ SV255 ) )
| ~ ! [SY594: $i,SY595: $i] :
( ~ ( in @ ( ordered_pair @ SY594 @ SY595 ) @ SV255 )
| ( in @ ( ordered_pair @ SY594 @ SY595 ) @ SV73 ) ) ) )
= $true )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1632]) ).
thf(1740,plain,
! [SV74: $i,SV211: $i,SV231: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK22_D @ SV231 @ SV211 @ SV74 ) @ SV231 )
| ( ( sK22_D @ SV231 @ SV211 @ SV74 )
!= SV74 ) )
| ~ ( ~ ( in @ ( sK22_D @ SV231 @ SV211 @ SV74 ) @ SV231 )
| ( ( sK22_D @ SV231 @ SV211 @ SV74 )
!= SV211 ) ) )
| ~ ( ( in @ ( sK22_D @ SV231 @ SV211 @ SV74 ) @ SV231 )
| ( ( sK22_D @ SV231 @ SV211 @ SV74 )
= SV74 )
| ( ( sK22_D @ SV231 @ SV211 @ SV74 )
= SV211 ) ) )
= $false )
| ( ( SV231
= ( unordered_pair @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1633]) ).
thf(1741,plain,
! [SV212: $i,SV74: $i,SV232: $i] :
( ( ( SV232
= ( unordered_pair @ SV74 @ SV212 ) )
= $false )
| ( ( ~ ( ~ ! [SY577: $i] :
( ~ ( in @ SY577 @ SV232 )
| ( SY577 = SV74 )
| ( SY577 = SV212 ) )
| ~ ~ ( ~ ! [SY578: $i] :
( ( SY578 != SV74 )
| ( in @ SY578 @ SV232 ) )
| ~ ! [SY579: $i] :
( ( SY579 != SV212 )
| ( in @ SY579 @ SV232 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1634]) ).
thf(1742,plain,
! [SV169: $i] :
( ( ( in @ ( sK25_B @ SV169 ) @ SV169 )
= $true )
| ( ( epsilon_transitive @ SV169 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1635]) ).
thf(1743,plain,
! [SV169: $i] :
( ( ( ~ ( subset @ ( sK25_B @ SV169 ) @ SV169 ) )
= $true )
| ( ( epsilon_transitive @ SV169 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1636]) ).
thf(1744,plain,
! [SV170: $i,SV256: $i] :
( ( ( ~ ( in @ SV256 @ SV170 ) )
= $true )
| ( ( subset @ SV256 @ SV170 )
= $true )
| ( ( epsilon_transitive @ SV170 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1637]) ).
thf(1745,plain,
! [SV75: $i,SV213: $i] :
( ( ( subset @ SV213 @ ( sK2_B @ SV75 ) )
= $false )
| ( ( are_equipotent @ SV213 @ ( sK2_B @ SV75 ) )
= $true )
| ( ( in @ SV213 @ ( sK2_B @ SV75 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1638]) ).
thf(1746,plain,
! [SV75: $i,SV275: $i] :
( ( ~ ( ~ ! [SY609: $i] :
( ~ ( subset @ SY609 @ SV275 )
| ( in @ SY609 @ ( sK3_SY270 @ SV275 @ SV75 ) ) )
| ~ ( in @ ( sK3_SY270 @ SV275 @ SV75 ) @ ( sK2_B @ SV75 ) ) )
| ~ ( in @ SV275 @ ( sK2_B @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1639]) ).
thf(1747,plain,
! [SV75: $i] :
( ( ~ ! [SY431: $i,SY432: $i] :
( ~ ( in @ SY431 @ ( sK2_B @ SV75 ) )
| ~ ( subset @ SY432 @ SY431 )
| ( in @ SY432 @ ( sK2_B @ SV75 ) ) )
| ~ ( in @ SV75 @ ( sK2_B @ SV75 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1640]) ).
thf(1748,plain,
! [SV214: $i,SV76: $i,SV233: $i] :
( ( ( relation @ SV233 )
= $false )
| ( ( ~ ( in @ SV76 @ ( relation_field @ ( relation_restriction @ SV233 @ SV214 ) ) )
| ( in @ SV76 @ ( relation_field @ SV233 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1641]) ).
thf(1749,plain,
! [SV215: $i,SV76: $i,SV234: $i] :
( ( ( relation @ SV234 )
= $false )
| ( ( ~ ( in @ SV76 @ ( relation_field @ ( relation_restriction @ SV234 @ SV215 ) ) )
| ( in @ SV76 @ SV215 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1642]) ).
thf(1750,plain,
! [SV77: $i,SV257: $i] :
( ( ( ~ ( relation @ SV257 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_C @ SV257 @ SV77 ) @ ( sK18_SY278 @ SV257 @ SV77 ) ) @ SV77 )
| ~ ~ ( in @ ( ordered_pair @ ( sK17_C @ SV257 @ SV77 ) @ ( sK18_SY278 @ SV257 @ SV77 ) ) @ SV257 ) )
| ( subset @ SV77 @ SV257 ) )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1643]) ).
thf(1751,plain,
! [SV77: $i,SV258: $i] :
( ( ( ~ ( relation @ SV258 ) )
= $true )
| ( ( ~ ( subset @ SV77 @ SV258 )
| ! [SY596: $i,SY597: $i] :
( ~ ( in @ ( ordered_pair @ SY596 @ SY597 ) @ SV77 )
| ( in @ ( ordered_pair @ SY596 @ SY597 ) @ SV258 ) ) )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1644]) ).
thf(1752,plain,
! [SV171: $i,SV216: $i] :
( ( ( ~ ( in @ ( sK16_C @ SV216 @ SV171 ) @ SV171 ) )
= $false )
| ( ( subset @ SV171 @ SV216 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1645]) ).
thf(1753,plain,
! [SV171: $i,SV216: $i] :
( ( ( ~ ~ ( in @ ( sK16_C @ SV216 @ SV171 ) @ SV216 ) )
= $false )
| ( ( subset @ SV171 @ SV216 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1645]) ).
thf(1754,plain,
! [SV217: $i,SV172: $i,SV276: $i] :
( ( ( ~ ( in @ SV276 @ SV172 )
| ( in @ SV276 @ SV217 ) )
= $true )
| ( ( subset @ SV172 @ SV217 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1646]) ).
thf(1755,plain,
! [SV78: $i,SV218: $i,SV235: $i] :
( ( ( ~ ( ~ ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV78 )
| ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV218 )
| ~ ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV235 ) )
| ~ ~ ( ~ ( ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV78 )
| ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV235 ) )
| ~ ( ~ ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV218 )
| ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV235 ) ) ) )
= $false )
| ( ( SV235
= ( set_difference @ SV78 @ SV218 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1647]) ).
thf(1756,plain,
! [SV219: $i,SV78: $i,SV236: $i] :
( ( ( SV236
= ( set_difference @ SV78 @ SV219 ) )
= $false )
| ( ( ~ ( ~ ! [SY580: $i] :
( ~ ( in @ SY580 @ SV78 )
| ( in @ SY580 @ SV219 )
| ( in @ SY580 @ SV236 ) )
| ~ ~ ( ~ ! [SY581: $i] :
( ~ ( in @ SY581 @ SV236 )
| ( in @ SY581 @ SV78 ) )
| ~ ! [SY582: $i] :
( ~ ( in @ SY582 @ SV236 )
| ~ ( in @ SY582 @ SV219 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1648]) ).
thf(1757,plain,
! [SV175: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK36_B @ SV175 ) @ ( sK37_SY285 @ SV175 ) ) @ SV175 )
| ~ ( in @ ( ordered_pair @ ( sK37_SY285 @ SV175 ) @ ( sK36_B @ SV175 ) ) @ SV175 ) )
| ~ ( ( ( sK36_B @ SV175 )
!= ( sK37_SY285 @ SV175 ) ) ) )
= $false )
| ( ( antisymmetric @ SV175 )
= $true )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1651]) ).
thf(1758,plain,
! [SV176: $i] :
( ( ( antisymmetric @ SV176 )
= $false )
| ( ( ! [SY526: $i,SY527: $i] :
( ~ ( in @ ( ordered_pair @ SY526 @ SY527 ) @ SV176 )
| ~ ( in @ ( ordered_pair @ SY527 @ SY526 ) @ SV176 )
| ( SY526 = SY527 ) ) )
= $true )
| ( ( relation @ SV176 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1652]) ).
thf(1759,plain,
! [SV222: $i,SV177: $i] :
( ( ( subset @ SV177 @ SV222 )
= $false )
| ( ( ~ ( subset @ SV222 @ SV177 ) )
= $true )
| ( ( SV177 = SV222 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1653]) ).
thf(1760,plain,
! [SV277: $i,SV259: $i] :
( ( ( SV259 != SV277 )
| ( subset @ SV259 @ SV277 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1654]) ).
thf(1761,plain,
! [SV278: $i,SV260: $i] :
( ( ( SV260 != SV278 )
| ( subset @ SV278 @ SV260 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1655]) ).
thf(1762,plain,
! [SV178: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK38_B @ SV178 ) @ ( sK39_SY286 @ SV178 ) ) @ SV178 )
| ~ ( in @ ( ordered_pair @ ( sK39_SY286 @ SV178 ) @ ( sK40_SY288 @ SV178 ) ) @ SV178 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK38_B @ SV178 ) @ ( sK40_SY288 @ SV178 ) ) @ SV178 ) )
= $false )
| ( ( transitive @ SV178 )
= $true )
| ( ( relation @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1656]) ).
thf(1763,plain,
! [SV179: $i] :
( ( ( transitive @ SV179 )
= $false )
| ( ( ! [SY529: $i,SY530: $i,SY531: $i] :
( ~ ( in @ ( ordered_pair @ SY529 @ SY530 ) @ SV179 )
| ~ ( in @ ( ordered_pair @ SY530 @ SY531 ) @ SV179 )
| ( in @ ( ordered_pair @ SY529 @ SY531 ) @ SV179 ) ) )
= $true )
| ( ( relation @ SV179 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1657]) ).
thf(1764,plain,
! [SV79: $i,SV124: $i] :
( ( ( in @ ( sK5_C @ SV124 @ SV79 ) @ SV79 )
= $false )
| ( ( ~ ( in @ ( sK5_C @ SV124 @ SV79 ) @ SV124 ) )
= $true )
| ( ( SV79 = SV124 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1658]) ).
thf(1765,plain,
! [SV261: $i] :
( ( ( ~ ( empty @ SV261 ) )
= $true )
| ( ( epsilon_connected @ SV261 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1660]) ).
thf(1766,plain,
! [SV262: $i] :
( ( ( ~ ( empty @ SV262 ) )
= $true )
| ( ( epsilon_transitive @ SV262 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1661]) ).
thf(1767,plain,
! [SV183: $i] :
( ( ( ~ ( ordinal @ ( sK50_B @ SV183 ) )
| ( SV183
!= ( succ @ ( sK50_B @ SV183 ) ) ) )
= $false )
| ( ( being_limit_ordinal @ SV183 )
= $true )
| ( ( ordinal @ SV183 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1662]) ).
thf(1768,plain,
! [SV279: $i,SV184: $i] :
( ( ( ( SV184
!= ( succ @ SV279 ) )
| ~ ( ordinal @ SV279 ) )
= $true )
| ( ( ~ ( being_limit_ordinal @ SV184 ) )
= $true )
| ( ( ordinal @ SV184 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1663]) ).
thf(1769,plain,
! [SV80: $i,SV125: $i,SV237: $i,SV263: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
!= SV237 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
!= SV80 ) )
| ~ ( ~ ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
!= SV125 ) ) ) )
| ~ ( ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
= SV237 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
= SV80 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
= SV125 ) ) ) )
= $true )
| ( ( SV263
= ( unordered_triple @ SV80 @ SV125 @ SV237 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1666]) ).
thf(1770,plain,
! [SV238: $i,SV125: $i,SV80: $i,SV264: $i] :
( ( ( SV264
!= ( unordered_triple @ SV80 @ SV125 @ SV238 ) )
= $true )
| ( ( ~ ( ~ ! [SY600: $i] :
( ~ ( in @ SY600 @ SV264 )
| ( SY600 = SV238 )
| ( SY600 = SV80 )
| ( SY600 = SV125 ) )
| ~ ~ ( ~ ! [SY601: $i] :
( ( SY601 != SV238 )
| ( in @ SY601 @ SV264 ) )
| ~ ~ ( ~ ! [SY602: $i] :
( ( SY602 != SV80 )
| ( in @ SY602 @ SV264 ) )
| ~ ! [SY603: $i] :
( ( SY603 != SV125 )
| ( in @ SY603 @ SV264 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1667]) ).
thf(1771,plain,
! [SV192: $i,SV225: $i,SV61: $i] :
( ( ( ~ ( in @ SV61 @ SV225 )
| ~ ( in @ SV61 @ ( cartesian_product2 @ SV192 @ SV192 ) ) )
= $true )
| ( ( in @ SV61 @ ( relation_restriction @ SV225 @ SV192 ) )
= $true )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1674]) ).
thf(1772,plain,
! [SV265: $i,SV61: $i,SV280: $i] :
( ( ~ ( relation @ SV280 )
| ~ ( in @ SV61 @ ( relation_restriction @ SV280 @ SV265 ) )
| ( in @ SV61 @ SV280 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1675]) ).
thf(1773,plain,
! [SV266: $i,SV61: $i,SV281: $i] :
( ( ~ ( relation @ SV281 )
| ~ ( in @ SV61 @ ( relation_restriction @ SV281 @ SV266 ) )
| ( in @ SV61 @ ( cartesian_product2 @ SV266 @ SV266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1676]) ).
thf(1774,plain,
! [SV144: $i] :
( ( ( ~ ( ordinal @ ( sK33_B @ SV144 ) ) )
= $false )
| ( ( being_limit_ordinal @ SV144 )
= $true )
| ( ( ordinal @ SV144 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1677]) ).
thf(1775,plain,
! [SV144: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK33_B @ SV144 ) @ SV144 )
| ~ ~ ( in @ ( succ @ ( sK33_B @ SV144 ) ) @ SV144 ) ) )
= $false )
| ( ( being_limit_ordinal @ SV144 )
= $true )
| ( ( ordinal @ SV144 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1677]) ).
thf(1776,plain,
! [SV145: $i,SV282: $i] :
( ( ( ~ ( ordinal @ SV282 )
| ~ ( in @ SV282 @ SV145 )
| ( in @ ( succ @ SV282 ) @ SV145 ) )
= $true )
| ( ( being_limit_ordinal @ SV145 )
= $false )
| ( ( ordinal @ SV145 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1678]) ).
thf(1777,plain,
! [SV62: $i,SV239: $i] :
( ( ( ordinal @ SV239 )
= $false )
| ( ( ~ ( in @ SV62 @ SV239 )
| ( ordinal_subset @ ( succ @ SV62 ) @ SV239 ) )
= $true )
| ( ( ordinal @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1679]) ).
thf(1778,plain,
! [SV62: $i,SV240: $i] :
( ( ( ordinal @ SV240 )
= $false )
| ( ( ~ ( ordinal_subset @ ( succ @ SV62 ) @ SV240 )
| ( in @ SV62 @ SV240 ) )
= $true )
| ( ( ordinal @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1680]) ).
thf(1779,plain,
! [SV120: $i,SV63: $i,SV267: $i] :
( ( ( ! [SY606: $i] :
( ( SV267 != SY606 )
| ~ ( ordinal @ SY606 )
| ~ ( in @ SY606 @ SV63 ) )
| ~ ( in @ SV267 @ ( succ @ SV120 ) ) )
= $true )
| ( ( in @ SV267 @ ( sK52_C @ SV120 @ SV63 ) )
= $true )
| ( ( ordinal @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1681]) ).
thf(1780,plain,
! [SV63: $i,SV120: $i] :
( ( ( ~ ! [SY473: $i] :
( ~ ( in @ SY473 @ ( sK52_C @ SV120 @ SV63 ) )
| ~ ( ~ ~ ( ( SY473
!= ( sK53_E @ SY473 @ SV120 @ SV63 ) )
| ~ ( ordinal @ ( sK53_E @ SY473 @ SV120 @ SV63 ) ) )
| ~ ( in @ ( sK53_E @ SY473 @ SV120 @ SV63 ) @ SV63 ) ) ) )
= $false )
| ( ( ordinal @ SV120 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1682]) ).
thf(1781,plain,
! [SV63: $i,SV120: $i] :
( ( ( ~ ! [SY474: $i] :
( ~ ( in @ SY474 @ ( sK52_C @ SV120 @ SV63 ) )
| ( in @ SY474 @ ( succ @ SV120 ) ) ) )
= $false )
| ( ( ordinal @ SV120 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1682]) ).
thf(1782,plain,
! [SV241: $i] :
( ( ( ordinal @ SV241 )
= $false )
| ( ( epsilon_connected @ SV241 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1686]) ).
thf(1783,plain,
! [SV242: $i] :
( ( ( ordinal @ SV242 )
= $false )
| ( ( epsilon_transitive @ SV242 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1687]) ).
thf(1784,plain,
! [SV195: $i,SV226: $i,SV65: $i] :
( ( ( in @ SV65 @ SV226 )
= $false )
| ( ( ~ ( in @ SV195 @ SV226 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV65 @ SV195 ) @ SV226 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1688]) ).
thf(1785,plain,
! [SV283: $i,SV270: $i,SV65: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV65 @ SV270 ) @ SV283 )
| ( in @ SV65 @ SV283 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1689]) ).
thf(1786,plain,
! [SV284: $i,SV271: $i,SV65: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV65 @ SV271 ) @ SV284 )
| ( in @ SV271 @ SV284 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1690]) ).
thf(1787,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( empty @ ( succ @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1691]) ).
thf(1788,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ ( succ @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1692]) ).
thf(1789,plain,
! [SV243: $i] :
( ( ( ordinal @ SV243 )
= $false )
| ( ( epsilon_connected @ ( succ @ SV243 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1693]) ).
thf(1790,plain,
! [SV148: $i,SV196: $i] :
( ( ( ! [SY539: $i] :
( ~ ( in @ ( sK13_C @ SV196 @ SV148 ) @ SY539 )
| ~ ( in @ SY539 @ SV148 ) )
| ~ ( in @ ( sK13_C @ SV196 @ SV148 ) @ SV196 ) )
= $true )
| ( ( SV196
= ( union @ SV148 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1694]) ).
thf(1791,plain,
! [SV148: $i,SV196: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_C @ SV196 @ SV148 ) @ ( sK14_SY277 @ SV196 @ SV148 ) )
| ~ ( in @ ( sK14_SY277 @ SV196 @ SV148 ) @ SV148 ) )
| ( in @ ( sK13_C @ SV196 @ SV148 ) @ SV196 ) )
= $true )
| ( ( SV196
= ( union @ SV148 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1695]) ).
thf(1792,plain,
! [SV197: $i,SV149: $i] :
( ( ( ~ ! [SY540: $i] :
( ! [SY498: $i] :
( ~ ( in @ SY540 @ SY498 )
| ~ ( in @ SY498 @ SV149 ) )
| ( in @ SY540 @ SV197 ) ) )
= $false )
| ( ( SV197
= ( union @ SV149 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1696]) ).
thf(1793,plain,
! [SV149: $i,SV197: $i] :
( ( ( ~ ! [SY542: $i] :
( ~ ( in @ SY542 @ SV197 )
| ~ ( ~ ( in @ SY542 @ ( sK12_D @ SY542 @ SV197 @ SV149 ) )
| ~ ( in @ ( sK12_D @ SY542 @ SV197 @ SV149 ) @ SV149 ) ) ) )
= $false )
| ( ( SV197
= ( union @ SV149 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1696]) ).
thf(1794,plain,
! [SV285: $i,SV150: $i] :
( ( ( ! [SY610: $i] :
( ( sK31_B @ SV150 )
!= ( ordered_pair @ SV285 @ SY610 ) ) )
= $true )
| ( ( relation @ SV150 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1697]) ).
thf(1795,plain,
! [SV151: $i,SV244: $i] :
( ( ( in @ SV244 @ SV151 )
= $false )
| ( ( SV244
= ( ordered_pair @ ( sK29_C @ SV244 @ SV151 ) @ ( sK30_SY281 @ SV244 @ SV151 ) ) )
= $true )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1699]) ).
thf(1796,plain,
! [SV152: $i] :
( ( ( ~ ( ( ( sK19_B @ SV152 )
!= ( sK20_SY279 @ SV152 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_B @ SV152 ) @ SV152 )
| ~ ( in @ ( sK20_SY279 @ SV152 ) @ SV152 ) )
| ~ ~ ( in @ ( sK19_B @ SV152 ) @ ( sK20_SY279 @ SV152 ) ) ) )
= $false )
| ( ( epsilon_connected @ SV152 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1700]) ).
thf(1797,plain,
! [SV152: $i] :
( ( ( in @ ( sK20_SY279 @ SV152 ) @ ( sK19_B @ SV152 ) )
= $false )
| ( ( epsilon_connected @ SV152 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1701]) ).
thf(1798,plain,
! [SV153: $i,SV272: $i,SV245: $i] :
( ( ( ( SV245 = SV272 )
| ~ ( in @ SV245 @ SV153 )
| ~ ( in @ SV272 @ SV153 )
| ( in @ SV245 @ SV272 ) )
= $true )
| ( ( in @ SV272 @ SV245 )
= $true )
| ( ( epsilon_connected @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1702]) ).
thf(1799,plain,
! [SV273: $i,SV246: $i] :
( ( ( ~ ( proper_subset @ SV246 @ SV273 ) )
= $true )
| ( ( SV246 != SV273 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1704]) ).
thf(1800,plain,
! [SV274: $i,SV247: $i] :
( ( ( ~ ( proper_subset @ SV247 @ SV274 ) )
= $true )
| ( ( subset @ SV247 @ SV274 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1705]) ).
thf(1801,plain,
! [SV155: $i] :
( ( ( ~ ( reflexive @ SV155 )
| ~ ( transitive @ SV155 )
| ~ ( antisymmetric @ SV155 ) )
= $true )
| ( ( ~ ( connected @ SV155 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV155 ) )
= $true )
| ( ( well_ordering @ SV155 )
= $true )
| ( ( relation @ SV155 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1706]) ).
thf(1802,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1707]) ).
thf(1803,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1708]) ).
thf(1804,plain,
! [SV248: $i] :
( ( ( relation @ SV248 )
= $false )
| ( ( ~ ( well_ordering @ SV248 )
| ( well_founded_relation @ SV248 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1709]) ).
thf(1805,plain,
! [SV67: $i,SV121: $i,SV249: $i] :
( ( ( in @ SV249 @ SV121 )
= $false )
| ( ( ~ ( in @ SV249 @ ( sK4_C @ SV121 @ SV67 ) ) )
= $true )
| ( ( ~ ( in @ SV67 @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1711]) ).
thf(1806,plain,
! [SV158: $i,SV199: $i] :
( ( ( in @ ( sK34_C @ SV199 @ SV158 ) @ SV158 )
= $true )
| ( ( disjoint @ SV158 @ SV199 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1713]) ).
thf(1807,plain,
! [SV158: $i,SV199: $i] :
( ( ( in @ ( sK34_C @ SV199 @ SV158 ) @ SV199 )
= $true )
| ( ( disjoint @ SV158 @ SV199 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1714]) ).
thf(1808,plain,
! [SV200: $i,SV159: $i,SV251: $i] :
( ( ( in @ SV251 @ SV159 )
= $false )
| ( ( ~ ( in @ SV251 @ SV200 ) )
= $true )
| ( ( ~ ( disjoint @ SV159 @ SV200 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1715]) ).
thf(1809,plain,
! [SV160: $i,SV201: $i] :
( ( ( ( ( sK28_C @ SV201 @ SV160 )
!= SV160 )
| ~ ( in @ ( sK28_C @ SV201 @ SV160 ) @ SV201 ) )
= $true )
| ( ( SV201
= ( singleton @ SV160 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1716]) ).
thf(1810,plain,
! [SV160: $i,SV201: $i] :
( ( ( ( ( sK28_C @ SV201 @ SV160 )
= SV160 )
| ( in @ ( sK28_C @ SV201 @ SV160 ) @ SV201 ) )
= $true )
| ( ( SV201
= ( singleton @ SV160 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1717]) ).
thf(1811,plain,
! [SV202: $i,SV161: $i] :
( ( ( ~ ! [SY544: $i] :
( ( SY544 != SV161 )
| ( in @ SY544 @ SV202 ) ) )
= $false )
| ( ( SV202
= ( singleton @ SV161 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1718]) ).
thf(1812,plain,
! [SV161: $i,SV202: $i] :
( ( ( ~ ! [SY545: $i] :
( ~ ( in @ SY545 @ SV202 )
| ( SY545 = SV161 ) ) )
= $false )
| ( ( SV202
= ( singleton @ SV161 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1718]) ).
thf(1813,plain,
( ( ~ ( empty @ sK7_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1719]) ).
thf(1814,plain,
( ( epsilon_transitive @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1720]) ).
thf(1815,plain,
! [SV122: $i,SV68: $i] :
( ( ( SV68 = empty_set )
= $true )
| ( ( ~ ( subset @ SV68 @ SV122 ) )
= $true )
| ( ( ordinal @ ( sK35_C @ SV122 @ SV68 ) )
= $true )
| ( ( ordinal @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1721]) ).
thf(1816,plain,
! [SV122: $i,SV68: $i] :
( ( ( ~ ! [SY476: $i] :
( ~ ( ordinal @ SY476 )
| ~ ( in @ SY476 @ SV68 )
| ( ordinal_subset @ ( sK35_C @ SV122 @ SV68 ) @ SY476 ) )
| ~ ( in @ ( sK35_C @ SV122 @ SV68 ) @ SV68 ) )
= $false )
| ( ( ( SV68 = empty_set )
| ~ ( subset @ SV68 @ SV122 ) )
= $true )
| ( ( ordinal @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1722]) ).
thf(1817,plain,
! [SV69: $i,SV203: $i,SV227: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV227 )
| ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV69 ) )
| ~ ( ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV227 )
| ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV203 ) ) ) )
= $false )
| ( ( SV227
= ( set_union2 @ SV69 @ SV203 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1723]) ).
thf(1818,plain,
! [SV69: $i,SV203: $i,SV227: $i] :
( ( ( ~ ( ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV227 )
| ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV69 )
| ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV203 ) ) )
= $false )
| ( ( SV227
= ( set_union2 @ SV69 @ SV203 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1723]) ).
thf(1819,plain,
! [SV204: $i,SV69: $i,SV228: $i] :
( ( ( ~ ! [SY571: $i] :
( ~ ( in @ SY571 @ SV228 )
| ( in @ SY571 @ SV69 )
| ( in @ SY571 @ SV204 ) )
| ~ ~ ( ~ ! [SY572: $i] :
( ~ ( in @ SY572 @ SV69 )
| ( in @ SY572 @ SV228 ) )
| ~ ! [SY573: $i] :
( ~ ( in @ SY573 @ SV204 )
| ( in @ SY573 @ SV228 ) ) ) )
= $false )
| ( ( SV228
= ( set_union2 @ SV69 @ SV204 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1724]) ).
thf(1820,plain,
! [SV162: $i,SV205: $i] :
( ( ( ~ ( in @ ( sK26_C @ SV205 @ SV162 ) @ SV205 )
| ~ ( subset @ ( sK26_C @ SV205 @ SV162 ) @ SV162 ) )
= $true )
| ( ( SV205
= ( powerset @ SV162 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1725]) ).
thf(1821,plain,
! [SV162: $i,SV205: $i] :
( ( ( ( in @ ( sK26_C @ SV205 @ SV162 ) @ SV205 )
| ( subset @ ( sK26_C @ SV205 @ SV162 ) @ SV162 ) )
= $true )
| ( ( SV205
= ( powerset @ SV162 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1726]) ).
thf(1822,plain,
! [SV163: $i,SV206: $i] :
( ( ( ~ ! [SY551: $i] :
( ~ ( in @ SY551 @ SV206 )
| ( subset @ SY551 @ SV163 ) ) )
= $false )
| ( ( SV206
= ( powerset @ SV163 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1727]) ).
thf(1823,plain,
! [SV206: $i,SV163: $i] :
( ( ( ~ ! [SY552: $i] :
( ~ ( subset @ SY552 @ SV163 )
| ( in @ SY552 @ SV206 ) ) )
= $false )
| ( ( SV206
= ( powerset @ SV163 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1727]) ).
thf(1824,plain,
! [SV70: $i,SV207: $i,SV229: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV70 )
| ~ ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV207 )
| ~ ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV229 ) ) )
= $false )
| ( ( SV229
= ( set_intersection2 @ SV70 @ SV207 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1728]) ).
thf(1825,plain,
! [SV70: $i,SV207: $i,SV229: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV70 )
| ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV229 ) )
| ~ ( ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV207 )
| ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV229 ) ) ) )
= $false )
| ( ( SV229
= ( set_intersection2 @ SV70 @ SV207 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1728]) ).
thf(1826,plain,
! [SV230: $i,SV208: $i,SV70: $i] :
( ( ( ~ ! [SY574: $i] :
( ~ ( in @ SY574 @ SV70 )
| ~ ( in @ SY574 @ SV208 )
| ( in @ SY574 @ SV230 ) )
| ~ ~ ( ~ ! [SY575: $i] :
( ~ ( in @ SY575 @ SV230 )
| ( in @ SY575 @ SV70 ) )
| ~ ! [SY576: $i] :
( ~ ( in @ SY576 @ SV230 )
| ( in @ SY576 @ SV208 ) ) ) )
= $false )
| ( ( SV230
= ( set_intersection2 @ SV70 @ SV208 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1729]) ).
thf(1827,plain,
! [SV252: $i] :
( ( ( ordinal @ SV252 )
= $false )
| ( ( epsilon_connected @ ( union @ SV252 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1730]) ).
thf(1828,plain,
! [SV253: $i] :
( ( ( ordinal @ SV253 )
= $false )
| ( ( epsilon_transitive @ ( union @ SV253 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1731]) ).
thf(1829,plain,
! [SV165: $i,SV209: $i] :
( ( ( ordinal @ SV209 )
= $false )
| ( ( ordinal @ SV165 )
= $false )
| ( ( ~ ( ordinal_subset @ SV165 @ SV209 )
| ( subset @ SV165 @ SV209 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1732]) ).
thf(1830,plain,
! [SV166: $i,SV210: $i] :
( ( ( ordinal @ SV210 )
= $false )
| ( ( ordinal @ SV166 )
= $false )
| ( ( ~ ( subset @ SV166 @ SV210 )
| ( ordinal_subset @ SV166 @ SV210 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1733]) ).
thf(1831,plain,
! [SV135: $i,SV71: $i] :
( ( ( ! [SY409: $i] :
( ~ ( ordinal @ SY409 )
| ~ ( in @ SY409 @ SV71 )
| ( ordinal_subset @ ( sK54_B @ SV71 ) @ SY409 ) ) )
= $true )
| ( ( in @ SV135 @ SV71 )
= $false )
| ( ( ordinal @ SV135 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1734]) ).
thf(1832,plain,
! [SV135: $i,SV71: $i] :
( ( ( ~ ( ~ ( in @ ( sK54_B @ SV71 ) @ SV71 )
| ~ ( ordinal @ ( sK54_B @ SV71 ) ) ) )
= $true )
| ( ( in @ SV135 @ SV71 )
= $false )
| ( ( ordinal @ SV135 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1735]) ).
thf(1833,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( sK44_C @ SV123 @ SV72 )
!= ( sK45_SY295 @ SV123 @ SV72 ) )
| ~ ~ ( ~ ~ ( ( ( sK45_SY295 @ SV123 @ SV72 )
!= ( sK48_SY300 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 ) ) )
| ( ( sK44_C @ SV123 @ SV72 )
!= ( sK46_SY299 @ SV123 @ SV72 ) ) )
| ~ ~ ( ~ ~ ( ( ( sK46_SY299 @ SV123 @ SV72 )
!= ( sK47_SY303 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1736]) ).
thf(1834,plain,
! [SV72: $i,SV123: $i] :
( ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1737]) ).
thf(1835,plain,
! [SV73: $i,SV254: $i] :
( ( ( relation @ SV254 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK23_C @ SV254 @ SV73 ) @ ( sK24_SY280 @ SV254 @ SV73 ) ) @ SV73 )
| ~ ( in @ ( ordered_pair @ ( sK23_C @ SV254 @ SV73 ) @ ( sK24_SY280 @ SV254 @ SV73 ) ) @ SV254 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK23_C @ SV254 @ SV73 ) @ ( sK24_SY280 @ SV254 @ SV73 ) ) @ SV73 )
| ( in @ ( ordered_pair @ ( sK23_C @ SV254 @ SV73 ) @ ( sK24_SY280 @ SV254 @ SV73 ) ) @ SV254 ) ) )
| ( SV73 = SV254 ) )
= $true )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1738]) ).
thf(1836,plain,
! [SV73: $i,SV255: $i] :
( ( ( relation @ SV255 )
= $false )
| ( ( ( SV73 != SV255 )
| ~ ( ~ ! [SY592: $i,SY593: $i] :
( ~ ( in @ ( ordered_pair @ SY592 @ SY593 ) @ SV73 )
| ( in @ ( ordered_pair @ SY592 @ SY593 ) @ SV255 ) )
| ~ ! [SY594: $i,SY595: $i] :
( ~ ( in @ ( ordered_pair @ SY594 @ SY595 ) @ SV255 )
| ( in @ ( ordered_pair @ SY594 @ SY595 ) @ SV73 ) ) ) )
= $true )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1739]) ).
thf(1837,plain,
! [SV74: $i,SV211: $i,SV231: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK22_D @ SV231 @ SV211 @ SV74 ) @ SV231 )
| ( ( sK22_D @ SV231 @ SV211 @ SV74 )
!= SV74 ) )
| ~ ( ~ ( in @ ( sK22_D @ SV231 @ SV211 @ SV74 ) @ SV231 )
| ( ( sK22_D @ SV231 @ SV211 @ SV74 )
!= SV211 ) ) ) )
= $false )
| ( ( SV231
= ( unordered_pair @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1740]) ).
thf(1838,plain,
! [SV74: $i,SV211: $i,SV231: $i] :
( ( ( ~ ( ( in @ ( sK22_D @ SV231 @ SV211 @ SV74 ) @ SV231 )
| ( ( sK22_D @ SV231 @ SV211 @ SV74 )
= SV74 )
| ( ( sK22_D @ SV231 @ SV211 @ SV74 )
= SV211 ) ) )
= $false )
| ( ( SV231
= ( unordered_pair @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1740]) ).
thf(1839,plain,
! [SV212: $i,SV74: $i,SV232: $i] :
( ( ( ~ ! [SY577: $i] :
( ~ ( in @ SY577 @ SV232 )
| ( SY577 = SV74 )
| ( SY577 = SV212 ) )
| ~ ~ ( ~ ! [SY578: $i] :
( ( SY578 != SV74 )
| ( in @ SY578 @ SV232 ) )
| ~ ! [SY579: $i] :
( ( SY579 != SV212 )
| ( in @ SY579 @ SV232 ) ) ) )
= $false )
| ( ( SV232
= ( unordered_pair @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1741]) ).
thf(1840,plain,
! [SV169: $i] :
( ( ( subset @ ( sK25_B @ SV169 ) @ SV169 )
= $false )
| ( ( epsilon_transitive @ SV169 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1743]) ).
thf(1841,plain,
! [SV170: $i,SV256: $i] :
( ( ( in @ SV256 @ SV170 )
= $false )
| ( ( subset @ SV256 @ SV170 )
= $true )
| ( ( epsilon_transitive @ SV170 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1744]) ).
thf(1842,plain,
! [SV75: $i,SV275: $i] :
( ( ( ~ ( ~ ! [SY609: $i] :
( ~ ( subset @ SY609 @ SV275 )
| ( in @ SY609 @ ( sK3_SY270 @ SV275 @ SV75 ) ) )
| ~ ( in @ ( sK3_SY270 @ SV275 @ SV75 ) @ ( sK2_B @ SV75 ) ) ) )
= $true )
| ( ( ~ ( in @ SV275 @ ( sK2_B @ SV75 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1746]) ).
thf(1843,plain,
! [SV75: $i] :
( ( ~ ! [SY431: $i,SY432: $i] :
( ~ ( in @ SY431 @ ( sK2_B @ SV75 ) )
| ~ ( subset @ SY432 @ SY431 )
| ( in @ SY432 @ ( sK2_B @ SV75 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1747]) ).
thf(1844,plain,
! [SV75: $i] :
( ( ~ ( in @ SV75 @ ( sK2_B @ SV75 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1747]) ).
thf(1845,plain,
! [SV214: $i,SV233: $i,SV76: $i] :
( ( ( ~ ( in @ SV76 @ ( relation_field @ ( relation_restriction @ SV233 @ SV214 ) ) ) )
= $true )
| ( ( in @ SV76 @ ( relation_field @ SV233 ) )
= $true )
| ( ( relation @ SV233 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1748]) ).
thf(1846,plain,
! [SV215: $i,SV234: $i,SV76: $i] :
( ( ( ~ ( in @ SV76 @ ( relation_field @ ( relation_restriction @ SV234 @ SV215 ) ) ) )
= $true )
| ( ( in @ SV76 @ SV215 )
= $true )
| ( ( relation @ SV234 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1749]) ).
thf(1847,plain,
! [SV77: $i,SV257: $i] :
( ( ( relation @ SV257 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_C @ SV257 @ SV77 ) @ ( sK18_SY278 @ SV257 @ SV77 ) ) @ SV77 )
| ~ ~ ( in @ ( ordered_pair @ ( sK17_C @ SV257 @ SV77 ) @ ( sK18_SY278 @ SV257 @ SV77 ) ) @ SV257 ) )
| ( subset @ SV77 @ SV257 ) )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1750]) ).
thf(1848,plain,
! [SV77: $i,SV258: $i] :
( ( ( relation @ SV258 )
= $false )
| ( ( ~ ( subset @ SV77 @ SV258 )
| ! [SY596: $i,SY597: $i] :
( ~ ( in @ ( ordered_pair @ SY596 @ SY597 ) @ SV77 )
| ( in @ ( ordered_pair @ SY596 @ SY597 ) @ SV258 ) ) )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1751]) ).
thf(1849,plain,
! [SV171: $i,SV216: $i] :
( ( ( in @ ( sK16_C @ SV216 @ SV171 ) @ SV171 )
= $true )
| ( ( subset @ SV171 @ SV216 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1752]) ).
thf(1850,plain,
! [SV171: $i,SV216: $i] :
( ( ( ~ ( in @ ( sK16_C @ SV216 @ SV171 ) @ SV216 ) )
= $true )
| ( ( subset @ SV171 @ SV216 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1753]) ).
thf(1851,plain,
! [SV217: $i,SV172: $i,SV276: $i] :
( ( ( ~ ( in @ SV276 @ SV172 ) )
= $true )
| ( ( in @ SV276 @ SV217 )
= $true )
| ( ( subset @ SV172 @ SV217 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1754]) ).
thf(1852,plain,
! [SV78: $i,SV218: $i,SV235: $i] :
( ( ( ~ ( ~ ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV78 )
| ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV218 )
| ~ ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV235 ) ) )
= $false )
| ( ( SV235
= ( set_difference @ SV78 @ SV218 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1755]) ).
thf(1853,plain,
! [SV78: $i,SV218: $i,SV235: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV78 )
| ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV235 ) )
| ~ ( ~ ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV218 )
| ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV235 ) ) ) )
= $false )
| ( ( SV235
= ( set_difference @ SV78 @ SV218 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1755]) ).
thf(1854,plain,
! [SV236: $i,SV219: $i,SV78: $i] :
( ( ( ~ ! [SY580: $i] :
( ~ ( in @ SY580 @ SV78 )
| ( in @ SY580 @ SV219 )
| ( in @ SY580 @ SV236 ) )
| ~ ~ ( ~ ! [SY581: $i] :
( ~ ( in @ SY581 @ SV236 )
| ( in @ SY581 @ SV78 ) )
| ~ ! [SY582: $i] :
( ~ ( in @ SY582 @ SV236 )
| ~ ( in @ SY582 @ SV219 ) ) ) )
= $false )
| ( ( SV236
= ( set_difference @ SV78 @ SV219 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1756]) ).
thf(1855,plain,
! [SV175: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK36_B @ SV175 ) @ ( sK37_SY285 @ SV175 ) ) @ SV175 )
| ~ ( in @ ( ordered_pair @ ( sK37_SY285 @ SV175 ) @ ( sK36_B @ SV175 ) ) @ SV175 ) ) )
= $false )
| ( ( antisymmetric @ SV175 )
= $true )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1757]) ).
thf(1856,plain,
! [SV175: $i] :
( ( ( ~ ( ( ( sK36_B @ SV175 )
!= ( sK37_SY285 @ SV175 ) ) ) )
= $false )
| ( ( antisymmetric @ SV175 )
= $true )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1757]) ).
thf(1857,plain,
! [SV176: $i,SV286: $i] :
( ( ( ! [SY611: $i] :
( ~ ( in @ ( ordered_pair @ SV286 @ SY611 ) @ SV176 )
| ~ ( in @ ( ordered_pair @ SY611 @ SV286 ) @ SV176 )
| ( SV286 = SY611 ) ) )
= $true )
| ( ( antisymmetric @ SV176 )
= $false )
| ( ( relation @ SV176 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1758]) ).
thf(1858,plain,
! [SV177: $i,SV222: $i] :
( ( ( subset @ SV222 @ SV177 )
= $false )
| ( ( subset @ SV177 @ SV222 )
= $false )
| ( ( SV177 = SV222 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1759]) ).
thf(1859,plain,
! [SV277: $i,SV259: $i] :
( ( ( SV259 != SV277 )
= $true )
| ( ( subset @ SV259 @ SV277 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1760]) ).
thf(1860,plain,
! [SV278: $i,SV260: $i] :
( ( ( SV260 != SV278 )
= $true )
| ( ( subset @ SV278 @ SV260 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1761]) ).
thf(1861,plain,
! [SV178: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK38_B @ SV178 ) @ ( sK39_SY286 @ SV178 ) ) @ SV178 )
| ~ ( in @ ( ordered_pair @ ( sK39_SY286 @ SV178 ) @ ( sK40_SY288 @ SV178 ) ) @ SV178 ) ) )
= $false )
| ( ( transitive @ SV178 )
= $true )
| ( ( relation @ SV178 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1762]) ).
thf(1862,plain,
! [SV178: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK38_B @ SV178 ) @ ( sK40_SY288 @ SV178 ) ) @ SV178 ) )
= $false )
| ( ( transitive @ SV178 )
= $true )
| ( ( relation @ SV178 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1762]) ).
thf(1863,plain,
! [SV179: $i,SV287: $i] :
( ( ( ! [SY612: $i,SY613: $i] :
( ~ ( in @ ( ordered_pair @ SV287 @ SY612 ) @ SV179 )
| ~ ( in @ ( ordered_pair @ SY612 @ SY613 ) @ SV179 )
| ( in @ ( ordered_pair @ SV287 @ SY613 ) @ SV179 ) ) )
= $true )
| ( ( transitive @ SV179 )
= $false )
| ( ( relation @ SV179 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1763]) ).
thf(1864,plain,
! [SV79: $i,SV124: $i] :
( ( ( in @ ( sK5_C @ SV124 @ SV79 ) @ SV124 )
= $false )
| ( ( in @ ( sK5_C @ SV124 @ SV79 ) @ SV79 )
= $false )
| ( ( SV79 = SV124 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1764]) ).
thf(1865,plain,
! [SV261: $i] :
( ( ( empty @ SV261 )
= $false )
| ( ( epsilon_connected @ SV261 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1765]) ).
thf(1866,plain,
! [SV262: $i] :
( ( ( empty @ SV262 )
= $false )
| ( ( epsilon_transitive @ SV262 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1766]) ).
thf(1867,plain,
! [SV183: $i] :
( ( ( ~ ( ordinal @ ( sK50_B @ SV183 ) ) )
= $false )
| ( ( being_limit_ordinal @ SV183 )
= $true )
| ( ( ordinal @ SV183 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1767]) ).
thf(1868,plain,
! [SV183: $i] :
( ( ( SV183
!= ( succ @ ( sK50_B @ SV183 ) ) )
= $false )
| ( ( being_limit_ordinal @ SV183 )
= $true )
| ( ( ordinal @ SV183 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1767]) ).
thf(1869,plain,
! [SV279: $i,SV184: $i] :
( ( ( SV184
!= ( succ @ SV279 ) )
= $true )
| ( ( ~ ( ordinal @ SV279 ) )
= $true )
| ( ( ~ ( being_limit_ordinal @ SV184 ) )
= $true )
| ( ( ordinal @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1768]) ).
thf(1870,plain,
! [SV80: $i,SV125: $i,SV237: $i,SV263: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
!= SV237 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
!= SV80 ) )
| ~ ( ~ ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
!= SV125 ) ) ) )
| ~ ( ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
= SV237 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
= SV80 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
= SV125 ) ) )
= $false )
| ( ( SV263
= ( unordered_triple @ SV80 @ SV125 @ SV237 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1769]) ).
thf(1871,plain,
! [SV238: $i,SV125: $i,SV80: $i,SV264: $i] :
( ( ( SV264
= ( unordered_triple @ SV80 @ SV125 @ SV238 ) )
= $false )
| ( ( ~ ( ~ ! [SY600: $i] :
( ~ ( in @ SY600 @ SV264 )
| ( SY600 = SV238 )
| ( SY600 = SV80 )
| ( SY600 = SV125 ) )
| ~ ~ ( ~ ! [SY601: $i] :
( ( SY601 != SV238 )
| ( in @ SY601 @ SV264 ) )
| ~ ~ ( ~ ! [SY602: $i] :
( ( SY602 != SV80 )
| ( in @ SY602 @ SV264 ) )
| ~ ! [SY603: $i] :
( ( SY603 != SV125 )
| ( in @ SY603 @ SV264 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1770]) ).
thf(1872,plain,
! [SV192: $i,SV225: $i,SV61: $i] :
( ( ( ~ ( in @ SV61 @ SV225 ) )
= $true )
| ( ( ~ ( in @ SV61 @ ( cartesian_product2 @ SV192 @ SV192 ) ) )
= $true )
| ( ( in @ SV61 @ ( relation_restriction @ SV225 @ SV192 ) )
= $true )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1771]) ).
thf(1873,plain,
! [SV265: $i,SV61: $i,SV280: $i] :
( ( ( ~ ( relation @ SV280 ) )
= $true )
| ( ( ~ ( in @ SV61 @ ( relation_restriction @ SV280 @ SV265 ) )
| ( in @ SV61 @ SV280 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1772]) ).
thf(1874,plain,
! [SV266: $i,SV61: $i,SV281: $i] :
( ( ( ~ ( relation @ SV281 ) )
= $true )
| ( ( ~ ( in @ SV61 @ ( relation_restriction @ SV281 @ SV266 ) )
| ( in @ SV61 @ ( cartesian_product2 @ SV266 @ SV266 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1773]) ).
thf(1875,plain,
! [SV144: $i] :
( ( ( ordinal @ ( sK33_B @ SV144 ) )
= $true )
| ( ( being_limit_ordinal @ SV144 )
= $true )
| ( ( ordinal @ SV144 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1774]) ).
thf(1876,plain,
! [SV144: $i] :
( ( ( ~ ( ~ ( in @ ( sK33_B @ SV144 ) @ SV144 )
| ~ ~ ( in @ ( succ @ ( sK33_B @ SV144 ) ) @ SV144 ) ) )
= $true )
| ( ( being_limit_ordinal @ SV144 )
= $true )
| ( ( ordinal @ SV144 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1775]) ).
thf(1877,plain,
! [SV145: $i,SV282: $i] :
( ( ( ~ ( ordinal @ SV282 ) )
= $true )
| ( ( ~ ( in @ SV282 @ SV145 )
| ( in @ ( succ @ SV282 ) @ SV145 ) )
= $true )
| ( ( being_limit_ordinal @ SV145 )
= $false )
| ( ( ordinal @ SV145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1776]) ).
thf(1878,plain,
! [SV239: $i,SV62: $i] :
( ( ( ~ ( in @ SV62 @ SV239 ) )
= $true )
| ( ( ordinal_subset @ ( succ @ SV62 ) @ SV239 )
= $true )
| ( ( ordinal @ SV239 )
= $false )
| ( ( ordinal @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1777]) ).
thf(1879,plain,
! [SV240: $i,SV62: $i] :
( ( ( ~ ( ordinal_subset @ ( succ @ SV62 ) @ SV240 ) )
= $true )
| ( ( in @ SV62 @ SV240 )
= $true )
| ( ( ordinal @ SV240 )
= $false )
| ( ( ordinal @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1778]) ).
thf(1880,plain,
! [SV120: $i,SV63: $i,SV267: $i] :
( ( ( ! [SY606: $i] :
( ( SV267 != SY606 )
| ~ ( ordinal @ SY606 )
| ~ ( in @ SY606 @ SV63 ) ) )
= $true )
| ( ( ~ ( in @ SV267 @ ( succ @ SV120 ) ) )
= $true )
| ( ( in @ SV267 @ ( sK52_C @ SV120 @ SV63 ) )
= $true )
| ( ( ordinal @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1779]) ).
thf(1881,plain,
! [SV63: $i,SV120: $i] :
( ( ( ! [SY473: $i] :
( ~ ( in @ SY473 @ ( sK52_C @ SV120 @ SV63 ) )
| ~ ( ~ ~ ( ( SY473
!= ( sK53_E @ SY473 @ SV120 @ SV63 ) )
| ~ ( ordinal @ ( sK53_E @ SY473 @ SV120 @ SV63 ) ) )
| ~ ( in @ ( sK53_E @ SY473 @ SV120 @ SV63 ) @ SV63 ) ) ) )
= $true )
| ( ( ordinal @ SV120 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1780]) ).
thf(1882,plain,
! [SV63: $i,SV120: $i] :
( ( ( ! [SY474: $i] :
( ~ ( in @ SY474 @ ( sK52_C @ SV120 @ SV63 ) )
| ( in @ SY474 @ ( succ @ SV120 ) ) ) )
= $true )
| ( ( ordinal @ SV120 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1781]) ).
thf(1883,plain,
! [SV65: $i,SV226: $i,SV195: $i] :
( ( ( in @ SV195 @ SV226 )
= $false )
| ( ( in @ SV65 @ SV226 )
= $false )
| ( ( subset @ ( unordered_pair @ SV65 @ SV195 ) @ SV226 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1784]) ).
thf(1884,plain,
! [SV283: $i,SV270: $i,SV65: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV65 @ SV270 ) @ SV283 ) )
= $true )
| ( ( in @ SV65 @ SV283 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1785]) ).
thf(1885,plain,
! [SV284: $i,SV271: $i,SV65: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV65 @ SV271 ) @ SV284 ) )
= $true )
| ( ( in @ SV271 @ SV284 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1786]) ).
thf(1886,plain,
! [SV288: $i] :
( ( ~ ( ordinal @ SV288 )
| ~ ( empty @ ( succ @ SV288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1787]) ).
thf(1887,plain,
! [SV289: $i] :
( ( ~ ( ordinal @ SV289 )
| ( epsilon_transitive @ ( succ @ SV289 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1788]) ).
thf(1888,plain,
! [SV148: $i,SV196: $i] :
( ( ( ! [SY539: $i] :
( ~ ( in @ ( sK13_C @ SV196 @ SV148 ) @ SY539 )
| ~ ( in @ SY539 @ SV148 ) ) )
= $true )
| ( ( ~ ( in @ ( sK13_C @ SV196 @ SV148 ) @ SV196 ) )
= $true )
| ( ( SV196
= ( union @ SV148 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1790]) ).
thf(1889,plain,
! [SV148: $i,SV196: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_C @ SV196 @ SV148 ) @ ( sK14_SY277 @ SV196 @ SV148 ) )
| ~ ( in @ ( sK14_SY277 @ SV196 @ SV148 ) @ SV148 ) ) )
= $true )
| ( ( in @ ( sK13_C @ SV196 @ SV148 ) @ SV196 )
= $true )
| ( ( SV196
= ( union @ SV148 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1791]) ).
thf(1890,plain,
! [SV197: $i,SV149: $i] :
( ( ( ! [SY540: $i] :
( ! [SY498: $i] :
( ~ ( in @ SY540 @ SY498 )
| ~ ( in @ SY498 @ SV149 ) )
| ( in @ SY540 @ SV197 ) ) )
= $true )
| ( ( SV197
= ( union @ SV149 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1792]) ).
thf(1891,plain,
! [SV149: $i,SV197: $i] :
( ( ( ! [SY542: $i] :
( ~ ( in @ SY542 @ SV197 )
| ~ ( ~ ( in @ SY542 @ ( sK12_D @ SY542 @ SV197 @ SV149 ) )
| ~ ( in @ ( sK12_D @ SY542 @ SV197 @ SV149 ) @ SV149 ) ) ) )
= $true )
| ( ( SV197
= ( union @ SV149 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1793]) ).
thf(1892,plain,
! [SV290: $i,SV285: $i,SV150: $i] :
( ( ( ( sK31_B @ SV150 )
!= ( ordered_pair @ SV285 @ SV290 ) )
= $true )
| ( ( relation @ SV150 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1794]) ).
thf(1893,plain,
! [SV152: $i] :
( ( ( ~ ( ( ( sK19_B @ SV152 )
!= ( sK20_SY279 @ SV152 ) ) ) )
= $false )
| ( ( epsilon_connected @ SV152 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1796]) ).
thf(1894,plain,
! [SV152: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_B @ SV152 ) @ SV152 )
| ~ ( in @ ( sK20_SY279 @ SV152 ) @ SV152 ) )
| ~ ~ ( in @ ( sK19_B @ SV152 ) @ ( sK20_SY279 @ SV152 ) ) ) )
= $false )
| ( ( epsilon_connected @ SV152 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1796]) ).
thf(1895,plain,
! [SV153: $i,SV272: $i,SV245: $i] :
( ( ( SV245 = SV272 )
= $true )
| ( ( ~ ( in @ SV245 @ SV153 )
| ~ ( in @ SV272 @ SV153 )
| ( in @ SV245 @ SV272 ) )
= $true )
| ( ( in @ SV272 @ SV245 )
= $true )
| ( ( epsilon_connected @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1798]) ).
thf(1896,plain,
! [SV273: $i,SV246: $i] :
( ( ( proper_subset @ SV246 @ SV273 )
= $false )
| ( ( SV246 != SV273 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1799]) ).
thf(1897,plain,
! [SV274: $i,SV247: $i] :
( ( ( proper_subset @ SV247 @ SV274 )
= $false )
| ( ( subset @ SV247 @ SV274 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1800]) ).
thf(1898,plain,
! [SV155: $i] :
( ( ( ~ ( reflexive @ SV155 )
| ~ ( transitive @ SV155 ) )
= $true )
| ( ( ~ ( antisymmetric @ SV155 ) )
= $true )
| ( ( ~ ( connected @ SV155 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV155 ) )
= $true )
| ( ( well_ordering @ SV155 )
= $true )
| ( ( relation @ SV155 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1801]) ).
thf(1899,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1802]) ).
thf(1900,plain,
! [SV291: $i] :
( ( ~ ( relation @ SV291 )
| ~ ( well_ordering @ SV291 )
| ( connected @ SV291 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1803]) ).
thf(1901,plain,
! [SV248: $i] :
( ( ( ~ ( well_ordering @ SV248 ) )
= $true )
| ( ( well_founded_relation @ SV248 )
= $true )
| ( ( relation @ SV248 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1804]) ).
thf(1902,plain,
! [SV67: $i,SV121: $i,SV249: $i] :
( ( ( in @ SV249 @ ( sK4_C @ SV121 @ SV67 ) )
= $false )
| ( ( in @ SV249 @ SV121 )
= $false )
| ( ( ~ ( in @ SV67 @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1805]) ).
thf(1903,plain,
! [SV159: $i,SV200: $i,SV251: $i] :
( ( ( in @ SV251 @ SV200 )
= $false )
| ( ( in @ SV251 @ SV159 )
= $false )
| ( ( ~ ( disjoint @ SV159 @ SV200 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1808]) ).
thf(1904,plain,
! [SV160: $i,SV201: $i] :
( ( ( ( sK28_C @ SV201 @ SV160 )
!= SV160 )
= $true )
| ( ( ~ ( in @ ( sK28_C @ SV201 @ SV160 ) @ SV201 ) )
= $true )
| ( ( SV201
= ( singleton @ SV160 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1809]) ).
thf(1905,plain,
! [SV160: $i,SV201: $i] :
( ( ( ( sK28_C @ SV201 @ SV160 )
= SV160 )
= $true )
| ( ( in @ ( sK28_C @ SV201 @ SV160 ) @ SV201 )
= $true )
| ( ( SV201
= ( singleton @ SV160 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1810]) ).
thf(1906,plain,
! [SV202: $i,SV161: $i] :
( ( ( ! [SY544: $i] :
( ( SY544 != SV161 )
| ( in @ SY544 @ SV202 ) ) )
= $true )
| ( ( SV202
= ( singleton @ SV161 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1811]) ).
thf(1907,plain,
! [SV161: $i,SV202: $i] :
( ( ( ! [SY545: $i] :
( ~ ( in @ SY545 @ SV202 )
| ( SY545 = SV161 ) ) )
= $true )
| ( ( SV202
= ( singleton @ SV161 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1812]) ).
thf(1908,plain,
( ( empty @ sK7_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1813]) ).
thf(1909,plain,
! [SV122: $i,SV68: $i] :
( ( ( subset @ SV68 @ SV122 )
= $false )
| ( ( SV68 = empty_set )
= $true )
| ( ( ordinal @ ( sK35_C @ SV122 @ SV68 ) )
= $true )
| ( ( ordinal @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1815]) ).
thf(1910,plain,
! [SV122: $i,SV68: $i] :
( ( ( ~ ! [SY476: $i] :
( ~ ( ordinal @ SY476 )
| ~ ( in @ SY476 @ SV68 )
| ( ordinal_subset @ ( sK35_C @ SV122 @ SV68 ) @ SY476 ) ) )
= $false )
| ( ( ( SV68 = empty_set )
| ~ ( subset @ SV68 @ SV122 ) )
= $true )
| ( ( ordinal @ SV122 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1816]) ).
thf(1911,plain,
! [SV68: $i,SV122: $i] :
( ( ( ~ ( in @ ( sK35_C @ SV122 @ SV68 ) @ SV68 ) )
= $false )
| ( ( ( SV68 = empty_set )
| ~ ( subset @ SV68 @ SV122 ) )
= $true )
| ( ( ordinal @ SV122 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1816]) ).
thf(1912,plain,
! [SV69: $i,SV203: $i,SV227: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV227 )
| ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV69 ) )
| ~ ( ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV227 )
| ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV203 ) ) ) )
= $true )
| ( ( SV227
= ( set_union2 @ SV69 @ SV203 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1817]) ).
thf(1913,plain,
! [SV69: $i,SV203: $i,SV227: $i] :
( ( ( ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV227 )
| ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV69 )
| ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV203 ) )
= $true )
| ( ( SV227
= ( set_union2 @ SV69 @ SV203 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1818]) ).
thf(1914,plain,
! [SV204: $i,SV69: $i,SV228: $i] :
( ( ( ~ ! [SY571: $i] :
( ~ ( in @ SY571 @ SV228 )
| ( in @ SY571 @ SV69 )
| ( in @ SY571 @ SV204 ) ) )
= $false )
| ( ( SV228
= ( set_union2 @ SV69 @ SV204 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1819]) ).
thf(1915,plain,
! [SV204: $i,SV228: $i,SV69: $i] :
( ( ( ~ ~ ( ~ ! [SY572: $i] :
( ~ ( in @ SY572 @ SV69 )
| ( in @ SY572 @ SV228 ) )
| ~ ! [SY573: $i] :
( ~ ( in @ SY573 @ SV204 )
| ( in @ SY573 @ SV228 ) ) ) )
= $false )
| ( ( SV228
= ( set_union2 @ SV69 @ SV204 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1819]) ).
thf(1916,plain,
! [SV162: $i,SV205: $i] :
( ( ( ~ ( in @ ( sK26_C @ SV205 @ SV162 ) @ SV205 ) )
= $true )
| ( ( ~ ( subset @ ( sK26_C @ SV205 @ SV162 ) @ SV162 ) )
= $true )
| ( ( SV205
= ( powerset @ SV162 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1820]) ).
thf(1917,plain,
! [SV162: $i,SV205: $i] :
( ( ( in @ ( sK26_C @ SV205 @ SV162 ) @ SV205 )
= $true )
| ( ( subset @ ( sK26_C @ SV205 @ SV162 ) @ SV162 )
= $true )
| ( ( SV205
= ( powerset @ SV162 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1821]) ).
thf(1918,plain,
! [SV163: $i,SV206: $i] :
( ( ( ! [SY551: $i] :
( ~ ( in @ SY551 @ SV206 )
| ( subset @ SY551 @ SV163 ) ) )
= $true )
| ( ( SV206
= ( powerset @ SV163 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1822]) ).
thf(1919,plain,
! [SV206: $i,SV163: $i] :
( ( ( ! [SY552: $i] :
( ~ ( subset @ SY552 @ SV163 )
| ( in @ SY552 @ SV206 ) ) )
= $true )
| ( ( SV206
= ( powerset @ SV163 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1823]) ).
thf(1920,plain,
! [SV70: $i,SV207: $i,SV229: $i] :
( ( ( ~ ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV70 )
| ~ ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV207 )
| ~ ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV229 ) )
= $true )
| ( ( SV229
= ( set_intersection2 @ SV70 @ SV207 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1824]) ).
thf(1921,plain,
! [SV70: $i,SV207: $i,SV229: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV70 )
| ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV229 ) )
| ~ ( ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV207 )
| ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV229 ) ) ) )
= $true )
| ( ( SV229
= ( set_intersection2 @ SV70 @ SV207 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1825]) ).
thf(1922,plain,
! [SV230: $i,SV208: $i,SV70: $i] :
( ( ( ~ ! [SY574: $i] :
( ~ ( in @ SY574 @ SV70 )
| ~ ( in @ SY574 @ SV208 )
| ( in @ SY574 @ SV230 ) ) )
= $false )
| ( ( SV230
= ( set_intersection2 @ SV70 @ SV208 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1826]) ).
thf(1923,plain,
! [SV208: $i,SV70: $i,SV230: $i] :
( ( ( ~ ~ ( ~ ! [SY575: $i] :
( ~ ( in @ SY575 @ SV230 )
| ( in @ SY575 @ SV70 ) )
| ~ ! [SY576: $i] :
( ~ ( in @ SY576 @ SV230 )
| ( in @ SY576 @ SV208 ) ) ) )
= $false )
| ( ( SV230
= ( set_intersection2 @ SV70 @ SV208 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1826]) ).
thf(1924,plain,
! [SV209: $i,SV165: $i] :
( ( ( ~ ( ordinal_subset @ SV165 @ SV209 ) )
= $true )
| ( ( subset @ SV165 @ SV209 )
= $true )
| ( ( ordinal @ SV165 )
= $false )
| ( ( ordinal @ SV209 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1829]) ).
thf(1925,plain,
! [SV210: $i,SV166: $i] :
( ( ( ~ ( subset @ SV166 @ SV210 ) )
= $true )
| ( ( ordinal_subset @ SV166 @ SV210 )
= $true )
| ( ( ordinal @ SV166 )
= $false )
| ( ( ordinal @ SV210 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1830]) ).
thf(1926,plain,
! [SV135: $i,SV71: $i,SV292: $i] :
( ( ( ~ ( ordinal @ SV292 )
| ~ ( in @ SV292 @ SV71 )
| ( ordinal_subset @ ( sK54_B @ SV71 ) @ SV292 ) )
= $true )
| ( ( in @ SV135 @ SV71 )
= $false )
| ( ( ordinal @ SV135 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1831]) ).
thf(1927,plain,
! [SV135: $i,SV71: $i] :
( ( ( ~ ( in @ ( sK54_B @ SV71 ) @ SV71 )
| ~ ( ordinal @ ( sK54_B @ SV71 ) ) )
= $false )
| ( ( in @ SV135 @ SV71 )
= $false )
| ( ( ordinal @ SV135 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1832]) ).
thf(1928,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( sK44_C @ SV123 @ SV72 )
!= ( sK45_SY295 @ SV123 @ SV72 ) )
| ~ ~ ( ~ ~ ( ( ( sK45_SY295 @ SV123 @ SV72 )
!= ( sK48_SY300 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 ) ) )
| ( ( sK44_C @ SV123 @ SV72 )
!= ( sK46_SY299 @ SV123 @ SV72 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1833]) ).
thf(1929,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( sK46_SY299 @ SV123 @ SV72 )
!= ( sK47_SY303 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1833]) ).
thf(1930,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1834]) ).
thf(1931,plain,
! [SV73: $i,SV254: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK23_C @ SV254 @ SV73 ) @ ( sK24_SY280 @ SV254 @ SV73 ) ) @ SV73 )
| ~ ( in @ ( ordered_pair @ ( sK23_C @ SV254 @ SV73 ) @ ( sK24_SY280 @ SV254 @ SV73 ) ) @ SV254 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK23_C @ SV254 @ SV73 ) @ ( sK24_SY280 @ SV254 @ SV73 ) ) @ SV73 )
| ( in @ ( ordered_pair @ ( sK23_C @ SV254 @ SV73 ) @ ( sK24_SY280 @ SV254 @ SV73 ) ) @ SV254 ) ) ) )
= $true )
| ( ( SV73 = SV254 )
= $true )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1835]) ).
thf(1932,plain,
! [SV255: $i,SV73: $i] :
( ( ( SV73 != SV255 )
= $true )
| ( ( ~ ( ~ ! [SY592: $i,SY593: $i] :
( ~ ( in @ ( ordered_pair @ SY592 @ SY593 ) @ SV73 )
| ( in @ ( ordered_pair @ SY592 @ SY593 ) @ SV255 ) )
| ~ ! [SY594: $i,SY595: $i] :
( ~ ( in @ ( ordered_pair @ SY594 @ SY595 ) @ SV255 )
| ( in @ ( ordered_pair @ SY594 @ SY595 ) @ SV73 ) ) ) )
= $true )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1836]) ).
thf(1933,plain,
! [SV74: $i,SV211: $i,SV231: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK22_D @ SV231 @ SV211 @ SV74 ) @ SV231 )
| ( ( sK22_D @ SV231 @ SV211 @ SV74 )
!= SV74 ) )
| ~ ( ~ ( in @ ( sK22_D @ SV231 @ SV211 @ SV74 ) @ SV231 )
| ( ( sK22_D @ SV231 @ SV211 @ SV74 )
!= SV211 ) ) ) )
= $true )
| ( ( SV231
= ( unordered_pair @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1837]) ).
thf(1934,plain,
! [SV74: $i,SV211: $i,SV231: $i] :
( ( ( ( in @ ( sK22_D @ SV231 @ SV211 @ SV74 ) @ SV231 )
| ( ( sK22_D @ SV231 @ SV211 @ SV74 )
= SV74 )
| ( ( sK22_D @ SV231 @ SV211 @ SV74 )
= SV211 ) )
= $true )
| ( ( SV231
= ( unordered_pair @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1838]) ).
thf(1935,plain,
! [SV212: $i,SV74: $i,SV232: $i] :
( ( ( ~ ! [SY577: $i] :
( ~ ( in @ SY577 @ SV232 )
| ( SY577 = SV74 )
| ( SY577 = SV212 ) ) )
= $false )
| ( ( SV232
= ( unordered_pair @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1839]) ).
thf(1936,plain,
! [SV212: $i,SV232: $i,SV74: $i] :
( ( ( ~ ~ ( ~ ! [SY578: $i] :
( ( SY578 != SV74 )
| ( in @ SY578 @ SV232 ) )
| ~ ! [SY579: $i] :
( ( SY579 != SV212 )
| ( in @ SY579 @ SV232 ) ) ) )
= $false )
| ( ( SV232
= ( unordered_pair @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1839]) ).
thf(1937,plain,
! [SV75: $i,SV275: $i] :
( ( ( ~ ! [SY609: $i] :
( ~ ( subset @ SY609 @ SV275 )
| ( in @ SY609 @ ( sK3_SY270 @ SV275 @ SV75 ) ) )
| ~ ( in @ ( sK3_SY270 @ SV275 @ SV75 ) @ ( sK2_B @ SV75 ) ) )
= $false )
| ( ( ~ ( in @ SV275 @ ( sK2_B @ SV75 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1842]) ).
thf(1938,plain,
! [SV75: $i] :
( ( ! [SY431: $i,SY432: $i] :
( ~ ( in @ SY431 @ ( sK2_B @ SV75 ) )
| ~ ( subset @ SY432 @ SY431 )
| ( in @ SY432 @ ( sK2_B @ SV75 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1843]) ).
thf(1939,plain,
! [SV75: $i] :
( ( in @ SV75 @ ( sK2_B @ SV75 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1844]) ).
thf(1940,plain,
! [SV214: $i,SV233: $i,SV76: $i] :
( ( ( in @ SV76 @ ( relation_field @ ( relation_restriction @ SV233 @ SV214 ) ) )
= $false )
| ( ( in @ SV76 @ ( relation_field @ SV233 ) )
= $true )
| ( ( relation @ SV233 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1845]) ).
thf(1941,plain,
! [SV215: $i,SV234: $i,SV76: $i] :
( ( ( in @ SV76 @ ( relation_field @ ( relation_restriction @ SV234 @ SV215 ) ) )
= $false )
| ( ( in @ SV76 @ SV215 )
= $true )
| ( ( relation @ SV234 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1846]) ).
thf(1942,plain,
! [SV77: $i,SV257: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_C @ SV257 @ SV77 ) @ ( sK18_SY278 @ SV257 @ SV77 ) ) @ SV77 )
| ~ ~ ( in @ ( ordered_pair @ ( sK17_C @ SV257 @ SV77 ) @ ( sK18_SY278 @ SV257 @ SV77 ) ) @ SV257 ) ) )
= $true )
| ( ( subset @ SV77 @ SV257 )
= $true )
| ( ( relation @ SV257 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1847]) ).
thf(1943,plain,
! [SV258: $i,SV77: $i] :
( ( ( ~ ( subset @ SV77 @ SV258 ) )
= $true )
| ( ( ! [SY596: $i,SY597: $i] :
( ~ ( in @ ( ordered_pair @ SY596 @ SY597 ) @ SV77 )
| ( in @ ( ordered_pair @ SY596 @ SY597 ) @ SV258 ) ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1848]) ).
thf(1944,plain,
! [SV171: $i,SV216: $i] :
( ( ( in @ ( sK16_C @ SV216 @ SV171 ) @ SV216 )
= $false )
| ( ( subset @ SV171 @ SV216 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1850]) ).
thf(1945,plain,
! [SV217: $i,SV172: $i,SV276: $i] :
( ( ( in @ SV276 @ SV172 )
= $false )
| ( ( in @ SV276 @ SV217 )
= $true )
| ( ( subset @ SV172 @ SV217 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1851]) ).
thf(1946,plain,
! [SV78: $i,SV218: $i,SV235: $i] :
( ( ( ~ ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV78 )
| ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV218 )
| ~ ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV235 ) )
= $true )
| ( ( SV235
= ( set_difference @ SV78 @ SV218 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1852]) ).
thf(1947,plain,
! [SV78: $i,SV218: $i,SV235: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV78 )
| ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV235 ) )
| ~ ( ~ ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV218 )
| ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV235 ) ) ) )
= $true )
| ( ( SV235
= ( set_difference @ SV78 @ SV218 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1853]) ).
thf(1948,plain,
! [SV236: $i,SV219: $i,SV78: $i] :
( ( ( ~ ! [SY580: $i] :
( ~ ( in @ SY580 @ SV78 )
| ( in @ SY580 @ SV219 )
| ( in @ SY580 @ SV236 ) ) )
= $false )
| ( ( SV236
= ( set_difference @ SV78 @ SV219 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1854]) ).
thf(1949,plain,
! [SV219: $i,SV78: $i,SV236: $i] :
( ( ( ~ ~ ( ~ ! [SY581: $i] :
( ~ ( in @ SY581 @ SV236 )
| ( in @ SY581 @ SV78 ) )
| ~ ! [SY582: $i] :
( ~ ( in @ SY582 @ SV236 )
| ~ ( in @ SY582 @ SV219 ) ) ) )
= $false )
| ( ( SV236
= ( set_difference @ SV78 @ SV219 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1854]) ).
thf(1950,plain,
! [SV175: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK36_B @ SV175 ) @ ( sK37_SY285 @ SV175 ) ) @ SV175 )
| ~ ( in @ ( ordered_pair @ ( sK37_SY285 @ SV175 ) @ ( sK36_B @ SV175 ) ) @ SV175 ) ) )
= $true )
| ( ( antisymmetric @ SV175 )
= $true )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1855]) ).
thf(1951,plain,
! [SV175: $i] :
( ( ( ( sK36_B @ SV175 )
!= ( sK37_SY285 @ SV175 ) )
= $true )
| ( ( antisymmetric @ SV175 )
= $true )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1856]) ).
thf(1952,plain,
! [SV176: $i,SV293: $i,SV286: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV286 @ SV293 ) @ SV176 )
| ~ ( in @ ( ordered_pair @ SV293 @ SV286 ) @ SV176 )
| ( SV286 = SV293 ) )
= $true )
| ( ( antisymmetric @ SV176 )
= $false )
| ( ( relation @ SV176 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1857]) ).
thf(1953,plain,
! [SV277: $i,SV259: $i] :
( ( ( SV259 = SV277 )
= $false )
| ( ( subset @ SV259 @ SV277 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1859]) ).
thf(1954,plain,
! [SV278: $i,SV260: $i] :
( ( ( SV260 = SV278 )
= $false )
| ( ( subset @ SV278 @ SV260 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1860]) ).
thf(1955,plain,
! [SV178: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK38_B @ SV178 ) @ ( sK39_SY286 @ SV178 ) ) @ SV178 )
| ~ ( in @ ( ordered_pair @ ( sK39_SY286 @ SV178 ) @ ( sK40_SY288 @ SV178 ) ) @ SV178 ) ) )
= $true )
| ( ( transitive @ SV178 )
= $true )
| ( ( relation @ SV178 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1861]) ).
thf(1956,plain,
! [SV178: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK38_B @ SV178 ) @ ( sK40_SY288 @ SV178 ) ) @ SV178 ) )
= $true )
| ( ( transitive @ SV178 )
= $true )
| ( ( relation @ SV178 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1862]) ).
thf(1957,plain,
! [SV179: $i,SV294: $i,SV287: $i] :
( ( ( ! [SY614: $i] :
( ~ ( in @ ( ordered_pair @ SV287 @ SV294 ) @ SV179 )
| ~ ( in @ ( ordered_pair @ SV294 @ SY614 ) @ SV179 )
| ( in @ ( ordered_pair @ SV287 @ SY614 ) @ SV179 ) ) )
= $true )
| ( ( transitive @ SV179 )
= $false )
| ( ( relation @ SV179 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1863]) ).
thf(1958,plain,
! [SV183: $i] :
( ( ( ordinal @ ( sK50_B @ SV183 ) )
= $true )
| ( ( being_limit_ordinal @ SV183 )
= $true )
| ( ( ordinal @ SV183 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1867]) ).
thf(1959,plain,
! [SV183: $i] :
( ( ( SV183
= ( succ @ ( sK50_B @ SV183 ) ) )
= $true )
| ( ( being_limit_ordinal @ SV183 )
= $true )
| ( ( ordinal @ SV183 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1868]) ).
thf(1960,plain,
! [SV279: $i,SV184: $i] :
( ( ( SV184
= ( succ @ SV279 ) )
= $false )
| ( ( ~ ( ordinal @ SV279 ) )
= $true )
| ( ( ~ ( being_limit_ordinal @ SV184 ) )
= $true )
| ( ( ordinal @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1869]) ).
thf(1961,plain,
! [SV80: $i,SV125: $i,SV237: $i,SV263: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
!= SV237 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
!= SV80 ) )
| ~ ( ~ ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
!= SV125 ) ) ) ) )
= $false )
| ( ( SV263
= ( unordered_triple @ SV80 @ SV125 @ SV237 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1870]) ).
thf(1962,plain,
! [SV80: $i,SV125: $i,SV237: $i,SV263: $i] :
( ( ( ~ ( ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
= SV237 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
= SV80 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
= SV125 ) ) )
= $false )
| ( ( SV263
= ( unordered_triple @ SV80 @ SV125 @ SV237 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1870]) ).
thf(1963,plain,
! [SV125: $i,SV80: $i,SV238: $i,SV264: $i] :
( ( ( ~ ! [SY600: $i] :
( ~ ( in @ SY600 @ SV264 )
| ( SY600 = SV238 )
| ( SY600 = SV80 )
| ( SY600 = SV125 ) )
| ~ ~ ( ~ ! [SY601: $i] :
( ( SY601 != SV238 )
| ( in @ SY601 @ SV264 ) )
| ~ ~ ( ~ ! [SY602: $i] :
( ( SY602 != SV80 )
| ( in @ SY602 @ SV264 ) )
| ~ ! [SY603: $i] :
( ( SY603 != SV125 )
| ( in @ SY603 @ SV264 ) ) ) ) )
= $false )
| ( ( SV264
= ( unordered_triple @ SV80 @ SV125 @ SV238 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1871]) ).
thf(1964,plain,
! [SV192: $i,SV225: $i,SV61: $i] :
( ( ( in @ SV61 @ SV225 )
= $false )
| ( ( ~ ( in @ SV61 @ ( cartesian_product2 @ SV192 @ SV192 ) ) )
= $true )
| ( ( in @ SV61 @ ( relation_restriction @ SV225 @ SV192 ) )
= $true )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1872]) ).
thf(1965,plain,
! [SV265: $i,SV61: $i,SV280: $i] :
( ( ( relation @ SV280 )
= $false )
| ( ( ~ ( in @ SV61 @ ( relation_restriction @ SV280 @ SV265 ) )
| ( in @ SV61 @ SV280 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1873]) ).
thf(1966,plain,
! [SV266: $i,SV61: $i,SV281: $i] :
( ( ( relation @ SV281 )
= $false )
| ( ( ~ ( in @ SV61 @ ( relation_restriction @ SV281 @ SV266 ) )
| ( in @ SV61 @ ( cartesian_product2 @ SV266 @ SV266 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1874]) ).
thf(1967,plain,
! [SV144: $i] :
( ( ( ~ ( in @ ( sK33_B @ SV144 ) @ SV144 )
| ~ ~ ( in @ ( succ @ ( sK33_B @ SV144 ) ) @ SV144 ) )
= $false )
| ( ( being_limit_ordinal @ SV144 )
= $true )
| ( ( ordinal @ SV144 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1876]) ).
thf(1968,plain,
! [SV145: $i,SV282: $i] :
( ( ( ordinal @ SV282 )
= $false )
| ( ( ~ ( in @ SV282 @ SV145 )
| ( in @ ( succ @ SV282 ) @ SV145 ) )
= $true )
| ( ( being_limit_ordinal @ SV145 )
= $false )
| ( ( ordinal @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1877]) ).
thf(1969,plain,
! [SV239: $i,SV62: $i] :
( ( ( in @ SV62 @ SV239 )
= $false )
| ( ( ordinal_subset @ ( succ @ SV62 ) @ SV239 )
= $true )
| ( ( ordinal @ SV239 )
= $false )
| ( ( ordinal @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1878]) ).
thf(1970,plain,
! [SV240: $i,SV62: $i] :
( ( ( ordinal_subset @ ( succ @ SV62 ) @ SV240 )
= $false )
| ( ( in @ SV62 @ SV240 )
= $true )
| ( ( ordinal @ SV240 )
= $false )
| ( ( ordinal @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1879]) ).
thf(1971,plain,
! [SV120: $i,SV63: $i,SV295: $i,SV267: $i] :
( ( ( ( SV267 != SV295 )
| ~ ( ordinal @ SV295 )
| ~ ( in @ SV295 @ SV63 ) )
= $true )
| ( ( ~ ( in @ SV267 @ ( succ @ SV120 ) ) )
= $true )
| ( ( in @ SV267 @ ( sK52_C @ SV120 @ SV63 ) )
= $true )
| ( ( ordinal @ SV120 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1880]) ).
thf(1972,plain,
! [SV63: $i,SV120: $i,SV296: $i] :
( ( ( ~ ( in @ SV296 @ ( sK52_C @ SV120 @ SV63 ) )
| ~ ( ~ ~ ( ( SV296
!= ( sK53_E @ SV296 @ SV120 @ SV63 ) )
| ~ ( ordinal @ ( sK53_E @ SV296 @ SV120 @ SV63 ) ) )
| ~ ( in @ ( sK53_E @ SV296 @ SV120 @ SV63 ) @ SV63 ) ) )
= $true )
| ( ( ordinal @ SV120 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1881]) ).
thf(1973,plain,
! [SV63: $i,SV120: $i,SV297: $i] :
( ( ( ~ ( in @ SV297 @ ( sK52_C @ SV120 @ SV63 ) )
| ( in @ SV297 @ ( succ @ SV120 ) ) )
= $true )
| ( ( ordinal @ SV120 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1882]) ).
thf(1974,plain,
! [SV283: $i,SV270: $i,SV65: $i] :
( ( ( subset @ ( unordered_pair @ SV65 @ SV270 ) @ SV283 )
= $false )
| ( ( in @ SV65 @ SV283 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1884]) ).
thf(1975,plain,
! [SV284: $i,SV271: $i,SV65: $i] :
( ( ( subset @ ( unordered_pair @ SV65 @ SV271 ) @ SV284 )
= $false )
| ( ( in @ SV271 @ SV284 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1885]) ).
thf(1976,plain,
! [SV288: $i] :
( ( ( ~ ( ordinal @ SV288 ) )
= $true )
| ( ( ~ ( empty @ ( succ @ SV288 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1886]) ).
thf(1977,plain,
! [SV289: $i] :
( ( ( ~ ( ordinal @ SV289 ) )
= $true )
| ( ( epsilon_transitive @ ( succ @ SV289 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1887]) ).
thf(1978,plain,
! [SV298: $i,SV148: $i,SV196: $i] :
( ( ( ~ ( in @ ( sK13_C @ SV196 @ SV148 ) @ SV298 )
| ~ ( in @ SV298 @ SV148 ) )
= $true )
| ( ( ~ ( in @ ( sK13_C @ SV196 @ SV148 ) @ SV196 ) )
= $true )
| ( ( SV196
= ( union @ SV148 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1888]) ).
thf(1979,plain,
! [SV148: $i,SV196: $i] :
( ( ( ~ ( in @ ( sK13_C @ SV196 @ SV148 ) @ ( sK14_SY277 @ SV196 @ SV148 ) )
| ~ ( in @ ( sK14_SY277 @ SV196 @ SV148 ) @ SV148 ) )
= $false )
| ( ( in @ ( sK13_C @ SV196 @ SV148 ) @ SV196 )
= $true )
| ( ( SV196
= ( union @ SV148 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1889]) ).
thf(1980,plain,
! [SV197: $i,SV149: $i,SV299: $i] :
( ( ( ! [SY615: $i] :
( ~ ( in @ SV299 @ SY615 )
| ~ ( in @ SY615 @ SV149 ) )
| ( in @ SV299 @ SV197 ) )
= $true )
| ( ( SV197
= ( union @ SV149 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1890]) ).
thf(1981,plain,
! [SV149: $i,SV197: $i,SV300: $i] :
( ( ( ~ ( in @ SV300 @ SV197 )
| ~ ( ~ ( in @ SV300 @ ( sK12_D @ SV300 @ SV197 @ SV149 ) )
| ~ ( in @ ( sK12_D @ SV300 @ SV197 @ SV149 ) @ SV149 ) ) )
= $true )
| ( ( SV197
= ( union @ SV149 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1891]) ).
thf(1982,plain,
! [SV290: $i,SV285: $i,SV150: $i] :
( ( ( ( sK31_B @ SV150 )
= ( ordered_pair @ SV285 @ SV290 ) )
= $false )
| ( ( relation @ SV150 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1892]) ).
thf(1983,plain,
! [SV152: $i] :
( ( ( ( sK19_B @ SV152 )
!= ( sK20_SY279 @ SV152 ) )
= $true )
| ( ( epsilon_connected @ SV152 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1893]) ).
thf(1984,plain,
! [SV152: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK19_B @ SV152 ) @ SV152 )
| ~ ( in @ ( sK20_SY279 @ SV152 ) @ SV152 ) )
| ~ ~ ( in @ ( sK19_B @ SV152 ) @ ( sK20_SY279 @ SV152 ) ) ) )
= $true )
| ( ( epsilon_connected @ SV152 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1894]) ).
thf(1985,plain,
! [SV272: $i,SV153: $i,SV245: $i] :
( ( ( ~ ( in @ SV245 @ SV153 )
| ~ ( in @ SV272 @ SV153 ) )
= $true )
| ( ( in @ SV245 @ SV272 )
= $true )
| ( ( SV245 = SV272 )
= $true )
| ( ( in @ SV272 @ SV245 )
= $true )
| ( ( epsilon_connected @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1895]) ).
thf(1986,plain,
! [SV273: $i,SV246: $i] :
( ( ( SV246 = SV273 )
= $false )
| ( ( proper_subset @ SV246 @ SV273 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1896]) ).
thf(1987,plain,
! [SV155: $i] :
( ( ( ~ ( reflexive @ SV155 ) )
= $true )
| ( ( ~ ( transitive @ SV155 ) )
= $true )
| ( ( ~ ( antisymmetric @ SV155 ) )
= $true )
| ( ( ~ ( connected @ SV155 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV155 ) )
= $true )
| ( ( well_ordering @ SV155 )
= $true )
| ( ( relation @ SV155 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1898]) ).
thf(1988,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1899]) ).
thf(1989,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1899]) ).
thf(1990,plain,
! [SV291: $i] :
( ( ( ~ ( relation @ SV291 ) )
= $true )
| ( ( ~ ( well_ordering @ SV291 )
| ( connected @ SV291 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1900]) ).
thf(1991,plain,
! [SV248: $i] :
( ( ( well_ordering @ SV248 )
= $false )
| ( ( well_founded_relation @ SV248 )
= $true )
| ( ( relation @ SV248 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1901]) ).
thf(1992,plain,
! [SV249: $i,SV121: $i,SV67: $i] :
( ( ( in @ SV67 @ SV121 )
= $false )
| ( ( in @ SV249 @ SV121 )
= $false )
| ( ( in @ SV249 @ ( sK4_C @ SV121 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1902]) ).
thf(1993,plain,
! [SV251: $i,SV200: $i,SV159: $i] :
( ( ( disjoint @ SV159 @ SV200 )
= $false )
| ( ( in @ SV251 @ SV159 )
= $false )
| ( ( in @ SV251 @ SV200 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1903]) ).
thf(1994,plain,
! [SV160: $i,SV201: $i] :
( ( ( ( sK28_C @ SV201 @ SV160 )
= SV160 )
= $false )
| ( ( ~ ( in @ ( sK28_C @ SV201 @ SV160 ) @ SV201 ) )
= $true )
| ( ( SV201
= ( singleton @ SV160 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1904]) ).
thf(1995,plain,
! [SV202: $i,SV161: $i,SV301: $i] :
( ( ( ( SV301 != SV161 )
| ( in @ SV301 @ SV202 ) )
= $true )
| ( ( SV202
= ( singleton @ SV161 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1906]) ).
thf(1996,plain,
! [SV161: $i,SV202: $i,SV302: $i] :
( ( ( ~ ( in @ SV302 @ SV202 )
| ( SV302 = SV161 ) )
= $true )
| ( ( SV202
= ( singleton @ SV161 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1907]) ).
thf(1997,plain,
! [SV122: $i,SV68: $i] :
( ( ( ! [SY476: $i] :
( ~ ( ordinal @ SY476 )
| ~ ( in @ SY476 @ SV68 )
| ( ordinal_subset @ ( sK35_C @ SV122 @ SV68 ) @ SY476 ) ) )
= $true )
| ( ( ( SV68 = empty_set )
| ~ ( subset @ SV68 @ SV122 ) )
= $true )
| ( ( ordinal @ SV122 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1910]) ).
thf(1998,plain,
! [SV68: $i,SV122: $i] :
( ( ( in @ ( sK35_C @ SV122 @ SV68 ) @ SV68 )
= $true )
| ( ( ( SV68 = empty_set )
| ~ ( subset @ SV68 @ SV122 ) )
= $true )
| ( ( ordinal @ SV122 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1911]) ).
thf(1999,plain,
! [SV69: $i,SV203: $i,SV227: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV227 )
| ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV69 ) )
| ~ ( ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV227 )
| ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV203 ) ) )
= $false )
| ( ( SV227
= ( set_union2 @ SV69 @ SV203 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1912]) ).
thf(2000,plain,
! [SV69: $i,SV203: $i,SV227: $i] :
( ( ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV227 )
= $true )
| ( ( ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV69 )
| ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV203 ) )
= $true )
| ( ( SV227
= ( set_union2 @ SV69 @ SV203 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1913]) ).
thf(2001,plain,
! [SV204: $i,SV69: $i,SV228: $i] :
( ( ( ! [SY571: $i] :
( ~ ( in @ SY571 @ SV228 )
| ( in @ SY571 @ SV69 )
| ( in @ SY571 @ SV204 ) ) )
= $true )
| ( ( SV228
= ( set_union2 @ SV69 @ SV204 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1914]) ).
thf(2002,plain,
! [SV204: $i,SV228: $i,SV69: $i] :
( ( ( ~ ( ~ ! [SY572: $i] :
( ~ ( in @ SY572 @ SV69 )
| ( in @ SY572 @ SV228 ) )
| ~ ! [SY573: $i] :
( ~ ( in @ SY573 @ SV204 )
| ( in @ SY573 @ SV228 ) ) ) )
= $true )
| ( ( SV228
= ( set_union2 @ SV69 @ SV204 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1915]) ).
thf(2003,plain,
! [SV162: $i,SV205: $i] :
( ( ( in @ ( sK26_C @ SV205 @ SV162 ) @ SV205 )
= $false )
| ( ( ~ ( subset @ ( sK26_C @ SV205 @ SV162 ) @ SV162 ) )
= $true )
| ( ( SV205
= ( powerset @ SV162 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1916]) ).
thf(2004,plain,
! [SV163: $i,SV206: $i,SV303: $i] :
( ( ( ~ ( in @ SV303 @ SV206 )
| ( subset @ SV303 @ SV163 ) )
= $true )
| ( ( SV206
= ( powerset @ SV163 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1918]) ).
thf(2005,plain,
! [SV206: $i,SV163: $i,SV304: $i] :
( ( ( ~ ( subset @ SV304 @ SV163 )
| ( in @ SV304 @ SV206 ) )
= $true )
| ( ( SV206
= ( powerset @ SV163 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1919]) ).
thf(2006,plain,
! [SV70: $i,SV207: $i,SV229: $i] :
( ( ( ~ ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV70 )
| ~ ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV207 ) )
= $true )
| ( ( ~ ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV229 ) )
= $true )
| ( ( SV229
= ( set_intersection2 @ SV70 @ SV207 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1920]) ).
thf(2007,plain,
! [SV70: $i,SV207: $i,SV229: $i] :
( ( ( ~ ( ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV70 )
| ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV229 ) )
| ~ ( ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV207 )
| ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV229 ) ) )
= $false )
| ( ( SV229
= ( set_intersection2 @ SV70 @ SV207 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1921]) ).
thf(2008,plain,
! [SV230: $i,SV208: $i,SV70: $i] :
( ( ( ! [SY574: $i] :
( ~ ( in @ SY574 @ SV70 )
| ~ ( in @ SY574 @ SV208 )
| ( in @ SY574 @ SV230 ) ) )
= $true )
| ( ( SV230
= ( set_intersection2 @ SV70 @ SV208 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1922]) ).
thf(2009,plain,
! [SV208: $i,SV70: $i,SV230: $i] :
( ( ( ~ ( ~ ! [SY575: $i] :
( ~ ( in @ SY575 @ SV230 )
| ( in @ SY575 @ SV70 ) )
| ~ ! [SY576: $i] :
( ~ ( in @ SY576 @ SV230 )
| ( in @ SY576 @ SV208 ) ) ) )
= $true )
| ( ( SV230
= ( set_intersection2 @ SV70 @ SV208 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1923]) ).
thf(2010,plain,
! [SV209: $i,SV165: $i] :
( ( ( ordinal_subset @ SV165 @ SV209 )
= $false )
| ( ( subset @ SV165 @ SV209 )
= $true )
| ( ( ordinal @ SV165 )
= $false )
| ( ( ordinal @ SV209 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1924]) ).
thf(2011,plain,
! [SV210: $i,SV166: $i] :
( ( ( subset @ SV166 @ SV210 )
= $false )
| ( ( ordinal_subset @ SV166 @ SV210 )
= $true )
| ( ( ordinal @ SV166 )
= $false )
| ( ( ordinal @ SV210 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1925]) ).
thf(2012,plain,
! [SV135: $i,SV71: $i,SV292: $i] :
( ( ( ~ ( ordinal @ SV292 ) )
= $true )
| ( ( ~ ( in @ SV292 @ SV71 )
| ( ordinal_subset @ ( sK54_B @ SV71 ) @ SV292 ) )
= $true )
| ( ( in @ SV135 @ SV71 )
= $false )
| ( ( ordinal @ SV135 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1926]) ).
thf(2013,plain,
! [SV135: $i,SV71: $i] :
( ( ( ~ ( in @ ( sK54_B @ SV71 ) @ SV71 ) )
= $false )
| ( ( in @ SV135 @ SV71 )
= $false )
| ( ( ordinal @ SV135 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1927]) ).
thf(2014,plain,
! [SV135: $i,SV71: $i] :
( ( ( ~ ( ordinal @ ( sK54_B @ SV71 ) ) )
= $false )
| ( ( in @ SV135 @ SV71 )
= $false )
| ( ( ordinal @ SV135 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1927]) ).
thf(2015,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ( ~ ~ ( ( ( sK44_C @ SV123 @ SV72 )
!= ( sK45_SY295 @ SV123 @ SV72 ) )
| ~ ~ ( ~ ~ ( ( ( sK45_SY295 @ SV123 @ SV72 )
!= ( sK48_SY300 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 ) ) )
| ( ( sK44_C @ SV123 @ SV72 )
!= ( sK46_SY299 @ SV123 @ SV72 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1928]) ).
thf(2016,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ( ~ ~ ( ( ( sK46_SY299 @ SV123 @ SV72 )
!= ( sK47_SY303 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1929]) ).
thf(2017,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1930]) ).
thf(2018,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1930]) ).
thf(2019,plain,
! [SV73: $i,SV254: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK23_C @ SV254 @ SV73 ) @ ( sK24_SY280 @ SV254 @ SV73 ) ) @ SV73 )
| ~ ( in @ ( ordered_pair @ ( sK23_C @ SV254 @ SV73 ) @ ( sK24_SY280 @ SV254 @ SV73 ) ) @ SV254 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK23_C @ SV254 @ SV73 ) @ ( sK24_SY280 @ SV254 @ SV73 ) ) @ SV73 )
| ( in @ ( ordered_pair @ ( sK23_C @ SV254 @ SV73 ) @ ( sK24_SY280 @ SV254 @ SV73 ) ) @ SV254 ) ) )
= $false )
| ( ( SV73 = SV254 )
= $true )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1931]) ).
thf(2020,plain,
! [SV255: $i,SV73: $i] :
( ( ( SV73 = SV255 )
= $false )
| ( ( ~ ( ~ ! [SY592: $i,SY593: $i] :
( ~ ( in @ ( ordered_pair @ SY592 @ SY593 ) @ SV73 )
| ( in @ ( ordered_pair @ SY592 @ SY593 ) @ SV255 ) )
| ~ ! [SY594: $i,SY595: $i] :
( ~ ( in @ ( ordered_pair @ SY594 @ SY595 ) @ SV255 )
| ( in @ ( ordered_pair @ SY594 @ SY595 ) @ SV73 ) ) ) )
= $true )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1932]) ).
thf(2021,plain,
! [SV74: $i,SV211: $i,SV231: $i] :
( ( ( ~ ( ~ ( in @ ( sK22_D @ SV231 @ SV211 @ SV74 ) @ SV231 )
| ( ( sK22_D @ SV231 @ SV211 @ SV74 )
!= SV74 ) )
| ~ ( ~ ( in @ ( sK22_D @ SV231 @ SV211 @ SV74 ) @ SV231 )
| ( ( sK22_D @ SV231 @ SV211 @ SV74 )
!= SV211 ) ) )
= $false )
| ( ( SV231
= ( unordered_pair @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1933]) ).
thf(2022,plain,
! [SV74: $i,SV211: $i,SV231: $i] :
( ( ( in @ ( sK22_D @ SV231 @ SV211 @ SV74 ) @ SV231 )
= $true )
| ( ( ( ( sK22_D @ SV231 @ SV211 @ SV74 )
= SV74 )
| ( ( sK22_D @ SV231 @ SV211 @ SV74 )
= SV211 ) )
= $true )
| ( ( SV231
= ( unordered_pair @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1934]) ).
thf(2023,plain,
! [SV212: $i,SV74: $i,SV232: $i] :
( ( ( ! [SY577: $i] :
( ~ ( in @ SY577 @ SV232 )
| ( SY577 = SV74 )
| ( SY577 = SV212 ) ) )
= $true )
| ( ( SV232
= ( unordered_pair @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1935]) ).
thf(2024,plain,
! [SV212: $i,SV232: $i,SV74: $i] :
( ( ( ~ ( ~ ! [SY578: $i] :
( ( SY578 != SV74 )
| ( in @ SY578 @ SV232 ) )
| ~ ! [SY579: $i] :
( ( SY579 != SV212 )
| ( in @ SY579 @ SV232 ) ) ) )
= $true )
| ( ( SV232
= ( unordered_pair @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1936]) ).
thf(2025,plain,
! [SV75: $i,SV275: $i] :
( ( ( ~ ! [SY609: $i] :
( ~ ( subset @ SY609 @ SV275 )
| ( in @ SY609 @ ( sK3_SY270 @ SV275 @ SV75 ) ) ) )
= $false )
| ( ( ~ ( in @ SV275 @ ( sK2_B @ SV75 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1937]) ).
thf(2026,plain,
! [SV75: $i,SV275: $i] :
( ( ( ~ ( in @ ( sK3_SY270 @ SV275 @ SV75 ) @ ( sK2_B @ SV75 ) ) )
= $false )
| ( ( ~ ( in @ SV275 @ ( sK2_B @ SV75 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1937]) ).
thf(2027,plain,
! [SV75: $i,SV305: $i] :
( ( ! [SY616: $i] :
( ~ ( in @ SV305 @ ( sK2_B @ SV75 ) )
| ~ ( subset @ SY616 @ SV305 )
| ( in @ SY616 @ ( sK2_B @ SV75 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1938]) ).
thf(2028,plain,
! [SV77: $i,SV257: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK17_C @ SV257 @ SV77 ) @ ( sK18_SY278 @ SV257 @ SV77 ) ) @ SV77 )
| ~ ~ ( in @ ( ordered_pair @ ( sK17_C @ SV257 @ SV77 ) @ ( sK18_SY278 @ SV257 @ SV77 ) ) @ SV257 ) )
= $false )
| ( ( subset @ SV77 @ SV257 )
= $true )
| ( ( relation @ SV257 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1942]) ).
thf(2029,plain,
! [SV258: $i,SV77: $i] :
( ( ( subset @ SV77 @ SV258 )
= $false )
| ( ( ! [SY596: $i,SY597: $i] :
( ~ ( in @ ( ordered_pair @ SY596 @ SY597 ) @ SV77 )
| ( in @ ( ordered_pair @ SY596 @ SY597 ) @ SV258 ) ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1943]) ).
thf(2030,plain,
! [SV78: $i,SV218: $i,SV235: $i] :
( ( ( ~ ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV78 )
| ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV218 ) )
= $true )
| ( ( ~ ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV235 ) )
= $true )
| ( ( SV235
= ( set_difference @ SV78 @ SV218 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1946]) ).
thf(2031,plain,
! [SV78: $i,SV218: $i,SV235: $i] :
( ( ( ~ ( ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV78 )
| ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV235 ) )
| ~ ( ~ ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV218 )
| ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV235 ) ) )
= $false )
| ( ( SV235
= ( set_difference @ SV78 @ SV218 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1947]) ).
thf(2032,plain,
! [SV236: $i,SV219: $i,SV78: $i] :
( ( ( ! [SY580: $i] :
( ~ ( in @ SY580 @ SV78 )
| ( in @ SY580 @ SV219 )
| ( in @ SY580 @ SV236 ) ) )
= $true )
| ( ( SV236
= ( set_difference @ SV78 @ SV219 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1948]) ).
thf(2033,plain,
! [SV219: $i,SV78: $i,SV236: $i] :
( ( ( ~ ( ~ ! [SY581: $i] :
( ~ ( in @ SY581 @ SV236 )
| ( in @ SY581 @ SV78 ) )
| ~ ! [SY582: $i] :
( ~ ( in @ SY582 @ SV236 )
| ~ ( in @ SY582 @ SV219 ) ) ) )
= $true )
| ( ( SV236
= ( set_difference @ SV78 @ SV219 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1949]) ).
thf(2034,plain,
! [SV175: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK36_B @ SV175 ) @ ( sK37_SY285 @ SV175 ) ) @ SV175 )
| ~ ( in @ ( ordered_pair @ ( sK37_SY285 @ SV175 ) @ ( sK36_B @ SV175 ) ) @ SV175 ) )
= $false )
| ( ( antisymmetric @ SV175 )
= $true )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1950]) ).
thf(2035,plain,
! [SV175: $i] :
( ( ( ( sK36_B @ SV175 )
= ( sK37_SY285 @ SV175 ) )
= $false )
| ( ( antisymmetric @ SV175 )
= $true )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1951]) ).
thf(2036,plain,
! [SV176: $i,SV293: $i,SV286: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV286 @ SV293 ) @ SV176 )
| ~ ( in @ ( ordered_pair @ SV293 @ SV286 ) @ SV176 ) )
= $true )
| ( ( SV286 = SV293 )
= $true )
| ( ( antisymmetric @ SV176 )
= $false )
| ( ( relation @ SV176 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1952]) ).
thf(2037,plain,
! [SV178: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK38_B @ SV178 ) @ ( sK39_SY286 @ SV178 ) ) @ SV178 )
| ~ ( in @ ( ordered_pair @ ( sK39_SY286 @ SV178 ) @ ( sK40_SY288 @ SV178 ) ) @ SV178 ) )
= $false )
| ( ( transitive @ SV178 )
= $true )
| ( ( relation @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1955]) ).
thf(2038,plain,
! [SV178: $i] :
( ( ( in @ ( ordered_pair @ ( sK38_B @ SV178 ) @ ( sK40_SY288 @ SV178 ) ) @ SV178 )
= $false )
| ( ( transitive @ SV178 )
= $true )
| ( ( relation @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1956]) ).
thf(2039,plain,
! [SV306: $i,SV179: $i,SV294: $i,SV287: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV287 @ SV294 ) @ SV179 )
| ~ ( in @ ( ordered_pair @ SV294 @ SV306 ) @ SV179 )
| ( in @ ( ordered_pair @ SV287 @ SV306 ) @ SV179 ) )
= $true )
| ( ( transitive @ SV179 )
= $false )
| ( ( relation @ SV179 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1957]) ).
thf(2040,plain,
! [SV184: $i,SV279: $i] :
( ( ( ordinal @ SV279 )
= $false )
| ( ( SV184
= ( succ @ SV279 ) )
= $false )
| ( ( ~ ( being_limit_ordinal @ SV184 ) )
= $true )
| ( ( ordinal @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1960]) ).
thf(2041,plain,
! [SV80: $i,SV125: $i,SV237: $i,SV263: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
!= SV237 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
!= SV80 ) )
| ~ ( ~ ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
!= SV125 ) ) ) ) )
= $true )
| ( ( SV263
= ( unordered_triple @ SV80 @ SV125 @ SV237 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1961]) ).
thf(2042,plain,
! [SV80: $i,SV125: $i,SV237: $i,SV263: $i] :
( ( ( ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
= SV237 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
= SV80 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
= SV125 ) )
= $true )
| ( ( SV263
= ( unordered_triple @ SV80 @ SV125 @ SV237 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1962]) ).
thf(2043,plain,
! [SV125: $i,SV80: $i,SV238: $i,SV264: $i] :
( ( ( ~ ! [SY600: $i] :
( ~ ( in @ SY600 @ SV264 )
| ( SY600 = SV238 )
| ( SY600 = SV80 )
| ( SY600 = SV125 ) ) )
= $false )
| ( ( SV264
= ( unordered_triple @ SV80 @ SV125 @ SV238 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1963]) ).
thf(2044,plain,
! [SV125: $i,SV80: $i,SV264: $i,SV238: $i] :
( ( ( ~ ~ ( ~ ! [SY601: $i] :
( ( SY601 != SV238 )
| ( in @ SY601 @ SV264 ) )
| ~ ~ ( ~ ! [SY602: $i] :
( ( SY602 != SV80 )
| ( in @ SY602 @ SV264 ) )
| ~ ! [SY603: $i] :
( ( SY603 != SV125 )
| ( in @ SY603 @ SV264 ) ) ) ) )
= $false )
| ( ( SV264
= ( unordered_triple @ SV80 @ SV125 @ SV238 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1963]) ).
thf(2045,plain,
! [SV225: $i,SV192: $i,SV61: $i] :
( ( ( in @ SV61 @ ( cartesian_product2 @ SV192 @ SV192 ) )
= $false )
| ( ( in @ SV61 @ SV225 )
= $false )
| ( ( in @ SV61 @ ( relation_restriction @ SV225 @ SV192 ) )
= $true )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1964]) ).
thf(2046,plain,
! [SV265: $i,SV280: $i,SV61: $i] :
( ( ( ~ ( in @ SV61 @ ( relation_restriction @ SV280 @ SV265 ) ) )
= $true )
| ( ( in @ SV61 @ SV280 )
= $true )
| ( ( relation @ SV280 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1965]) ).
thf(2047,plain,
! [SV266: $i,SV281: $i,SV61: $i] :
( ( ( ~ ( in @ SV61 @ ( relation_restriction @ SV281 @ SV266 ) ) )
= $true )
| ( ( in @ SV61 @ ( cartesian_product2 @ SV266 @ SV266 ) )
= $true )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1966]) ).
thf(2048,plain,
! [SV144: $i] :
( ( ( ~ ( in @ ( sK33_B @ SV144 ) @ SV144 ) )
= $false )
| ( ( being_limit_ordinal @ SV144 )
= $true )
| ( ( ordinal @ SV144 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1967]) ).
thf(2049,plain,
! [SV144: $i] :
( ( ( ~ ~ ( in @ ( succ @ ( sK33_B @ SV144 ) ) @ SV144 ) )
= $false )
| ( ( being_limit_ordinal @ SV144 )
= $true )
| ( ( ordinal @ SV144 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1967]) ).
thf(2050,plain,
! [SV145: $i,SV282: $i] :
( ( ( ~ ( in @ SV282 @ SV145 ) )
= $true )
| ( ( in @ ( succ @ SV282 ) @ SV145 )
= $true )
| ( ( ordinal @ SV282 )
= $false )
| ( ( being_limit_ordinal @ SV145 )
= $false )
| ( ( ordinal @ SV145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1968]) ).
thf(2051,plain,
! [SV120: $i,SV63: $i,SV295: $i,SV267: $i] :
( ( ( ( SV267 != SV295 )
| ~ ( ordinal @ SV295 ) )
= $true )
| ( ( ~ ( in @ SV295 @ SV63 ) )
= $true )
| ( ( ~ ( in @ SV267 @ ( succ @ SV120 ) ) )
= $true )
| ( ( in @ SV267 @ ( sK52_C @ SV120 @ SV63 ) )
= $true )
| ( ( ordinal @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1971]) ).
thf(2052,plain,
! [SV63: $i,SV120: $i,SV296: $i] :
( ( ( ~ ( in @ SV296 @ ( sK52_C @ SV120 @ SV63 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV296
!= ( sK53_E @ SV296 @ SV120 @ SV63 ) )
| ~ ( ordinal @ ( sK53_E @ SV296 @ SV120 @ SV63 ) ) )
| ~ ( in @ ( sK53_E @ SV296 @ SV120 @ SV63 ) @ SV63 ) ) )
= $true )
| ( ( ordinal @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1972]) ).
thf(2053,plain,
! [SV63: $i,SV120: $i,SV297: $i] :
( ( ( ~ ( in @ SV297 @ ( sK52_C @ SV120 @ SV63 ) ) )
= $true )
| ( ( in @ SV297 @ ( succ @ SV120 ) )
= $true )
| ( ( ordinal @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1973]) ).
thf(2054,plain,
! [SV288: $i] :
( ( ( ordinal @ SV288 )
= $false )
| ( ( ~ ( empty @ ( succ @ SV288 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1976]) ).
thf(2055,plain,
! [SV289: $i] :
( ( ( ordinal @ SV289 )
= $false )
| ( ( epsilon_transitive @ ( succ @ SV289 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1977]) ).
thf(2056,plain,
! [SV298: $i,SV148: $i,SV196: $i] :
( ( ( ~ ( in @ ( sK13_C @ SV196 @ SV148 ) @ SV298 ) )
= $true )
| ( ( ~ ( in @ SV298 @ SV148 ) )
= $true )
| ( ( ~ ( in @ ( sK13_C @ SV196 @ SV148 ) @ SV196 ) )
= $true )
| ( ( SV196
= ( union @ SV148 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1978]) ).
thf(2057,plain,
! [SV148: $i,SV196: $i] :
( ( ( ~ ( in @ ( sK13_C @ SV196 @ SV148 ) @ ( sK14_SY277 @ SV196 @ SV148 ) ) )
= $false )
| ( ( in @ ( sK13_C @ SV196 @ SV148 ) @ SV196 )
= $true )
| ( ( SV196
= ( union @ SV148 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1979]) ).
thf(2058,plain,
! [SV148: $i,SV196: $i] :
( ( ( ~ ( in @ ( sK14_SY277 @ SV196 @ SV148 ) @ SV148 ) )
= $false )
| ( ( in @ ( sK13_C @ SV196 @ SV148 ) @ SV196 )
= $true )
| ( ( SV196
= ( union @ SV148 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1979]) ).
thf(2059,plain,
! [SV197: $i,SV149: $i,SV299: $i] :
( ( ( ! [SY615: $i] :
( ~ ( in @ SV299 @ SY615 )
| ~ ( in @ SY615 @ SV149 ) ) )
= $true )
| ( ( in @ SV299 @ SV197 )
= $true )
| ( ( SV197
= ( union @ SV149 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1980]) ).
thf(2060,plain,
! [SV149: $i,SV197: $i,SV300: $i] :
( ( ( ~ ( in @ SV300 @ SV197 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV300 @ ( sK12_D @ SV300 @ SV197 @ SV149 ) )
| ~ ( in @ ( sK12_D @ SV300 @ SV197 @ SV149 ) @ SV149 ) ) )
= $true )
| ( ( SV197
= ( union @ SV149 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1981]) ).
thf(2061,plain,
! [SV152: $i] :
( ( ( ( sK19_B @ SV152 )
= ( sK20_SY279 @ SV152 ) )
= $false )
| ( ( epsilon_connected @ SV152 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1983]) ).
thf(2062,plain,
! [SV152: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK19_B @ SV152 ) @ SV152 )
| ~ ( in @ ( sK20_SY279 @ SV152 ) @ SV152 ) )
| ~ ~ ( in @ ( sK19_B @ SV152 ) @ ( sK20_SY279 @ SV152 ) ) )
= $false )
| ( ( epsilon_connected @ SV152 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1984]) ).
thf(2063,plain,
! [SV272: $i,SV153: $i,SV245: $i] :
( ( ( ~ ( in @ SV245 @ SV153 ) )
= $true )
| ( ( ~ ( in @ SV272 @ SV153 ) )
= $true )
| ( ( in @ SV245 @ SV272 )
= $true )
| ( ( SV245 = SV272 )
= $true )
| ( ( in @ SV272 @ SV245 )
= $true )
| ( ( epsilon_connected @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1985]) ).
thf(2064,plain,
! [SV155: $i] :
( ( ( reflexive @ SV155 )
= $false )
| ( ( ~ ( transitive @ SV155 ) )
= $true )
| ( ( ~ ( antisymmetric @ SV155 ) )
= $true )
| ( ( ~ ( connected @ SV155 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV155 ) )
= $true )
| ( ( well_ordering @ SV155 )
= $true )
| ( ( relation @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1987]) ).
thf(2065,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1988]) ).
thf(2066,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1989]) ).
thf(2067,plain,
! [SV291: $i] :
( ( ( relation @ SV291 )
= $false )
| ( ( ~ ( well_ordering @ SV291 )
| ( connected @ SV291 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1990]) ).
thf(2068,plain,
! [SV160: $i,SV201: $i] :
( ( ( in @ ( sK28_C @ SV201 @ SV160 ) @ SV201 )
= $false )
| ( ( ( sK28_C @ SV201 @ SV160 )
= SV160 )
= $false )
| ( ( SV201
= ( singleton @ SV160 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1994]) ).
thf(2069,plain,
! [SV202: $i,SV161: $i,SV301: $i] :
( ( ( SV301 != SV161 )
= $true )
| ( ( in @ SV301 @ SV202 )
= $true )
| ( ( SV202
= ( singleton @ SV161 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1995]) ).
thf(2070,plain,
! [SV161: $i,SV202: $i,SV302: $i] :
( ( ( ~ ( in @ SV302 @ SV202 ) )
= $true )
| ( ( SV302 = SV161 )
= $true )
| ( ( SV202
= ( singleton @ SV161 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1996]) ).
thf(2071,plain,
! [SV122: $i,SV68: $i,SV307: $i] :
( ( ( ~ ( ordinal @ SV307 )
| ~ ( in @ SV307 @ SV68 )
| ( ordinal_subset @ ( sK35_C @ SV122 @ SV68 ) @ SV307 ) )
= $true )
| ( ( ( SV68 = empty_set )
| ~ ( subset @ SV68 @ SV122 ) )
= $true )
| ( ( ordinal @ SV122 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1997]) ).
thf(2072,plain,
! [SV122: $i,SV68: $i] :
( ( ( SV68 = empty_set )
= $true )
| ( ( ~ ( subset @ SV68 @ SV122 ) )
= $true )
| ( ( in @ ( sK35_C @ SV122 @ SV68 ) @ SV68 )
= $true )
| ( ( ordinal @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1998]) ).
thf(2073,plain,
! [SV69: $i,SV203: $i,SV227: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV227 )
| ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV69 ) ) )
= $false )
| ( ( SV227
= ( set_union2 @ SV69 @ SV203 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1999]) ).
thf(2074,plain,
! [SV69: $i,SV203: $i,SV227: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV227 )
| ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV203 ) ) )
= $false )
| ( ( SV227
= ( set_union2 @ SV69 @ SV203 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1999]) ).
thf(2075,plain,
! [SV69: $i,SV203: $i,SV227: $i] :
( ( ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV69 )
= $true )
| ( ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV203 )
= $true )
| ( ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV227 )
= $true )
| ( ( SV227
= ( set_union2 @ SV69 @ SV203 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2000]) ).
thf(2076,plain,
! [SV204: $i,SV69: $i,SV228: $i,SV308: $i] :
( ( ( ~ ( in @ SV308 @ SV228 )
| ( in @ SV308 @ SV69 )
| ( in @ SV308 @ SV204 ) )
= $true )
| ( ( SV228
= ( set_union2 @ SV69 @ SV204 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2001]) ).
thf(2077,plain,
! [SV204: $i,SV228: $i,SV69: $i] :
( ( ( ~ ! [SY572: $i] :
( ~ ( in @ SY572 @ SV69 )
| ( in @ SY572 @ SV228 ) )
| ~ ! [SY573: $i] :
( ~ ( in @ SY573 @ SV204 )
| ( in @ SY573 @ SV228 ) ) )
= $false )
| ( ( SV228
= ( set_union2 @ SV69 @ SV204 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2002]) ).
thf(2078,plain,
! [SV162: $i,SV205: $i] :
( ( ( subset @ ( sK26_C @ SV205 @ SV162 ) @ SV162 )
= $false )
| ( ( in @ ( sK26_C @ SV205 @ SV162 ) @ SV205 )
= $false )
| ( ( SV205
= ( powerset @ SV162 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2003]) ).
thf(2079,plain,
! [SV163: $i,SV206: $i,SV303: $i] :
( ( ( ~ ( in @ SV303 @ SV206 ) )
= $true )
| ( ( subset @ SV303 @ SV163 )
= $true )
| ( ( SV206
= ( powerset @ SV163 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2004]) ).
thf(2080,plain,
! [SV206: $i,SV163: $i,SV304: $i] :
( ( ( ~ ( subset @ SV304 @ SV163 ) )
= $true )
| ( ( in @ SV304 @ SV206 )
= $true )
| ( ( SV206
= ( powerset @ SV163 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2005]) ).
thf(2081,plain,
! [SV70: $i,SV207: $i,SV229: $i] :
( ( ( ~ ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV70 ) )
= $true )
| ( ( ~ ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV207 ) )
= $true )
| ( ( ~ ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV229 ) )
= $true )
| ( ( SV229
= ( set_intersection2 @ SV70 @ SV207 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2006]) ).
thf(2082,plain,
! [SV70: $i,SV207: $i,SV229: $i] :
( ( ( ~ ( ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV70 )
| ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV229 ) ) )
= $false )
| ( ( SV229
= ( set_intersection2 @ SV70 @ SV207 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2007]) ).
thf(2083,plain,
! [SV70: $i,SV207: $i,SV229: $i] :
( ( ( ~ ( ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV207 )
| ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV229 ) ) )
= $false )
| ( ( SV229
= ( set_intersection2 @ SV70 @ SV207 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2007]) ).
thf(2084,plain,
! [SV230: $i,SV208: $i,SV70: $i,SV309: $i] :
( ( ( ~ ( in @ SV309 @ SV70 )
| ~ ( in @ SV309 @ SV208 )
| ( in @ SV309 @ SV230 ) )
= $true )
| ( ( SV230
= ( set_intersection2 @ SV70 @ SV208 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2008]) ).
thf(2085,plain,
! [SV208: $i,SV70: $i,SV230: $i] :
( ( ( ~ ! [SY575: $i] :
( ~ ( in @ SY575 @ SV230 )
| ( in @ SY575 @ SV70 ) )
| ~ ! [SY576: $i] :
( ~ ( in @ SY576 @ SV230 )
| ( in @ SY576 @ SV208 ) ) )
= $false )
| ( ( SV230
= ( set_intersection2 @ SV70 @ SV208 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2009]) ).
thf(2086,plain,
! [SV135: $i,SV71: $i,SV292: $i] :
( ( ( ordinal @ SV292 )
= $false )
| ( ( ~ ( in @ SV292 @ SV71 )
| ( ordinal_subset @ ( sK54_B @ SV71 ) @ SV292 ) )
= $true )
| ( ( in @ SV135 @ SV71 )
= $false )
| ( ( ordinal @ SV135 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2012]) ).
thf(2087,plain,
! [SV135: $i,SV71: $i] :
( ( ( in @ ( sK54_B @ SV71 ) @ SV71 )
= $true )
| ( ( in @ SV135 @ SV71 )
= $false )
| ( ( ordinal @ SV135 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2013]) ).
thf(2088,plain,
! [SV135: $i,SV71: $i] :
( ( ( ordinal @ ( sK54_B @ SV71 ) )
= $true )
| ( ( in @ SV135 @ SV71 )
= $false )
| ( ( ordinal @ SV135 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2014]) ).
thf(2089,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ~ ( ( ( sK44_C @ SV123 @ SV72 )
!= ( sK45_SY295 @ SV123 @ SV72 ) )
| ~ ~ ( ~ ~ ( ( ( sK45_SY295 @ SV123 @ SV72 )
!= ( sK48_SY300 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 ) ) )
| ( ( sK44_C @ SV123 @ SV72 )
!= ( sK46_SY299 @ SV123 @ SV72 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2015]) ).
thf(2090,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ~ ( ( ( sK46_SY299 @ SV123 @ SV72 )
!= ( sK47_SY303 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 ) )
= $false )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2016]) ).
thf(2091,plain,
! [SV72: $i,SV123: $i] :
( ( ( ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) ) )
= $true )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2017]) ).
thf(2092,plain,
! [SV72: $i,SV123: $i] :
( ( ( ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) )
= $true )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2018]) ).
thf(2093,plain,
! [SV73: $i,SV254: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK23_C @ SV254 @ SV73 ) @ ( sK24_SY280 @ SV254 @ SV73 ) ) @ SV73 )
| ~ ( in @ ( ordered_pair @ ( sK23_C @ SV254 @ SV73 ) @ ( sK24_SY280 @ SV254 @ SV73 ) ) @ SV254 ) ) )
= $false )
| ( ( SV73 = SV254 )
= $true )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2019]) ).
thf(2094,plain,
! [SV73: $i,SV254: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK23_C @ SV254 @ SV73 ) @ ( sK24_SY280 @ SV254 @ SV73 ) ) @ SV73 )
| ( in @ ( ordered_pair @ ( sK23_C @ SV254 @ SV73 ) @ ( sK24_SY280 @ SV254 @ SV73 ) ) @ SV254 ) ) )
= $false )
| ( ( SV73 = SV254 )
= $true )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2019]) ).
thf(2095,plain,
! [SV255: $i,SV73: $i] :
( ( ( ~ ! [SY592: $i,SY593: $i] :
( ~ ( in @ ( ordered_pair @ SY592 @ SY593 ) @ SV73 )
| ( in @ ( ordered_pair @ SY592 @ SY593 ) @ SV255 ) )
| ~ ! [SY594: $i,SY595: $i] :
( ~ ( in @ ( ordered_pair @ SY594 @ SY595 ) @ SV255 )
| ( in @ ( ordered_pair @ SY594 @ SY595 ) @ SV73 ) ) )
= $false )
| ( ( SV73 = SV255 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2020]) ).
thf(2096,plain,
! [SV74: $i,SV211: $i,SV231: $i] :
( ( ( ~ ( ~ ( in @ ( sK22_D @ SV231 @ SV211 @ SV74 ) @ SV231 )
| ( ( sK22_D @ SV231 @ SV211 @ SV74 )
!= SV74 ) ) )
= $false )
| ( ( SV231
= ( unordered_pair @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2021]) ).
thf(2097,plain,
! [SV74: $i,SV211: $i,SV231: $i] :
( ( ( ~ ( ~ ( in @ ( sK22_D @ SV231 @ SV211 @ SV74 ) @ SV231 )
| ( ( sK22_D @ SV231 @ SV211 @ SV74 )
!= SV211 ) ) )
= $false )
| ( ( SV231
= ( unordered_pair @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2021]) ).
thf(2098,plain,
! [SV74: $i,SV211: $i,SV231: $i] :
( ( ( ( sK22_D @ SV231 @ SV211 @ SV74 )
= SV74 )
= $true )
| ( ( ( sK22_D @ SV231 @ SV211 @ SV74 )
= SV211 )
= $true )
| ( ( in @ ( sK22_D @ SV231 @ SV211 @ SV74 ) @ SV231 )
= $true )
| ( ( SV231
= ( unordered_pair @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2022]) ).
thf(2099,plain,
! [SV212: $i,SV74: $i,SV232: $i,SV310: $i] :
( ( ( ~ ( in @ SV310 @ SV232 )
| ( SV310 = SV74 )
| ( SV310 = SV212 ) )
= $true )
| ( ( SV232
= ( unordered_pair @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2023]) ).
thf(2100,plain,
! [SV212: $i,SV232: $i,SV74: $i] :
( ( ( ~ ! [SY578: $i] :
( ( SY578 != SV74 )
| ( in @ SY578 @ SV232 ) )
| ~ ! [SY579: $i] :
( ( SY579 != SV212 )
| ( in @ SY579 @ SV232 ) ) )
= $false )
| ( ( SV232
= ( unordered_pair @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2024]) ).
thf(2101,plain,
! [SV75: $i,SV275: $i] :
( ( ( ! [SY609: $i] :
( ~ ( subset @ SY609 @ SV275 )
| ( in @ SY609 @ ( sK3_SY270 @ SV275 @ SV75 ) ) ) )
= $true )
| ( ( ~ ( in @ SV275 @ ( sK2_B @ SV75 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2025]) ).
thf(2102,plain,
! [SV75: $i,SV275: $i] :
( ( ( in @ ( sK3_SY270 @ SV275 @ SV75 ) @ ( sK2_B @ SV75 ) )
= $true )
| ( ( ~ ( in @ SV275 @ ( sK2_B @ SV75 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2026]) ).
thf(2103,plain,
! [SV311: $i,SV75: $i,SV305: $i] :
( ( ~ ( in @ SV305 @ ( sK2_B @ SV75 ) )
| ~ ( subset @ SV311 @ SV305 )
| ( in @ SV311 @ ( sK2_B @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2027]) ).
thf(2104,plain,
! [SV77: $i,SV257: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK17_C @ SV257 @ SV77 ) @ ( sK18_SY278 @ SV257 @ SV77 ) ) @ SV77 ) )
= $false )
| ( ( subset @ SV77 @ SV257 )
= $true )
| ( ( relation @ SV257 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2028]) ).
thf(2105,plain,
! [SV77: $i,SV257: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK17_C @ SV257 @ SV77 ) @ ( sK18_SY278 @ SV257 @ SV77 ) ) @ SV257 ) )
= $false )
| ( ( subset @ SV77 @ SV257 )
= $true )
| ( ( relation @ SV257 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2028]) ).
thf(2106,plain,
! [SV258: $i,SV77: $i,SV312: $i] :
( ( ( ! [SY617: $i] :
( ~ ( in @ ( ordered_pair @ SV312 @ SY617 ) @ SV77 )
| ( in @ ( ordered_pair @ SV312 @ SY617 ) @ SV258 ) ) )
= $true )
| ( ( subset @ SV77 @ SV258 )
= $false )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2029]) ).
thf(2107,plain,
! [SV78: $i,SV218: $i,SV235: $i] :
( ( ( ~ ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV78 ) )
= $true )
| ( ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV218 )
= $true )
| ( ( ~ ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV235 ) )
= $true )
| ( ( SV235
= ( set_difference @ SV78 @ SV218 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2030]) ).
thf(2108,plain,
! [SV78: $i,SV218: $i,SV235: $i] :
( ( ( ~ ( ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV78 )
| ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV235 ) ) )
= $false )
| ( ( SV235
= ( set_difference @ SV78 @ SV218 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2031]) ).
thf(2109,plain,
! [SV78: $i,SV218: $i,SV235: $i] :
( ( ( ~ ( ~ ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV218 )
| ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV235 ) ) )
= $false )
| ( ( SV235
= ( set_difference @ SV78 @ SV218 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2031]) ).
thf(2110,plain,
! [SV236: $i,SV219: $i,SV78: $i,SV313: $i] :
( ( ( ~ ( in @ SV313 @ SV78 )
| ( in @ SV313 @ SV219 )
| ( in @ SV313 @ SV236 ) )
= $true )
| ( ( SV236
= ( set_difference @ SV78 @ SV219 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2032]) ).
thf(2111,plain,
! [SV219: $i,SV78: $i,SV236: $i] :
( ( ( ~ ! [SY581: $i] :
( ~ ( in @ SY581 @ SV236 )
| ( in @ SY581 @ SV78 ) )
| ~ ! [SY582: $i] :
( ~ ( in @ SY582 @ SV236 )
| ~ ( in @ SY582 @ SV219 ) ) )
= $false )
| ( ( SV236
= ( set_difference @ SV78 @ SV219 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2033]) ).
thf(2112,plain,
! [SV175: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK36_B @ SV175 ) @ ( sK37_SY285 @ SV175 ) ) @ SV175 ) )
= $false )
| ( ( antisymmetric @ SV175 )
= $true )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2034]) ).
thf(2113,plain,
! [SV175: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK37_SY285 @ SV175 ) @ ( sK36_B @ SV175 ) ) @ SV175 ) )
= $false )
| ( ( antisymmetric @ SV175 )
= $true )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2034]) ).
thf(2114,plain,
! [SV176: $i,SV293: $i,SV286: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV286 @ SV293 ) @ SV176 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV293 @ SV286 ) @ SV176 ) )
= $true )
| ( ( SV286 = SV293 )
= $true )
| ( ( antisymmetric @ SV176 )
= $false )
| ( ( relation @ SV176 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2036]) ).
thf(2115,plain,
! [SV178: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK38_B @ SV178 ) @ ( sK39_SY286 @ SV178 ) ) @ SV178 ) )
= $false )
| ( ( transitive @ SV178 )
= $true )
| ( ( relation @ SV178 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2037]) ).
thf(2116,plain,
! [SV178: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK39_SY286 @ SV178 ) @ ( sK40_SY288 @ SV178 ) ) @ SV178 ) )
= $false )
| ( ( transitive @ SV178 )
= $true )
| ( ( relation @ SV178 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2037]) ).
thf(2117,plain,
! [SV306: $i,SV179: $i,SV294: $i,SV287: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV287 @ SV294 ) @ SV179 )
| ~ ( in @ ( ordered_pair @ SV294 @ SV306 ) @ SV179 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV287 @ SV306 ) @ SV179 )
= $true )
| ( ( transitive @ SV179 )
= $false )
| ( ( relation @ SV179 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2039]) ).
thf(2118,plain,
! [SV279: $i,SV184: $i] :
( ( ( being_limit_ordinal @ SV184 )
= $false )
| ( ( SV184
= ( succ @ SV279 ) )
= $false )
| ( ( ordinal @ SV279 )
= $false )
| ( ( ordinal @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2040]) ).
thf(2119,plain,
! [SV80: $i,SV125: $i,SV237: $i,SV263: $i] :
( ( ( ~ ( ~ ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
!= SV237 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
!= SV80 ) )
| ~ ( ~ ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
!= SV125 ) ) ) )
= $false )
| ( ( SV263
= ( unordered_triple @ SV80 @ SV125 @ SV237 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2041]) ).
thf(2120,plain,
! [SV80: $i,SV125: $i,SV237: $i,SV263: $i] :
( ( ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
= $true )
| ( ( ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
= SV237 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
= SV80 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
= SV125 ) )
= $true )
| ( ( SV263
= ( unordered_triple @ SV80 @ SV125 @ SV237 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2042]) ).
thf(2121,plain,
! [SV125: $i,SV80: $i,SV238: $i,SV264: $i] :
( ( ( ! [SY600: $i] :
( ~ ( in @ SY600 @ SV264 )
| ( SY600 = SV238 )
| ( SY600 = SV80 )
| ( SY600 = SV125 ) ) )
= $true )
| ( ( SV264
= ( unordered_triple @ SV80 @ SV125 @ SV238 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2043]) ).
thf(2122,plain,
! [SV125: $i,SV80: $i,SV264: $i,SV238: $i] :
( ( ( ~ ( ~ ! [SY601: $i] :
( ( SY601 != SV238 )
| ( in @ SY601 @ SV264 ) )
| ~ ~ ( ~ ! [SY602: $i] :
( ( SY602 != SV80 )
| ( in @ SY602 @ SV264 ) )
| ~ ! [SY603: $i] :
( ( SY603 != SV125 )
| ( in @ SY603 @ SV264 ) ) ) ) )
= $true )
| ( ( SV264
= ( unordered_triple @ SV80 @ SV125 @ SV238 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2044]) ).
thf(2123,plain,
! [SV265: $i,SV280: $i,SV61: $i] :
( ( ( in @ SV61 @ ( relation_restriction @ SV280 @ SV265 ) )
= $false )
| ( ( in @ SV61 @ SV280 )
= $true )
| ( ( relation @ SV280 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2046]) ).
thf(2124,plain,
! [SV266: $i,SV281: $i,SV61: $i] :
( ( ( in @ SV61 @ ( relation_restriction @ SV281 @ SV266 ) )
= $false )
| ( ( in @ SV61 @ ( cartesian_product2 @ SV266 @ SV266 ) )
= $true )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2047]) ).
thf(2125,plain,
! [SV144: $i] :
( ( ( in @ ( sK33_B @ SV144 ) @ SV144 )
= $true )
| ( ( being_limit_ordinal @ SV144 )
= $true )
| ( ( ordinal @ SV144 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2048]) ).
thf(2126,plain,
! [SV144: $i] :
( ( ( ~ ( in @ ( succ @ ( sK33_B @ SV144 ) ) @ SV144 ) )
= $true )
| ( ( being_limit_ordinal @ SV144 )
= $true )
| ( ( ordinal @ SV144 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2049]) ).
thf(2127,plain,
! [SV145: $i,SV282: $i] :
( ( ( in @ SV282 @ SV145 )
= $false )
| ( ( in @ ( succ @ SV282 ) @ SV145 )
= $true )
| ( ( ordinal @ SV282 )
= $false )
| ( ( being_limit_ordinal @ SV145 )
= $false )
| ( ( ordinal @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2050]) ).
thf(2128,plain,
! [SV120: $i,SV63: $i,SV295: $i,SV267: $i] :
( ( ( SV267 != SV295 )
= $true )
| ( ( ~ ( ordinal @ SV295 ) )
= $true )
| ( ( ~ ( in @ SV295 @ SV63 ) )
= $true )
| ( ( ~ ( in @ SV267 @ ( succ @ SV120 ) ) )
= $true )
| ( ( in @ SV267 @ ( sK52_C @ SV120 @ SV63 ) )
= $true )
| ( ( ordinal @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2051]) ).
thf(2129,plain,
! [SV63: $i,SV120: $i,SV296: $i] :
( ( ( in @ SV296 @ ( sK52_C @ SV120 @ SV63 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( SV296
!= ( sK53_E @ SV296 @ SV120 @ SV63 ) )
| ~ ( ordinal @ ( sK53_E @ SV296 @ SV120 @ SV63 ) ) )
| ~ ( in @ ( sK53_E @ SV296 @ SV120 @ SV63 ) @ SV63 ) ) )
= $true )
| ( ( ordinal @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2052]) ).
thf(2130,plain,
! [SV63: $i,SV120: $i,SV297: $i] :
( ( ( in @ SV297 @ ( sK52_C @ SV120 @ SV63 ) )
= $false )
| ( ( in @ SV297 @ ( succ @ SV120 ) )
= $true )
| ( ( ordinal @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2053]) ).
thf(2131,plain,
! [SV288: $i] :
( ( ( empty @ ( succ @ SV288 ) )
= $false )
| ( ( ordinal @ SV288 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2054]) ).
thf(2132,plain,
! [SV298: $i,SV148: $i,SV196: $i] :
( ( ( in @ ( sK13_C @ SV196 @ SV148 ) @ SV298 )
= $false )
| ( ( ~ ( in @ SV298 @ SV148 ) )
= $true )
| ( ( ~ ( in @ ( sK13_C @ SV196 @ SV148 ) @ SV196 ) )
= $true )
| ( ( SV196
= ( union @ SV148 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2056]) ).
thf(2133,plain,
! [SV148: $i,SV196: $i] :
( ( ( in @ ( sK13_C @ SV196 @ SV148 ) @ ( sK14_SY277 @ SV196 @ SV148 ) )
= $true )
| ( ( in @ ( sK13_C @ SV196 @ SV148 ) @ SV196 )
= $true )
| ( ( SV196
= ( union @ SV148 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2057]) ).
thf(2134,plain,
! [SV148: $i,SV196: $i] :
( ( ( in @ ( sK14_SY277 @ SV196 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ ( sK13_C @ SV196 @ SV148 ) @ SV196 )
= $true )
| ( ( SV196
= ( union @ SV148 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2058]) ).
thf(2135,plain,
! [SV197: $i,SV149: $i,SV314: $i,SV299: $i] :
( ( ( ~ ( in @ SV299 @ SV314 )
| ~ ( in @ SV314 @ SV149 ) )
= $true )
| ( ( in @ SV299 @ SV197 )
= $true )
| ( ( SV197
= ( union @ SV149 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2059]) ).
thf(2136,plain,
! [SV149: $i,SV197: $i,SV300: $i] :
( ( ( in @ SV300 @ SV197 )
= $false )
| ( ( ~ ( ~ ( in @ SV300 @ ( sK12_D @ SV300 @ SV197 @ SV149 ) )
| ~ ( in @ ( sK12_D @ SV300 @ SV197 @ SV149 ) @ SV149 ) ) )
= $true )
| ( ( SV197
= ( union @ SV149 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2060]) ).
thf(2137,plain,
! [SV152: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK19_B @ SV152 ) @ SV152 )
| ~ ( in @ ( sK20_SY279 @ SV152 ) @ SV152 ) ) )
= $false )
| ( ( epsilon_connected @ SV152 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2062]) ).
thf(2138,plain,
! [SV152: $i] :
( ( ( ~ ~ ( in @ ( sK19_B @ SV152 ) @ ( sK20_SY279 @ SV152 ) ) )
= $false )
| ( ( epsilon_connected @ SV152 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2062]) ).
thf(2139,plain,
! [SV272: $i,SV153: $i,SV245: $i] :
( ( ( in @ SV245 @ SV153 )
= $false )
| ( ( ~ ( in @ SV272 @ SV153 ) )
= $true )
| ( ( in @ SV245 @ SV272 )
= $true )
| ( ( SV245 = SV272 )
= $true )
| ( ( in @ SV272 @ SV245 )
= $true )
| ( ( epsilon_connected @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2063]) ).
thf(2140,plain,
! [SV155: $i] :
( ( ( transitive @ SV155 )
= $false )
| ( ( reflexive @ SV155 )
= $false )
| ( ( ~ ( antisymmetric @ SV155 ) )
= $true )
| ( ( ~ ( connected @ SV155 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV155 ) )
= $true )
| ( ( well_ordering @ SV155 )
= $true )
| ( ( relation @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2064]) ).
thf(2141,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2065]) ).
thf(2142,plain,
! [SV315: $i] :
( ( ~ ( relation @ SV315 )
| ~ ( well_ordering @ SV315 )
| ( antisymmetric @ SV315 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2066]) ).
thf(2143,plain,
! [SV291: $i] :
( ( ( ~ ( well_ordering @ SV291 ) )
= $true )
| ( ( connected @ SV291 )
= $true )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2067]) ).
thf(2144,plain,
! [SV202: $i,SV161: $i,SV301: $i] :
( ( ( SV301 = SV161 )
= $false )
| ( ( in @ SV301 @ SV202 )
= $true )
| ( ( SV202
= ( singleton @ SV161 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2069]) ).
thf(2145,plain,
! [SV161: $i,SV202: $i,SV302: $i] :
( ( ( in @ SV302 @ SV202 )
= $false )
| ( ( SV302 = SV161 )
= $true )
| ( ( SV202
= ( singleton @ SV161 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2070]) ).
thf(2146,plain,
! [SV122: $i,SV68: $i,SV307: $i] :
( ( ( ~ ( ordinal @ SV307 ) )
= $true )
| ( ( ~ ( in @ SV307 @ SV68 )
| ( ordinal_subset @ ( sK35_C @ SV122 @ SV68 ) @ SV307 ) )
= $true )
| ( ( ( SV68 = empty_set )
| ~ ( subset @ SV68 @ SV122 ) )
= $true )
| ( ( ordinal @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2071]) ).
thf(2147,plain,
! [SV122: $i,SV68: $i] :
( ( ( subset @ SV68 @ SV122 )
= $false )
| ( ( SV68 = empty_set )
= $true )
| ( ( in @ ( sK35_C @ SV122 @ SV68 ) @ SV68 )
= $true )
| ( ( ordinal @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2072]) ).
thf(2148,plain,
! [SV69: $i,SV203: $i,SV227: $i] :
( ( ( ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV227 )
| ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV69 ) )
= $true )
| ( ( SV227
= ( set_union2 @ SV69 @ SV203 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2073]) ).
thf(2149,plain,
! [SV69: $i,SV203: $i,SV227: $i] :
( ( ( ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV227 )
| ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV203 ) )
= $true )
| ( ( SV227
= ( set_union2 @ SV69 @ SV203 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2074]) ).
thf(2150,plain,
! [SV204: $i,SV69: $i,SV228: $i,SV308: $i] :
( ( ( ~ ( in @ SV308 @ SV228 ) )
= $true )
| ( ( ( in @ SV308 @ SV69 )
| ( in @ SV308 @ SV204 ) )
= $true )
| ( ( SV228
= ( set_union2 @ SV69 @ SV204 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2076]) ).
thf(2151,plain,
! [SV204: $i,SV228: $i,SV69: $i] :
( ( ( ~ ! [SY572: $i] :
( ~ ( in @ SY572 @ SV69 )
| ( in @ SY572 @ SV228 ) ) )
= $false )
| ( ( SV228
= ( set_union2 @ SV69 @ SV204 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2077]) ).
thf(2152,plain,
! [SV69: $i,SV228: $i,SV204: $i] :
( ( ( ~ ! [SY573: $i] :
( ~ ( in @ SY573 @ SV204 )
| ( in @ SY573 @ SV228 ) ) )
= $false )
| ( ( SV228
= ( set_union2 @ SV69 @ SV204 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2077]) ).
thf(2153,plain,
! [SV163: $i,SV206: $i,SV303: $i] :
( ( ( in @ SV303 @ SV206 )
= $false )
| ( ( subset @ SV303 @ SV163 )
= $true )
| ( ( SV206
= ( powerset @ SV163 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2079]) ).
thf(2154,plain,
! [SV206: $i,SV163: $i,SV304: $i] :
( ( ( subset @ SV304 @ SV163 )
= $false )
| ( ( in @ SV304 @ SV206 )
= $true )
| ( ( SV206
= ( powerset @ SV163 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2080]) ).
thf(2155,plain,
! [SV70: $i,SV207: $i,SV229: $i] :
( ( ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV70 )
= $false )
| ( ( ~ ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV207 ) )
= $true )
| ( ( ~ ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV229 ) )
= $true )
| ( ( SV229
= ( set_intersection2 @ SV70 @ SV207 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2081]) ).
thf(2156,plain,
! [SV70: $i,SV207: $i,SV229: $i] :
( ( ( ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV70 )
| ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV229 ) )
= $true )
| ( ( SV229
= ( set_intersection2 @ SV70 @ SV207 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2082]) ).
thf(2157,plain,
! [SV70: $i,SV207: $i,SV229: $i] :
( ( ( ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV207 )
| ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV229 ) )
= $true )
| ( ( SV229
= ( set_intersection2 @ SV70 @ SV207 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2083]) ).
thf(2158,plain,
! [SV230: $i,SV208: $i,SV70: $i,SV309: $i] :
( ( ( ~ ( in @ SV309 @ SV70 )
| ~ ( in @ SV309 @ SV208 ) )
= $true )
| ( ( in @ SV309 @ SV230 )
= $true )
| ( ( SV230
= ( set_intersection2 @ SV70 @ SV208 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2084]) ).
thf(2159,plain,
! [SV208: $i,SV70: $i,SV230: $i] :
( ( ( ~ ! [SY575: $i] :
( ~ ( in @ SY575 @ SV230 )
| ( in @ SY575 @ SV70 ) ) )
= $false )
| ( ( SV230
= ( set_intersection2 @ SV70 @ SV208 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2085]) ).
thf(2160,plain,
! [SV70: $i,SV208: $i,SV230: $i] :
( ( ( ~ ! [SY576: $i] :
( ~ ( in @ SY576 @ SV230 )
| ( in @ SY576 @ SV208 ) ) )
= $false )
| ( ( SV230
= ( set_intersection2 @ SV70 @ SV208 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2085]) ).
thf(2161,plain,
! [SV135: $i,SV71: $i,SV292: $i] :
( ( ( ~ ( in @ SV292 @ SV71 ) )
= $true )
| ( ( ordinal_subset @ ( sK54_B @ SV71 ) @ SV292 )
= $true )
| ( ( ordinal @ SV292 )
= $false )
| ( ( in @ SV135 @ SV71 )
= $false )
| ( ( ordinal @ SV135 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2086]) ).
thf(2162,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ~ ( ( ( sK44_C @ SV123 @ SV72 )
!= ( sK45_SY295 @ SV123 @ SV72 ) )
| ~ ~ ( ~ ~ ( ( ( sK45_SY295 @ SV123 @ SV72 )
!= ( sK48_SY300 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2089]) ).
thf(2163,plain,
! [SV72: $i,SV123: $i] :
( ( ( ( sK44_C @ SV123 @ SV72 )
!= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2089]) ).
thf(2164,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ~ ( ( ( sK46_SY299 @ SV123 @ SV72 )
!= ( sK47_SY303 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2090]) ).
thf(2165,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 ) )
= $false )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2090]) ).
thf(2166,plain,
! [SV72: $i,SV123: $i,SV316: $i] :
( ( ( ! [SY618: $i] :
( ( SY618 != SV316 )
| ~ ( in @ SY618 @ ( succ @ SV123 ) ) )
| ! [SY619: $i] :
( ( SV316 != SY619 )
| ~ ( ordinal @ SY619 )
| ~ ( in @ SY619 @ SV72 ) )
| ( in @ SV316 @ ( sK41_C @ SV123 @ SV72 ) ) )
= $true )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2091]) ).
thf(2167,plain,
! [SV72: $i,SV123: $i,SV317: $i] :
( ( ( ~ ( in @ SV317 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SV317 @ SV123 @ SV72 )
!= SV317 )
| ~ ( in @ ( sK43_E @ SV317 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SV317
!= ( sK42_H @ SV317 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV317 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV317 @ SV123 @ SV72 ) @ SV72 ) ) ) )
= $true )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2092]) ).
thf(2168,plain,
! [SV73: $i,SV254: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK23_C @ SV254 @ SV73 ) @ ( sK24_SY280 @ SV254 @ SV73 ) ) @ SV73 )
| ~ ( in @ ( ordered_pair @ ( sK23_C @ SV254 @ SV73 ) @ ( sK24_SY280 @ SV254 @ SV73 ) ) @ SV254 ) )
= $true )
| ( ( SV73 = SV254 )
= $true )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2093]) ).
thf(2169,plain,
! [SV73: $i,SV254: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK23_C @ SV254 @ SV73 ) @ ( sK24_SY280 @ SV254 @ SV73 ) ) @ SV73 )
| ( in @ ( ordered_pair @ ( sK23_C @ SV254 @ SV73 ) @ ( sK24_SY280 @ SV254 @ SV73 ) ) @ SV254 ) )
= $true )
| ( ( SV73 = SV254 )
= $true )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2094]) ).
thf(2170,plain,
! [SV255: $i,SV73: $i] :
( ( ( ~ ! [SY592: $i,SY593: $i] :
( ~ ( in @ ( ordered_pair @ SY592 @ SY593 ) @ SV73 )
| ( in @ ( ordered_pair @ SY592 @ SY593 ) @ SV255 ) ) )
= $false )
| ( ( SV73 = SV255 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2095]) ).
thf(2171,plain,
! [SV73: $i,SV255: $i] :
( ( ( ~ ! [SY594: $i,SY595: $i] :
( ~ ( in @ ( ordered_pair @ SY594 @ SY595 ) @ SV255 )
| ( in @ ( ordered_pair @ SY594 @ SY595 ) @ SV73 ) ) )
= $false )
| ( ( SV73 = SV255 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2095]) ).
thf(2172,plain,
! [SV74: $i,SV211: $i,SV231: $i] :
( ( ( ~ ( in @ ( sK22_D @ SV231 @ SV211 @ SV74 ) @ SV231 )
| ( ( sK22_D @ SV231 @ SV211 @ SV74 )
!= SV74 ) )
= $true )
| ( ( SV231
= ( unordered_pair @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2096]) ).
thf(2173,plain,
! [SV74: $i,SV211: $i,SV231: $i] :
( ( ( ~ ( in @ ( sK22_D @ SV231 @ SV211 @ SV74 ) @ SV231 )
| ( ( sK22_D @ SV231 @ SV211 @ SV74 )
!= SV211 ) )
= $true )
| ( ( SV231
= ( unordered_pair @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2097]) ).
thf(2174,plain,
! [SV212: $i,SV74: $i,SV232: $i,SV310: $i] :
( ( ( ~ ( in @ SV310 @ SV232 ) )
= $true )
| ( ( ( SV310 = SV74 )
| ( SV310 = SV212 ) )
= $true )
| ( ( SV232
= ( unordered_pair @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2099]) ).
thf(2175,plain,
! [SV212: $i,SV232: $i,SV74: $i] :
( ( ( ~ ! [SY578: $i] :
( ( SY578 != SV74 )
| ( in @ SY578 @ SV232 ) ) )
= $false )
| ( ( SV232
= ( unordered_pair @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2100]) ).
thf(2176,plain,
! [SV74: $i,SV232: $i,SV212: $i] :
( ( ( ~ ! [SY579: $i] :
( ( SY579 != SV212 )
| ( in @ SY579 @ SV232 ) ) )
= $false )
| ( ( SV232
= ( unordered_pair @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2100]) ).
thf(2177,plain,
! [SV75: $i,SV275: $i,SV318: $i] :
( ( ( ~ ( subset @ SV318 @ SV275 )
| ( in @ SV318 @ ( sK3_SY270 @ SV275 @ SV75 ) ) )
= $true )
| ( ( ~ ( in @ SV275 @ ( sK2_B @ SV75 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2101]) ).
thf(2178,plain,
! [SV75: $i,SV275: $i] :
( ( ( in @ SV275 @ ( sK2_B @ SV75 ) )
= $false )
| ( ( in @ ( sK3_SY270 @ SV275 @ SV75 ) @ ( sK2_B @ SV75 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2102]) ).
thf(2179,plain,
! [SV311: $i,SV75: $i,SV305: $i] :
( ( ( ~ ( in @ SV305 @ ( sK2_B @ SV75 ) )
| ~ ( subset @ SV311 @ SV305 ) )
= $true )
| ( ( in @ SV311 @ ( sK2_B @ SV75 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2103]) ).
thf(2180,plain,
! [SV77: $i,SV257: $i] :
( ( ( in @ ( ordered_pair @ ( sK17_C @ SV257 @ SV77 ) @ ( sK18_SY278 @ SV257 @ SV77 ) ) @ SV77 )
= $true )
| ( ( subset @ SV77 @ SV257 )
= $true )
| ( ( relation @ SV257 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2104]) ).
thf(2181,plain,
! [SV77: $i,SV257: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK17_C @ SV257 @ SV77 ) @ ( sK18_SY278 @ SV257 @ SV77 ) ) @ SV257 ) )
= $true )
| ( ( subset @ SV77 @ SV257 )
= $true )
| ( ( relation @ SV257 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2105]) ).
thf(2182,plain,
! [SV258: $i,SV77: $i,SV319: $i,SV312: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV312 @ SV319 ) @ SV77 )
| ( in @ ( ordered_pair @ SV312 @ SV319 ) @ SV258 ) )
= $true )
| ( ( subset @ SV77 @ SV258 )
= $false )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2106]) ).
thf(2183,plain,
! [SV78: $i,SV218: $i,SV235: $i] :
( ( ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV78 )
= $false )
| ( ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV218 )
= $true )
| ( ( ~ ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV235 ) )
= $true )
| ( ( SV235
= ( set_difference @ SV78 @ SV218 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2107]) ).
thf(2184,plain,
! [SV78: $i,SV218: $i,SV235: $i] :
( ( ( ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV78 )
| ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV235 ) )
= $true )
| ( ( SV235
= ( set_difference @ SV78 @ SV218 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2108]) ).
thf(2185,plain,
! [SV78: $i,SV218: $i,SV235: $i] :
( ( ( ~ ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV218 )
| ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV235 ) )
= $true )
| ( ( SV235
= ( set_difference @ SV78 @ SV218 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2109]) ).
thf(2186,plain,
! [SV236: $i,SV219: $i,SV78: $i,SV313: $i] :
( ( ( ~ ( in @ SV313 @ SV78 )
| ( in @ SV313 @ SV219 ) )
= $true )
| ( ( in @ SV313 @ SV236 )
= $true )
| ( ( SV236
= ( set_difference @ SV78 @ SV219 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2110]) ).
thf(2187,plain,
! [SV219: $i,SV78: $i,SV236: $i] :
( ( ( ~ ! [SY581: $i] :
( ~ ( in @ SY581 @ SV236 )
| ( in @ SY581 @ SV78 ) ) )
= $false )
| ( ( SV236
= ( set_difference @ SV78 @ SV219 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2111]) ).
thf(2188,plain,
! [SV78: $i,SV219: $i,SV236: $i] :
( ( ( ~ ! [SY582: $i] :
( ~ ( in @ SY582 @ SV236 )
| ~ ( in @ SY582 @ SV219 ) ) )
= $false )
| ( ( SV236
= ( set_difference @ SV78 @ SV219 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2111]) ).
thf(2189,plain,
! [SV175: $i] :
( ( ( in @ ( ordered_pair @ ( sK36_B @ SV175 ) @ ( sK37_SY285 @ SV175 ) ) @ SV175 )
= $true )
| ( ( antisymmetric @ SV175 )
= $true )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2112]) ).
thf(2190,plain,
! [SV175: $i] :
( ( ( in @ ( ordered_pair @ ( sK37_SY285 @ SV175 ) @ ( sK36_B @ SV175 ) ) @ SV175 )
= $true )
| ( ( antisymmetric @ SV175 )
= $true )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2113]) ).
thf(2191,plain,
! [SV176: $i,SV293: $i,SV286: $i] :
( ( ( in @ ( ordered_pair @ SV286 @ SV293 ) @ SV176 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV293 @ SV286 ) @ SV176 ) )
= $true )
| ( ( SV286 = SV293 )
= $true )
| ( ( antisymmetric @ SV176 )
= $false )
| ( ( relation @ SV176 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2114]) ).
thf(2192,plain,
! [SV178: $i] :
( ( ( in @ ( ordered_pair @ ( sK38_B @ SV178 ) @ ( sK39_SY286 @ SV178 ) ) @ SV178 )
= $true )
| ( ( transitive @ SV178 )
= $true )
| ( ( relation @ SV178 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2115]) ).
thf(2193,plain,
! [SV178: $i] :
( ( ( in @ ( ordered_pair @ ( sK39_SY286 @ SV178 ) @ ( sK40_SY288 @ SV178 ) ) @ SV178 )
= $true )
| ( ( transitive @ SV178 )
= $true )
| ( ( relation @ SV178 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2116]) ).
thf(2194,plain,
! [SV306: $i,SV179: $i,SV294: $i,SV287: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV287 @ SV294 ) @ SV179 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV294 @ SV306 ) @ SV179 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV287 @ SV306 ) @ SV179 )
= $true )
| ( ( transitive @ SV179 )
= $false )
| ( ( relation @ SV179 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2117]) ).
thf(2195,plain,
! [SV80: $i,SV125: $i,SV237: $i,SV263: $i] :
( ( ( ~ ( ~ ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
!= SV237 ) ) )
= $false )
| ( ( SV263
= ( unordered_triple @ SV80 @ SV125 @ SV237 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2119]) ).
thf(2196,plain,
! [SV80: $i,SV125: $i,SV237: $i,SV263: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
!= SV80 ) )
| ~ ( ~ ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
!= SV125 ) ) ) )
= $false )
| ( ( SV263
= ( unordered_triple @ SV80 @ SV125 @ SV237 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2119]) ).
thf(2197,plain,
! [SV80: $i,SV125: $i,SV237: $i,SV263: $i] :
( ( ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
= SV237 )
= $true )
| ( ( ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
= SV80 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
= SV125 ) )
= $true )
| ( ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
= $true )
| ( ( SV263
= ( unordered_triple @ SV80 @ SV125 @ SV237 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2120]) ).
thf(2198,plain,
! [SV125: $i,SV80: $i,SV238: $i,SV264: $i,SV320: $i] :
( ( ( ~ ( in @ SV320 @ SV264 )
| ( SV320 = SV238 )
| ( SV320 = SV80 )
| ( SV320 = SV125 ) )
= $true )
| ( ( SV264
= ( unordered_triple @ SV80 @ SV125 @ SV238 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2121]) ).
thf(2199,plain,
! [SV125: $i,SV80: $i,SV264: $i,SV238: $i] :
( ( ( ~ ! [SY601: $i] :
( ( SY601 != SV238 )
| ( in @ SY601 @ SV264 ) )
| ~ ~ ( ~ ! [SY602: $i] :
( ( SY602 != SV80 )
| ( in @ SY602 @ SV264 ) )
| ~ ! [SY603: $i] :
( ( SY603 != SV125 )
| ( in @ SY603 @ SV264 ) ) ) )
= $false )
| ( ( SV264
= ( unordered_triple @ SV80 @ SV125 @ SV238 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2122]) ).
thf(2200,plain,
! [SV144: $i] :
( ( ( in @ ( succ @ ( sK33_B @ SV144 ) ) @ SV144 )
= $false )
| ( ( being_limit_ordinal @ SV144 )
= $true )
| ( ( ordinal @ SV144 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2126]) ).
thf(2201,plain,
! [SV120: $i,SV63: $i,SV295: $i,SV267: $i] :
( ( ( SV267 = SV295 )
= $false )
| ( ( ~ ( ordinal @ SV295 ) )
= $true )
| ( ( ~ ( in @ SV295 @ SV63 ) )
= $true )
| ( ( ~ ( in @ SV267 @ ( succ @ SV120 ) ) )
= $true )
| ( ( in @ SV267 @ ( sK52_C @ SV120 @ SV63 ) )
= $true )
| ( ( ordinal @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2128]) ).
thf(2202,plain,
! [SV63: $i,SV120: $i,SV296: $i] :
( ( ( ~ ~ ( ( SV296
!= ( sK53_E @ SV296 @ SV120 @ SV63 ) )
| ~ ( ordinal @ ( sK53_E @ SV296 @ SV120 @ SV63 ) ) )
| ~ ( in @ ( sK53_E @ SV296 @ SV120 @ SV63 ) @ SV63 ) )
= $false )
| ( ( in @ SV296 @ ( sK52_C @ SV120 @ SV63 ) )
= $false )
| ( ( ordinal @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2129]) ).
thf(2203,plain,
! [SV196: $i,SV148: $i,SV298: $i] :
( ( ( in @ SV298 @ SV148 )
= $false )
| ( ( in @ ( sK13_C @ SV196 @ SV148 ) @ SV298 )
= $false )
| ( ( ~ ( in @ ( sK13_C @ SV196 @ SV148 ) @ SV196 ) )
= $true )
| ( ( SV196
= ( union @ SV148 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2132]) ).
thf(2204,plain,
! [SV197: $i,SV149: $i,SV314: $i,SV299: $i] :
( ( ( ~ ( in @ SV299 @ SV314 ) )
= $true )
| ( ( ~ ( in @ SV314 @ SV149 ) )
= $true )
| ( ( in @ SV299 @ SV197 )
= $true )
| ( ( SV197
= ( union @ SV149 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2135]) ).
thf(2205,plain,
! [SV149: $i,SV197: $i,SV300: $i] :
( ( ( ~ ( in @ SV300 @ ( sK12_D @ SV300 @ SV197 @ SV149 ) )
| ~ ( in @ ( sK12_D @ SV300 @ SV197 @ SV149 ) @ SV149 ) )
= $false )
| ( ( in @ SV300 @ SV197 )
= $false )
| ( ( SV197
= ( union @ SV149 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2136]) ).
thf(2206,plain,
! [SV152: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_B @ SV152 ) @ SV152 )
| ~ ( in @ ( sK20_SY279 @ SV152 ) @ SV152 ) ) )
= $true )
| ( ( epsilon_connected @ SV152 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2137]) ).
thf(2207,plain,
! [SV152: $i] :
( ( ( ~ ( in @ ( sK19_B @ SV152 ) @ ( sK20_SY279 @ SV152 ) ) )
= $true )
| ( ( epsilon_connected @ SV152 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2138]) ).
thf(2208,plain,
! [SV245: $i,SV153: $i,SV272: $i] :
( ( ( in @ SV272 @ SV153 )
= $false )
| ( ( in @ SV245 @ SV153 )
= $false )
| ( ( in @ SV245 @ SV272 )
= $true )
| ( ( SV245 = SV272 )
= $true )
| ( ( in @ SV272 @ SV245 )
= $true )
| ( ( epsilon_connected @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2139]) ).
thf(2209,plain,
! [SV155: $i] :
( ( ( antisymmetric @ SV155 )
= $false )
| ( ( reflexive @ SV155 )
= $false )
| ( ( transitive @ SV155 )
= $false )
| ( ( ~ ( connected @ SV155 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV155 ) )
= $true )
| ( ( well_ordering @ SV155 )
= $true )
| ( ( relation @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2140]) ).
thf(2210,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2141]) ).
thf(2211,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2141]) ).
thf(2212,plain,
! [SV315: $i] :
( ( ( ~ ( relation @ SV315 ) )
= $true )
| ( ( ~ ( well_ordering @ SV315 )
| ( antisymmetric @ SV315 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2142]) ).
thf(2213,plain,
! [SV291: $i] :
( ( ( well_ordering @ SV291 )
= $false )
| ( ( connected @ SV291 )
= $true )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2143]) ).
thf(2214,plain,
! [SV122: $i,SV68: $i,SV307: $i] :
( ( ( ordinal @ SV307 )
= $false )
| ( ( ~ ( in @ SV307 @ SV68 )
| ( ordinal_subset @ ( sK35_C @ SV122 @ SV68 ) @ SV307 ) )
= $true )
| ( ( ( SV68 = empty_set )
| ~ ( subset @ SV68 @ SV122 ) )
= $true )
| ( ( ordinal @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2146]) ).
thf(2215,plain,
! [SV69: $i,SV203: $i,SV227: $i] :
( ( ( ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV227 ) )
= $true )
| ( ( ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV69 ) )
= $true )
| ( ( SV227
= ( set_union2 @ SV69 @ SV203 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2148]) ).
thf(2216,plain,
! [SV69: $i,SV203: $i,SV227: $i] :
( ( ( ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV227 ) )
= $true )
| ( ( ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV203 ) )
= $true )
| ( ( SV227
= ( set_union2 @ SV69 @ SV203 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2149]) ).
thf(2217,plain,
! [SV204: $i,SV69: $i,SV228: $i,SV308: $i] :
( ( ( in @ SV308 @ SV228 )
= $false )
| ( ( ( in @ SV308 @ SV69 )
| ( in @ SV308 @ SV204 ) )
= $true )
| ( ( SV228
= ( set_union2 @ SV69 @ SV204 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2150]) ).
thf(2218,plain,
! [SV204: $i,SV228: $i,SV69: $i] :
( ( ( ! [SY572: $i] :
( ~ ( in @ SY572 @ SV69 )
| ( in @ SY572 @ SV228 ) ) )
= $true )
| ( ( SV228
= ( set_union2 @ SV69 @ SV204 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2151]) ).
thf(2219,plain,
! [SV69: $i,SV228: $i,SV204: $i] :
( ( ( ! [SY573: $i] :
( ~ ( in @ SY573 @ SV204 )
| ( in @ SY573 @ SV228 ) ) )
= $true )
| ( ( SV228
= ( set_union2 @ SV69 @ SV204 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2152]) ).
thf(2220,plain,
! [SV70: $i,SV207: $i,SV229: $i] :
( ( ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV207 )
= $false )
| ( ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV70 )
= $false )
| ( ( ~ ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV229 ) )
= $true )
| ( ( SV229
= ( set_intersection2 @ SV70 @ SV207 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2155]) ).
thf(2221,plain,
! [SV70: $i,SV207: $i,SV229: $i] :
( ( ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV70 )
= $true )
| ( ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV229 )
= $true )
| ( ( SV229
= ( set_intersection2 @ SV70 @ SV207 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2156]) ).
thf(2222,plain,
! [SV70: $i,SV207: $i,SV229: $i] :
( ( ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV207 )
= $true )
| ( ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV229 )
= $true )
| ( ( SV229
= ( set_intersection2 @ SV70 @ SV207 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2157]) ).
thf(2223,plain,
! [SV230: $i,SV208: $i,SV70: $i,SV309: $i] :
( ( ( ~ ( in @ SV309 @ SV70 ) )
= $true )
| ( ( ~ ( in @ SV309 @ SV208 ) )
= $true )
| ( ( in @ SV309 @ SV230 )
= $true )
| ( ( SV230
= ( set_intersection2 @ SV70 @ SV208 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2158]) ).
thf(2224,plain,
! [SV208: $i,SV70: $i,SV230: $i] :
( ( ( ! [SY575: $i] :
( ~ ( in @ SY575 @ SV230 )
| ( in @ SY575 @ SV70 ) ) )
= $true )
| ( ( SV230
= ( set_intersection2 @ SV70 @ SV208 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2159]) ).
thf(2225,plain,
! [SV70: $i,SV208: $i,SV230: $i] :
( ( ( ! [SY576: $i] :
( ~ ( in @ SY576 @ SV230 )
| ( in @ SY576 @ SV208 ) ) )
= $true )
| ( ( SV230
= ( set_intersection2 @ SV70 @ SV208 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2160]) ).
thf(2226,plain,
! [SV135: $i,SV71: $i,SV292: $i] :
( ( ( in @ SV292 @ SV71 )
= $false )
| ( ( ordinal_subset @ ( sK54_B @ SV71 ) @ SV292 )
= $true )
| ( ( ordinal @ SV292 )
= $false )
| ( ( in @ SV135 @ SV71 )
= $false )
| ( ( ordinal @ SV135 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2161]) ).
thf(2227,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ( ( ( sK44_C @ SV123 @ SV72 )
!= ( sK45_SY295 @ SV123 @ SV72 ) )
| ~ ~ ( ~ ~ ( ( ( sK45_SY295 @ SV123 @ SV72 )
!= ( sK48_SY300 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2162]) ).
thf(2228,plain,
! [SV72: $i,SV123: $i] :
( ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2163]) ).
thf(2229,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ( ( ( sK46_SY299 @ SV123 @ SV72 )
!= ( sK47_SY303 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2164]) ).
thf(2230,plain,
! [SV72: $i,SV123: $i] :
( ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2165]) ).
thf(2231,plain,
! [SV72: $i,SV123: $i,SV316: $i] :
( ( ( ! [SY618: $i] :
( ( SY618 != SV316 )
| ~ ( in @ SY618 @ ( succ @ SV123 ) ) )
| ! [SY619: $i] :
( ( SV316 != SY619 )
| ~ ( ordinal @ SY619 )
| ~ ( in @ SY619 @ SV72 ) ) )
= $true )
| ( ( in @ SV316 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2166]) ).
thf(2232,plain,
! [SV72: $i,SV123: $i,SV317: $i] :
( ( ( ~ ( in @ SV317 @ ( sK41_C @ SV123 @ SV72 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK43_E @ SV317 @ SV123 @ SV72 )
!= SV317 )
| ~ ( in @ ( sK43_E @ SV317 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SV317
!= ( sK42_H @ SV317 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV317 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV317 @ SV123 @ SV72 ) @ SV72 ) ) ) )
= $true )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2167]) ).
thf(2233,plain,
! [SV73: $i,SV254: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK23_C @ SV254 @ SV73 ) @ ( sK24_SY280 @ SV254 @ SV73 ) ) @ SV73 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK23_C @ SV254 @ SV73 ) @ ( sK24_SY280 @ SV254 @ SV73 ) ) @ SV254 ) )
= $true )
| ( ( SV73 = SV254 )
= $true )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2168]) ).
thf(2234,plain,
! [SV73: $i,SV254: $i] :
( ( ( in @ ( ordered_pair @ ( sK23_C @ SV254 @ SV73 ) @ ( sK24_SY280 @ SV254 @ SV73 ) ) @ SV73 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK23_C @ SV254 @ SV73 ) @ ( sK24_SY280 @ SV254 @ SV73 ) ) @ SV254 )
= $true )
| ( ( SV73 = SV254 )
= $true )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2169]) ).
thf(2235,plain,
! [SV255: $i,SV73: $i] :
( ( ( ! [SY592: $i,SY593: $i] :
( ~ ( in @ ( ordered_pair @ SY592 @ SY593 ) @ SV73 )
| ( in @ ( ordered_pair @ SY592 @ SY593 ) @ SV255 ) ) )
= $true )
| ( ( SV73 = SV255 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2170]) ).
thf(2236,plain,
! [SV73: $i,SV255: $i] :
( ( ( ! [SY594: $i,SY595: $i] :
( ~ ( in @ ( ordered_pair @ SY594 @ SY595 ) @ SV255 )
| ( in @ ( ordered_pair @ SY594 @ SY595 ) @ SV73 ) ) )
= $true )
| ( ( SV73 = SV255 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2171]) ).
thf(2237,plain,
! [SV74: $i,SV211: $i,SV231: $i] :
( ( ( ~ ( in @ ( sK22_D @ SV231 @ SV211 @ SV74 ) @ SV231 ) )
= $true )
| ( ( ( sK22_D @ SV231 @ SV211 @ SV74 )
!= SV74 )
= $true )
| ( ( SV231
= ( unordered_pair @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2172]) ).
thf(2238,plain,
! [SV74: $i,SV211: $i,SV231: $i] :
( ( ( ~ ( in @ ( sK22_D @ SV231 @ SV211 @ SV74 ) @ SV231 ) )
= $true )
| ( ( ( sK22_D @ SV231 @ SV211 @ SV74 )
!= SV211 )
= $true )
| ( ( SV231
= ( unordered_pair @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2173]) ).
thf(2239,plain,
! [SV212: $i,SV74: $i,SV232: $i,SV310: $i] :
( ( ( in @ SV310 @ SV232 )
= $false )
| ( ( ( SV310 = SV74 )
| ( SV310 = SV212 ) )
= $true )
| ( ( SV232
= ( unordered_pair @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2174]) ).
thf(2240,plain,
! [SV212: $i,SV232: $i,SV74: $i] :
( ( ( ! [SY578: $i] :
( ( SY578 != SV74 )
| ( in @ SY578 @ SV232 ) ) )
= $true )
| ( ( SV232
= ( unordered_pair @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2175]) ).
thf(2241,plain,
! [SV74: $i,SV232: $i,SV212: $i] :
( ( ( ! [SY579: $i] :
( ( SY579 != SV212 )
| ( in @ SY579 @ SV232 ) ) )
= $true )
| ( ( SV232
= ( unordered_pair @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2176]) ).
thf(2242,plain,
! [SV75: $i,SV275: $i,SV318: $i] :
( ( ( ~ ( subset @ SV318 @ SV275 ) )
= $true )
| ( ( in @ SV318 @ ( sK3_SY270 @ SV275 @ SV75 ) )
= $true )
| ( ( ~ ( in @ SV275 @ ( sK2_B @ SV75 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2177]) ).
thf(2243,plain,
! [SV311: $i,SV75: $i,SV305: $i] :
( ( ( ~ ( in @ SV305 @ ( sK2_B @ SV75 ) ) )
= $true )
| ( ( ~ ( subset @ SV311 @ SV305 ) )
= $true )
| ( ( in @ SV311 @ ( sK2_B @ SV75 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2179]) ).
thf(2244,plain,
! [SV77: $i,SV257: $i] :
( ( ( in @ ( ordered_pair @ ( sK17_C @ SV257 @ SV77 ) @ ( sK18_SY278 @ SV257 @ SV77 ) ) @ SV257 )
= $false )
| ( ( subset @ SV77 @ SV257 )
= $true )
| ( ( relation @ SV257 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2181]) ).
thf(2245,plain,
! [SV258: $i,SV77: $i,SV319: $i,SV312: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV312 @ SV319 ) @ SV77 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV312 @ SV319 ) @ SV258 )
= $true )
| ( ( subset @ SV77 @ SV258 )
= $false )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2182]) ).
thf(2246,plain,
! [SV78: $i,SV218: $i,SV235: $i] :
( ( ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV235 )
= $false )
| ( ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV218 )
= $true )
| ( ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV78 )
= $false )
| ( ( SV235
= ( set_difference @ SV78 @ SV218 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2183]) ).
thf(2247,plain,
! [SV78: $i,SV218: $i,SV235: $i] :
( ( ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV78 )
= $true )
| ( ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV235 )
= $true )
| ( ( SV235
= ( set_difference @ SV78 @ SV218 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2184]) ).
thf(2248,plain,
! [SV78: $i,SV218: $i,SV235: $i] :
( ( ( ~ ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV218 ) )
= $true )
| ( ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV235 )
= $true )
| ( ( SV235
= ( set_difference @ SV78 @ SV218 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2185]) ).
thf(2249,plain,
! [SV236: $i,SV219: $i,SV78: $i,SV313: $i] :
( ( ( ~ ( in @ SV313 @ SV78 ) )
= $true )
| ( ( in @ SV313 @ SV219 )
= $true )
| ( ( in @ SV313 @ SV236 )
= $true )
| ( ( SV236
= ( set_difference @ SV78 @ SV219 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2186]) ).
thf(2250,plain,
! [SV219: $i,SV78: $i,SV236: $i] :
( ( ( ! [SY581: $i] :
( ~ ( in @ SY581 @ SV236 )
| ( in @ SY581 @ SV78 ) ) )
= $true )
| ( ( SV236
= ( set_difference @ SV78 @ SV219 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2187]) ).
thf(2251,plain,
! [SV78: $i,SV219: $i,SV236: $i] :
( ( ( ! [SY582: $i] :
( ~ ( in @ SY582 @ SV236 )
| ~ ( in @ SY582 @ SV219 ) ) )
= $true )
| ( ( SV236
= ( set_difference @ SV78 @ SV219 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2188]) ).
thf(2252,plain,
! [SV176: $i,SV286: $i,SV293: $i] :
( ( ( in @ ( ordered_pair @ SV293 @ SV286 ) @ SV176 )
= $false )
| ( ( in @ ( ordered_pair @ SV286 @ SV293 ) @ SV176 )
= $false )
| ( ( SV286 = SV293 )
= $true )
| ( ( antisymmetric @ SV176 )
= $false )
| ( ( relation @ SV176 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2191]) ).
thf(2253,plain,
! [SV306: $i,SV179: $i,SV294: $i,SV287: $i] :
( ( ( in @ ( ordered_pair @ SV287 @ SV294 ) @ SV179 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV294 @ SV306 ) @ SV179 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV287 @ SV306 ) @ SV179 )
= $true )
| ( ( transitive @ SV179 )
= $false )
| ( ( relation @ SV179 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2194]) ).
thf(2254,plain,
! [SV80: $i,SV125: $i,SV237: $i,SV263: $i] :
( ( ( ~ ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
!= SV237 ) )
= $true )
| ( ( SV263
= ( unordered_triple @ SV80 @ SV125 @ SV237 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2195]) ).
thf(2255,plain,
! [SV80: $i,SV125: $i,SV237: $i,SV263: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
!= SV80 ) )
| ~ ( ~ ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
!= SV125 ) ) ) )
= $true )
| ( ( SV263
= ( unordered_triple @ SV80 @ SV125 @ SV237 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2196]) ).
thf(2256,plain,
! [SV80: $i,SV125: $i,SV237: $i,SV263: $i] :
( ( ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
= SV80 )
= $true )
| ( ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
= SV125 )
= $true )
| ( ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
= SV237 )
= $true )
| ( ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
= $true )
| ( ( SV263
= ( unordered_triple @ SV80 @ SV125 @ SV237 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2197]) ).
thf(2257,plain,
! [SV125: $i,SV80: $i,SV238: $i,SV264: $i,SV320: $i] :
( ( ( ~ ( in @ SV320 @ SV264 ) )
= $true )
| ( ( ( SV320 = SV238 )
| ( SV320 = SV80 )
| ( SV320 = SV125 ) )
= $true )
| ( ( SV264
= ( unordered_triple @ SV80 @ SV125 @ SV238 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2198]) ).
thf(2258,plain,
! [SV125: $i,SV80: $i,SV264: $i,SV238: $i] :
( ( ( ~ ! [SY601: $i] :
( ( SY601 != SV238 )
| ( in @ SY601 @ SV264 ) ) )
= $false )
| ( ( SV264
= ( unordered_triple @ SV80 @ SV125 @ SV238 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2199]) ).
thf(2259,plain,
! [SV238: $i,SV125: $i,SV264: $i,SV80: $i] :
( ( ( ~ ~ ( ~ ! [SY602: $i] :
( ( SY602 != SV80 )
| ( in @ SY602 @ SV264 ) )
| ~ ! [SY603: $i] :
( ( SY603 != SV125 )
| ( in @ SY603 @ SV264 ) ) ) )
= $false )
| ( ( SV264
= ( unordered_triple @ SV80 @ SV125 @ SV238 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2199]) ).
thf(2260,plain,
! [SV120: $i,SV63: $i,SV267: $i,SV295: $i] :
( ( ( ordinal @ SV295 )
= $false )
| ( ( SV267 = SV295 )
= $false )
| ( ( ~ ( in @ SV295 @ SV63 ) )
= $true )
| ( ( ~ ( in @ SV267 @ ( succ @ SV120 ) ) )
= $true )
| ( ( in @ SV267 @ ( sK52_C @ SV120 @ SV63 ) )
= $true )
| ( ( ordinal @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2201]) ).
thf(2261,plain,
! [SV63: $i,SV120: $i,SV296: $i] :
( ( ( ~ ~ ( ( SV296
!= ( sK53_E @ SV296 @ SV120 @ SV63 ) )
| ~ ( ordinal @ ( sK53_E @ SV296 @ SV120 @ SV63 ) ) ) )
= $false )
| ( ( in @ SV296 @ ( sK52_C @ SV120 @ SV63 ) )
= $false )
| ( ( ordinal @ SV120 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2202]) ).
thf(2262,plain,
! [SV63: $i,SV120: $i,SV296: $i] :
( ( ( ~ ( in @ ( sK53_E @ SV296 @ SV120 @ SV63 ) @ SV63 ) )
= $false )
| ( ( in @ SV296 @ ( sK52_C @ SV120 @ SV63 ) )
= $false )
| ( ( ordinal @ SV120 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2202]) ).
thf(2263,plain,
! [SV298: $i,SV148: $i,SV196: $i] :
( ( ( in @ ( sK13_C @ SV196 @ SV148 ) @ SV196 )
= $false )
| ( ( in @ ( sK13_C @ SV196 @ SV148 ) @ SV298 )
= $false )
| ( ( in @ SV298 @ SV148 )
= $false )
| ( ( SV196
= ( union @ SV148 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2203]) ).
thf(2264,plain,
! [SV197: $i,SV149: $i,SV314: $i,SV299: $i] :
( ( ( in @ SV299 @ SV314 )
= $false )
| ( ( ~ ( in @ SV314 @ SV149 ) )
= $true )
| ( ( in @ SV299 @ SV197 )
= $true )
| ( ( SV197
= ( union @ SV149 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2204]) ).
thf(2265,plain,
! [SV149: $i,SV197: $i,SV300: $i] :
( ( ( ~ ( in @ SV300 @ ( sK12_D @ SV300 @ SV197 @ SV149 ) ) )
= $false )
| ( ( in @ SV300 @ SV197 )
= $false )
| ( ( SV197
= ( union @ SV149 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2205]) ).
thf(2266,plain,
! [SV149: $i,SV197: $i,SV300: $i] :
( ( ( ~ ( in @ ( sK12_D @ SV300 @ SV197 @ SV149 ) @ SV149 ) )
= $false )
| ( ( in @ SV300 @ SV197 )
= $false )
| ( ( SV197
= ( union @ SV149 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2205]) ).
thf(2267,plain,
! [SV152: $i] :
( ( ( ~ ( in @ ( sK19_B @ SV152 ) @ SV152 )
| ~ ( in @ ( sK20_SY279 @ SV152 ) @ SV152 ) )
= $false )
| ( ( epsilon_connected @ SV152 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2206]) ).
thf(2268,plain,
! [SV152: $i] :
( ( ( in @ ( sK19_B @ SV152 ) @ ( sK20_SY279 @ SV152 ) )
= $false )
| ( ( epsilon_connected @ SV152 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2207]) ).
thf(2269,plain,
! [SV155: $i] :
( ( ( connected @ SV155 )
= $false )
| ( ( transitive @ SV155 )
= $false )
| ( ( reflexive @ SV155 )
= $false )
| ( ( antisymmetric @ SV155 )
= $false )
| ( ( ~ ( well_founded_relation @ SV155 ) )
= $true )
| ( ( well_ordering @ SV155 )
= $true )
| ( ( relation @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2209]) ).
thf(2270,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2210]) ).
thf(2271,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2211]) ).
thf(2272,plain,
! [SV315: $i] :
( ( ( relation @ SV315 )
= $false )
| ( ( ~ ( well_ordering @ SV315 )
| ( antisymmetric @ SV315 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2212]) ).
thf(2273,plain,
! [SV122: $i,SV68: $i,SV307: $i] :
( ( ( ~ ( in @ SV307 @ SV68 ) )
= $true )
| ( ( ordinal_subset @ ( sK35_C @ SV122 @ SV68 ) @ SV307 )
= $true )
| ( ( ordinal @ SV307 )
= $false )
| ( ( ( SV68 = empty_set )
| ~ ( subset @ SV68 @ SV122 ) )
= $true )
| ( ( ordinal @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2214]) ).
thf(2274,plain,
! [SV69: $i,SV203: $i,SV227: $i] :
( ( ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV227 )
= $false )
| ( ( ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV69 ) )
= $true )
| ( ( SV227
= ( set_union2 @ SV69 @ SV203 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2215]) ).
thf(2275,plain,
! [SV69: $i,SV203: $i,SV227: $i] :
( ( ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV227 )
= $false )
| ( ( ~ ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV203 ) )
= $true )
| ( ( SV227
= ( set_union2 @ SV69 @ SV203 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2216]) ).
thf(2276,plain,
! [SV228: $i,SV204: $i,SV69: $i,SV308: $i] :
( ( ( in @ SV308 @ SV69 )
= $true )
| ( ( in @ SV308 @ SV204 )
= $true )
| ( ( in @ SV308 @ SV228 )
= $false )
| ( ( SV228
= ( set_union2 @ SV69 @ SV204 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2217]) ).
thf(2277,plain,
! [SV204: $i,SV228: $i,SV69: $i,SV321: $i] :
( ( ( ~ ( in @ SV321 @ SV69 )
| ( in @ SV321 @ SV228 ) )
= $true )
| ( ( SV228
= ( set_union2 @ SV69 @ SV204 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2218]) ).
thf(2278,plain,
! [SV69: $i,SV228: $i,SV204: $i,SV322: $i] :
( ( ( ~ ( in @ SV322 @ SV204 )
| ( in @ SV322 @ SV228 ) )
= $true )
| ( ( SV228
= ( set_union2 @ SV69 @ SV204 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2219]) ).
thf(2279,plain,
! [SV70: $i,SV207: $i,SV229: $i] :
( ( ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV229 )
= $false )
| ( ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV70 )
= $false )
| ( ( in @ ( sK15_D @ SV229 @ SV207 @ SV70 ) @ SV207 )
= $false )
| ( ( SV229
= ( set_intersection2 @ SV70 @ SV207 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2220]) ).
thf(2280,plain,
! [SV230: $i,SV208: $i,SV70: $i,SV309: $i] :
( ( ( in @ SV309 @ SV70 )
= $false )
| ( ( ~ ( in @ SV309 @ SV208 ) )
= $true )
| ( ( in @ SV309 @ SV230 )
= $true )
| ( ( SV230
= ( set_intersection2 @ SV70 @ SV208 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2223]) ).
thf(2281,plain,
! [SV208: $i,SV70: $i,SV230: $i,SV323: $i] :
( ( ( ~ ( in @ SV323 @ SV230 )
| ( in @ SV323 @ SV70 ) )
= $true )
| ( ( SV230
= ( set_intersection2 @ SV70 @ SV208 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2224]) ).
thf(2282,plain,
! [SV70: $i,SV208: $i,SV230: $i,SV324: $i] :
( ( ( ~ ( in @ SV324 @ SV230 )
| ( in @ SV324 @ SV208 ) )
= $true )
| ( ( SV230
= ( set_intersection2 @ SV70 @ SV208 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2225]) ).
thf(2283,plain,
! [SV72: $i,SV123: $i] :
( ( ( ( ( sK44_C @ SV123 @ SV72 )
!= ( sK45_SY295 @ SV123 @ SV72 ) )
| ~ ~ ( ~ ~ ( ( ( sK45_SY295 @ SV123 @ SV72 )
!= ( sK48_SY300 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2227]) ).
thf(2284,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2228]) ).
thf(2285,plain,
! [SV72: $i,SV123: $i] :
( ( ( ( ( sK46_SY299 @ SV123 @ SV72 )
!= ( sK47_SY303 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2229]) ).
thf(2286,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) )
= $false )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2230]) ).
thf(2287,plain,
! [SV72: $i,SV123: $i,SV316: $i] :
( ( ( ! [SY618: $i] :
( ( SY618 != SV316 )
| ~ ( in @ SY618 @ ( succ @ SV123 ) ) ) )
= $true )
| ( ( ! [SY619: $i] :
( ( SV316 != SY619 )
| ~ ( ordinal @ SY619 )
| ~ ( in @ SY619 @ SV72 ) ) )
= $true )
| ( ( in @ SV316 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2231]) ).
thf(2288,plain,
! [SV72: $i,SV123: $i,SV317: $i] :
( ( ( in @ SV317 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK43_E @ SV317 @ SV123 @ SV72 )
!= SV317 )
| ~ ( in @ ( sK43_E @ SV317 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SV317
!= ( sK42_H @ SV317 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV317 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV317 @ SV123 @ SV72 ) @ SV72 ) ) ) )
= $true )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2232]) ).
thf(2289,plain,
! [SV73: $i,SV254: $i] :
( ( ( in @ ( ordered_pair @ ( sK23_C @ SV254 @ SV73 ) @ ( sK24_SY280 @ SV254 @ SV73 ) ) @ SV73 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK23_C @ SV254 @ SV73 ) @ ( sK24_SY280 @ SV254 @ SV73 ) ) @ SV254 ) )
= $true )
| ( ( SV73 = SV254 )
= $true )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2233]) ).
thf(2290,plain,
! [SV255: $i,SV73: $i,SV325: $i] :
( ( ( ! [SY620: $i] :
( ~ ( in @ ( ordered_pair @ SV325 @ SY620 ) @ SV73 )
| ( in @ ( ordered_pair @ SV325 @ SY620 ) @ SV255 ) ) )
= $true )
| ( ( SV73 = SV255 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2235]) ).
thf(2291,plain,
! [SV73: $i,SV255: $i,SV326: $i] :
( ( ( ! [SY621: $i] :
( ~ ( in @ ( ordered_pair @ SV326 @ SY621 ) @ SV255 )
| ( in @ ( ordered_pair @ SV326 @ SY621 ) @ SV73 ) ) )
= $true )
| ( ( SV73 = SV255 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2236]) ).
thf(2292,plain,
! [SV74: $i,SV211: $i,SV231: $i] :
( ( ( in @ ( sK22_D @ SV231 @ SV211 @ SV74 ) @ SV231 )
= $false )
| ( ( ( sK22_D @ SV231 @ SV211 @ SV74 )
!= SV74 )
= $true )
| ( ( SV231
= ( unordered_pair @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2237]) ).
thf(2293,plain,
! [SV74: $i,SV211: $i,SV231: $i] :
( ( ( in @ ( sK22_D @ SV231 @ SV211 @ SV74 ) @ SV231 )
= $false )
| ( ( ( sK22_D @ SV231 @ SV211 @ SV74 )
!= SV211 )
= $true )
| ( ( SV231
= ( unordered_pair @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2238]) ).
thf(2294,plain,
! [SV232: $i,SV212: $i,SV74: $i,SV310: $i] :
( ( ( SV310 = SV74 )
= $true )
| ( ( SV310 = SV212 )
= $true )
| ( ( in @ SV310 @ SV232 )
= $false )
| ( ( SV232
= ( unordered_pair @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2239]) ).
thf(2295,plain,
! [SV212: $i,SV232: $i,SV74: $i,SV327: $i] :
( ( ( ( SV327 != SV74 )
| ( in @ SV327 @ SV232 ) )
= $true )
| ( ( SV232
= ( unordered_pair @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2240]) ).
thf(2296,plain,
! [SV74: $i,SV232: $i,SV212: $i,SV328: $i] :
( ( ( ( SV328 != SV212 )
| ( in @ SV328 @ SV232 ) )
= $true )
| ( ( SV232
= ( unordered_pair @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2241]) ).
thf(2297,plain,
! [SV75: $i,SV275: $i,SV318: $i] :
( ( ( subset @ SV318 @ SV275 )
= $false )
| ( ( in @ SV318 @ ( sK3_SY270 @ SV275 @ SV75 ) )
= $true )
| ( ( ~ ( in @ SV275 @ ( sK2_B @ SV75 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2242]) ).
thf(2298,plain,
! [SV311: $i,SV75: $i,SV305: $i] :
( ( ( in @ SV305 @ ( sK2_B @ SV75 ) )
= $false )
| ( ( ~ ( subset @ SV311 @ SV305 ) )
= $true )
| ( ( in @ SV311 @ ( sK2_B @ SV75 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2243]) ).
thf(2299,plain,
! [SV258: $i,SV77: $i,SV319: $i,SV312: $i] :
( ( ( in @ ( ordered_pair @ SV312 @ SV319 ) @ SV77 )
= $false )
| ( ( in @ ( ordered_pair @ SV312 @ SV319 ) @ SV258 )
= $true )
| ( ( subset @ SV77 @ SV258 )
= $false )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2245]) ).
thf(2300,plain,
! [SV78: $i,SV218: $i,SV235: $i] :
( ( ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV218 )
= $false )
| ( ( in @ ( sK11_D @ SV235 @ SV218 @ SV78 ) @ SV235 )
= $true )
| ( ( SV235
= ( set_difference @ SV78 @ SV218 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2248]) ).
thf(2301,plain,
! [SV236: $i,SV219: $i,SV78: $i,SV313: $i] :
( ( ( in @ SV313 @ SV78 )
= $false )
| ( ( in @ SV313 @ SV219 )
= $true )
| ( ( in @ SV313 @ SV236 )
= $true )
| ( ( SV236
= ( set_difference @ SV78 @ SV219 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2249]) ).
thf(2302,plain,
! [SV219: $i,SV78: $i,SV236: $i,SV329: $i] :
( ( ( ~ ( in @ SV329 @ SV236 )
| ( in @ SV329 @ SV78 ) )
= $true )
| ( ( SV236
= ( set_difference @ SV78 @ SV219 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2250]) ).
thf(2303,plain,
! [SV78: $i,SV219: $i,SV236: $i,SV330: $i] :
( ( ( ~ ( in @ SV330 @ SV236 )
| ~ ( in @ SV330 @ SV219 ) )
= $true )
| ( ( SV236
= ( set_difference @ SV78 @ SV219 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2251]) ).
thf(2304,plain,
! [SV287: $i,SV179: $i,SV306: $i,SV294: $i] :
( ( ( in @ ( ordered_pair @ SV294 @ SV306 ) @ SV179 )
= $false )
| ( ( in @ ( ordered_pair @ SV287 @ SV294 ) @ SV179 )
= $false )
| ( ( in @ ( ordered_pair @ SV287 @ SV306 ) @ SV179 )
= $true )
| ( ( transitive @ SV179 )
= $false )
| ( ( relation @ SV179 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2253]) ).
thf(2305,plain,
! [SV80: $i,SV125: $i,SV237: $i,SV263: $i] :
( ( ( ~ ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 ) )
= $true )
| ( ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
!= SV237 )
= $true )
| ( ( SV263
= ( unordered_triple @ SV80 @ SV125 @ SV237 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2254]) ).
thf(2306,plain,
! [SV80: $i,SV125: $i,SV237: $i,SV263: $i] :
( ( ( ~ ( ~ ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
!= SV80 ) )
| ~ ( ~ ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
!= SV125 ) ) )
= $false )
| ( ( SV263
= ( unordered_triple @ SV80 @ SV125 @ SV237 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2255]) ).
thf(2307,plain,
! [SV125: $i,SV80: $i,SV238: $i,SV264: $i,SV320: $i] :
( ( ( in @ SV320 @ SV264 )
= $false )
| ( ( ( SV320 = SV238 )
| ( SV320 = SV80 )
| ( SV320 = SV125 ) )
= $true )
| ( ( SV264
= ( unordered_triple @ SV80 @ SV125 @ SV238 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2257]) ).
thf(2308,plain,
! [SV125: $i,SV80: $i,SV264: $i,SV238: $i] :
( ( ( ! [SY601: $i] :
( ( SY601 != SV238 )
| ( in @ SY601 @ SV264 ) ) )
= $true )
| ( ( SV264
= ( unordered_triple @ SV80 @ SV125 @ SV238 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2258]) ).
thf(2309,plain,
! [SV238: $i,SV125: $i,SV264: $i,SV80: $i] :
( ( ( ~ ( ~ ! [SY602: $i] :
( ( SY602 != SV80 )
| ( in @ SY602 @ SV264 ) )
| ~ ! [SY603: $i] :
( ( SY603 != SV125 )
| ( in @ SY603 @ SV264 ) ) ) )
= $true )
| ( ( SV264
= ( unordered_triple @ SV80 @ SV125 @ SV238 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2259]) ).
thf(2310,plain,
! [SV120: $i,SV267: $i,SV63: $i,SV295: $i] :
( ( ( in @ SV295 @ SV63 )
= $false )
| ( ( SV267 = SV295 )
= $false )
| ( ( ordinal @ SV295 )
= $false )
| ( ( ~ ( in @ SV267 @ ( succ @ SV120 ) ) )
= $true )
| ( ( in @ SV267 @ ( sK52_C @ SV120 @ SV63 ) )
= $true )
| ( ( ordinal @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2260]) ).
thf(2311,plain,
! [SV63: $i,SV120: $i,SV296: $i] :
( ( ( ~ ( ( SV296
!= ( sK53_E @ SV296 @ SV120 @ SV63 ) )
| ~ ( ordinal @ ( sK53_E @ SV296 @ SV120 @ SV63 ) ) ) )
= $true )
| ( ( in @ SV296 @ ( sK52_C @ SV120 @ SV63 ) )
= $false )
| ( ( ordinal @ SV120 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2261]) ).
thf(2312,plain,
! [SV63: $i,SV120: $i,SV296: $i] :
( ( ( in @ ( sK53_E @ SV296 @ SV120 @ SV63 ) @ SV63 )
= $true )
| ( ( in @ SV296 @ ( sK52_C @ SV120 @ SV63 ) )
= $false )
| ( ( ordinal @ SV120 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2262]) ).
thf(2313,plain,
! [SV197: $i,SV299: $i,SV149: $i,SV314: $i] :
( ( ( in @ SV314 @ SV149 )
= $false )
| ( ( in @ SV299 @ SV314 )
= $false )
| ( ( in @ SV299 @ SV197 )
= $true )
| ( ( SV197
= ( union @ SV149 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2264]) ).
thf(2314,plain,
! [SV149: $i,SV197: $i,SV300: $i] :
( ( ( in @ SV300 @ ( sK12_D @ SV300 @ SV197 @ SV149 ) )
= $true )
| ( ( in @ SV300 @ SV197 )
= $false )
| ( ( SV197
= ( union @ SV149 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2265]) ).
thf(2315,plain,
! [SV149: $i,SV197: $i,SV300: $i] :
( ( ( in @ ( sK12_D @ SV300 @ SV197 @ SV149 ) @ SV149 )
= $true )
| ( ( in @ SV300 @ SV197 )
= $false )
| ( ( SV197
= ( union @ SV149 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2266]) ).
thf(2316,plain,
! [SV152: $i] :
( ( ( ~ ( in @ ( sK19_B @ SV152 ) @ SV152 ) )
= $false )
| ( ( epsilon_connected @ SV152 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2267]) ).
thf(2317,plain,
! [SV152: $i] :
( ( ( ~ ( in @ ( sK20_SY279 @ SV152 ) @ SV152 ) )
= $false )
| ( ( epsilon_connected @ SV152 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2267]) ).
thf(2318,plain,
! [SV155: $i] :
( ( ( well_founded_relation @ SV155 )
= $false )
| ( ( antisymmetric @ SV155 )
= $false )
| ( ( reflexive @ SV155 )
= $false )
| ( ( transitive @ SV155 )
= $false )
| ( ( connected @ SV155 )
= $false )
| ( ( well_ordering @ SV155 )
= $true )
| ( ( relation @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2269]) ).
thf(2319,plain,
! [SV331: $i] :
( ( ~ ( relation @ SV331 )
| ~ ( well_ordering @ SV331 )
| ( reflexive @ SV331 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2270]) ).
thf(2320,plain,
! [SV332: $i] :
( ( ~ ( relation @ SV332 )
| ~ ( well_ordering @ SV332 )
| ( transitive @ SV332 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2271]) ).
thf(2321,plain,
! [SV315: $i] :
( ( ( ~ ( well_ordering @ SV315 ) )
= $true )
| ( ( antisymmetric @ SV315 )
= $true )
| ( ( relation @ SV315 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2272]) ).
thf(2322,plain,
! [SV122: $i,SV68: $i,SV307: $i] :
( ( ( in @ SV307 @ SV68 )
= $false )
| ( ( ordinal_subset @ ( sK35_C @ SV122 @ SV68 ) @ SV307 )
= $true )
| ( ( ordinal @ SV307 )
= $false )
| ( ( ( SV68 = empty_set )
| ~ ( subset @ SV68 @ SV122 ) )
= $true )
| ( ( ordinal @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2273]) ).
thf(2323,plain,
! [SV69: $i,SV203: $i,SV227: $i] :
( ( ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV69 )
= $false )
| ( ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV227 )
= $false )
| ( ( SV227
= ( set_union2 @ SV69 @ SV203 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2274]) ).
thf(2324,plain,
! [SV69: $i,SV203: $i,SV227: $i] :
( ( ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV203 )
= $false )
| ( ( in @ ( sK21_D @ SV227 @ SV203 @ SV69 ) @ SV227 )
= $false )
| ( ( SV227
= ( set_union2 @ SV69 @ SV203 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2275]) ).
thf(2325,plain,
! [SV204: $i,SV228: $i,SV69: $i,SV321: $i] :
( ( ( ~ ( in @ SV321 @ SV69 ) )
= $true )
| ( ( in @ SV321 @ SV228 )
= $true )
| ( ( SV228
= ( set_union2 @ SV69 @ SV204 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2277]) ).
thf(2326,plain,
! [SV69: $i,SV228: $i,SV204: $i,SV322: $i] :
( ( ( ~ ( in @ SV322 @ SV204 ) )
= $true )
| ( ( in @ SV322 @ SV228 )
= $true )
| ( ( SV228
= ( set_union2 @ SV69 @ SV204 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2278]) ).
thf(2327,plain,
! [SV230: $i,SV70: $i,SV208: $i,SV309: $i] :
( ( ( in @ SV309 @ SV208 )
= $false )
| ( ( in @ SV309 @ SV70 )
= $false )
| ( ( in @ SV309 @ SV230 )
= $true )
| ( ( SV230
= ( set_intersection2 @ SV70 @ SV208 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2280]) ).
thf(2328,plain,
! [SV208: $i,SV70: $i,SV230: $i,SV323: $i] :
( ( ( ~ ( in @ SV323 @ SV230 ) )
= $true )
| ( ( in @ SV323 @ SV70 )
= $true )
| ( ( SV230
= ( set_intersection2 @ SV70 @ SV208 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2281]) ).
thf(2329,plain,
! [SV70: $i,SV208: $i,SV230: $i,SV324: $i] :
( ( ( ~ ( in @ SV324 @ SV230 ) )
= $true )
| ( ( in @ SV324 @ SV208 )
= $true )
| ( ( SV230
= ( set_intersection2 @ SV70 @ SV208 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2282]) ).
thf(2330,plain,
! [SV72: $i,SV123: $i] :
( ( ( ( sK44_C @ SV123 @ SV72 )
!= ( sK45_SY295 @ SV123 @ SV72 ) )
= $false )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2283]) ).
thf(2331,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( sK45_SY295 @ SV123 @ SV72 )
!= ( sK48_SY300 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2283]) ).
thf(2332,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2284]) ).
thf(2333,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2284]) ).
thf(2334,plain,
! [SV72: $i,SV123: $i] :
( ( ( ( sK46_SY299 @ SV123 @ SV72 )
!= ( sK47_SY303 @ SV123 @ SV72 ) )
= $false )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2285]) ).
thf(2335,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2285]) ).
thf(2336,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) ) )
= $false )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2286]) ).
thf(2337,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) )
= $false )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2286]) ).
thf(2338,plain,
! [SV72: $i,SV123: $i,SV316: $i,SV333: $i] :
( ( ( ( SV333 != SV316 )
| ~ ( in @ SV333 @ ( succ @ SV123 ) ) )
= $true )
| ( ( ! [SY619: $i] :
( ( SV316 != SY619 )
| ~ ( ordinal @ SY619 )
| ~ ( in @ SY619 @ SV72 ) ) )
= $true )
| ( ( in @ SV316 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2287]) ).
thf(2339,plain,
! [SV72: $i,SV123: $i,SV317: $i] :
( ( ( ~ ~ ( ( ( sK43_E @ SV317 @ SV123 @ SV72 )
!= SV317 )
| ~ ( in @ ( sK43_E @ SV317 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SV317
!= ( sK42_H @ SV317 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV317 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV317 @ SV123 @ SV72 ) @ SV72 ) ) )
= $false )
| ( ( in @ SV317 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2288]) ).
thf(2340,plain,
! [SV73: $i,SV254: $i] :
( ( ( in @ ( ordered_pair @ ( sK23_C @ SV254 @ SV73 ) @ ( sK24_SY280 @ SV254 @ SV73 ) ) @ SV254 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK23_C @ SV254 @ SV73 ) @ ( sK24_SY280 @ SV254 @ SV73 ) ) @ SV73 )
= $false )
| ( ( SV73 = SV254 )
= $true )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2289]) ).
thf(2341,plain,
! [SV255: $i,SV73: $i,SV334: $i,SV325: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV325 @ SV334 ) @ SV73 )
| ( in @ ( ordered_pair @ SV325 @ SV334 ) @ SV255 ) )
= $true )
| ( ( SV73 = SV255 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2290]) ).
thf(2342,plain,
! [SV73: $i,SV255: $i,SV335: $i,SV326: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV326 @ SV335 ) @ SV255 )
| ( in @ ( ordered_pair @ SV326 @ SV335 ) @ SV73 ) )
= $true )
| ( ( SV73 = SV255 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2291]) ).
thf(2343,plain,
! [SV74: $i,SV211: $i,SV231: $i] :
( ( ( ( sK22_D @ SV231 @ SV211 @ SV74 )
= SV74 )
= $false )
| ( ( in @ ( sK22_D @ SV231 @ SV211 @ SV74 ) @ SV231 )
= $false )
| ( ( SV231
= ( unordered_pair @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2292]) ).
thf(2344,plain,
! [SV74: $i,SV211: $i,SV231: $i] :
( ( ( ( sK22_D @ SV231 @ SV211 @ SV74 )
= SV211 )
= $false )
| ( ( in @ ( sK22_D @ SV231 @ SV211 @ SV74 ) @ SV231 )
= $false )
| ( ( SV231
= ( unordered_pair @ SV74 @ SV211 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2293]) ).
thf(2345,plain,
! [SV212: $i,SV232: $i,SV74: $i,SV327: $i] :
( ( ( SV327 != SV74 )
= $true )
| ( ( in @ SV327 @ SV232 )
= $true )
| ( ( SV232
= ( unordered_pair @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2295]) ).
thf(2346,plain,
! [SV74: $i,SV232: $i,SV212: $i,SV328: $i] :
( ( ( SV328 != SV212 )
= $true )
| ( ( in @ SV328 @ SV232 )
= $true )
| ( ( SV232
= ( unordered_pair @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2296]) ).
thf(2347,plain,
! [SV318: $i,SV75: $i,SV275: $i] :
( ( ( in @ SV275 @ ( sK2_B @ SV75 ) )
= $false )
| ( ( in @ SV318 @ ( sK3_SY270 @ SV275 @ SV75 ) )
= $true )
| ( ( subset @ SV318 @ SV275 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2297]) ).
thf(2348,plain,
! [SV75: $i,SV305: $i,SV311: $i] :
( ( ( subset @ SV311 @ SV305 )
= $false )
| ( ( in @ SV305 @ ( sK2_B @ SV75 ) )
= $false )
| ( ( in @ SV311 @ ( sK2_B @ SV75 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2298]) ).
thf(2349,plain,
! [SV219: $i,SV78: $i,SV236: $i,SV329: $i] :
( ( ( ~ ( in @ SV329 @ SV236 ) )
= $true )
| ( ( in @ SV329 @ SV78 )
= $true )
| ( ( SV236
= ( set_difference @ SV78 @ SV219 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2302]) ).
thf(2350,plain,
! [SV78: $i,SV219: $i,SV236: $i,SV330: $i] :
( ( ( ~ ( in @ SV330 @ SV236 ) )
= $true )
| ( ( ~ ( in @ SV330 @ SV219 ) )
= $true )
| ( ( SV236
= ( set_difference @ SV78 @ SV219 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2303]) ).
thf(2351,plain,
! [SV80: $i,SV125: $i,SV237: $i,SV263: $i] :
( ( ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
= $false )
| ( ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
!= SV237 )
= $true )
| ( ( SV263
= ( unordered_triple @ SV80 @ SV125 @ SV237 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2305]) ).
thf(2352,plain,
! [SV80: $i,SV125: $i,SV237: $i,SV263: $i] :
( ( ( ~ ( ~ ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
!= SV80 ) ) )
= $false )
| ( ( SV263
= ( unordered_triple @ SV80 @ SV125 @ SV237 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2306]) ).
thf(2353,plain,
! [SV80: $i,SV125: $i,SV237: $i,SV263: $i] :
( ( ( ~ ( ~ ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
!= SV125 ) ) )
= $false )
| ( ( SV263
= ( unordered_triple @ SV80 @ SV125 @ SV237 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2306]) ).
thf(2354,plain,
! [SV264: $i,SV125: $i,SV80: $i,SV238: $i,SV320: $i] :
( ( ( SV320 = SV238 )
= $true )
| ( ( ( SV320 = SV80 )
| ( SV320 = SV125 ) )
= $true )
| ( ( in @ SV320 @ SV264 )
= $false )
| ( ( SV264
= ( unordered_triple @ SV80 @ SV125 @ SV238 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2307]) ).
thf(2355,plain,
! [SV125: $i,SV80: $i,SV264: $i,SV238: $i,SV336: $i] :
( ( ( ( SV336 != SV238 )
| ( in @ SV336 @ SV264 ) )
= $true )
| ( ( SV264
= ( unordered_triple @ SV80 @ SV125 @ SV238 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2308]) ).
thf(2356,plain,
! [SV238: $i,SV125: $i,SV264: $i,SV80: $i] :
( ( ( ~ ! [SY602: $i] :
( ( SY602 != SV80 )
| ( in @ SY602 @ SV264 ) )
| ~ ! [SY603: $i] :
( ( SY603 != SV125 )
| ( in @ SY603 @ SV264 ) ) )
= $false )
| ( ( SV264
= ( unordered_triple @ SV80 @ SV125 @ SV238 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2309]) ).
thf(2357,plain,
! [SV63: $i,SV295: $i,SV120: $i,SV267: $i] :
( ( ( in @ SV267 @ ( succ @ SV120 ) )
= $false )
| ( ( ordinal @ SV295 )
= $false )
| ( ( SV267 = SV295 )
= $false )
| ( ( in @ SV295 @ SV63 )
= $false )
| ( ( in @ SV267 @ ( sK52_C @ SV120 @ SV63 ) )
= $true )
| ( ( ordinal @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2310]) ).
thf(2358,plain,
! [SV63: $i,SV120: $i,SV296: $i] :
( ( ( ( SV296
!= ( sK53_E @ SV296 @ SV120 @ SV63 ) )
| ~ ( ordinal @ ( sK53_E @ SV296 @ SV120 @ SV63 ) ) )
= $false )
| ( ( in @ SV296 @ ( sK52_C @ SV120 @ SV63 ) )
= $false )
| ( ( ordinal @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2311]) ).
thf(2359,plain,
! [SV152: $i] :
( ( ( in @ ( sK19_B @ SV152 ) @ SV152 )
= $true )
| ( ( epsilon_connected @ SV152 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2316]) ).
thf(2360,plain,
! [SV152: $i] :
( ( ( in @ ( sK20_SY279 @ SV152 ) @ SV152 )
= $true )
| ( ( epsilon_connected @ SV152 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2317]) ).
thf(2361,plain,
! [SV331: $i] :
( ( ( ~ ( relation @ SV331 ) )
= $true )
| ( ( ~ ( well_ordering @ SV331 )
| ( reflexive @ SV331 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2319]) ).
thf(2362,plain,
! [SV332: $i] :
( ( ( ~ ( relation @ SV332 ) )
= $true )
| ( ( ~ ( well_ordering @ SV332 )
| ( transitive @ SV332 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2320]) ).
thf(2363,plain,
! [SV315: $i] :
( ( ( well_ordering @ SV315 )
= $false )
| ( ( antisymmetric @ SV315 )
= $true )
| ( ( relation @ SV315 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2321]) ).
thf(2364,plain,
! [SV307: $i,SV122: $i,SV68: $i] :
( ( ( SV68 = empty_set )
= $true )
| ( ( ~ ( subset @ SV68 @ SV122 ) )
= $true )
| ( ( ordinal @ SV307 )
= $false )
| ( ( ordinal_subset @ ( sK35_C @ SV122 @ SV68 ) @ SV307 )
= $true )
| ( ( in @ SV307 @ SV68 )
= $false )
| ( ( ordinal @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2322]) ).
thf(2365,plain,
! [SV204: $i,SV228: $i,SV69: $i,SV321: $i] :
( ( ( in @ SV321 @ SV69 )
= $false )
| ( ( in @ SV321 @ SV228 )
= $true )
| ( ( SV228
= ( set_union2 @ SV69 @ SV204 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2325]) ).
thf(2366,plain,
! [SV69: $i,SV228: $i,SV204: $i,SV322: $i] :
( ( ( in @ SV322 @ SV204 )
= $false )
| ( ( in @ SV322 @ SV228 )
= $true )
| ( ( SV228
= ( set_union2 @ SV69 @ SV204 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2326]) ).
thf(2367,plain,
! [SV208: $i,SV70: $i,SV230: $i,SV323: $i] :
( ( ( in @ SV323 @ SV230 )
= $false )
| ( ( in @ SV323 @ SV70 )
= $true )
| ( ( SV230
= ( set_intersection2 @ SV70 @ SV208 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2328]) ).
thf(2368,plain,
! [SV70: $i,SV208: $i,SV230: $i,SV324: $i] :
( ( ( in @ SV324 @ SV230 )
= $false )
| ( ( in @ SV324 @ SV208 )
= $true )
| ( ( SV230
= ( set_intersection2 @ SV70 @ SV208 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2329]) ).
thf(2369,plain,
! [SV72: $i,SV123: $i] :
( ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2330]) ).
thf(2370,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ( ~ ~ ( ( ( sK45_SY295 @ SV123 @ SV72 )
!= ( sK48_SY300 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2331]) ).
thf(2371,plain,
! [SV72: $i,SV123: $i] :
( ( ( ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) ) )
= $true )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2332]) ).
thf(2372,plain,
! [SV72: $i,SV123: $i] :
( ( ( ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) )
= $true )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2333]) ).
thf(2373,plain,
! [SV72: $i,SV123: $i] :
( ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2334]) ).
thf(2374,plain,
! [SV72: $i,SV123: $i] :
( ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2335]) ).
thf(2375,plain,
! [SV72: $i,SV123: $i] :
( ( ( ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) ) )
= $true )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2336]) ).
thf(2376,plain,
! [SV72: $i,SV123: $i] :
( ( ( ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) )
= $true )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2337]) ).
thf(2377,plain,
! [SV72: $i,SV123: $i,SV316: $i,SV333: $i] :
( ( ( SV333 != SV316 )
= $true )
| ( ( ~ ( in @ SV333 @ ( succ @ SV123 ) ) )
= $true )
| ( ( ! [SY619: $i] :
( ( SV316 != SY619 )
| ~ ( ordinal @ SY619 )
| ~ ( in @ SY619 @ SV72 ) ) )
= $true )
| ( ( in @ SV316 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2338]) ).
thf(2378,plain,
! [SV72: $i,SV123: $i,SV317: $i] :
( ( ( ~ ~ ( ( ( sK43_E @ SV317 @ SV123 @ SV72 )
!= SV317 )
| ~ ( in @ ( sK43_E @ SV317 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) ) )
= $false )
| ( ( in @ SV317 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2339]) ).
thf(2379,plain,
! [SV72: $i,SV123: $i,SV317: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV317
!= ( sK42_H @ SV317 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV317 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV317 @ SV123 @ SV72 ) @ SV72 ) ) )
= $false )
| ( ( in @ SV317 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2339]) ).
thf(2380,plain,
! [SV255: $i,SV73: $i,SV334: $i,SV325: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV325 @ SV334 ) @ SV73 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV325 @ SV334 ) @ SV255 )
= $true )
| ( ( SV73 = SV255 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2341]) ).
thf(2381,plain,
! [SV73: $i,SV255: $i,SV335: $i,SV326: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV326 @ SV335 ) @ SV255 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV326 @ SV335 ) @ SV73 )
= $true )
| ( ( SV73 = SV255 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2342]) ).
thf(2382,plain,
! [SV212: $i,SV232: $i,SV74: $i,SV327: $i] :
( ( ( SV327 = SV74 )
= $false )
| ( ( in @ SV327 @ SV232 )
= $true )
| ( ( SV232
= ( unordered_pair @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2345]) ).
thf(2383,plain,
! [SV74: $i,SV232: $i,SV212: $i,SV328: $i] :
( ( ( SV328 = SV212 )
= $false )
| ( ( in @ SV328 @ SV232 )
= $true )
| ( ( SV232
= ( unordered_pair @ SV74 @ SV212 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2346]) ).
thf(2384,plain,
! [SV219: $i,SV78: $i,SV236: $i,SV329: $i] :
( ( ( in @ SV329 @ SV236 )
= $false )
| ( ( in @ SV329 @ SV78 )
= $true )
| ( ( SV236
= ( set_difference @ SV78 @ SV219 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2349]) ).
thf(2385,plain,
! [SV78: $i,SV219: $i,SV236: $i,SV330: $i] :
( ( ( in @ SV330 @ SV236 )
= $false )
| ( ( ~ ( in @ SV330 @ SV219 ) )
= $true )
| ( ( SV236
= ( set_difference @ SV78 @ SV219 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2350]) ).
thf(2386,plain,
! [SV80: $i,SV125: $i,SV237: $i,SV263: $i] :
( ( ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
= SV237 )
= $false )
| ( ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
= $false )
| ( ( SV263
= ( unordered_triple @ SV80 @ SV125 @ SV237 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2351]) ).
thf(2387,plain,
! [SV80: $i,SV125: $i,SV237: $i,SV263: $i] :
( ( ( ~ ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
!= SV80 ) )
= $true )
| ( ( SV263
= ( unordered_triple @ SV80 @ SV125 @ SV237 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2352]) ).
thf(2388,plain,
! [SV80: $i,SV125: $i,SV237: $i,SV263: $i] :
( ( ( ~ ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
| ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
!= SV125 ) )
= $true )
| ( ( SV263
= ( unordered_triple @ SV80 @ SV125 @ SV237 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2353]) ).
thf(2389,plain,
! [SV264: $i,SV238: $i,SV125: $i,SV80: $i,SV320: $i] :
( ( ( SV320 = SV80 )
= $true )
| ( ( SV320 = SV125 )
= $true )
| ( ( SV320 = SV238 )
= $true )
| ( ( in @ SV320 @ SV264 )
= $false )
| ( ( SV264
= ( unordered_triple @ SV80 @ SV125 @ SV238 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2354]) ).
thf(2390,plain,
! [SV125: $i,SV80: $i,SV264: $i,SV238: $i,SV336: $i] :
( ( ( SV336 != SV238 )
= $true )
| ( ( in @ SV336 @ SV264 )
= $true )
| ( ( SV264
= ( unordered_triple @ SV80 @ SV125 @ SV238 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2355]) ).
thf(2391,plain,
! [SV238: $i,SV125: $i,SV264: $i,SV80: $i] :
( ( ( ~ ! [SY602: $i] :
( ( SY602 != SV80 )
| ( in @ SY602 @ SV264 ) ) )
= $false )
| ( ( SV264
= ( unordered_triple @ SV80 @ SV125 @ SV238 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2356]) ).
thf(2392,plain,
! [SV238: $i,SV80: $i,SV264: $i,SV125: $i] :
( ( ( ~ ! [SY603: $i] :
( ( SY603 != SV125 )
| ( in @ SY603 @ SV264 ) ) )
= $false )
| ( ( SV264
= ( unordered_triple @ SV80 @ SV125 @ SV238 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2356]) ).
thf(2393,plain,
! [SV63: $i,SV120: $i,SV296: $i] :
( ( ( SV296
!= ( sK53_E @ SV296 @ SV120 @ SV63 ) )
= $false )
| ( ( in @ SV296 @ ( sK52_C @ SV120 @ SV63 ) )
= $false )
| ( ( ordinal @ SV120 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2358]) ).
thf(2394,plain,
! [SV63: $i,SV120: $i,SV296: $i] :
( ( ( ~ ( ordinal @ ( sK53_E @ SV296 @ SV120 @ SV63 ) ) )
= $false )
| ( ( in @ SV296 @ ( sK52_C @ SV120 @ SV63 ) )
= $false )
| ( ( ordinal @ SV120 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2358]) ).
thf(2395,plain,
! [SV331: $i] :
( ( ( relation @ SV331 )
= $false )
| ( ( ~ ( well_ordering @ SV331 )
| ( reflexive @ SV331 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2361]) ).
thf(2396,plain,
! [SV332: $i] :
( ( ( relation @ SV332 )
= $false )
| ( ( ~ ( well_ordering @ SV332 )
| ( transitive @ SV332 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2362]) ).
thf(2397,plain,
! [SV307: $i,SV122: $i,SV68: $i] :
( ( ( subset @ SV68 @ SV122 )
= $false )
| ( ( SV68 = empty_set )
= $true )
| ( ( ordinal @ SV307 )
= $false )
| ( ( ordinal_subset @ ( sK35_C @ SV122 @ SV68 ) @ SV307 )
= $true )
| ( ( in @ SV307 @ SV68 )
= $false )
| ( ( ordinal @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2364]) ).
thf(2398,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2369]) ).
thf(2399,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ~ ( ( ( sK45_SY295 @ SV123 @ SV72 )
!= ( sK48_SY300 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 ) )
= $false )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2370]) ).
thf(2400,plain,
! [SV72: $i,SV123: $i,SV337: $i] :
( ( ( ! [SY622: $i] :
( ( SY622 != SV337 )
| ~ ( in @ SY622 @ ( succ @ SV123 ) ) )
| ! [SY623: $i] :
( ( SV337 != SY623 )
| ~ ( ordinal @ SY623 )
| ~ ( in @ SY623 @ SV72 ) )
| ( in @ SV337 @ ( sK41_C @ SV123 @ SV72 ) ) )
= $true )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2371]) ).
thf(2401,plain,
! [SV72: $i,SV123: $i,SV338: $i] :
( ( ( ~ ( in @ SV338 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SV338 @ SV123 @ SV72 )
!= SV338 )
| ~ ( in @ ( sK43_E @ SV338 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SV338
!= ( sK42_H @ SV338 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV338 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV338 @ SV123 @ SV72 ) @ SV72 ) ) ) )
= $true )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2372]) ).
thf(2402,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) )
= $false )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2373]) ).
thf(2403,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) )
= $false )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2374]) ).
thf(2404,plain,
! [SV72: $i,SV123: $i,SV339: $i] :
( ( ( ! [SY624: $i] :
( ( SY624 != SV339 )
| ~ ( in @ SY624 @ ( succ @ SV123 ) ) )
| ! [SY625: $i] :
( ( SV339 != SY625 )
| ~ ( ordinal @ SY625 )
| ~ ( in @ SY625 @ SV72 ) )
| ( in @ SV339 @ ( sK41_C @ SV123 @ SV72 ) ) )
= $true )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2375]) ).
thf(2405,plain,
! [SV72: $i,SV123: $i,SV340: $i] :
( ( ( ~ ( in @ SV340 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SV340 @ SV123 @ SV72 )
!= SV340 )
| ~ ( in @ ( sK43_E @ SV340 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SV340
!= ( sK42_H @ SV340 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV340 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV340 @ SV123 @ SV72 ) @ SV72 ) ) ) )
= $true )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2376]) ).
thf(2406,plain,
! [SV72: $i,SV123: $i,SV316: $i,SV333: $i] :
( ( ( SV333 = SV316 )
= $false )
| ( ( ~ ( in @ SV333 @ ( succ @ SV123 ) ) )
= $true )
| ( ( ! [SY619: $i] :
( ( SV316 != SY619 )
| ~ ( ordinal @ SY619 )
| ~ ( in @ SY619 @ SV72 ) ) )
= $true )
| ( ( in @ SV316 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2377]) ).
thf(2407,plain,
! [SV72: $i,SV123: $i,SV317: $i] :
( ( ( ~ ( ( ( sK43_E @ SV317 @ SV123 @ SV72 )
!= SV317 )
| ~ ( in @ ( sK43_E @ SV317 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) ) )
= $true )
| ( ( in @ SV317 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2378]) ).
thf(2408,plain,
! [SV72: $i,SV123: $i,SV317: $i] :
( ( ( ~ ( ~ ~ ( ( SV317
!= ( sK42_H @ SV317 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV317 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV317 @ SV123 @ SV72 ) @ SV72 ) ) )
= $true )
| ( ( in @ SV317 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2379]) ).
thf(2409,plain,
! [SV255: $i,SV73: $i,SV334: $i,SV325: $i] :
( ( ( in @ ( ordered_pair @ SV325 @ SV334 ) @ SV73 )
= $false )
| ( ( in @ ( ordered_pair @ SV325 @ SV334 ) @ SV255 )
= $true )
| ( ( SV73 = SV255 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2380]) ).
thf(2410,plain,
! [SV73: $i,SV255: $i,SV335: $i,SV326: $i] :
( ( ( in @ ( ordered_pair @ SV326 @ SV335 ) @ SV255 )
= $false )
| ( ( in @ ( ordered_pair @ SV326 @ SV335 ) @ SV73 )
= $true )
| ( ( SV73 = SV255 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2381]) ).
thf(2411,plain,
! [SV78: $i,SV236: $i,SV219: $i,SV330: $i] :
( ( ( in @ SV330 @ SV219 )
= $false )
| ( ( in @ SV330 @ SV236 )
= $false )
| ( ( SV236
= ( set_difference @ SV78 @ SV219 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2385]) ).
thf(2412,plain,
! [SV80: $i,SV125: $i,SV237: $i,SV263: $i] :
( ( ( ~ ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 ) )
= $true )
| ( ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
!= SV80 )
= $true )
| ( ( SV263
= ( unordered_triple @ SV80 @ SV125 @ SV237 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2387]) ).
thf(2413,plain,
! [SV80: $i,SV125: $i,SV237: $i,SV263: $i] :
( ( ( ~ ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 ) )
= $true )
| ( ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
!= SV125 )
= $true )
| ( ( SV263
= ( unordered_triple @ SV80 @ SV125 @ SV237 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2388]) ).
thf(2414,plain,
! [SV125: $i,SV80: $i,SV264: $i,SV238: $i,SV336: $i] :
( ( ( SV336 = SV238 )
= $false )
| ( ( in @ SV336 @ SV264 )
= $true )
| ( ( SV264
= ( unordered_triple @ SV80 @ SV125 @ SV238 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2390]) ).
thf(2415,plain,
! [SV238: $i,SV125: $i,SV264: $i,SV80: $i] :
( ( ( ! [SY602: $i] :
( ( SY602 != SV80 )
| ( in @ SY602 @ SV264 ) ) )
= $true )
| ( ( SV264
= ( unordered_triple @ SV80 @ SV125 @ SV238 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2391]) ).
thf(2416,plain,
! [SV238: $i,SV80: $i,SV264: $i,SV125: $i] :
( ( ( ! [SY603: $i] :
( ( SY603 != SV125 )
| ( in @ SY603 @ SV264 ) ) )
= $true )
| ( ( SV264
= ( unordered_triple @ SV80 @ SV125 @ SV238 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2392]) ).
thf(2417,plain,
! [SV63: $i,SV120: $i,SV296: $i] :
( ( ( SV296
= ( sK53_E @ SV296 @ SV120 @ SV63 ) )
= $true )
| ( ( in @ SV296 @ ( sK52_C @ SV120 @ SV63 ) )
= $false )
| ( ( ordinal @ SV120 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2393]) ).
thf(2418,plain,
! [SV63: $i,SV120: $i,SV296: $i] :
( ( ( ordinal @ ( sK53_E @ SV296 @ SV120 @ SV63 ) )
= $true )
| ( ( in @ SV296 @ ( sK52_C @ SV120 @ SV63 ) )
= $false )
| ( ( ordinal @ SV120 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2394]) ).
thf(2419,plain,
! [SV331: $i] :
( ( ( ~ ( well_ordering @ SV331 ) )
= $true )
| ( ( reflexive @ SV331 )
= $true )
| ( ( relation @ SV331 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2395]) ).
thf(2420,plain,
! [SV332: $i] :
( ( ( ~ ( well_ordering @ SV332 ) )
= $true )
| ( ( transitive @ SV332 )
= $true )
| ( ( relation @ SV332 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2396]) ).
thf(2421,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2398]) ).
thf(2422,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2398]) ).
thf(2423,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ~ ( ( ( sK45_SY295 @ SV123 @ SV72 )
!= ( sK48_SY300 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2399]) ).
thf(2424,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 ) )
= $false )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2399]) ).
thf(2425,plain,
! [SV72: $i,SV123: $i,SV337: $i] :
( ( ( ! [SY622: $i] :
( ( SY622 != SV337 )
| ~ ( in @ SY622 @ ( succ @ SV123 ) ) )
| ! [SY623: $i] :
( ( SV337 != SY623 )
| ~ ( ordinal @ SY623 )
| ~ ( in @ SY623 @ SV72 ) ) )
= $true )
| ( ( in @ SV337 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2400]) ).
thf(2426,plain,
! [SV72: $i,SV123: $i,SV338: $i] :
( ( ( ~ ( in @ SV338 @ ( sK41_C @ SV123 @ SV72 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK43_E @ SV338 @ SV123 @ SV72 )
!= SV338 )
| ~ ( in @ ( sK43_E @ SV338 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SV338
!= ( sK42_H @ SV338 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV338 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV338 @ SV123 @ SV72 ) @ SV72 ) ) ) )
= $true )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2401]) ).
thf(2427,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) ) )
= $false )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2402]) ).
thf(2428,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) )
= $false )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2402]) ).
thf(2429,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) ) )
= $false )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2403]) ).
thf(2430,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) )
= $false )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2403]) ).
thf(2431,plain,
! [SV72: $i,SV123: $i,SV339: $i] :
( ( ( ! [SY624: $i] :
( ( SY624 != SV339 )
| ~ ( in @ SY624 @ ( succ @ SV123 ) ) )
| ! [SY625: $i] :
( ( SV339 != SY625 )
| ~ ( ordinal @ SY625 )
| ~ ( in @ SY625 @ SV72 ) ) )
= $true )
| ( ( in @ SV339 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2404]) ).
thf(2432,plain,
! [SV72: $i,SV123: $i,SV340: $i] :
( ( ( ~ ( in @ SV340 @ ( sK41_C @ SV123 @ SV72 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK43_E @ SV340 @ SV123 @ SV72 )
!= SV340 )
| ~ ( in @ ( sK43_E @ SV340 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SV340
!= ( sK42_H @ SV340 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV340 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV340 @ SV123 @ SV72 ) @ SV72 ) ) ) )
= $true )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2405]) ).
thf(2433,plain,
! [SV72: $i,SV316: $i,SV123: $i,SV333: $i] :
( ( ( in @ SV333 @ ( succ @ SV123 ) )
= $false )
| ( ( SV333 = SV316 )
= $false )
| ( ( ! [SY619: $i] :
( ( SV316 != SY619 )
| ~ ( ordinal @ SY619 )
| ~ ( in @ SY619 @ SV72 ) ) )
= $true )
| ( ( in @ SV316 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2406]) ).
thf(2434,plain,
! [SV72: $i,SV123: $i,SV317: $i] :
( ( ( ( ( sK43_E @ SV317 @ SV123 @ SV72 )
!= SV317 )
| ~ ( in @ ( sK43_E @ SV317 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
= $false )
| ( ( in @ SV317 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2407]) ).
thf(2435,plain,
! [SV72: $i,SV123: $i,SV317: $i] :
( ( ( ~ ~ ( ( SV317
!= ( sK42_H @ SV317 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV317 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV317 @ SV123 @ SV72 ) @ SV72 ) )
= $false )
| ( ( in @ SV317 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2408]) ).
thf(2436,plain,
! [SV80: $i,SV125: $i,SV237: $i,SV263: $i] :
( ( ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
= $false )
| ( ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
!= SV80 )
= $true )
| ( ( SV263
= ( unordered_triple @ SV80 @ SV125 @ SV237 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2412]) ).
thf(2437,plain,
! [SV80: $i,SV125: $i,SV237: $i,SV263: $i] :
( ( ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
= $false )
| ( ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
!= SV125 )
= $true )
| ( ( SV263
= ( unordered_triple @ SV80 @ SV125 @ SV237 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2413]) ).
thf(2438,plain,
! [SV238: $i,SV125: $i,SV264: $i,SV80: $i,SV341: $i] :
( ( ( ( SV341 != SV80 )
| ( in @ SV341 @ SV264 ) )
= $true )
| ( ( SV264
= ( unordered_triple @ SV80 @ SV125 @ SV238 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2415]) ).
thf(2439,plain,
! [SV238: $i,SV80: $i,SV264: $i,SV125: $i,SV342: $i] :
( ( ( ( SV342 != SV125 )
| ( in @ SV342 @ SV264 ) )
= $true )
| ( ( SV264
= ( unordered_triple @ SV80 @ SV125 @ SV238 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2416]) ).
thf(2440,plain,
! [SV331: $i] :
( ( ( well_ordering @ SV331 )
= $false )
| ( ( reflexive @ SV331 )
= $true )
| ( ( relation @ SV331 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2419]) ).
thf(2441,plain,
! [SV332: $i] :
( ( ( well_ordering @ SV332 )
= $false )
| ( ( transitive @ SV332 )
= $true )
| ( ( relation @ SV332 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2420]) ).
thf(2442,plain,
! [SV72: $i,SV123: $i] :
( ( ( ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) ) )
= $true )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2421]) ).
thf(2443,plain,
! [SV72: $i,SV123: $i] :
( ( ( ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) )
= $true )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2422]) ).
thf(2444,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ( ( ( sK45_SY295 @ SV123 @ SV72 )
!= ( sK48_SY300 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2423]) ).
thf(2445,plain,
! [SV72: $i,SV123: $i] :
( ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2424]) ).
thf(2446,plain,
! [SV72: $i,SV123: $i,SV337: $i] :
( ( ( ! [SY622: $i] :
( ( SY622 != SV337 )
| ~ ( in @ SY622 @ ( succ @ SV123 ) ) ) )
= $true )
| ( ( ! [SY623: $i] :
( ( SV337 != SY623 )
| ~ ( ordinal @ SY623 )
| ~ ( in @ SY623 @ SV72 ) ) )
= $true )
| ( ( in @ SV337 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2425]) ).
thf(2447,plain,
! [SV72: $i,SV123: $i,SV338: $i] :
( ( ( in @ SV338 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK43_E @ SV338 @ SV123 @ SV72 )
!= SV338 )
| ~ ( in @ ( sK43_E @ SV338 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SV338
!= ( sK42_H @ SV338 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV338 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV338 @ SV123 @ SV72 ) @ SV72 ) ) ) )
= $true )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2426]) ).
thf(2448,plain,
! [SV72: $i,SV123: $i] :
( ( ( ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) ) )
= $true )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2427]) ).
thf(2449,plain,
! [SV72: $i,SV123: $i] :
( ( ( ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) )
= $true )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2428]) ).
thf(2450,plain,
! [SV72: $i,SV123: $i] :
( ( ( ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) ) )
= $true )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2429]) ).
thf(2451,plain,
! [SV72: $i,SV123: $i] :
( ( ( ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) )
= $true )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2430]) ).
thf(2452,plain,
! [SV72: $i,SV123: $i,SV339: $i] :
( ( ( ! [SY624: $i] :
( ( SY624 != SV339 )
| ~ ( in @ SY624 @ ( succ @ SV123 ) ) ) )
= $true )
| ( ( ! [SY625: $i] :
( ( SV339 != SY625 )
| ~ ( ordinal @ SY625 )
| ~ ( in @ SY625 @ SV72 ) ) )
= $true )
| ( ( in @ SV339 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2431]) ).
thf(2453,plain,
! [SV72: $i,SV123: $i,SV340: $i] :
( ( ( in @ SV340 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK43_E @ SV340 @ SV123 @ SV72 )
!= SV340 )
| ~ ( in @ ( sK43_E @ SV340 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SV340
!= ( sK42_H @ SV340 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV340 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV340 @ SV123 @ SV72 ) @ SV72 ) ) ) )
= $true )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2432]) ).
thf(2454,plain,
! [SV123: $i,SV333: $i,SV72: $i,SV343: $i,SV316: $i] :
( ( ( ( SV316 != SV343 )
| ~ ( ordinal @ SV343 )
| ~ ( in @ SV343 @ SV72 ) )
= $true )
| ( ( SV333 = SV316 )
= $false )
| ( ( in @ SV333 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV316 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2433]) ).
thf(2455,plain,
! [SV72: $i,SV123: $i,SV317: $i] :
( ( ( ( sK43_E @ SV317 @ SV123 @ SV72 )
!= SV317 )
= $false )
| ( ( in @ SV317 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2434]) ).
thf(2456,plain,
! [SV72: $i,SV123: $i,SV317: $i] :
( ( ( ~ ( in @ ( sK43_E @ SV317 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
= $false )
| ( ( in @ SV317 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2434]) ).
thf(2457,plain,
! [SV72: $i,SV123: $i,SV317: $i] :
( ( ( ~ ~ ( ( SV317
!= ( sK42_H @ SV317 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV317 @ SV123 @ SV72 ) ) ) )
= $false )
| ( ( in @ SV317 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2435]) ).
thf(2458,plain,
! [SV72: $i,SV123: $i,SV317: $i] :
( ( ( ~ ( in @ ( sK42_H @ SV317 @ SV123 @ SV72 ) @ SV72 ) )
= $false )
| ( ( in @ SV317 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2435]) ).
thf(2459,plain,
! [SV80: $i,SV125: $i,SV237: $i,SV263: $i] :
( ( ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
= SV80 )
= $false )
| ( ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
= $false )
| ( ( SV263
= ( unordered_triple @ SV80 @ SV125 @ SV237 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2436]) ).
thf(2460,plain,
! [SV80: $i,SV125: $i,SV237: $i,SV263: $i] :
( ( ( ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 )
= SV125 )
= $false )
| ( ( in @ ( sK32_E @ SV263 @ SV237 @ SV125 @ SV80 ) @ SV263 )
= $false )
| ( ( SV263
= ( unordered_triple @ SV80 @ SV125 @ SV237 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2437]) ).
thf(2461,plain,
! [SV238: $i,SV125: $i,SV264: $i,SV80: $i,SV341: $i] :
( ( ( SV341 != SV80 )
= $true )
| ( ( in @ SV341 @ SV264 )
= $true )
| ( ( SV264
= ( unordered_triple @ SV80 @ SV125 @ SV238 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2438]) ).
thf(2462,plain,
! [SV238: $i,SV80: $i,SV264: $i,SV125: $i,SV342: $i] :
( ( ( SV342 != SV125 )
= $true )
| ( ( in @ SV342 @ SV264 )
= $true )
| ( ( SV264
= ( unordered_triple @ SV80 @ SV125 @ SV238 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2439]) ).
thf(2463,plain,
! [SV72: $i,SV123: $i,SV344: $i] :
( ( ( ! [SY626: $i] :
( ( SY626 != SV344 )
| ~ ( in @ SY626 @ ( succ @ SV123 ) ) )
| ! [SY627: $i] :
( ( SV344 != SY627 )
| ~ ( ordinal @ SY627 )
| ~ ( in @ SY627 @ SV72 ) )
| ( in @ SV344 @ ( sK41_C @ SV123 @ SV72 ) ) )
= $true )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2442]) ).
thf(2464,plain,
! [SV72: $i,SV123: $i,SV345: $i] :
( ( ( ~ ( in @ SV345 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SV345 @ SV123 @ SV72 )
!= SV345 )
| ~ ( in @ ( sK43_E @ SV345 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SV345
!= ( sK42_H @ SV345 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV345 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV345 @ SV123 @ SV72 ) @ SV72 ) ) ) )
= $true )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2443]) ).
thf(2465,plain,
! [SV72: $i,SV123: $i] :
( ( ( ( ( sK45_SY295 @ SV123 @ SV72 )
!= ( sK48_SY300 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2444]) ).
thf(2466,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) )
= $false )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2445]) ).
thf(2467,plain,
! [SV72: $i,SV123: $i,SV337: $i,SV346: $i] :
( ( ( ( SV346 != SV337 )
| ~ ( in @ SV346 @ ( succ @ SV123 ) ) )
= $true )
| ( ( ! [SY623: $i] :
( ( SV337 != SY623 )
| ~ ( ordinal @ SY623 )
| ~ ( in @ SY623 @ SV72 ) ) )
= $true )
| ( ( in @ SV337 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2446]) ).
thf(2468,plain,
! [SV72: $i,SV123: $i,SV338: $i] :
( ( ( ~ ~ ( ( ( sK43_E @ SV338 @ SV123 @ SV72 )
!= SV338 )
| ~ ( in @ ( sK43_E @ SV338 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SV338
!= ( sK42_H @ SV338 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV338 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV338 @ SV123 @ SV72 ) @ SV72 ) ) )
= $false )
| ( ( in @ SV338 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2447]) ).
thf(2469,plain,
! [SV72: $i,SV123: $i,SV347: $i] :
( ( ( ! [SY628: $i] :
( ( SY628 != SV347 )
| ~ ( in @ SY628 @ ( succ @ SV123 ) ) )
| ! [SY629: $i] :
( ( SV347 != SY629 )
| ~ ( ordinal @ SY629 )
| ~ ( in @ SY629 @ SV72 ) )
| ( in @ SV347 @ ( sK41_C @ SV123 @ SV72 ) ) )
= $true )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2448]) ).
thf(2470,plain,
! [SV72: $i,SV123: $i,SV348: $i] :
( ( ( ~ ( in @ SV348 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SV348 @ SV123 @ SV72 )
!= SV348 )
| ~ ( in @ ( sK43_E @ SV348 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SV348
!= ( sK42_H @ SV348 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV348 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV348 @ SV123 @ SV72 ) @ SV72 ) ) ) )
= $true )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2449]) ).
thf(2471,plain,
! [SV72: $i,SV123: $i,SV349: $i] :
( ( ( ! [SY630: $i] :
( ( SY630 != SV349 )
| ~ ( in @ SY630 @ ( succ @ SV123 ) ) )
| ! [SY631: $i] :
( ( SV349 != SY631 )
| ~ ( ordinal @ SY631 )
| ~ ( in @ SY631 @ SV72 ) )
| ( in @ SV349 @ ( sK41_C @ SV123 @ SV72 ) ) )
= $true )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2450]) ).
thf(2472,plain,
! [SV72: $i,SV123: $i,SV350: $i] :
( ( ( ~ ( in @ SV350 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SV350 @ SV123 @ SV72 )
!= SV350 )
| ~ ( in @ ( sK43_E @ SV350 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SV350
!= ( sK42_H @ SV350 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV350 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV350 @ SV123 @ SV72 ) @ SV72 ) ) ) )
= $true )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2451]) ).
thf(2473,plain,
! [SV72: $i,SV123: $i,SV339: $i,SV351: $i] :
( ( ( ( SV351 != SV339 )
| ~ ( in @ SV351 @ ( succ @ SV123 ) ) )
= $true )
| ( ( ! [SY625: $i] :
( ( SV339 != SY625 )
| ~ ( ordinal @ SY625 )
| ~ ( in @ SY625 @ SV72 ) ) )
= $true )
| ( ( in @ SV339 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2452]) ).
thf(2474,plain,
! [SV72: $i,SV123: $i,SV340: $i] :
( ( ( ~ ~ ( ( ( sK43_E @ SV340 @ SV123 @ SV72 )
!= SV340 )
| ~ ( in @ ( sK43_E @ SV340 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SV340
!= ( sK42_H @ SV340 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV340 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV340 @ SV123 @ SV72 ) @ SV72 ) ) )
= $false )
| ( ( in @ SV340 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2453]) ).
thf(2475,plain,
! [SV123: $i,SV333: $i,SV72: $i,SV343: $i,SV316: $i] :
( ( ( ( SV316 != SV343 )
| ~ ( ordinal @ SV343 ) )
= $true )
| ( ( ~ ( in @ SV343 @ SV72 ) )
= $true )
| ( ( SV333 = SV316 )
= $false )
| ( ( in @ SV333 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV316 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2454]) ).
thf(2476,plain,
! [SV72: $i,SV123: $i,SV317: $i] :
( ( ( ( sK43_E @ SV317 @ SV123 @ SV72 )
= SV317 )
= $true )
| ( ( in @ SV317 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2455]) ).
thf(2477,plain,
! [SV72: $i,SV123: $i,SV317: $i] :
( ( ( in @ ( sK43_E @ SV317 @ SV123 @ SV72 ) @ ( succ @ SV123 ) )
= $true )
| ( ( in @ SV317 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2456]) ).
thf(2478,plain,
! [SV72: $i,SV123: $i,SV317: $i] :
( ( ( ~ ( ( SV317
!= ( sK42_H @ SV317 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV317 @ SV123 @ SV72 ) ) ) )
= $true )
| ( ( in @ SV317 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2457]) ).
thf(2479,plain,
! [SV72: $i,SV123: $i,SV317: $i] :
( ( ( in @ ( sK42_H @ SV317 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( in @ SV317 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2458]) ).
thf(2480,plain,
! [SV238: $i,SV125: $i,SV264: $i,SV80: $i,SV341: $i] :
( ( ( SV341 = SV80 )
= $false )
| ( ( in @ SV341 @ SV264 )
= $true )
| ( ( SV264
= ( unordered_triple @ SV80 @ SV125 @ SV238 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2461]) ).
thf(2481,plain,
! [SV238: $i,SV80: $i,SV264: $i,SV125: $i,SV342: $i] :
( ( ( SV342 = SV125 )
= $false )
| ( ( in @ SV342 @ SV264 )
= $true )
| ( ( SV264
= ( unordered_triple @ SV80 @ SV125 @ SV238 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2462]) ).
thf(2482,plain,
! [SV72: $i,SV123: $i,SV344: $i] :
( ( ( ! [SY626: $i] :
( ( SY626 != SV344 )
| ~ ( in @ SY626 @ ( succ @ SV123 ) ) )
| ! [SY627: $i] :
( ( SV344 != SY627 )
| ~ ( ordinal @ SY627 )
| ~ ( in @ SY627 @ SV72 ) ) )
= $true )
| ( ( in @ SV344 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2463]) ).
thf(2483,plain,
! [SV72: $i,SV123: $i,SV345: $i] :
( ( ( ~ ( in @ SV345 @ ( sK41_C @ SV123 @ SV72 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK43_E @ SV345 @ SV123 @ SV72 )
!= SV345 )
| ~ ( in @ ( sK43_E @ SV345 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SV345
!= ( sK42_H @ SV345 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV345 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV345 @ SV123 @ SV72 ) @ SV72 ) ) ) )
= $true )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2464]) ).
thf(2484,plain,
! [SV72: $i,SV123: $i] :
( ( ( ( sK45_SY295 @ SV123 @ SV72 )
!= ( sK48_SY300 @ SV123 @ SV72 ) )
= $false )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2465]) ).
thf(2485,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2465]) ).
thf(2486,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) ) )
= $false )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2466]) ).
thf(2487,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) )
= $false )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2466]) ).
thf(2488,plain,
! [SV72: $i,SV123: $i,SV337: $i,SV346: $i] :
( ( ( SV346 != SV337 )
= $true )
| ( ( ~ ( in @ SV346 @ ( succ @ SV123 ) ) )
= $true )
| ( ( ! [SY623: $i] :
( ( SV337 != SY623 )
| ~ ( ordinal @ SY623 )
| ~ ( in @ SY623 @ SV72 ) ) )
= $true )
| ( ( in @ SV337 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2467]) ).
thf(2489,plain,
! [SV72: $i,SV123: $i,SV338: $i] :
( ( ( ~ ~ ( ( ( sK43_E @ SV338 @ SV123 @ SV72 )
!= SV338 )
| ~ ( in @ ( sK43_E @ SV338 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) ) )
= $false )
| ( ( in @ SV338 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2468]) ).
thf(2490,plain,
! [SV72: $i,SV123: $i,SV338: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV338
!= ( sK42_H @ SV338 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV338 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV338 @ SV123 @ SV72 ) @ SV72 ) ) )
= $false )
| ( ( in @ SV338 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2468]) ).
thf(2491,plain,
! [SV72: $i,SV123: $i,SV347: $i] :
( ( ( ! [SY628: $i] :
( ( SY628 != SV347 )
| ~ ( in @ SY628 @ ( succ @ SV123 ) ) )
| ! [SY629: $i] :
( ( SV347 != SY629 )
| ~ ( ordinal @ SY629 )
| ~ ( in @ SY629 @ SV72 ) ) )
= $true )
| ( ( in @ SV347 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2469]) ).
thf(2492,plain,
! [SV72: $i,SV123: $i,SV348: $i] :
( ( ( ~ ( in @ SV348 @ ( sK41_C @ SV123 @ SV72 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK43_E @ SV348 @ SV123 @ SV72 )
!= SV348 )
| ~ ( in @ ( sK43_E @ SV348 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SV348
!= ( sK42_H @ SV348 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV348 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV348 @ SV123 @ SV72 ) @ SV72 ) ) ) )
= $true )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2470]) ).
thf(2493,plain,
! [SV72: $i,SV123: $i,SV349: $i] :
( ( ( ! [SY630: $i] :
( ( SY630 != SV349 )
| ~ ( in @ SY630 @ ( succ @ SV123 ) ) )
| ! [SY631: $i] :
( ( SV349 != SY631 )
| ~ ( ordinal @ SY631 )
| ~ ( in @ SY631 @ SV72 ) ) )
= $true )
| ( ( in @ SV349 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2471]) ).
thf(2494,plain,
! [SV72: $i,SV123: $i,SV350: $i] :
( ( ( ~ ( in @ SV350 @ ( sK41_C @ SV123 @ SV72 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK43_E @ SV350 @ SV123 @ SV72 )
!= SV350 )
| ~ ( in @ ( sK43_E @ SV350 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SV350
!= ( sK42_H @ SV350 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV350 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV350 @ SV123 @ SV72 ) @ SV72 ) ) ) )
= $true )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2472]) ).
thf(2495,plain,
! [SV72: $i,SV123: $i,SV339: $i,SV351: $i] :
( ( ( SV351 != SV339 )
= $true )
| ( ( ~ ( in @ SV351 @ ( succ @ SV123 ) ) )
= $true )
| ( ( ! [SY625: $i] :
( ( SV339 != SY625 )
| ~ ( ordinal @ SY625 )
| ~ ( in @ SY625 @ SV72 ) ) )
= $true )
| ( ( in @ SV339 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2473]) ).
thf(2496,plain,
! [SV72: $i,SV123: $i,SV340: $i] :
( ( ( ~ ~ ( ( ( sK43_E @ SV340 @ SV123 @ SV72 )
!= SV340 )
| ~ ( in @ ( sK43_E @ SV340 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) ) )
= $false )
| ( ( in @ SV340 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2474]) ).
thf(2497,plain,
! [SV72: $i,SV123: $i,SV340: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV340
!= ( sK42_H @ SV340 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV340 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV340 @ SV123 @ SV72 ) @ SV72 ) ) )
= $false )
| ( ( in @ SV340 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2474]) ).
thf(2498,plain,
! [SV123: $i,SV333: $i,SV72: $i,SV343: $i,SV316: $i] :
( ( ( SV316 != SV343 )
= $true )
| ( ( ~ ( ordinal @ SV343 ) )
= $true )
| ( ( ~ ( in @ SV343 @ SV72 ) )
= $true )
| ( ( SV333 = SV316 )
= $false )
| ( ( in @ SV333 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV316 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2475]) ).
thf(2499,plain,
! [SV72: $i,SV123: $i,SV317: $i] :
( ( ( ( SV317
!= ( sK42_H @ SV317 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV317 @ SV123 @ SV72 ) ) )
= $false )
| ( ( in @ SV317 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2478]) ).
thf(2500,plain,
! [SV72: $i,SV123: $i,SV344: $i] :
( ( ( ! [SY626: $i] :
( ( SY626 != SV344 )
| ~ ( in @ SY626 @ ( succ @ SV123 ) ) ) )
= $true )
| ( ( ! [SY627: $i] :
( ( SV344 != SY627 )
| ~ ( ordinal @ SY627 )
| ~ ( in @ SY627 @ SV72 ) ) )
= $true )
| ( ( in @ SV344 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2482]) ).
thf(2501,plain,
! [SV72: $i,SV123: $i,SV345: $i] :
( ( ( in @ SV345 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK43_E @ SV345 @ SV123 @ SV72 )
!= SV345 )
| ~ ( in @ ( sK43_E @ SV345 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SV345
!= ( sK42_H @ SV345 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV345 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV345 @ SV123 @ SV72 ) @ SV72 ) ) ) )
= $true )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2483]) ).
thf(2502,plain,
! [SV72: $i,SV123: $i] :
( ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2484]) ).
thf(2503,plain,
! [SV72: $i,SV123: $i] :
( ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ~ ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2485]) ).
thf(2504,plain,
! [SV72: $i,SV123: $i] :
( ( ( ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) ) )
= $true )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2486]) ).
thf(2505,plain,
! [SV72: $i,SV123: $i] :
( ( ( ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) )
= $true )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2487]) ).
thf(2506,plain,
! [SV72: $i,SV123: $i,SV337: $i,SV346: $i] :
( ( ( SV346 = SV337 )
= $false )
| ( ( ~ ( in @ SV346 @ ( succ @ SV123 ) ) )
= $true )
| ( ( ! [SY623: $i] :
( ( SV337 != SY623 )
| ~ ( ordinal @ SY623 )
| ~ ( in @ SY623 @ SV72 ) ) )
= $true )
| ( ( in @ SV337 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2488]) ).
thf(2507,plain,
! [SV72: $i,SV123: $i,SV338: $i] :
( ( ( ~ ( ( ( sK43_E @ SV338 @ SV123 @ SV72 )
!= SV338 )
| ~ ( in @ ( sK43_E @ SV338 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) ) )
= $true )
| ( ( in @ SV338 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2489]) ).
thf(2508,plain,
! [SV72: $i,SV123: $i,SV338: $i] :
( ( ( ~ ( ~ ~ ( ( SV338
!= ( sK42_H @ SV338 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV338 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV338 @ SV123 @ SV72 ) @ SV72 ) ) )
= $true )
| ( ( in @ SV338 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2490]) ).
thf(2509,plain,
! [SV72: $i,SV123: $i,SV347: $i] :
( ( ( ! [SY628: $i] :
( ( SY628 != SV347 )
| ~ ( in @ SY628 @ ( succ @ SV123 ) ) ) )
= $true )
| ( ( ! [SY629: $i] :
( ( SV347 != SY629 )
| ~ ( ordinal @ SY629 )
| ~ ( in @ SY629 @ SV72 ) ) )
= $true )
| ( ( in @ SV347 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2491]) ).
thf(2510,plain,
! [SV72: $i,SV123: $i,SV348: $i] :
( ( ( in @ SV348 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK43_E @ SV348 @ SV123 @ SV72 )
!= SV348 )
| ~ ( in @ ( sK43_E @ SV348 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SV348
!= ( sK42_H @ SV348 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV348 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV348 @ SV123 @ SV72 ) @ SV72 ) ) ) )
= $true )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2492]) ).
thf(2511,plain,
! [SV72: $i,SV123: $i,SV349: $i] :
( ( ( ! [SY630: $i] :
( ( SY630 != SV349 )
| ~ ( in @ SY630 @ ( succ @ SV123 ) ) ) )
= $true )
| ( ( ! [SY631: $i] :
( ( SV349 != SY631 )
| ~ ( ordinal @ SY631 )
| ~ ( in @ SY631 @ SV72 ) ) )
= $true )
| ( ( in @ SV349 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2493]) ).
thf(2512,plain,
! [SV72: $i,SV123: $i,SV350: $i] :
( ( ( in @ SV350 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK43_E @ SV350 @ SV123 @ SV72 )
!= SV350 )
| ~ ( in @ ( sK43_E @ SV350 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SV350
!= ( sK42_H @ SV350 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV350 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV350 @ SV123 @ SV72 ) @ SV72 ) ) ) )
= $true )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2494]) ).
thf(2513,plain,
! [SV72: $i,SV123: $i,SV339: $i,SV351: $i] :
( ( ( SV351 = SV339 )
= $false )
| ( ( ~ ( in @ SV351 @ ( succ @ SV123 ) ) )
= $true )
| ( ( ! [SY625: $i] :
( ( SV339 != SY625 )
| ~ ( ordinal @ SY625 )
| ~ ( in @ SY625 @ SV72 ) ) )
= $true )
| ( ( in @ SV339 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2495]) ).
thf(2514,plain,
! [SV72: $i,SV123: $i,SV340: $i] :
( ( ( ~ ( ( ( sK43_E @ SV340 @ SV123 @ SV72 )
!= SV340 )
| ~ ( in @ ( sK43_E @ SV340 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) ) )
= $true )
| ( ( in @ SV340 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2496]) ).
thf(2515,plain,
! [SV72: $i,SV123: $i,SV340: $i] :
( ( ( ~ ( ~ ~ ( ( SV340
!= ( sK42_H @ SV340 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV340 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV340 @ SV123 @ SV72 ) @ SV72 ) ) )
= $true )
| ( ( in @ SV340 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2497]) ).
thf(2516,plain,
! [SV123: $i,SV333: $i,SV72: $i,SV343: $i,SV316: $i] :
( ( ( SV316 = SV343 )
= $false )
| ( ( ~ ( ordinal @ SV343 ) )
= $true )
| ( ( ~ ( in @ SV343 @ SV72 ) )
= $true )
| ( ( SV333 = SV316 )
= $false )
| ( ( in @ SV333 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV316 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2498]) ).
thf(2517,plain,
! [SV72: $i,SV123: $i,SV317: $i] :
( ( ( SV317
!= ( sK42_H @ SV317 @ SV123 @ SV72 ) )
= $false )
| ( ( in @ SV317 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2499]) ).
thf(2518,plain,
! [SV72: $i,SV123: $i,SV317: $i] :
( ( ( ~ ( ordinal @ ( sK42_H @ SV317 @ SV123 @ SV72 ) ) )
= $false )
| ( ( in @ SV317 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2499]) ).
thf(2519,plain,
! [SV72: $i,SV123: $i,SV344: $i,SV352: $i] :
( ( ( ( SV352 != SV344 )
| ~ ( in @ SV352 @ ( succ @ SV123 ) ) )
= $true )
| ( ( ! [SY627: $i] :
( ( SV344 != SY627 )
| ~ ( ordinal @ SY627 )
| ~ ( in @ SY627 @ SV72 ) ) )
= $true )
| ( ( in @ SV344 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2500]) ).
thf(2520,plain,
! [SV72: $i,SV123: $i,SV345: $i] :
( ( ( ~ ~ ( ( ( sK43_E @ SV345 @ SV123 @ SV72 )
!= SV345 )
| ~ ( in @ ( sK43_E @ SV345 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SV345
!= ( sK42_H @ SV345 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV345 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV345 @ SV123 @ SV72 ) @ SV72 ) ) )
= $false )
| ( ( in @ SV345 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2501]) ).
thf(2521,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2502]) ).
thf(2522,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) )
| ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) )
= $false )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2503]) ).
thf(2523,plain,
! [SV72: $i,SV123: $i,SV353: $i] :
( ( ( ! [SY632: $i] :
( ( SY632 != SV353 )
| ~ ( in @ SY632 @ ( succ @ SV123 ) ) )
| ! [SY633: $i] :
( ( SV353 != SY633 )
| ~ ( ordinal @ SY633 )
| ~ ( in @ SY633 @ SV72 ) )
| ( in @ SV353 @ ( sK41_C @ SV123 @ SV72 ) ) )
= $true )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2504]) ).
thf(2524,plain,
! [SV72: $i,SV123: $i,SV354: $i] :
( ( ( ~ ( in @ SV354 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SV354 @ SV123 @ SV72 )
!= SV354 )
| ~ ( in @ ( sK43_E @ SV354 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SV354
!= ( sK42_H @ SV354 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV354 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV354 @ SV123 @ SV72 ) @ SV72 ) ) ) )
= $true )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2505]) ).
thf(2525,plain,
! [SV72: $i,SV337: $i,SV123: $i,SV346: $i] :
( ( ( in @ SV346 @ ( succ @ SV123 ) )
= $false )
| ( ( SV346 = SV337 )
= $false )
| ( ( ! [SY623: $i] :
( ( SV337 != SY623 )
| ~ ( ordinal @ SY623 )
| ~ ( in @ SY623 @ SV72 ) ) )
= $true )
| ( ( in @ SV337 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2506]) ).
thf(2526,plain,
! [SV72: $i,SV123: $i,SV338: $i] :
( ( ( ( ( sK43_E @ SV338 @ SV123 @ SV72 )
!= SV338 )
| ~ ( in @ ( sK43_E @ SV338 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
= $false )
| ( ( in @ SV338 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2507]) ).
thf(2527,plain,
! [SV72: $i,SV123: $i,SV338: $i] :
( ( ( ~ ~ ( ( SV338
!= ( sK42_H @ SV338 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV338 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV338 @ SV123 @ SV72 ) @ SV72 ) )
= $false )
| ( ( in @ SV338 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2508]) ).
thf(2528,plain,
! [SV72: $i,SV123: $i,SV347: $i,SV355: $i] :
( ( ( ( SV355 != SV347 )
| ~ ( in @ SV355 @ ( succ @ SV123 ) ) )
= $true )
| ( ( ! [SY629: $i] :
( ( SV347 != SY629 )
| ~ ( ordinal @ SY629 )
| ~ ( in @ SY629 @ SV72 ) ) )
= $true )
| ( ( in @ SV347 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2509]) ).
thf(2529,plain,
! [SV72: $i,SV123: $i,SV348: $i] :
( ( ( ~ ~ ( ( ( sK43_E @ SV348 @ SV123 @ SV72 )
!= SV348 )
| ~ ( in @ ( sK43_E @ SV348 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SV348
!= ( sK42_H @ SV348 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV348 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV348 @ SV123 @ SV72 ) @ SV72 ) ) )
= $false )
| ( ( in @ SV348 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2510]) ).
thf(2530,plain,
! [SV72: $i,SV123: $i,SV349: $i,SV356: $i] :
( ( ( ( SV356 != SV349 )
| ~ ( in @ SV356 @ ( succ @ SV123 ) ) )
= $true )
| ( ( ! [SY631: $i] :
( ( SV349 != SY631 )
| ~ ( ordinal @ SY631 )
| ~ ( in @ SY631 @ SV72 ) ) )
= $true )
| ( ( in @ SV349 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2511]) ).
thf(2531,plain,
! [SV72: $i,SV123: $i,SV350: $i] :
( ( ( ~ ~ ( ( ( sK43_E @ SV350 @ SV123 @ SV72 )
!= SV350 )
| ~ ( in @ ( sK43_E @ SV350 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SV350
!= ( sK42_H @ SV350 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV350 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV350 @ SV123 @ SV72 ) @ SV72 ) ) )
= $false )
| ( ( in @ SV350 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2512]) ).
thf(2532,plain,
! [SV72: $i,SV339: $i,SV123: $i,SV351: $i] :
( ( ( in @ SV351 @ ( succ @ SV123 ) )
= $false )
| ( ( SV351 = SV339 )
= $false )
| ( ( ! [SY625: $i] :
( ( SV339 != SY625 )
| ~ ( ordinal @ SY625 )
| ~ ( in @ SY625 @ SV72 ) ) )
= $true )
| ( ( in @ SV339 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2513]) ).
thf(2533,plain,
! [SV72: $i,SV123: $i,SV340: $i] :
( ( ( ( ( sK43_E @ SV340 @ SV123 @ SV72 )
!= SV340 )
| ~ ( in @ ( sK43_E @ SV340 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
= $false )
| ( ( in @ SV340 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2514]) ).
thf(2534,plain,
! [SV72: $i,SV123: $i,SV340: $i] :
( ( ( ~ ~ ( ( SV340
!= ( sK42_H @ SV340 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV340 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV340 @ SV123 @ SV72 ) @ SV72 ) )
= $false )
| ( ( in @ SV340 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2515]) ).
thf(2535,plain,
! [SV123: $i,SV333: $i,SV72: $i,SV316: $i,SV343: $i] :
( ( ( ordinal @ SV343 )
= $false )
| ( ( SV316 = SV343 )
= $false )
| ( ( ~ ( in @ SV343 @ SV72 ) )
= $true )
| ( ( SV333 = SV316 )
= $false )
| ( ( in @ SV333 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV316 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2516]) ).
thf(2536,plain,
! [SV72: $i,SV123: $i,SV317: $i] :
( ( ( SV317
= ( sK42_H @ SV317 @ SV123 @ SV72 ) )
= $true )
| ( ( in @ SV317 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2517]) ).
thf(2537,plain,
! [SV72: $i,SV123: $i,SV317: $i] :
( ( ( ordinal @ ( sK42_H @ SV317 @ SV123 @ SV72 ) )
= $true )
| ( ( in @ SV317 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2518]) ).
thf(2538,plain,
! [SV72: $i,SV123: $i,SV344: $i,SV352: $i] :
( ( ( SV352 != SV344 )
= $true )
| ( ( ~ ( in @ SV352 @ ( succ @ SV123 ) ) )
= $true )
| ( ( ! [SY627: $i] :
( ( SV344 != SY627 )
| ~ ( ordinal @ SY627 )
| ~ ( in @ SY627 @ SV72 ) ) )
= $true )
| ( ( in @ SV344 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2519]) ).
thf(2539,plain,
! [SV72: $i,SV123: $i,SV345: $i] :
( ( ( ~ ~ ( ( ( sK43_E @ SV345 @ SV123 @ SV72 )
!= SV345 )
| ~ ( in @ ( sK43_E @ SV345 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) ) )
= $false )
| ( ( in @ SV345 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2520]) ).
thf(2540,plain,
! [SV72: $i,SV123: $i,SV345: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV345
!= ( sK42_H @ SV345 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV345 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV345 @ SV123 @ SV72 ) @ SV72 ) ) )
= $false )
| ( ( in @ SV345 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2520]) ).
thf(2541,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2521]) ).
thf(2542,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2521]) ).
thf(2543,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) ) )
= $false )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2522]) ).
thf(2544,plain,
! [SV72: $i,SV123: $i] :
( ( ( ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) )
= $false )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2522]) ).
thf(2545,plain,
! [SV72: $i,SV123: $i,SV353: $i] :
( ( ( ! [SY632: $i] :
( ( SY632 != SV353 )
| ~ ( in @ SY632 @ ( succ @ SV123 ) ) )
| ! [SY633: $i] :
( ( SV353 != SY633 )
| ~ ( ordinal @ SY633 )
| ~ ( in @ SY633 @ SV72 ) ) )
= $true )
| ( ( in @ SV353 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2523]) ).
thf(2546,plain,
! [SV72: $i,SV123: $i,SV354: $i] :
( ( ( ~ ( in @ SV354 @ ( sK41_C @ SV123 @ SV72 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK43_E @ SV354 @ SV123 @ SV72 )
!= SV354 )
| ~ ( in @ ( sK43_E @ SV354 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SV354
!= ( sK42_H @ SV354 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV354 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV354 @ SV123 @ SV72 ) @ SV72 ) ) ) )
= $true )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2524]) ).
thf(2547,plain,
! [SV123: $i,SV346: $i,SV72: $i,SV357: $i,SV337: $i] :
( ( ( ( SV337 != SV357 )
| ~ ( ordinal @ SV357 )
| ~ ( in @ SV357 @ SV72 ) )
= $true )
| ( ( SV346 = SV337 )
= $false )
| ( ( in @ SV346 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV337 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2525]) ).
thf(2548,plain,
! [SV72: $i,SV123: $i,SV338: $i] :
( ( ( ( sK43_E @ SV338 @ SV123 @ SV72 )
!= SV338 )
= $false )
| ( ( in @ SV338 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2526]) ).
thf(2549,plain,
! [SV72: $i,SV123: $i,SV338: $i] :
( ( ( ~ ( in @ ( sK43_E @ SV338 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
= $false )
| ( ( in @ SV338 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2526]) ).
thf(2550,plain,
! [SV72: $i,SV123: $i,SV338: $i] :
( ( ( ~ ~ ( ( SV338
!= ( sK42_H @ SV338 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV338 @ SV123 @ SV72 ) ) ) )
= $false )
| ( ( in @ SV338 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2527]) ).
thf(2551,plain,
! [SV72: $i,SV123: $i,SV338: $i] :
( ( ( ~ ( in @ ( sK42_H @ SV338 @ SV123 @ SV72 ) @ SV72 ) )
= $false )
| ( ( in @ SV338 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2527]) ).
thf(2552,plain,
! [SV72: $i,SV123: $i,SV347: $i,SV355: $i] :
( ( ( SV355 != SV347 )
= $true )
| ( ( ~ ( in @ SV355 @ ( succ @ SV123 ) ) )
= $true )
| ( ( ! [SY629: $i] :
( ( SV347 != SY629 )
| ~ ( ordinal @ SY629 )
| ~ ( in @ SY629 @ SV72 ) ) )
= $true )
| ( ( in @ SV347 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2528]) ).
thf(2553,plain,
! [SV72: $i,SV123: $i,SV348: $i] :
( ( ( ~ ~ ( ( ( sK43_E @ SV348 @ SV123 @ SV72 )
!= SV348 )
| ~ ( in @ ( sK43_E @ SV348 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) ) )
= $false )
| ( ( in @ SV348 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2529]) ).
thf(2554,plain,
! [SV72: $i,SV123: $i,SV348: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV348
!= ( sK42_H @ SV348 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV348 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV348 @ SV123 @ SV72 ) @ SV72 ) ) )
= $false )
| ( ( in @ SV348 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2529]) ).
thf(2555,plain,
! [SV72: $i,SV123: $i,SV349: $i,SV356: $i] :
( ( ( SV356 != SV349 )
= $true )
| ( ( ~ ( in @ SV356 @ ( succ @ SV123 ) ) )
= $true )
| ( ( ! [SY631: $i] :
( ( SV349 != SY631 )
| ~ ( ordinal @ SY631 )
| ~ ( in @ SY631 @ SV72 ) ) )
= $true )
| ( ( in @ SV349 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2530]) ).
thf(2556,plain,
! [SV72: $i,SV123: $i,SV350: $i] :
( ( ( ~ ~ ( ( ( sK43_E @ SV350 @ SV123 @ SV72 )
!= SV350 )
| ~ ( in @ ( sK43_E @ SV350 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) ) )
= $false )
| ( ( in @ SV350 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2531]) ).
thf(2557,plain,
! [SV72: $i,SV123: $i,SV350: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV350
!= ( sK42_H @ SV350 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV350 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV350 @ SV123 @ SV72 ) @ SV72 ) ) )
= $false )
| ( ( in @ SV350 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2531]) ).
thf(2558,plain,
! [SV123: $i,SV351: $i,SV72: $i,SV358: $i,SV339: $i] :
( ( ( ( SV339 != SV358 )
| ~ ( ordinal @ SV358 )
| ~ ( in @ SV358 @ SV72 ) )
= $true )
| ( ( SV351 = SV339 )
= $false )
| ( ( in @ SV351 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV339 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2532]) ).
thf(2559,plain,
! [SV72: $i,SV123: $i,SV340: $i] :
( ( ( ( sK43_E @ SV340 @ SV123 @ SV72 )
!= SV340 )
= $false )
| ( ( in @ SV340 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2533]) ).
thf(2560,plain,
! [SV72: $i,SV123: $i,SV340: $i] :
( ( ( ~ ( in @ ( sK43_E @ SV340 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
= $false )
| ( ( in @ SV340 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2533]) ).
thf(2561,plain,
! [SV72: $i,SV123: $i,SV340: $i] :
( ( ( ~ ~ ( ( SV340
!= ( sK42_H @ SV340 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV340 @ SV123 @ SV72 ) ) ) )
= $false )
| ( ( in @ SV340 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2534]) ).
thf(2562,plain,
! [SV72: $i,SV123: $i,SV340: $i] :
( ( ( ~ ( in @ ( sK42_H @ SV340 @ SV123 @ SV72 ) @ SV72 ) )
= $false )
| ( ( in @ SV340 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2534]) ).
thf(2563,plain,
! [SV123: $i,SV333: $i,SV316: $i,SV72: $i,SV343: $i] :
( ( ( in @ SV343 @ SV72 )
= $false )
| ( ( SV316 = SV343 )
= $false )
| ( ( ordinal @ SV343 )
= $false )
| ( ( SV333 = SV316 )
= $false )
| ( ( in @ SV333 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV316 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2535]) ).
thf(2564,plain,
! [SV72: $i,SV123: $i,SV344: $i,SV352: $i] :
( ( ( SV352 = SV344 )
= $false )
| ( ( ~ ( in @ SV352 @ ( succ @ SV123 ) ) )
= $true )
| ( ( ! [SY627: $i] :
( ( SV344 != SY627 )
| ~ ( ordinal @ SY627 )
| ~ ( in @ SY627 @ SV72 ) ) )
= $true )
| ( ( in @ SV344 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2538]) ).
thf(2565,plain,
! [SV72: $i,SV123: $i,SV345: $i] :
( ( ( ~ ( ( ( sK43_E @ SV345 @ SV123 @ SV72 )
!= SV345 )
| ~ ( in @ ( sK43_E @ SV345 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) ) )
= $true )
| ( ( in @ SV345 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2539]) ).
thf(2566,plain,
! [SV72: $i,SV123: $i,SV345: $i] :
( ( ( ~ ( ~ ~ ( ( SV345
!= ( sK42_H @ SV345 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV345 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV345 @ SV123 @ SV72 ) @ SV72 ) ) )
= $true )
| ( ( in @ SV345 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2540]) ).
thf(2567,plain,
! [SV72: $i,SV123: $i] :
( ( ( ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) ) )
= $true )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2541]) ).
thf(2568,plain,
! [SV72: $i,SV123: $i] :
( ( ( ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) )
= $true )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2542]) ).
thf(2569,plain,
! [SV72: $i,SV123: $i] :
( ( ( ! [SY477: $i] :
( ! [SY478: $i] :
( ( SY478 != SY477 )
| ~ ( in @ SY478 @ ( succ @ SV123 ) ) )
| ! [SY413: $i] :
( ( SY477 != SY413 )
| ~ ( ordinal @ SY413 )
| ~ ( in @ SY413 @ SV72 ) )
| ( in @ SY477 @ ( sK41_C @ SV123 @ SV72 ) ) ) )
= $true )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2543]) ).
thf(2570,plain,
! [SV72: $i,SV123: $i] :
( ( ( ! [SY480: $i] :
( ~ ( in @ SY480 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SY480 @ SV123 @ SV72 )
!= SY480 )
| ~ ( in @ ( sK43_E @ SY480 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SY480
!= ( sK42_H @ SY480 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SY480 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SY480 @ SV123 @ SV72 ) @ SV72 ) ) ) ) )
= $true )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2544]) ).
thf(2571,plain,
! [SV72: $i,SV123: $i,SV353: $i] :
( ( ( ! [SY632: $i] :
( ( SY632 != SV353 )
| ~ ( in @ SY632 @ ( succ @ SV123 ) ) ) )
= $true )
| ( ( ! [SY633: $i] :
( ( SV353 != SY633 )
| ~ ( ordinal @ SY633 )
| ~ ( in @ SY633 @ SV72 ) ) )
= $true )
| ( ( in @ SV353 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2545]) ).
thf(2572,plain,
! [SV72: $i,SV123: $i,SV354: $i] :
( ( ( in @ SV354 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK43_E @ SV354 @ SV123 @ SV72 )
!= SV354 )
| ~ ( in @ ( sK43_E @ SV354 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SV354
!= ( sK42_H @ SV354 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV354 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV354 @ SV123 @ SV72 ) @ SV72 ) ) ) )
= $true )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2546]) ).
thf(2573,plain,
! [SV123: $i,SV346: $i,SV72: $i,SV357: $i,SV337: $i] :
( ( ( ( SV337 != SV357 )
| ~ ( ordinal @ SV357 ) )
= $true )
| ( ( ~ ( in @ SV357 @ SV72 ) )
= $true )
| ( ( SV346 = SV337 )
= $false )
| ( ( in @ SV346 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV337 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2547]) ).
thf(2574,plain,
! [SV72: $i,SV123: $i,SV338: $i] :
( ( ( ( sK43_E @ SV338 @ SV123 @ SV72 )
= SV338 )
= $true )
| ( ( in @ SV338 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2548]) ).
thf(2575,plain,
! [SV72: $i,SV123: $i,SV338: $i] :
( ( ( in @ ( sK43_E @ SV338 @ SV123 @ SV72 ) @ ( succ @ SV123 ) )
= $true )
| ( ( in @ SV338 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2549]) ).
thf(2576,plain,
! [SV72: $i,SV123: $i,SV338: $i] :
( ( ( ~ ( ( SV338
!= ( sK42_H @ SV338 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV338 @ SV123 @ SV72 ) ) ) )
= $true )
| ( ( in @ SV338 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2550]) ).
thf(2577,plain,
! [SV72: $i,SV123: $i,SV338: $i] :
( ( ( in @ ( sK42_H @ SV338 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( in @ SV338 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2551]) ).
thf(2578,plain,
! [SV72: $i,SV123: $i,SV347: $i,SV355: $i] :
( ( ( SV355 = SV347 )
= $false )
| ( ( ~ ( in @ SV355 @ ( succ @ SV123 ) ) )
= $true )
| ( ( ! [SY629: $i] :
( ( SV347 != SY629 )
| ~ ( ordinal @ SY629 )
| ~ ( in @ SY629 @ SV72 ) ) )
= $true )
| ( ( in @ SV347 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2552]) ).
thf(2579,plain,
! [SV72: $i,SV123: $i,SV348: $i] :
( ( ( ~ ( ( ( sK43_E @ SV348 @ SV123 @ SV72 )
!= SV348 )
| ~ ( in @ ( sK43_E @ SV348 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) ) )
= $true )
| ( ( in @ SV348 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2553]) ).
thf(2580,plain,
! [SV72: $i,SV123: $i,SV348: $i] :
( ( ( ~ ( ~ ~ ( ( SV348
!= ( sK42_H @ SV348 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV348 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV348 @ SV123 @ SV72 ) @ SV72 ) ) )
= $true )
| ( ( in @ SV348 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2554]) ).
thf(2581,plain,
! [SV72: $i,SV123: $i,SV349: $i,SV356: $i] :
( ( ( SV356 = SV349 )
= $false )
| ( ( ~ ( in @ SV356 @ ( succ @ SV123 ) ) )
= $true )
| ( ( ! [SY631: $i] :
( ( SV349 != SY631 )
| ~ ( ordinal @ SY631 )
| ~ ( in @ SY631 @ SV72 ) ) )
= $true )
| ( ( in @ SV349 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2555]) ).
thf(2582,plain,
! [SV72: $i,SV123: $i,SV350: $i] :
( ( ( ~ ( ( ( sK43_E @ SV350 @ SV123 @ SV72 )
!= SV350 )
| ~ ( in @ ( sK43_E @ SV350 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) ) )
= $true )
| ( ( in @ SV350 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2556]) ).
thf(2583,plain,
! [SV72: $i,SV123: $i,SV350: $i] :
( ( ( ~ ( ~ ~ ( ( SV350
!= ( sK42_H @ SV350 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV350 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV350 @ SV123 @ SV72 ) @ SV72 ) ) )
= $true )
| ( ( in @ SV350 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2557]) ).
thf(2584,plain,
! [SV123: $i,SV351: $i,SV72: $i,SV358: $i,SV339: $i] :
( ( ( ( SV339 != SV358 )
| ~ ( ordinal @ SV358 ) )
= $true )
| ( ( ~ ( in @ SV358 @ SV72 ) )
= $true )
| ( ( SV351 = SV339 )
= $false )
| ( ( in @ SV351 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV339 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2558]) ).
thf(2585,plain,
! [SV72: $i,SV123: $i,SV340: $i] :
( ( ( ( sK43_E @ SV340 @ SV123 @ SV72 )
= SV340 )
= $true )
| ( ( in @ SV340 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2559]) ).
thf(2586,plain,
! [SV72: $i,SV123: $i,SV340: $i] :
( ( ( in @ ( sK43_E @ SV340 @ SV123 @ SV72 ) @ ( succ @ SV123 ) )
= $true )
| ( ( in @ SV340 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2560]) ).
thf(2587,plain,
! [SV72: $i,SV123: $i,SV340: $i] :
( ( ( ~ ( ( SV340
!= ( sK42_H @ SV340 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV340 @ SV123 @ SV72 ) ) ) )
= $true )
| ( ( in @ SV340 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2561]) ).
thf(2588,plain,
! [SV72: $i,SV123: $i,SV340: $i] :
( ( ( in @ ( sK42_H @ SV340 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( in @ SV340 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2562]) ).
thf(2589,plain,
! [SV72: $i,SV344: $i,SV123: $i,SV352: $i] :
( ( ( in @ SV352 @ ( succ @ SV123 ) )
= $false )
| ( ( SV352 = SV344 )
= $false )
| ( ( ! [SY627: $i] :
( ( SV344 != SY627 )
| ~ ( ordinal @ SY627 )
| ~ ( in @ SY627 @ SV72 ) ) )
= $true )
| ( ( in @ SV344 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2564]) ).
thf(2590,plain,
! [SV72: $i,SV123: $i,SV345: $i] :
( ( ( ( ( sK43_E @ SV345 @ SV123 @ SV72 )
!= SV345 )
| ~ ( in @ ( sK43_E @ SV345 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
= $false )
| ( ( in @ SV345 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2565]) ).
thf(2591,plain,
! [SV72: $i,SV123: $i,SV345: $i] :
( ( ( ~ ~ ( ( SV345
!= ( sK42_H @ SV345 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV345 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV345 @ SV123 @ SV72 ) @ SV72 ) )
= $false )
| ( ( in @ SV345 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2566]) ).
thf(2592,plain,
! [SV72: $i,SV123: $i,SV359: $i] :
( ( ( ! [SY634: $i] :
( ( SY634 != SV359 )
| ~ ( in @ SY634 @ ( succ @ SV123 ) ) )
| ! [SY635: $i] :
( ( SV359 != SY635 )
| ~ ( ordinal @ SY635 )
| ~ ( in @ SY635 @ SV72 ) )
| ( in @ SV359 @ ( sK41_C @ SV123 @ SV72 ) ) )
= $true )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2567]) ).
thf(2593,plain,
! [SV72: $i,SV123: $i,SV360: $i] :
( ( ( ~ ( in @ SV360 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SV360 @ SV123 @ SV72 )
!= SV360 )
| ~ ( in @ ( sK43_E @ SV360 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SV360
!= ( sK42_H @ SV360 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV360 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV360 @ SV123 @ SV72 ) @ SV72 ) ) ) )
= $true )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2568]) ).
thf(2594,plain,
! [SV72: $i,SV123: $i,SV361: $i] :
( ( ( ! [SY636: $i] :
( ( SY636 != SV361 )
| ~ ( in @ SY636 @ ( succ @ SV123 ) ) )
| ! [SY637: $i] :
( ( SV361 != SY637 )
| ~ ( ordinal @ SY637 )
| ~ ( in @ SY637 @ SV72 ) )
| ( in @ SV361 @ ( sK41_C @ SV123 @ SV72 ) ) )
= $true )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2569]) ).
thf(2595,plain,
! [SV72: $i,SV123: $i,SV362: $i] :
( ( ( ~ ( in @ SV362 @ ( sK41_C @ SV123 @ SV72 ) )
| ~ ( ~ ~ ( ( ( sK43_E @ SV362 @ SV123 @ SV72 )
!= SV362 )
| ~ ( in @ ( sK43_E @ SV362 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SV362
!= ( sK42_H @ SV362 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV362 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV362 @ SV123 @ SV72 ) @ SV72 ) ) ) )
= $true )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2570]) ).
thf(2596,plain,
! [SV72: $i,SV123: $i,SV353: $i,SV363: $i] :
( ( ( ( SV363 != SV353 )
| ~ ( in @ SV363 @ ( succ @ SV123 ) ) )
= $true )
| ( ( ! [SY633: $i] :
( ( SV353 != SY633 )
| ~ ( ordinal @ SY633 )
| ~ ( in @ SY633 @ SV72 ) ) )
= $true )
| ( ( in @ SV353 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2571]) ).
thf(2597,plain,
! [SV72: $i,SV123: $i,SV354: $i] :
( ( ( ~ ~ ( ( ( sK43_E @ SV354 @ SV123 @ SV72 )
!= SV354 )
| ~ ( in @ ( sK43_E @ SV354 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SV354
!= ( sK42_H @ SV354 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV354 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV354 @ SV123 @ SV72 ) @ SV72 ) ) )
= $false )
| ( ( in @ SV354 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2572]) ).
thf(2598,plain,
! [SV123: $i,SV346: $i,SV72: $i,SV357: $i,SV337: $i] :
( ( ( SV337 != SV357 )
= $true )
| ( ( ~ ( ordinal @ SV357 ) )
= $true )
| ( ( ~ ( in @ SV357 @ SV72 ) )
= $true )
| ( ( SV346 = SV337 )
= $false )
| ( ( in @ SV346 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV337 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2573]) ).
thf(2599,plain,
! [SV72: $i,SV123: $i,SV338: $i] :
( ( ( ( SV338
!= ( sK42_H @ SV338 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV338 @ SV123 @ SV72 ) ) )
= $false )
| ( ( in @ SV338 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2576]) ).
thf(2600,plain,
! [SV72: $i,SV347: $i,SV123: $i,SV355: $i] :
( ( ( in @ SV355 @ ( succ @ SV123 ) )
= $false )
| ( ( SV355 = SV347 )
= $false )
| ( ( ! [SY629: $i] :
( ( SV347 != SY629 )
| ~ ( ordinal @ SY629 )
| ~ ( in @ SY629 @ SV72 ) ) )
= $true )
| ( ( in @ SV347 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2578]) ).
thf(2601,plain,
! [SV72: $i,SV123: $i,SV348: $i] :
( ( ( ( ( sK43_E @ SV348 @ SV123 @ SV72 )
!= SV348 )
| ~ ( in @ ( sK43_E @ SV348 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
= $false )
| ( ( in @ SV348 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2579]) ).
thf(2602,plain,
! [SV72: $i,SV123: $i,SV348: $i] :
( ( ( ~ ~ ( ( SV348
!= ( sK42_H @ SV348 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV348 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV348 @ SV123 @ SV72 ) @ SV72 ) )
= $false )
| ( ( in @ SV348 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2580]) ).
thf(2603,plain,
! [SV72: $i,SV349: $i,SV123: $i,SV356: $i] :
( ( ( in @ SV356 @ ( succ @ SV123 ) )
= $false )
| ( ( SV356 = SV349 )
= $false )
| ( ( ! [SY631: $i] :
( ( SV349 != SY631 )
| ~ ( ordinal @ SY631 )
| ~ ( in @ SY631 @ SV72 ) ) )
= $true )
| ( ( in @ SV349 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2581]) ).
thf(2604,plain,
! [SV72: $i,SV123: $i,SV350: $i] :
( ( ( ( ( sK43_E @ SV350 @ SV123 @ SV72 )
!= SV350 )
| ~ ( in @ ( sK43_E @ SV350 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
= $false )
| ( ( in @ SV350 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2582]) ).
thf(2605,plain,
! [SV72: $i,SV123: $i,SV350: $i] :
( ( ( ~ ~ ( ( SV350
!= ( sK42_H @ SV350 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV350 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV350 @ SV123 @ SV72 ) @ SV72 ) )
= $false )
| ( ( in @ SV350 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2583]) ).
thf(2606,plain,
! [SV123: $i,SV351: $i,SV72: $i,SV358: $i,SV339: $i] :
( ( ( SV339 != SV358 )
= $true )
| ( ( ~ ( ordinal @ SV358 ) )
= $true )
| ( ( ~ ( in @ SV358 @ SV72 ) )
= $true )
| ( ( SV351 = SV339 )
= $false )
| ( ( in @ SV351 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV339 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2584]) ).
thf(2607,plain,
! [SV72: $i,SV123: $i,SV340: $i] :
( ( ( ( SV340
!= ( sK42_H @ SV340 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV340 @ SV123 @ SV72 ) ) )
= $false )
| ( ( in @ SV340 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2587]) ).
thf(2608,plain,
! [SV123: $i,SV352: $i,SV72: $i,SV364: $i,SV344: $i] :
( ( ( ( SV344 != SV364 )
| ~ ( ordinal @ SV364 )
| ~ ( in @ SV364 @ SV72 ) )
= $true )
| ( ( SV352 = SV344 )
= $false )
| ( ( in @ SV352 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV344 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2589]) ).
thf(2609,plain,
! [SV72: $i,SV123: $i,SV345: $i] :
( ( ( ( sK43_E @ SV345 @ SV123 @ SV72 )
!= SV345 )
= $false )
| ( ( in @ SV345 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2590]) ).
thf(2610,plain,
! [SV72: $i,SV123: $i,SV345: $i] :
( ( ( ~ ( in @ ( sK43_E @ SV345 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
= $false )
| ( ( in @ SV345 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2590]) ).
thf(2611,plain,
! [SV72: $i,SV123: $i,SV345: $i] :
( ( ( ~ ~ ( ( SV345
!= ( sK42_H @ SV345 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV345 @ SV123 @ SV72 ) ) ) )
= $false )
| ( ( in @ SV345 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2591]) ).
thf(2612,plain,
! [SV72: $i,SV123: $i,SV345: $i] :
( ( ( ~ ( in @ ( sK42_H @ SV345 @ SV123 @ SV72 ) @ SV72 ) )
= $false )
| ( ( in @ SV345 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2591]) ).
thf(2613,plain,
! [SV72: $i,SV123: $i,SV359: $i] :
( ( ( ! [SY634: $i] :
( ( SY634 != SV359 )
| ~ ( in @ SY634 @ ( succ @ SV123 ) ) )
| ! [SY635: $i] :
( ( SV359 != SY635 )
| ~ ( ordinal @ SY635 )
| ~ ( in @ SY635 @ SV72 ) ) )
= $true )
| ( ( in @ SV359 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2592]) ).
thf(2614,plain,
! [SV72: $i,SV123: $i,SV360: $i] :
( ( ( ~ ( in @ SV360 @ ( sK41_C @ SV123 @ SV72 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK43_E @ SV360 @ SV123 @ SV72 )
!= SV360 )
| ~ ( in @ ( sK43_E @ SV360 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SV360
!= ( sK42_H @ SV360 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV360 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV360 @ SV123 @ SV72 ) @ SV72 ) ) ) )
= $true )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2593]) ).
thf(2615,plain,
! [SV72: $i,SV123: $i,SV361: $i] :
( ( ( ! [SY636: $i] :
( ( SY636 != SV361 )
| ~ ( in @ SY636 @ ( succ @ SV123 ) ) )
| ! [SY637: $i] :
( ( SV361 != SY637 )
| ~ ( ordinal @ SY637 )
| ~ ( in @ SY637 @ SV72 ) ) )
= $true )
| ( ( in @ SV361 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2594]) ).
thf(2616,plain,
! [SV72: $i,SV123: $i,SV362: $i] :
( ( ( ~ ( in @ SV362 @ ( sK41_C @ SV123 @ SV72 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK43_E @ SV362 @ SV123 @ SV72 )
!= SV362 )
| ~ ( in @ ( sK43_E @ SV362 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SV362
!= ( sK42_H @ SV362 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV362 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV362 @ SV123 @ SV72 ) @ SV72 ) ) ) )
= $true )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2595]) ).
thf(2617,plain,
! [SV72: $i,SV123: $i,SV353: $i,SV363: $i] :
( ( ( SV363 != SV353 )
= $true )
| ( ( ~ ( in @ SV363 @ ( succ @ SV123 ) ) )
= $true )
| ( ( ! [SY633: $i] :
( ( SV353 != SY633 )
| ~ ( ordinal @ SY633 )
| ~ ( in @ SY633 @ SV72 ) ) )
= $true )
| ( ( in @ SV353 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2596]) ).
thf(2618,plain,
! [SV72: $i,SV123: $i,SV354: $i] :
( ( ( ~ ~ ( ( ( sK43_E @ SV354 @ SV123 @ SV72 )
!= SV354 )
| ~ ( in @ ( sK43_E @ SV354 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) ) )
= $false )
| ( ( in @ SV354 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2597]) ).
thf(2619,plain,
! [SV72: $i,SV123: $i,SV354: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV354
!= ( sK42_H @ SV354 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV354 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV354 @ SV123 @ SV72 ) @ SV72 ) ) )
= $false )
| ( ( in @ SV354 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2597]) ).
thf(2620,plain,
! [SV123: $i,SV346: $i,SV72: $i,SV357: $i,SV337: $i] :
( ( ( SV337 = SV357 )
= $false )
| ( ( ~ ( ordinal @ SV357 ) )
= $true )
| ( ( ~ ( in @ SV357 @ SV72 ) )
= $true )
| ( ( SV346 = SV337 )
= $false )
| ( ( in @ SV346 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV337 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2598]) ).
thf(2621,plain,
! [SV72: $i,SV123: $i,SV338: $i] :
( ( ( SV338
!= ( sK42_H @ SV338 @ SV123 @ SV72 ) )
= $false )
| ( ( in @ SV338 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2599]) ).
thf(2622,plain,
! [SV72: $i,SV123: $i,SV338: $i] :
( ( ( ~ ( ordinal @ ( sK42_H @ SV338 @ SV123 @ SV72 ) ) )
= $false )
| ( ( in @ SV338 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2599]) ).
thf(2623,plain,
! [SV123: $i,SV355: $i,SV72: $i,SV365: $i,SV347: $i] :
( ( ( ( SV347 != SV365 )
| ~ ( ordinal @ SV365 )
| ~ ( in @ SV365 @ SV72 ) )
= $true )
| ( ( SV355 = SV347 )
= $false )
| ( ( in @ SV355 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV347 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2600]) ).
thf(2624,plain,
! [SV72: $i,SV123: $i,SV348: $i] :
( ( ( ( sK43_E @ SV348 @ SV123 @ SV72 )
!= SV348 )
= $false )
| ( ( in @ SV348 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2601]) ).
thf(2625,plain,
! [SV72: $i,SV123: $i,SV348: $i] :
( ( ( ~ ( in @ ( sK43_E @ SV348 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
= $false )
| ( ( in @ SV348 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2601]) ).
thf(2626,plain,
! [SV72: $i,SV123: $i,SV348: $i] :
( ( ( ~ ~ ( ( SV348
!= ( sK42_H @ SV348 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV348 @ SV123 @ SV72 ) ) ) )
= $false )
| ( ( in @ SV348 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2602]) ).
thf(2627,plain,
! [SV72: $i,SV123: $i,SV348: $i] :
( ( ( ~ ( in @ ( sK42_H @ SV348 @ SV123 @ SV72 ) @ SV72 ) )
= $false )
| ( ( in @ SV348 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2602]) ).
thf(2628,plain,
! [SV123: $i,SV356: $i,SV72: $i,SV366: $i,SV349: $i] :
( ( ( ( SV349 != SV366 )
| ~ ( ordinal @ SV366 )
| ~ ( in @ SV366 @ SV72 ) )
= $true )
| ( ( SV356 = SV349 )
= $false )
| ( ( in @ SV356 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV349 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2603]) ).
thf(2629,plain,
! [SV72: $i,SV123: $i,SV350: $i] :
( ( ( ( sK43_E @ SV350 @ SV123 @ SV72 )
!= SV350 )
= $false )
| ( ( in @ SV350 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2604]) ).
thf(2630,plain,
! [SV72: $i,SV123: $i,SV350: $i] :
( ( ( ~ ( in @ ( sK43_E @ SV350 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
= $false )
| ( ( in @ SV350 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2604]) ).
thf(2631,plain,
! [SV72: $i,SV123: $i,SV350: $i] :
( ( ( ~ ~ ( ( SV350
!= ( sK42_H @ SV350 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV350 @ SV123 @ SV72 ) ) ) )
= $false )
| ( ( in @ SV350 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2605]) ).
thf(2632,plain,
! [SV72: $i,SV123: $i,SV350: $i] :
( ( ( ~ ( in @ ( sK42_H @ SV350 @ SV123 @ SV72 ) @ SV72 ) )
= $false )
| ( ( in @ SV350 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2605]) ).
thf(2633,plain,
! [SV123: $i,SV351: $i,SV72: $i,SV358: $i,SV339: $i] :
( ( ( SV339 = SV358 )
= $false )
| ( ( ~ ( ordinal @ SV358 ) )
= $true )
| ( ( ~ ( in @ SV358 @ SV72 ) )
= $true )
| ( ( SV351 = SV339 )
= $false )
| ( ( in @ SV351 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV339 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2606]) ).
thf(2634,plain,
! [SV72: $i,SV123: $i,SV340: $i] :
( ( ( SV340
!= ( sK42_H @ SV340 @ SV123 @ SV72 ) )
= $false )
| ( ( in @ SV340 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2607]) ).
thf(2635,plain,
! [SV72: $i,SV123: $i,SV340: $i] :
( ( ( ~ ( ordinal @ ( sK42_H @ SV340 @ SV123 @ SV72 ) ) )
= $false )
| ( ( in @ SV340 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2607]) ).
thf(2636,plain,
! [SV123: $i,SV352: $i,SV72: $i,SV364: $i,SV344: $i] :
( ( ( ( SV344 != SV364 )
| ~ ( ordinal @ SV364 ) )
= $true )
| ( ( ~ ( in @ SV364 @ SV72 ) )
= $true )
| ( ( SV352 = SV344 )
= $false )
| ( ( in @ SV352 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV344 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2608]) ).
thf(2637,plain,
! [SV72: $i,SV123: $i,SV345: $i] :
( ( ( ( sK43_E @ SV345 @ SV123 @ SV72 )
= SV345 )
= $true )
| ( ( in @ SV345 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2609]) ).
thf(2638,plain,
! [SV72: $i,SV123: $i,SV345: $i] :
( ( ( in @ ( sK43_E @ SV345 @ SV123 @ SV72 ) @ ( succ @ SV123 ) )
= $true )
| ( ( in @ SV345 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2610]) ).
thf(2639,plain,
! [SV72: $i,SV123: $i,SV345: $i] :
( ( ( ~ ( ( SV345
!= ( sK42_H @ SV345 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV345 @ SV123 @ SV72 ) ) ) )
= $true )
| ( ( in @ SV345 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2611]) ).
thf(2640,plain,
! [SV72: $i,SV123: $i,SV345: $i] :
( ( ( in @ ( sK42_H @ SV345 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( in @ SV345 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2612]) ).
thf(2641,plain,
! [SV72: $i,SV123: $i,SV359: $i] :
( ( ( ! [SY634: $i] :
( ( SY634 != SV359 )
| ~ ( in @ SY634 @ ( succ @ SV123 ) ) ) )
= $true )
| ( ( ! [SY635: $i] :
( ( SV359 != SY635 )
| ~ ( ordinal @ SY635 )
| ~ ( in @ SY635 @ SV72 ) ) )
= $true )
| ( ( in @ SV359 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2613]) ).
thf(2642,plain,
! [SV72: $i,SV123: $i,SV360: $i] :
( ( ( in @ SV360 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK43_E @ SV360 @ SV123 @ SV72 )
!= SV360 )
| ~ ( in @ ( sK43_E @ SV360 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SV360
!= ( sK42_H @ SV360 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV360 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV360 @ SV123 @ SV72 ) @ SV72 ) ) ) )
= $true )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2614]) ).
thf(2643,plain,
! [SV72: $i,SV123: $i,SV361: $i] :
( ( ( ! [SY636: $i] :
( ( SY636 != SV361 )
| ~ ( in @ SY636 @ ( succ @ SV123 ) ) ) )
= $true )
| ( ( ! [SY637: $i] :
( ( SV361 != SY637 )
| ~ ( ordinal @ SY637 )
| ~ ( in @ SY637 @ SV72 ) ) )
= $true )
| ( ( in @ SV361 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2615]) ).
thf(2644,plain,
! [SV72: $i,SV123: $i,SV362: $i] :
( ( ( in @ SV362 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK43_E @ SV362 @ SV123 @ SV72 )
!= SV362 )
| ~ ( in @ ( sK43_E @ SV362 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SV362
!= ( sK42_H @ SV362 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV362 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV362 @ SV123 @ SV72 ) @ SV72 ) ) ) )
= $true )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2616]) ).
thf(2645,plain,
! [SV72: $i,SV123: $i,SV353: $i,SV363: $i] :
( ( ( SV363 = SV353 )
= $false )
| ( ( ~ ( in @ SV363 @ ( succ @ SV123 ) ) )
= $true )
| ( ( ! [SY633: $i] :
( ( SV353 != SY633 )
| ~ ( ordinal @ SY633 )
| ~ ( in @ SY633 @ SV72 ) ) )
= $true )
| ( ( in @ SV353 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2617]) ).
thf(2646,plain,
! [SV72: $i,SV123: $i,SV354: $i] :
( ( ( ~ ( ( ( sK43_E @ SV354 @ SV123 @ SV72 )
!= SV354 )
| ~ ( in @ ( sK43_E @ SV354 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) ) )
= $true )
| ( ( in @ SV354 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2618]) ).
thf(2647,plain,
! [SV72: $i,SV123: $i,SV354: $i] :
( ( ( ~ ( ~ ~ ( ( SV354
!= ( sK42_H @ SV354 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV354 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV354 @ SV123 @ SV72 ) @ SV72 ) ) )
= $true )
| ( ( in @ SV354 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2619]) ).
thf(2648,plain,
! [SV123: $i,SV346: $i,SV72: $i,SV337: $i,SV357: $i] :
( ( ( ordinal @ SV357 )
= $false )
| ( ( SV337 = SV357 )
= $false )
| ( ( ~ ( in @ SV357 @ SV72 ) )
= $true )
| ( ( SV346 = SV337 )
= $false )
| ( ( in @ SV346 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV337 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2620]) ).
thf(2649,plain,
! [SV72: $i,SV123: $i,SV338: $i] :
( ( ( SV338
= ( sK42_H @ SV338 @ SV123 @ SV72 ) )
= $true )
| ( ( in @ SV338 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2621]) ).
thf(2650,plain,
! [SV72: $i,SV123: $i,SV338: $i] :
( ( ( ordinal @ ( sK42_H @ SV338 @ SV123 @ SV72 ) )
= $true )
| ( ( in @ SV338 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2622]) ).
thf(2651,plain,
! [SV123: $i,SV355: $i,SV72: $i,SV365: $i,SV347: $i] :
( ( ( ( SV347 != SV365 )
| ~ ( ordinal @ SV365 ) )
= $true )
| ( ( ~ ( in @ SV365 @ SV72 ) )
= $true )
| ( ( SV355 = SV347 )
= $false )
| ( ( in @ SV355 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV347 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2623]) ).
thf(2652,plain,
! [SV72: $i,SV123: $i,SV348: $i] :
( ( ( ( sK43_E @ SV348 @ SV123 @ SV72 )
= SV348 )
= $true )
| ( ( in @ SV348 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2624]) ).
thf(2653,plain,
! [SV72: $i,SV123: $i,SV348: $i] :
( ( ( in @ ( sK43_E @ SV348 @ SV123 @ SV72 ) @ ( succ @ SV123 ) )
= $true )
| ( ( in @ SV348 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2625]) ).
thf(2654,plain,
! [SV72: $i,SV123: $i,SV348: $i] :
( ( ( ~ ( ( SV348
!= ( sK42_H @ SV348 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV348 @ SV123 @ SV72 ) ) ) )
= $true )
| ( ( in @ SV348 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2626]) ).
thf(2655,plain,
! [SV72: $i,SV123: $i,SV348: $i] :
( ( ( in @ ( sK42_H @ SV348 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( in @ SV348 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2627]) ).
thf(2656,plain,
! [SV123: $i,SV356: $i,SV72: $i,SV366: $i,SV349: $i] :
( ( ( ( SV349 != SV366 )
| ~ ( ordinal @ SV366 ) )
= $true )
| ( ( ~ ( in @ SV366 @ SV72 ) )
= $true )
| ( ( SV356 = SV349 )
= $false )
| ( ( in @ SV356 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV349 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2628]) ).
thf(2657,plain,
! [SV72: $i,SV123: $i,SV350: $i] :
( ( ( ( sK43_E @ SV350 @ SV123 @ SV72 )
= SV350 )
= $true )
| ( ( in @ SV350 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2629]) ).
thf(2658,plain,
! [SV72: $i,SV123: $i,SV350: $i] :
( ( ( in @ ( sK43_E @ SV350 @ SV123 @ SV72 ) @ ( succ @ SV123 ) )
= $true )
| ( ( in @ SV350 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2630]) ).
thf(2659,plain,
! [SV72: $i,SV123: $i,SV350: $i] :
( ( ( ~ ( ( SV350
!= ( sK42_H @ SV350 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV350 @ SV123 @ SV72 ) ) ) )
= $true )
| ( ( in @ SV350 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2631]) ).
thf(2660,plain,
! [SV72: $i,SV123: $i,SV350: $i] :
( ( ( in @ ( sK42_H @ SV350 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( in @ SV350 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2632]) ).
thf(2661,plain,
! [SV123: $i,SV351: $i,SV72: $i,SV339: $i,SV358: $i] :
( ( ( ordinal @ SV358 )
= $false )
| ( ( SV339 = SV358 )
= $false )
| ( ( ~ ( in @ SV358 @ SV72 ) )
= $true )
| ( ( SV351 = SV339 )
= $false )
| ( ( in @ SV351 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV339 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2633]) ).
thf(2662,plain,
! [SV72: $i,SV123: $i,SV340: $i] :
( ( ( SV340
= ( sK42_H @ SV340 @ SV123 @ SV72 ) )
= $true )
| ( ( in @ SV340 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2634]) ).
thf(2663,plain,
! [SV72: $i,SV123: $i,SV340: $i] :
( ( ( ordinal @ ( sK42_H @ SV340 @ SV123 @ SV72 ) )
= $true )
| ( ( in @ SV340 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2635]) ).
thf(2664,plain,
! [SV123: $i,SV352: $i,SV72: $i,SV364: $i,SV344: $i] :
( ( ( SV344 != SV364 )
= $true )
| ( ( ~ ( ordinal @ SV364 ) )
= $true )
| ( ( ~ ( in @ SV364 @ SV72 ) )
= $true )
| ( ( SV352 = SV344 )
= $false )
| ( ( in @ SV352 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV344 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2636]) ).
thf(2665,plain,
! [SV72: $i,SV123: $i,SV345: $i] :
( ( ( ( SV345
!= ( sK42_H @ SV345 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV345 @ SV123 @ SV72 ) ) )
= $false )
| ( ( in @ SV345 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2639]) ).
thf(2666,plain,
! [SV72: $i,SV123: $i,SV359: $i,SV367: $i] :
( ( ( ( SV367 != SV359 )
| ~ ( in @ SV367 @ ( succ @ SV123 ) ) )
= $true )
| ( ( ! [SY635: $i] :
( ( SV359 != SY635 )
| ~ ( ordinal @ SY635 )
| ~ ( in @ SY635 @ SV72 ) ) )
= $true )
| ( ( in @ SV359 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2641]) ).
thf(2667,plain,
! [SV72: $i,SV123: $i,SV360: $i] :
( ( ( ~ ~ ( ( ( sK43_E @ SV360 @ SV123 @ SV72 )
!= SV360 )
| ~ ( in @ ( sK43_E @ SV360 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SV360
!= ( sK42_H @ SV360 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV360 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV360 @ SV123 @ SV72 ) @ SV72 ) ) )
= $false )
| ( ( in @ SV360 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2642]) ).
thf(2668,plain,
! [SV72: $i,SV123: $i,SV361: $i,SV368: $i] :
( ( ( ( SV368 != SV361 )
| ~ ( in @ SV368 @ ( succ @ SV123 ) ) )
= $true )
| ( ( ! [SY637: $i] :
( ( SV361 != SY637 )
| ~ ( ordinal @ SY637 )
| ~ ( in @ SY637 @ SV72 ) ) )
= $true )
| ( ( in @ SV361 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2643]) ).
thf(2669,plain,
! [SV72: $i,SV123: $i,SV362: $i] :
( ( ( ~ ~ ( ( ( sK43_E @ SV362 @ SV123 @ SV72 )
!= SV362 )
| ~ ( in @ ( sK43_E @ SV362 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
| ~ ~ ( ~ ~ ( ( SV362
!= ( sK42_H @ SV362 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV362 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV362 @ SV123 @ SV72 ) @ SV72 ) ) )
= $false )
| ( ( in @ SV362 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2644]) ).
thf(2670,plain,
! [SV72: $i,SV353: $i,SV123: $i,SV363: $i] :
( ( ( in @ SV363 @ ( succ @ SV123 ) )
= $false )
| ( ( SV363 = SV353 )
= $false )
| ( ( ! [SY633: $i] :
( ( SV353 != SY633 )
| ~ ( ordinal @ SY633 )
| ~ ( in @ SY633 @ SV72 ) ) )
= $true )
| ( ( in @ SV353 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2645]) ).
thf(2671,plain,
! [SV72: $i,SV123: $i,SV354: $i] :
( ( ( ( ( sK43_E @ SV354 @ SV123 @ SV72 )
!= SV354 )
| ~ ( in @ ( sK43_E @ SV354 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
= $false )
| ( ( in @ SV354 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2646]) ).
thf(2672,plain,
! [SV72: $i,SV123: $i,SV354: $i] :
( ( ( ~ ~ ( ( SV354
!= ( sK42_H @ SV354 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV354 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV354 @ SV123 @ SV72 ) @ SV72 ) )
= $false )
| ( ( in @ SV354 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2647]) ).
thf(2673,plain,
! [SV123: $i,SV346: $i,SV337: $i,SV72: $i,SV357: $i] :
( ( ( in @ SV357 @ SV72 )
= $false )
| ( ( SV337 = SV357 )
= $false )
| ( ( ordinal @ SV357 )
= $false )
| ( ( SV346 = SV337 )
= $false )
| ( ( in @ SV346 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV337 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK46_SY299 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2648]) ).
thf(2674,plain,
! [SV123: $i,SV355: $i,SV72: $i,SV365: $i,SV347: $i] :
( ( ( SV347 != SV365 )
= $true )
| ( ( ~ ( ordinal @ SV365 ) )
= $true )
| ( ( ~ ( in @ SV365 @ SV72 ) )
= $true )
| ( ( SV355 = SV347 )
= $false )
| ( ( in @ SV355 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV347 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2651]) ).
thf(2675,plain,
! [SV72: $i,SV123: $i,SV348: $i] :
( ( ( ( SV348
!= ( sK42_H @ SV348 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV348 @ SV123 @ SV72 ) ) )
= $false )
| ( ( in @ SV348 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2654]) ).
thf(2676,plain,
! [SV123: $i,SV356: $i,SV72: $i,SV366: $i,SV349: $i] :
( ( ( SV349 != SV366 )
= $true )
| ( ( ~ ( ordinal @ SV366 ) )
= $true )
| ( ( ~ ( in @ SV366 @ SV72 ) )
= $true )
| ( ( SV356 = SV349 )
= $false )
| ( ( in @ SV356 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV349 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2656]) ).
thf(2677,plain,
! [SV72: $i,SV123: $i,SV350: $i] :
( ( ( ( SV350
!= ( sK42_H @ SV350 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV350 @ SV123 @ SV72 ) ) )
= $false )
| ( ( in @ SV350 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2659]) ).
thf(2678,plain,
! [SV123: $i,SV351: $i,SV339: $i,SV72: $i,SV358: $i] :
( ( ( in @ SV358 @ SV72 )
= $false )
| ( ( SV339 = SV358 )
= $false )
| ( ( ordinal @ SV358 )
= $false )
| ( ( SV351 = SV339 )
= $false )
| ( ( in @ SV351 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV339 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( in @ ( sK47_SY303 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2661]) ).
thf(2679,plain,
! [SV123: $i,SV352: $i,SV72: $i,SV364: $i,SV344: $i] :
( ( ( SV344 = SV364 )
= $false )
| ( ( ~ ( ordinal @ SV364 ) )
= $true )
| ( ( ~ ( in @ SV364 @ SV72 ) )
= $true )
| ( ( SV352 = SV344 )
= $false )
| ( ( in @ SV352 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV344 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2664]) ).
thf(2680,plain,
! [SV72: $i,SV123: $i,SV345: $i] :
( ( ( SV345
!= ( sK42_H @ SV345 @ SV123 @ SV72 ) )
= $false )
| ( ( in @ SV345 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2665]) ).
thf(2681,plain,
! [SV72: $i,SV123: $i,SV345: $i] :
( ( ( ~ ( ordinal @ ( sK42_H @ SV345 @ SV123 @ SV72 ) ) )
= $false )
| ( ( in @ SV345 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2665]) ).
thf(2682,plain,
! [SV72: $i,SV123: $i,SV359: $i,SV367: $i] :
( ( ( SV367 != SV359 )
= $true )
| ( ( ~ ( in @ SV367 @ ( succ @ SV123 ) ) )
= $true )
| ( ( ! [SY635: $i] :
( ( SV359 != SY635 )
| ~ ( ordinal @ SY635 )
| ~ ( in @ SY635 @ SV72 ) ) )
= $true )
| ( ( in @ SV359 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2666]) ).
thf(2683,plain,
! [SV72: $i,SV123: $i,SV360: $i] :
( ( ( ~ ~ ( ( ( sK43_E @ SV360 @ SV123 @ SV72 )
!= SV360 )
| ~ ( in @ ( sK43_E @ SV360 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) ) )
= $false )
| ( ( in @ SV360 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2667]) ).
thf(2684,plain,
! [SV72: $i,SV123: $i,SV360: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV360
!= ( sK42_H @ SV360 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV360 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV360 @ SV123 @ SV72 ) @ SV72 ) ) )
= $false )
| ( ( in @ SV360 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2667]) ).
thf(2685,plain,
! [SV72: $i,SV123: $i,SV361: $i,SV368: $i] :
( ( ( SV368 != SV361 )
= $true )
| ( ( ~ ( in @ SV368 @ ( succ @ SV123 ) ) )
= $true )
| ( ( ! [SY637: $i] :
( ( SV361 != SY637 )
| ~ ( ordinal @ SY637 )
| ~ ( in @ SY637 @ SV72 ) ) )
= $true )
| ( ( in @ SV361 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2668]) ).
thf(2686,plain,
! [SV72: $i,SV123: $i,SV362: $i] :
( ( ( ~ ~ ( ( ( sK43_E @ SV362 @ SV123 @ SV72 )
!= SV362 )
| ~ ( in @ ( sK43_E @ SV362 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) ) )
= $false )
| ( ( in @ SV362 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2669]) ).
thf(2687,plain,
! [SV72: $i,SV123: $i,SV362: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV362
!= ( sK42_H @ SV362 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV362 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV362 @ SV123 @ SV72 ) @ SV72 ) ) )
= $false )
| ( ( in @ SV362 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2669]) ).
thf(2688,plain,
! [SV123: $i,SV363: $i,SV72: $i,SV369: $i,SV353: $i] :
( ( ( ( SV353 != SV369 )
| ~ ( ordinal @ SV369 )
| ~ ( in @ SV369 @ SV72 ) )
= $true )
| ( ( SV363 = SV353 )
= $false )
| ( ( in @ SV363 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV353 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2670]) ).
thf(2689,plain,
! [SV72: $i,SV123: $i,SV354: $i] :
( ( ( ( sK43_E @ SV354 @ SV123 @ SV72 )
!= SV354 )
= $false )
| ( ( in @ SV354 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2671]) ).
thf(2690,plain,
! [SV72: $i,SV123: $i,SV354: $i] :
( ( ( ~ ( in @ ( sK43_E @ SV354 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
= $false )
| ( ( in @ SV354 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2671]) ).
thf(2691,plain,
! [SV72: $i,SV123: $i,SV354: $i] :
( ( ( ~ ~ ( ( SV354
!= ( sK42_H @ SV354 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV354 @ SV123 @ SV72 ) ) ) )
= $false )
| ( ( in @ SV354 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2672]) ).
thf(2692,plain,
! [SV72: $i,SV123: $i,SV354: $i] :
( ( ( ~ ( in @ ( sK42_H @ SV354 @ SV123 @ SV72 ) @ SV72 ) )
= $false )
| ( ( in @ SV354 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2672]) ).
thf(2693,plain,
! [SV123: $i,SV355: $i,SV72: $i,SV365: $i,SV347: $i] :
( ( ( SV347 = SV365 )
= $false )
| ( ( ~ ( ordinal @ SV365 ) )
= $true )
| ( ( ~ ( in @ SV365 @ SV72 ) )
= $true )
| ( ( SV355 = SV347 )
= $false )
| ( ( in @ SV355 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV347 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2674]) ).
thf(2694,plain,
! [SV72: $i,SV123: $i,SV348: $i] :
( ( ( SV348
!= ( sK42_H @ SV348 @ SV123 @ SV72 ) )
= $false )
| ( ( in @ SV348 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2675]) ).
thf(2695,plain,
! [SV72: $i,SV123: $i,SV348: $i] :
( ( ( ~ ( ordinal @ ( sK42_H @ SV348 @ SV123 @ SV72 ) ) )
= $false )
| ( ( in @ SV348 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2675]) ).
thf(2696,plain,
! [SV123: $i,SV356: $i,SV72: $i,SV366: $i,SV349: $i] :
( ( ( SV349 = SV366 )
= $false )
| ( ( ~ ( ordinal @ SV366 ) )
= $true )
| ( ( ~ ( in @ SV366 @ SV72 ) )
= $true )
| ( ( SV356 = SV349 )
= $false )
| ( ( in @ SV356 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV349 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2676]) ).
thf(2697,plain,
! [SV72: $i,SV123: $i,SV350: $i] :
( ( ( SV350
!= ( sK42_H @ SV350 @ SV123 @ SV72 ) )
= $false )
| ( ( in @ SV350 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2677]) ).
thf(2698,plain,
! [SV72: $i,SV123: $i,SV350: $i] :
( ( ( ~ ( ordinal @ ( sK42_H @ SV350 @ SV123 @ SV72 ) ) )
= $false )
| ( ( in @ SV350 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2677]) ).
thf(2699,plain,
! [SV123: $i,SV352: $i,SV72: $i,SV344: $i,SV364: $i] :
( ( ( ordinal @ SV364 )
= $false )
| ( ( SV344 = SV364 )
= $false )
| ( ( ~ ( in @ SV364 @ SV72 ) )
= $true )
| ( ( SV352 = SV344 )
= $false )
| ( ( in @ SV352 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV344 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2679]) ).
thf(2700,plain,
! [SV72: $i,SV123: $i,SV345: $i] :
( ( ( SV345
= ( sK42_H @ SV345 @ SV123 @ SV72 ) )
= $true )
| ( ( in @ SV345 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2680]) ).
thf(2701,plain,
! [SV72: $i,SV123: $i,SV345: $i] :
( ( ( ordinal @ ( sK42_H @ SV345 @ SV123 @ SV72 ) )
= $true )
| ( ( in @ SV345 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2681]) ).
thf(2702,plain,
! [SV72: $i,SV123: $i,SV359: $i,SV367: $i] :
( ( ( SV367 = SV359 )
= $false )
| ( ( ~ ( in @ SV367 @ ( succ @ SV123 ) ) )
= $true )
| ( ( ! [SY635: $i] :
( ( SV359 != SY635 )
| ~ ( ordinal @ SY635 )
| ~ ( in @ SY635 @ SV72 ) ) )
= $true )
| ( ( in @ SV359 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2682]) ).
thf(2703,plain,
! [SV72: $i,SV123: $i,SV360: $i] :
( ( ( ~ ( ( ( sK43_E @ SV360 @ SV123 @ SV72 )
!= SV360 )
| ~ ( in @ ( sK43_E @ SV360 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) ) )
= $true )
| ( ( in @ SV360 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2683]) ).
thf(2704,plain,
! [SV72: $i,SV123: $i,SV360: $i] :
( ( ( ~ ( ~ ~ ( ( SV360
!= ( sK42_H @ SV360 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV360 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV360 @ SV123 @ SV72 ) @ SV72 ) ) )
= $true )
| ( ( in @ SV360 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2684]) ).
thf(2705,plain,
! [SV72: $i,SV123: $i,SV361: $i,SV368: $i] :
( ( ( SV368 = SV361 )
= $false )
| ( ( ~ ( in @ SV368 @ ( succ @ SV123 ) ) )
= $true )
| ( ( ! [SY637: $i] :
( ( SV361 != SY637 )
| ~ ( ordinal @ SY637 )
| ~ ( in @ SY637 @ SV72 ) ) )
= $true )
| ( ( in @ SV361 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2685]) ).
thf(2706,plain,
! [SV72: $i,SV123: $i,SV362: $i] :
( ( ( ~ ( ( ( sK43_E @ SV362 @ SV123 @ SV72 )
!= SV362 )
| ~ ( in @ ( sK43_E @ SV362 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) ) )
= $true )
| ( ( in @ SV362 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2686]) ).
thf(2707,plain,
! [SV72: $i,SV123: $i,SV362: $i] :
( ( ( ~ ( ~ ~ ( ( SV362
!= ( sK42_H @ SV362 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV362 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV362 @ SV123 @ SV72 ) @ SV72 ) ) )
= $true )
| ( ( in @ SV362 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2687]) ).
thf(2708,plain,
! [SV123: $i,SV363: $i,SV72: $i,SV369: $i,SV353: $i] :
( ( ( ( SV353 != SV369 )
| ~ ( ordinal @ SV369 ) )
= $true )
| ( ( ~ ( in @ SV369 @ SV72 ) )
= $true )
| ( ( SV363 = SV353 )
= $false )
| ( ( in @ SV363 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV353 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2688]) ).
thf(2709,plain,
! [SV72: $i,SV123: $i,SV354: $i] :
( ( ( ( sK43_E @ SV354 @ SV123 @ SV72 )
= SV354 )
= $true )
| ( ( in @ SV354 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2689]) ).
thf(2710,plain,
! [SV72: $i,SV123: $i,SV354: $i] :
( ( ( in @ ( sK43_E @ SV354 @ SV123 @ SV72 ) @ ( succ @ SV123 ) )
= $true )
| ( ( in @ SV354 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2690]) ).
thf(2711,plain,
! [SV72: $i,SV123: $i,SV354: $i] :
( ( ( ~ ( ( SV354
!= ( sK42_H @ SV354 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV354 @ SV123 @ SV72 ) ) ) )
= $true )
| ( ( in @ SV354 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2691]) ).
thf(2712,plain,
! [SV72: $i,SV123: $i,SV354: $i] :
( ( ( in @ ( sK42_H @ SV354 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( in @ SV354 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2692]) ).
thf(2713,plain,
! [SV123: $i,SV355: $i,SV72: $i,SV347: $i,SV365: $i] :
( ( ( ordinal @ SV365 )
= $false )
| ( ( SV347 = SV365 )
= $false )
| ( ( ~ ( in @ SV365 @ SV72 ) )
= $true )
| ( ( SV355 = SV347 )
= $false )
| ( ( in @ SV355 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV347 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2693]) ).
thf(2714,plain,
! [SV72: $i,SV123: $i,SV348: $i] :
( ( ( SV348
= ( sK42_H @ SV348 @ SV123 @ SV72 ) )
= $true )
| ( ( in @ SV348 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2694]) ).
thf(2715,plain,
! [SV72: $i,SV123: $i,SV348: $i] :
( ( ( ordinal @ ( sK42_H @ SV348 @ SV123 @ SV72 ) )
= $true )
| ( ( in @ SV348 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2695]) ).
thf(2716,plain,
! [SV123: $i,SV356: $i,SV72: $i,SV349: $i,SV366: $i] :
( ( ( ordinal @ SV366 )
= $false )
| ( ( SV349 = SV366 )
= $false )
| ( ( ~ ( in @ SV366 @ SV72 ) )
= $true )
| ( ( SV356 = SV349 )
= $false )
| ( ( in @ SV356 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV349 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2696]) ).
thf(2717,plain,
! [SV72: $i,SV123: $i,SV350: $i] :
( ( ( SV350
= ( sK42_H @ SV350 @ SV123 @ SV72 ) )
= $true )
| ( ( in @ SV350 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2697]) ).
thf(2718,plain,
! [SV72: $i,SV123: $i,SV350: $i] :
( ( ( ordinal @ ( sK42_H @ SV350 @ SV123 @ SV72 ) )
= $true )
| ( ( in @ SV350 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2698]) ).
thf(2719,plain,
! [SV123: $i,SV352: $i,SV344: $i,SV72: $i,SV364: $i] :
( ( ( in @ SV364 @ SV72 )
= $false )
| ( ( SV344 = SV364 )
= $false )
| ( ( ordinal @ SV364 )
= $false )
| ( ( SV352 = SV344 )
= $false )
| ( ( in @ SV352 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV344 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK44_C @ SV123 @ SV72 )
= ( sK45_SY295 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2699]) ).
thf(2720,plain,
! [SV72: $i,SV359: $i,SV123: $i,SV367: $i] :
( ( ( in @ SV367 @ ( succ @ SV123 ) )
= $false )
| ( ( SV367 = SV359 )
= $false )
| ( ( ! [SY635: $i] :
( ( SV359 != SY635 )
| ~ ( ordinal @ SY635 )
| ~ ( in @ SY635 @ SV72 ) ) )
= $true )
| ( ( in @ SV359 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2702]) ).
thf(2721,plain,
! [SV72: $i,SV123: $i,SV360: $i] :
( ( ( ( ( sK43_E @ SV360 @ SV123 @ SV72 )
!= SV360 )
| ~ ( in @ ( sK43_E @ SV360 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
= $false )
| ( ( in @ SV360 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2703]) ).
thf(2722,plain,
! [SV72: $i,SV123: $i,SV360: $i] :
( ( ( ~ ~ ( ( SV360
!= ( sK42_H @ SV360 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV360 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV360 @ SV123 @ SV72 ) @ SV72 ) )
= $false )
| ( ( in @ SV360 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2704]) ).
thf(2723,plain,
! [SV72: $i,SV361: $i,SV123: $i,SV368: $i] :
( ( ( in @ SV368 @ ( succ @ SV123 ) )
= $false )
| ( ( SV368 = SV361 )
= $false )
| ( ( ! [SY637: $i] :
( ( SV361 != SY637 )
| ~ ( ordinal @ SY637 )
| ~ ( in @ SY637 @ SV72 ) ) )
= $true )
| ( ( in @ SV361 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2705]) ).
thf(2724,plain,
! [SV72: $i,SV123: $i,SV362: $i] :
( ( ( ( ( sK43_E @ SV362 @ SV123 @ SV72 )
!= SV362 )
| ~ ( in @ ( sK43_E @ SV362 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
= $false )
| ( ( in @ SV362 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2706]) ).
thf(2725,plain,
! [SV72: $i,SV123: $i,SV362: $i] :
( ( ( ~ ~ ( ( SV362
!= ( sK42_H @ SV362 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV362 @ SV123 @ SV72 ) ) )
| ~ ( in @ ( sK42_H @ SV362 @ SV123 @ SV72 ) @ SV72 ) )
= $false )
| ( ( in @ SV362 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2707]) ).
thf(2726,plain,
! [SV123: $i,SV363: $i,SV72: $i,SV369: $i,SV353: $i] :
( ( ( SV353 != SV369 )
= $true )
| ( ( ~ ( ordinal @ SV369 ) )
= $true )
| ( ( ~ ( in @ SV369 @ SV72 ) )
= $true )
| ( ( SV363 = SV353 )
= $false )
| ( ( in @ SV363 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV353 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2708]) ).
thf(2727,plain,
! [SV72: $i,SV123: $i,SV354: $i] :
( ( ( ( SV354
!= ( sK42_H @ SV354 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV354 @ SV123 @ SV72 ) ) )
= $false )
| ( ( in @ SV354 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2711]) ).
thf(2728,plain,
! [SV123: $i,SV355: $i,SV347: $i,SV72: $i,SV365: $i] :
( ( ( in @ SV365 @ SV72 )
= $false )
| ( ( SV347 = SV365 )
= $false )
| ( ( ordinal @ SV365 )
= $false )
| ( ( SV355 = SV347 )
= $false )
| ( ( in @ SV355 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV347 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK46_SY299 @ SV123 @ SV72 )
= ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2713]) ).
thf(2729,plain,
! [SV123: $i,SV356: $i,SV349: $i,SV72: $i,SV366: $i] :
( ( ( in @ SV366 @ SV72 )
= $false )
| ( ( SV349 = SV366 )
= $false )
| ( ( ordinal @ SV366 )
= $false )
| ( ( SV356 = SV349 )
= $false )
| ( ( in @ SV356 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV349 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ ( sK47_SY303 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2716]) ).
thf(2730,plain,
! [SV123: $i,SV367: $i,SV72: $i,SV370: $i,SV359: $i] :
( ( ( ( SV359 != SV370 )
| ~ ( ordinal @ SV370 )
| ~ ( in @ SV370 @ SV72 ) )
= $true )
| ( ( SV367 = SV359 )
= $false )
| ( ( in @ SV367 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV359 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2720]) ).
thf(2731,plain,
! [SV72: $i,SV123: $i,SV360: $i] :
( ( ( ( sK43_E @ SV360 @ SV123 @ SV72 )
!= SV360 )
= $false )
| ( ( in @ SV360 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2721]) ).
thf(2732,plain,
! [SV72: $i,SV123: $i,SV360: $i] :
( ( ( ~ ( in @ ( sK43_E @ SV360 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
= $false )
| ( ( in @ SV360 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2721]) ).
thf(2733,plain,
! [SV72: $i,SV123: $i,SV360: $i] :
( ( ( ~ ~ ( ( SV360
!= ( sK42_H @ SV360 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV360 @ SV123 @ SV72 ) ) ) )
= $false )
| ( ( in @ SV360 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2722]) ).
thf(2734,plain,
! [SV72: $i,SV123: $i,SV360: $i] :
( ( ( ~ ( in @ ( sK42_H @ SV360 @ SV123 @ SV72 ) @ SV72 ) )
= $false )
| ( ( in @ SV360 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2722]) ).
thf(2735,plain,
! [SV123: $i,SV368: $i,SV72: $i,SV371: $i,SV361: $i] :
( ( ( ( SV361 != SV371 )
| ~ ( ordinal @ SV371 )
| ~ ( in @ SV371 @ SV72 ) )
= $true )
| ( ( SV368 = SV361 )
= $false )
| ( ( in @ SV368 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV361 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2723]) ).
thf(2736,plain,
! [SV72: $i,SV123: $i,SV362: $i] :
( ( ( ( sK43_E @ SV362 @ SV123 @ SV72 )
!= SV362 )
= $false )
| ( ( in @ SV362 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2724]) ).
thf(2737,plain,
! [SV72: $i,SV123: $i,SV362: $i] :
( ( ( ~ ( in @ ( sK43_E @ SV362 @ SV123 @ SV72 ) @ ( succ @ SV123 ) ) )
= $false )
| ( ( in @ SV362 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2724]) ).
thf(2738,plain,
! [SV72: $i,SV123: $i,SV362: $i] :
( ( ( ~ ~ ( ( SV362
!= ( sK42_H @ SV362 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV362 @ SV123 @ SV72 ) ) ) )
= $false )
| ( ( in @ SV362 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2725]) ).
thf(2739,plain,
! [SV72: $i,SV123: $i,SV362: $i] :
( ( ( ~ ( in @ ( sK42_H @ SV362 @ SV123 @ SV72 ) @ SV72 ) )
= $false )
| ( ( in @ SV362 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2725]) ).
thf(2740,plain,
! [SV123: $i,SV363: $i,SV72: $i,SV369: $i,SV353: $i] :
( ( ( SV353 = SV369 )
= $false )
| ( ( ~ ( ordinal @ SV369 ) )
= $true )
| ( ( ~ ( in @ SV369 @ SV72 ) )
= $true )
| ( ( SV363 = SV353 )
= $false )
| ( ( in @ SV363 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV353 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2726]) ).
thf(2741,plain,
! [SV72: $i,SV123: $i,SV354: $i] :
( ( ( SV354
!= ( sK42_H @ SV354 @ SV123 @ SV72 ) )
= $false )
| ( ( in @ SV354 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2727]) ).
thf(2742,plain,
! [SV72: $i,SV123: $i,SV354: $i] :
( ( ( ~ ( ordinal @ ( sK42_H @ SV354 @ SV123 @ SV72 ) ) )
= $false )
| ( ( in @ SV354 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2727]) ).
thf(2743,plain,
! [SV123: $i,SV367: $i,SV72: $i,SV370: $i,SV359: $i] :
( ( ( ( SV359 != SV370 )
| ~ ( ordinal @ SV370 ) )
= $true )
| ( ( ~ ( in @ SV370 @ SV72 ) )
= $true )
| ( ( SV367 = SV359 )
= $false )
| ( ( in @ SV367 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV359 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2730]) ).
thf(2744,plain,
! [SV72: $i,SV123: $i,SV360: $i] :
( ( ( ( sK43_E @ SV360 @ SV123 @ SV72 )
= SV360 )
= $true )
| ( ( in @ SV360 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2731]) ).
thf(2745,plain,
! [SV72: $i,SV123: $i,SV360: $i] :
( ( ( in @ ( sK43_E @ SV360 @ SV123 @ SV72 ) @ ( succ @ SV123 ) )
= $true )
| ( ( in @ SV360 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2732]) ).
thf(2746,plain,
! [SV72: $i,SV123: $i,SV360: $i] :
( ( ( ~ ( ( SV360
!= ( sK42_H @ SV360 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV360 @ SV123 @ SV72 ) ) ) )
= $true )
| ( ( in @ SV360 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2733]) ).
thf(2747,plain,
! [SV72: $i,SV123: $i,SV360: $i] :
( ( ( in @ ( sK42_H @ SV360 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( in @ SV360 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2734]) ).
thf(2748,plain,
! [SV123: $i,SV368: $i,SV72: $i,SV371: $i,SV361: $i] :
( ( ( ( SV361 != SV371 )
| ~ ( ordinal @ SV371 ) )
= $true )
| ( ( ~ ( in @ SV371 @ SV72 ) )
= $true )
| ( ( SV368 = SV361 )
= $false )
| ( ( in @ SV368 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV361 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2735]) ).
thf(2749,plain,
! [SV72: $i,SV123: $i,SV362: $i] :
( ( ( ( sK43_E @ SV362 @ SV123 @ SV72 )
= SV362 )
= $true )
| ( ( in @ SV362 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2736]) ).
thf(2750,plain,
! [SV72: $i,SV123: $i,SV362: $i] :
( ( ( in @ ( sK43_E @ SV362 @ SV123 @ SV72 ) @ ( succ @ SV123 ) )
= $true )
| ( ( in @ SV362 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2737]) ).
thf(2751,plain,
! [SV72: $i,SV123: $i,SV362: $i] :
( ( ( ~ ( ( SV362
!= ( sK42_H @ SV362 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV362 @ SV123 @ SV72 ) ) ) )
= $true )
| ( ( in @ SV362 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2738]) ).
thf(2752,plain,
! [SV72: $i,SV123: $i,SV362: $i] :
( ( ( in @ ( sK42_H @ SV362 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( in @ SV362 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2739]) ).
thf(2753,plain,
! [SV123: $i,SV363: $i,SV72: $i,SV353: $i,SV369: $i] :
( ( ( ordinal @ SV369 )
= $false )
| ( ( SV353 = SV369 )
= $false )
| ( ( ~ ( in @ SV369 @ SV72 ) )
= $true )
| ( ( SV363 = SV353 )
= $false )
| ( ( in @ SV363 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV353 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2740]) ).
thf(2754,plain,
! [SV72: $i,SV123: $i,SV354: $i] :
( ( ( SV354
= ( sK42_H @ SV354 @ SV123 @ SV72 ) )
= $true )
| ( ( in @ SV354 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2741]) ).
thf(2755,plain,
! [SV72: $i,SV123: $i,SV354: $i] :
( ( ( ordinal @ ( sK42_H @ SV354 @ SV123 @ SV72 ) )
= $true )
| ( ( in @ SV354 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2742]) ).
thf(2756,plain,
! [SV123: $i,SV367: $i,SV72: $i,SV370: $i,SV359: $i] :
( ( ( SV359 != SV370 )
= $true )
| ( ( ~ ( ordinal @ SV370 ) )
= $true )
| ( ( ~ ( in @ SV370 @ SV72 ) )
= $true )
| ( ( SV367 = SV359 )
= $false )
| ( ( in @ SV367 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV359 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2743]) ).
thf(2757,plain,
! [SV72: $i,SV123: $i,SV360: $i] :
( ( ( ( SV360
!= ( sK42_H @ SV360 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV360 @ SV123 @ SV72 ) ) )
= $false )
| ( ( in @ SV360 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2746]) ).
thf(2758,plain,
! [SV123: $i,SV368: $i,SV72: $i,SV371: $i,SV361: $i] :
( ( ( SV361 != SV371 )
= $true )
| ( ( ~ ( ordinal @ SV371 ) )
= $true )
| ( ( ~ ( in @ SV371 @ SV72 ) )
= $true )
| ( ( SV368 = SV361 )
= $false )
| ( ( in @ SV368 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV361 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2748]) ).
thf(2759,plain,
! [SV72: $i,SV123: $i,SV362: $i] :
( ( ( ( SV362
!= ( sK42_H @ SV362 @ SV123 @ SV72 ) )
| ~ ( ordinal @ ( sK42_H @ SV362 @ SV123 @ SV72 ) ) )
= $false )
| ( ( in @ SV362 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2751]) ).
thf(2760,plain,
! [SV123: $i,SV363: $i,SV353: $i,SV72: $i,SV369: $i] :
( ( ( in @ SV369 @ SV72 )
= $false )
| ( ( SV353 = SV369 )
= $false )
| ( ( ordinal @ SV369 )
= $false )
| ( ( SV363 = SV353 )
= $false )
| ( ( in @ SV363 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV353 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( in @ ( sK48_SY300 @ SV123 @ SV72 ) @ SV72 )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2753]) ).
thf(2761,plain,
! [SV123: $i,SV367: $i,SV72: $i,SV370: $i,SV359: $i] :
( ( ( SV359 = SV370 )
= $false )
| ( ( ~ ( ordinal @ SV370 ) )
= $true )
| ( ( ~ ( in @ SV370 @ SV72 ) )
= $true )
| ( ( SV367 = SV359 )
= $false )
| ( ( in @ SV367 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV359 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2756]) ).
thf(2762,plain,
! [SV72: $i,SV123: $i,SV360: $i] :
( ( ( SV360
!= ( sK42_H @ SV360 @ SV123 @ SV72 ) )
= $false )
| ( ( in @ SV360 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2757]) ).
thf(2763,plain,
! [SV72: $i,SV123: $i,SV360: $i] :
( ( ( ~ ( ordinal @ ( sK42_H @ SV360 @ SV123 @ SV72 ) ) )
= $false )
| ( ( in @ SV360 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2757]) ).
thf(2764,plain,
! [SV123: $i,SV368: $i,SV72: $i,SV371: $i,SV361: $i] :
( ( ( SV361 = SV371 )
= $false )
| ( ( ~ ( ordinal @ SV371 ) )
= $true )
| ( ( ~ ( in @ SV371 @ SV72 ) )
= $true )
| ( ( SV368 = SV361 )
= $false )
| ( ( in @ SV368 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV361 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2758]) ).
thf(2765,plain,
! [SV72: $i,SV123: $i,SV362: $i] :
( ( ( SV362
!= ( sK42_H @ SV362 @ SV123 @ SV72 ) )
= $false )
| ( ( in @ SV362 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2759]) ).
thf(2766,plain,
! [SV72: $i,SV123: $i,SV362: $i] :
( ( ( ~ ( ordinal @ ( sK42_H @ SV362 @ SV123 @ SV72 ) ) )
= $false )
| ( ( in @ SV362 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2759]) ).
thf(2767,plain,
! [SV123: $i,SV367: $i,SV72: $i,SV359: $i,SV370: $i] :
( ( ( ordinal @ SV370 )
= $false )
| ( ( SV359 = SV370 )
= $false )
| ( ( ~ ( in @ SV370 @ SV72 ) )
= $true )
| ( ( SV367 = SV359 )
= $false )
| ( ( in @ SV367 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV359 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2761]) ).
thf(2768,plain,
! [SV72: $i,SV123: $i,SV360: $i] :
( ( ( SV360
= ( sK42_H @ SV360 @ SV123 @ SV72 ) )
= $true )
| ( ( in @ SV360 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2762]) ).
thf(2769,plain,
! [SV72: $i,SV123: $i,SV360: $i] :
( ( ( ordinal @ ( sK42_H @ SV360 @ SV123 @ SV72 ) )
= $true )
| ( ( in @ SV360 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2763]) ).
thf(2770,plain,
! [SV123: $i,SV368: $i,SV72: $i,SV361: $i,SV371: $i] :
( ( ( ordinal @ SV371 )
= $false )
| ( ( SV361 = SV371 )
= $false )
| ( ( ~ ( in @ SV371 @ SV72 ) )
= $true )
| ( ( SV368 = SV361 )
= $false )
| ( ( in @ SV368 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV361 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2764]) ).
thf(2771,plain,
! [SV72: $i,SV123: $i,SV362: $i] :
( ( ( SV362
= ( sK42_H @ SV362 @ SV123 @ SV72 ) )
= $true )
| ( ( in @ SV362 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2765]) ).
thf(2772,plain,
! [SV72: $i,SV123: $i,SV362: $i] :
( ( ( ordinal @ ( sK42_H @ SV362 @ SV123 @ SV72 ) )
= $true )
| ( ( in @ SV362 @ ( sK41_C @ SV123 @ SV72 ) )
= $false )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2766]) ).
thf(2773,plain,
! [SV123: $i,SV367: $i,SV359: $i,SV72: $i,SV370: $i] :
( ( ( in @ SV370 @ SV72 )
= $false )
| ( ( SV359 = SV370 )
= $false )
| ( ( ordinal @ SV370 )
= $false )
| ( ( SV367 = SV359 )
= $false )
| ( ( in @ SV367 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV359 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ( sK45_SY295 @ SV123 @ SV72 )
= ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2767]) ).
thf(2774,plain,
! [SV123: $i,SV368: $i,SV361: $i,SV72: $i,SV371: $i] :
( ( ( in @ SV371 @ SV72 )
= $false )
| ( ( SV361 = SV371 )
= $false )
| ( ( ordinal @ SV371 )
= $false )
| ( ( SV368 = SV361 )
= $false )
| ( ( in @ SV368 @ ( succ @ SV123 ) )
= $false )
| ( ( in @ SV361 @ ( sK41_C @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ ( sK48_SY300 @ SV123 @ SV72 ) )
= $true )
| ( ( ordinal @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2770]) ).
thf(2775,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[613,2774,2773,2772,2771,2769,2768,2760,2755,2754,2752,2750,2749,2747,2745,2744,2729,2728,2719,2718,2717,2715,2714,2712,2710,2709,2701,2700,2678,2673,2663,2662,2660,2658,2657,2655,2653,2652,2650,2649,2640,2638,2637,2588,2586,2585,2577,2575,2574,2563,2537,2536,2481,2480,2479,2477,2476,2460,2459,2441,2440,2418,2417,2414,2411,2410,2409,2397,2389,2386,2384,2383,2382,2368,2367,2366,2365,2363,2360,2359,2357,2348,2347,2344,2343,2340,2327,2324,2323,2318,2315,2314,2313,2312,2304,2301,2300,2299,2294,2279,2276,2268,2263,2256,2252,2247,2246,2244,2234,2226,2222,2221,2213,2208,2200,2193,2192,2190,2189,2180,2178,2154,2153,2147,2145,2144,2134,2133,2131,2130,2127,2125,2124,2123,2118,2098,2088,2087,2078,2075,2068,2061,2055,2045,2038,2035,2011,2010,1993,1992,1991,1986,1982,1975,1974,1970,1969,1959,1958,1954,1953,1945,1944,1941,1940,1939,1917,1909,1908,1905,1897,1883,1875,1866,1865,1864,1858,1849,1841,1840,1828,1827,1814,1807,1806,1797,1795,1789,1783,1782,1745,1742,1712,1710,1703,1698,1685,1684,1683,1673,1672,1671,1670,1669,1668,1665,1664,1659,1650,1649,1609,1573,1572,1571,1570,1566,1565,1564,1561,1553,1550,1549,1539,1538,1520,1519,1512,1502,1480,1458,1457,1456,1455,1450,1449,1448,1447,1446,1439,1437,1435,1371,1367,1335,1330,1327,1324,1322,1317,1308,1252,1217,1213,1212,1210,1208,1206,1205,1198,1186,1184,1183,1160,1127,1123,1121,1120,1117,1116,1089,1088,1081,1074,1072,1064,1040,1039,945,934,927,914,847,844,836,817,800,797,793,791,789,733,637,636,635,634,633,632,631,630,629,628,627,626,625,624,623,621,620,619,618,617,616,615,614]) ).
thf(2776,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[2775]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU275+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.05/0.18 % Computer : n015.cluster.edu
% 0.05/0.18 % Model : x86_64 x86_64
% 0.05/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.18 % Memory : 8046.5625MB
% 0.05/0.18 % OS : Linux 6.8.0-71-generic
% 0.05/0.18 % CPULimit : 300
% 0.05/0.18 % WCLimit : 300
% 0.05/0.18 % DateTime : Tue Oct 6 15:13:58 UTC 2026
% 0.05/0.18 % CPUTime :
% 0.05/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.37/3.95 ...
% 21.37/3.95
% 21.37/3.95 No.of.Axioms: 352
% 21.37/3.95
% 21.37/3.95 Length.of.Defs: 0
% 21.37/3.95
% 21.37/3.95 Contains.Choice.Funs: false
% 21.37/3.95 ...................................................................................................
% 21.37/3.95
% 21.37/3.95 ********************************
% 21.37/3.95 * All subproblems solved! *
% 21.37/3.95 ********************************
% 21.37/3.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:2,axioms:137,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2775,loop_count:0,foatp_calls:1,translation:fof_full)
% 21.37/3.95
% 21.37/3.95 %**** Beginning of derivation protocol ****
% 21.37/3.95 % SZS output start CNFRefutation
% See solution above
% 21.37/3.97
% 21.37/3.97 %**** End of derivation protocol ****
% 21.37/3.97 %**** no. of clauses in derivation: 2560 ****
% 21.37/3.97 %**** clause counter: 2775 ****
% 21.37/3.97
% 21.37/3.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:2,axioms:137,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2775,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------