%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU294+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 10:43:50 AM UTC 2026
% Result : Theorem 9.97s 1.93s
% Output : CNFRefutation 9.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 87
% Syntax : Number of formulae : 963 ( 531 unt; 0 typ; 0 def)
% Number of atoms : 5675 (1661 equ; 0 cnn)
% Maximal formula atoms : 11 ( 5 avg)
% Number of connectives : 10922 (2310 ~;1587 |; 101 &;6700 @)
% ( 51 <=>; 173 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 89 ( 86 usr; 6 con; 0-3 aty)
% Number of variables : 2204 ( 0 ^;2192 !; 12 ?;2204 :)
% 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_equipotent,type,
equipotent: $i > $i > $o ).
thf(tp_fiber,type,
fiber: $i > $i > $i ).
thf(tp_finite,type,
finite: $i > $o ).
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_natural,type,
natural: $i > $o ).
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_quasi_total,type,
quasi_total: $i > $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_SY258,type,
sK10_SY258: $i > $i > $i ).
thf(tp_sK11_SY290,type,
sK11_SY290: $i > $i > $i ).
thf(tp_sK12_SY295,type,
sK12_SY295: $i > $i > $i ).
thf(tp_sK13_SY292,type,
sK13_SY292: $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY155,type,
sK2_SY155: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SY211,type,
sK4_SY211: $i > $i ).
thf(tp_sK5_SY226,type,
sK5_SY226: $i > $i ).
thf(tp_sK6_SY193,type,
sK6_SY193: $i > $i ).
thf(tp_sK7_SY169,type,
sK7_SY169: $i > $i ).
thf(tp_sK8_SY171,type,
sK8_SY171: $i > $i ).
thf(tp_sK9_SY256,type,
sK9_SY256: $i > $i > $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_set_intersection2,type,
set_intersection2: $i > $i > $i ).
thf(tp_set_meet,type,
set_meet: $i > $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subset_complement,type,
subset_complement: $i > $i > $i ).
thf(tp_subset_difference,type,
subset_difference: $i > $i > $i > $i ).
thf(tp_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(9,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(26,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(29,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(40,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(55,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(97,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(98,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_relset_1) ).
thf(99,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_relat_1) ).
thf(109,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(110,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(113,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(114,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_tarski) ).
thf(116,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_relat_1) ).
thf(117,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(118,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(120,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(122,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(123,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_mcart_1) ).
thf(125,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(126,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(128,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_wellord1) ).
thf(129,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(130,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_setfam_1) ).
thf(131,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(132,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_ordinal1) ).
thf(133,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_mcart_1) ).
thf(134,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_funct_1) ).
thf(135,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_enumset1) ).
thf(136,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_relat_1) ).
thf(139,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(167,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(168,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(176,axiom,
! [A: $i] :
( ( epsilon_transitive @ A )
<=> ! [B: $i] :
( ( in @ B @ A )
=> ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
thf(178,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(184,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
<=> ( subset @ C @ ( cartesian_product2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relset_1) ).
thf(201,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(210,axiom,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(216,axiom,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(223,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_relat_1) ).
thf(225,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(228,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(231,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(234,axiom,
! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(241,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(249,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(251,axiom,
! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_xboole_1) ).
thf(274,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_xboole_1) ).
thf(275,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_relat_1) ).
thf(276,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_relat_1) ).
thf(281,axiom,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(285,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(288,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(289,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(290,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(292,axiom,
! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(296,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(301,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(303,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(305,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(307,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(311,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) )
& ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relat_1) ).
thf(321,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(326,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(329,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(330,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(333,axiom,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(335,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(338,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(339,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t167_relat_1) ).
thf(342,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( relation_of2_as_subset @ D @ C @ A )
=> ( ( subset @ ( relation_rng @ D ) @ B )
=> ( relation_of2_as_subset @ D @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_relset_1) ).
thf(348,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_relat_1) ).
thf(351,axiom,
! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( powerset @ C ) @ B ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_zfmisc_1) ).
thf(352,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(353,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( ( subset @ ( relation_dom @ C ) @ A )
& ( subset @ ( relation_rng @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_relset_1) ).
thf(354,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(356,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(357,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_relat_1) ).
thf(358,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(359,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_relat_1) ).
thf(379,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l50_zfmisc_1) ).
thf(380,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
thf(382,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_zfmisc_1) ).
thf(385,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_xboole_1) ).
thf(387,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(389,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_dom @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l29_wellord1) ).
thf(395,conjecture,
! [A: $i,B: $i] :
( ( ( subset @ A @ B )
& ( finite @ B ) )
=> ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_finset_1) ).
thf(396,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( ( subset @ A @ B )
& ( finite @ B ) )
=> ( finite @ A ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[395]) ).
thf(397,plain,
( ( ! [A: $i,B: $i] :
( ( ( subset @ A @ B )
& ( finite @ B ) )
=> ( finite @ A ) ) )
= $false ),
inference(unfold_def,[status(thm)],[396]) ).
thf(398,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(399,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(400,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(401,plain,
( ( ! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ( ordinal_subset @ A @ B )
<=> ( subset @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(402,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(403,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(404,plain,
$true = $true,
inference(unfold_def,[status(thm)],[97]) ).
thf(405,plain,
$true = $true,
inference(unfold_def,[status(thm)],[98]) ).
thf(406,plain,
$true = $true,
inference(unfold_def,[status(thm)],[99]) ).
thf(407,plain,
$true = $true,
inference(unfold_def,[status(thm)],[109]) ).
thf(408,plain,
$true = $true,
inference(unfold_def,[status(thm)],[110]) ).
thf(409,plain,
$true = $true,
inference(unfold_def,[status(thm)],[113]) ).
thf(410,plain,
$true = $true,
inference(unfold_def,[status(thm)],[114]) ).
thf(411,plain,
$true = $true,
inference(unfold_def,[status(thm)],[116]) ).
thf(412,plain,
$true = $true,
inference(unfold_def,[status(thm)],[117]) ).
thf(413,plain,
$true = $true,
inference(unfold_def,[status(thm)],[118]) ).
thf(414,plain,
$true = $true,
inference(unfold_def,[status(thm)],[120]) ).
thf(415,plain,
$true = $true,
inference(unfold_def,[status(thm)],[122]) ).
thf(416,plain,
$true = $true,
inference(unfold_def,[status(thm)],[123]) ).
thf(417,plain,
$true = $true,
inference(unfold_def,[status(thm)],[125]) ).
thf(418,plain,
$true = $true,
inference(unfold_def,[status(thm)],[126]) ).
thf(419,plain,
$true = $true,
inference(unfold_def,[status(thm)],[128]) ).
thf(420,plain,
$true = $true,
inference(unfold_def,[status(thm)],[129]) ).
thf(421,plain,
$true = $true,
inference(unfold_def,[status(thm)],[130]) ).
thf(422,plain,
$true = $true,
inference(unfold_def,[status(thm)],[131]) ).
thf(423,plain,
$true = $true,
inference(unfold_def,[status(thm)],[132]) ).
thf(424,plain,
$true = $true,
inference(unfold_def,[status(thm)],[133]) ).
thf(425,plain,
$true = $true,
inference(unfold_def,[status(thm)],[134]) ).
thf(426,plain,
$true = $true,
inference(unfold_def,[status(thm)],[135]) ).
thf(427,plain,
$true = $true,
inference(unfold_def,[status(thm)],[136]) ).
thf(428,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(429,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(430,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)],[168]) ).
thf(431,plain,
( ( ! [A: $i] :
( ( epsilon_transitive @ A )
<=> ! [B: $i] :
( ( in @ B @ A )
=> ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(432,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(433,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
<=> ( subset @ C @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(434,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(435,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(436,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[216]) ).
thf(437,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(438,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(439,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)],[228]) ).
thf(440,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(441,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(442,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[241]) ).
thf(443,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(444,plain,
( ( ! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(445,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[274]) ).
thf(446,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
thf(447,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[276]) ).
thf(448,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[281]) ).
thf(449,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[285]) ).
thf(450,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)],[288]) ).
thf(451,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(452,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(453,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(454,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)],[296]) ).
thf(455,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ( in @ B @ A )
=> ( ( ordinal @ B )
& ( subset @ B @ A ) ) )
=> ( ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(456,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(457,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[305]) ).
thf(458,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)],[307]) ).
thf(459,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) )
& ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311]) ).
thf(460,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)],[321]) ).
thf(461,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)],[326]) ).
thf(462,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(463,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)],[330]) ).
thf(464,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(465,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)],[335]) ).
thf(466,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)],[338]) ).
thf(467,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[339]) ).
thf(468,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( relation_of2_as_subset @ D @ C @ A )
=> ( ( subset @ ( relation_rng @ D ) @ B )
=> ( relation_of2_as_subset @ D @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(469,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[348]) ).
thf(470,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( powerset @ C ) @ B ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[351]) ).
thf(471,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(472,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( ( subset @ ( relation_dom @ C ) @ A )
& ( subset @ ( relation_rng @ C ) @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[353]) ).
thf(473,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)],[354]) ).
thf(474,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)],[356]) ).
thf(475,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[357]) ).
thf(476,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[358]) ).
thf(477,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359]) ).
thf(478,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[379]) ).
thf(479,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[380]) ).
thf(480,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[382]) ).
thf(481,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[385]) ).
thf(482,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[387]) ).
thf(483,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[389]) ).
thf(484,plain,
( ( ! [SY155: $i] :
( ( ( subset @ sK1_A @ SY155 )
& ( finite @ SY155 ) )
=> ( finite @ sK1_A ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[397]) ).
thf(485,plain,
( ( ( ( subset @ sK1_A @ sK2_SY155 )
& ( finite @ sK2_SY155 ) )
=> ( finite @ sK1_A ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[484]) ).
thf(486,plain,
( ( subset @ sK1_A @ sK2_SY155 )
= $true ),
inference(standard_cnf,[status(thm)],[485]) ).
thf(487,plain,
( ( finite @ sK2_SY155 )
= $true ),
inference(standard_cnf,[status(thm)],[485]) ).
thf(488,plain,
( ( finite @ sK1_A )
= $false ),
inference(standard_cnf,[status(thm)],[485]) ).
thf(489,plain,
( ( ~ ( finite @ sK1_A ) )
= $true ),
inference(polarity_switch,[status(thm)],[488]) ).
thf(490,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[483]) ).
thf(491,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[482]) ).
thf(492,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[481]) ).
thf(493,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[480]) ).
thf(494,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[479]) ).
thf(495,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[478]) ).
thf(496,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[477]) ).
thf(497,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[476]) ).
thf(498,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[475]) ).
thf(499,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(copy,[status(thm)],[474]) ).
thf(500,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)],[473]) ).
thf(501,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( ( subset @ ( relation_dom @ C ) @ A )
& ( subset @ ( relation_rng @ C ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[472]) ).
thf(502,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[471]) ).
thf(503,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( powerset @ C ) @ B ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[470]) ).
thf(504,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[469]) ).
thf(505,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( relation_of2_as_subset @ D @ C @ A )
=> ( ( subset @ ( relation_rng @ D ) @ B )
=> ( relation_of2_as_subset @ D @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[468]) ).
thf(506,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[467]) ).
thf(507,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)],[466]) ).
thf(508,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)],[465]) ).
thf(509,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[464]) ).
thf(510,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[463]) ).
thf(511,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[462]) ).
thf(512,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(copy,[status(thm)],[461]) ).
thf(513,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( subset @ ( fiber @ ( relation_restriction @ C @ A ) @ B ) @ ( fiber @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[460]) ).
thf(514,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) )
& ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[459]) ).
thf(515,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[458]) ).
thf(516,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[457]) ).
thf(517,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[456]) ).
thf(518,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ( in @ B @ A )
=> ( ( ordinal @ B )
& ( subset @ B @ A ) ) )
=> ( ordinal @ A ) ) )
= $true ),
inference(copy,[status(thm)],[455]) ).
thf(519,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[454]) ).
thf(520,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[453]) ).
thf(521,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[452]) ).
thf(522,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[451]) ).
thf(523,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ C )
& ( in @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[450]) ).
thf(524,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[449]) ).
thf(525,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[448]) ).
thf(526,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[447]) ).
thf(527,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[446]) ).
thf(528,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[445]) ).
thf(529,plain,
( ( ! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[444]) ).
thf(530,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[443]) ).
thf(531,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[442]) ).
thf(532,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[441]) ).
thf(533,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[440]) ).
thf(534,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[439]) ).
thf(535,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[438]) ).
thf(536,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[437]) ).
thf(537,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[436]) ).
thf(538,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[435]) ).
thf(539,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[434]) ).
thf(540,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
<=> ( subset @ C @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[433]) ).
thf(541,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[432]) ).
thf(542,plain,
( ( ! [A: $i] :
( ( epsilon_transitive @ A )
<=> ! [B: $i] :
( ( in @ B @ A )
=> ( subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[431]) ).
thf(543,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ A )
=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[430]) ).
thf(544,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[429]) ).
thf(545,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(copy,[status(thm)],[428]) ).
thf(546,plain,
$true = $true,
inference(copy,[status(thm)],[427]) ).
thf(547,plain,
$true = $true,
inference(copy,[status(thm)],[426]) ).
thf(548,plain,
$true = $true,
inference(copy,[status(thm)],[425]) ).
thf(549,plain,
$true = $true,
inference(copy,[status(thm)],[424]) ).
thf(550,plain,
$true = $true,
inference(copy,[status(thm)],[423]) ).
thf(551,plain,
$true = $true,
inference(copy,[status(thm)],[422]) ).
thf(552,plain,
$true = $true,
inference(copy,[status(thm)],[421]) ).
thf(553,plain,
$true = $true,
inference(copy,[status(thm)],[420]) ).
thf(554,plain,
$true = $true,
inference(copy,[status(thm)],[419]) ).
thf(555,plain,
$true = $true,
inference(copy,[status(thm)],[418]) ).
thf(556,plain,
$true = $true,
inference(copy,[status(thm)],[417]) ).
thf(557,plain,
$true = $true,
inference(copy,[status(thm)],[416]) ).
thf(558,plain,
$true = $true,
inference(copy,[status(thm)],[415]) ).
thf(559,plain,
$true = $true,
inference(copy,[status(thm)],[414]) ).
thf(560,plain,
$true = $true,
inference(copy,[status(thm)],[413]) ).
thf(561,plain,
$true = $true,
inference(copy,[status(thm)],[412]) ).
thf(562,plain,
$true = $true,
inference(copy,[status(thm)],[411]) ).
thf(563,plain,
$true = $true,
inference(copy,[status(thm)],[410]) ).
thf(564,plain,
$true = $true,
inference(copy,[status(thm)],[409]) ).
thf(565,plain,
$true = $true,
inference(copy,[status(thm)],[408]) ).
thf(566,plain,
$true = $true,
inference(copy,[status(thm)],[407]) ).
thf(567,plain,
$true = $true,
inference(copy,[status(thm)],[406]) ).
thf(568,plain,
$true = $true,
inference(copy,[status(thm)],[405]) ).
thf(569,plain,
$true = $true,
inference(copy,[status(thm)],[404]) ).
thf(570,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(571,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[402]) ).
thf(572,plain,
( ( ! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ( ordinal_subset @ A @ B )
<=> ( subset @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[401]) ).
thf(573,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[400]) ).
thf(574,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[399]) ).
thf(575,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
( ( subset @ E @ C )
=> ( in @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[398]) ).
thf(576,plain,
( ( finite @ sK2_SY155 )
= $true ),
inference(copy,[status(thm)],[487]) ).
thf(577,plain,
( ( subset @ sK1_A @ sK2_SY155 )
= $true ),
inference(copy,[status(thm)],[486]) ).
thf(578,plain,
( ( ~ ( finite @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[489]) ).
thf(579,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX0 @ SX2 ) )
| ( subset @ SX0 @ ( set_intersection2 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[510]) ).
thf(580,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ( ~ ( ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[524]) ).
thf(581,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ( ~ ( ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[494]) ).
thf(582,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ ( singleton @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[531]) ).
thf(583,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_rng @ ( relation_composition @ SX0 @ SX1 ) ) @ ( relation_rng @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[527]) ).
thf(584,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( ordinal @ SX0 )
| ~ ( ordinal @ SX1 ) )
| ~ ( ~ ( ~ ( ordinal_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ( ordinal_subset @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[572]) ).
thf(585,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ~ ( ~ ( subset @ ( relation_dom @ SX2 ) @ SX0 )
| ~ ( subset @ ( relation_rng @ SX2 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[501]) ).
thf(586,plain,
( ( ! [SX0: $i] :
( ~ ~ ( empty @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ SX1 ) )
| ~ ( finite @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[571]) ).
thf(587,plain,
( ( ! [SX0: $i] :
( ~ ( subset @ SX0 @ empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[525]) ).
thf(588,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( epsilon_transitive @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) )
| ( epsilon_transitive @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[542]) ).
thf(589,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( set_intersection2 @ SX0 @ SX2 ) @ ( set_intersection2 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[515]) ).
thf(590,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_inverse_image @ SX1 @ SX0 ) @ ( relation_dom @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[506]) ).
thf(591,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX1
!= ( powerset @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[541]) ).
thf(592,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_image @ SX1 @ SX0 ) @ ( relation_rng @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[504]) ).
thf(593,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( SX1
= ( set_union2 @ SX0 @ ( set_difference @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[528]) ).
thf(594,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[544]) ).
thf(595,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( relation_inverse_image @ SX2 @ SX0 ) @ ( relation_inverse_image @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[508]) ).
thf(596,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( finite @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[537]) ).
thf(597,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_dom_restriction @ SX1 @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[533]) ).
thf(598,plain,
( ( ! [SX0: $i] :
( ~ ( finite @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( finite @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[538]) ).
thf(599,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( relation_of2_as_subset @ SX3 @ SX2 @ SX0 )
| ~ ( subset @ ( relation_rng @ SX3 ) @ SX1 )
| ( relation_of2_as_subset @ SX3 @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[505]) ).
thf(600,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ SX0 @ ( union @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[495]) ).
thf(601,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( disjoint @ SX1 @ SX2 ) )
| ( disjoint @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[530]) ).
thf(602,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ~ ( ~ ( ordinal @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) ) )
| ( ordinal @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[518]) ).
thf(603,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( relation_of2_as_subset @ SX3 @ SX2 @ SX0 )
| ~ ( subset @ SX0 @ SX1 )
| ( relation_of2_as_subset @ SX3 @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[507]) ).
thf(604,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) )
| ~ ( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[491]) ).
thf(605,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SX0 @ SX1 ) ) @ ( relation_rng @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[498]) ).
thf(606,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( relation_of2 @ SX2 @ SX0 @ SX1 )
| ( subset @ SX2 @ ( cartesian_product2 @ SX0 @ SX1 ) ) )
| ~ ( ~ ( subset @ SX2 @ ( cartesian_product2 @ SX0 @ SX1 ) )
| ( relation_of2 @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[540]) ).
thf(607,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX0 != SX1 )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[539]) ).
thf(608,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_dom @ ( relation_rng_restriction @ SX0 @ SX1 ) ) @ ( relation_dom @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[490]) ).
thf(609,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX2 ) )
| ( subset @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[511]) ).
thf(610,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( ~ ( subset @ ( cartesian_product2 @ SX0 @ SX2 ) @ ( cartesian_product2 @ SX1 @ SX2 ) )
| ~ ( subset @ ( cartesian_product2 @ SX2 @ SX0 ) @ ( cartesian_product2 @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[499]) ).
thf(611,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( set_difference @ SX0 @ SX2 ) @ ( set_difference @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[519]) ).
thf(612,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[516]) ).
thf(613,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ SX1 @ SX0 ) ) @ ( relation_rng @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[536]) ).
thf(614,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ( subset @ SX3 @ SX2 ) )
| ( in @ SX3 @ SX1 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SX1 )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) ) ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SX2 @ SX1 )
| ~ ~ ( are_equipotent @ SX2 @ SX1 ) )
| ~ ~ ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[575]) ).
thf(615,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX2 @ SX3 ) )
| ( subset @ ( cartesian_product2 @ SX0 @ SX2 ) @ ( cartesian_product2 @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[500]) ).
thf(616,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_dom @ ( relation_composition @ SX0 @ SX1 ) ) @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[526]) ).
thf(617,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[574]) ).
thf(618,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( in @ SX2 @ SX0 )
| ( subset @ SX0 @ ( set_difference @ SX1 @ ( singleton @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[493]) ).
thf(619,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ~ ( ~ ( subset @ ( relation_dom @ SX0 ) @ ( relation_dom @ SX1 ) )
| ~ ( subset @ ( relation_rng @ SX0 ) @ ( relation_rng @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[514]) ).
thf(620,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ( subset @ SX3 @ SX2 ) )
| ( in @ SX3 @ SX1 ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ ( powerset @ SX2 ) @ SX1 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SX2 @ SX1 )
| ~ ~ ( are_equipotent @ SX2 @ SX1 ) )
| ~ ~ ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[503]) ).
thf(621,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( proper_subset @ SX0 @ SX1 )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) )
| ( proper_subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[545]) ).
thf(622,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_rng_restriction @ SX0 @ SX1 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[497]) ).
thf(623,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ( subset @ ( fiber @ ( relation_restriction @ SX2 @ SX0 ) @ SX1 ) @ ( fiber @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[513]) ).
thf(624,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_union2 @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[502]) ).
thf(625,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 )
| ~ ( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX2 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX2 ) )
| ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[523]) ).
thf(626,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( subset @ ( relation_field @ ( relation_restriction @ SX1 @ SX0 ) ) @ ( relation_field @ SX1 ) )
| ~ ( subset @ ( relation_field @ ( relation_restriction @ SX1 @ SX0 ) ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[512]) ).
thf(627,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SX0 @ SX1 ) ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[496]) ).
thf(628,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( finite @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[570]) ).
thf(629,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) )
| ~ ( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[522]) ).
thf(630,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ SX0 @ ( union @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[535]) ).
thf(631,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( proper_subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[529]) ).
thf(632,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[543]) ).
thf(633,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX2 @ SX1 ) )
| ( subset @ ( set_union2 @ SX0 @ SX2 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[534]) ).
thf(634,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[492]) ).
thf(635,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[521]) ).
thf(636,plain,
! [SV1: $i] :
( ( ! [SY156: $i] : ( subset @ ( set_intersection2 @ SV1 @ SY156 ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(637,plain,
! [SV2: $i] :
( ( subset @ empty_set @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(638,plain,
! [SV3: $i] :
( ( ! [SY157: $i] : ( subset @ ( set_difference @ SV3 @ SY157 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(639,plain,
! [SV4: $i] :
( ( ! [SY158: $i] : ( subset @ SV4 @ ( set_union2 @ SV4 @ SY158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(640,plain,
! [SV5: $i] :
( ( ! [SY159: $i] : ( subset @ SV5 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(641,plain,
( ( finite @ sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[578]) ).
thf(642,plain,
! [SV6: $i] :
( ( ! [SY160: $i,SY161: $i] :
( ~ ~ ( ~ ( subset @ SV6 @ SY160 )
| ~ ( subset @ SV6 @ SY161 ) )
| ( subset @ SV6 @ ( set_intersection2 @ SY160 @ SY161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[579]) ).
thf(643,plain,
! [SV7: $i] :
( ( ! [SY162: $i] :
~ ( ~ ( ~ ( subset @ SV7 @ ( singleton @ SY162 ) )
| ( SV7 = empty_set )
| ( SV7
= ( singleton @ SY162 ) ) )
| ~ ( ~ ( ( SV7 = empty_set )
| ( SV7
= ( singleton @ SY162 ) ) )
| ( subset @ SV7 @ ( singleton @ SY162 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(644,plain,
! [SV8: $i] :
( ( ! [SY163: $i] :
~ ( ~ ( ~ ( subset @ SV8 @ ( singleton @ SY163 ) )
| ( SV8 = empty_set )
| ( SV8
= ( singleton @ SY163 ) ) )
| ~ ( ~ ( ( SV8 = empty_set )
| ( SV8
= ( singleton @ SY163 ) ) )
| ( subset @ SV8 @ ( singleton @ SY163 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(645,plain,
! [SV9: $i] :
( ( ! [SY164: $i] :
( ~ ( subset @ ( singleton @ SV9 ) @ ( singleton @ SY164 ) )
| ( SV9 = SY164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(646,plain,
! [SV10: $i] :
( ( ~ ( relation @ SV10 )
| ! [SY165: $i] :
( ~ ( relation @ SY165 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV10 @ SY165 ) ) @ ( relation_rng @ SY165 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(647,plain,
! [SV11: $i] :
( ( ! [SY166: $i] :
( ~ ~ ( ~ ( ordinal @ SV11 )
| ~ ( ordinal @ SY166 ) )
| ~ ( ~ ( ~ ( ordinal_subset @ SV11 @ SY166 )
| ( subset @ SV11 @ SY166 ) )
| ~ ( ~ ( subset @ SV11 @ SY166 )
| ( ordinal_subset @ SV11 @ SY166 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(648,plain,
! [SV12: $i] :
( ( ! [SY167: $i,SY168: $i] :
( ~ ( relation_of2_as_subset @ SY168 @ SV12 @ SY167 )
| ~ ( ~ ( subset @ ( relation_dom @ SY168 ) @ SV12 )
| ~ ( subset @ ( relation_rng @ SY168 ) @ SY167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(649,plain,
! [SV13: $i] :
( ( ~ ~ ( empty @ SV13 )
| ~ ! [SY169: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY169 @ ( powerset @ SV13 ) )
| ~ ~ ( empty @ SY169 ) )
| ~ ( finite @ SY169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[586]) ).
thf(650,plain,
! [SV14: $i] :
( ( ~ ( subset @ SV14 @ empty_set )
| ( SV14 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(651,plain,
! [SV15: $i] :
( ( ~ ( ~ ( ~ ( epsilon_transitive @ SV15 )
| ! [SY170: $i] :
( ~ ( in @ SY170 @ SV15 )
| ( subset @ SY170 @ SV15 ) ) )
| ~ ( ~ ! [SY171: $i] :
( ~ ( in @ SY171 @ SV15 )
| ( subset @ SY171 @ SV15 ) )
| ( epsilon_transitive @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(652,plain,
! [SV16: $i] :
( ( ! [SY172: $i,SY173: $i] :
( ~ ( subset @ SV16 @ SY172 )
| ( subset @ ( set_intersection2 @ SV16 @ SY173 ) @ ( set_intersection2 @ SY172 @ SY173 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(653,plain,
! [SV17: $i] :
( ( ! [SY174: $i] :
( ~ ( relation @ SY174 )
| ( subset @ ( relation_inverse_image @ SY174 @ SV17 ) @ ( relation_dom @ SY174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(654,plain,
! [SV18: $i] :
( ( ! [SY175: $i] :
~ ( ~ ( ( SY175
!= ( powerset @ SV18 ) )
| ! [SY176: $i] :
~ ( ~ ( ~ ( in @ SY176 @ SY175 )
| ( subset @ SY176 @ SV18 ) )
| ~ ( ~ ( subset @ SY176 @ SV18 )
| ( in @ SY176 @ SY175 ) ) ) )
| ~ ( ~ ! [SY177: $i] :
~ ( ~ ( ~ ( in @ SY177 @ SY175 )
| ( subset @ SY177 @ SV18 ) )
| ~ ( ~ ( subset @ SY177 @ SV18 )
| ( in @ SY177 @ SY175 ) ) )
| ( SY175
= ( powerset @ SV18 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(655,plain,
! [SV19: $i] :
( ( ! [SY178: $i] :
( ~ ( relation @ SY178 )
| ( subset @ ( relation_image @ SY178 @ SV19 ) @ ( relation_rng @ SY178 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(656,plain,
! [SV20: $i] :
( ( ! [SY179: $i] :
( ~ ( subset @ SV20 @ SY179 )
| ( SY179
= ( set_union2 @ SV20 @ ( set_difference @ SY179 @ SV20 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(657,plain,
! [SV21: $i] :
( ( ! [SY180: $i] :
~ ( ~ ( ~ ( subset @ SV21 @ SY180 )
| ! [SY181: $i] :
( ~ ( in @ SY181 @ SV21 )
| ( in @ SY181 @ SY180 ) ) )
| ~ ( ~ ! [SY182: $i] :
( ~ ( in @ SY182 @ SV21 )
| ( in @ SY182 @ SY180 ) )
| ( subset @ SV21 @ SY180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(658,plain,
! [SV22: $i] :
( ( ! [SY183: $i,SY184: $i] :
( ~ ( relation @ SY184 )
| ~ ( subset @ SV22 @ SY183 )
| ( subset @ ( relation_inverse_image @ SY184 @ SV22 ) @ ( relation_inverse_image @ SY184 @ SY183 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(659,plain,
! [SV23: $i] :
( ( ~ ( empty @ SV23 )
| ( finite @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(660,plain,
! [SV24: $i] :
( ( ! [SY185: $i] :
( ~ ( relation @ SY185 )
| ( subset @ ( relation_dom_restriction @ SY185 @ SV24 ) @ SY185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(661,plain,
! [SV25: $i] :
( ( ~ ( finite @ SV25 )
| ! [SY186: $i] :
( ~ ( element @ SY186 @ ( powerset @ SV25 ) )
| ( finite @ SY186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(662,plain,
! [SV26: $i] :
( ( ! [SY187: $i,SY188: $i,SY189: $i] :
( ~ ( relation_of2_as_subset @ SY189 @ SY188 @ SV26 )
| ~ ( subset @ ( relation_rng @ SY189 ) @ SY187 )
| ( relation_of2_as_subset @ SY189 @ SY188 @ SY187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(663,plain,
! [SV27: $i] :
( ( ! [SY190: $i] :
( ~ ( in @ SV27 @ SY190 )
| ( subset @ SV27 @ ( union @ SY190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(664,plain,
! [SV28: $i] :
( ( ! [SY191: $i,SY192: $i] :
( ~ ~ ( ~ ( subset @ SV28 @ SY191 )
| ~ ( disjoint @ SY191 @ SY192 ) )
| ( disjoint @ SV28 @ SY192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(665,plain,
! [SV29: $i] :
( ( ~ ! [SY193: $i] :
( ~ ( in @ SY193 @ SV29 )
| ~ ( ~ ( ordinal @ SY193 )
| ~ ( subset @ SY193 @ SV29 ) ) )
| ( ordinal @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(666,plain,
! [SV30: $i] :
( ( ! [SY194: $i,SY195: $i,SY196: $i] :
( ~ ( relation_of2_as_subset @ SY196 @ SY195 @ SV30 )
| ~ ( subset @ SV30 @ SY194 )
| ( relation_of2_as_subset @ SY196 @ SY195 @ SY194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(667,plain,
! [SV31: $i] :
( ( ! [SY197: $i] :
~ ( ~ ( ~ ( subset @ ( singleton @ SV31 ) @ SY197 )
| ( in @ SV31 @ SY197 ) )
| ~ ( ~ ( in @ SV31 @ SY197 )
| ( subset @ ( singleton @ SV31 ) @ SY197 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(668,plain,
! [SV32: $i] :
( ( ! [SY198: $i] :
( ~ ( relation @ SY198 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV32 @ SY198 ) ) @ ( relation_rng @ SY198 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[605]) ).
thf(669,plain,
! [SV33: $i] :
( ( ! [SY199: $i,SY200: $i] :
~ ( ~ ( ~ ( relation_of2 @ SY200 @ SV33 @ SY199 )
| ( subset @ SY200 @ ( cartesian_product2 @ SV33 @ SY199 ) ) )
| ~ ( ~ ( subset @ SY200 @ ( cartesian_product2 @ SV33 @ SY199 ) )
| ( relation_of2 @ SY200 @ SV33 @ SY199 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(670,plain,
! [SV34: $i] :
( ( ! [SY201: $i] :
~ ( ~ ( ( SV34 != SY201 )
| ~ ( ~ ( subset @ SV34 @ SY201 )
| ~ ( subset @ SY201 @ SV34 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV34 @ SY201 )
| ~ ( subset @ SY201 @ SV34 ) )
| ( SV34 = SY201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(671,plain,
! [SV35: $i] :
( ( ! [SY202: $i] :
( ~ ( relation @ SY202 )
| ( subset @ ( relation_dom @ ( relation_rng_restriction @ SV35 @ SY202 ) ) @ ( relation_dom @ SY202 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(672,plain,
! [SV36: $i] :
( ( ! [SY203: $i,SY204: $i] :
( ~ ~ ( ~ ( subset @ SV36 @ SY203 )
| ~ ( subset @ SY203 @ SY204 ) )
| ( subset @ SV36 @ SY204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(673,plain,
! [SV37: $i] :
( ( ! [SY205: $i,SY206: $i] :
( ~ ( subset @ SV37 @ SY205 )
| ~ ( ~ ( subset @ ( cartesian_product2 @ SV37 @ SY206 ) @ ( cartesian_product2 @ SY205 @ SY206 ) )
| ~ ( subset @ ( cartesian_product2 @ SY206 @ SV37 ) @ ( cartesian_product2 @ SY206 @ SY205 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(674,plain,
! [SV38: $i] :
( ( ! [SY207: $i,SY208: $i] :
( ~ ( subset @ SV38 @ SY207 )
| ( subset @ ( set_difference @ SV38 @ SY208 ) @ ( set_difference @ SY207 @ SY208 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(675,plain,
! [SV39: $i] :
( ( ! [SY209: $i] :
( ~ ( subset @ SV39 @ SY209 )
| ( ( set_intersection2 @ SV39 @ SY209 )
= SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(676,plain,
! [SV40: $i] :
( ( ! [SY210: $i] :
( ~ ( relation @ SY210 )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ SY210 @ SV40 ) ) @ ( relation_rng @ SY210 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(677,plain,
! [SV41: $i] :
( ( ~ ! [SY211: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV41 @ SY211 )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY211 )
| ~ ( subset @ SX3 @ SX2 ) )
| ( in @ SX3 @ SY211 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SY211 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SY211 )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) ) ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SX2 @ SY211 )
| ~ ~ ( are_equipotent @ SX2 @ SY211 ) )
| ~ ~ ( in @ SX2 @ SY211 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(678,plain,
! [SV42: $i] :
( ( ! [SY218: $i,SY219: $i,SY220: $i] :
( ~ ~ ( ~ ( subset @ SV42 @ SY218 )
| ~ ( subset @ SY219 @ SY220 ) )
| ( subset @ ( cartesian_product2 @ SV42 @ SY219 ) @ ( cartesian_product2 @ SY218 @ SY220 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(679,plain,
! [SV43: $i] :
( ( ~ ( relation @ SV43 )
| ! [SY221: $i] :
( ~ ( relation @ SY221 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV43 @ SY221 ) ) @ ( relation_dom @ SV43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(680,plain,
! [SV44: $i] :
( ( ! [SY222: $i] :
~ ( ~ ( ~ ( element @ SV44 @ ( powerset @ SY222 ) )
| ( subset @ SV44 @ SY222 ) )
| ~ ( ~ ( subset @ SV44 @ SY222 )
| ( element @ SV44 @ ( powerset @ SY222 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(681,plain,
! [SV45: $i] :
( ( ! [SY223: $i,SY224: $i] :
( ~ ( subset @ SV45 @ SY223 )
| ( in @ SY224 @ SV45 )
| ( subset @ SV45 @ ( set_difference @ SY223 @ ( singleton @ SY224 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(682,plain,
! [SV46: $i] :
( ( ~ ( relation @ SV46 )
| ! [SY225: $i] :
( ~ ( relation @ SY225 )
| ~ ( subset @ SV46 @ SY225 )
| ~ ( ~ ( subset @ ( relation_dom @ SV46 ) @ ( relation_dom @ SY225 ) )
| ~ ( subset @ ( relation_rng @ SV46 ) @ ( relation_rng @ SY225 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(683,plain,
! [SV47: $i] :
( ( ~ ! [SY226: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV47 @ SY226 )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY226 )
| ~ ( subset @ SX3 @ SX2 ) )
| ( in @ SX3 @ SY226 ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY226 )
| ( in @ ( powerset @ SX2 ) @ SY226 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SX2 @ SY226 )
| ~ ~ ( are_equipotent @ SX2 @ SY226 ) )
| ~ ~ ( in @ SX2 @ SY226 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(684,plain,
! [SV48: $i] :
( ( ! [SY231: $i] :
~ ( ~ ( ~ ( proper_subset @ SV48 @ SY231 )
| ~ ( ~ ( subset @ SV48 @ SY231 )
| ~ ( ( SV48 != SY231 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV48 @ SY231 )
| ~ ( ( SV48 != SY231 ) ) )
| ( proper_subset @ SV48 @ SY231 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(685,plain,
! [SV49: $i] :
( ( ! [SY232: $i] :
( ~ ( relation @ SY232 )
| ( subset @ ( relation_rng_restriction @ SV49 @ SY232 ) @ SY232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(686,plain,
! [SV50: $i] :
( ( ! [SY233: $i,SY234: $i] :
( ~ ( relation @ SY234 )
| ( subset @ ( fiber @ ( relation_restriction @ SY234 @ SV50 ) @ SY233 ) @ ( fiber @ SY234 @ SY233 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(687,plain,
! [SV51: $i] :
( ( ! [SY235: $i] :
( ~ ( subset @ SV51 @ SY235 )
| ( ( set_union2 @ SV51 @ SY235 )
= SY235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(688,plain,
! [SV52: $i] :
( ( ! [SY236: $i,SY237: $i] :
~ ( ~ ( ~ ( subset @ ( unordered_pair @ SV52 @ SY236 ) @ SY237 )
| ~ ( ~ ( in @ SV52 @ SY237 )
| ~ ( in @ SY236 @ SY237 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV52 @ SY237 )
| ~ ( in @ SY236 @ SY237 ) )
| ( subset @ ( unordered_pair @ SV52 @ SY236 ) @ SY237 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(689,plain,
! [SV53: $i] :
( ( ! [SY238: $i] :
( ~ ( relation @ SY238 )
| ~ ( ~ ( subset @ ( relation_field @ ( relation_restriction @ SY238 @ SV53 ) ) @ ( relation_field @ SY238 ) )
| ~ ( subset @ ( relation_field @ ( relation_restriction @ SY238 @ SV53 ) ) @ SV53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(690,plain,
! [SV54: $i] :
( ( ! [SY239: $i] :
( ~ ( relation @ SY239 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV54 @ SY239 ) ) @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(691,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( finite @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[628]) ).
thf(692,plain,
! [SV55: $i] :
( ( ! [SY240: $i] :
~ ( ~ ( ~ ( subset @ ( singleton @ SV55 ) @ SY240 )
| ( in @ SV55 @ SY240 ) )
| ~ ( ~ ( in @ SV55 @ SY240 )
| ( subset @ ( singleton @ SV55 ) @ SY240 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(693,plain,
! [SV56: $i] :
( ( ! [SY241: $i] :
( ~ ( in @ SV56 @ SY241 )
| ( subset @ SV56 @ ( union @ SY241 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(694,plain,
! [SV57: $i] :
( ( ! [SY242: $i] :
~ ~ ( ~ ( subset @ SV57 @ SY242 )
| ~ ( proper_subset @ SY242 @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(695,plain,
! [SV58: $i] :
( ( ~ ( relation @ SV58 )
| ! [SY243: $i] :
( ~ ( relation @ SY243 )
| ~ ( ~ ( ~ ( subset @ SV58 @ SY243 )
| ! [SY244: $i,SY245: $i] :
( ~ ( in @ ( ordered_pair @ SY244 @ SY245 ) @ SV58 )
| ( in @ ( ordered_pair @ SY244 @ SY245 ) @ SY243 ) ) )
| ~ ( ~ ! [SY246: $i,SY247: $i] :
( ~ ( in @ ( ordered_pair @ SY246 @ SY247 ) @ SV58 )
| ( in @ ( ordered_pair @ SY246 @ SY247 ) @ SY243 ) )
| ( subset @ SV58 @ SY243 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(696,plain,
! [SV59: $i] :
( ( ! [SY248: $i,SY249: $i] :
( ~ ~ ( ~ ( subset @ SV59 @ SY248 )
| ~ ( subset @ SY249 @ SY248 ) )
| ( subset @ ( set_union2 @ SV59 @ SY249 ) @ SY248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(697,plain,
! [SV60: $i] :
( ( ! [SY250: $i] :
~ ( ~ ( ( ( set_difference @ SV60 @ SY250 )
!= empty_set )
| ( subset @ SV60 @ SY250 ) )
| ~ ( ~ ( subset @ SV60 @ SY250 )
| ( ( set_difference @ SV60 @ SY250 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(698,plain,
! [SV61: $i] :
( ( ! [SY251: $i] :
~ ( ~ ( ( ( set_difference @ SV61 @ SY251 )
!= empty_set )
| ( subset @ SV61 @ SY251 ) )
| ~ ( ~ ( subset @ SV61 @ SY251 )
| ( ( set_difference @ SV61 @ SY251 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(699,plain,
! [SV62: $i,SV1: $i] :
( ( subset @ ( set_intersection2 @ SV1 @ SV62 ) @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(700,plain,
! [SV63: $i,SV3: $i] :
( ( subset @ ( set_difference @ SV3 @ SV63 ) @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(701,plain,
! [SV64: $i,SV4: $i] :
( ( subset @ SV4 @ ( set_union2 @ SV4 @ SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(702,plain,
! [SV5: $i] :
( ( subset @ SV5 @ SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(703,plain,
! [SV66: $i,SV6: $i] :
( ( ! [SY252: $i] :
( ~ ~ ( ~ ( subset @ SV6 @ SV66 )
| ~ ( subset @ SV6 @ SY252 ) )
| ( subset @ SV6 @ ( set_intersection2 @ SV66 @ SY252 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(704,plain,
! [SV67: $i,SV7: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV7 @ ( singleton @ SV67 ) )
| ( SV7 = empty_set )
| ( SV7
= ( singleton @ SV67 ) ) )
| ~ ( ~ ( ( SV7 = empty_set )
| ( SV7
= ( singleton @ SV67 ) ) )
| ( subset @ SV7 @ ( singleton @ SV67 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(705,plain,
! [SV68: $i,SV8: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV8 @ ( singleton @ SV68 ) )
| ( SV8 = empty_set )
| ( SV8
= ( singleton @ SV68 ) ) )
| ~ ( ~ ( ( SV8 = empty_set )
| ( SV8
= ( singleton @ SV68 ) ) )
| ( subset @ SV8 @ ( singleton @ SV68 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(706,plain,
! [SV69: $i,SV9: $i] :
( ( ~ ( subset @ ( singleton @ SV9 ) @ ( singleton @ SV69 ) )
| ( SV9 = SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(707,plain,
! [SV10: $i] :
( ( ( ~ ( relation @ SV10 ) )
= $true )
| ( ( ! [SY165: $i] :
( ~ ( relation @ SY165 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV10 @ SY165 ) ) @ ( relation_rng @ SY165 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[646]) ).
thf(708,plain,
! [SV70: $i,SV11: $i] :
( ( ~ ~ ( ~ ( ordinal @ SV11 )
| ~ ( ordinal @ SV70 ) )
| ~ ( ~ ( ~ ( ordinal_subset @ SV11 @ SV70 )
| ( subset @ SV11 @ SV70 ) )
| ~ ( ~ ( subset @ SV11 @ SV70 )
| ( ordinal_subset @ SV11 @ SV70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(709,plain,
! [SV71: $i,SV12: $i] :
( ( ! [SY253: $i] :
( ~ ( relation_of2_as_subset @ SY253 @ SV12 @ SV71 )
| ~ ( ~ ( subset @ ( relation_dom @ SY253 ) @ SV12 )
| ~ ( subset @ ( relation_rng @ SY253 ) @ SV71 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(710,plain,
! [SV13: $i] :
( ( ( ~ ~ ( empty @ SV13 ) )
= $true )
| ( ( ~ ! [SY169: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY169 @ ( powerset @ SV13 ) )
| ~ ~ ( empty @ SY169 ) )
| ~ ( finite @ SY169 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[649]) ).
thf(711,plain,
! [SV14: $i] :
( ( ( ~ ( subset @ SV14 @ empty_set ) )
= $true )
| ( ( SV14 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[650]) ).
thf(712,plain,
! [SV15: $i] :
( ( ~ ( ~ ( epsilon_transitive @ SV15 )
| ! [SY170: $i] :
( ~ ( in @ SY170 @ SV15 )
| ( subset @ SY170 @ SV15 ) ) )
| ~ ( ~ ! [SY171: $i] :
( ~ ( in @ SY171 @ SV15 )
| ( subset @ SY171 @ SV15 ) )
| ( epsilon_transitive @ SV15 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[651]) ).
thf(713,plain,
! [SV72: $i,SV16: $i] :
( ( ! [SY254: $i] :
( ~ ( subset @ SV16 @ SV72 )
| ( subset @ ( set_intersection2 @ SV16 @ SY254 ) @ ( set_intersection2 @ SV72 @ SY254 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(714,plain,
! [SV17: $i,SV73: $i] :
( ( ~ ( relation @ SV73 )
| ( subset @ ( relation_inverse_image @ SV73 @ SV17 ) @ ( relation_dom @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(715,plain,
! [SV18: $i,SV74: $i] :
( ( ~ ( ~ ( ( SV74
!= ( powerset @ SV18 ) )
| ! [SY255: $i] :
~ ( ~ ( ~ ( in @ SY255 @ SV74 )
| ( subset @ SY255 @ SV18 ) )
| ~ ( ~ ( subset @ SY255 @ SV18 )
| ( in @ SY255 @ SV74 ) ) ) )
| ~ ( ~ ! [SY256: $i] :
~ ( ~ ( ~ ( in @ SY256 @ SV74 )
| ( subset @ SY256 @ SV18 ) )
| ~ ( ~ ( subset @ SY256 @ SV18 )
| ( in @ SY256 @ SV74 ) ) )
| ( SV74
= ( powerset @ SV18 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(716,plain,
! [SV19: $i,SV75: $i] :
( ( ~ ( relation @ SV75 )
| ( subset @ ( relation_image @ SV75 @ SV19 ) @ ( relation_rng @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(717,plain,
! [SV76: $i,SV20: $i] :
( ( ~ ( subset @ SV20 @ SV76 )
| ( SV76
= ( set_union2 @ SV20 @ ( set_difference @ SV76 @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(718,plain,
! [SV77: $i,SV21: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV21 @ SV77 )
| ! [SY257: $i] :
( ~ ( in @ SY257 @ SV21 )
| ( in @ SY257 @ SV77 ) ) )
| ~ ( ~ ! [SY258: $i] :
( ~ ( in @ SY258 @ SV21 )
| ( in @ SY258 @ SV77 ) )
| ( subset @ SV21 @ SV77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(719,plain,
! [SV78: $i,SV22: $i] :
( ( ! [SY259: $i] :
( ~ ( relation @ SY259 )
| ~ ( subset @ SV22 @ SV78 )
| ( subset @ ( relation_inverse_image @ SY259 @ SV22 ) @ ( relation_inverse_image @ SY259 @ SV78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(720,plain,
! [SV23: $i] :
( ( ( ~ ( empty @ SV23 ) )
= $true )
| ( ( finite @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[659]) ).
thf(721,plain,
! [SV24: $i,SV79: $i] :
( ( ~ ( relation @ SV79 )
| ( subset @ ( relation_dom_restriction @ SV79 @ SV24 ) @ SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(722,plain,
! [SV25: $i] :
( ( ( ~ ( finite @ SV25 ) )
= $true )
| ( ( ! [SY186: $i] :
( ~ ( element @ SY186 @ ( powerset @ SV25 ) )
| ( finite @ SY186 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[661]) ).
thf(723,plain,
! [SV80: $i,SV26: $i] :
( ( ! [SY260: $i,SY261: $i] :
( ~ ( relation_of2_as_subset @ SY261 @ SY260 @ SV26 )
| ~ ( subset @ ( relation_rng @ SY261 ) @ SV80 )
| ( relation_of2_as_subset @ SY261 @ SY260 @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(724,plain,
! [SV81: $i,SV27: $i] :
( ( ~ ( in @ SV27 @ SV81 )
| ( subset @ SV27 @ ( union @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(725,plain,
! [SV82: $i,SV28: $i] :
( ( ! [SY262: $i] :
( ~ ~ ( ~ ( subset @ SV28 @ SV82 )
| ~ ( disjoint @ SV82 @ SY262 ) )
| ( disjoint @ SV28 @ SY262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(726,plain,
! [SV29: $i] :
( ( ( ~ ! [SY193: $i] :
( ~ ( in @ SY193 @ SV29 )
| ~ ( ~ ( ordinal @ SY193 )
| ~ ( subset @ SY193 @ SV29 ) ) ) )
= $true )
| ( ( ordinal @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[665]) ).
thf(727,plain,
! [SV83: $i,SV30: $i] :
( ( ! [SY263: $i,SY264: $i] :
( ~ ( relation_of2_as_subset @ SY264 @ SY263 @ SV30 )
| ~ ( subset @ SV30 @ SV83 )
| ( relation_of2_as_subset @ SY264 @ SY263 @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(728,plain,
! [SV84: $i,SV31: $i] :
( ( ~ ( ~ ( ~ ( subset @ ( singleton @ SV31 ) @ SV84 )
| ( in @ SV31 @ SV84 ) )
| ~ ( ~ ( in @ SV31 @ SV84 )
| ( subset @ ( singleton @ SV31 ) @ SV84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(729,plain,
! [SV32: $i,SV85: $i] :
( ( ~ ( relation @ SV85 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV32 @ SV85 ) ) @ ( relation_rng @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(730,plain,
! [SV86: $i,SV33: $i] :
( ( ! [SY265: $i] :
~ ( ~ ( ~ ( relation_of2 @ SY265 @ SV33 @ SV86 )
| ( subset @ SY265 @ ( cartesian_product2 @ SV33 @ SV86 ) ) )
| ~ ( ~ ( subset @ SY265 @ ( cartesian_product2 @ SV33 @ SV86 ) )
| ( relation_of2 @ SY265 @ SV33 @ SV86 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(731,plain,
! [SV87: $i,SV34: $i] :
( ( ~ ( ~ ( ( SV34 != SV87 )
| ~ ( ~ ( subset @ SV34 @ SV87 )
| ~ ( subset @ SV87 @ SV34 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV34 @ SV87 )
| ~ ( subset @ SV87 @ SV34 ) )
| ( SV34 = SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(732,plain,
! [SV35: $i,SV88: $i] :
( ( ~ ( relation @ SV88 )
| ( subset @ ( relation_dom @ ( relation_rng_restriction @ SV35 @ SV88 ) ) @ ( relation_dom @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(733,plain,
! [SV89: $i,SV36: $i] :
( ( ! [SY266: $i] :
( ~ ~ ( ~ ( subset @ SV36 @ SV89 )
| ~ ( subset @ SV89 @ SY266 ) )
| ( subset @ SV36 @ SY266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(734,plain,
! [SV90: $i,SV37: $i] :
( ( ! [SY267: $i] :
( ~ ( subset @ SV37 @ SV90 )
| ~ ( ~ ( subset @ ( cartesian_product2 @ SV37 @ SY267 ) @ ( cartesian_product2 @ SV90 @ SY267 ) )
| ~ ( subset @ ( cartesian_product2 @ SY267 @ SV37 ) @ ( cartesian_product2 @ SY267 @ SV90 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(735,plain,
! [SV91: $i,SV38: $i] :
( ( ! [SY268: $i] :
( ~ ( subset @ SV38 @ SV91 )
| ( subset @ ( set_difference @ SV38 @ SY268 ) @ ( set_difference @ SV91 @ SY268 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(736,plain,
! [SV92: $i,SV39: $i] :
( ( ~ ( subset @ SV39 @ SV92 )
| ( ( set_intersection2 @ SV39 @ SV92 )
= SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(737,plain,
! [SV40: $i,SV93: $i] :
( ( ~ ( relation @ SV93 )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ SV93 @ SV40 ) ) @ ( relation_rng @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(738,plain,
! [SV41: $i] :
( ( ! [SY211: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV41 @ SY211 )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY211 )
| ~ ( subset @ SX3 @ SX2 ) )
| ( in @ SX3 @ SY211 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SY211 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SY211 )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) ) ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SX2 @ SY211 )
| ~ ~ ( are_equipotent @ SX2 @ SY211 ) )
| ~ ~ ( in @ SX2 @ SY211 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[677]) ).
thf(739,plain,
! [SV94: $i,SV42: $i] :
( ( ! [SY269: $i,SY270: $i] :
( ~ ~ ( ~ ( subset @ SV42 @ SV94 )
| ~ ( subset @ SY269 @ SY270 ) )
| ( subset @ ( cartesian_product2 @ SV42 @ SY269 ) @ ( cartesian_product2 @ SV94 @ SY270 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(740,plain,
! [SV43: $i] :
( ( ( ~ ( relation @ SV43 ) )
= $true )
| ( ( ! [SY221: $i] :
( ~ ( relation @ SY221 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV43 @ SY221 ) ) @ ( relation_dom @ SV43 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[679]) ).
thf(741,plain,
! [SV95: $i,SV44: $i] :
( ( ~ ( ~ ( ~ ( element @ SV44 @ ( powerset @ SV95 ) )
| ( subset @ SV44 @ SV95 ) )
| ~ ( ~ ( subset @ SV44 @ SV95 )
| ( element @ SV44 @ ( powerset @ SV95 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(742,plain,
! [SV96: $i,SV45: $i] :
( ( ! [SY271: $i] :
( ~ ( subset @ SV45 @ SV96 )
| ( in @ SY271 @ SV45 )
| ( subset @ SV45 @ ( set_difference @ SV96 @ ( singleton @ SY271 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(743,plain,
! [SV46: $i] :
( ( ( ~ ( relation @ SV46 ) )
= $true )
| ( ( ! [SY225: $i] :
( ~ ( relation @ SY225 )
| ~ ( subset @ SV46 @ SY225 )
| ~ ( ~ ( subset @ ( relation_dom @ SV46 ) @ ( relation_dom @ SY225 ) )
| ~ ( subset @ ( relation_rng @ SV46 ) @ ( relation_rng @ SY225 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[682]) ).
thf(744,plain,
! [SV47: $i] :
( ( ! [SY226: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV47 @ SY226 )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY226 )
| ~ ( subset @ SX3 @ SX2 ) )
| ( in @ SX3 @ SY226 ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY226 )
| ( in @ ( powerset @ SX2 ) @ SY226 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SX2 @ SY226 )
| ~ ~ ( are_equipotent @ SX2 @ SY226 ) )
| ~ ~ ( in @ SX2 @ SY226 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[683]) ).
thf(745,plain,
! [SV97: $i,SV48: $i] :
( ( ~ ( ~ ( ~ ( proper_subset @ SV48 @ SV97 )
| ~ ( ~ ( subset @ SV48 @ SV97 )
| ~ ( ( SV48 != SV97 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV48 @ SV97 )
| ~ ( ( SV48 != SV97 ) ) )
| ( proper_subset @ SV48 @ SV97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(746,plain,
! [SV49: $i,SV98: $i] :
( ( ~ ( relation @ SV98 )
| ( subset @ ( relation_rng_restriction @ SV49 @ SV98 ) @ SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(747,plain,
! [SV99: $i,SV50: $i] :
( ( ! [SY272: $i] :
( ~ ( relation @ SY272 )
| ( subset @ ( fiber @ ( relation_restriction @ SY272 @ SV50 ) @ SV99 ) @ ( fiber @ SY272 @ SV99 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(748,plain,
! [SV100: $i,SV51: $i] :
( ( ~ ( subset @ SV51 @ SV100 )
| ( ( set_union2 @ SV51 @ SV100 )
= SV100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(749,plain,
! [SV101: $i,SV52: $i] :
( ( ! [SY273: $i] :
~ ( ~ ( ~ ( subset @ ( unordered_pair @ SV52 @ SV101 ) @ SY273 )
| ~ ( ~ ( in @ SV52 @ SY273 )
| ~ ( in @ SV101 @ SY273 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV52 @ SY273 )
| ~ ( in @ SV101 @ SY273 ) )
| ( subset @ ( unordered_pair @ SV52 @ SV101 ) @ SY273 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(750,plain,
! [SV53: $i,SV102: $i] :
( ( ~ ( relation @ SV102 )
| ~ ( ~ ( subset @ ( relation_field @ ( relation_restriction @ SV102 @ SV53 ) ) @ ( relation_field @ SV102 ) )
| ~ ( subset @ ( relation_field @ ( relation_restriction @ SV102 @ SV53 ) ) @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(751,plain,
! [SV54: $i,SV103: $i] :
( ( ~ ( relation @ SV103 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV54 @ SV103 ) ) @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(752,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( finite @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[691]) ).
thf(753,plain,
! [SV104: $i,SV55: $i] :
( ( ~ ( ~ ( ~ ( subset @ ( singleton @ SV55 ) @ SV104 )
| ( in @ SV55 @ SV104 ) )
| ~ ( ~ ( in @ SV55 @ SV104 )
| ( subset @ ( singleton @ SV55 ) @ SV104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(754,plain,
! [SV105: $i,SV56: $i] :
( ( ~ ( in @ SV56 @ SV105 )
| ( subset @ SV56 @ ( union @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(755,plain,
! [SV106: $i,SV57: $i] :
( ( ~ ~ ( ~ ( subset @ SV57 @ SV106 )
| ~ ( proper_subset @ SV106 @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(756,plain,
! [SV58: $i] :
( ( ( ~ ( relation @ SV58 ) )
= $true )
| ( ( ! [SY243: $i] :
( ~ ( relation @ SY243 )
| ~ ( ~ ( ~ ( subset @ SV58 @ SY243 )
| ! [SY244: $i,SY245: $i] :
( ~ ( in @ ( ordered_pair @ SY244 @ SY245 ) @ SV58 )
| ( in @ ( ordered_pair @ SY244 @ SY245 ) @ SY243 ) ) )
| ~ ( ~ ! [SY246: $i,SY247: $i] :
( ~ ( in @ ( ordered_pair @ SY246 @ SY247 ) @ SV58 )
| ( in @ ( ordered_pair @ SY246 @ SY247 ) @ SY243 ) )
| ( subset @ SV58 @ SY243 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[695]) ).
thf(757,plain,
! [SV107: $i,SV59: $i] :
( ( ! [SY274: $i] :
( ~ ~ ( ~ ( subset @ SV59 @ SV107 )
| ~ ( subset @ SY274 @ SV107 ) )
| ( subset @ ( set_union2 @ SV59 @ SY274 ) @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(758,plain,
! [SV108: $i,SV60: $i] :
( ( ~ ( ~ ( ( ( set_difference @ SV60 @ SV108 )
!= empty_set )
| ( subset @ SV60 @ SV108 ) )
| ~ ( ~ ( subset @ SV60 @ SV108 )
| ( ( set_difference @ SV60 @ SV108 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(759,plain,
! [SV109: $i,SV61: $i] :
( ( ~ ( ~ ( ( ( set_difference @ SV61 @ SV109 )
!= empty_set )
| ( subset @ SV61 @ SV109 ) )
| ~ ( ~ ( subset @ SV61 @ SV109 )
| ( ( set_difference @ SV61 @ SV109 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(760,plain,
! [SV110: $i,SV66: $i,SV6: $i] :
( ( ~ ~ ( ~ ( subset @ SV6 @ SV66 )
| ~ ( subset @ SV6 @ SV110 ) )
| ( subset @ SV6 @ ( set_intersection2 @ SV66 @ SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(761,plain,
! [SV67: $i,SV7: $i] :
( ( ~ ( ~ ( subset @ SV7 @ ( singleton @ SV67 ) )
| ( SV7 = empty_set )
| ( SV7
= ( singleton @ SV67 ) ) )
| ~ ( ~ ( ( SV7 = empty_set )
| ( SV7
= ( singleton @ SV67 ) ) )
| ( subset @ SV7 @ ( singleton @ SV67 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[704]) ).
thf(762,plain,
! [SV68: $i,SV8: $i] :
( ( ~ ( ~ ( subset @ SV8 @ ( singleton @ SV68 ) )
| ( SV8 = empty_set )
| ( SV8
= ( singleton @ SV68 ) ) )
| ~ ( ~ ( ( SV8 = empty_set )
| ( SV8
= ( singleton @ SV68 ) ) )
| ( subset @ SV8 @ ( singleton @ SV68 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[705]) ).
thf(763,plain,
! [SV69: $i,SV9: $i] :
( ( ( ~ ( subset @ ( singleton @ SV9 ) @ ( singleton @ SV69 ) ) )
= $true )
| ( ( SV9 = SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[706]) ).
thf(764,plain,
! [SV10: $i] :
( ( ( relation @ SV10 )
= $false )
| ( ( ! [SY165: $i] :
( ~ ( relation @ SY165 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV10 @ SY165 ) ) @ ( relation_rng @ SY165 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[707]) ).
thf(765,plain,
! [SV70: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( ordinal @ SV11 )
| ~ ( ordinal @ SV70 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ordinal_subset @ SV11 @ SV70 )
| ( subset @ SV11 @ SV70 ) )
| ~ ( ~ ( subset @ SV11 @ SV70 )
| ( ordinal_subset @ SV11 @ SV70 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[708]) ).
thf(766,plain,
! [SV71: $i,SV12: $i,SV111: $i] :
( ( ~ ( relation_of2_as_subset @ SV111 @ SV12 @ SV71 )
| ~ ( ~ ( subset @ ( relation_dom @ SV111 ) @ SV12 )
| ~ ( subset @ ( relation_rng @ SV111 ) @ SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(767,plain,
! [SV13: $i] :
( ( ( ~ ( empty @ SV13 ) )
= $false )
| ( ( ~ ! [SY169: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY169 @ ( powerset @ SV13 ) )
| ~ ~ ( empty @ SY169 ) )
| ~ ( finite @ SY169 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[710]) ).
thf(768,plain,
! [SV14: $i] :
( ( ( subset @ SV14 @ empty_set )
= $false )
| ( ( SV14 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[711]) ).
thf(769,plain,
! [SV15: $i] :
( ( ~ ( ~ ( epsilon_transitive @ SV15 )
| ! [SY170: $i] :
( ~ ( in @ SY170 @ SV15 )
| ( subset @ SY170 @ SV15 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[712]) ).
thf(770,plain,
! [SV15: $i] :
( ( ~ ( ~ ! [SY171: $i] :
( ~ ( in @ SY171 @ SV15 )
| ( subset @ SY171 @ SV15 ) )
| ( epsilon_transitive @ SV15 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[712]) ).
thf(771,plain,
! [SV112: $i,SV72: $i,SV16: $i] :
( ( ~ ( subset @ SV16 @ SV72 )
| ( subset @ ( set_intersection2 @ SV16 @ SV112 ) @ ( set_intersection2 @ SV72 @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(772,plain,
! [SV17: $i,SV73: $i] :
( ( ( ~ ( relation @ SV73 ) )
= $true )
| ( ( subset @ ( relation_inverse_image @ SV73 @ SV17 ) @ ( relation_dom @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[714]) ).
thf(773,plain,
! [SV18: $i,SV74: $i] :
( ( ~ ( ( SV74
!= ( powerset @ SV18 ) )
| ! [SY255: $i] :
~ ( ~ ( ~ ( in @ SY255 @ SV74 )
| ( subset @ SY255 @ SV18 ) )
| ~ ( ~ ( subset @ SY255 @ SV18 )
| ( in @ SY255 @ SV74 ) ) ) )
| ~ ( ~ ! [SY256: $i] :
~ ( ~ ( ~ ( in @ SY256 @ SV74 )
| ( subset @ SY256 @ SV18 ) )
| ~ ( ~ ( subset @ SY256 @ SV18 )
| ( in @ SY256 @ SV74 ) ) )
| ( SV74
= ( powerset @ SV18 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[715]) ).
thf(774,plain,
! [SV19: $i,SV75: $i] :
( ( ( ~ ( relation @ SV75 ) )
= $true )
| ( ( subset @ ( relation_image @ SV75 @ SV19 ) @ ( relation_rng @ SV75 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[716]) ).
thf(775,plain,
! [SV76: $i,SV20: $i] :
( ( ( ~ ( subset @ SV20 @ SV76 ) )
= $true )
| ( ( SV76
= ( set_union2 @ SV20 @ ( set_difference @ SV76 @ SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[717]) ).
thf(776,plain,
! [SV77: $i,SV21: $i] :
( ( ~ ( ~ ( subset @ SV21 @ SV77 )
| ! [SY257: $i] :
( ~ ( in @ SY257 @ SV21 )
| ( in @ SY257 @ SV77 ) ) )
| ~ ( ~ ! [SY258: $i] :
( ~ ( in @ SY258 @ SV21 )
| ( in @ SY258 @ SV77 ) )
| ( subset @ SV21 @ SV77 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[718]) ).
thf(777,plain,
! [SV78: $i,SV22: $i,SV113: $i] :
( ( ~ ( relation @ SV113 )
| ~ ( subset @ SV22 @ SV78 )
| ( subset @ ( relation_inverse_image @ SV113 @ SV22 ) @ ( relation_inverse_image @ SV113 @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(778,plain,
! [SV23: $i] :
( ( ( empty @ SV23 )
= $false )
| ( ( finite @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[720]) ).
thf(779,plain,
! [SV24: $i,SV79: $i] :
( ( ( ~ ( relation @ SV79 ) )
= $true )
| ( ( subset @ ( relation_dom_restriction @ SV79 @ SV24 ) @ SV79 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[721]) ).
thf(780,plain,
! [SV25: $i] :
( ( ( finite @ SV25 )
= $false )
| ( ( ! [SY186: $i] :
( ~ ( element @ SY186 @ ( powerset @ SV25 ) )
| ( finite @ SY186 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[722]) ).
thf(781,plain,
! [SV80: $i,SV26: $i,SV114: $i] :
( ( ! [SY275: $i] :
( ~ ( relation_of2_as_subset @ SY275 @ SV114 @ SV26 )
| ~ ( subset @ ( relation_rng @ SY275 ) @ SV80 )
| ( relation_of2_as_subset @ SY275 @ SV114 @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(782,plain,
! [SV81: $i,SV27: $i] :
( ( ( ~ ( in @ SV27 @ SV81 ) )
= $true )
| ( ( subset @ SV27 @ ( union @ SV81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[724]) ).
thf(783,plain,
! [SV115: $i,SV82: $i,SV28: $i] :
( ( ~ ~ ( ~ ( subset @ SV28 @ SV82 )
| ~ ( disjoint @ SV82 @ SV115 ) )
| ( disjoint @ SV28 @ SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(784,plain,
! [SV29: $i] :
( ( ( ! [SY193: $i] :
( ~ ( in @ SY193 @ SV29 )
| ~ ( ~ ( ordinal @ SY193 )
| ~ ( subset @ SY193 @ SV29 ) ) ) )
= $false )
| ( ( ordinal @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[726]) ).
thf(785,plain,
! [SV83: $i,SV30: $i,SV116: $i] :
( ( ! [SY276: $i] :
( ~ ( relation_of2_as_subset @ SY276 @ SV116 @ SV30 )
| ~ ( subset @ SV30 @ SV83 )
| ( relation_of2_as_subset @ SY276 @ SV116 @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(786,plain,
! [SV84: $i,SV31: $i] :
( ( ~ ( ~ ( subset @ ( singleton @ SV31 ) @ SV84 )
| ( in @ SV31 @ SV84 ) )
| ~ ( ~ ( in @ SV31 @ SV84 )
| ( subset @ ( singleton @ SV31 ) @ SV84 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[728]) ).
thf(787,plain,
! [SV32: $i,SV85: $i] :
( ( ( ~ ( relation @ SV85 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV32 @ SV85 ) ) @ ( relation_rng @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[729]) ).
thf(788,plain,
! [SV86: $i,SV33: $i,SV117: $i] :
( ( ~ ( ~ ( ~ ( relation_of2 @ SV117 @ SV33 @ SV86 )
| ( subset @ SV117 @ ( cartesian_product2 @ SV33 @ SV86 ) ) )
| ~ ( ~ ( subset @ SV117 @ ( cartesian_product2 @ SV33 @ SV86 ) )
| ( relation_of2 @ SV117 @ SV33 @ SV86 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(789,plain,
! [SV87: $i,SV34: $i] :
( ( ~ ( ( SV34 != SV87 )
| ~ ( ~ ( subset @ SV34 @ SV87 )
| ~ ( subset @ SV87 @ SV34 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV34 @ SV87 )
| ~ ( subset @ SV87 @ SV34 ) )
| ( SV34 = SV87 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[731]) ).
thf(790,plain,
! [SV35: $i,SV88: $i] :
( ( ( ~ ( relation @ SV88 ) )
= $true )
| ( ( subset @ ( relation_dom @ ( relation_rng_restriction @ SV35 @ SV88 ) ) @ ( relation_dom @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[732]) ).
thf(791,plain,
! [SV118: $i,SV89: $i,SV36: $i] :
( ( ~ ~ ( ~ ( subset @ SV36 @ SV89 )
| ~ ( subset @ SV89 @ SV118 ) )
| ( subset @ SV36 @ SV118 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(792,plain,
! [SV119: $i,SV90: $i,SV37: $i] :
( ( ~ ( subset @ SV37 @ SV90 )
| ~ ( ~ ( subset @ ( cartesian_product2 @ SV37 @ SV119 ) @ ( cartesian_product2 @ SV90 @ SV119 ) )
| ~ ( subset @ ( cartesian_product2 @ SV119 @ SV37 ) @ ( cartesian_product2 @ SV119 @ SV90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(793,plain,
! [SV120: $i,SV91: $i,SV38: $i] :
( ( ~ ( subset @ SV38 @ SV91 )
| ( subset @ ( set_difference @ SV38 @ SV120 ) @ ( set_difference @ SV91 @ SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(794,plain,
! [SV92: $i,SV39: $i] :
( ( ( ~ ( subset @ SV39 @ SV92 ) )
= $true )
| ( ( ( set_intersection2 @ SV39 @ SV92 )
= SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[736]) ).
thf(795,plain,
! [SV40: $i,SV93: $i] :
( ( ( ~ ( relation @ SV93 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_dom_restriction @ SV93 @ SV40 ) ) @ ( relation_rng @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[737]) ).
thf(796,plain,
! [SV41: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV41 @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SY277: $i,SY278: $i] :
( ~ ~ ( ~ ( in @ SY277 @ ( sK4_SY211 @ SV41 ) )
| ~ ( subset @ SY278 @ SY277 ) )
| ( in @ SY278 @ ( sK4_SY211 @ SV41 ) ) ) )
| ~ ! [SY279: $i] :
~ ~ ( ~ ( in @ SY279 @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SY280: $i] :
~ ~ ( ~ ( in @ SY280 @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY279 )
| ( in @ SX4 @ SY280 ) ) ) ) )
| ~ ! [SY282: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY282 @ ( sK4_SY211 @ SV41 ) )
| ~ ~ ( are_equipotent @ SY282 @ ( sK4_SY211 @ SV41 ) ) )
| ~ ~ ( in @ SY282 @ ( sK4_SY211 @ SV41 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[738]) ).
thf(797,plain,
! [SV121: $i,SV94: $i,SV42: $i] :
( ( ! [SY283: $i] :
( ~ ~ ( ~ ( subset @ SV42 @ SV94 )
| ~ ( subset @ SV121 @ SY283 ) )
| ( subset @ ( cartesian_product2 @ SV42 @ SV121 ) @ ( cartesian_product2 @ SV94 @ SY283 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(798,plain,
! [SV43: $i] :
( ( ( relation @ SV43 )
= $false )
| ( ( ! [SY221: $i] :
( ~ ( relation @ SY221 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV43 @ SY221 ) ) @ ( relation_dom @ SV43 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[740]) ).
thf(799,plain,
! [SV95: $i,SV44: $i] :
( ( ~ ( ~ ( element @ SV44 @ ( powerset @ SV95 ) )
| ( subset @ SV44 @ SV95 ) )
| ~ ( ~ ( subset @ SV44 @ SV95 )
| ( element @ SV44 @ ( powerset @ SV95 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[741]) ).
thf(800,plain,
! [SV122: $i,SV96: $i,SV45: $i] :
( ( ~ ( subset @ SV45 @ SV96 )
| ( in @ SV122 @ SV45 )
| ( subset @ SV45 @ ( set_difference @ SV96 @ ( singleton @ SV122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(801,plain,
! [SV46: $i] :
( ( ( relation @ SV46 )
= $false )
| ( ( ! [SY225: $i] :
( ~ ( relation @ SY225 )
| ~ ( subset @ SV46 @ SY225 )
| ~ ( ~ ( subset @ ( relation_dom @ SV46 ) @ ( relation_dom @ SY225 ) )
| ~ ( subset @ ( relation_rng @ SV46 ) @ ( relation_rng @ SY225 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[743]) ).
thf(802,plain,
! [SV47: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV47 @ ( sK5_SY226 @ SV47 ) )
| ~ ! [SY284: $i,SY285: $i] :
( ~ ~ ( ~ ( in @ SY284 @ ( sK5_SY226 @ SV47 ) )
| ~ ( subset @ SY285 @ SY284 ) )
| ( in @ SY285 @ ( sK5_SY226 @ SV47 ) ) ) )
| ~ ! [SY286: $i] :
( ~ ( in @ SY286 @ ( sK5_SY226 @ SV47 ) )
| ( in @ ( powerset @ SY286 ) @ ( sK5_SY226 @ SV47 ) ) ) )
| ~ ! [SY287: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY287 @ ( sK5_SY226 @ SV47 ) )
| ~ ~ ( are_equipotent @ SY287 @ ( sK5_SY226 @ SV47 ) ) )
| ~ ~ ( in @ SY287 @ ( sK5_SY226 @ SV47 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[744]) ).
thf(803,plain,
! [SV97: $i,SV48: $i] :
( ( ~ ( ~ ( proper_subset @ SV48 @ SV97 )
| ~ ( ~ ( subset @ SV48 @ SV97 )
| ~ ( ( SV48 != SV97 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV48 @ SV97 )
| ~ ( ( SV48 != SV97 ) ) )
| ( proper_subset @ SV48 @ SV97 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[745]) ).
thf(804,plain,
! [SV49: $i,SV98: $i] :
( ( ( ~ ( relation @ SV98 ) )
= $true )
| ( ( subset @ ( relation_rng_restriction @ SV49 @ SV98 ) @ SV98 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[746]) ).
thf(805,plain,
! [SV99: $i,SV50: $i,SV123: $i] :
( ( ~ ( relation @ SV123 )
| ( subset @ ( fiber @ ( relation_restriction @ SV123 @ SV50 ) @ SV99 ) @ ( fiber @ SV123 @ SV99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(806,plain,
! [SV100: $i,SV51: $i] :
( ( ( ~ ( subset @ SV51 @ SV100 ) )
= $true )
| ( ( ( set_union2 @ SV51 @ SV100 )
= SV100 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[748]) ).
thf(807,plain,
! [SV124: $i,SV101: $i,SV52: $i] :
( ( ~ ( ~ ( ~ ( subset @ ( unordered_pair @ SV52 @ SV101 ) @ SV124 )
| ~ ( ~ ( in @ SV52 @ SV124 )
| ~ ( in @ SV101 @ SV124 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV52 @ SV124 )
| ~ ( in @ SV101 @ SV124 ) )
| ( subset @ ( unordered_pair @ SV52 @ SV101 ) @ SV124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(808,plain,
! [SV53: $i,SV102: $i] :
( ( ( ~ ( relation @ SV102 ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( relation_field @ ( relation_restriction @ SV102 @ SV53 ) ) @ ( relation_field @ SV102 ) )
| ~ ( subset @ ( relation_field @ ( relation_restriction @ SV102 @ SV53 ) ) @ SV53 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[750]) ).
thf(809,plain,
! [SV54: $i,SV103: $i] :
( ( ( ~ ( relation @ SV103 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV54 @ SV103 ) ) @ SV54 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[751]) ).
thf(810,plain,
( ( ~ ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( finite @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[752]) ).
thf(811,plain,
! [SV104: $i,SV55: $i] :
( ( ~ ( ~ ( subset @ ( singleton @ SV55 ) @ SV104 )
| ( in @ SV55 @ SV104 ) )
| ~ ( ~ ( in @ SV55 @ SV104 )
| ( subset @ ( singleton @ SV55 ) @ SV104 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[753]) ).
thf(812,plain,
! [SV105: $i,SV56: $i] :
( ( ( ~ ( in @ SV56 @ SV105 ) )
= $true )
| ( ( subset @ SV56 @ ( union @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[754]) ).
thf(813,plain,
! [SV106: $i,SV57: $i] :
( ( ~ ( ~ ( subset @ SV57 @ SV106 )
| ~ ( proper_subset @ SV106 @ SV57 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[755]) ).
thf(814,plain,
! [SV58: $i] :
( ( ( relation @ SV58 )
= $false )
| ( ( ! [SY243: $i] :
( ~ ( relation @ SY243 )
| ~ ( ~ ( ~ ( subset @ SV58 @ SY243 )
| ! [SY244: $i,SY245: $i] :
( ~ ( in @ ( ordered_pair @ SY244 @ SY245 ) @ SV58 )
| ( in @ ( ordered_pair @ SY244 @ SY245 ) @ SY243 ) ) )
| ~ ( ~ ! [SY246: $i,SY247: $i] :
( ~ ( in @ ( ordered_pair @ SY246 @ SY247 ) @ SV58 )
| ( in @ ( ordered_pair @ SY246 @ SY247 ) @ SY243 ) )
| ( subset @ SV58 @ SY243 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[756]) ).
thf(815,plain,
! [SV125: $i,SV107: $i,SV59: $i] :
( ( ~ ~ ( ~ ( subset @ SV59 @ SV107 )
| ~ ( subset @ SV125 @ SV107 ) )
| ( subset @ ( set_union2 @ SV59 @ SV125 ) @ SV107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(816,plain,
! [SV108: $i,SV60: $i] :
( ( ~ ( ( ( set_difference @ SV60 @ SV108 )
!= empty_set )
| ( subset @ SV60 @ SV108 ) )
| ~ ( ~ ( subset @ SV60 @ SV108 )
| ( ( set_difference @ SV60 @ SV108 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[758]) ).
thf(817,plain,
! [SV109: $i,SV61: $i] :
( ( ~ ( ( ( set_difference @ SV61 @ SV109 )
!= empty_set )
| ( subset @ SV61 @ SV109 ) )
| ~ ( ~ ( subset @ SV61 @ SV109 )
| ( ( set_difference @ SV61 @ SV109 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[759]) ).
thf(818,plain,
! [SV110: $i,SV66: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV6 @ SV66 )
| ~ ( subset @ SV6 @ SV110 ) ) )
= $true )
| ( ( subset @ SV6 @ ( set_intersection2 @ SV66 @ SV110 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[760]) ).
thf(819,plain,
! [SV67: $i,SV7: $i] :
( ( ~ ( ~ ( subset @ SV7 @ ( singleton @ SV67 ) )
| ( SV7 = empty_set )
| ( SV7
= ( singleton @ SV67 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[761]) ).
thf(820,plain,
! [SV67: $i,SV7: $i] :
( ( ~ ( ~ ( ( SV7 = empty_set )
| ( SV7
= ( singleton @ SV67 ) ) )
| ( subset @ SV7 @ ( singleton @ SV67 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[761]) ).
thf(821,plain,
! [SV68: $i,SV8: $i] :
( ( ~ ( ~ ( subset @ SV8 @ ( singleton @ SV68 ) )
| ( SV8 = empty_set )
| ( SV8
= ( singleton @ SV68 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[762]) ).
thf(822,plain,
! [SV68: $i,SV8: $i] :
( ( ~ ( ~ ( ( SV8 = empty_set )
| ( SV8
= ( singleton @ SV68 ) ) )
| ( subset @ SV8 @ ( singleton @ SV68 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[762]) ).
thf(823,plain,
! [SV69: $i,SV9: $i] :
( ( ( subset @ ( singleton @ SV9 ) @ ( singleton @ SV69 ) )
= $false )
| ( ( SV9 = SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[763]) ).
thf(824,plain,
! [SV10: $i,SV126: $i] :
( ( ( ~ ( relation @ SV126 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV10 @ SV126 ) ) @ ( relation_rng @ SV126 ) ) )
= $true )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(825,plain,
! [SV70: $i,SV11: $i] :
( ( ( ~ ( ~ ( ordinal @ SV11 )
| ~ ( ordinal @ SV70 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( ordinal_subset @ SV11 @ SV70 )
| ( subset @ SV11 @ SV70 ) )
| ~ ( ~ ( subset @ SV11 @ SV70 )
| ( ordinal_subset @ SV11 @ SV70 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[765]) ).
thf(826,plain,
! [SV71: $i,SV12: $i,SV111: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV111 @ SV12 @ SV71 ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( relation_dom @ SV111 ) @ SV12 )
| ~ ( subset @ ( relation_rng @ SV111 ) @ SV71 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[766]) ).
thf(827,plain,
! [SV13: $i] :
( ( ( empty @ SV13 )
= $true )
| ( ( ~ ! [SY169: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY169 @ ( powerset @ SV13 ) )
| ~ ~ ( empty @ SY169 ) )
| ~ ( finite @ SY169 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[767]) ).
thf(828,plain,
! [SV15: $i] :
( ( ~ ( epsilon_transitive @ SV15 )
| ! [SY170: $i] :
( ~ ( in @ SY170 @ SV15 )
| ( subset @ SY170 @ SV15 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[769]) ).
thf(829,plain,
! [SV15: $i] :
( ( ~ ! [SY171: $i] :
( ~ ( in @ SY171 @ SV15 )
| ( subset @ SY171 @ SV15 ) )
| ( epsilon_transitive @ SV15 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[770]) ).
thf(830,plain,
! [SV112: $i,SV72: $i,SV16: $i] :
( ( ( ~ ( subset @ SV16 @ SV72 ) )
= $true )
| ( ( subset @ ( set_intersection2 @ SV16 @ SV112 ) @ ( set_intersection2 @ SV72 @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[771]) ).
thf(831,plain,
! [SV17: $i,SV73: $i] :
( ( ( relation @ SV73 )
= $false )
| ( ( subset @ ( relation_inverse_image @ SV73 @ SV17 ) @ ( relation_dom @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[772]) ).
thf(832,plain,
! [SV18: $i,SV74: $i] :
( ( ~ ( ( SV74
!= ( powerset @ SV18 ) )
| ! [SY255: $i] :
~ ( ~ ( ~ ( in @ SY255 @ SV74 )
| ( subset @ SY255 @ SV18 ) )
| ~ ( ~ ( subset @ SY255 @ SV18 )
| ( in @ SY255 @ SV74 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[773]) ).
thf(833,plain,
! [SV18: $i,SV74: $i] :
( ( ~ ( ~ ! [SY256: $i] :
~ ( ~ ( ~ ( in @ SY256 @ SV74 )
| ( subset @ SY256 @ SV18 ) )
| ~ ( ~ ( subset @ SY256 @ SV18 )
| ( in @ SY256 @ SV74 ) ) )
| ( SV74
= ( powerset @ SV18 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[773]) ).
thf(834,plain,
! [SV19: $i,SV75: $i] :
( ( ( relation @ SV75 )
= $false )
| ( ( subset @ ( relation_image @ SV75 @ SV19 ) @ ( relation_rng @ SV75 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[774]) ).
thf(835,plain,
! [SV76: $i,SV20: $i] :
( ( ( subset @ SV20 @ SV76 )
= $false )
| ( ( SV76
= ( set_union2 @ SV20 @ ( set_difference @ SV76 @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[775]) ).
thf(836,plain,
! [SV77: $i,SV21: $i] :
( ( ~ ( ~ ( subset @ SV21 @ SV77 )
| ! [SY257: $i] :
( ~ ( in @ SY257 @ SV21 )
| ( in @ SY257 @ SV77 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[776]) ).
thf(837,plain,
! [SV77: $i,SV21: $i] :
( ( ~ ( ~ ! [SY258: $i] :
( ~ ( in @ SY258 @ SV21 )
| ( in @ SY258 @ SV77 ) )
| ( subset @ SV21 @ SV77 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[776]) ).
thf(838,plain,
! [SV78: $i,SV22: $i,SV113: $i] :
( ( ( ~ ( relation @ SV113 ) )
= $true )
| ( ( ~ ( subset @ SV22 @ SV78 )
| ( subset @ ( relation_inverse_image @ SV113 @ SV22 ) @ ( relation_inverse_image @ SV113 @ SV78 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[777]) ).
thf(839,plain,
! [SV24: $i,SV79: $i] :
( ( ( relation @ SV79 )
= $false )
| ( ( subset @ ( relation_dom_restriction @ SV79 @ SV24 ) @ SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[779]) ).
thf(840,plain,
! [SV25: $i,SV127: $i] :
( ( ( ~ ( element @ SV127 @ ( powerset @ SV25 ) )
| ( finite @ SV127 ) )
= $true )
| ( ( finite @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[780]) ).
thf(841,plain,
! [SV80: $i,SV26: $i,SV114: $i,SV128: $i] :
( ( ~ ( relation_of2_as_subset @ SV128 @ SV114 @ SV26 )
| ~ ( subset @ ( relation_rng @ SV128 ) @ SV80 )
| ( relation_of2_as_subset @ SV128 @ SV114 @ SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(842,plain,
! [SV81: $i,SV27: $i] :
( ( ( in @ SV27 @ SV81 )
= $false )
| ( ( subset @ SV27 @ ( union @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[782]) ).
thf(843,plain,
! [SV115: $i,SV82: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV28 @ SV82 )
| ~ ( disjoint @ SV82 @ SV115 ) ) )
= $true )
| ( ( disjoint @ SV28 @ SV115 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[783]) ).
thf(844,plain,
! [SV29: $i] :
( ( ( ~ ( in @ ( sK6_SY193 @ SV29 ) @ SV29 )
| ~ ( ~ ( ordinal @ ( sK6_SY193 @ SV29 ) )
| ~ ( subset @ ( sK6_SY193 @ SV29 ) @ SV29 ) ) )
= $false )
| ( ( ordinal @ SV29 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[784]) ).
thf(845,plain,
! [SV83: $i,SV30: $i,SV116: $i,SV129: $i] :
( ( ~ ( relation_of2_as_subset @ SV129 @ SV116 @ SV30 )
| ~ ( subset @ SV30 @ SV83 )
| ( relation_of2_as_subset @ SV129 @ SV116 @ SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(846,plain,
! [SV84: $i,SV31: $i] :
( ( ~ ( ~ ( subset @ ( singleton @ SV31 ) @ SV84 )
| ( in @ SV31 @ SV84 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[786]) ).
thf(847,plain,
! [SV84: $i,SV31: $i] :
( ( ~ ( ~ ( in @ SV31 @ SV84 )
| ( subset @ ( singleton @ SV31 ) @ SV84 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[786]) ).
thf(848,plain,
! [SV32: $i,SV85: $i] :
( ( ( relation @ SV85 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV32 @ SV85 ) ) @ ( relation_rng @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[787]) ).
thf(849,plain,
! [SV86: $i,SV33: $i,SV117: $i] :
( ( ~ ( ~ ( relation_of2 @ SV117 @ SV33 @ SV86 )
| ( subset @ SV117 @ ( cartesian_product2 @ SV33 @ SV86 ) ) )
| ~ ( ~ ( subset @ SV117 @ ( cartesian_product2 @ SV33 @ SV86 ) )
| ( relation_of2 @ SV117 @ SV33 @ SV86 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[788]) ).
thf(850,plain,
! [SV87: $i,SV34: $i] :
( ( ~ ( ( SV34 != SV87 )
| ~ ( ~ ( subset @ SV34 @ SV87 )
| ~ ( subset @ SV87 @ SV34 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[789]) ).
thf(851,plain,
! [SV87: $i,SV34: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV34 @ SV87 )
| ~ ( subset @ SV87 @ SV34 ) )
| ( SV34 = SV87 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[789]) ).
thf(852,plain,
! [SV35: $i,SV88: $i] :
( ( ( relation @ SV88 )
= $false )
| ( ( subset @ ( relation_dom @ ( relation_rng_restriction @ SV35 @ SV88 ) ) @ ( relation_dom @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[790]) ).
thf(853,plain,
! [SV118: $i,SV89: $i,SV36: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV36 @ SV89 )
| ~ ( subset @ SV89 @ SV118 ) ) )
= $true )
| ( ( subset @ SV36 @ SV118 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[791]) ).
thf(854,plain,
! [SV119: $i,SV90: $i,SV37: $i] :
( ( ( ~ ( subset @ SV37 @ SV90 ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( cartesian_product2 @ SV37 @ SV119 ) @ ( cartesian_product2 @ SV90 @ SV119 ) )
| ~ ( subset @ ( cartesian_product2 @ SV119 @ SV37 ) @ ( cartesian_product2 @ SV119 @ SV90 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[792]) ).
thf(855,plain,
! [SV120: $i,SV91: $i,SV38: $i] :
( ( ( ~ ( subset @ SV38 @ SV91 ) )
= $true )
| ( ( subset @ ( set_difference @ SV38 @ SV120 ) @ ( set_difference @ SV91 @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[793]) ).
thf(856,plain,
! [SV92: $i,SV39: $i] :
( ( ( subset @ SV39 @ SV92 )
= $false )
| ( ( ( set_intersection2 @ SV39 @ SV92 )
= SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[794]) ).
thf(857,plain,
! [SV40: $i,SV93: $i] :
( ( ( relation @ SV93 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_dom_restriction @ SV93 @ SV40 ) ) @ ( relation_rng @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[795]) ).
thf(858,plain,
! [SV41: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV41 @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SY277: $i,SY278: $i] :
( ~ ~ ( ~ ( in @ SY277 @ ( sK4_SY211 @ SV41 ) )
| ~ ( subset @ SY278 @ SY277 ) )
| ( in @ SY278 @ ( sK4_SY211 @ SV41 ) ) ) )
| ~ ! [SY279: $i] :
~ ~ ( ~ ( in @ SY279 @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SY280: $i] :
~ ~ ( ~ ( in @ SY280 @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY279 )
| ( in @ SX4 @ SY280 ) ) ) ) )
| ~ ! [SY282: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY282 @ ( sK4_SY211 @ SV41 ) )
| ~ ~ ( are_equipotent @ SY282 @ ( sK4_SY211 @ SV41 ) ) )
| ~ ~ ( in @ SY282 @ ( sK4_SY211 @ SV41 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[796]) ).
thf(859,plain,
! [SV130: $i,SV121: $i,SV94: $i,SV42: $i] :
( ( ~ ~ ( ~ ( subset @ SV42 @ SV94 )
| ~ ( subset @ SV121 @ SV130 ) )
| ( subset @ ( cartesian_product2 @ SV42 @ SV121 ) @ ( cartesian_product2 @ SV94 @ SV130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(860,plain,
! [SV43: $i,SV131: $i] :
( ( ( ~ ( relation @ SV131 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV43 @ SV131 ) ) @ ( relation_dom @ SV43 ) ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(861,plain,
! [SV95: $i,SV44: $i] :
( ( ~ ( ~ ( element @ SV44 @ ( powerset @ SV95 ) )
| ( subset @ SV44 @ SV95 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[799]) ).
thf(862,plain,
! [SV95: $i,SV44: $i] :
( ( ~ ( ~ ( subset @ SV44 @ SV95 )
| ( element @ SV44 @ ( powerset @ SV95 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[799]) ).
thf(863,plain,
! [SV122: $i,SV96: $i,SV45: $i] :
( ( ( ~ ( subset @ SV45 @ SV96 ) )
= $true )
| ( ( ( in @ SV122 @ SV45 )
| ( subset @ SV45 @ ( set_difference @ SV96 @ ( singleton @ SV122 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[800]) ).
thf(864,plain,
! [SV46: $i,SV132: $i] :
( ( ( ~ ( relation @ SV132 )
| ~ ( subset @ SV46 @ SV132 )
| ~ ( ~ ( subset @ ( relation_dom @ SV46 ) @ ( relation_dom @ SV132 ) )
| ~ ( subset @ ( relation_rng @ SV46 ) @ ( relation_rng @ SV132 ) ) ) )
= $true )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(865,plain,
! [SV47: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV47 @ ( sK5_SY226 @ SV47 ) )
| ~ ! [SY284: $i,SY285: $i] :
( ~ ~ ( ~ ( in @ SY284 @ ( sK5_SY226 @ SV47 ) )
| ~ ( subset @ SY285 @ SY284 ) )
| ( in @ SY285 @ ( sK5_SY226 @ SV47 ) ) ) )
| ~ ! [SY286: $i] :
( ~ ( in @ SY286 @ ( sK5_SY226 @ SV47 ) )
| ( in @ ( powerset @ SY286 ) @ ( sK5_SY226 @ SV47 ) ) ) )
| ~ ! [SY287: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY287 @ ( sK5_SY226 @ SV47 ) )
| ~ ~ ( are_equipotent @ SY287 @ ( sK5_SY226 @ SV47 ) ) )
| ~ ~ ( in @ SY287 @ ( sK5_SY226 @ SV47 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[802]) ).
thf(866,plain,
! [SV97: $i,SV48: $i] :
( ( ~ ( ~ ( proper_subset @ SV48 @ SV97 )
| ~ ( ~ ( subset @ SV48 @ SV97 )
| ~ ( ( SV48 != SV97 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[803]) ).
thf(867,plain,
! [SV97: $i,SV48: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV48 @ SV97 )
| ~ ( ( SV48 != SV97 ) ) )
| ( proper_subset @ SV48 @ SV97 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[803]) ).
thf(868,plain,
! [SV49: $i,SV98: $i] :
( ( ( relation @ SV98 )
= $false )
| ( ( subset @ ( relation_rng_restriction @ SV49 @ SV98 ) @ SV98 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[804]) ).
thf(869,plain,
! [SV99: $i,SV50: $i,SV123: $i] :
( ( ( ~ ( relation @ SV123 ) )
= $true )
| ( ( subset @ ( fiber @ ( relation_restriction @ SV123 @ SV50 ) @ SV99 ) @ ( fiber @ SV123 @ SV99 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[805]) ).
thf(870,plain,
! [SV100: $i,SV51: $i] :
( ( ( subset @ SV51 @ SV100 )
= $false )
| ( ( ( set_union2 @ SV51 @ SV100 )
= SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[806]) ).
thf(871,plain,
! [SV124: $i,SV101: $i,SV52: $i] :
( ( ~ ( ~ ( subset @ ( unordered_pair @ SV52 @ SV101 ) @ SV124 )
| ~ ( ~ ( in @ SV52 @ SV124 )
| ~ ( in @ SV101 @ SV124 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV52 @ SV124 )
| ~ ( in @ SV101 @ SV124 ) )
| ( subset @ ( unordered_pair @ SV52 @ SV101 ) @ SV124 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[807]) ).
thf(872,plain,
! [SV53: $i,SV102: $i] :
( ( ( relation @ SV102 )
= $false )
| ( ( ~ ( ~ ( subset @ ( relation_field @ ( relation_restriction @ SV102 @ SV53 ) ) @ ( relation_field @ SV102 ) )
| ~ ( subset @ ( relation_field @ ( relation_restriction @ SV102 @ SV53 ) ) @ SV53 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[808]) ).
thf(873,plain,
! [SV54: $i,SV103: $i] :
( ( ( relation @ SV103 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV54 @ SV103 ) ) @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[809]) ).
thf(874,plain,
( ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( finite @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[810]) ).
thf(875,plain,
! [SV104: $i,SV55: $i] :
( ( ~ ( ~ ( subset @ ( singleton @ SV55 ) @ SV104 )
| ( in @ SV55 @ SV104 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[811]) ).
thf(876,plain,
! [SV104: $i,SV55: $i] :
( ( ~ ( ~ ( in @ SV55 @ SV104 )
| ( subset @ ( singleton @ SV55 ) @ SV104 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[811]) ).
thf(877,plain,
! [SV105: $i,SV56: $i] :
( ( ( in @ SV56 @ SV105 )
= $false )
| ( ( subset @ SV56 @ ( union @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[812]) ).
thf(878,plain,
! [SV106: $i,SV57: $i] :
( ( ~ ( subset @ SV57 @ SV106 )
| ~ ( proper_subset @ SV106 @ SV57 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[813]) ).
thf(879,plain,
! [SV58: $i,SV133: $i] :
( ( ( ~ ( relation @ SV133 )
| ~ ( ~ ( ~ ( subset @ SV58 @ SV133 )
| ! [SY288: $i,SY289: $i] :
( ~ ( in @ ( ordered_pair @ SY288 @ SY289 ) @ SV58 )
| ( in @ ( ordered_pair @ SY288 @ SY289 ) @ SV133 ) ) )
| ~ ( ~ ! [SY290: $i,SY291: $i] :
( ~ ( in @ ( ordered_pair @ SY290 @ SY291 ) @ SV58 )
| ( in @ ( ordered_pair @ SY290 @ SY291 ) @ SV133 ) )
| ( subset @ SV58 @ SV133 ) ) ) )
= $true )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(880,plain,
! [SV125: $i,SV107: $i,SV59: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV59 @ SV107 )
| ~ ( subset @ SV125 @ SV107 ) ) )
= $true )
| ( ( subset @ ( set_union2 @ SV59 @ SV125 ) @ SV107 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[815]) ).
thf(881,plain,
! [SV108: $i,SV60: $i] :
( ( ~ ( ( ( set_difference @ SV60 @ SV108 )
!= empty_set )
| ( subset @ SV60 @ SV108 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[816]) ).
thf(882,plain,
! [SV108: $i,SV60: $i] :
( ( ~ ( ~ ( subset @ SV60 @ SV108 )
| ( ( set_difference @ SV60 @ SV108 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[816]) ).
thf(883,plain,
! [SV109: $i,SV61: $i] :
( ( ~ ( ( ( set_difference @ SV61 @ SV109 )
!= empty_set )
| ( subset @ SV61 @ SV109 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[817]) ).
thf(884,plain,
! [SV109: $i,SV61: $i] :
( ( ~ ( ~ ( subset @ SV61 @ SV109 )
| ( ( set_difference @ SV61 @ SV109 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[817]) ).
thf(885,plain,
! [SV110: $i,SV66: $i,SV6: $i] :
( ( ( ~ ( ~ ( subset @ SV6 @ SV66 )
| ~ ( subset @ SV6 @ SV110 ) ) )
= $false )
| ( ( subset @ SV6 @ ( set_intersection2 @ SV66 @ SV110 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[818]) ).
thf(886,plain,
! [SV67: $i,SV7: $i] :
( ( ~ ( subset @ SV7 @ ( singleton @ SV67 ) )
| ( SV7 = empty_set )
| ( SV7
= ( singleton @ SV67 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[819]) ).
thf(887,plain,
! [SV67: $i,SV7: $i] :
( ( ~ ( ( SV7 = empty_set )
| ( SV7
= ( singleton @ SV67 ) ) )
| ( subset @ SV7 @ ( singleton @ SV67 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[820]) ).
thf(888,plain,
! [SV68: $i,SV8: $i] :
( ( ~ ( subset @ SV8 @ ( singleton @ SV68 ) )
| ( SV8 = empty_set )
| ( SV8
= ( singleton @ SV68 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[821]) ).
thf(889,plain,
! [SV68: $i,SV8: $i] :
( ( ~ ( ( SV8 = empty_set )
| ( SV8
= ( singleton @ SV68 ) ) )
| ( subset @ SV8 @ ( singleton @ SV68 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[822]) ).
thf(890,plain,
! [SV10: $i,SV126: $i] :
( ( ( ~ ( relation @ SV126 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV10 @ SV126 ) ) @ ( relation_rng @ SV126 ) )
= $true )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[824]) ).
thf(891,plain,
! [SV70: $i,SV11: $i] :
( ( ( ~ ( ordinal @ SV11 )
| ~ ( ordinal @ SV70 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ordinal_subset @ SV11 @ SV70 )
| ( subset @ SV11 @ SV70 ) )
| ~ ( ~ ( subset @ SV11 @ SV70 )
| ( ordinal_subset @ SV11 @ SV70 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[825]) ).
thf(892,plain,
! [SV71: $i,SV12: $i,SV111: $i] :
( ( ( relation_of2_as_subset @ SV111 @ SV12 @ SV71 )
= $false )
| ( ( ~ ( ~ ( subset @ ( relation_dom @ SV111 ) @ SV12 )
| ~ ( subset @ ( relation_rng @ SV111 ) @ SV71 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[826]) ).
thf(893,plain,
! [SV13: $i] :
( ( ( ! [SY169: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY169 @ ( powerset @ SV13 ) )
| ~ ~ ( empty @ SY169 ) )
| ~ ( finite @ SY169 ) ) )
= $false )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[827]) ).
thf(894,plain,
! [SV15: $i] :
( ( ( ~ ( epsilon_transitive @ SV15 ) )
= $true )
| ( ( ! [SY170: $i] :
( ~ ( in @ SY170 @ SV15 )
| ( subset @ SY170 @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[828]) ).
thf(895,plain,
! [SV15: $i] :
( ( ( ~ ! [SY171: $i] :
( ~ ( in @ SY171 @ SV15 )
| ( subset @ SY171 @ SV15 ) ) )
= $true )
| ( ( epsilon_transitive @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[829]) ).
thf(896,plain,
! [SV112: $i,SV72: $i,SV16: $i] :
( ( ( subset @ SV16 @ SV72 )
= $false )
| ( ( subset @ ( set_intersection2 @ SV16 @ SV112 ) @ ( set_intersection2 @ SV72 @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[830]) ).
thf(897,plain,
! [SV18: $i,SV74: $i] :
( ( ( SV74
!= ( powerset @ SV18 ) )
| ! [SY255: $i] :
~ ( ~ ( ~ ( in @ SY255 @ SV74 )
| ( subset @ SY255 @ SV18 ) )
| ~ ( ~ ( subset @ SY255 @ SV18 )
| ( in @ SY255 @ SV74 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[832]) ).
thf(898,plain,
! [SV18: $i,SV74: $i] :
( ( ~ ! [SY256: $i] :
~ ( ~ ( ~ ( in @ SY256 @ SV74 )
| ( subset @ SY256 @ SV18 ) )
| ~ ( ~ ( subset @ SY256 @ SV18 )
| ( in @ SY256 @ SV74 ) ) )
| ( SV74
= ( powerset @ SV18 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[833]) ).
thf(899,plain,
! [SV77: $i,SV21: $i] :
( ( ~ ( subset @ SV21 @ SV77 )
| ! [SY257: $i] :
( ~ ( in @ SY257 @ SV21 )
| ( in @ SY257 @ SV77 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[836]) ).
thf(900,plain,
! [SV77: $i,SV21: $i] :
( ( ~ ! [SY258: $i] :
( ~ ( in @ SY258 @ SV21 )
| ( in @ SY258 @ SV77 ) )
| ( subset @ SV21 @ SV77 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[837]) ).
thf(901,plain,
! [SV78: $i,SV22: $i,SV113: $i] :
( ( ( relation @ SV113 )
= $false )
| ( ( ~ ( subset @ SV22 @ SV78 )
| ( subset @ ( relation_inverse_image @ SV113 @ SV22 ) @ ( relation_inverse_image @ SV113 @ SV78 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[838]) ).
thf(902,plain,
! [SV25: $i,SV127: $i] :
( ( ( ~ ( element @ SV127 @ ( powerset @ SV25 ) ) )
= $true )
| ( ( finite @ SV127 )
= $true )
| ( ( finite @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[840]) ).
thf(903,plain,
! [SV80: $i,SV26: $i,SV114: $i,SV128: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV128 @ SV114 @ SV26 ) )
= $true )
| ( ( ~ ( subset @ ( relation_rng @ SV128 ) @ SV80 )
| ( relation_of2_as_subset @ SV128 @ SV114 @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[841]) ).
thf(904,plain,
! [SV115: $i,SV82: $i,SV28: $i] :
( ( ( ~ ( ~ ( subset @ SV28 @ SV82 )
| ~ ( disjoint @ SV82 @ SV115 ) ) )
= $false )
| ( ( disjoint @ SV28 @ SV115 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[843]) ).
thf(905,plain,
! [SV29: $i] :
( ( ( ~ ( in @ ( sK6_SY193 @ SV29 ) @ SV29 ) )
= $false )
| ( ( ordinal @ SV29 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[844]) ).
thf(906,plain,
! [SV29: $i] :
( ( ( ~ ( ~ ( ordinal @ ( sK6_SY193 @ SV29 ) )
| ~ ( subset @ ( sK6_SY193 @ SV29 ) @ SV29 ) ) )
= $false )
| ( ( ordinal @ SV29 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[844]) ).
thf(907,plain,
! [SV83: $i,SV30: $i,SV116: $i,SV129: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV129 @ SV116 @ SV30 ) )
= $true )
| ( ( ~ ( subset @ SV30 @ SV83 )
| ( relation_of2_as_subset @ SV129 @ SV116 @ SV83 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[845]) ).
thf(908,plain,
! [SV84: $i,SV31: $i] :
( ( ~ ( subset @ ( singleton @ SV31 ) @ SV84 )
| ( in @ SV31 @ SV84 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[846]) ).
thf(909,plain,
! [SV84: $i,SV31: $i] :
( ( ~ ( in @ SV31 @ SV84 )
| ( subset @ ( singleton @ SV31 ) @ SV84 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[847]) ).
thf(910,plain,
! [SV86: $i,SV33: $i,SV117: $i] :
( ( ~ ( ~ ( relation_of2 @ SV117 @ SV33 @ SV86 )
| ( subset @ SV117 @ ( cartesian_product2 @ SV33 @ SV86 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[849]) ).
thf(911,plain,
! [SV86: $i,SV33: $i,SV117: $i] :
( ( ~ ( ~ ( subset @ SV117 @ ( cartesian_product2 @ SV33 @ SV86 ) )
| ( relation_of2 @ SV117 @ SV33 @ SV86 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[849]) ).
thf(912,plain,
! [SV87: $i,SV34: $i] :
( ( ( SV34 != SV87 )
| ~ ( ~ ( subset @ SV34 @ SV87 )
| ~ ( subset @ SV87 @ SV34 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[850]) ).
thf(913,plain,
! [SV87: $i,SV34: $i] :
( ( ~ ~ ( ~ ( subset @ SV34 @ SV87 )
| ~ ( subset @ SV87 @ SV34 ) )
| ( SV34 = SV87 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[851]) ).
thf(914,plain,
! [SV118: $i,SV89: $i,SV36: $i] :
( ( ( ~ ( ~ ( subset @ SV36 @ SV89 )
| ~ ( subset @ SV89 @ SV118 ) ) )
= $false )
| ( ( subset @ SV36 @ SV118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[853]) ).
thf(915,plain,
! [SV119: $i,SV90: $i,SV37: $i] :
( ( ( subset @ SV37 @ SV90 )
= $false )
| ( ( ~ ( ~ ( subset @ ( cartesian_product2 @ SV37 @ SV119 ) @ ( cartesian_product2 @ SV90 @ SV119 ) )
| ~ ( subset @ ( cartesian_product2 @ SV119 @ SV37 ) @ ( cartesian_product2 @ SV119 @ SV90 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[854]) ).
thf(916,plain,
! [SV120: $i,SV91: $i,SV38: $i] :
( ( ( subset @ SV38 @ SV91 )
= $false )
| ( ( subset @ ( set_difference @ SV38 @ SV120 ) @ ( set_difference @ SV91 @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[855]) ).
thf(917,plain,
! [SV41: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( in @ SV41 @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SY277: $i,SY278: $i] :
( ~ ~ ( ~ ( in @ SY277 @ ( sK4_SY211 @ SV41 ) )
| ~ ( subset @ SY278 @ SY277 ) )
| ( in @ SY278 @ ( sK4_SY211 @ SV41 ) ) ) )
| ~ ! [SY279: $i] :
~ ~ ( ~ ( in @ SY279 @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SY280: $i] :
~ ~ ( ~ ( in @ SY280 @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY279 )
| ( in @ SX4 @ SY280 ) ) ) ) )
| ~ ! [SY282: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY282 @ ( sK4_SY211 @ SV41 ) )
| ~ ~ ( are_equipotent @ SY282 @ ( sK4_SY211 @ SV41 ) ) )
| ~ ~ ( in @ SY282 @ ( sK4_SY211 @ SV41 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[858]) ).
thf(918,plain,
! [SV130: $i,SV121: $i,SV94: $i,SV42: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV42 @ SV94 )
| ~ ( subset @ SV121 @ SV130 ) ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV42 @ SV121 ) @ ( cartesian_product2 @ SV94 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[859]) ).
thf(919,plain,
! [SV43: $i,SV131: $i] :
( ( ( ~ ( relation @ SV131 ) )
= $true )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV43 @ SV131 ) ) @ ( relation_dom @ SV43 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[860]) ).
thf(920,plain,
! [SV95: $i,SV44: $i] :
( ( ~ ( element @ SV44 @ ( powerset @ SV95 ) )
| ( subset @ SV44 @ SV95 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[861]) ).
thf(921,plain,
! [SV95: $i,SV44: $i] :
( ( ~ ( subset @ SV44 @ SV95 )
| ( element @ SV44 @ ( powerset @ SV95 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[862]) ).
thf(922,plain,
! [SV122: $i,SV96: $i,SV45: $i] :
( ( ( subset @ SV45 @ SV96 )
= $false )
| ( ( ( in @ SV122 @ SV45 )
| ( subset @ SV45 @ ( set_difference @ SV96 @ ( singleton @ SV122 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[863]) ).
thf(923,plain,
! [SV46: $i,SV132: $i] :
( ( ( ~ ( relation @ SV132 ) )
= $true )
| ( ( ~ ( subset @ SV46 @ SV132 )
| ~ ( ~ ( subset @ ( relation_dom @ SV46 ) @ ( relation_dom @ SV132 ) )
| ~ ( subset @ ( relation_rng @ SV46 ) @ ( relation_rng @ SV132 ) ) ) )
= $true )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[864]) ).
thf(924,plain,
! [SV47: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( in @ SV47 @ ( sK5_SY226 @ SV47 ) )
| ~ ! [SY284: $i,SY285: $i] :
( ~ ~ ( ~ ( in @ SY284 @ ( sK5_SY226 @ SV47 ) )
| ~ ( subset @ SY285 @ SY284 ) )
| ( in @ SY285 @ ( sK5_SY226 @ SV47 ) ) ) )
| ~ ! [SY286: $i] :
( ~ ( in @ SY286 @ ( sK5_SY226 @ SV47 ) )
| ( in @ ( powerset @ SY286 ) @ ( sK5_SY226 @ SV47 ) ) ) )
| ~ ! [SY287: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY287 @ ( sK5_SY226 @ SV47 ) )
| ~ ~ ( are_equipotent @ SY287 @ ( sK5_SY226 @ SV47 ) ) )
| ~ ~ ( in @ SY287 @ ( sK5_SY226 @ SV47 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[865]) ).
thf(925,plain,
! [SV97: $i,SV48: $i] :
( ( ~ ( proper_subset @ SV48 @ SV97 )
| ~ ( ~ ( subset @ SV48 @ SV97 )
| ~ ( ( SV48 != SV97 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[866]) ).
thf(926,plain,
! [SV97: $i,SV48: $i] :
( ( ~ ~ ( ~ ( subset @ SV48 @ SV97 )
| ~ ( ( SV48 != SV97 ) ) )
| ( proper_subset @ SV48 @ SV97 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[867]) ).
thf(927,plain,
! [SV99: $i,SV50: $i,SV123: $i] :
( ( ( relation @ SV123 )
= $false )
| ( ( subset @ ( fiber @ ( relation_restriction @ SV123 @ SV50 ) @ SV99 ) @ ( fiber @ SV123 @ SV99 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[869]) ).
thf(928,plain,
! [SV124: $i,SV101: $i,SV52: $i] :
( ( ~ ( ~ ( subset @ ( unordered_pair @ SV52 @ SV101 ) @ SV124 )
| ~ ( ~ ( in @ SV52 @ SV124 )
| ~ ( in @ SV101 @ SV124 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[871]) ).
thf(929,plain,
! [SV101: $i,SV124: $i,SV52: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV52 @ SV124 )
| ~ ( in @ SV101 @ SV124 ) )
| ( subset @ ( unordered_pair @ SV52 @ SV101 ) @ SV124 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[871]) ).
thf(930,plain,
! [SV53: $i,SV102: $i] :
( ( ( ~ ( subset @ ( relation_field @ ( relation_restriction @ SV102 @ SV53 ) ) @ ( relation_field @ SV102 ) )
| ~ ( subset @ ( relation_field @ ( relation_restriction @ SV102 @ SV53 ) ) @ SV53 ) )
= $false )
| ( ( relation @ SV102 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[872]) ).
thf(931,plain,
( ( ~ ~ ( empty @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[874]) ).
thf(932,plain,
( ( ~ ( finite @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[874]) ).
thf(933,plain,
! [SV104: $i,SV55: $i] :
( ( ~ ( subset @ ( singleton @ SV55 ) @ SV104 )
| ( in @ SV55 @ SV104 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[875]) ).
thf(934,plain,
! [SV104: $i,SV55: $i] :
( ( ~ ( in @ SV55 @ SV104 )
| ( subset @ ( singleton @ SV55 ) @ SV104 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[876]) ).
thf(935,plain,
! [SV106: $i,SV57: $i] :
( ( ( ~ ( subset @ SV57 @ SV106 ) )
= $true )
| ( ( ~ ( proper_subset @ SV106 @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[878]) ).
thf(936,plain,
! [SV58: $i,SV133: $i] :
( ( ( ~ ( relation @ SV133 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( subset @ SV58 @ SV133 )
| ! [SY288: $i,SY289: $i] :
( ~ ( in @ ( ordered_pair @ SY288 @ SY289 ) @ SV58 )
| ( in @ ( ordered_pair @ SY288 @ SY289 ) @ SV133 ) ) )
| ~ ( ~ ! [SY290: $i,SY291: $i] :
( ~ ( in @ ( ordered_pair @ SY290 @ SY291 ) @ SV58 )
| ( in @ ( ordered_pair @ SY290 @ SY291 ) @ SV133 ) )
| ( subset @ SV58 @ SV133 ) ) ) )
= $true )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[879]) ).
thf(937,plain,
! [SV125: $i,SV107: $i,SV59: $i] :
( ( ( ~ ( ~ ( subset @ SV59 @ SV107 )
| ~ ( subset @ SV125 @ SV107 ) ) )
= $false )
| ( ( subset @ ( set_union2 @ SV59 @ SV125 ) @ SV107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[880]) ).
thf(938,plain,
! [SV108: $i,SV60: $i] :
( ( ( ( set_difference @ SV60 @ SV108 )
!= empty_set )
| ( subset @ SV60 @ SV108 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[881]) ).
thf(939,plain,
! [SV108: $i,SV60: $i] :
( ( ~ ( subset @ SV60 @ SV108 )
| ( ( set_difference @ SV60 @ SV108 )
= empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[882]) ).
thf(940,plain,
! [SV109: $i,SV61: $i] :
( ( ( ( set_difference @ SV61 @ SV109 )
!= empty_set )
| ( subset @ SV61 @ SV109 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[883]) ).
thf(941,plain,
! [SV109: $i,SV61: $i] :
( ( ~ ( subset @ SV61 @ SV109 )
| ( ( set_difference @ SV61 @ SV109 )
= empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[884]) ).
thf(942,plain,
! [SV110: $i,SV66: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ SV66 )
| ~ ( subset @ SV6 @ SV110 ) )
= $true )
| ( ( subset @ SV6 @ ( set_intersection2 @ SV66 @ SV110 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[885]) ).
thf(943,plain,
! [SV67: $i,SV7: $i] :
( ( ( ~ ( subset @ SV7 @ ( singleton @ SV67 ) ) )
= $true )
| ( ( ( SV7 = empty_set )
| ( SV7
= ( singleton @ SV67 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[886]) ).
thf(944,plain,
! [SV67: $i,SV7: $i] :
( ( ( ~ ( ( SV7 = empty_set )
| ( SV7
= ( singleton @ SV67 ) ) ) )
= $true )
| ( ( subset @ SV7 @ ( singleton @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[887]) ).
thf(945,plain,
! [SV68: $i,SV8: $i] :
( ( ( ~ ( subset @ SV8 @ ( singleton @ SV68 ) ) )
= $true )
| ( ( ( SV8 = empty_set )
| ( SV8
= ( singleton @ SV68 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[888]) ).
thf(946,plain,
! [SV68: $i,SV8: $i] :
( ( ( ~ ( ( SV8 = empty_set )
| ( SV8
= ( singleton @ SV68 ) ) ) )
= $true )
| ( ( subset @ SV8 @ ( singleton @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[889]) ).
thf(947,plain,
! [SV10: $i,SV126: $i] :
( ( ( relation @ SV126 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV10 @ SV126 ) ) @ ( relation_rng @ SV126 ) )
= $true )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[890]) ).
thf(948,plain,
! [SV70: $i,SV11: $i] :
( ( ( ~ ( ordinal @ SV11 ) )
= $true )
| ( ( ~ ( ordinal @ SV70 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ordinal_subset @ SV11 @ SV70 )
| ( subset @ SV11 @ SV70 ) )
| ~ ( ~ ( subset @ SV11 @ SV70 )
| ( ordinal_subset @ SV11 @ SV70 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[891]) ).
thf(949,plain,
! [SV71: $i,SV12: $i,SV111: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV111 ) @ SV12 )
| ~ ( subset @ ( relation_rng @ SV111 ) @ SV71 ) )
= $false )
| ( ( relation_of2_as_subset @ SV111 @ SV12 @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[892]) ).
thf(950,plain,
! [SV13: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK7_SY169 @ SV13 ) @ ( powerset @ SV13 ) )
| ~ ~ ( empty @ ( sK7_SY169 @ SV13 ) ) )
| ~ ( finite @ ( sK7_SY169 @ SV13 ) ) ) )
= $false )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[893]) ).
thf(951,plain,
! [SV15: $i] :
( ( ( epsilon_transitive @ SV15 )
= $false )
| ( ( ! [SY170: $i] :
( ~ ( in @ SY170 @ SV15 )
| ( subset @ SY170 @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[894]) ).
thf(952,plain,
! [SV15: $i] :
( ( ( ! [SY171: $i] :
( ~ ( in @ SY171 @ SV15 )
| ( subset @ SY171 @ SV15 ) ) )
= $false )
| ( ( epsilon_transitive @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[895]) ).
thf(953,plain,
! [SV18: $i,SV74: $i] :
( ( ( SV74
!= ( powerset @ SV18 ) )
= $true )
| ( ( ! [SY255: $i] :
~ ( ~ ( ~ ( in @ SY255 @ SV74 )
| ( subset @ SY255 @ SV18 ) )
| ~ ( ~ ( subset @ SY255 @ SV18 )
| ( in @ SY255 @ SV74 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[897]) ).
thf(954,plain,
! [SV18: $i,SV74: $i] :
( ( ( ~ ! [SY256: $i] :
~ ( ~ ( ~ ( in @ SY256 @ SV74 )
| ( subset @ SY256 @ SV18 ) )
| ~ ( ~ ( subset @ SY256 @ SV18 )
| ( in @ SY256 @ SV74 ) ) ) )
= $true )
| ( ( SV74
= ( powerset @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[898]) ).
thf(955,plain,
! [SV77: $i,SV21: $i] :
( ( ( ~ ( subset @ SV21 @ SV77 ) )
= $true )
| ( ( ! [SY257: $i] :
( ~ ( in @ SY257 @ SV21 )
| ( in @ SY257 @ SV77 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[899]) ).
thf(956,plain,
! [SV77: $i,SV21: $i] :
( ( ( ~ ! [SY258: $i] :
( ~ ( in @ SY258 @ SV21 )
| ( in @ SY258 @ SV77 ) ) )
= $true )
| ( ( subset @ SV21 @ SV77 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[900]) ).
thf(957,plain,
! [SV113: $i,SV78: $i,SV22: $i] :
( ( ( ~ ( subset @ SV22 @ SV78 ) )
= $true )
| ( ( subset @ ( relation_inverse_image @ SV113 @ SV22 ) @ ( relation_inverse_image @ SV113 @ SV78 ) )
= $true )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[901]) ).
thf(958,plain,
! [SV25: $i,SV127: $i] :
( ( ( element @ SV127 @ ( powerset @ SV25 ) )
= $false )
| ( ( finite @ SV127 )
= $true )
| ( ( finite @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(959,plain,
! [SV80: $i,SV26: $i,SV114: $i,SV128: $i] :
( ( ( relation_of2_as_subset @ SV128 @ SV114 @ SV26 )
= $false )
| ( ( ~ ( subset @ ( relation_rng @ SV128 ) @ SV80 )
| ( relation_of2_as_subset @ SV128 @ SV114 @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[903]) ).
thf(960,plain,
! [SV115: $i,SV82: $i,SV28: $i] :
( ( ( ~ ( subset @ SV28 @ SV82 )
| ~ ( disjoint @ SV82 @ SV115 ) )
= $true )
| ( ( disjoint @ SV28 @ SV115 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[904]) ).
thf(961,plain,
! [SV29: $i] :
( ( ( in @ ( sK6_SY193 @ SV29 ) @ SV29 )
= $true )
| ( ( ordinal @ SV29 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[905]) ).
thf(962,plain,
! [SV29: $i] :
( ( ( ~ ( ordinal @ ( sK6_SY193 @ SV29 ) )
| ~ ( subset @ ( sK6_SY193 @ SV29 ) @ SV29 ) )
= $true )
| ( ( ordinal @ SV29 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[906]) ).
thf(963,plain,
! [SV83: $i,SV30: $i,SV116: $i,SV129: $i] :
( ( ( relation_of2_as_subset @ SV129 @ SV116 @ SV30 )
= $false )
| ( ( ~ ( subset @ SV30 @ SV83 )
| ( relation_of2_as_subset @ SV129 @ SV116 @ SV83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[907]) ).
thf(964,plain,
! [SV84: $i,SV31: $i] :
( ( ( ~ ( subset @ ( singleton @ SV31 ) @ SV84 ) )
= $true )
| ( ( in @ SV31 @ SV84 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[908]) ).
thf(965,plain,
! [SV84: $i,SV31: $i] :
( ( ( ~ ( in @ SV31 @ SV84 ) )
= $true )
| ( ( subset @ ( singleton @ SV31 ) @ SV84 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[909]) ).
thf(966,plain,
! [SV86: $i,SV33: $i,SV117: $i] :
( ( ~ ( relation_of2 @ SV117 @ SV33 @ SV86 )
| ( subset @ SV117 @ ( cartesian_product2 @ SV33 @ SV86 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[910]) ).
thf(967,plain,
! [SV86: $i,SV33: $i,SV117: $i] :
( ( ~ ( subset @ SV117 @ ( cartesian_product2 @ SV33 @ SV86 ) )
| ( relation_of2 @ SV117 @ SV33 @ SV86 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[911]) ).
thf(968,plain,
! [SV87: $i,SV34: $i] :
( ( ( SV34 != SV87 )
= $true )
| ( ( ~ ( ~ ( subset @ SV34 @ SV87 )
| ~ ( subset @ SV87 @ SV34 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[912]) ).
thf(969,plain,
! [SV87: $i,SV34: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV34 @ SV87 )
| ~ ( subset @ SV87 @ SV34 ) ) )
= $true )
| ( ( SV34 = SV87 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[913]) ).
thf(970,plain,
! [SV118: $i,SV89: $i,SV36: $i] :
( ( ( ~ ( subset @ SV36 @ SV89 )
| ~ ( subset @ SV89 @ SV118 ) )
= $true )
| ( ( subset @ SV36 @ SV118 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[914]) ).
thf(971,plain,
! [SV90: $i,SV119: $i,SV37: $i] :
( ( ( ~ ( subset @ ( cartesian_product2 @ SV37 @ SV119 ) @ ( cartesian_product2 @ SV90 @ SV119 ) )
| ~ ( subset @ ( cartesian_product2 @ SV119 @ SV37 ) @ ( cartesian_product2 @ SV119 @ SV90 ) ) )
= $false )
| ( ( subset @ SV37 @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[915]) ).
thf(972,plain,
! [SV41: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( in @ SV41 @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SY277: $i,SY278: $i] :
( ~ ~ ( ~ ( in @ SY277 @ ( sK4_SY211 @ SV41 ) )
| ~ ( subset @ SY278 @ SY277 ) )
| ( in @ SY278 @ ( sK4_SY211 @ SV41 ) ) ) )
| ~ ! [SY279: $i] :
~ ~ ( ~ ( in @ SY279 @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SY280: $i] :
~ ~ ( ~ ( in @ SY280 @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY279 )
| ( in @ SX4 @ SY280 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[917]) ).
thf(973,plain,
! [SV41: $i] :
( ( ~ ! [SY282: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY282 @ ( sK4_SY211 @ SV41 ) )
| ~ ~ ( are_equipotent @ SY282 @ ( sK4_SY211 @ SV41 ) ) )
| ~ ~ ( in @ SY282 @ ( sK4_SY211 @ SV41 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[917]) ).
thf(974,plain,
! [SV130: $i,SV121: $i,SV94: $i,SV42: $i] :
( ( ( ~ ( ~ ( subset @ SV42 @ SV94 )
| ~ ( subset @ SV121 @ SV130 ) ) )
= $false )
| ( ( subset @ ( cartesian_product2 @ SV42 @ SV121 ) @ ( cartesian_product2 @ SV94 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[918]) ).
thf(975,plain,
! [SV43: $i,SV131: $i] :
( ( ( relation @ SV131 )
= $false )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV43 @ SV131 ) ) @ ( relation_dom @ SV43 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[919]) ).
thf(976,plain,
! [SV95: $i,SV44: $i] :
( ( ( ~ ( element @ SV44 @ ( powerset @ SV95 ) ) )
= $true )
| ( ( subset @ SV44 @ SV95 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[920]) ).
thf(977,plain,
! [SV95: $i,SV44: $i] :
( ( ( ~ ( subset @ SV44 @ SV95 ) )
= $true )
| ( ( element @ SV44 @ ( powerset @ SV95 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[921]) ).
thf(978,plain,
! [SV96: $i,SV45: $i,SV122: $i] :
( ( ( in @ SV122 @ SV45 )
= $true )
| ( ( subset @ SV45 @ ( set_difference @ SV96 @ ( singleton @ SV122 ) ) )
= $true )
| ( ( subset @ SV45 @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[922]) ).
thf(979,plain,
! [SV46: $i,SV132: $i] :
( ( ( relation @ SV132 )
= $false )
| ( ( ~ ( subset @ SV46 @ SV132 )
| ~ ( ~ ( subset @ ( relation_dom @ SV46 ) @ ( relation_dom @ SV132 ) )
| ~ ( subset @ ( relation_rng @ SV46 ) @ ( relation_rng @ SV132 ) ) ) )
= $true )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[923]) ).
thf(980,plain,
! [SV47: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( in @ SV47 @ ( sK5_SY226 @ SV47 ) )
| ~ ! [SY284: $i,SY285: $i] :
( ~ ~ ( ~ ( in @ SY284 @ ( sK5_SY226 @ SV47 ) )
| ~ ( subset @ SY285 @ SY284 ) )
| ( in @ SY285 @ ( sK5_SY226 @ SV47 ) ) ) )
| ~ ! [SY286: $i] :
( ~ ( in @ SY286 @ ( sK5_SY226 @ SV47 ) )
| ( in @ ( powerset @ SY286 ) @ ( sK5_SY226 @ SV47 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[924]) ).
thf(981,plain,
! [SV47: $i] :
( ( ~ ! [SY287: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY287 @ ( sK5_SY226 @ SV47 ) )
| ~ ~ ( are_equipotent @ SY287 @ ( sK5_SY226 @ SV47 ) ) )
| ~ ~ ( in @ SY287 @ ( sK5_SY226 @ SV47 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[924]) ).
thf(982,plain,
! [SV97: $i,SV48: $i] :
( ( ( ~ ( proper_subset @ SV48 @ SV97 ) )
= $true )
| ( ( ~ ( ~ ( subset @ SV48 @ SV97 )
| ~ ( ( SV48 != SV97 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[925]) ).
thf(983,plain,
! [SV97: $i,SV48: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV48 @ SV97 )
| ~ ( ( SV48 != SV97 ) ) ) )
= $true )
| ( ( proper_subset @ SV48 @ SV97 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[926]) ).
thf(984,plain,
! [SV124: $i,SV101: $i,SV52: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV52 @ SV101 ) @ SV124 )
| ~ ( ~ ( in @ SV52 @ SV124 )
| ~ ( in @ SV101 @ SV124 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[928]) ).
thf(985,plain,
! [SV101: $i,SV124: $i,SV52: $i] :
( ( ~ ~ ( ~ ( in @ SV52 @ SV124 )
| ~ ( in @ SV101 @ SV124 ) )
| ( subset @ ( unordered_pair @ SV52 @ SV101 ) @ SV124 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[929]) ).
thf(986,plain,
! [SV53: $i,SV102: $i] :
( ( ( ~ ( subset @ ( relation_field @ ( relation_restriction @ SV102 @ SV53 ) ) @ ( relation_field @ SV102 ) ) )
= $false )
| ( ( relation @ SV102 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[930]) ).
thf(987,plain,
! [SV53: $i,SV102: $i] :
( ( ( ~ ( subset @ ( relation_field @ ( relation_restriction @ SV102 @ SV53 ) ) @ SV53 ) )
= $false )
| ( ( relation @ SV102 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[930]) ).
thf(988,plain,
( ( ~ ( empty @ sK3_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[931]) ).
thf(989,plain,
( ( finite @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[932]) ).
thf(990,plain,
! [SV104: $i,SV55: $i] :
( ( ( ~ ( subset @ ( singleton @ SV55 ) @ SV104 ) )
= $true )
| ( ( in @ SV55 @ SV104 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[933]) ).
thf(991,plain,
! [SV104: $i,SV55: $i] :
( ( ( ~ ( in @ SV55 @ SV104 ) )
= $true )
| ( ( subset @ ( singleton @ SV55 ) @ SV104 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[934]) ).
thf(992,plain,
! [SV106: $i,SV57: $i] :
( ( ( subset @ SV57 @ SV106 )
= $false )
| ( ( ~ ( proper_subset @ SV106 @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[935]) ).
thf(993,plain,
! [SV58: $i,SV133: $i] :
( ( ( relation @ SV133 )
= $false )
| ( ( ~ ( ~ ( ~ ( subset @ SV58 @ SV133 )
| ! [SY288: $i,SY289: $i] :
( ~ ( in @ ( ordered_pair @ SY288 @ SY289 ) @ SV58 )
| ( in @ ( ordered_pair @ SY288 @ SY289 ) @ SV133 ) ) )
| ~ ( ~ ! [SY290: $i,SY291: $i] :
( ~ ( in @ ( ordered_pair @ SY290 @ SY291 ) @ SV58 )
| ( in @ ( ordered_pair @ SY290 @ SY291 ) @ SV133 ) )
| ( subset @ SV58 @ SV133 ) ) ) )
= $true )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[936]) ).
thf(994,plain,
! [SV125: $i,SV107: $i,SV59: $i] :
( ( ( ~ ( subset @ SV59 @ SV107 )
| ~ ( subset @ SV125 @ SV107 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV59 @ SV125 ) @ SV107 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[937]) ).
thf(995,plain,
! [SV108: $i,SV60: $i] :
( ( ( ( set_difference @ SV60 @ SV108 )
!= empty_set )
= $true )
| ( ( subset @ SV60 @ SV108 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[938]) ).
thf(996,plain,
! [SV108: $i,SV60: $i] :
( ( ( ~ ( subset @ SV60 @ SV108 ) )
= $true )
| ( ( ( set_difference @ SV60 @ SV108 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[939]) ).
thf(997,plain,
! [SV109: $i,SV61: $i] :
( ( ( ( set_difference @ SV61 @ SV109 )
!= empty_set )
= $true )
| ( ( subset @ SV61 @ SV109 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[940]) ).
thf(998,plain,
! [SV109: $i,SV61: $i] :
( ( ( ~ ( subset @ SV61 @ SV109 ) )
= $true )
| ( ( ( set_difference @ SV61 @ SV109 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[941]) ).
thf(999,plain,
! [SV110: $i,SV66: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ SV66 ) )
= $true )
| ( ( ~ ( subset @ SV6 @ SV110 ) )
= $true )
| ( ( subset @ SV6 @ ( set_intersection2 @ SV66 @ SV110 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[942]) ).
thf(1000,plain,
! [SV67: $i,SV7: $i] :
( ( ( subset @ SV7 @ ( singleton @ SV67 ) )
= $false )
| ( ( ( SV7 = empty_set )
| ( SV7
= ( singleton @ SV67 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[943]) ).
thf(1001,plain,
! [SV67: $i,SV7: $i] :
( ( ( ( SV7 = empty_set )
| ( SV7
= ( singleton @ SV67 ) ) )
= $false )
| ( ( subset @ SV7 @ ( singleton @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[944]) ).
thf(1002,plain,
! [SV68: $i,SV8: $i] :
( ( ( subset @ SV8 @ ( singleton @ SV68 ) )
= $false )
| ( ( ( SV8 = empty_set )
| ( SV8
= ( singleton @ SV68 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[945]) ).
thf(1003,plain,
! [SV68: $i,SV8: $i] :
( ( ( ( SV8 = empty_set )
| ( SV8
= ( singleton @ SV68 ) ) )
= $false )
| ( ( subset @ SV8 @ ( singleton @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[946]) ).
thf(1004,plain,
! [SV70: $i,SV11: $i] :
( ( ( ordinal @ SV11 )
= $false )
| ( ( ~ ( ordinal @ SV70 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ordinal_subset @ SV11 @ SV70 )
| ( subset @ SV11 @ SV70 ) )
| ~ ( ~ ( subset @ SV11 @ SV70 )
| ( ordinal_subset @ SV11 @ SV70 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[948]) ).
thf(1005,plain,
! [SV71: $i,SV12: $i,SV111: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV111 ) @ SV12 ) )
= $false )
| ( ( relation_of2_as_subset @ SV111 @ SV12 @ SV71 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[949]) ).
thf(1006,plain,
! [SV12: $i,SV71: $i,SV111: $i] :
( ( ( ~ ( subset @ ( relation_rng @ SV111 ) @ SV71 ) )
= $false )
| ( ( relation_of2_as_subset @ SV111 @ SV12 @ SV71 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[949]) ).
thf(1007,plain,
! [SV13: $i] :
( ( ( ~ ( ~ ~ ( ~ ( element @ ( sK7_SY169 @ SV13 ) @ ( powerset @ SV13 ) )
| ~ ~ ( empty @ ( sK7_SY169 @ SV13 ) ) )
| ~ ( finite @ ( sK7_SY169 @ SV13 ) ) ) )
= $true )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[950]) ).
thf(1008,plain,
! [SV15: $i,SV134: $i] :
( ( ( ~ ( in @ SV134 @ SV15 )
| ( subset @ SV134 @ SV15 ) )
= $true )
| ( ( epsilon_transitive @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(1009,plain,
! [SV15: $i] :
( ( ( ~ ( in @ ( sK8_SY171 @ SV15 ) @ SV15 )
| ( subset @ ( sK8_SY171 @ SV15 ) @ SV15 ) )
= $false )
| ( ( epsilon_transitive @ SV15 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[952]) ).
thf(1010,plain,
! [SV18: $i,SV74: $i] :
( ( ( SV74
= ( powerset @ SV18 ) )
= $false )
| ( ( ! [SY255: $i] :
~ ( ~ ( ~ ( in @ SY255 @ SV74 )
| ( subset @ SY255 @ SV18 ) )
| ~ ( ~ ( subset @ SY255 @ SV18 )
| ( in @ SY255 @ SV74 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[953]) ).
thf(1011,plain,
! [SV18: $i,SV74: $i] :
( ( ( ! [SY256: $i] :
~ ( ~ ( ~ ( in @ SY256 @ SV74 )
| ( subset @ SY256 @ SV18 ) )
| ~ ( ~ ( subset @ SY256 @ SV18 )
| ( in @ SY256 @ SV74 ) ) ) )
= $false )
| ( ( SV74
= ( powerset @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[954]) ).
thf(1012,plain,
! [SV77: $i,SV21: $i] :
( ( ( subset @ SV21 @ SV77 )
= $false )
| ( ( ! [SY257: $i] :
( ~ ( in @ SY257 @ SV21 )
| ( in @ SY257 @ SV77 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[955]) ).
thf(1013,plain,
! [SV77: $i,SV21: $i] :
( ( ( ! [SY258: $i] :
( ~ ( in @ SY258 @ SV21 )
| ( in @ SY258 @ SV77 ) ) )
= $false )
| ( ( subset @ SV21 @ SV77 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[956]) ).
thf(1014,plain,
! [SV113: $i,SV78: $i,SV22: $i] :
( ( ( subset @ SV22 @ SV78 )
= $false )
| ( ( subset @ ( relation_inverse_image @ SV113 @ SV22 ) @ ( relation_inverse_image @ SV113 @ SV78 ) )
= $true )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[957]) ).
thf(1015,plain,
! [SV26: $i,SV114: $i,SV80: $i,SV128: $i] :
( ( ( ~ ( subset @ ( relation_rng @ SV128 ) @ SV80 ) )
= $true )
| ( ( relation_of2_as_subset @ SV128 @ SV114 @ SV80 )
= $true )
| ( ( relation_of2_as_subset @ SV128 @ SV114 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[959]) ).
thf(1016,plain,
! [SV115: $i,SV82: $i,SV28: $i] :
( ( ( ~ ( subset @ SV28 @ SV82 ) )
= $true )
| ( ( ~ ( disjoint @ SV82 @ SV115 ) )
= $true )
| ( ( disjoint @ SV28 @ SV115 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[960]) ).
thf(1017,plain,
! [SV29: $i] :
( ( ( ~ ( ordinal @ ( sK6_SY193 @ SV29 ) ) )
= $true )
| ( ( ~ ( subset @ ( sK6_SY193 @ SV29 ) @ SV29 ) )
= $true )
| ( ( ordinal @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[962]) ).
thf(1018,plain,
! [SV116: $i,SV129: $i,SV83: $i,SV30: $i] :
( ( ( ~ ( subset @ SV30 @ SV83 ) )
= $true )
| ( ( relation_of2_as_subset @ SV129 @ SV116 @ SV83 )
= $true )
| ( ( relation_of2_as_subset @ SV129 @ SV116 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[963]) ).
thf(1019,plain,
! [SV84: $i,SV31: $i] :
( ( ( subset @ ( singleton @ SV31 ) @ SV84 )
= $false )
| ( ( in @ SV31 @ SV84 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[964]) ).
thf(1020,plain,
! [SV84: $i,SV31: $i] :
( ( ( in @ SV31 @ SV84 )
= $false )
| ( ( subset @ ( singleton @ SV31 ) @ SV84 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[965]) ).
thf(1021,plain,
! [SV86: $i,SV33: $i,SV117: $i] :
( ( ( ~ ( relation_of2 @ SV117 @ SV33 @ SV86 ) )
= $true )
| ( ( subset @ SV117 @ ( cartesian_product2 @ SV33 @ SV86 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[966]) ).
thf(1022,plain,
! [SV86: $i,SV33: $i,SV117: $i] :
( ( ( ~ ( subset @ SV117 @ ( cartesian_product2 @ SV33 @ SV86 ) ) )
= $true )
| ( ( relation_of2 @ SV117 @ SV33 @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[967]) ).
thf(1023,plain,
! [SV87: $i,SV34: $i] :
( ( ( SV34 = SV87 )
= $false )
| ( ( ~ ( ~ ( subset @ SV34 @ SV87 )
| ~ ( subset @ SV87 @ SV34 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[968]) ).
thf(1024,plain,
! [SV87: $i,SV34: $i] :
( ( ( ~ ( ~ ( subset @ SV34 @ SV87 )
| ~ ( subset @ SV87 @ SV34 ) ) )
= $false )
| ( ( SV34 = SV87 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[969]) ).
thf(1025,plain,
! [SV118: $i,SV89: $i,SV36: $i] :
( ( ( ~ ( subset @ SV36 @ SV89 ) )
= $true )
| ( ( ~ ( subset @ SV89 @ SV118 ) )
= $true )
| ( ( subset @ SV36 @ SV118 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[970]) ).
thf(1026,plain,
! [SV90: $i,SV119: $i,SV37: $i] :
( ( ( ~ ( subset @ ( cartesian_product2 @ SV37 @ SV119 ) @ ( cartesian_product2 @ SV90 @ SV119 ) ) )
= $false )
| ( ( subset @ SV37 @ SV90 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[971]) ).
thf(1027,plain,
! [SV90: $i,SV37: $i,SV119: $i] :
( ( ( ~ ( subset @ ( cartesian_product2 @ SV119 @ SV37 ) @ ( cartesian_product2 @ SV119 @ SV90 ) ) )
= $false )
| ( ( subset @ SV37 @ SV90 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[971]) ).
thf(1028,plain,
! [SV41: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV41 @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SY277: $i,SY278: $i] :
( ~ ~ ( ~ ( in @ SY277 @ ( sK4_SY211 @ SV41 ) )
| ~ ( subset @ SY278 @ SY277 ) )
| ( in @ SY278 @ ( sK4_SY211 @ SV41 ) ) ) )
| ~ ! [SY279: $i] :
~ ~ ( ~ ( in @ SY279 @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SY280: $i] :
~ ~ ( ~ ( in @ SY280 @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY279 )
| ( in @ SX4 @ SY280 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[972]) ).
thf(1029,plain,
! [SV41: $i] :
( ( ! [SY282: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY282 @ ( sK4_SY211 @ SV41 ) )
| ~ ~ ( are_equipotent @ SY282 @ ( sK4_SY211 @ SV41 ) ) )
| ~ ~ ( in @ SY282 @ ( sK4_SY211 @ SV41 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[973]) ).
thf(1030,plain,
! [SV130: $i,SV121: $i,SV94: $i,SV42: $i] :
( ( ( ~ ( subset @ SV42 @ SV94 )
| ~ ( subset @ SV121 @ SV130 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV42 @ SV121 ) @ ( cartesian_product2 @ SV94 @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[974]) ).
thf(1031,plain,
! [SV95: $i,SV44: $i] :
( ( ( element @ SV44 @ ( powerset @ SV95 ) )
= $false )
| ( ( subset @ SV44 @ SV95 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[976]) ).
thf(1032,plain,
! [SV95: $i,SV44: $i] :
( ( ( subset @ SV44 @ SV95 )
= $false )
| ( ( element @ SV44 @ ( powerset @ SV95 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[977]) ).
thf(1033,plain,
! [SV132: $i,SV46: $i] :
( ( ( ~ ( subset @ SV46 @ SV132 ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( relation_dom @ SV46 ) @ ( relation_dom @ SV132 ) )
| ~ ( subset @ ( relation_rng @ SV46 ) @ ( relation_rng @ SV132 ) ) ) )
= $true )
| ( ( relation @ SV132 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[979]) ).
thf(1034,plain,
! [SV47: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV47 @ ( sK5_SY226 @ SV47 ) )
| ~ ! [SY284: $i,SY285: $i] :
( ~ ~ ( ~ ( in @ SY284 @ ( sK5_SY226 @ SV47 ) )
| ~ ( subset @ SY285 @ SY284 ) )
| ( in @ SY285 @ ( sK5_SY226 @ SV47 ) ) ) )
| ~ ! [SY286: $i] :
( ~ ( in @ SY286 @ ( sK5_SY226 @ SV47 ) )
| ( in @ ( powerset @ SY286 ) @ ( sK5_SY226 @ SV47 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[980]) ).
thf(1035,plain,
! [SV47: $i] :
( ( ! [SY287: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY287 @ ( sK5_SY226 @ SV47 ) )
| ~ ~ ( are_equipotent @ SY287 @ ( sK5_SY226 @ SV47 ) ) )
| ~ ~ ( in @ SY287 @ ( sK5_SY226 @ SV47 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[981]) ).
thf(1036,plain,
! [SV97: $i,SV48: $i] :
( ( ( proper_subset @ SV48 @ SV97 )
= $false )
| ( ( ~ ( ~ ( subset @ SV48 @ SV97 )
| ~ ( ( SV48 != SV97 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(1037,plain,
! [SV97: $i,SV48: $i] :
( ( ( ~ ( ~ ( subset @ SV48 @ SV97 )
| ~ ( ( SV48 != SV97 ) ) ) )
= $false )
| ( ( proper_subset @ SV48 @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[983]) ).
thf(1038,plain,
! [SV124: $i,SV101: $i,SV52: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV52 @ SV101 ) @ SV124 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV52 @ SV124 )
| ~ ( in @ SV101 @ SV124 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[984]) ).
thf(1039,plain,
! [SV101: $i,SV124: $i,SV52: $i] :
( ( ( ~ ~ ( ~ ( in @ SV52 @ SV124 )
| ~ ( in @ SV101 @ SV124 ) ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV52 @ SV101 ) @ SV124 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[985]) ).
thf(1040,plain,
! [SV53: $i,SV102: $i] :
( ( ( subset @ ( relation_field @ ( relation_restriction @ SV102 @ SV53 ) ) @ ( relation_field @ SV102 ) )
= $true )
| ( ( relation @ SV102 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[986]) ).
thf(1041,plain,
! [SV53: $i,SV102: $i] :
( ( ( subset @ ( relation_field @ ( relation_restriction @ SV102 @ SV53 ) ) @ SV53 )
= $true )
| ( ( relation @ SV102 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[987]) ).
thf(1042,plain,
( ( empty @ sK3_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[988]) ).
thf(1043,plain,
! [SV104: $i,SV55: $i] :
( ( ( subset @ ( singleton @ SV55 ) @ SV104 )
= $false )
| ( ( in @ SV55 @ SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[990]) ).
thf(1044,plain,
! [SV104: $i,SV55: $i] :
( ( ( in @ SV55 @ SV104 )
= $false )
| ( ( subset @ ( singleton @ SV55 ) @ SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[991]) ).
thf(1045,plain,
! [SV57: $i,SV106: $i] :
( ( ( proper_subset @ SV106 @ SV57 )
= $false )
| ( ( subset @ SV57 @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[992]) ).
thf(1046,plain,
! [SV133: $i,SV58: $i] :
( ( ( ~ ( ~ ( subset @ SV58 @ SV133 )
| ! [SY288: $i,SY289: $i] :
( ~ ( in @ ( ordered_pair @ SY288 @ SY289 ) @ SV58 )
| ( in @ ( ordered_pair @ SY288 @ SY289 ) @ SV133 ) ) )
| ~ ( ~ ! [SY290: $i,SY291: $i] :
( ~ ( in @ ( ordered_pair @ SY290 @ SY291 ) @ SV58 )
| ( in @ ( ordered_pair @ SY290 @ SY291 ) @ SV133 ) )
| ( subset @ SV58 @ SV133 ) ) )
= $false )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[993]) ).
thf(1047,plain,
! [SV125: $i,SV107: $i,SV59: $i] :
( ( ( ~ ( subset @ SV59 @ SV107 ) )
= $true )
| ( ( ~ ( subset @ SV125 @ SV107 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV59 @ SV125 ) @ SV107 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[994]) ).
thf(1048,plain,
! [SV108: $i,SV60: $i] :
( ( ( ( set_difference @ SV60 @ SV108 )
= empty_set )
= $false )
| ( ( subset @ SV60 @ SV108 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[995]) ).
thf(1049,plain,
! [SV108: $i,SV60: $i] :
( ( ( subset @ SV60 @ SV108 )
= $false )
| ( ( ( set_difference @ SV60 @ SV108 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[996]) ).
thf(1050,plain,
! [SV109: $i,SV61: $i] :
( ( ( ( set_difference @ SV61 @ SV109 )
= empty_set )
= $false )
| ( ( subset @ SV61 @ SV109 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[997]) ).
thf(1051,plain,
! [SV109: $i,SV61: $i] :
( ( ( subset @ SV61 @ SV109 )
= $false )
| ( ( ( set_difference @ SV61 @ SV109 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[998]) ).
thf(1052,plain,
! [SV110: $i,SV66: $i,SV6: $i] :
( ( ( subset @ SV6 @ SV66 )
= $false )
| ( ( ~ ( subset @ SV6 @ SV110 ) )
= $true )
| ( ( subset @ SV6 @ ( set_intersection2 @ SV66 @ SV110 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[999]) ).
thf(1053,plain,
! [SV67: $i,SV7: $i] :
( ( ( SV7 = empty_set )
= $true )
| ( ( SV7
= ( singleton @ SV67 ) )
= $true )
| ( ( subset @ SV7 @ ( singleton @ SV67 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1000]) ).
thf(1054,plain,
! [SV67: $i,SV7: $i] :
( ( ( SV7 = empty_set )
= $false )
| ( ( subset @ SV7 @ ( singleton @ SV67 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1001]) ).
thf(1055,plain,
! [SV67: $i,SV7: $i] :
( ( ( SV7
= ( singleton @ SV67 ) )
= $false )
| ( ( subset @ SV7 @ ( singleton @ SV67 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1001]) ).
thf(1056,plain,
! [SV68: $i,SV8: $i] :
( ( ( SV8 = empty_set )
= $true )
| ( ( SV8
= ( singleton @ SV68 ) )
= $true )
| ( ( subset @ SV8 @ ( singleton @ SV68 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1002]) ).
thf(1057,plain,
! [SV68: $i,SV8: $i] :
( ( ( SV8 = empty_set )
= $false )
| ( ( subset @ SV8 @ ( singleton @ SV68 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1003]) ).
thf(1058,plain,
! [SV68: $i,SV8: $i] :
( ( ( SV8
= ( singleton @ SV68 ) )
= $false )
| ( ( subset @ SV8 @ ( singleton @ SV68 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1003]) ).
thf(1059,plain,
! [SV11: $i,SV70: $i] :
( ( ( ordinal @ SV70 )
= $false )
| ( ( ordinal @ SV11 )
= $false )
| ( ( ~ ( ~ ( ~ ( ordinal_subset @ SV11 @ SV70 )
| ( subset @ SV11 @ SV70 ) )
| ~ ( ~ ( subset @ SV11 @ SV70 )
| ( ordinal_subset @ SV11 @ SV70 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1004]) ).
thf(1060,plain,
! [SV71: $i,SV12: $i,SV111: $i] :
( ( ( subset @ ( relation_dom @ SV111 ) @ SV12 )
= $true )
| ( ( relation_of2_as_subset @ SV111 @ SV12 @ SV71 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1005]) ).
thf(1061,plain,
! [SV12: $i,SV71: $i,SV111: $i] :
( ( ( subset @ ( relation_rng @ SV111 ) @ SV71 )
= $true )
| ( ( relation_of2_as_subset @ SV111 @ SV12 @ SV71 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1006]) ).
thf(1062,plain,
! [SV13: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK7_SY169 @ SV13 ) @ ( powerset @ SV13 ) )
| ~ ~ ( empty @ ( sK7_SY169 @ SV13 ) ) )
| ~ ( finite @ ( sK7_SY169 @ SV13 ) ) )
= $false )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1007]) ).
thf(1063,plain,
! [SV15: $i,SV134: $i] :
( ( ( ~ ( in @ SV134 @ SV15 ) )
= $true )
| ( ( subset @ SV134 @ SV15 )
= $true )
| ( ( epsilon_transitive @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1008]) ).
thf(1064,plain,
! [SV15: $i] :
( ( ( ~ ( in @ ( sK8_SY171 @ SV15 ) @ SV15 ) )
= $false )
| ( ( epsilon_transitive @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1009]) ).
thf(1065,plain,
! [SV15: $i] :
( ( ( subset @ ( sK8_SY171 @ SV15 ) @ SV15 )
= $false )
| ( ( epsilon_transitive @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1009]) ).
thf(1066,plain,
! [SV18: $i,SV74: $i,SV135: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV135 @ SV74 )
| ( subset @ SV135 @ SV18 ) )
| ~ ( ~ ( subset @ SV135 @ SV18 )
| ( in @ SV135 @ SV74 ) ) ) )
= $true )
| ( ( SV74
= ( powerset @ SV18 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1067,plain,
! [SV74: $i,SV18: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV74 )
| ( subset @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV18 ) )
| ~ ( ~ ( subset @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV18 )
| ( in @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV74 ) ) ) )
= $false )
| ( ( SV74
= ( powerset @ SV18 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1011]) ).
thf(1068,plain,
! [SV77: $i,SV21: $i,SV136: $i] :
( ( ( ~ ( in @ SV136 @ SV21 )
| ( in @ SV136 @ SV77 ) )
= $true )
| ( ( subset @ SV21 @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1069,plain,
! [SV21: $i,SV77: $i] :
( ( ( ~ ( in @ ( sK10_SY258 @ SV77 @ SV21 ) @ SV21 )
| ( in @ ( sK10_SY258 @ SV77 @ SV21 ) @ SV77 ) )
= $false )
| ( ( subset @ SV21 @ SV77 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1013]) ).
thf(1070,plain,
! [SV26: $i,SV114: $i,SV80: $i,SV128: $i] :
( ( ( subset @ ( relation_rng @ SV128 ) @ SV80 )
= $false )
| ( ( relation_of2_as_subset @ SV128 @ SV114 @ SV80 )
= $true )
| ( ( relation_of2_as_subset @ SV128 @ SV114 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1015]) ).
thf(1071,plain,
! [SV115: $i,SV82: $i,SV28: $i] :
( ( ( subset @ SV28 @ SV82 )
= $false )
| ( ( ~ ( disjoint @ SV82 @ SV115 ) )
= $true )
| ( ( disjoint @ SV28 @ SV115 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1016]) ).
thf(1072,plain,
! [SV29: $i] :
( ( ( ordinal @ ( sK6_SY193 @ SV29 ) )
= $false )
| ( ( ~ ( subset @ ( sK6_SY193 @ SV29 ) @ SV29 ) )
= $true )
| ( ( ordinal @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1017]) ).
thf(1073,plain,
! [SV116: $i,SV129: $i,SV83: $i,SV30: $i] :
( ( ( subset @ SV30 @ SV83 )
= $false )
| ( ( relation_of2_as_subset @ SV129 @ SV116 @ SV83 )
= $true )
| ( ( relation_of2_as_subset @ SV129 @ SV116 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1018]) ).
thf(1074,plain,
! [SV86: $i,SV33: $i,SV117: $i] :
( ( ( relation_of2 @ SV117 @ SV33 @ SV86 )
= $false )
| ( ( subset @ SV117 @ ( cartesian_product2 @ SV33 @ SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1021]) ).
thf(1075,plain,
! [SV86: $i,SV33: $i,SV117: $i] :
( ( ( subset @ SV117 @ ( cartesian_product2 @ SV33 @ SV86 ) )
= $false )
| ( ( relation_of2 @ SV117 @ SV33 @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1022]) ).
thf(1076,plain,
! [SV87: $i,SV34: $i] :
( ( ( ~ ( subset @ SV34 @ SV87 )
| ~ ( subset @ SV87 @ SV34 ) )
= $false )
| ( ( SV34 = SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1023]) ).
thf(1077,plain,
! [SV87: $i,SV34: $i] :
( ( ( ~ ( subset @ SV34 @ SV87 )
| ~ ( subset @ SV87 @ SV34 ) )
= $true )
| ( ( SV34 = SV87 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1024]) ).
thf(1078,plain,
! [SV118: $i,SV89: $i,SV36: $i] :
( ( ( subset @ SV36 @ SV89 )
= $false )
| ( ( ~ ( subset @ SV89 @ SV118 ) )
= $true )
| ( ( subset @ SV36 @ SV118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1025]) ).
thf(1079,plain,
! [SV90: $i,SV119: $i,SV37: $i] :
( ( ( subset @ ( cartesian_product2 @ SV37 @ SV119 ) @ ( cartesian_product2 @ SV90 @ SV119 ) )
= $true )
| ( ( subset @ SV37 @ SV90 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1026]) ).
thf(1080,plain,
! [SV90: $i,SV37: $i,SV119: $i] :
( ( ( subset @ ( cartesian_product2 @ SV119 @ SV37 ) @ ( cartesian_product2 @ SV119 @ SV90 ) )
= $true )
| ( ( subset @ SV37 @ SV90 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1027]) ).
thf(1081,plain,
! [SV41: $i] :
( ( ~ ~ ( ~ ( in @ SV41 @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SY277: $i,SY278: $i] :
( ~ ~ ( ~ ( in @ SY277 @ ( sK4_SY211 @ SV41 ) )
| ~ ( subset @ SY278 @ SY277 ) )
| ( in @ SY278 @ ( sK4_SY211 @ SV41 ) ) ) )
| ~ ! [SY279: $i] :
~ ~ ( ~ ( in @ SY279 @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SY280: $i] :
~ ~ ( ~ ( in @ SY280 @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY279 )
| ( in @ SX4 @ SY280 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1028]) ).
thf(1082,plain,
! [SV41: $i,SV137: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( subset @ SV137 @ ( sK4_SY211 @ SV41 ) )
| ~ ~ ( are_equipotent @ SV137 @ ( sK4_SY211 @ SV41 ) ) )
| ~ ~ ( in @ SV137 @ ( sK4_SY211 @ SV41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1029]) ).
thf(1083,plain,
! [SV130: $i,SV121: $i,SV94: $i,SV42: $i] :
( ( ( ~ ( subset @ SV42 @ SV94 ) )
= $true )
| ( ( ~ ( subset @ SV121 @ SV130 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV42 @ SV121 ) @ ( cartesian_product2 @ SV94 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1030]) ).
thf(1084,plain,
! [SV132: $i,SV46: $i] :
( ( ( subset @ SV46 @ SV132 )
= $false )
| ( ( ~ ( ~ ( subset @ ( relation_dom @ SV46 ) @ ( relation_dom @ SV132 ) )
| ~ ( subset @ ( relation_rng @ SV46 ) @ ( relation_rng @ SV132 ) ) ) )
= $true )
| ( ( relation @ SV132 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1033]) ).
thf(1085,plain,
! [SV47: $i] :
( ( ~ ~ ( ~ ( in @ SV47 @ ( sK5_SY226 @ SV47 ) )
| ~ ! [SY284: $i,SY285: $i] :
( ~ ~ ( ~ ( in @ SY284 @ ( sK5_SY226 @ SV47 ) )
| ~ ( subset @ SY285 @ SY284 ) )
| ( in @ SY285 @ ( sK5_SY226 @ SV47 ) ) ) )
| ~ ! [SY286: $i] :
( ~ ( in @ SY286 @ ( sK5_SY226 @ SV47 ) )
| ( in @ ( powerset @ SY286 ) @ ( sK5_SY226 @ SV47 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1034]) ).
thf(1086,plain,
! [SV47: $i,SV138: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( subset @ SV138 @ ( sK5_SY226 @ SV47 ) )
| ~ ~ ( are_equipotent @ SV138 @ ( sK5_SY226 @ SV47 ) ) )
| ~ ~ ( in @ SV138 @ ( sK5_SY226 @ SV47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1087,plain,
! [SV97: $i,SV48: $i] :
( ( ( ~ ( subset @ SV48 @ SV97 )
| ~ ( ( SV48 != SV97 ) ) )
= $false )
| ( ( proper_subset @ SV48 @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1036]) ).
thf(1088,plain,
! [SV97: $i,SV48: $i] :
( ( ( ~ ( subset @ SV48 @ SV97 )
| ~ ( ( SV48 != SV97 ) ) )
= $true )
| ( ( proper_subset @ SV48 @ SV97 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1037]) ).
thf(1089,plain,
! [SV124: $i,SV101: $i,SV52: $i] :
( ( ( subset @ ( unordered_pair @ SV52 @ SV101 ) @ SV124 )
= $false )
| ( ( ~ ( ~ ( in @ SV52 @ SV124 )
| ~ ( in @ SV101 @ SV124 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1038]) ).
thf(1090,plain,
! [SV101: $i,SV124: $i,SV52: $i] :
( ( ( ~ ( ~ ( in @ SV52 @ SV124 )
| ~ ( in @ SV101 @ SV124 ) ) )
= $false )
| ( ( subset @ ( unordered_pair @ SV52 @ SV101 ) @ SV124 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1039]) ).
thf(1091,plain,
! [SV133: $i,SV58: $i] :
( ( ( ~ ( ~ ( subset @ SV58 @ SV133 )
| ! [SY288: $i,SY289: $i] :
( ~ ( in @ ( ordered_pair @ SY288 @ SY289 ) @ SV58 )
| ( in @ ( ordered_pair @ SY288 @ SY289 ) @ SV133 ) ) ) )
= $false )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1046]) ).
thf(1092,plain,
! [SV133: $i,SV58: $i] :
( ( ( ~ ( ~ ! [SY290: $i,SY291: $i] :
( ~ ( in @ ( ordered_pair @ SY290 @ SY291 ) @ SV58 )
| ( in @ ( ordered_pair @ SY290 @ SY291 ) @ SV133 ) )
| ( subset @ SV58 @ SV133 ) ) )
= $false )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1046]) ).
thf(1093,plain,
! [SV125: $i,SV107: $i,SV59: $i] :
( ( ( subset @ SV59 @ SV107 )
= $false )
| ( ( ~ ( subset @ SV125 @ SV107 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV59 @ SV125 ) @ SV107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1047]) ).
thf(1094,plain,
! [SV66: $i,SV110: $i,SV6: $i] :
( ( ( subset @ SV6 @ SV110 )
= $false )
| ( ( subset @ SV6 @ SV66 )
= $false )
| ( ( subset @ SV6 @ ( set_intersection2 @ SV66 @ SV110 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1052]) ).
thf(1095,plain,
! [SV70: $i,SV11: $i] :
( ( ( ~ ( ~ ( ordinal_subset @ SV11 @ SV70 )
| ( subset @ SV11 @ SV70 ) )
| ~ ( ~ ( subset @ SV11 @ SV70 )
| ( ordinal_subset @ SV11 @ SV70 ) ) )
= $false )
| ( ( ordinal @ SV11 )
= $false )
| ( ( ordinal @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1059]) ).
thf(1096,plain,
! [SV13: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK7_SY169 @ SV13 ) @ ( powerset @ SV13 ) )
| ~ ~ ( empty @ ( sK7_SY169 @ SV13 ) ) ) )
= $false )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1062]) ).
thf(1097,plain,
! [SV13: $i] :
( ( ( ~ ( finite @ ( sK7_SY169 @ SV13 ) ) )
= $false )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1062]) ).
thf(1098,plain,
! [SV15: $i,SV134: $i] :
( ( ( in @ SV134 @ SV15 )
= $false )
| ( ( subset @ SV134 @ SV15 )
= $true )
| ( ( epsilon_transitive @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1063]) ).
thf(1099,plain,
! [SV15: $i] :
( ( ( in @ ( sK8_SY171 @ SV15 ) @ SV15 )
= $true )
| ( ( epsilon_transitive @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1064]) ).
thf(1100,plain,
! [SV18: $i,SV74: $i,SV135: $i] :
( ( ( ~ ( ~ ( in @ SV135 @ SV74 )
| ( subset @ SV135 @ SV18 ) )
| ~ ( ~ ( subset @ SV135 @ SV18 )
| ( in @ SV135 @ SV74 ) ) )
= $false )
| ( ( SV74
= ( powerset @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1066]) ).
thf(1101,plain,
! [SV74: $i,SV18: $i] :
( ( ( ~ ( ~ ( in @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV74 )
| ( subset @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV18 ) )
| ~ ( ~ ( subset @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV18 )
| ( in @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV74 ) ) )
= $true )
| ( ( SV74
= ( powerset @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1067]) ).
thf(1102,plain,
! [SV77: $i,SV21: $i,SV136: $i] :
( ( ( ~ ( in @ SV136 @ SV21 ) )
= $true )
| ( ( in @ SV136 @ SV77 )
= $true )
| ( ( subset @ SV21 @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1068]) ).
thf(1103,plain,
! [SV21: $i,SV77: $i] :
( ( ( ~ ( in @ ( sK10_SY258 @ SV77 @ SV21 ) @ SV21 ) )
= $false )
| ( ( subset @ SV21 @ SV77 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1069]) ).
thf(1104,plain,
! [SV21: $i,SV77: $i] :
( ( ( in @ ( sK10_SY258 @ SV77 @ SV21 ) @ SV77 )
= $false )
| ( ( subset @ SV21 @ SV77 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1069]) ).
thf(1105,plain,
! [SV28: $i,SV115: $i,SV82: $i] :
( ( ( disjoint @ SV82 @ SV115 )
= $false )
| ( ( subset @ SV28 @ SV82 )
= $false )
| ( ( disjoint @ SV28 @ SV115 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1071]) ).
thf(1106,plain,
! [SV29: $i] :
( ( ( subset @ ( sK6_SY193 @ SV29 ) @ SV29 )
= $false )
| ( ( ordinal @ ( sK6_SY193 @ SV29 ) )
= $false )
| ( ( ordinal @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1072]) ).
thf(1107,plain,
! [SV87: $i,SV34: $i] :
( ( ( ~ ( subset @ SV34 @ SV87 ) )
= $false )
| ( ( SV34 = SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1076]) ).
thf(1108,plain,
! [SV34: $i,SV87: $i] :
( ( ( ~ ( subset @ SV87 @ SV34 ) )
= $false )
| ( ( SV34 = SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1076]) ).
thf(1109,plain,
! [SV87: $i,SV34: $i] :
( ( ( ~ ( subset @ SV34 @ SV87 ) )
= $true )
| ( ( ~ ( subset @ SV87 @ SV34 ) )
= $true )
| ( ( SV34 = SV87 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1077]) ).
thf(1110,plain,
! [SV36: $i,SV118: $i,SV89: $i] :
( ( ( subset @ SV89 @ SV118 )
= $false )
| ( ( subset @ SV36 @ SV89 )
= $false )
| ( ( subset @ SV36 @ SV118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1078]) ).
thf(1111,plain,
! [SV41: $i] :
( ( ~ ~ ( ~ ( in @ SV41 @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SY277: $i,SY278: $i] :
( ~ ~ ( ~ ( in @ SY277 @ ( sK4_SY211 @ SV41 ) )
| ~ ( subset @ SY278 @ SY277 ) )
| ( in @ SY278 @ ( sK4_SY211 @ SV41 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1081]) ).
thf(1112,plain,
! [SV41: $i] :
( ( ~ ! [SY279: $i] :
~ ~ ( ~ ( in @ SY279 @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SY280: $i] :
~ ~ ( ~ ( in @ SY280 @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY279 )
| ( in @ SX4 @ SY280 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1081]) ).
thf(1113,plain,
! [SV41: $i,SV137: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV137 @ ( sK4_SY211 @ SV41 ) )
| ~ ~ ( are_equipotent @ SV137 @ ( sK4_SY211 @ SV41 ) ) )
| ~ ~ ( in @ SV137 @ ( sK4_SY211 @ SV41 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1082]) ).
thf(1114,plain,
! [SV130: $i,SV121: $i,SV94: $i,SV42: $i] :
( ( ( subset @ SV42 @ SV94 )
= $false )
| ( ( ~ ( subset @ SV121 @ SV130 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV42 @ SV121 ) @ ( cartesian_product2 @ SV94 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1083]) ).
thf(1115,plain,
! [SV132: $i,SV46: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV46 ) @ ( relation_dom @ SV132 ) )
| ~ ( subset @ ( relation_rng @ SV46 ) @ ( relation_rng @ SV132 ) ) )
= $false )
| ( ( subset @ SV46 @ SV132 )
= $false )
| ( ( relation @ SV132 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1084]) ).
thf(1116,plain,
! [SV47: $i] :
( ( ~ ~ ( ~ ( in @ SV47 @ ( sK5_SY226 @ SV47 ) )
| ~ ! [SY284: $i,SY285: $i] :
( ~ ~ ( ~ ( in @ SY284 @ ( sK5_SY226 @ SV47 ) )
| ~ ( subset @ SY285 @ SY284 ) )
| ( in @ SY285 @ ( sK5_SY226 @ SV47 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1085]) ).
thf(1117,plain,
! [SV47: $i] :
( ( ~ ! [SY286: $i] :
( ~ ( in @ SY286 @ ( sK5_SY226 @ SV47 ) )
| ( in @ ( powerset @ SY286 ) @ ( sK5_SY226 @ SV47 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1085]) ).
thf(1118,plain,
! [SV47: $i,SV138: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV138 @ ( sK5_SY226 @ SV47 ) )
| ~ ~ ( are_equipotent @ SV138 @ ( sK5_SY226 @ SV47 ) ) )
| ~ ~ ( in @ SV138 @ ( sK5_SY226 @ SV47 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1086]) ).
thf(1119,plain,
! [SV97: $i,SV48: $i] :
( ( ( ~ ( subset @ SV48 @ SV97 ) )
= $false )
| ( ( proper_subset @ SV48 @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1087]) ).
thf(1120,plain,
! [SV97: $i,SV48: $i] :
( ( ( ~ ( ( SV48 != SV97 ) ) )
= $false )
| ( ( proper_subset @ SV48 @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1087]) ).
thf(1121,plain,
! [SV97: $i,SV48: $i] :
( ( ( ~ ( subset @ SV48 @ SV97 ) )
= $true )
| ( ( ~ ( ( SV48 != SV97 ) ) )
= $true )
| ( ( proper_subset @ SV48 @ SV97 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1088]) ).
thf(1122,plain,
! [SV101: $i,SV124: $i,SV52: $i] :
( ( ( ~ ( in @ SV52 @ SV124 )
| ~ ( in @ SV101 @ SV124 ) )
= $false )
| ( ( subset @ ( unordered_pair @ SV52 @ SV101 ) @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1089]) ).
thf(1123,plain,
! [SV101: $i,SV124: $i,SV52: $i] :
( ( ( ~ ( in @ SV52 @ SV124 )
| ~ ( in @ SV101 @ SV124 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV52 @ SV101 ) @ SV124 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1090]) ).
thf(1124,plain,
! [SV133: $i,SV58: $i] :
( ( ( ~ ( subset @ SV58 @ SV133 )
| ! [SY288: $i,SY289: $i] :
( ~ ( in @ ( ordered_pair @ SY288 @ SY289 ) @ SV58 )
| ( in @ ( ordered_pair @ SY288 @ SY289 ) @ SV133 ) ) )
= $true )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1091]) ).
thf(1125,plain,
! [SV133: $i,SV58: $i] :
( ( ( ~ ! [SY290: $i,SY291: $i] :
( ~ ( in @ ( ordered_pair @ SY290 @ SY291 ) @ SV58 )
| ( in @ ( ordered_pair @ SY290 @ SY291 ) @ SV133 ) )
| ( subset @ SV58 @ SV133 ) )
= $true )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1092]) ).
thf(1126,plain,
! [SV59: $i,SV107: $i,SV125: $i] :
( ( ( subset @ SV125 @ SV107 )
= $false )
| ( ( subset @ SV59 @ SV107 )
= $false )
| ( ( subset @ ( set_union2 @ SV59 @ SV125 ) @ SV107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1093]) ).
thf(1127,plain,
! [SV70: $i,SV11: $i] :
( ( ( ~ ( ~ ( ordinal_subset @ SV11 @ SV70 )
| ( subset @ SV11 @ SV70 ) ) )
= $false )
| ( ( ordinal @ SV11 )
= $false )
| ( ( ordinal @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1095]) ).
thf(1128,plain,
! [SV70: $i,SV11: $i] :
( ( ( ~ ( ~ ( subset @ SV11 @ SV70 )
| ( ordinal_subset @ SV11 @ SV70 ) ) )
= $false )
| ( ( ordinal @ SV11 )
= $false )
| ( ( ordinal @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1095]) ).
thf(1129,plain,
! [SV13: $i] :
( ( ( ~ ( ~ ( element @ ( sK7_SY169 @ SV13 ) @ ( powerset @ SV13 ) )
| ~ ~ ( empty @ ( sK7_SY169 @ SV13 ) ) ) )
= $true )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1096]) ).
thf(1130,plain,
! [SV13: $i] :
( ( ( finite @ ( sK7_SY169 @ SV13 ) )
= $true )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1097]) ).
thf(1131,plain,
! [SV18: $i,SV74: $i,SV135: $i] :
( ( ( ~ ( ~ ( in @ SV135 @ SV74 )
| ( subset @ SV135 @ SV18 ) ) )
= $false )
| ( ( SV74
= ( powerset @ SV18 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1100]) ).
thf(1132,plain,
! [SV74: $i,SV18: $i,SV135: $i] :
( ( ( ~ ( ~ ( subset @ SV135 @ SV18 )
| ( in @ SV135 @ SV74 ) ) )
= $false )
| ( ( SV74
= ( powerset @ SV18 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1100]) ).
thf(1133,plain,
! [SV74: $i,SV18: $i] :
( ( ( ~ ( ~ ( in @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV74 )
| ( subset @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV18 ) ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV18 )
| ( in @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV74 ) ) )
= $true )
| ( ( SV74
= ( powerset @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1101]) ).
thf(1134,plain,
! [SV77: $i,SV21: $i,SV136: $i] :
( ( ( in @ SV136 @ SV21 )
= $false )
| ( ( in @ SV136 @ SV77 )
= $true )
| ( ( subset @ SV21 @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1102]) ).
thf(1135,plain,
! [SV21: $i,SV77: $i] :
( ( ( in @ ( sK10_SY258 @ SV77 @ SV21 ) @ SV21 )
= $true )
| ( ( subset @ SV21 @ SV77 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1103]) ).
thf(1136,plain,
! [SV87: $i,SV34: $i] :
( ( ( subset @ SV34 @ SV87 )
= $true )
| ( ( SV34 = SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1107]) ).
thf(1137,plain,
! [SV34: $i,SV87: $i] :
( ( ( subset @ SV87 @ SV34 )
= $true )
| ( ( SV34 = SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1108]) ).
thf(1138,plain,
! [SV87: $i,SV34: $i] :
( ( ( subset @ SV34 @ SV87 )
= $false )
| ( ( ~ ( subset @ SV87 @ SV34 ) )
= $true )
| ( ( SV34 = SV87 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1109]) ).
thf(1139,plain,
! [SV41: $i] :
( ( ~ ( ~ ( in @ SV41 @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SY277: $i,SY278: $i] :
( ~ ~ ( ~ ( in @ SY277 @ ( sK4_SY211 @ SV41 ) )
| ~ ( subset @ SY278 @ SY277 ) )
| ( in @ SY278 @ ( sK4_SY211 @ SV41 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1111]) ).
thf(1140,plain,
! [SV41: $i] :
( ( ! [SY279: $i] :
~ ~ ( ~ ( in @ SY279 @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SY280: $i] :
~ ~ ( ~ ( in @ SY280 @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SX4: $i] :
( ~ ( subset @ SX4 @ SY279 )
| ( in @ SX4 @ SY280 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1112]) ).
thf(1141,plain,
! [SV41: $i,SV137: $i] :
( ( ~ ~ ( ~ ( subset @ SV137 @ ( sK4_SY211 @ SV41 ) )
| ~ ~ ( are_equipotent @ SV137 @ ( sK4_SY211 @ SV41 ) ) )
| ~ ~ ( in @ SV137 @ ( sK4_SY211 @ SV41 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1113]) ).
thf(1142,plain,
! [SV94: $i,SV42: $i,SV130: $i,SV121: $i] :
( ( ( subset @ SV121 @ SV130 )
= $false )
| ( ( subset @ SV42 @ SV94 )
= $false )
| ( ( subset @ ( cartesian_product2 @ SV42 @ SV121 ) @ ( cartesian_product2 @ SV94 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1114]) ).
thf(1143,plain,
! [SV132: $i,SV46: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV46 ) @ ( relation_dom @ SV132 ) ) )
= $false )
| ( ( subset @ SV46 @ SV132 )
= $false )
| ( ( relation @ SV132 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1115]) ).
thf(1144,plain,
! [SV132: $i,SV46: $i] :
( ( ( ~ ( subset @ ( relation_rng @ SV46 ) @ ( relation_rng @ SV132 ) ) )
= $false )
| ( ( subset @ SV46 @ SV132 )
= $false )
| ( ( relation @ SV132 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1115]) ).
thf(1145,plain,
! [SV47: $i] :
( ( ~ ( ~ ( in @ SV47 @ ( sK5_SY226 @ SV47 ) )
| ~ ! [SY284: $i,SY285: $i] :
( ~ ~ ( ~ ( in @ SY284 @ ( sK5_SY226 @ SV47 ) )
| ~ ( subset @ SY285 @ SY284 ) )
| ( in @ SY285 @ ( sK5_SY226 @ SV47 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1116]) ).
thf(1146,plain,
! [SV47: $i] :
( ( ! [SY286: $i] :
( ~ ( in @ SY286 @ ( sK5_SY226 @ SV47 ) )
| ( in @ ( powerset @ SY286 ) @ ( sK5_SY226 @ SV47 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1117]) ).
thf(1147,plain,
! [SV47: $i,SV138: $i] :
( ( ~ ~ ( ~ ( subset @ SV138 @ ( sK5_SY226 @ SV47 ) )
| ~ ~ ( are_equipotent @ SV138 @ ( sK5_SY226 @ SV47 ) ) )
| ~ ~ ( in @ SV138 @ ( sK5_SY226 @ SV47 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1118]) ).
thf(1148,plain,
! [SV97: $i,SV48: $i] :
( ( ( subset @ SV48 @ SV97 )
= $true )
| ( ( proper_subset @ SV48 @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1119]) ).
thf(1149,plain,
! [SV97: $i,SV48: $i] :
( ( ( SV48 != SV97 )
= $true )
| ( ( proper_subset @ SV48 @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1120]) ).
thf(1150,plain,
! [SV97: $i,SV48: $i] :
( ( ( subset @ SV48 @ SV97 )
= $false )
| ( ( ~ ( ( SV48 != SV97 ) ) )
= $true )
| ( ( proper_subset @ SV48 @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1121]) ).
thf(1151,plain,
! [SV101: $i,SV124: $i,SV52: $i] :
( ( ( ~ ( in @ SV52 @ SV124 ) )
= $false )
| ( ( subset @ ( unordered_pair @ SV52 @ SV101 ) @ SV124 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1122]) ).
thf(1152,plain,
! [SV52: $i,SV124: $i,SV101: $i] :
( ( ( ~ ( in @ SV101 @ SV124 ) )
= $false )
| ( ( subset @ ( unordered_pair @ SV52 @ SV101 ) @ SV124 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1122]) ).
thf(1153,plain,
! [SV101: $i,SV124: $i,SV52: $i] :
( ( ( ~ ( in @ SV52 @ SV124 ) )
= $true )
| ( ( ~ ( in @ SV101 @ SV124 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV52 @ SV101 ) @ SV124 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1123]) ).
thf(1154,plain,
! [SV133: $i,SV58: $i] :
( ( ( ~ ( subset @ SV58 @ SV133 ) )
= $true )
| ( ( ! [SY288: $i,SY289: $i] :
( ~ ( in @ ( ordered_pair @ SY288 @ SY289 ) @ SV58 )
| ( in @ ( ordered_pair @ SY288 @ SY289 ) @ SV133 ) ) )
= $true )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1124]) ).
thf(1155,plain,
! [SV133: $i,SV58: $i] :
( ( ( ~ ! [SY290: $i,SY291: $i] :
( ~ ( in @ ( ordered_pair @ SY290 @ SY291 ) @ SV58 )
| ( in @ ( ordered_pair @ SY290 @ SY291 ) @ SV133 ) ) )
= $true )
| ( ( subset @ SV58 @ SV133 )
= $true )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1125]) ).
thf(1156,plain,
! [SV70: $i,SV11: $i] :
( ( ( ~ ( ordinal_subset @ SV11 @ SV70 )
| ( subset @ SV11 @ SV70 ) )
= $true )
| ( ( ordinal @ SV11 )
= $false )
| ( ( ordinal @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1127]) ).
thf(1157,plain,
! [SV70: $i,SV11: $i] :
( ( ( ~ ( subset @ SV11 @ SV70 )
| ( ordinal_subset @ SV11 @ SV70 ) )
= $true )
| ( ( ordinal @ SV11 )
= $false )
| ( ( ordinal @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1128]) ).
thf(1158,plain,
! [SV13: $i] :
( ( ( ~ ( element @ ( sK7_SY169 @ SV13 ) @ ( powerset @ SV13 ) )
| ~ ~ ( empty @ ( sK7_SY169 @ SV13 ) ) )
= $false )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1129]) ).
thf(1159,plain,
! [SV18: $i,SV74: $i,SV135: $i] :
( ( ( ~ ( in @ SV135 @ SV74 )
| ( subset @ SV135 @ SV18 ) )
= $true )
| ( ( SV74
= ( powerset @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1131]) ).
thf(1160,plain,
! [SV74: $i,SV18: $i,SV135: $i] :
( ( ( ~ ( subset @ SV135 @ SV18 )
| ( in @ SV135 @ SV74 ) )
= $true )
| ( ( SV74
= ( powerset @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1132]) ).
thf(1161,plain,
! [SV74: $i,SV18: $i] :
( ( ( ~ ( in @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV74 )
| ( subset @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV18 ) )
= $false )
| ( ( ~ ( ~ ( subset @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV18 )
| ( in @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV74 ) ) )
= $true )
| ( ( SV74
= ( powerset @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1133]) ).
thf(1162,plain,
! [SV34: $i,SV87: $i] :
( ( ( subset @ SV87 @ SV34 )
= $false )
| ( ( subset @ SV34 @ SV87 )
= $false )
| ( ( SV34 = SV87 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1138]) ).
thf(1163,plain,
! [SV41: $i] :
( ( ~ ( in @ SV41 @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SY277: $i,SY278: $i] :
( ~ ~ ( ~ ( in @ SY277 @ ( sK4_SY211 @ SV41 ) )
| ~ ( subset @ SY278 @ SY277 ) )
| ( in @ SY278 @ ( sK4_SY211 @ SV41 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1139]) ).
thf(1164,plain,
! [SV41: $i,SV139: $i] :
( ( ~ ~ ( ~ ( in @ SV139 @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SY292: $i] :
~ ~ ( ~ ( in @ SY292 @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SY293: $i] :
( ~ ( subset @ SY293 @ SV139 )
| ( in @ SY293 @ SY292 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1165,plain,
! [SV41: $i,SV137: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV137 @ ( sK4_SY211 @ SV41 ) )
| ~ ~ ( are_equipotent @ SV137 @ ( sK4_SY211 @ SV41 ) ) ) )
= $true )
| ( ( ~ ~ ( in @ SV137 @ ( sK4_SY211 @ SV41 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1141]) ).
thf(1166,plain,
! [SV132: $i,SV46: $i] :
( ( ( subset @ ( relation_dom @ SV46 ) @ ( relation_dom @ SV132 ) )
= $true )
| ( ( subset @ SV46 @ SV132 )
= $false )
| ( ( relation @ SV132 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1143]) ).
thf(1167,plain,
! [SV132: $i,SV46: $i] :
( ( ( subset @ ( relation_rng @ SV46 ) @ ( relation_rng @ SV132 ) )
= $true )
| ( ( subset @ SV46 @ SV132 )
= $false )
| ( ( relation @ SV132 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1144]) ).
thf(1168,plain,
! [SV47: $i] :
( ( ~ ( in @ SV47 @ ( sK5_SY226 @ SV47 ) )
| ~ ! [SY284: $i,SY285: $i] :
( ~ ~ ( ~ ( in @ SY284 @ ( sK5_SY226 @ SV47 ) )
| ~ ( subset @ SY285 @ SY284 ) )
| ( in @ SY285 @ ( sK5_SY226 @ SV47 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1145]) ).
thf(1169,plain,
! [SV47: $i,SV140: $i] :
( ( ~ ( in @ SV140 @ ( sK5_SY226 @ SV47 ) )
| ( in @ ( powerset @ SV140 ) @ ( sK5_SY226 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1170,plain,
! [SV47: $i,SV138: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV138 @ ( sK5_SY226 @ SV47 ) )
| ~ ~ ( are_equipotent @ SV138 @ ( sK5_SY226 @ SV47 ) ) ) )
= $true )
| ( ( ~ ~ ( in @ SV138 @ ( sK5_SY226 @ SV47 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1147]) ).
thf(1171,plain,
! [SV97: $i,SV48: $i] :
( ( ( SV48 = SV97 )
= $false )
| ( ( proper_subset @ SV48 @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1149]) ).
thf(1172,plain,
! [SV97: $i,SV48: $i] :
( ( ( SV48 != SV97 )
= $false )
| ( ( subset @ SV48 @ SV97 )
= $false )
| ( ( proper_subset @ SV48 @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1150]) ).
thf(1173,plain,
! [SV101: $i,SV124: $i,SV52: $i] :
( ( ( in @ SV52 @ SV124 )
= $true )
| ( ( subset @ ( unordered_pair @ SV52 @ SV101 ) @ SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1151]) ).
thf(1174,plain,
! [SV52: $i,SV124: $i,SV101: $i] :
( ( ( in @ SV101 @ SV124 )
= $true )
| ( ( subset @ ( unordered_pair @ SV52 @ SV101 ) @ SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1152]) ).
thf(1175,plain,
! [SV101: $i,SV124: $i,SV52: $i] :
( ( ( in @ SV52 @ SV124 )
= $false )
| ( ( ~ ( in @ SV101 @ SV124 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV52 @ SV101 ) @ SV124 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1153]) ).
thf(1176,plain,
! [SV133: $i,SV58: $i] :
( ( ( subset @ SV58 @ SV133 )
= $false )
| ( ( ! [SY288: $i,SY289: $i] :
( ~ ( in @ ( ordered_pair @ SY288 @ SY289 ) @ SV58 )
| ( in @ ( ordered_pair @ SY288 @ SY289 ) @ SV133 ) ) )
= $true )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1154]) ).
thf(1177,plain,
! [SV133: $i,SV58: $i] :
( ( ( ! [SY290: $i,SY291: $i] :
( ~ ( in @ ( ordered_pair @ SY290 @ SY291 ) @ SV58 )
| ( in @ ( ordered_pair @ SY290 @ SY291 ) @ SV133 ) ) )
= $false )
| ( ( subset @ SV58 @ SV133 )
= $true )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1155]) ).
thf(1178,plain,
! [SV70: $i,SV11: $i] :
( ( ( ~ ( ordinal_subset @ SV11 @ SV70 ) )
= $true )
| ( ( subset @ SV11 @ SV70 )
= $true )
| ( ( ordinal @ SV11 )
= $false )
| ( ( ordinal @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1156]) ).
thf(1179,plain,
! [SV70: $i,SV11: $i] :
( ( ( ~ ( subset @ SV11 @ SV70 ) )
= $true )
| ( ( ordinal_subset @ SV11 @ SV70 )
= $true )
| ( ( ordinal @ SV11 )
= $false )
| ( ( ordinal @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1157]) ).
thf(1180,plain,
! [SV13: $i] :
( ( ( ~ ( element @ ( sK7_SY169 @ SV13 ) @ ( powerset @ SV13 ) ) )
= $false )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1158]) ).
thf(1181,plain,
! [SV13: $i] :
( ( ( ~ ~ ( empty @ ( sK7_SY169 @ SV13 ) ) )
= $false )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1158]) ).
thf(1182,plain,
! [SV18: $i,SV74: $i,SV135: $i] :
( ( ( ~ ( in @ SV135 @ SV74 ) )
= $true )
| ( ( subset @ SV135 @ SV18 )
= $true )
| ( ( SV74
= ( powerset @ SV18 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1159]) ).
thf(1183,plain,
! [SV74: $i,SV18: $i,SV135: $i] :
( ( ( ~ ( subset @ SV135 @ SV18 ) )
= $true )
| ( ( in @ SV135 @ SV74 )
= $true )
| ( ( SV74
= ( powerset @ SV18 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1160]) ).
thf(1184,plain,
! [SV74: $i,SV18: $i] :
( ( ( ~ ( in @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV74 ) )
= $false )
| ( ( ~ ( ~ ( subset @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV18 )
| ( in @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV74 ) ) )
= $true )
| ( ( SV74
= ( powerset @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1161]) ).
thf(1185,plain,
! [SV74: $i,SV18: $i] :
( ( ( subset @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV18 )
= $false )
| ( ( ~ ( ~ ( subset @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV18 )
| ( in @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV74 ) ) )
= $true )
| ( ( SV74
= ( powerset @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1161]) ).
thf(1186,plain,
! [SV41: $i] :
( ( ~ ( in @ SV41 @ ( sK4_SY211 @ SV41 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1163]) ).
thf(1187,plain,
! [SV41: $i] :
( ( ~ ! [SY277: $i,SY278: $i] :
( ~ ~ ( ~ ( in @ SY277 @ ( sK4_SY211 @ SV41 ) )
| ~ ( subset @ SY278 @ SY277 ) )
| ( in @ SY278 @ ( sK4_SY211 @ SV41 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1163]) ).
thf(1188,plain,
! [SV41: $i,SV139: $i] :
( ( ~ ( ~ ( in @ SV139 @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SY292: $i] :
~ ~ ( ~ ( in @ SY292 @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SY293: $i] :
( ~ ( subset @ SY293 @ SV139 )
| ( in @ SY293 @ SY292 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1164]) ).
thf(1189,plain,
! [SV41: $i,SV137: $i] :
( ( ( ~ ( ~ ( subset @ SV137 @ ( sK4_SY211 @ SV41 ) )
| ~ ~ ( are_equipotent @ SV137 @ ( sK4_SY211 @ SV41 ) ) ) )
= $false )
| ( ( ~ ~ ( in @ SV137 @ ( sK4_SY211 @ SV41 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1165]) ).
thf(1190,plain,
! [SV47: $i] :
( ( ~ ( in @ SV47 @ ( sK5_SY226 @ SV47 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1168]) ).
thf(1191,plain,
! [SV47: $i] :
( ( ~ ! [SY284: $i,SY285: $i] :
( ~ ~ ( ~ ( in @ SY284 @ ( sK5_SY226 @ SV47 ) )
| ~ ( subset @ SY285 @ SY284 ) )
| ( in @ SY285 @ ( sK5_SY226 @ SV47 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1168]) ).
thf(1192,plain,
! [SV47: $i,SV140: $i] :
( ( ( ~ ( in @ SV140 @ ( sK5_SY226 @ SV47 ) ) )
= $true )
| ( ( in @ ( powerset @ SV140 ) @ ( sK5_SY226 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1169]) ).
thf(1193,plain,
! [SV47: $i,SV138: $i] :
( ( ( ~ ( ~ ( subset @ SV138 @ ( sK5_SY226 @ SV47 ) )
| ~ ~ ( are_equipotent @ SV138 @ ( sK5_SY226 @ SV47 ) ) ) )
= $false )
| ( ( ~ ~ ( in @ SV138 @ ( sK5_SY226 @ SV47 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1170]) ).
thf(1194,plain,
! [SV97: $i,SV48: $i] :
( ( ( SV48 = SV97 )
= $true )
| ( ( subset @ SV48 @ SV97 )
= $false )
| ( ( proper_subset @ SV48 @ SV97 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1172]) ).
thf(1195,plain,
! [SV52: $i,SV124: $i,SV101: $i] :
( ( ( in @ SV101 @ SV124 )
= $false )
| ( ( in @ SV52 @ SV124 )
= $false )
| ( ( subset @ ( unordered_pair @ SV52 @ SV101 ) @ SV124 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1175]) ).
thf(1196,plain,
! [SV133: $i,SV58: $i,SV141: $i] :
( ( ( ! [SY294: $i] :
( ~ ( in @ ( ordered_pair @ SV141 @ SY294 ) @ SV58 )
| ( in @ ( ordered_pair @ SV141 @ SY294 ) @ SV133 ) ) )
= $true )
| ( ( subset @ SV58 @ SV133 )
= $false )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1176]) ).
thf(1197,plain,
! [SV58: $i,SV133: $i] :
( ( ( ! [SY295: $i] :
( ~ ( in @ ( ordered_pair @ ( sK11_SY290 @ SV133 @ SV58 ) @ SY295 ) @ SV58 )
| ( in @ ( ordered_pair @ ( sK11_SY290 @ SV133 @ SV58 ) @ SY295 ) @ SV133 ) ) )
= $false )
| ( ( subset @ SV58 @ SV133 )
= $true )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1177]) ).
thf(1198,plain,
! [SV70: $i,SV11: $i] :
( ( ( ordinal_subset @ SV11 @ SV70 )
= $false )
| ( ( subset @ SV11 @ SV70 )
= $true )
| ( ( ordinal @ SV11 )
= $false )
| ( ( ordinal @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1178]) ).
thf(1199,plain,
! [SV70: $i,SV11: $i] :
( ( ( subset @ SV11 @ SV70 )
= $false )
| ( ( ordinal_subset @ SV11 @ SV70 )
= $true )
| ( ( ordinal @ SV11 )
= $false )
| ( ( ordinal @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1179]) ).
thf(1200,plain,
! [SV13: $i] :
( ( ( element @ ( sK7_SY169 @ SV13 ) @ ( powerset @ SV13 ) )
= $true )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1180]) ).
thf(1201,plain,
! [SV13: $i] :
( ( ( ~ ( empty @ ( sK7_SY169 @ SV13 ) ) )
= $true )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1181]) ).
thf(1202,plain,
! [SV18: $i,SV74: $i,SV135: $i] :
( ( ( in @ SV135 @ SV74 )
= $false )
| ( ( subset @ SV135 @ SV18 )
= $true )
| ( ( SV74
= ( powerset @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1182]) ).
thf(1203,plain,
! [SV74: $i,SV18: $i,SV135: $i] :
( ( ( subset @ SV135 @ SV18 )
= $false )
| ( ( in @ SV135 @ SV74 )
= $true )
| ( ( SV74
= ( powerset @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1183]) ).
thf(1204,plain,
! [SV74: $i,SV18: $i] :
( ( ( in @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV74 )
= $true )
| ( ( ~ ( ~ ( subset @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV18 )
| ( in @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV74 ) ) )
= $true )
| ( ( SV74
= ( powerset @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1184]) ).
thf(1205,plain,
! [SV74: $i,SV18: $i] :
( ( ( ~ ( subset @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV18 )
| ( in @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV74 ) )
= $false )
| ( ( subset @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV18 )
= $false )
| ( ( SV74
= ( powerset @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1185]) ).
thf(1206,plain,
! [SV41: $i] :
( ( in @ SV41 @ ( sK4_SY211 @ SV41 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1186]) ).
thf(1207,plain,
! [SV41: $i] :
( ( ! [SY277: $i,SY278: $i] :
( ~ ~ ( ~ ( in @ SY277 @ ( sK4_SY211 @ SV41 ) )
| ~ ( subset @ SY278 @ SY277 ) )
| ( in @ SY278 @ ( sK4_SY211 @ SV41 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1187]) ).
thf(1208,plain,
! [SV41: $i,SV139: $i] :
( ( ~ ( in @ SV139 @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SY292: $i] :
~ ~ ( ~ ( in @ SY292 @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SY293: $i] :
( ~ ( subset @ SY293 @ SV139 )
| ( in @ SY293 @ SY292 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1188]) ).
thf(1209,plain,
! [SV41: $i,SV137: $i] :
( ( ( ~ ( subset @ SV137 @ ( sK4_SY211 @ SV41 ) )
| ~ ~ ( are_equipotent @ SV137 @ ( sK4_SY211 @ SV41 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV137 @ ( sK4_SY211 @ SV41 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1189]) ).
thf(1210,plain,
! [SV47: $i] :
( ( in @ SV47 @ ( sK5_SY226 @ SV47 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1190]) ).
thf(1211,plain,
! [SV47: $i] :
( ( ! [SY284: $i,SY285: $i] :
( ~ ~ ( ~ ( in @ SY284 @ ( sK5_SY226 @ SV47 ) )
| ~ ( subset @ SY285 @ SY284 ) )
| ( in @ SY285 @ ( sK5_SY226 @ SV47 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1191]) ).
thf(1212,plain,
! [SV47: $i,SV140: $i] :
( ( ( in @ SV140 @ ( sK5_SY226 @ SV47 ) )
= $false )
| ( ( in @ ( powerset @ SV140 ) @ ( sK5_SY226 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1192]) ).
thf(1213,plain,
! [SV47: $i,SV138: $i] :
( ( ( ~ ( subset @ SV138 @ ( sK5_SY226 @ SV47 ) )
| ~ ~ ( are_equipotent @ SV138 @ ( sK5_SY226 @ SV47 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV138 @ ( sK5_SY226 @ SV47 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1193]) ).
thf(1214,plain,
! [SV133: $i,SV58: $i,SV142: $i,SV141: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV141 @ SV142 ) @ SV58 )
| ( in @ ( ordered_pair @ SV141 @ SV142 ) @ SV133 ) )
= $true )
| ( ( subset @ SV58 @ SV133 )
= $false )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1196]) ).
thf(1215,plain,
! [SV58: $i,SV133: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK11_SY290 @ SV133 @ SV58 ) @ ( sK12_SY295 @ SV58 @ SV133 ) ) @ SV58 )
| ( in @ ( ordered_pair @ ( sK11_SY290 @ SV133 @ SV58 ) @ ( sK12_SY295 @ SV58 @ SV133 ) ) @ SV133 ) )
= $false )
| ( ( subset @ SV58 @ SV133 )
= $true )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1197]) ).
thf(1216,plain,
! [SV13: $i] :
( ( ( empty @ ( sK7_SY169 @ SV13 ) )
= $false )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1201]) ).
thf(1217,plain,
! [SV74: $i,SV18: $i] :
( ( ( ~ ( subset @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV18 )
| ( in @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV74 ) )
= $false )
| ( ( in @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV74 )
= $true )
| ( ( SV74
= ( powerset @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1204]) ).
thf(1218,plain,
! [SV74: $i,SV18: $i] :
( ( ( ~ ( subset @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV18 ) )
= $false )
| ( ( subset @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV18 )
= $false )
| ( ( SV74
= ( powerset @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1205]) ).
thf(1219,plain,
! [SV74: $i,SV18: $i] :
( ( ( in @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV74 )
= $false )
| ( ( subset @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV18 )
= $false )
| ( ( SV74
= ( powerset @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1205]) ).
thf(1220,plain,
! [SV41: $i,SV143: $i] :
( ( ! [SY296: $i] :
( ~ ~ ( ~ ( in @ SV143 @ ( sK4_SY211 @ SV41 ) )
| ~ ( subset @ SY296 @ SV143 ) )
| ( in @ SY296 @ ( sK4_SY211 @ SV41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1207]) ).
thf(1221,plain,
! [SV41: $i,SV139: $i] :
( ( ( ~ ( in @ SV139 @ ( sK4_SY211 @ SV41 ) ) )
= $true )
| ( ( ~ ! [SY292: $i] :
~ ~ ( ~ ( in @ SY292 @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SY293: $i] :
( ~ ( subset @ SY293 @ SV139 )
| ( in @ SY293 @ SY292 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1208]) ).
thf(1222,plain,
! [SV41: $i,SV137: $i] :
( ( ( ~ ( subset @ SV137 @ ( sK4_SY211 @ SV41 ) ) )
= $true )
| ( ( ~ ~ ( are_equipotent @ SV137 @ ( sK4_SY211 @ SV41 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV137 @ ( sK4_SY211 @ SV41 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1209]) ).
thf(1223,plain,
! [SV47: $i,SV144: $i] :
( ( ! [SY297: $i] :
( ~ ~ ( ~ ( in @ SV144 @ ( sK5_SY226 @ SV47 ) )
| ~ ( subset @ SY297 @ SV144 ) )
| ( in @ SY297 @ ( sK5_SY226 @ SV47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1211]) ).
thf(1224,plain,
! [SV47: $i,SV138: $i] :
( ( ( ~ ( subset @ SV138 @ ( sK5_SY226 @ SV47 ) ) )
= $true )
| ( ( ~ ~ ( are_equipotent @ SV138 @ ( sK5_SY226 @ SV47 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV138 @ ( sK5_SY226 @ SV47 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1213]) ).
thf(1225,plain,
! [SV133: $i,SV58: $i,SV142: $i,SV141: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV141 @ SV142 ) @ SV58 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV141 @ SV142 ) @ SV133 )
= $true )
| ( ( subset @ SV58 @ SV133 )
= $false )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1214]) ).
thf(1226,plain,
! [SV58: $i,SV133: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK11_SY290 @ SV133 @ SV58 ) @ ( sK12_SY295 @ SV58 @ SV133 ) ) @ SV58 ) )
= $false )
| ( ( subset @ SV58 @ SV133 )
= $true )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1215]) ).
thf(1227,plain,
! [SV58: $i,SV133: $i] :
( ( ( in @ ( ordered_pair @ ( sK11_SY290 @ SV133 @ SV58 ) @ ( sK12_SY295 @ SV58 @ SV133 ) ) @ SV133 )
= $false )
| ( ( subset @ SV58 @ SV133 )
= $true )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1215]) ).
thf(1228,plain,
! [SV74: $i,SV18: $i] :
( ( ( ~ ( subset @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV18 ) )
= $false )
| ( ( in @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV74 )
= $true )
| ( ( SV74
= ( powerset @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1217]) ).
thf(1229,plain,
! [SV74: $i,SV18: $i] :
( ( ( in @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV74 )
= $false )
| ( ( in @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV74 )
= $true )
| ( ( SV74
= ( powerset @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1217]) ).
thf(1230,plain,
! [SV74: $i,SV18: $i] :
( ( ( subset @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV18 )
= $true )
| ( ( subset @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV18 )
= $false )
| ( ( SV74
= ( powerset @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1218]) ).
thf(1231,plain,
! [SV145: $i,SV41: $i,SV143: $i] :
( ( ~ ~ ( ~ ( in @ SV143 @ ( sK4_SY211 @ SV41 ) )
| ~ ( subset @ SV145 @ SV143 ) )
| ( in @ SV145 @ ( sK4_SY211 @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1220]) ).
thf(1232,plain,
! [SV41: $i,SV139: $i] :
( ( ( in @ SV139 @ ( sK4_SY211 @ SV41 ) )
= $false )
| ( ( ~ ! [SY292: $i] :
~ ~ ( ~ ( in @ SY292 @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SY293: $i] :
( ~ ( subset @ SY293 @ SV139 )
| ( in @ SY293 @ SY292 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1221]) ).
thf(1233,plain,
! [SV41: $i,SV137: $i] :
( ( ( subset @ SV137 @ ( sK4_SY211 @ SV41 ) )
= $false )
| ( ( ~ ~ ( are_equipotent @ SV137 @ ( sK4_SY211 @ SV41 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV137 @ ( sK4_SY211 @ SV41 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1222]) ).
thf(1234,plain,
! [SV146: $i,SV47: $i,SV144: $i] :
( ( ~ ~ ( ~ ( in @ SV144 @ ( sK5_SY226 @ SV47 ) )
| ~ ( subset @ SV146 @ SV144 ) )
| ( in @ SV146 @ ( sK5_SY226 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1223]) ).
thf(1235,plain,
! [SV47: $i,SV138: $i] :
( ( ( subset @ SV138 @ ( sK5_SY226 @ SV47 ) )
= $false )
| ( ( ~ ~ ( are_equipotent @ SV138 @ ( sK5_SY226 @ SV47 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV138 @ ( sK5_SY226 @ SV47 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1224]) ).
thf(1236,plain,
! [SV133: $i,SV58: $i,SV142: $i,SV141: $i] :
( ( ( in @ ( ordered_pair @ SV141 @ SV142 ) @ SV58 )
= $false )
| ( ( in @ ( ordered_pair @ SV141 @ SV142 ) @ SV133 )
= $true )
| ( ( subset @ SV58 @ SV133 )
= $false )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1225]) ).
thf(1237,plain,
! [SV58: $i,SV133: $i] :
( ( ( in @ ( ordered_pair @ ( sK11_SY290 @ SV133 @ SV58 ) @ ( sK12_SY295 @ SV58 @ SV133 ) ) @ SV58 )
= $true )
| ( ( subset @ SV58 @ SV133 )
= $true )
| ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1226]) ).
thf(1238,plain,
! [SV74: $i,SV18: $i] :
( ( ( subset @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV18 )
= $true )
| ( ( in @ ( sK9_SY256 @ SV18 @ SV74 ) @ SV74 )
= $true )
| ( ( SV74
= ( powerset @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1228]) ).
thf(1239,plain,
! [SV145: $i,SV41: $i,SV143: $i] :
( ( ( ~ ~ ( ~ ( in @ SV143 @ ( sK4_SY211 @ SV41 ) )
| ~ ( subset @ SV145 @ SV143 ) ) )
= $true )
| ( ( in @ SV145 @ ( sK4_SY211 @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1231]) ).
thf(1240,plain,
! [SV139: $i,SV41: $i] :
( ( ( ! [SY292: $i] :
~ ~ ( ~ ( in @ SY292 @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SY293: $i] :
( ~ ( subset @ SY293 @ SV139 )
| ( in @ SY293 @ SY292 ) ) ) )
= $false )
| ( ( in @ SV139 @ ( sK4_SY211 @ SV41 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1232]) ).
thf(1241,plain,
! [SV41: $i,SV137: $i] :
( ( ( ~ ( are_equipotent @ SV137 @ ( sK4_SY211 @ SV41 ) ) )
= $false )
| ( ( subset @ SV137 @ ( sK4_SY211 @ SV41 ) )
= $false )
| ( ( ~ ~ ( in @ SV137 @ ( sK4_SY211 @ SV41 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1233]) ).
thf(1242,plain,
! [SV146: $i,SV47: $i,SV144: $i] :
( ( ( ~ ~ ( ~ ( in @ SV144 @ ( sK5_SY226 @ SV47 ) )
| ~ ( subset @ SV146 @ SV144 ) ) )
= $true )
| ( ( in @ SV146 @ ( sK5_SY226 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1234]) ).
thf(1243,plain,
! [SV47: $i,SV138: $i] :
( ( ( ~ ( are_equipotent @ SV138 @ ( sK5_SY226 @ SV47 ) ) )
= $false )
| ( ( subset @ SV138 @ ( sK5_SY226 @ SV47 ) )
= $false )
| ( ( ~ ~ ( in @ SV138 @ ( sK5_SY226 @ SV47 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1235]) ).
thf(1244,plain,
! [SV145: $i,SV41: $i,SV143: $i] :
( ( ( ~ ( ~ ( in @ SV143 @ ( sK4_SY211 @ SV41 ) )
| ~ ( subset @ SV145 @ SV143 ) ) )
= $false )
| ( ( in @ SV145 @ ( sK4_SY211 @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1239]) ).
thf(1245,plain,
! [SV41: $i,SV139: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK13_SY292 @ SV139 @ SV41 ) @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SY298: $i] :
( ~ ( subset @ SY298 @ SV139 )
| ( in @ SY298 @ ( sK13_SY292 @ SV139 @ SV41 ) ) ) ) )
= $false )
| ( ( in @ SV139 @ ( sK4_SY211 @ SV41 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1240]) ).
thf(1246,plain,
! [SV41: $i,SV137: $i] :
( ( ( are_equipotent @ SV137 @ ( sK4_SY211 @ SV41 ) )
= $true )
| ( ( subset @ SV137 @ ( sK4_SY211 @ SV41 ) )
= $false )
| ( ( ~ ~ ( in @ SV137 @ ( sK4_SY211 @ SV41 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1241]) ).
thf(1247,plain,
! [SV146: $i,SV47: $i,SV144: $i] :
( ( ( ~ ( ~ ( in @ SV144 @ ( sK5_SY226 @ SV47 ) )
| ~ ( subset @ SV146 @ SV144 ) ) )
= $false )
| ( ( in @ SV146 @ ( sK5_SY226 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1242]) ).
thf(1248,plain,
! [SV47: $i,SV138: $i] :
( ( ( are_equipotent @ SV138 @ ( sK5_SY226 @ SV47 ) )
= $true )
| ( ( subset @ SV138 @ ( sK5_SY226 @ SV47 ) )
= $false )
| ( ( ~ ~ ( in @ SV138 @ ( sK5_SY226 @ SV47 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1243]) ).
thf(1249,plain,
! [SV145: $i,SV41: $i,SV143: $i] :
( ( ( ~ ( in @ SV143 @ ( sK4_SY211 @ SV41 ) )
| ~ ( subset @ SV145 @ SV143 ) )
= $true )
| ( ( in @ SV145 @ ( sK4_SY211 @ SV41 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1244]) ).
thf(1250,plain,
! [SV41: $i,SV139: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_SY292 @ SV139 @ SV41 ) @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SY298: $i] :
( ~ ( subset @ SY298 @ SV139 )
| ( in @ SY298 @ ( sK13_SY292 @ SV139 @ SV41 ) ) ) ) )
= $true )
| ( ( in @ SV139 @ ( sK4_SY211 @ SV41 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1245]) ).
thf(1251,plain,
! [SV41: $i,SV137: $i] :
( ( ( ~ ( in @ SV137 @ ( sK4_SY211 @ SV41 ) ) )
= $false )
| ( ( subset @ SV137 @ ( sK4_SY211 @ SV41 ) )
= $false )
| ( ( are_equipotent @ SV137 @ ( sK4_SY211 @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1246]) ).
thf(1252,plain,
! [SV146: $i,SV47: $i,SV144: $i] :
( ( ( ~ ( in @ SV144 @ ( sK5_SY226 @ SV47 ) )
| ~ ( subset @ SV146 @ SV144 ) )
= $true )
| ( ( in @ SV146 @ ( sK5_SY226 @ SV47 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1247]) ).
thf(1253,plain,
! [SV47: $i,SV138: $i] :
( ( ( ~ ( in @ SV138 @ ( sK5_SY226 @ SV47 ) ) )
= $false )
| ( ( subset @ SV138 @ ( sK5_SY226 @ SV47 ) )
= $false )
| ( ( are_equipotent @ SV138 @ ( sK5_SY226 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1248]) ).
thf(1254,plain,
! [SV145: $i,SV41: $i,SV143: $i] :
( ( ( ~ ( in @ SV143 @ ( sK4_SY211 @ SV41 ) ) )
= $true )
| ( ( ~ ( subset @ SV145 @ SV143 ) )
= $true )
| ( ( in @ SV145 @ ( sK4_SY211 @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1249]) ).
thf(1255,plain,
! [SV41: $i,SV139: $i] :
( ( ( ~ ( in @ ( sK13_SY292 @ SV139 @ SV41 ) @ ( sK4_SY211 @ SV41 ) )
| ~ ! [SY298: $i] :
( ~ ( subset @ SY298 @ SV139 )
| ( in @ SY298 @ ( sK13_SY292 @ SV139 @ SV41 ) ) ) )
= $false )
| ( ( in @ SV139 @ ( sK4_SY211 @ SV41 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1250]) ).
thf(1256,plain,
! [SV41: $i,SV137: $i] :
( ( ( in @ SV137 @ ( sK4_SY211 @ SV41 ) )
= $true )
| ( ( subset @ SV137 @ ( sK4_SY211 @ SV41 ) )
= $false )
| ( ( are_equipotent @ SV137 @ ( sK4_SY211 @ SV41 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1251]) ).
thf(1257,plain,
! [SV146: $i,SV47: $i,SV144: $i] :
( ( ( ~ ( in @ SV144 @ ( sK5_SY226 @ SV47 ) ) )
= $true )
| ( ( ~ ( subset @ SV146 @ SV144 ) )
= $true )
| ( ( in @ SV146 @ ( sK5_SY226 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1252]) ).
thf(1258,plain,
! [SV47: $i,SV138: $i] :
( ( ( in @ SV138 @ ( sK5_SY226 @ SV47 ) )
= $true )
| ( ( subset @ SV138 @ ( sK5_SY226 @ SV47 ) )
= $false )
| ( ( are_equipotent @ SV138 @ ( sK5_SY226 @ SV47 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1253]) ).
thf(1259,plain,
! [SV145: $i,SV41: $i,SV143: $i] :
( ( ( in @ SV143 @ ( sK4_SY211 @ SV41 ) )
= $false )
| ( ( ~ ( subset @ SV145 @ SV143 ) )
= $true )
| ( ( in @ SV145 @ ( sK4_SY211 @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1254]) ).
thf(1260,plain,
! [SV41: $i,SV139: $i] :
( ( ( ~ ( in @ ( sK13_SY292 @ SV139 @ SV41 ) @ ( sK4_SY211 @ SV41 ) ) )
= $false )
| ( ( in @ SV139 @ ( sK4_SY211 @ SV41 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1255]) ).
thf(1261,plain,
! [SV41: $i,SV139: $i] :
( ( ( ~ ! [SY298: $i] :
( ~ ( subset @ SY298 @ SV139 )
| ( in @ SY298 @ ( sK13_SY292 @ SV139 @ SV41 ) ) ) )
= $false )
| ( ( in @ SV139 @ ( sK4_SY211 @ SV41 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1255]) ).
thf(1262,plain,
! [SV146: $i,SV47: $i,SV144: $i] :
( ( ( in @ SV144 @ ( sK5_SY226 @ SV47 ) )
= $false )
| ( ( ~ ( subset @ SV146 @ SV144 ) )
= $true )
| ( ( in @ SV146 @ ( sK5_SY226 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1257]) ).
thf(1263,plain,
! [SV41: $i,SV143: $i,SV145: $i] :
( ( ( subset @ SV145 @ SV143 )
= $false )
| ( ( in @ SV143 @ ( sK4_SY211 @ SV41 ) )
= $false )
| ( ( in @ SV145 @ ( sK4_SY211 @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1259]) ).
thf(1264,plain,
! [SV41: $i,SV139: $i] :
( ( ( in @ ( sK13_SY292 @ SV139 @ SV41 ) @ ( sK4_SY211 @ SV41 ) )
= $true )
| ( ( in @ SV139 @ ( sK4_SY211 @ SV41 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1260]) ).
thf(1265,plain,
! [SV41: $i,SV139: $i] :
( ( ( ! [SY298: $i] :
( ~ ( subset @ SY298 @ SV139 )
| ( in @ SY298 @ ( sK13_SY292 @ SV139 @ SV41 ) ) ) )
= $true )
| ( ( in @ SV139 @ ( sK4_SY211 @ SV41 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1261]) ).
thf(1266,plain,
! [SV47: $i,SV144: $i,SV146: $i] :
( ( ( subset @ SV146 @ SV144 )
= $false )
| ( ( in @ SV144 @ ( sK5_SY226 @ SV47 ) )
= $false )
| ( ( in @ SV146 @ ( sK5_SY226 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1262]) ).
thf(1267,plain,
! [SV41: $i,SV139: $i,SV147: $i] :
( ( ( ~ ( subset @ SV147 @ SV139 )
| ( in @ SV147 @ ( sK13_SY292 @ SV139 @ SV41 ) ) )
= $true )
| ( ( in @ SV139 @ ( sK4_SY211 @ SV41 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1265]) ).
thf(1268,plain,
! [SV41: $i,SV139: $i,SV147: $i] :
( ( ( ~ ( subset @ SV147 @ SV139 ) )
= $true )
| ( ( in @ SV147 @ ( sK13_SY292 @ SV139 @ SV41 ) )
= $true )
| ( ( in @ SV139 @ ( sK4_SY211 @ SV41 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1267]) ).
thf(1269,plain,
! [SV41: $i,SV139: $i,SV147: $i] :
( ( ( subset @ SV147 @ SV139 )
= $false )
| ( ( in @ SV147 @ ( sK13_SY292 @ SV139 @ SV41 ) )
= $true )
| ( ( in @ SV139 @ ( sK4_SY211 @ SV41 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1268]) ).
thf(1270,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[546,1269,1266,1264,1263,1258,1256,1238,1237,1236,1230,1229,1227,1219,1216,1212,1210,1206,1203,1202,1200,1199,1198,1195,1194,1174,1173,1171,1167,1166,1162,1148,1142,1137,1136,1135,1134,1130,1126,1110,1106,1105,1104,1099,1098,1094,1080,1079,1075,1074,1073,1070,1065,1061,1060,1058,1057,1056,1055,1054,1053,1051,1050,1049,1048,1045,1044,1043,1042,1041,1040,1032,1031,1020,1019,1014,989,978,975,961,958,947,927,916,896,877,873,870,868,857,856,852,848,842,839,835,834,831,823,778,768,702,701,700,699,641,637,577,576,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547]) ).
thf(1271,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1270]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU294+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
% 0.09/0.21 % Computer : n015.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Oct 6 15:15:43 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.97/1.93 ...
% 9.97/1.93
% 9.97/1.93 No.of.Axioms: 86
% 9.97/1.93
% 9.97/1.93 Length.of.Defs: 0
% 9.97/1.93
% 9.97/1.93 Contains.Choice.Funs: false
% 9.97/1.93 ................................
% 9.97/1.93
% 9.97/1.93 ********************************
% 9.97/1.93 * All subproblems solved! *
% 9.97/1.93 ********************************
% 9.97/1.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:88,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1270,loop_count:0,foatp_calls:1,translation:fof_full)
% 9.97/1.93
% 9.97/1.93 %**** Beginning of derivation protocol ****
% 9.97/1.93 % SZS output start CNFRefutation
% See solution above
% 9.97/1.93
% 9.97/1.93 %**** End of derivation protocol ****
% 9.97/1.93 %**** no. of clauses in derivation: 963 ****
% 9.97/1.93 %**** clause counter: 1270 ****
% 9.97/1.93
% 9.97/1.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:88,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1270,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------