TSTP Solution File: SEU264+2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU264+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 12:09:17 EDT 2022
% Result : Theorem 242.21s 242.51s
% Output : CNFRefutation 242.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 156
% Syntax : Number of formulae : 1222 ( 613 unt; 83 typ; 0 def)
% Number of atoms : 7582 (2306 equ; 0 cnn)
% Maximal formula atoms : 11 ( 6 avg)
% Number of connectives : 15078 (2465 ~;2405 |; 186 &;9818 @)
% ( 42 <=>; 162 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 130 ( 130 >; 0 *; 0 +; 0 <<)
% Number of symbols : 86 ( 83 usr; 7 con; 0-3 aty)
% Number of variables : 3018 ( 0 ^3012 !; 6 ?;3018 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_antisymmetric,type,
antisymmetric: $i > $o ).
thf(tp_apply,type,
apply: $i > $i > $i ).
thf(tp_are_equipotent,type,
are_equipotent: $i > $i > $o ).
thf(tp_being_limit_ordinal,type,
being_limit_ordinal: $i > $o ).
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_cast_to_subset,type,
cast_to_subset: $i > $i ).
thf(tp_complements_of_subsets,type,
complements_of_subsets: $i > $i > $i ).
thf(tp_connected,type,
connected: $i > $o ).
thf(tp_disjoint,type,
disjoint: $i > $i > $o ).
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_epsilon_connected,type,
epsilon_connected: $i > $o ).
thf(tp_epsilon_transitive,type,
epsilon_transitive: $i > $o ).
thf(tp_fiber,type,
fiber: $i > $i > $i ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_function_inverse,type,
function_inverse: $i > $i ).
thf(tp_identity_relation,type,
identity_relation: $i > $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_is_antisymmetric_in,type,
is_antisymmetric_in: $i > $i > $o ).
thf(tp_is_connected_in,type,
is_connected_in: $i > $i > $o ).
thf(tp_is_reflexive_in,type,
is_reflexive_in: $i > $i > $o ).
thf(tp_is_transitive_in,type,
is_transitive_in: $i > $i > $o ).
thf(tp_is_well_founded_in,type,
is_well_founded_in: $i > $i > $o ).
thf(tp_meet_of_subsets,type,
meet_of_subsets: $i > $i > $i ).
thf(tp_one_to_one,type,
one_to_one: $i > $o ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_ordinal,type,
ordinal: $i > $o ).
thf(tp_ordinal_subset,type,
ordinal_subset: $i > $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_proper_subset,type,
proper_subset: $i > $i > $o ).
thf(tp_reflexive,type,
reflexive: $i > $o ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_composition,type,
relation_composition: $i > $i > $i ).
thf(tp_relation_dom,type,
relation_dom: $i > $i ).
thf(tp_relation_dom_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_restriction,type,
relation_rng_restriction: $i > $i > $i ).
thf(tp_sK10_C,type,
sK10_C: $i > $i > $i ).
thf(tp_sK11_C,type,
sK11_C: $i > $i > $i ).
thf(tp_sK12_SY3639,type,
sK12_SY3639: $i > $i > $i ).
thf(tp_sK13_C,type,
sK13_C: $i > $i > $i ).
thf(tp_sK14_B,type,
sK14_B: $i > $i ).
thf(tp_sK15_B,type,
sK15_B: $i > $i ).
thf(tp_sK16_C,type,
sK16_C: $i > $i > $i ).
thf(tp_sK17_C,type,
sK17_C: $i > $i > $i ).
thf(tp_sK18_B,type,
sK18_B: $i > $i ).
thf(tp_sK19_B,type,
sK19_B: $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY3625,type,
sK2_SY3625: $i ).
thf(tp_sK3_SY3628,type,
sK3_SY3628: $i ).
thf(tp_sK4_SY3630,type,
sK4_SY3630: $i ).
thf(tp_sK5_B,type,
sK5_B: $i > $i ).
thf(tp_sK6_SY3633,type,
sK6_SY3633: $i > $i > $i ).
thf(tp_sK7_C,type,
sK7_C: $i > $i > $i ).
thf(tp_sK8_D,type,
sK8_D: $i > $i > $i > $i ).
thf(tp_sK9_C,type,
sK9_C: $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(17,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ( ordinal_subset @ A @ B )
<=> ( subset @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
<=> ( relation_of2 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(74,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(115,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(141,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( is_well_founded_in @ A @ B )
<=> ! [C: $i] :
~ ( ( subset @ C @ B )
& ( C != empty_set )
& ! [D: $i] :
~ ( ( in @ D @ C )
& ( disjoint @ ( fiber @ A @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_wellord1) ).
thf(142,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(143,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(147,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( well_founded_relation @ A )
<=> ! [B: $i] :
~ ( ( subset @ B @ ( relation_field @ A ) )
& ( B != empty_set )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ( disjoint @ ( fiber @ A @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_wellord1) ).
thf(151,axiom,
! [A: $i] :
( ( epsilon_transitive @ A )
<=> ! [B: $i] :
( ( in @ B @ A )
=> ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
thf(152,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(157,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(171,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(188,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(190,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(193,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(196,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(199,axiom,
! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(204,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(210,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(212,axiom,
! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_xboole_1) ).
thf(228,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_rng @ B ) )
=> ( ( relation_rng @ ( relation_composition @ B @ A ) )
= ( relation_rng @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_relat_1) ).
thf(231,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ ( relation_rng @ A ) @ ( relation_dom @ B ) )
=> ( ( relation_dom @ ( relation_composition @ A @ B ) )
= ( relation_dom @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_relat_1) ).
thf(232,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(233,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(234,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(235,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ( ( disjoint @ B @ C )
<=> ( subset @ B @ ( subset_complement @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_subset_1) ).
thf(239,axiom,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(242,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(244,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( ( well_ordering @ B )
& ( subset @ A @ ( relation_field @ B ) ) )
=> ( ( relation_field @ ( relation_restriction @ B @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_wellord1) ).
thf(245,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(246,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(247,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(249,axiom,
! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(253,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(256,axiom,
! [A: $i,B: $i] :
( ( ordinal @ B )
=> ~ ( ( subset @ A @ B )
& ( A != empty_set )
& ! [C: $i] :
( ( ordinal @ C )
=> ~ ( ( in @ C @ A )
& ! [D: $i] :
( ( ordinal @ D )
=> ( ( in @ D @ A )
=> ( ordinal_subset @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_ordinal1) ).
thf(258,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(260,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(261,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(262,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(264,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(272,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(273,axiom,
! [A: $i] :
( ( relation @ A )
=> ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relat_1) ).
thf(276,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(279,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(280,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(283,axiom,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(285,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(286,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ~ ( ( A != empty_set )
& ( subset @ A @ ( relation_rng @ B ) )
& ( ( relation_inverse_image @ B @ A )
= empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t174_relat_1) ).
thf(288,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(291,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(292,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( subset @ A @ ( relation_rng @ B ) )
=> ( ( relation_image @ B @ ( relation_inverse_image @ B @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t147_funct_1) ).
thf(294,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ ( relation_dom @ B ) )
=> ( subset @ A @ ( relation_inverse_image @ B @ ( relation_image @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_funct_1) ).
thf(296,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( subset @ ( relation_image @ B @ ( relation_inverse_image @ B @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_funct_1) ).
thf(297,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(300,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(301,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(302,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(303,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(305,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(306,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(307,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(308,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(316,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l50_zfmisc_1) ).
thf(317,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(319,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(322,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(323,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(325,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(331,conjecture,
! [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(332,negated_conjecture,
( ( ! [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 ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[331]) ).
thf(333,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 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[332]) ).
thf(334,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(335,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(336,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(337,plain,
( ( ! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ( ordinal_subset @ A @ B )
<=> ( subset @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(338,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
<=> ( relation_of2 @ C @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(339,plain,
( ( ! [A: $i,B: $i] :
? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(340,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(341,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(342,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( is_well_founded_in @ A @ B )
<=> ! [C: $i] :
~ ( ( subset @ C @ B )
& ( C != empty_set )
& ! [D: $i] :
~ ( ( in @ D @ C )
& ( disjoint @ ( fiber @ A @ D ) @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(343,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(344,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)],[143]) ).
thf(345,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( well_founded_relation @ A )
<=> ! [B: $i] :
~ ( ( subset @ B @ ( relation_field @ A ) )
& ( B != empty_set )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ( disjoint @ ( fiber @ A @ C ) @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(346,plain,
( ( ! [A: $i] :
( ( epsilon_transitive @ A )
<=> ! [B: $i] :
( ( in @ B @ A )
=> ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(347,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(348,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
<=> ( subset @ C @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(349,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(350,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(351,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(352,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)],[193]) ).
thf(353,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(354,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(355,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[204]) ).
thf(356,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(357,plain,
( ( ! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(358,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_rng @ B ) )
=> ( ( relation_rng @ ( relation_composition @ B @ A ) )
= ( relation_rng @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[228]) ).
thf(359,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ ( relation_rng @ A ) @ ( relation_dom @ B ) )
=> ( ( relation_dom @ ( relation_composition @ A @ B ) )
= ( relation_dom @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(360,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(361,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)],[233]) ).
thf(362,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)],[234]) ).
thf(363,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ( ( disjoint @ B @ C )
<=> ( subset @ B @ ( subset_complement @ A @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(364,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(365,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[242]) ).
thf(366,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( ( well_ordering @ B )
& ( subset @ A @ ( relation_field @ B ) ) )
=> ( ( relation_field @ ( relation_restriction @ B @ A ) )
= A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[244]) ).
thf(367,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)],[245]) ).
thf(368,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(369,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(370,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(371,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)],[253]) ).
thf(372,plain,
( ( ! [A: $i,B: $i] :
( ( ordinal @ B )
=> ~ ( ( subset @ A @ B )
& ( A != empty_set )
& ! [C: $i] :
( ( ordinal @ C )
=> ~ ( ( in @ C @ A )
& ! [D: $i] :
( ( ordinal @ D )
=> ( ( in @ D @ A )
=> ( ordinal_subset @ C @ D ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[256]) ).
thf(373,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ( in @ B @ A )
=> ( ( ordinal @ B )
& ( subset @ B @ A ) ) )
=> ( ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(374,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(375,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(376,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)],[262]) ).
thf(377,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)],[264]) ).
thf(378,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)],[272]) ).
thf(379,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[273]) ).
thf(380,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)],[276]) ).
thf(381,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[279]) ).
thf(382,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)],[280]) ).
thf(383,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(384,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)],[285]) ).
thf(385,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ~ ( ( A != empty_set )
& ( subset @ A @ ( relation_rng @ B ) )
& ( ( relation_inverse_image @ B @ A )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286]) ).
thf(386,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(387,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)],[291]) ).
thf(388,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( subset @ A @ ( relation_rng @ B ) )
=> ( ( relation_image @ B @ ( relation_inverse_image @ B @ A ) )
= A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(389,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ ( relation_dom @ B ) )
=> ( subset @ A @ ( relation_inverse_image @ B @ ( relation_image @ B @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(390,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( subset @ ( relation_image @ B @ ( relation_inverse_image @ B @ A ) ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(391,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(392,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)],[300]) ).
thf(393,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(394,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)],[302]) ).
thf(395,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)],[303]) ).
thf(396,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)],[305]) ).
thf(397,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(398,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(399,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(400,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[316]) ).
thf(401,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317]) ).
thf(402,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)],[319]) ).
thf(403,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[322]) ).
thf(404,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[323]) ).
thf(405,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[325]) ).
thf(406,plain,
( ( ! [SY3625: $i,SY3626: $i,SY3627: $i] :
( ( relation_of2_as_subset @ SY3627 @ SY3626 @ sK1_A )
=> ( ( subset @ sK1_A @ SY3625 )
=> ( relation_of2_as_subset @ SY3627 @ SY3626 @ SY3625 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[333]) ).
thf(407,plain,
( ( ! [SY3628: $i,SY3629: $i] :
( ( relation_of2_as_subset @ SY3629 @ SY3628 @ sK1_A )
=> ( ( subset @ sK1_A @ sK2_SY3625 )
=> ( relation_of2_as_subset @ SY3629 @ SY3628 @ sK2_SY3625 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[406]) ).
thf(408,plain,
( ( ! [SY3630: $i] :
( ( relation_of2_as_subset @ SY3630 @ sK3_SY3628 @ sK1_A )
=> ( ( subset @ sK1_A @ sK2_SY3625 )
=> ( relation_of2_as_subset @ SY3630 @ sK3_SY3628 @ sK2_SY3625 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[407]) ).
thf(409,plain,
( ( ( relation_of2_as_subset @ sK4_SY3630 @ sK3_SY3628 @ sK1_A )
=> ( ( subset @ sK1_A @ sK2_SY3625 )
=> ( relation_of2_as_subset @ sK4_SY3630 @ sK3_SY3628 @ sK2_SY3625 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[408]) ).
thf(410,plain,
( ( relation_of2_as_subset @ sK4_SY3630 @ sK3_SY3628 @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[409]) ).
thf(411,plain,
( ( subset @ sK1_A @ sK2_SY3625 )
= $true ),
inference(standard_cnf,[status(thm)],[409]) ).
thf(412,plain,
( ( relation_of2_as_subset @ sK4_SY3630 @ sK3_SY3628 @ sK2_SY3625 )
= $false ),
inference(standard_cnf,[status(thm)],[409]) ).
thf(413,plain,
( ( ~ ( relation_of2_as_subset @ sK4_SY3630 @ sK3_SY3628 @ sK2_SY3625 ) )
= $true ),
inference(polarity_switch,[status(thm)],[412]) ).
thf(414,plain,
( ( ! [A: $i] :
( ! [SY3631: $i] :
( ~ ( subset @ SY3631 @ ( sK5_B @ A ) )
| ( are_equipotent @ SY3631 @ ( sK5_B @ A ) )
| ( in @ SY3631 @ ( sK5_B @ A ) ) )
& ! [SY3632: $i] :
( ( ! [SY3637: $i] :
( ~ ( subset @ SY3637 @ SY3632 )
| ( in @ SY3637 @ ( sK6_SY3633 @ SY3632 @ A ) ) )
& ( in @ ( sK6_SY3633 @ SY3632 @ A ) @ ( sK5_B @ A ) ) )
| ~ ( in @ SY3632 @ ( sK5_B @ A ) ) )
& ! [SY3635: $i,SY3636: $i] :
( ~ ( in @ SY3635 @ ( sK5_B @ A ) )
| ~ ( subset @ SY3636 @ SY3635 )
| ( in @ SY3636 @ ( sK5_B @ A ) ) )
& ( in @ A @ ( sK5_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[334]) ).
thf(415,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[335]) ).
thf(416,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[336]) ).
thf(417,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ordinal @ A )
| ~ ( ordinal @ B )
| ~ ( ordinal_subset @ A @ B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( ordinal @ A )
| ~ ( ordinal @ B )
| ~ ( subset @ A @ B )
| ( ordinal_subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[337]) ).
thf(418,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( relation_of2_as_subset @ C @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( relation_of2 @ C @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[338]) ).
thf(419,plain,
( ( ! [A: $i,B: $i] : ( relation_of2_as_subset @ ( sK7_C @ B @ A ) @ A @ B ) )
= $true ),
inference(extcnf_combined,[status(esa)],[339]) ).
thf(420,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[340]) ).
thf(421,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ( proper_subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( A != B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[341]) ).
thf(422,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ! [SY3638: $i] :
( ~ ( disjoint @ ( fiber @ A @ SY3638 ) @ ( sK9_C @ B @ A ) )
| ~ ( in @ SY3638 @ ( sK9_C @ B @ A ) ) )
& ( ( sK9_C @ B @ A )
!= empty_set )
& ( subset @ ( sK9_C @ B @ A ) @ B ) )
| ( is_well_founded_in @ A @ B ) )
& ! [B: $i] :
( ~ ( is_well_founded_in @ A @ B )
| ! [C: $i] :
( ( ( disjoint @ ( fiber @ A @ ( sK8_D @ C @ B @ A ) ) @ C )
& ( in @ ( sK8_D @ C @ B @ A ) @ C ) )
| ( C = empty_set )
| ~ ( subset @ C @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[342]) ).
thf(423,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK10_C @ B @ A ) @ A )
& ~ ( in @ ( sK10_C @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[343]) ).
thf(424,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( in @ ( ordered_pair @ ( sK11_C @ B @ A ) @ ( sK12_SY3639 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK11_C @ B @ A ) @ ( sK12_SY3639 @ B @ A ) ) @ B ) )
| ( subset @ A @ B ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ B )
| ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[344]) ).
thf(425,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [SY3640: $i] :
( ~ ( disjoint @ ( fiber @ A @ SY3640 ) @ ( sK14_B @ A ) )
| ~ ( in @ SY3640 @ ( sK14_B @ A ) ) )
& ( ( sK14_B @ A )
!= empty_set )
& ( subset @ ( sK14_B @ A ) @ ( relation_field @ A ) ) )
| ( well_founded_relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_founded_relation @ A )
| ! [B: $i] :
( ( ( disjoint @ ( fiber @ A @ ( sK13_C @ B @ A ) ) @ B )
& ( in @ ( sK13_C @ B @ A ) @ B ) )
| ( B = empty_set )
| ~ ( subset @ B @ ( relation_field @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[345]) ).
thf(426,plain,
( ( ! [A: $i] :
( ( ( in @ ( sK15_B @ A ) @ A )
& ~ ( subset @ ( sK15_B @ A ) @ A ) )
| ( epsilon_transitive @ A ) )
& ! [A: $i] :
( ~ ( epsilon_transitive @ A )
| ! [B: $i] :
( ~ ( in @ B @ A )
| ( subset @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[346]) ).
thf(427,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK16_C @ B @ A ) @ B )
| ~ ( subset @ ( sK16_C @ B @ A ) @ A ) )
& ( ( in @ ( sK16_C @ B @ A ) @ B )
| ( subset @ ( sK16_C @ B @ A ) @ A ) ) )
| ( B
= ( powerset @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( powerset @ A ) )
| ( ! [C: $i] :
( ~ ( in @ C @ B )
| ( subset @ C @ A ) )
& ! [C: $i] :
( ~ ( subset @ C @ A )
| ( in @ C @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[347]) ).
thf(428,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( subset @ C @ ( cartesian_product2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ C @ ( cartesian_product2 @ A @ B ) )
| ( relation_of2 @ C @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[348]) ).
thf(429,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[349]) ).
thf(430,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[350]) ).
thf(431,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[351]) ).
thf(432,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ B )
| ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[352]) ).
thf(433,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[353]) ).
thf(434,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[355]) ).
thf(435,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[356]) ).
thf(436,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[357]) ).
thf(437,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ ( relation_dom @ A ) @ ( relation_rng @ B ) )
| ( ( relation_rng @ ( relation_composition @ B @ A ) )
= ( relation_rng @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[358]) ).
thf(438,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ ( relation_rng @ A ) @ ( relation_dom @ B ) )
| ( ( relation_dom @ ( relation_composition @ A @ B ) )
= ( relation_dom @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[359]) ).
thf(439,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[360]) ).
thf(440,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[361]) ).
thf(441,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[362]) ).
thf(442,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ! [C: $i] :
( ~ ( element @ C @ ( powerset @ A ) )
| ~ ( disjoint @ B @ C )
| ( subset @ B @ ( subset_complement @ A @ C ) ) )
& ! [C: $i] :
( ~ ( element @ C @ ( powerset @ A ) )
| ~ ( subset @ B @ ( subset_complement @ A @ C ) )
| ( disjoint @ B @ C ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[363]) ).
thf(443,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[364]) ).
thf(444,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[365]) ).
thf(445,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ ( relation_field @ B ) )
| ~ ( well_ordering @ B )
| ( ( relation_field @ ( relation_restriction @ B @ A ) )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[366]) ).
thf(446,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ C )
| ( subset @ ( unordered_pair @ A @ B ) @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ A @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[367]) ).
thf(447,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[368]) ).
thf(448,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[369]) ).
thf(449,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[371]) ).
thf(450,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ordinal @ B )
| ( ( ordinal @ ( sK17_C @ B @ A ) )
& ! [SY3641: $i] :
( ~ ( ordinal @ SY3641 )
| ~ ( in @ SY3641 @ A )
| ( ordinal_subset @ ( sK17_C @ B @ A ) @ SY3641 ) )
& ( in @ ( sK17_C @ B @ A ) @ A ) )
| ( A = empty_set )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[372]) ).
thf(451,plain,
( ( ! [A: $i] :
( ( ( in @ ( sK18_B @ A ) @ A )
& ( ~ ( ordinal @ ( sK18_B @ A ) )
| ~ ( subset @ ( sK18_B @ A ) @ A ) ) )
| ( ordinal @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[373]) ).
thf(452,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[375]) ).
thf(453,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[376]) ).
thf(454,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[377]) ).
thf(455,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation @ C )
| ( subset @ ( fiber @ ( relation_restriction @ C @ A ) @ B ) @ ( fiber @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[378]) ).
thf(456,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[379]) ).
thf(457,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_field @ ( relation_restriction @ B @ A ) ) @ ( relation_field @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_field @ ( relation_restriction @ B @ A ) ) @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[380]) ).
thf(458,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[381]) ).
thf(459,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ A @ C )
| ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[382]) ).
thf(460,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_inverse_image @ C @ A ) @ ( relation_inverse_image @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[384]) ).
thf(461,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( A = empty_set )
| ~ ( subset @ A @ ( relation_rng @ B ) )
| ( ( relation_inverse_image @ B @ A )
!= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[385]) ).
thf(462,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[386]) ).
thf(463,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(extcnf_combined,[status(esa)],[387]) ).
thf(464,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ~ ( subset @ A @ ( relation_rng @ B ) )
| ( ( relation_image @ B @ ( relation_inverse_image @ B @ A ) )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[388]) ).
thf(465,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ ( relation_dom @ B ) )
| ( subset @ A @ ( relation_inverse_image @ B @ ( relation_image @ B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[389]) ).
thf(466,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( subset @ ( relation_image @ B @ ( relation_inverse_image @ B @ A ) ) @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[390]) ).
thf(467,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[391]) ).
thf(468,plain,
( ( ! [A: $i] :
( ! [SY3642: $i] :
( ~ ( subset @ SY3642 @ ( sK19_B @ A ) )
| ( are_equipotent @ SY3642 @ ( sK19_B @ A ) )
| ( in @ SY3642 @ ( sK19_B @ A ) ) )
& ! [SY3643: $i] :
( ~ ( in @ SY3643 @ ( sK19_B @ A ) )
| ( in @ ( powerset @ SY3643 ) @ ( sK19_B @ A ) ) )
& ! [SY3644: $i,SY3645: $i] :
( ~ ( in @ SY3644 @ ( sK19_B @ A ) )
| ~ ( subset @ SY3645 @ SY3644 )
| ( in @ SY3645 @ ( sK19_B @ A ) ) )
& ( in @ A @ ( sK19_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[392]) ).
thf(469,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[393]) ).
thf(470,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( subset @ ( relation_dom @ C ) @ A ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( subset @ ( relation_rng @ C ) @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[394]) ).
thf(471,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ D )
| ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[395]) ).
thf(472,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) ) )
& ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[396]) ).
thf(473,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[397]) ).
thf(474,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[398]) ).
thf(475,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[399]) ).
thf(476,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[400]) ).
thf(477,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[401]) ).
thf(478,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[402]) ).
thf(479,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[403]) ).
thf(480,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[404]) ).
thf(481,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[405]) ).
thf(482,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[481]) ).
thf(483,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[480]) ).
thf(484,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[479]) ).
thf(485,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[478]) ).
thf(486,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[477]) ).
thf(487,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[476]) ).
thf(488,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[475]) ).
thf(489,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[474]) ).
thf(490,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[473]) ).
thf(491,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) ) )
& ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[472]) ).
thf(492,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)],[471]) ).
thf(493,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( subset @ ( relation_dom @ C ) @ A ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( subset @ ( relation_rng @ C ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[470]) ).
thf(494,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[469]) ).
thf(495,plain,
( ( ! [A: $i] :
( ! [SY3642: $i] :
( ~ ( subset @ SY3642 @ ( sK19_B @ A ) )
| ( are_equipotent @ SY3642 @ ( sK19_B @ A ) )
| ( in @ SY3642 @ ( sK19_B @ A ) ) )
& ! [SY3643: $i] :
( ~ ( in @ SY3643 @ ( sK19_B @ A ) )
| ( in @ ( powerset @ SY3643 ) @ ( sK19_B @ A ) ) )
& ! [SY3644: $i,SY3645: $i] :
( ~ ( in @ SY3644 @ ( sK19_B @ A ) )
| ~ ( subset @ SY3645 @ SY3644 )
| ( in @ SY3645 @ ( sK19_B @ A ) ) )
& ( in @ A @ ( sK19_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[468]) ).
thf(496,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[467]) ).
thf(497,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( subset @ ( relation_image @ B @ ( relation_inverse_image @ B @ A ) ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[466]) ).
thf(498,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ ( relation_dom @ B ) )
| ( subset @ A @ ( relation_inverse_image @ B @ ( relation_image @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[465]) ).
thf(499,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ~ ( subset @ A @ ( relation_rng @ B ) )
| ( ( relation_image @ B @ ( relation_inverse_image @ B @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[464]) ).
thf(500,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)],[463]) ).
thf(501,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[462]) ).
thf(502,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( A = empty_set )
| ~ ( subset @ A @ ( relation_rng @ B ) )
| ( ( relation_inverse_image @ B @ A )
!= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[461]) ).
thf(503,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)],[460]) ).
thf(504,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[383]) ).
thf(505,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ A @ C )
| ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[459]) ).
thf(506,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[458]) ).
thf(507,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_field @ ( relation_restriction @ B @ A ) ) @ ( relation_field @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_field @ ( relation_restriction @ B @ A ) ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[457]) ).
thf(508,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[456]) ).
thf(509,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation @ C )
| ( subset @ ( fiber @ ( relation_restriction @ C @ A ) @ B ) @ ( fiber @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[455]) ).
thf(510,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[454]) ).
thf(511,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[453]) ).
thf(512,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[452]) ).
thf(513,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[374]) ).
thf(514,plain,
( ( ! [A: $i] :
( ( ( in @ ( sK18_B @ A ) @ A )
& ( ~ ( ordinal @ ( sK18_B @ A ) )
| ~ ( subset @ ( sK18_B @ A ) @ A ) ) )
| ( ordinal @ A ) ) )
= $true ),
inference(copy,[status(thm)],[451]) ).
thf(515,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ordinal @ B )
| ( ( ordinal @ ( sK17_C @ B @ A ) )
& ! [SY3641: $i] :
( ~ ( ordinal @ SY3641 )
| ~ ( in @ SY3641 @ A )
| ( ordinal_subset @ ( sK17_C @ B @ A ) @ SY3641 ) )
& ( in @ ( sK17_C @ B @ A ) @ A ) )
| ( A = empty_set )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[450]) ).
thf(516,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[449]) ).
thf(517,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(518,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[448]) ).
thf(519,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[447]) ).
thf(520,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ C )
| ( subset @ ( unordered_pair @ A @ B ) @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ A @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[446]) ).
thf(521,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ ( relation_field @ B ) )
| ~ ( well_ordering @ B )
| ( ( relation_field @ ( relation_restriction @ B @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[445]) ).
thf(522,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[444]) ).
thf(523,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[443]) ).
thf(524,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ! [C: $i] :
( ~ ( element @ C @ ( powerset @ A ) )
| ~ ( disjoint @ B @ C )
| ( subset @ B @ ( subset_complement @ A @ C ) ) )
& ! [C: $i] :
( ~ ( element @ C @ ( powerset @ A ) )
| ~ ( subset @ B @ ( subset_complement @ A @ C ) )
| ( disjoint @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[442]) ).
thf(525,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[441]) ).
thf(526,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[440]) ).
thf(527,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[439]) ).
thf(528,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ ( relation_rng @ A ) @ ( relation_dom @ B ) )
| ( ( relation_dom @ ( relation_composition @ A @ B ) )
= ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[438]) ).
thf(529,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ ( relation_dom @ A ) @ ( relation_rng @ B ) )
| ( ( relation_rng @ ( relation_composition @ B @ A ) )
= ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[437]) ).
thf(530,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[436]) ).
thf(531,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[435]) ).
thf(532,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[434]) ).
thf(533,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[354]) ).
thf(534,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[433]) ).
thf(535,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ B )
| ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[432]) ).
thf(536,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[431]) ).
thf(537,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[430]) ).
thf(538,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[429]) ).
thf(539,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( subset @ C @ ( cartesian_product2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ C @ ( cartesian_product2 @ A @ B ) )
| ( relation_of2 @ C @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[428]) ).
thf(540,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK16_C @ B @ A ) @ B )
| ~ ( subset @ ( sK16_C @ B @ A ) @ A ) )
& ( ( in @ ( sK16_C @ B @ A ) @ B )
| ( subset @ ( sK16_C @ B @ A ) @ A ) ) )
| ( B
= ( powerset @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( powerset @ A ) )
| ( ! [C: $i] :
( ~ ( in @ C @ B )
| ( subset @ C @ A ) )
& ! [C: $i] :
( ~ ( subset @ C @ A )
| ( in @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[427]) ).
thf(541,plain,
( ( ! [A: $i] :
( ( ( in @ ( sK15_B @ A ) @ A )
& ~ ( subset @ ( sK15_B @ A ) @ A ) )
| ( epsilon_transitive @ A ) )
& ! [A: $i] :
( ~ ( epsilon_transitive @ A )
| ! [B: $i] :
( ~ ( in @ B @ A )
| ( subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[426]) ).
thf(542,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [SY3640: $i] :
( ~ ( disjoint @ ( fiber @ A @ SY3640 ) @ ( sK14_B @ A ) )
| ~ ( in @ SY3640 @ ( sK14_B @ A ) ) )
& ( ( sK14_B @ A )
!= empty_set )
& ( subset @ ( sK14_B @ A ) @ ( relation_field @ A ) ) )
| ( well_founded_relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_founded_relation @ A )
| ! [B: $i] :
( ( ( disjoint @ ( fiber @ A @ ( sK13_C @ B @ A ) ) @ B )
& ( in @ ( sK13_C @ B @ A ) @ B ) )
| ( B = empty_set )
| ~ ( subset @ B @ ( relation_field @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[425]) ).
thf(543,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( in @ ( ordered_pair @ ( sK11_C @ B @ A ) @ ( sK12_SY3639 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK11_C @ B @ A ) @ ( sK12_SY3639 @ B @ A ) ) @ B ) )
| ( subset @ A @ B ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ B )
| ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[424]) ).
thf(544,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK10_C @ B @ A ) @ A )
& ~ ( in @ ( sK10_C @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[423]) ).
thf(545,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ! [SY3638: $i] :
( ~ ( disjoint @ ( fiber @ A @ SY3638 ) @ ( sK9_C @ B @ A ) )
| ~ ( in @ SY3638 @ ( sK9_C @ B @ A ) ) )
& ( ( sK9_C @ B @ A )
!= empty_set )
& ( subset @ ( sK9_C @ B @ A ) @ B ) )
| ( is_well_founded_in @ A @ B ) )
& ! [B: $i] :
( ~ ( is_well_founded_in @ A @ B )
| ! [C: $i] :
( ( ( disjoint @ ( fiber @ A @ ( sK8_D @ C @ B @ A ) ) @ C )
& ( in @ ( sK8_D @ C @ B @ A ) @ C ) )
| ( C = empty_set )
| ~ ( subset @ C @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[422]) ).
thf(546,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ( proper_subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( A != B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[421]) ).
thf(547,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[420]) ).
thf(548,plain,
( ( ! [A: $i,B: $i] : ( relation_of2_as_subset @ ( sK7_C @ B @ A ) @ A @ B ) )
= $true ),
inference(copy,[status(thm)],[419]) ).
thf(549,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( relation_of2_as_subset @ C @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( relation_of2 @ C @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[418]) ).
thf(550,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ordinal @ A )
| ~ ( ordinal @ B )
| ~ ( ordinal_subset @ A @ B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( ordinal @ A )
| ~ ( ordinal @ B )
| ~ ( subset @ A @ B )
| ( ordinal_subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[417]) ).
thf(551,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[416]) ).
thf(552,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[415]) ).
thf(553,plain,
( ( ! [A: $i] :
( ! [SY3631: $i] :
( ~ ( subset @ SY3631 @ ( sK5_B @ A ) )
| ( are_equipotent @ SY3631 @ ( sK5_B @ A ) )
| ( in @ SY3631 @ ( sK5_B @ A ) ) )
& ! [SY3632: $i] :
( ( ! [SY3637: $i] :
( ~ ( subset @ SY3637 @ SY3632 )
| ( in @ SY3637 @ ( sK6_SY3633 @ SY3632 @ A ) ) )
& ( in @ ( sK6_SY3633 @ SY3632 @ A ) @ ( sK5_B @ A ) ) )
| ~ ( in @ SY3632 @ ( sK5_B @ A ) ) )
& ! [SY3635: $i,SY3636: $i] :
( ~ ( in @ SY3635 @ ( sK5_B @ A ) )
| ~ ( subset @ SY3636 @ SY3635 )
| ( in @ SY3636 @ ( sK5_B @ A ) ) )
& ( in @ A @ ( sK5_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[414]) ).
thf(554,plain,
( ( subset @ sK1_A @ sK2_SY3625 )
= $true ),
inference(copy,[status(thm)],[411]) ).
thf(555,plain,
( ( relation_of2_as_subset @ sK4_SY3630 @ sK3_SY3628 @ sK1_A )
= $true ),
inference(copy,[status(thm)],[410]) ).
thf(556,plain,
( ( ~ ( relation_of2_as_subset @ sK4_SY3630 @ sK3_SY3628 @ sK2_SY3625 ) )
= $true ),
inference(copy,[status(thm)],[413]) ).
thf(557,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[486]) ).
thf(558,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( relation_dom @ SX0 ) @ ( relation_dom @ SX1 ) ) )
| ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( relation_rng @ SX0 ) @ ( relation_rng @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[510]) ).
thf(559,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ ( powerset @ SX0 ) )
| ~ ( disjoint @ SX1 @ SX2 )
| ( subset @ SX1 @ ( subset_complement @ SX0 @ SX2 ) ) )
| ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ ( powerset @ SX0 ) )
| ~ ( subset @ SX1 @ ( subset_complement @ SX0 @ SX2 ) )
| ( disjoint @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[524]) ).
thf(560,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2 @ SX2 @ SX0 @ SX1 )
| ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( relation_of2 @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[549]) ).
thf(561,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[546]) ).
thf(562,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( disjoint @ ( fiber @ SX0 @ SX1 ) @ ( sK14_B @ SX0 ) )
| ~ ( in @ SX1 @ ( sK14_B @ SX0 ) ) )
| ~ ~ ( ~ ( ( ( sK14_B @ SX0 )
!= empty_set ) )
| ~ ( subset @ ( sK14_B @ SX0 ) @ ( relation_field @ SX0 ) ) ) )
| ( well_founded_relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ! [SX1: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SX0 @ ( sK13_C @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) )
| ( SX1 = empty_set )
| ~ ( subset @ SX1 @ ( relation_field @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[542]) ).
thf(563,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ordinal @ SX1 )
| ~ ( ~ ( ordinal @ ( sK17_C @ SX1 @ SX0 ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ~ ( ordinal @ SX2 )
| ~ ( in @ SX2 @ SX0 )
| ( ordinal_subset @ ( sK17_C @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX0 = empty_set )
| ~ ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[515]) ).
thf(564,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ( in @ ( sK15_B @ SX0 ) @ SX0 )
| ~ ~ ( subset @ ( sK15_B @ SX0 ) @ SX0 ) )
| ( epsilon_transitive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( epsilon_transitive @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[541]) ).
thf(565,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX2 )
| ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX0 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[520]) ).
thf(566,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[544]) ).
thf(567,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[538]) ).
thf(568,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX1 @ ( sK19_B @ SX0 ) )
| ( are_equipotent @ SX1 @ ( sK19_B @ SX0 ) )
| ( in @ SX1 @ ( sK19_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK19_B @ SX0 ) )
| ( in @ ( powerset @ SX1 ) @ ( sK19_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( sK19_B @ SX0 ) )
| ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK19_B @ SX0 ) ) )
| ~ ( in @ SX0 @ ( sK19_B @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[495]) ).
thf(569,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[483]) ).
thf(570,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[518]) ).
thf(571,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[552]) ).
thf(572,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_field @ ( relation_restriction @ SX1 @ SX0 ) ) @ ( relation_field @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_field @ ( relation_restriction @ SX1 @ SX0 ) ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[507]) ).
thf(573,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] : ( subset @ ( cartesian_product2 @ SX0 @ SX2 ) @ ( cartesian_product2 @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] : ( subset @ ( cartesian_product2 @ SX2 @ SX0 ) @ ( cartesian_product2 @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[491]) ).
thf(574,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK16_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK16_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK16_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK16_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[540]) ).
thf(575,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2 @ SX2 @ SX0 @ SX1 )
| ( subset @ SX2 @ ( cartesian_product2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( subset @ SX2 @ ( cartesian_product2 @ SX0 @ SX1 ) )
| ( relation_of2 @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[539]) ).
thf(576,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[519]) ).
thf(577,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( subset @ ( relation_dom @ SX2 ) @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( subset @ ( relation_rng @ SX2 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[493]) ).
thf(578,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ( in @ ( sK18_B @ SX0 ) @ SX0 )
| ~ ( ~ ( ordinal @ ( sK18_B @ SX0 ) )
| ~ ( subset @ ( sK18_B @ SX0 ) @ SX0 ) ) )
| ( ordinal @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[514]) ).
thf(579,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ! [SX2: $i] :
( ~ ( disjoint @ ( fiber @ SX0 @ SX2 ) @ ( sK9_C @ SX1 @ SX0 ) )
| ~ ( in @ SX2 @ ( sK9_C @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ( ( sK9_C @ SX1 @ SX0 )
!= empty_set ) )
| ~ ( subset @ ( sK9_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( is_well_founded_in @ SX0 @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( is_well_founded_in @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SX0 @ ( sK8_D @ SX2 @ SX1 @ SX0 ) ) @ SX2 )
| ~ ( in @ ( sK8_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ( SX2 = empty_set )
| ~ ( subset @ SX2 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[545]) ).
thf(580,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX1 @ ( sK5_B @ SX0 ) )
| ( are_equipotent @ SX1 @ ( sK5_B @ SX0 ) )
| ( in @ SX1 @ ( sK5_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK6_SY3633 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK6_SY3633 @ SX1 @ SX0 ) @ ( sK5_B @ SX0 ) ) )
| ~ ( in @ SX1 @ ( sK5_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( sK5_B @ SX0 ) )
| ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK5_B @ SX0 ) ) )
| ~ ( in @ SX0 @ ( sK5_B @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[553]) ).
thf(581,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[522]) ).
thf(582,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SX1 @ SX0 ) @ ( sK12_SY3639 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( in @ ( ordered_pair @ ( sK11_C @ SX1 @ SX0 ) @ ( sK12_SY3639 @ SX1 @ SX0 ) ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[543]) ).
thf(583,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ordinal @ SX1 )
| ~ ( ordinal_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ordinal @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( ordinal_subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[550]) ).
thf(584,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[484]) ).
thf(585,plain,
! [SV1: $i] :
( ( ! [SY3646: $i] :
( ~ ( relation @ SY3646 )
| ( subset @ ( relation_dom @ ( relation_rng_restriction @ SV1 @ SY3646 ) ) @ ( relation_dom @ SY3646 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(586,plain,
! [SV2: $i] :
( ( ! [SY3647: $i] :
( ~ ( subset @ SV2 @ SY3647 )
| ! [SY3648: $i] :
( ( in @ SY3648 @ SV2 )
| ( subset @ SV2 @ ( set_difference @ SY3647 @ ( singleton @ SY3648 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(587,plain,
! [SV3: $i] :
( ( ! [SY3649: $i] :
( ~ ( in @ SV3 @ SY3649 )
| ( subset @ SV3 @ ( union @ SY3649 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(588,plain,
! [SV4: $i] :
( ( ! [SY3650: $i] :
( ~ ( relation @ SY3650 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV4 @ SY3650 ) ) @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(589,plain,
! [SV5: $i] :
( ( ! [SY3651: $i] :
( ~ ( relation @ SY3651 )
| ( subset @ ( relation_rng_restriction @ SV5 @ SY3651 ) @ SY3651 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(590,plain,
! [SV6: $i] :
( ( ! [SY3652: $i] :
( ~ ( relation @ SY3652 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV6 @ SY3652 ) ) @ ( relation_rng @ SY3652 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(591,plain,
! [SV7: $i] :
( ( ! [SY3653: $i,SY3654: $i,SY3655: $i] :
( ~ ( subset @ SV7 @ SY3653 )
| ~ ( subset @ SY3654 @ SY3655 )
| ( subset @ ( cartesian_product2 @ SV7 @ SY3654 ) @ ( cartesian_product2 @ SY3653 @ SY3655 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(592,plain,
! [SV8: $i] :
( ( ! [SY3656: $i] :
( ~ ( subset @ SV8 @ SY3656 )
| ( ( set_union2 @ SV8 @ SY3656 )
= SY3656 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(593,plain,
! [SV9: $i] :
( ( ! [SY3657: $i] :
( ~ ( relation @ SY3657 )
| ( subset @ ( relation_image @ SY3657 @ SV9 ) @ ( relation_rng @ SY3657 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(594,plain,
! [SV10: $i] :
( ( ! [SY3658: $i] :
( ~ ( function @ SY3658 )
| ~ ( relation @ SY3658 )
| ( subset @ ( relation_image @ SY3658 @ ( relation_inverse_image @ SY3658 @ SV10 ) ) @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(595,plain,
! [SV11: $i] :
( ( ! [SY3659: $i] :
( ~ ( relation @ SY3659 )
| ~ ( subset @ SV11 @ ( relation_dom @ SY3659 ) )
| ( subset @ SV11 @ ( relation_inverse_image @ SY3659 @ ( relation_image @ SY3659 @ SV11 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(596,plain,
! [SV12: $i] :
( ( ! [SY3660: $i] :
( ~ ( function @ SY3660 )
| ~ ( relation @ SY3660 )
| ~ ( subset @ SV12 @ ( relation_rng @ SY3660 ) )
| ( ( relation_image @ SY3660 @ ( relation_inverse_image @ SY3660 @ SV12 ) )
= SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(597,plain,
! [SV13: $i] :
( ( ! [SY3661: $i,SY3662: $i,SY3663: $i] :
( ~ ( relation_of2_as_subset @ SY3663 @ SY3662 @ SV13 )
| ~ ( subset @ ( relation_rng @ SY3663 ) @ SY3661 )
| ( relation_of2_as_subset @ SY3663 @ SY3662 @ SY3661 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(598,plain,
! [SV14: $i] :
( ( ! [SY3664: $i] :
( ~ ( relation @ SY3664 )
| ( subset @ ( relation_inverse_image @ SY3664 @ SV14 ) @ ( relation_dom @ SY3664 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(599,plain,
! [SV15: $i] :
( ( ! [SY3665: $i] :
( ~ ( relation @ SY3665 )
| ( SV15 = empty_set )
| ~ ( subset @ SV15 @ ( relation_rng @ SY3665 ) )
| ( ( relation_inverse_image @ SY3665 @ SV15 )
!= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(600,plain,
! [SV16: $i] :
( ( ! [SY3666: $i,SY3667: $i] :
( ~ ( relation @ SY3667 )
| ~ ( subset @ SV16 @ SY3666 )
| ( subset @ ( relation_inverse_image @ SY3667 @ SV16 ) @ ( relation_inverse_image @ SY3667 @ SY3666 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(601,plain,
! [SV17: $i] :
( ( ! [SY3668: $i] : ( subset @ ( set_intersection2 @ SV17 @ SY3668 ) @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(602,plain,
! [SV18: $i] :
( ( ! [SY3669: $i,SY3670: $i] :
( ~ ( subset @ SV18 @ SY3669 )
| ~ ( subset @ SV18 @ SY3670 )
| ( subset @ SV18 @ ( set_intersection2 @ SY3669 @ SY3670 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(603,plain,
! [SV19: $i] :
( ( ! [SY3671: $i,SY3672: $i] :
( ~ ( subset @ SV19 @ SY3671 )
| ~ ( subset @ SY3671 @ SY3672 )
| ( subset @ SV19 @ SY3672 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(604,plain,
! [SV20: $i] :
( ( ~ ( relation @ SV20 )
| ( subset @ SV20 @ ( cartesian_product2 @ ( relation_dom @ SV20 ) @ ( relation_rng @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(605,plain,
! [SV21: $i] :
( ( ! [SY3673: $i,SY3674: $i] :
( ~ ( relation @ SY3674 )
| ( subset @ ( fiber @ ( relation_restriction @ SY3674 @ SV21 ) @ SY3673 ) @ ( fiber @ SY3674 @ SY3673 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(606,plain,
! [SV22: $i] :
( ( ! [SY3675: $i] :
( ~ ( subset @ SV22 @ SY3675 )
| ! [SY3676: $i] : ( subset @ ( set_intersection2 @ SV22 @ SY3676 ) @ ( set_intersection2 @ SY3675 @ SY3676 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(607,plain,
! [SV23: $i] :
( ( ! [SY3677: $i] :
( ~ ( subset @ SV23 @ SY3677 )
| ( ( set_intersection2 @ SV23 @ SY3677 )
= SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(608,plain,
! [SV24: $i] :
( ( subset @ empty_set @ SV24 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(609,plain,
! [SV25: $i] :
( ( ! [SY3678: $i] :
( ~ ( subset @ SV25 @ SY3678 )
| ! [SY3679: $i] : ( subset @ ( set_difference @ SV25 @ SY3679 ) @ ( set_difference @ SY3678 @ SY3679 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(610,plain,
! [SV26: $i] :
( ( ! [SY3680: $i] : ( subset @ ( set_difference @ SV26 @ SY3680 ) @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(611,plain,
! [SV27: $i] :
( ( ! [SY3681: $i] :
( ~ ( relation @ SY3681 )
| ~ ( subset @ SV27 @ ( relation_field @ SY3681 ) )
| ~ ( well_ordering @ SY3681 )
| ( ( relation_field @ ( relation_restriction @ SY3681 @ SV27 ) )
= SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(612,plain,
! [SV28: $i] :
( ( ~ ( subset @ SV28 @ empty_set )
| ( SV28 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(613,plain,
! [SV29: $i] :
( ( ~ ( relation @ SV29 )
| ! [SY3682: $i] :
( ~ ( relation @ SY3682 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV29 @ SY3682 ) ) @ ( relation_dom @ SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(614,plain,
! [SV30: $i] :
( ( ~ ( relation @ SV30 )
| ! [SY3683: $i] :
( ~ ( relation @ SY3683 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV30 @ SY3683 ) ) @ ( relation_rng @ SY3683 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(615,plain,
! [SV31: $i] :
( ( ! [SY3684: $i] :
( ~ ( subset @ SV31 @ SY3684 )
| ( SY3684
= ( set_union2 @ SV31 @ ( set_difference @ SY3684 @ SV31 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(616,plain,
! [SV32: $i] :
( ( ~ ( relation @ SV32 )
| ! [SY3685: $i] :
( ~ ( relation @ SY3685 )
| ~ ( subset @ ( relation_rng @ SV32 ) @ ( relation_dom @ SY3685 ) )
| ( ( relation_dom @ ( relation_composition @ SV32 @ SY3685 ) )
= ( relation_dom @ SV32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(617,plain,
! [SV33: $i] :
( ( ~ ( relation @ SV33 )
| ! [SY3686: $i] :
( ~ ( relation @ SY3686 )
| ~ ( subset @ ( relation_dom @ SV33 ) @ ( relation_rng @ SY3686 ) )
| ( ( relation_rng @ ( relation_composition @ SY3686 @ SV33 ) )
= ( relation_rng @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(618,plain,
! [SV34: $i] :
( ( ! [SY3687: $i] :
( ~ ( proper_subset @ SY3687 @ SV34 )
| ~ ( subset @ SV34 @ SY3687 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(619,plain,
! [SV35: $i] :
( ( ! [SY3688: $i,SY3689: $i] :
( ~ ( disjoint @ SY3688 @ SY3689 )
| ~ ( subset @ SV35 @ SY3688 )
| ( disjoint @ SV35 @ SY3689 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(620,plain,
! [SV36: $i] :
( ( ! [SY3690: $i] :
( ~ ( subset @ ( singleton @ SV36 ) @ ( singleton @ SY3690 ) )
| ( SV36 = SY3690 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(621,plain,
! [SV37: $i] :
( ( ! [SY3691: $i] : ( subset @ SV37 @ ( set_union2 @ SV37 @ SY3691 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(622,plain,
! [SV38: $i] :
( ( ! [SY3692: $i] :
( ~ ( relation @ SY3692 )
| ( subset @ ( relation_dom_restriction @ SY3692 @ SV38 ) @ SY3692 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(623,plain,
! [SV39: $i] :
( ( ! [SY3693: $i,SY3694: $i] :
( ~ ( subset @ SV39 @ SY3693 )
| ~ ( subset @ SY3694 @ SY3693 )
| ( subset @ ( set_union2 @ SV39 @ SY3694 ) @ SY3693 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(624,plain,
! [SV40: $i] :
( ( ! [SY3695: $i] :
( ~ ( in @ SV40 @ SY3695 )
| ( subset @ SV40 @ ( union @ SY3695 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(625,plain,
! [SV41: $i] :
( ( ! [SY3696: $i] :
( ~ ( relation @ SY3696 )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ SY3696 @ SV41 ) ) @ ( relation_rng @ SY3696 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(626,plain,
! [SV42: $i] :
( ( ! [SY3697: $i,SY3698: $i] :
( ~ ( relation_of2_as_subset @ SY3698 @ SV42 @ SY3697 )
| ( element @ SY3698 @ ( powerset @ ( cartesian_product2 @ SV42 @ SY3697 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(627,plain,
! [SV43: $i] :
( ( ! [SY3699: $i] : ( relation_of2_as_subset @ ( sK7_C @ SY3699 @ SV43 ) @ SV43 @ SY3699 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(628,plain,
! [SV44: $i] :
( ( subset @ SV44 @ SV44 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(629,plain,
( ( relation_of2_as_subset @ sK4_SY3630 @ sK3_SY3628 @ sK2_SY3625 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[556]) ).
thf(630,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[557]) ).
thf(631,plain,
! [SV45: $i] :
( ( ~ ( relation @ SV45 )
| ~ ( ~ ! [SY3700: $i] :
( ~ ( relation @ SY3700 )
| ~ ( subset @ SV45 @ SY3700 )
| ( subset @ ( relation_dom @ SV45 ) @ ( relation_dom @ SY3700 ) ) )
| ~ ! [SY3701: $i] :
( ~ ( relation @ SY3701 )
| ~ ( subset @ SV45 @ SY3701 )
| ( subset @ ( relation_rng @ SV45 ) @ ( relation_rng @ SY3701 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(632,plain,
! [SV46: $i] :
( ( ! [SY3702: $i] :
( ~ ( element @ SY3702 @ ( powerset @ SV46 ) )
| ~ ( ~ ! [SY3703: $i] :
( ~ ( element @ SY3703 @ ( powerset @ SV46 ) )
| ~ ( disjoint @ SY3702 @ SY3703 )
| ( subset @ SY3702 @ ( subset_complement @ SV46 @ SY3703 ) ) )
| ~ ! [SY3704: $i] :
( ~ ( element @ SY3704 @ ( powerset @ SV46 ) )
| ~ ( subset @ SY3702 @ ( subset_complement @ SV46 @ SY3704 ) )
| ( disjoint @ SY3702 @ SY3704 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(633,plain,
! [SV47: $i] :
( ( ~ ( ~ ! [SY3705: $i,SY3706: $i] :
( ~ ( relation_of2 @ SY3706 @ SV47 @ SY3705 )
| ( relation_of2_as_subset @ SY3706 @ SV47 @ SY3705 ) )
| ~ ! [SY3707: $i,SY3708: $i] :
( ~ ( relation_of2_as_subset @ SY3708 @ SV47 @ SY3707 )
| ( relation_of2 @ SY3708 @ SV47 @ SY3707 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(634,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[561]) ).
thf(635,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( disjoint @ ( fiber @ SX0 @ SX1 ) @ ( sK14_B @ SX0 ) )
| ~ ( in @ SX1 @ ( sK14_B @ SX0 ) ) )
| ~ ~ ( ~ ( ( ( sK14_B @ SX0 )
!= empty_set ) )
| ~ ( subset @ ( sK14_B @ SX0 ) @ ( relation_field @ SX0 ) ) ) )
| ( well_founded_relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ! [SX1: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SX0 @ ( sK13_C @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) )
| ( SX1 = empty_set )
| ~ ( subset @ SX1 @ ( relation_field @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[562]) ).
thf(636,plain,
! [SV48: $i] :
( ( ! [SY3709: $i] :
( ~ ( ordinal @ SY3709 )
| ~ ( ~ ( ordinal @ ( sK17_C @ SY3709 @ SV48 ) )
| ~ ~ ( ~ ! [SY3710: $i] :
( ~ ( ordinal @ SY3710 )
| ~ ( in @ SY3710 @ SV48 )
| ( ordinal_subset @ ( sK17_C @ SY3709 @ SV48 ) @ SY3710 ) )
| ~ ( in @ ( sK17_C @ SY3709 @ SV48 ) @ SV48 ) ) )
| ( SV48 = empty_set )
| ~ ( subset @ SV48 @ SY3709 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(637,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ( in @ ( sK15_B @ SX0 ) @ SX0 )
| ~ ~ ( subset @ ( sK15_B @ SX0 ) @ SX0 ) )
| ( epsilon_transitive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( epsilon_transitive @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[564]) ).
thf(638,plain,
! [SV49: $i] :
( ( ~ ( ~ ! [SY3711: $i,SY3712: $i] :
( ~ ( in @ SV49 @ SY3712 )
| ~ ( in @ SY3711 @ SY3712 )
| ( subset @ ( unordered_pair @ SV49 @ SY3711 ) @ SY3712 ) )
| ~ ~ ( ~ ! [SY3713: $i,SY3714: $i] :
( ~ ( subset @ ( unordered_pair @ SV49 @ SY3713 ) @ SY3714 )
| ( in @ SV49 @ SY3714 ) )
| ~ ! [SY3715: $i,SY3716: $i] :
( ~ ( subset @ ( unordered_pair @ SV49 @ SY3715 ) @ SY3716 )
| ( in @ SY3715 @ SY3716 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(639,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[566]) ).
thf(640,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[567]) ).
thf(641,plain,
! [SV50: $i] :
( ( ~ ( ~ ! [SY3717: $i] :
( ~ ( subset @ SY3717 @ ( sK19_B @ SV50 ) )
| ( are_equipotent @ SY3717 @ ( sK19_B @ SV50 ) )
| ( in @ SY3717 @ ( sK19_B @ SV50 ) ) )
| ~ ~ ( ~ ! [SY3718: $i] :
( ~ ( in @ SY3718 @ ( sK19_B @ SV50 ) )
| ( in @ ( powerset @ SY3718 ) @ ( sK19_B @ SV50 ) ) )
| ~ ~ ( ~ ! [SY3719: $i,SY3720: $i] :
( ~ ( in @ SY3719 @ ( sK19_B @ SV50 ) )
| ~ ( subset @ SY3720 @ SY3719 )
| ( in @ SY3720 @ ( sK19_B @ SV50 ) ) )
| ~ ( in @ SV50 @ ( sK19_B @ SV50 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(642,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[569]) ).
thf(643,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[570]) ).
thf(644,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(645,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_field @ ( relation_restriction @ SX1 @ SX0 ) ) @ ( relation_field @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_field @ ( relation_restriction @ SX1 @ SX0 ) ) @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[572]) ).
thf(646,plain,
! [SV51: $i] :
( ( ~ ( ~ ! [SY3721: $i] :
( ~ ( subset @ SV51 @ SY3721 )
| ! [SY3722: $i] : ( subset @ ( cartesian_product2 @ SV51 @ SY3722 ) @ ( cartesian_product2 @ SY3721 @ SY3722 ) ) )
| ~ ! [SY3723: $i] :
( ~ ( subset @ SV51 @ SY3723 )
| ! [SY3724: $i] : ( subset @ ( cartesian_product2 @ SY3724 @ SV51 ) @ ( cartesian_product2 @ SY3724 @ SY3723 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(647,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK16_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK16_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK16_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK16_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[574]) ).
thf(648,plain,
! [SV52: $i] :
( ( ~ ( ~ ! [SY3725: $i,SY3726: $i] :
( ~ ( relation_of2 @ SY3726 @ SV52 @ SY3725 )
| ( subset @ SY3726 @ ( cartesian_product2 @ SV52 @ SY3725 ) ) )
| ~ ! [SY3727: $i,SY3728: $i] :
( ~ ( subset @ SY3728 @ ( cartesian_product2 @ SV52 @ SY3727 ) )
| ( relation_of2 @ SY3728 @ SV52 @ SY3727 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(649,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(650,plain,
! [SV53: $i] :
( ( ~ ( ~ ! [SY3729: $i,SY3730: $i] :
( ~ ( relation_of2_as_subset @ SY3730 @ SV53 @ SY3729 )
| ( subset @ ( relation_dom @ SY3730 ) @ SV53 ) )
| ~ ! [SY3731: $i,SY3732: $i] :
( ~ ( relation_of2_as_subset @ SY3732 @ SV53 @ SY3731 )
| ( subset @ ( relation_rng @ SY3732 ) @ SY3731 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(651,plain,
! [SV54: $i] :
( ( ~ ( ~ ( in @ ( sK18_B @ SV54 ) @ SV54 )
| ~ ( ~ ( ordinal @ ( sK18_B @ SV54 ) )
| ~ ( subset @ ( sK18_B @ SV54 ) @ SV54 ) ) )
| ( ordinal @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(652,plain,
! [SV55: $i] :
( ( ~ ( relation @ SV55 )
| ~ ( ~ ! [SY3733: $i] :
( ~ ( ~ ! [SY3734: $i] :
( ~ ( disjoint @ ( fiber @ SV55 @ SY3734 ) @ ( sK9_C @ SY3733 @ SV55 ) )
| ~ ( in @ SY3734 @ ( sK9_C @ SY3733 @ SV55 ) ) )
| ~ ~ ( ~ ( ( ( sK9_C @ SY3733 @ SV55 )
!= empty_set ) )
| ~ ( subset @ ( sK9_C @ SY3733 @ SV55 ) @ SY3733 ) ) )
| ( is_well_founded_in @ SV55 @ SY3733 ) )
| ~ ! [SY3735: $i] :
( ~ ( is_well_founded_in @ SV55 @ SY3735 )
| ! [SY3736: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV55 @ ( sK8_D @ SY3736 @ SY3735 @ SV55 ) ) @ SY3736 )
| ~ ( in @ ( sK8_D @ SY3736 @ SY3735 @ SV55 ) @ SY3736 ) )
| ( SY3736 = empty_set )
| ~ ( subset @ SY3736 @ SY3735 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[579]) ).
thf(653,plain,
! [SV56: $i] :
( ( ~ ( ~ ! [SY3737: $i] :
( ~ ( subset @ SY3737 @ ( sK5_B @ SV56 ) )
| ( are_equipotent @ SY3737 @ ( sK5_B @ SV56 ) )
| ( in @ SY3737 @ ( sK5_B @ SV56 ) ) )
| ~ ~ ( ~ ! [SY3738: $i] :
( ~ ( ~ ! [SY3739: $i] :
( ~ ( subset @ SY3739 @ SY3738 )
| ( in @ SY3739 @ ( sK6_SY3633 @ SY3738 @ SV56 ) ) )
| ~ ( in @ ( sK6_SY3633 @ SY3738 @ SV56 ) @ ( sK5_B @ SV56 ) ) )
| ~ ( in @ SY3738 @ ( sK5_B @ SV56 ) ) )
| ~ ~ ( ~ ! [SY3740: $i,SY3741: $i] :
( ~ ( in @ SY3740 @ ( sK5_B @ SV56 ) )
| ~ ( subset @ SY3741 @ SY3740 )
| ( in @ SY3741 @ ( sK5_B @ SV56 ) ) )
| ~ ( in @ SV56 @ ( sK5_B @ SV56 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(654,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[581]) ).
thf(655,plain,
! [SV57: $i] :
( ( ~ ( relation @ SV57 )
| ~ ( ~ ! [SY3742: $i] :
( ~ ( relation @ SY3742 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SY3742 @ SV57 ) @ ( sK12_SY3639 @ SY3742 @ SV57 ) ) @ SV57 )
| ~ ~ ( in @ ( ordered_pair @ ( sK11_C @ SY3742 @ SV57 ) @ ( sK12_SY3639 @ SY3742 @ SV57 ) ) @ SY3742 ) )
| ( subset @ SV57 @ SY3742 ) )
| ~ ! [SY3743: $i] :
( ~ ( relation @ SY3743 )
| ~ ( subset @ SV57 @ SY3743 )
| ! [SY3744: $i,SY3745: $i] :
( ~ ( in @ ( ordered_pair @ SY3744 @ SY3745 ) @ SV57 )
| ( in @ ( ordered_pair @ SY3744 @ SY3745 ) @ SY3743 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(656,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ordinal @ SX1 )
| ~ ( ordinal_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ordinal @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( ordinal_subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[583]) ).
thf(657,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[584]) ).
thf(658,plain,
! [SV1: $i,SV58: $i] :
( ( ~ ( relation @ SV58 )
| ( subset @ ( relation_dom @ ( relation_rng_restriction @ SV1 @ SV58 ) ) @ ( relation_dom @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(659,plain,
! [SV59: $i,SV2: $i] :
( ( ~ ( subset @ SV2 @ SV59 )
| ! [SY3746: $i] :
( ( in @ SY3746 @ SV2 )
| ( subset @ SV2 @ ( set_difference @ SV59 @ ( singleton @ SY3746 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[586]) ).
thf(660,plain,
! [SV60: $i,SV3: $i] :
( ( ~ ( in @ SV3 @ SV60 )
| ( subset @ SV3 @ ( union @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(661,plain,
! [SV4: $i,SV61: $i] :
( ( ~ ( relation @ SV61 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV4 @ SV61 ) ) @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(662,plain,
! [SV5: $i,SV62: $i] :
( ( ~ ( relation @ SV62 )
| ( subset @ ( relation_rng_restriction @ SV5 @ SV62 ) @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(663,plain,
! [SV6: $i,SV63: $i] :
( ( ~ ( relation @ SV63 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV6 @ SV63 ) ) @ ( relation_rng @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(664,plain,
! [SV64: $i,SV7: $i] :
( ( ! [SY3747: $i,SY3748: $i] :
( ~ ( subset @ SV7 @ SV64 )
| ~ ( subset @ SY3747 @ SY3748 )
| ( subset @ ( cartesian_product2 @ SV7 @ SY3747 ) @ ( cartesian_product2 @ SV64 @ SY3748 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(665,plain,
! [SV65: $i,SV8: $i] :
( ( ~ ( subset @ SV8 @ SV65 )
| ( ( set_union2 @ SV8 @ SV65 )
= SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(666,plain,
! [SV9: $i,SV66: $i] :
( ( ~ ( relation @ SV66 )
| ( subset @ ( relation_image @ SV66 @ SV9 ) @ ( relation_rng @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(667,plain,
! [SV10: $i,SV67: $i] :
( ( ~ ( function @ SV67 )
| ~ ( relation @ SV67 )
| ( subset @ ( relation_image @ SV67 @ ( relation_inverse_image @ SV67 @ SV10 ) ) @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(668,plain,
! [SV11: $i,SV68: $i] :
( ( ~ ( relation @ SV68 )
| ~ ( subset @ SV11 @ ( relation_dom @ SV68 ) )
| ( subset @ SV11 @ ( relation_inverse_image @ SV68 @ ( relation_image @ SV68 @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(669,plain,
! [SV12: $i,SV69: $i] :
( ( ~ ( function @ SV69 )
| ~ ( relation @ SV69 )
| ~ ( subset @ SV12 @ ( relation_rng @ SV69 ) )
| ( ( relation_image @ SV69 @ ( relation_inverse_image @ SV69 @ SV12 ) )
= SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(670,plain,
! [SV70: $i,SV13: $i] :
( ( ! [SY3749: $i,SY3750: $i] :
( ~ ( relation_of2_as_subset @ SY3750 @ SY3749 @ SV13 )
| ~ ( subset @ ( relation_rng @ SY3750 ) @ SV70 )
| ( relation_of2_as_subset @ SY3750 @ SY3749 @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(671,plain,
! [SV14: $i,SV71: $i] :
( ( ~ ( relation @ SV71 )
| ( subset @ ( relation_inverse_image @ SV71 @ SV14 ) @ ( relation_dom @ SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(672,plain,
! [SV15: $i,SV72: $i] :
( ( ~ ( relation @ SV72 )
| ( SV15 = empty_set )
| ~ ( subset @ SV15 @ ( relation_rng @ SV72 ) )
| ( ( relation_inverse_image @ SV72 @ SV15 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(673,plain,
! [SV73: $i,SV16: $i] :
( ( ! [SY3751: $i] :
( ~ ( relation @ SY3751 )
| ~ ( subset @ SV16 @ SV73 )
| ( subset @ ( relation_inverse_image @ SY3751 @ SV16 ) @ ( relation_inverse_image @ SY3751 @ SV73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(674,plain,
! [SV74: $i,SV17: $i] :
( ( subset @ ( set_intersection2 @ SV17 @ SV74 ) @ SV17 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(675,plain,
! [SV75: $i,SV18: $i] :
( ( ! [SY3752: $i] :
( ~ ( subset @ SV18 @ SV75 )
| ~ ( subset @ SV18 @ SY3752 )
| ( subset @ SV18 @ ( set_intersection2 @ SV75 @ SY3752 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(676,plain,
! [SV76: $i,SV19: $i] :
( ( ! [SY3753: $i] :
( ~ ( subset @ SV19 @ SV76 )
| ~ ( subset @ SV76 @ SY3753 )
| ( subset @ SV19 @ SY3753 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(677,plain,
! [SV20: $i] :
( ( ( ~ ( relation @ SV20 ) )
= $true )
| ( ( subset @ SV20 @ ( cartesian_product2 @ ( relation_dom @ SV20 ) @ ( relation_rng @ SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[604]) ).
thf(678,plain,
! [SV77: $i,SV21: $i] :
( ( ! [SY3754: $i] :
( ~ ( relation @ SY3754 )
| ( subset @ ( fiber @ ( relation_restriction @ SY3754 @ SV21 ) @ SV77 ) @ ( fiber @ SY3754 @ SV77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[605]) ).
thf(679,plain,
! [SV78: $i,SV22: $i] :
( ( ~ ( subset @ SV22 @ SV78 )
| ! [SY3755: $i] : ( subset @ ( set_intersection2 @ SV22 @ SY3755 ) @ ( set_intersection2 @ SV78 @ SY3755 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(680,plain,
! [SV79: $i,SV23: $i] :
( ( ~ ( subset @ SV23 @ SV79 )
| ( ( set_intersection2 @ SV23 @ SV79 )
= SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(681,plain,
! [SV80: $i,SV25: $i] :
( ( ~ ( subset @ SV25 @ SV80 )
| ! [SY3756: $i] : ( subset @ ( set_difference @ SV25 @ SY3756 ) @ ( set_difference @ SV80 @ SY3756 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(682,plain,
! [SV81: $i,SV26: $i] :
( ( subset @ ( set_difference @ SV26 @ SV81 ) @ SV26 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(683,plain,
! [SV27: $i,SV82: $i] :
( ( ~ ( relation @ SV82 )
| ~ ( subset @ SV27 @ ( relation_field @ SV82 ) )
| ~ ( well_ordering @ SV82 )
| ( ( relation_field @ ( relation_restriction @ SV82 @ SV27 ) )
= SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(684,plain,
! [SV28: $i] :
( ( ( ~ ( subset @ SV28 @ empty_set ) )
= $true )
| ( ( SV28 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[612]) ).
thf(685,plain,
! [SV29: $i] :
( ( ( ~ ( relation @ SV29 ) )
= $true )
| ( ( ! [SY3682: $i] :
( ~ ( relation @ SY3682 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV29 @ SY3682 ) ) @ ( relation_dom @ SV29 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[613]) ).
thf(686,plain,
! [SV30: $i] :
( ( ( ~ ( relation @ SV30 ) )
= $true )
| ( ( ! [SY3683: $i] :
( ~ ( relation @ SY3683 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV30 @ SY3683 ) ) @ ( relation_rng @ SY3683 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[614]) ).
thf(687,plain,
! [SV83: $i,SV31: $i] :
( ( ~ ( subset @ SV31 @ SV83 )
| ( SV83
= ( set_union2 @ SV31 @ ( set_difference @ SV83 @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(688,plain,
! [SV32: $i] :
( ( ( ~ ( relation @ SV32 ) )
= $true )
| ( ( ! [SY3685: $i] :
( ~ ( relation @ SY3685 )
| ~ ( subset @ ( relation_rng @ SV32 ) @ ( relation_dom @ SY3685 ) )
| ( ( relation_dom @ ( relation_composition @ SV32 @ SY3685 ) )
= ( relation_dom @ SV32 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[616]) ).
thf(689,plain,
! [SV33: $i] :
( ( ( ~ ( relation @ SV33 ) )
= $true )
| ( ( ! [SY3686: $i] :
( ~ ( relation @ SY3686 )
| ~ ( subset @ ( relation_dom @ SV33 ) @ ( relation_rng @ SY3686 ) )
| ( ( relation_rng @ ( relation_composition @ SY3686 @ SV33 ) )
= ( relation_rng @ SV33 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[617]) ).
thf(690,plain,
! [SV34: $i,SV84: $i] :
( ( ~ ( proper_subset @ SV84 @ SV34 )
| ~ ( subset @ SV34 @ SV84 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(691,plain,
! [SV35: $i,SV85: $i] :
( ( ! [SY3757: $i] :
( ~ ( disjoint @ SV85 @ SY3757 )
| ~ ( subset @ SV35 @ SV85 )
| ( disjoint @ SV35 @ SY3757 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(692,plain,
! [SV86: $i,SV36: $i] :
( ( ~ ( subset @ ( singleton @ SV36 ) @ ( singleton @ SV86 ) )
| ( SV36 = SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(693,plain,
! [SV87: $i,SV37: $i] :
( ( subset @ SV37 @ ( set_union2 @ SV37 @ SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(694,plain,
! [SV38: $i,SV88: $i] :
( ( ~ ( relation @ SV88 )
| ( subset @ ( relation_dom_restriction @ SV88 @ SV38 ) @ SV88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(695,plain,
! [SV89: $i,SV39: $i] :
( ( ! [SY3758: $i] :
( ~ ( subset @ SV39 @ SV89 )
| ~ ( subset @ SY3758 @ SV89 )
| ( subset @ ( set_union2 @ SV39 @ SY3758 ) @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(696,plain,
! [SV90: $i,SV40: $i] :
( ( ~ ( in @ SV40 @ SV90 )
| ( subset @ SV40 @ ( union @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(697,plain,
! [SV41: $i,SV91: $i] :
( ( ~ ( relation @ SV91 )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ SV91 @ SV41 ) ) @ ( relation_rng @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(698,plain,
! [SV92: $i,SV42: $i] :
( ( ! [SY3759: $i] :
( ~ ( relation_of2_as_subset @ SY3759 @ SV42 @ SV92 )
| ( element @ SY3759 @ ( powerset @ ( cartesian_product2 @ SV42 @ SV92 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(699,plain,
! [SV43: $i,SV93: $i] :
( ( relation_of2_as_subset @ ( sK7_C @ SV93 @ SV43 ) @ SV43 @ SV93 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(700,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[630]) ).
thf(701,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[630]) ).
thf(702,plain,
! [SV45: $i] :
( ( ( ~ ( relation @ SV45 ) )
= $true )
| ( ( ~ ( ~ ! [SY3700: $i] :
( ~ ( relation @ SY3700 )
| ~ ( subset @ SV45 @ SY3700 )
| ( subset @ ( relation_dom @ SV45 ) @ ( relation_dom @ SY3700 ) ) )
| ~ ! [SY3701: $i] :
( ~ ( relation @ SY3701 )
| ~ ( subset @ SV45 @ SY3701 )
| ( subset @ ( relation_rng @ SV45 ) @ ( relation_rng @ SY3701 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[631]) ).
thf(703,plain,
! [SV46: $i,SV94: $i] :
( ( ~ ( element @ SV94 @ ( powerset @ SV46 ) )
| ~ ( ~ ! [SY3760: $i] :
( ~ ( element @ SY3760 @ ( powerset @ SV46 ) )
| ~ ( disjoint @ SV94 @ SY3760 )
| ( subset @ SV94 @ ( subset_complement @ SV46 @ SY3760 ) ) )
| ~ ! [SY3761: $i] :
( ~ ( element @ SY3761 @ ( powerset @ SV46 ) )
| ~ ( subset @ SV94 @ ( subset_complement @ SV46 @ SY3761 ) )
| ( disjoint @ SV94 @ SY3761 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(704,plain,
! [SV47: $i] :
( ( ~ ! [SY3705: $i,SY3706: $i] :
( ~ ( relation_of2 @ SY3706 @ SV47 @ SY3705 )
| ( relation_of2_as_subset @ SY3706 @ SV47 @ SY3705 ) )
| ~ ! [SY3707: $i,SY3708: $i] :
( ~ ( relation_of2_as_subset @ SY3708 @ SV47 @ SY3707 )
| ( relation_of2 @ SY3708 @ SV47 @ SY3707 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[633]) ).
thf(705,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[634]) ).
thf(706,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[634]) ).
thf(707,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( disjoint @ ( fiber @ SX0 @ SX1 ) @ ( sK14_B @ SX0 ) )
| ~ ( in @ SX1 @ ( sK14_B @ SX0 ) ) )
| ~ ~ ( ~ ( ( ( sK14_B @ SX0 )
!= empty_set ) )
| ~ ( subset @ ( sK14_B @ SX0 ) @ ( relation_field @ SX0 ) ) ) )
| ( well_founded_relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[635]) ).
thf(708,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ! [SX1: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SX0 @ ( sK13_C @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) )
| ( SX1 = empty_set )
| ~ ( subset @ SX1 @ ( relation_field @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[635]) ).
thf(709,plain,
! [SV48: $i,SV95: $i] :
( ( ~ ( ordinal @ SV95 )
| ~ ( ~ ( ordinal @ ( sK17_C @ SV95 @ SV48 ) )
| ~ ~ ( ~ ! [SY3762: $i] :
( ~ ( ordinal @ SY3762 )
| ~ ( in @ SY3762 @ SV48 )
| ( ordinal_subset @ ( sK17_C @ SV95 @ SV48 ) @ SY3762 ) )
| ~ ( in @ ( sK17_C @ SV95 @ SV48 ) @ SV48 ) ) )
| ( SV48 = empty_set )
| ~ ( subset @ SV48 @ SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(710,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ( in @ ( sK15_B @ SX0 ) @ SX0 )
| ~ ~ ( subset @ ( sK15_B @ SX0 ) @ SX0 ) )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[637]) ).
thf(711,plain,
( ( ~ ! [SX0: $i] :
( ~ ( epsilon_transitive @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[637]) ).
thf(712,plain,
! [SV49: $i] :
( ( ~ ! [SY3711: $i,SY3712: $i] :
( ~ ( in @ SV49 @ SY3712 )
| ~ ( in @ SY3711 @ SY3712 )
| ( subset @ ( unordered_pair @ SV49 @ SY3711 ) @ SY3712 ) )
| ~ ~ ( ~ ! [SY3713: $i,SY3714: $i] :
( ~ ( subset @ ( unordered_pair @ SV49 @ SY3713 ) @ SY3714 )
| ( in @ SV49 @ SY3714 ) )
| ~ ! [SY3715: $i,SY3716: $i] :
( ~ ( subset @ ( unordered_pair @ SV49 @ SY3715 ) @ SY3716 )
| ( in @ SY3715 @ SY3716 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[638]) ).
thf(713,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[639]) ).
thf(714,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[639]) ).
thf(715,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[640]) ).
thf(716,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[640]) ).
thf(717,plain,
! [SV50: $i] :
( ( ~ ! [SY3717: $i] :
( ~ ( subset @ SY3717 @ ( sK19_B @ SV50 ) )
| ( are_equipotent @ SY3717 @ ( sK19_B @ SV50 ) )
| ( in @ SY3717 @ ( sK19_B @ SV50 ) ) )
| ~ ~ ( ~ ! [SY3718: $i] :
( ~ ( in @ SY3718 @ ( sK19_B @ SV50 ) )
| ( in @ ( powerset @ SY3718 ) @ ( sK19_B @ SV50 ) ) )
| ~ ~ ( ~ ! [SY3719: $i,SY3720: $i] :
( ~ ( in @ SY3719 @ ( sK19_B @ SV50 ) )
| ~ ( subset @ SY3720 @ SY3719 )
| ( in @ SY3720 @ ( sK19_B @ SV50 ) ) )
| ~ ( in @ SV50 @ ( sK19_B @ SV50 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[641]) ).
thf(718,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[642]) ).
thf(719,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[642]) ).
thf(720,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[643]) ).
thf(721,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[643]) ).
thf(722,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[644]) ).
thf(723,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[644]) ).
thf(724,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_field @ ( relation_restriction @ SX1 @ SX0 ) ) @ ( relation_field @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[645]) ).
thf(725,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_field @ ( relation_restriction @ SX1 @ SX0 ) ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[645]) ).
thf(726,plain,
! [SV51: $i] :
( ( ~ ! [SY3721: $i] :
( ~ ( subset @ SV51 @ SY3721 )
| ! [SY3722: $i] : ( subset @ ( cartesian_product2 @ SV51 @ SY3722 ) @ ( cartesian_product2 @ SY3721 @ SY3722 ) ) )
| ~ ! [SY3723: $i] :
( ~ ( subset @ SV51 @ SY3723 )
| ! [SY3724: $i] : ( subset @ ( cartesian_product2 @ SY3724 @ SV51 ) @ ( cartesian_product2 @ SY3724 @ SY3723 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[646]) ).
thf(727,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK16_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK16_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK16_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK16_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[647]) ).
thf(728,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[647]) ).
thf(729,plain,
! [SV52: $i] :
( ( ~ ! [SY3725: $i,SY3726: $i] :
( ~ ( relation_of2 @ SY3726 @ SV52 @ SY3725 )
| ( subset @ SY3726 @ ( cartesian_product2 @ SV52 @ SY3725 ) ) )
| ~ ! [SY3727: $i,SY3728: $i] :
( ~ ( subset @ SY3728 @ ( cartesian_product2 @ SV52 @ SY3727 ) )
| ( relation_of2 @ SY3728 @ SV52 @ SY3727 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[648]) ).
thf(730,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[649]) ).
thf(731,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[649]) ).
thf(732,plain,
! [SV53: $i] :
( ( ~ ! [SY3729: $i,SY3730: $i] :
( ~ ( relation_of2_as_subset @ SY3730 @ SV53 @ SY3729 )
| ( subset @ ( relation_dom @ SY3730 ) @ SV53 ) )
| ~ ! [SY3731: $i,SY3732: $i] :
( ~ ( relation_of2_as_subset @ SY3732 @ SV53 @ SY3731 )
| ( subset @ ( relation_rng @ SY3732 ) @ SY3731 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[650]) ).
thf(733,plain,
! [SV54: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_B @ SV54 ) @ SV54 )
| ~ ( ~ ( ordinal @ ( sK18_B @ SV54 ) )
| ~ ( subset @ ( sK18_B @ SV54 ) @ SV54 ) ) ) )
= $true )
| ( ( ordinal @ SV54 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[651]) ).
thf(734,plain,
! [SV55: $i] :
( ( ( ~ ( relation @ SV55 ) )
= $true )
| ( ( ~ ( ~ ! [SY3733: $i] :
( ~ ( ~ ! [SY3734: $i] :
( ~ ( disjoint @ ( fiber @ SV55 @ SY3734 ) @ ( sK9_C @ SY3733 @ SV55 ) )
| ~ ( in @ SY3734 @ ( sK9_C @ SY3733 @ SV55 ) ) )
| ~ ~ ( ~ ( ( ( sK9_C @ SY3733 @ SV55 )
!= empty_set ) )
| ~ ( subset @ ( sK9_C @ SY3733 @ SV55 ) @ SY3733 ) ) )
| ( is_well_founded_in @ SV55 @ SY3733 ) )
| ~ ! [SY3735: $i] :
( ~ ( is_well_founded_in @ SV55 @ SY3735 )
| ! [SY3736: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV55 @ ( sK8_D @ SY3736 @ SY3735 @ SV55 ) ) @ SY3736 )
| ~ ( in @ ( sK8_D @ SY3736 @ SY3735 @ SV55 ) @ SY3736 ) )
| ( SY3736 = empty_set )
| ~ ( subset @ SY3736 @ SY3735 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[652]) ).
thf(735,plain,
! [SV56: $i] :
( ( ~ ! [SY3737: $i] :
( ~ ( subset @ SY3737 @ ( sK5_B @ SV56 ) )
| ( are_equipotent @ SY3737 @ ( sK5_B @ SV56 ) )
| ( in @ SY3737 @ ( sK5_B @ SV56 ) ) )
| ~ ~ ( ~ ! [SY3738: $i] :
( ~ ( ~ ! [SY3739: $i] :
( ~ ( subset @ SY3739 @ SY3738 )
| ( in @ SY3739 @ ( sK6_SY3633 @ SY3738 @ SV56 ) ) )
| ~ ( in @ ( sK6_SY3633 @ SY3738 @ SV56 ) @ ( sK5_B @ SV56 ) ) )
| ~ ( in @ SY3738 @ ( sK5_B @ SV56 ) ) )
| ~ ~ ( ~ ! [SY3740: $i,SY3741: $i] :
( ~ ( in @ SY3740 @ ( sK5_B @ SV56 ) )
| ~ ( subset @ SY3741 @ SY3740 )
| ( in @ SY3741 @ ( sK5_B @ SV56 ) ) )
| ~ ( in @ SV56 @ ( sK5_B @ SV56 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[653]) ).
thf(736,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[654]) ).
thf(737,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[654]) ).
thf(738,plain,
! [SV57: $i] :
( ( ( ~ ( relation @ SV57 ) )
= $true )
| ( ( ~ ( ~ ! [SY3742: $i] :
( ~ ( relation @ SY3742 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SY3742 @ SV57 ) @ ( sK12_SY3639 @ SY3742 @ SV57 ) ) @ SV57 )
| ~ ~ ( in @ ( ordered_pair @ ( sK11_C @ SY3742 @ SV57 ) @ ( sK12_SY3639 @ SY3742 @ SV57 ) ) @ SY3742 ) )
| ( subset @ SV57 @ SY3742 ) )
| ~ ! [SY3743: $i] :
( ~ ( relation @ SY3743 )
| ~ ( subset @ SV57 @ SY3743 )
| ! [SY3744: $i,SY3745: $i] :
( ~ ( in @ ( ordered_pair @ SY3744 @ SY3745 ) @ SV57 )
| ( in @ ( ordered_pair @ SY3744 @ SY3745 ) @ SY3743 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[655]) ).
thf(739,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ordinal @ SX1 )
| ~ ( ordinal_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[656]) ).
thf(740,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ordinal @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( ordinal_subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[656]) ).
thf(741,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[657]) ).
thf(742,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[657]) ).
thf(743,plain,
! [SV1: $i,SV58: $i] :
( ( ( ~ ( relation @ SV58 ) )
= $true )
| ( ( subset @ ( relation_dom @ ( relation_rng_restriction @ SV1 @ SV58 ) ) @ ( relation_dom @ SV58 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[658]) ).
thf(744,plain,
! [SV59: $i,SV2: $i] :
( ( ( ~ ( subset @ SV2 @ SV59 ) )
= $true )
| ( ( ! [SY3746: $i] :
( ( in @ SY3746 @ SV2 )
| ( subset @ SV2 @ ( set_difference @ SV59 @ ( singleton @ SY3746 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[659]) ).
thf(745,plain,
! [SV60: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV60 ) )
= $true )
| ( ( subset @ SV3 @ ( union @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[660]) ).
thf(746,plain,
! [SV4: $i,SV61: $i] :
( ( ( ~ ( relation @ SV61 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV4 @ SV61 ) ) @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[661]) ).
thf(747,plain,
! [SV5: $i,SV62: $i] :
( ( ( ~ ( relation @ SV62 ) )
= $true )
| ( ( subset @ ( relation_rng_restriction @ SV5 @ SV62 ) @ SV62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[662]) ).
thf(748,plain,
! [SV6: $i,SV63: $i] :
( ( ( ~ ( relation @ SV63 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV6 @ SV63 ) ) @ ( relation_rng @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[663]) ).
thf(749,plain,
! [SV96: $i,SV64: $i,SV7: $i] :
( ( ! [SY3763: $i] :
( ~ ( subset @ SV7 @ SV64 )
| ~ ( subset @ SV96 @ SY3763 )
| ( subset @ ( cartesian_product2 @ SV7 @ SV96 ) @ ( cartesian_product2 @ SV64 @ SY3763 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(750,plain,
! [SV65: $i,SV8: $i] :
( ( ( ~ ( subset @ SV8 @ SV65 ) )
= $true )
| ( ( ( set_union2 @ SV8 @ SV65 )
= SV65 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[665]) ).
thf(751,plain,
! [SV9: $i,SV66: $i] :
( ( ( ~ ( relation @ SV66 ) )
= $true )
| ( ( subset @ ( relation_image @ SV66 @ SV9 ) @ ( relation_rng @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[666]) ).
thf(752,plain,
! [SV10: $i,SV67: $i] :
( ( ( ~ ( function @ SV67 )
| ~ ( relation @ SV67 ) )
= $true )
| ( ( subset @ ( relation_image @ SV67 @ ( relation_inverse_image @ SV67 @ SV10 ) ) @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[667]) ).
thf(753,plain,
! [SV11: $i,SV68: $i] :
( ( ( ~ ( relation @ SV68 ) )
= $true )
| ( ( ~ ( subset @ SV11 @ ( relation_dom @ SV68 ) )
| ( subset @ SV11 @ ( relation_inverse_image @ SV68 @ ( relation_image @ SV68 @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[668]) ).
thf(754,plain,
! [SV12: $i,SV69: $i] :
( ( ( ~ ( function @ SV69 )
| ~ ( relation @ SV69 ) )
= $true )
| ( ( ~ ( subset @ SV12 @ ( relation_rng @ SV69 ) )
| ( ( relation_image @ SV69 @ ( relation_inverse_image @ SV69 @ SV12 ) )
= SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[669]) ).
thf(755,plain,
! [SV70: $i,SV13: $i,SV97: $i] :
( ( ! [SY3764: $i] :
( ~ ( relation_of2_as_subset @ SY3764 @ SV97 @ SV13 )
| ~ ( subset @ ( relation_rng @ SY3764 ) @ SV70 )
| ( relation_of2_as_subset @ SY3764 @ SV97 @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(756,plain,
! [SV14: $i,SV71: $i] :
( ( ( ~ ( relation @ SV71 ) )
= $true )
| ( ( subset @ ( relation_inverse_image @ SV71 @ SV14 ) @ ( relation_dom @ SV71 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[671]) ).
thf(757,plain,
! [SV15: $i,SV72: $i] :
( ( ( ~ ( relation @ SV72 ) )
= $true )
| ( ( ( SV15 = empty_set )
| ~ ( subset @ SV15 @ ( relation_rng @ SV72 ) )
| ( ( relation_inverse_image @ SV72 @ SV15 )
!= empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[672]) ).
thf(758,plain,
! [SV73: $i,SV16: $i,SV98: $i] :
( ( ~ ( relation @ SV98 )
| ~ ( subset @ SV16 @ SV73 )
| ( subset @ ( relation_inverse_image @ SV98 @ SV16 ) @ ( relation_inverse_image @ SV98 @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(759,plain,
! [SV99: $i,SV75: $i,SV18: $i] :
( ( ~ ( subset @ SV18 @ SV75 )
| ~ ( subset @ SV18 @ SV99 )
| ( subset @ SV18 @ ( set_intersection2 @ SV75 @ SV99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(760,plain,
! [SV100: $i,SV76: $i,SV19: $i] :
( ( ~ ( subset @ SV19 @ SV76 )
| ~ ( subset @ SV76 @ SV100 )
| ( subset @ SV19 @ SV100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(761,plain,
! [SV20: $i] :
( ( ( relation @ SV20 )
= $false )
| ( ( subset @ SV20 @ ( cartesian_product2 @ ( relation_dom @ SV20 ) @ ( relation_rng @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[677]) ).
thf(762,plain,
! [SV77: $i,SV21: $i,SV101: $i] :
( ( ~ ( relation @ SV101 )
| ( subset @ ( fiber @ ( relation_restriction @ SV101 @ SV21 ) @ SV77 ) @ ( fiber @ SV101 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(763,plain,
! [SV78: $i,SV22: $i] :
( ( ( ~ ( subset @ SV22 @ SV78 ) )
= $true )
| ( ( ! [SY3755: $i] : ( subset @ ( set_intersection2 @ SV22 @ SY3755 ) @ ( set_intersection2 @ SV78 @ SY3755 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[679]) ).
thf(764,plain,
! [SV79: $i,SV23: $i] :
( ( ( ~ ( subset @ SV23 @ SV79 ) )
= $true )
| ( ( ( set_intersection2 @ SV23 @ SV79 )
= SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[680]) ).
thf(765,plain,
! [SV80: $i,SV25: $i] :
( ( ( ~ ( subset @ SV25 @ SV80 ) )
= $true )
| ( ( ! [SY3756: $i] : ( subset @ ( set_difference @ SV25 @ SY3756 ) @ ( set_difference @ SV80 @ SY3756 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[681]) ).
thf(766,plain,
! [SV27: $i,SV82: $i] :
( ( ( ~ ( relation @ SV82 ) )
= $true )
| ( ( ~ ( subset @ SV27 @ ( relation_field @ SV82 ) )
| ~ ( well_ordering @ SV82 )
| ( ( relation_field @ ( relation_restriction @ SV82 @ SV27 ) )
= SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[683]) ).
thf(767,plain,
! [SV28: $i] :
( ( ( subset @ SV28 @ empty_set )
= $false )
| ( ( SV28 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[684]) ).
thf(768,plain,
! [SV29: $i] :
( ( ( relation @ SV29 )
= $false )
| ( ( ! [SY3682: $i] :
( ~ ( relation @ SY3682 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV29 @ SY3682 ) ) @ ( relation_dom @ SV29 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[685]) ).
thf(769,plain,
! [SV30: $i] :
( ( ( relation @ SV30 )
= $false )
| ( ( ! [SY3683: $i] :
( ~ ( relation @ SY3683 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV30 @ SY3683 ) ) @ ( relation_rng @ SY3683 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[686]) ).
thf(770,plain,
! [SV83: $i,SV31: $i] :
( ( ( ~ ( subset @ SV31 @ SV83 ) )
= $true )
| ( ( SV83
= ( set_union2 @ SV31 @ ( set_difference @ SV83 @ SV31 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[687]) ).
thf(771,plain,
! [SV32: $i] :
( ( ( relation @ SV32 )
= $false )
| ( ( ! [SY3685: $i] :
( ~ ( relation @ SY3685 )
| ~ ( subset @ ( relation_rng @ SV32 ) @ ( relation_dom @ SY3685 ) )
| ( ( relation_dom @ ( relation_composition @ SV32 @ SY3685 ) )
= ( relation_dom @ SV32 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[688]) ).
thf(772,plain,
! [SV33: $i] :
( ( ( relation @ SV33 )
= $false )
| ( ( ! [SY3686: $i] :
( ~ ( relation @ SY3686 )
| ~ ( subset @ ( relation_dom @ SV33 ) @ ( relation_rng @ SY3686 ) )
| ( ( relation_rng @ ( relation_composition @ SY3686 @ SV33 ) )
= ( relation_rng @ SV33 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[689]) ).
thf(773,plain,
! [SV34: $i,SV84: $i] :
( ( ( ~ ( proper_subset @ SV84 @ SV34 ) )
= $true )
| ( ( ~ ( subset @ SV34 @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[690]) ).
thf(774,plain,
! [SV35: $i,SV102: $i,SV85: $i] :
( ( ~ ( disjoint @ SV85 @ SV102 )
| ~ ( subset @ SV35 @ SV85 )
| ( disjoint @ SV35 @ SV102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(775,plain,
! [SV86: $i,SV36: $i] :
( ( ( ~ ( subset @ ( singleton @ SV36 ) @ ( singleton @ SV86 ) ) )
= $true )
| ( ( SV36 = SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[692]) ).
thf(776,plain,
! [SV38: $i,SV88: $i] :
( ( ( ~ ( relation @ SV88 ) )
= $true )
| ( ( subset @ ( relation_dom_restriction @ SV88 @ SV38 ) @ SV88 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[694]) ).
thf(777,plain,
! [SV103: $i,SV89: $i,SV39: $i] :
( ( ~ ( subset @ SV39 @ SV89 )
| ~ ( subset @ SV103 @ SV89 )
| ( subset @ ( set_union2 @ SV39 @ SV103 ) @ SV89 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(778,plain,
! [SV90: $i,SV40: $i] :
( ( ( ~ ( in @ SV40 @ SV90 ) )
= $true )
| ( ( subset @ SV40 @ ( union @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[696]) ).
thf(779,plain,
! [SV41: $i,SV91: $i] :
( ( ( ~ ( relation @ SV91 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_dom_restriction @ SV91 @ SV41 ) ) @ ( relation_rng @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[697]) ).
thf(780,plain,
! [SV92: $i,SV42: $i,SV104: $i] :
( ( ~ ( relation_of2_as_subset @ SV104 @ SV42 @ SV92 )
| ( element @ SV104 @ ( powerset @ ( cartesian_product2 @ SV42 @ SV92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(781,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[700]) ).
thf(782,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[701]) ).
thf(783,plain,
! [SV45: $i] :
( ( ( relation @ SV45 )
= $false )
| ( ( ~ ( ~ ! [SY3700: $i] :
( ~ ( relation @ SY3700 )
| ~ ( subset @ SV45 @ SY3700 )
| ( subset @ ( relation_dom @ SV45 ) @ ( relation_dom @ SY3700 ) ) )
| ~ ! [SY3701: $i] :
( ~ ( relation @ SY3701 )
| ~ ( subset @ SV45 @ SY3701 )
| ( subset @ ( relation_rng @ SV45 ) @ ( relation_rng @ SY3701 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[702]) ).
thf(784,plain,
! [SV46: $i,SV94: $i] :
( ( ( ~ ( element @ SV94 @ ( powerset @ SV46 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3760: $i] :
( ~ ( element @ SY3760 @ ( powerset @ SV46 ) )
| ~ ( disjoint @ SV94 @ SY3760 )
| ( subset @ SV94 @ ( subset_complement @ SV46 @ SY3760 ) ) )
| ~ ! [SY3761: $i] :
( ~ ( element @ SY3761 @ ( powerset @ SV46 ) )
| ~ ( subset @ SV94 @ ( subset_complement @ SV46 @ SY3761 ) )
| ( disjoint @ SV94 @ SY3761 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[703]) ).
thf(785,plain,
! [SV47: $i] :
( ( ~ ! [SY3705: $i,SY3706: $i] :
( ~ ( relation_of2 @ SY3706 @ SV47 @ SY3705 )
| ( relation_of2_as_subset @ SY3706 @ SV47 @ SY3705 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[704]) ).
thf(786,plain,
! [SV47: $i] :
( ( ~ ! [SY3707: $i,SY3708: $i] :
( ~ ( relation_of2_as_subset @ SY3708 @ SV47 @ SY3707 )
| ( relation_of2 @ SY3708 @ SV47 @ SY3707 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[704]) ).
thf(787,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[705]) ).
thf(788,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[706]) ).
thf(789,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( disjoint @ ( fiber @ SX0 @ SX1 ) @ ( sK14_B @ SX0 ) )
| ~ ( in @ SX1 @ ( sK14_B @ SX0 ) ) )
| ~ ~ ( ~ ( ( ( sK14_B @ SX0 )
!= empty_set ) )
| ~ ( subset @ ( sK14_B @ SX0 ) @ ( relation_field @ SX0 ) ) ) )
| ( well_founded_relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[707]) ).
thf(790,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ! [SX1: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SX0 @ ( sK13_C @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) )
| ( SX1 = empty_set )
| ~ ( subset @ SX1 @ ( relation_field @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[708]) ).
thf(791,plain,
! [SV48: $i,SV95: $i] :
( ( ( ~ ( ordinal @ SV95 ) )
= $true )
| ( ( ~ ( ~ ( ordinal @ ( sK17_C @ SV95 @ SV48 ) )
| ~ ~ ( ~ ! [SY3762: $i] :
( ~ ( ordinal @ SY3762 )
| ~ ( in @ SY3762 @ SV48 )
| ( ordinal_subset @ ( sK17_C @ SV95 @ SV48 ) @ SY3762 ) )
| ~ ( in @ ( sK17_C @ SV95 @ SV48 ) @ SV48 ) ) )
| ( SV48 = empty_set )
| ~ ( subset @ SV48 @ SV95 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[709]) ).
thf(792,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ( in @ ( sK15_B @ SX0 ) @ SX0 )
| ~ ~ ( subset @ ( sK15_B @ SX0 ) @ SX0 ) )
| ( epsilon_transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[710]) ).
thf(793,plain,
( ( ! [SX0: $i] :
( ~ ( epsilon_transitive @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[711]) ).
thf(794,plain,
! [SV49: $i] :
( ( ~ ! [SY3711: $i,SY3712: $i] :
( ~ ( in @ SV49 @ SY3712 )
| ~ ( in @ SY3711 @ SY3712 )
| ( subset @ ( unordered_pair @ SV49 @ SY3711 ) @ SY3712 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[712]) ).
thf(795,plain,
! [SV49: $i] :
( ( ~ ~ ( ~ ! [SY3713: $i,SY3714: $i] :
( ~ ( subset @ ( unordered_pair @ SV49 @ SY3713 ) @ SY3714 )
| ( in @ SV49 @ SY3714 ) )
| ~ ! [SY3715: $i,SY3716: $i] :
( ~ ( subset @ ( unordered_pair @ SV49 @ SY3715 ) @ SY3716 )
| ( in @ SY3715 @ SY3716 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[712]) ).
thf(796,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[713]) ).
thf(797,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[714]) ).
thf(798,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[715]) ).
thf(799,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[716]) ).
thf(800,plain,
! [SV50: $i] :
( ( ~ ! [SY3717: $i] :
( ~ ( subset @ SY3717 @ ( sK19_B @ SV50 ) )
| ( are_equipotent @ SY3717 @ ( sK19_B @ SV50 ) )
| ( in @ SY3717 @ ( sK19_B @ SV50 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[717]) ).
thf(801,plain,
! [SV50: $i] :
( ( ~ ~ ( ~ ! [SY3718: $i] :
( ~ ( in @ SY3718 @ ( sK19_B @ SV50 ) )
| ( in @ ( powerset @ SY3718 ) @ ( sK19_B @ SV50 ) ) )
| ~ ~ ( ~ ! [SY3719: $i,SY3720: $i] :
( ~ ( in @ SY3719 @ ( sK19_B @ SV50 ) )
| ~ ( subset @ SY3720 @ SY3719 )
| ( in @ SY3720 @ ( sK19_B @ SV50 ) ) )
| ~ ( in @ SV50 @ ( sK19_B @ SV50 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[717]) ).
thf(802,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[718]) ).
thf(803,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[719]) ).
thf(804,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[720]) ).
thf(805,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[721]) ).
thf(806,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[722]) ).
thf(807,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[723]) ).
thf(808,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_field @ ( relation_restriction @ SX1 @ SX0 ) ) @ ( relation_field @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[724]) ).
thf(809,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_field @ ( relation_restriction @ SX1 @ SX0 ) ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[725]) ).
thf(810,plain,
! [SV51: $i] :
( ( ~ ! [SY3721: $i] :
( ~ ( subset @ SV51 @ SY3721 )
| ! [SY3722: $i] : ( subset @ ( cartesian_product2 @ SV51 @ SY3722 ) @ ( cartesian_product2 @ SY3721 @ SY3722 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[726]) ).
thf(811,plain,
! [SV51: $i] :
( ( ~ ! [SY3723: $i] :
( ~ ( subset @ SV51 @ SY3723 )
| ! [SY3724: $i] : ( subset @ ( cartesian_product2 @ SY3724 @ SV51 ) @ ( cartesian_product2 @ SY3724 @ SY3723 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[726]) ).
thf(812,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK16_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK16_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK16_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK16_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[727]) ).
thf(813,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[728]) ).
thf(814,plain,
! [SV52: $i] :
( ( ~ ! [SY3725: $i,SY3726: $i] :
( ~ ( relation_of2 @ SY3726 @ SV52 @ SY3725 )
| ( subset @ SY3726 @ ( cartesian_product2 @ SV52 @ SY3725 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[729]) ).
thf(815,plain,
! [SV52: $i] :
( ( ~ ! [SY3727: $i,SY3728: $i] :
( ~ ( subset @ SY3728 @ ( cartesian_product2 @ SV52 @ SY3727 ) )
| ( relation_of2 @ SY3728 @ SV52 @ SY3727 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[729]) ).
thf(816,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[730]) ).
thf(817,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[731]) ).
thf(818,plain,
! [SV53: $i] :
( ( ~ ! [SY3729: $i,SY3730: $i] :
( ~ ( relation_of2_as_subset @ SY3730 @ SV53 @ SY3729 )
| ( subset @ ( relation_dom @ SY3730 ) @ SV53 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[732]) ).
thf(819,plain,
! [SV53: $i] :
( ( ~ ! [SY3731: $i,SY3732: $i] :
( ~ ( relation_of2_as_subset @ SY3732 @ SV53 @ SY3731 )
| ( subset @ ( relation_rng @ SY3732 ) @ SY3731 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[732]) ).
thf(820,plain,
! [SV54: $i] :
( ( ( ~ ( in @ ( sK18_B @ SV54 ) @ SV54 )
| ~ ( ~ ( ordinal @ ( sK18_B @ SV54 ) )
| ~ ( subset @ ( sK18_B @ SV54 ) @ SV54 ) ) )
= $false )
| ( ( ordinal @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[733]) ).
thf(821,plain,
! [SV55: $i] :
( ( ( relation @ SV55 )
= $false )
| ( ( ~ ( ~ ! [SY3733: $i] :
( ~ ( ~ ! [SY3734: $i] :
( ~ ( disjoint @ ( fiber @ SV55 @ SY3734 ) @ ( sK9_C @ SY3733 @ SV55 ) )
| ~ ( in @ SY3734 @ ( sK9_C @ SY3733 @ SV55 ) ) )
| ~ ~ ( ~ ( ( ( sK9_C @ SY3733 @ SV55 )
!= empty_set ) )
| ~ ( subset @ ( sK9_C @ SY3733 @ SV55 ) @ SY3733 ) ) )
| ( is_well_founded_in @ SV55 @ SY3733 ) )
| ~ ! [SY3735: $i] :
( ~ ( is_well_founded_in @ SV55 @ SY3735 )
| ! [SY3736: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV55 @ ( sK8_D @ SY3736 @ SY3735 @ SV55 ) ) @ SY3736 )
| ~ ( in @ ( sK8_D @ SY3736 @ SY3735 @ SV55 ) @ SY3736 ) )
| ( SY3736 = empty_set )
| ~ ( subset @ SY3736 @ SY3735 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[734]) ).
thf(822,plain,
! [SV56: $i] :
( ( ~ ! [SY3737: $i] :
( ~ ( subset @ SY3737 @ ( sK5_B @ SV56 ) )
| ( are_equipotent @ SY3737 @ ( sK5_B @ SV56 ) )
| ( in @ SY3737 @ ( sK5_B @ SV56 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[735]) ).
thf(823,plain,
! [SV56: $i] :
( ( ~ ~ ( ~ ! [SY3738: $i] :
( ~ ( ~ ! [SY3739: $i] :
( ~ ( subset @ SY3739 @ SY3738 )
| ( in @ SY3739 @ ( sK6_SY3633 @ SY3738 @ SV56 ) ) )
| ~ ( in @ ( sK6_SY3633 @ SY3738 @ SV56 ) @ ( sK5_B @ SV56 ) ) )
| ~ ( in @ SY3738 @ ( sK5_B @ SV56 ) ) )
| ~ ~ ( ~ ! [SY3740: $i,SY3741: $i] :
( ~ ( in @ SY3740 @ ( sK5_B @ SV56 ) )
| ~ ( subset @ SY3741 @ SY3740 )
| ( in @ SY3741 @ ( sK5_B @ SV56 ) ) )
| ~ ( in @ SV56 @ ( sK5_B @ SV56 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[735]) ).
thf(824,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[736]) ).
thf(825,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[737]) ).
thf(826,plain,
! [SV57: $i] :
( ( ( relation @ SV57 )
= $false )
| ( ( ~ ( ~ ! [SY3742: $i] :
( ~ ( relation @ SY3742 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SY3742 @ SV57 ) @ ( sK12_SY3639 @ SY3742 @ SV57 ) ) @ SV57 )
| ~ ~ ( in @ ( ordered_pair @ ( sK11_C @ SY3742 @ SV57 ) @ ( sK12_SY3639 @ SY3742 @ SV57 ) ) @ SY3742 ) )
| ( subset @ SV57 @ SY3742 ) )
| ~ ! [SY3743: $i] :
( ~ ( relation @ SY3743 )
| ~ ( subset @ SV57 @ SY3743 )
| ! [SY3744: $i,SY3745: $i] :
( ~ ( in @ ( ordered_pair @ SY3744 @ SY3745 ) @ SV57 )
| ( in @ ( ordered_pair @ SY3744 @ SY3745 ) @ SY3743 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[738]) ).
thf(827,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ordinal @ SX1 )
| ~ ( ordinal_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[739]) ).
thf(828,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ordinal @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( ordinal_subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[740]) ).
thf(829,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[741]) ).
thf(830,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[742]) ).
thf(831,plain,
! [SV1: $i,SV58: $i] :
( ( ( relation @ SV58 )
= $false )
| ( ( subset @ ( relation_dom @ ( relation_rng_restriction @ SV1 @ SV58 ) ) @ ( relation_dom @ SV58 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[743]) ).
thf(832,plain,
! [SV59: $i,SV2: $i] :
( ( ( subset @ SV2 @ SV59 )
= $false )
| ( ( ! [SY3746: $i] :
( ( in @ SY3746 @ SV2 )
| ( subset @ SV2 @ ( set_difference @ SV59 @ ( singleton @ SY3746 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[744]) ).
thf(833,plain,
! [SV60: $i,SV3: $i] :
( ( ( in @ SV3 @ SV60 )
= $false )
| ( ( subset @ SV3 @ ( union @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[745]) ).
thf(834,plain,
! [SV4: $i,SV61: $i] :
( ( ( relation @ SV61 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV4 @ SV61 ) ) @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[746]) ).
thf(835,plain,
! [SV5: $i,SV62: $i] :
( ( ( relation @ SV62 )
= $false )
| ( ( subset @ ( relation_rng_restriction @ SV5 @ SV62 ) @ SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[747]) ).
thf(836,plain,
! [SV6: $i,SV63: $i] :
( ( ( relation @ SV63 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV6 @ SV63 ) ) @ ( relation_rng @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[748]) ).
thf(837,plain,
! [SV105: $i,SV96: $i,SV64: $i,SV7: $i] :
( ( ~ ( subset @ SV7 @ SV64 )
| ~ ( subset @ SV96 @ SV105 )
| ( subset @ ( cartesian_product2 @ SV7 @ SV96 ) @ ( cartesian_product2 @ SV64 @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(838,plain,
! [SV65: $i,SV8: $i] :
( ( ( subset @ SV8 @ SV65 )
= $false )
| ( ( ( set_union2 @ SV8 @ SV65 )
= SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[750]) ).
thf(839,plain,
! [SV9: $i,SV66: $i] :
( ( ( relation @ SV66 )
= $false )
| ( ( subset @ ( relation_image @ SV66 @ SV9 ) @ ( relation_rng @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[751]) ).
thf(840,plain,
! [SV10: $i,SV67: $i] :
( ( ( ~ ( function @ SV67 ) )
= $true )
| ( ( ~ ( relation @ SV67 ) )
= $true )
| ( ( subset @ ( relation_image @ SV67 @ ( relation_inverse_image @ SV67 @ SV10 ) ) @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[752]) ).
thf(841,plain,
! [SV11: $i,SV68: $i] :
( ( ( relation @ SV68 )
= $false )
| ( ( ~ ( subset @ SV11 @ ( relation_dom @ SV68 ) )
| ( subset @ SV11 @ ( relation_inverse_image @ SV68 @ ( relation_image @ SV68 @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[753]) ).
thf(842,plain,
! [SV12: $i,SV69: $i] :
( ( ( ~ ( function @ SV69 ) )
= $true )
| ( ( ~ ( relation @ SV69 ) )
= $true )
| ( ( ~ ( subset @ SV12 @ ( relation_rng @ SV69 ) )
| ( ( relation_image @ SV69 @ ( relation_inverse_image @ SV69 @ SV12 ) )
= SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[754]) ).
thf(843,plain,
! [SV70: $i,SV13: $i,SV97: $i,SV106: $i] :
( ( ~ ( relation_of2_as_subset @ SV106 @ SV97 @ SV13 )
| ~ ( subset @ ( relation_rng @ SV106 ) @ SV70 )
| ( relation_of2_as_subset @ SV106 @ SV97 @ SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(844,plain,
! [SV14: $i,SV71: $i] :
( ( ( relation @ SV71 )
= $false )
| ( ( subset @ ( relation_inverse_image @ SV71 @ SV14 ) @ ( relation_dom @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[756]) ).
thf(845,plain,
! [SV15: $i,SV72: $i] :
( ( ( relation @ SV72 )
= $false )
| ( ( ( SV15 = empty_set )
| ~ ( subset @ SV15 @ ( relation_rng @ SV72 ) )
| ( ( relation_inverse_image @ SV72 @ SV15 )
!= empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[757]) ).
thf(846,plain,
! [SV73: $i,SV16: $i,SV98: $i] :
( ( ( ~ ( relation @ SV98 ) )
= $true )
| ( ( ~ ( subset @ SV16 @ SV73 )
| ( subset @ ( relation_inverse_image @ SV98 @ SV16 ) @ ( relation_inverse_image @ SV98 @ SV73 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[758]) ).
thf(847,plain,
! [SV99: $i,SV75: $i,SV18: $i] :
( ( ( ~ ( subset @ SV18 @ SV75 )
| ~ ( subset @ SV18 @ SV99 ) )
= $true )
| ( ( subset @ SV18 @ ( set_intersection2 @ SV75 @ SV99 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[759]) ).
thf(848,plain,
! [SV100: $i,SV76: $i,SV19: $i] :
( ( ( ~ ( subset @ SV19 @ SV76 )
| ~ ( subset @ SV76 @ SV100 ) )
= $true )
| ( ( subset @ SV19 @ SV100 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[760]) ).
thf(849,plain,
! [SV77: $i,SV21: $i,SV101: $i] :
( ( ( ~ ( relation @ SV101 ) )
= $true )
| ( ( subset @ ( fiber @ ( relation_restriction @ SV101 @ SV21 ) @ SV77 ) @ ( fiber @ SV101 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[762]) ).
thf(850,plain,
! [SV78: $i,SV22: $i] :
( ( ( subset @ SV22 @ SV78 )
= $false )
| ( ( ! [SY3755: $i] : ( subset @ ( set_intersection2 @ SV22 @ SY3755 ) @ ( set_intersection2 @ SV78 @ SY3755 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[763]) ).
thf(851,plain,
! [SV79: $i,SV23: $i] :
( ( ( subset @ SV23 @ SV79 )
= $false )
| ( ( ( set_intersection2 @ SV23 @ SV79 )
= SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[764]) ).
thf(852,plain,
! [SV80: $i,SV25: $i] :
( ( ( subset @ SV25 @ SV80 )
= $false )
| ( ( ! [SY3756: $i] : ( subset @ ( set_difference @ SV25 @ SY3756 ) @ ( set_difference @ SV80 @ SY3756 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[765]) ).
thf(853,plain,
! [SV27: $i,SV82: $i] :
( ( ( relation @ SV82 )
= $false )
| ( ( ~ ( subset @ SV27 @ ( relation_field @ SV82 ) )
| ~ ( well_ordering @ SV82 )
| ( ( relation_field @ ( relation_restriction @ SV82 @ SV27 ) )
= SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[766]) ).
thf(854,plain,
! [SV29: $i,SV107: $i] :
( ( ( ~ ( relation @ SV107 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV29 @ SV107 ) ) @ ( relation_dom @ SV29 ) ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(855,plain,
! [SV30: $i,SV108: $i] :
( ( ( ~ ( relation @ SV108 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV30 @ SV108 ) ) @ ( relation_rng @ SV108 ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(856,plain,
! [SV83: $i,SV31: $i] :
( ( ( subset @ SV31 @ SV83 )
= $false )
| ( ( SV83
= ( set_union2 @ SV31 @ ( set_difference @ SV83 @ SV31 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[770]) ).
thf(857,plain,
! [SV32: $i,SV109: $i] :
( ( ( ~ ( relation @ SV109 )
| ~ ( subset @ ( relation_rng @ SV32 ) @ ( relation_dom @ SV109 ) )
| ( ( relation_dom @ ( relation_composition @ SV32 @ SV109 ) )
= ( relation_dom @ SV32 ) ) )
= $true )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(858,plain,
! [SV33: $i,SV110: $i] :
( ( ( ~ ( relation @ SV110 )
| ~ ( subset @ ( relation_dom @ SV33 ) @ ( relation_rng @ SV110 ) )
| ( ( relation_rng @ ( relation_composition @ SV110 @ SV33 ) )
= ( relation_rng @ SV33 ) ) )
= $true )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(859,plain,
! [SV34: $i,SV84: $i] :
( ( ( proper_subset @ SV84 @ SV34 )
= $false )
| ( ( ~ ( subset @ SV34 @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[773]) ).
thf(860,plain,
! [SV35: $i,SV102: $i,SV85: $i] :
( ( ( ~ ( disjoint @ SV85 @ SV102 )
| ~ ( subset @ SV35 @ SV85 ) )
= $true )
| ( ( disjoint @ SV35 @ SV102 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[774]) ).
thf(861,plain,
! [SV86: $i,SV36: $i] :
( ( ( subset @ ( singleton @ SV36 ) @ ( singleton @ SV86 ) )
= $false )
| ( ( SV36 = SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[775]) ).
thf(862,plain,
! [SV38: $i,SV88: $i] :
( ( ( relation @ SV88 )
= $false )
| ( ( subset @ ( relation_dom_restriction @ SV88 @ SV38 ) @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[776]) ).
thf(863,plain,
! [SV103: $i,SV89: $i,SV39: $i] :
( ( ( ~ ( subset @ SV39 @ SV89 )
| ~ ( subset @ SV103 @ SV89 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV39 @ SV103 ) @ SV89 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[777]) ).
thf(864,plain,
! [SV90: $i,SV40: $i] :
( ( ( in @ SV40 @ SV90 )
= $false )
| ( ( subset @ SV40 @ ( union @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[778]) ).
thf(865,plain,
! [SV41: $i,SV91: $i] :
( ( ( relation @ SV91 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_dom_restriction @ SV91 @ SV41 ) ) @ ( relation_rng @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[779]) ).
thf(866,plain,
! [SV92: $i,SV42: $i,SV104: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV104 @ SV42 @ SV92 ) )
= $true )
| ( ( element @ SV104 @ ( powerset @ ( cartesian_product2 @ SV42 @ SV92 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[780]) ).
thf(867,plain,
! [SV111: $i] :
( ( ! [SY3765: $i] :
( ~ ( subset @ SV111 @ ( singleton @ SY3765 ) )
| ( SV111 = empty_set )
| ( SV111
= ( singleton @ SY3765 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(868,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[782]) ).
thf(869,plain,
! [SV45: $i] :
( ( ( ~ ! [SY3700: $i] :
( ~ ( relation @ SY3700 )
| ~ ( subset @ SV45 @ SY3700 )
| ( subset @ ( relation_dom @ SV45 ) @ ( relation_dom @ SY3700 ) ) )
| ~ ! [SY3701: $i] :
( ~ ( relation @ SY3701 )
| ~ ( subset @ SV45 @ SY3701 )
| ( subset @ ( relation_rng @ SV45 ) @ ( relation_rng @ SY3701 ) ) ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[783]) ).
thf(870,plain,
! [SV46: $i,SV94: $i] :
( ( ( element @ SV94 @ ( powerset @ SV46 ) )
= $false )
| ( ( ~ ( ~ ! [SY3760: $i] :
( ~ ( element @ SY3760 @ ( powerset @ SV46 ) )
| ~ ( disjoint @ SV94 @ SY3760 )
| ( subset @ SV94 @ ( subset_complement @ SV46 @ SY3760 ) ) )
| ~ ! [SY3761: $i] :
( ~ ( element @ SY3761 @ ( powerset @ SV46 ) )
| ~ ( subset @ SV94 @ ( subset_complement @ SV46 @ SY3761 ) )
| ( disjoint @ SV94 @ SY3761 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[784]) ).
thf(871,plain,
! [SV47: $i] :
( ( ! [SY3705: $i,SY3706: $i] :
( ~ ( relation_of2 @ SY3706 @ SV47 @ SY3705 )
| ( relation_of2_as_subset @ SY3706 @ SV47 @ SY3705 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[785]) ).
thf(872,plain,
! [SV47: $i] :
( ( ! [SY3707: $i,SY3708: $i] :
( ~ ( relation_of2_as_subset @ SY3708 @ SV47 @ SY3707 )
| ( relation_of2 @ SY3708 @ SV47 @ SY3707 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[786]) ).
thf(873,plain,
! [SV112: $i] :
( ( ! [SY3766: $i] :
( ( SV112 = SY3766 )
| ~ ( subset @ SV112 @ SY3766 )
| ( proper_subset @ SV112 @ SY3766 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(874,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[788]) ).
thf(875,plain,
! [SV113: $i] :
( ( ~ ( relation @ SV113 )
| ~ ( ~ ! [SY3767: $i] :
( ~ ( disjoint @ ( fiber @ SV113 @ SY3767 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ SY3767 @ ( sK14_B @ SV113 ) ) )
| ~ ~ ( ~ ( ( ( sK14_B @ SV113 )
!= empty_set ) )
| ~ ( subset @ ( sK14_B @ SV113 ) @ ( relation_field @ SV113 ) ) ) )
| ( well_founded_relation @ SV113 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[789]) ).
thf(876,plain,
! [SV114: $i] :
( ( ~ ( relation @ SV114 )
| ~ ( well_founded_relation @ SV114 )
| ! [SY3768: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV114 @ ( sK13_C @ SY3768 @ SV114 ) ) @ SY3768 )
| ~ ( in @ ( sK13_C @ SY3768 @ SV114 ) @ SY3768 ) )
| ( SY3768 = empty_set )
| ~ ( subset @ SY3768 @ ( relation_field @ SV114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(877,plain,
! [SV48: $i,SV95: $i] :
( ( ( ordinal @ SV95 )
= $false )
| ( ( ~ ( ~ ( ordinal @ ( sK17_C @ SV95 @ SV48 ) )
| ~ ~ ( ~ ! [SY3762: $i] :
( ~ ( ordinal @ SY3762 )
| ~ ( in @ SY3762 @ SV48 )
| ( ordinal_subset @ ( sK17_C @ SV95 @ SV48 ) @ SY3762 ) )
| ~ ( in @ ( sK17_C @ SV95 @ SV48 ) @ SV48 ) ) )
| ( SV48 = empty_set )
| ~ ( subset @ SV48 @ SV95 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[791]) ).
thf(878,plain,
! [SV115: $i] :
( ( ~ ( ~ ( in @ ( sK15_B @ SV115 ) @ SV115 )
| ~ ~ ( subset @ ( sK15_B @ SV115 ) @ SV115 ) )
| ( epsilon_transitive @ SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(879,plain,
! [SV116: $i] :
( ( ~ ( epsilon_transitive @ SV116 )
| ! [SY3769: $i] :
( ~ ( in @ SY3769 @ SV116 )
| ( subset @ SY3769 @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(880,plain,
! [SV49: $i] :
( ( ! [SY3711: $i,SY3712: $i] :
( ~ ( in @ SV49 @ SY3712 )
| ~ ( in @ SY3711 @ SY3712 )
| ( subset @ ( unordered_pair @ SV49 @ SY3711 ) @ SY3712 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[794]) ).
thf(881,plain,
! [SV49: $i] :
( ( ~ ( ~ ! [SY3713: $i,SY3714: $i] :
( ~ ( subset @ ( unordered_pair @ SV49 @ SY3713 ) @ SY3714 )
| ( in @ SV49 @ SY3714 ) )
| ~ ! [SY3715: $i,SY3716: $i] :
( ~ ( subset @ ( unordered_pair @ SV49 @ SY3715 ) @ SY3716 )
| ( in @ SY3715 @ SY3716 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[795]) ).
thf(882,plain,
! [SV117: $i] :
( ( ! [SY3770: $i] :
( ~ ( ~ ( in @ ( sK10_C @ SY3770 @ SV117 ) @ SV117 )
| ~ ~ ( in @ ( sK10_C @ SY3770 @ SV117 ) @ SY3770 ) )
| ( subset @ SV117 @ SY3770 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(883,plain,
! [SV118: $i] :
( ( ! [SY3771: $i] :
( ~ ( subset @ SV118 @ SY3771 )
| ! [SY3772: $i] :
( ~ ( in @ SY3772 @ SV118 )
| ( in @ SY3772 @ SY3771 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(884,plain,
! [SV119: $i] :
( ( ! [SY3773: $i] :
( ~ ( subset @ SV119 @ SY3773 )
| ~ ( subset @ SY3773 @ SV119 )
| ( SV119 = SY3773 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(885,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[799]) ).
thf(886,plain,
! [SV50: $i] :
( ( ! [SY3717: $i] :
( ~ ( subset @ SY3717 @ ( sK19_B @ SV50 ) )
| ( are_equipotent @ SY3717 @ ( sK19_B @ SV50 ) )
| ( in @ SY3717 @ ( sK19_B @ SV50 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[800]) ).
thf(887,plain,
! [SV50: $i] :
( ( ~ ( ~ ! [SY3718: $i] :
( ~ ( in @ SY3718 @ ( sK19_B @ SV50 ) )
| ( in @ ( powerset @ SY3718 ) @ ( sK19_B @ SV50 ) ) )
| ~ ~ ( ~ ! [SY3719: $i,SY3720: $i] :
( ~ ( in @ SY3719 @ ( sK19_B @ SV50 ) )
| ~ ( subset @ SY3720 @ SY3719 )
| ( in @ SY3720 @ ( sK19_B @ SV50 ) ) )
| ~ ( in @ SV50 @ ( sK19_B @ SV50 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[801]) ).
thf(888,plain,
! [SV120: $i] :
( ( ! [SY3774: $i] :
( ~ ( in @ SV120 @ SY3774 )
| ( subset @ ( singleton @ SV120 ) @ SY3774 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(889,plain,
! [SV121: $i] :
( ( ! [SY3775: $i] :
( ~ ( subset @ ( singleton @ SV121 ) @ SY3775 )
| ( in @ SV121 @ SY3775 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(890,plain,
! [SV122: $i] :
( ( ! [SY3776: $i] :
( ( ( set_difference @ SV122 @ SY3776 )
!= empty_set )
| ( subset @ SV122 @ SY3776 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(891,plain,
! [SV123: $i] :
( ( ! [SY3777: $i] :
( ~ ( subset @ SV123 @ SY3777 )
| ( ( set_difference @ SV123 @ SY3777 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(892,plain,
! [SV124: $i] :
( ( ! [SY3778: $i] :
( ~ ( element @ SV124 @ ( powerset @ SY3778 ) )
| ( subset @ SV124 @ SY3778 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(893,plain,
! [SV125: $i] :
( ( ! [SY3779: $i] :
( ~ ( subset @ SV125 @ SY3779 )
| ( element @ SV125 @ ( powerset @ SY3779 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(894,plain,
! [SV126: $i] :
( ( ! [SY3780: $i] :
( ~ ( relation @ SY3780 )
| ( subset @ ( relation_field @ ( relation_restriction @ SY3780 @ SV126 ) ) @ ( relation_field @ SY3780 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(895,plain,
! [SV127: $i] :
( ( ! [SY3781: $i] :
( ~ ( relation @ SY3781 )
| ( subset @ ( relation_field @ ( relation_restriction @ SY3781 @ SV127 ) ) @ SV127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(896,plain,
! [SV51: $i] :
( ( ! [SY3721: $i] :
( ~ ( subset @ SV51 @ SY3721 )
| ! [SY3722: $i] : ( subset @ ( cartesian_product2 @ SV51 @ SY3722 ) @ ( cartesian_product2 @ SY3721 @ SY3722 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[810]) ).
thf(897,plain,
! [SV51: $i] :
( ( ! [SY3723: $i] :
( ~ ( subset @ SV51 @ SY3723 )
| ! [SY3724: $i] : ( subset @ ( cartesian_product2 @ SY3724 @ SV51 ) @ ( cartesian_product2 @ SY3724 @ SY3723 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[811]) ).
thf(898,plain,
! [SV128: $i] :
( ( ! [SY3782: $i] :
( ~ ( ~ ( ~ ( in @ ( sK16_C @ SY3782 @ SV128 ) @ SY3782 )
| ~ ( subset @ ( sK16_C @ SY3782 @ SV128 ) @ SV128 ) )
| ~ ( ( in @ ( sK16_C @ SY3782 @ SV128 ) @ SY3782 )
| ( subset @ ( sK16_C @ SY3782 @ SV128 ) @ SV128 ) ) )
| ( SY3782
= ( powerset @ SV128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(899,plain,
! [SV129: $i] :
( ( ! [SY3783: $i] :
( ( SY3783
!= ( powerset @ SV129 ) )
| ~ ( ~ ! [SY3784: $i] :
( ~ ( in @ SY3784 @ SY3783 )
| ( subset @ SY3784 @ SV129 ) )
| ~ ! [SY3785: $i] :
( ~ ( subset @ SY3785 @ SV129 )
| ( in @ SY3785 @ SY3783 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(900,plain,
! [SV52: $i] :
( ( ! [SY3725: $i,SY3726: $i] :
( ~ ( relation_of2 @ SY3726 @ SV52 @ SY3725 )
| ( subset @ SY3726 @ ( cartesian_product2 @ SV52 @ SY3725 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[814]) ).
thf(901,plain,
! [SV52: $i] :
( ( ! [SY3727: $i,SY3728: $i] :
( ~ ( subset @ SY3728 @ ( cartesian_product2 @ SV52 @ SY3727 ) )
| ( relation_of2 @ SY3728 @ SV52 @ SY3727 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[815]) ).
thf(902,plain,
! [SV130: $i] :
( ( ! [SY3786: $i] :
( ~ ( in @ SV130 @ SY3786 )
| ( subset @ ( singleton @ SV130 ) @ SY3786 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(903,plain,
! [SV131: $i] :
( ( ! [SY3787: $i] :
( ~ ( subset @ ( singleton @ SV131 ) @ SY3787 )
| ( in @ SV131 @ SY3787 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(904,plain,
! [SV53: $i] :
( ( ! [SY3729: $i,SY3730: $i] :
( ~ ( relation_of2_as_subset @ SY3730 @ SV53 @ SY3729 )
| ( subset @ ( relation_dom @ SY3730 ) @ SV53 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[818]) ).
thf(905,plain,
! [SV53: $i] :
( ( ! [SY3731: $i,SY3732: $i] :
( ~ ( relation_of2_as_subset @ SY3732 @ SV53 @ SY3731 )
| ( subset @ ( relation_rng @ SY3732 ) @ SY3731 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[819]) ).
thf(906,plain,
! [SV54: $i] :
( ( ( ~ ( in @ ( sK18_B @ SV54 ) @ SV54 ) )
= $false )
| ( ( ordinal @ SV54 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[820]) ).
thf(907,plain,
! [SV54: $i] :
( ( ( ~ ( ~ ( ordinal @ ( sK18_B @ SV54 ) )
| ~ ( subset @ ( sK18_B @ SV54 ) @ SV54 ) ) )
= $false )
| ( ( ordinal @ SV54 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[820]) ).
thf(908,plain,
! [SV55: $i] :
( ( ( ~ ! [SY3733: $i] :
( ~ ( ~ ! [SY3734: $i] :
( ~ ( disjoint @ ( fiber @ SV55 @ SY3734 ) @ ( sK9_C @ SY3733 @ SV55 ) )
| ~ ( in @ SY3734 @ ( sK9_C @ SY3733 @ SV55 ) ) )
| ~ ~ ( ~ ( ( ( sK9_C @ SY3733 @ SV55 )
!= empty_set ) )
| ~ ( subset @ ( sK9_C @ SY3733 @ SV55 ) @ SY3733 ) ) )
| ( is_well_founded_in @ SV55 @ SY3733 ) )
| ~ ! [SY3735: $i] :
( ~ ( is_well_founded_in @ SV55 @ SY3735 )
| ! [SY3736: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV55 @ ( sK8_D @ SY3736 @ SY3735 @ SV55 ) ) @ SY3736 )
| ~ ( in @ ( sK8_D @ SY3736 @ SY3735 @ SV55 ) @ SY3736 ) )
| ( SY3736 = empty_set )
| ~ ( subset @ SY3736 @ SY3735 ) ) ) )
= $false )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[821]) ).
thf(909,plain,
! [SV56: $i] :
( ( ! [SY3737: $i] :
( ~ ( subset @ SY3737 @ ( sK5_B @ SV56 ) )
| ( are_equipotent @ SY3737 @ ( sK5_B @ SV56 ) )
| ( in @ SY3737 @ ( sK5_B @ SV56 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[822]) ).
thf(910,plain,
! [SV56: $i] :
( ( ~ ( ~ ! [SY3738: $i] :
( ~ ( ~ ! [SY3739: $i] :
( ~ ( subset @ SY3739 @ SY3738 )
| ( in @ SY3739 @ ( sK6_SY3633 @ SY3738 @ SV56 ) ) )
| ~ ( in @ ( sK6_SY3633 @ SY3738 @ SV56 ) @ ( sK5_B @ SV56 ) ) )
| ~ ( in @ SY3738 @ ( sK5_B @ SV56 ) ) )
| ~ ~ ( ~ ! [SY3740: $i,SY3741: $i] :
( ~ ( in @ SY3740 @ ( sK5_B @ SV56 ) )
| ~ ( subset @ SY3741 @ SY3740 )
| ( in @ SY3741 @ ( sK5_B @ SV56 ) ) )
| ~ ( in @ SV56 @ ( sK5_B @ SV56 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[823]) ).
thf(911,plain,
! [SV132: $i] :
( ( ! [SY3788: $i] :
( ~ ( subset @ SV132 @ ( singleton @ SY3788 ) )
| ( SV132 = empty_set )
| ( SV132
= ( singleton @ SY3788 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(912,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[825]) ).
thf(913,plain,
! [SV57: $i] :
( ( ( ~ ! [SY3742: $i] :
( ~ ( relation @ SY3742 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SY3742 @ SV57 ) @ ( sK12_SY3639 @ SY3742 @ SV57 ) ) @ SV57 )
| ~ ~ ( in @ ( ordered_pair @ ( sK11_C @ SY3742 @ SV57 ) @ ( sK12_SY3639 @ SY3742 @ SV57 ) ) @ SY3742 ) )
| ( subset @ SV57 @ SY3742 ) )
| ~ ! [SY3743: $i] :
( ~ ( relation @ SY3743 )
| ~ ( subset @ SV57 @ SY3743 )
| ! [SY3744: $i,SY3745: $i] :
( ~ ( in @ ( ordered_pair @ SY3744 @ SY3745 ) @ SV57 )
| ( in @ ( ordered_pair @ SY3744 @ SY3745 ) @ SY3743 ) ) ) )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[826]) ).
thf(914,plain,
! [SV133: $i] :
( ( ! [SY3789: $i] :
( ~ ( ordinal @ SV133 )
| ~ ( ordinal @ SY3789 )
| ~ ( ordinal_subset @ SV133 @ SY3789 )
| ( subset @ SV133 @ SY3789 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(915,plain,
! [SV134: $i] :
( ( ! [SY3790: $i] :
( ~ ( ordinal @ SV134 )
| ~ ( ordinal @ SY3790 )
| ~ ( subset @ SV134 @ SY3790 )
| ( ordinal_subset @ SV134 @ SY3790 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(916,plain,
! [SV135: $i] :
( ( ! [SY3791: $i] :
( ( ( set_difference @ SV135 @ SY3791 )
!= empty_set )
| ( subset @ SV135 @ SY3791 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(917,plain,
! [SV136: $i] :
( ( ! [SY3792: $i] :
( ~ ( subset @ SV136 @ SY3792 )
| ( ( set_difference @ SV136 @ SY3792 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(918,plain,
! [SV59: $i,SV2: $i,SV137: $i] :
( ( ( ( in @ SV137 @ SV2 )
| ( subset @ SV2 @ ( set_difference @ SV59 @ ( singleton @ SV137 ) ) ) )
= $true )
| ( ( subset @ SV2 @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(919,plain,
! [SV105: $i,SV96: $i,SV64: $i,SV7: $i] :
( ( ( ~ ( subset @ SV7 @ SV64 )
| ~ ( subset @ SV96 @ SV105 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV7 @ SV96 ) @ ( cartesian_product2 @ SV64 @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[837]) ).
thf(920,plain,
! [SV10: $i,SV67: $i] :
( ( ( function @ SV67 )
= $false )
| ( ( ~ ( relation @ SV67 ) )
= $true )
| ( ( subset @ ( relation_image @ SV67 @ ( relation_inverse_image @ SV67 @ SV10 ) ) @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[840]) ).
thf(921,plain,
! [SV68: $i,SV11: $i] :
( ( ( ~ ( subset @ SV11 @ ( relation_dom @ SV68 ) ) )
= $true )
| ( ( subset @ SV11 @ ( relation_inverse_image @ SV68 @ ( relation_image @ SV68 @ SV11 ) ) )
= $true )
| ( ( relation @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[841]) ).
thf(922,plain,
! [SV12: $i,SV69: $i] :
( ( ( function @ SV69 )
= $false )
| ( ( ~ ( relation @ SV69 ) )
= $true )
| ( ( ~ ( subset @ SV12 @ ( relation_rng @ SV69 ) )
| ( ( relation_image @ SV69 @ ( relation_inverse_image @ SV69 @ SV12 ) )
= SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[842]) ).
thf(923,plain,
! [SV70: $i,SV13: $i,SV97: $i,SV106: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV106 @ SV97 @ SV13 ) )
= $true )
| ( ( ~ ( subset @ ( relation_rng @ SV106 ) @ SV70 )
| ( relation_of2_as_subset @ SV106 @ SV97 @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[843]) ).
thf(924,plain,
! [SV72: $i,SV15: $i] :
( ( ( ( SV15 = empty_set )
| ~ ( subset @ SV15 @ ( relation_rng @ SV72 ) ) )
= $true )
| ( ( ( ( relation_inverse_image @ SV72 @ SV15 )
!= empty_set ) )
= $true )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[845]) ).
thf(925,plain,
! [SV73: $i,SV16: $i,SV98: $i] :
( ( ( relation @ SV98 )
= $false )
| ( ( ~ ( subset @ SV16 @ SV73 )
| ( subset @ ( relation_inverse_image @ SV98 @ SV16 ) @ ( relation_inverse_image @ SV98 @ SV73 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[846]) ).
thf(926,plain,
! [SV99: $i,SV75: $i,SV18: $i] :
( ( ( ~ ( subset @ SV18 @ SV75 ) )
= $true )
| ( ( ~ ( subset @ SV18 @ SV99 ) )
= $true )
| ( ( subset @ SV18 @ ( set_intersection2 @ SV75 @ SV99 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[847]) ).
thf(927,plain,
! [SV100: $i,SV76: $i,SV19: $i] :
( ( ( ~ ( subset @ SV19 @ SV76 ) )
= $true )
| ( ( ~ ( subset @ SV76 @ SV100 ) )
= $true )
| ( ( subset @ SV19 @ SV100 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[848]) ).
thf(928,plain,
! [SV77: $i,SV21: $i,SV101: $i] :
( ( ( relation @ SV101 )
= $false )
| ( ( subset @ ( fiber @ ( relation_restriction @ SV101 @ SV21 ) @ SV77 ) @ ( fiber @ SV101 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[849]) ).
thf(929,plain,
! [SV78: $i,SV138: $i,SV22: $i] :
( ( ( subset @ ( set_intersection2 @ SV22 @ SV138 ) @ ( set_intersection2 @ SV78 @ SV138 ) )
= $true )
| ( ( subset @ SV22 @ SV78 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(930,plain,
! [SV80: $i,SV139: $i,SV25: $i] :
( ( ( subset @ ( set_difference @ SV25 @ SV139 ) @ ( set_difference @ SV80 @ SV139 ) )
= $true )
| ( ( subset @ SV25 @ SV80 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(931,plain,
! [SV82: $i,SV27: $i] :
( ( ( ~ ( subset @ SV27 @ ( relation_field @ SV82 ) )
| ~ ( well_ordering @ SV82 ) )
= $true )
| ( ( ( relation_field @ ( relation_restriction @ SV82 @ SV27 ) )
= SV27 )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[853]) ).
thf(932,plain,
! [SV29: $i,SV107: $i] :
( ( ( ~ ( relation @ SV107 ) )
= $true )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV29 @ SV107 ) ) @ ( relation_dom @ SV29 ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[854]) ).
thf(933,plain,
! [SV30: $i,SV108: $i] :
( ( ( ~ ( relation @ SV108 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV30 @ SV108 ) ) @ ( relation_rng @ SV108 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[855]) ).
thf(934,plain,
! [SV32: $i,SV109: $i] :
( ( ( ~ ( relation @ SV109 ) )
= $true )
| ( ( ~ ( subset @ ( relation_rng @ SV32 ) @ ( relation_dom @ SV109 ) )
| ( ( relation_dom @ ( relation_composition @ SV32 @ SV109 ) )
= ( relation_dom @ SV32 ) ) )
= $true )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[857]) ).
thf(935,plain,
! [SV33: $i,SV110: $i] :
( ( ( ~ ( relation @ SV110 ) )
= $true )
| ( ( ~ ( subset @ ( relation_dom @ SV33 ) @ ( relation_rng @ SV110 ) )
| ( ( relation_rng @ ( relation_composition @ SV110 @ SV33 ) )
= ( relation_rng @ SV33 ) ) )
= $true )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[858]) ).
thf(936,plain,
! [SV84: $i,SV34: $i] :
( ( ( subset @ SV34 @ SV84 )
= $false )
| ( ( proper_subset @ SV84 @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[859]) ).
thf(937,plain,
! [SV35: $i,SV102: $i,SV85: $i] :
( ( ( ~ ( disjoint @ SV85 @ SV102 ) )
= $true )
| ( ( ~ ( subset @ SV35 @ SV85 ) )
= $true )
| ( ( disjoint @ SV35 @ SV102 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[860]) ).
thf(938,plain,
! [SV103: $i,SV89: $i,SV39: $i] :
( ( ( ~ ( subset @ SV39 @ SV89 ) )
= $true )
| ( ( ~ ( subset @ SV103 @ SV89 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV39 @ SV103 ) @ SV89 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[863]) ).
thf(939,plain,
! [SV92: $i,SV42: $i,SV104: $i] :
( ( ( relation_of2_as_subset @ SV104 @ SV42 @ SV92 )
= $false )
| ( ( element @ SV104 @ ( powerset @ ( cartesian_product2 @ SV42 @ SV92 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[866]) ).
thf(940,plain,
! [SV140: $i,SV111: $i] :
( ( ~ ( subset @ SV111 @ ( singleton @ SV140 ) )
| ( SV111 = empty_set )
| ( SV111
= ( singleton @ SV140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(941,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[868]) ).
thf(942,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[868]) ).
thf(943,plain,
! [SV45: $i] :
( ( ( ~ ! [SY3700: $i] :
( ~ ( relation @ SY3700 )
| ~ ( subset @ SV45 @ SY3700 )
| ( subset @ ( relation_dom @ SV45 ) @ ( relation_dom @ SY3700 ) ) ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[869]) ).
thf(944,plain,
! [SV45: $i] :
( ( ( ~ ! [SY3701: $i] :
( ~ ( relation @ SY3701 )
| ~ ( subset @ SV45 @ SY3701 )
| ( subset @ ( relation_rng @ SV45 ) @ ( relation_rng @ SY3701 ) ) ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[869]) ).
thf(945,plain,
! [SV94: $i,SV46: $i] :
( ( ( ~ ! [SY3760: $i] :
( ~ ( element @ SY3760 @ ( powerset @ SV46 ) )
| ~ ( disjoint @ SV94 @ SY3760 )
| ( subset @ SV94 @ ( subset_complement @ SV46 @ SY3760 ) ) )
| ~ ! [SY3761: $i] :
( ~ ( element @ SY3761 @ ( powerset @ SV46 ) )
| ~ ( subset @ SV94 @ ( subset_complement @ SV46 @ SY3761 ) )
| ( disjoint @ SV94 @ SY3761 ) ) )
= $false )
| ( ( element @ SV94 @ ( powerset @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[870]) ).
thf(946,plain,
! [SV141: $i,SV47: $i] :
( ( ! [SY3793: $i] :
( ~ ( relation_of2 @ SY3793 @ SV47 @ SV141 )
| ( relation_of2_as_subset @ SY3793 @ SV47 @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[871]) ).
thf(947,plain,
! [SV142: $i,SV47: $i] :
( ( ! [SY3794: $i] :
( ~ ( relation_of2_as_subset @ SY3794 @ SV47 @ SV142 )
| ( relation_of2 @ SY3794 @ SV47 @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[872]) ).
thf(948,plain,
! [SV143: $i,SV112: $i] :
( ( ( SV112 = SV143 )
| ~ ( subset @ SV112 @ SV143 )
| ( proper_subset @ SV112 @ SV143 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[873]) ).
thf(949,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[874]) ).
thf(950,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[874]) ).
thf(951,plain,
! [SV113: $i] :
( ( ( ~ ( relation @ SV113 ) )
= $true )
| ( ( ~ ( ~ ! [SY3767: $i] :
( ~ ( disjoint @ ( fiber @ SV113 @ SY3767 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ SY3767 @ ( sK14_B @ SV113 ) ) )
| ~ ~ ( ~ ( ( ( sK14_B @ SV113 )
!= empty_set ) )
| ~ ( subset @ ( sK14_B @ SV113 ) @ ( relation_field @ SV113 ) ) ) )
| ( well_founded_relation @ SV113 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[875]) ).
thf(952,plain,
! [SV114: $i] :
( ( ( ~ ( relation @ SV114 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV114 )
| ! [SY3768: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV114 @ ( sK13_C @ SY3768 @ SV114 ) ) @ SY3768 )
| ~ ( in @ ( sK13_C @ SY3768 @ SV114 ) @ SY3768 ) )
| ( SY3768 = empty_set )
| ~ ( subset @ SY3768 @ ( relation_field @ SV114 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[876]) ).
thf(953,plain,
! [SV48: $i,SV95: $i] :
( ( ( ~ ( ~ ( ordinal @ ( sK17_C @ SV95 @ SV48 ) )
| ~ ~ ( ~ ! [SY3762: $i] :
( ~ ( ordinal @ SY3762 )
| ~ ( in @ SY3762 @ SV48 )
| ( ordinal_subset @ ( sK17_C @ SV95 @ SV48 ) @ SY3762 ) )
| ~ ( in @ ( sK17_C @ SV95 @ SV48 ) @ SV48 ) ) ) )
= $true )
| ( ( ( SV48 = empty_set )
| ~ ( subset @ SV48 @ SV95 ) )
= $true )
| ( ( ordinal @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[877]) ).
thf(954,plain,
! [SV115: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_B @ SV115 ) @ SV115 )
| ~ ~ ( subset @ ( sK15_B @ SV115 ) @ SV115 ) ) )
= $true )
| ( ( epsilon_transitive @ SV115 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[878]) ).
thf(955,plain,
! [SV116: $i] :
( ( ( ~ ( epsilon_transitive @ SV116 ) )
= $true )
| ( ( ! [SY3769: $i] :
( ~ ( in @ SY3769 @ SV116 )
| ( subset @ SY3769 @ SV116 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[879]) ).
thf(956,plain,
! [SV144: $i,SV49: $i] :
( ( ! [SY3795: $i] :
( ~ ( in @ SV49 @ SY3795 )
| ~ ( in @ SV144 @ SY3795 )
| ( subset @ ( unordered_pair @ SV49 @ SV144 ) @ SY3795 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(957,plain,
! [SV49: $i] :
( ( ~ ! [SY3713: $i,SY3714: $i] :
( ~ ( subset @ ( unordered_pair @ SV49 @ SY3713 ) @ SY3714 )
| ( in @ SV49 @ SY3714 ) )
| ~ ! [SY3715: $i,SY3716: $i] :
( ~ ( subset @ ( unordered_pair @ SV49 @ SY3715 ) @ SY3716 )
| ( in @ SY3715 @ SY3716 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[881]) ).
thf(958,plain,
! [SV117: $i,SV145: $i] :
( ( ~ ( ~ ( in @ ( sK10_C @ SV145 @ SV117 ) @ SV117 )
| ~ ~ ( in @ ( sK10_C @ SV145 @ SV117 ) @ SV145 ) )
| ( subset @ SV117 @ SV145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[882]) ).
thf(959,plain,
! [SV146: $i,SV118: $i] :
( ( ~ ( subset @ SV118 @ SV146 )
| ! [SY3796: $i] :
( ~ ( in @ SY3796 @ SV118 )
| ( in @ SY3796 @ SV146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(960,plain,
! [SV147: $i,SV119: $i] :
( ( ~ ( subset @ SV119 @ SV147 )
| ~ ( subset @ SV147 @ SV119 )
| ( SV119 = SV147 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[884]) ).
thf(961,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[885]) ).
thf(962,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[885]) ).
thf(963,plain,
! [SV50: $i,SV148: $i] :
( ( ~ ( subset @ SV148 @ ( sK19_B @ SV50 ) )
| ( are_equipotent @ SV148 @ ( sK19_B @ SV50 ) )
| ( in @ SV148 @ ( sK19_B @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[886]) ).
thf(964,plain,
! [SV50: $i] :
( ( ~ ! [SY3718: $i] :
( ~ ( in @ SY3718 @ ( sK19_B @ SV50 ) )
| ( in @ ( powerset @ SY3718 ) @ ( sK19_B @ SV50 ) ) )
| ~ ~ ( ~ ! [SY3719: $i,SY3720: $i] :
( ~ ( in @ SY3719 @ ( sK19_B @ SV50 ) )
| ~ ( subset @ SY3720 @ SY3719 )
| ( in @ SY3720 @ ( sK19_B @ SV50 ) ) )
| ~ ( in @ SV50 @ ( sK19_B @ SV50 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[887]) ).
thf(965,plain,
! [SV149: $i,SV120: $i] :
( ( ~ ( in @ SV120 @ SV149 )
| ( subset @ ( singleton @ SV120 ) @ SV149 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[888]) ).
thf(966,plain,
! [SV150: $i,SV121: $i] :
( ( ~ ( subset @ ( singleton @ SV121 ) @ SV150 )
| ( in @ SV121 @ SV150 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(967,plain,
! [SV151: $i,SV122: $i] :
( ( ( ( set_difference @ SV122 @ SV151 )
!= empty_set )
| ( subset @ SV122 @ SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(968,plain,
! [SV152: $i,SV123: $i] :
( ( ~ ( subset @ SV123 @ SV152 )
| ( ( set_difference @ SV123 @ SV152 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(969,plain,
! [SV153: $i,SV124: $i] :
( ( ~ ( element @ SV124 @ ( powerset @ SV153 ) )
| ( subset @ SV124 @ SV153 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[892]) ).
thf(970,plain,
! [SV154: $i,SV125: $i] :
( ( ~ ( subset @ SV125 @ SV154 )
| ( element @ SV125 @ ( powerset @ SV154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(971,plain,
! [SV126: $i,SV155: $i] :
( ( ~ ( relation @ SV155 )
| ( subset @ ( relation_field @ ( relation_restriction @ SV155 @ SV126 ) ) @ ( relation_field @ SV155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(972,plain,
! [SV127: $i,SV156: $i] :
( ( ~ ( relation @ SV156 )
| ( subset @ ( relation_field @ ( relation_restriction @ SV156 @ SV127 ) ) @ SV127 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[895]) ).
thf(973,plain,
! [SV157: $i,SV51: $i] :
( ( ~ ( subset @ SV51 @ SV157 )
| ! [SY3797: $i] : ( subset @ ( cartesian_product2 @ SV51 @ SY3797 ) @ ( cartesian_product2 @ SV157 @ SY3797 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(974,plain,
! [SV158: $i,SV51: $i] :
( ( ~ ( subset @ SV51 @ SV158 )
| ! [SY3798: $i] : ( subset @ ( cartesian_product2 @ SY3798 @ SV51 ) @ ( cartesian_product2 @ SY3798 @ SV158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(975,plain,
! [SV128: $i,SV159: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK16_C @ SV159 @ SV128 ) @ SV159 )
| ~ ( subset @ ( sK16_C @ SV159 @ SV128 ) @ SV128 ) )
| ~ ( ( in @ ( sK16_C @ SV159 @ SV128 ) @ SV159 )
| ( subset @ ( sK16_C @ SV159 @ SV128 ) @ SV128 ) ) )
| ( SV159
= ( powerset @ SV128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[898]) ).
thf(976,plain,
! [SV129: $i,SV160: $i] :
( ( ( SV160
!= ( powerset @ SV129 ) )
| ~ ( ~ ! [SY3799: $i] :
( ~ ( in @ SY3799 @ SV160 )
| ( subset @ SY3799 @ SV129 ) )
| ~ ! [SY3800: $i] :
( ~ ( subset @ SY3800 @ SV129 )
| ( in @ SY3800 @ SV160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(977,plain,
! [SV161: $i,SV52: $i] :
( ( ! [SY3801: $i] :
( ~ ( relation_of2 @ SY3801 @ SV52 @ SV161 )
| ( subset @ SY3801 @ ( cartesian_product2 @ SV52 @ SV161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(978,plain,
! [SV162: $i,SV52: $i] :
( ( ! [SY3802: $i] :
( ~ ( subset @ SY3802 @ ( cartesian_product2 @ SV52 @ SV162 ) )
| ( relation_of2 @ SY3802 @ SV52 @ SV162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(979,plain,
! [SV163: $i,SV130: $i] :
( ( ~ ( in @ SV130 @ SV163 )
| ( subset @ ( singleton @ SV130 ) @ SV163 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[902]) ).
thf(980,plain,
! [SV164: $i,SV131: $i] :
( ( ~ ( subset @ ( singleton @ SV131 ) @ SV164 )
| ( in @ SV131 @ SV164 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(981,plain,
! [SV165: $i,SV53: $i] :
( ( ! [SY3803: $i] :
( ~ ( relation_of2_as_subset @ SY3803 @ SV53 @ SV165 )
| ( subset @ ( relation_dom @ SY3803 ) @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[904]) ).
thf(982,plain,
! [SV166: $i,SV53: $i] :
( ( ! [SY3804: $i] :
( ~ ( relation_of2_as_subset @ SY3804 @ SV53 @ SV166 )
| ( subset @ ( relation_rng @ SY3804 ) @ SV166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(983,plain,
! [SV54: $i] :
( ( ( in @ ( sK18_B @ SV54 ) @ SV54 )
= $true )
| ( ( ordinal @ SV54 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[906]) ).
thf(984,plain,
! [SV54: $i] :
( ( ( ~ ( ordinal @ ( sK18_B @ SV54 ) )
| ~ ( subset @ ( sK18_B @ SV54 ) @ SV54 ) )
= $true )
| ( ( ordinal @ SV54 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[907]) ).
thf(985,plain,
! [SV55: $i] :
( ( ( ~ ! [SY3733: $i] :
( ~ ( ~ ! [SY3734: $i] :
( ~ ( disjoint @ ( fiber @ SV55 @ SY3734 ) @ ( sK9_C @ SY3733 @ SV55 ) )
| ~ ( in @ SY3734 @ ( sK9_C @ SY3733 @ SV55 ) ) )
| ~ ~ ( ~ ( ( ( sK9_C @ SY3733 @ SV55 )
!= empty_set ) )
| ~ ( subset @ ( sK9_C @ SY3733 @ SV55 ) @ SY3733 ) ) )
| ( is_well_founded_in @ SV55 @ SY3733 ) ) )
= $false )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[908]) ).
thf(986,plain,
! [SV55: $i] :
( ( ( ~ ! [SY3735: $i] :
( ~ ( is_well_founded_in @ SV55 @ SY3735 )
| ! [SY3736: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV55 @ ( sK8_D @ SY3736 @ SY3735 @ SV55 ) ) @ SY3736 )
| ~ ( in @ ( sK8_D @ SY3736 @ SY3735 @ SV55 ) @ SY3736 ) )
| ( SY3736 = empty_set )
| ~ ( subset @ SY3736 @ SY3735 ) ) ) )
= $false )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[908]) ).
thf(987,plain,
! [SV56: $i,SV167: $i] :
( ( ~ ( subset @ SV167 @ ( sK5_B @ SV56 ) )
| ( are_equipotent @ SV167 @ ( sK5_B @ SV56 ) )
| ( in @ SV167 @ ( sK5_B @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[909]) ).
thf(988,plain,
! [SV56: $i] :
( ( ~ ! [SY3738: $i] :
( ~ ( ~ ! [SY3739: $i] :
( ~ ( subset @ SY3739 @ SY3738 )
| ( in @ SY3739 @ ( sK6_SY3633 @ SY3738 @ SV56 ) ) )
| ~ ( in @ ( sK6_SY3633 @ SY3738 @ SV56 ) @ ( sK5_B @ SV56 ) ) )
| ~ ( in @ SY3738 @ ( sK5_B @ SV56 ) ) )
| ~ ~ ( ~ ! [SY3740: $i,SY3741: $i] :
( ~ ( in @ SY3740 @ ( sK5_B @ SV56 ) )
| ~ ( subset @ SY3741 @ SY3740 )
| ( in @ SY3741 @ ( sK5_B @ SV56 ) ) )
| ~ ( in @ SV56 @ ( sK5_B @ SV56 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[910]) ).
thf(989,plain,
! [SV168: $i,SV132: $i] :
( ( ~ ( subset @ SV132 @ ( singleton @ SV168 ) )
| ( SV132 = empty_set )
| ( SV132
= ( singleton @ SV168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(990,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[912]) ).
thf(991,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[912]) ).
thf(992,plain,
! [SV57: $i] :
( ( ( ~ ! [SY3742: $i] :
( ~ ( relation @ SY3742 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SY3742 @ SV57 ) @ ( sK12_SY3639 @ SY3742 @ SV57 ) ) @ SV57 )
| ~ ~ ( in @ ( ordered_pair @ ( sK11_C @ SY3742 @ SV57 ) @ ( sK12_SY3639 @ SY3742 @ SV57 ) ) @ SY3742 ) )
| ( subset @ SV57 @ SY3742 ) ) )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[913]) ).
thf(993,plain,
! [SV57: $i] :
( ( ( ~ ! [SY3743: $i] :
( ~ ( relation @ SY3743 )
| ~ ( subset @ SV57 @ SY3743 )
| ! [SY3744: $i,SY3745: $i] :
( ~ ( in @ ( ordered_pair @ SY3744 @ SY3745 ) @ SV57 )
| ( in @ ( ordered_pair @ SY3744 @ SY3745 ) @ SY3743 ) ) ) )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[913]) ).
thf(994,plain,
! [SV169: $i,SV133: $i] :
( ( ~ ( ordinal @ SV133 )
| ~ ( ordinal @ SV169 )
| ~ ( ordinal_subset @ SV133 @ SV169 )
| ( subset @ SV133 @ SV169 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(995,plain,
! [SV170: $i,SV134: $i] :
( ( ~ ( ordinal @ SV134 )
| ~ ( ordinal @ SV170 )
| ~ ( subset @ SV134 @ SV170 )
| ( ordinal_subset @ SV134 @ SV170 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(996,plain,
! [SV171: $i,SV135: $i] :
( ( ( ( set_difference @ SV135 @ SV171 )
!= empty_set )
| ( subset @ SV135 @ SV171 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(997,plain,
! [SV172: $i,SV136: $i] :
( ( ~ ( subset @ SV136 @ SV172 )
| ( ( set_difference @ SV136 @ SV172 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[917]) ).
thf(998,plain,
! [SV59: $i,SV2: $i,SV137: $i] :
( ( ( in @ SV137 @ SV2 )
= $true )
| ( ( subset @ SV2 @ ( set_difference @ SV59 @ ( singleton @ SV137 ) ) )
= $true )
| ( ( subset @ SV2 @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[918]) ).
thf(999,plain,
! [SV105: $i,SV96: $i,SV64: $i,SV7: $i] :
( ( ( ~ ( subset @ SV7 @ SV64 ) )
= $true )
| ( ( ~ ( subset @ SV96 @ SV105 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV7 @ SV96 ) @ ( cartesian_product2 @ SV64 @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[919]) ).
thf(1000,plain,
! [SV10: $i,SV67: $i] :
( ( ( relation @ SV67 )
= $false )
| ( ( function @ SV67 )
= $false )
| ( ( subset @ ( relation_image @ SV67 @ ( relation_inverse_image @ SV67 @ SV10 ) ) @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[920]) ).
thf(1001,plain,
! [SV68: $i,SV11: $i] :
( ( ( subset @ SV11 @ ( relation_dom @ SV68 ) )
= $false )
| ( ( subset @ SV11 @ ( relation_inverse_image @ SV68 @ ( relation_image @ SV68 @ SV11 ) ) )
= $true )
| ( ( relation @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[921]) ).
thf(1002,plain,
! [SV12: $i,SV69: $i] :
( ( ( relation @ SV69 )
= $false )
| ( ( function @ SV69 )
= $false )
| ( ( ~ ( subset @ SV12 @ ( relation_rng @ SV69 ) )
| ( ( relation_image @ SV69 @ ( relation_inverse_image @ SV69 @ SV12 ) )
= SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[922]) ).
thf(1003,plain,
! [SV70: $i,SV13: $i,SV97: $i,SV106: $i] :
( ( ( relation_of2_as_subset @ SV106 @ SV97 @ SV13 )
= $false )
| ( ( ~ ( subset @ ( relation_rng @ SV106 ) @ SV70 )
| ( relation_of2_as_subset @ SV106 @ SV97 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[923]) ).
thf(1004,plain,
! [SV72: $i,SV15: $i] :
( ( ( SV15 = empty_set )
= $true )
| ( ( ~ ( subset @ SV15 @ ( relation_rng @ SV72 ) ) )
= $true )
| ( ( ( ( relation_inverse_image @ SV72 @ SV15 )
!= empty_set ) )
= $true )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[924]) ).
thf(1005,plain,
! [SV98: $i,SV73: $i,SV16: $i] :
( ( ( ~ ( subset @ SV16 @ SV73 ) )
= $true )
| ( ( subset @ ( relation_inverse_image @ SV98 @ SV16 ) @ ( relation_inverse_image @ SV98 @ SV73 ) )
= $true )
| ( ( relation @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[925]) ).
thf(1006,plain,
! [SV99: $i,SV75: $i,SV18: $i] :
( ( ( subset @ SV18 @ SV75 )
= $false )
| ( ( ~ ( subset @ SV18 @ SV99 ) )
= $true )
| ( ( subset @ SV18 @ ( set_intersection2 @ SV75 @ SV99 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[926]) ).
thf(1007,plain,
! [SV100: $i,SV76: $i,SV19: $i] :
( ( ( subset @ SV19 @ SV76 )
= $false )
| ( ( ~ ( subset @ SV76 @ SV100 ) )
= $true )
| ( ( subset @ SV19 @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[927]) ).
thf(1008,plain,
! [SV82: $i,SV27: $i] :
( ( ( ~ ( subset @ SV27 @ ( relation_field @ SV82 ) ) )
= $true )
| ( ( ~ ( well_ordering @ SV82 ) )
= $true )
| ( ( ( relation_field @ ( relation_restriction @ SV82 @ SV27 ) )
= SV27 )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[931]) ).
thf(1009,plain,
! [SV29: $i,SV107: $i] :
( ( ( relation @ SV107 )
= $false )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV29 @ SV107 ) ) @ ( relation_dom @ SV29 ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[932]) ).
thf(1010,plain,
! [SV30: $i,SV108: $i] :
( ( ( relation @ SV108 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV30 @ SV108 ) ) @ ( relation_rng @ SV108 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[933]) ).
thf(1011,plain,
! [SV32: $i,SV109: $i] :
( ( ( relation @ SV109 )
= $false )
| ( ( ~ ( subset @ ( relation_rng @ SV32 ) @ ( relation_dom @ SV109 ) )
| ( ( relation_dom @ ( relation_composition @ SV32 @ SV109 ) )
= ( relation_dom @ SV32 ) ) )
= $true )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[934]) ).
thf(1012,plain,
! [SV33: $i,SV110: $i] :
( ( ( relation @ SV110 )
= $false )
| ( ( ~ ( subset @ ( relation_dom @ SV33 ) @ ( relation_rng @ SV110 ) )
| ( ( relation_rng @ ( relation_composition @ SV110 @ SV33 ) )
= ( relation_rng @ SV33 ) ) )
= $true )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[935]) ).
thf(1013,plain,
! [SV35: $i,SV102: $i,SV85: $i] :
( ( ( disjoint @ SV85 @ SV102 )
= $false )
| ( ( ~ ( subset @ SV35 @ SV85 ) )
= $true )
| ( ( disjoint @ SV35 @ SV102 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[937]) ).
thf(1014,plain,
! [SV103: $i,SV89: $i,SV39: $i] :
( ( ( subset @ SV39 @ SV89 )
= $false )
| ( ( ~ ( subset @ SV103 @ SV89 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV39 @ SV103 ) @ SV89 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[938]) ).
thf(1015,plain,
! [SV140: $i,SV111: $i] :
( ( ( ~ ( subset @ SV111 @ ( singleton @ SV140 ) ) )
= $true )
| ( ( ( SV111 = empty_set )
| ( SV111
= ( singleton @ SV140 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[940]) ).
thf(1016,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[941]) ).
thf(1017,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[942]) ).
thf(1018,plain,
! [SV45: $i] :
( ( ( ! [SY3700: $i] :
( ~ ( relation @ SY3700 )
| ~ ( subset @ SV45 @ SY3700 )
| ( subset @ ( relation_dom @ SV45 ) @ ( relation_dom @ SY3700 ) ) ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[943]) ).
thf(1019,plain,
! [SV45: $i] :
( ( ( ! [SY3701: $i] :
( ~ ( relation @ SY3701 )
| ~ ( subset @ SV45 @ SY3701 )
| ( subset @ ( relation_rng @ SV45 ) @ ( relation_rng @ SY3701 ) ) ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[944]) ).
thf(1020,plain,
! [SV94: $i,SV46: $i] :
( ( ( ~ ! [SY3760: $i] :
( ~ ( element @ SY3760 @ ( powerset @ SV46 ) )
| ~ ( disjoint @ SV94 @ SY3760 )
| ( subset @ SV94 @ ( subset_complement @ SV46 @ SY3760 ) ) ) )
= $false )
| ( ( element @ SV94 @ ( powerset @ SV46 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[945]) ).
thf(1021,plain,
! [SV94: $i,SV46: $i] :
( ( ( ~ ! [SY3761: $i] :
( ~ ( element @ SY3761 @ ( powerset @ SV46 ) )
| ~ ( subset @ SV94 @ ( subset_complement @ SV46 @ SY3761 ) )
| ( disjoint @ SV94 @ SY3761 ) ) )
= $false )
| ( ( element @ SV94 @ ( powerset @ SV46 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[945]) ).
thf(1022,plain,
! [SV141: $i,SV47: $i,SV173: $i] :
( ( ~ ( relation_of2 @ SV173 @ SV47 @ SV141 )
| ( relation_of2_as_subset @ SV173 @ SV47 @ SV141 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(1023,plain,
! [SV142: $i,SV47: $i,SV174: $i] :
( ( ~ ( relation_of2_as_subset @ SV174 @ SV47 @ SV142 )
| ( relation_of2 @ SV174 @ SV47 @ SV142 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(1024,plain,
! [SV143: $i,SV112: $i] :
( ( ( ( SV112 = SV143 )
| ~ ( subset @ SV112 @ SV143 ) )
= $true )
| ( ( proper_subset @ SV112 @ SV143 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[948]) ).
thf(1025,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[949]) ).
thf(1026,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[950]) ).
thf(1027,plain,
! [SV113: $i] :
( ( ( relation @ SV113 )
= $false )
| ( ( ~ ( ~ ! [SY3767: $i] :
( ~ ( disjoint @ ( fiber @ SV113 @ SY3767 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ SY3767 @ ( sK14_B @ SV113 ) ) )
| ~ ~ ( ~ ( ( ( sK14_B @ SV113 )
!= empty_set ) )
| ~ ( subset @ ( sK14_B @ SV113 ) @ ( relation_field @ SV113 ) ) ) )
| ( well_founded_relation @ SV113 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[951]) ).
thf(1028,plain,
! [SV114: $i] :
( ( ( relation @ SV114 )
= $false )
| ( ( ~ ( well_founded_relation @ SV114 )
| ! [SY3768: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV114 @ ( sK13_C @ SY3768 @ SV114 ) ) @ SY3768 )
| ~ ( in @ ( sK13_C @ SY3768 @ SV114 ) @ SY3768 ) )
| ( SY3768 = empty_set )
| ~ ( subset @ SY3768 @ ( relation_field @ SV114 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[952]) ).
thf(1029,plain,
! [SV48: $i,SV95: $i] :
( ( ( ~ ( ordinal @ ( sK17_C @ SV95 @ SV48 ) )
| ~ ~ ( ~ ! [SY3762: $i] :
( ~ ( ordinal @ SY3762 )
| ~ ( in @ SY3762 @ SV48 )
| ( ordinal_subset @ ( sK17_C @ SV95 @ SV48 ) @ SY3762 ) )
| ~ ( in @ ( sK17_C @ SV95 @ SV48 ) @ SV48 ) ) )
= $false )
| ( ( ( SV48 = empty_set )
| ~ ( subset @ SV48 @ SV95 ) )
= $true )
| ( ( ordinal @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[953]) ).
thf(1030,plain,
! [SV115: $i] :
( ( ( ~ ( in @ ( sK15_B @ SV115 ) @ SV115 )
| ~ ~ ( subset @ ( sK15_B @ SV115 ) @ SV115 ) )
= $false )
| ( ( epsilon_transitive @ SV115 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[954]) ).
thf(1031,plain,
! [SV116: $i] :
( ( ( epsilon_transitive @ SV116 )
= $false )
| ( ( ! [SY3769: $i] :
( ~ ( in @ SY3769 @ SV116 )
| ( subset @ SY3769 @ SV116 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[955]) ).
thf(1032,plain,
! [SV144: $i,SV175: $i,SV49: $i] :
( ( ~ ( in @ SV49 @ SV175 )
| ~ ( in @ SV144 @ SV175 )
| ( subset @ ( unordered_pair @ SV49 @ SV144 ) @ SV175 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[956]) ).
thf(1033,plain,
! [SV49: $i] :
( ( ~ ! [SY3713: $i,SY3714: $i] :
( ~ ( subset @ ( unordered_pair @ SV49 @ SY3713 ) @ SY3714 )
| ( in @ SV49 @ SY3714 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[957]) ).
thf(1034,plain,
! [SV49: $i] :
( ( ~ ! [SY3715: $i,SY3716: $i] :
( ~ ( subset @ ( unordered_pair @ SV49 @ SY3715 ) @ SY3716 )
| ( in @ SY3715 @ SY3716 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[957]) ).
thf(1035,plain,
! [SV117: $i,SV145: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_C @ SV145 @ SV117 ) @ SV117 )
| ~ ~ ( in @ ( sK10_C @ SV145 @ SV117 ) @ SV145 ) ) )
= $true )
| ( ( subset @ SV117 @ SV145 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[958]) ).
thf(1036,plain,
! [SV146: $i,SV118: $i] :
( ( ( ~ ( subset @ SV118 @ SV146 ) )
= $true )
| ( ( ! [SY3796: $i] :
( ~ ( in @ SY3796 @ SV118 )
| ( in @ SY3796 @ SV146 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[959]) ).
thf(1037,plain,
! [SV147: $i,SV119: $i] :
( ( ( ~ ( subset @ SV119 @ SV147 )
| ~ ( subset @ SV147 @ SV119 ) )
= $true )
| ( ( SV119 = SV147 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[960]) ).
thf(1038,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[961]) ).
thf(1039,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[962]) ).
thf(1040,plain,
! [SV50: $i,SV148: $i] :
( ( ( ~ ( subset @ SV148 @ ( sK19_B @ SV50 ) )
| ( are_equipotent @ SV148 @ ( sK19_B @ SV50 ) ) )
= $true )
| ( ( in @ SV148 @ ( sK19_B @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[963]) ).
thf(1041,plain,
! [SV50: $i] :
( ( ~ ! [SY3718: $i] :
( ~ ( in @ SY3718 @ ( sK19_B @ SV50 ) )
| ( in @ ( powerset @ SY3718 ) @ ( sK19_B @ SV50 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[964]) ).
thf(1042,plain,
! [SV50: $i] :
( ( ~ ~ ( ~ ! [SY3719: $i,SY3720: $i] :
( ~ ( in @ SY3719 @ ( sK19_B @ SV50 ) )
| ~ ( subset @ SY3720 @ SY3719 )
| ( in @ SY3720 @ ( sK19_B @ SV50 ) ) )
| ~ ( in @ SV50 @ ( sK19_B @ SV50 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[964]) ).
thf(1043,plain,
! [SV149: $i,SV120: $i] :
( ( ( ~ ( in @ SV120 @ SV149 ) )
= $true )
| ( ( subset @ ( singleton @ SV120 ) @ SV149 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[965]) ).
thf(1044,plain,
! [SV150: $i,SV121: $i] :
( ( ( ~ ( subset @ ( singleton @ SV121 ) @ SV150 ) )
= $true )
| ( ( in @ SV121 @ SV150 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[966]) ).
thf(1045,plain,
! [SV151: $i,SV122: $i] :
( ( ( ( ( set_difference @ SV122 @ SV151 )
!= empty_set ) )
= $true )
| ( ( subset @ SV122 @ SV151 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[967]) ).
thf(1046,plain,
! [SV152: $i,SV123: $i] :
( ( ( ~ ( subset @ SV123 @ SV152 ) )
= $true )
| ( ( ( set_difference @ SV123 @ SV152 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[968]) ).
thf(1047,plain,
! [SV153: $i,SV124: $i] :
( ( ( ~ ( element @ SV124 @ ( powerset @ SV153 ) ) )
= $true )
| ( ( subset @ SV124 @ SV153 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[969]) ).
thf(1048,plain,
! [SV154: $i,SV125: $i] :
( ( ( ~ ( subset @ SV125 @ SV154 ) )
= $true )
| ( ( element @ SV125 @ ( powerset @ SV154 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[970]) ).
thf(1049,plain,
! [SV126: $i,SV155: $i] :
( ( ( ~ ( relation @ SV155 ) )
= $true )
| ( ( subset @ ( relation_field @ ( relation_restriction @ SV155 @ SV126 ) ) @ ( relation_field @ SV155 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[971]) ).
thf(1050,plain,
! [SV127: $i,SV156: $i] :
( ( ( ~ ( relation @ SV156 ) )
= $true )
| ( ( subset @ ( relation_field @ ( relation_restriction @ SV156 @ SV127 ) ) @ SV127 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[972]) ).
thf(1051,plain,
! [SV157: $i,SV51: $i] :
( ( ( ~ ( subset @ SV51 @ SV157 ) )
= $true )
| ( ( ! [SY3797: $i] : ( subset @ ( cartesian_product2 @ SV51 @ SY3797 ) @ ( cartesian_product2 @ SV157 @ SY3797 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[973]) ).
thf(1052,plain,
! [SV158: $i,SV51: $i] :
( ( ( ~ ( subset @ SV51 @ SV158 ) )
= $true )
| ( ( ! [SY3798: $i] : ( subset @ ( cartesian_product2 @ SY3798 @ SV51 ) @ ( cartesian_product2 @ SY3798 @ SV158 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[974]) ).
thf(1053,plain,
! [SV128: $i,SV159: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK16_C @ SV159 @ SV128 ) @ SV159 )
| ~ ( subset @ ( sK16_C @ SV159 @ SV128 ) @ SV128 ) )
| ~ ( ( in @ ( sK16_C @ SV159 @ SV128 ) @ SV159 )
| ( subset @ ( sK16_C @ SV159 @ SV128 ) @ SV128 ) ) ) )
= $true )
| ( ( SV159
= ( powerset @ SV128 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[975]) ).
thf(1054,plain,
! [SV129: $i,SV160: $i] :
( ( ( ( SV160
!= ( powerset @ SV129 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3799: $i] :
( ~ ( in @ SY3799 @ SV160 )
| ( subset @ SY3799 @ SV129 ) )
| ~ ! [SY3800: $i] :
( ~ ( subset @ SY3800 @ SV129 )
| ( in @ SY3800 @ SV160 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[976]) ).
thf(1055,plain,
! [SV161: $i,SV52: $i,SV176: $i] :
( ( ~ ( relation_of2 @ SV176 @ SV52 @ SV161 )
| ( subset @ SV176 @ ( cartesian_product2 @ SV52 @ SV161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[977]) ).
thf(1056,plain,
! [SV162: $i,SV52: $i,SV177: $i] :
( ( ~ ( subset @ SV177 @ ( cartesian_product2 @ SV52 @ SV162 ) )
| ( relation_of2 @ SV177 @ SV52 @ SV162 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(1057,plain,
! [SV163: $i,SV130: $i] :
( ( ( ~ ( in @ SV130 @ SV163 ) )
= $true )
| ( ( subset @ ( singleton @ SV130 ) @ SV163 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[979]) ).
thf(1058,plain,
! [SV164: $i,SV131: $i] :
( ( ( ~ ( subset @ ( singleton @ SV131 ) @ SV164 ) )
= $true )
| ( ( in @ SV131 @ SV164 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[980]) ).
thf(1059,plain,
! [SV165: $i,SV53: $i,SV178: $i] :
( ( ~ ( relation_of2_as_subset @ SV178 @ SV53 @ SV165 )
| ( subset @ ( relation_dom @ SV178 ) @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[981]) ).
thf(1060,plain,
! [SV166: $i,SV53: $i,SV179: $i] :
( ( ~ ( relation_of2_as_subset @ SV179 @ SV53 @ SV166 )
| ( subset @ ( relation_rng @ SV179 ) @ SV166 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[982]) ).
thf(1061,plain,
! [SV54: $i] :
( ( ( ~ ( ordinal @ ( sK18_B @ SV54 ) ) )
= $true )
| ( ( ~ ( subset @ ( sK18_B @ SV54 ) @ SV54 ) )
= $true )
| ( ( ordinal @ SV54 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[984]) ).
thf(1062,plain,
! [SV55: $i] :
( ( ( ! [SY3733: $i] :
( ~ ( ~ ! [SY3734: $i] :
( ~ ( disjoint @ ( fiber @ SV55 @ SY3734 ) @ ( sK9_C @ SY3733 @ SV55 ) )
| ~ ( in @ SY3734 @ ( sK9_C @ SY3733 @ SV55 ) ) )
| ~ ~ ( ~ ( ( ( sK9_C @ SY3733 @ SV55 )
!= empty_set ) )
| ~ ( subset @ ( sK9_C @ SY3733 @ SV55 ) @ SY3733 ) ) )
| ( is_well_founded_in @ SV55 @ SY3733 ) ) )
= $true )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[985]) ).
thf(1063,plain,
! [SV55: $i] :
( ( ( ! [SY3735: $i] :
( ~ ( is_well_founded_in @ SV55 @ SY3735 )
| ! [SY3736: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV55 @ ( sK8_D @ SY3736 @ SY3735 @ SV55 ) ) @ SY3736 )
| ~ ( in @ ( sK8_D @ SY3736 @ SY3735 @ SV55 ) @ SY3736 ) )
| ( SY3736 = empty_set )
| ~ ( subset @ SY3736 @ SY3735 ) ) ) )
= $true )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[986]) ).
thf(1064,plain,
! [SV56: $i,SV167: $i] :
( ( ( ~ ( subset @ SV167 @ ( sK5_B @ SV56 ) )
| ( are_equipotent @ SV167 @ ( sK5_B @ SV56 ) ) )
= $true )
| ( ( in @ SV167 @ ( sK5_B @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[987]) ).
thf(1065,plain,
! [SV56: $i] :
( ( ~ ! [SY3738: $i] :
( ~ ( ~ ! [SY3739: $i] :
( ~ ( subset @ SY3739 @ SY3738 )
| ( in @ SY3739 @ ( sK6_SY3633 @ SY3738 @ SV56 ) ) )
| ~ ( in @ ( sK6_SY3633 @ SY3738 @ SV56 ) @ ( sK5_B @ SV56 ) ) )
| ~ ( in @ SY3738 @ ( sK5_B @ SV56 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[988]) ).
thf(1066,plain,
! [SV56: $i] :
( ( ~ ~ ( ~ ! [SY3740: $i,SY3741: $i] :
( ~ ( in @ SY3740 @ ( sK5_B @ SV56 ) )
| ~ ( subset @ SY3741 @ SY3740 )
| ( in @ SY3741 @ ( sK5_B @ SV56 ) ) )
| ~ ( in @ SV56 @ ( sK5_B @ SV56 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[988]) ).
thf(1067,plain,
! [SV168: $i,SV132: $i] :
( ( ( ~ ( subset @ SV132 @ ( singleton @ SV168 ) ) )
= $true )
| ( ( ( SV132 = empty_set )
| ( SV132
= ( singleton @ SV168 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[989]) ).
thf(1068,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[990]) ).
thf(1069,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[991]) ).
thf(1070,plain,
! [SV57: $i] :
( ( ( ! [SY3742: $i] :
( ~ ( relation @ SY3742 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SY3742 @ SV57 ) @ ( sK12_SY3639 @ SY3742 @ SV57 ) ) @ SV57 )
| ~ ~ ( in @ ( ordered_pair @ ( sK11_C @ SY3742 @ SV57 ) @ ( sK12_SY3639 @ SY3742 @ SV57 ) ) @ SY3742 ) )
| ( subset @ SV57 @ SY3742 ) ) )
= $true )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[992]) ).
thf(1071,plain,
! [SV57: $i] :
( ( ( ! [SY3743: $i] :
( ~ ( relation @ SY3743 )
| ~ ( subset @ SV57 @ SY3743 )
| ! [SY3744: $i,SY3745: $i] :
( ~ ( in @ ( ordered_pair @ SY3744 @ SY3745 ) @ SV57 )
| ( in @ ( ordered_pair @ SY3744 @ SY3745 ) @ SY3743 ) ) ) )
= $true )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[993]) ).
thf(1072,plain,
! [SV169: $i,SV133: $i] :
( ( ( ~ ( ordinal @ SV133 )
| ~ ( ordinal @ SV169 ) )
= $true )
| ( ( ~ ( ordinal_subset @ SV133 @ SV169 )
| ( subset @ SV133 @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[994]) ).
thf(1073,plain,
! [SV170: $i,SV134: $i] :
( ( ( ~ ( ordinal @ SV134 )
| ~ ( ordinal @ SV170 ) )
= $true )
| ( ( ~ ( subset @ SV134 @ SV170 )
| ( ordinal_subset @ SV134 @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[995]) ).
thf(1074,plain,
! [SV171: $i,SV135: $i] :
( ( ( ( ( set_difference @ SV135 @ SV171 )
!= empty_set ) )
= $true )
| ( ( subset @ SV135 @ SV171 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[996]) ).
thf(1075,plain,
! [SV172: $i,SV136: $i] :
( ( ( ~ ( subset @ SV136 @ SV172 ) )
= $true )
| ( ( ( set_difference @ SV136 @ SV172 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[997]) ).
thf(1076,plain,
! [SV105: $i,SV96: $i,SV64: $i,SV7: $i] :
( ( ( subset @ SV7 @ SV64 )
= $false )
| ( ( ~ ( subset @ SV96 @ SV105 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV7 @ SV96 ) @ ( cartesian_product2 @ SV64 @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[999]) ).
thf(1077,plain,
! [SV69: $i,SV12: $i] :
( ( ( ~ ( subset @ SV12 @ ( relation_rng @ SV69 ) ) )
= $true )
| ( ( ( relation_image @ SV69 @ ( relation_inverse_image @ SV69 @ SV12 ) )
= SV12 )
= $true )
| ( ( function @ SV69 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1002]) ).
thf(1078,plain,
! [SV13: $i,SV97: $i,SV70: $i,SV106: $i] :
( ( ( ~ ( subset @ ( relation_rng @ SV106 ) @ SV70 ) )
= $true )
| ( ( relation_of2_as_subset @ SV106 @ SV97 @ SV70 )
= $true )
| ( ( relation_of2_as_subset @ SV106 @ SV97 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1003]) ).
thf(1079,plain,
! [SV72: $i,SV15: $i] :
( ( ( subset @ SV15 @ ( relation_rng @ SV72 ) )
= $false )
| ( ( SV15 = empty_set )
= $true )
| ( ( ( ( relation_inverse_image @ SV72 @ SV15 )
!= empty_set ) )
= $true )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1004]) ).
thf(1080,plain,
! [SV98: $i,SV73: $i,SV16: $i] :
( ( ( subset @ SV16 @ SV73 )
= $false )
| ( ( subset @ ( relation_inverse_image @ SV98 @ SV16 ) @ ( relation_inverse_image @ SV98 @ SV73 ) )
= $true )
| ( ( relation @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1005]) ).
thf(1081,plain,
! [SV75: $i,SV99: $i,SV18: $i] :
( ( ( subset @ SV18 @ SV99 )
= $false )
| ( ( subset @ SV18 @ SV75 )
= $false )
| ( ( subset @ SV18 @ ( set_intersection2 @ SV75 @ SV99 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1006]) ).
thf(1082,plain,
! [SV19: $i,SV100: $i,SV76: $i] :
( ( ( subset @ SV76 @ SV100 )
= $false )
| ( ( subset @ SV19 @ SV76 )
= $false )
| ( ( subset @ SV19 @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1007]) ).
thf(1083,plain,
! [SV82: $i,SV27: $i] :
( ( ( subset @ SV27 @ ( relation_field @ SV82 ) )
= $false )
| ( ( ~ ( well_ordering @ SV82 ) )
= $true )
| ( ( ( relation_field @ ( relation_restriction @ SV82 @ SV27 ) )
= SV27 )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1008]) ).
thf(1084,plain,
! [SV109: $i,SV32: $i] :
( ( ( ~ ( subset @ ( relation_rng @ SV32 ) @ ( relation_dom @ SV109 ) ) )
= $true )
| ( ( ( relation_dom @ ( relation_composition @ SV32 @ SV109 ) )
= ( relation_dom @ SV32 ) )
= $true )
| ( ( relation @ SV109 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1011]) ).
thf(1085,plain,
! [SV110: $i,SV33: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV33 ) @ ( relation_rng @ SV110 ) ) )
= $true )
| ( ( ( relation_rng @ ( relation_composition @ SV110 @ SV33 ) )
= ( relation_rng @ SV33 ) )
= $true )
| ( ( relation @ SV110 )
= $false )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1012]) ).
thf(1086,plain,
! [SV102: $i,SV85: $i,SV35: $i] :
( ( ( subset @ SV35 @ SV85 )
= $false )
| ( ( disjoint @ SV85 @ SV102 )
= $false )
| ( ( disjoint @ SV35 @ SV102 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1013]) ).
thf(1087,plain,
! [SV39: $i,SV89: $i,SV103: $i] :
( ( ( subset @ SV103 @ SV89 )
= $false )
| ( ( subset @ SV39 @ SV89 )
= $false )
| ( ( subset @ ( set_union2 @ SV39 @ SV103 ) @ SV89 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1014]) ).
thf(1088,plain,
! [SV140: $i,SV111: $i] :
( ( ( subset @ SV111 @ ( singleton @ SV140 ) )
= $false )
| ( ( ( SV111 = empty_set )
| ( SV111
= ( singleton @ SV140 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1015]) ).
thf(1089,plain,
! [SV180: $i] :
( ( ( SV180 != empty_set )
| ! [SY3805: $i] : ( subset @ SV180 @ ( singleton @ SY3805 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1090,plain,
! [SV181: $i] :
( ( ! [SY3806: $i] :
( ( SV181
!= ( singleton @ SY3806 ) )
| ( subset @ SV181 @ ( singleton @ SY3806 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1091,plain,
! [SV45: $i,SV182: $i] :
( ( ( ~ ( relation @ SV182 )
| ~ ( subset @ SV45 @ SV182 )
| ( subset @ ( relation_dom @ SV45 ) @ ( relation_dom @ SV182 ) ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1092,plain,
! [SV45: $i,SV183: $i] :
( ( ( ~ ( relation @ SV183 )
| ~ ( subset @ SV45 @ SV183 )
| ( subset @ ( relation_rng @ SV45 ) @ ( relation_rng @ SV183 ) ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1019]) ).
thf(1093,plain,
! [SV94: $i,SV46: $i] :
( ( ( ! [SY3760: $i] :
( ~ ( element @ SY3760 @ ( powerset @ SV46 ) )
| ~ ( disjoint @ SV94 @ SY3760 )
| ( subset @ SV94 @ ( subset_complement @ SV46 @ SY3760 ) ) ) )
= $true )
| ( ( element @ SV94 @ ( powerset @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1020]) ).
thf(1094,plain,
! [SV94: $i,SV46: $i] :
( ( ( ! [SY3761: $i] :
( ~ ( element @ SY3761 @ ( powerset @ SV46 ) )
| ~ ( subset @ SV94 @ ( subset_complement @ SV46 @ SY3761 ) )
| ( disjoint @ SV94 @ SY3761 ) ) )
= $true )
| ( ( element @ SV94 @ ( powerset @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1021]) ).
thf(1095,plain,
! [SV141: $i,SV47: $i,SV173: $i] :
( ( ( ~ ( relation_of2 @ SV173 @ SV47 @ SV141 ) )
= $true )
| ( ( relation_of2_as_subset @ SV173 @ SV47 @ SV141 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1022]) ).
thf(1096,plain,
! [SV142: $i,SV47: $i,SV174: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV174 @ SV47 @ SV142 ) )
= $true )
| ( ( relation_of2 @ SV174 @ SV47 @ SV142 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1023]) ).
thf(1097,plain,
! [SV143: $i,SV112: $i] :
( ( ( SV112 = SV143 )
= $true )
| ( ( ~ ( subset @ SV112 @ SV143 ) )
= $true )
| ( ( proper_subset @ SV112 @ SV143 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1024]) ).
thf(1098,plain,
! [SV184: $i] :
( ( ! [SY3807: $i] :
( ~ ( proper_subset @ SV184 @ SY3807 )
| ( SV184 != SY3807 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1099,plain,
! [SV185: $i] :
( ( ! [SY3808: $i] :
( ~ ( proper_subset @ SV185 @ SY3808 )
| ( subset @ SV185 @ SY3808 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1100,plain,
! [SV113: $i] :
( ( ( ~ ( ~ ! [SY3767: $i] :
( ~ ( disjoint @ ( fiber @ SV113 @ SY3767 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ SY3767 @ ( sK14_B @ SV113 ) ) )
| ~ ~ ( ~ ( ( ( sK14_B @ SV113 )
!= empty_set ) )
| ~ ( subset @ ( sK14_B @ SV113 ) @ ( relation_field @ SV113 ) ) ) ) )
= $true )
| ( ( well_founded_relation @ SV113 )
= $true )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1027]) ).
thf(1101,plain,
! [SV114: $i] :
( ( ( ~ ( well_founded_relation @ SV114 ) )
= $true )
| ( ( ! [SY3768: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV114 @ ( sK13_C @ SY3768 @ SV114 ) ) @ SY3768 )
| ~ ( in @ ( sK13_C @ SY3768 @ SV114 ) @ SY3768 ) )
| ( SY3768 = empty_set )
| ~ ( subset @ SY3768 @ ( relation_field @ SV114 ) ) ) )
= $true )
| ( ( relation @ SV114 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1028]) ).
thf(1102,plain,
! [SV48: $i,SV95: $i] :
( ( ( ~ ( ordinal @ ( sK17_C @ SV95 @ SV48 ) ) )
= $false )
| ( ( ( SV48 = empty_set )
| ~ ( subset @ SV48 @ SV95 ) )
= $true )
| ( ( ordinal @ SV95 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1029]) ).
thf(1103,plain,
! [SV95: $i,SV48: $i] :
( ( ( ~ ~ ( ~ ! [SY3762: $i] :
( ~ ( ordinal @ SY3762 )
| ~ ( in @ SY3762 @ SV48 )
| ( ordinal_subset @ ( sK17_C @ SV95 @ SV48 ) @ SY3762 ) )
| ~ ( in @ ( sK17_C @ SV95 @ SV48 ) @ SV48 ) ) )
= $false )
| ( ( ( SV48 = empty_set )
| ~ ( subset @ SV48 @ SV95 ) )
= $true )
| ( ( ordinal @ SV95 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1029]) ).
thf(1104,plain,
! [SV115: $i] :
( ( ( ~ ( in @ ( sK15_B @ SV115 ) @ SV115 ) )
= $false )
| ( ( epsilon_transitive @ SV115 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1030]) ).
thf(1105,plain,
! [SV115: $i] :
( ( ( ~ ~ ( subset @ ( sK15_B @ SV115 ) @ SV115 ) )
= $false )
| ( ( epsilon_transitive @ SV115 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1030]) ).
thf(1106,plain,
! [SV116: $i,SV186: $i] :
( ( ( ~ ( in @ SV186 @ SV116 )
| ( subset @ SV186 @ SV116 ) )
= $true )
| ( ( epsilon_transitive @ SV116 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1107,plain,
! [SV144: $i,SV175: $i,SV49: $i] :
( ( ( ~ ( in @ SV49 @ SV175 )
| ~ ( in @ SV144 @ SV175 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV49 @ SV144 ) @ SV175 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1032]) ).
thf(1108,plain,
! [SV49: $i] :
( ( ! [SY3713: $i,SY3714: $i] :
( ~ ( subset @ ( unordered_pair @ SV49 @ SY3713 ) @ SY3714 )
| ( in @ SV49 @ SY3714 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1033]) ).
thf(1109,plain,
! [SV49: $i] :
( ( ! [SY3715: $i,SY3716: $i] :
( ~ ( subset @ ( unordered_pair @ SV49 @ SY3715 ) @ SY3716 )
| ( in @ SY3715 @ SY3716 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1034]) ).
thf(1110,plain,
! [SV117: $i,SV145: $i] :
( ( ( ~ ( in @ ( sK10_C @ SV145 @ SV117 ) @ SV117 )
| ~ ~ ( in @ ( sK10_C @ SV145 @ SV117 ) @ SV145 ) )
= $false )
| ( ( subset @ SV117 @ SV145 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1035]) ).
thf(1111,plain,
! [SV146: $i,SV118: $i] :
( ( ( subset @ SV118 @ SV146 )
= $false )
| ( ( ! [SY3796: $i] :
( ~ ( in @ SY3796 @ SV118 )
| ( in @ SY3796 @ SV146 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1036]) ).
thf(1112,plain,
! [SV147: $i,SV119: $i] :
( ( ( ~ ( subset @ SV119 @ SV147 ) )
= $true )
| ( ( ~ ( subset @ SV147 @ SV119 ) )
= $true )
| ( ( SV119 = SV147 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1037]) ).
thf(1113,plain,
! [SV187: $i] :
( ( ! [SY3809: $i] :
( ( SV187 != SY3809 )
| ( subset @ SV187 @ SY3809 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1114,plain,
! [SV188: $i] :
( ( ! [SY3810: $i] :
( ( SV188 != SY3810 )
| ( subset @ SY3810 @ SV188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1115,plain,
! [SV50: $i,SV148: $i] :
( ( ( ~ ( subset @ SV148 @ ( sK19_B @ SV50 ) ) )
= $true )
| ( ( are_equipotent @ SV148 @ ( sK19_B @ SV50 ) )
= $true )
| ( ( in @ SV148 @ ( sK19_B @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1040]) ).
thf(1116,plain,
! [SV50: $i] :
( ( ! [SY3718: $i] :
( ~ ( in @ SY3718 @ ( sK19_B @ SV50 ) )
| ( in @ ( powerset @ SY3718 ) @ ( sK19_B @ SV50 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1041]) ).
thf(1117,plain,
! [SV50: $i] :
( ( ~ ( ~ ! [SY3719: $i,SY3720: $i] :
( ~ ( in @ SY3719 @ ( sK19_B @ SV50 ) )
| ~ ( subset @ SY3720 @ SY3719 )
| ( in @ SY3720 @ ( sK19_B @ SV50 ) ) )
| ~ ( in @ SV50 @ ( sK19_B @ SV50 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1042]) ).
thf(1118,plain,
! [SV149: $i,SV120: $i] :
( ( ( in @ SV120 @ SV149 )
= $false )
| ( ( subset @ ( singleton @ SV120 ) @ SV149 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1043]) ).
thf(1119,plain,
! [SV150: $i,SV121: $i] :
( ( ( subset @ ( singleton @ SV121 ) @ SV150 )
= $false )
| ( ( in @ SV121 @ SV150 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1044]) ).
thf(1120,plain,
! [SV151: $i,SV122: $i] :
( ( ( ( set_difference @ SV122 @ SV151 )
= empty_set )
= $false )
| ( ( subset @ SV122 @ SV151 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1045]) ).
thf(1121,plain,
! [SV152: $i,SV123: $i] :
( ( ( subset @ SV123 @ SV152 )
= $false )
| ( ( ( set_difference @ SV123 @ SV152 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1046]) ).
thf(1122,plain,
! [SV153: $i,SV124: $i] :
( ( ( element @ SV124 @ ( powerset @ SV153 ) )
= $false )
| ( ( subset @ SV124 @ SV153 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1047]) ).
thf(1123,plain,
! [SV154: $i,SV125: $i] :
( ( ( subset @ SV125 @ SV154 )
= $false )
| ( ( element @ SV125 @ ( powerset @ SV154 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1048]) ).
thf(1124,plain,
! [SV126: $i,SV155: $i] :
( ( ( relation @ SV155 )
= $false )
| ( ( subset @ ( relation_field @ ( relation_restriction @ SV155 @ SV126 ) ) @ ( relation_field @ SV155 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1049]) ).
thf(1125,plain,
! [SV127: $i,SV156: $i] :
( ( ( relation @ SV156 )
= $false )
| ( ( subset @ ( relation_field @ ( relation_restriction @ SV156 @ SV127 ) ) @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1050]) ).
thf(1126,plain,
! [SV157: $i,SV51: $i] :
( ( ( subset @ SV51 @ SV157 )
= $false )
| ( ( ! [SY3797: $i] : ( subset @ ( cartesian_product2 @ SV51 @ SY3797 ) @ ( cartesian_product2 @ SV157 @ SY3797 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1051]) ).
thf(1127,plain,
! [SV158: $i,SV51: $i] :
( ( ( subset @ SV51 @ SV158 )
= $false )
| ( ( ! [SY3798: $i] : ( subset @ ( cartesian_product2 @ SY3798 @ SV51 ) @ ( cartesian_product2 @ SY3798 @ SV158 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1052]) ).
thf(1128,plain,
! [SV128: $i,SV159: $i] :
( ( ( ~ ( ~ ( in @ ( sK16_C @ SV159 @ SV128 ) @ SV159 )
| ~ ( subset @ ( sK16_C @ SV159 @ SV128 ) @ SV128 ) )
| ~ ( ( in @ ( sK16_C @ SV159 @ SV128 ) @ SV159 )
| ( subset @ ( sK16_C @ SV159 @ SV128 ) @ SV128 ) ) )
= $false )
| ( ( SV159
= ( powerset @ SV128 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1053]) ).
thf(1129,plain,
! [SV129: $i,SV160: $i] :
( ( ( SV160
= ( powerset @ SV129 ) )
= $false )
| ( ( ~ ( ~ ! [SY3799: $i] :
( ~ ( in @ SY3799 @ SV160 )
| ( subset @ SY3799 @ SV129 ) )
| ~ ! [SY3800: $i] :
( ~ ( subset @ SY3800 @ SV129 )
| ( in @ SY3800 @ SV160 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1054]) ).
thf(1130,plain,
! [SV161: $i,SV52: $i,SV176: $i] :
( ( ( ~ ( relation_of2 @ SV176 @ SV52 @ SV161 ) )
= $true )
| ( ( subset @ SV176 @ ( cartesian_product2 @ SV52 @ SV161 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1055]) ).
thf(1131,plain,
! [SV162: $i,SV52: $i,SV177: $i] :
( ( ( ~ ( subset @ SV177 @ ( cartesian_product2 @ SV52 @ SV162 ) ) )
= $true )
| ( ( relation_of2 @ SV177 @ SV52 @ SV162 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1056]) ).
thf(1132,plain,
! [SV163: $i,SV130: $i] :
( ( ( in @ SV130 @ SV163 )
= $false )
| ( ( subset @ ( singleton @ SV130 ) @ SV163 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1057]) ).
thf(1133,plain,
! [SV164: $i,SV131: $i] :
( ( ( subset @ ( singleton @ SV131 ) @ SV164 )
= $false )
| ( ( in @ SV131 @ SV164 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1058]) ).
thf(1134,plain,
! [SV165: $i,SV53: $i,SV178: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV178 @ SV53 @ SV165 ) )
= $true )
| ( ( subset @ ( relation_dom @ SV178 ) @ SV53 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1059]) ).
thf(1135,plain,
! [SV166: $i,SV53: $i,SV179: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV179 @ SV53 @ SV166 ) )
= $true )
| ( ( subset @ ( relation_rng @ SV179 ) @ SV166 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1060]) ).
thf(1136,plain,
! [SV54: $i] :
( ( ( ordinal @ ( sK18_B @ SV54 ) )
= $false )
| ( ( ~ ( subset @ ( sK18_B @ SV54 ) @ SV54 ) )
= $true )
| ( ( ordinal @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1061]) ).
thf(1137,plain,
! [SV189: $i,SV55: $i] :
( ( ( ~ ( ~ ! [SY3811: $i] :
( ~ ( disjoint @ ( fiber @ SV55 @ SY3811 ) @ ( sK9_C @ SV189 @ SV55 ) )
| ~ ( in @ SY3811 @ ( sK9_C @ SV189 @ SV55 ) ) )
| ~ ~ ( ~ ( ( ( sK9_C @ SV189 @ SV55 )
!= empty_set ) )
| ~ ( subset @ ( sK9_C @ SV189 @ SV55 ) @ SV189 ) ) )
| ( is_well_founded_in @ SV55 @ SV189 ) )
= $true )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1062]) ).
thf(1138,plain,
! [SV190: $i,SV55: $i] :
( ( ( ~ ( is_well_founded_in @ SV55 @ SV190 )
| ! [SY3812: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV55 @ ( sK8_D @ SY3812 @ SV190 @ SV55 ) ) @ SY3812 )
| ~ ( in @ ( sK8_D @ SY3812 @ SV190 @ SV55 ) @ SY3812 ) )
| ( SY3812 = empty_set )
| ~ ( subset @ SY3812 @ SV190 ) ) )
= $true )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1139,plain,
! [SV56: $i,SV167: $i] :
( ( ( ~ ( subset @ SV167 @ ( sK5_B @ SV56 ) ) )
= $true )
| ( ( are_equipotent @ SV167 @ ( sK5_B @ SV56 ) )
= $true )
| ( ( in @ SV167 @ ( sK5_B @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1064]) ).
thf(1140,plain,
! [SV56: $i] :
( ( ! [SY3738: $i] :
( ~ ( ~ ! [SY3739: $i] :
( ~ ( subset @ SY3739 @ SY3738 )
| ( in @ SY3739 @ ( sK6_SY3633 @ SY3738 @ SV56 ) ) )
| ~ ( in @ ( sK6_SY3633 @ SY3738 @ SV56 ) @ ( sK5_B @ SV56 ) ) )
| ~ ( in @ SY3738 @ ( sK5_B @ SV56 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1065]) ).
thf(1141,plain,
! [SV56: $i] :
( ( ~ ( ~ ! [SY3740: $i,SY3741: $i] :
( ~ ( in @ SY3740 @ ( sK5_B @ SV56 ) )
| ~ ( subset @ SY3741 @ SY3740 )
| ( in @ SY3741 @ ( sK5_B @ SV56 ) ) )
| ~ ( in @ SV56 @ ( sK5_B @ SV56 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1066]) ).
thf(1142,plain,
! [SV168: $i,SV132: $i] :
( ( ( subset @ SV132 @ ( singleton @ SV168 ) )
= $false )
| ( ( ( SV132 = empty_set )
| ( SV132
= ( singleton @ SV168 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1067]) ).
thf(1143,plain,
! [SV191: $i] :
( ( ( SV191 != empty_set )
| ! [SY3813: $i] : ( subset @ SV191 @ ( singleton @ SY3813 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1068]) ).
thf(1144,plain,
! [SV192: $i] :
( ( ! [SY3814: $i] :
( ( SV192
!= ( singleton @ SY3814 ) )
| ( subset @ SV192 @ ( singleton @ SY3814 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1069]) ).
thf(1145,plain,
! [SV57: $i,SV193: $i] :
( ( ( ~ ( relation @ SV193 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SV193 @ SV57 ) @ ( sK12_SY3639 @ SV193 @ SV57 ) ) @ SV57 )
| ~ ~ ( in @ ( ordered_pair @ ( sK11_C @ SV193 @ SV57 ) @ ( sK12_SY3639 @ SV193 @ SV57 ) ) @ SV193 ) )
| ( subset @ SV57 @ SV193 ) )
= $true )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1070]) ).
thf(1146,plain,
! [SV57: $i,SV194: $i] :
( ( ( ~ ( relation @ SV194 )
| ~ ( subset @ SV57 @ SV194 )
| ! [SY3815: $i,SY3816: $i] :
( ~ ( in @ ( ordered_pair @ SY3815 @ SY3816 ) @ SV57 )
| ( in @ ( ordered_pair @ SY3815 @ SY3816 ) @ SV194 ) ) )
= $true )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1071]) ).
thf(1147,plain,
! [SV169: $i,SV133: $i] :
( ( ( ~ ( ordinal @ SV133 ) )
= $true )
| ( ( ~ ( ordinal @ SV169 ) )
= $true )
| ( ( ~ ( ordinal_subset @ SV133 @ SV169 )
| ( subset @ SV133 @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1072]) ).
thf(1148,plain,
! [SV170: $i,SV134: $i] :
( ( ( ~ ( ordinal @ SV134 ) )
= $true )
| ( ( ~ ( ordinal @ SV170 ) )
= $true )
| ( ( ~ ( subset @ SV134 @ SV170 )
| ( ordinal_subset @ SV134 @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1073]) ).
thf(1149,plain,
! [SV171: $i,SV135: $i] :
( ( ( ( set_difference @ SV135 @ SV171 )
= empty_set )
= $false )
| ( ( subset @ SV135 @ SV171 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1074]) ).
thf(1150,plain,
! [SV172: $i,SV136: $i] :
( ( ( subset @ SV136 @ SV172 )
= $false )
| ( ( ( set_difference @ SV136 @ SV172 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1075]) ).
thf(1151,plain,
! [SV64: $i,SV7: $i,SV105: $i,SV96: $i] :
( ( ( subset @ SV96 @ SV105 )
= $false )
| ( ( subset @ SV7 @ SV64 )
= $false )
| ( ( subset @ ( cartesian_product2 @ SV7 @ SV96 ) @ ( cartesian_product2 @ SV64 @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1076]) ).
thf(1152,plain,
! [SV69: $i,SV12: $i] :
( ( ( subset @ SV12 @ ( relation_rng @ SV69 ) )
= $false )
| ( ( ( relation_image @ SV69 @ ( relation_inverse_image @ SV69 @ SV12 ) )
= SV12 )
= $true )
| ( ( function @ SV69 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1077]) ).
thf(1153,plain,
! [SV13: $i,SV97: $i,SV70: $i,SV106: $i] :
( ( ( subset @ ( relation_rng @ SV106 ) @ SV70 )
= $false )
| ( ( relation_of2_as_subset @ SV106 @ SV97 @ SV70 )
= $true )
| ( ( relation_of2_as_subset @ SV106 @ SV97 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1078]) ).
thf(1154,plain,
! [SV15: $i,SV72: $i] :
( ( ( ( relation_inverse_image @ SV72 @ SV15 )
= empty_set )
= $false )
| ( ( SV15 = empty_set )
= $true )
| ( ( subset @ SV15 @ ( relation_rng @ SV72 ) )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1079]) ).
thf(1155,plain,
! [SV27: $i,SV82: $i] :
( ( ( well_ordering @ SV82 )
= $false )
| ( ( subset @ SV27 @ ( relation_field @ SV82 ) )
= $false )
| ( ( ( relation_field @ ( relation_restriction @ SV82 @ SV27 ) )
= SV27 )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1083]) ).
thf(1156,plain,
! [SV109: $i,SV32: $i] :
( ( ( subset @ ( relation_rng @ SV32 ) @ ( relation_dom @ SV109 ) )
= $false )
| ( ( ( relation_dom @ ( relation_composition @ SV32 @ SV109 ) )
= ( relation_dom @ SV32 ) )
= $true )
| ( ( relation @ SV109 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1084]) ).
thf(1157,plain,
! [SV110: $i,SV33: $i] :
( ( ( subset @ ( relation_dom @ SV33 ) @ ( relation_rng @ SV110 ) )
= $false )
| ( ( ( relation_rng @ ( relation_composition @ SV110 @ SV33 ) )
= ( relation_rng @ SV33 ) )
= $true )
| ( ( relation @ SV110 )
= $false )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1085]) ).
thf(1158,plain,
! [SV140: $i,SV111: $i] :
( ( ( SV111 = empty_set )
= $true )
| ( ( SV111
= ( singleton @ SV140 ) )
= $true )
| ( ( subset @ SV111 @ ( singleton @ SV140 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1088]) ).
thf(1159,plain,
! [SV180: $i] :
( ( ( ( SV180 != empty_set ) )
= $true )
| ( ( ! [SY3805: $i] : ( subset @ SV180 @ ( singleton @ SY3805 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1089]) ).
thf(1160,plain,
! [SV195: $i,SV181: $i] :
( ( ( SV181
!= ( singleton @ SV195 ) )
| ( subset @ SV181 @ ( singleton @ SV195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1090]) ).
thf(1161,plain,
! [SV45: $i,SV182: $i] :
( ( ( ~ ( relation @ SV182 ) )
= $true )
| ( ( ~ ( subset @ SV45 @ SV182 )
| ( subset @ ( relation_dom @ SV45 ) @ ( relation_dom @ SV182 ) ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1091]) ).
thf(1162,plain,
! [SV45: $i,SV183: $i] :
( ( ( ~ ( relation @ SV183 ) )
= $true )
| ( ( ~ ( subset @ SV45 @ SV183 )
| ( subset @ ( relation_rng @ SV45 ) @ ( relation_rng @ SV183 ) ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1092]) ).
thf(1163,plain,
! [SV94: $i,SV46: $i,SV196: $i] :
( ( ( ~ ( element @ SV196 @ ( powerset @ SV46 ) )
| ~ ( disjoint @ SV94 @ SV196 )
| ( subset @ SV94 @ ( subset_complement @ SV46 @ SV196 ) ) )
= $true )
| ( ( element @ SV94 @ ( powerset @ SV46 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1093]) ).
thf(1164,plain,
! [SV94: $i,SV46: $i,SV197: $i] :
( ( ( ~ ( element @ SV197 @ ( powerset @ SV46 ) )
| ~ ( subset @ SV94 @ ( subset_complement @ SV46 @ SV197 ) )
| ( disjoint @ SV94 @ SV197 ) )
= $true )
| ( ( element @ SV94 @ ( powerset @ SV46 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1165,plain,
! [SV141: $i,SV47: $i,SV173: $i] :
( ( ( relation_of2 @ SV173 @ SV47 @ SV141 )
= $false )
| ( ( relation_of2_as_subset @ SV173 @ SV47 @ SV141 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1095]) ).
thf(1166,plain,
! [SV142: $i,SV47: $i,SV174: $i] :
( ( ( relation_of2_as_subset @ SV174 @ SV47 @ SV142 )
= $false )
| ( ( relation_of2 @ SV174 @ SV47 @ SV142 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1096]) ).
thf(1167,plain,
! [SV143: $i,SV112: $i] :
( ( ( subset @ SV112 @ SV143 )
= $false )
| ( ( SV112 = SV143 )
= $true )
| ( ( proper_subset @ SV112 @ SV143 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1097]) ).
thf(1168,plain,
! [SV198: $i,SV184: $i] :
( ( ~ ( proper_subset @ SV184 @ SV198 )
| ( SV184 != SV198 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1098]) ).
thf(1169,plain,
! [SV199: $i,SV185: $i] :
( ( ~ ( proper_subset @ SV185 @ SV199 )
| ( subset @ SV185 @ SV199 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1099]) ).
thf(1170,plain,
! [SV113: $i] :
( ( ( ~ ! [SY3767: $i] :
( ~ ( disjoint @ ( fiber @ SV113 @ SY3767 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ SY3767 @ ( sK14_B @ SV113 ) ) )
| ~ ~ ( ~ ( ( ( sK14_B @ SV113 )
!= empty_set ) )
| ~ ( subset @ ( sK14_B @ SV113 ) @ ( relation_field @ SV113 ) ) ) )
= $false )
| ( ( well_founded_relation @ SV113 )
= $true )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1100]) ).
thf(1171,plain,
! [SV114: $i] :
( ( ( well_founded_relation @ SV114 )
= $false )
| ( ( ! [SY3768: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV114 @ ( sK13_C @ SY3768 @ SV114 ) ) @ SY3768 )
| ~ ( in @ ( sK13_C @ SY3768 @ SV114 ) @ SY3768 ) )
| ( SY3768 = empty_set )
| ~ ( subset @ SY3768 @ ( relation_field @ SV114 ) ) ) )
= $true )
| ( ( relation @ SV114 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1101]) ).
thf(1172,plain,
! [SV48: $i,SV95: $i] :
( ( ( ordinal @ ( sK17_C @ SV95 @ SV48 ) )
= $true )
| ( ( ( SV48 = empty_set )
| ~ ( subset @ SV48 @ SV95 ) )
= $true )
| ( ( ordinal @ SV95 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1102]) ).
thf(1173,plain,
! [SV95: $i,SV48: $i] :
( ( ( ~ ( ~ ! [SY3762: $i] :
( ~ ( ordinal @ SY3762 )
| ~ ( in @ SY3762 @ SV48 )
| ( ordinal_subset @ ( sK17_C @ SV95 @ SV48 ) @ SY3762 ) )
| ~ ( in @ ( sK17_C @ SV95 @ SV48 ) @ SV48 ) ) )
= $true )
| ( ( ( SV48 = empty_set )
| ~ ( subset @ SV48 @ SV95 ) )
= $true )
| ( ( ordinal @ SV95 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1103]) ).
thf(1174,plain,
! [SV115: $i] :
( ( ( in @ ( sK15_B @ SV115 ) @ SV115 )
= $true )
| ( ( epsilon_transitive @ SV115 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1104]) ).
thf(1175,plain,
! [SV115: $i] :
( ( ( ~ ( subset @ ( sK15_B @ SV115 ) @ SV115 ) )
= $true )
| ( ( epsilon_transitive @ SV115 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1105]) ).
thf(1176,plain,
! [SV116: $i,SV186: $i] :
( ( ( ~ ( in @ SV186 @ SV116 ) )
= $true )
| ( ( subset @ SV186 @ SV116 )
= $true )
| ( ( epsilon_transitive @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1106]) ).
thf(1177,plain,
! [SV144: $i,SV175: $i,SV49: $i] :
( ( ( ~ ( in @ SV49 @ SV175 ) )
= $true )
| ( ( ~ ( in @ SV144 @ SV175 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV49 @ SV144 ) @ SV175 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1107]) ).
thf(1178,plain,
! [SV200: $i,SV49: $i] :
( ( ! [SY3817: $i] :
( ~ ( subset @ ( unordered_pair @ SV49 @ SV200 ) @ SY3817 )
| ( in @ SV49 @ SY3817 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1179,plain,
! [SV201: $i,SV49: $i] :
( ( ! [SY3818: $i] :
( ~ ( subset @ ( unordered_pair @ SV49 @ SV201 ) @ SY3818 )
| ( in @ SV201 @ SY3818 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1109]) ).
thf(1180,plain,
! [SV117: $i,SV145: $i] :
( ( ( ~ ( in @ ( sK10_C @ SV145 @ SV117 ) @ SV117 ) )
= $false )
| ( ( subset @ SV117 @ SV145 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1110]) ).
thf(1181,plain,
! [SV117: $i,SV145: $i] :
( ( ( ~ ~ ( in @ ( sK10_C @ SV145 @ SV117 ) @ SV145 ) )
= $false )
| ( ( subset @ SV117 @ SV145 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1110]) ).
thf(1182,plain,
! [SV146: $i,SV118: $i,SV202: $i] :
( ( ( ~ ( in @ SV202 @ SV118 )
| ( in @ SV202 @ SV146 ) )
= $true )
| ( ( subset @ SV118 @ SV146 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1111]) ).
thf(1183,plain,
! [SV147: $i,SV119: $i] :
( ( ( subset @ SV119 @ SV147 )
= $false )
| ( ( ~ ( subset @ SV147 @ SV119 ) )
= $true )
| ( ( SV119 = SV147 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1112]) ).
thf(1184,plain,
! [SV203: $i,SV187: $i] :
( ( ( SV187 != SV203 )
| ( subset @ SV187 @ SV203 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1113]) ).
thf(1185,plain,
! [SV204: $i,SV188: $i] :
( ( ( SV188 != SV204 )
| ( subset @ SV204 @ SV188 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1114]) ).
thf(1186,plain,
! [SV50: $i,SV148: $i] :
( ( ( subset @ SV148 @ ( sK19_B @ SV50 ) )
= $false )
| ( ( are_equipotent @ SV148 @ ( sK19_B @ SV50 ) )
= $true )
| ( ( in @ SV148 @ ( sK19_B @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1115]) ).
thf(1187,plain,
! [SV50: $i,SV205: $i] :
( ( ~ ( in @ SV205 @ ( sK19_B @ SV50 ) )
| ( in @ ( powerset @ SV205 ) @ ( sK19_B @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1188,plain,
! [SV50: $i] :
( ( ~ ! [SY3719: $i,SY3720: $i] :
( ~ ( in @ SY3719 @ ( sK19_B @ SV50 ) )
| ~ ( subset @ SY3720 @ SY3719 )
| ( in @ SY3720 @ ( sK19_B @ SV50 ) ) )
| ~ ( in @ SV50 @ ( sK19_B @ SV50 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1117]) ).
thf(1189,plain,
! [SV157: $i,SV206: $i,SV51: $i] :
( ( ( subset @ ( cartesian_product2 @ SV51 @ SV206 ) @ ( cartesian_product2 @ SV157 @ SV206 ) )
= $true )
| ( ( subset @ SV51 @ SV157 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1190,plain,
! [SV158: $i,SV51: $i,SV207: $i] :
( ( ( subset @ ( cartesian_product2 @ SV207 @ SV51 ) @ ( cartesian_product2 @ SV207 @ SV158 ) )
= $true )
| ( ( subset @ SV51 @ SV158 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1191,plain,
! [SV128: $i,SV159: $i] :
( ( ( ~ ( ~ ( in @ ( sK16_C @ SV159 @ SV128 ) @ SV159 )
| ~ ( subset @ ( sK16_C @ SV159 @ SV128 ) @ SV128 ) ) )
= $false )
| ( ( SV159
= ( powerset @ SV128 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1128]) ).
thf(1192,plain,
! [SV128: $i,SV159: $i] :
( ( ( ~ ( ( in @ ( sK16_C @ SV159 @ SV128 ) @ SV159 )
| ( subset @ ( sK16_C @ SV159 @ SV128 ) @ SV128 ) ) )
= $false )
| ( ( SV159
= ( powerset @ SV128 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1128]) ).
thf(1193,plain,
! [SV129: $i,SV160: $i] :
( ( ( ~ ! [SY3799: $i] :
( ~ ( in @ SY3799 @ SV160 )
| ( subset @ SY3799 @ SV129 ) )
| ~ ! [SY3800: $i] :
( ~ ( subset @ SY3800 @ SV129 )
| ( in @ SY3800 @ SV160 ) ) )
= $false )
| ( ( SV160
= ( powerset @ SV129 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1129]) ).
thf(1194,plain,
! [SV161: $i,SV52: $i,SV176: $i] :
( ( ( relation_of2 @ SV176 @ SV52 @ SV161 )
= $false )
| ( ( subset @ SV176 @ ( cartesian_product2 @ SV52 @ SV161 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1130]) ).
thf(1195,plain,
! [SV162: $i,SV52: $i,SV177: $i] :
( ( ( subset @ SV177 @ ( cartesian_product2 @ SV52 @ SV162 ) )
= $false )
| ( ( relation_of2 @ SV177 @ SV52 @ SV162 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1131]) ).
thf(1196,plain,
! [SV165: $i,SV53: $i,SV178: $i] :
( ( ( relation_of2_as_subset @ SV178 @ SV53 @ SV165 )
= $false )
| ( ( subset @ ( relation_dom @ SV178 ) @ SV53 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1134]) ).
thf(1197,plain,
! [SV166: $i,SV53: $i,SV179: $i] :
( ( ( relation_of2_as_subset @ SV179 @ SV53 @ SV166 )
= $false )
| ( ( subset @ ( relation_rng @ SV179 ) @ SV166 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1135]) ).
thf(1198,plain,
! [SV54: $i] :
( ( ( subset @ ( sK18_B @ SV54 ) @ SV54 )
= $false )
| ( ( ordinal @ ( sK18_B @ SV54 ) )
= $false )
| ( ( ordinal @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1136]) ).
thf(1199,plain,
! [SV189: $i,SV55: $i] :
( ( ( ~ ( ~ ! [SY3811: $i] :
( ~ ( disjoint @ ( fiber @ SV55 @ SY3811 ) @ ( sK9_C @ SV189 @ SV55 ) )
| ~ ( in @ SY3811 @ ( sK9_C @ SV189 @ SV55 ) ) )
| ~ ~ ( ~ ( ( ( sK9_C @ SV189 @ SV55 )
!= empty_set ) )
| ~ ( subset @ ( sK9_C @ SV189 @ SV55 ) @ SV189 ) ) ) )
= $true )
| ( ( is_well_founded_in @ SV55 @ SV189 )
= $true )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1137]) ).
thf(1200,plain,
! [SV190: $i,SV55: $i] :
( ( ( ~ ( is_well_founded_in @ SV55 @ SV190 ) )
= $true )
| ( ( ! [SY3812: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV55 @ ( sK8_D @ SY3812 @ SV190 @ SV55 ) ) @ SY3812 )
| ~ ( in @ ( sK8_D @ SY3812 @ SV190 @ SV55 ) @ SY3812 ) )
| ( SY3812 = empty_set )
| ~ ( subset @ SY3812 @ SV190 ) ) )
= $true )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1138]) ).
thf(1201,plain,
! [SV56: $i,SV167: $i] :
( ( ( subset @ SV167 @ ( sK5_B @ SV56 ) )
= $false )
| ( ( are_equipotent @ SV167 @ ( sK5_B @ SV56 ) )
= $true )
| ( ( in @ SV167 @ ( sK5_B @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1139]) ).
thf(1202,plain,
! [SV56: $i,SV208: $i] :
( ( ~ ( ~ ! [SY3819: $i] :
( ~ ( subset @ SY3819 @ SV208 )
| ( in @ SY3819 @ ( sK6_SY3633 @ SV208 @ SV56 ) ) )
| ~ ( in @ ( sK6_SY3633 @ SV208 @ SV56 ) @ ( sK5_B @ SV56 ) ) )
| ~ ( in @ SV208 @ ( sK5_B @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1203,plain,
! [SV56: $i] :
( ( ~ ! [SY3740: $i,SY3741: $i] :
( ~ ( in @ SY3740 @ ( sK5_B @ SV56 ) )
| ~ ( subset @ SY3741 @ SY3740 )
| ( in @ SY3741 @ ( sK5_B @ SV56 ) ) )
| ~ ( in @ SV56 @ ( sK5_B @ SV56 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1141]) ).
thf(1204,plain,
! [SV168: $i,SV132: $i] :
( ( ( SV132 = empty_set )
= $true )
| ( ( SV132
= ( singleton @ SV168 ) )
= $true )
| ( ( subset @ SV132 @ ( singleton @ SV168 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1142]) ).
thf(1205,plain,
! [SV191: $i] :
( ( ( ( SV191 != empty_set ) )
= $true )
| ( ( ! [SY3813: $i] : ( subset @ SV191 @ ( singleton @ SY3813 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1143]) ).
thf(1206,plain,
! [SV209: $i,SV192: $i] :
( ( ( SV192
!= ( singleton @ SV209 ) )
| ( subset @ SV192 @ ( singleton @ SV209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1144]) ).
thf(1207,plain,
! [SV57: $i,SV193: $i] :
( ( ( ~ ( relation @ SV193 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SV193 @ SV57 ) @ ( sK12_SY3639 @ SV193 @ SV57 ) ) @ SV57 )
| ~ ~ ( in @ ( ordered_pair @ ( sK11_C @ SV193 @ SV57 ) @ ( sK12_SY3639 @ SV193 @ SV57 ) ) @ SV193 ) )
| ( subset @ SV57 @ SV193 ) )
= $true )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1145]) ).
thf(1208,plain,
! [SV57: $i,SV194: $i] :
( ( ( ~ ( relation @ SV194 ) )
= $true )
| ( ( ~ ( subset @ SV57 @ SV194 )
| ! [SY3815: $i,SY3816: $i] :
( ~ ( in @ ( ordered_pair @ SY3815 @ SY3816 ) @ SV57 )
| ( in @ ( ordered_pair @ SY3815 @ SY3816 ) @ SV194 ) ) )
= $true )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1146]) ).
thf(1209,plain,
! [SV169: $i,SV133: $i] :
( ( ( ordinal @ SV133 )
= $false )
| ( ( ~ ( ordinal @ SV169 ) )
= $true )
| ( ( ~ ( ordinal_subset @ SV133 @ SV169 )
| ( subset @ SV133 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1147]) ).
thf(1210,plain,
! [SV170: $i,SV134: $i] :
( ( ( ordinal @ SV134 )
= $false )
| ( ( ~ ( ordinal @ SV170 ) )
= $true )
| ( ( ~ ( subset @ SV134 @ SV170 )
| ( ordinal_subset @ SV134 @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1148]) ).
thf(1211,plain,
! [SV180: $i] :
( ( ( SV180 = empty_set )
= $false )
| ( ( ! [SY3805: $i] : ( subset @ SV180 @ ( singleton @ SY3805 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1159]) ).
thf(1212,plain,
! [SV195: $i,SV181: $i] :
( ( ( ( SV181
!= ( singleton @ SV195 ) ) )
= $true )
| ( ( subset @ SV181 @ ( singleton @ SV195 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1160]) ).
thf(1213,plain,
! [SV45: $i,SV182: $i] :
( ( ( relation @ SV182 )
= $false )
| ( ( ~ ( subset @ SV45 @ SV182 )
| ( subset @ ( relation_dom @ SV45 ) @ ( relation_dom @ SV182 ) ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1161]) ).
thf(1214,plain,
! [SV45: $i,SV183: $i] :
( ( ( relation @ SV183 )
= $false )
| ( ( ~ ( subset @ SV45 @ SV183 )
| ( subset @ ( relation_rng @ SV45 ) @ ( relation_rng @ SV183 ) ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1162]) ).
thf(1215,plain,
! [SV94: $i,SV46: $i,SV196: $i] :
( ( ( ~ ( element @ SV196 @ ( powerset @ SV46 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV94 @ SV196 )
| ( subset @ SV94 @ ( subset_complement @ SV46 @ SV196 ) ) )
= $true )
| ( ( element @ SV94 @ ( powerset @ SV46 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1163]) ).
thf(1216,plain,
! [SV94: $i,SV46: $i,SV197: $i] :
( ( ( ~ ( element @ SV197 @ ( powerset @ SV46 ) ) )
= $true )
| ( ( ~ ( subset @ SV94 @ ( subset_complement @ SV46 @ SV197 ) )
| ( disjoint @ SV94 @ SV197 ) )
= $true )
| ( ( element @ SV94 @ ( powerset @ SV46 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1164]) ).
thf(1217,plain,
! [SV198: $i,SV184: $i] :
( ( ( ~ ( proper_subset @ SV184 @ SV198 ) )
= $true )
| ( ( ( SV184 != SV198 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1168]) ).
thf(1218,plain,
! [SV199: $i,SV185: $i] :
( ( ( ~ ( proper_subset @ SV185 @ SV199 ) )
= $true )
| ( ( subset @ SV185 @ SV199 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1169]) ).
thf(1219,plain,
! [SV113: $i] :
( ( ( ~ ! [SY3767: $i] :
( ~ ( disjoint @ ( fiber @ SV113 @ SY3767 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ SY3767 @ ( sK14_B @ SV113 ) ) ) )
= $false )
| ( ( well_founded_relation @ SV113 )
= $true )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1170]) ).
thf(1220,plain,
! [SV113: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK14_B @ SV113 )
!= empty_set ) )
| ~ ( subset @ ( sK14_B @ SV113 ) @ ( relation_field @ SV113 ) ) ) )
= $false )
| ( ( well_founded_relation @ SV113 )
= $true )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1170]) ).
thf(1221,plain,
! [SV210: $i,SV114: $i] :
( ( ( ~ ( ~ ( disjoint @ ( fiber @ SV114 @ ( sK13_C @ SV210 @ SV114 ) ) @ SV210 )
| ~ ( in @ ( sK13_C @ SV210 @ SV114 ) @ SV210 ) )
| ( SV210 = empty_set )
| ~ ( subset @ SV210 @ ( relation_field @ SV114 ) ) )
= $true )
| ( ( well_founded_relation @ SV114 )
= $false )
| ( ( relation @ SV114 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1171]) ).
thf(1222,plain,
! [SV95: $i,SV48: $i] :
( ( ( SV48 = empty_set )
= $true )
| ( ( ~ ( subset @ SV48 @ SV95 ) )
= $true )
| ( ( ordinal @ ( sK17_C @ SV95 @ SV48 ) )
= $true )
| ( ( ordinal @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1172]) ).
thf(1223,plain,
! [SV95: $i,SV48: $i] :
( ( ( ~ ! [SY3762: $i] :
( ~ ( ordinal @ SY3762 )
| ~ ( in @ SY3762 @ SV48 )
| ( ordinal_subset @ ( sK17_C @ SV95 @ SV48 ) @ SY3762 ) )
| ~ ( in @ ( sK17_C @ SV95 @ SV48 ) @ SV48 ) )
= $false )
| ( ( ( SV48 = empty_set )
| ~ ( subset @ SV48 @ SV95 ) )
= $true )
| ( ( ordinal @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1173]) ).
thf(1224,plain,
! [SV115: $i] :
( ( ( subset @ ( sK15_B @ SV115 ) @ SV115 )
= $false )
| ( ( epsilon_transitive @ SV115 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1175]) ).
thf(1225,plain,
! [SV116: $i,SV186: $i] :
( ( ( in @ SV186 @ SV116 )
= $false )
| ( ( subset @ SV186 @ SV116 )
= $true )
| ( ( epsilon_transitive @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1176]) ).
thf(1226,plain,
! [SV144: $i,SV175: $i,SV49: $i] :
( ( ( in @ SV49 @ SV175 )
= $false )
| ( ( ~ ( in @ SV144 @ SV175 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV49 @ SV144 ) @ SV175 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1177]) ).
thf(1227,plain,
! [SV211: $i,SV200: $i,SV49: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV49 @ SV200 ) @ SV211 )
| ( in @ SV49 @ SV211 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1178]) ).
thf(1228,plain,
! [SV212: $i,SV201: $i,SV49: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV49 @ SV201 ) @ SV212 )
| ( in @ SV201 @ SV212 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1179]) ).
thf(1229,plain,
! [SV117: $i,SV145: $i] :
( ( ( in @ ( sK10_C @ SV145 @ SV117 ) @ SV117 )
= $true )
| ( ( subset @ SV117 @ SV145 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1180]) ).
thf(1230,plain,
! [SV117: $i,SV145: $i] :
( ( ( ~ ( in @ ( sK10_C @ SV145 @ SV117 ) @ SV145 ) )
= $true )
| ( ( subset @ SV117 @ SV145 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1181]) ).
thf(1231,plain,
! [SV146: $i,SV118: $i,SV202: $i] :
( ( ( ~ ( in @ SV202 @ SV118 ) )
= $true )
| ( ( in @ SV202 @ SV146 )
= $true )
| ( ( subset @ SV118 @ SV146 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1182]) ).
thf(1232,plain,
! [SV119: $i,SV147: $i] :
( ( ( subset @ SV147 @ SV119 )
= $false )
| ( ( subset @ SV119 @ SV147 )
= $false )
| ( ( SV119 = SV147 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1183]) ).
thf(1233,plain,
! [SV203: $i,SV187: $i] :
( ( ( ( SV187 != SV203 ) )
= $true )
| ( ( subset @ SV187 @ SV203 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1184]) ).
thf(1234,plain,
! [SV204: $i,SV188: $i] :
( ( ( ( SV188 != SV204 ) )
= $true )
| ( ( subset @ SV204 @ SV188 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1185]) ).
thf(1235,plain,
! [SV50: $i,SV205: $i] :
( ( ( ~ ( in @ SV205 @ ( sK19_B @ SV50 ) ) )
= $true )
| ( ( in @ ( powerset @ SV205 ) @ ( sK19_B @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1187]) ).
thf(1236,plain,
! [SV50: $i] :
( ( ~ ! [SY3719: $i,SY3720: $i] :
( ~ ( in @ SY3719 @ ( sK19_B @ SV50 ) )
| ~ ( subset @ SY3720 @ SY3719 )
| ( in @ SY3720 @ ( sK19_B @ SV50 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1188]) ).
thf(1237,plain,
! [SV50: $i] :
( ( ~ ( in @ SV50 @ ( sK19_B @ SV50 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1188]) ).
thf(1238,plain,
! [SV128: $i,SV159: $i] :
( ( ( ~ ( in @ ( sK16_C @ SV159 @ SV128 ) @ SV159 )
| ~ ( subset @ ( sK16_C @ SV159 @ SV128 ) @ SV128 ) )
= $true )
| ( ( SV159
= ( powerset @ SV128 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1191]) ).
thf(1239,plain,
! [SV128: $i,SV159: $i] :
( ( ( ( in @ ( sK16_C @ SV159 @ SV128 ) @ SV159 )
| ( subset @ ( sK16_C @ SV159 @ SV128 ) @ SV128 ) )
= $true )
| ( ( SV159
= ( powerset @ SV128 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1192]) ).
thf(1240,plain,
! [SV129: $i,SV160: $i] :
( ( ( ~ ! [SY3799: $i] :
( ~ ( in @ SY3799 @ SV160 )
| ( subset @ SY3799 @ SV129 ) ) )
= $false )
| ( ( SV160
= ( powerset @ SV129 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1193]) ).
thf(1241,plain,
! [SV160: $i,SV129: $i] :
( ( ( ~ ! [SY3800: $i] :
( ~ ( subset @ SY3800 @ SV129 )
| ( in @ SY3800 @ SV160 ) ) )
= $false )
| ( ( SV160
= ( powerset @ SV129 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1193]) ).
thf(1242,plain,
! [SV189: $i,SV55: $i] :
( ( ( ~ ! [SY3811: $i] :
( ~ ( disjoint @ ( fiber @ SV55 @ SY3811 ) @ ( sK9_C @ SV189 @ SV55 ) )
| ~ ( in @ SY3811 @ ( sK9_C @ SV189 @ SV55 ) ) )
| ~ ~ ( ~ ( ( ( sK9_C @ SV189 @ SV55 )
!= empty_set ) )
| ~ ( subset @ ( sK9_C @ SV189 @ SV55 ) @ SV189 ) ) )
= $false )
| ( ( is_well_founded_in @ SV55 @ SV189 )
= $true )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1199]) ).
thf(1243,plain,
! [SV190: $i,SV55: $i] :
( ( ( is_well_founded_in @ SV55 @ SV190 )
= $false )
| ( ( ! [SY3812: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV55 @ ( sK8_D @ SY3812 @ SV190 @ SV55 ) ) @ SY3812 )
| ~ ( in @ ( sK8_D @ SY3812 @ SV190 @ SV55 ) @ SY3812 ) )
| ( SY3812 = empty_set )
| ~ ( subset @ SY3812 @ SV190 ) ) )
= $true )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1200]) ).
thf(1244,plain,
! [SV56: $i,SV208: $i] :
( ( ( ~ ( ~ ! [SY3819: $i] :
( ~ ( subset @ SY3819 @ SV208 )
| ( in @ SY3819 @ ( sK6_SY3633 @ SV208 @ SV56 ) ) )
| ~ ( in @ ( sK6_SY3633 @ SV208 @ SV56 ) @ ( sK5_B @ SV56 ) ) ) )
= $true )
| ( ( ~ ( in @ SV208 @ ( sK5_B @ SV56 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1202]) ).
thf(1245,plain,
! [SV56: $i] :
( ( ~ ! [SY3740: $i,SY3741: $i] :
( ~ ( in @ SY3740 @ ( sK5_B @ SV56 ) )
| ~ ( subset @ SY3741 @ SY3740 )
| ( in @ SY3741 @ ( sK5_B @ SV56 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1203]) ).
thf(1246,plain,
! [SV56: $i] :
( ( ~ ( in @ SV56 @ ( sK5_B @ SV56 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1203]) ).
thf(1247,plain,
! [SV191: $i] :
( ( ( SV191 = empty_set )
= $false )
| ( ( ! [SY3813: $i] : ( subset @ SV191 @ ( singleton @ SY3813 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1205]) ).
thf(1248,plain,
! [SV209: $i,SV192: $i] :
( ( ( ( SV192
!= ( singleton @ SV209 ) ) )
= $true )
| ( ( subset @ SV192 @ ( singleton @ SV209 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1206]) ).
thf(1249,plain,
! [SV57: $i,SV193: $i] :
( ( ( relation @ SV193 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SV193 @ SV57 ) @ ( sK12_SY3639 @ SV193 @ SV57 ) ) @ SV57 )
| ~ ~ ( in @ ( ordered_pair @ ( sK11_C @ SV193 @ SV57 ) @ ( sK12_SY3639 @ SV193 @ SV57 ) ) @ SV193 ) )
| ( subset @ SV57 @ SV193 ) )
= $true )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1207]) ).
thf(1250,plain,
! [SV57: $i,SV194: $i] :
( ( ( relation @ SV194 )
= $false )
| ( ( ~ ( subset @ SV57 @ SV194 )
| ! [SY3815: $i,SY3816: $i] :
( ~ ( in @ ( ordered_pair @ SY3815 @ SY3816 ) @ SV57 )
| ( in @ ( ordered_pair @ SY3815 @ SY3816 ) @ SV194 ) ) )
= $true )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1208]) ).
thf(1251,plain,
! [SV133: $i,SV169: $i] :
( ( ( ordinal @ SV169 )
= $false )
| ( ( ordinal @ SV133 )
= $false )
| ( ( ~ ( ordinal_subset @ SV133 @ SV169 )
| ( subset @ SV133 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1209]) ).
thf(1252,plain,
! [SV134: $i,SV170: $i] :
( ( ( ordinal @ SV170 )
= $false )
| ( ( ordinal @ SV134 )
= $false )
| ( ( ~ ( subset @ SV134 @ SV170 )
| ( ordinal_subset @ SV134 @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1210]) ).
thf(1253,plain,
! [SV213: $i,SV180: $i] :
( ( ( subset @ SV180 @ ( singleton @ SV213 ) )
= $true )
| ( ( SV180 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1211]) ).
thf(1254,plain,
! [SV195: $i,SV181: $i] :
( ( ( SV181
= ( singleton @ SV195 ) )
= $false )
| ( ( subset @ SV181 @ ( singleton @ SV195 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1212]) ).
thf(1255,plain,
! [SV182: $i,SV45: $i] :
( ( ( ~ ( subset @ SV45 @ SV182 ) )
= $true )
| ( ( subset @ ( relation_dom @ SV45 ) @ ( relation_dom @ SV182 ) )
= $true )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1213]) ).
thf(1256,plain,
! [SV183: $i,SV45: $i] :
( ( ( ~ ( subset @ SV45 @ SV183 ) )
= $true )
| ( ( subset @ ( relation_rng @ SV45 ) @ ( relation_rng @ SV183 ) )
= $true )
| ( ( relation @ SV183 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1214]) ).
thf(1257,plain,
! [SV94: $i,SV46: $i,SV196: $i] :
( ( ( element @ SV196 @ ( powerset @ SV46 ) )
= $false )
| ( ( ~ ( disjoint @ SV94 @ SV196 )
| ( subset @ SV94 @ ( subset_complement @ SV46 @ SV196 ) ) )
= $true )
| ( ( element @ SV94 @ ( powerset @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1215]) ).
thf(1258,plain,
! [SV94: $i,SV46: $i,SV197: $i] :
( ( ( element @ SV197 @ ( powerset @ SV46 ) )
= $false )
| ( ( ~ ( subset @ SV94 @ ( subset_complement @ SV46 @ SV197 ) )
| ( disjoint @ SV94 @ SV197 ) )
= $true )
| ( ( element @ SV94 @ ( powerset @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1216]) ).
thf(1259,plain,
! [SV198: $i,SV184: $i] :
( ( ( proper_subset @ SV184 @ SV198 )
= $false )
| ( ( ( SV184 != SV198 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1217]) ).
thf(1260,plain,
! [SV199: $i,SV185: $i] :
( ( ( proper_subset @ SV185 @ SV199 )
= $false )
| ( ( subset @ SV185 @ SV199 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1218]) ).
thf(1261,plain,
! [SV113: $i] :
( ( ( ! [SY3767: $i] :
( ~ ( disjoint @ ( fiber @ SV113 @ SY3767 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ SY3767 @ ( sK14_B @ SV113 ) ) ) )
= $true )
| ( ( well_founded_relation @ SV113 )
= $true )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1219]) ).
thf(1262,plain,
! [SV113: $i] :
( ( ( ~ ( ~ ( ( ( sK14_B @ SV113 )
!= empty_set ) )
| ~ ( subset @ ( sK14_B @ SV113 ) @ ( relation_field @ SV113 ) ) ) )
= $true )
| ( ( well_founded_relation @ SV113 )
= $true )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1220]) ).
thf(1263,plain,
! [SV210: $i,SV114: $i] :
( ( ( ~ ( ~ ( disjoint @ ( fiber @ SV114 @ ( sK13_C @ SV210 @ SV114 ) ) @ SV210 )
| ~ ( in @ ( sK13_C @ SV210 @ SV114 ) @ SV210 ) ) )
= $true )
| ( ( ( SV210 = empty_set )
| ~ ( subset @ SV210 @ ( relation_field @ SV114 ) ) )
= $true )
| ( ( well_founded_relation @ SV114 )
= $false )
| ( ( relation @ SV114 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1221]) ).
thf(1264,plain,
! [SV95: $i,SV48: $i] :
( ( ( subset @ SV48 @ SV95 )
= $false )
| ( ( SV48 = empty_set )
= $true )
| ( ( ordinal @ ( sK17_C @ SV95 @ SV48 ) )
= $true )
| ( ( ordinal @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1222]) ).
thf(1265,plain,
! [SV95: $i,SV48: $i] :
( ( ( ~ ! [SY3762: $i] :
( ~ ( ordinal @ SY3762 )
| ~ ( in @ SY3762 @ SV48 )
| ( ordinal_subset @ ( sK17_C @ SV95 @ SV48 ) @ SY3762 ) ) )
= $false )
| ( ( ( SV48 = empty_set )
| ~ ( subset @ SV48 @ SV95 ) )
= $true )
| ( ( ordinal @ SV95 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1223]) ).
thf(1266,plain,
! [SV48: $i,SV95: $i] :
( ( ( ~ ( in @ ( sK17_C @ SV95 @ SV48 ) @ SV48 ) )
= $false )
| ( ( ( SV48 = empty_set )
| ~ ( subset @ SV48 @ SV95 ) )
= $true )
| ( ( ordinal @ SV95 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1223]) ).
thf(1267,plain,
! [SV49: $i,SV175: $i,SV144: $i] :
( ( ( in @ SV144 @ SV175 )
= $false )
| ( ( in @ SV49 @ SV175 )
= $false )
| ( ( subset @ ( unordered_pair @ SV49 @ SV144 ) @ SV175 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1226]) ).
thf(1268,plain,
! [SV211: $i,SV200: $i,SV49: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV49 @ SV200 ) @ SV211 ) )
= $true )
| ( ( in @ SV49 @ SV211 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1227]) ).
thf(1269,plain,
! [SV212: $i,SV201: $i,SV49: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV49 @ SV201 ) @ SV212 ) )
= $true )
| ( ( in @ SV201 @ SV212 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1228]) ).
thf(1270,plain,
! [SV117: $i,SV145: $i] :
( ( ( in @ ( sK10_C @ SV145 @ SV117 ) @ SV145 )
= $false )
| ( ( subset @ SV117 @ SV145 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1230]) ).
thf(1271,plain,
! [SV146: $i,SV118: $i,SV202: $i] :
( ( ( in @ SV202 @ SV118 )
= $false )
| ( ( in @ SV202 @ SV146 )
= $true )
| ( ( subset @ SV118 @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1231]) ).
thf(1272,plain,
! [SV203: $i,SV187: $i] :
( ( ( SV187 = SV203 )
= $false )
| ( ( subset @ SV187 @ SV203 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1233]) ).
thf(1273,plain,
! [SV204: $i,SV188: $i] :
( ( ( SV188 = SV204 )
= $false )
| ( ( subset @ SV204 @ SV188 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1234]) ).
thf(1274,plain,
! [SV50: $i,SV205: $i] :
( ( ( in @ SV205 @ ( sK19_B @ SV50 ) )
= $false )
| ( ( in @ ( powerset @ SV205 ) @ ( sK19_B @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1235]) ).
thf(1275,plain,
! [SV50: $i] :
( ( ! [SY3719: $i,SY3720: $i] :
( ~ ( in @ SY3719 @ ( sK19_B @ SV50 ) )
| ~ ( subset @ SY3720 @ SY3719 )
| ( in @ SY3720 @ ( sK19_B @ SV50 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1236]) ).
thf(1276,plain,
! [SV50: $i] :
( ( in @ SV50 @ ( sK19_B @ SV50 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1237]) ).
thf(1277,plain,
! [SV128: $i,SV159: $i] :
( ( ( ~ ( in @ ( sK16_C @ SV159 @ SV128 ) @ SV159 ) )
= $true )
| ( ( ~ ( subset @ ( sK16_C @ SV159 @ SV128 ) @ SV128 ) )
= $true )
| ( ( SV159
= ( powerset @ SV128 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1238]) ).
thf(1278,plain,
! [SV128: $i,SV159: $i] :
( ( ( in @ ( sK16_C @ SV159 @ SV128 ) @ SV159 )
= $true )
| ( ( subset @ ( sK16_C @ SV159 @ SV128 ) @ SV128 )
= $true )
| ( ( SV159
= ( powerset @ SV128 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1239]) ).
thf(1279,plain,
! [SV129: $i,SV160: $i] :
( ( ( ! [SY3799: $i] :
( ~ ( in @ SY3799 @ SV160 )
| ( subset @ SY3799 @ SV129 ) ) )
= $true )
| ( ( SV160
= ( powerset @ SV129 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1240]) ).
thf(1280,plain,
! [SV160: $i,SV129: $i] :
( ( ( ! [SY3800: $i] :
( ~ ( subset @ SY3800 @ SV129 )
| ( in @ SY3800 @ SV160 ) ) )
= $true )
| ( ( SV160
= ( powerset @ SV129 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1241]) ).
thf(1281,plain,
! [SV189: $i,SV55: $i] :
( ( ( ~ ! [SY3811: $i] :
( ~ ( disjoint @ ( fiber @ SV55 @ SY3811 ) @ ( sK9_C @ SV189 @ SV55 ) )
| ~ ( in @ SY3811 @ ( sK9_C @ SV189 @ SV55 ) ) ) )
= $false )
| ( ( is_well_founded_in @ SV55 @ SV189 )
= $true )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1242]) ).
thf(1282,plain,
! [SV55: $i,SV189: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK9_C @ SV189 @ SV55 )
!= empty_set ) )
| ~ ( subset @ ( sK9_C @ SV189 @ SV55 ) @ SV189 ) ) )
= $false )
| ( ( is_well_founded_in @ SV55 @ SV189 )
= $true )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1242]) ).
thf(1283,plain,
! [SV190: $i,SV214: $i,SV55: $i] :
( ( ( ~ ( ~ ( disjoint @ ( fiber @ SV55 @ ( sK8_D @ SV214 @ SV190 @ SV55 ) ) @ SV214 )
| ~ ( in @ ( sK8_D @ SV214 @ SV190 @ SV55 ) @ SV214 ) )
| ( SV214 = empty_set )
| ~ ( subset @ SV214 @ SV190 ) )
= $true )
| ( ( is_well_founded_in @ SV55 @ SV190 )
= $false )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1243]) ).
thf(1284,plain,
! [SV56: $i,SV208: $i] :
( ( ( ~ ! [SY3819: $i] :
( ~ ( subset @ SY3819 @ SV208 )
| ( in @ SY3819 @ ( sK6_SY3633 @ SV208 @ SV56 ) ) )
| ~ ( in @ ( sK6_SY3633 @ SV208 @ SV56 ) @ ( sK5_B @ SV56 ) ) )
= $false )
| ( ( ~ ( in @ SV208 @ ( sK5_B @ SV56 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1244]) ).
thf(1285,plain,
! [SV56: $i] :
( ( ! [SY3740: $i,SY3741: $i] :
( ~ ( in @ SY3740 @ ( sK5_B @ SV56 ) )
| ~ ( subset @ SY3741 @ SY3740 )
| ( in @ SY3741 @ ( sK5_B @ SV56 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1245]) ).
thf(1286,plain,
! [SV56: $i] :
( ( in @ SV56 @ ( sK5_B @ SV56 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1246]) ).
thf(1287,plain,
! [SV215: $i,SV191: $i] :
( ( ( subset @ SV191 @ ( singleton @ SV215 ) )
= $true )
| ( ( SV191 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1247]) ).
thf(1288,plain,
! [SV209: $i,SV192: $i] :
( ( ( SV192
= ( singleton @ SV209 ) )
= $false )
| ( ( subset @ SV192 @ ( singleton @ SV209 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1248]) ).
thf(1289,plain,
! [SV57: $i,SV193: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SV193 @ SV57 ) @ ( sK12_SY3639 @ SV193 @ SV57 ) ) @ SV57 )
| ~ ~ ( in @ ( ordered_pair @ ( sK11_C @ SV193 @ SV57 ) @ ( sK12_SY3639 @ SV193 @ SV57 ) ) @ SV193 ) ) )
= $true )
| ( ( subset @ SV57 @ SV193 )
= $true )
| ( ( relation @ SV193 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1249]) ).
thf(1290,plain,
! [SV194: $i,SV57: $i] :
( ( ( ~ ( subset @ SV57 @ SV194 ) )
= $true )
| ( ( ! [SY3815: $i,SY3816: $i] :
( ~ ( in @ ( ordered_pair @ SY3815 @ SY3816 ) @ SV57 )
| ( in @ ( ordered_pair @ SY3815 @ SY3816 ) @ SV194 ) ) )
= $true )
| ( ( relation @ SV194 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1250]) ).
thf(1291,plain,
! [SV169: $i,SV133: $i] :
( ( ( ~ ( ordinal_subset @ SV133 @ SV169 ) )
= $true )
| ( ( subset @ SV133 @ SV169 )
= $true )
| ( ( ordinal @ SV133 )
= $false )
| ( ( ordinal @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1251]) ).
thf(1292,plain,
! [SV170: $i,SV134: $i] :
( ( ( ~ ( subset @ SV134 @ SV170 ) )
= $true )
| ( ( ordinal_subset @ SV134 @ SV170 )
= $true )
| ( ( ordinal @ SV134 )
= $false )
| ( ( ordinal @ SV170 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1252]) ).
thf(1293,plain,
! [SV182: $i,SV45: $i] :
( ( ( subset @ SV45 @ SV182 )
= $false )
| ( ( subset @ ( relation_dom @ SV45 ) @ ( relation_dom @ SV182 ) )
= $true )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1255]) ).
thf(1294,plain,
! [SV183: $i,SV45: $i] :
( ( ( subset @ SV45 @ SV183 )
= $false )
| ( ( subset @ ( relation_rng @ SV45 ) @ ( relation_rng @ SV183 ) )
= $true )
| ( ( relation @ SV183 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1256]) ).
thf(1295,plain,
! [SV46: $i,SV196: $i,SV94: $i] :
( ( ( ~ ( disjoint @ SV94 @ SV196 ) )
= $true )
| ( ( subset @ SV94 @ ( subset_complement @ SV46 @ SV196 ) )
= $true )
| ( ( element @ SV196 @ ( powerset @ SV46 ) )
= $false )
| ( ( element @ SV94 @ ( powerset @ SV46 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1257]) ).
thf(1296,plain,
! [SV197: $i,SV46: $i,SV94: $i] :
( ( ( ~ ( subset @ SV94 @ ( subset_complement @ SV46 @ SV197 ) ) )
= $true )
| ( ( disjoint @ SV94 @ SV197 )
= $true )
| ( ( element @ SV197 @ ( powerset @ SV46 ) )
= $false )
| ( ( element @ SV94 @ ( powerset @ SV46 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1258]) ).
thf(1297,plain,
! [SV198: $i,SV184: $i] :
( ( ( SV184 = SV198 )
= $false )
| ( ( proper_subset @ SV184 @ SV198 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1259]) ).
thf(1298,plain,
! [SV216: $i,SV113: $i] :
( ( ( ~ ( disjoint @ ( fiber @ SV113 @ SV216 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ SV216 @ ( sK14_B @ SV113 ) ) )
= $true )
| ( ( well_founded_relation @ SV113 )
= $true )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(1299,plain,
! [SV113: $i] :
( ( ( ~ ( ( ( sK14_B @ SV113 )
!= empty_set ) )
| ~ ( subset @ ( sK14_B @ SV113 ) @ ( relation_field @ SV113 ) ) )
= $false )
| ( ( well_founded_relation @ SV113 )
= $true )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1262]) ).
thf(1300,plain,
! [SV210: $i,SV114: $i] :
( ( ( ~ ( disjoint @ ( fiber @ SV114 @ ( sK13_C @ SV210 @ SV114 ) ) @ SV210 )
| ~ ( in @ ( sK13_C @ SV210 @ SV114 ) @ SV210 ) )
= $false )
| ( ( ( SV210 = empty_set )
| ~ ( subset @ SV210 @ ( relation_field @ SV114 ) ) )
= $true )
| ( ( well_founded_relation @ SV114 )
= $false )
| ( ( relation @ SV114 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1263]) ).
thf(1301,plain,
! [SV95: $i,SV48: $i] :
( ( ( ! [SY3762: $i] :
( ~ ( ordinal @ SY3762 )
| ~ ( in @ SY3762 @ SV48 )
| ( ordinal_subset @ ( sK17_C @ SV95 @ SV48 ) @ SY3762 ) ) )
= $true )
| ( ( ( SV48 = empty_set )
| ~ ( subset @ SV48 @ SV95 ) )
= $true )
| ( ( ordinal @ SV95 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1265]) ).
thf(1302,plain,
! [SV48: $i,SV95: $i] :
( ( ( in @ ( sK17_C @ SV95 @ SV48 ) @ SV48 )
= $true )
| ( ( ( SV48 = empty_set )
| ~ ( subset @ SV48 @ SV95 ) )
= $true )
| ( ( ordinal @ SV95 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1266]) ).
thf(1303,plain,
! [SV211: $i,SV200: $i,SV49: $i] :
( ( ( subset @ ( unordered_pair @ SV49 @ SV200 ) @ SV211 )
= $false )
| ( ( in @ SV49 @ SV211 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1268]) ).
thf(1304,plain,
! [SV212: $i,SV201: $i,SV49: $i] :
( ( ( subset @ ( unordered_pair @ SV49 @ SV201 ) @ SV212 )
= $false )
| ( ( in @ SV201 @ SV212 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1269]) ).
thf(1305,plain,
! [SV50: $i,SV217: $i] :
( ( ! [SY3820: $i] :
( ~ ( in @ SV217 @ ( sK19_B @ SV50 ) )
| ~ ( subset @ SY3820 @ SV217 )
| ( in @ SY3820 @ ( sK19_B @ SV50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1275]) ).
thf(1306,plain,
! [SV128: $i,SV159: $i] :
( ( ( in @ ( sK16_C @ SV159 @ SV128 ) @ SV159 )
= $false )
| ( ( ~ ( subset @ ( sK16_C @ SV159 @ SV128 ) @ SV128 ) )
= $true )
| ( ( SV159
= ( powerset @ SV128 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1277]) ).
thf(1307,plain,
! [SV129: $i,SV160: $i,SV218: $i] :
( ( ( ~ ( in @ SV218 @ SV160 )
| ( subset @ SV218 @ SV129 ) )
= $true )
| ( ( SV160
= ( powerset @ SV129 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1279]) ).
thf(1308,plain,
! [SV160: $i,SV129: $i,SV219: $i] :
( ( ( ~ ( subset @ SV219 @ SV129 )
| ( in @ SV219 @ SV160 ) )
= $true )
| ( ( SV160
= ( powerset @ SV129 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1280]) ).
thf(1309,plain,
! [SV189: $i,SV55: $i] :
( ( ( ! [SY3811: $i] :
( ~ ( disjoint @ ( fiber @ SV55 @ SY3811 ) @ ( sK9_C @ SV189 @ SV55 ) )
| ~ ( in @ SY3811 @ ( sK9_C @ SV189 @ SV55 ) ) ) )
= $true )
| ( ( is_well_founded_in @ SV55 @ SV189 )
= $true )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1281]) ).
thf(1310,plain,
! [SV55: $i,SV189: $i] :
( ( ( ~ ( ~ ( ( ( sK9_C @ SV189 @ SV55 )
!= empty_set ) )
| ~ ( subset @ ( sK9_C @ SV189 @ SV55 ) @ SV189 ) ) )
= $true )
| ( ( is_well_founded_in @ SV55 @ SV189 )
= $true )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1282]) ).
thf(1311,plain,
! [SV190: $i,SV214: $i,SV55: $i] :
( ( ( ~ ( ~ ( disjoint @ ( fiber @ SV55 @ ( sK8_D @ SV214 @ SV190 @ SV55 ) ) @ SV214 )
| ~ ( in @ ( sK8_D @ SV214 @ SV190 @ SV55 ) @ SV214 ) ) )
= $true )
| ( ( ( SV214 = empty_set )
| ~ ( subset @ SV214 @ SV190 ) )
= $true )
| ( ( is_well_founded_in @ SV55 @ SV190 )
= $false )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1283]) ).
thf(1312,plain,
! [SV56: $i,SV208: $i] :
( ( ( ~ ! [SY3819: $i] :
( ~ ( subset @ SY3819 @ SV208 )
| ( in @ SY3819 @ ( sK6_SY3633 @ SV208 @ SV56 ) ) ) )
= $false )
| ( ( ~ ( in @ SV208 @ ( sK5_B @ SV56 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1284]) ).
thf(1313,plain,
! [SV56: $i,SV208: $i] :
( ( ( ~ ( in @ ( sK6_SY3633 @ SV208 @ SV56 ) @ ( sK5_B @ SV56 ) ) )
= $false )
| ( ( ~ ( in @ SV208 @ ( sK5_B @ SV56 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1284]) ).
thf(1314,plain,
! [SV56: $i,SV220: $i] :
( ( ! [SY3821: $i] :
( ~ ( in @ SV220 @ ( sK5_B @ SV56 ) )
| ~ ( subset @ SY3821 @ SV220 )
| ( in @ SY3821 @ ( sK5_B @ SV56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1285]) ).
thf(1315,plain,
! [SV57: $i,SV193: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SV193 @ SV57 ) @ ( sK12_SY3639 @ SV193 @ SV57 ) ) @ SV57 )
| ~ ~ ( in @ ( ordered_pair @ ( sK11_C @ SV193 @ SV57 ) @ ( sK12_SY3639 @ SV193 @ SV57 ) ) @ SV193 ) )
= $false )
| ( ( subset @ SV57 @ SV193 )
= $true )
| ( ( relation @ SV193 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1289]) ).
thf(1316,plain,
! [SV194: $i,SV57: $i] :
( ( ( subset @ SV57 @ SV194 )
= $false )
| ( ( ! [SY3815: $i,SY3816: $i] :
( ~ ( in @ ( ordered_pair @ SY3815 @ SY3816 ) @ SV57 )
| ( in @ ( ordered_pair @ SY3815 @ SY3816 ) @ SV194 ) ) )
= $true )
| ( ( relation @ SV194 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1290]) ).
thf(1317,plain,
! [SV169: $i,SV133: $i] :
( ( ( ordinal_subset @ SV133 @ SV169 )
= $false )
| ( ( subset @ SV133 @ SV169 )
= $true )
| ( ( ordinal @ SV133 )
= $false )
| ( ( ordinal @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1291]) ).
thf(1318,plain,
! [SV170: $i,SV134: $i] :
( ( ( subset @ SV134 @ SV170 )
= $false )
| ( ( ordinal_subset @ SV134 @ SV170 )
= $true )
| ( ( ordinal @ SV134 )
= $false )
| ( ( ordinal @ SV170 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1292]) ).
thf(1319,plain,
! [SV46: $i,SV196: $i,SV94: $i] :
( ( ( disjoint @ SV94 @ SV196 )
= $false )
| ( ( subset @ SV94 @ ( subset_complement @ SV46 @ SV196 ) )
= $true )
| ( ( element @ SV196 @ ( powerset @ SV46 ) )
= $false )
| ( ( element @ SV94 @ ( powerset @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1295]) ).
thf(1320,plain,
! [SV197: $i,SV46: $i,SV94: $i] :
( ( ( subset @ SV94 @ ( subset_complement @ SV46 @ SV197 ) )
= $false )
| ( ( disjoint @ SV94 @ SV197 )
= $true )
| ( ( element @ SV197 @ ( powerset @ SV46 ) )
= $false )
| ( ( element @ SV94 @ ( powerset @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1296]) ).
thf(1321,plain,
! [SV216: $i,SV113: $i] :
( ( ( ~ ( disjoint @ ( fiber @ SV113 @ SV216 ) @ ( sK14_B @ SV113 ) ) )
= $true )
| ( ( ~ ( in @ SV216 @ ( sK14_B @ SV113 ) ) )
= $true )
| ( ( well_founded_relation @ SV113 )
= $true )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1298]) ).
thf(1322,plain,
! [SV113: $i] :
( ( ( ~ ( ( ( sK14_B @ SV113 )
!= empty_set ) ) )
= $false )
| ( ( well_founded_relation @ SV113 )
= $true )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1299]) ).
thf(1323,plain,
! [SV113: $i] :
( ( ( ~ ( subset @ ( sK14_B @ SV113 ) @ ( relation_field @ SV113 ) ) )
= $false )
| ( ( well_founded_relation @ SV113 )
= $true )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1299]) ).
thf(1324,plain,
! [SV210: $i,SV114: $i] :
( ( ( ~ ( disjoint @ ( fiber @ SV114 @ ( sK13_C @ SV210 @ SV114 ) ) @ SV210 ) )
= $false )
| ( ( ( SV210 = empty_set )
| ~ ( subset @ SV210 @ ( relation_field @ SV114 ) ) )
= $true )
| ( ( well_founded_relation @ SV114 )
= $false )
| ( ( relation @ SV114 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1300]) ).
thf(1325,plain,
! [SV114: $i,SV210: $i] :
( ( ( ~ ( in @ ( sK13_C @ SV210 @ SV114 ) @ SV210 ) )
= $false )
| ( ( ( SV210 = empty_set )
| ~ ( subset @ SV210 @ ( relation_field @ SV114 ) ) )
= $true )
| ( ( well_founded_relation @ SV114 )
= $false )
| ( ( relation @ SV114 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1300]) ).
thf(1326,plain,
! [SV95: $i,SV48: $i,SV221: $i] :
( ( ( ~ ( ordinal @ SV221 )
| ~ ( in @ SV221 @ SV48 )
| ( ordinal_subset @ ( sK17_C @ SV95 @ SV48 ) @ SV221 ) )
= $true )
| ( ( ( SV48 = empty_set )
| ~ ( subset @ SV48 @ SV95 ) )
= $true )
| ( ( ordinal @ SV95 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1301]) ).
thf(1327,plain,
! [SV95: $i,SV48: $i] :
( ( ( SV48 = empty_set )
= $true )
| ( ( ~ ( subset @ SV48 @ SV95 ) )
= $true )
| ( ( in @ ( sK17_C @ SV95 @ SV48 ) @ SV48 )
= $true )
| ( ( ordinal @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1302]) ).
thf(1328,plain,
! [SV222: $i,SV50: $i,SV217: $i] :
( ( ~ ( in @ SV217 @ ( sK19_B @ SV50 ) )
| ~ ( subset @ SV222 @ SV217 )
| ( in @ SV222 @ ( sK19_B @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1305]) ).
thf(1329,plain,
! [SV128: $i,SV159: $i] :
( ( ( subset @ ( sK16_C @ SV159 @ SV128 ) @ SV128 )
= $false )
| ( ( in @ ( sK16_C @ SV159 @ SV128 ) @ SV159 )
= $false )
| ( ( SV159
= ( powerset @ SV128 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1306]) ).
thf(1330,plain,
! [SV129: $i,SV160: $i,SV218: $i] :
( ( ( ~ ( in @ SV218 @ SV160 ) )
= $true )
| ( ( subset @ SV218 @ SV129 )
= $true )
| ( ( SV160
= ( powerset @ SV129 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1307]) ).
thf(1331,plain,
! [SV160: $i,SV129: $i,SV219: $i] :
( ( ( ~ ( subset @ SV219 @ SV129 ) )
= $true )
| ( ( in @ SV219 @ SV160 )
= $true )
| ( ( SV160
= ( powerset @ SV129 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1308]) ).
thf(1332,plain,
! [SV189: $i,SV223: $i,SV55: $i] :
( ( ( ~ ( disjoint @ ( fiber @ SV55 @ SV223 ) @ ( sK9_C @ SV189 @ SV55 ) )
| ~ ( in @ SV223 @ ( sK9_C @ SV189 @ SV55 ) ) )
= $true )
| ( ( is_well_founded_in @ SV55 @ SV189 )
= $true )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1309]) ).
thf(1333,plain,
! [SV55: $i,SV189: $i] :
( ( ( ~ ( ( ( sK9_C @ SV189 @ SV55 )
!= empty_set ) )
| ~ ( subset @ ( sK9_C @ SV189 @ SV55 ) @ SV189 ) )
= $false )
| ( ( is_well_founded_in @ SV55 @ SV189 )
= $true )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1310]) ).
thf(1334,plain,
! [SV190: $i,SV214: $i,SV55: $i] :
( ( ( ~ ( disjoint @ ( fiber @ SV55 @ ( sK8_D @ SV214 @ SV190 @ SV55 ) ) @ SV214 )
| ~ ( in @ ( sK8_D @ SV214 @ SV190 @ SV55 ) @ SV214 ) )
= $false )
| ( ( ( SV214 = empty_set )
| ~ ( subset @ SV214 @ SV190 ) )
= $true )
| ( ( is_well_founded_in @ SV55 @ SV190 )
= $false )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1311]) ).
thf(1335,plain,
! [SV56: $i,SV208: $i] :
( ( ( ! [SY3819: $i] :
( ~ ( subset @ SY3819 @ SV208 )
| ( in @ SY3819 @ ( sK6_SY3633 @ SV208 @ SV56 ) ) ) )
= $true )
| ( ( ~ ( in @ SV208 @ ( sK5_B @ SV56 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1312]) ).
thf(1336,plain,
! [SV56: $i,SV208: $i] :
( ( ( in @ ( sK6_SY3633 @ SV208 @ SV56 ) @ ( sK5_B @ SV56 ) )
= $true )
| ( ( ~ ( in @ SV208 @ ( sK5_B @ SV56 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1313]) ).
thf(1337,plain,
! [SV224: $i,SV56: $i,SV220: $i] :
( ( ~ ( in @ SV220 @ ( sK5_B @ SV56 ) )
| ~ ( subset @ SV224 @ SV220 )
| ( in @ SV224 @ ( sK5_B @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1314]) ).
thf(1338,plain,
! [SV57: $i,SV193: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SV193 @ SV57 ) @ ( sK12_SY3639 @ SV193 @ SV57 ) ) @ SV57 ) )
= $false )
| ( ( subset @ SV57 @ SV193 )
= $true )
| ( ( relation @ SV193 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1315]) ).
thf(1339,plain,
! [SV57: $i,SV193: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK11_C @ SV193 @ SV57 ) @ ( sK12_SY3639 @ SV193 @ SV57 ) ) @ SV193 ) )
= $false )
| ( ( subset @ SV57 @ SV193 )
= $true )
| ( ( relation @ SV193 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1315]) ).
thf(1340,plain,
! [SV194: $i,SV57: $i,SV225: $i] :
( ( ( ! [SY3822: $i] :
( ~ ( in @ ( ordered_pair @ SV225 @ SY3822 ) @ SV57 )
| ( in @ ( ordered_pair @ SV225 @ SY3822 ) @ SV194 ) ) )
= $true )
| ( ( subset @ SV57 @ SV194 )
= $false )
| ( ( relation @ SV194 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1316]) ).
thf(1341,plain,
! [SV216: $i,SV113: $i] :
( ( ( disjoint @ ( fiber @ SV113 @ SV216 ) @ ( sK14_B @ SV113 ) )
= $false )
| ( ( ~ ( in @ SV216 @ ( sK14_B @ SV113 ) ) )
= $true )
| ( ( well_founded_relation @ SV113 )
= $true )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1321]) ).
thf(1342,plain,
! [SV113: $i] :
( ( ( ( ( sK14_B @ SV113 )
!= empty_set ) )
= $true )
| ( ( well_founded_relation @ SV113 )
= $true )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1322]) ).
thf(1343,plain,
! [SV113: $i] :
( ( ( subset @ ( sK14_B @ SV113 ) @ ( relation_field @ SV113 ) )
= $true )
| ( ( well_founded_relation @ SV113 )
= $true )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1323]) ).
thf(1344,plain,
! [SV210: $i,SV114: $i] :
( ( ( disjoint @ ( fiber @ SV114 @ ( sK13_C @ SV210 @ SV114 ) ) @ SV210 )
= $true )
| ( ( ( SV210 = empty_set )
| ~ ( subset @ SV210 @ ( relation_field @ SV114 ) ) )
= $true )
| ( ( well_founded_relation @ SV114 )
= $false )
| ( ( relation @ SV114 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1324]) ).
thf(1345,plain,
! [SV114: $i,SV210: $i] :
( ( ( in @ ( sK13_C @ SV210 @ SV114 ) @ SV210 )
= $true )
| ( ( ( SV210 = empty_set )
| ~ ( subset @ SV210 @ ( relation_field @ SV114 ) ) )
= $true )
| ( ( well_founded_relation @ SV114 )
= $false )
| ( ( relation @ SV114 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1325]) ).
thf(1346,plain,
! [SV95: $i,SV48: $i,SV221: $i] :
( ( ( ~ ( ordinal @ SV221 ) )
= $true )
| ( ( ~ ( in @ SV221 @ SV48 )
| ( ordinal_subset @ ( sK17_C @ SV95 @ SV48 ) @ SV221 ) )
= $true )
| ( ( ( SV48 = empty_set )
| ~ ( subset @ SV48 @ SV95 ) )
= $true )
| ( ( ordinal @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1326]) ).
thf(1347,plain,
! [SV95: $i,SV48: $i] :
( ( ( subset @ SV48 @ SV95 )
= $false )
| ( ( SV48 = empty_set )
= $true )
| ( ( in @ ( sK17_C @ SV95 @ SV48 ) @ SV48 )
= $true )
| ( ( ordinal @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1327]) ).
thf(1348,plain,
! [SV222: $i,SV50: $i,SV217: $i] :
( ( ( ~ ( in @ SV217 @ ( sK19_B @ SV50 ) )
| ~ ( subset @ SV222 @ SV217 ) )
= $true )
| ( ( in @ SV222 @ ( sK19_B @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1328]) ).
thf(1349,plain,
! [SV129: $i,SV160: $i,SV218: $i] :
( ( ( in @ SV218 @ SV160 )
= $false )
| ( ( subset @ SV218 @ SV129 )
= $true )
| ( ( SV160
= ( powerset @ SV129 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1330]) ).
thf(1350,plain,
! [SV160: $i,SV129: $i,SV219: $i] :
( ( ( subset @ SV219 @ SV129 )
= $false )
| ( ( in @ SV219 @ SV160 )
= $true )
| ( ( SV160
= ( powerset @ SV129 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1331]) ).
thf(1351,plain,
! [SV189: $i,SV223: $i,SV55: $i] :
( ( ( ~ ( disjoint @ ( fiber @ SV55 @ SV223 ) @ ( sK9_C @ SV189 @ SV55 ) ) )
= $true )
| ( ( ~ ( in @ SV223 @ ( sK9_C @ SV189 @ SV55 ) ) )
= $true )
| ( ( is_well_founded_in @ SV55 @ SV189 )
= $true )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1332]) ).
thf(1352,plain,
! [SV55: $i,SV189: $i] :
( ( ( ~ ( ( ( sK9_C @ SV189 @ SV55 )
!= empty_set ) ) )
= $false )
| ( ( is_well_founded_in @ SV55 @ SV189 )
= $true )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1333]) ).
thf(1353,plain,
! [SV55: $i,SV189: $i] :
( ( ( ~ ( subset @ ( sK9_C @ SV189 @ SV55 ) @ SV189 ) )
= $false )
| ( ( is_well_founded_in @ SV55 @ SV189 )
= $true )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1333]) ).
thf(1354,plain,
! [SV190: $i,SV214: $i,SV55: $i] :
( ( ( ~ ( disjoint @ ( fiber @ SV55 @ ( sK8_D @ SV214 @ SV190 @ SV55 ) ) @ SV214 ) )
= $false )
| ( ( ( SV214 = empty_set )
| ~ ( subset @ SV214 @ SV190 ) )
= $true )
| ( ( is_well_founded_in @ SV55 @ SV190 )
= $false )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1334]) ).
thf(1355,plain,
! [SV55: $i,SV190: $i,SV214: $i] :
( ( ( ~ ( in @ ( sK8_D @ SV214 @ SV190 @ SV55 ) @ SV214 ) )
= $false )
| ( ( ( SV214 = empty_set )
| ~ ( subset @ SV214 @ SV190 ) )
= $true )
| ( ( is_well_founded_in @ SV55 @ SV190 )
= $false )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1334]) ).
thf(1356,plain,
! [SV56: $i,SV208: $i,SV226: $i] :
( ( ( ~ ( subset @ SV226 @ SV208 )
| ( in @ SV226 @ ( sK6_SY3633 @ SV208 @ SV56 ) ) )
= $true )
| ( ( ~ ( in @ SV208 @ ( sK5_B @ SV56 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1335]) ).
thf(1357,plain,
! [SV56: $i,SV208: $i] :
( ( ( in @ SV208 @ ( sK5_B @ SV56 ) )
= $false )
| ( ( in @ ( sK6_SY3633 @ SV208 @ SV56 ) @ ( sK5_B @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1336]) ).
thf(1358,plain,
! [SV224: $i,SV56: $i,SV220: $i] :
( ( ( ~ ( in @ SV220 @ ( sK5_B @ SV56 ) )
| ~ ( subset @ SV224 @ SV220 ) )
= $true )
| ( ( in @ SV224 @ ( sK5_B @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1337]) ).
thf(1359,plain,
! [SV57: $i,SV193: $i] :
( ( ( in @ ( ordered_pair @ ( sK11_C @ SV193 @ SV57 ) @ ( sK12_SY3639 @ SV193 @ SV57 ) ) @ SV57 )
= $true )
| ( ( subset @ SV57 @ SV193 )
= $true )
| ( ( relation @ SV193 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1338]) ).
thf(1360,plain,
! [SV57: $i,SV193: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SV193 @ SV57 ) @ ( sK12_SY3639 @ SV193 @ SV57 ) ) @ SV193 ) )
= $true )
| ( ( subset @ SV57 @ SV193 )
= $true )
| ( ( relation @ SV193 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1339]) ).
thf(1361,plain,
! [SV194: $i,SV57: $i,SV227: $i,SV225: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV225 @ SV227 ) @ SV57 )
| ( in @ ( ordered_pair @ SV225 @ SV227 ) @ SV194 ) )
= $true )
| ( ( subset @ SV57 @ SV194 )
= $false )
| ( ( relation @ SV194 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1340]) ).
thf(1362,plain,
! [SV113: $i,SV216: $i] :
( ( ( in @ SV216 @ ( sK14_B @ SV113 ) )
= $false )
| ( ( disjoint @ ( fiber @ SV113 @ SV216 ) @ ( sK14_B @ SV113 ) )
= $false )
| ( ( well_founded_relation @ SV113 )
= $true )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1341]) ).
thf(1363,plain,
! [SV113: $i] :
( ( ( ( sK14_B @ SV113 )
= empty_set )
= $false )
| ( ( well_founded_relation @ SV113 )
= $true )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1342]) ).
thf(1364,plain,
! [SV114: $i,SV210: $i] :
( ( ( SV210 = empty_set )
= $true )
| ( ( ~ ( subset @ SV210 @ ( relation_field @ SV114 ) ) )
= $true )
| ( ( disjoint @ ( fiber @ SV114 @ ( sK13_C @ SV210 @ SV114 ) ) @ SV210 )
= $true )
| ( ( well_founded_relation @ SV114 )
= $false )
| ( ( relation @ SV114 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1344]) ).
thf(1365,plain,
! [SV114: $i,SV210: $i] :
( ( ( SV210 = empty_set )
= $true )
| ( ( ~ ( subset @ SV210 @ ( relation_field @ SV114 ) ) )
= $true )
| ( ( in @ ( sK13_C @ SV210 @ SV114 ) @ SV210 )
= $true )
| ( ( well_founded_relation @ SV114 )
= $false )
| ( ( relation @ SV114 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1345]) ).
thf(1366,plain,
! [SV95: $i,SV48: $i,SV221: $i] :
( ( ( ordinal @ SV221 )
= $false )
| ( ( ~ ( in @ SV221 @ SV48 )
| ( ordinal_subset @ ( sK17_C @ SV95 @ SV48 ) @ SV221 ) )
= $true )
| ( ( ( SV48 = empty_set )
| ~ ( subset @ SV48 @ SV95 ) )
= $true )
| ( ( ordinal @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1346]) ).
thf(1367,plain,
! [SV222: $i,SV50: $i,SV217: $i] :
( ( ( ~ ( in @ SV217 @ ( sK19_B @ SV50 ) ) )
= $true )
| ( ( ~ ( subset @ SV222 @ SV217 ) )
= $true )
| ( ( in @ SV222 @ ( sK19_B @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1348]) ).
thf(1368,plain,
! [SV189: $i,SV223: $i,SV55: $i] :
( ( ( disjoint @ ( fiber @ SV55 @ SV223 ) @ ( sK9_C @ SV189 @ SV55 ) )
= $false )
| ( ( ~ ( in @ SV223 @ ( sK9_C @ SV189 @ SV55 ) ) )
= $true )
| ( ( is_well_founded_in @ SV55 @ SV189 )
= $true )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1351]) ).
thf(1369,plain,
! [SV55: $i,SV189: $i] :
( ( ( ( ( sK9_C @ SV189 @ SV55 )
!= empty_set ) )
= $true )
| ( ( is_well_founded_in @ SV55 @ SV189 )
= $true )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1352]) ).
thf(1370,plain,
! [SV55: $i,SV189: $i] :
( ( ( subset @ ( sK9_C @ SV189 @ SV55 ) @ SV189 )
= $true )
| ( ( is_well_founded_in @ SV55 @ SV189 )
= $true )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1353]) ).
thf(1371,plain,
! [SV190: $i,SV214: $i,SV55: $i] :
( ( ( disjoint @ ( fiber @ SV55 @ ( sK8_D @ SV214 @ SV190 @ SV55 ) ) @ SV214 )
= $true )
| ( ( ( SV214 = empty_set )
| ~ ( subset @ SV214 @ SV190 ) )
= $true )
| ( ( is_well_founded_in @ SV55 @ SV190 )
= $false )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1354]) ).
thf(1372,plain,
! [SV55: $i,SV190: $i,SV214: $i] :
( ( ( in @ ( sK8_D @ SV214 @ SV190 @ SV55 ) @ SV214 )
= $true )
| ( ( ( SV214 = empty_set )
| ~ ( subset @ SV214 @ SV190 ) )
= $true )
| ( ( is_well_founded_in @ SV55 @ SV190 )
= $false )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1355]) ).
thf(1373,plain,
! [SV56: $i,SV208: $i,SV226: $i] :
( ( ( ~ ( subset @ SV226 @ SV208 ) )
= $true )
| ( ( in @ SV226 @ ( sK6_SY3633 @ SV208 @ SV56 ) )
= $true )
| ( ( ~ ( in @ SV208 @ ( sK5_B @ SV56 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1356]) ).
thf(1374,plain,
! [SV224: $i,SV56: $i,SV220: $i] :
( ( ( ~ ( in @ SV220 @ ( sK5_B @ SV56 ) ) )
= $true )
| ( ( ~ ( subset @ SV224 @ SV220 ) )
= $true )
| ( ( in @ SV224 @ ( sK5_B @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1358]) ).
thf(1375,plain,
! [SV57: $i,SV193: $i] :
( ( ( in @ ( ordered_pair @ ( sK11_C @ SV193 @ SV57 ) @ ( sK12_SY3639 @ SV193 @ SV57 ) ) @ SV193 )
= $false )
| ( ( subset @ SV57 @ SV193 )
= $true )
| ( ( relation @ SV193 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1360]) ).
thf(1376,plain,
! [SV194: $i,SV57: $i,SV227: $i,SV225: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV225 @ SV227 ) @ SV57 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV225 @ SV227 ) @ SV194 )
= $true )
| ( ( subset @ SV57 @ SV194 )
= $false )
| ( ( relation @ SV194 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1361]) ).
thf(1377,plain,
! [SV114: $i,SV210: $i] :
( ( ( subset @ SV210 @ ( relation_field @ SV114 ) )
= $false )
| ( ( SV210 = empty_set )
= $true )
| ( ( disjoint @ ( fiber @ SV114 @ ( sK13_C @ SV210 @ SV114 ) ) @ SV210 )
= $true )
| ( ( well_founded_relation @ SV114 )
= $false )
| ( ( relation @ SV114 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1364]) ).
thf(1378,plain,
! [SV114: $i,SV210: $i] :
( ( ( subset @ SV210 @ ( relation_field @ SV114 ) )
= $false )
| ( ( SV210 = empty_set )
= $true )
| ( ( in @ ( sK13_C @ SV210 @ SV114 ) @ SV210 )
= $true )
| ( ( well_founded_relation @ SV114 )
= $false )
| ( ( relation @ SV114 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1365]) ).
thf(1379,plain,
! [SV95: $i,SV48: $i,SV221: $i] :
( ( ( ~ ( in @ SV221 @ SV48 ) )
= $true )
| ( ( ordinal_subset @ ( sK17_C @ SV95 @ SV48 ) @ SV221 )
= $true )
| ( ( ordinal @ SV221 )
= $false )
| ( ( ( SV48 = empty_set )
| ~ ( subset @ SV48 @ SV95 ) )
= $true )
| ( ( ordinal @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1366]) ).
thf(1380,plain,
! [SV222: $i,SV50: $i,SV217: $i] :
( ( ( in @ SV217 @ ( sK19_B @ SV50 ) )
= $false )
| ( ( ~ ( subset @ SV222 @ SV217 ) )
= $true )
| ( ( in @ SV222 @ ( sK19_B @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1367]) ).
thf(1381,plain,
! [SV55: $i,SV189: $i,SV223: $i] :
( ( ( in @ SV223 @ ( sK9_C @ SV189 @ SV55 ) )
= $false )
| ( ( disjoint @ ( fiber @ SV55 @ SV223 ) @ ( sK9_C @ SV189 @ SV55 ) )
= $false )
| ( ( is_well_founded_in @ SV55 @ SV189 )
= $true )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1368]) ).
thf(1382,plain,
! [SV55: $i,SV189: $i] :
( ( ( ( sK9_C @ SV189 @ SV55 )
= empty_set )
= $false )
| ( ( is_well_founded_in @ SV55 @ SV189 )
= $true )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1369]) ).
thf(1383,plain,
! [SV55: $i,SV190: $i,SV214: $i] :
( ( ( SV214 = empty_set )
= $true )
| ( ( ~ ( subset @ SV214 @ SV190 ) )
= $true )
| ( ( disjoint @ ( fiber @ SV55 @ ( sK8_D @ SV214 @ SV190 @ SV55 ) ) @ SV214 )
= $true )
| ( ( is_well_founded_in @ SV55 @ SV190 )
= $false )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1371]) ).
thf(1384,plain,
! [SV55: $i,SV190: $i,SV214: $i] :
( ( ( SV214 = empty_set )
= $true )
| ( ( ~ ( subset @ SV214 @ SV190 ) )
= $true )
| ( ( in @ ( sK8_D @ SV214 @ SV190 @ SV55 ) @ SV214 )
= $true )
| ( ( is_well_founded_in @ SV55 @ SV190 )
= $false )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1372]) ).
thf(1385,plain,
! [SV56: $i,SV208: $i,SV226: $i] :
( ( ( subset @ SV226 @ SV208 )
= $false )
| ( ( in @ SV226 @ ( sK6_SY3633 @ SV208 @ SV56 ) )
= $true )
| ( ( ~ ( in @ SV208 @ ( sK5_B @ SV56 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1373]) ).
thf(1386,plain,
! [SV224: $i,SV56: $i,SV220: $i] :
( ( ( in @ SV220 @ ( sK5_B @ SV56 ) )
= $false )
| ( ( ~ ( subset @ SV224 @ SV220 ) )
= $true )
| ( ( in @ SV224 @ ( sK5_B @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1374]) ).
thf(1387,plain,
! [SV194: $i,SV57: $i,SV227: $i,SV225: $i] :
( ( ( in @ ( ordered_pair @ SV225 @ SV227 ) @ SV57 )
= $false )
| ( ( in @ ( ordered_pair @ SV225 @ SV227 ) @ SV194 )
= $true )
| ( ( subset @ SV57 @ SV194 )
= $false )
| ( ( relation @ SV194 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1376]) ).
thf(1388,plain,
! [SV95: $i,SV48: $i,SV221: $i] :
( ( ( in @ SV221 @ SV48 )
= $false )
| ( ( ordinal_subset @ ( sK17_C @ SV95 @ SV48 ) @ SV221 )
= $true )
| ( ( ordinal @ SV221 )
= $false )
| ( ( ( SV48 = empty_set )
| ~ ( subset @ SV48 @ SV95 ) )
= $true )
| ( ( ordinal @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1379]) ).
thf(1389,plain,
! [SV50: $i,SV217: $i,SV222: $i] :
( ( ( subset @ SV222 @ SV217 )
= $false )
| ( ( in @ SV217 @ ( sK19_B @ SV50 ) )
= $false )
| ( ( in @ SV222 @ ( sK19_B @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1380]) ).
thf(1390,plain,
! [SV55: $i,SV190: $i,SV214: $i] :
( ( ( subset @ SV214 @ SV190 )
= $false )
| ( ( SV214 = empty_set )
= $true )
| ( ( disjoint @ ( fiber @ SV55 @ ( sK8_D @ SV214 @ SV190 @ SV55 ) ) @ SV214 )
= $true )
| ( ( is_well_founded_in @ SV55 @ SV190 )
= $false )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1383]) ).
thf(1391,plain,
! [SV55: $i,SV190: $i,SV214: $i] :
( ( ( subset @ SV214 @ SV190 )
= $false )
| ( ( SV214 = empty_set )
= $true )
| ( ( in @ ( sK8_D @ SV214 @ SV190 @ SV55 ) @ SV214 )
= $true )
| ( ( is_well_founded_in @ SV55 @ SV190 )
= $false )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1384]) ).
thf(1392,plain,
! [SV226: $i,SV56: $i,SV208: $i] :
( ( ( in @ SV208 @ ( sK5_B @ SV56 ) )
= $false )
| ( ( in @ SV226 @ ( sK6_SY3633 @ SV208 @ SV56 ) )
= $true )
| ( ( subset @ SV226 @ SV208 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1385]) ).
thf(1393,plain,
! [SV56: $i,SV220: $i,SV224: $i] :
( ( ( subset @ SV224 @ SV220 )
= $false )
| ( ( in @ SV220 @ ( sK5_B @ SV56 ) )
= $false )
| ( ( in @ SV224 @ ( sK5_B @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1386]) ).
thf(1394,plain,
! [SV221: $i,SV95: $i,SV48: $i] :
( ( ( SV48 = empty_set )
= $true )
| ( ( ~ ( subset @ SV48 @ SV95 ) )
= $true )
| ( ( ordinal @ SV221 )
= $false )
| ( ( ordinal_subset @ ( sK17_C @ SV95 @ SV48 ) @ SV221 )
= $true )
| ( ( in @ SV221 @ SV48 )
= $false )
| ( ( ordinal @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1388]) ).
thf(1395,plain,
! [SV221: $i,SV95: $i,SV48: $i] :
( ( ( subset @ SV48 @ SV95 )
= $false )
| ( ( SV48 = empty_set )
= $true )
| ( ( ordinal @ SV221 )
= $false )
| ( ( ordinal_subset @ ( sK17_C @ SV95 @ SV48 ) @ SV221 )
= $true )
| ( ( in @ SV221 @ SV48 )
= $false )
| ( ( ordinal @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1394]) ).
thf(1396,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[554,1395,1393,1392,1391,1390,1389,1387,1382,1381,1378,1377,1375,1370,1363,1362,1359,1357,1350,1349,1347,1343,1329,1320,1319,1318,1317,1304,1303,1297,1294,1293,1288,1287,1286,1278,1276,1274,1273,1272,1271,1270,1267,1264,1260,1254,1253,1232,1229,1225,1224,1204,1201,1198,1197,1196,1195,1194,1190,1189,1186,1174,1167,1166,1165,1158,1157,1156,1155,1154,1153,1152,1151,1150,1149,1133,1132,1125,1124,1123,1122,1121,1120,1119,1118,1087,1086,1082,1081,1080,1010,1009,1001,1000,998,983,939,936,930,929,928,865,864,862,861,856,851,844,839,838,836,835,834,833,831,767,761,699,693,682,674,629,628,608,555]) ).
thf(1397,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1396]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SEU264+2 : TPTP v8.1.0. Released v3.3.0.
% 0.09/0.11 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.09/0.31 % Computer : n020.cluster.edu
% 0.09/0.31 % Model : x86_64 x86_64
% 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31 % Memory : 8042.1875MB
% 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31 % CPULimit : 300
% 0.09/0.31 % WCLimit : 600
% 0.09/0.31 % DateTime : Mon Jun 20 13:26:33 EDT 2022
% 0.09/0.31 % CPUTime :
% 0.15/0.42 .........
% 0.15/0.55
% 0.15/0.55 No.of.Axioms: 330
% 0.15/0.55
% 0.15/0.55 Length.of.Defs: 0
% 0.15/0.55
% 0.15/0.55 Contains.Choice.Funs: false
% 0.45/0.69 ....................
% 0.61/0.80 (rf:2,axioms:214,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:332,loop_count:0,foatp_calls:0,translation:fof_full)......................................................................................................................................................................................................................................................eprover: CPU time limit exceeded, terminating
% 75.11/75.35 ...............ignored arguments false
% 75.33/75.56 ..........
% 75.51/75.73 (rf:0,axioms:330,ps:0,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:false,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:332,loop_count:0,foatp_calls:0,translation:fof_full)......................................................................................................................................................................................................................................................................................................................................................................................................................................................................eprover: CPU time limit exceeded, terminating
% 150.51/150.75 .......................................
% 150.78/151.01 (rf:2,axioms:214,ps:0,u:1,ude:true,rLeibEQ:false,rAndEQ:false,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:332,loop_count:0,foatp_calls:0,translation:fof_full).....................................................................................................................................................................................................................................................eprover: CPU time limit exceeded, terminating
% 224.98/225.28 ..............................
% 225.19/225.53 (rf:-1,axioms:72,ps:0,u:1,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:332,loop_count:0,foatp_calls:0,translation:fof_full)........................................................................
% 242.21/242.51
% 242.21/242.51 ********************************
% 242.21/242.51 * All subproblems solved! *
% 242.21/242.51 ********************************
% 242.21/242.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:-1,axioms:74,ps:0,u:1,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:1396,loop_count:0,foatp_calls:1,translation:fof_full)
% 242.61/242.89
% 242.61/242.89 %**** Beginning of derivation protocol ****
% 242.61/242.89 % SZS output start CNFRefutation
% See solution above
% 242.61/242.89
% 242.61/242.89 %**** End of derivation protocol ****
% 242.61/242.89 %**** no. of clauses in derivation: 1139 ****
% 242.61/242.89 %**** clause counter: 1396 ****
% 242.61/242.89
% 242.61/242.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:-1,axioms:74,ps:0,u:1,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:1396,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------