TSTP Solution File: SET020+1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET020+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 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 02:58:04 EDT 2022
% Result : Theorem 0.74s 1.03s
% Output : CNFRefutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 85
% Syntax : Number of formulae : 1431 ( 926 unt; 41 typ; 0 def)
% Number of atoms : 8159 (2484 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 19788 (3210 ~;2644 |; 209 &;13663 @)
% ( 38 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 47 ( 47 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 41 usr; 12 con; 0-3 aty)
% Number of variables : 3983 ( 0 ^3973 !; 10 ?;3983 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_apply,type,
apply: $i > $i > $i ).
thf(tp_complement,type,
complement: $i > $i ).
thf(tp_compose,type,
compose: $i > $i > $i ).
thf(tp_cross_product,type,
cross_product: $i > $i > $i ).
thf(tp_disjoint,type,
disjoint: $i > $i > $o ).
thf(tp_domain_of,type,
domain_of: $i > $i ).
thf(tp_element_relation,type,
element_relation: $i ).
thf(tp_first,type,
first: $i > $i ).
thf(tp_flip,type,
flip: $i > $i ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_identity_relation,type,
identity_relation: $i ).
thf(tp_image,type,
image: $i > $i > $i ).
thf(tp_inductive,type,
inductive: $i > $o ).
thf(tp_intersection,type,
intersection: $i > $i > $i ).
thf(tp_inverse,type,
inverse: $i > $i ).
thf(tp_member,type,
member: $i > $i > $o ).
thf(tp_null_class,type,
null_class: $i ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_power_class,type,
power_class: $i > $i ).
thf(tp_range_of,type,
range_of: $i > $i ).
thf(tp_restrict,type,
restrict: $i > $i > $i > $i ).
thf(tp_rotate,type,
rotate: $i > $i ).
thf(tp_sK10_U,type,
sK10_U: $i > $i > $i ).
thf(tp_sK1_U,type,
sK1_U: $i ).
thf(tp_sK2_SY89,type,
sK2_SY89: $i ).
thf(tp_sK3_SY91,type,
sK3_SY91: $i ).
thf(tp_sK4_XF,type,
sK4_XF: $i ).
thf(tp_sK5_U,type,
sK5_U: $i > $i ).
thf(tp_sK6_U,type,
sK6_U: $i > $i > $i ).
thf(tp_sK7_X,type,
sK7_X: $i > $i ).
thf(tp_sK8_Y,type,
sK8_Y: $i > $i > $i ).
thf(tp_sK9_X,type,
sK9_X: $i ).
thf(tp_second,type,
second: $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subclass,type,
subclass: $i > $i > $o ).
thf(tp_successor,type,
successor: $i > $i ).
thf(tp_successor_relation,type,
successor_relation: $i ).
thf(tp_sum_class,type,
sum_class: $i > $i ).
thf(tp_union,type,
union: $i > $i > $i ).
thf(tp_universal_class,type,
universal_class: $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(1,axiom,
? [XF: $i] :
( ( function @ XF )
& ! [Y: $i] :
( ( member @ Y @ universal_class )
=> ( ( Y = null_class )
| ( member @ ( apply @ XF @ Y ) @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice) ).
thf(2,axiom,
! [XF: $i,Y: $i] :
( ( apply @ XF @ Y )
= ( sum_class @ ( image @ XF @ ( singleton @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply_defn) ).
thf(3,axiom,
! [X: $i] :
( ( X != null_class )
=> ? [U: $i] :
( ( member @ U @ universal_class )
& ( member @ U @ X )
& ( disjoint @ U @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity) ).
thf(4,axiom,
! [X: $i,Y: $i] :
( ( disjoint @ X @ Y )
<=> ! [U: $i] :
~ ( ( member @ U @ X )
& ( member @ U @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint_defn) ).
thf(5,axiom,
! [X: $i,XF: $i] :
( ( ( member @ X @ universal_class )
& ( function @ XF ) )
=> ( member @ ( image @ XF @ X ) @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replacement) ).
thf(6,axiom,
! [XF: $i] :
( ( function @ XF )
<=> ( ( subclass @ XF @ ( cross_product @ universal_class @ universal_class ) )
& ( subclass @ ( compose @ XF @ ( inverse @ XF ) ) @ identity_relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function_defn) ).
thf(7,axiom,
! [Z: $i] :
( ( member @ Z @ identity_relation )
<=> ? [X: $i] :
( ( member @ X @ universal_class )
& ( Z
= ( ordered_pair @ X @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_relation) ).
thf(8,axiom,
! [XR: $i,YR: $i,U: $i,V: $i] :
( ( member @ ( ordered_pair @ U @ V ) @ ( compose @ YR @ XR ) )
<=> ( ( member @ U @ universal_class )
& ( member @ V @ ( image @ YR @ ( image @ XR @ ( singleton @ U ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_defn2) ).
thf(9,axiom,
! [XR: $i,YR: $i] : ( subclass @ ( compose @ YR @ XR ) @ ( cross_product @ universal_class @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_defn1) ).
thf(10,axiom,
! [U: $i] :
( ( member @ U @ universal_class )
=> ( member @ ( power_class @ U ) @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_class) ).
thf(11,axiom,
! [U: $i,X: $i] :
( ( member @ U @ ( power_class @ X ) )
<=> ( ( member @ U @ universal_class )
& ( subclass @ U @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_class_defn) ).
thf(12,axiom,
! [X: $i] :
( ( member @ X @ universal_class )
=> ( member @ ( sum_class @ X ) @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class) ).
thf(13,axiom,
! [U: $i,X: $i] :
( ( member @ U @ ( sum_class @ X ) )
<=> ? [Y: $i] :
( ( member @ U @ Y )
& ( member @ Y @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class_defn) ).
thf(14,axiom,
? [X: $i] :
( ( member @ X @ universal_class )
& ( inductive @ X )
& ! [Y: $i] :
( ( inductive @ Y )
=> ( subclass @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infinity) ).
thf(15,axiom,
! [X: $i] :
( ( inductive @ X )
<=> ( ( member @ null_class @ X )
& ( subclass @ ( image @ successor_relation @ X ) @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive_defn) ).
thf(16,axiom,
! [X: $i,XR: $i] :
( ( image @ XR @ X )
= ( range_of @ ( restrict @ XR @ X @ universal_class ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image_defn) ).
thf(17,axiom,
! [Z: $i] :
( ( range_of @ Z )
= ( domain_of @ ( inverse @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',range_of_defn) ).
thf(18,axiom,
! [Y: $i] :
( ( inverse @ Y )
= ( domain_of @ ( flip @ ( cross_product @ Y @ universal_class ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_defn) ).
thf(19,axiom,
! [X: $i,Y: $i] :
( ( member @ ( ordered_pair @ X @ Y ) @ successor_relation )
<=> ( ( member @ X @ universal_class )
& ( member @ Y @ universal_class )
& ( ( successor @ X )
= Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation_defn2) ).
thf(20,axiom,
subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation_defn1) ).
thf(21,axiom,
! [X: $i] :
( ( successor @ X )
= ( union @ X @ ( singleton @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_defn) ).
thf(22,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( member @ Z @ ( union @ X @ Y ) )
<=> ( ( member @ Z @ X )
| ( member @ Z @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
thf(23,axiom,
! [X: $i] : ( subclass @ ( flip @ X ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip) ).
thf(24,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( flip @ X ) )
<=> ( ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
& ( member @ ( ordered_pair @ ( ordered_pair @ V @ U ) @ W ) @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip_defn) ).
thf(25,axiom,
! [X: $i] : ( subclass @ ( rotate @ X ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate) ).
thf(26,axiom,
! [X: $i,U: $i,V: $i,W: $i] :
( ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( rotate @ X ) )
<=> ( ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
& ( member @ ( ordered_pair @ ( ordered_pair @ V @ W ) @ U ) @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate_defn) ).
thf(27,axiom,
! [X: $i,Z: $i] :
( ( member @ Z @ ( domain_of @ X ) )
<=> ( ( member @ Z @ universal_class )
& ( ( restrict @ X @ ( singleton @ Z ) @ universal_class )
!= null_class ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_of) ).
thf(28,axiom,
! [X: $i] :
~ ( member @ X @ null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_defn) ).
thf(29,axiom,
! [X: $i,XR: $i,Y: $i] :
( ( restrict @ XR @ X @ Y )
= ( intersection @ XR @ ( cross_product @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',restrict_defn) ).
thf(30,axiom,
! [X: $i,Z: $i] :
( ( member @ Z @ ( complement @ X ) )
<=> ( ( member @ Z @ universal_class )
& ~ ( member @ Z @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement) ).
thf(31,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( member @ Z @ ( intersection @ X @ Y ) )
<=> ( ( member @ Z @ X )
& ( member @ Z @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).
thf(32,axiom,
subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation) ).
thf(33,axiom,
! [X: $i,Y: $i] :
( ( member @ ( ordered_pair @ X @ Y ) @ element_relation )
<=> ( ( member @ Y @ universal_class )
& ( member @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation_defn) ).
thf(34,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( member @ Z @ ( cross_product @ X @ Y ) )
=> ( Z
= ( ordered_pair @ ( first @ Z ) @ ( second @ Z ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cross_product) ).
thf(35,axiom,
! [X: $i,Y: $i] :
( ( ( member @ X @ universal_class )
& ( member @ Y @ universal_class ) )
=> ( ( ( first @ ( ordered_pair @ X @ Y ) )
= X )
& ( ( second @ ( ordered_pair @ X @ Y ) )
= Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first_second) ).
thf(36,axiom,
! [U: $i,V: $i,X: $i,Y: $i] :
( ( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) )
<=> ( ( member @ U @ X )
& ( member @ V @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cross_product_defn) ).
thf(37,axiom,
! [X: $i,Y: $i] :
( ( ordered_pair @ X @ Y )
= ( unordered_pair @ ( singleton @ X ) @ ( unordered_pair @ X @ ( singleton @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_defn) ).
thf(38,axiom,
! [X: $i] :
( ( singleton @ X )
= ( unordered_pair @ X @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set_defn) ).
thf(39,axiom,
! [X: $i,Y: $i] : ( member @ ( unordered_pair @ X @ Y ) @ universal_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair) ).
thf(40,axiom,
! [U: $i,X: $i,Y: $i] :
( ( member @ U @ ( unordered_pair @ X @ Y ) )
<=> ( ( member @ U @ universal_class )
& ( ( U = X )
| ( U = Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_defn) ).
thf(41,axiom,
! [X: $i,Y: $i] :
( ( X = Y )
<=> ( ( subclass @ X @ Y )
& ( subclass @ Y @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality) ).
thf(42,axiom,
! [X: $i] : ( subclass @ X @ universal_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
thf(43,axiom,
! [X: $i,Y: $i] :
( ( subclass @ X @ Y )
<=> ! [U: $i] :
( ( member @ U @ X )
=> ( member @ U @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_defn) ).
thf(44,conjecture,
! [U: $i,V: $i,X: $i] :
( ( ( member @ U @ universal_class )
& ( member @ V @ universal_class )
& ( X
= ( ordered_pair @ U @ V ) ) )
=> ( ( ( first @ X )
= U )
& ( ( second @ X )
= V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_1st_and_2nd_in_pair_of_sets1) ).
thf(45,negated_conjecture,
( ( ! [U: $i,V: $i,X: $i] :
( ( ( member @ U @ universal_class )
& ( member @ V @ universal_class )
& ( X
= ( ordered_pair @ U @ V ) ) )
=> ( ( ( first @ X )
= U )
& ( ( second @ X )
= V ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[44]) ).
thf(46,plain,
( ( ! [U: $i,V: $i,X: $i] :
( ( ( member @ U @ universal_class )
& ( member @ V @ universal_class )
& ( X
= ( ordered_pair @ U @ V ) ) )
=> ( ( ( first @ X )
= U )
& ( ( second @ X )
= V ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[45]) ).
thf(47,plain,
( ( ? [XF: $i] :
( ( function @ XF )
& ! [Y: $i] :
( ( member @ Y @ universal_class )
=> ( ( Y = null_class )
| ( member @ ( apply @ XF @ Y ) @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(48,plain,
( ( ! [XF: $i,Y: $i] :
( ( apply @ XF @ Y )
= ( sum_class @ ( image @ XF @ ( singleton @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(49,plain,
( ( ! [X: $i] :
( ( X != null_class )
=> ? [U: $i] :
( ( member @ U @ universal_class )
& ( member @ U @ X )
& ( disjoint @ U @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(50,plain,
( ( ! [X: $i,Y: $i] :
( ( disjoint @ X @ Y )
<=> ! [U: $i] :
~ ( ( member @ U @ X )
& ( member @ U @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(51,plain,
( ( ! [X: $i,XF: $i] :
( ( ( member @ X @ universal_class )
& ( function @ XF ) )
=> ( member @ ( image @ XF @ X ) @ universal_class ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(52,plain,
( ( ! [XF: $i] :
( ( function @ XF )
<=> ( ( subclass @ XF @ ( cross_product @ universal_class @ universal_class ) )
& ( subclass @ ( compose @ XF @ ( inverse @ XF ) ) @ identity_relation ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(53,plain,
( ( ! [Z: $i] :
( ( member @ Z @ identity_relation )
<=> ? [X: $i] :
( ( member @ X @ universal_class )
& ( Z
= ( ordered_pair @ X @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(54,plain,
( ( ! [XR: $i,YR: $i,U: $i,V: $i] :
( ( member @ ( ordered_pair @ U @ V ) @ ( compose @ YR @ XR ) )
<=> ( ( member @ U @ universal_class )
& ( member @ V @ ( image @ YR @ ( image @ XR @ ( singleton @ U ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(55,plain,
( ( ! [XR: $i,YR: $i] : ( subclass @ ( compose @ YR @ XR ) @ ( cross_product @ universal_class @ universal_class ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(56,plain,
( ( ! [U: $i] :
( ( member @ U @ universal_class )
=> ( member @ ( power_class @ U ) @ universal_class ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(57,plain,
( ( ! [U: $i,X: $i] :
( ( member @ U @ ( power_class @ X ) )
<=> ( ( member @ U @ universal_class )
& ( subclass @ U @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(58,plain,
( ( ! [X: $i] :
( ( member @ X @ universal_class )
=> ( member @ ( sum_class @ X ) @ universal_class ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(59,plain,
( ( ! [U: $i,X: $i] :
( ( member @ U @ ( sum_class @ X ) )
<=> ? [Y: $i] :
( ( member @ U @ Y )
& ( member @ Y @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(60,plain,
( ( ? [X: $i] :
( ( member @ X @ universal_class )
& ( inductive @ X )
& ! [Y: $i] :
( ( inductive @ Y )
=> ( subclass @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(61,plain,
( ( ! [X: $i] :
( ( inductive @ X )
<=> ( ( member @ null_class @ X )
& ( subclass @ ( image @ successor_relation @ X ) @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(62,plain,
( ( ! [X: $i,XR: $i] :
( ( image @ XR @ X )
= ( range_of @ ( restrict @ XR @ X @ universal_class ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(63,plain,
( ( ! [Z: $i] :
( ( range_of @ Z )
= ( domain_of @ ( inverse @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(64,plain,
( ( ! [Y: $i] :
( ( inverse @ Y )
= ( domain_of @ ( flip @ ( cross_product @ Y @ universal_class ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(65,plain,
( ( ! [X: $i,Y: $i] :
( ( member @ ( ordered_pair @ X @ Y ) @ successor_relation )
<=> ( ( member @ X @ universal_class )
& ( member @ Y @ universal_class )
& ( ( successor @ X )
= Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(66,plain,
( ( subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(67,plain,
( ( ! [X: $i] :
( ( successor @ X )
= ( union @ X @ ( singleton @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(68,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( member @ Z @ ( union @ X @ Y ) )
<=> ( ( member @ Z @ X )
| ( member @ Z @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(69,plain,
( ( ! [X: $i] : ( subclass @ ( flip @ X ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(70,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( flip @ X ) )
<=> ( ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
& ( member @ ( ordered_pair @ ( ordered_pair @ V @ U ) @ W ) @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(71,plain,
( ( ! [X: $i] : ( subclass @ ( rotate @ X ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(72,plain,
( ( ! [X: $i,U: $i,V: $i,W: $i] :
( ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( rotate @ X ) )
<=> ( ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
& ( member @ ( ordered_pair @ ( ordered_pair @ V @ W ) @ U ) @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(73,plain,
( ( ! [X: $i,Z: $i] :
( ( member @ Z @ ( domain_of @ X ) )
<=> ( ( member @ Z @ universal_class )
& ( ( restrict @ X @ ( singleton @ Z ) @ universal_class )
!= null_class ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(74,plain,
( ( ! [X: $i] :
~ ( member @ X @ null_class ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(75,plain,
( ( ! [X: $i,XR: $i,Y: $i] :
( ( restrict @ XR @ X @ Y )
= ( intersection @ XR @ ( cross_product @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(76,plain,
( ( ! [X: $i,Z: $i] :
( ( member @ Z @ ( complement @ X ) )
<=> ( ( member @ Z @ universal_class )
& ~ ( member @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(77,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( member @ Z @ ( intersection @ X @ Y ) )
<=> ( ( member @ Z @ X )
& ( member @ Z @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(78,plain,
( ( subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(79,plain,
( ( ! [X: $i,Y: $i] :
( ( member @ ( ordered_pair @ X @ Y ) @ element_relation )
<=> ( ( member @ Y @ universal_class )
& ( member @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(80,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( member @ Z @ ( cross_product @ X @ Y ) )
=> ( Z
= ( ordered_pair @ ( first @ Z ) @ ( second @ Z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(81,plain,
( ( ! [X: $i,Y: $i] :
( ( ( member @ X @ universal_class )
& ( member @ Y @ universal_class ) )
=> ( ( ( first @ ( ordered_pair @ X @ Y ) )
= X )
& ( ( second @ ( ordered_pair @ X @ Y ) )
= Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(82,plain,
( ( ! [U: $i,V: $i,X: $i,Y: $i] :
( ( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) )
<=> ( ( member @ U @ X )
& ( member @ V @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(83,plain,
( ( ! [X: $i,Y: $i] :
( ( ordered_pair @ X @ Y )
= ( unordered_pair @ ( singleton @ X ) @ ( unordered_pair @ X @ ( singleton @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(84,plain,
( ( ! [X: $i] :
( ( singleton @ X )
= ( unordered_pair @ X @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(85,plain,
( ( ! [X: $i,Y: $i] : ( member @ ( unordered_pair @ X @ Y ) @ universal_class ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(86,plain,
( ( ! [U: $i,X: $i,Y: $i] :
( ( member @ U @ ( unordered_pair @ X @ Y ) )
<=> ( ( member @ U @ universal_class )
& ( ( U = X )
| ( U = Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(87,plain,
( ( ! [X: $i,Y: $i] :
( ( X = Y )
<=> ( ( subclass @ X @ Y )
& ( subclass @ Y @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(88,plain,
( ( ! [X: $i] : ( subclass @ X @ universal_class ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(89,plain,
( ( ! [X: $i,Y: $i] :
( ( subclass @ X @ Y )
<=> ! [U: $i] :
( ( member @ U @ X )
=> ( member @ U @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(90,plain,
( ( ! [SY89: $i,SY90: $i] :
( ( ( member @ sK1_U @ universal_class )
& ( member @ SY89 @ universal_class )
& ( SY90
= ( ordered_pair @ sK1_U @ SY89 ) ) )
=> ( ( ( first @ SY90 )
= sK1_U )
& ( ( second @ SY90 )
= SY89 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[46]) ).
thf(91,plain,
( ( ! [SY91: $i] :
( ( ( member @ sK1_U @ universal_class )
& ( member @ sK2_SY89 @ universal_class )
& ( SY91
= ( ordered_pair @ sK1_U @ sK2_SY89 ) ) )
=> ( ( ( first @ SY91 )
= sK1_U )
& ( ( second @ SY91 )
= sK2_SY89 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[90]) ).
thf(92,plain,
( ( ( ( member @ sK1_U @ universal_class )
& ( member @ sK2_SY89 @ universal_class )
& ( sK3_SY91
= ( ordered_pair @ sK1_U @ sK2_SY89 ) ) )
=> ( ( ( first @ sK3_SY91 )
= sK1_U )
& ( ( second @ sK3_SY91 )
= sK2_SY89 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[91]) ).
thf(93,plain,
( ( member @ sK1_U @ universal_class )
= $true ),
inference(standard_cnf,[status(thm)],[92]) ).
thf(94,plain,
( ( member @ sK2_SY89 @ universal_class )
= $true ),
inference(standard_cnf,[status(thm)],[92]) ).
thf(95,plain,
( ( sK3_SY91
= ( ordered_pair @ sK1_U @ sK2_SY89 ) )
= $true ),
inference(standard_cnf,[status(thm)],[92]) ).
thf(96,plain,
( ( ( ( first @ sK3_SY91 )
= sK1_U )
& ( ( second @ sK3_SY91 )
= sK2_SY89 ) )
= $false ),
inference(standard_cnf,[status(thm)],[92]) ).
thf(97,plain,
( ( ( first @ sK3_SY91 )
= sK1_U )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[96]) ).
thf(98,plain,
( ( ( second @ sK3_SY91 )
= sK2_SY89 )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[96]) ).
thf(99,plain,
( ( ( ( first @ sK3_SY91 )
!= sK1_U ) )
= $true ),
inference(polarity_switch,[status(thm)],[97]) ).
thf(100,plain,
( ( ( ( second @ sK3_SY91 )
!= sK2_SY89 ) )
= $true ),
inference(polarity_switch,[status(thm)],[98]) ).
thf(101,plain,
( ( ! [SY92: $i] :
( ~ ( member @ SY92 @ universal_class )
| ( SY92 = null_class )
| ( member @ ( apply @ sK4_XF @ SY92 ) @ SY92 ) )
& ( function @ sK4_XF ) )
= $true ),
inference(extcnf_combined,[status(esa)],[47]) ).
thf(102,plain,
( ( ! [X: $i] :
( ( X = null_class )
| ( ( member @ ( sK5_U @ X ) @ universal_class )
& ( member @ ( sK5_U @ X ) @ X )
& ( disjoint @ ( sK5_U @ X ) @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(103,plain,
( ( ! [X: $i,Y: $i] :
( ( ( member @ ( sK6_U @ Y @ X ) @ X )
& ( member @ ( sK6_U @ Y @ X ) @ Y ) )
| ( disjoint @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( disjoint @ X @ Y )
| ! [U: $i] :
( ~ ( member @ U @ X )
| ~ ( member @ U @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(104,plain,
( ( ! [X: $i,XF: $i] :
( ~ ( function @ XF )
| ~ ( member @ X @ universal_class )
| ( member @ ( image @ XF @ X ) @ universal_class ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[51]) ).
thf(105,plain,
( ( ! [XF: $i] :
( ~ ( subclass @ XF @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ XF @ ( inverse @ XF ) ) @ identity_relation )
| ( function @ XF ) )
& ! [XF: $i] :
( ~ ( function @ XF )
| ( subclass @ XF @ ( cross_product @ universal_class @ universal_class ) ) )
& ! [XF: $i] :
( ~ ( function @ XF )
| ( subclass @ ( compose @ XF @ ( inverse @ XF ) ) @ identity_relation ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[52]) ).
thf(106,plain,
( ( ! [Z: $i] :
( ! [X: $i] :
( ( Z
!= ( ordered_pair @ X @ X ) )
| ~ ( member @ X @ universal_class ) )
| ( member @ Z @ identity_relation ) )
& ! [Z: $i] :
( ~ ( member @ Z @ identity_relation )
| ( ( Z
= ( ordered_pair @ ( sK7_X @ Z ) @ ( sK7_X @ Z ) ) )
& ( member @ ( sK7_X @ Z ) @ universal_class ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[53]) ).
thf(107,plain,
( ( ! [XR: $i,YR: $i] :
( ! [U: $i,V: $i] :
( ~ ( member @ U @ universal_class )
| ~ ( member @ V @ ( image @ YR @ ( image @ XR @ ( singleton @ U ) ) ) )
| ( member @ ( ordered_pair @ U @ V ) @ ( compose @ YR @ XR ) ) )
& ! [U: $i] :
( ! [V: $i] :
~ ( member @ ( ordered_pair @ U @ V ) @ ( compose @ YR @ XR ) )
| ( member @ U @ universal_class ) )
& ! [U: $i,V: $i] :
( ~ ( member @ ( ordered_pair @ U @ V ) @ ( compose @ YR @ XR ) )
| ( member @ V @ ( image @ YR @ ( image @ XR @ ( singleton @ U ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[54]) ).
thf(108,plain,
( ( ! [U: $i] :
( ~ ( member @ U @ universal_class )
| ( member @ ( power_class @ U ) @ universal_class ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[56]) ).
thf(109,plain,
( ( ! [U: $i,X: $i] :
( ~ ( member @ U @ universal_class )
| ~ ( subclass @ U @ X )
| ( member @ U @ ( power_class @ X ) ) )
& ! [U: $i] :
( ! [X: $i] :
~ ( member @ U @ ( power_class @ X ) )
| ( member @ U @ universal_class ) )
& ! [U: $i,X: $i] :
( ~ ( member @ U @ ( power_class @ X ) )
| ( subclass @ U @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[57]) ).
thf(110,plain,
( ( ! [X: $i] :
( ~ ( member @ X @ universal_class )
| ( member @ ( sum_class @ X ) @ universal_class ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[58]) ).
thf(111,plain,
( ( ! [U: $i,X: $i] :
( ! [Y: $i] :
( ~ ( member @ U @ Y )
| ~ ( member @ Y @ X ) )
| ( member @ U @ ( sum_class @ X ) ) )
& ! [U: $i,X: $i] :
( ~ ( member @ U @ ( sum_class @ X ) )
| ( ( member @ U @ ( sK8_Y @ X @ U ) )
& ( member @ ( sK8_Y @ X @ U ) @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[59]) ).
thf(112,plain,
( ( ! [SY93: $i] :
( ~ ( inductive @ SY93 )
| ( subclass @ sK9_X @ SY93 ) )
& ( inductive @ sK9_X )
& ( member @ sK9_X @ universal_class ) )
= $true ),
inference(extcnf_combined,[status(esa)],[60]) ).
thf(113,plain,
( ( ! [X: $i] :
( ~ ( member @ null_class @ X )
| ~ ( subclass @ ( image @ successor_relation @ X ) @ X )
| ( inductive @ X ) )
& ! [X: $i] :
( ~ ( inductive @ X )
| ( member @ null_class @ X ) )
& ! [X: $i] :
( ~ ( inductive @ X )
| ( subclass @ ( image @ successor_relation @ X ) @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[61]) ).
thf(114,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( member @ X @ universal_class )
| ~ ( member @ Y @ universal_class )
| ( ( successor @ X )
!= Y )
| ( member @ ( ordered_pair @ X @ Y ) @ successor_relation ) )
& ! [X: $i] :
( ! [Y: $i] :
~ ( member @ ( ordered_pair @ X @ Y ) @ successor_relation )
| ( member @ X @ universal_class ) )
& ! [X: $i,Y: $i] :
( ~ ( member @ ( ordered_pair @ X @ Y ) @ successor_relation )
| ( member @ Y @ universal_class ) )
& ! [X: $i,Y: $i] :
( ~ ( member @ ( ordered_pair @ X @ Y ) @ successor_relation )
| ( ( successor @ X )
= Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[65]) ).
thf(115,plain,
( ( ! [X: $i] :
( ! [Y: $i,Z: $i] :
( ~ ( member @ Z @ ( union @ X @ Y ) )
| ( member @ Z @ X )
| ( member @ Z @ Y ) )
& ! [Y: $i,Z: $i] :
( ~ ( member @ Z @ X )
| ( member @ Z @ ( union @ X @ Y ) ) )
& ! [Y: $i,Z: $i] :
( ~ ( member @ Z @ Y )
| ( member @ Z @ ( union @ X @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[68]) ).
thf(116,plain,
( ( ! [U: $i,V: $i] :
( ! [W: $i,X: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ V @ U ) @ W ) @ X )
| ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( flip @ X ) ) )
& ! [W: $i] :
( ! [X: $i] :
~ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( flip @ X ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
& ! [W: $i,X: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( flip @ X ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ V @ U ) @ W ) @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[70]) ).
thf(117,plain,
( ( ! [X: $i,U: $i] :
( ! [V: $i,W: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ V @ W ) @ U ) @ X )
| ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( rotate @ X ) ) )
& ! [V: $i,W: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( rotate @ X ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
& ! [V: $i,W: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( rotate @ X ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ V @ W ) @ U ) @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[72]) ).
thf(118,plain,
( ( ! [X: $i,Z: $i] :
( ( ( restrict @ X @ ( singleton @ Z ) @ universal_class )
= null_class )
| ~ ( member @ Z @ universal_class )
| ( member @ Z @ ( domain_of @ X ) ) )
& ! [X: $i,Z: $i] :
( ~ ( member @ Z @ ( domain_of @ X ) )
| ( ( restrict @ X @ ( singleton @ Z ) @ universal_class )
!= null_class ) )
& ! [X: $i,Z: $i] :
( ~ ( member @ Z @ ( domain_of @ X ) )
| ( member @ Z @ universal_class ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[73]) ).
thf(119,plain,
( ( ! [X: $i,Z: $i] :
( ~ ( member @ Z @ universal_class )
| ( member @ Z @ X )
| ( member @ Z @ ( complement @ X ) ) )
& ! [X: $i,Z: $i] :
( ~ ( member @ Z @ ( complement @ X ) )
| ( member @ Z @ universal_class ) )
& ! [X: $i,Z: $i] :
( ~ ( member @ Z @ ( complement @ X ) )
| ~ ( member @ Z @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[76]) ).
thf(120,plain,
( ( ! [X: $i] :
( ! [Y: $i,Z: $i] :
( ~ ( member @ Z @ X )
| ~ ( member @ Z @ Y )
| ( member @ Z @ ( intersection @ X @ Y ) ) )
& ! [Y: $i,Z: $i] :
( ~ ( member @ Z @ ( intersection @ X @ Y ) )
| ( member @ Z @ X ) )
& ! [Y: $i,Z: $i] :
( ~ ( member @ Z @ ( intersection @ X @ Y ) )
| ( member @ Z @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[77]) ).
thf(121,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( member @ Y @ universal_class )
| ~ ( member @ X @ Y )
| ( member @ ( ordered_pair @ X @ Y ) @ element_relation ) )
& ! [X: $i,Y: $i] :
( ~ ( member @ ( ordered_pair @ X @ Y ) @ element_relation )
| ( member @ Y @ universal_class ) )
& ! [X: $i,Y: $i] :
( ~ ( member @ ( ordered_pair @ X @ Y ) @ element_relation )
| ( member @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[79]) ).
thf(122,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( member @ Z @ ( cross_product @ X @ Y ) )
| ( Z
= ( ordered_pair @ ( first @ Z ) @ ( second @ Z ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[80]) ).
thf(123,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( member @ X @ universal_class )
| ~ ( member @ Y @ universal_class )
| ( ( first @ ( ordered_pair @ X @ Y ) )
= X ) )
& ! [X: $i,Y: $i] :
( ~ ( member @ X @ universal_class )
| ~ ( member @ Y @ universal_class )
| ( ( second @ ( ordered_pair @ X @ Y ) )
= Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[81]) ).
thf(124,plain,
( ( ! [U: $i,V: $i] :
( ! [X: $i,Y: $i] :
( ~ ( member @ U @ X )
| ~ ( member @ V @ Y )
| ( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) ) )
& ! [X: $i] :
( ! [Y: $i] :
~ ( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) )
| ( member @ U @ X ) )
& ! [X: $i,Y: $i] :
( ~ ( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) )
| ( member @ V @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[82]) ).
thf(125,plain,
( ( ! [U: $i] :
( ! [X: $i] :
( ~ ( member @ U @ universal_class )
| ( U != X )
| ! [Y: $i] : ( member @ U @ ( unordered_pair @ X @ Y ) ) )
& ! [X: $i,Y: $i] :
( ~ ( member @ U @ universal_class )
| ( U != Y )
| ( member @ U @ ( unordered_pair @ X @ Y ) ) )
& ( ! [X: $i,Y: $i] :
~ ( member @ U @ ( unordered_pair @ X @ Y ) )
| ( member @ U @ universal_class ) )
& ! [X: $i,Y: $i] :
( ~ ( member @ U @ ( unordered_pair @ X @ Y ) )
| ( U = X )
| ( U = Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[86]) ).
thf(126,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( subclass @ X @ Y )
| ~ ( subclass @ Y @ X )
| ( X = Y ) )
& ! [X: $i,Y: $i] :
( ( X != Y )
| ( subclass @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( X != Y )
| ( subclass @ Y @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[87]) ).
thf(127,plain,
( ( ! [X: $i,Y: $i] :
( ( ( member @ ( sK10_U @ Y @ X ) @ X )
& ~ ( member @ ( sK10_U @ Y @ X ) @ Y ) )
| ( subclass @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( subclass @ X @ Y )
| ! [U: $i] :
( ~ ( member @ U @ X )
| ( member @ U @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[89]) ).
thf(128,plain,
( ( ! [X: $i,Y: $i] :
( ( ( member @ ( sK10_U @ Y @ X ) @ X )
& ~ ( member @ ( sK10_U @ Y @ X ) @ Y ) )
| ( subclass @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( subclass @ X @ Y )
| ! [U: $i] :
( ~ ( member @ U @ X )
| ( member @ U @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(129,plain,
( ( ! [X: $i] : ( subclass @ X @ universal_class ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(130,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( subclass @ X @ Y )
| ~ ( subclass @ Y @ X )
| ( X = Y ) )
& ! [X: $i,Y: $i] :
( ( X != Y )
| ( subclass @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( X != Y )
| ( subclass @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(131,plain,
( ( ! [U: $i] :
( ! [X: $i] :
( ~ ( member @ U @ universal_class )
| ( U != X )
| ! [Y: $i] : ( member @ U @ ( unordered_pair @ X @ Y ) ) )
& ! [X: $i,Y: $i] :
( ~ ( member @ U @ universal_class )
| ( U != Y )
| ( member @ U @ ( unordered_pair @ X @ Y ) ) )
& ( ! [X: $i,Y: $i] :
~ ( member @ U @ ( unordered_pair @ X @ Y ) )
| ( member @ U @ universal_class ) )
& ! [X: $i,Y: $i] :
( ~ ( member @ U @ ( unordered_pair @ X @ Y ) )
| ( U = X )
| ( U = Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(132,plain,
( ( ! [X: $i,Y: $i] : ( member @ ( unordered_pair @ X @ Y ) @ universal_class ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(133,plain,
( ( ! [X: $i] :
( ( singleton @ X )
= ( unordered_pair @ X @ X ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(134,plain,
( ( ! [X: $i,Y: $i] :
( ( ordered_pair @ X @ Y )
= ( unordered_pair @ ( singleton @ X ) @ ( unordered_pair @ X @ ( singleton @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(135,plain,
( ( ! [U: $i,V: $i] :
( ! [X: $i,Y: $i] :
( ~ ( member @ U @ X )
| ~ ( member @ V @ Y )
| ( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) ) )
& ! [X: $i] :
( ! [Y: $i] :
~ ( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) )
| ( member @ U @ X ) )
& ! [X: $i,Y: $i] :
( ~ ( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) )
| ( member @ V @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(136,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( member @ X @ universal_class )
| ~ ( member @ Y @ universal_class )
| ( ( first @ ( ordered_pair @ X @ Y ) )
= X ) )
& ! [X: $i,Y: $i] :
( ~ ( member @ X @ universal_class )
| ~ ( member @ Y @ universal_class )
| ( ( second @ ( ordered_pair @ X @ Y ) )
= Y ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(137,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( member @ Z @ ( cross_product @ X @ Y ) )
| ( Z
= ( ordered_pair @ ( first @ Z ) @ ( second @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(138,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( member @ Y @ universal_class )
| ~ ( member @ X @ Y )
| ( member @ ( ordered_pair @ X @ Y ) @ element_relation ) )
& ! [X: $i,Y: $i] :
( ~ ( member @ ( ordered_pair @ X @ Y ) @ element_relation )
| ( member @ Y @ universal_class ) )
& ! [X: $i,Y: $i] :
( ~ ( member @ ( ordered_pair @ X @ Y ) @ element_relation )
| ( member @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(139,plain,
( ( subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(140,plain,
( ( ! [X: $i] :
( ! [Y: $i,Z: $i] :
( ~ ( member @ Z @ X )
| ~ ( member @ Z @ Y )
| ( member @ Z @ ( intersection @ X @ Y ) ) )
& ! [Y: $i,Z: $i] :
( ~ ( member @ Z @ ( intersection @ X @ Y ) )
| ( member @ Z @ X ) )
& ! [Y: $i,Z: $i] :
( ~ ( member @ Z @ ( intersection @ X @ Y ) )
| ( member @ Z @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(141,plain,
( ( ! [X: $i,Z: $i] :
( ~ ( member @ Z @ universal_class )
| ( member @ Z @ X )
| ( member @ Z @ ( complement @ X ) ) )
& ! [X: $i,Z: $i] :
( ~ ( member @ Z @ ( complement @ X ) )
| ( member @ Z @ universal_class ) )
& ! [X: $i,Z: $i] :
( ~ ( member @ Z @ ( complement @ X ) )
| ~ ( member @ Z @ X ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(142,plain,
( ( ! [X: $i,XR: $i,Y: $i] :
( ( restrict @ XR @ X @ Y )
= ( intersection @ XR @ ( cross_product @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(143,plain,
( ( ! [X: $i] :
~ ( member @ X @ null_class ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(144,plain,
( ( ! [X: $i,Z: $i] :
( ( ( restrict @ X @ ( singleton @ Z ) @ universal_class )
= null_class )
| ~ ( member @ Z @ universal_class )
| ( member @ Z @ ( domain_of @ X ) ) )
& ! [X: $i,Z: $i] :
( ~ ( member @ Z @ ( domain_of @ X ) )
| ( ( restrict @ X @ ( singleton @ Z ) @ universal_class )
!= null_class ) )
& ! [X: $i,Z: $i] :
( ~ ( member @ Z @ ( domain_of @ X ) )
| ( member @ Z @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(145,plain,
( ( ! [X: $i,U: $i] :
( ! [V: $i,W: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ V @ W ) @ U ) @ X )
| ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( rotate @ X ) ) )
& ! [V: $i,W: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( rotate @ X ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
& ! [V: $i,W: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( rotate @ X ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ V @ W ) @ U ) @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(146,plain,
( ( ! [X: $i] : ( subclass @ ( rotate @ X ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(147,plain,
( ( ! [U: $i,V: $i] :
( ! [W: $i,X: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ V @ U ) @ W ) @ X )
| ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( flip @ X ) ) )
& ! [W: $i] :
( ! [X: $i] :
~ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( flip @ X ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
& ! [W: $i,X: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( flip @ X ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ V @ U ) @ W ) @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(148,plain,
( ( ! [X: $i] : ( subclass @ ( flip @ X ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(149,plain,
( ( ! [X: $i] :
( ! [Y: $i,Z: $i] :
( ~ ( member @ Z @ ( union @ X @ Y ) )
| ( member @ Z @ X )
| ( member @ Z @ Y ) )
& ! [Y: $i,Z: $i] :
( ~ ( member @ Z @ X )
| ( member @ Z @ ( union @ X @ Y ) ) )
& ! [Y: $i,Z: $i] :
( ~ ( member @ Z @ Y )
| ( member @ Z @ ( union @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(150,plain,
( ( ! [X: $i] :
( ( successor @ X )
= ( union @ X @ ( singleton @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(151,plain,
( ( subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(152,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( member @ X @ universal_class )
| ~ ( member @ Y @ universal_class )
| ( ( successor @ X )
!= Y )
| ( member @ ( ordered_pair @ X @ Y ) @ successor_relation ) )
& ! [X: $i] :
( ! [Y: $i] :
~ ( member @ ( ordered_pair @ X @ Y ) @ successor_relation )
| ( member @ X @ universal_class ) )
& ! [X: $i,Y: $i] :
( ~ ( member @ ( ordered_pair @ X @ Y ) @ successor_relation )
| ( member @ Y @ universal_class ) )
& ! [X: $i,Y: $i] :
( ~ ( member @ ( ordered_pair @ X @ Y ) @ successor_relation )
| ( ( successor @ X )
= Y ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(153,plain,
( ( ! [Y: $i] :
( ( inverse @ Y )
= ( domain_of @ ( flip @ ( cross_product @ Y @ universal_class ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(154,plain,
( ( ! [Z: $i] :
( ( range_of @ Z )
= ( domain_of @ ( inverse @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(155,plain,
( ( ! [X: $i,XR: $i] :
( ( image @ XR @ X )
= ( range_of @ ( restrict @ XR @ X @ universal_class ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(156,plain,
( ( ! [X: $i] :
( ~ ( member @ null_class @ X )
| ~ ( subclass @ ( image @ successor_relation @ X ) @ X )
| ( inductive @ X ) )
& ! [X: $i] :
( ~ ( inductive @ X )
| ( member @ null_class @ X ) )
& ! [X: $i] :
( ~ ( inductive @ X )
| ( subclass @ ( image @ successor_relation @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(157,plain,
( ( ! [SY93: $i] :
( ~ ( inductive @ SY93 )
| ( subclass @ sK9_X @ SY93 ) )
& ( inductive @ sK9_X )
& ( member @ sK9_X @ universal_class ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(158,plain,
( ( ! [U: $i,X: $i] :
( ! [Y: $i] :
( ~ ( member @ U @ Y )
| ~ ( member @ Y @ X ) )
| ( member @ U @ ( sum_class @ X ) ) )
& ! [U: $i,X: $i] :
( ~ ( member @ U @ ( sum_class @ X ) )
| ( ( member @ U @ ( sK8_Y @ X @ U ) )
& ( member @ ( sK8_Y @ X @ U ) @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(159,plain,
( ( ! [X: $i] :
( ~ ( member @ X @ universal_class )
| ( member @ ( sum_class @ X ) @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(160,plain,
( ( ! [U: $i,X: $i] :
( ~ ( member @ U @ universal_class )
| ~ ( subclass @ U @ X )
| ( member @ U @ ( power_class @ X ) ) )
& ! [U: $i] :
( ! [X: $i] :
~ ( member @ U @ ( power_class @ X ) )
| ( member @ U @ universal_class ) )
& ! [U: $i,X: $i] :
( ~ ( member @ U @ ( power_class @ X ) )
| ( subclass @ U @ X ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(161,plain,
( ( ! [U: $i] :
( ~ ( member @ U @ universal_class )
| ( member @ ( power_class @ U ) @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(162,plain,
( ( ! [XR: $i,YR: $i] : ( subclass @ ( compose @ YR @ XR ) @ ( cross_product @ universal_class @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(163,plain,
( ( ! [XR: $i,YR: $i] :
( ! [U: $i,V: $i] :
( ~ ( member @ U @ universal_class )
| ~ ( member @ V @ ( image @ YR @ ( image @ XR @ ( singleton @ U ) ) ) )
| ( member @ ( ordered_pair @ U @ V ) @ ( compose @ YR @ XR ) ) )
& ! [U: $i] :
( ! [V: $i] :
~ ( member @ ( ordered_pair @ U @ V ) @ ( compose @ YR @ XR ) )
| ( member @ U @ universal_class ) )
& ! [U: $i,V: $i] :
( ~ ( member @ ( ordered_pair @ U @ V ) @ ( compose @ YR @ XR ) )
| ( member @ V @ ( image @ YR @ ( image @ XR @ ( singleton @ U ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(164,plain,
( ( ! [Z: $i] :
( ! [X: $i] :
( ( Z
!= ( ordered_pair @ X @ X ) )
| ~ ( member @ X @ universal_class ) )
| ( member @ Z @ identity_relation ) )
& ! [Z: $i] :
( ~ ( member @ Z @ identity_relation )
| ( ( Z
= ( ordered_pair @ ( sK7_X @ Z ) @ ( sK7_X @ Z ) ) )
& ( member @ ( sK7_X @ Z ) @ universal_class ) ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(165,plain,
( ( ! [XF: $i] :
( ~ ( subclass @ XF @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ XF @ ( inverse @ XF ) ) @ identity_relation )
| ( function @ XF ) )
& ! [XF: $i] :
( ~ ( function @ XF )
| ( subclass @ XF @ ( cross_product @ universal_class @ universal_class ) ) )
& ! [XF: $i] :
( ~ ( function @ XF )
| ( subclass @ ( compose @ XF @ ( inverse @ XF ) ) @ identity_relation ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(166,plain,
( ( ! [X: $i,XF: $i] :
( ~ ( function @ XF )
| ~ ( member @ X @ universal_class )
| ( member @ ( image @ XF @ X ) @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(167,plain,
( ( ! [X: $i,Y: $i] :
( ( ( member @ ( sK6_U @ Y @ X ) @ X )
& ( member @ ( sK6_U @ Y @ X ) @ Y ) )
| ( disjoint @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( disjoint @ X @ Y )
| ! [U: $i] :
( ~ ( member @ U @ X )
| ~ ( member @ U @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(168,plain,
( ( ! [X: $i] :
( ( X = null_class )
| ( ( member @ ( sK5_U @ X ) @ universal_class )
& ( member @ ( sK5_U @ X ) @ X )
& ( disjoint @ ( sK5_U @ X ) @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(169,plain,
( ( ! [XF: $i,Y: $i] :
( ( apply @ XF @ Y )
= ( sum_class @ ( image @ XF @ ( singleton @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(170,plain,
( ( ! [SY92: $i] :
( ~ ( member @ SY92 @ universal_class )
| ( SY92 = null_class )
| ( member @ ( apply @ sK4_XF @ SY92 ) @ SY92 ) )
& ( function @ sK4_XF ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(171,plain,
( ( sK3_SY91
= ( ordered_pair @ sK1_U @ sK2_SY89 ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(172,plain,
( ( member @ sK2_SY89 @ universal_class )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(173,plain,
( ( member @ sK1_U @ universal_class )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(174,plain,
( ( ( ( first @ sK3_SY91 )
!= sK1_U ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(175,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ ( union @ SX0 @ SX1 ) )
| ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ ( union @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ ( union @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(176,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( member @ SX2 @ universal_class )
| ~ ( member @ SX3 @ ( image @ SX1 @ ( image @ SX0 @ ( singleton @ SX2 ) ) ) )
| ( member @ ( ordered_pair @ SX2 @ SX3 ) @ ( compose @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( member @ ( ordered_pair @ SX2 @ SX3 ) @ ( compose @ SX1 @ SX0 ) )
| ( member @ SX2 @ universal_class ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( member @ ( ordered_pair @ SX2 @ SX3 ) @ ( compose @ SX1 @ SX0 ) )
| ( member @ SX3 @ ( image @ SX1 @ ( image @ SX0 @ ( singleton @ SX2 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(177,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SX1 @ SX0 ) @ SX2 ) @ SX3 )
| ( member @ ( ordered_pair @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 ) @ ( flip @ SX3 ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( member @ ( ordered_pair @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 ) @ ( flip @ SX3 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 ) @ ( flip @ SX3 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SX1 @ SX0 ) @ SX2 ) @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(178,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ universal_class )
| ( SX0 = null_class )
| ( member @ ( apply @ sK4_XF @ SX0 ) @ SX0 ) )
| ~ ( function @ sK4_XF ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(179,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ universal_class )
| ~ ( member @ SX0 @ SX1 )
| ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation )
| ( member @ SX1 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation )
| ( member @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(180,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX0 @ SX2 )
| ~ ( member @ SX2 @ SX1 ) )
| ( member @ SX0 @ ( sum_class @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( sum_class @ SX1 ) )
| ~ ( ~ ( member @ SX0 @ ( sK8_Y @ SX1 @ SX0 ) )
| ~ ( member @ ( sK8_Y @ SX1 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(181,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( subclass @ SX0 @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ SX0 @ ( inverse @ SX0 ) ) @ identity_relation )
| ( function @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ( subclass @ SX0 @ ( cross_product @ universal_class @ universal_class ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ( subclass @ ( compose @ SX0 @ ( inverse @ SX0 ) ) @ identity_relation ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(182,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( member @ null_class @ SX0 )
| ~ ( subclass @ ( image @ successor_relation @ SX0 ) @ SX0 )
| ( inductive @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( inductive @ SX0 )
| ( member @ null_class @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( inductive @ SX0 )
| ( subclass @ ( image @ successor_relation @ SX0 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(183,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK6_U @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK6_U @ SX1 @ SX0 ) @ SX1 ) )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(184,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK10_U @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK10_U @ SX1 @ SX0 ) @ SX1 ) )
| ( subclass @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subclass @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(185,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( SX0
!= ( ordered_pair @ SX1 @ SX1 ) )
| ~ ( member @ SX1 @ universal_class ) )
| ( member @ SX0 @ identity_relation ) )
| ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ identity_relation )
| ~ ( ( SX0
!= ( ordered_pair @ ( sK7_X @ SX0 ) @ ( sK7_X @ SX0 ) ) )
| ~ ( member @ ( sK7_X @ SX0 ) @ universal_class ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(186,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subclass @ SX0 @ SX1 )
| ~ ( subclass @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subclass @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subclass @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(187,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ universal_class )
| ~ ( member @ SX1 @ universal_class )
| ( ( first @ ( ordered_pair @ SX0 @ SX1 ) )
= SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ universal_class )
| ~ ( member @ SX1 @ universal_class )
| ( ( second @ ( ordered_pair @ SX0 @ SX1 ) )
= SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(188,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( inductive @ SX0 )
| ( subclass @ sK9_X @ SX0 ) )
| ~ ~ ( ~ ( inductive @ sK9_X )
| ~ ( member @ sK9_X @ universal_class ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(189,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( restrict @ SX0 @ ( singleton @ SX1 ) @ universal_class )
= null_class )
| ~ ( member @ SX1 @ universal_class )
| ( member @ SX1 @ ( domain_of @ SX0 ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( domain_of @ SX0 ) )
| ( ( restrict @ SX0 @ ( singleton @ SX1 ) @ universal_class )
!= null_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( domain_of @ SX0 ) )
| ( member @ SX1 @ universal_class ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(190,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( member @ SX0 @ SX2 )
| ~ ( member @ SX1 @ SX3 )
| ( member @ ( ordered_pair @ SX0 @ SX1 ) @ ( cross_product @ SX2 @ SX3 ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ ( cross_product @ SX2 @ SX3 ) )
| ( member @ SX0 @ SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ ( cross_product @ SX2 @ SX3 ) )
| ( member @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(191,plain,
( ( ! [SX0: $i] :
~ ( ~ ~ ( ~ ! [SX1: $i] :
( ~ ( member @ SX0 @ universal_class )
| ( SX0 != SX1 )
| ! [SX2: $i] : ( member @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ universal_class )
| ( SX0 != SX2 )
| ( member @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) ) ) )
| ~ ~ ( ~ ( ! [SX1: $i,SX2: $i] :
~ ( member @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) )
| ( member @ SX0 @ universal_class ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) )
| ( SX0 = SX1 )
| ( SX0 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(192,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ ( intersection @ SX0 @ SX1 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ ( intersection @ SX0 @ SX1 ) )
| ( member @ SX2 @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ ( intersection @ SX0 @ SX1 ) )
| ( member @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(193,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ universal_class )
| ~ ( subclass @ SX0 @ SX1 )
| ( member @ SX0 @ ( power_class @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( member @ SX0 @ ( power_class @ SX1 ) )
| ( member @ SX0 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( power_class @ SX1 ) )
| ( subclass @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(194,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ universal_class )
| ~ ( member @ SX1 @ universal_class )
| ( ( successor @ SX0 )
!= SX1 )
| ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX0 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX1 @ universal_class ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( ( successor @ SX0 )
= SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(195,plain,
( ( ! [SX0: $i] :
( ( SX0 = null_class )
| ~ ( ~ ~ ( ~ ( member @ ( sK5_U @ SX0 ) @ universal_class )
| ~ ( member @ ( sK5_U @ SX0 ) @ SX0 ) )
| ~ ( disjoint @ ( sK5_U @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(196,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ universal_class )
| ( member @ SX1 @ SX0 )
| ( member @ SX1 @ ( complement @ SX0 ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( complement @ SX0 ) )
| ( member @ SX1 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( complement @ SX0 ) )
| ~ ( member @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(197,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SX1 @ SX2 ) @ SX3 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) @ SX0 )
| ( member @ ( ordered_pair @ ( ordered_pair @ SX1 @ SX2 ) @ SX3 ) @ ( rotate @ SX0 ) ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SX1 @ SX2 ) @ SX3 ) @ ( rotate @ SX0 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SX1 @ SX2 ) @ SX3 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SX1 @ SX2 ) @ SX3 ) @ ( rotate @ SX0 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(198,plain,
! [SV1: $i] :
( ( subclass @ SV1 @ universal_class )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(199,plain,
! [SV2: $i] :
( ( ! [SY94: $i] : ( member @ ( unordered_pair @ SV2 @ SY94 ) @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(200,plain,
! [SV3: $i] :
( ( ( singleton @ SV3 )
= ( unordered_pair @ SV3 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(201,plain,
! [SV4: $i] :
( ( ! [SY95: $i] :
( ( ordered_pair @ SV4 @ SY95 )
= ( unordered_pair @ ( singleton @ SV4 ) @ ( unordered_pair @ SV4 @ ( singleton @ SY95 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(202,plain,
! [SV5: $i] :
( ( ! [SY96: $i,SY97: $i] :
( ~ ( member @ SY97 @ ( cross_product @ SV5 @ SY96 ) )
| ( SY97
= ( ordered_pair @ ( first @ SY97 ) @ ( second @ SY97 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(203,plain,
! [SV6: $i] :
( ( ! [SY98: $i,SY99: $i] :
( ( restrict @ SY98 @ SV6 @ SY99 )
= ( intersection @ SY98 @ ( cross_product @ SV6 @ SY99 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(204,plain,
! [SV7: $i] :
( ( ~ ( member @ SV7 @ null_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(205,plain,
! [SV8: $i] :
( ( subclass @ ( rotate @ SV8 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(206,plain,
! [SV9: $i] :
( ( subclass @ ( flip @ SV9 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(207,plain,
! [SV10: $i] :
( ( ( successor @ SV10 )
= ( union @ SV10 @ ( singleton @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(208,plain,
! [SV11: $i] :
( ( ( inverse @ SV11 )
= ( domain_of @ ( flip @ ( cross_product @ SV11 @ universal_class ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(209,plain,
! [SV12: $i] :
( ( ( range_of @ SV12 )
= ( domain_of @ ( inverse @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(210,plain,
! [SV13: $i] :
( ( ! [SY100: $i] :
( ( image @ SY100 @ SV13 )
= ( range_of @ ( restrict @ SY100 @ SV13 @ universal_class ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(211,plain,
! [SV14: $i] :
( ( ~ ( member @ SV14 @ universal_class )
| ( member @ ( sum_class @ SV14 ) @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(212,plain,
! [SV15: $i] :
( ( ~ ( member @ SV15 @ universal_class )
| ( member @ ( power_class @ SV15 ) @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(213,plain,
! [SV16: $i] :
( ( ! [SY101: $i] : ( subclass @ ( compose @ SY101 @ SV16 ) @ ( cross_product @ universal_class @ universal_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(214,plain,
! [SV17: $i] :
( ( ! [SY102: $i] :
( ~ ( function @ SY102 )
| ~ ( member @ SV17 @ universal_class )
| ( member @ ( image @ SY102 @ SV17 ) @ universal_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(215,plain,
! [SV18: $i] :
( ( ! [SY103: $i] :
( ( apply @ SV18 @ SY103 )
= ( sum_class @ ( image @ SV18 @ ( singleton @ SY103 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(216,plain,
( ( ( first @ sK3_SY91 )
= sK1_U )
= $false ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(217,plain,
! [SV19: $i] :
( ( ~ ( ~ ! [SY104: $i,SY105: $i] :
( ~ ( member @ SY105 @ ( union @ SV19 @ SY104 ) )
| ( member @ SY105 @ SV19 )
| ( member @ SY105 @ SY104 ) )
| ~ ~ ( ~ ! [SY106: $i,SY107: $i] :
( ~ ( member @ SY107 @ SV19 )
| ( member @ SY107 @ ( union @ SV19 @ SY106 ) ) )
| ~ ! [SY108: $i,SY109: $i] :
( ~ ( member @ SY109 @ SY108 )
| ( member @ SY109 @ ( union @ SV19 @ SY108 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(218,plain,
! [SV20: $i] :
( ( ! [SY110: $i] :
~ ( ~ ! [SY111: $i,SY112: $i] :
( ~ ( member @ SY111 @ universal_class )
| ~ ( member @ SY112 @ ( image @ SY110 @ ( image @ SV20 @ ( singleton @ SY111 ) ) ) )
| ( member @ ( ordered_pair @ SY111 @ SY112 ) @ ( compose @ SY110 @ SV20 ) ) )
| ~ ~ ( ~ ! [SY113: $i] :
( ! [SY114: $i] :
~ ( member @ ( ordered_pair @ SY113 @ SY114 ) @ ( compose @ SY110 @ SV20 ) )
| ( member @ SY113 @ universal_class ) )
| ~ ! [SY115: $i,SY116: $i] :
( ~ ( member @ ( ordered_pair @ SY115 @ SY116 ) @ ( compose @ SY110 @ SV20 ) )
| ( member @ SY116 @ ( image @ SY110 @ ( image @ SV20 @ ( singleton @ SY115 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(219,plain,
! [SV21: $i] :
( ( ! [SY117: $i] :
~ ( ~ ! [SY118: $i,SY119: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SY117 ) @ SY118 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SY117 @ SV21 ) @ SY118 ) @ SY119 )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SY117 ) @ SY118 ) @ ( flip @ SY119 ) ) )
| ~ ~ ( ~ ! [SY120: $i] :
( ! [SY121: $i] :
~ ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SY117 ) @ SY120 ) @ ( flip @ SY121 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SY117 ) @ SY120 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
| ~ ! [SY122: $i,SY123: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SY117 ) @ SY122 ) @ ( flip @ SY123 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SY117 @ SV21 ) @ SY122 ) @ SY123 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(220,plain,
( ( ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ universal_class )
| ( SX0 = null_class )
| ( member @ ( apply @ sK4_XF @ SX0 ) @ SX0 ) )
| ~ ( function @ sK4_XF ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(221,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ universal_class )
| ~ ( member @ SX0 @ SX1 )
| ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation )
| ( member @ SX1 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation )
| ( member @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(222,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX0 @ SX2 )
| ~ ( member @ SX2 @ SX1 ) )
| ( member @ SX0 @ ( sum_class @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( sum_class @ SX1 ) )
| ~ ( ~ ( member @ SX0 @ ( sK8_Y @ SX1 @ SX0 ) )
| ~ ( member @ ( sK8_Y @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(223,plain,
( ( ~ ! [SX0: $i] :
( ~ ( subclass @ SX0 @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ SX0 @ ( inverse @ SX0 ) ) @ identity_relation )
| ( function @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ( subclass @ SX0 @ ( cross_product @ universal_class @ universal_class ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ( subclass @ ( compose @ SX0 @ ( inverse @ SX0 ) ) @ identity_relation ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(224,plain,
( ( ~ ! [SX0: $i] :
( ~ ( member @ null_class @ SX0 )
| ~ ( subclass @ ( image @ successor_relation @ SX0 ) @ SX0 )
| ( inductive @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( inductive @ SX0 )
| ( member @ null_class @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( inductive @ SX0 )
| ( subclass @ ( image @ successor_relation @ SX0 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(225,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK6_U @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK6_U @ SX1 @ SX0 ) @ SX1 ) )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(226,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK10_U @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK10_U @ SX1 @ SX0 ) @ SX1 ) )
| ( subclass @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subclass @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(227,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( SX0
!= ( ordered_pair @ SX1 @ SX1 ) )
| ~ ( member @ SX1 @ universal_class ) )
| ( member @ SX0 @ identity_relation ) )
| ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ identity_relation )
| ~ ( ( SX0
!= ( ordered_pair @ ( sK7_X @ SX0 ) @ ( sK7_X @ SX0 ) ) )
| ~ ( member @ ( sK7_X @ SX0 ) @ universal_class ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(228,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subclass @ SX0 @ SX1 )
| ~ ( subclass @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subclass @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subclass @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(229,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ universal_class )
| ~ ( member @ SX1 @ universal_class )
| ( ( first @ ( ordered_pair @ SX0 @ SX1 ) )
= SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ universal_class )
| ~ ( member @ SX1 @ universal_class )
| ( ( second @ ( ordered_pair @ SX0 @ SX1 ) )
= SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(230,plain,
( ( ~ ! [SX0: $i] :
( ~ ( inductive @ SX0 )
| ( subclass @ sK9_X @ SX0 ) )
| ~ ~ ( ~ ( inductive @ sK9_X )
| ~ ( member @ sK9_X @ universal_class ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(231,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( restrict @ SX0 @ ( singleton @ SX1 ) @ universal_class )
= null_class )
| ~ ( member @ SX1 @ universal_class )
| ( member @ SX1 @ ( domain_of @ SX0 ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( domain_of @ SX0 ) )
| ( ( restrict @ SX0 @ ( singleton @ SX1 ) @ universal_class )
!= null_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( domain_of @ SX0 ) )
| ( member @ SX1 @ universal_class ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(232,plain,
! [SV22: $i] :
( ( ! [SY124: $i] :
~ ( ~ ! [SY125: $i,SY126: $i] :
( ~ ( member @ SV22 @ SY125 )
| ~ ( member @ SY124 @ SY126 )
| ( member @ ( ordered_pair @ SV22 @ SY124 ) @ ( cross_product @ SY125 @ SY126 ) ) )
| ~ ~ ( ~ ! [SY127: $i] :
( ! [SY128: $i] :
~ ( member @ ( ordered_pair @ SV22 @ SY124 ) @ ( cross_product @ SY127 @ SY128 ) )
| ( member @ SV22 @ SY127 ) )
| ~ ! [SY129: $i,SY130: $i] :
( ~ ( member @ ( ordered_pair @ SV22 @ SY124 ) @ ( cross_product @ SY129 @ SY130 ) )
| ( member @ SY124 @ SY130 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(233,plain,
! [SV23: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY131: $i] :
( ~ ( member @ SV23 @ universal_class )
| ( SV23 != SY131 )
| ! [SY132: $i] : ( member @ SV23 @ ( unordered_pair @ SY131 @ SY132 ) ) )
| ~ ! [SY133: $i,SY134: $i] :
( ~ ( member @ SV23 @ universal_class )
| ( SV23 != SY134 )
| ( member @ SV23 @ ( unordered_pair @ SY133 @ SY134 ) ) ) )
| ~ ~ ( ~ ( ! [SY135: $i,SY136: $i] :
~ ( member @ SV23 @ ( unordered_pair @ SY135 @ SY136 ) )
| ( member @ SV23 @ universal_class ) )
| ~ ! [SY137: $i,SY138: $i] :
( ~ ( member @ SV23 @ ( unordered_pair @ SY137 @ SY138 ) )
| ( SV23 = SY137 )
| ( SV23 = SY138 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(234,plain,
! [SV24: $i] :
( ( ~ ( ~ ! [SY139: $i,SY140: $i] :
( ~ ( member @ SY140 @ SV24 )
| ~ ( member @ SY140 @ SY139 )
| ( member @ SY140 @ ( intersection @ SV24 @ SY139 ) ) )
| ~ ~ ( ~ ! [SY141: $i,SY142: $i] :
( ~ ( member @ SY142 @ ( intersection @ SV24 @ SY141 ) )
| ( member @ SY142 @ SV24 ) )
| ~ ! [SY143: $i,SY144: $i] :
( ~ ( member @ SY144 @ ( intersection @ SV24 @ SY143 ) )
| ( member @ SY144 @ SY143 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(235,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ universal_class )
| ~ ( subclass @ SX0 @ SX1 )
| ( member @ SX0 @ ( power_class @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( member @ SX0 @ ( power_class @ SX1 ) )
| ( member @ SX0 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( power_class @ SX1 ) )
| ( subclass @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(236,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ universal_class )
| ~ ( member @ SX1 @ universal_class )
| ( ( successor @ SX0 )
!= SX1 )
| ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX0 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX1 @ universal_class ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( ( successor @ SX0 )
= SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(237,plain,
! [SV25: $i] :
( ( ( SV25 = null_class )
| ~ ( ~ ~ ( ~ ( member @ ( sK5_U @ SV25 ) @ universal_class )
| ~ ( member @ ( sK5_U @ SV25 ) @ SV25 ) )
| ~ ( disjoint @ ( sK5_U @ SV25 ) @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(238,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ universal_class )
| ( member @ SX1 @ SX0 )
| ( member @ SX1 @ ( complement @ SX0 ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( complement @ SX0 ) )
| ( member @ SX1 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( complement @ SX0 ) )
| ~ ( member @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(239,plain,
! [SV26: $i] :
( ( ! [SY145: $i] :
~ ( ~ ! [SY146: $i,SY147: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SY145 @ SY146 ) @ SY147 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SY146 @ SY147 ) @ SY145 ) @ SV26 )
| ( member @ ( ordered_pair @ ( ordered_pair @ SY145 @ SY146 ) @ SY147 ) @ ( rotate @ SV26 ) ) )
| ~ ~ ( ~ ! [SY148: $i,SY149: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SY145 @ SY148 ) @ SY149 ) @ ( rotate @ SV26 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SY145 @ SY148 ) @ SY149 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
| ~ ! [SY150: $i,SY151: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SY145 @ SY150 ) @ SY151 ) @ ( rotate @ SV26 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SY150 @ SY151 ) @ SY145 ) @ SV26 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(240,plain,
! [SV27: $i,SV2: $i] :
( ( member @ ( unordered_pair @ SV2 @ SV27 ) @ universal_class )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(241,plain,
! [SV28: $i,SV4: $i] :
( ( ( ordered_pair @ SV4 @ SV28 )
= ( unordered_pair @ ( singleton @ SV4 ) @ ( unordered_pair @ SV4 @ ( singleton @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(242,plain,
! [SV29: $i,SV5: $i] :
( ( ! [SY152: $i] :
( ~ ( member @ SY152 @ ( cross_product @ SV5 @ SV29 ) )
| ( SY152
= ( ordered_pair @ ( first @ SY152 ) @ ( second @ SY152 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(243,plain,
! [SV6: $i,SV30: $i] :
( ( ! [SY153: $i] :
( ( restrict @ SV30 @ SV6 @ SY153 )
= ( intersection @ SV30 @ ( cross_product @ SV6 @ SY153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(244,plain,
! [SV7: $i] :
( ( member @ SV7 @ null_class )
= $false ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(245,plain,
! [SV13: $i,SV31: $i] :
( ( ( image @ SV31 @ SV13 )
= ( range_of @ ( restrict @ SV31 @ SV13 @ universal_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(246,plain,
! [SV14: $i] :
( ( ( ~ ( member @ SV14 @ universal_class ) )
= $true )
| ( ( member @ ( sum_class @ SV14 ) @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(247,plain,
! [SV15: $i] :
( ( ( ~ ( member @ SV15 @ universal_class ) )
= $true )
| ( ( member @ ( power_class @ SV15 ) @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(248,plain,
! [SV16: $i,SV32: $i] :
( ( subclass @ ( compose @ SV32 @ SV16 ) @ ( cross_product @ universal_class @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(249,plain,
! [SV17: $i,SV33: $i] :
( ( ~ ( function @ SV33 )
| ~ ( member @ SV17 @ universal_class )
| ( member @ ( image @ SV33 @ SV17 ) @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(250,plain,
! [SV34: $i,SV18: $i] :
( ( ( apply @ SV18 @ SV34 )
= ( sum_class @ ( image @ SV18 @ ( singleton @ SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(251,plain,
! [SV19: $i] :
( ( ~ ! [SY104: $i,SY105: $i] :
( ~ ( member @ SY105 @ ( union @ SV19 @ SY104 ) )
| ( member @ SY105 @ SV19 )
| ( member @ SY105 @ SY104 ) )
| ~ ~ ( ~ ! [SY106: $i,SY107: $i] :
( ~ ( member @ SY107 @ SV19 )
| ( member @ SY107 @ ( union @ SV19 @ SY106 ) ) )
| ~ ! [SY108: $i,SY109: $i] :
( ~ ( member @ SY109 @ SY108 )
| ( member @ SY109 @ ( union @ SV19 @ SY108 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(252,plain,
! [SV20: $i,SV35: $i] :
( ( ~ ( ~ ! [SY154: $i,SY155: $i] :
( ~ ( member @ SY154 @ universal_class )
| ~ ( member @ SY155 @ ( image @ SV35 @ ( image @ SV20 @ ( singleton @ SY154 ) ) ) )
| ( member @ ( ordered_pair @ SY154 @ SY155 ) @ ( compose @ SV35 @ SV20 ) ) )
| ~ ~ ( ~ ! [SY156: $i] :
( ! [SY157: $i] :
~ ( member @ ( ordered_pair @ SY156 @ SY157 ) @ ( compose @ SV35 @ SV20 ) )
| ( member @ SY156 @ universal_class ) )
| ~ ! [SY158: $i,SY159: $i] :
( ~ ( member @ ( ordered_pair @ SY158 @ SY159 ) @ ( compose @ SV35 @ SV20 ) )
| ( member @ SY159 @ ( image @ SV35 @ ( image @ SV20 @ ( singleton @ SY158 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(253,plain,
! [SV36: $i,SV21: $i] :
( ( ~ ( ~ ! [SY160: $i,SY161: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SY160 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV36 @ SV21 ) @ SY160 ) @ SY161 )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SY160 ) @ ( flip @ SY161 ) ) )
| ~ ~ ( ~ ! [SY162: $i] :
( ! [SY163: $i] :
~ ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SY162 ) @ ( flip @ SY163 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SY162 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
| ~ ! [SY164: $i,SY165: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SY164 ) @ ( flip @ SY165 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV36 @ SV21 ) @ SY164 ) @ SY165 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(254,plain,
( ( ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ universal_class )
| ( SX0 = null_class )
| ( member @ ( apply @ sK4_XF @ SX0 ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[220]) ).
thf(255,plain,
( ( ~ ( function @ sK4_XF ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[220]) ).
thf(256,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ universal_class )
| ~ ( member @ SX0 @ SX1 )
| ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[221]) ).
thf(257,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation )
| ( member @ SX1 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation )
| ( member @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[221]) ).
thf(258,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX0 @ SX2 )
| ~ ( member @ SX2 @ SX1 ) )
| ( member @ SX0 @ ( sum_class @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(259,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( sum_class @ SX1 ) )
| ~ ( ~ ( member @ SX0 @ ( sK8_Y @ SX1 @ SX0 ) )
| ~ ( member @ ( sK8_Y @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(260,plain,
( ( ~ ! [SX0: $i] :
( ~ ( subclass @ SX0 @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ SX0 @ ( inverse @ SX0 ) ) @ identity_relation )
| ( function @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[223]) ).
thf(261,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ( subclass @ SX0 @ ( cross_product @ universal_class @ universal_class ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ( subclass @ ( compose @ SX0 @ ( inverse @ SX0 ) ) @ identity_relation ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[223]) ).
thf(262,plain,
( ( ~ ! [SX0: $i] :
( ~ ( member @ null_class @ SX0 )
| ~ ( subclass @ ( image @ successor_relation @ SX0 ) @ SX0 )
| ( inductive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(263,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( inductive @ SX0 )
| ( member @ null_class @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( inductive @ SX0 )
| ( subclass @ ( image @ successor_relation @ SX0 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(264,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK6_U @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK6_U @ SX1 @ SX0 ) @ SX1 ) )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[225]) ).
thf(265,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[225]) ).
thf(266,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK10_U @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK10_U @ SX1 @ SX0 ) @ SX1 ) )
| ( subclass @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[226]) ).
thf(267,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subclass @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[226]) ).
thf(268,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( SX0
!= ( ordered_pair @ SX1 @ SX1 ) )
| ~ ( member @ SX1 @ universal_class ) )
| ( member @ SX0 @ identity_relation ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[227]) ).
thf(269,plain,
( ( ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ identity_relation )
| ~ ( ( SX0
!= ( ordered_pair @ ( sK7_X @ SX0 ) @ ( sK7_X @ SX0 ) ) )
| ~ ( member @ ( sK7_X @ SX0 ) @ universal_class ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[227]) ).
thf(270,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subclass @ SX0 @ SX1 )
| ~ ( subclass @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[228]) ).
thf(271,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subclass @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subclass @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[228]) ).
thf(272,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ universal_class )
| ~ ( member @ SX1 @ universal_class )
| ( ( first @ ( ordered_pair @ SX0 @ SX1 ) )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[229]) ).
thf(273,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ universal_class )
| ~ ( member @ SX1 @ universal_class )
| ( ( second @ ( ordered_pair @ SX0 @ SX1 ) )
= SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[229]) ).
thf(274,plain,
( ( ~ ! [SX0: $i] :
( ~ ( inductive @ SX0 )
| ( subclass @ sK9_X @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[230]) ).
thf(275,plain,
( ( ~ ~ ( ~ ( inductive @ sK9_X )
| ~ ( member @ sK9_X @ universal_class ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[230]) ).
thf(276,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( restrict @ SX0 @ ( singleton @ SX1 ) @ universal_class )
= null_class )
| ~ ( member @ SX1 @ universal_class )
| ( member @ SX1 @ ( domain_of @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[231]) ).
thf(277,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( domain_of @ SX0 ) )
| ( ( restrict @ SX0 @ ( singleton @ SX1 ) @ universal_class )
!= null_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( domain_of @ SX0 ) )
| ( member @ SX1 @ universal_class ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[231]) ).
thf(278,plain,
! [SV37: $i,SV22: $i] :
( ( ~ ( ~ ! [SY166: $i,SY167: $i] :
( ~ ( member @ SV22 @ SY166 )
| ~ ( member @ SV37 @ SY167 )
| ( member @ ( ordered_pair @ SV22 @ SV37 ) @ ( cross_product @ SY166 @ SY167 ) ) )
| ~ ~ ( ~ ! [SY168: $i] :
( ! [SY169: $i] :
~ ( member @ ( ordered_pair @ SV22 @ SV37 ) @ ( cross_product @ SY168 @ SY169 ) )
| ( member @ SV22 @ SY168 ) )
| ~ ! [SY170: $i,SY171: $i] :
( ~ ( member @ ( ordered_pair @ SV22 @ SV37 ) @ ( cross_product @ SY170 @ SY171 ) )
| ( member @ SV37 @ SY171 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(279,plain,
! [SV23: $i] :
( ( ~ ~ ( ~ ! [SY131: $i] :
( ~ ( member @ SV23 @ universal_class )
| ( SV23 != SY131 )
| ! [SY132: $i] : ( member @ SV23 @ ( unordered_pair @ SY131 @ SY132 ) ) )
| ~ ! [SY133: $i,SY134: $i] :
( ~ ( member @ SV23 @ universal_class )
| ( SV23 != SY134 )
| ( member @ SV23 @ ( unordered_pair @ SY133 @ SY134 ) ) ) )
| ~ ~ ( ~ ( ! [SY135: $i,SY136: $i] :
~ ( member @ SV23 @ ( unordered_pair @ SY135 @ SY136 ) )
| ( member @ SV23 @ universal_class ) )
| ~ ! [SY137: $i,SY138: $i] :
( ~ ( member @ SV23 @ ( unordered_pair @ SY137 @ SY138 ) )
| ( SV23 = SY137 )
| ( SV23 = SY138 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(280,plain,
! [SV24: $i] :
( ( ~ ! [SY139: $i,SY140: $i] :
( ~ ( member @ SY140 @ SV24 )
| ~ ( member @ SY140 @ SY139 )
| ( member @ SY140 @ ( intersection @ SV24 @ SY139 ) ) )
| ~ ~ ( ~ ! [SY141: $i,SY142: $i] :
( ~ ( member @ SY142 @ ( intersection @ SV24 @ SY141 ) )
| ( member @ SY142 @ SV24 ) )
| ~ ! [SY143: $i,SY144: $i] :
( ~ ( member @ SY144 @ ( intersection @ SV24 @ SY143 ) )
| ( member @ SY144 @ SY143 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(281,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ universal_class )
| ~ ( subclass @ SX0 @ SX1 )
| ( member @ SX0 @ ( power_class @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(282,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( member @ SX0 @ ( power_class @ SX1 ) )
| ( member @ SX0 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( power_class @ SX1 ) )
| ( subclass @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(283,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ universal_class )
| ~ ( member @ SX1 @ universal_class )
| ( ( successor @ SX0 )
!= SX1 )
| ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(284,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX0 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX1 @ universal_class ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( ( successor @ SX0 )
= SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(285,plain,
! [SV25: $i] :
( ( ( SV25 = null_class )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( member @ ( sK5_U @ SV25 ) @ universal_class )
| ~ ( member @ ( sK5_U @ SV25 ) @ SV25 ) )
| ~ ( disjoint @ ( sK5_U @ SV25 ) @ SV25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[237]) ).
thf(286,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ universal_class )
| ( member @ SX1 @ SX0 )
| ( member @ SX1 @ ( complement @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[238]) ).
thf(287,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( complement @ SX0 ) )
| ( member @ SX1 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( complement @ SX0 ) )
| ~ ( member @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[238]) ).
thf(288,plain,
! [SV26: $i,SV38: $i] :
( ( ~ ( ~ ! [SY172: $i,SY173: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SY172 ) @ SY173 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SY172 @ SY173 ) @ SV38 ) @ SV26 )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SY172 ) @ SY173 ) @ ( rotate @ SV26 ) ) )
| ~ ~ ( ~ ! [SY174: $i,SY175: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SY174 ) @ SY175 ) @ ( rotate @ SV26 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SY174 ) @ SY175 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
| ~ ! [SY176: $i,SY177: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SY176 ) @ SY177 ) @ ( rotate @ SV26 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SY176 @ SY177 ) @ SV38 ) @ SV26 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(289,plain,
! [SV29: $i,SV5: $i,SV39: $i] :
( ( ~ ( member @ SV39 @ ( cross_product @ SV5 @ SV29 ) )
| ( SV39
= ( ordered_pair @ ( first @ SV39 ) @ ( second @ SV39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(290,plain,
! [SV40: $i,SV6: $i,SV30: $i] :
( ( ( restrict @ SV30 @ SV6 @ SV40 )
= ( intersection @ SV30 @ ( cross_product @ SV6 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(291,plain,
! [SV14: $i] :
( ( ( member @ SV14 @ universal_class )
= $false )
| ( ( member @ ( sum_class @ SV14 ) @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(292,plain,
! [SV15: $i] :
( ( ( member @ SV15 @ universal_class )
= $false )
| ( ( member @ ( power_class @ SV15 ) @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(293,plain,
! [SV17: $i,SV33: $i] :
( ( ( ~ ( function @ SV33 )
| ~ ( member @ SV17 @ universal_class ) )
= $true )
| ( ( member @ ( image @ SV33 @ SV17 ) @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[249]) ).
thf(294,plain,
! [SV19: $i] :
( ( ~ ! [SY104: $i,SY105: $i] :
( ~ ( member @ SY105 @ ( union @ SV19 @ SY104 ) )
| ( member @ SY105 @ SV19 )
| ( member @ SY105 @ SY104 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[251]) ).
thf(295,plain,
! [SV19: $i] :
( ( ~ ~ ( ~ ! [SY106: $i,SY107: $i] :
( ~ ( member @ SY107 @ SV19 )
| ( member @ SY107 @ ( union @ SV19 @ SY106 ) ) )
| ~ ! [SY108: $i,SY109: $i] :
( ~ ( member @ SY109 @ SY108 )
| ( member @ SY109 @ ( union @ SV19 @ SY108 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[251]) ).
thf(296,plain,
! [SV20: $i,SV35: $i] :
( ( ~ ! [SY154: $i,SY155: $i] :
( ~ ( member @ SY154 @ universal_class )
| ~ ( member @ SY155 @ ( image @ SV35 @ ( image @ SV20 @ ( singleton @ SY154 ) ) ) )
| ( member @ ( ordered_pair @ SY154 @ SY155 ) @ ( compose @ SV35 @ SV20 ) ) )
| ~ ~ ( ~ ! [SY156: $i] :
( ! [SY157: $i] :
~ ( member @ ( ordered_pair @ SY156 @ SY157 ) @ ( compose @ SV35 @ SV20 ) )
| ( member @ SY156 @ universal_class ) )
| ~ ! [SY158: $i,SY159: $i] :
( ~ ( member @ ( ordered_pair @ SY158 @ SY159 ) @ ( compose @ SV35 @ SV20 ) )
| ( member @ SY159 @ ( image @ SV35 @ ( image @ SV20 @ ( singleton @ SY158 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(297,plain,
! [SV36: $i,SV21: $i] :
( ( ~ ! [SY160: $i,SY161: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SY160 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV36 @ SV21 ) @ SY160 ) @ SY161 )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SY160 ) @ ( flip @ SY161 ) ) )
| ~ ~ ( ~ ! [SY162: $i] :
( ! [SY163: $i] :
~ ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SY162 ) @ ( flip @ SY163 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SY162 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
| ~ ! [SY164: $i,SY165: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SY164 ) @ ( flip @ SY165 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV36 @ SV21 ) @ SY164 ) @ SY165 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(298,plain,
( ( ! [SX0: $i] :
( ~ ( member @ SX0 @ universal_class )
| ( SX0 = null_class )
| ( member @ ( apply @ sK4_XF @ SX0 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(299,plain,
( ( function @ sK4_XF )
= $true ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(300,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ universal_class )
| ~ ( member @ SX0 @ SX1 )
| ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[256]) ).
thf(301,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation )
| ( member @ SX1 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation )
| ( member @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[257]) ).
thf(302,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX0 @ SX2 )
| ~ ( member @ SX2 @ SX1 ) )
| ( member @ SX0 @ ( sum_class @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[258]) ).
thf(303,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( sum_class @ SX1 ) )
| ~ ( ~ ( member @ SX0 @ ( sK8_Y @ SX1 @ SX0 ) )
| ~ ( member @ ( sK8_Y @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[259]) ).
thf(304,plain,
( ( ! [SX0: $i] :
( ~ ( subclass @ SX0 @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ SX0 @ ( inverse @ SX0 ) ) @ identity_relation )
| ( function @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[260]) ).
thf(305,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ( subclass @ SX0 @ ( cross_product @ universal_class @ universal_class ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ( subclass @ ( compose @ SX0 @ ( inverse @ SX0 ) ) @ identity_relation ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(306,plain,
( ( ! [SX0: $i] :
( ~ ( member @ null_class @ SX0 )
| ~ ( subclass @ ( image @ successor_relation @ SX0 ) @ SX0 )
| ( inductive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[262]) ).
thf(307,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( inductive @ SX0 )
| ( member @ null_class @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( inductive @ SX0 )
| ( subclass @ ( image @ successor_relation @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[263]) ).
thf(308,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK6_U @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK6_U @ SX1 @ SX0 ) @ SX1 ) )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[264]) ).
thf(309,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[265]) ).
thf(310,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK10_U @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK10_U @ SX1 @ SX0 ) @ SX1 ) )
| ( subclass @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[266]) ).
thf(311,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subclass @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[267]) ).
thf(312,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
( ( SX0
!= ( ordered_pair @ SX1 @ SX1 ) )
| ~ ( member @ SX1 @ universal_class ) )
| ( member @ SX0 @ identity_relation ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[268]) ).
thf(313,plain,
( ( ! [SX0: $i] :
( ~ ( member @ SX0 @ identity_relation )
| ~ ( ( SX0
!= ( ordered_pair @ ( sK7_X @ SX0 ) @ ( sK7_X @ SX0 ) ) )
| ~ ( member @ ( sK7_X @ SX0 ) @ universal_class ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[269]) ).
thf(314,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subclass @ SX0 @ SX1 )
| ~ ( subclass @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[270]) ).
thf(315,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subclass @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subclass @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[271]) ).
thf(316,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ universal_class )
| ~ ( member @ SX1 @ universal_class )
| ( ( first @ ( ordered_pair @ SX0 @ SX1 ) )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[272]) ).
thf(317,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ universal_class )
| ~ ( member @ SX1 @ universal_class )
| ( ( second @ ( ordered_pair @ SX0 @ SX1 ) )
= SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[273]) ).
thf(318,plain,
( ( ! [SX0: $i] :
( ~ ( inductive @ SX0 )
| ( subclass @ sK9_X @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[274]) ).
thf(319,plain,
( ( ~ ( ~ ( inductive @ sK9_X )
| ~ ( member @ sK9_X @ universal_class ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[275]) ).
thf(320,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( restrict @ SX0 @ ( singleton @ SX1 ) @ universal_class )
= null_class )
| ~ ( member @ SX1 @ universal_class )
| ( member @ SX1 @ ( domain_of @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[276]) ).
thf(321,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( domain_of @ SX0 ) )
| ( ( restrict @ SX0 @ ( singleton @ SX1 ) @ universal_class )
!= null_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( domain_of @ SX0 ) )
| ( member @ SX1 @ universal_class ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[277]) ).
thf(322,plain,
! [SV37: $i,SV22: $i] :
( ( ~ ! [SY166: $i,SY167: $i] :
( ~ ( member @ SV22 @ SY166 )
| ~ ( member @ SV37 @ SY167 )
| ( member @ ( ordered_pair @ SV22 @ SV37 ) @ ( cross_product @ SY166 @ SY167 ) ) )
| ~ ~ ( ~ ! [SY168: $i] :
( ! [SY169: $i] :
~ ( member @ ( ordered_pair @ SV22 @ SV37 ) @ ( cross_product @ SY168 @ SY169 ) )
| ( member @ SV22 @ SY168 ) )
| ~ ! [SY170: $i,SY171: $i] :
( ~ ( member @ ( ordered_pair @ SV22 @ SV37 ) @ ( cross_product @ SY170 @ SY171 ) )
| ( member @ SV37 @ SY171 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(323,plain,
! [SV23: $i] :
( ( ~ ~ ( ~ ! [SY131: $i] :
( ~ ( member @ SV23 @ universal_class )
| ( SV23 != SY131 )
| ! [SY132: $i] : ( member @ SV23 @ ( unordered_pair @ SY131 @ SY132 ) ) )
| ~ ! [SY133: $i,SY134: $i] :
( ~ ( member @ SV23 @ universal_class )
| ( SV23 != SY134 )
| ( member @ SV23 @ ( unordered_pair @ SY133 @ SY134 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[279]) ).
thf(324,plain,
! [SV23: $i] :
( ( ~ ~ ( ~ ( ! [SY135: $i,SY136: $i] :
~ ( member @ SV23 @ ( unordered_pair @ SY135 @ SY136 ) )
| ( member @ SV23 @ universal_class ) )
| ~ ! [SY137: $i,SY138: $i] :
( ~ ( member @ SV23 @ ( unordered_pair @ SY137 @ SY138 ) )
| ( SV23 = SY137 )
| ( SV23 = SY138 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[279]) ).
thf(325,plain,
! [SV24: $i] :
( ( ~ ! [SY139: $i,SY140: $i] :
( ~ ( member @ SY140 @ SV24 )
| ~ ( member @ SY140 @ SY139 )
| ( member @ SY140 @ ( intersection @ SV24 @ SY139 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[280]) ).
thf(326,plain,
! [SV24: $i] :
( ( ~ ~ ( ~ ! [SY141: $i,SY142: $i] :
( ~ ( member @ SY142 @ ( intersection @ SV24 @ SY141 ) )
| ( member @ SY142 @ SV24 ) )
| ~ ! [SY143: $i,SY144: $i] :
( ~ ( member @ SY144 @ ( intersection @ SV24 @ SY143 ) )
| ( member @ SY144 @ SY143 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[280]) ).
thf(327,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ universal_class )
| ~ ( subclass @ SX0 @ SX1 )
| ( member @ SX0 @ ( power_class @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[281]) ).
thf(328,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( member @ SX0 @ ( power_class @ SX1 ) )
| ( member @ SX0 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( power_class @ SX1 ) )
| ( subclass @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[282]) ).
thf(329,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ universal_class )
| ~ ( member @ SX1 @ universal_class )
| ( ( successor @ SX0 )
!= SX1 )
| ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[283]) ).
thf(330,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX0 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX1 @ universal_class ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( ( successor @ SX0 )
= SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[284]) ).
thf(331,plain,
! [SV25: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK5_U @ SV25 ) @ universal_class )
| ~ ( member @ ( sK5_U @ SV25 ) @ SV25 ) )
| ~ ( disjoint @ ( sK5_U @ SV25 ) @ SV25 ) )
= $false )
| ( ( SV25 = null_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(332,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ universal_class )
| ( member @ SX1 @ SX0 )
| ( member @ SX1 @ ( complement @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(333,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( complement @ SX0 ) )
| ( member @ SX1 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( complement @ SX0 ) )
| ~ ( member @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[287]) ).
thf(334,plain,
! [SV26: $i,SV38: $i] :
( ( ~ ! [SY172: $i,SY173: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SY172 ) @ SY173 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SY172 @ SY173 ) @ SV38 ) @ SV26 )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SY172 ) @ SY173 ) @ ( rotate @ SV26 ) ) )
| ~ ~ ( ~ ! [SY174: $i,SY175: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SY174 ) @ SY175 ) @ ( rotate @ SV26 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SY174 ) @ SY175 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
| ~ ! [SY176: $i,SY177: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SY176 ) @ SY177 ) @ ( rotate @ SV26 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SY176 @ SY177 ) @ SV38 ) @ SV26 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(335,plain,
! [SV29: $i,SV5: $i,SV39: $i] :
( ( ( ~ ( member @ SV39 @ ( cross_product @ SV5 @ SV29 ) ) )
= $true )
| ( ( SV39
= ( ordered_pair @ ( first @ SV39 ) @ ( second @ SV39 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(336,plain,
! [SV17: $i,SV33: $i] :
( ( ( ~ ( function @ SV33 ) )
= $true )
| ( ( ~ ( member @ SV17 @ universal_class ) )
= $true )
| ( ( member @ ( image @ SV33 @ SV17 ) @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[293]) ).
thf(337,plain,
! [SV19: $i] :
( ( ! [SY104: $i,SY105: $i] :
( ~ ( member @ SY105 @ ( union @ SV19 @ SY104 ) )
| ( member @ SY105 @ SV19 )
| ( member @ SY105 @ SY104 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[294]) ).
thf(338,plain,
! [SV19: $i] :
( ( ~ ( ~ ! [SY106: $i,SY107: $i] :
( ~ ( member @ SY107 @ SV19 )
| ( member @ SY107 @ ( union @ SV19 @ SY106 ) ) )
| ~ ! [SY108: $i,SY109: $i] :
( ~ ( member @ SY109 @ SY108 )
| ( member @ SY109 @ ( union @ SV19 @ SY108 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[295]) ).
thf(339,plain,
! [SV20: $i,SV35: $i] :
( ( ~ ! [SY154: $i,SY155: $i] :
( ~ ( member @ SY154 @ universal_class )
| ~ ( member @ SY155 @ ( image @ SV35 @ ( image @ SV20 @ ( singleton @ SY154 ) ) ) )
| ( member @ ( ordered_pair @ SY154 @ SY155 ) @ ( compose @ SV35 @ SV20 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(340,plain,
! [SV20: $i,SV35: $i] :
( ( ~ ~ ( ~ ! [SY156: $i] :
( ! [SY157: $i] :
~ ( member @ ( ordered_pair @ SY156 @ SY157 ) @ ( compose @ SV35 @ SV20 ) )
| ( member @ SY156 @ universal_class ) )
| ~ ! [SY158: $i,SY159: $i] :
( ~ ( member @ ( ordered_pair @ SY158 @ SY159 ) @ ( compose @ SV35 @ SV20 ) )
| ( member @ SY159 @ ( image @ SV35 @ ( image @ SV20 @ ( singleton @ SY158 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(341,plain,
! [SV36: $i,SV21: $i] :
( ( ~ ! [SY160: $i,SY161: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SY160 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV36 @ SV21 ) @ SY160 ) @ SY161 )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SY160 ) @ ( flip @ SY161 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[297]) ).
thf(342,plain,
! [SV36: $i,SV21: $i] :
( ( ~ ~ ( ~ ! [SY162: $i] :
( ! [SY163: $i] :
~ ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SY162 ) @ ( flip @ SY163 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SY162 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
| ~ ! [SY164: $i,SY165: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SY164 ) @ ( flip @ SY165 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV36 @ SV21 ) @ SY164 ) @ SY165 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[297]) ).
thf(343,plain,
! [SV41: $i] :
( ( ~ ( member @ SV41 @ universal_class )
| ( SV41 = null_class )
| ( member @ ( apply @ sK4_XF @ SV41 ) @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(344,plain,
! [SV42: $i] :
( ( ! [SY178: $i] :
( ~ ( member @ SY178 @ universal_class )
| ~ ( member @ SV42 @ SY178 )
| ( member @ ( ordered_pair @ SV42 @ SY178 ) @ element_relation ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(345,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation )
| ( member @ SX1 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation )
| ( member @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(346,plain,
! [SV43: $i] :
( ( ! [SY179: $i] :
( ! [SY180: $i] :
( ~ ( member @ SV43 @ SY180 )
| ~ ( member @ SY180 @ SY179 ) )
| ( member @ SV43 @ ( sum_class @ SY179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(347,plain,
! [SV44: $i] :
( ( ! [SY181: $i] :
( ~ ( member @ SV44 @ ( sum_class @ SY181 ) )
| ~ ( ~ ( member @ SV44 @ ( sK8_Y @ SY181 @ SV44 ) )
| ~ ( member @ ( sK8_Y @ SY181 @ SV44 ) @ SY181 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(348,plain,
! [SV45: $i] :
( ( ~ ( subclass @ SV45 @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ SV45 @ ( inverse @ SV45 ) ) @ identity_relation )
| ( function @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(349,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ( subclass @ SX0 @ ( cross_product @ universal_class @ universal_class ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ( subclass @ ( compose @ SX0 @ ( inverse @ SX0 ) ) @ identity_relation ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(350,plain,
! [SV46: $i] :
( ( ~ ( member @ null_class @ SV46 )
| ~ ( subclass @ ( image @ successor_relation @ SV46 ) @ SV46 )
| ( inductive @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(351,plain,
( ( ~ ! [SX0: $i] :
( ~ ( inductive @ SX0 )
| ( member @ null_class @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( inductive @ SX0 )
| ( subclass @ ( image @ successor_relation @ SX0 ) @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(352,plain,
! [SV47: $i] :
( ( ! [SY182: $i] :
( ~ ( ~ ( member @ ( sK6_U @ SY182 @ SV47 ) @ SV47 )
| ~ ( member @ ( sK6_U @ SY182 @ SV47 ) @ SY182 ) )
| ( disjoint @ SV47 @ SY182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(353,plain,
! [SV48: $i] :
( ( ! [SY183: $i] :
( ~ ( disjoint @ SV48 @ SY183 )
| ! [SY184: $i] :
( ~ ( member @ SY184 @ SV48 )
| ~ ( member @ SY184 @ SY183 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(354,plain,
! [SV49: $i] :
( ( ! [SY185: $i] :
( ~ ( ~ ( member @ ( sK10_U @ SY185 @ SV49 ) @ SV49 )
| ~ ~ ( member @ ( sK10_U @ SY185 @ SV49 ) @ SY185 ) )
| ( subclass @ SV49 @ SY185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(355,plain,
! [SV50: $i] :
( ( ! [SY186: $i] :
( ~ ( subclass @ SV50 @ SY186 )
| ! [SY187: $i] :
( ~ ( member @ SY187 @ SV50 )
| ( member @ SY187 @ SY186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(356,plain,
! [SV51: $i] :
( ( ! [SY188: $i] :
( ( SV51
!= ( ordered_pair @ SY188 @ SY188 ) )
| ~ ( member @ SY188 @ universal_class ) )
| ( member @ SV51 @ identity_relation ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(357,plain,
! [SV52: $i] :
( ( ~ ( member @ SV52 @ identity_relation )
| ~ ( ( SV52
!= ( ordered_pair @ ( sK7_X @ SV52 ) @ ( sK7_X @ SV52 ) ) )
| ~ ( member @ ( sK7_X @ SV52 ) @ universal_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(358,plain,
! [SV53: $i] :
( ( ! [SY189: $i] :
( ~ ( subclass @ SV53 @ SY189 )
| ~ ( subclass @ SY189 @ SV53 )
| ( SV53 = SY189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(359,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subclass @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subclass @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(360,plain,
! [SV54: $i] :
( ( ! [SY190: $i] :
( ~ ( member @ SV54 @ universal_class )
| ~ ( member @ SY190 @ universal_class )
| ( ( first @ ( ordered_pair @ SV54 @ SY190 ) )
= SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(361,plain,
! [SV55: $i] :
( ( ! [SY191: $i] :
( ~ ( member @ SV55 @ universal_class )
| ~ ( member @ SY191 @ universal_class )
| ( ( second @ ( ordered_pair @ SV55 @ SY191 ) )
= SY191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(362,plain,
! [SV56: $i] :
( ( ~ ( inductive @ SV56 )
| ( subclass @ sK9_X @ SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(363,plain,
( ( ~ ( inductive @ sK9_X )
| ~ ( member @ sK9_X @ universal_class ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(364,plain,
! [SV57: $i] :
( ( ! [SY192: $i] :
( ( ( restrict @ SV57 @ ( singleton @ SY192 ) @ universal_class )
= null_class )
| ~ ( member @ SY192 @ universal_class )
| ( member @ SY192 @ ( domain_of @ SV57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(365,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( domain_of @ SX0 ) )
| ( ( restrict @ SX0 @ ( singleton @ SX1 ) @ universal_class )
!= null_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( domain_of @ SX0 ) )
| ( member @ SX1 @ universal_class ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(366,plain,
! [SV37: $i,SV22: $i] :
( ( ~ ! [SY166: $i,SY167: $i] :
( ~ ( member @ SV22 @ SY166 )
| ~ ( member @ SV37 @ SY167 )
| ( member @ ( ordered_pair @ SV22 @ SV37 ) @ ( cross_product @ SY166 @ SY167 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[322]) ).
thf(367,plain,
! [SV37: $i,SV22: $i] :
( ( ~ ~ ( ~ ! [SY168: $i] :
( ! [SY169: $i] :
~ ( member @ ( ordered_pair @ SV22 @ SV37 ) @ ( cross_product @ SY168 @ SY169 ) )
| ( member @ SV22 @ SY168 ) )
| ~ ! [SY170: $i,SY171: $i] :
( ~ ( member @ ( ordered_pair @ SV22 @ SV37 ) @ ( cross_product @ SY170 @ SY171 ) )
| ( member @ SV37 @ SY171 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[322]) ).
thf(368,plain,
! [SV23: $i] :
( ( ~ ( ~ ! [SY131: $i] :
( ~ ( member @ SV23 @ universal_class )
| ( SV23 != SY131 )
| ! [SY132: $i] : ( member @ SV23 @ ( unordered_pair @ SY131 @ SY132 ) ) )
| ~ ! [SY133: $i,SY134: $i] :
( ~ ( member @ SV23 @ universal_class )
| ( SV23 != SY134 )
| ( member @ SV23 @ ( unordered_pair @ SY133 @ SY134 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[323]) ).
thf(369,plain,
! [SV23: $i] :
( ( ~ ( ~ ( ! [SY135: $i,SY136: $i] :
~ ( member @ SV23 @ ( unordered_pair @ SY135 @ SY136 ) )
| ( member @ SV23 @ universal_class ) )
| ~ ! [SY137: $i,SY138: $i] :
( ~ ( member @ SV23 @ ( unordered_pair @ SY137 @ SY138 ) )
| ( SV23 = SY137 )
| ( SV23 = SY138 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[324]) ).
thf(370,plain,
! [SV24: $i] :
( ( ! [SY139: $i,SY140: $i] :
( ~ ( member @ SY140 @ SV24 )
| ~ ( member @ SY140 @ SY139 )
| ( member @ SY140 @ ( intersection @ SV24 @ SY139 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[325]) ).
thf(371,plain,
! [SV24: $i] :
( ( ~ ( ~ ! [SY141: $i,SY142: $i] :
( ~ ( member @ SY142 @ ( intersection @ SV24 @ SY141 ) )
| ( member @ SY142 @ SV24 ) )
| ~ ! [SY143: $i,SY144: $i] :
( ~ ( member @ SY144 @ ( intersection @ SV24 @ SY143 ) )
| ( member @ SY144 @ SY143 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[326]) ).
thf(372,plain,
! [SV58: $i] :
( ( ! [SY193: $i] :
( ~ ( member @ SV58 @ universal_class )
| ~ ( subclass @ SV58 @ SY193 )
| ( member @ SV58 @ ( power_class @ SY193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(373,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( member @ SX0 @ ( power_class @ SX1 ) )
| ( member @ SX0 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( power_class @ SX1 ) )
| ( subclass @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(374,plain,
! [SV59: $i] :
( ( ! [SY194: $i] :
( ~ ( member @ SV59 @ universal_class )
| ~ ( member @ SY194 @ universal_class )
| ( ( successor @ SV59 )
!= SY194 )
| ( member @ ( ordered_pair @ SV59 @ SY194 ) @ successor_relation ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(375,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX0 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX1 @ universal_class ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( ( successor @ SX0 )
= SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(376,plain,
! [SV25: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK5_U @ SV25 ) @ universal_class )
| ~ ( member @ ( sK5_U @ SV25 ) @ SV25 ) ) )
= $false )
| ( ( SV25 = null_class )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[331]) ).
thf(377,plain,
! [SV25: $i] :
( ( ( ~ ( disjoint @ ( sK5_U @ SV25 ) @ SV25 ) )
= $false )
| ( ( SV25 = null_class )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[331]) ).
thf(378,plain,
! [SV60: $i] :
( ( ! [SY195: $i] :
( ~ ( member @ SY195 @ universal_class )
| ( member @ SY195 @ SV60 )
| ( member @ SY195 @ ( complement @ SV60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(379,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( complement @ SX0 ) )
| ( member @ SX1 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( complement @ SX0 ) )
| ~ ( member @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(380,plain,
! [SV26: $i,SV38: $i] :
( ( ~ ! [SY172: $i,SY173: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SY172 ) @ SY173 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SY172 @ SY173 ) @ SV38 ) @ SV26 )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SY172 ) @ SY173 ) @ ( rotate @ SV26 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[334]) ).
thf(381,plain,
! [SV26: $i,SV38: $i] :
( ( ~ ~ ( ~ ! [SY174: $i,SY175: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SY174 ) @ SY175 ) @ ( rotate @ SV26 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SY174 ) @ SY175 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
| ~ ! [SY176: $i,SY177: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SY176 ) @ SY177 ) @ ( rotate @ SV26 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SY176 @ SY177 ) @ SV38 ) @ SV26 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[334]) ).
thf(382,plain,
! [SV29: $i,SV5: $i,SV39: $i] :
( ( ( member @ SV39 @ ( cross_product @ SV5 @ SV29 ) )
= $false )
| ( ( SV39
= ( ordered_pair @ ( first @ SV39 ) @ ( second @ SV39 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(383,plain,
! [SV17: $i,SV33: $i] :
( ( ( function @ SV33 )
= $false )
| ( ( ~ ( member @ SV17 @ universal_class ) )
= $true )
| ( ( member @ ( image @ SV33 @ SV17 ) @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(384,plain,
! [SV61: $i,SV19: $i] :
( ( ! [SY196: $i] :
( ~ ( member @ SY196 @ ( union @ SV19 @ SV61 ) )
| ( member @ SY196 @ SV19 )
| ( member @ SY196 @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(385,plain,
! [SV19: $i] :
( ( ~ ! [SY106: $i,SY107: $i] :
( ~ ( member @ SY107 @ SV19 )
| ( member @ SY107 @ ( union @ SV19 @ SY106 ) ) )
| ~ ! [SY108: $i,SY109: $i] :
( ~ ( member @ SY109 @ SY108 )
| ( member @ SY109 @ ( union @ SV19 @ SY108 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(386,plain,
! [SV20: $i,SV35: $i] :
( ( ! [SY154: $i,SY155: $i] :
( ~ ( member @ SY154 @ universal_class )
| ~ ( member @ SY155 @ ( image @ SV35 @ ( image @ SV20 @ ( singleton @ SY154 ) ) ) )
| ( member @ ( ordered_pair @ SY154 @ SY155 ) @ ( compose @ SV35 @ SV20 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[339]) ).
thf(387,plain,
! [SV20: $i,SV35: $i] :
( ( ~ ( ~ ! [SY156: $i] :
( ! [SY157: $i] :
~ ( member @ ( ordered_pair @ SY156 @ SY157 ) @ ( compose @ SV35 @ SV20 ) )
| ( member @ SY156 @ universal_class ) )
| ~ ! [SY158: $i,SY159: $i] :
( ~ ( member @ ( ordered_pair @ SY158 @ SY159 ) @ ( compose @ SV35 @ SV20 ) )
| ( member @ SY159 @ ( image @ SV35 @ ( image @ SV20 @ ( singleton @ SY158 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[340]) ).
thf(388,plain,
! [SV36: $i,SV21: $i] :
( ( ! [SY160: $i,SY161: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SY160 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV36 @ SV21 ) @ SY160 ) @ SY161 )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SY160 ) @ ( flip @ SY161 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[341]) ).
thf(389,plain,
! [SV36: $i,SV21: $i] :
( ( ~ ( ~ ! [SY162: $i] :
( ! [SY163: $i] :
~ ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SY162 ) @ ( flip @ SY163 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SY162 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
| ~ ! [SY164: $i,SY165: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SY164 ) @ ( flip @ SY165 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV36 @ SV21 ) @ SY164 ) @ SY165 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[342]) ).
thf(390,plain,
! [SV41: $i] :
( ( ( ~ ( member @ SV41 @ universal_class ) )
= $true )
| ( ( ( SV41 = null_class )
| ( member @ ( apply @ sK4_XF @ SV41 ) @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[343]) ).
thf(391,plain,
! [SV42: $i,SV62: $i] :
( ( ~ ( member @ SV62 @ universal_class )
| ~ ( member @ SV42 @ SV62 )
| ( member @ ( ordered_pair @ SV42 @ SV62 ) @ element_relation ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(392,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation )
| ( member @ SX1 @ universal_class ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[345]) ).
thf(393,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation )
| ( member @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[345]) ).
thf(394,plain,
! [SV63: $i,SV43: $i] :
( ( ! [SY197: $i] :
( ~ ( member @ SV43 @ SY197 )
| ~ ( member @ SY197 @ SV63 ) )
| ( member @ SV43 @ ( sum_class @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(395,plain,
! [SV64: $i,SV44: $i] :
( ( ~ ( member @ SV44 @ ( sum_class @ SV64 ) )
| ~ ( ~ ( member @ SV44 @ ( sK8_Y @ SV64 @ SV44 ) )
| ~ ( member @ ( sK8_Y @ SV64 @ SV44 ) @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(396,plain,
! [SV45: $i] :
( ( ( ~ ( subclass @ SV45 @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ SV45 @ ( inverse @ SV45 ) ) @ identity_relation ) )
= $true )
| ( ( function @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[348]) ).
thf(397,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ( subclass @ SX0 @ ( cross_product @ universal_class @ universal_class ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[349]) ).
thf(398,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ( subclass @ ( compose @ SX0 @ ( inverse @ SX0 ) ) @ identity_relation ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[349]) ).
thf(399,plain,
! [SV46: $i] :
( ( ( ~ ( member @ null_class @ SV46 )
| ~ ( subclass @ ( image @ successor_relation @ SV46 ) @ SV46 ) )
= $true )
| ( ( inductive @ SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[350]) ).
thf(400,plain,
( ( ~ ! [SX0: $i] :
( ~ ( inductive @ SX0 )
| ( member @ null_class @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[351]) ).
thf(401,plain,
( ( ~ ! [SX0: $i] :
( ~ ( inductive @ SX0 )
| ( subclass @ ( image @ successor_relation @ SX0 ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[351]) ).
thf(402,plain,
! [SV47: $i,SV65: $i] :
( ( ~ ( ~ ( member @ ( sK6_U @ SV65 @ SV47 ) @ SV47 )
| ~ ( member @ ( sK6_U @ SV65 @ SV47 ) @ SV65 ) )
| ( disjoint @ SV47 @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(403,plain,
! [SV66: $i,SV48: $i] :
( ( ~ ( disjoint @ SV48 @ SV66 )
| ! [SY198: $i] :
( ~ ( member @ SY198 @ SV48 )
| ~ ( member @ SY198 @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(404,plain,
! [SV49: $i,SV67: $i] :
( ( ~ ( ~ ( member @ ( sK10_U @ SV67 @ SV49 ) @ SV49 )
| ~ ~ ( member @ ( sK10_U @ SV67 @ SV49 ) @ SV67 ) )
| ( subclass @ SV49 @ SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(405,plain,
! [SV68: $i,SV50: $i] :
( ( ~ ( subclass @ SV50 @ SV68 )
| ! [SY199: $i] :
( ~ ( member @ SY199 @ SV50 )
| ( member @ SY199 @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(406,plain,
! [SV51: $i] :
( ( ( ! [SY188: $i] :
( ( SV51
!= ( ordered_pair @ SY188 @ SY188 ) )
| ~ ( member @ SY188 @ universal_class ) ) )
= $true )
| ( ( member @ SV51 @ identity_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[356]) ).
thf(407,plain,
! [SV52: $i] :
( ( ( ~ ( member @ SV52 @ identity_relation ) )
= $true )
| ( ( ~ ( ( SV52
!= ( ordered_pair @ ( sK7_X @ SV52 ) @ ( sK7_X @ SV52 ) ) )
| ~ ( member @ ( sK7_X @ SV52 ) @ universal_class ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(408,plain,
! [SV69: $i,SV53: $i] :
( ( ~ ( subclass @ SV53 @ SV69 )
| ~ ( subclass @ SV69 @ SV53 )
| ( SV53 = SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(409,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subclass @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[359]) ).
thf(410,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subclass @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[359]) ).
thf(411,plain,
! [SV70: $i,SV54: $i] :
( ( ~ ( member @ SV54 @ universal_class )
| ~ ( member @ SV70 @ universal_class )
| ( ( first @ ( ordered_pair @ SV54 @ SV70 ) )
= SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(412,plain,
! [SV71: $i,SV55: $i] :
( ( ~ ( member @ SV55 @ universal_class )
| ~ ( member @ SV71 @ universal_class )
| ( ( second @ ( ordered_pair @ SV55 @ SV71 ) )
= SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(413,plain,
! [SV56: $i] :
( ( ( ~ ( inductive @ SV56 ) )
= $true )
| ( ( subclass @ sK9_X @ SV56 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[362]) ).
thf(414,plain,
( ( ~ ( inductive @ sK9_X ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[363]) ).
thf(415,plain,
( ( ~ ( member @ sK9_X @ universal_class ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[363]) ).
thf(416,plain,
! [SV72: $i,SV57: $i] :
( ( ( ( restrict @ SV57 @ ( singleton @ SV72 ) @ universal_class )
= null_class )
| ~ ( member @ SV72 @ universal_class )
| ( member @ SV72 @ ( domain_of @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(417,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( domain_of @ SX0 ) )
| ( ( restrict @ SX0 @ ( singleton @ SX1 ) @ universal_class )
!= null_class ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[365]) ).
thf(418,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( domain_of @ SX0 ) )
| ( member @ SX1 @ universal_class ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[365]) ).
thf(419,plain,
! [SV37: $i,SV22: $i] :
( ( ! [SY166: $i,SY167: $i] :
( ~ ( member @ SV22 @ SY166 )
| ~ ( member @ SV37 @ SY167 )
| ( member @ ( ordered_pair @ SV22 @ SV37 ) @ ( cross_product @ SY166 @ SY167 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[366]) ).
thf(420,plain,
! [SV37: $i,SV22: $i] :
( ( ~ ( ~ ! [SY168: $i] :
( ! [SY169: $i] :
~ ( member @ ( ordered_pair @ SV22 @ SV37 ) @ ( cross_product @ SY168 @ SY169 ) )
| ( member @ SV22 @ SY168 ) )
| ~ ! [SY170: $i,SY171: $i] :
( ~ ( member @ ( ordered_pair @ SV22 @ SV37 ) @ ( cross_product @ SY170 @ SY171 ) )
| ( member @ SV37 @ SY171 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[367]) ).
thf(421,plain,
! [SV23: $i] :
( ( ~ ! [SY131: $i] :
( ~ ( member @ SV23 @ universal_class )
| ( SV23 != SY131 )
| ! [SY132: $i] : ( member @ SV23 @ ( unordered_pair @ SY131 @ SY132 ) ) )
| ~ ! [SY133: $i,SY134: $i] :
( ~ ( member @ SV23 @ universal_class )
| ( SV23 != SY134 )
| ( member @ SV23 @ ( unordered_pair @ SY133 @ SY134 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(422,plain,
! [SV23: $i] :
( ( ~ ( ! [SY135: $i,SY136: $i] :
~ ( member @ SV23 @ ( unordered_pair @ SY135 @ SY136 ) )
| ( member @ SV23 @ universal_class ) )
| ~ ! [SY137: $i,SY138: $i] :
( ~ ( member @ SV23 @ ( unordered_pair @ SY137 @ SY138 ) )
| ( SV23 = SY137 )
| ( SV23 = SY138 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(423,plain,
! [SV73: $i,SV24: $i] :
( ( ! [SY200: $i] :
( ~ ( member @ SY200 @ SV24 )
| ~ ( member @ SY200 @ SV73 )
| ( member @ SY200 @ ( intersection @ SV24 @ SV73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(424,plain,
! [SV24: $i] :
( ( ~ ! [SY141: $i,SY142: $i] :
( ~ ( member @ SY142 @ ( intersection @ SV24 @ SY141 ) )
| ( member @ SY142 @ SV24 ) )
| ~ ! [SY143: $i,SY144: $i] :
( ~ ( member @ SY144 @ ( intersection @ SV24 @ SY143 ) )
| ( member @ SY144 @ SY143 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[371]) ).
thf(425,plain,
! [SV74: $i,SV58: $i] :
( ( ~ ( member @ SV58 @ universal_class )
| ~ ( subclass @ SV58 @ SV74 )
| ( member @ SV58 @ ( power_class @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(426,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( member @ SX0 @ ( power_class @ SX1 ) )
| ( member @ SX0 @ universal_class ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[373]) ).
thf(427,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( power_class @ SX1 ) )
| ( subclass @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[373]) ).
thf(428,plain,
! [SV75: $i,SV59: $i] :
( ( ~ ( member @ SV59 @ universal_class )
| ~ ( member @ SV75 @ universal_class )
| ( ( successor @ SV59 )
!= SV75 )
| ( member @ ( ordered_pair @ SV59 @ SV75 ) @ successor_relation ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(429,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX0 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX1 @ universal_class ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[375]) ).
thf(430,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( ( successor @ SX0 )
= SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[375]) ).
thf(431,plain,
! [SV25: $i] :
( ( ( ~ ( ~ ( member @ ( sK5_U @ SV25 ) @ universal_class )
| ~ ( member @ ( sK5_U @ SV25 ) @ SV25 ) ) )
= $true )
| ( ( SV25 = null_class )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[376]) ).
thf(432,plain,
! [SV25: $i] :
( ( ( disjoint @ ( sK5_U @ SV25 ) @ SV25 )
= $true )
| ( ( SV25 = null_class )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[377]) ).
thf(433,plain,
! [SV60: $i,SV76: $i] :
( ( ~ ( member @ SV76 @ universal_class )
| ( member @ SV76 @ SV60 )
| ( member @ SV76 @ ( complement @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(434,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( complement @ SX0 ) )
| ( member @ SX1 @ universal_class ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[379]) ).
thf(435,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( complement @ SX0 ) )
| ~ ( member @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[379]) ).
thf(436,plain,
! [SV26: $i,SV38: $i] :
( ( ! [SY172: $i,SY173: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SY172 ) @ SY173 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SY172 @ SY173 ) @ SV38 ) @ SV26 )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SY172 ) @ SY173 ) @ ( rotate @ SV26 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[380]) ).
thf(437,plain,
! [SV26: $i,SV38: $i] :
( ( ~ ( ~ ! [SY174: $i,SY175: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SY174 ) @ SY175 ) @ ( rotate @ SV26 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SY174 ) @ SY175 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
| ~ ! [SY176: $i,SY177: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SY176 ) @ SY177 ) @ ( rotate @ SV26 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SY176 @ SY177 ) @ SV38 ) @ SV26 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[381]) ).
thf(438,plain,
! [SV33: $i,SV17: $i] :
( ( ( member @ SV17 @ universal_class )
= $false )
| ( ( function @ SV33 )
= $false )
| ( ( member @ ( image @ SV33 @ SV17 ) @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(439,plain,
! [SV61: $i,SV19: $i,SV77: $i] :
( ( ~ ( member @ SV77 @ ( union @ SV19 @ SV61 ) )
| ( member @ SV77 @ SV19 )
| ( member @ SV77 @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(440,plain,
! [SV19: $i] :
( ( ~ ! [SY106: $i,SY107: $i] :
( ~ ( member @ SY107 @ SV19 )
| ( member @ SY107 @ ( union @ SV19 @ SY106 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[385]) ).
thf(441,plain,
! [SV19: $i] :
( ( ~ ! [SY108: $i,SY109: $i] :
( ~ ( member @ SY109 @ SY108 )
| ( member @ SY109 @ ( union @ SV19 @ SY108 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[385]) ).
thf(442,plain,
! [SV20: $i,SV35: $i,SV78: $i] :
( ( ! [SY201: $i] :
( ~ ( member @ SV78 @ universal_class )
| ~ ( member @ SY201 @ ( image @ SV35 @ ( image @ SV20 @ ( singleton @ SV78 ) ) ) )
| ( member @ ( ordered_pair @ SV78 @ SY201 ) @ ( compose @ SV35 @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(443,plain,
! [SV20: $i,SV35: $i] :
( ( ~ ! [SY156: $i] :
( ! [SY157: $i] :
~ ( member @ ( ordered_pair @ SY156 @ SY157 ) @ ( compose @ SV35 @ SV20 ) )
| ( member @ SY156 @ universal_class ) )
| ~ ! [SY158: $i,SY159: $i] :
( ~ ( member @ ( ordered_pair @ SY158 @ SY159 ) @ ( compose @ SV35 @ SV20 ) )
| ( member @ SY159 @ ( image @ SV35 @ ( image @ SV20 @ ( singleton @ SY158 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(444,plain,
! [SV79: $i,SV36: $i,SV21: $i] :
( ( ! [SY202: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SV79 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV36 @ SV21 ) @ SV79 ) @ SY202 )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SV79 ) @ ( flip @ SY202 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(445,plain,
! [SV36: $i,SV21: $i] :
( ( ~ ! [SY162: $i] :
( ! [SY163: $i] :
~ ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SY162 ) @ ( flip @ SY163 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SY162 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
| ~ ! [SY164: $i,SY165: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SY164 ) @ ( flip @ SY165 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV36 @ SV21 ) @ SY164 ) @ SY165 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(446,plain,
! [SV41: $i] :
( ( ( member @ SV41 @ universal_class )
= $false )
| ( ( ( SV41 = null_class )
| ( member @ ( apply @ sK4_XF @ SV41 ) @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(447,plain,
! [SV42: $i,SV62: $i] :
( ( ( ~ ( member @ SV62 @ universal_class )
| ~ ( member @ SV42 @ SV62 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV42 @ SV62 ) @ element_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[391]) ).
thf(448,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation )
| ( member @ SX1 @ universal_class ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[392]) ).
thf(449,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation )
| ( member @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[393]) ).
thf(450,plain,
! [SV63: $i,SV43: $i] :
( ( ( ! [SY197: $i] :
( ~ ( member @ SV43 @ SY197 )
| ~ ( member @ SY197 @ SV63 ) ) )
= $true )
| ( ( member @ SV43 @ ( sum_class @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[394]) ).
thf(451,plain,
! [SV64: $i,SV44: $i] :
( ( ( ~ ( member @ SV44 @ ( sum_class @ SV64 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ SV44 @ ( sK8_Y @ SV64 @ SV44 ) )
| ~ ( member @ ( sK8_Y @ SV64 @ SV44 ) @ SV64 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[395]) ).
thf(452,plain,
! [SV45: $i] :
( ( ( ~ ( subclass @ SV45 @ ( cross_product @ universal_class @ universal_class ) ) )
= $true )
| ( ( ~ ( subclass @ ( compose @ SV45 @ ( inverse @ SV45 ) ) @ identity_relation ) )
= $true )
| ( ( function @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[396]) ).
thf(453,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ( subclass @ SX0 @ ( cross_product @ universal_class @ universal_class ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[397]) ).
thf(454,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ( subclass @ ( compose @ SX0 @ ( inverse @ SX0 ) ) @ identity_relation ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[398]) ).
thf(455,plain,
! [SV46: $i] :
( ( ( ~ ( member @ null_class @ SV46 ) )
= $true )
| ( ( ~ ( subclass @ ( image @ successor_relation @ SV46 ) @ SV46 ) )
= $true )
| ( ( inductive @ SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[399]) ).
thf(456,plain,
( ( ! [SX0: $i] :
( ~ ( inductive @ SX0 )
| ( member @ null_class @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[400]) ).
thf(457,plain,
( ( ! [SX0: $i] :
( ~ ( inductive @ SX0 )
| ( subclass @ ( image @ successor_relation @ SX0 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[401]) ).
thf(458,plain,
! [SV47: $i,SV65: $i] :
( ( ( ~ ( ~ ( member @ ( sK6_U @ SV65 @ SV47 ) @ SV47 )
| ~ ( member @ ( sK6_U @ SV65 @ SV47 ) @ SV65 ) ) )
= $true )
| ( ( disjoint @ SV47 @ SV65 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[402]) ).
thf(459,plain,
! [SV66: $i,SV48: $i] :
( ( ( ~ ( disjoint @ SV48 @ SV66 ) )
= $true )
| ( ( ! [SY198: $i] :
( ~ ( member @ SY198 @ SV48 )
| ~ ( member @ SY198 @ SV66 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[403]) ).
thf(460,plain,
! [SV49: $i,SV67: $i] :
( ( ( ~ ( ~ ( member @ ( sK10_U @ SV67 @ SV49 ) @ SV49 )
| ~ ~ ( member @ ( sK10_U @ SV67 @ SV49 ) @ SV67 ) ) )
= $true )
| ( ( subclass @ SV49 @ SV67 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[404]) ).
thf(461,plain,
! [SV68: $i,SV50: $i] :
( ( ( ~ ( subclass @ SV50 @ SV68 ) )
= $true )
| ( ( ! [SY199: $i] :
( ~ ( member @ SY199 @ SV50 )
| ( member @ SY199 @ SV68 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[405]) ).
thf(462,plain,
! [SV80: $i,SV51: $i] :
( ( ( ( SV51
!= ( ordered_pair @ SV80 @ SV80 ) )
| ~ ( member @ SV80 @ universal_class ) )
= $true )
| ( ( member @ SV51 @ identity_relation )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(463,plain,
! [SV52: $i] :
( ( ( member @ SV52 @ identity_relation )
= $false )
| ( ( ~ ( ( SV52
!= ( ordered_pair @ ( sK7_X @ SV52 ) @ ( sK7_X @ SV52 ) ) )
| ~ ( member @ ( sK7_X @ SV52 ) @ universal_class ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(464,plain,
! [SV69: $i,SV53: $i] :
( ( ( ~ ( subclass @ SV53 @ SV69 )
| ~ ( subclass @ SV69 @ SV53 ) )
= $true )
| ( ( SV53 = SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[408]) ).
thf(465,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subclass @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[409]) ).
thf(466,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subclass @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[410]) ).
thf(467,plain,
! [SV70: $i,SV54: $i] :
( ( ( ~ ( member @ SV54 @ universal_class )
| ~ ( member @ SV70 @ universal_class ) )
= $true )
| ( ( ( first @ ( ordered_pair @ SV54 @ SV70 ) )
= SV54 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[411]) ).
thf(468,plain,
! [SV71: $i,SV55: $i] :
( ( ( ~ ( member @ SV55 @ universal_class )
| ~ ( member @ SV71 @ universal_class ) )
= $true )
| ( ( ( second @ ( ordered_pair @ SV55 @ SV71 ) )
= SV71 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[412]) ).
thf(469,plain,
! [SV56: $i] :
( ( ( inductive @ SV56 )
= $false )
| ( ( subclass @ sK9_X @ SV56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[413]) ).
thf(470,plain,
( ( inductive @ sK9_X )
= $true ),
inference(extcnf_not_neg,[status(thm)],[414]) ).
thf(471,plain,
( ( member @ sK9_X @ universal_class )
= $true ),
inference(extcnf_not_neg,[status(thm)],[415]) ).
thf(472,plain,
! [SV72: $i,SV57: $i] :
( ( ( ( ( restrict @ SV57 @ ( singleton @ SV72 ) @ universal_class )
= null_class )
| ~ ( member @ SV72 @ universal_class ) )
= $true )
| ( ( member @ SV72 @ ( domain_of @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[416]) ).
thf(473,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( domain_of @ SX0 ) )
| ( ( restrict @ SX0 @ ( singleton @ SX1 ) @ universal_class )
!= null_class ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[417]) ).
thf(474,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( domain_of @ SX0 ) )
| ( member @ SX1 @ universal_class ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[418]) ).
thf(475,plain,
! [SV37: $i,SV81: $i,SV22: $i] :
( ( ! [SY203: $i] :
( ~ ( member @ SV22 @ SV81 )
| ~ ( member @ SV37 @ SY203 )
| ( member @ ( ordered_pair @ SV22 @ SV37 ) @ ( cross_product @ SV81 @ SY203 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(476,plain,
! [SV37: $i,SV22: $i] :
( ( ~ ! [SY168: $i] :
( ! [SY169: $i] :
~ ( member @ ( ordered_pair @ SV22 @ SV37 ) @ ( cross_product @ SY168 @ SY169 ) )
| ( member @ SV22 @ SY168 ) )
| ~ ! [SY170: $i,SY171: $i] :
( ~ ( member @ ( ordered_pair @ SV22 @ SV37 ) @ ( cross_product @ SY170 @ SY171 ) )
| ( member @ SV37 @ SY171 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(477,plain,
! [SV23: $i] :
( ( ~ ! [SY131: $i] :
( ~ ( member @ SV23 @ universal_class )
| ( SV23 != SY131 )
| ! [SY132: $i] : ( member @ SV23 @ ( unordered_pair @ SY131 @ SY132 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[421]) ).
thf(478,plain,
! [SV23: $i] :
( ( ~ ! [SY133: $i,SY134: $i] :
( ~ ( member @ SV23 @ universal_class )
| ( SV23 != SY134 )
| ( member @ SV23 @ ( unordered_pair @ SY133 @ SY134 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[421]) ).
thf(479,plain,
! [SV23: $i] :
( ( ~ ( ! [SY135: $i,SY136: $i] :
~ ( member @ SV23 @ ( unordered_pair @ SY135 @ SY136 ) )
| ( member @ SV23 @ universal_class ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[422]) ).
thf(480,plain,
! [SV23: $i] :
( ( ~ ! [SY137: $i,SY138: $i] :
( ~ ( member @ SV23 @ ( unordered_pair @ SY137 @ SY138 ) )
| ( SV23 = SY137 )
| ( SV23 = SY138 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[422]) ).
thf(481,plain,
! [SV73: $i,SV24: $i,SV82: $i] :
( ( ~ ( member @ SV82 @ SV24 )
| ~ ( member @ SV82 @ SV73 )
| ( member @ SV82 @ ( intersection @ SV24 @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(482,plain,
! [SV24: $i] :
( ( ~ ! [SY141: $i,SY142: $i] :
( ~ ( member @ SY142 @ ( intersection @ SV24 @ SY141 ) )
| ( member @ SY142 @ SV24 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[424]) ).
thf(483,plain,
! [SV24: $i] :
( ( ~ ! [SY143: $i,SY144: $i] :
( ~ ( member @ SY144 @ ( intersection @ SV24 @ SY143 ) )
| ( member @ SY144 @ SY143 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[424]) ).
thf(484,plain,
! [SV74: $i,SV58: $i] :
( ( ( ~ ( member @ SV58 @ universal_class )
| ~ ( subclass @ SV58 @ SV74 ) )
= $true )
| ( ( member @ SV58 @ ( power_class @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[425]) ).
thf(485,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( member @ SX0 @ ( power_class @ SX1 ) )
| ( member @ SX0 @ universal_class ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[426]) ).
thf(486,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( power_class @ SX1 ) )
| ( subclass @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[427]) ).
thf(487,plain,
! [SV75: $i,SV59: $i] :
( ( ( ~ ( member @ SV59 @ universal_class )
| ~ ( member @ SV75 @ universal_class )
| ( ( successor @ SV59 )
!= SV75 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV59 @ SV75 ) @ successor_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[428]) ).
thf(488,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX0 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX1 @ universal_class ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[429]) ).
thf(489,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( ( successor @ SX0 )
= SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[430]) ).
thf(490,plain,
! [SV25: $i] :
( ( ( ~ ( member @ ( sK5_U @ SV25 ) @ universal_class )
| ~ ( member @ ( sK5_U @ SV25 ) @ SV25 ) )
= $false )
| ( ( SV25 = null_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[431]) ).
thf(491,plain,
! [SV60: $i,SV76: $i] :
( ( ( ~ ( member @ SV76 @ universal_class )
| ( member @ SV76 @ SV60 ) )
= $true )
| ( ( member @ SV76 @ ( complement @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[433]) ).
thf(492,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( complement @ SX0 ) )
| ( member @ SX1 @ universal_class ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[434]) ).
thf(493,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( complement @ SX0 ) )
| ~ ( member @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[435]) ).
thf(494,plain,
! [SV26: $i,SV83: $i,SV38: $i] :
( ( ! [SY204: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SV83 ) @ SY204 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV83 @ SY204 ) @ SV38 ) @ SV26 )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SV83 ) @ SY204 ) @ ( rotate @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(495,plain,
! [SV26: $i,SV38: $i] :
( ( ~ ! [SY174: $i,SY175: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SY174 ) @ SY175 ) @ ( rotate @ SV26 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SY174 ) @ SY175 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
| ~ ! [SY176: $i,SY177: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SY176 ) @ SY177 ) @ ( rotate @ SV26 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SY176 @ SY177 ) @ SV38 ) @ SV26 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(496,plain,
! [SV61: $i,SV19: $i,SV77: $i] :
( ( ( ~ ( member @ SV77 @ ( union @ SV19 @ SV61 ) ) )
= $true )
| ( ( ( member @ SV77 @ SV19 )
| ( member @ SV77 @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[439]) ).
thf(497,plain,
! [SV19: $i] :
( ( ! [SY106: $i,SY107: $i] :
( ~ ( member @ SY107 @ SV19 )
| ( member @ SY107 @ ( union @ SV19 @ SY106 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[440]) ).
thf(498,plain,
! [SV19: $i] :
( ( ! [SY108: $i,SY109: $i] :
( ~ ( member @ SY109 @ SY108 )
| ( member @ SY109 @ ( union @ SV19 @ SY108 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[441]) ).
thf(499,plain,
! [SV20: $i,SV35: $i,SV84: $i,SV78: $i] :
( ( ~ ( member @ SV78 @ universal_class )
| ~ ( member @ SV84 @ ( image @ SV35 @ ( image @ SV20 @ ( singleton @ SV78 ) ) ) )
| ( member @ ( ordered_pair @ SV78 @ SV84 ) @ ( compose @ SV35 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(500,plain,
! [SV20: $i,SV35: $i] :
( ( ~ ! [SY156: $i] :
( ! [SY157: $i] :
~ ( member @ ( ordered_pair @ SY156 @ SY157 ) @ ( compose @ SV35 @ SV20 ) )
| ( member @ SY156 @ universal_class ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[443]) ).
thf(501,plain,
! [SV20: $i,SV35: $i] :
( ( ~ ! [SY158: $i,SY159: $i] :
( ~ ( member @ ( ordered_pair @ SY158 @ SY159 ) @ ( compose @ SV35 @ SV20 ) )
| ( member @ SY159 @ ( image @ SV35 @ ( image @ SV20 @ ( singleton @ SY158 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[443]) ).
thf(502,plain,
! [SV85: $i,SV79: $i,SV36: $i,SV21: $i] :
( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SV79 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV36 @ SV21 ) @ SV79 ) @ SV85 )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SV79 ) @ ( flip @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(503,plain,
! [SV36: $i,SV21: $i] :
( ( ~ ! [SY162: $i] :
( ! [SY163: $i] :
~ ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SY162 ) @ ( flip @ SY163 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SY162 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[445]) ).
thf(504,plain,
! [SV36: $i,SV21: $i] :
( ( ~ ! [SY164: $i,SY165: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SY164 ) @ ( flip @ SY165 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV36 @ SV21 ) @ SY164 ) @ SY165 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[445]) ).
thf(505,plain,
! [SV41: $i] :
( ( ( SV41 = null_class )
= $true )
| ( ( member @ ( apply @ sK4_XF @ SV41 ) @ SV41 )
= $true )
| ( ( member @ SV41 @ universal_class )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[446]) ).
thf(506,plain,
! [SV42: $i,SV62: $i] :
( ( ( ~ ( member @ SV62 @ universal_class ) )
= $true )
| ( ( ~ ( member @ SV42 @ SV62 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV42 @ SV62 ) @ element_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[447]) ).
thf(507,plain,
! [SV86: $i] :
( ( ! [SY205: $i] :
( ~ ( member @ ( ordered_pair @ SV86 @ SY205 ) @ element_relation )
| ( member @ SY205 @ universal_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(508,plain,
! [SV87: $i] :
( ( ! [SY206: $i] :
( ~ ( member @ ( ordered_pair @ SV87 @ SY206 ) @ element_relation )
| ( member @ SV87 @ SY206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(509,plain,
! [SV63: $i,SV88: $i,SV43: $i] :
( ( ( ~ ( member @ SV43 @ SV88 )
| ~ ( member @ SV88 @ SV63 ) )
= $true )
| ( ( member @ SV43 @ ( sum_class @ SV63 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(510,plain,
! [SV64: $i,SV44: $i] :
( ( ( member @ SV44 @ ( sum_class @ SV64 ) )
= $false )
| ( ( ~ ( ~ ( member @ SV44 @ ( sK8_Y @ SV64 @ SV44 ) )
| ~ ( member @ ( sK8_Y @ SV64 @ SV44 ) @ SV64 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[451]) ).
thf(511,plain,
! [SV45: $i] :
( ( ( subclass @ SV45 @ ( cross_product @ universal_class @ universal_class ) )
= $false )
| ( ( ~ ( subclass @ ( compose @ SV45 @ ( inverse @ SV45 ) ) @ identity_relation ) )
= $true )
| ( ( function @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[452]) ).
thf(512,plain,
! [SV89: $i] :
( ( ~ ( function @ SV89 )
| ( subclass @ SV89 @ ( cross_product @ universal_class @ universal_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(513,plain,
! [SV90: $i] :
( ( ~ ( function @ SV90 )
| ( subclass @ ( compose @ SV90 @ ( inverse @ SV90 ) ) @ identity_relation ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(514,plain,
! [SV46: $i] :
( ( ( member @ null_class @ SV46 )
= $false )
| ( ( ~ ( subclass @ ( image @ successor_relation @ SV46 ) @ SV46 ) )
= $true )
| ( ( inductive @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(515,plain,
! [SV91: $i] :
( ( ~ ( inductive @ SV91 )
| ( member @ null_class @ SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(516,plain,
! [SV92: $i] :
( ( ~ ( inductive @ SV92 )
| ( subclass @ ( image @ successor_relation @ SV92 ) @ SV92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(517,plain,
! [SV47: $i,SV65: $i] :
( ( ( ~ ( member @ ( sK6_U @ SV65 @ SV47 ) @ SV47 )
| ~ ( member @ ( sK6_U @ SV65 @ SV47 ) @ SV65 ) )
= $false )
| ( ( disjoint @ SV47 @ SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[458]) ).
thf(518,plain,
! [SV66: $i,SV48: $i] :
( ( ( disjoint @ SV48 @ SV66 )
= $false )
| ( ( ! [SY198: $i] :
( ~ ( member @ SY198 @ SV48 )
| ~ ( member @ SY198 @ SV66 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[459]) ).
thf(519,plain,
! [SV49: $i,SV67: $i] :
( ( ( ~ ( member @ ( sK10_U @ SV67 @ SV49 ) @ SV49 )
| ~ ~ ( member @ ( sK10_U @ SV67 @ SV49 ) @ SV67 ) )
= $false )
| ( ( subclass @ SV49 @ SV67 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[460]) ).
thf(520,plain,
! [SV68: $i,SV50: $i] :
( ( ( subclass @ SV50 @ SV68 )
= $false )
| ( ( ! [SY199: $i] :
( ~ ( member @ SY199 @ SV50 )
| ( member @ SY199 @ SV68 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[461]) ).
thf(521,plain,
! [SV80: $i,SV51: $i] :
( ( ( ( SV51
!= ( ordered_pair @ SV80 @ SV80 ) ) )
= $true )
| ( ( ~ ( member @ SV80 @ universal_class ) )
= $true )
| ( ( member @ SV51 @ identity_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[462]) ).
thf(522,plain,
! [SV52: $i] :
( ( ( ( SV52
!= ( ordered_pair @ ( sK7_X @ SV52 ) @ ( sK7_X @ SV52 ) ) )
| ~ ( member @ ( sK7_X @ SV52 ) @ universal_class ) )
= $false )
| ( ( member @ SV52 @ identity_relation )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[463]) ).
thf(523,plain,
! [SV69: $i,SV53: $i] :
( ( ( ~ ( subclass @ SV53 @ SV69 ) )
= $true )
| ( ( ~ ( subclass @ SV69 @ SV53 ) )
= $true )
| ( ( SV53 = SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[464]) ).
thf(524,plain,
! [SV93: $i] :
( ( ! [SY207: $i] :
( ( SV93 != SY207 )
| ( subclass @ SV93 @ SY207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(525,plain,
! [SV94: $i] :
( ( ! [SY208: $i] :
( ( SV94 != SY208 )
| ( subclass @ SY208 @ SV94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(526,plain,
! [SV70: $i,SV54: $i] :
( ( ( ~ ( member @ SV54 @ universal_class ) )
= $true )
| ( ( ~ ( member @ SV70 @ universal_class ) )
= $true )
| ( ( ( first @ ( ordered_pair @ SV54 @ SV70 ) )
= SV54 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[467]) ).
thf(527,plain,
! [SV71: $i,SV55: $i] :
( ( ( ~ ( member @ SV55 @ universal_class ) )
= $true )
| ( ( ~ ( member @ SV71 @ universal_class ) )
= $true )
| ( ( ( second @ ( ordered_pair @ SV55 @ SV71 ) )
= SV71 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[468]) ).
thf(528,plain,
! [SV72: $i,SV57: $i] :
( ( ( ( restrict @ SV57 @ ( singleton @ SV72 ) @ universal_class )
= null_class )
= $true )
| ( ( ~ ( member @ SV72 @ universal_class ) )
= $true )
| ( ( member @ SV72 @ ( domain_of @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[472]) ).
thf(529,plain,
! [SV95: $i] :
( ( ! [SY209: $i] :
( ~ ( member @ SY209 @ ( domain_of @ SV95 ) )
| ( ( restrict @ SV95 @ ( singleton @ SY209 ) @ universal_class )
!= null_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(530,plain,
! [SV96: $i] :
( ( ! [SY210: $i] :
( ~ ( member @ SY210 @ ( domain_of @ SV96 ) )
| ( member @ SY210 @ universal_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(531,plain,
! [SV97: $i,SV37: $i,SV81: $i,SV22: $i] :
( ( ~ ( member @ SV22 @ SV81 )
| ~ ( member @ SV37 @ SV97 )
| ( member @ ( ordered_pair @ SV22 @ SV37 ) @ ( cross_product @ SV81 @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(532,plain,
! [SV37: $i,SV22: $i] :
( ( ~ ! [SY168: $i] :
( ! [SY169: $i] :
~ ( member @ ( ordered_pair @ SV22 @ SV37 ) @ ( cross_product @ SY168 @ SY169 ) )
| ( member @ SV22 @ SY168 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[476]) ).
thf(533,plain,
! [SV37: $i,SV22: $i] :
( ( ~ ! [SY170: $i,SY171: $i] :
( ~ ( member @ ( ordered_pair @ SV22 @ SV37 ) @ ( cross_product @ SY170 @ SY171 ) )
| ( member @ SV37 @ SY171 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[476]) ).
thf(534,plain,
! [SV23: $i] :
( ( ! [SY131: $i] :
( ~ ( member @ SV23 @ universal_class )
| ( SV23 != SY131 )
| ! [SY132: $i] : ( member @ SV23 @ ( unordered_pair @ SY131 @ SY132 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[477]) ).
thf(535,plain,
! [SV23: $i] :
( ( ! [SY133: $i,SY134: $i] :
( ~ ( member @ SV23 @ universal_class )
| ( SV23 != SY134 )
| ( member @ SV23 @ ( unordered_pair @ SY133 @ SY134 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[478]) ).
thf(536,plain,
! [SV23: $i] :
( ( ! [SY135: $i,SY136: $i] :
~ ( member @ SV23 @ ( unordered_pair @ SY135 @ SY136 ) )
| ( member @ SV23 @ universal_class ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[479]) ).
thf(537,plain,
! [SV23: $i] :
( ( ! [SY137: $i,SY138: $i] :
( ~ ( member @ SV23 @ ( unordered_pair @ SY137 @ SY138 ) )
| ( SV23 = SY137 )
| ( SV23 = SY138 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[480]) ).
thf(538,plain,
! [SV73: $i,SV24: $i,SV82: $i] :
( ( ( ~ ( member @ SV82 @ SV24 )
| ~ ( member @ SV82 @ SV73 ) )
= $true )
| ( ( member @ SV82 @ ( intersection @ SV24 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[481]) ).
thf(539,plain,
! [SV24: $i] :
( ( ! [SY141: $i,SY142: $i] :
( ~ ( member @ SY142 @ ( intersection @ SV24 @ SY141 ) )
| ( member @ SY142 @ SV24 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[482]) ).
thf(540,plain,
! [SV24: $i] :
( ( ! [SY143: $i,SY144: $i] :
( ~ ( member @ SY144 @ ( intersection @ SV24 @ SY143 ) )
| ( member @ SY144 @ SY143 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[483]) ).
thf(541,plain,
! [SV74: $i,SV58: $i] :
( ( ( ~ ( member @ SV58 @ universal_class ) )
= $true )
| ( ( ~ ( subclass @ SV58 @ SV74 ) )
= $true )
| ( ( member @ SV58 @ ( power_class @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[484]) ).
thf(542,plain,
! [SV98: $i] :
( ( ! [SY211: $i] :
~ ( member @ SV98 @ ( power_class @ SY211 ) )
| ( member @ SV98 @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(543,plain,
! [SV99: $i] :
( ( ! [SY212: $i] :
( ~ ( member @ SV99 @ ( power_class @ SY212 ) )
| ( subclass @ SV99 @ SY212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(544,plain,
! [SV75: $i,SV59: $i] :
( ( ( ~ ( member @ SV59 @ universal_class )
| ~ ( member @ SV75 @ universal_class ) )
= $true )
| ( ( ( ( successor @ SV59 )
!= SV75 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV59 @ SV75 ) @ successor_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[487]) ).
thf(545,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX0 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX1 @ universal_class ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[488]) ).
thf(546,plain,
! [SV100: $i] :
( ( ! [SY213: $i] :
( ~ ( member @ ( ordered_pair @ SV100 @ SY213 ) @ successor_relation )
| ( ( successor @ SV100 )
= SY213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(547,plain,
! [SV25: $i] :
( ( ( ~ ( member @ ( sK5_U @ SV25 ) @ universal_class ) )
= $false )
| ( ( SV25 = null_class )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[490]) ).
thf(548,plain,
! [SV25: $i] :
( ( ( ~ ( member @ ( sK5_U @ SV25 ) @ SV25 ) )
= $false )
| ( ( SV25 = null_class )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[490]) ).
thf(549,plain,
! [SV60: $i,SV76: $i] :
( ( ( ~ ( member @ SV76 @ universal_class ) )
= $true )
| ( ( member @ SV76 @ SV60 )
= $true )
| ( ( member @ SV76 @ ( complement @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[491]) ).
thf(550,plain,
! [SV101: $i] :
( ( ! [SY214: $i] :
( ~ ( member @ SY214 @ ( complement @ SV101 ) )
| ( member @ SY214 @ universal_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(551,plain,
! [SV102: $i] :
( ( ! [SY215: $i] :
( ~ ( member @ SY215 @ ( complement @ SV102 ) )
| ~ ( member @ SY215 @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(552,plain,
! [SV26: $i,SV103: $i,SV83: $i,SV38: $i] :
( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SV83 ) @ SV103 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV83 @ SV103 ) @ SV38 ) @ SV26 )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SV83 ) @ SV103 ) @ ( rotate @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(553,plain,
! [SV26: $i,SV38: $i] :
( ( ~ ! [SY174: $i,SY175: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SY174 ) @ SY175 ) @ ( rotate @ SV26 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SY174 ) @ SY175 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[495]) ).
thf(554,plain,
! [SV26: $i,SV38: $i] :
( ( ~ ! [SY176: $i,SY177: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SY176 ) @ SY177 ) @ ( rotate @ SV26 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SY176 @ SY177 ) @ SV38 ) @ SV26 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[495]) ).
thf(555,plain,
! [SV61: $i,SV19: $i,SV77: $i] :
( ( ( member @ SV77 @ ( union @ SV19 @ SV61 ) )
= $false )
| ( ( ( member @ SV77 @ SV19 )
| ( member @ SV77 @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(556,plain,
! [SV104: $i,SV19: $i] :
( ( ! [SY216: $i] :
( ~ ( member @ SY216 @ SV19 )
| ( member @ SY216 @ ( union @ SV19 @ SV104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(557,plain,
! [SV19: $i,SV105: $i] :
( ( ! [SY217: $i] :
( ~ ( member @ SY217 @ SV105 )
| ( member @ SY217 @ ( union @ SV19 @ SV105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(558,plain,
! [SV20: $i,SV35: $i,SV84: $i,SV78: $i] :
( ( ( ~ ( member @ SV78 @ universal_class )
| ~ ( member @ SV84 @ ( image @ SV35 @ ( image @ SV20 @ ( singleton @ SV78 ) ) ) ) )
= $true )
| ( ( member @ ( ordered_pair @ SV78 @ SV84 ) @ ( compose @ SV35 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[499]) ).
thf(559,plain,
! [SV20: $i,SV35: $i] :
( ( ! [SY156: $i] :
( ! [SY157: $i] :
~ ( member @ ( ordered_pair @ SY156 @ SY157 ) @ ( compose @ SV35 @ SV20 ) )
| ( member @ SY156 @ universal_class ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[500]) ).
thf(560,plain,
! [SV20: $i,SV35: $i] :
( ( ! [SY158: $i,SY159: $i] :
( ~ ( member @ ( ordered_pair @ SY158 @ SY159 ) @ ( compose @ SV35 @ SV20 ) )
| ( member @ SY159 @ ( image @ SV35 @ ( image @ SV20 @ ( singleton @ SY158 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[501]) ).
thf(561,plain,
! [SV85: $i,SV79: $i,SV36: $i,SV21: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SV79 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV36 @ SV21 ) @ SV79 ) @ SV85 ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SV79 ) @ ( flip @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[502]) ).
thf(562,plain,
! [SV36: $i,SV21: $i] :
( ( ! [SY162: $i] :
( ! [SY163: $i] :
~ ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SY162 ) @ ( flip @ SY163 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SY162 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[503]) ).
thf(563,plain,
! [SV36: $i,SV21: $i] :
( ( ! [SY164: $i,SY165: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SY164 ) @ ( flip @ SY165 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV36 @ SV21 ) @ SY164 ) @ SY165 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[504]) ).
thf(564,plain,
! [SV42: $i,SV62: $i] :
( ( ( member @ SV62 @ universal_class )
= $false )
| ( ( ~ ( member @ SV42 @ SV62 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV42 @ SV62 ) @ element_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[506]) ).
thf(565,plain,
! [SV106: $i,SV86: $i] :
( ( ~ ( member @ ( ordered_pair @ SV86 @ SV106 ) @ element_relation )
| ( member @ SV106 @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(566,plain,
! [SV107: $i,SV87: $i] :
( ( ~ ( member @ ( ordered_pair @ SV87 @ SV107 ) @ element_relation )
| ( member @ SV87 @ SV107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(567,plain,
! [SV63: $i,SV88: $i,SV43: $i] :
( ( ( ~ ( member @ SV43 @ SV88 ) )
= $true )
| ( ( ~ ( member @ SV88 @ SV63 ) )
= $true )
| ( ( member @ SV43 @ ( sum_class @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[509]) ).
thf(568,plain,
! [SV64: $i,SV44: $i] :
( ( ( ~ ( member @ SV44 @ ( sK8_Y @ SV64 @ SV44 ) )
| ~ ( member @ ( sK8_Y @ SV64 @ SV44 ) @ SV64 ) )
= $false )
| ( ( member @ SV44 @ ( sum_class @ SV64 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(569,plain,
! [SV45: $i] :
( ( ( subclass @ ( compose @ SV45 @ ( inverse @ SV45 ) ) @ identity_relation )
= $false )
| ( ( subclass @ SV45 @ ( cross_product @ universal_class @ universal_class ) )
= $false )
| ( ( function @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[511]) ).
thf(570,plain,
! [SV89: $i] :
( ( ( ~ ( function @ SV89 ) )
= $true )
| ( ( subclass @ SV89 @ ( cross_product @ universal_class @ universal_class ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[512]) ).
thf(571,plain,
! [SV90: $i] :
( ( ( ~ ( function @ SV90 ) )
= $true )
| ( ( subclass @ ( compose @ SV90 @ ( inverse @ SV90 ) ) @ identity_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[513]) ).
thf(572,plain,
! [SV46: $i] :
( ( ( subclass @ ( image @ successor_relation @ SV46 ) @ SV46 )
= $false )
| ( ( member @ null_class @ SV46 )
= $false )
| ( ( inductive @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[514]) ).
thf(573,plain,
! [SV91: $i] :
( ( ( ~ ( inductive @ SV91 ) )
= $true )
| ( ( member @ null_class @ SV91 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[515]) ).
thf(574,plain,
! [SV92: $i] :
( ( ( ~ ( inductive @ SV92 ) )
= $true )
| ( ( subclass @ ( image @ successor_relation @ SV92 ) @ SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[516]) ).
thf(575,plain,
! [SV47: $i,SV65: $i] :
( ( ( ~ ( member @ ( sK6_U @ SV65 @ SV47 ) @ SV47 ) )
= $false )
| ( ( disjoint @ SV47 @ SV65 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[517]) ).
thf(576,plain,
! [SV47: $i,SV65: $i] :
( ( ( ~ ( member @ ( sK6_U @ SV65 @ SV47 ) @ SV65 ) )
= $false )
| ( ( disjoint @ SV47 @ SV65 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[517]) ).
thf(577,plain,
! [SV66: $i,SV48: $i,SV108: $i] :
( ( ( ~ ( member @ SV108 @ SV48 )
| ~ ( member @ SV108 @ SV66 ) )
= $true )
| ( ( disjoint @ SV48 @ SV66 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(578,plain,
! [SV49: $i,SV67: $i] :
( ( ( ~ ( member @ ( sK10_U @ SV67 @ SV49 ) @ SV49 ) )
= $false )
| ( ( subclass @ SV49 @ SV67 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[519]) ).
thf(579,plain,
! [SV49: $i,SV67: $i] :
( ( ( ~ ~ ( member @ ( sK10_U @ SV67 @ SV49 ) @ SV67 ) )
= $false )
| ( ( subclass @ SV49 @ SV67 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[519]) ).
thf(580,plain,
! [SV68: $i,SV50: $i,SV109: $i] :
( ( ( ~ ( member @ SV109 @ SV50 )
| ( member @ SV109 @ SV68 ) )
= $true )
| ( ( subclass @ SV50 @ SV68 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(581,plain,
! [SV80: $i,SV51: $i] :
( ( ( SV51
= ( ordered_pair @ SV80 @ SV80 ) )
= $false )
| ( ( ~ ( member @ SV80 @ universal_class ) )
= $true )
| ( ( member @ SV51 @ identity_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[521]) ).
thf(582,plain,
! [SV52: $i] :
( ( ( ( SV52
!= ( ordered_pair @ ( sK7_X @ SV52 ) @ ( sK7_X @ SV52 ) ) ) )
= $false )
| ( ( member @ SV52 @ identity_relation )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[522]) ).
thf(583,plain,
! [SV52: $i] :
( ( ( ~ ( member @ ( sK7_X @ SV52 ) @ universal_class ) )
= $false )
| ( ( member @ SV52 @ identity_relation )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[522]) ).
thf(584,plain,
! [SV69: $i,SV53: $i] :
( ( ( subclass @ SV53 @ SV69 )
= $false )
| ( ( ~ ( subclass @ SV69 @ SV53 ) )
= $true )
| ( ( SV53 = SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[523]) ).
thf(585,plain,
! [SV110: $i,SV93: $i] :
( ( ( SV93 != SV110 )
| ( subclass @ SV93 @ SV110 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(586,plain,
! [SV111: $i,SV94: $i] :
( ( ( SV94 != SV111 )
| ( subclass @ SV111 @ SV94 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(587,plain,
! [SV70: $i,SV54: $i] :
( ( ( member @ SV54 @ universal_class )
= $false )
| ( ( ~ ( member @ SV70 @ universal_class ) )
= $true )
| ( ( ( first @ ( ordered_pair @ SV54 @ SV70 ) )
= SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(588,plain,
! [SV71: $i,SV55: $i] :
( ( ( member @ SV55 @ universal_class )
= $false )
| ( ( ~ ( member @ SV71 @ universal_class ) )
= $true )
| ( ( ( second @ ( ordered_pair @ SV55 @ SV71 ) )
= SV71 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[527]) ).
thf(589,plain,
! [SV57: $i,SV72: $i] :
( ( ( member @ SV72 @ universal_class )
= $false )
| ( ( ( restrict @ SV57 @ ( singleton @ SV72 ) @ universal_class )
= null_class )
= $true )
| ( ( member @ SV72 @ ( domain_of @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[528]) ).
thf(590,plain,
! [SV95: $i,SV112: $i] :
( ( ~ ( member @ SV112 @ ( domain_of @ SV95 ) )
| ( ( restrict @ SV95 @ ( singleton @ SV112 ) @ universal_class )
!= null_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(591,plain,
! [SV96: $i,SV113: $i] :
( ( ~ ( member @ SV113 @ ( domain_of @ SV96 ) )
| ( member @ SV113 @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(592,plain,
! [SV97: $i,SV37: $i,SV81: $i,SV22: $i] :
( ( ( ~ ( member @ SV22 @ SV81 )
| ~ ( member @ SV37 @ SV97 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV22 @ SV37 ) @ ( cross_product @ SV81 @ SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[531]) ).
thf(593,plain,
! [SV37: $i,SV22: $i] :
( ( ! [SY168: $i] :
( ! [SY169: $i] :
~ ( member @ ( ordered_pair @ SV22 @ SV37 ) @ ( cross_product @ SY168 @ SY169 ) )
| ( member @ SV22 @ SY168 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[532]) ).
thf(594,plain,
! [SV37: $i,SV22: $i] :
( ( ! [SY170: $i,SY171: $i] :
( ~ ( member @ ( ordered_pair @ SV22 @ SV37 ) @ ( cross_product @ SY170 @ SY171 ) )
| ( member @ SV37 @ SY171 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[533]) ).
thf(595,plain,
! [SV114: $i,SV23: $i] :
( ( ~ ( member @ SV23 @ universal_class )
| ( SV23 != SV114 )
| ! [SY218: $i] : ( member @ SV23 @ ( unordered_pair @ SV114 @ SY218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(596,plain,
! [SV115: $i,SV23: $i] :
( ( ! [SY219: $i] :
( ~ ( member @ SV23 @ universal_class )
| ( SV23 != SY219 )
| ( member @ SV23 @ ( unordered_pair @ SV115 @ SY219 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(597,plain,
! [SV23: $i] :
( ( ( ! [SY135: $i,SY136: $i] :
~ ( member @ SV23 @ ( unordered_pair @ SY135 @ SY136 ) ) )
= $true )
| ( ( member @ SV23 @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[536]) ).
thf(598,plain,
! [SV116: $i,SV23: $i] :
( ( ! [SY220: $i] :
( ~ ( member @ SV23 @ ( unordered_pair @ SV116 @ SY220 ) )
| ( SV23 = SV116 )
| ( SV23 = SY220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(599,plain,
! [SV73: $i,SV24: $i,SV82: $i] :
( ( ( ~ ( member @ SV82 @ SV24 ) )
= $true )
| ( ( ~ ( member @ SV82 @ SV73 ) )
= $true )
| ( ( member @ SV82 @ ( intersection @ SV24 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[538]) ).
thf(600,plain,
! [SV117: $i,SV24: $i] :
( ( ! [SY221: $i] :
( ~ ( member @ SY221 @ ( intersection @ SV24 @ SV117 ) )
| ( member @ SY221 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(601,plain,
! [SV118: $i,SV24: $i] :
( ( ! [SY222: $i] :
( ~ ( member @ SY222 @ ( intersection @ SV24 @ SV118 ) )
| ( member @ SY222 @ SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(602,plain,
! [SV74: $i,SV58: $i] :
( ( ( member @ SV58 @ universal_class )
= $false )
| ( ( ~ ( subclass @ SV58 @ SV74 ) )
= $true )
| ( ( member @ SV58 @ ( power_class @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[541]) ).
thf(603,plain,
! [SV98: $i] :
( ( ( ! [SY211: $i] :
~ ( member @ SV98 @ ( power_class @ SY211 ) ) )
= $true )
| ( ( member @ SV98 @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[542]) ).
thf(604,plain,
! [SV119: $i,SV99: $i] :
( ( ~ ( member @ SV99 @ ( power_class @ SV119 ) )
| ( subclass @ SV99 @ SV119 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(605,plain,
! [SV75: $i,SV59: $i] :
( ( ( ~ ( member @ SV59 @ universal_class ) )
= $true )
| ( ( ~ ( member @ SV75 @ universal_class ) )
= $true )
| ( ( ( ( successor @ SV59 )
!= SV75 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV59 @ SV75 ) @ successor_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[544]) ).
thf(606,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX0 @ universal_class ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[545]) ).
thf(607,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX1 @ universal_class ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[545]) ).
thf(608,plain,
! [SV120: $i,SV100: $i] :
( ( ~ ( member @ ( ordered_pair @ SV100 @ SV120 ) @ successor_relation )
| ( ( successor @ SV100 )
= SV120 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(609,plain,
! [SV25: $i] :
( ( ( member @ ( sK5_U @ SV25 ) @ universal_class )
= $true )
| ( ( SV25 = null_class )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[547]) ).
thf(610,plain,
! [SV25: $i] :
( ( ( member @ ( sK5_U @ SV25 ) @ SV25 )
= $true )
| ( ( SV25 = null_class )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[548]) ).
thf(611,plain,
! [SV60: $i,SV76: $i] :
( ( ( member @ SV76 @ universal_class )
= $false )
| ( ( member @ SV76 @ SV60 )
= $true )
| ( ( member @ SV76 @ ( complement @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[549]) ).
thf(612,plain,
! [SV101: $i,SV121: $i] :
( ( ~ ( member @ SV121 @ ( complement @ SV101 ) )
| ( member @ SV121 @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(613,plain,
! [SV102: $i,SV122: $i] :
( ( ~ ( member @ SV122 @ ( complement @ SV102 ) )
| ~ ( member @ SV122 @ SV102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(614,plain,
! [SV26: $i,SV103: $i,SV83: $i,SV38: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SV83 ) @ SV103 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV83 @ SV103 ) @ SV38 ) @ SV26 ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SV83 ) @ SV103 ) @ ( rotate @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[552]) ).
thf(615,plain,
! [SV26: $i,SV38: $i] :
( ( ! [SY174: $i,SY175: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SY174 ) @ SY175 ) @ ( rotate @ SV26 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SY174 ) @ SY175 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[553]) ).
thf(616,plain,
! [SV26: $i,SV38: $i] :
( ( ! [SY176: $i,SY177: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SY176 ) @ SY177 ) @ ( rotate @ SV26 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SY176 @ SY177 ) @ SV38 ) @ SV26 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[554]) ).
thf(617,plain,
! [SV61: $i,SV19: $i,SV77: $i] :
( ( ( member @ SV77 @ SV19 )
= $true )
| ( ( member @ SV77 @ SV61 )
= $true )
| ( ( member @ SV77 @ ( union @ SV19 @ SV61 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[555]) ).
thf(618,plain,
! [SV104: $i,SV19: $i,SV123: $i] :
( ( ~ ( member @ SV123 @ SV19 )
| ( member @ SV123 @ ( union @ SV19 @ SV104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(619,plain,
! [SV19: $i,SV105: $i,SV124: $i] :
( ( ~ ( member @ SV124 @ SV105 )
| ( member @ SV124 @ ( union @ SV19 @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(620,plain,
! [SV20: $i,SV35: $i,SV84: $i,SV78: $i] :
( ( ( ~ ( member @ SV78 @ universal_class ) )
= $true )
| ( ( ~ ( member @ SV84 @ ( image @ SV35 @ ( image @ SV20 @ ( singleton @ SV78 ) ) ) ) )
= $true )
| ( ( member @ ( ordered_pair @ SV78 @ SV84 ) @ ( compose @ SV35 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[558]) ).
thf(621,plain,
! [SV20: $i,SV35: $i,SV125: $i] :
( ( ! [SY223: $i] :
~ ( member @ ( ordered_pair @ SV125 @ SY223 ) @ ( compose @ SV35 @ SV20 ) )
| ( member @ SV125 @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(622,plain,
! [SV20: $i,SV35: $i,SV126: $i] :
( ( ! [SY224: $i] :
( ~ ( member @ ( ordered_pair @ SV126 @ SY224 ) @ ( compose @ SV35 @ SV20 ) )
| ( member @ SY224 @ ( image @ SV35 @ ( image @ SV20 @ ( singleton @ SV126 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(623,plain,
! [SV85: $i,SV79: $i,SV36: $i,SV21: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SV79 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV36 @ SV21 ) @ SV79 ) @ SV85 ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SV79 ) @ ( flip @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[561]) ).
thf(624,plain,
! [SV127: $i,SV36: $i,SV21: $i] :
( ( ! [SY225: $i] :
~ ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SV127 ) @ ( flip @ SY225 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SV127 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(625,plain,
! [SV128: $i,SV36: $i,SV21: $i] :
( ( ! [SY226: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SV128 ) @ ( flip @ SY226 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV36 @ SV21 ) @ SV128 ) @ SY226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(626,plain,
! [SV62: $i,SV42: $i] :
( ( ( member @ SV42 @ SV62 )
= $false )
| ( ( member @ SV62 @ universal_class )
= $false )
| ( ( member @ ( ordered_pair @ SV42 @ SV62 ) @ element_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[564]) ).
thf(627,plain,
! [SV106: $i,SV86: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV86 @ SV106 ) @ element_relation ) )
= $true )
| ( ( member @ SV106 @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[565]) ).
thf(628,plain,
! [SV107: $i,SV87: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV87 @ SV107 ) @ element_relation ) )
= $true )
| ( ( member @ SV87 @ SV107 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[566]) ).
thf(629,plain,
! [SV63: $i,SV88: $i,SV43: $i] :
( ( ( member @ SV43 @ SV88 )
= $false )
| ( ( ~ ( member @ SV88 @ SV63 ) )
= $true )
| ( ( member @ SV43 @ ( sum_class @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[567]) ).
thf(630,plain,
! [SV64: $i,SV44: $i] :
( ( ( ~ ( member @ SV44 @ ( sK8_Y @ SV64 @ SV44 ) ) )
= $false )
| ( ( member @ SV44 @ ( sum_class @ SV64 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[568]) ).
thf(631,plain,
! [SV44: $i,SV64: $i] :
( ( ( ~ ( member @ ( sK8_Y @ SV64 @ SV44 ) @ SV64 ) )
= $false )
| ( ( member @ SV44 @ ( sum_class @ SV64 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[568]) ).
thf(632,plain,
! [SV89: $i] :
( ( ( function @ SV89 )
= $false )
| ( ( subclass @ SV89 @ ( cross_product @ universal_class @ universal_class ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[570]) ).
thf(633,plain,
! [SV90: $i] :
( ( ( function @ SV90 )
= $false )
| ( ( subclass @ ( compose @ SV90 @ ( inverse @ SV90 ) ) @ identity_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(634,plain,
! [SV91: $i] :
( ( ( inductive @ SV91 )
= $false )
| ( ( member @ null_class @ SV91 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[573]) ).
thf(635,plain,
! [SV92: $i] :
( ( ( inductive @ SV92 )
= $false )
| ( ( subclass @ ( image @ successor_relation @ SV92 ) @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[574]) ).
thf(636,plain,
! [SV47: $i,SV65: $i] :
( ( ( member @ ( sK6_U @ SV65 @ SV47 ) @ SV47 )
= $true )
| ( ( disjoint @ SV47 @ SV65 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[575]) ).
thf(637,plain,
! [SV47: $i,SV65: $i] :
( ( ( member @ ( sK6_U @ SV65 @ SV47 ) @ SV65 )
= $true )
| ( ( disjoint @ SV47 @ SV65 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[576]) ).
thf(638,plain,
! [SV66: $i,SV48: $i,SV108: $i] :
( ( ( ~ ( member @ SV108 @ SV48 ) )
= $true )
| ( ( ~ ( member @ SV108 @ SV66 ) )
= $true )
| ( ( disjoint @ SV48 @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[577]) ).
thf(639,plain,
! [SV49: $i,SV67: $i] :
( ( ( member @ ( sK10_U @ SV67 @ SV49 ) @ SV49 )
= $true )
| ( ( subclass @ SV49 @ SV67 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[578]) ).
thf(640,plain,
! [SV49: $i,SV67: $i] :
( ( ( ~ ( member @ ( sK10_U @ SV67 @ SV49 ) @ SV67 ) )
= $true )
| ( ( subclass @ SV49 @ SV67 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[579]) ).
thf(641,plain,
! [SV68: $i,SV50: $i,SV109: $i] :
( ( ( ~ ( member @ SV109 @ SV50 ) )
= $true )
| ( ( member @ SV109 @ SV68 )
= $true )
| ( ( subclass @ SV50 @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[580]) ).
thf(642,plain,
! [SV51: $i,SV80: $i] :
( ( ( member @ SV80 @ universal_class )
= $false )
| ( ( SV51
= ( ordered_pair @ SV80 @ SV80 ) )
= $false )
| ( ( member @ SV51 @ identity_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[581]) ).
thf(643,plain,
! [SV52: $i] :
( ( ( SV52
= ( ordered_pair @ ( sK7_X @ SV52 ) @ ( sK7_X @ SV52 ) ) )
= $true )
| ( ( member @ SV52 @ identity_relation )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[582]) ).
thf(644,plain,
! [SV52: $i] :
( ( ( member @ ( sK7_X @ SV52 ) @ universal_class )
= $true )
| ( ( member @ SV52 @ identity_relation )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[583]) ).
thf(645,plain,
! [SV53: $i,SV69: $i] :
( ( ( subclass @ SV69 @ SV53 )
= $false )
| ( ( subclass @ SV53 @ SV69 )
= $false )
| ( ( SV53 = SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[584]) ).
thf(646,plain,
! [SV110: $i,SV93: $i] :
( ( ( ( SV93 != SV110 ) )
= $true )
| ( ( subclass @ SV93 @ SV110 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[585]) ).
thf(647,plain,
! [SV111: $i,SV94: $i] :
( ( ( ( SV94 != SV111 ) )
= $true )
| ( ( subclass @ SV111 @ SV94 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[586]) ).
thf(648,plain,
! [SV54: $i,SV70: $i] :
( ( ( member @ SV70 @ universal_class )
= $false )
| ( ( member @ SV54 @ universal_class )
= $false )
| ( ( ( first @ ( ordered_pair @ SV54 @ SV70 ) )
= SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[587]) ).
thf(649,plain,
! [SV55: $i,SV71: $i] :
( ( ( member @ SV71 @ universal_class )
= $false )
| ( ( member @ SV55 @ universal_class )
= $false )
| ( ( ( second @ ( ordered_pair @ SV55 @ SV71 ) )
= SV71 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[588]) ).
thf(650,plain,
! [SV95: $i,SV112: $i] :
( ( ( ~ ( member @ SV112 @ ( domain_of @ SV95 ) ) )
= $true )
| ( ( ( ( restrict @ SV95 @ ( singleton @ SV112 ) @ universal_class )
!= null_class ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[590]) ).
thf(651,plain,
! [SV96: $i,SV113: $i] :
( ( ( ~ ( member @ SV113 @ ( domain_of @ SV96 ) ) )
= $true )
| ( ( member @ SV113 @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[591]) ).
thf(652,plain,
! [SV97: $i,SV37: $i,SV81: $i,SV22: $i] :
( ( ( ~ ( member @ SV22 @ SV81 ) )
= $true )
| ( ( ~ ( member @ SV37 @ SV97 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV22 @ SV37 ) @ ( cross_product @ SV81 @ SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[592]) ).
thf(653,plain,
! [SV129: $i,SV37: $i,SV22: $i] :
( ( ! [SY227: $i] :
~ ( member @ ( ordered_pair @ SV22 @ SV37 ) @ ( cross_product @ SV129 @ SY227 ) )
| ( member @ SV22 @ SV129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(654,plain,
! [SV130: $i,SV37: $i,SV22: $i] :
( ( ! [SY228: $i] :
( ~ ( member @ ( ordered_pair @ SV22 @ SV37 ) @ ( cross_product @ SV130 @ SY228 ) )
| ( member @ SV37 @ SY228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(655,plain,
! [SV114: $i,SV23: $i] :
( ( ( ~ ( member @ SV23 @ universal_class )
| ( SV23 != SV114 ) )
= $true )
| ( ( ! [SY218: $i] : ( member @ SV23 @ ( unordered_pair @ SV114 @ SY218 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[595]) ).
thf(656,plain,
! [SV115: $i,SV131: $i,SV23: $i] :
( ( ~ ( member @ SV23 @ universal_class )
| ( SV23 != SV131 )
| ( member @ SV23 @ ( unordered_pair @ SV115 @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(657,plain,
! [SV132: $i,SV23: $i] :
( ( ( ! [SY229: $i] :
~ ( member @ SV23 @ ( unordered_pair @ SV132 @ SY229 ) ) )
= $true )
| ( ( member @ SV23 @ universal_class )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(658,plain,
! [SV133: $i,SV116: $i,SV23: $i] :
( ( ~ ( member @ SV23 @ ( unordered_pair @ SV116 @ SV133 ) )
| ( SV23 = SV116 )
| ( SV23 = SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(659,plain,
! [SV73: $i,SV24: $i,SV82: $i] :
( ( ( member @ SV82 @ SV24 )
= $false )
| ( ( ~ ( member @ SV82 @ SV73 ) )
= $true )
| ( ( member @ SV82 @ ( intersection @ SV24 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[599]) ).
thf(660,plain,
! [SV117: $i,SV24: $i,SV134: $i] :
( ( ~ ( member @ SV134 @ ( intersection @ SV24 @ SV117 ) )
| ( member @ SV134 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(661,plain,
! [SV118: $i,SV24: $i,SV135: $i] :
( ( ~ ( member @ SV135 @ ( intersection @ SV24 @ SV118 ) )
| ( member @ SV135 @ SV118 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(662,plain,
! [SV74: $i,SV58: $i] :
( ( ( subclass @ SV58 @ SV74 )
= $false )
| ( ( member @ SV58 @ universal_class )
= $false )
| ( ( member @ SV58 @ ( power_class @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[602]) ).
thf(663,plain,
! [SV136: $i,SV98: $i] :
( ( ( ~ ( member @ SV98 @ ( power_class @ SV136 ) ) )
= $true )
| ( ( member @ SV98 @ universal_class )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(664,plain,
! [SV119: $i,SV99: $i] :
( ( ( ~ ( member @ SV99 @ ( power_class @ SV119 ) ) )
= $true )
| ( ( subclass @ SV99 @ SV119 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[604]) ).
thf(665,plain,
! [SV75: $i,SV59: $i] :
( ( ( member @ SV59 @ universal_class )
= $false )
| ( ( ~ ( member @ SV75 @ universal_class ) )
= $true )
| ( ( ( ( successor @ SV59 )
!= SV75 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV59 @ SV75 ) @ successor_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[605]) ).
thf(666,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX0 @ universal_class ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[606]) ).
thf(667,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX1 @ universal_class ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[607]) ).
thf(668,plain,
! [SV120: $i,SV100: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV100 @ SV120 ) @ successor_relation ) )
= $true )
| ( ( ( successor @ SV100 )
= SV120 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[608]) ).
thf(669,plain,
! [SV101: $i,SV121: $i] :
( ( ( ~ ( member @ SV121 @ ( complement @ SV101 ) ) )
= $true )
| ( ( member @ SV121 @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[612]) ).
thf(670,plain,
! [SV102: $i,SV122: $i] :
( ( ( ~ ( member @ SV122 @ ( complement @ SV102 ) ) )
= $true )
| ( ( ~ ( member @ SV122 @ SV102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[613]) ).
thf(671,plain,
! [SV26: $i,SV103: $i,SV83: $i,SV38: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SV83 ) @ SV103 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV83 @ SV103 ) @ SV38 ) @ SV26 ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SV83 ) @ SV103 ) @ ( rotate @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[614]) ).
thf(672,plain,
! [SV26: $i,SV137: $i,SV38: $i] :
( ( ! [SY230: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SV137 ) @ SY230 ) @ ( rotate @ SV26 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SV137 ) @ SY230 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(673,plain,
! [SV26: $i,SV138: $i,SV38: $i] :
( ( ! [SY231: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SV138 ) @ SY231 ) @ ( rotate @ SV26 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV138 @ SY231 ) @ SV38 ) @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(674,plain,
! [SV104: $i,SV19: $i,SV123: $i] :
( ( ( ~ ( member @ SV123 @ SV19 ) )
= $true )
| ( ( member @ SV123 @ ( union @ SV19 @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[618]) ).
thf(675,plain,
! [SV19: $i,SV105: $i,SV124: $i] :
( ( ( ~ ( member @ SV124 @ SV105 ) )
= $true )
| ( ( member @ SV124 @ ( union @ SV19 @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[619]) ).
thf(676,plain,
! [SV20: $i,SV35: $i,SV84: $i,SV78: $i] :
( ( ( member @ SV78 @ universal_class )
= $false )
| ( ( ~ ( member @ SV84 @ ( image @ SV35 @ ( image @ SV20 @ ( singleton @ SV78 ) ) ) ) )
= $true )
| ( ( member @ ( ordered_pair @ SV78 @ SV84 ) @ ( compose @ SV35 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[620]) ).
thf(677,plain,
! [SV20: $i,SV35: $i,SV125: $i] :
( ( ( ! [SY223: $i] :
~ ( member @ ( ordered_pair @ SV125 @ SY223 ) @ ( compose @ SV35 @ SV20 ) ) )
= $true )
| ( ( member @ SV125 @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[621]) ).
thf(678,plain,
! [SV20: $i,SV35: $i,SV139: $i,SV126: $i] :
( ( ~ ( member @ ( ordered_pair @ SV126 @ SV139 ) @ ( compose @ SV35 @ SV20 ) )
| ( member @ SV139 @ ( image @ SV35 @ ( image @ SV20 @ ( singleton @ SV126 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(679,plain,
! [SV85: $i,SV79: $i,SV36: $i,SV21: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SV79 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV36 @ SV21 ) @ SV79 ) @ SV85 ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SV79 ) @ ( flip @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[623]) ).
thf(680,plain,
! [SV127: $i,SV36: $i,SV21: $i] :
( ( ( ! [SY225: $i] :
~ ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SV127 ) @ ( flip @ SY225 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SV127 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[624]) ).
thf(681,plain,
! [SV140: $i,SV128: $i,SV36: $i,SV21: $i] :
( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SV128 ) @ ( flip @ SV140 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV36 @ SV21 ) @ SV128 ) @ SV140 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(682,plain,
! [SV106: $i,SV86: $i] :
( ( ( member @ ( ordered_pair @ SV86 @ SV106 ) @ element_relation )
= $false )
| ( ( member @ SV106 @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[627]) ).
thf(683,plain,
! [SV107: $i,SV87: $i] :
( ( ( member @ ( ordered_pair @ SV87 @ SV107 ) @ element_relation )
= $false )
| ( ( member @ SV87 @ SV107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[628]) ).
thf(684,plain,
! [SV43: $i,SV63: $i,SV88: $i] :
( ( ( member @ SV88 @ SV63 )
= $false )
| ( ( member @ SV43 @ SV88 )
= $false )
| ( ( member @ SV43 @ ( sum_class @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[629]) ).
thf(685,plain,
! [SV64: $i,SV44: $i] :
( ( ( member @ SV44 @ ( sK8_Y @ SV64 @ SV44 ) )
= $true )
| ( ( member @ SV44 @ ( sum_class @ SV64 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[630]) ).
thf(686,plain,
! [SV44: $i,SV64: $i] :
( ( ( member @ ( sK8_Y @ SV64 @ SV44 ) @ SV64 )
= $true )
| ( ( member @ SV44 @ ( sum_class @ SV64 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[631]) ).
thf(687,plain,
! [SV66: $i,SV48: $i,SV108: $i] :
( ( ( member @ SV108 @ SV48 )
= $false )
| ( ( ~ ( member @ SV108 @ SV66 ) )
= $true )
| ( ( disjoint @ SV48 @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[638]) ).
thf(688,plain,
! [SV49: $i,SV67: $i] :
( ( ( member @ ( sK10_U @ SV67 @ SV49 ) @ SV67 )
= $false )
| ( ( subclass @ SV49 @ SV67 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[640]) ).
thf(689,plain,
! [SV68: $i,SV50: $i,SV109: $i] :
( ( ( member @ SV109 @ SV50 )
= $false )
| ( ( member @ SV109 @ SV68 )
= $true )
| ( ( subclass @ SV50 @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[641]) ).
thf(690,plain,
! [SV110: $i,SV93: $i] :
( ( ( SV93 = SV110 )
= $false )
| ( ( subclass @ SV93 @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[646]) ).
thf(691,plain,
! [SV111: $i,SV94: $i] :
( ( ( SV94 = SV111 )
= $false )
| ( ( subclass @ SV111 @ SV94 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[647]) ).
thf(692,plain,
! [SV95: $i,SV112: $i] :
( ( ( member @ SV112 @ ( domain_of @ SV95 ) )
= $false )
| ( ( ( ( restrict @ SV95 @ ( singleton @ SV112 ) @ universal_class )
!= null_class ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[650]) ).
thf(693,plain,
! [SV96: $i,SV113: $i] :
( ( ( member @ SV113 @ ( domain_of @ SV96 ) )
= $false )
| ( ( member @ SV113 @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[651]) ).
thf(694,plain,
! [SV97: $i,SV37: $i,SV81: $i,SV22: $i] :
( ( ( member @ SV22 @ SV81 )
= $false )
| ( ( ~ ( member @ SV37 @ SV97 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV22 @ SV37 ) @ ( cross_product @ SV81 @ SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[652]) ).
thf(695,plain,
! [SV129: $i,SV37: $i,SV22: $i] :
( ( ( ! [SY227: $i] :
~ ( member @ ( ordered_pair @ SV22 @ SV37 ) @ ( cross_product @ SV129 @ SY227 ) ) )
= $true )
| ( ( member @ SV22 @ SV129 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[653]) ).
thf(696,plain,
! [SV141: $i,SV130: $i,SV37: $i,SV22: $i] :
( ( ~ ( member @ ( ordered_pair @ SV22 @ SV37 ) @ ( cross_product @ SV130 @ SV141 ) )
| ( member @ SV37 @ SV141 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(697,plain,
! [SV114: $i,SV23: $i] :
( ( ( ~ ( member @ SV23 @ universal_class ) )
= $true )
| ( ( ( SV23 != SV114 ) )
= $true )
| ( ( ! [SY218: $i] : ( member @ SV23 @ ( unordered_pair @ SV114 @ SY218 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[655]) ).
thf(698,plain,
! [SV115: $i,SV131: $i,SV23: $i] :
( ( ( ~ ( member @ SV23 @ universal_class )
| ( SV23 != SV131 ) )
= $true )
| ( ( member @ SV23 @ ( unordered_pair @ SV115 @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[656]) ).
thf(699,plain,
! [SV142: $i,SV132: $i,SV23: $i] :
( ( ( ~ ( member @ SV23 @ ( unordered_pair @ SV132 @ SV142 ) ) )
= $true )
| ( ( member @ SV23 @ universal_class )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(700,plain,
! [SV133: $i,SV116: $i,SV23: $i] :
( ( ( ~ ( member @ SV23 @ ( unordered_pair @ SV116 @ SV133 ) ) )
= $true )
| ( ( ( SV23 = SV116 )
| ( SV23 = SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[658]) ).
thf(701,plain,
! [SV24: $i,SV73: $i,SV82: $i] :
( ( ( member @ SV82 @ SV73 )
= $false )
| ( ( member @ SV82 @ SV24 )
= $false )
| ( ( member @ SV82 @ ( intersection @ SV24 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[659]) ).
thf(702,plain,
! [SV117: $i,SV24: $i,SV134: $i] :
( ( ( ~ ( member @ SV134 @ ( intersection @ SV24 @ SV117 ) ) )
= $true )
| ( ( member @ SV134 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[660]) ).
thf(703,plain,
! [SV118: $i,SV24: $i,SV135: $i] :
( ( ( ~ ( member @ SV135 @ ( intersection @ SV24 @ SV118 ) ) )
= $true )
| ( ( member @ SV135 @ SV118 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[661]) ).
thf(704,plain,
! [SV136: $i,SV98: $i] :
( ( ( member @ SV98 @ ( power_class @ SV136 ) )
= $false )
| ( ( member @ SV98 @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[663]) ).
thf(705,plain,
! [SV119: $i,SV99: $i] :
( ( ( member @ SV99 @ ( power_class @ SV119 ) )
= $false )
| ( ( subclass @ SV99 @ SV119 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[664]) ).
thf(706,plain,
! [SV59: $i,SV75: $i] :
( ( ( member @ SV75 @ universal_class )
= $false )
| ( ( member @ SV59 @ universal_class )
= $false )
| ( ( ( ( successor @ SV59 )
!= SV75 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV59 @ SV75 ) @ successor_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[665]) ).
thf(707,plain,
! [SV143: $i] :
( ( ! [SY232: $i] :
~ ( member @ ( ordered_pair @ SV143 @ SY232 ) @ successor_relation )
| ( member @ SV143 @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(708,plain,
! [SV144: $i] :
( ( ! [SY233: $i] :
( ~ ( member @ ( ordered_pair @ SV144 @ SY233 ) @ successor_relation )
| ( member @ SY233 @ universal_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(709,plain,
! [SV120: $i,SV100: $i] :
( ( ( member @ ( ordered_pair @ SV100 @ SV120 ) @ successor_relation )
= $false )
| ( ( ( successor @ SV100 )
= SV120 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[668]) ).
thf(710,plain,
! [SV101: $i,SV121: $i] :
( ( ( member @ SV121 @ ( complement @ SV101 ) )
= $false )
| ( ( member @ SV121 @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[669]) ).
thf(711,plain,
! [SV102: $i,SV122: $i] :
( ( ( member @ SV122 @ ( complement @ SV102 ) )
= $false )
| ( ( ~ ( member @ SV122 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[670]) ).
thf(712,plain,
! [SV26: $i,SV103: $i,SV83: $i,SV38: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SV83 ) @ SV103 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV83 @ SV103 ) @ SV38 ) @ SV26 ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SV83 ) @ SV103 ) @ ( rotate @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[671]) ).
thf(713,plain,
! [SV26: $i,SV145: $i,SV137: $i,SV38: $i] :
( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SV137 ) @ SV145 ) @ ( rotate @ SV26 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SV137 ) @ SV145 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(714,plain,
! [SV26: $i,SV146: $i,SV138: $i,SV38: $i] :
( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SV138 ) @ SV146 ) @ ( rotate @ SV26 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV138 @ SV146 ) @ SV38 ) @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(715,plain,
! [SV104: $i,SV19: $i,SV123: $i] :
( ( ( member @ SV123 @ SV19 )
= $false )
| ( ( member @ SV123 @ ( union @ SV19 @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[674]) ).
thf(716,plain,
! [SV19: $i,SV105: $i,SV124: $i] :
( ( ( member @ SV124 @ SV105 )
= $false )
| ( ( member @ SV124 @ ( union @ SV19 @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[675]) ).
thf(717,plain,
! [SV78: $i,SV20: $i,SV35: $i,SV84: $i] :
( ( ( member @ SV84 @ ( image @ SV35 @ ( image @ SV20 @ ( singleton @ SV78 ) ) ) )
= $false )
| ( ( member @ SV78 @ universal_class )
= $false )
| ( ( member @ ( ordered_pair @ SV78 @ SV84 ) @ ( compose @ SV35 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[676]) ).
thf(718,plain,
! [SV20: $i,SV35: $i,SV147: $i,SV125: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV125 @ SV147 ) @ ( compose @ SV35 @ SV20 ) ) )
= $true )
| ( ( member @ SV125 @ universal_class )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(719,plain,
! [SV20: $i,SV35: $i,SV139: $i,SV126: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV126 @ SV139 ) @ ( compose @ SV35 @ SV20 ) ) )
= $true )
| ( ( member @ SV139 @ ( image @ SV35 @ ( image @ SV20 @ ( singleton @ SV126 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[678]) ).
thf(720,plain,
! [SV85: $i,SV79: $i,SV21: $i,SV36: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ SV36 @ SV21 ) @ SV79 ) @ SV85 )
= $false )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SV79 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
= $false )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SV79 ) @ ( flip @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[679]) ).
thf(721,plain,
! [SV148: $i,SV127: $i,SV36: $i,SV21: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SV127 ) @ ( flip @ SV148 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SV127 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(722,plain,
! [SV140: $i,SV128: $i,SV36: $i,SV21: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SV128 ) @ ( flip @ SV140 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV36 @ SV21 ) @ SV128 ) @ SV140 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[681]) ).
thf(723,plain,
! [SV48: $i,SV66: $i,SV108: $i] :
( ( ( member @ SV108 @ SV66 )
= $false )
| ( ( member @ SV108 @ SV48 )
= $false )
| ( ( disjoint @ SV48 @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[687]) ).
thf(724,plain,
! [SV112: $i,SV95: $i] :
( ( ( ( restrict @ SV95 @ ( singleton @ SV112 ) @ universal_class )
= null_class )
= $false )
| ( ( member @ SV112 @ ( domain_of @ SV95 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[692]) ).
thf(725,plain,
! [SV81: $i,SV22: $i,SV97: $i,SV37: $i] :
( ( ( member @ SV37 @ SV97 )
= $false )
| ( ( member @ SV22 @ SV81 )
= $false )
| ( ( member @ ( ordered_pair @ SV22 @ SV37 ) @ ( cross_product @ SV81 @ SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[694]) ).
thf(726,plain,
! [SV149: $i,SV129: $i,SV37: $i,SV22: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV22 @ SV37 ) @ ( cross_product @ SV129 @ SV149 ) ) )
= $true )
| ( ( member @ SV22 @ SV129 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(727,plain,
! [SV141: $i,SV130: $i,SV37: $i,SV22: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV22 @ SV37 ) @ ( cross_product @ SV130 @ SV141 ) ) )
= $true )
| ( ( member @ SV37 @ SV141 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[696]) ).
thf(728,plain,
! [SV114: $i,SV23: $i] :
( ( ( member @ SV23 @ universal_class )
= $false )
| ( ( ( SV23 != SV114 ) )
= $true )
| ( ( ! [SY218: $i] : ( member @ SV23 @ ( unordered_pair @ SV114 @ SY218 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[697]) ).
thf(729,plain,
! [SV115: $i,SV131: $i,SV23: $i] :
( ( ( ~ ( member @ SV23 @ universal_class ) )
= $true )
| ( ( ( SV23 != SV131 ) )
= $true )
| ( ( member @ SV23 @ ( unordered_pair @ SV115 @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[698]) ).
thf(730,plain,
! [SV142: $i,SV132: $i,SV23: $i] :
( ( ( member @ SV23 @ ( unordered_pair @ SV132 @ SV142 ) )
= $false )
| ( ( member @ SV23 @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[699]) ).
thf(731,plain,
! [SV133: $i,SV116: $i,SV23: $i] :
( ( ( member @ SV23 @ ( unordered_pair @ SV116 @ SV133 ) )
= $false )
| ( ( ( SV23 = SV116 )
| ( SV23 = SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[700]) ).
thf(732,plain,
! [SV117: $i,SV24: $i,SV134: $i] :
( ( ( member @ SV134 @ ( intersection @ SV24 @ SV117 ) )
= $false )
| ( ( member @ SV134 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[702]) ).
thf(733,plain,
! [SV118: $i,SV24: $i,SV135: $i] :
( ( ( member @ SV135 @ ( intersection @ SV24 @ SV118 ) )
= $false )
| ( ( member @ SV135 @ SV118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[703]) ).
thf(734,plain,
! [SV75: $i,SV59: $i] :
( ( ( ( successor @ SV59 )
= SV75 )
= $false )
| ( ( member @ SV59 @ universal_class )
= $false )
| ( ( member @ SV75 @ universal_class )
= $false )
| ( ( member @ ( ordered_pair @ SV59 @ SV75 ) @ successor_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[706]) ).
thf(735,plain,
! [SV143: $i] :
( ( ( ! [SY232: $i] :
~ ( member @ ( ordered_pair @ SV143 @ SY232 ) @ successor_relation ) )
= $true )
| ( ( member @ SV143 @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[707]) ).
thf(736,plain,
! [SV150: $i,SV144: $i] :
( ( ~ ( member @ ( ordered_pair @ SV144 @ SV150 ) @ successor_relation )
| ( member @ SV150 @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(737,plain,
! [SV102: $i,SV122: $i] :
( ( ( member @ SV122 @ SV102 )
= $false )
| ( ( member @ SV122 @ ( complement @ SV102 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[711]) ).
thf(738,plain,
! [SV26: $i,SV38: $i,SV103: $i,SV83: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ SV83 @ SV103 ) @ SV38 ) @ SV26 )
= $false )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SV83 ) @ SV103 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
= $false )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SV83 ) @ SV103 ) @ ( rotate @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[712]) ).
thf(739,plain,
! [SV26: $i,SV145: $i,SV137: $i,SV38: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SV137 ) @ SV145 ) @ ( rotate @ SV26 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SV137 ) @ SV145 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[713]) ).
thf(740,plain,
! [SV26: $i,SV146: $i,SV138: $i,SV38: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SV138 ) @ SV146 ) @ ( rotate @ SV26 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV138 @ SV146 ) @ SV38 ) @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[714]) ).
thf(741,plain,
! [SV20: $i,SV35: $i,SV147: $i,SV125: $i] :
( ( ( member @ ( ordered_pair @ SV125 @ SV147 ) @ ( compose @ SV35 @ SV20 ) )
= $false )
| ( ( member @ SV125 @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[718]) ).
thf(742,plain,
! [SV20: $i,SV35: $i,SV139: $i,SV126: $i] :
( ( ( member @ ( ordered_pair @ SV126 @ SV139 ) @ ( compose @ SV35 @ SV20 ) )
= $false )
| ( ( member @ SV139 @ ( image @ SV35 @ ( image @ SV20 @ ( singleton @ SV126 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[719]) ).
thf(743,plain,
! [SV148: $i,SV127: $i,SV36: $i,SV21: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SV127 ) @ ( flip @ SV148 ) )
= $false )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SV127 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[721]) ).
thf(744,plain,
! [SV140: $i,SV128: $i,SV36: $i,SV21: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ SV21 @ SV36 ) @ SV128 ) @ ( flip @ SV140 ) )
= $false )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV36 @ SV21 ) @ SV128 ) @ SV140 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[722]) ).
thf(745,plain,
! [SV149: $i,SV129: $i,SV37: $i,SV22: $i] :
( ( ( member @ ( ordered_pair @ SV22 @ SV37 ) @ ( cross_product @ SV129 @ SV149 ) )
= $false )
| ( ( member @ SV22 @ SV129 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[726]) ).
thf(746,plain,
! [SV141: $i,SV130: $i,SV37: $i,SV22: $i] :
( ( ( member @ ( ordered_pair @ SV22 @ SV37 ) @ ( cross_product @ SV130 @ SV141 ) )
= $false )
| ( ( member @ SV37 @ SV141 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[727]) ).
thf(747,plain,
! [SV114: $i,SV23: $i] :
( ( ( SV23 = SV114 )
= $false )
| ( ( member @ SV23 @ universal_class )
= $false )
| ( ( ! [SY218: $i] : ( member @ SV23 @ ( unordered_pair @ SV114 @ SY218 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[728]) ).
thf(748,plain,
! [SV115: $i,SV131: $i,SV23: $i] :
( ( ( member @ SV23 @ universal_class )
= $false )
| ( ( ( SV23 != SV131 ) )
= $true )
| ( ( member @ SV23 @ ( unordered_pair @ SV115 @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[729]) ).
thf(749,plain,
! [SV133: $i,SV116: $i,SV23: $i] :
( ( ( SV23 = SV116 )
= $true )
| ( ( SV23 = SV133 )
= $true )
| ( ( member @ SV23 @ ( unordered_pair @ SV116 @ SV133 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[731]) ).
thf(750,plain,
! [SV151: $i,SV143: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV143 @ SV151 ) @ successor_relation ) )
= $true )
| ( ( member @ SV143 @ universal_class )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(751,plain,
! [SV150: $i,SV144: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV144 @ SV150 ) @ successor_relation ) )
= $true )
| ( ( member @ SV150 @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[736]) ).
thf(752,plain,
! [SV26: $i,SV145: $i,SV137: $i,SV38: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SV137 ) @ SV145 ) @ ( rotate @ SV26 ) )
= $false )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SV137 ) @ SV145 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[739]) ).
thf(753,plain,
! [SV26: $i,SV146: $i,SV138: $i,SV38: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ SV38 @ SV138 ) @ SV146 ) @ ( rotate @ SV26 ) )
= $false )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV138 @ SV146 ) @ SV38 ) @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[740]) ).
thf(754,plain,
! [SV152: $i,SV114: $i,SV23: $i] :
( ( ( member @ SV23 @ ( unordered_pair @ SV114 @ SV152 ) )
= $true )
| ( ( member @ SV23 @ universal_class )
= $false )
| ( ( SV23 = SV114 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(755,plain,
! [SV115: $i,SV131: $i,SV23: $i] :
( ( ( SV23 = SV131 )
= $false )
| ( ( member @ SV23 @ universal_class )
= $false )
| ( ( member @ SV23 @ ( unordered_pair @ SV115 @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[748]) ).
thf(756,plain,
! [SV151: $i,SV143: $i] :
( ( ( member @ ( ordered_pair @ SV143 @ SV151 ) @ successor_relation )
= $false )
| ( ( member @ SV143 @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[750]) ).
thf(757,plain,
! [SV150: $i,SV144: $i] :
( ( ( member @ ( ordered_pair @ SV144 @ SV150 ) @ successor_relation )
= $false )
| ( ( member @ SV150 @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[751]) ).
thf(758,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[139,757,756,755,754,753,752,749,746,745,744,743,742,741,738,737,734,733,732,730,725,724,723,720,717,716,715,710,709,705,704,701,693,691,690,689,688,686,685,684,683,682,662,649,648,645,644,643,642,639,637,636,635,634,633,632,626,617,611,610,609,589,572,569,505,471,470,469,438,432,382,299,292,291,290,250,248,245,244,241,240,216,209,208,207,206,205,200,198,173,172,171,151]) ).
thf(759,plain,
( ( ! [X: $i,Y: $i] :
( ( ( member @ ( sK10_U @ Y @ X ) @ X )
& ~ ( member @ ( sK10_U @ Y @ X ) @ Y ) )
| ( subclass @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( subclass @ X @ Y )
| ! [U: $i] :
( ~ ( member @ U @ X )
| ( member @ U @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(760,plain,
( ( ! [X: $i] : ( subclass @ X @ universal_class ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(761,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( subclass @ X @ Y )
| ~ ( subclass @ Y @ X )
| ( X = Y ) )
& ! [X: $i,Y: $i] :
( ( X != Y )
| ( subclass @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ( X != Y )
| ( subclass @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(762,plain,
( ( ! [U: $i] :
( ! [X: $i] :
( ~ ( member @ U @ universal_class )
| ( U != X )
| ! [Y: $i] : ( member @ U @ ( unordered_pair @ X @ Y ) ) )
& ! [X: $i,Y: $i] :
( ~ ( member @ U @ universal_class )
| ( U != Y )
| ( member @ U @ ( unordered_pair @ X @ Y ) ) )
& ( ! [X: $i,Y: $i] :
~ ( member @ U @ ( unordered_pair @ X @ Y ) )
| ( member @ U @ universal_class ) )
& ! [X: $i,Y: $i] :
( ~ ( member @ U @ ( unordered_pair @ X @ Y ) )
| ( U = X )
| ( U = Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(763,plain,
( ( ! [X: $i,Y: $i] : ( member @ ( unordered_pair @ X @ Y ) @ universal_class ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(764,plain,
( ( ! [X: $i] :
( ( singleton @ X )
= ( unordered_pair @ X @ X ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(765,plain,
( ( ! [X: $i,Y: $i] :
( ( ordered_pair @ X @ Y )
= ( unordered_pair @ ( singleton @ X ) @ ( unordered_pair @ X @ ( singleton @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(766,plain,
( ( ! [U: $i,V: $i] :
( ! [X: $i,Y: $i] :
( ~ ( member @ U @ X )
| ~ ( member @ V @ Y )
| ( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) ) )
& ! [X: $i] :
( ! [Y: $i] :
~ ( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) )
| ( member @ U @ X ) )
& ! [X: $i,Y: $i] :
( ~ ( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) )
| ( member @ V @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(767,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( member @ X @ universal_class )
| ~ ( member @ Y @ universal_class )
| ( ( first @ ( ordered_pair @ X @ Y ) )
= X ) )
& ! [X: $i,Y: $i] :
( ~ ( member @ X @ universal_class )
| ~ ( member @ Y @ universal_class )
| ( ( second @ ( ordered_pair @ X @ Y ) )
= Y ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(768,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( member @ Z @ ( cross_product @ X @ Y ) )
| ( Z
= ( ordered_pair @ ( first @ Z ) @ ( second @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(769,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( member @ Y @ universal_class )
| ~ ( member @ X @ Y )
| ( member @ ( ordered_pair @ X @ Y ) @ element_relation ) )
& ! [X: $i,Y: $i] :
( ~ ( member @ ( ordered_pair @ X @ Y ) @ element_relation )
| ( member @ Y @ universal_class ) )
& ! [X: $i,Y: $i] :
( ~ ( member @ ( ordered_pair @ X @ Y ) @ element_relation )
| ( member @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(770,plain,
( ( subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(771,plain,
( ( ! [X: $i] :
( ! [Y: $i,Z: $i] :
( ~ ( member @ Z @ X )
| ~ ( member @ Z @ Y )
| ( member @ Z @ ( intersection @ X @ Y ) ) )
& ! [Y: $i,Z: $i] :
( ~ ( member @ Z @ ( intersection @ X @ Y ) )
| ( member @ Z @ X ) )
& ! [Y: $i,Z: $i] :
( ~ ( member @ Z @ ( intersection @ X @ Y ) )
| ( member @ Z @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(772,plain,
( ( ! [X: $i,Z: $i] :
( ~ ( member @ Z @ universal_class )
| ( member @ Z @ X )
| ( member @ Z @ ( complement @ X ) ) )
& ! [X: $i,Z: $i] :
( ~ ( member @ Z @ ( complement @ X ) )
| ( member @ Z @ universal_class ) )
& ! [X: $i,Z: $i] :
( ~ ( member @ Z @ ( complement @ X ) )
| ~ ( member @ Z @ X ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(773,plain,
( ( ! [X: $i,XR: $i,Y: $i] :
( ( restrict @ XR @ X @ Y )
= ( intersection @ XR @ ( cross_product @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(774,plain,
( ( ! [X: $i] :
~ ( member @ X @ null_class ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(775,plain,
( ( ! [X: $i,Z: $i] :
( ( ( restrict @ X @ ( singleton @ Z ) @ universal_class )
= null_class )
| ~ ( member @ Z @ universal_class )
| ( member @ Z @ ( domain_of @ X ) ) )
& ! [X: $i,Z: $i] :
( ~ ( member @ Z @ ( domain_of @ X ) )
| ( ( restrict @ X @ ( singleton @ Z ) @ universal_class )
!= null_class ) )
& ! [X: $i,Z: $i] :
( ~ ( member @ Z @ ( domain_of @ X ) )
| ( member @ Z @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(776,plain,
( ( ! [X: $i,U: $i] :
( ! [V: $i,W: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ V @ W ) @ U ) @ X )
| ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( rotate @ X ) ) )
& ! [V: $i,W: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( rotate @ X ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
& ! [V: $i,W: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( rotate @ X ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ V @ W ) @ U ) @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(777,plain,
( ( ! [X: $i] : ( subclass @ ( rotate @ X ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(778,plain,
( ( ! [U: $i,V: $i] :
( ! [W: $i,X: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ V @ U ) @ W ) @ X )
| ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( flip @ X ) ) )
& ! [W: $i] :
( ! [X: $i] :
~ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( flip @ X ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
& ! [W: $i,X: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( flip @ X ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ V @ U ) @ W ) @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(779,plain,
( ( ! [X: $i] : ( subclass @ ( flip @ X ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(780,plain,
( ( ! [X: $i] :
( ! [Y: $i,Z: $i] :
( ~ ( member @ Z @ ( union @ X @ Y ) )
| ( member @ Z @ X )
| ( member @ Z @ Y ) )
& ! [Y: $i,Z: $i] :
( ~ ( member @ Z @ X )
| ( member @ Z @ ( union @ X @ Y ) ) )
& ! [Y: $i,Z: $i] :
( ~ ( member @ Z @ Y )
| ( member @ Z @ ( union @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(781,plain,
( ( ! [X: $i] :
( ( successor @ X )
= ( union @ X @ ( singleton @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(782,plain,
( ( subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(783,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( member @ X @ universal_class )
| ~ ( member @ Y @ universal_class )
| ( ( successor @ X )
!= Y )
| ( member @ ( ordered_pair @ X @ Y ) @ successor_relation ) )
& ! [X: $i] :
( ! [Y: $i] :
~ ( member @ ( ordered_pair @ X @ Y ) @ successor_relation )
| ( member @ X @ universal_class ) )
& ! [X: $i,Y: $i] :
( ~ ( member @ ( ordered_pair @ X @ Y ) @ successor_relation )
| ( member @ Y @ universal_class ) )
& ! [X: $i,Y: $i] :
( ~ ( member @ ( ordered_pair @ X @ Y ) @ successor_relation )
| ( ( successor @ X )
= Y ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(784,plain,
( ( ! [Y: $i] :
( ( inverse @ Y )
= ( domain_of @ ( flip @ ( cross_product @ Y @ universal_class ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(785,plain,
( ( ! [Z: $i] :
( ( range_of @ Z )
= ( domain_of @ ( inverse @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(786,plain,
( ( ! [X: $i,XR: $i] :
( ( image @ XR @ X )
= ( range_of @ ( restrict @ XR @ X @ universal_class ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(787,plain,
( ( ! [X: $i] :
( ~ ( member @ null_class @ X )
| ~ ( subclass @ ( image @ successor_relation @ X ) @ X )
| ( inductive @ X ) )
& ! [X: $i] :
( ~ ( inductive @ X )
| ( member @ null_class @ X ) )
& ! [X: $i] :
( ~ ( inductive @ X )
| ( subclass @ ( image @ successor_relation @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(788,plain,
( ( ! [SY93: $i] :
( ~ ( inductive @ SY93 )
| ( subclass @ sK9_X @ SY93 ) )
& ( inductive @ sK9_X )
& ( member @ sK9_X @ universal_class ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(789,plain,
( ( ! [U: $i,X: $i] :
( ! [Y: $i] :
( ~ ( member @ U @ Y )
| ~ ( member @ Y @ X ) )
| ( member @ U @ ( sum_class @ X ) ) )
& ! [U: $i,X: $i] :
( ~ ( member @ U @ ( sum_class @ X ) )
| ( ( member @ U @ ( sK8_Y @ X @ U ) )
& ( member @ ( sK8_Y @ X @ U ) @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(790,plain,
( ( ! [X: $i] :
( ~ ( member @ X @ universal_class )
| ( member @ ( sum_class @ X ) @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(791,plain,
( ( ! [U: $i,X: $i] :
( ~ ( member @ U @ universal_class )
| ~ ( subclass @ U @ X )
| ( member @ U @ ( power_class @ X ) ) )
& ! [U: $i] :
( ! [X: $i] :
~ ( member @ U @ ( power_class @ X ) )
| ( member @ U @ universal_class ) )
& ! [U: $i,X: $i] :
( ~ ( member @ U @ ( power_class @ X ) )
| ( subclass @ U @ X ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(792,plain,
( ( ! [U: $i] :
( ~ ( member @ U @ universal_class )
| ( member @ ( power_class @ U ) @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(793,plain,
( ( ! [XR: $i,YR: $i] : ( subclass @ ( compose @ YR @ XR ) @ ( cross_product @ universal_class @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(794,plain,
( ( ! [XR: $i,YR: $i] :
( ! [U: $i,V: $i] :
( ~ ( member @ U @ universal_class )
| ~ ( member @ V @ ( image @ YR @ ( image @ XR @ ( singleton @ U ) ) ) )
| ( member @ ( ordered_pair @ U @ V ) @ ( compose @ YR @ XR ) ) )
& ! [U: $i] :
( ! [V: $i] :
~ ( member @ ( ordered_pair @ U @ V ) @ ( compose @ YR @ XR ) )
| ( member @ U @ universal_class ) )
& ! [U: $i,V: $i] :
( ~ ( member @ ( ordered_pair @ U @ V ) @ ( compose @ YR @ XR ) )
| ( member @ V @ ( image @ YR @ ( image @ XR @ ( singleton @ U ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(795,plain,
( ( ! [Z: $i] :
( ! [X: $i] :
( ( Z
!= ( ordered_pair @ X @ X ) )
| ~ ( member @ X @ universal_class ) )
| ( member @ Z @ identity_relation ) )
& ! [Z: $i] :
( ~ ( member @ Z @ identity_relation )
| ( ( Z
= ( ordered_pair @ ( sK7_X @ Z ) @ ( sK7_X @ Z ) ) )
& ( member @ ( sK7_X @ Z ) @ universal_class ) ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(796,plain,
( ( ! [XF: $i] :
( ~ ( subclass @ XF @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ XF @ ( inverse @ XF ) ) @ identity_relation )
| ( function @ XF ) )
& ! [XF: $i] :
( ~ ( function @ XF )
| ( subclass @ XF @ ( cross_product @ universal_class @ universal_class ) ) )
& ! [XF: $i] :
( ~ ( function @ XF )
| ( subclass @ ( compose @ XF @ ( inverse @ XF ) ) @ identity_relation ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(797,plain,
( ( ! [X: $i,XF: $i] :
( ~ ( function @ XF )
| ~ ( member @ X @ universal_class )
| ( member @ ( image @ XF @ X ) @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(798,plain,
( ( ! [X: $i,Y: $i] :
( ( ( member @ ( sK6_U @ Y @ X ) @ X )
& ( member @ ( sK6_U @ Y @ X ) @ Y ) )
| ( disjoint @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( disjoint @ X @ Y )
| ! [U: $i] :
( ~ ( member @ U @ X )
| ~ ( member @ U @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(799,plain,
( ( ! [X: $i] :
( ( X = null_class )
| ( ( member @ ( sK5_U @ X ) @ universal_class )
& ( member @ ( sK5_U @ X ) @ X )
& ( disjoint @ ( sK5_U @ X ) @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(800,plain,
( ( ! [XF: $i,Y: $i] :
( ( apply @ XF @ Y )
= ( sum_class @ ( image @ XF @ ( singleton @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(801,plain,
( ( ! [SY92: $i] :
( ~ ( member @ SY92 @ universal_class )
| ( SY92 = null_class )
| ( member @ ( apply @ sK4_XF @ SY92 ) @ SY92 ) )
& ( function @ sK4_XF ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(802,plain,
( ( sK3_SY91
= ( ordered_pair @ sK1_U @ sK2_SY89 ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(803,plain,
( ( member @ sK2_SY89 @ universal_class )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(804,plain,
( ( member @ sK1_U @ universal_class )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(805,plain,
( ( ( ( second @ sK3_SY91 )
!= sK2_SY89 ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(806,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ ( intersection @ SX0 @ SX1 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ ( intersection @ SX0 @ SX1 ) )
| ( member @ SX2 @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ ( intersection @ SX0 @ SX1 ) )
| ( member @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[771]) ).
thf(807,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( restrict @ SX0 @ ( singleton @ SX1 ) @ universal_class )
= null_class )
| ~ ( member @ SX1 @ universal_class )
| ( member @ SX1 @ ( domain_of @ SX0 ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( domain_of @ SX0 ) )
| ( ( restrict @ SX0 @ ( singleton @ SX1 ) @ universal_class )
!= null_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( domain_of @ SX0 ) )
| ( member @ SX1 @ universal_class ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[775]) ).
thf(808,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ universal_class )
| ~ ( member @ SX0 @ SX1 )
| ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation )
| ( member @ SX1 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation )
| ( member @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[769]) ).
thf(809,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( subclass @ SX0 @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ SX0 @ ( inverse @ SX0 ) ) @ identity_relation )
| ( function @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ( subclass @ SX0 @ ( cross_product @ universal_class @ universal_class ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ( subclass @ ( compose @ SX0 @ ( inverse @ SX0 ) ) @ identity_relation ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[796]) ).
thf(810,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( inductive @ SX0 )
| ( subclass @ sK9_X @ SX0 ) )
| ~ ~ ( ~ ( inductive @ sK9_X )
| ~ ( member @ sK9_X @ universal_class ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[788]) ).
thf(811,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( SX0
!= ( ordered_pair @ SX1 @ SX1 ) )
| ~ ( member @ SX1 @ universal_class ) )
| ( member @ SX0 @ identity_relation ) )
| ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ identity_relation )
| ~ ( ( SX0
!= ( ordered_pair @ ( sK7_X @ SX0 ) @ ( sK7_X @ SX0 ) ) )
| ~ ( member @ ( sK7_X @ SX0 ) @ universal_class ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[795]) ).
thf(812,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ universal_class )
| ( SX0 = null_class )
| ( member @ ( apply @ sK4_XF @ SX0 ) @ SX0 ) )
| ~ ( function @ sK4_XF ) ) )
= $true ),
inference(unfold_def,[status(thm)],[801]) ).
thf(813,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK6_U @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK6_U @ SX1 @ SX0 ) @ SX1 ) )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[798]) ).
thf(814,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ universal_class )
| ~ ( member @ SX1 @ universal_class )
| ( ( successor @ SX0 )
!= SX1 )
| ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX0 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX1 @ universal_class ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( ( successor @ SX0 )
= SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[783]) ).
thf(815,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX0 @ SX2 )
| ~ ( member @ SX2 @ SX1 ) )
| ( member @ SX0 @ ( sum_class @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( sum_class @ SX1 ) )
| ~ ( ~ ( member @ SX0 @ ( sK8_Y @ SX1 @ SX0 ) )
| ~ ( member @ ( sK8_Y @ SX1 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[789]) ).
thf(816,plain,
( ( ! [SX0: $i] :
( ( SX0 = null_class )
| ~ ( ~ ~ ( ~ ( member @ ( sK5_U @ SX0 ) @ universal_class )
| ~ ( member @ ( sK5_U @ SX0 ) @ SX0 ) )
| ~ ( disjoint @ ( sK5_U @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[799]) ).
thf(817,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SX1 @ SX0 ) @ SX2 ) @ SX3 )
| ( member @ ( ordered_pair @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 ) @ ( flip @ SX3 ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( member @ ( ordered_pair @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 ) @ ( flip @ SX3 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 ) @ ( flip @ SX3 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SX1 @ SX0 ) @ SX2 ) @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[778]) ).
thf(818,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( member @ SX2 @ universal_class )
| ~ ( member @ SX3 @ ( image @ SX1 @ ( image @ SX0 @ ( singleton @ SX2 ) ) ) )
| ( member @ ( ordered_pair @ SX2 @ SX3 ) @ ( compose @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( member @ ( ordered_pair @ SX2 @ SX3 ) @ ( compose @ SX1 @ SX0 ) )
| ( member @ SX2 @ universal_class ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( member @ ( ordered_pair @ SX2 @ SX3 ) @ ( compose @ SX1 @ SX0 ) )
| ( member @ SX3 @ ( image @ SX1 @ ( image @ SX0 @ ( singleton @ SX2 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[794]) ).
thf(819,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subclass @ SX0 @ SX1 )
| ~ ( subclass @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subclass @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subclass @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[761]) ).
thf(820,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ universal_class )
| ( member @ SX1 @ SX0 )
| ( member @ SX1 @ ( complement @ SX0 ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( complement @ SX0 ) )
| ( member @ SX1 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( complement @ SX0 ) )
| ~ ( member @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[772]) ).
thf(821,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK10_U @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK10_U @ SX1 @ SX0 ) @ SX1 ) )
| ( subclass @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subclass @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[759]) ).
thf(822,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( member @ SX0 @ SX2 )
| ~ ( member @ SX1 @ SX3 )
| ( member @ ( ordered_pair @ SX0 @ SX1 ) @ ( cross_product @ SX2 @ SX3 ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ ( cross_product @ SX2 @ SX3 ) )
| ( member @ SX0 @ SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ ( cross_product @ SX2 @ SX3 ) )
| ( member @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[766]) ).
thf(823,plain,
( ( ! [SX0: $i] :
~ ( ~ ~ ( ~ ! [SX1: $i] :
( ~ ( member @ SX0 @ universal_class )
| ( SX0 != SX1 )
| ! [SX2: $i] : ( member @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ universal_class )
| ( SX0 != SX2 )
| ( member @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) ) ) )
| ~ ~ ( ~ ( ! [SX1: $i,SX2: $i] :
~ ( member @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) )
| ( member @ SX0 @ universal_class ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) )
| ( SX0 = SX1 )
| ( SX0 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[762]) ).
thf(824,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( member @ null_class @ SX0 )
| ~ ( subclass @ ( image @ successor_relation @ SX0 ) @ SX0 )
| ( inductive @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( inductive @ SX0 )
| ( member @ null_class @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( inductive @ SX0 )
| ( subclass @ ( image @ successor_relation @ SX0 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[787]) ).
thf(825,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SX1 @ SX2 ) @ SX3 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) @ SX0 )
| ( member @ ( ordered_pair @ ( ordered_pair @ SX1 @ SX2 ) @ SX3 ) @ ( rotate @ SX0 ) ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SX1 @ SX2 ) @ SX3 ) @ ( rotate @ SX0 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SX1 @ SX2 ) @ SX3 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SX1 @ SX2 ) @ SX3 ) @ ( rotate @ SX0 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[776]) ).
thf(826,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ universal_class )
| ~ ( member @ SX1 @ universal_class )
| ( ( first @ ( ordered_pair @ SX0 @ SX1 ) )
= SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ universal_class )
| ~ ( member @ SX1 @ universal_class )
| ( ( second @ ( ordered_pair @ SX0 @ SX1 ) )
= SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[767]) ).
thf(827,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ universal_class )
| ~ ( subclass @ SX0 @ SX1 )
| ( member @ SX0 @ ( power_class @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( member @ SX0 @ ( power_class @ SX1 ) )
| ( member @ SX0 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( power_class @ SX1 ) )
| ( subclass @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[791]) ).
thf(828,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ ( union @ SX0 @ SX1 ) )
| ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ ( union @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ ( union @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[780]) ).
thf(829,plain,
! [SV153: $i] :
( ( subclass @ SV153 @ universal_class )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(830,plain,
! [SV154: $i] :
( ( ! [SY234: $i] : ( member @ ( unordered_pair @ SV154 @ SY234 ) @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(831,plain,
! [SV155: $i] :
( ( ( singleton @ SV155 )
= ( unordered_pair @ SV155 @ SV155 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(832,plain,
! [SV156: $i] :
( ( ! [SY235: $i] :
( ( ordered_pair @ SV156 @ SY235 )
= ( unordered_pair @ ( singleton @ SV156 ) @ ( unordered_pair @ SV156 @ ( singleton @ SY235 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(833,plain,
! [SV157: $i] :
( ( ! [SY236: $i,SY237: $i] :
( ~ ( member @ SY237 @ ( cross_product @ SV157 @ SY236 ) )
| ( SY237
= ( ordered_pair @ ( first @ SY237 ) @ ( second @ SY237 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(834,plain,
! [SV158: $i] :
( ( ! [SY238: $i,SY239: $i] :
( ( restrict @ SY238 @ SV158 @ SY239 )
= ( intersection @ SY238 @ ( cross_product @ SV158 @ SY239 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(835,plain,
! [SV159: $i] :
( ( ~ ( member @ SV159 @ null_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(836,plain,
! [SV160: $i] :
( ( subclass @ ( rotate @ SV160 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(837,plain,
! [SV161: $i] :
( ( subclass @ ( flip @ SV161 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(838,plain,
! [SV162: $i] :
( ( ( successor @ SV162 )
= ( union @ SV162 @ ( singleton @ SV162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(839,plain,
! [SV163: $i] :
( ( ( inverse @ SV163 )
= ( domain_of @ ( flip @ ( cross_product @ SV163 @ universal_class ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(840,plain,
! [SV164: $i] :
( ( ( range_of @ SV164 )
= ( domain_of @ ( inverse @ SV164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(841,plain,
! [SV165: $i] :
( ( ! [SY240: $i] :
( ( image @ SY240 @ SV165 )
= ( range_of @ ( restrict @ SY240 @ SV165 @ universal_class ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(842,plain,
! [SV166: $i] :
( ( ~ ( member @ SV166 @ universal_class )
| ( member @ ( sum_class @ SV166 ) @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(843,plain,
! [SV167: $i] :
( ( ~ ( member @ SV167 @ universal_class )
| ( member @ ( power_class @ SV167 ) @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(844,plain,
! [SV168: $i] :
( ( ! [SY241: $i] : ( subclass @ ( compose @ SY241 @ SV168 ) @ ( cross_product @ universal_class @ universal_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(845,plain,
! [SV169: $i] :
( ( ! [SY242: $i] :
( ~ ( function @ SY242 )
| ~ ( member @ SV169 @ universal_class )
| ( member @ ( image @ SY242 @ SV169 ) @ universal_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(846,plain,
! [SV170: $i] :
( ( ! [SY243: $i] :
( ( apply @ SV170 @ SY243 )
= ( sum_class @ ( image @ SV170 @ ( singleton @ SY243 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(847,plain,
( ( ( second @ sK3_SY91 )
= sK2_SY89 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[805]) ).
thf(848,plain,
! [SV171: $i] :
( ( ~ ( ~ ! [SY244: $i,SY245: $i] :
( ~ ( member @ SY245 @ SV171 )
| ~ ( member @ SY245 @ SY244 )
| ( member @ SY245 @ ( intersection @ SV171 @ SY244 ) ) )
| ~ ~ ( ~ ! [SY246: $i,SY247: $i] :
( ~ ( member @ SY247 @ ( intersection @ SV171 @ SY246 ) )
| ( member @ SY247 @ SV171 ) )
| ~ ! [SY248: $i,SY249: $i] :
( ~ ( member @ SY249 @ ( intersection @ SV171 @ SY248 ) )
| ( member @ SY249 @ SY248 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(849,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( restrict @ SX0 @ ( singleton @ SX1 ) @ universal_class )
= null_class )
| ~ ( member @ SX1 @ universal_class )
| ( member @ SX1 @ ( domain_of @ SX0 ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( domain_of @ SX0 ) )
| ( ( restrict @ SX0 @ ( singleton @ SX1 ) @ universal_class )
!= null_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( domain_of @ SX0 ) )
| ( member @ SX1 @ universal_class ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[807]) ).
thf(850,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ universal_class )
| ~ ( member @ SX0 @ SX1 )
| ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation )
| ( member @ SX1 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation )
| ( member @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[808]) ).
thf(851,plain,
( ( ~ ! [SX0: $i] :
( ~ ( subclass @ SX0 @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ SX0 @ ( inverse @ SX0 ) ) @ identity_relation )
| ( function @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ( subclass @ SX0 @ ( cross_product @ universal_class @ universal_class ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ( subclass @ ( compose @ SX0 @ ( inverse @ SX0 ) ) @ identity_relation ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[809]) ).
thf(852,plain,
( ( ~ ! [SX0: $i] :
( ~ ( inductive @ SX0 )
| ( subclass @ sK9_X @ SX0 ) )
| ~ ~ ( ~ ( inductive @ sK9_X )
| ~ ( member @ sK9_X @ universal_class ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[810]) ).
thf(853,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( SX0
!= ( ordered_pair @ SX1 @ SX1 ) )
| ~ ( member @ SX1 @ universal_class ) )
| ( member @ SX0 @ identity_relation ) )
| ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ identity_relation )
| ~ ( ( SX0
!= ( ordered_pair @ ( sK7_X @ SX0 ) @ ( sK7_X @ SX0 ) ) )
| ~ ( member @ ( sK7_X @ SX0 ) @ universal_class ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[811]) ).
thf(854,plain,
( ( ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ universal_class )
| ( SX0 = null_class )
| ( member @ ( apply @ sK4_XF @ SX0 ) @ SX0 ) )
| ~ ( function @ sK4_XF ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[812]) ).
thf(855,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK6_U @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK6_U @ SX1 @ SX0 ) @ SX1 ) )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[813]) ).
thf(856,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ universal_class )
| ~ ( member @ SX1 @ universal_class )
| ( ( successor @ SX0 )
!= SX1 )
| ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX0 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX1 @ universal_class ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( ( successor @ SX0 )
= SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[814]) ).
thf(857,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX0 @ SX2 )
| ~ ( member @ SX2 @ SX1 ) )
| ( member @ SX0 @ ( sum_class @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( sum_class @ SX1 ) )
| ~ ( ~ ( member @ SX0 @ ( sK8_Y @ SX1 @ SX0 ) )
| ~ ( member @ ( sK8_Y @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[815]) ).
thf(858,plain,
! [SV172: $i] :
( ( ( SV172 = null_class )
| ~ ( ~ ~ ( ~ ( member @ ( sK5_U @ SV172 ) @ universal_class )
| ~ ( member @ ( sK5_U @ SV172 ) @ SV172 ) )
| ~ ( disjoint @ ( sK5_U @ SV172 ) @ SV172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(859,plain,
! [SV173: $i] :
( ( ! [SY250: $i] :
~ ( ~ ! [SY251: $i,SY252: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SY250 ) @ SY251 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SY250 @ SV173 ) @ SY251 ) @ SY252 )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SY250 ) @ SY251 ) @ ( flip @ SY252 ) ) )
| ~ ~ ( ~ ! [SY253: $i] :
( ! [SY254: $i] :
~ ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SY250 ) @ SY253 ) @ ( flip @ SY254 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SY250 ) @ SY253 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
| ~ ! [SY255: $i,SY256: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SY250 ) @ SY255 ) @ ( flip @ SY256 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SY250 @ SV173 ) @ SY255 ) @ SY256 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(860,plain,
! [SV174: $i] :
( ( ! [SY257: $i] :
~ ( ~ ! [SY258: $i,SY259: $i] :
( ~ ( member @ SY258 @ universal_class )
| ~ ( member @ SY259 @ ( image @ SY257 @ ( image @ SV174 @ ( singleton @ SY258 ) ) ) )
| ( member @ ( ordered_pair @ SY258 @ SY259 ) @ ( compose @ SY257 @ SV174 ) ) )
| ~ ~ ( ~ ! [SY260: $i] :
( ! [SY261: $i] :
~ ( member @ ( ordered_pair @ SY260 @ SY261 ) @ ( compose @ SY257 @ SV174 ) )
| ( member @ SY260 @ universal_class ) )
| ~ ! [SY262: $i,SY263: $i] :
( ~ ( member @ ( ordered_pair @ SY262 @ SY263 ) @ ( compose @ SY257 @ SV174 ) )
| ( member @ SY263 @ ( image @ SY257 @ ( image @ SV174 @ ( singleton @ SY262 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(861,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subclass @ SX0 @ SX1 )
| ~ ( subclass @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subclass @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subclass @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[819]) ).
thf(862,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ universal_class )
| ( member @ SX1 @ SX0 )
| ( member @ SX1 @ ( complement @ SX0 ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( complement @ SX0 ) )
| ( member @ SX1 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( complement @ SX0 ) )
| ~ ( member @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[820]) ).
thf(863,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK10_U @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK10_U @ SX1 @ SX0 ) @ SX1 ) )
| ( subclass @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subclass @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[821]) ).
thf(864,plain,
! [SV175: $i] :
( ( ! [SY264: $i] :
~ ( ~ ! [SY265: $i,SY266: $i] :
( ~ ( member @ SV175 @ SY265 )
| ~ ( member @ SY264 @ SY266 )
| ( member @ ( ordered_pair @ SV175 @ SY264 ) @ ( cross_product @ SY265 @ SY266 ) ) )
| ~ ~ ( ~ ! [SY267: $i] :
( ! [SY268: $i] :
~ ( member @ ( ordered_pair @ SV175 @ SY264 ) @ ( cross_product @ SY267 @ SY268 ) )
| ( member @ SV175 @ SY267 ) )
| ~ ! [SY269: $i,SY270: $i] :
( ~ ( member @ ( ordered_pair @ SV175 @ SY264 ) @ ( cross_product @ SY269 @ SY270 ) )
| ( member @ SY264 @ SY270 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(865,plain,
! [SV176: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY271: $i] :
( ~ ( member @ SV176 @ universal_class )
| ( SV176 != SY271 )
| ! [SY272: $i] : ( member @ SV176 @ ( unordered_pair @ SY271 @ SY272 ) ) )
| ~ ! [SY273: $i,SY274: $i] :
( ~ ( member @ SV176 @ universal_class )
| ( SV176 != SY274 )
| ( member @ SV176 @ ( unordered_pair @ SY273 @ SY274 ) ) ) )
| ~ ~ ( ~ ( ! [SY275: $i,SY276: $i] :
~ ( member @ SV176 @ ( unordered_pair @ SY275 @ SY276 ) )
| ( member @ SV176 @ universal_class ) )
| ~ ! [SY277: $i,SY278: $i] :
( ~ ( member @ SV176 @ ( unordered_pair @ SY277 @ SY278 ) )
| ( SV176 = SY277 )
| ( SV176 = SY278 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(866,plain,
( ( ~ ! [SX0: $i] :
( ~ ( member @ null_class @ SX0 )
| ~ ( subclass @ ( image @ successor_relation @ SX0 ) @ SX0 )
| ( inductive @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( inductive @ SX0 )
| ( member @ null_class @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( inductive @ SX0 )
| ( subclass @ ( image @ successor_relation @ SX0 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[824]) ).
thf(867,plain,
! [SV177: $i] :
( ( ! [SY279: $i] :
~ ( ~ ! [SY280: $i,SY281: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SY279 @ SY280 ) @ SY281 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SY280 @ SY281 ) @ SY279 ) @ SV177 )
| ( member @ ( ordered_pair @ ( ordered_pair @ SY279 @ SY280 ) @ SY281 ) @ ( rotate @ SV177 ) ) )
| ~ ~ ( ~ ! [SY282: $i,SY283: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SY279 @ SY282 ) @ SY283 ) @ ( rotate @ SV177 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SY279 @ SY282 ) @ SY283 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
| ~ ! [SY284: $i,SY285: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SY279 @ SY284 ) @ SY285 ) @ ( rotate @ SV177 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SY284 @ SY285 ) @ SY279 ) @ SV177 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(868,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ universal_class )
| ~ ( member @ SX1 @ universal_class )
| ( ( first @ ( ordered_pair @ SX0 @ SX1 ) )
= SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ universal_class )
| ~ ( member @ SX1 @ universal_class )
| ( ( second @ ( ordered_pair @ SX0 @ SX1 ) )
= SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[826]) ).
thf(869,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ universal_class )
| ~ ( subclass @ SX0 @ SX1 )
| ( member @ SX0 @ ( power_class @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( member @ SX0 @ ( power_class @ SX1 ) )
| ( member @ SX0 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( power_class @ SX1 ) )
| ( subclass @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[827]) ).
thf(870,plain,
! [SV178: $i] :
( ( ~ ( ~ ! [SY286: $i,SY287: $i] :
( ~ ( member @ SY287 @ ( union @ SV178 @ SY286 ) )
| ( member @ SY287 @ SV178 )
| ( member @ SY287 @ SY286 ) )
| ~ ~ ( ~ ! [SY288: $i,SY289: $i] :
( ~ ( member @ SY289 @ SV178 )
| ( member @ SY289 @ ( union @ SV178 @ SY288 ) ) )
| ~ ! [SY290: $i,SY291: $i] :
( ~ ( member @ SY291 @ SY290 )
| ( member @ SY291 @ ( union @ SV178 @ SY290 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(871,plain,
! [SV179: $i,SV154: $i] :
( ( member @ ( unordered_pair @ SV154 @ SV179 ) @ universal_class )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(872,plain,
! [SV180: $i,SV156: $i] :
( ( ( ordered_pair @ SV156 @ SV180 )
= ( unordered_pair @ ( singleton @ SV156 ) @ ( unordered_pair @ SV156 @ ( singleton @ SV180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(873,plain,
! [SV181: $i,SV157: $i] :
( ( ! [SY292: $i] :
( ~ ( member @ SY292 @ ( cross_product @ SV157 @ SV181 ) )
| ( SY292
= ( ordered_pair @ ( first @ SY292 ) @ ( second @ SY292 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(874,plain,
! [SV158: $i,SV182: $i] :
( ( ! [SY293: $i] :
( ( restrict @ SV182 @ SV158 @ SY293 )
= ( intersection @ SV182 @ ( cross_product @ SV158 @ SY293 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(875,plain,
! [SV159: $i] :
( ( member @ SV159 @ null_class )
= $false ),
inference(extcnf_not_pos,[status(thm)],[835]) ).
thf(876,plain,
! [SV165: $i,SV183: $i] :
( ( ( image @ SV183 @ SV165 )
= ( range_of @ ( restrict @ SV183 @ SV165 @ universal_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(877,plain,
! [SV166: $i] :
( ( ( ~ ( member @ SV166 @ universal_class ) )
= $true )
| ( ( member @ ( sum_class @ SV166 ) @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[842]) ).
thf(878,plain,
! [SV167: $i] :
( ( ( ~ ( member @ SV167 @ universal_class ) )
= $true )
| ( ( member @ ( power_class @ SV167 ) @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[843]) ).
thf(879,plain,
! [SV168: $i,SV184: $i] :
( ( subclass @ ( compose @ SV184 @ SV168 ) @ ( cross_product @ universal_class @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(880,plain,
! [SV169: $i,SV185: $i] :
( ( ~ ( function @ SV185 )
| ~ ( member @ SV169 @ universal_class )
| ( member @ ( image @ SV185 @ SV169 ) @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(881,plain,
! [SV186: $i,SV170: $i] :
( ( ( apply @ SV170 @ SV186 )
= ( sum_class @ ( image @ SV170 @ ( singleton @ SV186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(882,plain,
! [SV171: $i] :
( ( ~ ! [SY244: $i,SY245: $i] :
( ~ ( member @ SY245 @ SV171 )
| ~ ( member @ SY245 @ SY244 )
| ( member @ SY245 @ ( intersection @ SV171 @ SY244 ) ) )
| ~ ~ ( ~ ! [SY246: $i,SY247: $i] :
( ~ ( member @ SY247 @ ( intersection @ SV171 @ SY246 ) )
| ( member @ SY247 @ SV171 ) )
| ~ ! [SY248: $i,SY249: $i] :
( ~ ( member @ SY249 @ ( intersection @ SV171 @ SY248 ) )
| ( member @ SY249 @ SY248 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[848]) ).
thf(883,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( restrict @ SX0 @ ( singleton @ SX1 ) @ universal_class )
= null_class )
| ~ ( member @ SX1 @ universal_class )
| ( member @ SX1 @ ( domain_of @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[849]) ).
thf(884,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( domain_of @ SX0 ) )
| ( ( restrict @ SX0 @ ( singleton @ SX1 ) @ universal_class )
!= null_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( domain_of @ SX0 ) )
| ( member @ SX1 @ universal_class ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[849]) ).
thf(885,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ universal_class )
| ~ ( member @ SX0 @ SX1 )
| ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[850]) ).
thf(886,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation )
| ( member @ SX1 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation )
| ( member @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[850]) ).
thf(887,plain,
( ( ~ ! [SX0: $i] :
( ~ ( subclass @ SX0 @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ SX0 @ ( inverse @ SX0 ) ) @ identity_relation )
| ( function @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[851]) ).
thf(888,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ( subclass @ SX0 @ ( cross_product @ universal_class @ universal_class ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ( subclass @ ( compose @ SX0 @ ( inverse @ SX0 ) ) @ identity_relation ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[851]) ).
thf(889,plain,
( ( ~ ! [SX0: $i] :
( ~ ( inductive @ SX0 )
| ( subclass @ sK9_X @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[852]) ).
thf(890,plain,
( ( ~ ~ ( ~ ( inductive @ sK9_X )
| ~ ( member @ sK9_X @ universal_class ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[852]) ).
thf(891,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( SX0
!= ( ordered_pair @ SX1 @ SX1 ) )
| ~ ( member @ SX1 @ universal_class ) )
| ( member @ SX0 @ identity_relation ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[853]) ).
thf(892,plain,
( ( ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ identity_relation )
| ~ ( ( SX0
!= ( ordered_pair @ ( sK7_X @ SX0 ) @ ( sK7_X @ SX0 ) ) )
| ~ ( member @ ( sK7_X @ SX0 ) @ universal_class ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[853]) ).
thf(893,plain,
( ( ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ universal_class )
| ( SX0 = null_class )
| ( member @ ( apply @ sK4_XF @ SX0 ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[854]) ).
thf(894,plain,
( ( ~ ( function @ sK4_XF ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[854]) ).
thf(895,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK6_U @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK6_U @ SX1 @ SX0 ) @ SX1 ) )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[855]) ).
thf(896,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[855]) ).
thf(897,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ universal_class )
| ~ ( member @ SX1 @ universal_class )
| ( ( successor @ SX0 )
!= SX1 )
| ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[856]) ).
thf(898,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX0 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX1 @ universal_class ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( ( successor @ SX0 )
= SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[856]) ).
thf(899,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX0 @ SX2 )
| ~ ( member @ SX2 @ SX1 ) )
| ( member @ SX0 @ ( sum_class @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[857]) ).
thf(900,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( sum_class @ SX1 ) )
| ~ ( ~ ( member @ SX0 @ ( sK8_Y @ SX1 @ SX0 ) )
| ~ ( member @ ( sK8_Y @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[857]) ).
thf(901,plain,
! [SV172: $i] :
( ( ( SV172 = null_class )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( member @ ( sK5_U @ SV172 ) @ universal_class )
| ~ ( member @ ( sK5_U @ SV172 ) @ SV172 ) )
| ~ ( disjoint @ ( sK5_U @ SV172 ) @ SV172 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[858]) ).
thf(902,plain,
! [SV187: $i,SV173: $i] :
( ( ~ ( ~ ! [SY294: $i,SY295: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SY294 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV187 @ SV173 ) @ SY294 ) @ SY295 )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SY294 ) @ ( flip @ SY295 ) ) )
| ~ ~ ( ~ ! [SY296: $i] :
( ! [SY297: $i] :
~ ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SY296 ) @ ( flip @ SY297 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SY296 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
| ~ ! [SY298: $i,SY299: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SY298 ) @ ( flip @ SY299 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV187 @ SV173 ) @ SY298 ) @ SY299 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(903,plain,
! [SV174: $i,SV188: $i] :
( ( ~ ( ~ ! [SY300: $i,SY301: $i] :
( ~ ( member @ SY300 @ universal_class )
| ~ ( member @ SY301 @ ( image @ SV188 @ ( image @ SV174 @ ( singleton @ SY300 ) ) ) )
| ( member @ ( ordered_pair @ SY300 @ SY301 ) @ ( compose @ SV188 @ SV174 ) ) )
| ~ ~ ( ~ ! [SY302: $i] :
( ! [SY303: $i] :
~ ( member @ ( ordered_pair @ SY302 @ SY303 ) @ ( compose @ SV188 @ SV174 ) )
| ( member @ SY302 @ universal_class ) )
| ~ ! [SY304: $i,SY305: $i] :
( ~ ( member @ ( ordered_pair @ SY304 @ SY305 ) @ ( compose @ SV188 @ SV174 ) )
| ( member @ SY305 @ ( image @ SV188 @ ( image @ SV174 @ ( singleton @ SY304 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(904,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subclass @ SX0 @ SX1 )
| ~ ( subclass @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[861]) ).
thf(905,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subclass @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subclass @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[861]) ).
thf(906,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ universal_class )
| ( member @ SX1 @ SX0 )
| ( member @ SX1 @ ( complement @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[862]) ).
thf(907,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( complement @ SX0 ) )
| ( member @ SX1 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( complement @ SX0 ) )
| ~ ( member @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[862]) ).
thf(908,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK10_U @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK10_U @ SX1 @ SX0 ) @ SX1 ) )
| ( subclass @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[863]) ).
thf(909,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subclass @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[863]) ).
thf(910,plain,
! [SV189: $i,SV175: $i] :
( ( ~ ( ~ ! [SY306: $i,SY307: $i] :
( ~ ( member @ SV175 @ SY306 )
| ~ ( member @ SV189 @ SY307 )
| ( member @ ( ordered_pair @ SV175 @ SV189 ) @ ( cross_product @ SY306 @ SY307 ) ) )
| ~ ~ ( ~ ! [SY308: $i] :
( ! [SY309: $i] :
~ ( member @ ( ordered_pair @ SV175 @ SV189 ) @ ( cross_product @ SY308 @ SY309 ) )
| ( member @ SV175 @ SY308 ) )
| ~ ! [SY310: $i,SY311: $i] :
( ~ ( member @ ( ordered_pair @ SV175 @ SV189 ) @ ( cross_product @ SY310 @ SY311 ) )
| ( member @ SV189 @ SY311 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(911,plain,
! [SV176: $i] :
( ( ~ ~ ( ~ ! [SY271: $i] :
( ~ ( member @ SV176 @ universal_class )
| ( SV176 != SY271 )
| ! [SY272: $i] : ( member @ SV176 @ ( unordered_pair @ SY271 @ SY272 ) ) )
| ~ ! [SY273: $i,SY274: $i] :
( ~ ( member @ SV176 @ universal_class )
| ( SV176 != SY274 )
| ( member @ SV176 @ ( unordered_pair @ SY273 @ SY274 ) ) ) )
| ~ ~ ( ~ ( ! [SY275: $i,SY276: $i] :
~ ( member @ SV176 @ ( unordered_pair @ SY275 @ SY276 ) )
| ( member @ SV176 @ universal_class ) )
| ~ ! [SY277: $i,SY278: $i] :
( ~ ( member @ SV176 @ ( unordered_pair @ SY277 @ SY278 ) )
| ( SV176 = SY277 )
| ( SV176 = SY278 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[865]) ).
thf(912,plain,
( ( ~ ! [SX0: $i] :
( ~ ( member @ null_class @ SX0 )
| ~ ( subclass @ ( image @ successor_relation @ SX0 ) @ SX0 )
| ( inductive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[866]) ).
thf(913,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( inductive @ SX0 )
| ( member @ null_class @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( inductive @ SX0 )
| ( subclass @ ( image @ successor_relation @ SX0 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[866]) ).
thf(914,plain,
! [SV177: $i,SV190: $i] :
( ( ~ ( ~ ! [SY312: $i,SY313: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SY312 ) @ SY313 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SY312 @ SY313 ) @ SV190 ) @ SV177 )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SY312 ) @ SY313 ) @ ( rotate @ SV177 ) ) )
| ~ ~ ( ~ ! [SY314: $i,SY315: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SY314 ) @ SY315 ) @ ( rotate @ SV177 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SY314 ) @ SY315 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
| ~ ! [SY316: $i,SY317: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SY316 ) @ SY317 ) @ ( rotate @ SV177 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SY316 @ SY317 ) @ SV190 ) @ SV177 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(915,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ universal_class )
| ~ ( member @ SX1 @ universal_class )
| ( ( first @ ( ordered_pair @ SX0 @ SX1 ) )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[868]) ).
thf(916,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ universal_class )
| ~ ( member @ SX1 @ universal_class )
| ( ( second @ ( ordered_pair @ SX0 @ SX1 ) )
= SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[868]) ).
thf(917,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ universal_class )
| ~ ( subclass @ SX0 @ SX1 )
| ( member @ SX0 @ ( power_class @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[869]) ).
thf(918,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( member @ SX0 @ ( power_class @ SX1 ) )
| ( member @ SX0 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( power_class @ SX1 ) )
| ( subclass @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[869]) ).
thf(919,plain,
! [SV178: $i] :
( ( ~ ! [SY286: $i,SY287: $i] :
( ~ ( member @ SY287 @ ( union @ SV178 @ SY286 ) )
| ( member @ SY287 @ SV178 )
| ( member @ SY287 @ SY286 ) )
| ~ ~ ( ~ ! [SY288: $i,SY289: $i] :
( ~ ( member @ SY289 @ SV178 )
| ( member @ SY289 @ ( union @ SV178 @ SY288 ) ) )
| ~ ! [SY290: $i,SY291: $i] :
( ~ ( member @ SY291 @ SY290 )
| ( member @ SY291 @ ( union @ SV178 @ SY290 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[870]) ).
thf(920,plain,
! [SV181: $i,SV157: $i,SV191: $i] :
( ( ~ ( member @ SV191 @ ( cross_product @ SV157 @ SV181 ) )
| ( SV191
= ( ordered_pair @ ( first @ SV191 ) @ ( second @ SV191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[873]) ).
thf(921,plain,
! [SV192: $i,SV158: $i,SV182: $i] :
( ( ( restrict @ SV182 @ SV158 @ SV192 )
= ( intersection @ SV182 @ ( cross_product @ SV158 @ SV192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(922,plain,
! [SV166: $i] :
( ( ( member @ SV166 @ universal_class )
= $false )
| ( ( member @ ( sum_class @ SV166 ) @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[877]) ).
thf(923,plain,
! [SV167: $i] :
( ( ( member @ SV167 @ universal_class )
= $false )
| ( ( member @ ( power_class @ SV167 ) @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[878]) ).
thf(924,plain,
! [SV169: $i,SV185: $i] :
( ( ( ~ ( function @ SV185 )
| ~ ( member @ SV169 @ universal_class ) )
= $true )
| ( ( member @ ( image @ SV185 @ SV169 ) @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[880]) ).
thf(925,plain,
! [SV171: $i] :
( ( ~ ! [SY244: $i,SY245: $i] :
( ~ ( member @ SY245 @ SV171 )
| ~ ( member @ SY245 @ SY244 )
| ( member @ SY245 @ ( intersection @ SV171 @ SY244 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[882]) ).
thf(926,plain,
! [SV171: $i] :
( ( ~ ~ ( ~ ! [SY246: $i,SY247: $i] :
( ~ ( member @ SY247 @ ( intersection @ SV171 @ SY246 ) )
| ( member @ SY247 @ SV171 ) )
| ~ ! [SY248: $i,SY249: $i] :
( ~ ( member @ SY249 @ ( intersection @ SV171 @ SY248 ) )
| ( member @ SY249 @ SY248 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[882]) ).
thf(927,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( restrict @ SX0 @ ( singleton @ SX1 ) @ universal_class )
= null_class )
| ~ ( member @ SX1 @ universal_class )
| ( member @ SX1 @ ( domain_of @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[883]) ).
thf(928,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( domain_of @ SX0 ) )
| ( ( restrict @ SX0 @ ( singleton @ SX1 ) @ universal_class )
!= null_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( domain_of @ SX0 ) )
| ( member @ SX1 @ universal_class ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[884]) ).
thf(929,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ universal_class )
| ~ ( member @ SX0 @ SX1 )
| ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[885]) ).
thf(930,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation )
| ( member @ SX1 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation )
| ( member @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[886]) ).
thf(931,plain,
( ( ! [SX0: $i] :
( ~ ( subclass @ SX0 @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ SX0 @ ( inverse @ SX0 ) ) @ identity_relation )
| ( function @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[887]) ).
thf(932,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ( subclass @ SX0 @ ( cross_product @ universal_class @ universal_class ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ( subclass @ ( compose @ SX0 @ ( inverse @ SX0 ) ) @ identity_relation ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[888]) ).
thf(933,plain,
( ( ! [SX0: $i] :
( ~ ( inductive @ SX0 )
| ( subclass @ sK9_X @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[889]) ).
thf(934,plain,
( ( ~ ( ~ ( inductive @ sK9_X )
| ~ ( member @ sK9_X @ universal_class ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[890]) ).
thf(935,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
( ( SX0
!= ( ordered_pair @ SX1 @ SX1 ) )
| ~ ( member @ SX1 @ universal_class ) )
| ( member @ SX0 @ identity_relation ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[891]) ).
thf(936,plain,
( ( ! [SX0: $i] :
( ~ ( member @ SX0 @ identity_relation )
| ~ ( ( SX0
!= ( ordered_pair @ ( sK7_X @ SX0 ) @ ( sK7_X @ SX0 ) ) )
| ~ ( member @ ( sK7_X @ SX0 ) @ universal_class ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[892]) ).
thf(937,plain,
( ( ! [SX0: $i] :
( ~ ( member @ SX0 @ universal_class )
| ( SX0 = null_class )
| ( member @ ( apply @ sK4_XF @ SX0 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[893]) ).
thf(938,plain,
( ( function @ sK4_XF )
= $true ),
inference(extcnf_not_neg,[status(thm)],[894]) ).
thf(939,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK6_U @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK6_U @ SX1 @ SX0 ) @ SX1 ) )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[895]) ).
thf(940,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[896]) ).
thf(941,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ universal_class )
| ~ ( member @ SX1 @ universal_class )
| ( ( successor @ SX0 )
!= SX1 )
| ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[897]) ).
thf(942,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX0 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX1 @ universal_class ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( ( successor @ SX0 )
= SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[898]) ).
thf(943,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX0 @ SX2 )
| ~ ( member @ SX2 @ SX1 ) )
| ( member @ SX0 @ ( sum_class @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[899]) ).
thf(944,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( sum_class @ SX1 ) )
| ~ ( ~ ( member @ SX0 @ ( sK8_Y @ SX1 @ SX0 ) )
| ~ ( member @ ( sK8_Y @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[900]) ).
thf(945,plain,
! [SV172: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK5_U @ SV172 ) @ universal_class )
| ~ ( member @ ( sK5_U @ SV172 ) @ SV172 ) )
| ~ ( disjoint @ ( sK5_U @ SV172 ) @ SV172 ) )
= $false )
| ( ( SV172 = null_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[901]) ).
thf(946,plain,
! [SV187: $i,SV173: $i] :
( ( ~ ! [SY294: $i,SY295: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SY294 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV187 @ SV173 ) @ SY294 ) @ SY295 )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SY294 ) @ ( flip @ SY295 ) ) )
| ~ ~ ( ~ ! [SY296: $i] :
( ! [SY297: $i] :
~ ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SY296 ) @ ( flip @ SY297 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SY296 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
| ~ ! [SY298: $i,SY299: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SY298 ) @ ( flip @ SY299 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV187 @ SV173 ) @ SY298 ) @ SY299 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(947,plain,
! [SV174: $i,SV188: $i] :
( ( ~ ! [SY300: $i,SY301: $i] :
( ~ ( member @ SY300 @ universal_class )
| ~ ( member @ SY301 @ ( image @ SV188 @ ( image @ SV174 @ ( singleton @ SY300 ) ) ) )
| ( member @ ( ordered_pair @ SY300 @ SY301 ) @ ( compose @ SV188 @ SV174 ) ) )
| ~ ~ ( ~ ! [SY302: $i] :
( ! [SY303: $i] :
~ ( member @ ( ordered_pair @ SY302 @ SY303 ) @ ( compose @ SV188 @ SV174 ) )
| ( member @ SY302 @ universal_class ) )
| ~ ! [SY304: $i,SY305: $i] :
( ~ ( member @ ( ordered_pair @ SY304 @ SY305 ) @ ( compose @ SV188 @ SV174 ) )
| ( member @ SY305 @ ( image @ SV188 @ ( image @ SV174 @ ( singleton @ SY304 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[903]) ).
thf(948,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subclass @ SX0 @ SX1 )
| ~ ( subclass @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[904]) ).
thf(949,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subclass @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subclass @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[905]) ).
thf(950,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ universal_class )
| ( member @ SX1 @ SX0 )
| ( member @ SX1 @ ( complement @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[906]) ).
thf(951,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( complement @ SX0 ) )
| ( member @ SX1 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( complement @ SX0 ) )
| ~ ( member @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[907]) ).
thf(952,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK10_U @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK10_U @ SX1 @ SX0 ) @ SX1 ) )
| ( subclass @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[908]) ).
thf(953,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subclass @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[909]) ).
thf(954,plain,
! [SV189: $i,SV175: $i] :
( ( ~ ! [SY306: $i,SY307: $i] :
( ~ ( member @ SV175 @ SY306 )
| ~ ( member @ SV189 @ SY307 )
| ( member @ ( ordered_pair @ SV175 @ SV189 ) @ ( cross_product @ SY306 @ SY307 ) ) )
| ~ ~ ( ~ ! [SY308: $i] :
( ! [SY309: $i] :
~ ( member @ ( ordered_pair @ SV175 @ SV189 ) @ ( cross_product @ SY308 @ SY309 ) )
| ( member @ SV175 @ SY308 ) )
| ~ ! [SY310: $i,SY311: $i] :
( ~ ( member @ ( ordered_pair @ SV175 @ SV189 ) @ ( cross_product @ SY310 @ SY311 ) )
| ( member @ SV189 @ SY311 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[910]) ).
thf(955,plain,
! [SV176: $i] :
( ( ~ ~ ( ~ ! [SY271: $i] :
( ~ ( member @ SV176 @ universal_class )
| ( SV176 != SY271 )
| ! [SY272: $i] : ( member @ SV176 @ ( unordered_pair @ SY271 @ SY272 ) ) )
| ~ ! [SY273: $i,SY274: $i] :
( ~ ( member @ SV176 @ universal_class )
| ( SV176 != SY274 )
| ( member @ SV176 @ ( unordered_pair @ SY273 @ SY274 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[911]) ).
thf(956,plain,
! [SV176: $i] :
( ( ~ ~ ( ~ ( ! [SY275: $i,SY276: $i] :
~ ( member @ SV176 @ ( unordered_pair @ SY275 @ SY276 ) )
| ( member @ SV176 @ universal_class ) )
| ~ ! [SY277: $i,SY278: $i] :
( ~ ( member @ SV176 @ ( unordered_pair @ SY277 @ SY278 ) )
| ( SV176 = SY277 )
| ( SV176 = SY278 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[911]) ).
thf(957,plain,
( ( ! [SX0: $i] :
( ~ ( member @ null_class @ SX0 )
| ~ ( subclass @ ( image @ successor_relation @ SX0 ) @ SX0 )
| ( inductive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[912]) ).
thf(958,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( inductive @ SX0 )
| ( member @ null_class @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( inductive @ SX0 )
| ( subclass @ ( image @ successor_relation @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[913]) ).
thf(959,plain,
! [SV177: $i,SV190: $i] :
( ( ~ ! [SY312: $i,SY313: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SY312 ) @ SY313 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SY312 @ SY313 ) @ SV190 ) @ SV177 )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SY312 ) @ SY313 ) @ ( rotate @ SV177 ) ) )
| ~ ~ ( ~ ! [SY314: $i,SY315: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SY314 ) @ SY315 ) @ ( rotate @ SV177 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SY314 ) @ SY315 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
| ~ ! [SY316: $i,SY317: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SY316 ) @ SY317 ) @ ( rotate @ SV177 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SY316 @ SY317 ) @ SV190 ) @ SV177 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[914]) ).
thf(960,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ universal_class )
| ~ ( member @ SX1 @ universal_class )
| ( ( first @ ( ordered_pair @ SX0 @ SX1 ) )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[915]) ).
thf(961,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ universal_class )
| ~ ( member @ SX1 @ universal_class )
| ( ( second @ ( ordered_pair @ SX0 @ SX1 ) )
= SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[916]) ).
thf(962,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ universal_class )
| ~ ( subclass @ SX0 @ SX1 )
| ( member @ SX0 @ ( power_class @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[917]) ).
thf(963,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( member @ SX0 @ ( power_class @ SX1 ) )
| ( member @ SX0 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( power_class @ SX1 ) )
| ( subclass @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[918]) ).
thf(964,plain,
! [SV178: $i] :
( ( ~ ! [SY286: $i,SY287: $i] :
( ~ ( member @ SY287 @ ( union @ SV178 @ SY286 ) )
| ( member @ SY287 @ SV178 )
| ( member @ SY287 @ SY286 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[919]) ).
thf(965,plain,
! [SV178: $i] :
( ( ~ ~ ( ~ ! [SY288: $i,SY289: $i] :
( ~ ( member @ SY289 @ SV178 )
| ( member @ SY289 @ ( union @ SV178 @ SY288 ) ) )
| ~ ! [SY290: $i,SY291: $i] :
( ~ ( member @ SY291 @ SY290 )
| ( member @ SY291 @ ( union @ SV178 @ SY290 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[919]) ).
thf(966,plain,
! [SV181: $i,SV157: $i,SV191: $i] :
( ( ( ~ ( member @ SV191 @ ( cross_product @ SV157 @ SV181 ) ) )
= $true )
| ( ( SV191
= ( ordered_pair @ ( first @ SV191 ) @ ( second @ SV191 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[920]) ).
thf(967,plain,
! [SV169: $i,SV185: $i] :
( ( ( ~ ( function @ SV185 ) )
= $true )
| ( ( ~ ( member @ SV169 @ universal_class ) )
= $true )
| ( ( member @ ( image @ SV185 @ SV169 ) @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[924]) ).
thf(968,plain,
! [SV171: $i] :
( ( ! [SY244: $i,SY245: $i] :
( ~ ( member @ SY245 @ SV171 )
| ~ ( member @ SY245 @ SY244 )
| ( member @ SY245 @ ( intersection @ SV171 @ SY244 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[925]) ).
thf(969,plain,
! [SV171: $i] :
( ( ~ ( ~ ! [SY246: $i,SY247: $i] :
( ~ ( member @ SY247 @ ( intersection @ SV171 @ SY246 ) )
| ( member @ SY247 @ SV171 ) )
| ~ ! [SY248: $i,SY249: $i] :
( ~ ( member @ SY249 @ ( intersection @ SV171 @ SY248 ) )
| ( member @ SY249 @ SY248 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[926]) ).
thf(970,plain,
! [SV193: $i] :
( ( ! [SY318: $i] :
( ( ( restrict @ SV193 @ ( singleton @ SY318 ) @ universal_class )
= null_class )
| ~ ( member @ SY318 @ universal_class )
| ( member @ SY318 @ ( domain_of @ SV193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(971,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( domain_of @ SX0 ) )
| ( ( restrict @ SX0 @ ( singleton @ SX1 ) @ universal_class )
!= null_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( domain_of @ SX0 ) )
| ( member @ SX1 @ universal_class ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[928]) ).
thf(972,plain,
! [SV194: $i] :
( ( ! [SY319: $i] :
( ~ ( member @ SY319 @ universal_class )
| ~ ( member @ SV194 @ SY319 )
| ( member @ ( ordered_pair @ SV194 @ SY319 ) @ element_relation ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(973,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation )
| ( member @ SX1 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation )
| ( member @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[930]) ).
thf(974,plain,
! [SV195: $i] :
( ( ~ ( subclass @ SV195 @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ SV195 @ ( inverse @ SV195 ) ) @ identity_relation )
| ( function @ SV195 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(975,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ( subclass @ SX0 @ ( cross_product @ universal_class @ universal_class ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ( subclass @ ( compose @ SX0 @ ( inverse @ SX0 ) ) @ identity_relation ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[932]) ).
thf(976,plain,
! [SV196: $i] :
( ( ~ ( inductive @ SV196 )
| ( subclass @ sK9_X @ SV196 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(977,plain,
( ( ~ ( inductive @ sK9_X )
| ~ ( member @ sK9_X @ universal_class ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[934]) ).
thf(978,plain,
! [SV197: $i] :
( ( ! [SY320: $i] :
( ( SV197
!= ( ordered_pair @ SY320 @ SY320 ) )
| ~ ( member @ SY320 @ universal_class ) )
| ( member @ SV197 @ identity_relation ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[935]) ).
thf(979,plain,
! [SV198: $i] :
( ( ~ ( member @ SV198 @ identity_relation )
| ~ ( ( SV198
!= ( ordered_pair @ ( sK7_X @ SV198 ) @ ( sK7_X @ SV198 ) ) )
| ~ ( member @ ( sK7_X @ SV198 ) @ universal_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(980,plain,
! [SV199: $i] :
( ( ~ ( member @ SV199 @ universal_class )
| ( SV199 = null_class )
| ( member @ ( apply @ sK4_XF @ SV199 ) @ SV199 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[937]) ).
thf(981,plain,
! [SV200: $i] :
( ( ! [SY321: $i] :
( ~ ( ~ ( member @ ( sK6_U @ SY321 @ SV200 ) @ SV200 )
| ~ ( member @ ( sK6_U @ SY321 @ SV200 ) @ SY321 ) )
| ( disjoint @ SV200 @ SY321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(982,plain,
! [SV201: $i] :
( ( ! [SY322: $i] :
( ~ ( disjoint @ SV201 @ SY322 )
| ! [SY323: $i] :
( ~ ( member @ SY323 @ SV201 )
| ~ ( member @ SY323 @ SY322 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[940]) ).
thf(983,plain,
! [SV202: $i] :
( ( ! [SY324: $i] :
( ~ ( member @ SV202 @ universal_class )
| ~ ( member @ SY324 @ universal_class )
| ( ( successor @ SV202 )
!= SY324 )
| ( member @ ( ordered_pair @ SV202 @ SY324 ) @ successor_relation ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[941]) ).
thf(984,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX0 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX1 @ universal_class ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( ( successor @ SX0 )
= SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[942]) ).
thf(985,plain,
! [SV203: $i] :
( ( ! [SY325: $i] :
( ! [SY326: $i] :
( ~ ( member @ SV203 @ SY326 )
| ~ ( member @ SY326 @ SY325 ) )
| ( member @ SV203 @ ( sum_class @ SY325 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(986,plain,
! [SV204: $i] :
( ( ! [SY327: $i] :
( ~ ( member @ SV204 @ ( sum_class @ SY327 ) )
| ~ ( ~ ( member @ SV204 @ ( sK8_Y @ SY327 @ SV204 ) )
| ~ ( member @ ( sK8_Y @ SY327 @ SV204 ) @ SY327 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[944]) ).
thf(987,plain,
! [SV172: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK5_U @ SV172 ) @ universal_class )
| ~ ( member @ ( sK5_U @ SV172 ) @ SV172 ) ) )
= $false )
| ( ( SV172 = null_class )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[945]) ).
thf(988,plain,
! [SV172: $i] :
( ( ( ~ ( disjoint @ ( sK5_U @ SV172 ) @ SV172 ) )
= $false )
| ( ( SV172 = null_class )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[945]) ).
thf(989,plain,
! [SV187: $i,SV173: $i] :
( ( ~ ! [SY294: $i,SY295: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SY294 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV187 @ SV173 ) @ SY294 ) @ SY295 )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SY294 ) @ ( flip @ SY295 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[946]) ).
thf(990,plain,
! [SV187: $i,SV173: $i] :
( ( ~ ~ ( ~ ! [SY296: $i] :
( ! [SY297: $i] :
~ ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SY296 ) @ ( flip @ SY297 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SY296 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
| ~ ! [SY298: $i,SY299: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SY298 ) @ ( flip @ SY299 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV187 @ SV173 ) @ SY298 ) @ SY299 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[946]) ).
thf(991,plain,
! [SV174: $i,SV188: $i] :
( ( ~ ! [SY300: $i,SY301: $i] :
( ~ ( member @ SY300 @ universal_class )
| ~ ( member @ SY301 @ ( image @ SV188 @ ( image @ SV174 @ ( singleton @ SY300 ) ) ) )
| ( member @ ( ordered_pair @ SY300 @ SY301 ) @ ( compose @ SV188 @ SV174 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[947]) ).
thf(992,plain,
! [SV174: $i,SV188: $i] :
( ( ~ ~ ( ~ ! [SY302: $i] :
( ! [SY303: $i] :
~ ( member @ ( ordered_pair @ SY302 @ SY303 ) @ ( compose @ SV188 @ SV174 ) )
| ( member @ SY302 @ universal_class ) )
| ~ ! [SY304: $i,SY305: $i] :
( ~ ( member @ ( ordered_pair @ SY304 @ SY305 ) @ ( compose @ SV188 @ SV174 ) )
| ( member @ SY305 @ ( image @ SV188 @ ( image @ SV174 @ ( singleton @ SY304 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[947]) ).
thf(993,plain,
! [SV205: $i] :
( ( ! [SY328: $i] :
( ~ ( subclass @ SV205 @ SY328 )
| ~ ( subclass @ SY328 @ SV205 )
| ( SV205 = SY328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(994,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subclass @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subclass @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[949]) ).
thf(995,plain,
! [SV206: $i] :
( ( ! [SY329: $i] :
( ~ ( member @ SY329 @ universal_class )
| ( member @ SY329 @ SV206 )
| ( member @ SY329 @ ( complement @ SV206 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(996,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( complement @ SX0 ) )
| ( member @ SX1 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( complement @ SX0 ) )
| ~ ( member @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[951]) ).
thf(997,plain,
! [SV207: $i] :
( ( ! [SY330: $i] :
( ~ ( ~ ( member @ ( sK10_U @ SY330 @ SV207 ) @ SV207 )
| ~ ~ ( member @ ( sK10_U @ SY330 @ SV207 ) @ SY330 ) )
| ( subclass @ SV207 @ SY330 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(998,plain,
! [SV208: $i] :
( ( ! [SY331: $i] :
( ~ ( subclass @ SV208 @ SY331 )
| ! [SY332: $i] :
( ~ ( member @ SY332 @ SV208 )
| ( member @ SY332 @ SY331 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(999,plain,
! [SV189: $i,SV175: $i] :
( ( ~ ! [SY306: $i,SY307: $i] :
( ~ ( member @ SV175 @ SY306 )
| ~ ( member @ SV189 @ SY307 )
| ( member @ ( ordered_pair @ SV175 @ SV189 ) @ ( cross_product @ SY306 @ SY307 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[954]) ).
thf(1000,plain,
! [SV189: $i,SV175: $i] :
( ( ~ ~ ( ~ ! [SY308: $i] :
( ! [SY309: $i] :
~ ( member @ ( ordered_pair @ SV175 @ SV189 ) @ ( cross_product @ SY308 @ SY309 ) )
| ( member @ SV175 @ SY308 ) )
| ~ ! [SY310: $i,SY311: $i] :
( ~ ( member @ ( ordered_pair @ SV175 @ SV189 ) @ ( cross_product @ SY310 @ SY311 ) )
| ( member @ SV189 @ SY311 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[954]) ).
thf(1001,plain,
! [SV176: $i] :
( ( ~ ( ~ ! [SY271: $i] :
( ~ ( member @ SV176 @ universal_class )
| ( SV176 != SY271 )
| ! [SY272: $i] : ( member @ SV176 @ ( unordered_pair @ SY271 @ SY272 ) ) )
| ~ ! [SY273: $i,SY274: $i] :
( ~ ( member @ SV176 @ universal_class )
| ( SV176 != SY274 )
| ( member @ SV176 @ ( unordered_pair @ SY273 @ SY274 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[955]) ).
thf(1002,plain,
! [SV176: $i] :
( ( ~ ( ~ ( ! [SY275: $i,SY276: $i] :
~ ( member @ SV176 @ ( unordered_pair @ SY275 @ SY276 ) )
| ( member @ SV176 @ universal_class ) )
| ~ ! [SY277: $i,SY278: $i] :
( ~ ( member @ SV176 @ ( unordered_pair @ SY277 @ SY278 ) )
| ( SV176 = SY277 )
| ( SV176 = SY278 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[956]) ).
thf(1003,plain,
! [SV209: $i] :
( ( ~ ( member @ null_class @ SV209 )
| ~ ( subclass @ ( image @ successor_relation @ SV209 ) @ SV209 )
| ( inductive @ SV209 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(1004,plain,
( ( ~ ! [SX0: $i] :
( ~ ( inductive @ SX0 )
| ( member @ null_class @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( inductive @ SX0 )
| ( subclass @ ( image @ successor_relation @ SX0 ) @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[958]) ).
thf(1005,plain,
! [SV177: $i,SV190: $i] :
( ( ~ ! [SY312: $i,SY313: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SY312 ) @ SY313 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SY312 @ SY313 ) @ SV190 ) @ SV177 )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SY312 ) @ SY313 ) @ ( rotate @ SV177 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[959]) ).
thf(1006,plain,
! [SV177: $i,SV190: $i] :
( ( ~ ~ ( ~ ! [SY314: $i,SY315: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SY314 ) @ SY315 ) @ ( rotate @ SV177 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SY314 ) @ SY315 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
| ~ ! [SY316: $i,SY317: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SY316 ) @ SY317 ) @ ( rotate @ SV177 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SY316 @ SY317 ) @ SV190 ) @ SV177 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[959]) ).
thf(1007,plain,
! [SV210: $i] :
( ( ! [SY333: $i] :
( ~ ( member @ SV210 @ universal_class )
| ~ ( member @ SY333 @ universal_class )
| ( ( first @ ( ordered_pair @ SV210 @ SY333 ) )
= SV210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[960]) ).
thf(1008,plain,
! [SV211: $i] :
( ( ! [SY334: $i] :
( ~ ( member @ SV211 @ universal_class )
| ~ ( member @ SY334 @ universal_class )
| ( ( second @ ( ordered_pair @ SV211 @ SY334 ) )
= SY334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1009,plain,
! [SV212: $i] :
( ( ! [SY335: $i] :
( ~ ( member @ SV212 @ universal_class )
| ~ ( subclass @ SV212 @ SY335 )
| ( member @ SV212 @ ( power_class @ SY335 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1010,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( member @ SX0 @ ( power_class @ SX1 ) )
| ( member @ SX0 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( power_class @ SX1 ) )
| ( subclass @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[963]) ).
thf(1011,plain,
! [SV178: $i] :
( ( ! [SY286: $i,SY287: $i] :
( ~ ( member @ SY287 @ ( union @ SV178 @ SY286 ) )
| ( member @ SY287 @ SV178 )
| ( member @ SY287 @ SY286 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[964]) ).
thf(1012,plain,
! [SV178: $i] :
( ( ~ ( ~ ! [SY288: $i,SY289: $i] :
( ~ ( member @ SY289 @ SV178 )
| ( member @ SY289 @ ( union @ SV178 @ SY288 ) ) )
| ~ ! [SY290: $i,SY291: $i] :
( ~ ( member @ SY291 @ SY290 )
| ( member @ SY291 @ ( union @ SV178 @ SY290 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[965]) ).
thf(1013,plain,
! [SV181: $i,SV157: $i,SV191: $i] :
( ( ( member @ SV191 @ ( cross_product @ SV157 @ SV181 ) )
= $false )
| ( ( SV191
= ( ordered_pair @ ( first @ SV191 ) @ ( second @ SV191 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[966]) ).
thf(1014,plain,
! [SV169: $i,SV185: $i] :
( ( ( function @ SV185 )
= $false )
| ( ( ~ ( member @ SV169 @ universal_class ) )
= $true )
| ( ( member @ ( image @ SV185 @ SV169 ) @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[967]) ).
thf(1015,plain,
! [SV213: $i,SV171: $i] :
( ( ! [SY336: $i] :
( ~ ( member @ SY336 @ SV171 )
| ~ ( member @ SY336 @ SV213 )
| ( member @ SY336 @ ( intersection @ SV171 @ SV213 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1016,plain,
! [SV171: $i] :
( ( ~ ! [SY246: $i,SY247: $i] :
( ~ ( member @ SY247 @ ( intersection @ SV171 @ SY246 ) )
| ( member @ SY247 @ SV171 ) )
| ~ ! [SY248: $i,SY249: $i] :
( ~ ( member @ SY249 @ ( intersection @ SV171 @ SY248 ) )
| ( member @ SY249 @ SY248 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[969]) ).
thf(1017,plain,
! [SV214: $i,SV193: $i] :
( ( ( ( restrict @ SV193 @ ( singleton @ SV214 ) @ universal_class )
= null_class )
| ~ ( member @ SV214 @ universal_class )
| ( member @ SV214 @ ( domain_of @ SV193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1018,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( domain_of @ SX0 ) )
| ( ( restrict @ SX0 @ ( singleton @ SX1 ) @ universal_class )
!= null_class ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[971]) ).
thf(1019,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( domain_of @ SX0 ) )
| ( member @ SX1 @ universal_class ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[971]) ).
thf(1020,plain,
! [SV194: $i,SV215: $i] :
( ( ~ ( member @ SV215 @ universal_class )
| ~ ( member @ SV194 @ SV215 )
| ( member @ ( ordered_pair @ SV194 @ SV215 ) @ element_relation ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1021,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation )
| ( member @ SX1 @ universal_class ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[973]) ).
thf(1022,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation )
| ( member @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[973]) ).
thf(1023,plain,
! [SV195: $i] :
( ( ( ~ ( subclass @ SV195 @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ SV195 @ ( inverse @ SV195 ) ) @ identity_relation ) )
= $true )
| ( ( function @ SV195 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[974]) ).
thf(1024,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ( subclass @ SX0 @ ( cross_product @ universal_class @ universal_class ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[975]) ).
thf(1025,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ( subclass @ ( compose @ SX0 @ ( inverse @ SX0 ) ) @ identity_relation ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[975]) ).
thf(1026,plain,
! [SV196: $i] :
( ( ( ~ ( inductive @ SV196 ) )
= $true )
| ( ( subclass @ sK9_X @ SV196 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[976]) ).
thf(1027,plain,
( ( ~ ( inductive @ sK9_X ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[977]) ).
thf(1028,plain,
( ( ~ ( member @ sK9_X @ universal_class ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[977]) ).
thf(1029,plain,
! [SV197: $i] :
( ( ( ! [SY320: $i] :
( ( SV197
!= ( ordered_pair @ SY320 @ SY320 ) )
| ~ ( member @ SY320 @ universal_class ) ) )
= $true )
| ( ( member @ SV197 @ identity_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[978]) ).
thf(1030,plain,
! [SV198: $i] :
( ( ( ~ ( member @ SV198 @ identity_relation ) )
= $true )
| ( ( ~ ( ( SV198
!= ( ordered_pair @ ( sK7_X @ SV198 ) @ ( sK7_X @ SV198 ) ) )
| ~ ( member @ ( sK7_X @ SV198 ) @ universal_class ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[979]) ).
thf(1031,plain,
! [SV199: $i] :
( ( ( ~ ( member @ SV199 @ universal_class ) )
= $true )
| ( ( ( SV199 = null_class )
| ( member @ ( apply @ sK4_XF @ SV199 ) @ SV199 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[980]) ).
thf(1032,plain,
! [SV200: $i,SV216: $i] :
( ( ~ ( ~ ( member @ ( sK6_U @ SV216 @ SV200 ) @ SV200 )
| ~ ( member @ ( sK6_U @ SV216 @ SV200 ) @ SV216 ) )
| ( disjoint @ SV200 @ SV216 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[981]) ).
thf(1033,plain,
! [SV217: $i,SV201: $i] :
( ( ~ ( disjoint @ SV201 @ SV217 )
| ! [SY337: $i] :
( ~ ( member @ SY337 @ SV201 )
| ~ ( member @ SY337 @ SV217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[982]) ).
thf(1034,plain,
! [SV218: $i,SV202: $i] :
( ( ~ ( member @ SV202 @ universal_class )
| ~ ( member @ SV218 @ universal_class )
| ( ( successor @ SV202 )
!= SV218 )
| ( member @ ( ordered_pair @ SV202 @ SV218 ) @ successor_relation ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1035,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX0 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX1 @ universal_class ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[984]) ).
thf(1036,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( ( successor @ SX0 )
= SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[984]) ).
thf(1037,plain,
! [SV219: $i,SV203: $i] :
( ( ! [SY338: $i] :
( ~ ( member @ SV203 @ SY338 )
| ~ ( member @ SY338 @ SV219 ) )
| ( member @ SV203 @ ( sum_class @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1038,plain,
! [SV220: $i,SV204: $i] :
( ( ~ ( member @ SV204 @ ( sum_class @ SV220 ) )
| ~ ( ~ ( member @ SV204 @ ( sK8_Y @ SV220 @ SV204 ) )
| ~ ( member @ ( sK8_Y @ SV220 @ SV204 ) @ SV220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1039,plain,
! [SV172: $i] :
( ( ( ~ ( ~ ( member @ ( sK5_U @ SV172 ) @ universal_class )
| ~ ( member @ ( sK5_U @ SV172 ) @ SV172 ) ) )
= $true )
| ( ( SV172 = null_class )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[987]) ).
thf(1040,plain,
! [SV172: $i] :
( ( ( disjoint @ ( sK5_U @ SV172 ) @ SV172 )
= $true )
| ( ( SV172 = null_class )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[988]) ).
thf(1041,plain,
! [SV187: $i,SV173: $i] :
( ( ! [SY294: $i,SY295: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SY294 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV187 @ SV173 ) @ SY294 ) @ SY295 )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SY294 ) @ ( flip @ SY295 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[989]) ).
thf(1042,plain,
! [SV187: $i,SV173: $i] :
( ( ~ ( ~ ! [SY296: $i] :
( ! [SY297: $i] :
~ ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SY296 ) @ ( flip @ SY297 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SY296 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
| ~ ! [SY298: $i,SY299: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SY298 ) @ ( flip @ SY299 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV187 @ SV173 ) @ SY298 ) @ SY299 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[990]) ).
thf(1043,plain,
! [SV174: $i,SV188: $i] :
( ( ! [SY300: $i,SY301: $i] :
( ~ ( member @ SY300 @ universal_class )
| ~ ( member @ SY301 @ ( image @ SV188 @ ( image @ SV174 @ ( singleton @ SY300 ) ) ) )
| ( member @ ( ordered_pair @ SY300 @ SY301 ) @ ( compose @ SV188 @ SV174 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[991]) ).
thf(1044,plain,
! [SV174: $i,SV188: $i] :
( ( ~ ( ~ ! [SY302: $i] :
( ! [SY303: $i] :
~ ( member @ ( ordered_pair @ SY302 @ SY303 ) @ ( compose @ SV188 @ SV174 ) )
| ( member @ SY302 @ universal_class ) )
| ~ ! [SY304: $i,SY305: $i] :
( ~ ( member @ ( ordered_pair @ SY304 @ SY305 ) @ ( compose @ SV188 @ SV174 ) )
| ( member @ SY305 @ ( image @ SV188 @ ( image @ SV174 @ ( singleton @ SY304 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[992]) ).
thf(1045,plain,
! [SV221: $i,SV205: $i] :
( ( ~ ( subclass @ SV205 @ SV221 )
| ~ ( subclass @ SV221 @ SV205 )
| ( SV205 = SV221 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1046,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subclass @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[994]) ).
thf(1047,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subclass @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[994]) ).
thf(1048,plain,
! [SV206: $i,SV222: $i] :
( ( ~ ( member @ SV222 @ universal_class )
| ( member @ SV222 @ SV206 )
| ( member @ SV222 @ ( complement @ SV206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1049,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( complement @ SX0 ) )
| ( member @ SX1 @ universal_class ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[996]) ).
thf(1050,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( complement @ SX0 ) )
| ~ ( member @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[996]) ).
thf(1051,plain,
! [SV207: $i,SV223: $i] :
( ( ~ ( ~ ( member @ ( sK10_U @ SV223 @ SV207 ) @ SV207 )
| ~ ~ ( member @ ( sK10_U @ SV223 @ SV207 ) @ SV223 ) )
| ( subclass @ SV207 @ SV223 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[997]) ).
thf(1052,plain,
! [SV224: $i,SV208: $i] :
( ( ~ ( subclass @ SV208 @ SV224 )
| ! [SY339: $i] :
( ~ ( member @ SY339 @ SV208 )
| ( member @ SY339 @ SV224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1053,plain,
! [SV189: $i,SV175: $i] :
( ( ! [SY306: $i,SY307: $i] :
( ~ ( member @ SV175 @ SY306 )
| ~ ( member @ SV189 @ SY307 )
| ( member @ ( ordered_pair @ SV175 @ SV189 ) @ ( cross_product @ SY306 @ SY307 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[999]) ).
thf(1054,plain,
! [SV189: $i,SV175: $i] :
( ( ~ ( ~ ! [SY308: $i] :
( ! [SY309: $i] :
~ ( member @ ( ordered_pair @ SV175 @ SV189 ) @ ( cross_product @ SY308 @ SY309 ) )
| ( member @ SV175 @ SY308 ) )
| ~ ! [SY310: $i,SY311: $i] :
( ~ ( member @ ( ordered_pair @ SV175 @ SV189 ) @ ( cross_product @ SY310 @ SY311 ) )
| ( member @ SV189 @ SY311 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1000]) ).
thf(1055,plain,
! [SV176: $i] :
( ( ~ ! [SY271: $i] :
( ~ ( member @ SV176 @ universal_class )
| ( SV176 != SY271 )
| ! [SY272: $i] : ( member @ SV176 @ ( unordered_pair @ SY271 @ SY272 ) ) )
| ~ ! [SY273: $i,SY274: $i] :
( ~ ( member @ SV176 @ universal_class )
| ( SV176 != SY274 )
| ( member @ SV176 @ ( unordered_pair @ SY273 @ SY274 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1001]) ).
thf(1056,plain,
! [SV176: $i] :
( ( ~ ( ! [SY275: $i,SY276: $i] :
~ ( member @ SV176 @ ( unordered_pair @ SY275 @ SY276 ) )
| ( member @ SV176 @ universal_class ) )
| ~ ! [SY277: $i,SY278: $i] :
( ~ ( member @ SV176 @ ( unordered_pair @ SY277 @ SY278 ) )
| ( SV176 = SY277 )
| ( SV176 = SY278 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1002]) ).
thf(1057,plain,
! [SV209: $i] :
( ( ( ~ ( member @ null_class @ SV209 )
| ~ ( subclass @ ( image @ successor_relation @ SV209 ) @ SV209 ) )
= $true )
| ( ( inductive @ SV209 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1003]) ).
thf(1058,plain,
( ( ~ ! [SX0: $i] :
( ~ ( inductive @ SX0 )
| ( member @ null_class @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1004]) ).
thf(1059,plain,
( ( ~ ! [SX0: $i] :
( ~ ( inductive @ SX0 )
| ( subclass @ ( image @ successor_relation @ SX0 ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1004]) ).
thf(1060,plain,
! [SV177: $i,SV190: $i] :
( ( ! [SY312: $i,SY313: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SY312 ) @ SY313 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SY312 @ SY313 ) @ SV190 ) @ SV177 )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SY312 ) @ SY313 ) @ ( rotate @ SV177 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1005]) ).
thf(1061,plain,
! [SV177: $i,SV190: $i] :
( ( ~ ( ~ ! [SY314: $i,SY315: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SY314 ) @ SY315 ) @ ( rotate @ SV177 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SY314 ) @ SY315 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
| ~ ! [SY316: $i,SY317: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SY316 ) @ SY317 ) @ ( rotate @ SV177 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SY316 @ SY317 ) @ SV190 ) @ SV177 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1006]) ).
thf(1062,plain,
! [SV225: $i,SV210: $i] :
( ( ~ ( member @ SV210 @ universal_class )
| ~ ( member @ SV225 @ universal_class )
| ( ( first @ ( ordered_pair @ SV210 @ SV225 ) )
= SV210 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1007]) ).
thf(1063,plain,
! [SV226: $i,SV211: $i] :
( ( ~ ( member @ SV211 @ universal_class )
| ~ ( member @ SV226 @ universal_class )
| ( ( second @ ( ordered_pair @ SV211 @ SV226 ) )
= SV226 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1064,plain,
! [SV227: $i,SV212: $i] :
( ( ~ ( member @ SV212 @ universal_class )
| ~ ( subclass @ SV212 @ SV227 )
| ( member @ SV212 @ ( power_class @ SV227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1009]) ).
thf(1065,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( member @ SX0 @ ( power_class @ SX1 ) )
| ( member @ SX0 @ universal_class ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1010]) ).
thf(1066,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( power_class @ SX1 ) )
| ( subclass @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1010]) ).
thf(1067,plain,
! [SV228: $i,SV178: $i] :
( ( ! [SY340: $i] :
( ~ ( member @ SY340 @ ( union @ SV178 @ SV228 ) )
| ( member @ SY340 @ SV178 )
| ( member @ SY340 @ SV228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1068,plain,
! [SV178: $i] :
( ( ~ ! [SY288: $i,SY289: $i] :
( ~ ( member @ SY289 @ SV178 )
| ( member @ SY289 @ ( union @ SV178 @ SY288 ) ) )
| ~ ! [SY290: $i,SY291: $i] :
( ~ ( member @ SY291 @ SY290 )
| ( member @ SY291 @ ( union @ SV178 @ SY290 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1012]) ).
thf(1069,plain,
! [SV185: $i,SV169: $i] :
( ( ( member @ SV169 @ universal_class )
= $false )
| ( ( function @ SV185 )
= $false )
| ( ( member @ ( image @ SV185 @ SV169 ) @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1014]) ).
thf(1070,plain,
! [SV213: $i,SV171: $i,SV229: $i] :
( ( ~ ( member @ SV229 @ SV171 )
| ~ ( member @ SV229 @ SV213 )
| ( member @ SV229 @ ( intersection @ SV171 @ SV213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1015]) ).
thf(1071,plain,
! [SV171: $i] :
( ( ~ ! [SY246: $i,SY247: $i] :
( ~ ( member @ SY247 @ ( intersection @ SV171 @ SY246 ) )
| ( member @ SY247 @ SV171 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1016]) ).
thf(1072,plain,
! [SV171: $i] :
( ( ~ ! [SY248: $i,SY249: $i] :
( ~ ( member @ SY249 @ ( intersection @ SV171 @ SY248 ) )
| ( member @ SY249 @ SY248 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1016]) ).
thf(1073,plain,
! [SV214: $i,SV193: $i] :
( ( ( ( ( restrict @ SV193 @ ( singleton @ SV214 ) @ universal_class )
= null_class )
| ~ ( member @ SV214 @ universal_class ) )
= $true )
| ( ( member @ SV214 @ ( domain_of @ SV193 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1017]) ).
thf(1074,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( domain_of @ SX0 ) )
| ( ( restrict @ SX0 @ ( singleton @ SX1 ) @ universal_class )
!= null_class ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1018]) ).
thf(1075,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( domain_of @ SX0 ) )
| ( member @ SX1 @ universal_class ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1019]) ).
thf(1076,plain,
! [SV194: $i,SV215: $i] :
( ( ( ~ ( member @ SV215 @ universal_class )
| ~ ( member @ SV194 @ SV215 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV194 @ SV215 ) @ element_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1020]) ).
thf(1077,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation )
| ( member @ SX1 @ universal_class ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1021]) ).
thf(1078,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation )
| ( member @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1022]) ).
thf(1079,plain,
! [SV195: $i] :
( ( ( ~ ( subclass @ SV195 @ ( cross_product @ universal_class @ universal_class ) ) )
= $true )
| ( ( ~ ( subclass @ ( compose @ SV195 @ ( inverse @ SV195 ) ) @ identity_relation ) )
= $true )
| ( ( function @ SV195 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1023]) ).
thf(1080,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ( subclass @ SX0 @ ( cross_product @ universal_class @ universal_class ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1024]) ).
thf(1081,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ( subclass @ ( compose @ SX0 @ ( inverse @ SX0 ) ) @ identity_relation ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1025]) ).
thf(1082,plain,
! [SV196: $i] :
( ( ( inductive @ SV196 )
= $false )
| ( ( subclass @ sK9_X @ SV196 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1026]) ).
thf(1083,plain,
( ( inductive @ sK9_X )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1027]) ).
thf(1084,plain,
( ( member @ sK9_X @ universal_class )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1028]) ).
thf(1085,plain,
! [SV230: $i,SV197: $i] :
( ( ( ( SV197
!= ( ordered_pair @ SV230 @ SV230 ) )
| ~ ( member @ SV230 @ universal_class ) )
= $true )
| ( ( member @ SV197 @ identity_relation )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1029]) ).
thf(1086,plain,
! [SV198: $i] :
( ( ( member @ SV198 @ identity_relation )
= $false )
| ( ( ~ ( ( SV198
!= ( ordered_pair @ ( sK7_X @ SV198 ) @ ( sK7_X @ SV198 ) ) )
| ~ ( member @ ( sK7_X @ SV198 ) @ universal_class ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1030]) ).
thf(1087,plain,
! [SV199: $i] :
( ( ( member @ SV199 @ universal_class )
= $false )
| ( ( ( SV199 = null_class )
| ( member @ ( apply @ sK4_XF @ SV199 ) @ SV199 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1031]) ).
thf(1088,plain,
! [SV200: $i,SV216: $i] :
( ( ( ~ ( ~ ( member @ ( sK6_U @ SV216 @ SV200 ) @ SV200 )
| ~ ( member @ ( sK6_U @ SV216 @ SV200 ) @ SV216 ) ) )
= $true )
| ( ( disjoint @ SV200 @ SV216 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1032]) ).
thf(1089,plain,
! [SV217: $i,SV201: $i] :
( ( ( ~ ( disjoint @ SV201 @ SV217 ) )
= $true )
| ( ( ! [SY337: $i] :
( ~ ( member @ SY337 @ SV201 )
| ~ ( member @ SY337 @ SV217 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1033]) ).
thf(1090,plain,
! [SV218: $i,SV202: $i] :
( ( ( ~ ( member @ SV202 @ universal_class )
| ~ ( member @ SV218 @ universal_class )
| ( ( successor @ SV202 )
!= SV218 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV202 @ SV218 ) @ successor_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1034]) ).
thf(1091,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX0 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX1 @ universal_class ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1035]) ).
thf(1092,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( ( successor @ SX0 )
= SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1036]) ).
thf(1093,plain,
! [SV219: $i,SV203: $i] :
( ( ( ! [SY338: $i] :
( ~ ( member @ SV203 @ SY338 )
| ~ ( member @ SY338 @ SV219 ) ) )
= $true )
| ( ( member @ SV203 @ ( sum_class @ SV219 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1037]) ).
thf(1094,plain,
! [SV220: $i,SV204: $i] :
( ( ( ~ ( member @ SV204 @ ( sum_class @ SV220 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ SV204 @ ( sK8_Y @ SV220 @ SV204 ) )
| ~ ( member @ ( sK8_Y @ SV220 @ SV204 ) @ SV220 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1038]) ).
thf(1095,plain,
! [SV172: $i] :
( ( ( ~ ( member @ ( sK5_U @ SV172 ) @ universal_class )
| ~ ( member @ ( sK5_U @ SV172 ) @ SV172 ) )
= $false )
| ( ( SV172 = null_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1039]) ).
thf(1096,plain,
! [SV231: $i,SV187: $i,SV173: $i] :
( ( ! [SY341: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SV231 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV187 @ SV173 ) @ SV231 ) @ SY341 )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SV231 ) @ ( flip @ SY341 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1097,plain,
! [SV187: $i,SV173: $i] :
( ( ~ ! [SY296: $i] :
( ! [SY297: $i] :
~ ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SY296 ) @ ( flip @ SY297 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SY296 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
| ~ ! [SY298: $i,SY299: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SY298 ) @ ( flip @ SY299 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV187 @ SV173 ) @ SY298 ) @ SY299 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1042]) ).
thf(1098,plain,
! [SV174: $i,SV188: $i,SV232: $i] :
( ( ! [SY342: $i] :
( ~ ( member @ SV232 @ universal_class )
| ~ ( member @ SY342 @ ( image @ SV188 @ ( image @ SV174 @ ( singleton @ SV232 ) ) ) )
| ( member @ ( ordered_pair @ SV232 @ SY342 ) @ ( compose @ SV188 @ SV174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1099,plain,
! [SV174: $i,SV188: $i] :
( ( ~ ! [SY302: $i] :
( ! [SY303: $i] :
~ ( member @ ( ordered_pair @ SY302 @ SY303 ) @ ( compose @ SV188 @ SV174 ) )
| ( member @ SY302 @ universal_class ) )
| ~ ! [SY304: $i,SY305: $i] :
( ~ ( member @ ( ordered_pair @ SY304 @ SY305 ) @ ( compose @ SV188 @ SV174 ) )
| ( member @ SY305 @ ( image @ SV188 @ ( image @ SV174 @ ( singleton @ SY304 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1044]) ).
thf(1100,plain,
! [SV221: $i,SV205: $i] :
( ( ( ~ ( subclass @ SV205 @ SV221 )
| ~ ( subclass @ SV221 @ SV205 ) )
= $true )
| ( ( SV205 = SV221 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1045]) ).
thf(1101,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subclass @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1046]) ).
thf(1102,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subclass @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1047]) ).
thf(1103,plain,
! [SV206: $i,SV222: $i] :
( ( ( ~ ( member @ SV222 @ universal_class )
| ( member @ SV222 @ SV206 ) )
= $true )
| ( ( member @ SV222 @ ( complement @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1048]) ).
thf(1104,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( complement @ SX0 ) )
| ( member @ SX1 @ universal_class ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1049]) ).
thf(1105,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( complement @ SX0 ) )
| ~ ( member @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1050]) ).
thf(1106,plain,
! [SV207: $i,SV223: $i] :
( ( ( ~ ( ~ ( member @ ( sK10_U @ SV223 @ SV207 ) @ SV207 )
| ~ ~ ( member @ ( sK10_U @ SV223 @ SV207 ) @ SV223 ) ) )
= $true )
| ( ( subclass @ SV207 @ SV223 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1051]) ).
thf(1107,plain,
! [SV224: $i,SV208: $i] :
( ( ( ~ ( subclass @ SV208 @ SV224 ) )
= $true )
| ( ( ! [SY339: $i] :
( ~ ( member @ SY339 @ SV208 )
| ( member @ SY339 @ SV224 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1052]) ).
thf(1108,plain,
! [SV189: $i,SV233: $i,SV175: $i] :
( ( ! [SY343: $i] :
( ~ ( member @ SV175 @ SV233 )
| ~ ( member @ SV189 @ SY343 )
| ( member @ ( ordered_pair @ SV175 @ SV189 ) @ ( cross_product @ SV233 @ SY343 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1053]) ).
thf(1109,plain,
! [SV189: $i,SV175: $i] :
( ( ~ ! [SY308: $i] :
( ! [SY309: $i] :
~ ( member @ ( ordered_pair @ SV175 @ SV189 ) @ ( cross_product @ SY308 @ SY309 ) )
| ( member @ SV175 @ SY308 ) )
| ~ ! [SY310: $i,SY311: $i] :
( ~ ( member @ ( ordered_pair @ SV175 @ SV189 ) @ ( cross_product @ SY310 @ SY311 ) )
| ( member @ SV189 @ SY311 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1054]) ).
thf(1110,plain,
! [SV176: $i] :
( ( ~ ! [SY271: $i] :
( ~ ( member @ SV176 @ universal_class )
| ( SV176 != SY271 )
| ! [SY272: $i] : ( member @ SV176 @ ( unordered_pair @ SY271 @ SY272 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1055]) ).
thf(1111,plain,
! [SV176: $i] :
( ( ~ ! [SY273: $i,SY274: $i] :
( ~ ( member @ SV176 @ universal_class )
| ( SV176 != SY274 )
| ( member @ SV176 @ ( unordered_pair @ SY273 @ SY274 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1055]) ).
thf(1112,plain,
! [SV176: $i] :
( ( ~ ( ! [SY275: $i,SY276: $i] :
~ ( member @ SV176 @ ( unordered_pair @ SY275 @ SY276 ) )
| ( member @ SV176 @ universal_class ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1056]) ).
thf(1113,plain,
! [SV176: $i] :
( ( ~ ! [SY277: $i,SY278: $i] :
( ~ ( member @ SV176 @ ( unordered_pair @ SY277 @ SY278 ) )
| ( SV176 = SY277 )
| ( SV176 = SY278 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1056]) ).
thf(1114,plain,
! [SV209: $i] :
( ( ( ~ ( member @ null_class @ SV209 ) )
= $true )
| ( ( ~ ( subclass @ ( image @ successor_relation @ SV209 ) @ SV209 ) )
= $true )
| ( ( inductive @ SV209 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1057]) ).
thf(1115,plain,
( ( ! [SX0: $i] :
( ~ ( inductive @ SX0 )
| ( member @ null_class @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1058]) ).
thf(1116,plain,
( ( ! [SX0: $i] :
( ~ ( inductive @ SX0 )
| ( subclass @ ( image @ successor_relation @ SX0 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1059]) ).
thf(1117,plain,
! [SV177: $i,SV234: $i,SV190: $i] :
( ( ! [SY344: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SV234 ) @ SY344 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV234 @ SY344 ) @ SV190 ) @ SV177 )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SV234 ) @ SY344 ) @ ( rotate @ SV177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1060]) ).
thf(1118,plain,
! [SV177: $i,SV190: $i] :
( ( ~ ! [SY314: $i,SY315: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SY314 ) @ SY315 ) @ ( rotate @ SV177 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SY314 ) @ SY315 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
| ~ ! [SY316: $i,SY317: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SY316 ) @ SY317 ) @ ( rotate @ SV177 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SY316 @ SY317 ) @ SV190 ) @ SV177 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1061]) ).
thf(1119,plain,
! [SV225: $i,SV210: $i] :
( ( ( ~ ( member @ SV210 @ universal_class )
| ~ ( member @ SV225 @ universal_class ) )
= $true )
| ( ( ( first @ ( ordered_pair @ SV210 @ SV225 ) )
= SV210 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1062]) ).
thf(1120,plain,
! [SV226: $i,SV211: $i] :
( ( ( ~ ( member @ SV211 @ universal_class )
| ~ ( member @ SV226 @ universal_class ) )
= $true )
| ( ( ( second @ ( ordered_pair @ SV211 @ SV226 ) )
= SV226 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1063]) ).
thf(1121,plain,
! [SV227: $i,SV212: $i] :
( ( ( ~ ( member @ SV212 @ universal_class )
| ~ ( subclass @ SV212 @ SV227 ) )
= $true )
| ( ( member @ SV212 @ ( power_class @ SV227 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1064]) ).
thf(1122,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( member @ SX0 @ ( power_class @ SX1 ) )
| ( member @ SX0 @ universal_class ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1065]) ).
thf(1123,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( power_class @ SX1 ) )
| ( subclass @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1066]) ).
thf(1124,plain,
! [SV228: $i,SV178: $i,SV235: $i] :
( ( ~ ( member @ SV235 @ ( union @ SV178 @ SV228 ) )
| ( member @ SV235 @ SV178 )
| ( member @ SV235 @ SV228 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1125,plain,
! [SV178: $i] :
( ( ~ ! [SY288: $i,SY289: $i] :
( ~ ( member @ SY289 @ SV178 )
| ( member @ SY289 @ ( union @ SV178 @ SY288 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1068]) ).
thf(1126,plain,
! [SV178: $i] :
( ( ~ ! [SY290: $i,SY291: $i] :
( ~ ( member @ SY291 @ SY290 )
| ( member @ SY291 @ ( union @ SV178 @ SY290 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1068]) ).
thf(1127,plain,
! [SV213: $i,SV171: $i,SV229: $i] :
( ( ( ~ ( member @ SV229 @ SV171 )
| ~ ( member @ SV229 @ SV213 ) )
= $true )
| ( ( member @ SV229 @ ( intersection @ SV171 @ SV213 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1070]) ).
thf(1128,plain,
! [SV171: $i] :
( ( ! [SY246: $i,SY247: $i] :
( ~ ( member @ SY247 @ ( intersection @ SV171 @ SY246 ) )
| ( member @ SY247 @ SV171 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1071]) ).
thf(1129,plain,
! [SV171: $i] :
( ( ! [SY248: $i,SY249: $i] :
( ~ ( member @ SY249 @ ( intersection @ SV171 @ SY248 ) )
| ( member @ SY249 @ SY248 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1072]) ).
thf(1130,plain,
! [SV214: $i,SV193: $i] :
( ( ( ( restrict @ SV193 @ ( singleton @ SV214 ) @ universal_class )
= null_class )
= $true )
| ( ( ~ ( member @ SV214 @ universal_class ) )
= $true )
| ( ( member @ SV214 @ ( domain_of @ SV193 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1073]) ).
thf(1131,plain,
! [SV236: $i] :
( ( ! [SY345: $i] :
( ~ ( member @ SY345 @ ( domain_of @ SV236 ) )
| ( ( restrict @ SV236 @ ( singleton @ SY345 ) @ universal_class )
!= null_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1074]) ).
thf(1132,plain,
! [SV237: $i] :
( ( ! [SY346: $i] :
( ~ ( member @ SY346 @ ( domain_of @ SV237 ) )
| ( member @ SY346 @ universal_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1133,plain,
! [SV194: $i,SV215: $i] :
( ( ( ~ ( member @ SV215 @ universal_class ) )
= $true )
| ( ( ~ ( member @ SV194 @ SV215 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV194 @ SV215 ) @ element_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1076]) ).
thf(1134,plain,
! [SV238: $i] :
( ( ! [SY347: $i] :
( ~ ( member @ ( ordered_pair @ SV238 @ SY347 ) @ element_relation )
| ( member @ SY347 @ universal_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1077]) ).
thf(1135,plain,
! [SV239: $i] :
( ( ! [SY348: $i] :
( ~ ( member @ ( ordered_pair @ SV239 @ SY348 ) @ element_relation )
| ( member @ SV239 @ SY348 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1078]) ).
thf(1136,plain,
! [SV195: $i] :
( ( ( subclass @ SV195 @ ( cross_product @ universal_class @ universal_class ) )
= $false )
| ( ( ~ ( subclass @ ( compose @ SV195 @ ( inverse @ SV195 ) ) @ identity_relation ) )
= $true )
| ( ( function @ SV195 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1079]) ).
thf(1137,plain,
! [SV240: $i] :
( ( ~ ( function @ SV240 )
| ( subclass @ SV240 @ ( cross_product @ universal_class @ universal_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1138,plain,
! [SV241: $i] :
( ( ~ ( function @ SV241 )
| ( subclass @ ( compose @ SV241 @ ( inverse @ SV241 ) ) @ identity_relation ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1081]) ).
thf(1139,plain,
! [SV230: $i,SV197: $i] :
( ( ( ( SV197
!= ( ordered_pair @ SV230 @ SV230 ) ) )
= $true )
| ( ( ~ ( member @ SV230 @ universal_class ) )
= $true )
| ( ( member @ SV197 @ identity_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1085]) ).
thf(1140,plain,
! [SV198: $i] :
( ( ( ( SV198
!= ( ordered_pair @ ( sK7_X @ SV198 ) @ ( sK7_X @ SV198 ) ) )
| ~ ( member @ ( sK7_X @ SV198 ) @ universal_class ) )
= $false )
| ( ( member @ SV198 @ identity_relation )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1086]) ).
thf(1141,plain,
! [SV199: $i] :
( ( ( SV199 = null_class )
= $true )
| ( ( member @ ( apply @ sK4_XF @ SV199 ) @ SV199 )
= $true )
| ( ( member @ SV199 @ universal_class )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1087]) ).
thf(1142,plain,
! [SV200: $i,SV216: $i] :
( ( ( ~ ( member @ ( sK6_U @ SV216 @ SV200 ) @ SV200 )
| ~ ( member @ ( sK6_U @ SV216 @ SV200 ) @ SV216 ) )
= $false )
| ( ( disjoint @ SV200 @ SV216 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1088]) ).
thf(1143,plain,
! [SV217: $i,SV201: $i] :
( ( ( disjoint @ SV201 @ SV217 )
= $false )
| ( ( ! [SY337: $i] :
( ~ ( member @ SY337 @ SV201 )
| ~ ( member @ SY337 @ SV217 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1089]) ).
thf(1144,plain,
! [SV218: $i,SV202: $i] :
( ( ( ~ ( member @ SV202 @ universal_class )
| ~ ( member @ SV218 @ universal_class ) )
= $true )
| ( ( ( ( successor @ SV202 )
!= SV218 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV202 @ SV218 ) @ successor_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1090]) ).
thf(1145,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX0 @ universal_class ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX1 @ universal_class ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1091]) ).
thf(1146,plain,
! [SV242: $i] :
( ( ! [SY349: $i] :
( ~ ( member @ ( ordered_pair @ SV242 @ SY349 ) @ successor_relation )
| ( ( successor @ SV242 )
= SY349 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1092]) ).
thf(1147,plain,
! [SV219: $i,SV243: $i,SV203: $i] :
( ( ( ~ ( member @ SV203 @ SV243 )
| ~ ( member @ SV243 @ SV219 ) )
= $true )
| ( ( member @ SV203 @ ( sum_class @ SV219 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1093]) ).
thf(1148,plain,
! [SV220: $i,SV204: $i] :
( ( ( member @ SV204 @ ( sum_class @ SV220 ) )
= $false )
| ( ( ~ ( ~ ( member @ SV204 @ ( sK8_Y @ SV220 @ SV204 ) )
| ~ ( member @ ( sK8_Y @ SV220 @ SV204 ) @ SV220 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1094]) ).
thf(1149,plain,
! [SV172: $i] :
( ( ( ~ ( member @ ( sK5_U @ SV172 ) @ universal_class ) )
= $false )
| ( ( SV172 = null_class )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1095]) ).
thf(1150,plain,
! [SV172: $i] :
( ( ( ~ ( member @ ( sK5_U @ SV172 ) @ SV172 ) )
= $false )
| ( ( SV172 = null_class )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1095]) ).
thf(1151,plain,
! [SV244: $i,SV231: $i,SV187: $i,SV173: $i] :
( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SV231 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV187 @ SV173 ) @ SV231 ) @ SV244 )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SV231 ) @ ( flip @ SV244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1096]) ).
thf(1152,plain,
! [SV187: $i,SV173: $i] :
( ( ~ ! [SY296: $i] :
( ! [SY297: $i] :
~ ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SY296 ) @ ( flip @ SY297 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SY296 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1097]) ).
thf(1153,plain,
! [SV187: $i,SV173: $i] :
( ( ~ ! [SY298: $i,SY299: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SY298 ) @ ( flip @ SY299 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV187 @ SV173 ) @ SY298 ) @ SY299 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1097]) ).
thf(1154,plain,
! [SV174: $i,SV188: $i,SV245: $i,SV232: $i] :
( ( ~ ( member @ SV232 @ universal_class )
| ~ ( member @ SV245 @ ( image @ SV188 @ ( image @ SV174 @ ( singleton @ SV232 ) ) ) )
| ( member @ ( ordered_pair @ SV232 @ SV245 ) @ ( compose @ SV188 @ SV174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1098]) ).
thf(1155,plain,
! [SV174: $i,SV188: $i] :
( ( ~ ! [SY302: $i] :
( ! [SY303: $i] :
~ ( member @ ( ordered_pair @ SY302 @ SY303 ) @ ( compose @ SV188 @ SV174 ) )
| ( member @ SY302 @ universal_class ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1099]) ).
thf(1156,plain,
! [SV174: $i,SV188: $i] :
( ( ~ ! [SY304: $i,SY305: $i] :
( ~ ( member @ ( ordered_pair @ SY304 @ SY305 ) @ ( compose @ SV188 @ SV174 ) )
| ( member @ SY305 @ ( image @ SV188 @ ( image @ SV174 @ ( singleton @ SY304 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1099]) ).
thf(1157,plain,
! [SV221: $i,SV205: $i] :
( ( ( ~ ( subclass @ SV205 @ SV221 ) )
= $true )
| ( ( ~ ( subclass @ SV221 @ SV205 ) )
= $true )
| ( ( SV205 = SV221 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1100]) ).
thf(1158,plain,
! [SV246: $i] :
( ( ! [SY350: $i] :
( ( SV246 != SY350 )
| ( subclass @ SV246 @ SY350 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1159,plain,
! [SV247: $i] :
( ( ! [SY351: $i] :
( ( SV247 != SY351 )
| ( subclass @ SY351 @ SV247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1102]) ).
thf(1160,plain,
! [SV206: $i,SV222: $i] :
( ( ( ~ ( member @ SV222 @ universal_class ) )
= $true )
| ( ( member @ SV222 @ SV206 )
= $true )
| ( ( member @ SV222 @ ( complement @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1103]) ).
thf(1161,plain,
! [SV248: $i] :
( ( ! [SY352: $i] :
( ~ ( member @ SY352 @ ( complement @ SV248 ) )
| ( member @ SY352 @ universal_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1162,plain,
! [SV249: $i] :
( ( ! [SY353: $i] :
( ~ ( member @ SY353 @ ( complement @ SV249 ) )
| ~ ( member @ SY353 @ SV249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1105]) ).
thf(1163,plain,
! [SV207: $i,SV223: $i] :
( ( ( ~ ( member @ ( sK10_U @ SV223 @ SV207 ) @ SV207 )
| ~ ~ ( member @ ( sK10_U @ SV223 @ SV207 ) @ SV223 ) )
= $false )
| ( ( subclass @ SV207 @ SV223 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1106]) ).
thf(1164,plain,
! [SV224: $i,SV208: $i] :
( ( ( subclass @ SV208 @ SV224 )
= $false )
| ( ( ! [SY339: $i] :
( ~ ( member @ SY339 @ SV208 )
| ( member @ SY339 @ SV224 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1107]) ).
thf(1165,plain,
! [SV250: $i,SV189: $i,SV233: $i,SV175: $i] :
( ( ~ ( member @ SV175 @ SV233 )
| ~ ( member @ SV189 @ SV250 )
| ( member @ ( ordered_pair @ SV175 @ SV189 ) @ ( cross_product @ SV233 @ SV250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1166,plain,
! [SV189: $i,SV175: $i] :
( ( ~ ! [SY308: $i] :
( ! [SY309: $i] :
~ ( member @ ( ordered_pair @ SV175 @ SV189 ) @ ( cross_product @ SY308 @ SY309 ) )
| ( member @ SV175 @ SY308 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1109]) ).
thf(1167,plain,
! [SV189: $i,SV175: $i] :
( ( ~ ! [SY310: $i,SY311: $i] :
( ~ ( member @ ( ordered_pair @ SV175 @ SV189 ) @ ( cross_product @ SY310 @ SY311 ) )
| ( member @ SV189 @ SY311 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1109]) ).
thf(1168,plain,
! [SV176: $i] :
( ( ! [SY271: $i] :
( ~ ( member @ SV176 @ universal_class )
| ( SV176 != SY271 )
| ! [SY272: $i] : ( member @ SV176 @ ( unordered_pair @ SY271 @ SY272 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1110]) ).
thf(1169,plain,
! [SV176: $i] :
( ( ! [SY273: $i,SY274: $i] :
( ~ ( member @ SV176 @ universal_class )
| ( SV176 != SY274 )
| ( member @ SV176 @ ( unordered_pair @ SY273 @ SY274 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1111]) ).
thf(1170,plain,
! [SV176: $i] :
( ( ! [SY275: $i,SY276: $i] :
~ ( member @ SV176 @ ( unordered_pair @ SY275 @ SY276 ) )
| ( member @ SV176 @ universal_class ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1112]) ).
thf(1171,plain,
! [SV176: $i] :
( ( ! [SY277: $i,SY278: $i] :
( ~ ( member @ SV176 @ ( unordered_pair @ SY277 @ SY278 ) )
| ( SV176 = SY277 )
| ( SV176 = SY278 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1113]) ).
thf(1172,plain,
! [SV209: $i] :
( ( ( member @ null_class @ SV209 )
= $false )
| ( ( ~ ( subclass @ ( image @ successor_relation @ SV209 ) @ SV209 ) )
= $true )
| ( ( inductive @ SV209 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1114]) ).
thf(1173,plain,
! [SV251: $i] :
( ( ~ ( inductive @ SV251 )
| ( member @ null_class @ SV251 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1174,plain,
! [SV252: $i] :
( ( ~ ( inductive @ SV252 )
| ( subclass @ ( image @ successor_relation @ SV252 ) @ SV252 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1175,plain,
! [SV177: $i,SV253: $i,SV234: $i,SV190: $i] :
( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SV234 ) @ SV253 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV234 @ SV253 ) @ SV190 ) @ SV177 )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SV234 ) @ SV253 ) @ ( rotate @ SV177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1176,plain,
! [SV177: $i,SV190: $i] :
( ( ~ ! [SY314: $i,SY315: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SY314 ) @ SY315 ) @ ( rotate @ SV177 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SY314 ) @ SY315 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1118]) ).
thf(1177,plain,
! [SV177: $i,SV190: $i] :
( ( ~ ! [SY316: $i,SY317: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SY316 ) @ SY317 ) @ ( rotate @ SV177 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SY316 @ SY317 ) @ SV190 ) @ SV177 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1118]) ).
thf(1178,plain,
! [SV225: $i,SV210: $i] :
( ( ( ~ ( member @ SV210 @ universal_class ) )
= $true )
| ( ( ~ ( member @ SV225 @ universal_class ) )
= $true )
| ( ( ( first @ ( ordered_pair @ SV210 @ SV225 ) )
= SV210 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1119]) ).
thf(1179,plain,
! [SV226: $i,SV211: $i] :
( ( ( ~ ( member @ SV211 @ universal_class ) )
= $true )
| ( ( ~ ( member @ SV226 @ universal_class ) )
= $true )
| ( ( ( second @ ( ordered_pair @ SV211 @ SV226 ) )
= SV226 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1120]) ).
thf(1180,plain,
! [SV227: $i,SV212: $i] :
( ( ( ~ ( member @ SV212 @ universal_class ) )
= $true )
| ( ( ~ ( subclass @ SV212 @ SV227 ) )
= $true )
| ( ( member @ SV212 @ ( power_class @ SV227 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1121]) ).
thf(1181,plain,
! [SV254: $i] :
( ( ! [SY354: $i] :
~ ( member @ SV254 @ ( power_class @ SY354 ) )
| ( member @ SV254 @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1182,plain,
! [SV255: $i] :
( ( ! [SY355: $i] :
( ~ ( member @ SV255 @ ( power_class @ SY355 ) )
| ( subclass @ SV255 @ SY355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1123]) ).
thf(1183,plain,
! [SV228: $i,SV178: $i,SV235: $i] :
( ( ( ~ ( member @ SV235 @ ( union @ SV178 @ SV228 ) ) )
= $true )
| ( ( ( member @ SV235 @ SV178 )
| ( member @ SV235 @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1124]) ).
thf(1184,plain,
! [SV178: $i] :
( ( ! [SY288: $i,SY289: $i] :
( ~ ( member @ SY289 @ SV178 )
| ( member @ SY289 @ ( union @ SV178 @ SY288 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1125]) ).
thf(1185,plain,
! [SV178: $i] :
( ( ! [SY290: $i,SY291: $i] :
( ~ ( member @ SY291 @ SY290 )
| ( member @ SY291 @ ( union @ SV178 @ SY290 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1126]) ).
thf(1186,plain,
! [SV213: $i,SV171: $i,SV229: $i] :
( ( ( ~ ( member @ SV229 @ SV171 ) )
= $true )
| ( ( ~ ( member @ SV229 @ SV213 ) )
= $true )
| ( ( member @ SV229 @ ( intersection @ SV171 @ SV213 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1127]) ).
thf(1187,plain,
! [SV256: $i,SV171: $i] :
( ( ! [SY356: $i] :
( ~ ( member @ SY356 @ ( intersection @ SV171 @ SV256 ) )
| ( member @ SY356 @ SV171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1188,plain,
! [SV257: $i,SV171: $i] :
( ( ! [SY357: $i] :
( ~ ( member @ SY357 @ ( intersection @ SV171 @ SV257 ) )
| ( member @ SY357 @ SV257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1129]) ).
thf(1189,plain,
! [SV193: $i,SV214: $i] :
( ( ( member @ SV214 @ universal_class )
= $false )
| ( ( ( restrict @ SV193 @ ( singleton @ SV214 ) @ universal_class )
= null_class )
= $true )
| ( ( member @ SV214 @ ( domain_of @ SV193 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1130]) ).
thf(1190,plain,
! [SV236: $i,SV258: $i] :
( ( ~ ( member @ SV258 @ ( domain_of @ SV236 ) )
| ( ( restrict @ SV236 @ ( singleton @ SV258 ) @ universal_class )
!= null_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1131]) ).
thf(1191,plain,
! [SV237: $i,SV259: $i] :
( ( ~ ( member @ SV259 @ ( domain_of @ SV237 ) )
| ( member @ SV259 @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1192,plain,
! [SV194: $i,SV215: $i] :
( ( ( member @ SV215 @ universal_class )
= $false )
| ( ( ~ ( member @ SV194 @ SV215 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV194 @ SV215 ) @ element_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1133]) ).
thf(1193,plain,
! [SV260: $i,SV238: $i] :
( ( ~ ( member @ ( ordered_pair @ SV238 @ SV260 ) @ element_relation )
| ( member @ SV260 @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1194,plain,
! [SV261: $i,SV239: $i] :
( ( ~ ( member @ ( ordered_pair @ SV239 @ SV261 ) @ element_relation )
| ( member @ SV239 @ SV261 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1135]) ).
thf(1195,plain,
! [SV195: $i] :
( ( ( subclass @ ( compose @ SV195 @ ( inverse @ SV195 ) ) @ identity_relation )
= $false )
| ( ( subclass @ SV195 @ ( cross_product @ universal_class @ universal_class ) )
= $false )
| ( ( function @ SV195 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1136]) ).
thf(1196,plain,
! [SV240: $i] :
( ( ( ~ ( function @ SV240 ) )
= $true )
| ( ( subclass @ SV240 @ ( cross_product @ universal_class @ universal_class ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1137]) ).
thf(1197,plain,
! [SV241: $i] :
( ( ( ~ ( function @ SV241 ) )
= $true )
| ( ( subclass @ ( compose @ SV241 @ ( inverse @ SV241 ) ) @ identity_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1138]) ).
thf(1198,plain,
! [SV230: $i,SV197: $i] :
( ( ( SV197
= ( ordered_pair @ SV230 @ SV230 ) )
= $false )
| ( ( ~ ( member @ SV230 @ universal_class ) )
= $true )
| ( ( member @ SV197 @ identity_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1139]) ).
thf(1199,plain,
! [SV198: $i] :
( ( ( ( SV198
!= ( ordered_pair @ ( sK7_X @ SV198 ) @ ( sK7_X @ SV198 ) ) ) )
= $false )
| ( ( member @ SV198 @ identity_relation )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1140]) ).
thf(1200,plain,
! [SV198: $i] :
( ( ( ~ ( member @ ( sK7_X @ SV198 ) @ universal_class ) )
= $false )
| ( ( member @ SV198 @ identity_relation )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1140]) ).
thf(1201,plain,
! [SV200: $i,SV216: $i] :
( ( ( ~ ( member @ ( sK6_U @ SV216 @ SV200 ) @ SV200 ) )
= $false )
| ( ( disjoint @ SV200 @ SV216 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1142]) ).
thf(1202,plain,
! [SV200: $i,SV216: $i] :
( ( ( ~ ( member @ ( sK6_U @ SV216 @ SV200 ) @ SV216 ) )
= $false )
| ( ( disjoint @ SV200 @ SV216 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1142]) ).
thf(1203,plain,
! [SV217: $i,SV201: $i,SV262: $i] :
( ( ( ~ ( member @ SV262 @ SV201 )
| ~ ( member @ SV262 @ SV217 ) )
= $true )
| ( ( disjoint @ SV201 @ SV217 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1143]) ).
thf(1204,plain,
! [SV218: $i,SV202: $i] :
( ( ( ~ ( member @ SV202 @ universal_class ) )
= $true )
| ( ( ~ ( member @ SV218 @ universal_class ) )
= $true )
| ( ( ( ( successor @ SV202 )
!= SV218 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV202 @ SV218 ) @ successor_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1144]) ).
thf(1205,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX0 @ universal_class ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1145]) ).
thf(1206,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX1 @ universal_class ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1145]) ).
thf(1207,plain,
! [SV263: $i,SV242: $i] :
( ( ~ ( member @ ( ordered_pair @ SV242 @ SV263 ) @ successor_relation )
| ( ( successor @ SV242 )
= SV263 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1208,plain,
! [SV219: $i,SV243: $i,SV203: $i] :
( ( ( ~ ( member @ SV203 @ SV243 ) )
= $true )
| ( ( ~ ( member @ SV243 @ SV219 ) )
= $true )
| ( ( member @ SV203 @ ( sum_class @ SV219 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1147]) ).
thf(1209,plain,
! [SV220: $i,SV204: $i] :
( ( ( ~ ( member @ SV204 @ ( sK8_Y @ SV220 @ SV204 ) )
| ~ ( member @ ( sK8_Y @ SV220 @ SV204 ) @ SV220 ) )
= $false )
| ( ( member @ SV204 @ ( sum_class @ SV220 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1148]) ).
thf(1210,plain,
! [SV172: $i] :
( ( ( member @ ( sK5_U @ SV172 ) @ universal_class )
= $true )
| ( ( SV172 = null_class )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1149]) ).
thf(1211,plain,
! [SV172: $i] :
( ( ( member @ ( sK5_U @ SV172 ) @ SV172 )
= $true )
| ( ( SV172 = null_class )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1150]) ).
thf(1212,plain,
! [SV244: $i,SV231: $i,SV187: $i,SV173: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SV231 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV187 @ SV173 ) @ SV231 ) @ SV244 ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SV231 ) @ ( flip @ SV244 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1151]) ).
thf(1213,plain,
! [SV187: $i,SV173: $i] :
( ( ! [SY296: $i] :
( ! [SY297: $i] :
~ ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SY296 ) @ ( flip @ SY297 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SY296 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1152]) ).
thf(1214,plain,
! [SV187: $i,SV173: $i] :
( ( ! [SY298: $i,SY299: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SY298 ) @ ( flip @ SY299 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV187 @ SV173 ) @ SY298 ) @ SY299 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1153]) ).
thf(1215,plain,
! [SV174: $i,SV188: $i,SV245: $i,SV232: $i] :
( ( ( ~ ( member @ SV232 @ universal_class )
| ~ ( member @ SV245 @ ( image @ SV188 @ ( image @ SV174 @ ( singleton @ SV232 ) ) ) ) )
= $true )
| ( ( member @ ( ordered_pair @ SV232 @ SV245 ) @ ( compose @ SV188 @ SV174 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1154]) ).
thf(1216,plain,
! [SV174: $i,SV188: $i] :
( ( ! [SY302: $i] :
( ! [SY303: $i] :
~ ( member @ ( ordered_pair @ SY302 @ SY303 ) @ ( compose @ SV188 @ SV174 ) )
| ( member @ SY302 @ universal_class ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1155]) ).
thf(1217,plain,
! [SV174: $i,SV188: $i] :
( ( ! [SY304: $i,SY305: $i] :
( ~ ( member @ ( ordered_pair @ SY304 @ SY305 ) @ ( compose @ SV188 @ SV174 ) )
| ( member @ SY305 @ ( image @ SV188 @ ( image @ SV174 @ ( singleton @ SY304 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1156]) ).
thf(1218,plain,
! [SV221: $i,SV205: $i] :
( ( ( subclass @ SV205 @ SV221 )
= $false )
| ( ( ~ ( subclass @ SV221 @ SV205 ) )
= $true )
| ( ( SV205 = SV221 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1157]) ).
thf(1219,plain,
! [SV264: $i,SV246: $i] :
( ( ( SV246 != SV264 )
| ( subclass @ SV246 @ SV264 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1158]) ).
thf(1220,plain,
! [SV265: $i,SV247: $i] :
( ( ( SV247 != SV265 )
| ( subclass @ SV265 @ SV247 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1159]) ).
thf(1221,plain,
! [SV206: $i,SV222: $i] :
( ( ( member @ SV222 @ universal_class )
= $false )
| ( ( member @ SV222 @ SV206 )
= $true )
| ( ( member @ SV222 @ ( complement @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1160]) ).
thf(1222,plain,
! [SV248: $i,SV266: $i] :
( ( ~ ( member @ SV266 @ ( complement @ SV248 ) )
| ( member @ SV266 @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1223,plain,
! [SV249: $i,SV267: $i] :
( ( ~ ( member @ SV267 @ ( complement @ SV249 ) )
| ~ ( member @ SV267 @ SV249 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1162]) ).
thf(1224,plain,
! [SV207: $i,SV223: $i] :
( ( ( ~ ( member @ ( sK10_U @ SV223 @ SV207 ) @ SV207 ) )
= $false )
| ( ( subclass @ SV207 @ SV223 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1163]) ).
thf(1225,plain,
! [SV207: $i,SV223: $i] :
( ( ( ~ ~ ( member @ ( sK10_U @ SV223 @ SV207 ) @ SV223 ) )
= $false )
| ( ( subclass @ SV207 @ SV223 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1163]) ).
thf(1226,plain,
! [SV224: $i,SV208: $i,SV268: $i] :
( ( ( ~ ( member @ SV268 @ SV208 )
| ( member @ SV268 @ SV224 ) )
= $true )
| ( ( subclass @ SV208 @ SV224 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1164]) ).
thf(1227,plain,
! [SV250: $i,SV189: $i,SV233: $i,SV175: $i] :
( ( ( ~ ( member @ SV175 @ SV233 )
| ~ ( member @ SV189 @ SV250 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV175 @ SV189 ) @ ( cross_product @ SV233 @ SV250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1165]) ).
thf(1228,plain,
! [SV189: $i,SV175: $i] :
( ( ! [SY308: $i] :
( ! [SY309: $i] :
~ ( member @ ( ordered_pair @ SV175 @ SV189 ) @ ( cross_product @ SY308 @ SY309 ) )
| ( member @ SV175 @ SY308 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1166]) ).
thf(1229,plain,
! [SV189: $i,SV175: $i] :
( ( ! [SY310: $i,SY311: $i] :
( ~ ( member @ ( ordered_pair @ SV175 @ SV189 ) @ ( cross_product @ SY310 @ SY311 ) )
| ( member @ SV189 @ SY311 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1167]) ).
thf(1230,plain,
! [SV269: $i,SV176: $i] :
( ( ~ ( member @ SV176 @ universal_class )
| ( SV176 != SV269 )
| ! [SY358: $i] : ( member @ SV176 @ ( unordered_pair @ SV269 @ SY358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1168]) ).
thf(1231,plain,
! [SV270: $i,SV176: $i] :
( ( ! [SY359: $i] :
( ~ ( member @ SV176 @ universal_class )
| ( SV176 != SY359 )
| ( member @ SV176 @ ( unordered_pair @ SV270 @ SY359 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1169]) ).
thf(1232,plain,
! [SV176: $i] :
( ( ( ! [SY275: $i,SY276: $i] :
~ ( member @ SV176 @ ( unordered_pair @ SY275 @ SY276 ) ) )
= $true )
| ( ( member @ SV176 @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1170]) ).
thf(1233,plain,
! [SV271: $i,SV176: $i] :
( ( ! [SY360: $i] :
( ~ ( member @ SV176 @ ( unordered_pair @ SV271 @ SY360 ) )
| ( SV176 = SV271 )
| ( SV176 = SY360 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1171]) ).
thf(1234,plain,
! [SV209: $i] :
( ( ( subclass @ ( image @ successor_relation @ SV209 ) @ SV209 )
= $false )
| ( ( member @ null_class @ SV209 )
= $false )
| ( ( inductive @ SV209 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1172]) ).
thf(1235,plain,
! [SV251: $i] :
( ( ( ~ ( inductive @ SV251 ) )
= $true )
| ( ( member @ null_class @ SV251 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1173]) ).
thf(1236,plain,
! [SV252: $i] :
( ( ( ~ ( inductive @ SV252 ) )
= $true )
| ( ( subclass @ ( image @ successor_relation @ SV252 ) @ SV252 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1174]) ).
thf(1237,plain,
! [SV177: $i,SV253: $i,SV234: $i,SV190: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SV234 ) @ SV253 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV234 @ SV253 ) @ SV190 ) @ SV177 ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SV234 ) @ SV253 ) @ ( rotate @ SV177 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1175]) ).
thf(1238,plain,
! [SV177: $i,SV190: $i] :
( ( ! [SY314: $i,SY315: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SY314 ) @ SY315 ) @ ( rotate @ SV177 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SY314 ) @ SY315 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1176]) ).
thf(1239,plain,
! [SV177: $i,SV190: $i] :
( ( ! [SY316: $i,SY317: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SY316 ) @ SY317 ) @ ( rotate @ SV177 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SY316 @ SY317 ) @ SV190 ) @ SV177 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1177]) ).
thf(1240,plain,
! [SV225: $i,SV210: $i] :
( ( ( member @ SV210 @ universal_class )
= $false )
| ( ( ~ ( member @ SV225 @ universal_class ) )
= $true )
| ( ( ( first @ ( ordered_pair @ SV210 @ SV225 ) )
= SV210 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1178]) ).
thf(1241,plain,
! [SV226: $i,SV211: $i] :
( ( ( member @ SV211 @ universal_class )
= $false )
| ( ( ~ ( member @ SV226 @ universal_class ) )
= $true )
| ( ( ( second @ ( ordered_pair @ SV211 @ SV226 ) )
= SV226 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1179]) ).
thf(1242,plain,
! [SV227: $i,SV212: $i] :
( ( ( member @ SV212 @ universal_class )
= $false )
| ( ( ~ ( subclass @ SV212 @ SV227 ) )
= $true )
| ( ( member @ SV212 @ ( power_class @ SV227 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1180]) ).
thf(1243,plain,
! [SV254: $i] :
( ( ( ! [SY354: $i] :
~ ( member @ SV254 @ ( power_class @ SY354 ) ) )
= $true )
| ( ( member @ SV254 @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1181]) ).
thf(1244,plain,
! [SV272: $i,SV255: $i] :
( ( ~ ( member @ SV255 @ ( power_class @ SV272 ) )
| ( subclass @ SV255 @ SV272 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1182]) ).
thf(1245,plain,
! [SV228: $i,SV178: $i,SV235: $i] :
( ( ( member @ SV235 @ ( union @ SV178 @ SV228 ) )
= $false )
| ( ( ( member @ SV235 @ SV178 )
| ( member @ SV235 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1183]) ).
thf(1246,plain,
! [SV273: $i,SV178: $i] :
( ( ! [SY361: $i] :
( ~ ( member @ SY361 @ SV178 )
| ( member @ SY361 @ ( union @ SV178 @ SV273 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1184]) ).
thf(1247,plain,
! [SV178: $i,SV274: $i] :
( ( ! [SY362: $i] :
( ~ ( member @ SY362 @ SV274 )
| ( member @ SY362 @ ( union @ SV178 @ SV274 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1185]) ).
thf(1248,plain,
! [SV213: $i,SV171: $i,SV229: $i] :
( ( ( member @ SV229 @ SV171 )
= $false )
| ( ( ~ ( member @ SV229 @ SV213 ) )
= $true )
| ( ( member @ SV229 @ ( intersection @ SV171 @ SV213 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1186]) ).
thf(1249,plain,
! [SV256: $i,SV171: $i,SV275: $i] :
( ( ~ ( member @ SV275 @ ( intersection @ SV171 @ SV256 ) )
| ( member @ SV275 @ SV171 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1187]) ).
thf(1250,plain,
! [SV257: $i,SV171: $i,SV276: $i] :
( ( ~ ( member @ SV276 @ ( intersection @ SV171 @ SV257 ) )
| ( member @ SV276 @ SV257 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1188]) ).
thf(1251,plain,
! [SV236: $i,SV258: $i] :
( ( ( ~ ( member @ SV258 @ ( domain_of @ SV236 ) ) )
= $true )
| ( ( ( ( restrict @ SV236 @ ( singleton @ SV258 ) @ universal_class )
!= null_class ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1190]) ).
thf(1252,plain,
! [SV237: $i,SV259: $i] :
( ( ( ~ ( member @ SV259 @ ( domain_of @ SV237 ) ) )
= $true )
| ( ( member @ SV259 @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1191]) ).
thf(1253,plain,
! [SV215: $i,SV194: $i] :
( ( ( member @ SV194 @ SV215 )
= $false )
| ( ( member @ SV215 @ universal_class )
= $false )
| ( ( member @ ( ordered_pair @ SV194 @ SV215 ) @ element_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1192]) ).
thf(1254,plain,
! [SV260: $i,SV238: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV238 @ SV260 ) @ element_relation ) )
= $true )
| ( ( member @ SV260 @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1193]) ).
thf(1255,plain,
! [SV261: $i,SV239: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV239 @ SV261 ) @ element_relation ) )
= $true )
| ( ( member @ SV239 @ SV261 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1194]) ).
thf(1256,plain,
! [SV240: $i] :
( ( ( function @ SV240 )
= $false )
| ( ( subclass @ SV240 @ ( cross_product @ universal_class @ universal_class ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1196]) ).
thf(1257,plain,
! [SV241: $i] :
( ( ( function @ SV241 )
= $false )
| ( ( subclass @ ( compose @ SV241 @ ( inverse @ SV241 ) ) @ identity_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1197]) ).
thf(1258,plain,
! [SV197: $i,SV230: $i] :
( ( ( member @ SV230 @ universal_class )
= $false )
| ( ( SV197
= ( ordered_pair @ SV230 @ SV230 ) )
= $false )
| ( ( member @ SV197 @ identity_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1198]) ).
thf(1259,plain,
! [SV198: $i] :
( ( ( SV198
= ( ordered_pair @ ( sK7_X @ SV198 ) @ ( sK7_X @ SV198 ) ) )
= $true )
| ( ( member @ SV198 @ identity_relation )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1199]) ).
thf(1260,plain,
! [SV198: $i] :
( ( ( member @ ( sK7_X @ SV198 ) @ universal_class )
= $true )
| ( ( member @ SV198 @ identity_relation )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1200]) ).
thf(1261,plain,
! [SV200: $i,SV216: $i] :
( ( ( member @ ( sK6_U @ SV216 @ SV200 ) @ SV200 )
= $true )
| ( ( disjoint @ SV200 @ SV216 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1201]) ).
thf(1262,plain,
! [SV200: $i,SV216: $i] :
( ( ( member @ ( sK6_U @ SV216 @ SV200 ) @ SV216 )
= $true )
| ( ( disjoint @ SV200 @ SV216 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1202]) ).
thf(1263,plain,
! [SV217: $i,SV201: $i,SV262: $i] :
( ( ( ~ ( member @ SV262 @ SV201 ) )
= $true )
| ( ( ~ ( member @ SV262 @ SV217 ) )
= $true )
| ( ( disjoint @ SV201 @ SV217 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1203]) ).
thf(1264,plain,
! [SV218: $i,SV202: $i] :
( ( ( member @ SV202 @ universal_class )
= $false )
| ( ( ~ ( member @ SV218 @ universal_class ) )
= $true )
| ( ( ( ( successor @ SV202 )
!= SV218 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV202 @ SV218 ) @ successor_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1204]) ).
thf(1265,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX0 @ universal_class ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1205]) ).
thf(1266,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ( member @ SX1 @ universal_class ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1206]) ).
thf(1267,plain,
! [SV263: $i,SV242: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV242 @ SV263 ) @ successor_relation ) )
= $true )
| ( ( ( successor @ SV242 )
= SV263 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1207]) ).
thf(1268,plain,
! [SV219: $i,SV243: $i,SV203: $i] :
( ( ( member @ SV203 @ SV243 )
= $false )
| ( ( ~ ( member @ SV243 @ SV219 ) )
= $true )
| ( ( member @ SV203 @ ( sum_class @ SV219 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1208]) ).
thf(1269,plain,
! [SV220: $i,SV204: $i] :
( ( ( ~ ( member @ SV204 @ ( sK8_Y @ SV220 @ SV204 ) ) )
= $false )
| ( ( member @ SV204 @ ( sum_class @ SV220 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1209]) ).
thf(1270,plain,
! [SV204: $i,SV220: $i] :
( ( ( ~ ( member @ ( sK8_Y @ SV220 @ SV204 ) @ SV220 ) )
= $false )
| ( ( member @ SV204 @ ( sum_class @ SV220 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1209]) ).
thf(1271,plain,
! [SV244: $i,SV231: $i,SV187: $i,SV173: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SV231 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV187 @ SV173 ) @ SV231 ) @ SV244 ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SV231 ) @ ( flip @ SV244 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1212]) ).
thf(1272,plain,
! [SV277: $i,SV187: $i,SV173: $i] :
( ( ! [SY363: $i] :
~ ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SV277 ) @ ( flip @ SY363 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SV277 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1213]) ).
thf(1273,plain,
! [SV278: $i,SV187: $i,SV173: $i] :
( ( ! [SY364: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SV278 ) @ ( flip @ SY364 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV187 @ SV173 ) @ SV278 ) @ SY364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1214]) ).
thf(1274,plain,
! [SV174: $i,SV188: $i,SV245: $i,SV232: $i] :
( ( ( ~ ( member @ SV232 @ universal_class ) )
= $true )
| ( ( ~ ( member @ SV245 @ ( image @ SV188 @ ( image @ SV174 @ ( singleton @ SV232 ) ) ) ) )
= $true )
| ( ( member @ ( ordered_pair @ SV232 @ SV245 ) @ ( compose @ SV188 @ SV174 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1215]) ).
thf(1275,plain,
! [SV174: $i,SV188: $i,SV279: $i] :
( ( ! [SY365: $i] :
~ ( member @ ( ordered_pair @ SV279 @ SY365 ) @ ( compose @ SV188 @ SV174 ) )
| ( member @ SV279 @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1216]) ).
thf(1276,plain,
! [SV174: $i,SV188: $i,SV280: $i] :
( ( ! [SY366: $i] :
( ~ ( member @ ( ordered_pair @ SV280 @ SY366 ) @ ( compose @ SV188 @ SV174 ) )
| ( member @ SY366 @ ( image @ SV188 @ ( image @ SV174 @ ( singleton @ SV280 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1217]) ).
thf(1277,plain,
! [SV205: $i,SV221: $i] :
( ( ( subclass @ SV221 @ SV205 )
= $false )
| ( ( subclass @ SV205 @ SV221 )
= $false )
| ( ( SV205 = SV221 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1218]) ).
thf(1278,plain,
! [SV264: $i,SV246: $i] :
( ( ( ( SV246 != SV264 ) )
= $true )
| ( ( subclass @ SV246 @ SV264 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1219]) ).
thf(1279,plain,
! [SV265: $i,SV247: $i] :
( ( ( ( SV247 != SV265 ) )
= $true )
| ( ( subclass @ SV265 @ SV247 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1220]) ).
thf(1280,plain,
! [SV248: $i,SV266: $i] :
( ( ( ~ ( member @ SV266 @ ( complement @ SV248 ) ) )
= $true )
| ( ( member @ SV266 @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1222]) ).
thf(1281,plain,
! [SV249: $i,SV267: $i] :
( ( ( ~ ( member @ SV267 @ ( complement @ SV249 ) ) )
= $true )
| ( ( ~ ( member @ SV267 @ SV249 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1223]) ).
thf(1282,plain,
! [SV207: $i,SV223: $i] :
( ( ( member @ ( sK10_U @ SV223 @ SV207 ) @ SV207 )
= $true )
| ( ( subclass @ SV207 @ SV223 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1224]) ).
thf(1283,plain,
! [SV207: $i,SV223: $i] :
( ( ( ~ ( member @ ( sK10_U @ SV223 @ SV207 ) @ SV223 ) )
= $true )
| ( ( subclass @ SV207 @ SV223 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1225]) ).
thf(1284,plain,
! [SV224: $i,SV208: $i,SV268: $i] :
( ( ( ~ ( member @ SV268 @ SV208 ) )
= $true )
| ( ( member @ SV268 @ SV224 )
= $true )
| ( ( subclass @ SV208 @ SV224 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1226]) ).
thf(1285,plain,
! [SV250: $i,SV189: $i,SV233: $i,SV175: $i] :
( ( ( ~ ( member @ SV175 @ SV233 ) )
= $true )
| ( ( ~ ( member @ SV189 @ SV250 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV175 @ SV189 ) @ ( cross_product @ SV233 @ SV250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1227]) ).
thf(1286,plain,
! [SV281: $i,SV189: $i,SV175: $i] :
( ( ! [SY367: $i] :
~ ( member @ ( ordered_pair @ SV175 @ SV189 ) @ ( cross_product @ SV281 @ SY367 ) )
| ( member @ SV175 @ SV281 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1228]) ).
thf(1287,plain,
! [SV282: $i,SV189: $i,SV175: $i] :
( ( ! [SY368: $i] :
( ~ ( member @ ( ordered_pair @ SV175 @ SV189 ) @ ( cross_product @ SV282 @ SY368 ) )
| ( member @ SV189 @ SY368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1229]) ).
thf(1288,plain,
! [SV269: $i,SV176: $i] :
( ( ( ~ ( member @ SV176 @ universal_class )
| ( SV176 != SV269 ) )
= $true )
| ( ( ! [SY358: $i] : ( member @ SV176 @ ( unordered_pair @ SV269 @ SY358 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1230]) ).
thf(1289,plain,
! [SV270: $i,SV283: $i,SV176: $i] :
( ( ~ ( member @ SV176 @ universal_class )
| ( SV176 != SV283 )
| ( member @ SV176 @ ( unordered_pair @ SV270 @ SV283 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1231]) ).
thf(1290,plain,
! [SV284: $i,SV176: $i] :
( ( ( ! [SY369: $i] :
~ ( member @ SV176 @ ( unordered_pair @ SV284 @ SY369 ) ) )
= $true )
| ( ( member @ SV176 @ universal_class )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1232]) ).
thf(1291,plain,
! [SV285: $i,SV271: $i,SV176: $i] :
( ( ~ ( member @ SV176 @ ( unordered_pair @ SV271 @ SV285 ) )
| ( SV176 = SV271 )
| ( SV176 = SV285 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1233]) ).
thf(1292,plain,
! [SV251: $i] :
( ( ( inductive @ SV251 )
= $false )
| ( ( member @ null_class @ SV251 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1235]) ).
thf(1293,plain,
! [SV252: $i] :
( ( ( inductive @ SV252 )
= $false )
| ( ( subclass @ ( image @ successor_relation @ SV252 ) @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1236]) ).
thf(1294,plain,
! [SV177: $i,SV253: $i,SV234: $i,SV190: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SV234 ) @ SV253 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV234 @ SV253 ) @ SV190 ) @ SV177 ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SV234 ) @ SV253 ) @ ( rotate @ SV177 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1237]) ).
thf(1295,plain,
! [SV177: $i,SV286: $i,SV190: $i] :
( ( ! [SY370: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SV286 ) @ SY370 ) @ ( rotate @ SV177 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SV286 ) @ SY370 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1238]) ).
thf(1296,plain,
! [SV177: $i,SV287: $i,SV190: $i] :
( ( ! [SY371: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SV287 ) @ SY371 ) @ ( rotate @ SV177 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV287 @ SY371 ) @ SV190 ) @ SV177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1239]) ).
thf(1297,plain,
! [SV210: $i,SV225: $i] :
( ( ( member @ SV225 @ universal_class )
= $false )
| ( ( member @ SV210 @ universal_class )
= $false )
| ( ( ( first @ ( ordered_pair @ SV210 @ SV225 ) )
= SV210 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1240]) ).
thf(1298,plain,
! [SV211: $i,SV226: $i] :
( ( ( member @ SV226 @ universal_class )
= $false )
| ( ( member @ SV211 @ universal_class )
= $false )
| ( ( ( second @ ( ordered_pair @ SV211 @ SV226 ) )
= SV226 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1241]) ).
thf(1299,plain,
! [SV227: $i,SV212: $i] :
( ( ( subclass @ SV212 @ SV227 )
= $false )
| ( ( member @ SV212 @ universal_class )
= $false )
| ( ( member @ SV212 @ ( power_class @ SV227 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1242]) ).
thf(1300,plain,
! [SV288: $i,SV254: $i] :
( ( ( ~ ( member @ SV254 @ ( power_class @ SV288 ) ) )
= $true )
| ( ( member @ SV254 @ universal_class )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1243]) ).
thf(1301,plain,
! [SV272: $i,SV255: $i] :
( ( ( ~ ( member @ SV255 @ ( power_class @ SV272 ) ) )
= $true )
| ( ( subclass @ SV255 @ SV272 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1244]) ).
thf(1302,plain,
! [SV228: $i,SV178: $i,SV235: $i] :
( ( ( member @ SV235 @ SV178 )
= $true )
| ( ( member @ SV235 @ SV228 )
= $true )
| ( ( member @ SV235 @ ( union @ SV178 @ SV228 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1245]) ).
thf(1303,plain,
! [SV273: $i,SV178: $i,SV289: $i] :
( ( ~ ( member @ SV289 @ SV178 )
| ( member @ SV289 @ ( union @ SV178 @ SV273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1246]) ).
thf(1304,plain,
! [SV178: $i,SV274: $i,SV290: $i] :
( ( ~ ( member @ SV290 @ SV274 )
| ( member @ SV290 @ ( union @ SV178 @ SV274 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1247]) ).
thf(1305,plain,
! [SV171: $i,SV213: $i,SV229: $i] :
( ( ( member @ SV229 @ SV213 )
= $false )
| ( ( member @ SV229 @ SV171 )
= $false )
| ( ( member @ SV229 @ ( intersection @ SV171 @ SV213 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1248]) ).
thf(1306,plain,
! [SV256: $i,SV171: $i,SV275: $i] :
( ( ( ~ ( member @ SV275 @ ( intersection @ SV171 @ SV256 ) ) )
= $true )
| ( ( member @ SV275 @ SV171 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1249]) ).
thf(1307,plain,
! [SV257: $i,SV171: $i,SV276: $i] :
( ( ( ~ ( member @ SV276 @ ( intersection @ SV171 @ SV257 ) ) )
= $true )
| ( ( member @ SV276 @ SV257 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1250]) ).
thf(1308,plain,
! [SV236: $i,SV258: $i] :
( ( ( member @ SV258 @ ( domain_of @ SV236 ) )
= $false )
| ( ( ( ( restrict @ SV236 @ ( singleton @ SV258 ) @ universal_class )
!= null_class ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1251]) ).
thf(1309,plain,
! [SV237: $i,SV259: $i] :
( ( ( member @ SV259 @ ( domain_of @ SV237 ) )
= $false )
| ( ( member @ SV259 @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1252]) ).
thf(1310,plain,
! [SV260: $i,SV238: $i] :
( ( ( member @ ( ordered_pair @ SV238 @ SV260 ) @ element_relation )
= $false )
| ( ( member @ SV260 @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1254]) ).
thf(1311,plain,
! [SV261: $i,SV239: $i] :
( ( ( member @ ( ordered_pair @ SV239 @ SV261 ) @ element_relation )
= $false )
| ( ( member @ SV239 @ SV261 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1255]) ).
thf(1312,plain,
! [SV217: $i,SV201: $i,SV262: $i] :
( ( ( member @ SV262 @ SV201 )
= $false )
| ( ( ~ ( member @ SV262 @ SV217 ) )
= $true )
| ( ( disjoint @ SV201 @ SV217 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1263]) ).
thf(1313,plain,
! [SV202: $i,SV218: $i] :
( ( ( member @ SV218 @ universal_class )
= $false )
| ( ( member @ SV202 @ universal_class )
= $false )
| ( ( ( ( successor @ SV202 )
!= SV218 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV202 @ SV218 ) @ successor_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1264]) ).
thf(1314,plain,
! [SV291: $i] :
( ( ! [SY372: $i] :
~ ( member @ ( ordered_pair @ SV291 @ SY372 ) @ successor_relation )
| ( member @ SV291 @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1265]) ).
thf(1315,plain,
! [SV292: $i] :
( ( ! [SY373: $i] :
( ~ ( member @ ( ordered_pair @ SV292 @ SY373 ) @ successor_relation )
| ( member @ SY373 @ universal_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1266]) ).
thf(1316,plain,
! [SV263: $i,SV242: $i] :
( ( ( member @ ( ordered_pair @ SV242 @ SV263 ) @ successor_relation )
= $false )
| ( ( ( successor @ SV242 )
= SV263 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1267]) ).
thf(1317,plain,
! [SV203: $i,SV219: $i,SV243: $i] :
( ( ( member @ SV243 @ SV219 )
= $false )
| ( ( member @ SV203 @ SV243 )
= $false )
| ( ( member @ SV203 @ ( sum_class @ SV219 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1268]) ).
thf(1318,plain,
! [SV220: $i,SV204: $i] :
( ( ( member @ SV204 @ ( sK8_Y @ SV220 @ SV204 ) )
= $true )
| ( ( member @ SV204 @ ( sum_class @ SV220 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1269]) ).
thf(1319,plain,
! [SV204: $i,SV220: $i] :
( ( ( member @ ( sK8_Y @ SV220 @ SV204 ) @ SV220 )
= $true )
| ( ( member @ SV204 @ ( sum_class @ SV220 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1270]) ).
thf(1320,plain,
! [SV244: $i,SV231: $i,SV187: $i,SV173: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SV231 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV187 @ SV173 ) @ SV231 ) @ SV244 ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SV231 ) @ ( flip @ SV244 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1271]) ).
thf(1321,plain,
! [SV277: $i,SV187: $i,SV173: $i] :
( ( ( ! [SY363: $i] :
~ ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SV277 ) @ ( flip @ SY363 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SV277 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1272]) ).
thf(1322,plain,
! [SV293: $i,SV278: $i,SV187: $i,SV173: $i] :
( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SV278 ) @ ( flip @ SV293 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV187 @ SV173 ) @ SV278 ) @ SV293 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1273]) ).
thf(1323,plain,
! [SV174: $i,SV188: $i,SV245: $i,SV232: $i] :
( ( ( member @ SV232 @ universal_class )
= $false )
| ( ( ~ ( member @ SV245 @ ( image @ SV188 @ ( image @ SV174 @ ( singleton @ SV232 ) ) ) ) )
= $true )
| ( ( member @ ( ordered_pair @ SV232 @ SV245 ) @ ( compose @ SV188 @ SV174 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1274]) ).
thf(1324,plain,
! [SV174: $i,SV188: $i,SV279: $i] :
( ( ( ! [SY365: $i] :
~ ( member @ ( ordered_pair @ SV279 @ SY365 ) @ ( compose @ SV188 @ SV174 ) ) )
= $true )
| ( ( member @ SV279 @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1275]) ).
thf(1325,plain,
! [SV174: $i,SV188: $i,SV294: $i,SV280: $i] :
( ( ~ ( member @ ( ordered_pair @ SV280 @ SV294 ) @ ( compose @ SV188 @ SV174 ) )
| ( member @ SV294 @ ( image @ SV188 @ ( image @ SV174 @ ( singleton @ SV280 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1276]) ).
thf(1326,plain,
! [SV264: $i,SV246: $i] :
( ( ( SV246 = SV264 )
= $false )
| ( ( subclass @ SV246 @ SV264 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1278]) ).
thf(1327,plain,
! [SV265: $i,SV247: $i] :
( ( ( SV247 = SV265 )
= $false )
| ( ( subclass @ SV265 @ SV247 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1279]) ).
thf(1328,plain,
! [SV248: $i,SV266: $i] :
( ( ( member @ SV266 @ ( complement @ SV248 ) )
= $false )
| ( ( member @ SV266 @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1280]) ).
thf(1329,plain,
! [SV249: $i,SV267: $i] :
( ( ( member @ SV267 @ ( complement @ SV249 ) )
= $false )
| ( ( ~ ( member @ SV267 @ SV249 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1281]) ).
thf(1330,plain,
! [SV207: $i,SV223: $i] :
( ( ( member @ ( sK10_U @ SV223 @ SV207 ) @ SV223 )
= $false )
| ( ( subclass @ SV207 @ SV223 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1283]) ).
thf(1331,plain,
! [SV224: $i,SV208: $i,SV268: $i] :
( ( ( member @ SV268 @ SV208 )
= $false )
| ( ( member @ SV268 @ SV224 )
= $true )
| ( ( subclass @ SV208 @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1284]) ).
thf(1332,plain,
! [SV250: $i,SV189: $i,SV233: $i,SV175: $i] :
( ( ( member @ SV175 @ SV233 )
= $false )
| ( ( ~ ( member @ SV189 @ SV250 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV175 @ SV189 ) @ ( cross_product @ SV233 @ SV250 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1285]) ).
thf(1333,plain,
! [SV281: $i,SV189: $i,SV175: $i] :
( ( ( ! [SY367: $i] :
~ ( member @ ( ordered_pair @ SV175 @ SV189 ) @ ( cross_product @ SV281 @ SY367 ) ) )
= $true )
| ( ( member @ SV175 @ SV281 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1286]) ).
thf(1334,plain,
! [SV295: $i,SV282: $i,SV189: $i,SV175: $i] :
( ( ~ ( member @ ( ordered_pair @ SV175 @ SV189 ) @ ( cross_product @ SV282 @ SV295 ) )
| ( member @ SV189 @ SV295 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1287]) ).
thf(1335,plain,
! [SV269: $i,SV176: $i] :
( ( ( ~ ( member @ SV176 @ universal_class ) )
= $true )
| ( ( ( SV176 != SV269 ) )
= $true )
| ( ( ! [SY358: $i] : ( member @ SV176 @ ( unordered_pair @ SV269 @ SY358 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1288]) ).
thf(1336,plain,
! [SV270: $i,SV283: $i,SV176: $i] :
( ( ( ~ ( member @ SV176 @ universal_class )
| ( SV176 != SV283 ) )
= $true )
| ( ( member @ SV176 @ ( unordered_pair @ SV270 @ SV283 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1289]) ).
thf(1337,plain,
! [SV296: $i,SV284: $i,SV176: $i] :
( ( ( ~ ( member @ SV176 @ ( unordered_pair @ SV284 @ SV296 ) ) )
= $true )
| ( ( member @ SV176 @ universal_class )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1290]) ).
thf(1338,plain,
! [SV285: $i,SV271: $i,SV176: $i] :
( ( ( ~ ( member @ SV176 @ ( unordered_pair @ SV271 @ SV285 ) ) )
= $true )
| ( ( ( SV176 = SV271 )
| ( SV176 = SV285 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1291]) ).
thf(1339,plain,
! [SV177: $i,SV253: $i,SV234: $i,SV190: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SV234 ) @ SV253 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV234 @ SV253 ) @ SV190 ) @ SV177 ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SV234 ) @ SV253 ) @ ( rotate @ SV177 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1294]) ).
thf(1340,plain,
! [SV177: $i,SV297: $i,SV286: $i,SV190: $i] :
( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SV286 ) @ SV297 ) @ ( rotate @ SV177 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SV286 ) @ SV297 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1295]) ).
thf(1341,plain,
! [SV177: $i,SV298: $i,SV287: $i,SV190: $i] :
( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SV287 ) @ SV298 ) @ ( rotate @ SV177 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV287 @ SV298 ) @ SV190 ) @ SV177 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1296]) ).
thf(1342,plain,
! [SV288: $i,SV254: $i] :
( ( ( member @ SV254 @ ( power_class @ SV288 ) )
= $false )
| ( ( member @ SV254 @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1300]) ).
thf(1343,plain,
! [SV272: $i,SV255: $i] :
( ( ( member @ SV255 @ ( power_class @ SV272 ) )
= $false )
| ( ( subclass @ SV255 @ SV272 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1301]) ).
thf(1344,plain,
! [SV273: $i,SV178: $i,SV289: $i] :
( ( ( ~ ( member @ SV289 @ SV178 ) )
= $true )
| ( ( member @ SV289 @ ( union @ SV178 @ SV273 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1303]) ).
thf(1345,plain,
! [SV178: $i,SV274: $i,SV290: $i] :
( ( ( ~ ( member @ SV290 @ SV274 ) )
= $true )
| ( ( member @ SV290 @ ( union @ SV178 @ SV274 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1304]) ).
thf(1346,plain,
! [SV256: $i,SV171: $i,SV275: $i] :
( ( ( member @ SV275 @ ( intersection @ SV171 @ SV256 ) )
= $false )
| ( ( member @ SV275 @ SV171 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1306]) ).
thf(1347,plain,
! [SV257: $i,SV171: $i,SV276: $i] :
( ( ( member @ SV276 @ ( intersection @ SV171 @ SV257 ) )
= $false )
| ( ( member @ SV276 @ SV257 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1307]) ).
thf(1348,plain,
! [SV258: $i,SV236: $i] :
( ( ( ( restrict @ SV236 @ ( singleton @ SV258 ) @ universal_class )
= null_class )
= $false )
| ( ( member @ SV258 @ ( domain_of @ SV236 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1308]) ).
thf(1349,plain,
! [SV201: $i,SV217: $i,SV262: $i] :
( ( ( member @ SV262 @ SV217 )
= $false )
| ( ( member @ SV262 @ SV201 )
= $false )
| ( ( disjoint @ SV201 @ SV217 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1312]) ).
thf(1350,plain,
! [SV218: $i,SV202: $i] :
( ( ( ( successor @ SV202 )
= SV218 )
= $false )
| ( ( member @ SV202 @ universal_class )
= $false )
| ( ( member @ SV218 @ universal_class )
= $false )
| ( ( member @ ( ordered_pair @ SV202 @ SV218 ) @ successor_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1313]) ).
thf(1351,plain,
! [SV291: $i] :
( ( ( ! [SY372: $i] :
~ ( member @ ( ordered_pair @ SV291 @ SY372 ) @ successor_relation ) )
= $true )
| ( ( member @ SV291 @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1314]) ).
thf(1352,plain,
! [SV299: $i,SV292: $i] :
( ( ~ ( member @ ( ordered_pair @ SV292 @ SV299 ) @ successor_relation )
| ( member @ SV299 @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1315]) ).
thf(1353,plain,
! [SV244: $i,SV231: $i,SV173: $i,SV187: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ SV187 @ SV173 ) @ SV231 ) @ SV244 )
= $false )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SV231 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
= $false )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SV231 ) @ ( flip @ SV244 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1320]) ).
thf(1354,plain,
! [SV300: $i,SV277: $i,SV187: $i,SV173: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SV277 ) @ ( flip @ SV300 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SV277 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1321]) ).
thf(1355,plain,
! [SV293: $i,SV278: $i,SV187: $i,SV173: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SV278 ) @ ( flip @ SV293 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV187 @ SV173 ) @ SV278 ) @ SV293 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1322]) ).
thf(1356,plain,
! [SV232: $i,SV174: $i,SV188: $i,SV245: $i] :
( ( ( member @ SV245 @ ( image @ SV188 @ ( image @ SV174 @ ( singleton @ SV232 ) ) ) )
= $false )
| ( ( member @ SV232 @ universal_class )
= $false )
| ( ( member @ ( ordered_pair @ SV232 @ SV245 ) @ ( compose @ SV188 @ SV174 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1323]) ).
thf(1357,plain,
! [SV174: $i,SV188: $i,SV301: $i,SV279: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV279 @ SV301 ) @ ( compose @ SV188 @ SV174 ) ) )
= $true )
| ( ( member @ SV279 @ universal_class )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1324]) ).
thf(1358,plain,
! [SV174: $i,SV188: $i,SV294: $i,SV280: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV280 @ SV294 ) @ ( compose @ SV188 @ SV174 ) ) )
= $true )
| ( ( member @ SV294 @ ( image @ SV188 @ ( image @ SV174 @ ( singleton @ SV280 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1325]) ).
thf(1359,plain,
! [SV249: $i,SV267: $i] :
( ( ( member @ SV267 @ SV249 )
= $false )
| ( ( member @ SV267 @ ( complement @ SV249 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1329]) ).
thf(1360,plain,
! [SV233: $i,SV175: $i,SV250: $i,SV189: $i] :
( ( ( member @ SV189 @ SV250 )
= $false )
| ( ( member @ SV175 @ SV233 )
= $false )
| ( ( member @ ( ordered_pair @ SV175 @ SV189 ) @ ( cross_product @ SV233 @ SV250 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1332]) ).
thf(1361,plain,
! [SV302: $i,SV281: $i,SV189: $i,SV175: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV175 @ SV189 ) @ ( cross_product @ SV281 @ SV302 ) ) )
= $true )
| ( ( member @ SV175 @ SV281 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1333]) ).
thf(1362,plain,
! [SV295: $i,SV282: $i,SV189: $i,SV175: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV175 @ SV189 ) @ ( cross_product @ SV282 @ SV295 ) ) )
= $true )
| ( ( member @ SV189 @ SV295 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1334]) ).
thf(1363,plain,
! [SV269: $i,SV176: $i] :
( ( ( member @ SV176 @ universal_class )
= $false )
| ( ( ( SV176 != SV269 ) )
= $true )
| ( ( ! [SY358: $i] : ( member @ SV176 @ ( unordered_pair @ SV269 @ SY358 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1335]) ).
thf(1364,plain,
! [SV270: $i,SV283: $i,SV176: $i] :
( ( ( ~ ( member @ SV176 @ universal_class ) )
= $true )
| ( ( ( SV176 != SV283 ) )
= $true )
| ( ( member @ SV176 @ ( unordered_pair @ SV270 @ SV283 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1336]) ).
thf(1365,plain,
! [SV296: $i,SV284: $i,SV176: $i] :
( ( ( member @ SV176 @ ( unordered_pair @ SV284 @ SV296 ) )
= $false )
| ( ( member @ SV176 @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1337]) ).
thf(1366,plain,
! [SV285: $i,SV271: $i,SV176: $i] :
( ( ( member @ SV176 @ ( unordered_pair @ SV271 @ SV285 ) )
= $false )
| ( ( ( SV176 = SV271 )
| ( SV176 = SV285 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1338]) ).
thf(1367,plain,
! [SV177: $i,SV190: $i,SV253: $i,SV234: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ SV234 @ SV253 ) @ SV190 ) @ SV177 )
= $false )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SV234 ) @ SV253 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
= $false )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SV234 ) @ SV253 ) @ ( rotate @ SV177 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1339]) ).
thf(1368,plain,
! [SV177: $i,SV297: $i,SV286: $i,SV190: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SV286 ) @ SV297 ) @ ( rotate @ SV177 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SV286 ) @ SV297 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1340]) ).
thf(1369,plain,
! [SV177: $i,SV298: $i,SV287: $i,SV190: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SV287 ) @ SV298 ) @ ( rotate @ SV177 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV287 @ SV298 ) @ SV190 ) @ SV177 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1341]) ).
thf(1370,plain,
! [SV273: $i,SV178: $i,SV289: $i] :
( ( ( member @ SV289 @ SV178 )
= $false )
| ( ( member @ SV289 @ ( union @ SV178 @ SV273 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1344]) ).
thf(1371,plain,
! [SV178: $i,SV274: $i,SV290: $i] :
( ( ( member @ SV290 @ SV274 )
= $false )
| ( ( member @ SV290 @ ( union @ SV178 @ SV274 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1345]) ).
thf(1372,plain,
! [SV303: $i,SV291: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV291 @ SV303 ) @ successor_relation ) )
= $true )
| ( ( member @ SV291 @ universal_class )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1351]) ).
thf(1373,plain,
! [SV299: $i,SV292: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV292 @ SV299 ) @ successor_relation ) )
= $true )
| ( ( member @ SV299 @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1352]) ).
thf(1374,plain,
! [SV300: $i,SV277: $i,SV187: $i,SV173: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SV277 ) @ ( flip @ SV300 ) )
= $false )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SV277 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1354]) ).
thf(1375,plain,
! [SV293: $i,SV278: $i,SV187: $i,SV173: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ SV173 @ SV187 ) @ SV278 ) @ ( flip @ SV293 ) )
= $false )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV187 @ SV173 ) @ SV278 ) @ SV293 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1355]) ).
thf(1376,plain,
! [SV174: $i,SV188: $i,SV301: $i,SV279: $i] :
( ( ( member @ ( ordered_pair @ SV279 @ SV301 ) @ ( compose @ SV188 @ SV174 ) )
= $false )
| ( ( member @ SV279 @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1357]) ).
thf(1377,plain,
! [SV174: $i,SV188: $i,SV294: $i,SV280: $i] :
( ( ( member @ ( ordered_pair @ SV280 @ SV294 ) @ ( compose @ SV188 @ SV174 ) )
= $false )
| ( ( member @ SV294 @ ( image @ SV188 @ ( image @ SV174 @ ( singleton @ SV280 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1358]) ).
thf(1378,plain,
! [SV302: $i,SV281: $i,SV189: $i,SV175: $i] :
( ( ( member @ ( ordered_pair @ SV175 @ SV189 ) @ ( cross_product @ SV281 @ SV302 ) )
= $false )
| ( ( member @ SV175 @ SV281 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1361]) ).
thf(1379,plain,
! [SV295: $i,SV282: $i,SV189: $i,SV175: $i] :
( ( ( member @ ( ordered_pair @ SV175 @ SV189 ) @ ( cross_product @ SV282 @ SV295 ) )
= $false )
| ( ( member @ SV189 @ SV295 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1362]) ).
thf(1380,plain,
! [SV269: $i,SV176: $i] :
( ( ( SV176 = SV269 )
= $false )
| ( ( member @ SV176 @ universal_class )
= $false )
| ( ( ! [SY358: $i] : ( member @ SV176 @ ( unordered_pair @ SV269 @ SY358 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1363]) ).
thf(1381,plain,
! [SV270: $i,SV283: $i,SV176: $i] :
( ( ( member @ SV176 @ universal_class )
= $false )
| ( ( ( SV176 != SV283 ) )
= $true )
| ( ( member @ SV176 @ ( unordered_pair @ SV270 @ SV283 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1364]) ).
thf(1382,plain,
! [SV285: $i,SV271: $i,SV176: $i] :
( ( ( SV176 = SV271 )
= $true )
| ( ( SV176 = SV285 )
= $true )
| ( ( member @ SV176 @ ( unordered_pair @ SV271 @ SV285 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1366]) ).
thf(1383,plain,
! [SV177: $i,SV297: $i,SV286: $i,SV190: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SV286 ) @ SV297 ) @ ( rotate @ SV177 ) )
= $false )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SV286 ) @ SV297 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1368]) ).
thf(1384,plain,
! [SV177: $i,SV298: $i,SV287: $i,SV190: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ SV190 @ SV287 ) @ SV298 ) @ ( rotate @ SV177 ) )
= $false )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV287 @ SV298 ) @ SV190 ) @ SV177 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1369]) ).
thf(1385,plain,
! [SV303: $i,SV291: $i] :
( ( ( member @ ( ordered_pair @ SV291 @ SV303 ) @ successor_relation )
= $false )
| ( ( member @ SV291 @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1372]) ).
thf(1386,plain,
! [SV299: $i,SV292: $i] :
( ( ( member @ ( ordered_pair @ SV292 @ SV299 ) @ successor_relation )
= $false )
| ( ( member @ SV299 @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1373]) ).
thf(1387,plain,
! [SV304: $i,SV269: $i,SV176: $i] :
( ( ( member @ SV176 @ ( unordered_pair @ SV269 @ SV304 ) )
= $true )
| ( ( member @ SV176 @ universal_class )
= $false )
| ( ( SV176 = SV269 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1380]) ).
thf(1388,plain,
! [SV270: $i,SV283: $i,SV176: $i] :
( ( ( SV176 = SV283 )
= $false )
| ( ( member @ SV176 @ universal_class )
= $false )
| ( ( member @ SV176 @ ( unordered_pair @ SV270 @ SV283 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1381]) ).
thf(1389,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[770,1388,1387,1386,1385,1384,1383,1382,1379,1378,1377,1376,1375,1374,1371,1370,1367,1365,1360,1359,1356,1353,1350,1349,1348,1347,1346,1343,1342,1331,1330,1328,1327,1326,1319,1318,1317,1316,1311,1310,1309,1305,1302,1299,1298,1297,1293,1292,1282,1277,1262,1261,1260,1259,1258,1257,1256,1253,1234,1221,1211,1210,1195,1189,1141,1084,1083,1082,1069,1040,1013,938,923,922,921,881,879,876,875,872,871,847,840,839,838,837,836,831,829,804,803,802,782]) ).
thf(1390,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1389,758]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET020+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.03/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 11 01:25:43 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.37 .
% 0.19/0.37
% 0.19/0.37 No.of.Axioms: 43
% 0.19/0.37
% 0.19/0.37 Length.of.Defs: 0
% 0.19/0.37
% 0.19/0.37 Contains.Choice.Funs: false
% 0.19/0.40 .
% 0.19/0.40 (rf:0,axioms:43,ps:3,u:6,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:45,loop_count:0,foatp_calls:0,translation:fof_full).........................................................................................
% 0.74/1.03
% 0.74/1.03 ********************************
% 0.74/1.03 * All subproblems solved! *
% 0.74/1.03 ********************************
% 0.74/1.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:46,ps:3,u:6,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:1389,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.51/1.74
% 1.51/1.74 %**** Beginning of derivation protocol ****
% 1.51/1.74 % SZS output start CNFRefutation
% See solution above
% 1.51/1.74
% 1.51/1.74 %**** End of derivation protocol ****
% 1.51/1.74 %**** no. of clauses in derivation: 1390 ****
% 1.51/1.74 %**** clause counter: 1389 ****
% 1.51/1.74
% 1.51/1.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:46,ps:3,u:6,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:1389,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------