%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET101+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:39:34 AM UTC 2026
% Result : Theorem 6.32s 1.39s
% Output : CNFRefutation 6.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 44
% Syntax : Number of formulae : 677 ( 335 unt; 0 typ; 0 def)
% Number of atoms : 4146 (1313 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 9891 (2118 ~;1255 |; 78 &;6356 @)
% ( 57 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 40 usr; 11 con; 0-3 aty)
% Number of variables : 1554 ( 0 ^;1539 !; 15 ?;1554 :)
% 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_sK1_X,type,
sK1_X: $i ).
thf(tp_sK2_SY88,type,
sK2_SY88: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SX0,type,
sK4_SX0: $i ).
thf(tp_sK5_SY118,type,
sK5_SY118: $i > $i ).
thf(tp_sK6_SY145,type,
sK6_SY145: $i > $i > $i ).
thf(tp_sK7_SY120,type,
sK7_SY120: $i > $i ).
thf(tp_sK8_SY150,type,
sK8_SY150: $i > $i > $i ).
thf(tp_sK9_SY138,type,
sK9_SY138: $i > $i > $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/sandbox2/benchmark/theBenchmark.p',choice) ).
thf(2,axiom,
! [XF: $i,Y: $i] :
( ( apply @ XF @ Y )
= ( sum_class @ ( image @ XF @ ( singleton @ Y ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',compose_defn1) ).
thf(10,axiom,
! [U: $i] :
( ( member @ U @ universal_class )
=> ( member @ ( power_class @ U ) @ universal_class ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',power_class_defn) ).
thf(12,axiom,
! [X: $i] :
( ( member @ X @ universal_class )
=> ( member @ ( sum_class @ X ) @ universal_class ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',infinity) ).
thf(15,axiom,
! [X: $i] :
( ( inductive @ X )
<=> ( ( member @ null_class @ X )
& ( subclass @ ( image @ successor_relation @ X ) @ X ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',image_defn) ).
thf(17,axiom,
! [Z: $i] :
( ( range_of @ Z )
= ( domain_of @ ( inverse @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range_of_defn) ).
thf(18,axiom,
! [Y: $i] :
( ( inverse @ Y )
= ( domain_of @ ( flip @ ( cross_product @ Y @ universal_class ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',successor_relation_defn2) ).
thf(20,axiom,
subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation_defn1) ).
thf(21,axiom,
! [X: $i] :
( ( successor @ X )
= ( union @ X @ ( singleton @ X ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',domain_of) ).
thf(28,axiom,
! [X: $i] :
~ ( member @ X @ null_class ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',intersection) ).
thf(32,axiom,
subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ordered_pair_defn) ).
thf(38,axiom,
! [X: $i] :
( ( singleton @ X )
= ( unordered_pair @ X @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set_defn) ).
thf(39,axiom,
! [X: $i,Y: $i] : ( member @ ( unordered_pair @ X @ Y ) @ universal_class ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',unordered_pair_defn) ).
thf(41,axiom,
! [X: $i,Y: $i] :
( ( X = Y )
<=> ( ( subclass @ X @ Y )
& ( subclass @ Y @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality) ).
thf(42,axiom,
! [X: $i] : ( subclass @ X @ universal_class ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',subclass_defn) ).
thf(44,conjecture,
! [X: $i,Y: $i] : ( member @ ( singleton @ X ) @ ( ordered_pair @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_member_of_ordered_pair) ).
thf(45,negated_conjecture,
( ( ! [X: $i,Y: $i] : ( member @ ( singleton @ X ) @ ( ordered_pair @ X @ Y ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[44]) ).
thf(46,plain,
( ( ! [X: $i,Y: $i] : ( member @ ( singleton @ X ) @ ( ordered_pair @ X @ Y ) ) )
= $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,
( ( ! [SY88: $i] : ( member @ ( singleton @ sK1_X ) @ ( ordered_pair @ sK1_X @ SY88 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[46]) ).
thf(91,plain,
( ( member @ ( singleton @ sK1_X ) @ ( ordered_pair @ sK1_X @ sK2_SY88 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[90]) ).
thf(92,plain,
( ( ~ ( member @ ( singleton @ sK1_X ) @ ( ordered_pair @ sK1_X @ sK2_SY88 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[91]) ).
thf(93,plain,
( ( ! [X: $i,Y: $i] :
( ( subclass @ X @ Y )
<=> ! [U: $i] :
( ( member @ U @ X )
=> ( member @ U @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(94,plain,
( ( ! [X: $i] : ( subclass @ X @ universal_class ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(95,plain,
( ( ! [X: $i,Y: $i] :
( ( X = Y )
<=> ( ( subclass @ X @ Y )
& ( subclass @ Y @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(96,plain,
( ( ! [U: $i,X: $i,Y: $i] :
( ( member @ U @ ( unordered_pair @ X @ Y ) )
<=> ( ( member @ U @ universal_class )
& ( ( U = X )
| ( U = Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(97,plain,
( ( ! [X: $i,Y: $i] : ( member @ ( unordered_pair @ X @ Y ) @ universal_class ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(98,plain,
( ( ! [X: $i] :
( ( singleton @ X )
= ( unordered_pair @ X @ X ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(99,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(100,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(copy,[status(thm)],[82]) ).
thf(101,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(copy,[status(thm)],[81]) ).
thf(102,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)],[80]) ).
thf(103,plain,
( ( ! [X: $i,Y: $i] :
( ( member @ ( ordered_pair @ X @ Y ) @ element_relation )
<=> ( ( member @ Y @ universal_class )
& ( member @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(104,plain,
( ( subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(105,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( member @ Z @ ( intersection @ X @ Y ) )
<=> ( ( member @ Z @ X )
& ( member @ Z @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(106,plain,
( ( ! [X: $i,Z: $i] :
( ( member @ Z @ ( complement @ X ) )
<=> ( ( member @ Z @ universal_class )
& ~ ( member @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(107,plain,
( ( ! [X: $i,XR: $i,Y: $i] :
( ( restrict @ XR @ X @ Y )
= ( intersection @ XR @ ( cross_product @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(108,plain,
( ( ! [X: $i] :
~ ( member @ X @ null_class ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(109,plain,
( ( ! [X: $i,Z: $i] :
( ( member @ Z @ ( domain_of @ X ) )
<=> ( ( member @ Z @ universal_class )
& ( ( restrict @ X @ ( singleton @ Z ) @ universal_class )
!= null_class ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(110,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(copy,[status(thm)],[72]) ).
thf(111,plain,
( ( ! [X: $i] : ( subclass @ ( rotate @ X ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(112,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(copy,[status(thm)],[70]) ).
thf(113,plain,
( ( ! [X: $i] : ( subclass @ ( flip @ X ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(114,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( member @ Z @ ( union @ X @ Y ) )
<=> ( ( member @ Z @ X )
| ( member @ Z @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(115,plain,
( ( ! [X: $i] :
( ( successor @ X )
= ( union @ X @ ( singleton @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(116,plain,
( ( subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(117,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(copy,[status(thm)],[65]) ).
thf(118,plain,
( ( ! [Y: $i] :
( ( inverse @ Y )
= ( domain_of @ ( flip @ ( cross_product @ Y @ universal_class ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(119,plain,
( ( ! [Z: $i] :
( ( range_of @ Z )
= ( domain_of @ ( inverse @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(120,plain,
( ( ! [X: $i,XR: $i] :
( ( image @ XR @ X )
= ( range_of @ ( restrict @ XR @ X @ universal_class ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(121,plain,
( ( ! [X: $i] :
( ( inductive @ X )
<=> ( ( member @ null_class @ X )
& ( subclass @ ( image @ successor_relation @ X ) @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(122,plain,
( ( ? [X: $i] :
( ( member @ X @ universal_class )
& ( inductive @ X )
& ! [Y: $i] :
( ( inductive @ Y )
=> ( subclass @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(123,plain,
( ( ! [U: $i,X: $i] :
( ( member @ U @ ( sum_class @ X ) )
<=> ? [Y: $i] :
( ( member @ U @ Y )
& ( member @ Y @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(124,plain,
( ( ! [X: $i] :
( ( member @ X @ universal_class )
=> ( member @ ( sum_class @ X ) @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(125,plain,
( ( ! [U: $i,X: $i] :
( ( member @ U @ ( power_class @ X ) )
<=> ( ( member @ U @ universal_class )
& ( subclass @ U @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(126,plain,
( ( ! [U: $i] :
( ( member @ U @ universal_class )
=> ( member @ ( power_class @ U ) @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(127,plain,
( ( ! [XR: $i,YR: $i] : ( subclass @ ( compose @ YR @ XR ) @ ( cross_product @ universal_class @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(128,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(copy,[status(thm)],[54]) ).
thf(129,plain,
( ( ! [Z: $i] :
( ( member @ Z @ identity_relation )
<=> ? [X: $i] :
( ( member @ X @ universal_class )
& ( Z
= ( ordered_pair @ X @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(130,plain,
( ( ! [XF: $i] :
( ( function @ XF )
<=> ( ( subclass @ XF @ ( cross_product @ universal_class @ universal_class ) )
& ( subclass @ ( compose @ XF @ ( inverse @ XF ) ) @ identity_relation ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(131,plain,
( ( ! [X: $i,XF: $i] :
( ( ( member @ X @ universal_class )
& ( function @ XF ) )
=> ( member @ ( image @ XF @ X ) @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(132,plain,
( ( ! [X: $i,Y: $i] :
( ( disjoint @ X @ Y )
<=> ! [U: $i] :
~ ( ( member @ U @ X )
& ( member @ U @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(133,plain,
( ( ! [X: $i] :
( ( X != null_class )
=> ? [U: $i] :
( ( member @ U @ universal_class )
& ( member @ U @ X )
& ( disjoint @ U @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(134,plain,
( ( ! [XF: $i,Y: $i] :
( ( apply @ XF @ Y )
= ( sum_class @ ( image @ XF @ ( singleton @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(135,plain,
( ( ? [XF: $i] :
( ( function @ XF )
& ! [Y: $i] :
( ( member @ Y @ universal_class )
=> ( ( Y = null_class )
| ( member @ ( apply @ XF @ Y ) @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(136,plain,
( ( ~ ( member @ ( singleton @ sK1_X ) @ ( ordered_pair @ sK1_X @ sK2_SY88 ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(137,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX0 != SX1 )
| ~ ( ~ ( subclass @ SX0 @ SX1 )
| ~ ( subclass @ SX1 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( subclass @ SX0 @ SX1 )
| ~ ( subclass @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(138,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( member @ SX2 @ ( union @ SX0 @ SX1 ) )
| ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ( ~ ( ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ( member @ SX2 @ ( union @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(139,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( sum_class @ SX1 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( member @ SX0 @ SX2 )
| ~ ( member @ SX2 @ SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( member @ SX0 @ SX2 )
| ~ ( member @ SX2 @ SX1 ) )
| ( member @ SX0 @ ( sum_class @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(140,plain,
( ( ! [SX0: $i,SX1: $i,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 ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SX1 @ SX0 ) @ SX2 ) @ SX3 ) ) )
| ~ ( ~ ~ ( ~ ( 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 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(141,plain,
( ( ! [SX0: $i,SX1: $i,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 ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( 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 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(142,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( disjoint @ SX0 @ SX1 )
| ! [SX2: $i] :
~ ~ ( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ~ ( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) )
| ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(143,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( member @ SX1 @ ( domain_of @ SX0 ) )
| ~ ( ~ ( member @ SX1 @ universal_class )
| ~ ( ( ( restrict @ SX0 @ ( singleton @ SX1 ) @ universal_class )
!= null_class ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SX1 @ universal_class )
| ~ ( ( ( restrict @ SX0 @ ( singleton @ SX1 ) @ universal_class )
!= null_class ) ) )
| ( member @ SX1 @ ( domain_of @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(144,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( member @ ( ordered_pair @ SX2 @ SX3 ) @ ( compose @ SX1 @ SX0 ) )
| ~ ( ~ ( member @ SX2 @ universal_class )
| ~ ( member @ SX3 @ ( image @ SX1 @ ( image @ SX0 @ ( singleton @ SX2 ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SX2 @ universal_class )
| ~ ( member @ SX3 @ ( image @ SX1 @ ( image @ SX0 @ ( singleton @ SX2 ) ) ) ) )
| ( member @ ( ordered_pair @ SX2 @ SX3 ) @ ( compose @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(145,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) )
| ~ ( ~ ( member @ SX0 @ universal_class )
| ~ ( ( SX0 = SX1 )
| ( SX0 = SX2 ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SX0 @ universal_class )
| ~ ( ( SX0 = SX1 )
| ( SX0 = SX2 ) ) )
| ( member @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(146,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( member @ SX0 @ universal_class )
| ~ ( member @ SX1 @ universal_class ) )
| ~ ( ( ( first @ ( ordered_pair @ SX0 @ SX1 ) )
!= SX0 )
| ( ( second @ ( ordered_pair @ SX0 @ SX1 ) )
!= SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(147,plain,
( ( ! [SX0: $i] :
( ~ ( ( SX0 != null_class ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SX1 @ universal_class )
| ~ ( member @ SX1 @ SX0 ) )
| ~ ( disjoint @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(148,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( member @ SX1 @ ( complement @ SX0 ) )
| ~ ( ~ ( member @ SX1 @ universal_class )
| ~ ~ ( member @ SX1 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SX1 @ universal_class )
| ~ ~ ( member @ SX1 @ SX0 ) )
| ( member @ SX1 @ ( complement @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(149,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( function @ SX0 )
| ~ ( ~ ( subclass @ SX0 @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ SX0 @ ( inverse @ SX0 ) ) @ identity_relation ) ) )
| ~ ( ~ ~ ( ~ ( subclass @ SX0 @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ SX0 @ ( inverse @ SX0 ) ) @ identity_relation ) )
| ( function @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(150,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( member @ SX0 @ identity_relation )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( member @ SX1 @ universal_class )
| ( SX0
!= ( ordered_pair @ SX1 @ SX1 ) ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( member @ SX1 @ universal_class )
| ( SX0
!= ( ordered_pair @ SX1 @ SX1 ) ) )
| ( member @ SX0 @ identity_relation ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(151,plain,
( ( ! [SX0: $i] :
( ~ ( member @ SX0 @ universal_class )
| ( member @ ( power_class @ SX0 ) @ universal_class ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(152,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subclass @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ( subclass @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(153,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation )
| ~ ( ~ ~ ( ~ ( member @ SX0 @ universal_class )
| ~ ( member @ SX1 @ universal_class ) )
| ( ( successor @ SX0 )
!= SX1 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SX0 @ universal_class )
| ~ ( member @ SX1 @ universal_class ) )
| ( ( successor @ SX0 )
!= SX1 ) )
| ( member @ ( ordered_pair @ SX0 @ SX1 ) @ successor_relation ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(154,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( power_class @ SX1 ) )
| ~ ( ~ ( member @ SX0 @ universal_class )
| ~ ( subclass @ SX0 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SX0 @ universal_class )
| ~ ( subclass @ SX0 @ SX1 ) )
| ( member @ SX0 @ ( power_class @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(155,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( function @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( member @ SX1 @ universal_class )
| ( SX1 = null_class )
| ( member @ ( apply @ SX0 @ SX1 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(156,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( member @ SX2 @ ( intersection @ SX0 @ SX1 ) )
| ~ ( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) )
| ( member @ SX2 @ ( intersection @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(157,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ ( cross_product @ SX2 @ SX3 ) )
| ~ ( ~ ( member @ SX0 @ SX2 )
| ~ ( member @ SX1 @ SX3 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SX0 @ SX2 )
| ~ ( member @ SX1 @ SX3 ) )
| ( member @ ( ordered_pair @ SX0 @ SX1 ) @ ( cross_product @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(158,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SX0 @ universal_class )
| ~ ( inductive @ SX0 ) )
| ~ ! [SX1: $i] :
( ~ ( inductive @ SX1 )
| ( subclass @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(159,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( member @ SX0 @ universal_class )
| ~ ( function @ SX1 ) )
| ( member @ ( image @ SX1 @ SX0 ) @ universal_class ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(160,plain,
( ( ! [SX0: $i] :
( ~ ( member @ SX0 @ universal_class )
| ( member @ ( sum_class @ SX0 ) @ universal_class ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(161,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( inductive @ SX0 )
| ~ ( ~ ( member @ null_class @ SX0 )
| ~ ( subclass @ ( image @ successor_relation @ SX0 ) @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( member @ null_class @ SX0 )
| ~ ( subclass @ ( image @ successor_relation @ SX0 ) @ SX0 ) )
| ( inductive @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(162,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ ( cross_product @ SX0 @ SX1 ) )
| ( SX2
= ( ordered_pair @ ( first @ SX2 ) @ ( second @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(163,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation )
| ~ ( ~ ( member @ SX1 @ universal_class )
| ~ ( member @ SX0 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SX1 @ universal_class )
| ~ ( member @ SX0 @ SX1 ) )
| ( member @ ( ordered_pair @ SX0 @ SX1 ) @ element_relation ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(164,plain,
! [SV1: $i] :
( ( subclass @ SV1 @ universal_class )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(165,plain,
! [SV2: $i] :
( ( ! [SY89: $i] : ( member @ ( unordered_pair @ SV2 @ SY89 ) @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(166,plain,
! [SV3: $i] :
( ( ( singleton @ SV3 )
= ( unordered_pair @ SV3 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(167,plain,
! [SV4: $i] :
( ( ! [SY90: $i] :
( ( ordered_pair @ SV4 @ SY90 )
= ( unordered_pair @ ( singleton @ SV4 ) @ ( unordered_pair @ SV4 @ ( singleton @ SY90 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(168,plain,
! [SV5: $i] :
( ( ! [SY91: $i,SY92: $i] :
( ( restrict @ SY91 @ SV5 @ SY92 )
= ( intersection @ SY91 @ ( cross_product @ SV5 @ SY92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(169,plain,
! [SV6: $i] :
( ( ~ ( member @ SV6 @ null_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(170,plain,
! [SV7: $i] :
( ( subclass @ ( rotate @ SV7 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(171,plain,
! [SV8: $i] :
( ( subclass @ ( flip @ SV8 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(172,plain,
! [SV9: $i] :
( ( ( successor @ SV9 )
= ( union @ SV9 @ ( singleton @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(173,plain,
! [SV10: $i] :
( ( ( inverse @ SV10 )
= ( domain_of @ ( flip @ ( cross_product @ SV10 @ universal_class ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(174,plain,
! [SV11: $i] :
( ( ( range_of @ SV11 )
= ( domain_of @ ( inverse @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(175,plain,
! [SV12: $i] :
( ( ! [SY93: $i] :
( ( image @ SY93 @ SV12 )
= ( range_of @ ( restrict @ SY93 @ SV12 @ universal_class ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(176,plain,
! [SV13: $i] :
( ( ! [SY94: $i] : ( subclass @ ( compose @ SY94 @ SV13 ) @ ( cross_product @ universal_class @ universal_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(177,plain,
! [SV14: $i] :
( ( ! [SY95: $i] :
( ( apply @ SV14 @ SY95 )
= ( sum_class @ ( image @ SV14 @ ( singleton @ SY95 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(178,plain,
( ( member @ ( singleton @ sK1_X ) @ ( ordered_pair @ sK1_X @ sK2_SY88 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(179,plain,
! [SV15: $i] :
( ( ! [SY96: $i] :
~ ( ~ ( ( SV15 != SY96 )
| ~ ( ~ ( subclass @ SV15 @ SY96 )
| ~ ( subclass @ SY96 @ SV15 ) ) )
| ~ ( ~ ~ ( ~ ( subclass @ SV15 @ SY96 )
| ~ ( subclass @ SY96 @ SV15 ) )
| ( SV15 = SY96 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(180,plain,
! [SV16: $i] :
( ( ! [SY97: $i,SY98: $i] :
~ ( ~ ( ~ ( member @ SY98 @ ( union @ SV16 @ SY97 ) )
| ( member @ SY98 @ SV16 )
| ( member @ SY98 @ SY97 ) )
| ~ ( ~ ( ( member @ SY98 @ SV16 )
| ( member @ SY98 @ SY97 ) )
| ( member @ SY98 @ ( union @ SV16 @ SY97 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(181,plain,
! [SV17: $i] :
( ( ! [SY99: $i] :
~ ( ~ ( ~ ( member @ SV17 @ ( sum_class @ SY99 ) )
| ~ ! [SY100: $i] :
~ ~ ( ~ ( member @ SV17 @ SY100 )
| ~ ( member @ SY100 @ SY99 ) ) )
| ~ ( ~ ~ ! [SY101: $i] :
~ ~ ( ~ ( member @ SV17 @ SY101 )
| ~ ( member @ SY101 @ SY99 ) )
| ( member @ SV17 @ ( sum_class @ SY99 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(182,plain,
! [SV18: $i] :
( ( ! [SY102: $i,SY103: $i,SY104: $i] :
~ ( ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SY102 ) @ SY103 ) @ ( flip @ SY104 ) )
| ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SY102 ) @ SY103 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SY102 @ SV18 ) @ SY103 ) @ SY104 ) ) )
| ~ ( ~ ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SY102 ) @ SY103 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SY102 @ SV18 ) @ SY103 ) @ SY104 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SY102 ) @ SY103 ) @ ( flip @ SY104 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(183,plain,
! [SV19: $i] :
( ( ! [SY105: $i,SY106: $i,SY107: $i] :
~ ( ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SY105 @ SY106 ) @ SY107 ) @ ( rotate @ SV19 ) )
| ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SY105 @ SY106 ) @ SY107 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SY106 @ SY107 ) @ SY105 ) @ SV19 ) ) )
| ~ ( ~ ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SY105 @ SY106 ) @ SY107 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SY106 @ SY107 ) @ SY105 ) @ SV19 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SY105 @ SY106 ) @ SY107 ) @ ( rotate @ SV19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(184,plain,
! [SV20: $i] :
( ( ! [SY108: $i] :
~ ( ~ ( ~ ( disjoint @ SV20 @ SY108 )
| ! [SY109: $i] :
~ ~ ( ~ ( member @ SY109 @ SV20 )
| ~ ( member @ SY109 @ SY108 ) ) )
| ~ ( ~ ! [SY110: $i] :
~ ~ ( ~ ( member @ SY110 @ SV20 )
| ~ ( member @ SY110 @ SY108 ) )
| ( disjoint @ SV20 @ SY108 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(185,plain,
! [SV21: $i] :
( ( ! [SY111: $i] :
~ ( ~ ( ~ ( member @ SY111 @ ( domain_of @ SV21 ) )
| ~ ( ~ ( member @ SY111 @ universal_class )
| ~ ( ( ( restrict @ SV21 @ ( singleton @ SY111 ) @ universal_class )
!= null_class ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY111 @ universal_class )
| ~ ( ( ( restrict @ SV21 @ ( singleton @ SY111 ) @ universal_class )
!= null_class ) ) )
| ( member @ SY111 @ ( domain_of @ SV21 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(186,plain,
! [SV22: $i] :
( ( ! [SY112: $i,SY113: $i,SY114: $i] :
~ ( ~ ( ~ ( member @ ( ordered_pair @ SY113 @ SY114 ) @ ( compose @ SY112 @ SV22 ) )
| ~ ( ~ ( member @ SY113 @ universal_class )
| ~ ( member @ SY114 @ ( image @ SY112 @ ( image @ SV22 @ ( singleton @ SY113 ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY113 @ universal_class )
| ~ ( member @ SY114 @ ( image @ SY112 @ ( image @ SV22 @ ( singleton @ SY113 ) ) ) ) )
| ( member @ ( ordered_pair @ SY113 @ SY114 ) @ ( compose @ SY112 @ SV22 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(187,plain,
! [SV23: $i] :
( ( ! [SY115: $i,SY116: $i] :
~ ( ~ ( ~ ( member @ SV23 @ ( unordered_pair @ SY115 @ SY116 ) )
| ~ ( ~ ( member @ SV23 @ universal_class )
| ~ ( ( SV23 = SY115 )
| ( SV23 = SY116 ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV23 @ universal_class )
| ~ ( ( SV23 = SY115 )
| ( SV23 = SY116 ) ) )
| ( member @ SV23 @ ( unordered_pair @ SY115 @ SY116 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(188,plain,
! [SV24: $i] :
( ( ! [SY117: $i] :
( ~ ~ ( ~ ( member @ SV24 @ universal_class )
| ~ ( member @ SY117 @ universal_class ) )
| ~ ( ( ( first @ ( ordered_pair @ SV24 @ SY117 ) )
!= SV24 )
| ( ( second @ ( ordered_pair @ SV24 @ SY117 ) )
!= SY117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(189,plain,
! [SV25: $i] :
( ( ~ ( ( SV25 != null_class ) )
| ~ ! [SY118: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY118 @ universal_class )
| ~ ( member @ SY118 @ SV25 ) )
| ~ ( disjoint @ SY118 @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(190,plain,
! [SV26: $i] :
( ( ! [SY119: $i] :
~ ( ~ ( ~ ( member @ SY119 @ ( complement @ SV26 ) )
| ~ ( ~ ( member @ SY119 @ universal_class )
| ~ ~ ( member @ SY119 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY119 @ universal_class )
| ~ ~ ( member @ SY119 @ SV26 ) )
| ( member @ SY119 @ ( complement @ SV26 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(191,plain,
! [SV27: $i] :
( ( ~ ( ~ ( ~ ( function @ SV27 )
| ~ ( ~ ( subclass @ SV27 @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ SV27 @ ( inverse @ SV27 ) ) @ identity_relation ) ) )
| ~ ( ~ ~ ( ~ ( subclass @ SV27 @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ SV27 @ ( inverse @ SV27 ) ) @ identity_relation ) )
| ( function @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(192,plain,
! [SV28: $i] :
( ( ~ ( ~ ( ~ ( member @ SV28 @ identity_relation )
| ~ ! [SY120: $i] :
~ ~ ( ~ ( member @ SY120 @ universal_class )
| ( SV28
!= ( ordered_pair @ SY120 @ SY120 ) ) ) )
| ~ ( ~ ~ ! [SY121: $i] :
~ ~ ( ~ ( member @ SY121 @ universal_class )
| ( SV28
!= ( ordered_pair @ SY121 @ SY121 ) ) )
| ( member @ SV28 @ identity_relation ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(193,plain,
! [SV29: $i] :
( ( ~ ( member @ SV29 @ universal_class )
| ( member @ ( power_class @ SV29 ) @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(194,plain,
! [SV30: $i] :
( ( ! [SY122: $i] :
~ ( ~ ( ~ ( subclass @ SV30 @ SY122 )
| ! [SY123: $i] :
( ~ ( member @ SY123 @ SV30 )
| ( member @ SY123 @ SY122 ) ) )
| ~ ( ~ ! [SY124: $i] :
( ~ ( member @ SY124 @ SV30 )
| ( member @ SY124 @ SY122 ) )
| ( subclass @ SV30 @ SY122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(195,plain,
! [SV31: $i] :
( ( ! [SY125: $i] :
~ ( ~ ( ~ ( member @ ( ordered_pair @ SV31 @ SY125 ) @ successor_relation )
| ~ ( ~ ~ ( ~ ( member @ SV31 @ universal_class )
| ~ ( member @ SY125 @ universal_class ) )
| ( ( successor @ SV31 )
!= SY125 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV31 @ universal_class )
| ~ ( member @ SY125 @ universal_class ) )
| ( ( successor @ SV31 )
!= SY125 ) )
| ( member @ ( ordered_pair @ SV31 @ SY125 ) @ successor_relation ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(196,plain,
! [SV32: $i] :
( ( ! [SY126: $i] :
~ ( ~ ( ~ ( member @ SV32 @ ( power_class @ SY126 ) )
| ~ ( ~ ( member @ SV32 @ universal_class )
| ~ ( subclass @ SV32 @ SY126 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV32 @ universal_class )
| ~ ( subclass @ SV32 @ SY126 ) )
| ( member @ SV32 @ ( power_class @ SY126 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(197,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( function @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( member @ SX1 @ universal_class )
| ( SX1 = null_class )
| ( member @ ( apply @ SX0 @ SX1 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(198,plain,
! [SV33: $i] :
( ( ! [SY127: $i,SY128: $i] :
~ ( ~ ( ~ ( member @ SY128 @ ( intersection @ SV33 @ SY127 ) )
| ~ ( ~ ( member @ SY128 @ SV33 )
| ~ ( member @ SY128 @ SY127 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY128 @ SV33 )
| ~ ( member @ SY128 @ SY127 ) )
| ( member @ SY128 @ ( intersection @ SV33 @ SY127 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(199,plain,
! [SV34: $i] :
( ( ! [SY129: $i,SY130: $i,SY131: $i] :
~ ( ~ ( ~ ( member @ ( ordered_pair @ SV34 @ SY129 ) @ ( cross_product @ SY130 @ SY131 ) )
| ~ ( ~ ( member @ SV34 @ SY130 )
| ~ ( member @ SY129 @ SY131 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV34 @ SY130 )
| ~ ( member @ SY129 @ SY131 ) )
| ( member @ ( ordered_pair @ SV34 @ SY129 ) @ ( cross_product @ SY130 @ SY131 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(200,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SX0 @ universal_class )
| ~ ( inductive @ SX0 ) )
| ~ ! [SX1: $i] :
( ~ ( inductive @ SX1 )
| ( subclass @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(201,plain,
! [SV35: $i] :
( ( ! [SY132: $i] :
( ~ ~ ( ~ ( member @ SV35 @ universal_class )
| ~ ( function @ SY132 ) )
| ( member @ ( image @ SY132 @ SV35 ) @ universal_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(202,plain,
! [SV36: $i] :
( ( ~ ( member @ SV36 @ universal_class )
| ( member @ ( sum_class @ SV36 ) @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(203,plain,
! [SV37: $i] :
( ( ~ ( ~ ( ~ ( inductive @ SV37 )
| ~ ( ~ ( member @ null_class @ SV37 )
| ~ ( subclass @ ( image @ successor_relation @ SV37 ) @ SV37 ) ) )
| ~ ( ~ ~ ( ~ ( member @ null_class @ SV37 )
| ~ ( subclass @ ( image @ successor_relation @ SV37 ) @ SV37 ) )
| ( inductive @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(204,plain,
! [SV38: $i] :
( ( ! [SY133: $i,SY134: $i] :
( ~ ( member @ SY134 @ ( cross_product @ SV38 @ SY133 ) )
| ( SY134
= ( ordered_pair @ ( first @ SY134 ) @ ( second @ SY134 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(205,plain,
! [SV39: $i] :
( ( ! [SY135: $i] :
~ ( ~ ( ~ ( member @ ( ordered_pair @ SV39 @ SY135 ) @ element_relation )
| ~ ( ~ ( member @ SY135 @ universal_class )
| ~ ( member @ SV39 @ SY135 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY135 @ universal_class )
| ~ ( member @ SV39 @ SY135 ) )
| ( member @ ( ordered_pair @ SV39 @ SY135 ) @ element_relation ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(206,plain,
! [SV40: $i,SV2: $i] :
( ( member @ ( unordered_pair @ SV2 @ SV40 ) @ universal_class )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(207,plain,
! [SV41: $i,SV4: $i] :
( ( ( ordered_pair @ SV4 @ SV41 )
= ( unordered_pair @ ( singleton @ SV4 ) @ ( unordered_pair @ SV4 @ ( singleton @ SV41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(208,plain,
! [SV5: $i,SV42: $i] :
( ( ! [SY136: $i] :
( ( restrict @ SV42 @ SV5 @ SY136 )
= ( intersection @ SV42 @ ( cross_product @ SV5 @ SY136 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(209,plain,
! [SV6: $i] :
( ( member @ SV6 @ null_class )
= $false ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(210,plain,
! [SV12: $i,SV43: $i] :
( ( ( image @ SV43 @ SV12 )
= ( range_of @ ( restrict @ SV43 @ SV12 @ universal_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(211,plain,
! [SV13: $i,SV44: $i] :
( ( subclass @ ( compose @ SV44 @ SV13 ) @ ( cross_product @ universal_class @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(212,plain,
! [SV45: $i,SV14: $i] :
( ( ( apply @ SV14 @ SV45 )
= ( sum_class @ ( image @ SV14 @ ( singleton @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(213,plain,
! [SV46: $i,SV15: $i] :
( ( ~ ( ~ ( ( SV15 != SV46 )
| ~ ( ~ ( subclass @ SV15 @ SV46 )
| ~ ( subclass @ SV46 @ SV15 ) ) )
| ~ ( ~ ~ ( ~ ( subclass @ SV15 @ SV46 )
| ~ ( subclass @ SV46 @ SV15 ) )
| ( SV15 = SV46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(214,plain,
! [SV47: $i,SV16: $i] :
( ( ! [SY137: $i] :
~ ( ~ ( ~ ( member @ SY137 @ ( union @ SV16 @ SV47 ) )
| ( member @ SY137 @ SV16 )
| ( member @ SY137 @ SV47 ) )
| ~ ( ~ ( ( member @ SY137 @ SV16 )
| ( member @ SY137 @ SV47 ) )
| ( member @ SY137 @ ( union @ SV16 @ SV47 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(215,plain,
! [SV48: $i,SV17: $i] :
( ( ~ ( ~ ( ~ ( member @ SV17 @ ( sum_class @ SV48 ) )
| ~ ! [SY138: $i] :
~ ~ ( ~ ( member @ SV17 @ SY138 )
| ~ ( member @ SY138 @ SV48 ) ) )
| ~ ( ~ ~ ! [SY139: $i] :
~ ~ ( ~ ( member @ SV17 @ SY139 )
| ~ ( member @ SY139 @ SV48 ) )
| ( member @ SV17 @ ( sum_class @ SV48 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(216,plain,
! [SV49: $i,SV18: $i] :
( ( ! [SY140: $i,SY141: $i] :
~ ( ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SY140 ) @ ( flip @ SY141 ) )
| ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SY140 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV49 @ SV18 ) @ SY140 ) @ SY141 ) ) )
| ~ ( ~ ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SY140 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV49 @ SV18 ) @ SY140 ) @ SY141 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SY140 ) @ ( flip @ SY141 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(217,plain,
! [SV19: $i,SV50: $i] :
( ( ! [SY142: $i,SY143: $i] :
~ ( ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SY142 ) @ SY143 ) @ ( rotate @ SV19 ) )
| ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SY142 ) @ SY143 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SY142 @ SY143 ) @ SV50 ) @ SV19 ) ) )
| ~ ( ~ ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SY142 ) @ SY143 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SY142 @ SY143 ) @ SV50 ) @ SV19 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SY142 ) @ SY143 ) @ ( rotate @ SV19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(218,plain,
! [SV51: $i,SV20: $i] :
( ( ~ ( ~ ( ~ ( disjoint @ SV20 @ SV51 )
| ! [SY144: $i] :
~ ~ ( ~ ( member @ SY144 @ SV20 )
| ~ ( member @ SY144 @ SV51 ) ) )
| ~ ( ~ ! [SY145: $i] :
~ ~ ( ~ ( member @ SY145 @ SV20 )
| ~ ( member @ SY145 @ SV51 ) )
| ( disjoint @ SV20 @ SV51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(219,plain,
! [SV21: $i,SV52: $i] :
( ( ~ ( ~ ( ~ ( member @ SV52 @ ( domain_of @ SV21 ) )
| ~ ( ~ ( member @ SV52 @ universal_class )
| ~ ( ( ( restrict @ SV21 @ ( singleton @ SV52 ) @ universal_class )
!= null_class ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV52 @ universal_class )
| ~ ( ( ( restrict @ SV21 @ ( singleton @ SV52 ) @ universal_class )
!= null_class ) ) )
| ( member @ SV52 @ ( domain_of @ SV21 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(220,plain,
! [SV22: $i,SV53: $i] :
( ( ! [SY146: $i,SY147: $i] :
~ ( ~ ( ~ ( member @ ( ordered_pair @ SY146 @ SY147 ) @ ( compose @ SV53 @ SV22 ) )
| ~ ( ~ ( member @ SY146 @ universal_class )
| ~ ( member @ SY147 @ ( image @ SV53 @ ( image @ SV22 @ ( singleton @ SY146 ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY146 @ universal_class )
| ~ ( member @ SY147 @ ( image @ SV53 @ ( image @ SV22 @ ( singleton @ SY146 ) ) ) ) )
| ( member @ ( ordered_pair @ SY146 @ SY147 ) @ ( compose @ SV53 @ SV22 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(221,plain,
! [SV54: $i,SV23: $i] :
( ( ! [SY148: $i] :
~ ( ~ ( ~ ( member @ SV23 @ ( unordered_pair @ SV54 @ SY148 ) )
| ~ ( ~ ( member @ SV23 @ universal_class )
| ~ ( ( SV23 = SV54 )
| ( SV23 = SY148 ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV23 @ universal_class )
| ~ ( ( SV23 = SV54 )
| ( SV23 = SY148 ) ) )
| ( member @ SV23 @ ( unordered_pair @ SV54 @ SY148 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(222,plain,
! [SV55: $i,SV24: $i] :
( ( ~ ~ ( ~ ( member @ SV24 @ universal_class )
| ~ ( member @ SV55 @ universal_class ) )
| ~ ( ( ( first @ ( ordered_pair @ SV24 @ SV55 ) )
!= SV24 )
| ( ( second @ ( ordered_pair @ SV24 @ SV55 ) )
!= SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(223,plain,
! [SV25: $i] :
( ( ( ~ ( ( SV25 != null_class ) ) )
= $true )
| ( ( ~ ! [SY118: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY118 @ universal_class )
| ~ ( member @ SY118 @ SV25 ) )
| ~ ( disjoint @ SY118 @ SV25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(224,plain,
! [SV26: $i,SV56: $i] :
( ( ~ ( ~ ( ~ ( member @ SV56 @ ( complement @ SV26 ) )
| ~ ( ~ ( member @ SV56 @ universal_class )
| ~ ~ ( member @ SV56 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV56 @ universal_class )
| ~ ~ ( member @ SV56 @ SV26 ) )
| ( member @ SV56 @ ( complement @ SV26 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(225,plain,
! [SV27: $i] :
( ( ~ ( ~ ( function @ SV27 )
| ~ ( ~ ( subclass @ SV27 @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ SV27 @ ( inverse @ SV27 ) ) @ identity_relation ) ) )
| ~ ( ~ ~ ( ~ ( subclass @ SV27 @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ SV27 @ ( inverse @ SV27 ) ) @ identity_relation ) )
| ( function @ SV27 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(226,plain,
! [SV28: $i] :
( ( ~ ( ~ ( member @ SV28 @ identity_relation )
| ~ ! [SY120: $i] :
~ ~ ( ~ ( member @ SY120 @ universal_class )
| ( SV28
!= ( ordered_pair @ SY120 @ SY120 ) ) ) )
| ~ ( ~ ~ ! [SY121: $i] :
~ ~ ( ~ ( member @ SY121 @ universal_class )
| ( SV28
!= ( ordered_pair @ SY121 @ SY121 ) ) )
| ( member @ SV28 @ identity_relation ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(227,plain,
! [SV29: $i] :
( ( ( ~ ( member @ SV29 @ universal_class ) )
= $true )
| ( ( member @ ( power_class @ SV29 ) @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(228,plain,
! [SV57: $i,SV30: $i] :
( ( ~ ( ~ ( ~ ( subclass @ SV30 @ SV57 )
| ! [SY149: $i] :
( ~ ( member @ SY149 @ SV30 )
| ( member @ SY149 @ SV57 ) ) )
| ~ ( ~ ! [SY150: $i] :
( ~ ( member @ SY150 @ SV30 )
| ( member @ SY150 @ SV57 ) )
| ( subclass @ SV30 @ SV57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(229,plain,
! [SV58: $i,SV31: $i] :
( ( ~ ( ~ ( ~ ( member @ ( ordered_pair @ SV31 @ SV58 ) @ successor_relation )
| ~ ( ~ ~ ( ~ ( member @ SV31 @ universal_class )
| ~ ( member @ SV58 @ universal_class ) )
| ( ( successor @ SV31 )
!= SV58 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV31 @ universal_class )
| ~ ( member @ SV58 @ universal_class ) )
| ( ( successor @ SV31 )
!= SV58 ) )
| ( member @ ( ordered_pair @ SV31 @ SV58 ) @ successor_relation ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(230,plain,
! [SV59: $i,SV32: $i] :
( ( ~ ( ~ ( ~ ( member @ SV32 @ ( power_class @ SV59 ) )
| ~ ( ~ ( member @ SV32 @ universal_class )
| ~ ( subclass @ SV32 @ SV59 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV32 @ universal_class )
| ~ ( subclass @ SV32 @ SV59 ) )
| ( member @ SV32 @ ( power_class @ SV59 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(231,plain,
( ( ~ ~ ( ~ ( function @ sK3_SX0 )
| ~ ! [SY151: $i] :
( ~ ( member @ SY151 @ universal_class )
| ( SY151 = null_class )
| ( member @ ( apply @ sK3_SX0 @ SY151 ) @ SY151 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[197]) ).
thf(232,plain,
! [SV60: $i,SV33: $i] :
( ( ! [SY152: $i] :
~ ( ~ ( ~ ( member @ SY152 @ ( intersection @ SV33 @ SV60 ) )
| ~ ( ~ ( member @ SY152 @ SV33 )
| ~ ( member @ SY152 @ SV60 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY152 @ SV33 )
| ~ ( member @ SY152 @ SV60 ) )
| ( member @ SY152 @ ( intersection @ SV33 @ SV60 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(233,plain,
! [SV61: $i,SV34: $i] :
( ( ! [SY153: $i,SY154: $i] :
~ ( ~ ( ~ ( member @ ( ordered_pair @ SV34 @ SV61 ) @ ( cross_product @ SY153 @ SY154 ) )
| ~ ( ~ ( member @ SV34 @ SY153 )
| ~ ( member @ SV61 @ SY154 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV34 @ SY153 )
| ~ ( member @ SV61 @ SY154 ) )
| ( member @ ( ordered_pair @ SV34 @ SV61 ) @ ( cross_product @ SY153 @ SY154 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(234,plain,
( ( ~ ~ ( ~ ~ ( ~ ( member @ sK4_SX0 @ universal_class )
| ~ ( inductive @ sK4_SX0 ) )
| ~ ! [SY155: $i] :
( ~ ( inductive @ SY155 )
| ( subclass @ sK4_SX0 @ SY155 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[200]) ).
thf(235,plain,
! [SV62: $i,SV35: $i] :
( ( ~ ~ ( ~ ( member @ SV35 @ universal_class )
| ~ ( function @ SV62 ) )
| ( member @ ( image @ SV62 @ SV35 ) @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(236,plain,
! [SV36: $i] :
( ( ( ~ ( member @ SV36 @ universal_class ) )
= $true )
| ( ( member @ ( sum_class @ SV36 ) @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(237,plain,
! [SV37: $i] :
( ( ~ ( ~ ( inductive @ SV37 )
| ~ ( ~ ( member @ null_class @ SV37 )
| ~ ( subclass @ ( image @ successor_relation @ SV37 ) @ SV37 ) ) )
| ~ ( ~ ~ ( ~ ( member @ null_class @ SV37 )
| ~ ( subclass @ ( image @ successor_relation @ SV37 ) @ SV37 ) )
| ( inductive @ SV37 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(238,plain,
! [SV63: $i,SV38: $i] :
( ( ! [SY156: $i] :
( ~ ( member @ SY156 @ ( cross_product @ SV38 @ SV63 ) )
| ( SY156
= ( ordered_pair @ ( first @ SY156 ) @ ( second @ SY156 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(239,plain,
! [SV64: $i,SV39: $i] :
( ( ~ ( ~ ( ~ ( member @ ( ordered_pair @ SV39 @ SV64 ) @ element_relation )
| ~ ( ~ ( member @ SV64 @ universal_class )
| ~ ( member @ SV39 @ SV64 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV64 @ universal_class )
| ~ ( member @ SV39 @ SV64 ) )
| ( member @ ( ordered_pair @ SV39 @ SV64 ) @ element_relation ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(240,plain,
! [SV65: $i,SV5: $i,SV42: $i] :
( ( ( restrict @ SV42 @ SV5 @ SV65 )
= ( intersection @ SV42 @ ( cross_product @ SV5 @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(241,plain,
! [SV46: $i,SV15: $i] :
( ( ~ ( ( SV15 != SV46 )
| ~ ( ~ ( subclass @ SV15 @ SV46 )
| ~ ( subclass @ SV46 @ SV15 ) ) )
| ~ ( ~ ~ ( ~ ( subclass @ SV15 @ SV46 )
| ~ ( subclass @ SV46 @ SV15 ) )
| ( SV15 = SV46 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(242,plain,
! [SV47: $i,SV16: $i,SV66: $i] :
( ( ~ ( ~ ( ~ ( member @ SV66 @ ( union @ SV16 @ SV47 ) )
| ( member @ SV66 @ SV16 )
| ( member @ SV66 @ SV47 ) )
| ~ ( ~ ( ( member @ SV66 @ SV16 )
| ( member @ SV66 @ SV47 ) )
| ( member @ SV66 @ ( union @ SV16 @ SV47 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(243,plain,
! [SV48: $i,SV17: $i] :
( ( ~ ( ~ ( member @ SV17 @ ( sum_class @ SV48 ) )
| ~ ! [SY138: $i] :
~ ~ ( ~ ( member @ SV17 @ SY138 )
| ~ ( member @ SY138 @ SV48 ) ) )
| ~ ( ~ ~ ! [SY139: $i] :
~ ~ ( ~ ( member @ SV17 @ SY139 )
| ~ ( member @ SY139 @ SV48 ) )
| ( member @ SV17 @ ( sum_class @ SV48 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(244,plain,
! [SV67: $i,SV49: $i,SV18: $i] :
( ( ! [SY157: $i] :
~ ( ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( flip @ SY157 ) )
| ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV49 @ SV18 ) @ SV67 ) @ SY157 ) ) )
| ~ ( ~ ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV49 @ SV18 ) @ SV67 ) @ SY157 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( flip @ SY157 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(245,plain,
! [SV19: $i,SV68: $i,SV50: $i] :
( ( ! [SY158: $i] :
~ ( ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SY158 ) @ ( rotate @ SV19 ) )
| ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SY158 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV68 @ SY158 ) @ SV50 ) @ SV19 ) ) )
| ~ ( ~ ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SY158 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV68 @ SY158 ) @ SV50 ) @ SV19 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SY158 ) @ ( rotate @ SV19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(246,plain,
! [SV51: $i,SV20: $i] :
( ( ~ ( ~ ( disjoint @ SV20 @ SV51 )
| ! [SY144: $i] :
~ ~ ( ~ ( member @ SY144 @ SV20 )
| ~ ( member @ SY144 @ SV51 ) ) )
| ~ ( ~ ! [SY145: $i] :
~ ~ ( ~ ( member @ SY145 @ SV20 )
| ~ ( member @ SY145 @ SV51 ) )
| ( disjoint @ SV20 @ SV51 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(247,plain,
! [SV21: $i,SV52: $i] :
( ( ~ ( ~ ( member @ SV52 @ ( domain_of @ SV21 ) )
| ~ ( ~ ( member @ SV52 @ universal_class )
| ~ ( ( ( restrict @ SV21 @ ( singleton @ SV52 ) @ universal_class )
!= null_class ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV52 @ universal_class )
| ~ ( ( ( restrict @ SV21 @ ( singleton @ SV52 ) @ universal_class )
!= null_class ) ) )
| ( member @ SV52 @ ( domain_of @ SV21 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(248,plain,
! [SV22: $i,SV53: $i,SV69: $i] :
( ( ! [SY159: $i] :
~ ( ~ ( ~ ( member @ ( ordered_pair @ SV69 @ SY159 ) @ ( compose @ SV53 @ SV22 ) )
| ~ ( ~ ( member @ SV69 @ universal_class )
| ~ ( member @ SY159 @ ( image @ SV53 @ ( image @ SV22 @ ( singleton @ SV69 ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV69 @ universal_class )
| ~ ( member @ SY159 @ ( image @ SV53 @ ( image @ SV22 @ ( singleton @ SV69 ) ) ) ) )
| ( member @ ( ordered_pair @ SV69 @ SY159 ) @ ( compose @ SV53 @ SV22 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(249,plain,
! [SV70: $i,SV54: $i,SV23: $i] :
( ( ~ ( ~ ( ~ ( member @ SV23 @ ( unordered_pair @ SV54 @ SV70 ) )
| ~ ( ~ ( member @ SV23 @ universal_class )
| ~ ( ( SV23 = SV54 )
| ( SV23 = SV70 ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV23 @ universal_class )
| ~ ( ( SV23 = SV54 )
| ( SV23 = SV70 ) ) )
| ( member @ SV23 @ ( unordered_pair @ SV54 @ SV70 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(250,plain,
! [SV55: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( member @ SV24 @ universal_class )
| ~ ( member @ SV55 @ universal_class ) ) )
= $true )
| ( ( ~ ( ( ( first @ ( ordered_pair @ SV24 @ SV55 ) )
!= SV24 )
| ( ( second @ ( ordered_pair @ SV24 @ SV55 ) )
!= SV55 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(251,plain,
! [SV25: $i] :
( ( ( SV25 != null_class )
= $false )
| ( ( ~ ! [SY118: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY118 @ universal_class )
| ~ ( member @ SY118 @ SV25 ) )
| ~ ( disjoint @ SY118 @ SV25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(252,plain,
! [SV26: $i,SV56: $i] :
( ( ~ ( ~ ( member @ SV56 @ ( complement @ SV26 ) )
| ~ ( ~ ( member @ SV56 @ universal_class )
| ~ ~ ( member @ SV56 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV56 @ universal_class )
| ~ ~ ( member @ SV56 @ SV26 ) )
| ( member @ SV56 @ ( complement @ SV26 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(253,plain,
! [SV27: $i] :
( ( ~ ( ~ ( function @ SV27 )
| ~ ( ~ ( subclass @ SV27 @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ SV27 @ ( inverse @ SV27 ) ) @ identity_relation ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[225]) ).
thf(254,plain,
! [SV27: $i] :
( ( ~ ( ~ ~ ( ~ ( subclass @ SV27 @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ SV27 @ ( inverse @ SV27 ) ) @ identity_relation ) )
| ( function @ SV27 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[225]) ).
thf(255,plain,
! [SV28: $i] :
( ( ~ ( ~ ( member @ SV28 @ identity_relation )
| ~ ! [SY120: $i] :
~ ~ ( ~ ( member @ SY120 @ universal_class )
| ( SV28
!= ( ordered_pair @ SY120 @ SY120 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[226]) ).
thf(256,plain,
! [SV28: $i] :
( ( ~ ( ~ ~ ! [SY121: $i] :
~ ~ ( ~ ( member @ SY121 @ universal_class )
| ( SV28
!= ( ordered_pair @ SY121 @ SY121 ) ) )
| ( member @ SV28 @ identity_relation ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[226]) ).
thf(257,plain,
! [SV29: $i] :
( ( ( member @ SV29 @ universal_class )
= $false )
| ( ( member @ ( power_class @ SV29 ) @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(258,plain,
! [SV57: $i,SV30: $i] :
( ( ~ ( ~ ( subclass @ SV30 @ SV57 )
| ! [SY149: $i] :
( ~ ( member @ SY149 @ SV30 )
| ( member @ SY149 @ SV57 ) ) )
| ~ ( ~ ! [SY150: $i] :
( ~ ( member @ SY150 @ SV30 )
| ( member @ SY150 @ SV57 ) )
| ( subclass @ SV30 @ SV57 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(259,plain,
! [SV58: $i,SV31: $i] :
( ( ~ ( ~ ( member @ ( ordered_pair @ SV31 @ SV58 ) @ successor_relation )
| ~ ( ~ ~ ( ~ ( member @ SV31 @ universal_class )
| ~ ( member @ SV58 @ universal_class ) )
| ( ( successor @ SV31 )
!= SV58 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV31 @ universal_class )
| ~ ( member @ SV58 @ universal_class ) )
| ( ( successor @ SV31 )
!= SV58 ) )
| ( member @ ( ordered_pair @ SV31 @ SV58 ) @ successor_relation ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(260,plain,
! [SV59: $i,SV32: $i] :
( ( ~ ( ~ ( member @ SV32 @ ( power_class @ SV59 ) )
| ~ ( ~ ( member @ SV32 @ universal_class )
| ~ ( subclass @ SV32 @ SV59 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV32 @ universal_class )
| ~ ( subclass @ SV32 @ SV59 ) )
| ( member @ SV32 @ ( power_class @ SV59 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(261,plain,
( ( ~ ( ~ ( function @ sK3_SX0 )
| ~ ! [SY151: $i] :
( ~ ( member @ SY151 @ universal_class )
| ( SY151 = null_class )
| ( member @ ( apply @ sK3_SX0 @ SY151 ) @ SY151 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(262,plain,
! [SV60: $i,SV33: $i,SV71: $i] :
( ( ~ ( ~ ( ~ ( member @ SV71 @ ( intersection @ SV33 @ SV60 ) )
| ~ ( ~ ( member @ SV71 @ SV33 )
| ~ ( member @ SV71 @ SV60 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV71 @ SV33 )
| ~ ( member @ SV71 @ SV60 ) )
| ( member @ SV71 @ ( intersection @ SV33 @ SV60 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(263,plain,
! [SV72: $i,SV61: $i,SV34: $i] :
( ( ! [SY160: $i] :
~ ( ~ ( ~ ( member @ ( ordered_pair @ SV34 @ SV61 ) @ ( cross_product @ SV72 @ SY160 ) )
| ~ ( ~ ( member @ SV34 @ SV72 )
| ~ ( member @ SV61 @ SY160 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV34 @ SV72 )
| ~ ( member @ SV61 @ SY160 ) )
| ( member @ ( ordered_pair @ SV34 @ SV61 ) @ ( cross_product @ SV72 @ SY160 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(264,plain,
( ( ~ ( ~ ~ ( ~ ( member @ sK4_SX0 @ universal_class )
| ~ ( inductive @ sK4_SX0 ) )
| ~ ! [SY155: $i] :
( ~ ( inductive @ SY155 )
| ( subclass @ sK4_SX0 @ SY155 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[234]) ).
thf(265,plain,
! [SV62: $i,SV35: $i] :
( ( ( ~ ~ ( ~ ( member @ SV35 @ universal_class )
| ~ ( function @ SV62 ) ) )
= $true )
| ( ( member @ ( image @ SV62 @ SV35 ) @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(266,plain,
! [SV36: $i] :
( ( ( member @ SV36 @ universal_class )
= $false )
| ( ( member @ ( sum_class @ SV36 ) @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(267,plain,
! [SV37: $i] :
( ( ~ ( ~ ( inductive @ SV37 )
| ~ ( ~ ( member @ null_class @ SV37 )
| ~ ( subclass @ ( image @ successor_relation @ SV37 ) @ SV37 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[237]) ).
thf(268,plain,
! [SV37: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ null_class @ SV37 )
| ~ ( subclass @ ( image @ successor_relation @ SV37 ) @ SV37 ) )
| ( inductive @ SV37 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[237]) ).
thf(269,plain,
! [SV63: $i,SV38: $i,SV73: $i] :
( ( ~ ( member @ SV73 @ ( cross_product @ SV38 @ SV63 ) )
| ( SV73
= ( ordered_pair @ ( first @ SV73 ) @ ( second @ SV73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(270,plain,
! [SV64: $i,SV39: $i] :
( ( ~ ( ~ ( member @ ( ordered_pair @ SV39 @ SV64 ) @ element_relation )
| ~ ( ~ ( member @ SV64 @ universal_class )
| ~ ( member @ SV39 @ SV64 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV64 @ universal_class )
| ~ ( member @ SV39 @ SV64 ) )
| ( member @ ( ordered_pair @ SV39 @ SV64 ) @ element_relation ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(271,plain,
! [SV46: $i,SV15: $i] :
( ( ~ ( ( SV15 != SV46 )
| ~ ( ~ ( subclass @ SV15 @ SV46 )
| ~ ( subclass @ SV46 @ SV15 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[241]) ).
thf(272,plain,
! [SV46: $i,SV15: $i] :
( ( ~ ( ~ ~ ( ~ ( subclass @ SV15 @ SV46 )
| ~ ( subclass @ SV46 @ SV15 ) )
| ( SV15 = SV46 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[241]) ).
thf(273,plain,
! [SV47: $i,SV16: $i,SV66: $i] :
( ( ~ ( ~ ( member @ SV66 @ ( union @ SV16 @ SV47 ) )
| ( member @ SV66 @ SV16 )
| ( member @ SV66 @ SV47 ) )
| ~ ( ~ ( ( member @ SV66 @ SV16 )
| ( member @ SV66 @ SV47 ) )
| ( member @ SV66 @ ( union @ SV16 @ SV47 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(274,plain,
! [SV48: $i,SV17: $i] :
( ( ~ ( ~ ( member @ SV17 @ ( sum_class @ SV48 ) )
| ~ ! [SY138: $i] :
~ ~ ( ~ ( member @ SV17 @ SY138 )
| ~ ( member @ SY138 @ SV48 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(275,plain,
! [SV48: $i,SV17: $i] :
( ( ~ ( ~ ~ ! [SY139: $i] :
~ ~ ( ~ ( member @ SV17 @ SY139 )
| ~ ( member @ SY139 @ SV48 ) )
| ( member @ SV17 @ ( sum_class @ SV48 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(276,plain,
! [SV74: $i,SV67: $i,SV49: $i,SV18: $i] :
( ( ~ ( ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( flip @ SV74 ) )
| ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV49 @ SV18 ) @ SV67 ) @ SV74 ) ) )
| ~ ( ~ ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV49 @ SV18 ) @ SV67 ) @ SV74 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( flip @ SV74 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(277,plain,
! [SV19: $i,SV75: $i,SV68: $i,SV50: $i] :
( ( ~ ( ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( rotate @ SV19 ) )
| ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV68 @ SV75 ) @ SV50 ) @ SV19 ) ) )
| ~ ( ~ ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV68 @ SV75 ) @ SV50 ) @ SV19 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( rotate @ SV19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(278,plain,
! [SV51: $i,SV20: $i] :
( ( ~ ( ~ ( disjoint @ SV20 @ SV51 )
| ! [SY144: $i] :
~ ~ ( ~ ( member @ SY144 @ SV20 )
| ~ ( member @ SY144 @ SV51 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[246]) ).
thf(279,plain,
! [SV51: $i,SV20: $i] :
( ( ~ ( ~ ! [SY145: $i] :
~ ~ ( ~ ( member @ SY145 @ SV20 )
| ~ ( member @ SY145 @ SV51 ) )
| ( disjoint @ SV20 @ SV51 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[246]) ).
thf(280,plain,
! [SV21: $i,SV52: $i] :
( ( ~ ( ~ ( member @ SV52 @ ( domain_of @ SV21 ) )
| ~ ( ~ ( member @ SV52 @ universal_class )
| ~ ( ( ( restrict @ SV21 @ ( singleton @ SV52 ) @ universal_class )
!= null_class ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[247]) ).
thf(281,plain,
! [SV21: $i,SV52: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV52 @ universal_class )
| ~ ( ( ( restrict @ SV21 @ ( singleton @ SV52 ) @ universal_class )
!= null_class ) ) )
| ( member @ SV52 @ ( domain_of @ SV21 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[247]) ).
thf(282,plain,
! [SV22: $i,SV53: $i,SV76: $i,SV69: $i] :
( ( ~ ( ~ ( ~ ( member @ ( ordered_pair @ SV69 @ SV76 ) @ ( compose @ SV53 @ SV22 ) )
| ~ ( ~ ( member @ SV69 @ universal_class )
| ~ ( member @ SV76 @ ( image @ SV53 @ ( image @ SV22 @ ( singleton @ SV69 ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV69 @ universal_class )
| ~ ( member @ SV76 @ ( image @ SV53 @ ( image @ SV22 @ ( singleton @ SV69 ) ) ) ) )
| ( member @ ( ordered_pair @ SV69 @ SV76 ) @ ( compose @ SV53 @ SV22 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(283,plain,
! [SV70: $i,SV54: $i,SV23: $i] :
( ( ~ ( ~ ( member @ SV23 @ ( unordered_pair @ SV54 @ SV70 ) )
| ~ ( ~ ( member @ SV23 @ universal_class )
| ~ ( ( SV23 = SV54 )
| ( SV23 = SV70 ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV23 @ universal_class )
| ~ ( ( SV23 = SV54 )
| ( SV23 = SV70 ) ) )
| ( member @ SV23 @ ( unordered_pair @ SV54 @ SV70 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(284,plain,
! [SV55: $i,SV24: $i] :
( ( ( ~ ( ~ ( member @ SV24 @ universal_class )
| ~ ( member @ SV55 @ universal_class ) ) )
= $false )
| ( ( ~ ( ( ( first @ ( ordered_pair @ SV24 @ SV55 ) )
!= SV24 )
| ( ( second @ ( ordered_pair @ SV24 @ SV55 ) )
!= SV55 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(285,plain,
! [SV25: $i] :
( ( ( SV25 = null_class )
= $true )
| ( ( ~ ! [SY118: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY118 @ universal_class )
| ~ ( member @ SY118 @ SV25 ) )
| ~ ( disjoint @ SY118 @ SV25 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(286,plain,
! [SV26: $i,SV56: $i] :
( ( ~ ( ~ ( member @ SV56 @ ( complement @ SV26 ) )
| ~ ( ~ ( member @ SV56 @ universal_class )
| ~ ~ ( member @ SV56 @ SV26 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[252]) ).
thf(287,plain,
! [SV26: $i,SV56: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV56 @ universal_class )
| ~ ~ ( member @ SV56 @ SV26 ) )
| ( member @ SV56 @ ( complement @ SV26 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[252]) ).
thf(288,plain,
! [SV27: $i] :
( ( ~ ( function @ SV27 )
| ~ ( ~ ( subclass @ SV27 @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ SV27 @ ( inverse @ SV27 ) ) @ identity_relation ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(289,plain,
! [SV27: $i] :
( ( ~ ~ ( ~ ( subclass @ SV27 @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ SV27 @ ( inverse @ SV27 ) ) @ identity_relation ) )
| ( function @ SV27 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(290,plain,
! [SV28: $i] :
( ( ~ ( member @ SV28 @ identity_relation )
| ~ ! [SY120: $i] :
~ ~ ( ~ ( member @ SY120 @ universal_class )
| ( SV28
!= ( ordered_pair @ SY120 @ SY120 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(291,plain,
! [SV28: $i] :
( ( ~ ~ ! [SY121: $i] :
~ ~ ( ~ ( member @ SY121 @ universal_class )
| ( SV28
!= ( ordered_pair @ SY121 @ SY121 ) ) )
| ( member @ SV28 @ identity_relation ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[256]) ).
thf(292,plain,
! [SV57: $i,SV30: $i] :
( ( ~ ( ~ ( subclass @ SV30 @ SV57 )
| ! [SY149: $i] :
( ~ ( member @ SY149 @ SV30 )
| ( member @ SY149 @ SV57 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[258]) ).
thf(293,plain,
! [SV57: $i,SV30: $i] :
( ( ~ ( ~ ! [SY150: $i] :
( ~ ( member @ SY150 @ SV30 )
| ( member @ SY150 @ SV57 ) )
| ( subclass @ SV30 @ SV57 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[258]) ).
thf(294,plain,
! [SV58: $i,SV31: $i] :
( ( ~ ( ~ ( member @ ( ordered_pair @ SV31 @ SV58 ) @ successor_relation )
| ~ ( ~ ~ ( ~ ( member @ SV31 @ universal_class )
| ~ ( member @ SV58 @ universal_class ) )
| ( ( successor @ SV31 )
!= SV58 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[259]) ).
thf(295,plain,
! [SV58: $i,SV31: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV31 @ universal_class )
| ~ ( member @ SV58 @ universal_class ) )
| ( ( successor @ SV31 )
!= SV58 ) )
| ( member @ ( ordered_pair @ SV31 @ SV58 ) @ successor_relation ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[259]) ).
thf(296,plain,
! [SV59: $i,SV32: $i] :
( ( ~ ( ~ ( member @ SV32 @ ( power_class @ SV59 ) )
| ~ ( ~ ( member @ SV32 @ universal_class )
| ~ ( subclass @ SV32 @ SV59 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[260]) ).
thf(297,plain,
! [SV59: $i,SV32: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV32 @ universal_class )
| ~ ( subclass @ SV32 @ SV59 ) )
| ( member @ SV32 @ ( power_class @ SV59 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[260]) ).
thf(298,plain,
( ( ~ ( function @ sK3_SX0 )
| ~ ! [SY151: $i] :
( ~ ( member @ SY151 @ universal_class )
| ( SY151 = null_class )
| ( member @ ( apply @ sK3_SX0 @ SY151 ) @ SY151 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(299,plain,
! [SV60: $i,SV33: $i,SV71: $i] :
( ( ~ ( ~ ( member @ SV71 @ ( intersection @ SV33 @ SV60 ) )
| ~ ( ~ ( member @ SV71 @ SV33 )
| ~ ( member @ SV71 @ SV60 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV71 @ SV33 )
| ~ ( member @ SV71 @ SV60 ) )
| ( member @ SV71 @ ( intersection @ SV33 @ SV60 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(300,plain,
! [SV77: $i,SV72: $i,SV61: $i,SV34: $i] :
( ( ~ ( ~ ( ~ ( member @ ( ordered_pair @ SV34 @ SV61 ) @ ( cross_product @ SV72 @ SV77 ) )
| ~ ( ~ ( member @ SV34 @ SV72 )
| ~ ( member @ SV61 @ SV77 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV34 @ SV72 )
| ~ ( member @ SV61 @ SV77 ) )
| ( member @ ( ordered_pair @ SV34 @ SV61 ) @ ( cross_product @ SV72 @ SV77 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(301,plain,
( ( ~ ~ ( ~ ( member @ sK4_SX0 @ universal_class )
| ~ ( inductive @ sK4_SX0 ) )
| ~ ! [SY155: $i] :
( ~ ( inductive @ SY155 )
| ( subclass @ sK4_SX0 @ SY155 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(302,plain,
! [SV62: $i,SV35: $i] :
( ( ( ~ ( ~ ( member @ SV35 @ universal_class )
| ~ ( function @ SV62 ) ) )
= $false )
| ( ( member @ ( image @ SV62 @ SV35 ) @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(303,plain,
! [SV37: $i] :
( ( ~ ( inductive @ SV37 )
| ~ ( ~ ( member @ null_class @ SV37 )
| ~ ( subclass @ ( image @ successor_relation @ SV37 ) @ SV37 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[267]) ).
thf(304,plain,
! [SV37: $i] :
( ( ~ ~ ( ~ ( member @ null_class @ SV37 )
| ~ ( subclass @ ( image @ successor_relation @ SV37 ) @ SV37 ) )
| ( inductive @ SV37 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[268]) ).
thf(305,plain,
! [SV63: $i,SV38: $i,SV73: $i] :
( ( ( ~ ( member @ SV73 @ ( cross_product @ SV38 @ SV63 ) ) )
= $true )
| ( ( SV73
= ( ordered_pair @ ( first @ SV73 ) @ ( second @ SV73 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[269]) ).
thf(306,plain,
! [SV64: $i,SV39: $i] :
( ( ~ ( ~ ( member @ ( ordered_pair @ SV39 @ SV64 ) @ element_relation )
| ~ ( ~ ( member @ SV64 @ universal_class )
| ~ ( member @ SV39 @ SV64 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[270]) ).
thf(307,plain,
! [SV39: $i,SV64: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV64 @ universal_class )
| ~ ( member @ SV39 @ SV64 ) )
| ( member @ ( ordered_pair @ SV39 @ SV64 ) @ element_relation ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[270]) ).
thf(308,plain,
! [SV46: $i,SV15: $i] :
( ( ( SV15 != SV46 )
| ~ ( ~ ( subclass @ SV15 @ SV46 )
| ~ ( subclass @ SV46 @ SV15 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[271]) ).
thf(309,plain,
! [SV46: $i,SV15: $i] :
( ( ~ ~ ( ~ ( subclass @ SV15 @ SV46 )
| ~ ( subclass @ SV46 @ SV15 ) )
| ( SV15 = SV46 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[272]) ).
thf(310,plain,
! [SV47: $i,SV16: $i,SV66: $i] :
( ( ~ ( ~ ( member @ SV66 @ ( union @ SV16 @ SV47 ) )
| ( member @ SV66 @ SV16 )
| ( member @ SV66 @ SV47 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[273]) ).
thf(311,plain,
! [SV47: $i,SV16: $i,SV66: $i] :
( ( ~ ( ~ ( ( member @ SV66 @ SV16 )
| ( member @ SV66 @ SV47 ) )
| ( member @ SV66 @ ( union @ SV16 @ SV47 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[273]) ).
thf(312,plain,
! [SV48: $i,SV17: $i] :
( ( ~ ( member @ SV17 @ ( sum_class @ SV48 ) )
| ~ ! [SY138: $i] :
~ ~ ( ~ ( member @ SV17 @ SY138 )
| ~ ( member @ SY138 @ SV48 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[274]) ).
thf(313,plain,
! [SV48: $i,SV17: $i] :
( ( ~ ~ ! [SY139: $i] :
~ ~ ( ~ ( member @ SV17 @ SY139 )
| ~ ( member @ SY139 @ SV48 ) )
| ( member @ SV17 @ ( sum_class @ SV48 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[275]) ).
thf(314,plain,
! [SV74: $i,SV67: $i,SV49: $i,SV18: $i] :
( ( ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( flip @ SV74 ) )
| ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV49 @ SV18 ) @ SV67 ) @ SV74 ) ) )
| ~ ( ~ ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV49 @ SV18 ) @ SV67 ) @ SV74 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( flip @ SV74 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(315,plain,
! [SV19: $i,SV75: $i,SV68: $i,SV50: $i] :
( ( ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( rotate @ SV19 ) )
| ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV68 @ SV75 ) @ SV50 ) @ SV19 ) ) )
| ~ ( ~ ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV68 @ SV75 ) @ SV50 ) @ SV19 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( rotate @ SV19 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(316,plain,
! [SV51: $i,SV20: $i] :
( ( ~ ( disjoint @ SV20 @ SV51 )
| ! [SY144: $i] :
~ ~ ( ~ ( member @ SY144 @ SV20 )
| ~ ( member @ SY144 @ SV51 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[278]) ).
thf(317,plain,
! [SV51: $i,SV20: $i] :
( ( ~ ! [SY145: $i] :
~ ~ ( ~ ( member @ SY145 @ SV20 )
| ~ ( member @ SY145 @ SV51 ) )
| ( disjoint @ SV20 @ SV51 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[279]) ).
thf(318,plain,
! [SV21: $i,SV52: $i] :
( ( ~ ( member @ SV52 @ ( domain_of @ SV21 ) )
| ~ ( ~ ( member @ SV52 @ universal_class )
| ~ ( ( ( restrict @ SV21 @ ( singleton @ SV52 ) @ universal_class )
!= null_class ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[280]) ).
thf(319,plain,
! [SV21: $i,SV52: $i] :
( ( ~ ~ ( ~ ( member @ SV52 @ universal_class )
| ~ ( ( ( restrict @ SV21 @ ( singleton @ SV52 ) @ universal_class )
!= null_class ) ) )
| ( member @ SV52 @ ( domain_of @ SV21 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[281]) ).
thf(320,plain,
! [SV22: $i,SV53: $i,SV76: $i,SV69: $i] :
( ( ~ ( ~ ( member @ ( ordered_pair @ SV69 @ SV76 ) @ ( compose @ SV53 @ SV22 ) )
| ~ ( ~ ( member @ SV69 @ universal_class )
| ~ ( member @ SV76 @ ( image @ SV53 @ ( image @ SV22 @ ( singleton @ SV69 ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV69 @ universal_class )
| ~ ( member @ SV76 @ ( image @ SV53 @ ( image @ SV22 @ ( singleton @ SV69 ) ) ) ) )
| ( member @ ( ordered_pair @ SV69 @ SV76 ) @ ( compose @ SV53 @ SV22 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(321,plain,
! [SV70: $i,SV54: $i,SV23: $i] :
( ( ~ ( ~ ( member @ SV23 @ ( unordered_pair @ SV54 @ SV70 ) )
| ~ ( ~ ( member @ SV23 @ universal_class )
| ~ ( ( SV23 = SV54 )
| ( SV23 = SV70 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[283]) ).
thf(322,plain,
! [SV70: $i,SV54: $i,SV23: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV23 @ universal_class )
| ~ ( ( SV23 = SV54 )
| ( SV23 = SV70 ) ) )
| ( member @ SV23 @ ( unordered_pair @ SV54 @ SV70 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[283]) ).
thf(323,plain,
! [SV55: $i,SV24: $i] :
( ( ( ~ ( member @ SV24 @ universal_class )
| ~ ( member @ SV55 @ universal_class ) )
= $true )
| ( ( ~ ( ( ( first @ ( ordered_pair @ SV24 @ SV55 ) )
!= SV24 )
| ( ( second @ ( ordered_pair @ SV24 @ SV55 ) )
!= SV55 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[284]) ).
thf(324,plain,
! [SV25: $i] :
( ( ( ! [SY118: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY118 @ universal_class )
| ~ ( member @ SY118 @ SV25 ) )
| ~ ( disjoint @ SY118 @ SV25 ) ) )
= $false )
| ( ( SV25 = null_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(325,plain,
! [SV26: $i,SV56: $i] :
( ( ~ ( member @ SV56 @ ( complement @ SV26 ) )
| ~ ( ~ ( member @ SV56 @ universal_class )
| ~ ~ ( member @ SV56 @ SV26 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(326,plain,
! [SV26: $i,SV56: $i] :
( ( ~ ~ ( ~ ( member @ SV56 @ universal_class )
| ~ ~ ( member @ SV56 @ SV26 ) )
| ( member @ SV56 @ ( complement @ SV26 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[287]) ).
thf(327,plain,
! [SV27: $i] :
( ( ( ~ ( function @ SV27 ) )
= $true )
| ( ( ~ ( ~ ( subclass @ SV27 @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ SV27 @ ( inverse @ SV27 ) ) @ identity_relation ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(328,plain,
! [SV27: $i] :
( ( ( ~ ~ ( ~ ( subclass @ SV27 @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ SV27 @ ( inverse @ SV27 ) ) @ identity_relation ) ) )
= $true )
| ( ( function @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(329,plain,
! [SV28: $i] :
( ( ( ~ ( member @ SV28 @ identity_relation ) )
= $true )
| ( ( ~ ! [SY120: $i] :
~ ~ ( ~ ( member @ SY120 @ universal_class )
| ( SV28
!= ( ordered_pair @ SY120 @ SY120 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[290]) ).
thf(330,plain,
! [SV28: $i] :
( ( ( ~ ~ ! [SY121: $i] :
~ ~ ( ~ ( member @ SY121 @ universal_class )
| ( SV28
!= ( ordered_pair @ SY121 @ SY121 ) ) ) )
= $true )
| ( ( member @ SV28 @ identity_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[291]) ).
thf(331,plain,
! [SV57: $i,SV30: $i] :
( ( ~ ( subclass @ SV30 @ SV57 )
| ! [SY149: $i] :
( ~ ( member @ SY149 @ SV30 )
| ( member @ SY149 @ SV57 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[292]) ).
thf(332,plain,
! [SV57: $i,SV30: $i] :
( ( ~ ! [SY150: $i] :
( ~ ( member @ SY150 @ SV30 )
| ( member @ SY150 @ SV57 ) )
| ( subclass @ SV30 @ SV57 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[293]) ).
thf(333,plain,
! [SV58: $i,SV31: $i] :
( ( ~ ( member @ ( ordered_pair @ SV31 @ SV58 ) @ successor_relation )
| ~ ( ~ ~ ( ~ ( member @ SV31 @ universal_class )
| ~ ( member @ SV58 @ universal_class ) )
| ( ( successor @ SV31 )
!= SV58 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[294]) ).
thf(334,plain,
! [SV58: $i,SV31: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( member @ SV31 @ universal_class )
| ~ ( member @ SV58 @ universal_class ) )
| ( ( successor @ SV31 )
!= SV58 ) )
| ( member @ ( ordered_pair @ SV31 @ SV58 ) @ successor_relation ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[295]) ).
thf(335,plain,
! [SV59: $i,SV32: $i] :
( ( ~ ( member @ SV32 @ ( power_class @ SV59 ) )
| ~ ( ~ ( member @ SV32 @ universal_class )
| ~ ( subclass @ SV32 @ SV59 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[296]) ).
thf(336,plain,
! [SV59: $i,SV32: $i] :
( ( ~ ~ ( ~ ( member @ SV32 @ universal_class )
| ~ ( subclass @ SV32 @ SV59 ) )
| ( member @ SV32 @ ( power_class @ SV59 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[297]) ).
thf(337,plain,
( ( ~ ( function @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[298]) ).
thf(338,plain,
( ( ~ ! [SY151: $i] :
( ~ ( member @ SY151 @ universal_class )
| ( SY151 = null_class )
| ( member @ ( apply @ sK3_SX0 @ SY151 ) @ SY151 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[298]) ).
thf(339,plain,
! [SV60: $i,SV33: $i,SV71: $i] :
( ( ~ ( ~ ( member @ SV71 @ ( intersection @ SV33 @ SV60 ) )
| ~ ( ~ ( member @ SV71 @ SV33 )
| ~ ( member @ SV71 @ SV60 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[299]) ).
thf(340,plain,
! [SV60: $i,SV33: $i,SV71: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV71 @ SV33 )
| ~ ( member @ SV71 @ SV60 ) )
| ( member @ SV71 @ ( intersection @ SV33 @ SV60 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[299]) ).
thf(341,plain,
! [SV77: $i,SV72: $i,SV61: $i,SV34: $i] :
( ( ~ ( ~ ( member @ ( ordered_pair @ SV34 @ SV61 ) @ ( cross_product @ SV72 @ SV77 ) )
| ~ ( ~ ( member @ SV34 @ SV72 )
| ~ ( member @ SV61 @ SV77 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV34 @ SV72 )
| ~ ( member @ SV61 @ SV77 ) )
| ( member @ ( ordered_pair @ SV34 @ SV61 ) @ ( cross_product @ SV72 @ SV77 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(342,plain,
( ( ~ ~ ( ~ ( member @ sK4_SX0 @ universal_class )
| ~ ( inductive @ sK4_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[301]) ).
thf(343,plain,
( ( ~ ! [SY155: $i] :
( ~ ( inductive @ SY155 )
| ( subclass @ sK4_SX0 @ SY155 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[301]) ).
thf(344,plain,
! [SV62: $i,SV35: $i] :
( ( ( ~ ( member @ SV35 @ universal_class )
| ~ ( function @ SV62 ) )
= $true )
| ( ( member @ ( image @ SV62 @ SV35 ) @ universal_class )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[302]) ).
thf(345,plain,
! [SV37: $i] :
( ( ( ~ ( inductive @ SV37 ) )
= $true )
| ( ( ~ ( ~ ( member @ null_class @ SV37 )
| ~ ( subclass @ ( image @ successor_relation @ SV37 ) @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[303]) ).
thf(346,plain,
! [SV37: $i] :
( ( ( ~ ~ ( ~ ( member @ null_class @ SV37 )
| ~ ( subclass @ ( image @ successor_relation @ SV37 ) @ SV37 ) ) )
= $true )
| ( ( inductive @ SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(347,plain,
! [SV63: $i,SV38: $i,SV73: $i] :
( ( ( member @ SV73 @ ( cross_product @ SV38 @ SV63 ) )
= $false )
| ( ( SV73
= ( ordered_pair @ ( first @ SV73 ) @ ( second @ SV73 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(348,plain,
! [SV64: $i,SV39: $i] :
( ( ~ ( member @ ( ordered_pair @ SV39 @ SV64 ) @ element_relation )
| ~ ( ~ ( member @ SV64 @ universal_class )
| ~ ( member @ SV39 @ SV64 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[306]) ).
thf(349,plain,
! [SV39: $i,SV64: $i] :
( ( ~ ~ ( ~ ( member @ SV64 @ universal_class )
| ~ ( member @ SV39 @ SV64 ) )
| ( member @ ( ordered_pair @ SV39 @ SV64 ) @ element_relation ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[307]) ).
thf(350,plain,
! [SV46: $i,SV15: $i] :
( ( ( SV15 != SV46 )
= $true )
| ( ( ~ ( ~ ( subclass @ SV15 @ SV46 )
| ~ ( subclass @ SV46 @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[308]) ).
thf(351,plain,
! [SV46: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ( subclass @ SV15 @ SV46 )
| ~ ( subclass @ SV46 @ SV15 ) ) )
= $true )
| ( ( SV15 = SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[309]) ).
thf(352,plain,
! [SV47: $i,SV16: $i,SV66: $i] :
( ( ~ ( member @ SV66 @ ( union @ SV16 @ SV47 ) )
| ( member @ SV66 @ SV16 )
| ( member @ SV66 @ SV47 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[310]) ).
thf(353,plain,
! [SV47: $i,SV16: $i,SV66: $i] :
( ( ~ ( ( member @ SV66 @ SV16 )
| ( member @ SV66 @ SV47 ) )
| ( member @ SV66 @ ( union @ SV16 @ SV47 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[311]) ).
thf(354,plain,
! [SV48: $i,SV17: $i] :
( ( ( ~ ( member @ SV17 @ ( sum_class @ SV48 ) ) )
= $true )
| ( ( ~ ! [SY138: $i] :
~ ~ ( ~ ( member @ SV17 @ SY138 )
| ~ ( member @ SY138 @ SV48 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[312]) ).
thf(355,plain,
! [SV48: $i,SV17: $i] :
( ( ( ~ ~ ! [SY139: $i] :
~ ~ ( ~ ( member @ SV17 @ SY139 )
| ~ ( member @ SY139 @ SV48 ) ) )
= $true )
| ( ( member @ SV17 @ ( sum_class @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(356,plain,
! [SV74: $i,SV67: $i,SV49: $i,SV18: $i] :
( ( ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( flip @ SV74 ) )
| ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV49 @ SV18 ) @ SV67 ) @ SV74 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[314]) ).
thf(357,plain,
! [SV74: $i,SV67: $i,SV49: $i,SV18: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV49 @ SV18 ) @ SV67 ) @ SV74 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( flip @ SV74 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[314]) ).
thf(358,plain,
! [SV19: $i,SV75: $i,SV68: $i,SV50: $i] :
( ( ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( rotate @ SV19 ) )
| ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV68 @ SV75 ) @ SV50 ) @ SV19 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[315]) ).
thf(359,plain,
! [SV19: $i,SV75: $i,SV68: $i,SV50: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV68 @ SV75 ) @ SV50 ) @ SV19 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( rotate @ SV19 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[315]) ).
thf(360,plain,
! [SV51: $i,SV20: $i] :
( ( ( ~ ( disjoint @ SV20 @ SV51 ) )
= $true )
| ( ( ! [SY144: $i] :
~ ~ ( ~ ( member @ SY144 @ SV20 )
| ~ ( member @ SY144 @ SV51 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[316]) ).
thf(361,plain,
! [SV51: $i,SV20: $i] :
( ( ( ~ ! [SY145: $i] :
~ ~ ( ~ ( member @ SY145 @ SV20 )
| ~ ( member @ SY145 @ SV51 ) ) )
= $true )
| ( ( disjoint @ SV20 @ SV51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[317]) ).
thf(362,plain,
! [SV21: $i,SV52: $i] :
( ( ( ~ ( member @ SV52 @ ( domain_of @ SV21 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ SV52 @ universal_class )
| ~ ( ( ( restrict @ SV21 @ ( singleton @ SV52 ) @ universal_class )
!= null_class ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(363,plain,
! [SV21: $i,SV52: $i] :
( ( ( ~ ~ ( ~ ( member @ SV52 @ universal_class )
| ~ ( ( ( restrict @ SV21 @ ( singleton @ SV52 ) @ universal_class )
!= null_class ) ) ) )
= $true )
| ( ( member @ SV52 @ ( domain_of @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[319]) ).
thf(364,plain,
! [SV22: $i,SV53: $i,SV76: $i,SV69: $i] :
( ( ~ ( ~ ( member @ ( ordered_pair @ SV69 @ SV76 ) @ ( compose @ SV53 @ SV22 ) )
| ~ ( ~ ( member @ SV69 @ universal_class )
| ~ ( member @ SV76 @ ( image @ SV53 @ ( image @ SV22 @ ( singleton @ SV69 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[320]) ).
thf(365,plain,
! [SV22: $i,SV53: $i,SV76: $i,SV69: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV69 @ universal_class )
| ~ ( member @ SV76 @ ( image @ SV53 @ ( image @ SV22 @ ( singleton @ SV69 ) ) ) ) )
| ( member @ ( ordered_pair @ SV69 @ SV76 ) @ ( compose @ SV53 @ SV22 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[320]) ).
thf(366,plain,
! [SV70: $i,SV54: $i,SV23: $i] :
( ( ~ ( member @ SV23 @ ( unordered_pair @ SV54 @ SV70 ) )
| ~ ( ~ ( member @ SV23 @ universal_class )
| ~ ( ( SV23 = SV54 )
| ( SV23 = SV70 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[321]) ).
thf(367,plain,
! [SV70: $i,SV54: $i,SV23: $i] :
( ( ~ ~ ( ~ ( member @ SV23 @ universal_class )
| ~ ( ( SV23 = SV54 )
| ( SV23 = SV70 ) ) )
| ( member @ SV23 @ ( unordered_pair @ SV54 @ SV70 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[322]) ).
thf(368,plain,
! [SV55: $i,SV24: $i] :
( ( ( ~ ( member @ SV24 @ universal_class ) )
= $true )
| ( ( ~ ( member @ SV55 @ universal_class ) )
= $true )
| ( ( ~ ( ( ( first @ ( ordered_pair @ SV24 @ SV55 ) )
!= SV24 )
| ( ( second @ ( ordered_pair @ SV24 @ SV55 ) )
!= SV55 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[323]) ).
thf(369,plain,
! [SV25: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK5_SY118 @ SV25 ) @ universal_class )
| ~ ( member @ ( sK5_SY118 @ SV25 ) @ SV25 ) )
| ~ ( disjoint @ ( sK5_SY118 @ SV25 ) @ SV25 ) ) )
= $false )
| ( ( SV25 = null_class )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[324]) ).
thf(370,plain,
! [SV26: $i,SV56: $i] :
( ( ( ~ ( member @ SV56 @ ( complement @ SV26 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ SV56 @ universal_class )
| ~ ~ ( member @ SV56 @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(371,plain,
! [SV26: $i,SV56: $i] :
( ( ( ~ ~ ( ~ ( member @ SV56 @ universal_class )
| ~ ~ ( member @ SV56 @ SV26 ) ) )
= $true )
| ( ( member @ SV56 @ ( complement @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[326]) ).
thf(372,plain,
! [SV27: $i] :
( ( ( function @ SV27 )
= $false )
| ( ( ~ ( ~ ( subclass @ SV27 @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ SV27 @ ( inverse @ SV27 ) ) @ identity_relation ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(373,plain,
! [SV27: $i] :
( ( ( ~ ( ~ ( subclass @ SV27 @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ SV27 @ ( inverse @ SV27 ) ) @ identity_relation ) ) )
= $false )
| ( ( function @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(374,plain,
! [SV28: $i] :
( ( ( member @ SV28 @ identity_relation )
= $false )
| ( ( ~ ! [SY120: $i] :
~ ~ ( ~ ( member @ SY120 @ universal_class )
| ( SV28
!= ( ordered_pair @ SY120 @ SY120 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(375,plain,
! [SV28: $i] :
( ( ( ~ ! [SY121: $i] :
~ ~ ( ~ ( member @ SY121 @ universal_class )
| ( SV28
!= ( ordered_pair @ SY121 @ SY121 ) ) ) )
= $false )
| ( ( member @ SV28 @ identity_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(376,plain,
! [SV57: $i,SV30: $i] :
( ( ( ~ ( subclass @ SV30 @ SV57 ) )
= $true )
| ( ( ! [SY149: $i] :
( ~ ( member @ SY149 @ SV30 )
| ( member @ SY149 @ SV57 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[331]) ).
thf(377,plain,
! [SV57: $i,SV30: $i] :
( ( ( ~ ! [SY150: $i] :
( ~ ( member @ SY150 @ SV30 )
| ( member @ SY150 @ SV57 ) ) )
= $true )
| ( ( subclass @ SV30 @ SV57 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[332]) ).
thf(378,plain,
! [SV58: $i,SV31: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV31 @ SV58 ) @ successor_relation ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( member @ SV31 @ universal_class )
| ~ ( member @ SV58 @ universal_class ) )
| ( ( successor @ SV31 )
!= SV58 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(379,plain,
! [SV58: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV31 @ universal_class )
| ~ ( member @ SV58 @ universal_class ) )
| ( ( successor @ SV31 )
!= SV58 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ SV31 @ SV58 ) @ successor_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[334]) ).
thf(380,plain,
! [SV59: $i,SV32: $i] :
( ( ( ~ ( member @ SV32 @ ( power_class @ SV59 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ SV32 @ universal_class )
| ~ ( subclass @ SV32 @ SV59 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[335]) ).
thf(381,plain,
! [SV59: $i,SV32: $i] :
( ( ( ~ ~ ( ~ ( member @ SV32 @ universal_class )
| ~ ( subclass @ SV32 @ SV59 ) ) )
= $true )
| ( ( member @ SV32 @ ( power_class @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(382,plain,
( ( function @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[337]) ).
thf(383,plain,
( ( ! [SY151: $i] :
( ~ ( member @ SY151 @ universal_class )
| ( SY151 = null_class )
| ( member @ ( apply @ sK3_SX0 @ SY151 ) @ SY151 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[338]) ).
thf(384,plain,
! [SV60: $i,SV33: $i,SV71: $i] :
( ( ~ ( member @ SV71 @ ( intersection @ SV33 @ SV60 ) )
| ~ ( ~ ( member @ SV71 @ SV33 )
| ~ ( member @ SV71 @ SV60 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[339]) ).
thf(385,plain,
! [SV60: $i,SV33: $i,SV71: $i] :
( ( ~ ~ ( ~ ( member @ SV71 @ SV33 )
| ~ ( member @ SV71 @ SV60 ) )
| ( member @ SV71 @ ( intersection @ SV33 @ SV60 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[340]) ).
thf(386,plain,
! [SV77: $i,SV72: $i,SV61: $i,SV34: $i] :
( ( ~ ( ~ ( member @ ( ordered_pair @ SV34 @ SV61 ) @ ( cross_product @ SV72 @ SV77 ) )
| ~ ( ~ ( member @ SV34 @ SV72 )
| ~ ( member @ SV61 @ SV77 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[341]) ).
thf(387,plain,
! [SV77: $i,SV61: $i,SV72: $i,SV34: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV34 @ SV72 )
| ~ ( member @ SV61 @ SV77 ) )
| ( member @ ( ordered_pair @ SV34 @ SV61 ) @ ( cross_product @ SV72 @ SV77 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[341]) ).
thf(388,plain,
( ( ~ ( ~ ( member @ sK4_SX0 @ universal_class )
| ~ ( inductive @ sK4_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[342]) ).
thf(389,plain,
( ( ! [SY155: $i] :
( ~ ( inductive @ SY155 )
| ( subclass @ sK4_SX0 @ SY155 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[343]) ).
thf(390,plain,
! [SV62: $i,SV35: $i] :
( ( ( ~ ( member @ SV35 @ universal_class ) )
= $true )
| ( ( ~ ( function @ SV62 ) )
= $true )
| ( ( member @ ( image @ SV62 @ SV35 ) @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[344]) ).
thf(391,plain,
! [SV37: $i] :
( ( ( inductive @ SV37 )
= $false )
| ( ( ~ ( ~ ( member @ null_class @ SV37 )
| ~ ( subclass @ ( image @ successor_relation @ SV37 ) @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(392,plain,
! [SV37: $i] :
( ( ( ~ ( ~ ( member @ null_class @ SV37 )
| ~ ( subclass @ ( image @ successor_relation @ SV37 ) @ SV37 ) ) )
= $false )
| ( ( inductive @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(393,plain,
! [SV64: $i,SV39: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV39 @ SV64 ) @ element_relation ) )
= $true )
| ( ( ~ ( ~ ( member @ SV64 @ universal_class )
| ~ ( member @ SV39 @ SV64 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[348]) ).
thf(394,plain,
! [SV39: $i,SV64: $i] :
( ( ( ~ ~ ( ~ ( member @ SV64 @ universal_class )
| ~ ( member @ SV39 @ SV64 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ SV39 @ SV64 ) @ element_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(395,plain,
! [SV46: $i,SV15: $i] :
( ( ( SV15 = SV46 )
= $false )
| ( ( ~ ( ~ ( subclass @ SV15 @ SV46 )
| ~ ( subclass @ SV46 @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(396,plain,
! [SV46: $i,SV15: $i] :
( ( ( ~ ( ~ ( subclass @ SV15 @ SV46 )
| ~ ( subclass @ SV46 @ SV15 ) ) )
= $false )
| ( ( SV15 = SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(397,plain,
! [SV47: $i,SV16: $i,SV66: $i] :
( ( ( ~ ( member @ SV66 @ ( union @ SV16 @ SV47 ) ) )
= $true )
| ( ( ( member @ SV66 @ SV16 )
| ( member @ SV66 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[352]) ).
thf(398,plain,
! [SV47: $i,SV16: $i,SV66: $i] :
( ( ( ~ ( ( member @ SV66 @ SV16 )
| ( member @ SV66 @ SV47 ) ) )
= $true )
| ( ( member @ SV66 @ ( union @ SV16 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[353]) ).
thf(399,plain,
! [SV48: $i,SV17: $i] :
( ( ( member @ SV17 @ ( sum_class @ SV48 ) )
= $false )
| ( ( ~ ! [SY138: $i] :
~ ~ ( ~ ( member @ SV17 @ SY138 )
| ~ ( member @ SY138 @ SV48 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[354]) ).
thf(400,plain,
! [SV48: $i,SV17: $i] :
( ( ( ~ ! [SY139: $i] :
~ ~ ( ~ ( member @ SV17 @ SY139 )
| ~ ( member @ SY139 @ SV48 ) ) )
= $false )
| ( ( member @ SV17 @ ( sum_class @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(401,plain,
! [SV74: $i,SV67: $i,SV49: $i,SV18: $i] :
( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( flip @ SV74 ) )
| ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV49 @ SV18 ) @ SV67 ) @ SV74 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[356]) ).
thf(402,plain,
! [SV74: $i,SV67: $i,SV49: $i,SV18: $i] :
( ( ~ ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV49 @ SV18 ) @ SV67 ) @ SV74 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( flip @ SV74 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[357]) ).
thf(403,plain,
! [SV19: $i,SV75: $i,SV68: $i,SV50: $i] :
( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( rotate @ SV19 ) )
| ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV68 @ SV75 ) @ SV50 ) @ SV19 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[358]) ).
thf(404,plain,
! [SV19: $i,SV75: $i,SV68: $i,SV50: $i] :
( ( ~ ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV68 @ SV75 ) @ SV50 ) @ SV19 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( rotate @ SV19 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[359]) ).
thf(405,plain,
! [SV51: $i,SV20: $i] :
( ( ( disjoint @ SV20 @ SV51 )
= $false )
| ( ( ! [SY144: $i] :
~ ~ ( ~ ( member @ SY144 @ SV20 )
| ~ ( member @ SY144 @ SV51 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(406,plain,
! [SV51: $i,SV20: $i] :
( ( ( ! [SY145: $i] :
~ ~ ( ~ ( member @ SY145 @ SV20 )
| ~ ( member @ SY145 @ SV51 ) ) )
= $false )
| ( ( disjoint @ SV20 @ SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(407,plain,
! [SV21: $i,SV52: $i] :
( ( ( member @ SV52 @ ( domain_of @ SV21 ) )
= $false )
| ( ( ~ ( ~ ( member @ SV52 @ universal_class )
| ~ ( ( ( restrict @ SV21 @ ( singleton @ SV52 ) @ universal_class )
!= null_class ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(408,plain,
! [SV21: $i,SV52: $i] :
( ( ( ~ ( ~ ( member @ SV52 @ universal_class )
| ~ ( ( ( restrict @ SV21 @ ( singleton @ SV52 ) @ universal_class )
!= null_class ) ) ) )
= $false )
| ( ( member @ SV52 @ ( domain_of @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(409,plain,
! [SV22: $i,SV53: $i,SV76: $i,SV69: $i] :
( ( ~ ( member @ ( ordered_pair @ SV69 @ SV76 ) @ ( compose @ SV53 @ SV22 ) )
| ~ ( ~ ( member @ SV69 @ universal_class )
| ~ ( member @ SV76 @ ( image @ SV53 @ ( image @ SV22 @ ( singleton @ SV69 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[364]) ).
thf(410,plain,
! [SV22: $i,SV53: $i,SV76: $i,SV69: $i] :
( ( ~ ~ ( ~ ( member @ SV69 @ universal_class )
| ~ ( member @ SV76 @ ( image @ SV53 @ ( image @ SV22 @ ( singleton @ SV69 ) ) ) ) )
| ( member @ ( ordered_pair @ SV69 @ SV76 ) @ ( compose @ SV53 @ SV22 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[365]) ).
thf(411,plain,
! [SV70: $i,SV54: $i,SV23: $i] :
( ( ( ~ ( member @ SV23 @ ( unordered_pair @ SV54 @ SV70 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ SV23 @ universal_class )
| ~ ( ( SV23 = SV54 )
| ( SV23 = SV70 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[366]) ).
thf(412,plain,
! [SV70: $i,SV54: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( member @ SV23 @ universal_class )
| ~ ( ( SV23 = SV54 )
| ( SV23 = SV70 ) ) ) )
= $true )
| ( ( member @ SV23 @ ( unordered_pair @ SV54 @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[367]) ).
thf(413,plain,
! [SV55: $i,SV24: $i] :
( ( ( member @ SV24 @ universal_class )
= $false )
| ( ( ~ ( member @ SV55 @ universal_class ) )
= $true )
| ( ( ~ ( ( ( first @ ( ordered_pair @ SV24 @ SV55 ) )
!= SV24 )
| ( ( second @ ( ordered_pair @ SV24 @ SV55 ) )
!= SV55 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(414,plain,
! [SV25: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK5_SY118 @ SV25 ) @ universal_class )
| ~ ( member @ ( sK5_SY118 @ SV25 ) @ SV25 ) )
| ~ ( disjoint @ ( sK5_SY118 @ SV25 ) @ SV25 ) ) )
= $true )
| ( ( SV25 = null_class )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[369]) ).
thf(415,plain,
! [SV26: $i,SV56: $i] :
( ( ( member @ SV56 @ ( complement @ SV26 ) )
= $false )
| ( ( ~ ( ~ ( member @ SV56 @ universal_class )
| ~ ~ ( member @ SV56 @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(416,plain,
! [SV26: $i,SV56: $i] :
( ( ( ~ ( ~ ( member @ SV56 @ universal_class )
| ~ ~ ( member @ SV56 @ SV26 ) ) )
= $false )
| ( ( member @ SV56 @ ( complement @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[371]) ).
thf(417,plain,
! [SV27: $i] :
( ( ( ~ ( subclass @ SV27 @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ SV27 @ ( inverse @ SV27 ) ) @ identity_relation ) )
= $false )
| ( ( function @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[372]) ).
thf(418,plain,
! [SV27: $i] :
( ( ( ~ ( subclass @ SV27 @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ SV27 @ ( inverse @ SV27 ) ) @ identity_relation ) )
= $true )
| ( ( function @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[373]) ).
thf(419,plain,
! [SV28: $i] :
( ( ( ! [SY120: $i] :
~ ~ ( ~ ( member @ SY120 @ universal_class )
| ( SV28
!= ( ordered_pair @ SY120 @ SY120 ) ) ) )
= $false )
| ( ( member @ SV28 @ identity_relation )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(420,plain,
! [SV28: $i] :
( ( ( ! [SY121: $i] :
~ ~ ( ~ ( member @ SY121 @ universal_class )
| ( SV28
!= ( ordered_pair @ SY121 @ SY121 ) ) ) )
= $true )
| ( ( member @ SV28 @ identity_relation )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[375]) ).
thf(421,plain,
! [SV57: $i,SV30: $i] :
( ( ( subclass @ SV30 @ SV57 )
= $false )
| ( ( ! [SY149: $i] :
( ~ ( member @ SY149 @ SV30 )
| ( member @ SY149 @ SV57 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(422,plain,
! [SV57: $i,SV30: $i] :
( ( ( ! [SY150: $i] :
( ~ ( member @ SY150 @ SV30 )
| ( member @ SY150 @ SV57 ) ) )
= $false )
| ( ( subclass @ SV30 @ SV57 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(423,plain,
! [SV58: $i,SV31: $i] :
( ( ( member @ ( ordered_pair @ SV31 @ SV58 ) @ successor_relation )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( member @ SV31 @ universal_class )
| ~ ( member @ SV58 @ universal_class ) )
| ( ( successor @ SV31 )
!= SV58 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(424,plain,
! [SV58: $i,SV31: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ SV31 @ universal_class )
| ~ ( member @ SV58 @ universal_class ) )
| ( ( successor @ SV31 )
!= SV58 ) ) )
= $false )
| ( ( member @ ( ordered_pair @ SV31 @ SV58 ) @ successor_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(425,plain,
! [SV59: $i,SV32: $i] :
( ( ( member @ SV32 @ ( power_class @ SV59 ) )
= $false )
| ( ( ~ ( ~ ( member @ SV32 @ universal_class )
| ~ ( subclass @ SV32 @ SV59 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(426,plain,
! [SV59: $i,SV32: $i] :
( ( ( ~ ( ~ ( member @ SV32 @ universal_class )
| ~ ( subclass @ SV32 @ SV59 ) ) )
= $false )
| ( ( member @ SV32 @ ( power_class @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(427,plain,
! [SV78: $i] :
( ( ~ ( member @ SV78 @ universal_class )
| ( SV78 = null_class )
| ( member @ ( apply @ sK3_SX0 @ SV78 ) @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(428,plain,
! [SV60: $i,SV33: $i,SV71: $i] :
( ( ( ~ ( member @ SV71 @ ( intersection @ SV33 @ SV60 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ SV71 @ SV33 )
| ~ ( member @ SV71 @ SV60 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[384]) ).
thf(429,plain,
! [SV60: $i,SV33: $i,SV71: $i] :
( ( ( ~ ~ ( ~ ( member @ SV71 @ SV33 )
| ~ ( member @ SV71 @ SV60 ) ) )
= $true )
| ( ( member @ SV71 @ ( intersection @ SV33 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[385]) ).
thf(430,plain,
! [SV77: $i,SV72: $i,SV61: $i,SV34: $i] :
( ( ~ ( member @ ( ordered_pair @ SV34 @ SV61 ) @ ( cross_product @ SV72 @ SV77 ) )
| ~ ( ~ ( member @ SV34 @ SV72 )
| ~ ( member @ SV61 @ SV77 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[386]) ).
thf(431,plain,
! [SV77: $i,SV61: $i,SV72: $i,SV34: $i] :
( ( ~ ~ ( ~ ( member @ SV34 @ SV72 )
| ~ ( member @ SV61 @ SV77 ) )
| ( member @ ( ordered_pair @ SV34 @ SV61 ) @ ( cross_product @ SV72 @ SV77 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[387]) ).
thf(432,plain,
( ( ~ ( member @ sK4_SX0 @ universal_class )
| ~ ( inductive @ sK4_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(433,plain,
! [SV79: $i] :
( ( ~ ( inductive @ SV79 )
| ( subclass @ sK4_SX0 @ SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(434,plain,
! [SV62: $i,SV35: $i] :
( ( ( member @ SV35 @ universal_class )
= $false )
| ( ( ~ ( function @ SV62 ) )
= $true )
| ( ( member @ ( image @ SV62 @ SV35 ) @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(435,plain,
! [SV37: $i] :
( ( ( ~ ( member @ null_class @ SV37 )
| ~ ( subclass @ ( image @ successor_relation @ SV37 ) @ SV37 ) )
= $false )
| ( ( inductive @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[391]) ).
thf(436,plain,
! [SV37: $i] :
( ( ( ~ ( member @ null_class @ SV37 )
| ~ ( subclass @ ( image @ successor_relation @ SV37 ) @ SV37 ) )
= $true )
| ( ( inductive @ SV37 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[392]) ).
thf(437,plain,
! [SV64: $i,SV39: $i] :
( ( ( member @ ( ordered_pair @ SV39 @ SV64 ) @ element_relation )
= $false )
| ( ( ~ ( ~ ( member @ SV64 @ universal_class )
| ~ ( member @ SV39 @ SV64 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(438,plain,
! [SV39: $i,SV64: $i] :
( ( ( ~ ( ~ ( member @ SV64 @ universal_class )
| ~ ( member @ SV39 @ SV64 ) ) )
= $false )
| ( ( member @ ( ordered_pair @ SV39 @ SV64 ) @ element_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[394]) ).
thf(439,plain,
! [SV46: $i,SV15: $i] :
( ( ( ~ ( subclass @ SV15 @ SV46 )
| ~ ( subclass @ SV46 @ SV15 ) )
= $false )
| ( ( SV15 = SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(440,plain,
! [SV46: $i,SV15: $i] :
( ( ( ~ ( subclass @ SV15 @ SV46 )
| ~ ( subclass @ SV46 @ SV15 ) )
= $true )
| ( ( SV15 = SV46 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[396]) ).
thf(441,plain,
! [SV47: $i,SV16: $i,SV66: $i] :
( ( ( member @ SV66 @ ( union @ SV16 @ SV47 ) )
= $false )
| ( ( ( member @ SV66 @ SV16 )
| ( member @ SV66 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(442,plain,
! [SV47: $i,SV16: $i,SV66: $i] :
( ( ( ( member @ SV66 @ SV16 )
| ( member @ SV66 @ SV47 ) )
= $false )
| ( ( member @ SV66 @ ( union @ SV16 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(443,plain,
! [SV48: $i,SV17: $i] :
( ( ( ! [SY138: $i] :
~ ~ ( ~ ( member @ SV17 @ SY138 )
| ~ ( member @ SY138 @ SV48 ) ) )
= $false )
| ( ( member @ SV17 @ ( sum_class @ SV48 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(444,plain,
! [SV48: $i,SV17: $i] :
( ( ( ! [SY139: $i] :
~ ~ ( ~ ( member @ SV17 @ SY139 )
| ~ ( member @ SY139 @ SV48 ) ) )
= $true )
| ( ( member @ SV17 @ ( sum_class @ SV48 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[400]) ).
thf(445,plain,
! [SV74: $i,SV67: $i,SV49: $i,SV18: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( flip @ SV74 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV49 @ SV18 ) @ SV67 ) @ SV74 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[401]) ).
thf(446,plain,
! [SV74: $i,SV67: $i,SV49: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV49 @ SV18 ) @ SV67 ) @ SV74 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( flip @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[402]) ).
thf(447,plain,
! [SV19: $i,SV75: $i,SV68: $i,SV50: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( rotate @ SV19 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV68 @ SV75 ) @ SV50 ) @ SV19 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[403]) ).
thf(448,plain,
! [SV19: $i,SV75: $i,SV68: $i,SV50: $i] :
( ( ( ~ ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV68 @ SV75 ) @ SV50 ) @ SV19 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( rotate @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[404]) ).
thf(449,plain,
! [SV51: $i,SV20: $i,SV80: $i] :
( ( ( ~ ~ ( ~ ( member @ SV80 @ SV20 )
| ~ ( member @ SV80 @ SV51 ) ) )
= $true )
| ( ( disjoint @ SV20 @ SV51 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(450,plain,
! [SV20: $i,SV51: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK6_SY145 @ SV51 @ SV20 ) @ SV20 )
| ~ ( member @ ( sK6_SY145 @ SV51 @ SV20 ) @ SV51 ) ) )
= $false )
| ( ( disjoint @ SV20 @ SV51 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[406]) ).
thf(451,plain,
! [SV21: $i,SV52: $i] :
( ( ( ~ ( member @ SV52 @ universal_class )
| ~ ( ( ( restrict @ SV21 @ ( singleton @ SV52 ) @ universal_class )
!= null_class ) ) )
= $false )
| ( ( member @ SV52 @ ( domain_of @ SV21 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(452,plain,
! [SV21: $i,SV52: $i] :
( ( ( ~ ( member @ SV52 @ universal_class )
| ~ ( ( ( restrict @ SV21 @ ( singleton @ SV52 ) @ universal_class )
!= null_class ) ) )
= $true )
| ( ( member @ SV52 @ ( domain_of @ SV21 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[408]) ).
thf(453,plain,
! [SV22: $i,SV53: $i,SV76: $i,SV69: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV69 @ SV76 ) @ ( compose @ SV53 @ SV22 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ SV69 @ universal_class )
| ~ ( member @ SV76 @ ( image @ SV53 @ ( image @ SV22 @ ( singleton @ SV69 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[409]) ).
thf(454,plain,
! [SV22: $i,SV53: $i,SV76: $i,SV69: $i] :
( ( ( ~ ~ ( ~ ( member @ SV69 @ universal_class )
| ~ ( member @ SV76 @ ( image @ SV53 @ ( image @ SV22 @ ( singleton @ SV69 ) ) ) ) ) )
= $true )
| ( ( member @ ( ordered_pair @ SV69 @ SV76 ) @ ( compose @ SV53 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[410]) ).
thf(455,plain,
! [SV70: $i,SV54: $i,SV23: $i] :
( ( ( member @ SV23 @ ( unordered_pair @ SV54 @ SV70 ) )
= $false )
| ( ( ~ ( ~ ( member @ SV23 @ universal_class )
| ~ ( ( SV23 = SV54 )
| ( SV23 = SV70 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[411]) ).
thf(456,plain,
! [SV70: $i,SV54: $i,SV23: $i] :
( ( ( ~ ( ~ ( member @ SV23 @ universal_class )
| ~ ( ( SV23 = SV54 )
| ( SV23 = SV70 ) ) ) )
= $false )
| ( ( member @ SV23 @ ( unordered_pair @ SV54 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[412]) ).
thf(457,plain,
! [SV24: $i,SV55: $i] :
( ( ( member @ SV55 @ universal_class )
= $false )
| ( ( member @ SV24 @ universal_class )
= $false )
| ( ( ~ ( ( ( first @ ( ordered_pair @ SV24 @ SV55 ) )
!= SV24 )
| ( ( second @ ( ordered_pair @ SV24 @ SV55 ) )
!= SV55 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[413]) ).
thf(458,plain,
! [SV25: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK5_SY118 @ SV25 ) @ universal_class )
| ~ ( member @ ( sK5_SY118 @ SV25 ) @ SV25 ) )
| ~ ( disjoint @ ( sK5_SY118 @ SV25 ) @ SV25 ) )
= $false )
| ( ( SV25 = null_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(459,plain,
! [SV26: $i,SV56: $i] :
( ( ( ~ ( member @ SV56 @ universal_class )
| ~ ~ ( member @ SV56 @ SV26 ) )
= $false )
| ( ( member @ SV56 @ ( complement @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(460,plain,
! [SV26: $i,SV56: $i] :
( ( ( ~ ( member @ SV56 @ universal_class )
| ~ ~ ( member @ SV56 @ SV26 ) )
= $true )
| ( ( member @ SV56 @ ( complement @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[416]) ).
thf(461,plain,
! [SV27: $i] :
( ( ( ~ ( subclass @ SV27 @ ( cross_product @ universal_class @ universal_class ) ) )
= $false )
| ( ( function @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[417]) ).
thf(462,plain,
! [SV27: $i] :
( ( ( ~ ( subclass @ ( compose @ SV27 @ ( inverse @ SV27 ) ) @ identity_relation ) )
= $false )
| ( ( function @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[417]) ).
thf(463,plain,
! [SV27: $i] :
( ( ( ~ ( subclass @ SV27 @ ( cross_product @ universal_class @ universal_class ) ) )
= $true )
| ( ( ~ ( subclass @ ( compose @ SV27 @ ( inverse @ SV27 ) ) @ identity_relation ) )
= $true )
| ( ( function @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[418]) ).
thf(464,plain,
! [SV28: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK7_SY120 @ SV28 ) @ universal_class )
| ( SV28
!= ( ordered_pair @ ( sK7_SY120 @ SV28 ) @ ( sK7_SY120 @ SV28 ) ) ) ) )
= $false )
| ( ( member @ SV28 @ identity_relation )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[419]) ).
thf(465,plain,
! [SV28: $i,SV81: $i] :
( ( ( ~ ~ ( ~ ( member @ SV81 @ universal_class )
| ( SV28
!= ( ordered_pair @ SV81 @ SV81 ) ) ) )
= $true )
| ( ( member @ SV28 @ identity_relation )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(466,plain,
! [SV57: $i,SV30: $i,SV82: $i] :
( ( ( ~ ( member @ SV82 @ SV30 )
| ( member @ SV82 @ SV57 ) )
= $true )
| ( ( subclass @ SV30 @ SV57 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(467,plain,
! [SV30: $i,SV57: $i] :
( ( ( ~ ( member @ ( sK8_SY150 @ SV57 @ SV30 ) @ SV30 )
| ( member @ ( sK8_SY150 @ SV57 @ SV30 ) @ SV57 ) )
= $false )
| ( ( subclass @ SV30 @ SV57 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[422]) ).
thf(468,plain,
! [SV58: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ( member @ SV31 @ universal_class )
| ~ ( member @ SV58 @ universal_class ) )
| ( ( successor @ SV31 )
!= SV58 ) )
= $false )
| ( ( member @ ( ordered_pair @ SV31 @ SV58 ) @ successor_relation )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[423]) ).
thf(469,plain,
! [SV58: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ( member @ SV31 @ universal_class )
| ~ ( member @ SV58 @ universal_class ) )
| ( ( successor @ SV31 )
!= SV58 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV31 @ SV58 ) @ successor_relation )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[424]) ).
thf(470,plain,
! [SV59: $i,SV32: $i] :
( ( ( ~ ( member @ SV32 @ universal_class )
| ~ ( subclass @ SV32 @ SV59 ) )
= $false )
| ( ( member @ SV32 @ ( power_class @ SV59 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(471,plain,
! [SV59: $i,SV32: $i] :
( ( ( ~ ( member @ SV32 @ universal_class )
| ~ ( subclass @ SV32 @ SV59 ) )
= $true )
| ( ( member @ SV32 @ ( power_class @ SV59 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[426]) ).
thf(472,plain,
! [SV78: $i] :
( ( ( ~ ( member @ SV78 @ universal_class ) )
= $true )
| ( ( ( SV78 = null_class )
| ( member @ ( apply @ sK3_SX0 @ SV78 ) @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[427]) ).
thf(473,plain,
! [SV60: $i,SV33: $i,SV71: $i] :
( ( ( member @ SV71 @ ( intersection @ SV33 @ SV60 ) )
= $false )
| ( ( ~ ( ~ ( member @ SV71 @ SV33 )
| ~ ( member @ SV71 @ SV60 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[428]) ).
thf(474,plain,
! [SV60: $i,SV33: $i,SV71: $i] :
( ( ( ~ ( ~ ( member @ SV71 @ SV33 )
| ~ ( member @ SV71 @ SV60 ) ) )
= $false )
| ( ( member @ SV71 @ ( intersection @ SV33 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[429]) ).
thf(475,plain,
! [SV77: $i,SV72: $i,SV61: $i,SV34: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV34 @ SV61 ) @ ( cross_product @ SV72 @ SV77 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ SV34 @ SV72 )
| ~ ( member @ SV61 @ SV77 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[430]) ).
thf(476,plain,
! [SV77: $i,SV61: $i,SV72: $i,SV34: $i] :
( ( ( ~ ~ ( ~ ( member @ SV34 @ SV72 )
| ~ ( member @ SV61 @ SV77 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ SV34 @ SV61 ) @ ( cross_product @ SV72 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[431]) ).
thf(477,plain,
( ( ~ ( member @ sK4_SX0 @ universal_class ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[432]) ).
thf(478,plain,
( ( ~ ( inductive @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[432]) ).
thf(479,plain,
! [SV79: $i] :
( ( ( ~ ( inductive @ SV79 ) )
= $true )
| ( ( subclass @ sK4_SX0 @ SV79 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[433]) ).
thf(480,plain,
! [SV35: $i,SV62: $i] :
( ( ( function @ SV62 )
= $false )
| ( ( member @ SV35 @ universal_class )
= $false )
| ( ( member @ ( image @ SV62 @ SV35 ) @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[434]) ).
thf(481,plain,
! [SV37: $i] :
( ( ( ~ ( member @ null_class @ SV37 ) )
= $false )
| ( ( inductive @ SV37 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[435]) ).
thf(482,plain,
! [SV37: $i] :
( ( ( ~ ( subclass @ ( image @ successor_relation @ SV37 ) @ SV37 ) )
= $false )
| ( ( inductive @ SV37 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[435]) ).
thf(483,plain,
! [SV37: $i] :
( ( ( ~ ( member @ null_class @ SV37 ) )
= $true )
| ( ( ~ ( subclass @ ( image @ successor_relation @ SV37 ) @ SV37 ) )
= $true )
| ( ( inductive @ SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[436]) ).
thf(484,plain,
! [SV39: $i,SV64: $i] :
( ( ( ~ ( member @ SV64 @ universal_class )
| ~ ( member @ SV39 @ SV64 ) )
= $false )
| ( ( member @ ( ordered_pair @ SV39 @ SV64 ) @ element_relation )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(485,plain,
! [SV39: $i,SV64: $i] :
( ( ( ~ ( member @ SV64 @ universal_class )
| ~ ( member @ SV39 @ SV64 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV39 @ SV64 ) @ element_relation )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[438]) ).
thf(486,plain,
! [SV46: $i,SV15: $i] :
( ( ( ~ ( subclass @ SV15 @ SV46 ) )
= $false )
| ( ( SV15 = SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[439]) ).
thf(487,plain,
! [SV15: $i,SV46: $i] :
( ( ( ~ ( subclass @ SV46 @ SV15 ) )
= $false )
| ( ( SV15 = SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[439]) ).
thf(488,plain,
! [SV46: $i,SV15: $i] :
( ( ( ~ ( subclass @ SV15 @ SV46 ) )
= $true )
| ( ( ~ ( subclass @ SV46 @ SV15 ) )
= $true )
| ( ( SV15 = SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[440]) ).
thf(489,plain,
! [SV47: $i,SV16: $i,SV66: $i] :
( ( ( member @ SV66 @ SV16 )
= $true )
| ( ( member @ SV66 @ SV47 )
= $true )
| ( ( member @ SV66 @ ( union @ SV16 @ SV47 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[441]) ).
thf(490,plain,
! [SV47: $i,SV16: $i,SV66: $i] :
( ( ( member @ SV66 @ SV16 )
= $false )
| ( ( member @ SV66 @ ( union @ SV16 @ SV47 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[442]) ).
thf(491,plain,
! [SV16: $i,SV47: $i,SV66: $i] :
( ( ( member @ SV66 @ SV47 )
= $false )
| ( ( member @ SV66 @ ( union @ SV16 @ SV47 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[442]) ).
thf(492,plain,
! [SV48: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( member @ SV17 @ ( sK9_SY138 @ SV48 @ SV17 ) )
| ~ ( member @ ( sK9_SY138 @ SV48 @ SV17 ) @ SV48 ) ) )
= $false )
| ( ( member @ SV17 @ ( sum_class @ SV48 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[443]) ).
thf(493,plain,
! [SV48: $i,SV83: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( member @ SV17 @ SV83 )
| ~ ( member @ SV83 @ SV48 ) ) )
= $true )
| ( ( member @ SV17 @ ( sum_class @ SV48 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(494,plain,
! [SV74: $i,SV67: $i,SV49: $i,SV18: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( flip @ SV74 ) )
= $false )
| ( ( ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV49 @ SV18 ) @ SV67 ) @ SV74 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(495,plain,
! [SV74: $i,SV67: $i,SV49: $i,SV18: $i] :
( ( ( ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV49 @ SV18 ) @ SV67 ) @ SV74 ) ) )
= $false )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( flip @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(496,plain,
! [SV19: $i,SV75: $i,SV68: $i,SV50: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( rotate @ SV19 ) )
= $false )
| ( ( ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV68 @ SV75 ) @ SV50 ) @ SV19 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(497,plain,
! [SV19: $i,SV75: $i,SV68: $i,SV50: $i] :
( ( ( ~ ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV68 @ SV75 ) @ SV50 ) @ SV19 ) ) )
= $false )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( rotate @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(498,plain,
! [SV51: $i,SV20: $i,SV80: $i] :
( ( ( ~ ( ~ ( member @ SV80 @ SV20 )
| ~ ( member @ SV80 @ SV51 ) ) )
= $false )
| ( ( disjoint @ SV20 @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[449]) ).
thf(499,plain,
! [SV20: $i,SV51: $i] :
( ( ( ~ ( ~ ( member @ ( sK6_SY145 @ SV51 @ SV20 ) @ SV20 )
| ~ ( member @ ( sK6_SY145 @ SV51 @ SV20 ) @ SV51 ) ) )
= $true )
| ( ( disjoint @ SV20 @ SV51 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[450]) ).
thf(500,plain,
! [SV21: $i,SV52: $i] :
( ( ( ~ ( member @ SV52 @ universal_class ) )
= $false )
| ( ( member @ SV52 @ ( domain_of @ SV21 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[451]) ).
thf(501,plain,
! [SV52: $i,SV21: $i] :
( ( ( ~ ( ( ( restrict @ SV21 @ ( singleton @ SV52 ) @ universal_class )
!= null_class ) ) )
= $false )
| ( ( member @ SV52 @ ( domain_of @ SV21 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[451]) ).
thf(502,plain,
! [SV21: $i,SV52: $i] :
( ( ( ~ ( member @ SV52 @ universal_class ) )
= $true )
| ( ( ~ ( ( ( restrict @ SV21 @ ( singleton @ SV52 ) @ universal_class )
!= null_class ) ) )
= $true )
| ( ( member @ SV52 @ ( domain_of @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[452]) ).
thf(503,plain,
! [SV22: $i,SV53: $i,SV76: $i,SV69: $i] :
( ( ( member @ ( ordered_pair @ SV69 @ SV76 ) @ ( compose @ SV53 @ SV22 ) )
= $false )
| ( ( ~ ( ~ ( member @ SV69 @ universal_class )
| ~ ( member @ SV76 @ ( image @ SV53 @ ( image @ SV22 @ ( singleton @ SV69 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[453]) ).
thf(504,plain,
! [SV22: $i,SV53: $i,SV76: $i,SV69: $i] :
( ( ( ~ ( ~ ( member @ SV69 @ universal_class )
| ~ ( member @ SV76 @ ( image @ SV53 @ ( image @ SV22 @ ( singleton @ SV69 ) ) ) ) ) )
= $false )
| ( ( member @ ( ordered_pair @ SV69 @ SV76 ) @ ( compose @ SV53 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(505,plain,
! [SV70: $i,SV54: $i,SV23: $i] :
( ( ( ~ ( member @ SV23 @ universal_class )
| ~ ( ( SV23 = SV54 )
| ( SV23 = SV70 ) ) )
= $false )
| ( ( member @ SV23 @ ( unordered_pair @ SV54 @ SV70 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(506,plain,
! [SV70: $i,SV54: $i,SV23: $i] :
( ( ( ~ ( member @ SV23 @ universal_class )
| ~ ( ( SV23 = SV54 )
| ( SV23 = SV70 ) ) )
= $true )
| ( ( member @ SV23 @ ( unordered_pair @ SV54 @ SV70 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[456]) ).
thf(507,plain,
! [SV55: $i,SV24: $i] :
( ( ( ( ( first @ ( ordered_pair @ SV24 @ SV55 ) )
!= SV24 )
| ( ( second @ ( ordered_pair @ SV24 @ SV55 ) )
!= SV55 ) )
= $false )
| ( ( member @ SV24 @ universal_class )
= $false )
| ( ( member @ SV55 @ universal_class )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[457]) ).
thf(508,plain,
! [SV25: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK5_SY118 @ SV25 ) @ universal_class )
| ~ ( member @ ( sK5_SY118 @ SV25 ) @ SV25 ) ) )
= $false )
| ( ( SV25 = null_class )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[458]) ).
thf(509,plain,
! [SV25: $i] :
( ( ( ~ ( disjoint @ ( sK5_SY118 @ SV25 ) @ SV25 ) )
= $false )
| ( ( SV25 = null_class )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[458]) ).
thf(510,plain,
! [SV26: $i,SV56: $i] :
( ( ( ~ ( member @ SV56 @ universal_class ) )
= $false )
| ( ( member @ SV56 @ ( complement @ SV26 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[459]) ).
thf(511,plain,
! [SV26: $i,SV56: $i] :
( ( ( ~ ~ ( member @ SV56 @ SV26 ) )
= $false )
| ( ( member @ SV56 @ ( complement @ SV26 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[459]) ).
thf(512,plain,
! [SV26: $i,SV56: $i] :
( ( ( ~ ( member @ SV56 @ universal_class ) )
= $true )
| ( ( ~ ~ ( member @ SV56 @ SV26 ) )
= $true )
| ( ( member @ SV56 @ ( complement @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[460]) ).
thf(513,plain,
! [SV27: $i] :
( ( ( subclass @ SV27 @ ( cross_product @ universal_class @ universal_class ) )
= $true )
| ( ( function @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[461]) ).
thf(514,plain,
! [SV27: $i] :
( ( ( subclass @ ( compose @ SV27 @ ( inverse @ SV27 ) ) @ identity_relation )
= $true )
| ( ( function @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[462]) ).
thf(515,plain,
! [SV27: $i] :
( ( ( subclass @ SV27 @ ( cross_product @ universal_class @ universal_class ) )
= $false )
| ( ( ~ ( subclass @ ( compose @ SV27 @ ( inverse @ SV27 ) ) @ identity_relation ) )
= $true )
| ( ( function @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[463]) ).
thf(516,plain,
! [SV28: $i] :
( ( ( ~ ( ~ ( member @ ( sK7_SY120 @ SV28 ) @ universal_class )
| ( SV28
!= ( ordered_pair @ ( sK7_SY120 @ SV28 ) @ ( sK7_SY120 @ SV28 ) ) ) ) )
= $true )
| ( ( member @ SV28 @ identity_relation )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[464]) ).
thf(517,plain,
! [SV28: $i,SV81: $i] :
( ( ( ~ ( ~ ( member @ SV81 @ universal_class )
| ( SV28
!= ( ordered_pair @ SV81 @ SV81 ) ) ) )
= $false )
| ( ( member @ SV28 @ identity_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(518,plain,
! [SV57: $i,SV30: $i,SV82: $i] :
( ( ( ~ ( member @ SV82 @ SV30 ) )
= $true )
| ( ( member @ SV82 @ SV57 )
= $true )
| ( ( subclass @ SV30 @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[466]) ).
thf(519,plain,
! [SV30: $i,SV57: $i] :
( ( ( ~ ( member @ ( sK8_SY150 @ SV57 @ SV30 ) @ SV30 ) )
= $false )
| ( ( subclass @ SV30 @ SV57 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[467]) ).
thf(520,plain,
! [SV30: $i,SV57: $i] :
( ( ( member @ ( sK8_SY150 @ SV57 @ SV30 ) @ SV57 )
= $false )
| ( ( subclass @ SV30 @ SV57 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[467]) ).
thf(521,plain,
! [SV58: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ( member @ SV31 @ universal_class )
| ~ ( member @ SV58 @ universal_class ) ) )
= $false )
| ( ( member @ ( ordered_pair @ SV31 @ SV58 ) @ successor_relation )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[468]) ).
thf(522,plain,
! [SV58: $i,SV31: $i] :
( ( ( ( successor @ SV31 )
!= SV58 )
= $false )
| ( ( member @ ( ordered_pair @ SV31 @ SV58 ) @ successor_relation )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[468]) ).
thf(523,plain,
! [SV58: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ( member @ SV31 @ universal_class )
| ~ ( member @ SV58 @ universal_class ) ) )
= $true )
| ( ( ( successor @ SV31 )
!= SV58 )
= $true )
| ( ( member @ ( ordered_pair @ SV31 @ SV58 ) @ successor_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[469]) ).
thf(524,plain,
! [SV59: $i,SV32: $i] :
( ( ( ~ ( member @ SV32 @ universal_class ) )
= $false )
| ( ( member @ SV32 @ ( power_class @ SV59 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[470]) ).
thf(525,plain,
! [SV59: $i,SV32: $i] :
( ( ( ~ ( subclass @ SV32 @ SV59 ) )
= $false )
| ( ( member @ SV32 @ ( power_class @ SV59 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[470]) ).
thf(526,plain,
! [SV59: $i,SV32: $i] :
( ( ( ~ ( member @ SV32 @ universal_class ) )
= $true )
| ( ( ~ ( subclass @ SV32 @ SV59 ) )
= $true )
| ( ( member @ SV32 @ ( power_class @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[471]) ).
thf(527,plain,
! [SV78: $i] :
( ( ( member @ SV78 @ universal_class )
= $false )
| ( ( ( SV78 = null_class )
| ( member @ ( apply @ sK3_SX0 @ SV78 ) @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[472]) ).
thf(528,plain,
! [SV60: $i,SV33: $i,SV71: $i] :
( ( ( ~ ( member @ SV71 @ SV33 )
| ~ ( member @ SV71 @ SV60 ) )
= $false )
| ( ( member @ SV71 @ ( intersection @ SV33 @ SV60 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[473]) ).
thf(529,plain,
! [SV60: $i,SV33: $i,SV71: $i] :
( ( ( ~ ( member @ SV71 @ SV33 )
| ~ ( member @ SV71 @ SV60 ) )
= $true )
| ( ( member @ SV71 @ ( intersection @ SV33 @ SV60 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[474]) ).
thf(530,plain,
! [SV77: $i,SV72: $i,SV61: $i,SV34: $i] :
( ( ( member @ ( ordered_pair @ SV34 @ SV61 ) @ ( cross_product @ SV72 @ SV77 ) )
= $false )
| ( ( ~ ( ~ ( member @ SV34 @ SV72 )
| ~ ( member @ SV61 @ SV77 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(531,plain,
! [SV77: $i,SV61: $i,SV72: $i,SV34: $i] :
( ( ( ~ ( ~ ( member @ SV34 @ SV72 )
| ~ ( member @ SV61 @ SV77 ) ) )
= $false )
| ( ( member @ ( ordered_pair @ SV34 @ SV61 ) @ ( cross_product @ SV72 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[476]) ).
thf(532,plain,
( ( member @ sK4_SX0 @ universal_class )
= $true ),
inference(extcnf_not_neg,[status(thm)],[477]) ).
thf(533,plain,
( ( inductive @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[478]) ).
thf(534,plain,
! [SV79: $i] :
( ( ( inductive @ SV79 )
= $false )
| ( ( subclass @ sK4_SX0 @ SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(535,plain,
! [SV37: $i] :
( ( ( member @ null_class @ SV37 )
= $true )
| ( ( inductive @ SV37 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[481]) ).
thf(536,plain,
! [SV37: $i] :
( ( ( subclass @ ( image @ successor_relation @ SV37 ) @ SV37 )
= $true )
| ( ( inductive @ SV37 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[482]) ).
thf(537,plain,
! [SV37: $i] :
( ( ( member @ null_class @ SV37 )
= $false )
| ( ( ~ ( subclass @ ( image @ successor_relation @ SV37 ) @ SV37 ) )
= $true )
| ( ( inductive @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[483]) ).
thf(538,plain,
! [SV39: $i,SV64: $i] :
( ( ( ~ ( member @ SV64 @ universal_class ) )
= $false )
| ( ( member @ ( ordered_pair @ SV39 @ SV64 ) @ element_relation )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[484]) ).
thf(539,plain,
! [SV64: $i,SV39: $i] :
( ( ( ~ ( member @ SV39 @ SV64 ) )
= $false )
| ( ( member @ ( ordered_pair @ SV39 @ SV64 ) @ element_relation )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[484]) ).
thf(540,plain,
! [SV39: $i,SV64: $i] :
( ( ( ~ ( member @ SV64 @ universal_class ) )
= $true )
| ( ( ~ ( member @ SV39 @ SV64 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV39 @ SV64 ) @ element_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[485]) ).
thf(541,plain,
! [SV46: $i,SV15: $i] :
( ( ( subclass @ SV15 @ SV46 )
= $true )
| ( ( SV15 = SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[486]) ).
thf(542,plain,
! [SV15: $i,SV46: $i] :
( ( ( subclass @ SV46 @ SV15 )
= $true )
| ( ( SV15 = SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[487]) ).
thf(543,plain,
! [SV46: $i,SV15: $i] :
( ( ( subclass @ SV15 @ SV46 )
= $false )
| ( ( ~ ( subclass @ SV46 @ SV15 ) )
= $true )
| ( ( SV15 = SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[488]) ).
thf(544,plain,
! [SV48: $i,SV17: $i] :
( ( ( ~ ( ~ ( member @ SV17 @ ( sK9_SY138 @ SV48 @ SV17 ) )
| ~ ( member @ ( sK9_SY138 @ SV48 @ SV17 ) @ SV48 ) ) )
= $true )
| ( ( member @ SV17 @ ( sum_class @ SV48 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[492]) ).
thf(545,plain,
! [SV48: $i,SV83: $i,SV17: $i] :
( ( ( ~ ( ~ ( member @ SV17 @ SV83 )
| ~ ( member @ SV83 @ SV48 ) ) )
= $false )
| ( ( member @ SV17 @ ( sum_class @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[493]) ).
thf(546,plain,
! [SV74: $i,SV67: $i,SV49: $i,SV18: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV49 @ SV18 ) @ SV67 ) @ SV74 ) )
= $false )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( flip @ SV74 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[494]) ).
thf(547,plain,
! [SV74: $i,SV67: $i,SV49: $i,SV18: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV49 @ SV18 ) @ SV67 ) @ SV74 ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( flip @ SV74 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[495]) ).
thf(548,plain,
! [SV19: $i,SV75: $i,SV68: $i,SV50: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV68 @ SV75 ) @ SV50 ) @ SV19 ) )
= $false )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( rotate @ SV19 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(549,plain,
! [SV19: $i,SV75: $i,SV68: $i,SV50: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV68 @ SV75 ) @ SV50 ) @ SV19 ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( rotate @ SV19 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[497]) ).
thf(550,plain,
! [SV51: $i,SV20: $i,SV80: $i] :
( ( ( ~ ( member @ SV80 @ SV20 )
| ~ ( member @ SV80 @ SV51 ) )
= $true )
| ( ( disjoint @ SV20 @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[498]) ).
thf(551,plain,
! [SV20: $i,SV51: $i] :
( ( ( ~ ( member @ ( sK6_SY145 @ SV51 @ SV20 ) @ SV20 )
| ~ ( member @ ( sK6_SY145 @ SV51 @ SV20 ) @ SV51 ) )
= $false )
| ( ( disjoint @ SV20 @ SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[499]) ).
thf(552,plain,
! [SV21: $i,SV52: $i] :
( ( ( member @ SV52 @ universal_class )
= $true )
| ( ( member @ SV52 @ ( domain_of @ SV21 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[500]) ).
thf(553,plain,
! [SV52: $i,SV21: $i] :
( ( ( ( restrict @ SV21 @ ( singleton @ SV52 ) @ universal_class )
!= null_class )
= $true )
| ( ( member @ SV52 @ ( domain_of @ SV21 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[501]) ).
thf(554,plain,
! [SV21: $i,SV52: $i] :
( ( ( member @ SV52 @ universal_class )
= $false )
| ( ( ~ ( ( ( restrict @ SV21 @ ( singleton @ SV52 ) @ universal_class )
!= null_class ) ) )
= $true )
| ( ( member @ SV52 @ ( domain_of @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(555,plain,
! [SV22: $i,SV53: $i,SV76: $i,SV69: $i] :
( ( ( ~ ( member @ SV69 @ universal_class )
| ~ ( member @ SV76 @ ( image @ SV53 @ ( image @ SV22 @ ( singleton @ SV69 ) ) ) ) )
= $false )
| ( ( member @ ( ordered_pair @ SV69 @ SV76 ) @ ( compose @ SV53 @ SV22 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(556,plain,
! [SV22: $i,SV53: $i,SV76: $i,SV69: $i] :
( ( ( ~ ( member @ SV69 @ universal_class )
| ~ ( member @ SV76 @ ( image @ SV53 @ ( image @ SV22 @ ( singleton @ SV69 ) ) ) ) )
= $true )
| ( ( member @ ( ordered_pair @ SV69 @ SV76 ) @ ( compose @ SV53 @ SV22 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[504]) ).
thf(557,plain,
! [SV70: $i,SV54: $i,SV23: $i] :
( ( ( ~ ( member @ SV23 @ universal_class ) )
= $false )
| ( ( member @ SV23 @ ( unordered_pair @ SV54 @ SV70 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[505]) ).
thf(558,plain,
! [SV70: $i,SV54: $i,SV23: $i] :
( ( ( ~ ( ( SV23 = SV54 )
| ( SV23 = SV70 ) ) )
= $false )
| ( ( member @ SV23 @ ( unordered_pair @ SV54 @ SV70 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[505]) ).
thf(559,plain,
! [SV70: $i,SV54: $i,SV23: $i] :
( ( ( ~ ( member @ SV23 @ universal_class ) )
= $true )
| ( ( ~ ( ( SV23 = SV54 )
| ( SV23 = SV70 ) ) )
= $true )
| ( ( member @ SV23 @ ( unordered_pair @ SV54 @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[506]) ).
thf(560,plain,
! [SV55: $i,SV24: $i] :
( ( ( ( first @ ( ordered_pair @ SV24 @ SV55 ) )
!= SV24 )
= $false )
| ( ( member @ SV24 @ universal_class )
= $false )
| ( ( member @ SV55 @ universal_class )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[507]) ).
thf(561,plain,
! [SV55: $i,SV24: $i] :
( ( ( ( second @ ( ordered_pair @ SV24 @ SV55 ) )
!= SV55 )
= $false )
| ( ( member @ SV24 @ universal_class )
= $false )
| ( ( member @ SV55 @ universal_class )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[507]) ).
thf(562,plain,
! [SV25: $i] :
( ( ( ~ ( ~ ( member @ ( sK5_SY118 @ SV25 ) @ universal_class )
| ~ ( member @ ( sK5_SY118 @ SV25 ) @ SV25 ) ) )
= $true )
| ( ( SV25 = null_class )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[508]) ).
thf(563,plain,
! [SV25: $i] :
( ( ( disjoint @ ( sK5_SY118 @ SV25 ) @ SV25 )
= $true )
| ( ( SV25 = null_class )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[509]) ).
thf(564,plain,
! [SV26: $i,SV56: $i] :
( ( ( member @ SV56 @ universal_class )
= $true )
| ( ( member @ SV56 @ ( complement @ SV26 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[510]) ).
thf(565,plain,
! [SV26: $i,SV56: $i] :
( ( ( ~ ( member @ SV56 @ SV26 ) )
= $true )
| ( ( member @ SV56 @ ( complement @ SV26 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[511]) ).
thf(566,plain,
! [SV26: $i,SV56: $i] :
( ( ( member @ SV56 @ universal_class )
= $false )
| ( ( ~ ~ ( member @ SV56 @ SV26 ) )
= $true )
| ( ( member @ SV56 @ ( complement @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[512]) ).
thf(567,plain,
! [SV27: $i] :
( ( ( subclass @ ( compose @ SV27 @ ( inverse @ SV27 ) ) @ identity_relation )
= $false )
| ( ( subclass @ SV27 @ ( cross_product @ universal_class @ universal_class ) )
= $false )
| ( ( function @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[515]) ).
thf(568,plain,
! [SV28: $i] :
( ( ( ~ ( member @ ( sK7_SY120 @ SV28 ) @ universal_class )
| ( SV28
!= ( ordered_pair @ ( sK7_SY120 @ SV28 ) @ ( sK7_SY120 @ SV28 ) ) ) )
= $false )
| ( ( member @ SV28 @ identity_relation )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[516]) ).
thf(569,plain,
! [SV28: $i,SV81: $i] :
( ( ( ~ ( member @ SV81 @ universal_class )
| ( SV28
!= ( ordered_pair @ SV81 @ SV81 ) ) )
= $true )
| ( ( member @ SV28 @ identity_relation )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[517]) ).
thf(570,plain,
! [SV57: $i,SV30: $i,SV82: $i] :
( ( ( member @ SV82 @ SV30 )
= $false )
| ( ( member @ SV82 @ SV57 )
= $true )
| ( ( subclass @ SV30 @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(571,plain,
! [SV30: $i,SV57: $i] :
( ( ( member @ ( sK8_SY150 @ SV57 @ SV30 ) @ SV30 )
= $true )
| ( ( subclass @ SV30 @ SV57 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[519]) ).
thf(572,plain,
! [SV58: $i,SV31: $i] :
( ( ( ~ ( ~ ( member @ SV31 @ universal_class )
| ~ ( member @ SV58 @ universal_class ) ) )
= $true )
| ( ( member @ ( ordered_pair @ SV31 @ SV58 ) @ successor_relation )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[521]) ).
thf(573,plain,
! [SV58: $i,SV31: $i] :
( ( ( ( successor @ SV31 )
= SV58 )
= $true )
| ( ( member @ ( ordered_pair @ SV31 @ SV58 ) @ successor_relation )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[522]) ).
thf(574,plain,
! [SV58: $i,SV31: $i] :
( ( ( ~ ( ~ ( member @ SV31 @ universal_class )
| ~ ( member @ SV58 @ universal_class ) ) )
= $false )
| ( ( ( successor @ SV31 )
!= SV58 )
= $true )
| ( ( member @ ( ordered_pair @ SV31 @ SV58 ) @ successor_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[523]) ).
thf(575,plain,
! [SV59: $i,SV32: $i] :
( ( ( member @ SV32 @ universal_class )
= $true )
| ( ( member @ SV32 @ ( power_class @ SV59 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[524]) ).
thf(576,plain,
! [SV59: $i,SV32: $i] :
( ( ( subclass @ SV32 @ SV59 )
= $true )
| ( ( member @ SV32 @ ( power_class @ SV59 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[525]) ).
thf(577,plain,
! [SV59: $i,SV32: $i] :
( ( ( member @ SV32 @ universal_class )
= $false )
| ( ( ~ ( subclass @ SV32 @ SV59 ) )
= $true )
| ( ( member @ SV32 @ ( power_class @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(578,plain,
! [SV78: $i] :
( ( ( SV78 = null_class )
= $true )
| ( ( member @ ( apply @ sK3_SX0 @ SV78 ) @ SV78 )
= $true )
| ( ( member @ SV78 @ universal_class )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[527]) ).
thf(579,plain,
! [SV60: $i,SV33: $i,SV71: $i] :
( ( ( ~ ( member @ SV71 @ SV33 ) )
= $false )
| ( ( member @ SV71 @ ( intersection @ SV33 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[528]) ).
thf(580,plain,
! [SV33: $i,SV60: $i,SV71: $i] :
( ( ( ~ ( member @ SV71 @ SV60 ) )
= $false )
| ( ( member @ SV71 @ ( intersection @ SV33 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[528]) ).
thf(581,plain,
! [SV60: $i,SV33: $i,SV71: $i] :
( ( ( ~ ( member @ SV71 @ SV33 ) )
= $true )
| ( ( ~ ( member @ SV71 @ SV60 ) )
= $true )
| ( ( member @ SV71 @ ( intersection @ SV33 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[529]) ).
thf(582,plain,
! [SV77: $i,SV61: $i,SV72: $i,SV34: $i] :
( ( ( ~ ( member @ SV34 @ SV72 )
| ~ ( member @ SV61 @ SV77 ) )
= $false )
| ( ( member @ ( ordered_pair @ SV34 @ SV61 ) @ ( cross_product @ SV72 @ SV77 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[530]) ).
thf(583,plain,
! [SV77: $i,SV61: $i,SV72: $i,SV34: $i] :
( ( ( ~ ( member @ SV34 @ SV72 )
| ~ ( member @ SV61 @ SV77 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV34 @ SV61 ) @ ( cross_product @ SV72 @ SV77 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[531]) ).
thf(584,plain,
! [SV37: $i] :
( ( ( subclass @ ( image @ successor_relation @ SV37 ) @ SV37 )
= $false )
| ( ( member @ null_class @ SV37 )
= $false )
| ( ( inductive @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[537]) ).
thf(585,plain,
! [SV39: $i,SV64: $i] :
( ( ( member @ SV64 @ universal_class )
= $true )
| ( ( member @ ( ordered_pair @ SV39 @ SV64 ) @ element_relation )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[538]) ).
thf(586,plain,
! [SV64: $i,SV39: $i] :
( ( ( member @ SV39 @ SV64 )
= $true )
| ( ( member @ ( ordered_pair @ SV39 @ SV64 ) @ element_relation )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[539]) ).
thf(587,plain,
! [SV39: $i,SV64: $i] :
( ( ( member @ SV64 @ universal_class )
= $false )
| ( ( ~ ( member @ SV39 @ SV64 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV39 @ SV64 ) @ element_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[540]) ).
thf(588,plain,
! [SV15: $i,SV46: $i] :
( ( ( subclass @ SV46 @ SV15 )
= $false )
| ( ( subclass @ SV15 @ SV46 )
= $false )
| ( ( SV15 = SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[543]) ).
thf(589,plain,
! [SV48: $i,SV17: $i] :
( ( ( ~ ( member @ SV17 @ ( sK9_SY138 @ SV48 @ SV17 ) )
| ~ ( member @ ( sK9_SY138 @ SV48 @ SV17 ) @ SV48 ) )
= $false )
| ( ( member @ SV17 @ ( sum_class @ SV48 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[544]) ).
thf(590,plain,
! [SV48: $i,SV83: $i,SV17: $i] :
( ( ( ~ ( member @ SV17 @ SV83 )
| ~ ( member @ SV83 @ SV48 ) )
= $true )
| ( ( member @ SV17 @ ( sum_class @ SV48 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[545]) ).
thf(591,plain,
! [SV74: $i,SV67: $i,SV49: $i,SV18: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
= $false )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( flip @ SV74 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[546]) ).
thf(592,plain,
! [SV74: $i,SV67: $i,SV18: $i,SV49: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV49 @ SV18 ) @ SV67 ) @ SV74 ) )
= $false )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( flip @ SV74 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[546]) ).
thf(593,plain,
! [SV74: $i,SV67: $i,SV49: $i,SV18: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV49 @ SV18 ) @ SV67 ) @ SV74 ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( flip @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[547]) ).
thf(594,plain,
! [SV19: $i,SV75: $i,SV68: $i,SV50: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
= $false )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( rotate @ SV19 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[548]) ).
thf(595,plain,
! [SV19: $i,SV50: $i,SV75: $i,SV68: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV68 @ SV75 ) @ SV50 ) @ SV19 ) )
= $false )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( rotate @ SV19 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[548]) ).
thf(596,plain,
! [SV19: $i,SV75: $i,SV68: $i,SV50: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV68 @ SV75 ) @ SV50 ) @ SV19 ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( rotate @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[549]) ).
thf(597,plain,
! [SV51: $i,SV20: $i,SV80: $i] :
( ( ( ~ ( member @ SV80 @ SV20 ) )
= $true )
| ( ( ~ ( member @ SV80 @ SV51 ) )
= $true )
| ( ( disjoint @ SV20 @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[550]) ).
thf(598,plain,
! [SV20: $i,SV51: $i] :
( ( ( ~ ( member @ ( sK6_SY145 @ SV51 @ SV20 ) @ SV20 ) )
= $false )
| ( ( disjoint @ SV20 @ SV51 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[551]) ).
thf(599,plain,
! [SV20: $i,SV51: $i] :
( ( ( ~ ( member @ ( sK6_SY145 @ SV51 @ SV20 ) @ SV51 ) )
= $false )
| ( ( disjoint @ SV20 @ SV51 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[551]) ).
thf(600,plain,
! [SV52: $i,SV21: $i] :
( ( ( ( restrict @ SV21 @ ( singleton @ SV52 ) @ universal_class )
= null_class )
= $false )
| ( ( member @ SV52 @ ( domain_of @ SV21 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(601,plain,
! [SV52: $i,SV21: $i] :
( ( ( ( restrict @ SV21 @ ( singleton @ SV52 ) @ universal_class )
!= null_class )
= $false )
| ( ( member @ SV52 @ universal_class )
= $false )
| ( ( member @ SV52 @ ( domain_of @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[554]) ).
thf(602,plain,
! [SV22: $i,SV53: $i,SV76: $i,SV69: $i] :
( ( ( ~ ( member @ SV69 @ universal_class ) )
= $false )
| ( ( member @ ( ordered_pair @ SV69 @ SV76 ) @ ( compose @ SV53 @ SV22 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[555]) ).
thf(603,plain,
! [SV69: $i,SV22: $i,SV53: $i,SV76: $i] :
( ( ( ~ ( member @ SV76 @ ( image @ SV53 @ ( image @ SV22 @ ( singleton @ SV69 ) ) ) ) )
= $false )
| ( ( member @ ( ordered_pair @ SV69 @ SV76 ) @ ( compose @ SV53 @ SV22 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[555]) ).
thf(604,plain,
! [SV22: $i,SV53: $i,SV76: $i,SV69: $i] :
( ( ( ~ ( member @ SV69 @ universal_class ) )
= $true )
| ( ( ~ ( member @ SV76 @ ( image @ SV53 @ ( image @ SV22 @ ( singleton @ SV69 ) ) ) ) )
= $true )
| ( ( member @ ( ordered_pair @ SV69 @ SV76 ) @ ( compose @ SV53 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[556]) ).
thf(605,plain,
! [SV70: $i,SV54: $i,SV23: $i] :
( ( ( member @ SV23 @ universal_class )
= $true )
| ( ( member @ SV23 @ ( unordered_pair @ SV54 @ SV70 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[557]) ).
thf(606,plain,
! [SV70: $i,SV54: $i,SV23: $i] :
( ( ( ( SV23 = SV54 )
| ( SV23 = SV70 ) )
= $true )
| ( ( member @ SV23 @ ( unordered_pair @ SV54 @ SV70 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[558]) ).
thf(607,plain,
! [SV70: $i,SV54: $i,SV23: $i] :
( ( ( member @ SV23 @ universal_class )
= $false )
| ( ( ~ ( ( SV23 = SV54 )
| ( SV23 = SV70 ) ) )
= $true )
| ( ( member @ SV23 @ ( unordered_pair @ SV54 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[559]) ).
thf(608,plain,
! [SV55: $i,SV24: $i] :
( ( ( ( first @ ( ordered_pair @ SV24 @ SV55 ) )
= SV24 )
= $true )
| ( ( member @ SV24 @ universal_class )
= $false )
| ( ( member @ SV55 @ universal_class )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[560]) ).
thf(609,plain,
! [SV55: $i,SV24: $i] :
( ( ( ( second @ ( ordered_pair @ SV24 @ SV55 ) )
= SV55 )
= $true )
| ( ( member @ SV24 @ universal_class )
= $false )
| ( ( member @ SV55 @ universal_class )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[561]) ).
thf(610,plain,
! [SV25: $i] :
( ( ( ~ ( member @ ( sK5_SY118 @ SV25 ) @ universal_class )
| ~ ( member @ ( sK5_SY118 @ SV25 ) @ SV25 ) )
= $false )
| ( ( SV25 = null_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[562]) ).
thf(611,plain,
! [SV26: $i,SV56: $i] :
( ( ( member @ SV56 @ SV26 )
= $false )
| ( ( member @ SV56 @ ( complement @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[565]) ).
thf(612,plain,
! [SV26: $i,SV56: $i] :
( ( ( ~ ( member @ SV56 @ SV26 ) )
= $false )
| ( ( member @ SV56 @ universal_class )
= $false )
| ( ( member @ SV56 @ ( complement @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[566]) ).
thf(613,plain,
! [SV28: $i] :
( ( ( ~ ( member @ ( sK7_SY120 @ SV28 ) @ universal_class ) )
= $false )
| ( ( member @ SV28 @ identity_relation )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[568]) ).
thf(614,plain,
! [SV28: $i] :
( ( ( SV28
!= ( ordered_pair @ ( sK7_SY120 @ SV28 ) @ ( sK7_SY120 @ SV28 ) ) )
= $false )
| ( ( member @ SV28 @ identity_relation )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[568]) ).
thf(615,plain,
! [SV28: $i,SV81: $i] :
( ( ( ~ ( member @ SV81 @ universal_class ) )
= $true )
| ( ( SV28
!= ( ordered_pair @ SV81 @ SV81 ) )
= $true )
| ( ( member @ SV28 @ identity_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[569]) ).
thf(616,plain,
! [SV58: $i,SV31: $i] :
( ( ( ~ ( member @ SV31 @ universal_class )
| ~ ( member @ SV58 @ universal_class ) )
= $false )
| ( ( member @ ( ordered_pair @ SV31 @ SV58 ) @ successor_relation )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[572]) ).
thf(617,plain,
! [SV58: $i,SV31: $i] :
( ( ( ~ ( member @ SV31 @ universal_class )
| ~ ( member @ SV58 @ universal_class ) )
= $true )
| ( ( ( successor @ SV31 )
!= SV58 )
= $true )
| ( ( member @ ( ordered_pair @ SV31 @ SV58 ) @ successor_relation )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[574]) ).
thf(618,plain,
! [SV59: $i,SV32: $i] :
( ( ( subclass @ SV32 @ SV59 )
= $false )
| ( ( member @ SV32 @ universal_class )
= $false )
| ( ( member @ SV32 @ ( power_class @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[577]) ).
thf(619,plain,
! [SV60: $i,SV33: $i,SV71: $i] :
( ( ( member @ SV71 @ SV33 )
= $true )
| ( ( member @ SV71 @ ( intersection @ SV33 @ SV60 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[579]) ).
thf(620,plain,
! [SV33: $i,SV60: $i,SV71: $i] :
( ( ( member @ SV71 @ SV60 )
= $true )
| ( ( member @ SV71 @ ( intersection @ SV33 @ SV60 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[580]) ).
thf(621,plain,
! [SV60: $i,SV33: $i,SV71: $i] :
( ( ( member @ SV71 @ SV33 )
= $false )
| ( ( ~ ( member @ SV71 @ SV60 ) )
= $true )
| ( ( member @ SV71 @ ( intersection @ SV33 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[581]) ).
thf(622,plain,
! [SV77: $i,SV61: $i,SV72: $i,SV34: $i] :
( ( ( ~ ( member @ SV34 @ SV72 ) )
= $false )
| ( ( member @ ( ordered_pair @ SV34 @ SV61 ) @ ( cross_product @ SV72 @ SV77 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[582]) ).
thf(623,plain,
! [SV72: $i,SV34: $i,SV77: $i,SV61: $i] :
( ( ( ~ ( member @ SV61 @ SV77 ) )
= $false )
| ( ( member @ ( ordered_pair @ SV34 @ SV61 ) @ ( cross_product @ SV72 @ SV77 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[582]) ).
thf(624,plain,
! [SV77: $i,SV61: $i,SV72: $i,SV34: $i] :
( ( ( ~ ( member @ SV34 @ SV72 ) )
= $true )
| ( ( ~ ( member @ SV61 @ SV77 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV34 @ SV61 ) @ ( cross_product @ SV72 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[583]) ).
thf(625,plain,
! [SV64: $i,SV39: $i] :
( ( ( member @ SV39 @ SV64 )
= $false )
| ( ( member @ SV64 @ universal_class )
= $false )
| ( ( member @ ( ordered_pair @ SV39 @ SV64 ) @ element_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[587]) ).
thf(626,plain,
! [SV48: $i,SV17: $i] :
( ( ( ~ ( member @ SV17 @ ( sK9_SY138 @ SV48 @ SV17 ) ) )
= $false )
| ( ( member @ SV17 @ ( sum_class @ SV48 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[589]) ).
thf(627,plain,
! [SV17: $i,SV48: $i] :
( ( ( ~ ( member @ ( sK9_SY138 @ SV48 @ SV17 ) @ SV48 ) )
= $false )
| ( ( member @ SV17 @ ( sum_class @ SV48 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[589]) ).
thf(628,plain,
! [SV48: $i,SV83: $i,SV17: $i] :
( ( ( ~ ( member @ SV17 @ SV83 ) )
= $true )
| ( ( ~ ( member @ SV83 @ SV48 ) )
= $true )
| ( ( member @ SV17 @ ( sum_class @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[590]) ).
thf(629,plain,
! [SV74: $i,SV67: $i,SV49: $i,SV18: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( flip @ SV74 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[591]) ).
thf(630,plain,
! [SV74: $i,SV67: $i,SV18: $i,SV49: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ SV49 @ SV18 ) @ SV67 ) @ SV74 )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( flip @ SV74 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[592]) ).
thf(631,plain,
! [SV74: $i,SV67: $i,SV49: $i,SV18: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV49 @ SV18 ) @ SV67 ) @ SV74 ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( flip @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[593]) ).
thf(632,plain,
! [SV19: $i,SV75: $i,SV68: $i,SV50: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( rotate @ SV19 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[594]) ).
thf(633,plain,
! [SV19: $i,SV50: $i,SV75: $i,SV68: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ SV68 @ SV75 ) @ SV50 ) @ SV19 )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( rotate @ SV19 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[595]) ).
thf(634,plain,
! [SV19: $i,SV75: $i,SV68: $i,SV50: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV68 @ SV75 ) @ SV50 ) @ SV19 ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( rotate @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[596]) ).
thf(635,plain,
! [SV51: $i,SV20: $i,SV80: $i] :
( ( ( member @ SV80 @ SV20 )
= $false )
| ( ( ~ ( member @ SV80 @ SV51 ) )
= $true )
| ( ( disjoint @ SV20 @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[597]) ).
thf(636,plain,
! [SV20: $i,SV51: $i] :
( ( ( member @ ( sK6_SY145 @ SV51 @ SV20 ) @ SV20 )
= $true )
| ( ( disjoint @ SV20 @ SV51 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[598]) ).
thf(637,plain,
! [SV20: $i,SV51: $i] :
( ( ( member @ ( sK6_SY145 @ SV51 @ SV20 ) @ SV51 )
= $true )
| ( ( disjoint @ SV20 @ SV51 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[599]) ).
thf(638,plain,
! [SV52: $i,SV21: $i] :
( ( ( ( restrict @ SV21 @ ( singleton @ SV52 ) @ universal_class )
= null_class )
= $true )
| ( ( member @ SV52 @ universal_class )
= $false )
| ( ( member @ SV52 @ ( domain_of @ SV21 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[601]) ).
thf(639,plain,
! [SV22: $i,SV53: $i,SV76: $i,SV69: $i] :
( ( ( member @ SV69 @ universal_class )
= $true )
| ( ( member @ ( ordered_pair @ SV69 @ SV76 ) @ ( compose @ SV53 @ SV22 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[602]) ).
thf(640,plain,
! [SV69: $i,SV22: $i,SV53: $i,SV76: $i] :
( ( ( member @ SV76 @ ( image @ SV53 @ ( image @ SV22 @ ( singleton @ SV69 ) ) ) )
= $true )
| ( ( member @ ( ordered_pair @ SV69 @ SV76 ) @ ( compose @ SV53 @ SV22 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[603]) ).
thf(641,plain,
! [SV22: $i,SV53: $i,SV76: $i,SV69: $i] :
( ( ( member @ SV69 @ universal_class )
= $false )
| ( ( ~ ( member @ SV76 @ ( image @ SV53 @ ( image @ SV22 @ ( singleton @ SV69 ) ) ) ) )
= $true )
| ( ( member @ ( ordered_pair @ SV69 @ SV76 ) @ ( compose @ SV53 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(642,plain,
! [SV70: $i,SV54: $i,SV23: $i] :
( ( ( SV23 = SV54 )
= $true )
| ( ( SV23 = SV70 )
= $true )
| ( ( member @ SV23 @ ( unordered_pair @ SV54 @ SV70 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[606]) ).
thf(643,plain,
! [SV70: $i,SV54: $i,SV23: $i] :
( ( ( ( SV23 = SV54 )
| ( SV23 = SV70 ) )
= $false )
| ( ( member @ SV23 @ universal_class )
= $false )
| ( ( member @ SV23 @ ( unordered_pair @ SV54 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[607]) ).
thf(644,plain,
! [SV25: $i] :
( ( ( ~ ( member @ ( sK5_SY118 @ SV25 ) @ universal_class ) )
= $false )
| ( ( SV25 = null_class )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[610]) ).
thf(645,plain,
! [SV25: $i] :
( ( ( ~ ( member @ ( sK5_SY118 @ SV25 ) @ SV25 ) )
= $false )
| ( ( SV25 = null_class )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[610]) ).
thf(646,plain,
! [SV26: $i,SV56: $i] :
( ( ( member @ SV56 @ SV26 )
= $true )
| ( ( member @ SV56 @ universal_class )
= $false )
| ( ( member @ SV56 @ ( complement @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[612]) ).
thf(647,plain,
! [SV28: $i] :
( ( ( member @ ( sK7_SY120 @ SV28 ) @ universal_class )
= $true )
| ( ( member @ SV28 @ identity_relation )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[613]) ).
thf(648,plain,
! [SV28: $i] :
( ( ( SV28
= ( ordered_pair @ ( sK7_SY120 @ SV28 ) @ ( sK7_SY120 @ SV28 ) ) )
= $true )
| ( ( member @ SV28 @ identity_relation )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[614]) ).
thf(649,plain,
! [SV28: $i,SV81: $i] :
( ( ( member @ SV81 @ universal_class )
= $false )
| ( ( SV28
!= ( ordered_pair @ SV81 @ SV81 ) )
= $true )
| ( ( member @ SV28 @ identity_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[615]) ).
thf(650,plain,
! [SV58: $i,SV31: $i] :
( ( ( ~ ( member @ SV31 @ universal_class ) )
= $false )
| ( ( member @ ( ordered_pair @ SV31 @ SV58 ) @ successor_relation )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[616]) ).
thf(651,plain,
! [SV31: $i,SV58: $i] :
( ( ( ~ ( member @ SV58 @ universal_class ) )
= $false )
| ( ( member @ ( ordered_pair @ SV31 @ SV58 ) @ successor_relation )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[616]) ).
thf(652,plain,
! [SV58: $i,SV31: $i] :
( ( ( ~ ( member @ SV31 @ universal_class ) )
= $true )
| ( ( ~ ( member @ SV58 @ universal_class ) )
= $true )
| ( ( ( successor @ SV31 )
!= SV58 )
= $true )
| ( ( member @ ( ordered_pair @ SV31 @ SV58 ) @ successor_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[617]) ).
thf(653,plain,
! [SV33: $i,SV60: $i,SV71: $i] :
( ( ( member @ SV71 @ SV60 )
= $false )
| ( ( member @ SV71 @ SV33 )
= $false )
| ( ( member @ SV71 @ ( intersection @ SV33 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[621]) ).
thf(654,plain,
! [SV77: $i,SV61: $i,SV72: $i,SV34: $i] :
( ( ( member @ SV34 @ SV72 )
= $true )
| ( ( member @ ( ordered_pair @ SV34 @ SV61 ) @ ( cross_product @ SV72 @ SV77 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[622]) ).
thf(655,plain,
! [SV72: $i,SV34: $i,SV77: $i,SV61: $i] :
( ( ( member @ SV61 @ SV77 )
= $true )
| ( ( member @ ( ordered_pair @ SV34 @ SV61 ) @ ( cross_product @ SV72 @ SV77 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[623]) ).
thf(656,plain,
! [SV77: $i,SV61: $i,SV72: $i,SV34: $i] :
( ( ( member @ SV34 @ SV72 )
= $false )
| ( ( ~ ( member @ SV61 @ SV77 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV34 @ SV61 ) @ ( cross_product @ SV72 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[624]) ).
thf(657,plain,
! [SV48: $i,SV17: $i] :
( ( ( member @ SV17 @ ( sK9_SY138 @ SV48 @ SV17 ) )
= $true )
| ( ( member @ SV17 @ ( sum_class @ SV48 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[626]) ).
thf(658,plain,
! [SV17: $i,SV48: $i] :
( ( ( member @ ( sK9_SY138 @ SV48 @ SV17 ) @ SV48 )
= $true )
| ( ( member @ SV17 @ ( sum_class @ SV48 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[627]) ).
thf(659,plain,
! [SV48: $i,SV83: $i,SV17: $i] :
( ( ( member @ SV17 @ SV83 )
= $false )
| ( ( ~ ( member @ SV83 @ SV48 ) )
= $true )
| ( ( member @ SV17 @ ( sum_class @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[628]) ).
thf(660,plain,
! [SV74: $i,SV67: $i,SV18: $i,SV49: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ SV49 @ SV18 ) @ SV67 ) @ SV74 )
= $false )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
= $false )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV18 @ SV49 ) @ SV67 ) @ ( flip @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[631]) ).
thf(661,plain,
! [SV19: $i,SV50: $i,SV75: $i,SV68: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ SV68 @ SV75 ) @ SV50 ) @ SV19 )
= $false )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
= $false )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV50 @ SV68 ) @ SV75 ) @ ( rotate @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[634]) ).
thf(662,plain,
! [SV20: $i,SV51: $i,SV80: $i] :
( ( ( member @ SV80 @ SV51 )
= $false )
| ( ( member @ SV80 @ SV20 )
= $false )
| ( ( disjoint @ SV20 @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[635]) ).
thf(663,plain,
! [SV69: $i,SV22: $i,SV53: $i,SV76: $i] :
( ( ( member @ SV76 @ ( image @ SV53 @ ( image @ SV22 @ ( singleton @ SV69 ) ) ) )
= $false )
| ( ( member @ SV69 @ universal_class )
= $false )
| ( ( member @ ( ordered_pair @ SV69 @ SV76 ) @ ( compose @ SV53 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[641]) ).
thf(664,plain,
! [SV70: $i,SV54: $i,SV23: $i] :
( ( ( SV23 = SV54 )
= $false )
| ( ( member @ SV23 @ universal_class )
= $false )
| ( ( member @ SV23 @ ( unordered_pair @ SV54 @ SV70 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[643]) ).
thf(665,plain,
! [SV54: $i,SV70: $i,SV23: $i] :
( ( ( SV23 = SV70 )
= $false )
| ( ( member @ SV23 @ universal_class )
= $false )
| ( ( member @ SV23 @ ( unordered_pair @ SV54 @ SV70 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[643]) ).
thf(666,plain,
! [SV25: $i] :
( ( ( member @ ( sK5_SY118 @ SV25 ) @ universal_class )
= $true )
| ( ( SV25 = null_class )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[644]) ).
thf(667,plain,
! [SV25: $i] :
( ( ( member @ ( sK5_SY118 @ SV25 ) @ SV25 )
= $true )
| ( ( SV25 = null_class )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[645]) ).
thf(668,plain,
! [SV81: $i,SV28: $i] :
( ( ( SV28
= ( ordered_pair @ SV81 @ SV81 ) )
= $false )
| ( ( member @ SV81 @ universal_class )
= $false )
| ( ( member @ SV28 @ identity_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[649]) ).
thf(669,plain,
! [SV58: $i,SV31: $i] :
( ( ( member @ SV31 @ universal_class )
= $true )
| ( ( member @ ( ordered_pair @ SV31 @ SV58 ) @ successor_relation )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[650]) ).
thf(670,plain,
! [SV31: $i,SV58: $i] :
( ( ( member @ SV58 @ universal_class )
= $true )
| ( ( member @ ( ordered_pair @ SV31 @ SV58 ) @ successor_relation )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[651]) ).
thf(671,plain,
! [SV58: $i,SV31: $i] :
( ( ( member @ SV31 @ universal_class )
= $false )
| ( ( ~ ( member @ SV58 @ universal_class ) )
= $true )
| ( ( ( successor @ SV31 )
!= SV58 )
= $true )
| ( ( member @ ( ordered_pair @ SV31 @ SV58 ) @ successor_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[652]) ).
thf(672,plain,
! [SV72: $i,SV34: $i,SV77: $i,SV61: $i] :
( ( ( member @ SV61 @ SV77 )
= $false )
| ( ( member @ SV34 @ SV72 )
= $false )
| ( ( member @ ( ordered_pair @ SV34 @ SV61 ) @ ( cross_product @ SV72 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[656]) ).
thf(673,plain,
! [SV17: $i,SV48: $i,SV83: $i] :
( ( ( member @ SV83 @ SV48 )
= $false )
| ( ( member @ SV17 @ SV83 )
= $false )
| ( ( member @ SV17 @ ( sum_class @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[659]) ).
thf(674,plain,
! [SV31: $i,SV58: $i] :
( ( ( member @ SV58 @ universal_class )
= $false )
| ( ( member @ SV31 @ universal_class )
= $false )
| ( ( ( successor @ SV31 )
!= SV58 )
= $true )
| ( ( member @ ( ordered_pair @ SV31 @ SV58 ) @ successor_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[671]) ).
thf(675,plain,
! [SV58: $i,SV31: $i] :
( ( ( ( successor @ SV31 )
= SV58 )
= $false )
| ( ( member @ SV31 @ universal_class )
= $false )
| ( ( member @ SV58 @ universal_class )
= $false )
| ( ( member @ ( ordered_pair @ SV31 @ SV58 ) @ successor_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[674]) ).
thf(676,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[104,675,673,672,670,669,668,667,666,665,664,663,662,661,660,658,657,655,654,653,648,647,646,642,640,639,638,637,636,633,632,630,629,625,620,619,618,611,609,608,605,600,588,586,585,584,578,576,575,573,571,570,567,564,563,552,542,541,536,535,534,533,532,520,514,513,491,490,489,480,382,347,266,257,240,212,211,210,209,207,206,178,174,173,172,171,170,166,164,116]) ).
thf(677,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[676]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET101+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.17 % Computer : n015.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Oct 6 14:34:13 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.32/1.39
% 6.32/1.39 No.of.Axioms: 43
% 6.32/1.39
% 6.32/1.39 Length.of.Defs: 0
% 6.32/1.39
% 6.32/1.39 Contains.Choice.Funs: false
% 6.32/1.39 ....................
% 6.32/1.39
% 6.32/1.39 ********************************
% 6.32/1.39 * All subproblems solved! *
% 6.32/1.39 ********************************
% 6.32/1.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:43,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:676,loop_count:0,foatp_calls:1,translation:fof_full)
% 6.32/1.39
% 6.32/1.39 %**** Beginning of derivation protocol ****
% 6.32/1.39 % SZS output start CNFRefutation
% See solution above
% 6.32/1.39
% 6.32/1.39 %**** End of derivation protocol ****
% 6.32/1.39 %**** no. of clauses in derivation: 677 ****
% 6.32/1.39 %**** clause counter: 676 ****
% 6.32/1.39
% 6.32/1.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:43,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:676,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------