%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET020+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 10:38:57 AM UTC 2026
% Result : Theorem 2.13s 0.64s
% Output : CNFRefutation 2.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 18
% Syntax : Number of formulae : 615 ( 280 unt; 0 typ; 0 def)
% Number of atoms : 3986 (1271 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 8257 (2032 ~;1258 |; 59 &;4842 @)
% ( 40 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 42 usr; 10 con; 0-3 aty)
% Number of variables : 1538 ( 0 ^;1530 !; 8 ?;1538 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_apply,type,
apply: $i > $i > $i ).
thf(tp_complement,type,
complement: $i > $i ).
thf(tp_compose,type,
compose: $i > $i > $i ).
thf(tp_cross_product,type,
cross_product: $i > $i > $i ).
thf(tp_disjoint,type,
disjoint: $i > $i > $o ).
thf(tp_domain_of,type,
domain_of: $i > $i ).
thf(tp_element_relation,type,
element_relation: $i ).
thf(tp_first,type,
first: $i > $i ).
thf(tp_flip,type,
flip: $i > $i ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_identity_relation,type,
identity_relation: $i ).
thf(tp_image,type,
image: $i > $i > $i ).
thf(tp_inductive,type,
inductive: $i > $o ).
thf(tp_intersection,type,
intersection: $i > $i > $i ).
thf(tp_inverse,type,
inverse: $i > $i ).
thf(tp_member,type,
member: $i > $i > $o ).
thf(tp_null_class,type,
null_class: $i ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_power_class,type,
power_class: $i > $i ).
thf(tp_range_of,type,
range_of: $i > $i ).
thf(tp_restrict,type,
restrict: $i > $i > $i > $i ).
thf(tp_rotate,type,
rotate: $i > $i ).
thf(tp_sK10_SY119,type,
sK10_SY119: $i > $i > $i ).
thf(tp_sK11_SY114,type,
sK11_SY114: $i > $i > $i ).
thf(tp_sK1_U,type,
sK1_U: $i ).
thf(tp_sK2_SY42,type,
sK2_SY42: $i ).
thf(tp_sK3_SY44,type,
sK3_SY44: $i ).
thf(tp_sK4_SY74,type,
sK4_SY74: $i > $i > $i ).
thf(tp_sK5_SY76,type,
sK5_SY76: $i > $i > $i ).
thf(tp_sK6_SY60,type,
sK6_SY60: $i > $i ).
thf(tp_sK7_SY77,type,
sK7_SY77: $i > $i > $i ).
thf(tp_sK8_SY113,type,
sK8_SY113: $i > $i > $i ).
thf(tp_sK9_SY97,type,
sK9_SY97: $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(4,axiom,
! [X: $i,Y: $i] :
( ( disjoint @ X @ Y )
<=> ! [U: $i] :
~ ( ( member @ U @ X )
& ( member @ U @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint_defn) ).
thf(7,axiom,
! [Z: $i] :
( ( member @ Z @ identity_relation )
<=> ? [X: $i] :
( ( member @ X @ universal_class )
& ( Z
= ( ordered_pair @ X @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_relation) ).
thf(10,axiom,
! [U: $i] :
( ( member @ U @ universal_class )
=> ( member @ ( power_class @ U ) @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_class) ).
thf(12,axiom,
! [X: $i] :
( ( member @ X @ universal_class )
=> ( member @ ( sum_class @ X ) @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class) ).
thf(13,axiom,
! [U: $i,X: $i] :
( ( member @ U @ ( sum_class @ X ) )
<=> ? [Y: $i] :
( ( member @ U @ Y )
& ( member @ Y @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class_defn) ).
thf(22,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( member @ Z @ ( union @ X @ Y ) )
<=> ( ( member @ Z @ X )
| ( member @ Z @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
thf(28,axiom,
! [X: $i] :
~ ( member @ X @ null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_defn) ).
thf(30,axiom,
! [X: $i,Z: $i] :
( ( member @ Z @ ( complement @ X ) )
<=> ( ( member @ Z @ universal_class )
& ~ ( member @ Z @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement) ).
thf(31,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( member @ Z @ ( intersection @ X @ Y ) )
<=> ( ( member @ Z @ X )
& ( member @ Z @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).
thf(33,axiom,
! [X: $i,Y: $i] :
( ( member @ ( ordered_pair @ X @ Y ) @ element_relation )
<=> ( ( member @ Y @ universal_class )
& ( member @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation_defn) ).
thf(34,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( member @ Z @ ( cross_product @ X @ Y ) )
=> ( Z
= ( ordered_pair @ ( first @ Z ) @ ( second @ Z ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cross_product) ).
thf(35,axiom,
! [X: $i,Y: $i] :
( ( ( member @ X @ universal_class )
& ( member @ Y @ universal_class ) )
=> ( ( ( first @ ( ordered_pair @ X @ Y ) )
= X )
& ( ( second @ ( ordered_pair @ X @ Y ) )
= Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first_second) ).
thf(36,axiom,
! [U: $i,V: $i,X: $i,Y: $i] :
( ( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) )
<=> ( ( member @ U @ X )
& ( member @ V @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cross_product_defn) ).
thf(39,axiom,
! [X: $i,Y: $i] : ( member @ ( unordered_pair @ X @ Y ) @ universal_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair) ).
thf(40,axiom,
! [U: $i,X: $i,Y: $i] :
( ( member @ U @ ( unordered_pair @ X @ Y ) )
<=> ( ( member @ U @ universal_class )
& ( ( U = X )
| ( U = Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_defn) ).
thf(42,axiom,
! [X: $i] : ( subclass @ X @ universal_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
thf(43,axiom,
! [X: $i,Y: $i] :
( ( subclass @ X @ Y )
<=> ! [U: $i] :
( ( member @ U @ X )
=> ( member @ U @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_defn) ).
thf(44,conjecture,
! [U: $i,V: $i,X: $i] :
( ( ( member @ U @ universal_class )
& ( member @ V @ universal_class )
& ( X
= ( ordered_pair @ U @ V ) ) )
=> ( ( ( first @ X )
= U )
& ( ( second @ X )
= V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_1st_and_2nd_in_pair_of_sets1) ).
thf(45,negated_conjecture,
( ( ! [U: $i,V: $i,X: $i] :
( ( ( member @ U @ universal_class )
& ( member @ V @ universal_class )
& ( X
= ( ordered_pair @ U @ V ) ) )
=> ( ( ( first @ X )
= U )
& ( ( second @ X )
= V ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[44]) ).
thf(46,plain,
( ( ! [U: $i,V: $i,X: $i] :
( ( ( member @ U @ universal_class )
& ( member @ V @ universal_class )
& ( X
= ( ordered_pair @ U @ V ) ) )
=> ( ( ( first @ X )
= U )
& ( ( second @ X )
= V ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[45]) ).
thf(47,plain,
( ( ! [X: $i,Y: $i] :
( ( disjoint @ X @ Y )
<=> ! [U: $i] :
~ ( ( member @ U @ X )
& ( member @ U @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(48,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(49,plain,
( ( ! [U: $i] :
( ( member @ U @ universal_class )
=> ( member @ ( power_class @ U ) @ universal_class ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(50,plain,
( ( ! [X: $i] :
( ( member @ X @ universal_class )
=> ( member @ ( sum_class @ X ) @ universal_class ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(51,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(52,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(53,plain,
( ( ! [X: $i] :
~ ( member @ X @ null_class ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(54,plain,
( ( ! [X: $i,Z: $i] :
( ( member @ Z @ ( complement @ X ) )
<=> ( ( member @ Z @ universal_class )
& ~ ( member @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(55,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(56,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(57,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(58,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(59,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(60,plain,
( ( ! [X: $i,Y: $i] : ( member @ ( unordered_pair @ X @ Y ) @ universal_class ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(61,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(62,plain,
( ( ! [X: $i] : ( subclass @ X @ universal_class ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(63,plain,
( ( ! [X: $i,Y: $i] :
( ( subclass @ X @ Y )
<=> ! [U: $i] :
( ( member @ U @ X )
=> ( member @ U @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(64,plain,
( ( ! [SY42: $i,SY43: $i] :
( ( ( member @ sK1_U @ universal_class )
& ( member @ SY42 @ universal_class )
& ( SY43
= ( ordered_pair @ sK1_U @ SY42 ) ) )
=> ( ( ( first @ SY43 )
= sK1_U )
& ( ( second @ SY43 )
= SY42 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[46]) ).
thf(65,plain,
( ( ! [SY44: $i] :
( ( ( member @ sK1_U @ universal_class )
& ( member @ sK2_SY42 @ universal_class )
& ( SY44
= ( ordered_pair @ sK1_U @ sK2_SY42 ) ) )
=> ( ( ( first @ SY44 )
= sK1_U )
& ( ( second @ SY44 )
= sK2_SY42 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[64]) ).
thf(66,plain,
( ( ( ( member @ sK1_U @ universal_class )
& ( member @ sK2_SY42 @ universal_class )
& ( sK3_SY44
= ( ordered_pair @ sK1_U @ sK2_SY42 ) ) )
=> ( ( ( first @ sK3_SY44 )
= sK1_U )
& ( ( second @ sK3_SY44 )
= sK2_SY42 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[65]) ).
thf(67,plain,
( ( member @ sK1_U @ universal_class )
= $true ),
inference(standard_cnf,[status(thm)],[66]) ).
thf(68,plain,
( ( member @ sK2_SY42 @ universal_class )
= $true ),
inference(standard_cnf,[status(thm)],[66]) ).
thf(69,plain,
( ( sK3_SY44
= ( ordered_pair @ sK1_U @ sK2_SY42 ) )
= $true ),
inference(standard_cnf,[status(thm)],[66]) ).
thf(70,plain,
( ( ( ( first @ sK3_SY44 )
= sK1_U )
& ( ( second @ sK3_SY44 )
= sK2_SY42 ) )
= $false ),
inference(standard_cnf,[status(thm)],[66]) ).
thf(71,plain,
( ( ( first @ sK3_SY44 )
= sK1_U )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[70]) ).
thf(72,plain,
( ( ( second @ sK3_SY44 )
= sK2_SY42 )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[70]) ).
thf(73,plain,
( ( ( first @ sK3_SY44 )
!= sK1_U )
= $true ),
inference(polarity_switch,[status(thm)],[71]) ).
thf(74,plain,
( ( ( second @ sK3_SY44 )
!= sK2_SY42 )
= $true ),
inference(polarity_switch,[status(thm)],[72]) ).
thf(75,plain,
( ( ! [X: $i,Y: $i] :
( ( subclass @ X @ Y )
<=> ! [U: $i] :
( ( member @ U @ X )
=> ( member @ U @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(76,plain,
( ( ! [X: $i] : ( subclass @ X @ universal_class ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(77,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)],[61]) ).
thf(78,plain,
( ( ! [X: $i,Y: $i] : ( member @ ( unordered_pair @ X @ Y ) @ universal_class ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(79,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)],[59]) ).
thf(80,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)],[58]) ).
thf(81,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)],[57]) ).
thf(82,plain,
( ( ! [X: $i,Y: $i] :
( ( member @ ( ordered_pair @ X @ Y ) @ element_relation )
<=> ( ( member @ Y @ universal_class )
& ( member @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(83,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( member @ Z @ ( intersection @ X @ Y ) )
<=> ( ( member @ Z @ X )
& ( member @ Z @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(84,plain,
( ( ! [X: $i,Z: $i] :
( ( member @ Z @ ( complement @ X ) )
<=> ( ( member @ Z @ universal_class )
& ~ ( member @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(85,plain,
( ( ! [X: $i] :
~ ( member @ X @ null_class ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(86,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( member @ Z @ ( union @ X @ Y ) )
<=> ( ( member @ Z @ X )
| ( member @ Z @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(87,plain,
( ( ! [U: $i,X: $i] :
( ( member @ U @ ( sum_class @ X ) )
<=> ? [Y: $i] :
( ( member @ U @ Y )
& ( member @ Y @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(88,plain,
( ( ! [X: $i] :
( ( member @ X @ universal_class )
=> ( member @ ( sum_class @ X ) @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(89,plain,
( ( ! [U: $i] :
( ( member @ U @ universal_class )
=> ( member @ ( power_class @ U ) @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(90,plain,
( ( ! [Z: $i] :
( ( member @ Z @ identity_relation )
<=> ? [X: $i] :
( ( member @ X @ universal_class )
& ( Z
= ( ordered_pair @ X @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(91,plain,
( ( ! [X: $i,Y: $i] :
( ( disjoint @ X @ Y )
<=> ! [U: $i] :
~ ( ( member @ U @ X )
& ( member @ U @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(92,plain,
( ( sK3_SY44
= ( ordered_pair @ sK1_U @ sK2_SY42 ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(93,plain,
( ( member @ sK2_SY42 @ universal_class )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(94,plain,
( ( member @ sK1_U @ universal_class )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(95,plain,
( ( ( first @ sK3_SY44 )
!= sK1_U )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(96,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)],[86]) ).
thf(97,plain,
( ( ! [SX0: $i] :
( ~ ( member @ SX0 @ universal_class )
| ( member @ ( sum_class @ SX0 ) @ universal_class ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(98,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)],[83]) ).
thf(99,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)],[91]) ).
thf(100,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)],[75]) ).
thf(101,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)],[84]) ).
thf(102,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)],[87]) ).
thf(103,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)],[90]) ).
thf(104,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)],[77]) ).
thf(105,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)],[81]) ).
thf(106,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)],[79]) ).
thf(107,plain,
( ( ! [SX0: $i] :
( ~ ( member @ SX0 @ universal_class )
| ( member @ ( power_class @ SX0 ) @ universal_class ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(108,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)],[82]) ).
thf(109,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)],[80]) ).
thf(110,plain,
! [SV1: $i] :
( ( subclass @ SV1 @ universal_class )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(111,plain,
! [SV2: $i] :
( ( ! [SY45: $i] : ( member @ ( unordered_pair @ SV2 @ SY45 ) @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(112,plain,
! [SV3: $i] :
( ( ~ ( member @ SV3 @ null_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(113,plain,
( ( ( first @ sK3_SY44 )
= sK1_U )
= $false ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(114,plain,
! [SV4: $i] :
( ( ! [SY46: $i,SY47: $i] :
~ ( ~ ( ~ ( member @ SY47 @ ( union @ SV4 @ SY46 ) )
| ( member @ SY47 @ SV4 )
| ( member @ SY47 @ SY46 ) )
| ~ ( ~ ( ( member @ SY47 @ SV4 )
| ( member @ SY47 @ SY46 ) )
| ( member @ SY47 @ ( union @ SV4 @ SY46 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(115,plain,
! [SV5: $i] :
( ( ~ ( member @ SV5 @ universal_class )
| ( member @ ( sum_class @ SV5 ) @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(116,plain,
! [SV6: $i] :
( ( ! [SY48: $i,SY49: $i] :
~ ( ~ ( ~ ( member @ SY49 @ ( intersection @ SV6 @ SY48 ) )
| ~ ( ~ ( member @ SY49 @ SV6 )
| ~ ( member @ SY49 @ SY48 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY49 @ SV6 )
| ~ ( member @ SY49 @ SY48 ) )
| ( member @ SY49 @ ( intersection @ SV6 @ SY48 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(117,plain,
! [SV7: $i] :
( ( ! [SY50: $i] :
~ ( ~ ( ~ ( disjoint @ SV7 @ SY50 )
| ! [SY51: $i] :
~ ~ ( ~ ( member @ SY51 @ SV7 )
| ~ ( member @ SY51 @ SY50 ) ) )
| ~ ( ~ ! [SY52: $i] :
~ ~ ( ~ ( member @ SY52 @ SV7 )
| ~ ( member @ SY52 @ SY50 ) )
| ( disjoint @ SV7 @ SY50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(118,plain,
! [SV8: $i] :
( ( ! [SY53: $i] :
~ ( ~ ( ~ ( subclass @ SV8 @ SY53 )
| ! [SY54: $i] :
( ~ ( member @ SY54 @ SV8 )
| ( member @ SY54 @ SY53 ) ) )
| ~ ( ~ ! [SY55: $i] :
( ~ ( member @ SY55 @ SV8 )
| ( member @ SY55 @ SY53 ) )
| ( subclass @ SV8 @ SY53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(119,plain,
! [SV9: $i] :
( ( ! [SY56: $i] :
~ ( ~ ( ~ ( member @ SY56 @ ( complement @ SV9 ) )
| ~ ( ~ ( member @ SY56 @ universal_class )
| ~ ~ ( member @ SY56 @ SV9 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY56 @ universal_class )
| ~ ~ ( member @ SY56 @ SV9 ) )
| ( member @ SY56 @ ( complement @ SV9 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(120,plain,
! [SV10: $i] :
( ( ! [SY57: $i] :
~ ( ~ ( ~ ( member @ SV10 @ ( sum_class @ SY57 ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( member @ SV10 @ SY58 )
| ~ ( member @ SY58 @ SY57 ) ) )
| ~ ( ~ ~ ! [SY59: $i] :
~ ~ ( ~ ( member @ SV10 @ SY59 )
| ~ ( member @ SY59 @ SY57 ) )
| ( member @ SV10 @ ( sum_class @ SY57 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(121,plain,
! [SV11: $i] :
( ( ~ ( ~ ( ~ ( member @ SV11 @ identity_relation )
| ~ ! [SY60: $i] :
~ ~ ( ~ ( member @ SY60 @ universal_class )
| ( SV11
!= ( ordered_pair @ SY60 @ SY60 ) ) ) )
| ~ ( ~ ~ ! [SY61: $i] :
~ ~ ( ~ ( member @ SY61 @ universal_class )
| ( SV11
!= ( ordered_pair @ SY61 @ SY61 ) ) )
| ( member @ SV11 @ identity_relation ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(122,plain,
! [SV12: $i] :
( ( ! [SY62: $i,SY63: $i] :
~ ( ~ ( ~ ( member @ SV12 @ ( unordered_pair @ SY62 @ SY63 ) )
| ~ ( ~ ( member @ SV12 @ universal_class )
| ~ ( ( SV12 = SY62 )
| ( SV12 = SY63 ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV12 @ universal_class )
| ~ ( ( SV12 = SY62 )
| ( SV12 = SY63 ) ) )
| ( member @ SV12 @ ( unordered_pair @ SY62 @ SY63 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(123,plain,
! [SV13: $i] :
( ( ! [SY64: $i,SY65: $i] :
( ~ ( member @ SY65 @ ( cross_product @ SV13 @ SY64 ) )
| ( SY65
= ( ordered_pair @ ( first @ SY65 ) @ ( second @ SY65 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(124,plain,
! [SV14: $i] :
( ( ! [SY66: $i,SY67: $i,SY68: $i] :
~ ( ~ ( ~ ( member @ ( ordered_pair @ SV14 @ SY66 ) @ ( cross_product @ SY67 @ SY68 ) )
| ~ ( ~ ( member @ SV14 @ SY67 )
| ~ ( member @ SY66 @ SY68 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV14 @ SY67 )
| ~ ( member @ SY66 @ SY68 ) )
| ( member @ ( ordered_pair @ SV14 @ SY66 ) @ ( cross_product @ SY67 @ SY68 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(125,plain,
! [SV15: $i] :
( ( ~ ( member @ SV15 @ universal_class )
| ( member @ ( power_class @ SV15 ) @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(126,plain,
! [SV16: $i] :
( ( ! [SY69: $i] :
~ ( ~ ( ~ ( member @ ( ordered_pair @ SV16 @ SY69 ) @ element_relation )
| ~ ( ~ ( member @ SY69 @ universal_class )
| ~ ( member @ SV16 @ SY69 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY69 @ universal_class )
| ~ ( member @ SV16 @ SY69 ) )
| ( member @ ( ordered_pair @ SV16 @ SY69 ) @ element_relation ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(127,plain,
! [SV17: $i] :
( ( ! [SY70: $i] :
( ~ ~ ( ~ ( member @ SV17 @ universal_class )
| ~ ( member @ SY70 @ universal_class ) )
| ~ ( ( ( first @ ( ordered_pair @ SV17 @ SY70 ) )
!= SV17 )
| ( ( second @ ( ordered_pair @ SV17 @ SY70 ) )
!= SY70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(128,plain,
! [SV18: $i,SV2: $i] :
( ( member @ ( unordered_pair @ SV2 @ SV18 ) @ universal_class )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(129,plain,
! [SV3: $i] :
( ( member @ SV3 @ null_class )
= $false ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(130,plain,
! [SV19: $i,SV4: $i] :
( ( ! [SY71: $i] :
~ ( ~ ( ~ ( member @ SY71 @ ( union @ SV4 @ SV19 ) )
| ( member @ SY71 @ SV4 )
| ( member @ SY71 @ SV19 ) )
| ~ ( ~ ( ( member @ SY71 @ SV4 )
| ( member @ SY71 @ SV19 ) )
| ( member @ SY71 @ ( union @ SV4 @ SV19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(131,plain,
! [SV5: $i] :
( ( ( ~ ( member @ SV5 @ universal_class ) )
= $true )
| ( ( member @ ( sum_class @ SV5 ) @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(132,plain,
! [SV20: $i,SV6: $i] :
( ( ! [SY72: $i] :
~ ( ~ ( ~ ( member @ SY72 @ ( intersection @ SV6 @ SV20 ) )
| ~ ( ~ ( member @ SY72 @ SV6 )
| ~ ( member @ SY72 @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY72 @ SV6 )
| ~ ( member @ SY72 @ SV20 ) )
| ( member @ SY72 @ ( intersection @ SV6 @ SV20 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(133,plain,
! [SV21: $i,SV7: $i] :
( ( ~ ( ~ ( ~ ( disjoint @ SV7 @ SV21 )
| ! [SY73: $i] :
~ ~ ( ~ ( member @ SY73 @ SV7 )
| ~ ( member @ SY73 @ SV21 ) ) )
| ~ ( ~ ! [SY74: $i] :
~ ~ ( ~ ( member @ SY74 @ SV7 )
| ~ ( member @ SY74 @ SV21 ) )
| ( disjoint @ SV7 @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(134,plain,
! [SV22: $i,SV8: $i] :
( ( ~ ( ~ ( ~ ( subclass @ SV8 @ SV22 )
| ! [SY75: $i] :
( ~ ( member @ SY75 @ SV8 )
| ( member @ SY75 @ SV22 ) ) )
| ~ ( ~ ! [SY76: $i] :
( ~ ( member @ SY76 @ SV8 )
| ( member @ SY76 @ SV22 ) )
| ( subclass @ SV8 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(135,plain,
! [SV9: $i,SV23: $i] :
( ( ~ ( ~ ( ~ ( member @ SV23 @ ( complement @ SV9 ) )
| ~ ( ~ ( member @ SV23 @ universal_class )
| ~ ~ ( member @ SV23 @ SV9 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV23 @ universal_class )
| ~ ~ ( member @ SV23 @ SV9 ) )
| ( member @ SV23 @ ( complement @ SV9 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(136,plain,
! [SV24: $i,SV10: $i] :
( ( ~ ( ~ ( ~ ( member @ SV10 @ ( sum_class @ SV24 ) )
| ~ ! [SY77: $i] :
~ ~ ( ~ ( member @ SV10 @ SY77 )
| ~ ( member @ SY77 @ SV24 ) ) )
| ~ ( ~ ~ ! [SY78: $i] :
~ ~ ( ~ ( member @ SV10 @ SY78 )
| ~ ( member @ SY78 @ SV24 ) )
| ( member @ SV10 @ ( sum_class @ SV24 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(137,plain,
! [SV11: $i] :
( ( ~ ( ~ ( member @ SV11 @ identity_relation )
| ~ ! [SY60: $i] :
~ ~ ( ~ ( member @ SY60 @ universal_class )
| ( SV11
!= ( ordered_pair @ SY60 @ SY60 ) ) ) )
| ~ ( ~ ~ ! [SY61: $i] :
~ ~ ( ~ ( member @ SY61 @ universal_class )
| ( SV11
!= ( ordered_pair @ SY61 @ SY61 ) ) )
| ( member @ SV11 @ identity_relation ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(138,plain,
! [SV25: $i,SV12: $i] :
( ( ! [SY79: $i] :
~ ( ~ ( ~ ( member @ SV12 @ ( unordered_pair @ SV25 @ SY79 ) )
| ~ ( ~ ( member @ SV12 @ universal_class )
| ~ ( ( SV12 = SV25 )
| ( SV12 = SY79 ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV12 @ universal_class )
| ~ ( ( SV12 = SV25 )
| ( SV12 = SY79 ) ) )
| ( member @ SV12 @ ( unordered_pair @ SV25 @ SY79 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(139,plain,
! [SV26: $i,SV13: $i] :
( ( ! [SY80: $i] :
( ~ ( member @ SY80 @ ( cross_product @ SV13 @ SV26 ) )
| ( SY80
= ( ordered_pair @ ( first @ SY80 ) @ ( second @ SY80 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(140,plain,
! [SV27: $i,SV14: $i] :
( ( ! [SY81: $i,SY82: $i] :
~ ( ~ ( ~ ( member @ ( ordered_pair @ SV14 @ SV27 ) @ ( cross_product @ SY81 @ SY82 ) )
| ~ ( ~ ( member @ SV14 @ SY81 )
| ~ ( member @ SV27 @ SY82 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV14 @ SY81 )
| ~ ( member @ SV27 @ SY82 ) )
| ( member @ ( ordered_pair @ SV14 @ SV27 ) @ ( cross_product @ SY81 @ SY82 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(141,plain,
! [SV15: $i] :
( ( ( ~ ( member @ SV15 @ universal_class ) )
= $true )
| ( ( member @ ( power_class @ SV15 ) @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(142,plain,
! [SV28: $i,SV16: $i] :
( ( ~ ( ~ ( ~ ( member @ ( ordered_pair @ SV16 @ SV28 ) @ element_relation )
| ~ ( ~ ( member @ SV28 @ universal_class )
| ~ ( member @ SV16 @ SV28 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV28 @ universal_class )
| ~ ( member @ SV16 @ SV28 ) )
| ( member @ ( ordered_pair @ SV16 @ SV28 ) @ element_relation ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(143,plain,
! [SV29: $i,SV17: $i] :
( ( ~ ~ ( ~ ( member @ SV17 @ universal_class )
| ~ ( member @ SV29 @ universal_class ) )
| ~ ( ( ( first @ ( ordered_pair @ SV17 @ SV29 ) )
!= SV17 )
| ( ( second @ ( ordered_pair @ SV17 @ SV29 ) )
!= SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(144,plain,
! [SV19: $i,SV4: $i,SV30: $i] :
( ( ~ ( ~ ( ~ ( member @ SV30 @ ( union @ SV4 @ SV19 ) )
| ( member @ SV30 @ SV4 )
| ( member @ SV30 @ SV19 ) )
| ~ ( ~ ( ( member @ SV30 @ SV4 )
| ( member @ SV30 @ SV19 ) )
| ( member @ SV30 @ ( union @ SV4 @ SV19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(145,plain,
! [SV5: $i] :
( ( ( member @ SV5 @ universal_class )
= $false )
| ( ( member @ ( sum_class @ SV5 ) @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(146,plain,
! [SV20: $i,SV6: $i,SV31: $i] :
( ( ~ ( ~ ( ~ ( member @ SV31 @ ( intersection @ SV6 @ SV20 ) )
| ~ ( ~ ( member @ SV31 @ SV6 )
| ~ ( member @ SV31 @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV31 @ SV6 )
| ~ ( member @ SV31 @ SV20 ) )
| ( member @ SV31 @ ( intersection @ SV6 @ SV20 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(147,plain,
! [SV21: $i,SV7: $i] :
( ( ~ ( ~ ( disjoint @ SV7 @ SV21 )
| ! [SY73: $i] :
~ ~ ( ~ ( member @ SY73 @ SV7 )
| ~ ( member @ SY73 @ SV21 ) ) )
| ~ ( ~ ! [SY74: $i] :
~ ~ ( ~ ( member @ SY74 @ SV7 )
| ~ ( member @ SY74 @ SV21 ) )
| ( disjoint @ SV7 @ SV21 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(148,plain,
! [SV22: $i,SV8: $i] :
( ( ~ ( ~ ( subclass @ SV8 @ SV22 )
| ! [SY75: $i] :
( ~ ( member @ SY75 @ SV8 )
| ( member @ SY75 @ SV22 ) ) )
| ~ ( ~ ! [SY76: $i] :
( ~ ( member @ SY76 @ SV8 )
| ( member @ SY76 @ SV22 ) )
| ( subclass @ SV8 @ SV22 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(149,plain,
! [SV9: $i,SV23: $i] :
( ( ~ ( ~ ( member @ SV23 @ ( complement @ SV9 ) )
| ~ ( ~ ( member @ SV23 @ universal_class )
| ~ ~ ( member @ SV23 @ SV9 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV23 @ universal_class )
| ~ ~ ( member @ SV23 @ SV9 ) )
| ( member @ SV23 @ ( complement @ SV9 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(150,plain,
! [SV24: $i,SV10: $i] :
( ( ~ ( ~ ( member @ SV10 @ ( sum_class @ SV24 ) )
| ~ ! [SY77: $i] :
~ ~ ( ~ ( member @ SV10 @ SY77 )
| ~ ( member @ SY77 @ SV24 ) ) )
| ~ ( ~ ~ ! [SY78: $i] :
~ ~ ( ~ ( member @ SV10 @ SY78 )
| ~ ( member @ SY78 @ SV24 ) )
| ( member @ SV10 @ ( sum_class @ SV24 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(151,plain,
! [SV11: $i] :
( ( ~ ( ~ ( member @ SV11 @ identity_relation )
| ~ ! [SY60: $i] :
~ ~ ( ~ ( member @ SY60 @ universal_class )
| ( SV11
!= ( ordered_pair @ SY60 @ SY60 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(152,plain,
! [SV11: $i] :
( ( ~ ( ~ ~ ! [SY61: $i] :
~ ~ ( ~ ( member @ SY61 @ universal_class )
| ( SV11
!= ( ordered_pair @ SY61 @ SY61 ) ) )
| ( member @ SV11 @ identity_relation ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(153,plain,
! [SV32: $i,SV25: $i,SV12: $i] :
( ( ~ ( ~ ( ~ ( member @ SV12 @ ( unordered_pair @ SV25 @ SV32 ) )
| ~ ( ~ ( member @ SV12 @ universal_class )
| ~ ( ( SV12 = SV25 )
| ( SV12 = SV32 ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV12 @ universal_class )
| ~ ( ( SV12 = SV25 )
| ( SV12 = SV32 ) ) )
| ( member @ SV12 @ ( unordered_pair @ SV25 @ SV32 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(154,plain,
! [SV26: $i,SV13: $i,SV33: $i] :
( ( ~ ( member @ SV33 @ ( cross_product @ SV13 @ SV26 ) )
| ( SV33
= ( ordered_pair @ ( first @ SV33 ) @ ( second @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(155,plain,
! [SV34: $i,SV27: $i,SV14: $i] :
( ( ! [SY83: $i] :
~ ( ~ ( ~ ( member @ ( ordered_pair @ SV14 @ SV27 ) @ ( cross_product @ SV34 @ SY83 ) )
| ~ ( ~ ( member @ SV14 @ SV34 )
| ~ ( member @ SV27 @ SY83 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV14 @ SV34 )
| ~ ( member @ SV27 @ SY83 ) )
| ( member @ ( ordered_pair @ SV14 @ SV27 ) @ ( cross_product @ SV34 @ SY83 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(156,plain,
! [SV15: $i] :
( ( ( member @ SV15 @ universal_class )
= $false )
| ( ( member @ ( power_class @ SV15 ) @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(157,plain,
! [SV28: $i,SV16: $i] :
( ( ~ ( ~ ( member @ ( ordered_pair @ SV16 @ SV28 ) @ element_relation )
| ~ ( ~ ( member @ SV28 @ universal_class )
| ~ ( member @ SV16 @ SV28 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV28 @ universal_class )
| ~ ( member @ SV16 @ SV28 ) )
| ( member @ ( ordered_pair @ SV16 @ SV28 ) @ element_relation ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(158,plain,
! [SV29: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( member @ SV17 @ universal_class )
| ~ ( member @ SV29 @ universal_class ) ) )
= $true )
| ( ( ~ ( ( ( first @ ( ordered_pair @ SV17 @ SV29 ) )
!= SV17 )
| ( ( second @ ( ordered_pair @ SV17 @ SV29 ) )
!= SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(159,plain,
! [SV19: $i,SV4: $i,SV30: $i] :
( ( ~ ( ~ ( member @ SV30 @ ( union @ SV4 @ SV19 ) )
| ( member @ SV30 @ SV4 )
| ( member @ SV30 @ SV19 ) )
| ~ ( ~ ( ( member @ SV30 @ SV4 )
| ( member @ SV30 @ SV19 ) )
| ( member @ SV30 @ ( union @ SV4 @ SV19 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(160,plain,
! [SV20: $i,SV6: $i,SV31: $i] :
( ( ~ ( ~ ( member @ SV31 @ ( intersection @ SV6 @ SV20 ) )
| ~ ( ~ ( member @ SV31 @ SV6 )
| ~ ( member @ SV31 @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV31 @ SV6 )
| ~ ( member @ SV31 @ SV20 ) )
| ( member @ SV31 @ ( intersection @ SV6 @ SV20 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(161,plain,
! [SV21: $i,SV7: $i] :
( ( ~ ( ~ ( disjoint @ SV7 @ SV21 )
| ! [SY73: $i] :
~ ~ ( ~ ( member @ SY73 @ SV7 )
| ~ ( member @ SY73 @ SV21 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(162,plain,
! [SV21: $i,SV7: $i] :
( ( ~ ( ~ ! [SY74: $i] :
~ ~ ( ~ ( member @ SY74 @ SV7 )
| ~ ( member @ SY74 @ SV21 ) )
| ( disjoint @ SV7 @ SV21 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(163,plain,
! [SV22: $i,SV8: $i] :
( ( ~ ( ~ ( subclass @ SV8 @ SV22 )
| ! [SY75: $i] :
( ~ ( member @ SY75 @ SV8 )
| ( member @ SY75 @ SV22 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[148]) ).
thf(164,plain,
! [SV22: $i,SV8: $i] :
( ( ~ ( ~ ! [SY76: $i] :
( ~ ( member @ SY76 @ SV8 )
| ( member @ SY76 @ SV22 ) )
| ( subclass @ SV8 @ SV22 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[148]) ).
thf(165,plain,
! [SV9: $i,SV23: $i] :
( ( ~ ( ~ ( member @ SV23 @ ( complement @ SV9 ) )
| ~ ( ~ ( member @ SV23 @ universal_class )
| ~ ~ ( member @ SV23 @ SV9 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[149]) ).
thf(166,plain,
! [SV9: $i,SV23: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV23 @ universal_class )
| ~ ~ ( member @ SV23 @ SV9 ) )
| ( member @ SV23 @ ( complement @ SV9 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[149]) ).
thf(167,plain,
! [SV24: $i,SV10: $i] :
( ( ~ ( ~ ( member @ SV10 @ ( sum_class @ SV24 ) )
| ~ ! [SY77: $i] :
~ ~ ( ~ ( member @ SV10 @ SY77 )
| ~ ( member @ SY77 @ SV24 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[150]) ).
thf(168,plain,
! [SV24: $i,SV10: $i] :
( ( ~ ( ~ ~ ! [SY78: $i] :
~ ~ ( ~ ( member @ SV10 @ SY78 )
| ~ ( member @ SY78 @ SV24 ) )
| ( member @ SV10 @ ( sum_class @ SV24 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[150]) ).
thf(169,plain,
! [SV11: $i] :
( ( ~ ( member @ SV11 @ identity_relation )
| ~ ! [SY60: $i] :
~ ~ ( ~ ( member @ SY60 @ universal_class )
| ( SV11
!= ( ordered_pair @ SY60 @ SY60 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(170,plain,
! [SV11: $i] :
( ( ~ ~ ! [SY61: $i] :
~ ~ ( ~ ( member @ SY61 @ universal_class )
| ( SV11
!= ( ordered_pair @ SY61 @ SY61 ) ) )
| ( member @ SV11 @ identity_relation ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(171,plain,
! [SV32: $i,SV25: $i,SV12: $i] :
( ( ~ ( ~ ( member @ SV12 @ ( unordered_pair @ SV25 @ SV32 ) )
| ~ ( ~ ( member @ SV12 @ universal_class )
| ~ ( ( SV12 = SV25 )
| ( SV12 = SV32 ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV12 @ universal_class )
| ~ ( ( SV12 = SV25 )
| ( SV12 = SV32 ) ) )
| ( member @ SV12 @ ( unordered_pair @ SV25 @ SV32 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(172,plain,
! [SV26: $i,SV13: $i,SV33: $i] :
( ( ( ~ ( member @ SV33 @ ( cross_product @ SV13 @ SV26 ) ) )
= $true )
| ( ( SV33
= ( ordered_pair @ ( first @ SV33 ) @ ( second @ SV33 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(173,plain,
! [SV35: $i,SV34: $i,SV27: $i,SV14: $i] :
( ( ~ ( ~ ( ~ ( member @ ( ordered_pair @ SV14 @ SV27 ) @ ( cross_product @ SV34 @ SV35 ) )
| ~ ( ~ ( member @ SV14 @ SV34 )
| ~ ( member @ SV27 @ SV35 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV14 @ SV34 )
| ~ ( member @ SV27 @ SV35 ) )
| ( member @ ( ordered_pair @ SV14 @ SV27 ) @ ( cross_product @ SV34 @ SV35 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(174,plain,
! [SV28: $i,SV16: $i] :
( ( ~ ( ~ ( member @ ( ordered_pair @ SV16 @ SV28 ) @ element_relation )
| ~ ( ~ ( member @ SV28 @ universal_class )
| ~ ( member @ SV16 @ SV28 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[157]) ).
thf(175,plain,
! [SV16: $i,SV28: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV28 @ universal_class )
| ~ ( member @ SV16 @ SV28 ) )
| ( member @ ( ordered_pair @ SV16 @ SV28 ) @ element_relation ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[157]) ).
thf(176,plain,
! [SV29: $i,SV17: $i] :
( ( ( ~ ( ~ ( member @ SV17 @ universal_class )
| ~ ( member @ SV29 @ universal_class ) ) )
= $false )
| ( ( ~ ( ( ( first @ ( ordered_pair @ SV17 @ SV29 ) )
!= SV17 )
| ( ( second @ ( ordered_pair @ SV17 @ SV29 ) )
!= SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(177,plain,
! [SV19: $i,SV4: $i,SV30: $i] :
( ( ~ ( ~ ( member @ SV30 @ ( union @ SV4 @ SV19 ) )
| ( member @ SV30 @ SV4 )
| ( member @ SV30 @ SV19 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[159]) ).
thf(178,plain,
! [SV19: $i,SV4: $i,SV30: $i] :
( ( ~ ( ~ ( ( member @ SV30 @ SV4 )
| ( member @ SV30 @ SV19 ) )
| ( member @ SV30 @ ( union @ SV4 @ SV19 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[159]) ).
thf(179,plain,
! [SV20: $i,SV6: $i,SV31: $i] :
( ( ~ ( ~ ( member @ SV31 @ ( intersection @ SV6 @ SV20 ) )
| ~ ( ~ ( member @ SV31 @ SV6 )
| ~ ( member @ SV31 @ SV20 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[160]) ).
thf(180,plain,
! [SV20: $i,SV6: $i,SV31: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV31 @ SV6 )
| ~ ( member @ SV31 @ SV20 ) )
| ( member @ SV31 @ ( intersection @ SV6 @ SV20 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[160]) ).
thf(181,plain,
! [SV21: $i,SV7: $i] :
( ( ~ ( disjoint @ SV7 @ SV21 )
| ! [SY73: $i] :
~ ~ ( ~ ( member @ SY73 @ SV7 )
| ~ ( member @ SY73 @ SV21 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[161]) ).
thf(182,plain,
! [SV21: $i,SV7: $i] :
( ( ~ ! [SY74: $i] :
~ ~ ( ~ ( member @ SY74 @ SV7 )
| ~ ( member @ SY74 @ SV21 ) )
| ( disjoint @ SV7 @ SV21 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[162]) ).
thf(183,plain,
! [SV22: $i,SV8: $i] :
( ( ~ ( subclass @ SV8 @ SV22 )
| ! [SY75: $i] :
( ~ ( member @ SY75 @ SV8 )
| ( member @ SY75 @ SV22 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[163]) ).
thf(184,plain,
! [SV22: $i,SV8: $i] :
( ( ~ ! [SY76: $i] :
( ~ ( member @ SY76 @ SV8 )
| ( member @ SY76 @ SV22 ) )
| ( subclass @ SV8 @ SV22 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[164]) ).
thf(185,plain,
! [SV9: $i,SV23: $i] :
( ( ~ ( member @ SV23 @ ( complement @ SV9 ) )
| ~ ( ~ ( member @ SV23 @ universal_class )
| ~ ~ ( member @ SV23 @ SV9 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[165]) ).
thf(186,plain,
! [SV9: $i,SV23: $i] :
( ( ~ ~ ( ~ ( member @ SV23 @ universal_class )
| ~ ~ ( member @ SV23 @ SV9 ) )
| ( member @ SV23 @ ( complement @ SV9 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[166]) ).
thf(187,plain,
! [SV24: $i,SV10: $i] :
( ( ~ ( member @ SV10 @ ( sum_class @ SV24 ) )
| ~ ! [SY77: $i] :
~ ~ ( ~ ( member @ SV10 @ SY77 )
| ~ ( member @ SY77 @ SV24 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(188,plain,
! [SV24: $i,SV10: $i] :
( ( ~ ~ ! [SY78: $i] :
~ ~ ( ~ ( member @ SV10 @ SY78 )
| ~ ( member @ SY78 @ SV24 ) )
| ( member @ SV10 @ ( sum_class @ SV24 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[168]) ).
thf(189,plain,
! [SV11: $i] :
( ( ( ~ ( member @ SV11 @ identity_relation ) )
= $true )
| ( ( ~ ! [SY60: $i] :
~ ~ ( ~ ( member @ SY60 @ universal_class )
| ( SV11
!= ( ordered_pair @ SY60 @ SY60 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(190,plain,
! [SV11: $i] :
( ( ( ~ ~ ! [SY61: $i] :
~ ~ ( ~ ( member @ SY61 @ universal_class )
| ( SV11
!= ( ordered_pair @ SY61 @ SY61 ) ) ) )
= $true )
| ( ( member @ SV11 @ identity_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(191,plain,
! [SV32: $i,SV25: $i,SV12: $i] :
( ( ~ ( ~ ( member @ SV12 @ ( unordered_pair @ SV25 @ SV32 ) )
| ~ ( ~ ( member @ SV12 @ universal_class )
| ~ ( ( SV12 = SV25 )
| ( SV12 = SV32 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[171]) ).
thf(192,plain,
! [SV32: $i,SV25: $i,SV12: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV12 @ universal_class )
| ~ ( ( SV12 = SV25 )
| ( SV12 = SV32 ) ) )
| ( member @ SV12 @ ( unordered_pair @ SV25 @ SV32 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[171]) ).
thf(193,plain,
! [SV26: $i,SV13: $i,SV33: $i] :
( ( ( member @ SV33 @ ( cross_product @ SV13 @ SV26 ) )
= $false )
| ( ( SV33
= ( ordered_pair @ ( first @ SV33 ) @ ( second @ SV33 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(194,plain,
! [SV35: $i,SV34: $i,SV27: $i,SV14: $i] :
( ( ~ ( ~ ( member @ ( ordered_pair @ SV14 @ SV27 ) @ ( cross_product @ SV34 @ SV35 ) )
| ~ ( ~ ( member @ SV14 @ SV34 )
| ~ ( member @ SV27 @ SV35 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV14 @ SV34 )
| ~ ( member @ SV27 @ SV35 ) )
| ( member @ ( ordered_pair @ SV14 @ SV27 ) @ ( cross_product @ SV34 @ SV35 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(195,plain,
! [SV28: $i,SV16: $i] :
( ( ~ ( member @ ( ordered_pair @ SV16 @ SV28 ) @ element_relation )
| ~ ( ~ ( member @ SV28 @ universal_class )
| ~ ( member @ SV16 @ SV28 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(196,plain,
! [SV16: $i,SV28: $i] :
( ( ~ ~ ( ~ ( member @ SV28 @ universal_class )
| ~ ( member @ SV16 @ SV28 ) )
| ( member @ ( ordered_pair @ SV16 @ SV28 ) @ element_relation ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(197,plain,
! [SV29: $i,SV17: $i] :
( ( ( ~ ( member @ SV17 @ universal_class )
| ~ ( member @ SV29 @ universal_class ) )
= $true )
| ( ( ~ ( ( ( first @ ( ordered_pair @ SV17 @ SV29 ) )
!= SV17 )
| ( ( second @ ( ordered_pair @ SV17 @ SV29 ) )
!= SV29 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(198,plain,
! [SV19: $i,SV4: $i,SV30: $i] :
( ( ~ ( member @ SV30 @ ( union @ SV4 @ SV19 ) )
| ( member @ SV30 @ SV4 )
| ( member @ SV30 @ SV19 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[177]) ).
thf(199,plain,
! [SV19: $i,SV4: $i,SV30: $i] :
( ( ~ ( ( member @ SV30 @ SV4 )
| ( member @ SV30 @ SV19 ) )
| ( member @ SV30 @ ( union @ SV4 @ SV19 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[178]) ).
thf(200,plain,
! [SV20: $i,SV6: $i,SV31: $i] :
( ( ~ ( member @ SV31 @ ( intersection @ SV6 @ SV20 ) )
| ~ ( ~ ( member @ SV31 @ SV6 )
| ~ ( member @ SV31 @ SV20 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(201,plain,
! [SV20: $i,SV6: $i,SV31: $i] :
( ( ~ ~ ( ~ ( member @ SV31 @ SV6 )
| ~ ( member @ SV31 @ SV20 ) )
| ( member @ SV31 @ ( intersection @ SV6 @ SV20 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[180]) ).
thf(202,plain,
! [SV21: $i,SV7: $i] :
( ( ( ~ ( disjoint @ SV7 @ SV21 ) )
= $true )
| ( ( ! [SY73: $i] :
~ ~ ( ~ ( member @ SY73 @ SV7 )
| ~ ( member @ SY73 @ SV21 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(203,plain,
! [SV21: $i,SV7: $i] :
( ( ( ~ ! [SY74: $i] :
~ ~ ( ~ ( member @ SY74 @ SV7 )
| ~ ( member @ SY74 @ SV21 ) ) )
= $true )
| ( ( disjoint @ SV7 @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(204,plain,
! [SV22: $i,SV8: $i] :
( ( ( ~ ( subclass @ SV8 @ SV22 ) )
= $true )
| ( ( ! [SY75: $i] :
( ~ ( member @ SY75 @ SV8 )
| ( member @ SY75 @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(205,plain,
! [SV22: $i,SV8: $i] :
( ( ( ~ ! [SY76: $i] :
( ~ ( member @ SY76 @ SV8 )
| ( member @ SY76 @ SV22 ) ) )
= $true )
| ( ( subclass @ SV8 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(206,plain,
! [SV9: $i,SV23: $i] :
( ( ( ~ ( member @ SV23 @ ( complement @ SV9 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ SV23 @ universal_class )
| ~ ~ ( member @ SV23 @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(207,plain,
! [SV9: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( member @ SV23 @ universal_class )
| ~ ~ ( member @ SV23 @ SV9 ) ) )
= $true )
| ( ( member @ SV23 @ ( complement @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(208,plain,
! [SV24: $i,SV10: $i] :
( ( ( ~ ( member @ SV10 @ ( sum_class @ SV24 ) ) )
= $true )
| ( ( ~ ! [SY77: $i] :
~ ~ ( ~ ( member @ SV10 @ SY77 )
| ~ ( member @ SY77 @ SV24 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(209,plain,
! [SV24: $i,SV10: $i] :
( ( ( ~ ~ ! [SY78: $i] :
~ ~ ( ~ ( member @ SV10 @ SY78 )
| ~ ( member @ SY78 @ SV24 ) ) )
= $true )
| ( ( member @ SV10 @ ( sum_class @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(210,plain,
! [SV11: $i] :
( ( ( member @ SV11 @ identity_relation )
= $false )
| ( ( ~ ! [SY60: $i] :
~ ~ ( ~ ( member @ SY60 @ universal_class )
| ( SV11
!= ( ordered_pair @ SY60 @ SY60 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(211,plain,
! [SV11: $i] :
( ( ( ~ ! [SY61: $i] :
~ ~ ( ~ ( member @ SY61 @ universal_class )
| ( SV11
!= ( ordered_pair @ SY61 @ SY61 ) ) ) )
= $false )
| ( ( member @ SV11 @ identity_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(212,plain,
! [SV32: $i,SV25: $i,SV12: $i] :
( ( ~ ( member @ SV12 @ ( unordered_pair @ SV25 @ SV32 ) )
| ~ ( ~ ( member @ SV12 @ universal_class )
| ~ ( ( SV12 = SV25 )
| ( SV12 = SV32 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[191]) ).
thf(213,plain,
! [SV32: $i,SV25: $i,SV12: $i] :
( ( ~ ~ ( ~ ( member @ SV12 @ universal_class )
| ~ ( ( SV12 = SV25 )
| ( SV12 = SV32 ) ) )
| ( member @ SV12 @ ( unordered_pair @ SV25 @ SV32 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[192]) ).
thf(214,plain,
! [SV35: $i,SV34: $i,SV27: $i,SV14: $i] :
( ( ~ ( ~ ( member @ ( ordered_pair @ SV14 @ SV27 ) @ ( cross_product @ SV34 @ SV35 ) )
| ~ ( ~ ( member @ SV14 @ SV34 )
| ~ ( member @ SV27 @ SV35 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(215,plain,
! [SV35: $i,SV27: $i,SV34: $i,SV14: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV14 @ SV34 )
| ~ ( member @ SV27 @ SV35 ) )
| ( member @ ( ordered_pair @ SV14 @ SV27 ) @ ( cross_product @ SV34 @ SV35 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(216,plain,
! [SV28: $i,SV16: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV16 @ SV28 ) @ element_relation ) )
= $true )
| ( ( ~ ( ~ ( member @ SV28 @ universal_class )
| ~ ( member @ SV16 @ SV28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(217,plain,
! [SV16: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ( member @ SV28 @ universal_class )
| ~ ( member @ SV16 @ SV28 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ SV16 @ SV28 ) @ element_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(218,plain,
! [SV29: $i,SV17: $i] :
( ( ( ~ ( member @ SV17 @ universal_class ) )
= $true )
| ( ( ~ ( member @ SV29 @ universal_class ) )
= $true )
| ( ( ~ ( ( ( first @ ( ordered_pair @ SV17 @ SV29 ) )
!= SV17 )
| ( ( second @ ( ordered_pair @ SV17 @ SV29 ) )
!= SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(219,plain,
! [SV19: $i,SV4: $i,SV30: $i] :
( ( ( ~ ( member @ SV30 @ ( union @ SV4 @ SV19 ) ) )
= $true )
| ( ( ( member @ SV30 @ SV4 )
| ( member @ SV30 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(220,plain,
! [SV19: $i,SV4: $i,SV30: $i] :
( ( ( ~ ( ( member @ SV30 @ SV4 )
| ( member @ SV30 @ SV19 ) ) )
= $true )
| ( ( member @ SV30 @ ( union @ SV4 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(221,plain,
! [SV20: $i,SV6: $i,SV31: $i] :
( ( ( ~ ( member @ SV31 @ ( intersection @ SV6 @ SV20 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ SV31 @ SV6 )
| ~ ( member @ SV31 @ SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(222,plain,
! [SV20: $i,SV6: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ( member @ SV31 @ SV6 )
| ~ ( member @ SV31 @ SV20 ) ) )
= $true )
| ( ( member @ SV31 @ ( intersection @ SV6 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(223,plain,
! [SV21: $i,SV7: $i] :
( ( ( disjoint @ SV7 @ SV21 )
= $false )
| ( ( ! [SY73: $i] :
~ ~ ( ~ ( member @ SY73 @ SV7 )
| ~ ( member @ SY73 @ SV21 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(224,plain,
! [SV21: $i,SV7: $i] :
( ( ( ! [SY74: $i] :
~ ~ ( ~ ( member @ SY74 @ SV7 )
| ~ ( member @ SY74 @ SV21 ) ) )
= $false )
| ( ( disjoint @ SV7 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(225,plain,
! [SV22: $i,SV8: $i] :
( ( ( subclass @ SV8 @ SV22 )
= $false )
| ( ( ! [SY75: $i] :
( ~ ( member @ SY75 @ SV8 )
| ( member @ SY75 @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(226,plain,
! [SV22: $i,SV8: $i] :
( ( ( ! [SY76: $i] :
( ~ ( member @ SY76 @ SV8 )
| ( member @ SY76 @ SV22 ) ) )
= $false )
| ( ( subclass @ SV8 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(227,plain,
! [SV9: $i,SV23: $i] :
( ( ( member @ SV23 @ ( complement @ SV9 ) )
= $false )
| ( ( ~ ( ~ ( member @ SV23 @ universal_class )
| ~ ~ ( member @ SV23 @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(228,plain,
! [SV9: $i,SV23: $i] :
( ( ( ~ ( ~ ( member @ SV23 @ universal_class )
| ~ ~ ( member @ SV23 @ SV9 ) ) )
= $false )
| ( ( member @ SV23 @ ( complement @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(229,plain,
! [SV24: $i,SV10: $i] :
( ( ( member @ SV10 @ ( sum_class @ SV24 ) )
= $false )
| ( ( ~ ! [SY77: $i] :
~ ~ ( ~ ( member @ SV10 @ SY77 )
| ~ ( member @ SY77 @ SV24 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(230,plain,
! [SV24: $i,SV10: $i] :
( ( ( ~ ! [SY78: $i] :
~ ~ ( ~ ( member @ SV10 @ SY78 )
| ~ ( member @ SY78 @ SV24 ) ) )
= $false )
| ( ( member @ SV10 @ ( sum_class @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(231,plain,
! [SV11: $i] :
( ( ( ! [SY60: $i] :
~ ~ ( ~ ( member @ SY60 @ universal_class )
| ( SV11
!= ( ordered_pair @ SY60 @ SY60 ) ) ) )
= $false )
| ( ( member @ SV11 @ identity_relation )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(232,plain,
! [SV11: $i] :
( ( ( ! [SY61: $i] :
~ ~ ( ~ ( member @ SY61 @ universal_class )
| ( SV11
!= ( ordered_pair @ SY61 @ SY61 ) ) ) )
= $true )
| ( ( member @ SV11 @ identity_relation )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[211]) ).
thf(233,plain,
! [SV32: $i,SV25: $i,SV12: $i] :
( ( ( ~ ( member @ SV12 @ ( unordered_pair @ SV25 @ SV32 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ SV12 @ universal_class )
| ~ ( ( SV12 = SV25 )
| ( SV12 = SV32 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(234,plain,
! [SV32: $i,SV25: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( member @ SV12 @ universal_class )
| ~ ( ( SV12 = SV25 )
| ( SV12 = SV32 ) ) ) )
= $true )
| ( ( member @ SV12 @ ( unordered_pair @ SV25 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(235,plain,
! [SV35: $i,SV34: $i,SV27: $i,SV14: $i] :
( ( ~ ( member @ ( ordered_pair @ SV14 @ SV27 ) @ ( cross_product @ SV34 @ SV35 ) )
| ~ ( ~ ( member @ SV14 @ SV34 )
| ~ ( member @ SV27 @ SV35 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(236,plain,
! [SV35: $i,SV27: $i,SV34: $i,SV14: $i] :
( ( ~ ~ ( ~ ( member @ SV14 @ SV34 )
| ~ ( member @ SV27 @ SV35 ) )
| ( member @ ( ordered_pair @ SV14 @ SV27 ) @ ( cross_product @ SV34 @ SV35 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[215]) ).
thf(237,plain,
! [SV28: $i,SV16: $i] :
( ( ( member @ ( ordered_pair @ SV16 @ SV28 ) @ element_relation )
= $false )
| ( ( ~ ( ~ ( member @ SV28 @ universal_class )
| ~ ( member @ SV16 @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(238,plain,
! [SV16: $i,SV28: $i] :
( ( ( ~ ( ~ ( member @ SV28 @ universal_class )
| ~ ( member @ SV16 @ SV28 ) ) )
= $false )
| ( ( member @ ( ordered_pair @ SV16 @ SV28 ) @ element_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(239,plain,
! [SV29: $i,SV17: $i] :
( ( ( member @ SV17 @ universal_class )
= $false )
| ( ( ~ ( member @ SV29 @ universal_class ) )
= $true )
| ( ( ~ ( ( ( first @ ( ordered_pair @ SV17 @ SV29 ) )
!= SV17 )
| ( ( second @ ( ordered_pair @ SV17 @ SV29 ) )
!= SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(240,plain,
! [SV19: $i,SV4: $i,SV30: $i] :
( ( ( member @ SV30 @ ( union @ SV4 @ SV19 ) )
= $false )
| ( ( ( member @ SV30 @ SV4 )
| ( member @ SV30 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(241,plain,
! [SV19: $i,SV4: $i,SV30: $i] :
( ( ( ( member @ SV30 @ SV4 )
| ( member @ SV30 @ SV19 ) )
= $false )
| ( ( member @ SV30 @ ( union @ SV4 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(242,plain,
! [SV20: $i,SV6: $i,SV31: $i] :
( ( ( member @ SV31 @ ( intersection @ SV6 @ SV20 ) )
= $false )
| ( ( ~ ( ~ ( member @ SV31 @ SV6 )
| ~ ( member @ SV31 @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(243,plain,
! [SV20: $i,SV6: $i,SV31: $i] :
( ( ( ~ ( ~ ( member @ SV31 @ SV6 )
| ~ ( member @ SV31 @ SV20 ) ) )
= $false )
| ( ( member @ SV31 @ ( intersection @ SV6 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(244,plain,
! [SV21: $i,SV7: $i,SV36: $i] :
( ( ( ~ ~ ( ~ ( member @ SV36 @ SV7 )
| ~ ( member @ SV36 @ SV21 ) ) )
= $true )
| ( ( disjoint @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(245,plain,
! [SV7: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK4_SY74 @ SV21 @ SV7 ) @ SV7 )
| ~ ( member @ ( sK4_SY74 @ SV21 @ SV7 ) @ SV21 ) ) )
= $false )
| ( ( disjoint @ SV7 @ SV21 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[224]) ).
thf(246,plain,
! [SV22: $i,SV8: $i,SV37: $i] :
( ( ( ~ ( member @ SV37 @ SV8 )
| ( member @ SV37 @ SV22 ) )
= $true )
| ( ( subclass @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(247,plain,
! [SV8: $i,SV22: $i] :
( ( ( ~ ( member @ ( sK5_SY76 @ SV22 @ SV8 ) @ SV8 )
| ( member @ ( sK5_SY76 @ SV22 @ SV8 ) @ SV22 ) )
= $false )
| ( ( subclass @ SV8 @ SV22 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[226]) ).
thf(248,plain,
! [SV9: $i,SV23: $i] :
( ( ( ~ ( member @ SV23 @ universal_class )
| ~ ~ ( member @ SV23 @ SV9 ) )
= $false )
| ( ( member @ SV23 @ ( complement @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(249,plain,
! [SV9: $i,SV23: $i] :
( ( ( ~ ( member @ SV23 @ universal_class )
| ~ ~ ( member @ SV23 @ SV9 ) )
= $true )
| ( ( member @ SV23 @ ( complement @ SV9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(250,plain,
! [SV24: $i,SV10: $i] :
( ( ( ! [SY77: $i] :
~ ~ ( ~ ( member @ SV10 @ SY77 )
| ~ ( member @ SY77 @ SV24 ) ) )
= $false )
| ( ( member @ SV10 @ ( sum_class @ SV24 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(251,plain,
! [SV24: $i,SV10: $i] :
( ( ( ! [SY78: $i] :
~ ~ ( ~ ( member @ SV10 @ SY78 )
| ~ ( member @ SY78 @ SV24 ) ) )
= $true )
| ( ( member @ SV10 @ ( sum_class @ SV24 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[230]) ).
thf(252,plain,
! [SV11: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK6_SY60 @ SV11 ) @ universal_class )
| ( SV11
!= ( ordered_pair @ ( sK6_SY60 @ SV11 ) @ ( sK6_SY60 @ SV11 ) ) ) ) )
= $false )
| ( ( member @ SV11 @ identity_relation )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[231]) ).
thf(253,plain,
! [SV11: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ( member @ SV38 @ universal_class )
| ( SV11
!= ( ordered_pair @ SV38 @ SV38 ) ) ) )
= $true )
| ( ( member @ SV11 @ identity_relation )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(254,plain,
! [SV32: $i,SV25: $i,SV12: $i] :
( ( ( member @ SV12 @ ( unordered_pair @ SV25 @ SV32 ) )
= $false )
| ( ( ~ ( ~ ( member @ SV12 @ universal_class )
| ~ ( ( SV12 = SV25 )
| ( SV12 = SV32 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(255,plain,
! [SV32: $i,SV25: $i,SV12: $i] :
( ( ( ~ ( ~ ( member @ SV12 @ universal_class )
| ~ ( ( SV12 = SV25 )
| ( SV12 = SV32 ) ) ) )
= $false )
| ( ( member @ SV12 @ ( unordered_pair @ SV25 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(256,plain,
! [SV35: $i,SV34: $i,SV27: $i,SV14: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV14 @ SV27 ) @ ( cross_product @ SV34 @ SV35 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ SV14 @ SV34 )
| ~ ( member @ SV27 @ SV35 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(257,plain,
! [SV35: $i,SV27: $i,SV34: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( member @ SV14 @ SV34 )
| ~ ( member @ SV27 @ SV35 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ SV14 @ SV27 ) @ ( cross_product @ SV34 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(258,plain,
! [SV16: $i,SV28: $i] :
( ( ( ~ ( member @ SV28 @ universal_class )
| ~ ( member @ SV16 @ SV28 ) )
= $false )
| ( ( member @ ( ordered_pair @ SV16 @ SV28 ) @ element_relation )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(259,plain,
! [SV16: $i,SV28: $i] :
( ( ( ~ ( member @ SV28 @ universal_class )
| ~ ( member @ SV16 @ SV28 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV16 @ SV28 ) @ element_relation )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[238]) ).
thf(260,plain,
! [SV17: $i,SV29: $i] :
( ( ( member @ SV29 @ universal_class )
= $false )
| ( ( member @ SV17 @ universal_class )
= $false )
| ( ( ~ ( ( ( first @ ( ordered_pair @ SV17 @ SV29 ) )
!= SV17 )
| ( ( second @ ( ordered_pair @ SV17 @ SV29 ) )
!= SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(261,plain,
! [SV19: $i,SV4: $i,SV30: $i] :
( ( ( member @ SV30 @ SV4 )
= $true )
| ( ( member @ SV30 @ SV19 )
= $true )
| ( ( member @ SV30 @ ( union @ SV4 @ SV19 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[240]) ).
thf(262,plain,
! [SV19: $i,SV4: $i,SV30: $i] :
( ( ( member @ SV30 @ SV4 )
= $false )
| ( ( member @ SV30 @ ( union @ SV4 @ SV19 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[241]) ).
thf(263,plain,
! [SV4: $i,SV19: $i,SV30: $i] :
( ( ( member @ SV30 @ SV19 )
= $false )
| ( ( member @ SV30 @ ( union @ SV4 @ SV19 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[241]) ).
thf(264,plain,
! [SV20: $i,SV6: $i,SV31: $i] :
( ( ( ~ ( member @ SV31 @ SV6 )
| ~ ( member @ SV31 @ SV20 ) )
= $false )
| ( ( member @ SV31 @ ( intersection @ SV6 @ SV20 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(265,plain,
! [SV20: $i,SV6: $i,SV31: $i] :
( ( ( ~ ( member @ SV31 @ SV6 )
| ~ ( member @ SV31 @ SV20 ) )
= $true )
| ( ( member @ SV31 @ ( intersection @ SV6 @ SV20 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[243]) ).
thf(266,plain,
! [SV21: $i,SV7: $i,SV36: $i] :
( ( ( ~ ( ~ ( member @ SV36 @ SV7 )
| ~ ( member @ SV36 @ SV21 ) ) )
= $false )
| ( ( disjoint @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(267,plain,
! [SV7: $i,SV21: $i] :
( ( ( ~ ( ~ ( member @ ( sK4_SY74 @ SV21 @ SV7 ) @ SV7 )
| ~ ( member @ ( sK4_SY74 @ SV21 @ SV7 ) @ SV21 ) ) )
= $true )
| ( ( disjoint @ SV7 @ SV21 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[245]) ).
thf(268,plain,
! [SV22: $i,SV8: $i,SV37: $i] :
( ( ( ~ ( member @ SV37 @ SV8 ) )
= $true )
| ( ( member @ SV37 @ SV22 )
= $true )
| ( ( subclass @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(269,plain,
! [SV8: $i,SV22: $i] :
( ( ( ~ ( member @ ( sK5_SY76 @ SV22 @ SV8 ) @ SV8 ) )
= $false )
| ( ( subclass @ SV8 @ SV22 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[247]) ).
thf(270,plain,
! [SV8: $i,SV22: $i] :
( ( ( member @ ( sK5_SY76 @ SV22 @ SV8 ) @ SV22 )
= $false )
| ( ( subclass @ SV8 @ SV22 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[247]) ).
thf(271,plain,
! [SV9: $i,SV23: $i] :
( ( ( ~ ( member @ SV23 @ universal_class ) )
= $false )
| ( ( member @ SV23 @ ( complement @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[248]) ).
thf(272,plain,
! [SV9: $i,SV23: $i] :
( ( ( ~ ~ ( member @ SV23 @ SV9 ) )
= $false )
| ( ( member @ SV23 @ ( complement @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[248]) ).
thf(273,plain,
! [SV9: $i,SV23: $i] :
( ( ( ~ ( member @ SV23 @ universal_class ) )
= $true )
| ( ( ~ ~ ( member @ SV23 @ SV9 ) )
= $true )
| ( ( member @ SV23 @ ( complement @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[249]) ).
thf(274,plain,
! [SV24: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( member @ SV10 @ ( sK7_SY77 @ SV24 @ SV10 ) )
| ~ ( member @ ( sK7_SY77 @ SV24 @ SV10 ) @ SV24 ) ) )
= $false )
| ( ( member @ SV10 @ ( sum_class @ SV24 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[250]) ).
thf(275,plain,
! [SV24: $i,SV39: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( member @ SV10 @ SV39 )
| ~ ( member @ SV39 @ SV24 ) ) )
= $true )
| ( ( member @ SV10 @ ( sum_class @ SV24 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(276,plain,
! [SV11: $i] :
( ( ( ~ ( ~ ( member @ ( sK6_SY60 @ SV11 ) @ universal_class )
| ( SV11
!= ( ordered_pair @ ( sK6_SY60 @ SV11 ) @ ( sK6_SY60 @ SV11 ) ) ) ) )
= $true )
| ( ( member @ SV11 @ identity_relation )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[252]) ).
thf(277,plain,
! [SV11: $i,SV38: $i] :
( ( ( ~ ( ~ ( member @ SV38 @ universal_class )
| ( SV11
!= ( ordered_pair @ SV38 @ SV38 ) ) ) )
= $false )
| ( ( member @ SV11 @ identity_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(278,plain,
! [SV32: $i,SV25: $i,SV12: $i] :
( ( ( ~ ( member @ SV12 @ universal_class )
| ~ ( ( SV12 = SV25 )
| ( SV12 = SV32 ) ) )
= $false )
| ( ( member @ SV12 @ ( unordered_pair @ SV25 @ SV32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(279,plain,
! [SV32: $i,SV25: $i,SV12: $i] :
( ( ( ~ ( member @ SV12 @ universal_class )
| ~ ( ( SV12 = SV25 )
| ( SV12 = SV32 ) ) )
= $true )
| ( ( member @ SV12 @ ( unordered_pair @ SV25 @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(280,plain,
! [SV35: $i,SV34: $i,SV27: $i,SV14: $i] :
( ( ( member @ ( ordered_pair @ SV14 @ SV27 ) @ ( cross_product @ SV34 @ SV35 ) )
= $false )
| ( ( ~ ( ~ ( member @ SV14 @ SV34 )
| ~ ( member @ SV27 @ SV35 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(281,plain,
! [SV35: $i,SV27: $i,SV34: $i,SV14: $i] :
( ( ( ~ ( ~ ( member @ SV14 @ SV34 )
| ~ ( member @ SV27 @ SV35 ) ) )
= $false )
| ( ( member @ ( ordered_pair @ SV14 @ SV27 ) @ ( cross_product @ SV34 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(282,plain,
! [SV16: $i,SV28: $i] :
( ( ( ~ ( member @ SV28 @ universal_class ) )
= $false )
| ( ( member @ ( ordered_pair @ SV16 @ SV28 ) @ element_relation )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[258]) ).
thf(283,plain,
! [SV28: $i,SV16: $i] :
( ( ( ~ ( member @ SV16 @ SV28 ) )
= $false )
| ( ( member @ ( ordered_pair @ SV16 @ SV28 ) @ element_relation )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[258]) ).
thf(284,plain,
! [SV16: $i,SV28: $i] :
( ( ( ~ ( member @ SV28 @ universal_class ) )
= $true )
| ( ( ~ ( member @ SV16 @ SV28 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV16 @ SV28 ) @ element_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(285,plain,
! [SV29: $i,SV17: $i] :
( ( ( ( ( first @ ( ordered_pair @ SV17 @ SV29 ) )
!= SV17 )
| ( ( second @ ( ordered_pair @ SV17 @ SV29 ) )
!= SV29 ) )
= $false )
| ( ( member @ SV17 @ universal_class )
= $false )
| ( ( member @ SV29 @ universal_class )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(286,plain,
! [SV20: $i,SV6: $i,SV31: $i] :
( ( ( ~ ( member @ SV31 @ SV6 ) )
= $false )
| ( ( member @ SV31 @ ( intersection @ SV6 @ SV20 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[264]) ).
thf(287,plain,
! [SV6: $i,SV20: $i,SV31: $i] :
( ( ( ~ ( member @ SV31 @ SV20 ) )
= $false )
| ( ( member @ SV31 @ ( intersection @ SV6 @ SV20 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[264]) ).
thf(288,plain,
! [SV20: $i,SV6: $i,SV31: $i] :
( ( ( ~ ( member @ SV31 @ SV6 ) )
= $true )
| ( ( ~ ( member @ SV31 @ SV20 ) )
= $true )
| ( ( member @ SV31 @ ( intersection @ SV6 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(289,plain,
! [SV21: $i,SV7: $i,SV36: $i] :
( ( ( ~ ( member @ SV36 @ SV7 )
| ~ ( member @ SV36 @ SV21 ) )
= $true )
| ( ( disjoint @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[266]) ).
thf(290,plain,
! [SV7: $i,SV21: $i] :
( ( ( ~ ( member @ ( sK4_SY74 @ SV21 @ SV7 ) @ SV7 )
| ~ ( member @ ( sK4_SY74 @ SV21 @ SV7 ) @ SV21 ) )
= $false )
| ( ( disjoint @ SV7 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(291,plain,
! [SV22: $i,SV8: $i,SV37: $i] :
( ( ( member @ SV37 @ SV8 )
= $false )
| ( ( member @ SV37 @ SV22 )
= $true )
| ( ( subclass @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(292,plain,
! [SV8: $i,SV22: $i] :
( ( ( member @ ( sK5_SY76 @ SV22 @ SV8 ) @ SV8 )
= $true )
| ( ( subclass @ SV8 @ SV22 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[269]) ).
thf(293,plain,
! [SV9: $i,SV23: $i] :
( ( ( member @ SV23 @ universal_class )
= $true )
| ( ( member @ SV23 @ ( complement @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[271]) ).
thf(294,plain,
! [SV9: $i,SV23: $i] :
( ( ( ~ ( member @ SV23 @ SV9 ) )
= $true )
| ( ( member @ SV23 @ ( complement @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[272]) ).
thf(295,plain,
! [SV9: $i,SV23: $i] :
( ( ( member @ SV23 @ universal_class )
= $false )
| ( ( ~ ~ ( member @ SV23 @ SV9 ) )
= $true )
| ( ( member @ SV23 @ ( complement @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(296,plain,
! [SV24: $i,SV10: $i] :
( ( ( ~ ( ~ ( member @ SV10 @ ( sK7_SY77 @ SV24 @ SV10 ) )
| ~ ( member @ ( sK7_SY77 @ SV24 @ SV10 ) @ SV24 ) ) )
= $true )
| ( ( member @ SV10 @ ( sum_class @ SV24 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[274]) ).
thf(297,plain,
! [SV24: $i,SV39: $i,SV10: $i] :
( ( ( ~ ( ~ ( member @ SV10 @ SV39 )
| ~ ( member @ SV39 @ SV24 ) ) )
= $false )
| ( ( member @ SV10 @ ( sum_class @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(298,plain,
! [SV11: $i] :
( ( ( ~ ( member @ ( sK6_SY60 @ SV11 ) @ universal_class )
| ( SV11
!= ( ordered_pair @ ( sK6_SY60 @ SV11 ) @ ( sK6_SY60 @ SV11 ) ) ) )
= $false )
| ( ( member @ SV11 @ identity_relation )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(299,plain,
! [SV11: $i,SV38: $i] :
( ( ( ~ ( member @ SV38 @ universal_class )
| ( SV11
!= ( ordered_pair @ SV38 @ SV38 ) ) )
= $true )
| ( ( member @ SV11 @ identity_relation )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[277]) ).
thf(300,plain,
! [SV32: $i,SV25: $i,SV12: $i] :
( ( ( ~ ( member @ SV12 @ universal_class ) )
= $false )
| ( ( member @ SV12 @ ( unordered_pair @ SV25 @ SV32 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[278]) ).
thf(301,plain,
! [SV32: $i,SV25: $i,SV12: $i] :
( ( ( ~ ( ( SV12 = SV25 )
| ( SV12 = SV32 ) ) )
= $false )
| ( ( member @ SV12 @ ( unordered_pair @ SV25 @ SV32 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[278]) ).
thf(302,plain,
! [SV32: $i,SV25: $i,SV12: $i] :
( ( ( ~ ( member @ SV12 @ universal_class ) )
= $true )
| ( ( ~ ( ( SV12 = SV25 )
| ( SV12 = SV32 ) ) )
= $true )
| ( ( member @ SV12 @ ( unordered_pair @ SV25 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(303,plain,
! [SV35: $i,SV27: $i,SV34: $i,SV14: $i] :
( ( ( ~ ( member @ SV14 @ SV34 )
| ~ ( member @ SV27 @ SV35 ) )
= $false )
| ( ( member @ ( ordered_pair @ SV14 @ SV27 ) @ ( cross_product @ SV34 @ SV35 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(304,plain,
! [SV35: $i,SV27: $i,SV34: $i,SV14: $i] :
( ( ( ~ ( member @ SV14 @ SV34 )
| ~ ( member @ SV27 @ SV35 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV14 @ SV27 ) @ ( cross_product @ SV34 @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[281]) ).
thf(305,plain,
! [SV16: $i,SV28: $i] :
( ( ( member @ SV28 @ universal_class )
= $true )
| ( ( member @ ( ordered_pair @ SV16 @ SV28 ) @ element_relation )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[282]) ).
thf(306,plain,
! [SV28: $i,SV16: $i] :
( ( ( member @ SV16 @ SV28 )
= $true )
| ( ( member @ ( ordered_pair @ SV16 @ SV28 ) @ element_relation )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[283]) ).
thf(307,plain,
! [SV16: $i,SV28: $i] :
( ( ( member @ SV28 @ universal_class )
= $false )
| ( ( ~ ( member @ SV16 @ SV28 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV16 @ SV28 ) @ element_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(308,plain,
! [SV29: $i,SV17: $i] :
( ( ( ( first @ ( ordered_pair @ SV17 @ SV29 ) )
!= SV17 )
= $false )
| ( ( member @ SV17 @ universal_class )
= $false )
| ( ( member @ SV29 @ universal_class )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[285]) ).
thf(309,plain,
! [SV29: $i,SV17: $i] :
( ( ( ( second @ ( ordered_pair @ SV17 @ SV29 ) )
!= SV29 )
= $false )
| ( ( member @ SV17 @ universal_class )
= $false )
| ( ( member @ SV29 @ universal_class )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[285]) ).
thf(310,plain,
! [SV20: $i,SV6: $i,SV31: $i] :
( ( ( member @ SV31 @ SV6 )
= $true )
| ( ( member @ SV31 @ ( intersection @ SV6 @ SV20 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(311,plain,
! [SV6: $i,SV20: $i,SV31: $i] :
( ( ( member @ SV31 @ SV20 )
= $true )
| ( ( member @ SV31 @ ( intersection @ SV6 @ SV20 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[287]) ).
thf(312,plain,
! [SV20: $i,SV6: $i,SV31: $i] :
( ( ( member @ SV31 @ SV6 )
= $false )
| ( ( ~ ( member @ SV31 @ SV20 ) )
= $true )
| ( ( member @ SV31 @ ( intersection @ SV6 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(313,plain,
! [SV21: $i,SV7: $i,SV36: $i] :
( ( ( ~ ( member @ SV36 @ SV7 ) )
= $true )
| ( ( ~ ( member @ SV36 @ SV21 ) )
= $true )
| ( ( disjoint @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(314,plain,
! [SV7: $i,SV21: $i] :
( ( ( ~ ( member @ ( sK4_SY74 @ SV21 @ SV7 ) @ SV7 ) )
= $false )
| ( ( disjoint @ SV7 @ SV21 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[290]) ).
thf(315,plain,
! [SV7: $i,SV21: $i] :
( ( ( ~ ( member @ ( sK4_SY74 @ SV21 @ SV7 ) @ SV21 ) )
= $false )
| ( ( disjoint @ SV7 @ SV21 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[290]) ).
thf(316,plain,
! [SV9: $i,SV23: $i] :
( ( ( member @ SV23 @ SV9 )
= $false )
| ( ( member @ SV23 @ ( complement @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(317,plain,
! [SV9: $i,SV23: $i] :
( ( ( ~ ( member @ SV23 @ SV9 ) )
= $false )
| ( ( member @ SV23 @ universal_class )
= $false )
| ( ( member @ SV23 @ ( complement @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(318,plain,
! [SV24: $i,SV10: $i] :
( ( ( ~ ( member @ SV10 @ ( sK7_SY77 @ SV24 @ SV10 ) )
| ~ ( member @ ( sK7_SY77 @ SV24 @ SV10 ) @ SV24 ) )
= $false )
| ( ( member @ SV10 @ ( sum_class @ SV24 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(319,plain,
! [SV24: $i,SV39: $i,SV10: $i] :
( ( ( ~ ( member @ SV10 @ SV39 )
| ~ ( member @ SV39 @ SV24 ) )
= $true )
| ( ( member @ SV10 @ ( sum_class @ SV24 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[297]) ).
thf(320,plain,
! [SV11: $i] :
( ( ( ~ ( member @ ( sK6_SY60 @ SV11 ) @ universal_class ) )
= $false )
| ( ( member @ SV11 @ identity_relation )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[298]) ).
thf(321,plain,
! [SV11: $i] :
( ( ( SV11
!= ( ordered_pair @ ( sK6_SY60 @ SV11 ) @ ( sK6_SY60 @ SV11 ) ) )
= $false )
| ( ( member @ SV11 @ identity_relation )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[298]) ).
thf(322,plain,
! [SV11: $i,SV38: $i] :
( ( ( ~ ( member @ SV38 @ universal_class ) )
= $true )
| ( ( SV11
!= ( ordered_pair @ SV38 @ SV38 ) )
= $true )
| ( ( member @ SV11 @ identity_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(323,plain,
! [SV32: $i,SV25: $i,SV12: $i] :
( ( ( member @ SV12 @ universal_class )
= $true )
| ( ( member @ SV12 @ ( unordered_pair @ SV25 @ SV32 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[300]) ).
thf(324,plain,
! [SV32: $i,SV25: $i,SV12: $i] :
( ( ( ( SV12 = SV25 )
| ( SV12 = SV32 ) )
= $true )
| ( ( member @ SV12 @ ( unordered_pair @ SV25 @ SV32 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[301]) ).
thf(325,plain,
! [SV32: $i,SV25: $i,SV12: $i] :
( ( ( member @ SV12 @ universal_class )
= $false )
| ( ( ~ ( ( SV12 = SV25 )
| ( SV12 = SV32 ) ) )
= $true )
| ( ( member @ SV12 @ ( unordered_pair @ SV25 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(326,plain,
! [SV35: $i,SV27: $i,SV34: $i,SV14: $i] :
( ( ( ~ ( member @ SV14 @ SV34 ) )
= $false )
| ( ( member @ ( ordered_pair @ SV14 @ SV27 ) @ ( cross_product @ SV34 @ SV35 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[303]) ).
thf(327,plain,
! [SV34: $i,SV14: $i,SV35: $i,SV27: $i] :
( ( ( ~ ( member @ SV27 @ SV35 ) )
= $false )
| ( ( member @ ( ordered_pair @ SV14 @ SV27 ) @ ( cross_product @ SV34 @ SV35 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[303]) ).
thf(328,plain,
! [SV35: $i,SV27: $i,SV34: $i,SV14: $i] :
( ( ( ~ ( member @ SV14 @ SV34 ) )
= $true )
| ( ( ~ ( member @ SV27 @ SV35 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV14 @ SV27 ) @ ( cross_product @ SV34 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(329,plain,
! [SV28: $i,SV16: $i] :
( ( ( member @ SV16 @ SV28 )
= $false )
| ( ( member @ SV28 @ universal_class )
= $false )
| ( ( member @ ( ordered_pair @ SV16 @ SV28 ) @ element_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(330,plain,
! [SV29: $i,SV17: $i] :
( ( ( ( first @ ( ordered_pair @ SV17 @ SV29 ) )
= SV17 )
= $true )
| ( ( member @ SV17 @ universal_class )
= $false )
| ( ( member @ SV29 @ universal_class )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[308]) ).
thf(331,plain,
! [SV29: $i,SV17: $i] :
( ( ( ( second @ ( ordered_pair @ SV17 @ SV29 ) )
= SV29 )
= $true )
| ( ( member @ SV17 @ universal_class )
= $false )
| ( ( member @ SV29 @ universal_class )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[309]) ).
thf(332,plain,
! [SV6: $i,SV20: $i,SV31: $i] :
( ( ( member @ SV31 @ SV20 )
= $false )
| ( ( member @ SV31 @ SV6 )
= $false )
| ( ( member @ SV31 @ ( intersection @ SV6 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(333,plain,
! [SV21: $i,SV7: $i,SV36: $i] :
( ( ( member @ SV36 @ SV7 )
= $false )
| ( ( ~ ( member @ SV36 @ SV21 ) )
= $true )
| ( ( disjoint @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(334,plain,
! [SV7: $i,SV21: $i] :
( ( ( member @ ( sK4_SY74 @ SV21 @ SV7 ) @ SV7 )
= $true )
| ( ( disjoint @ SV7 @ SV21 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[314]) ).
thf(335,plain,
! [SV7: $i,SV21: $i] :
( ( ( member @ ( sK4_SY74 @ SV21 @ SV7 ) @ SV21 )
= $true )
| ( ( disjoint @ SV7 @ SV21 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[315]) ).
thf(336,plain,
! [SV9: $i,SV23: $i] :
( ( ( member @ SV23 @ SV9 )
= $true )
| ( ( member @ SV23 @ universal_class )
= $false )
| ( ( member @ SV23 @ ( complement @ SV9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[317]) ).
thf(337,plain,
! [SV24: $i,SV10: $i] :
( ( ( ~ ( member @ SV10 @ ( sK7_SY77 @ SV24 @ SV10 ) ) )
= $false )
| ( ( member @ SV10 @ ( sum_class @ SV24 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[318]) ).
thf(338,plain,
! [SV10: $i,SV24: $i] :
( ( ( ~ ( member @ ( sK7_SY77 @ SV24 @ SV10 ) @ SV24 ) )
= $false )
| ( ( member @ SV10 @ ( sum_class @ SV24 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[318]) ).
thf(339,plain,
! [SV24: $i,SV39: $i,SV10: $i] :
( ( ( ~ ( member @ SV10 @ SV39 ) )
= $true )
| ( ( ~ ( member @ SV39 @ SV24 ) )
= $true )
| ( ( member @ SV10 @ ( sum_class @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[319]) ).
thf(340,plain,
! [SV11: $i] :
( ( ( member @ ( sK6_SY60 @ SV11 ) @ universal_class )
= $true )
| ( ( member @ SV11 @ identity_relation )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[320]) ).
thf(341,plain,
! [SV11: $i] :
( ( ( SV11
= ( ordered_pair @ ( sK6_SY60 @ SV11 ) @ ( sK6_SY60 @ SV11 ) ) )
= $true )
| ( ( member @ SV11 @ identity_relation )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[321]) ).
thf(342,plain,
! [SV11: $i,SV38: $i] :
( ( ( member @ SV38 @ universal_class )
= $false )
| ( ( SV11
!= ( ordered_pair @ SV38 @ SV38 ) )
= $true )
| ( ( member @ SV11 @ identity_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(343,plain,
! [SV32: $i,SV25: $i,SV12: $i] :
( ( ( SV12 = SV25 )
= $true )
| ( ( SV12 = SV32 )
= $true )
| ( ( member @ SV12 @ ( unordered_pair @ SV25 @ SV32 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[324]) ).
thf(344,plain,
! [SV32: $i,SV25: $i,SV12: $i] :
( ( ( ( SV12 = SV25 )
| ( SV12 = SV32 ) )
= $false )
| ( ( member @ SV12 @ universal_class )
= $false )
| ( ( member @ SV12 @ ( unordered_pair @ SV25 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(345,plain,
! [SV35: $i,SV27: $i,SV34: $i,SV14: $i] :
( ( ( member @ SV14 @ SV34 )
= $true )
| ( ( member @ ( ordered_pair @ SV14 @ SV27 ) @ ( cross_product @ SV34 @ SV35 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[326]) ).
thf(346,plain,
! [SV34: $i,SV14: $i,SV35: $i,SV27: $i] :
( ( ( member @ SV27 @ SV35 )
= $true )
| ( ( member @ ( ordered_pair @ SV14 @ SV27 ) @ ( cross_product @ SV34 @ SV35 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[327]) ).
thf(347,plain,
! [SV35: $i,SV27: $i,SV34: $i,SV14: $i] :
( ( ( member @ SV14 @ SV34 )
= $false )
| ( ( ~ ( member @ SV27 @ SV35 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV14 @ SV27 ) @ ( cross_product @ SV34 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(348,plain,
! [SV7: $i,SV21: $i,SV36: $i] :
( ( ( member @ SV36 @ SV21 )
= $false )
| ( ( member @ SV36 @ SV7 )
= $false )
| ( ( disjoint @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(349,plain,
! [SV24: $i,SV10: $i] :
( ( ( member @ SV10 @ ( sK7_SY77 @ SV24 @ SV10 ) )
= $true )
| ( ( member @ SV10 @ ( sum_class @ SV24 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[337]) ).
thf(350,plain,
! [SV10: $i,SV24: $i] :
( ( ( member @ ( sK7_SY77 @ SV24 @ SV10 ) @ SV24 )
= $true )
| ( ( member @ SV10 @ ( sum_class @ SV24 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[338]) ).
thf(351,plain,
! [SV24: $i,SV39: $i,SV10: $i] :
( ( ( member @ SV10 @ SV39 )
= $false )
| ( ( ~ ( member @ SV39 @ SV24 ) )
= $true )
| ( ( member @ SV10 @ ( sum_class @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(352,plain,
! [SV38: $i,SV11: $i] :
( ( ( SV11
= ( ordered_pair @ SV38 @ SV38 ) )
= $false )
| ( ( member @ SV38 @ universal_class )
= $false )
| ( ( member @ SV11 @ identity_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(353,plain,
! [SV32: $i,SV25: $i,SV12: $i] :
( ( ( SV12 = SV25 )
= $false )
| ( ( member @ SV12 @ universal_class )
= $false )
| ( ( member @ SV12 @ ( unordered_pair @ SV25 @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[344]) ).
thf(354,plain,
! [SV25: $i,SV32: $i,SV12: $i] :
( ( ( SV12 = SV32 )
= $false )
| ( ( member @ SV12 @ universal_class )
= $false )
| ( ( member @ SV12 @ ( unordered_pair @ SV25 @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[344]) ).
thf(355,plain,
! [SV34: $i,SV14: $i,SV35: $i,SV27: $i] :
( ( ( member @ SV27 @ SV35 )
= $false )
| ( ( member @ SV14 @ SV34 )
= $false )
| ( ( member @ ( ordered_pair @ SV14 @ SV27 ) @ ( cross_product @ SV34 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(356,plain,
! [SV10: $i,SV24: $i,SV39: $i] :
( ( ( member @ SV39 @ SV24 )
= $false )
| ( ( member @ SV10 @ SV39 )
= $false )
| ( ( member @ SV10 @ ( sum_class @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(357,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[92,356,355,354,353,352,350,349,348,346,345,343,341,340,336,335,334,332,331,330,329,323,316,311,310,306,305,293,292,291,270,263,262,261,193,156,145,129,128,113,110,94,93]) ).
thf(358,plain,
( ( ! [X: $i,Y: $i] :
( ( subclass @ X @ Y )
<=> ! [U: $i] :
( ( member @ U @ X )
=> ( member @ U @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(359,plain,
( ( ! [X: $i] : ( subclass @ X @ universal_class ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(360,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)],[61]) ).
thf(361,plain,
( ( ! [X: $i,Y: $i] : ( member @ ( unordered_pair @ X @ Y ) @ universal_class ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(362,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)],[59]) ).
thf(363,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)],[58]) ).
thf(364,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)],[57]) ).
thf(365,plain,
( ( ! [X: $i,Y: $i] :
( ( member @ ( ordered_pair @ X @ Y ) @ element_relation )
<=> ( ( member @ Y @ universal_class )
& ( member @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(366,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( member @ Z @ ( intersection @ X @ Y ) )
<=> ( ( member @ Z @ X )
& ( member @ Z @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(367,plain,
( ( ! [X: $i,Z: $i] :
( ( member @ Z @ ( complement @ X ) )
<=> ( ( member @ Z @ universal_class )
& ~ ( member @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(368,plain,
( ( ! [X: $i] :
~ ( member @ X @ null_class ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(369,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( member @ Z @ ( union @ X @ Y ) )
<=> ( ( member @ Z @ X )
| ( member @ Z @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(370,plain,
( ( ! [U: $i,X: $i] :
( ( member @ U @ ( sum_class @ X ) )
<=> ? [Y: $i] :
( ( member @ U @ Y )
& ( member @ Y @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(371,plain,
( ( ! [X: $i] :
( ( member @ X @ universal_class )
=> ( member @ ( sum_class @ X ) @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(372,plain,
( ( ! [U: $i] :
( ( member @ U @ universal_class )
=> ( member @ ( power_class @ U ) @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(373,plain,
( ( ! [Z: $i] :
( ( member @ Z @ identity_relation )
<=> ? [X: $i] :
( ( member @ X @ universal_class )
& ( Z
= ( ordered_pair @ X @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(374,plain,
( ( ! [X: $i,Y: $i] :
( ( disjoint @ X @ Y )
<=> ! [U: $i] :
~ ( ( member @ U @ X )
& ( member @ U @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(375,plain,
( ( sK3_SY44
= ( ordered_pair @ sK1_U @ sK2_SY42 ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(376,plain,
( ( member @ sK2_SY42 @ universal_class )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(377,plain,
( ( member @ sK1_U @ universal_class )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(378,plain,
( ( ( second @ sK3_SY44 )
!= sK2_SY42 )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(379,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)],[360]) ).
thf(380,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)],[369]) ).
thf(381,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)],[358]) ).
thf(382,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)],[367]) ).
thf(383,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)],[370]) ).
thf(384,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)],[363]) ).
thf(385,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)],[373]) ).
thf(386,plain,
( ( ! [SX0: $i] :
( ~ ( member @ SX0 @ universal_class )
| ( member @ ( power_class @ SX0 ) @ universal_class ) ) )
= $true ),
inference(unfold_def,[status(thm)],[372]) ).
thf(387,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)],[362]) ).
thf(388,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)],[374]) ).
thf(389,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)],[366]) ).
thf(390,plain,
( ( ! [SX0: $i] :
( ~ ( member @ SX0 @ universal_class )
| ( member @ ( sum_class @ SX0 ) @ universal_class ) ) )
= $true ),
inference(unfold_def,[status(thm)],[371]) ).
thf(391,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)],[365]) ).
thf(392,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)],[364]) ).
thf(393,plain,
! [SV40: $i] :
( ( subclass @ SV40 @ universal_class )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(394,plain,
! [SV41: $i] :
( ( ! [SY84: $i] : ( member @ ( unordered_pair @ SV41 @ SY84 ) @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(395,plain,
! [SV42: $i] :
( ( ~ ( member @ SV42 @ null_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(396,plain,
( ( ( second @ sK3_SY44 )
= sK2_SY42 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(397,plain,
! [SV43: $i] :
( ( ! [SY85: $i,SY86: $i] :
~ ( ~ ( ~ ( member @ SV43 @ ( unordered_pair @ SY85 @ SY86 ) )
| ~ ( ~ ( member @ SV43 @ universal_class )
| ~ ( ( SV43 = SY85 )
| ( SV43 = SY86 ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV43 @ universal_class )
| ~ ( ( SV43 = SY85 )
| ( SV43 = SY86 ) ) )
| ( member @ SV43 @ ( unordered_pair @ SY85 @ SY86 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(398,plain,
! [SV44: $i] :
( ( ! [SY87: $i,SY88: $i] :
~ ( ~ ( ~ ( member @ SY88 @ ( union @ SV44 @ SY87 ) )
| ( member @ SY88 @ SV44 )
| ( member @ SY88 @ SY87 ) )
| ~ ( ~ ( ( member @ SY88 @ SV44 )
| ( member @ SY88 @ SY87 ) )
| ( member @ SY88 @ ( union @ SV44 @ SY87 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(399,plain,
! [SV45: $i] :
( ( ! [SY89: $i] :
~ ( ~ ( ~ ( subclass @ SV45 @ SY89 )
| ! [SY90: $i] :
( ~ ( member @ SY90 @ SV45 )
| ( member @ SY90 @ SY89 ) ) )
| ~ ( ~ ! [SY91: $i] :
( ~ ( member @ SY91 @ SV45 )
| ( member @ SY91 @ SY89 ) )
| ( subclass @ SV45 @ SY89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(400,plain,
! [SV46: $i] :
( ( ! [SY92: $i] :
~ ( ~ ( ~ ( member @ SY92 @ ( complement @ SV46 ) )
| ~ ( ~ ( member @ SY92 @ universal_class )
| ~ ~ ( member @ SY92 @ SV46 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY92 @ universal_class )
| ~ ~ ( member @ SY92 @ SV46 ) )
| ( member @ SY92 @ ( complement @ SV46 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(401,plain,
! [SV47: $i] :
( ( ! [SY93: $i] :
~ ( ~ ( ~ ( member @ SV47 @ ( sum_class @ SY93 ) )
| ~ ! [SY94: $i] :
~ ~ ( ~ ( member @ SV47 @ SY94 )
| ~ ( member @ SY94 @ SY93 ) ) )
| ~ ( ~ ~ ! [SY95: $i] :
~ ~ ( ~ ( member @ SV47 @ SY95 )
| ~ ( member @ SY95 @ SY93 ) )
| ( member @ SV47 @ ( sum_class @ SY93 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(402,plain,
! [SV48: $i] :
( ( ! [SY96: $i] :
( ~ ~ ( ~ ( member @ SV48 @ universal_class )
| ~ ( member @ SY96 @ universal_class ) )
| ~ ( ( ( first @ ( ordered_pair @ SV48 @ SY96 ) )
!= SV48 )
| ( ( second @ ( ordered_pair @ SV48 @ SY96 ) )
!= SY96 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(403,plain,
! [SV49: $i] :
( ( ~ ( ~ ( ~ ( member @ SV49 @ identity_relation )
| ~ ! [SY97: $i] :
~ ~ ( ~ ( member @ SY97 @ universal_class )
| ( SV49
!= ( ordered_pair @ SY97 @ SY97 ) ) ) )
| ~ ( ~ ~ ! [SY98: $i] :
~ ~ ( ~ ( member @ SY98 @ universal_class )
| ( SV49
!= ( ordered_pair @ SY98 @ SY98 ) ) )
| ( member @ SV49 @ identity_relation ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(404,plain,
! [SV50: $i] :
( ( ~ ( member @ SV50 @ universal_class )
| ( member @ ( power_class @ SV50 ) @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(405,plain,
! [SV51: $i] :
( ( ! [SY99: $i,SY100: $i,SY101: $i] :
~ ( ~ ( ~ ( member @ ( ordered_pair @ SV51 @ SY99 ) @ ( cross_product @ SY100 @ SY101 ) )
| ~ ( ~ ( member @ SV51 @ SY100 )
| ~ ( member @ SY99 @ SY101 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV51 @ SY100 )
| ~ ( member @ SY99 @ SY101 ) )
| ( member @ ( ordered_pair @ SV51 @ SY99 ) @ ( cross_product @ SY100 @ SY101 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(406,plain,
! [SV52: $i] :
( ( ! [SY102: $i] :
~ ( ~ ( ~ ( disjoint @ SV52 @ SY102 )
| ! [SY103: $i] :
~ ~ ( ~ ( member @ SY103 @ SV52 )
| ~ ( member @ SY103 @ SY102 ) ) )
| ~ ( ~ ! [SY104: $i] :
~ ~ ( ~ ( member @ SY104 @ SV52 )
| ~ ( member @ SY104 @ SY102 ) )
| ( disjoint @ SV52 @ SY102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(407,plain,
! [SV53: $i] :
( ( ! [SY105: $i,SY106: $i] :
~ ( ~ ( ~ ( member @ SY106 @ ( intersection @ SV53 @ SY105 ) )
| ~ ( ~ ( member @ SY106 @ SV53 )
| ~ ( member @ SY106 @ SY105 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY106 @ SV53 )
| ~ ( member @ SY106 @ SY105 ) )
| ( member @ SY106 @ ( intersection @ SV53 @ SY105 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(408,plain,
! [SV54: $i] :
( ( ~ ( member @ SV54 @ universal_class )
| ( member @ ( sum_class @ SV54 ) @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(409,plain,
! [SV55: $i] :
( ( ! [SY107: $i] :
~ ( ~ ( ~ ( member @ ( ordered_pair @ SV55 @ SY107 ) @ element_relation )
| ~ ( ~ ( member @ SY107 @ universal_class )
| ~ ( member @ SV55 @ SY107 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY107 @ universal_class )
| ~ ( member @ SV55 @ SY107 ) )
| ( member @ ( ordered_pair @ SV55 @ SY107 ) @ element_relation ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(410,plain,
! [SV56: $i] :
( ( ! [SY108: $i,SY109: $i] :
( ~ ( member @ SY109 @ ( cross_product @ SV56 @ SY108 ) )
| ( SY109
= ( ordered_pair @ ( first @ SY109 ) @ ( second @ SY109 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(411,plain,
! [SV57: $i,SV41: $i] :
( ( member @ ( unordered_pair @ SV41 @ SV57 ) @ universal_class )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(412,plain,
! [SV42: $i] :
( ( member @ SV42 @ null_class )
= $false ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(413,plain,
! [SV58: $i,SV43: $i] :
( ( ! [SY110: $i] :
~ ( ~ ( ~ ( member @ SV43 @ ( unordered_pair @ SV58 @ SY110 ) )
| ~ ( ~ ( member @ SV43 @ universal_class )
| ~ ( ( SV43 = SV58 )
| ( SV43 = SY110 ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV43 @ universal_class )
| ~ ( ( SV43 = SV58 )
| ( SV43 = SY110 ) ) )
| ( member @ SV43 @ ( unordered_pair @ SV58 @ SY110 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(414,plain,
! [SV59: $i,SV44: $i] :
( ( ! [SY111: $i] :
~ ( ~ ( ~ ( member @ SY111 @ ( union @ SV44 @ SV59 ) )
| ( member @ SY111 @ SV44 )
| ( member @ SY111 @ SV59 ) )
| ~ ( ~ ( ( member @ SY111 @ SV44 )
| ( member @ SY111 @ SV59 ) )
| ( member @ SY111 @ ( union @ SV44 @ SV59 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(415,plain,
! [SV60: $i,SV45: $i] :
( ( ~ ( ~ ( ~ ( subclass @ SV45 @ SV60 )
| ! [SY112: $i] :
( ~ ( member @ SY112 @ SV45 )
| ( member @ SY112 @ SV60 ) ) )
| ~ ( ~ ! [SY113: $i] :
( ~ ( member @ SY113 @ SV45 )
| ( member @ SY113 @ SV60 ) )
| ( subclass @ SV45 @ SV60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(416,plain,
! [SV46: $i,SV61: $i] :
( ( ~ ( ~ ( ~ ( member @ SV61 @ ( complement @ SV46 ) )
| ~ ( ~ ( member @ SV61 @ universal_class )
| ~ ~ ( member @ SV61 @ SV46 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV61 @ universal_class )
| ~ ~ ( member @ SV61 @ SV46 ) )
| ( member @ SV61 @ ( complement @ SV46 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(417,plain,
! [SV62: $i,SV47: $i] :
( ( ~ ( ~ ( ~ ( member @ SV47 @ ( sum_class @ SV62 ) )
| ~ ! [SY114: $i] :
~ ~ ( ~ ( member @ SV47 @ SY114 )
| ~ ( member @ SY114 @ SV62 ) ) )
| ~ ( ~ ~ ! [SY115: $i] :
~ ~ ( ~ ( member @ SV47 @ SY115 )
| ~ ( member @ SY115 @ SV62 ) )
| ( member @ SV47 @ ( sum_class @ SV62 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(418,plain,
! [SV63: $i,SV48: $i] :
( ( ~ ~ ( ~ ( member @ SV48 @ universal_class )
| ~ ( member @ SV63 @ universal_class ) )
| ~ ( ( ( first @ ( ordered_pair @ SV48 @ SV63 ) )
!= SV48 )
| ( ( second @ ( ordered_pair @ SV48 @ SV63 ) )
!= SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(419,plain,
! [SV49: $i] :
( ( ~ ( ~ ( member @ SV49 @ identity_relation )
| ~ ! [SY97: $i] :
~ ~ ( ~ ( member @ SY97 @ universal_class )
| ( SV49
!= ( ordered_pair @ SY97 @ SY97 ) ) ) )
| ~ ( ~ ~ ! [SY98: $i] :
~ ~ ( ~ ( member @ SY98 @ universal_class )
| ( SV49
!= ( ordered_pair @ SY98 @ SY98 ) ) )
| ( member @ SV49 @ identity_relation ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(420,plain,
! [SV50: $i] :
( ( ( ~ ( member @ SV50 @ universal_class ) )
= $true )
| ( ( member @ ( power_class @ SV50 ) @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[404]) ).
thf(421,plain,
! [SV64: $i,SV51: $i] :
( ( ! [SY116: $i,SY117: $i] :
~ ( ~ ( ~ ( member @ ( ordered_pair @ SV51 @ SV64 ) @ ( cross_product @ SY116 @ SY117 ) )
| ~ ( ~ ( member @ SV51 @ SY116 )
| ~ ( member @ SV64 @ SY117 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV51 @ SY116 )
| ~ ( member @ SV64 @ SY117 ) )
| ( member @ ( ordered_pair @ SV51 @ SV64 ) @ ( cross_product @ SY116 @ SY117 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(422,plain,
! [SV65: $i,SV52: $i] :
( ( ~ ( ~ ( ~ ( disjoint @ SV52 @ SV65 )
| ! [SY118: $i] :
~ ~ ( ~ ( member @ SY118 @ SV52 )
| ~ ( member @ SY118 @ SV65 ) ) )
| ~ ( ~ ! [SY119: $i] :
~ ~ ( ~ ( member @ SY119 @ SV52 )
| ~ ( member @ SY119 @ SV65 ) )
| ( disjoint @ SV52 @ SV65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(423,plain,
! [SV66: $i,SV53: $i] :
( ( ! [SY120: $i] :
~ ( ~ ( ~ ( member @ SY120 @ ( intersection @ SV53 @ SV66 ) )
| ~ ( ~ ( member @ SY120 @ SV53 )
| ~ ( member @ SY120 @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY120 @ SV53 )
| ~ ( member @ SY120 @ SV66 ) )
| ( member @ SY120 @ ( intersection @ SV53 @ SV66 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(424,plain,
! [SV54: $i] :
( ( ( ~ ( member @ SV54 @ universal_class ) )
= $true )
| ( ( member @ ( sum_class @ SV54 ) @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[408]) ).
thf(425,plain,
! [SV67: $i,SV55: $i] :
( ( ~ ( ~ ( ~ ( member @ ( ordered_pair @ SV55 @ SV67 ) @ element_relation )
| ~ ( ~ ( member @ SV67 @ universal_class )
| ~ ( member @ SV55 @ SV67 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV67 @ universal_class )
| ~ ( member @ SV55 @ SV67 ) )
| ( member @ ( ordered_pair @ SV55 @ SV67 ) @ element_relation ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(426,plain,
! [SV68: $i,SV56: $i] :
( ( ! [SY121: $i] :
( ~ ( member @ SY121 @ ( cross_product @ SV56 @ SV68 ) )
| ( SY121
= ( ordered_pair @ ( first @ SY121 ) @ ( second @ SY121 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(427,plain,
! [SV69: $i,SV58: $i,SV43: $i] :
( ( ~ ( ~ ( ~ ( member @ SV43 @ ( unordered_pair @ SV58 @ SV69 ) )
| ~ ( ~ ( member @ SV43 @ universal_class )
| ~ ( ( SV43 = SV58 )
| ( SV43 = SV69 ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV43 @ universal_class )
| ~ ( ( SV43 = SV58 )
| ( SV43 = SV69 ) ) )
| ( member @ SV43 @ ( unordered_pair @ SV58 @ SV69 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(428,plain,
! [SV59: $i,SV44: $i,SV70: $i] :
( ( ~ ( ~ ( ~ ( member @ SV70 @ ( union @ SV44 @ SV59 ) )
| ( member @ SV70 @ SV44 )
| ( member @ SV70 @ SV59 ) )
| ~ ( ~ ( ( member @ SV70 @ SV44 )
| ( member @ SV70 @ SV59 ) )
| ( member @ SV70 @ ( union @ SV44 @ SV59 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(429,plain,
! [SV60: $i,SV45: $i] :
( ( ~ ( ~ ( subclass @ SV45 @ SV60 )
| ! [SY112: $i] :
( ~ ( member @ SY112 @ SV45 )
| ( member @ SY112 @ SV60 ) ) )
| ~ ( ~ ! [SY113: $i] :
( ~ ( member @ SY113 @ SV45 )
| ( member @ SY113 @ SV60 ) )
| ( subclass @ SV45 @ SV60 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(430,plain,
! [SV46: $i,SV61: $i] :
( ( ~ ( ~ ( member @ SV61 @ ( complement @ SV46 ) )
| ~ ( ~ ( member @ SV61 @ universal_class )
| ~ ~ ( member @ SV61 @ SV46 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV61 @ universal_class )
| ~ ~ ( member @ SV61 @ SV46 ) )
| ( member @ SV61 @ ( complement @ SV46 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[416]) ).
thf(431,plain,
! [SV62: $i,SV47: $i] :
( ( ~ ( ~ ( member @ SV47 @ ( sum_class @ SV62 ) )
| ~ ! [SY114: $i] :
~ ~ ( ~ ( member @ SV47 @ SY114 )
| ~ ( member @ SY114 @ SV62 ) ) )
| ~ ( ~ ~ ! [SY115: $i] :
~ ~ ( ~ ( member @ SV47 @ SY115 )
| ~ ( member @ SY115 @ SV62 ) )
| ( member @ SV47 @ ( sum_class @ SV62 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(432,plain,
! [SV63: $i,SV48: $i] :
( ( ( ~ ~ ( ~ ( member @ SV48 @ universal_class )
| ~ ( member @ SV63 @ universal_class ) ) )
= $true )
| ( ( ~ ( ( ( first @ ( ordered_pair @ SV48 @ SV63 ) )
!= SV48 )
| ( ( second @ ( ordered_pair @ SV48 @ SV63 ) )
!= SV63 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[418]) ).
thf(433,plain,
! [SV49: $i] :
( ( ~ ( ~ ( member @ SV49 @ identity_relation )
| ~ ! [SY97: $i] :
~ ~ ( ~ ( member @ SY97 @ universal_class )
| ( SV49
!= ( ordered_pair @ SY97 @ SY97 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[419]) ).
thf(434,plain,
! [SV49: $i] :
( ( ~ ( ~ ~ ! [SY98: $i] :
~ ~ ( ~ ( member @ SY98 @ universal_class )
| ( SV49
!= ( ordered_pair @ SY98 @ SY98 ) ) )
| ( member @ SV49 @ identity_relation ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[419]) ).
thf(435,plain,
! [SV50: $i] :
( ( ( member @ SV50 @ universal_class )
= $false )
| ( ( member @ ( power_class @ SV50 ) @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(436,plain,
! [SV71: $i,SV64: $i,SV51: $i] :
( ( ! [SY122: $i] :
~ ( ~ ( ~ ( member @ ( ordered_pair @ SV51 @ SV64 ) @ ( cross_product @ SV71 @ SY122 ) )
| ~ ( ~ ( member @ SV51 @ SV71 )
| ~ ( member @ SV64 @ SY122 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV51 @ SV71 )
| ~ ( member @ SV64 @ SY122 ) )
| ( member @ ( ordered_pair @ SV51 @ SV64 ) @ ( cross_product @ SV71 @ SY122 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(437,plain,
! [SV65: $i,SV52: $i] :
( ( ~ ( ~ ( disjoint @ SV52 @ SV65 )
| ! [SY118: $i] :
~ ~ ( ~ ( member @ SY118 @ SV52 )
| ~ ( member @ SY118 @ SV65 ) ) )
| ~ ( ~ ! [SY119: $i] :
~ ~ ( ~ ( member @ SY119 @ SV52 )
| ~ ( member @ SY119 @ SV65 ) )
| ( disjoint @ SV52 @ SV65 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[422]) ).
thf(438,plain,
! [SV66: $i,SV53: $i,SV72: $i] :
( ( ~ ( ~ ( ~ ( member @ SV72 @ ( intersection @ SV53 @ SV66 ) )
| ~ ( ~ ( member @ SV72 @ SV53 )
| ~ ( member @ SV72 @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV72 @ SV53 )
| ~ ( member @ SV72 @ SV66 ) )
| ( member @ SV72 @ ( intersection @ SV53 @ SV66 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(439,plain,
! [SV54: $i] :
( ( ( member @ SV54 @ universal_class )
= $false )
| ( ( member @ ( sum_class @ SV54 ) @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(440,plain,
! [SV67: $i,SV55: $i] :
( ( ~ ( ~ ( member @ ( ordered_pair @ SV55 @ SV67 ) @ element_relation )
| ~ ( ~ ( member @ SV67 @ universal_class )
| ~ ( member @ SV55 @ SV67 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV67 @ universal_class )
| ~ ( member @ SV55 @ SV67 ) )
| ( member @ ( ordered_pair @ SV55 @ SV67 ) @ element_relation ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(441,plain,
! [SV68: $i,SV56: $i,SV73: $i] :
( ( ~ ( member @ SV73 @ ( cross_product @ SV56 @ SV68 ) )
| ( SV73
= ( ordered_pair @ ( first @ SV73 ) @ ( second @ SV73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(442,plain,
! [SV69: $i,SV58: $i,SV43: $i] :
( ( ~ ( ~ ( member @ SV43 @ ( unordered_pair @ SV58 @ SV69 ) )
| ~ ( ~ ( member @ SV43 @ universal_class )
| ~ ( ( SV43 = SV58 )
| ( SV43 = SV69 ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV43 @ universal_class )
| ~ ( ( SV43 = SV58 )
| ( SV43 = SV69 ) ) )
| ( member @ SV43 @ ( unordered_pair @ SV58 @ SV69 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[427]) ).
thf(443,plain,
! [SV59: $i,SV44: $i,SV70: $i] :
( ( ~ ( ~ ( member @ SV70 @ ( union @ SV44 @ SV59 ) )
| ( member @ SV70 @ SV44 )
| ( member @ SV70 @ SV59 ) )
| ~ ( ~ ( ( member @ SV70 @ SV44 )
| ( member @ SV70 @ SV59 ) )
| ( member @ SV70 @ ( union @ SV44 @ SV59 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[428]) ).
thf(444,plain,
! [SV60: $i,SV45: $i] :
( ( ~ ( ~ ( subclass @ SV45 @ SV60 )
| ! [SY112: $i] :
( ~ ( member @ SY112 @ SV45 )
| ( member @ SY112 @ SV60 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[429]) ).
thf(445,plain,
! [SV60: $i,SV45: $i] :
( ( ~ ( ~ ! [SY113: $i] :
( ~ ( member @ SY113 @ SV45 )
| ( member @ SY113 @ SV60 ) )
| ( subclass @ SV45 @ SV60 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[429]) ).
thf(446,plain,
! [SV46: $i,SV61: $i] :
( ( ~ ( ~ ( member @ SV61 @ ( complement @ SV46 ) )
| ~ ( ~ ( member @ SV61 @ universal_class )
| ~ ~ ( member @ SV61 @ SV46 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[430]) ).
thf(447,plain,
! [SV46: $i,SV61: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV61 @ universal_class )
| ~ ~ ( member @ SV61 @ SV46 ) )
| ( member @ SV61 @ ( complement @ SV46 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[430]) ).
thf(448,plain,
! [SV62: $i,SV47: $i] :
( ( ~ ( ~ ( member @ SV47 @ ( sum_class @ SV62 ) )
| ~ ! [SY114: $i] :
~ ~ ( ~ ( member @ SV47 @ SY114 )
| ~ ( member @ SY114 @ SV62 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[431]) ).
thf(449,plain,
! [SV62: $i,SV47: $i] :
( ( ~ ( ~ ~ ! [SY115: $i] :
~ ~ ( ~ ( member @ SV47 @ SY115 )
| ~ ( member @ SY115 @ SV62 ) )
| ( member @ SV47 @ ( sum_class @ SV62 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[431]) ).
thf(450,plain,
! [SV63: $i,SV48: $i] :
( ( ( ~ ( ~ ( member @ SV48 @ universal_class )
| ~ ( member @ SV63 @ universal_class ) ) )
= $false )
| ( ( ~ ( ( ( first @ ( ordered_pair @ SV48 @ SV63 ) )
!= SV48 )
| ( ( second @ ( ordered_pair @ SV48 @ SV63 ) )
!= SV63 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(451,plain,
! [SV49: $i] :
( ( ~ ( member @ SV49 @ identity_relation )
| ~ ! [SY97: $i] :
~ ~ ( ~ ( member @ SY97 @ universal_class )
| ( SV49
!= ( ordered_pair @ SY97 @ SY97 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[433]) ).
thf(452,plain,
! [SV49: $i] :
( ( ~ ~ ! [SY98: $i] :
~ ~ ( ~ ( member @ SY98 @ universal_class )
| ( SV49
!= ( ordered_pair @ SY98 @ SY98 ) ) )
| ( member @ SV49 @ identity_relation ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[434]) ).
thf(453,plain,
! [SV74: $i,SV71: $i,SV64: $i,SV51: $i] :
( ( ~ ( ~ ( ~ ( member @ ( ordered_pair @ SV51 @ SV64 ) @ ( cross_product @ SV71 @ SV74 ) )
| ~ ( ~ ( member @ SV51 @ SV71 )
| ~ ( member @ SV64 @ SV74 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV51 @ SV71 )
| ~ ( member @ SV64 @ SV74 ) )
| ( member @ ( ordered_pair @ SV51 @ SV64 ) @ ( cross_product @ SV71 @ SV74 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(454,plain,
! [SV65: $i,SV52: $i] :
( ( ~ ( ~ ( disjoint @ SV52 @ SV65 )
| ! [SY118: $i] :
~ ~ ( ~ ( member @ SY118 @ SV52 )
| ~ ( member @ SY118 @ SV65 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[437]) ).
thf(455,plain,
! [SV65: $i,SV52: $i] :
( ( ~ ( ~ ! [SY119: $i] :
~ ~ ( ~ ( member @ SY119 @ SV52 )
| ~ ( member @ SY119 @ SV65 ) )
| ( disjoint @ SV52 @ SV65 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[437]) ).
thf(456,plain,
! [SV66: $i,SV53: $i,SV72: $i] :
( ( ~ ( ~ ( member @ SV72 @ ( intersection @ SV53 @ SV66 ) )
| ~ ( ~ ( member @ SV72 @ SV53 )
| ~ ( member @ SV72 @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV72 @ SV53 )
| ~ ( member @ SV72 @ SV66 ) )
| ( member @ SV72 @ ( intersection @ SV53 @ SV66 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(457,plain,
! [SV67: $i,SV55: $i] :
( ( ~ ( ~ ( member @ ( ordered_pair @ SV55 @ SV67 ) @ element_relation )
| ~ ( ~ ( member @ SV67 @ universal_class )
| ~ ( member @ SV55 @ SV67 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[440]) ).
thf(458,plain,
! [SV55: $i,SV67: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV67 @ universal_class )
| ~ ( member @ SV55 @ SV67 ) )
| ( member @ ( ordered_pair @ SV55 @ SV67 ) @ element_relation ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[440]) ).
thf(459,plain,
! [SV68: $i,SV56: $i,SV73: $i] :
( ( ( ~ ( member @ SV73 @ ( cross_product @ SV56 @ SV68 ) ) )
= $true )
| ( ( SV73
= ( ordered_pair @ ( first @ SV73 ) @ ( second @ SV73 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[441]) ).
thf(460,plain,
! [SV69: $i,SV58: $i,SV43: $i] :
( ( ~ ( ~ ( member @ SV43 @ ( unordered_pair @ SV58 @ SV69 ) )
| ~ ( ~ ( member @ SV43 @ universal_class )
| ~ ( ( SV43 = SV58 )
| ( SV43 = SV69 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[442]) ).
thf(461,plain,
! [SV69: $i,SV58: $i,SV43: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV43 @ universal_class )
| ~ ( ( SV43 = SV58 )
| ( SV43 = SV69 ) ) )
| ( member @ SV43 @ ( unordered_pair @ SV58 @ SV69 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[442]) ).
thf(462,plain,
! [SV59: $i,SV44: $i,SV70: $i] :
( ( ~ ( ~ ( member @ SV70 @ ( union @ SV44 @ SV59 ) )
| ( member @ SV70 @ SV44 )
| ( member @ SV70 @ SV59 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[443]) ).
thf(463,plain,
! [SV59: $i,SV44: $i,SV70: $i] :
( ( ~ ( ~ ( ( member @ SV70 @ SV44 )
| ( member @ SV70 @ SV59 ) )
| ( member @ SV70 @ ( union @ SV44 @ SV59 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[443]) ).
thf(464,plain,
! [SV60: $i,SV45: $i] :
( ( ~ ( subclass @ SV45 @ SV60 )
| ! [SY112: $i] :
( ~ ( member @ SY112 @ SV45 )
| ( member @ SY112 @ SV60 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[444]) ).
thf(465,plain,
! [SV60: $i,SV45: $i] :
( ( ~ ! [SY113: $i] :
( ~ ( member @ SY113 @ SV45 )
| ( member @ SY113 @ SV60 ) )
| ( subclass @ SV45 @ SV60 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[445]) ).
thf(466,plain,
! [SV46: $i,SV61: $i] :
( ( ~ ( member @ SV61 @ ( complement @ SV46 ) )
| ~ ( ~ ( member @ SV61 @ universal_class )
| ~ ~ ( member @ SV61 @ SV46 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[446]) ).
thf(467,plain,
! [SV46: $i,SV61: $i] :
( ( ~ ~ ( ~ ( member @ SV61 @ universal_class )
| ~ ~ ( member @ SV61 @ SV46 ) )
| ( member @ SV61 @ ( complement @ SV46 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[447]) ).
thf(468,plain,
! [SV62: $i,SV47: $i] :
( ( ~ ( member @ SV47 @ ( sum_class @ SV62 ) )
| ~ ! [SY114: $i] :
~ ~ ( ~ ( member @ SV47 @ SY114 )
| ~ ( member @ SY114 @ SV62 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[448]) ).
thf(469,plain,
! [SV62: $i,SV47: $i] :
( ( ~ ~ ! [SY115: $i] :
~ ~ ( ~ ( member @ SV47 @ SY115 )
| ~ ( member @ SY115 @ SV62 ) )
| ( member @ SV47 @ ( sum_class @ SV62 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[449]) ).
thf(470,plain,
! [SV63: $i,SV48: $i] :
( ( ( ~ ( member @ SV48 @ universal_class )
| ~ ( member @ SV63 @ universal_class ) )
= $true )
| ( ( ~ ( ( ( first @ ( ordered_pair @ SV48 @ SV63 ) )
!= SV48 )
| ( ( second @ ( ordered_pair @ SV48 @ SV63 ) )
!= SV63 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[450]) ).
thf(471,plain,
! [SV49: $i] :
( ( ( ~ ( member @ SV49 @ identity_relation ) )
= $true )
| ( ( ~ ! [SY97: $i] :
~ ~ ( ~ ( member @ SY97 @ universal_class )
| ( SV49
!= ( ordered_pair @ SY97 @ SY97 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[451]) ).
thf(472,plain,
! [SV49: $i] :
( ( ( ~ ~ ! [SY98: $i] :
~ ~ ( ~ ( member @ SY98 @ universal_class )
| ( SV49
!= ( ordered_pair @ SY98 @ SY98 ) ) ) )
= $true )
| ( ( member @ SV49 @ identity_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[452]) ).
thf(473,plain,
! [SV74: $i,SV71: $i,SV64: $i,SV51: $i] :
( ( ~ ( ~ ( member @ ( ordered_pair @ SV51 @ SV64 ) @ ( cross_product @ SV71 @ SV74 ) )
| ~ ( ~ ( member @ SV51 @ SV71 )
| ~ ( member @ SV64 @ SV74 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV51 @ SV71 )
| ~ ( member @ SV64 @ SV74 ) )
| ( member @ ( ordered_pair @ SV51 @ SV64 ) @ ( cross_product @ SV71 @ SV74 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[453]) ).
thf(474,plain,
! [SV65: $i,SV52: $i] :
( ( ~ ( disjoint @ SV52 @ SV65 )
| ! [SY118: $i] :
~ ~ ( ~ ( member @ SY118 @ SV52 )
| ~ ( member @ SY118 @ SV65 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[454]) ).
thf(475,plain,
! [SV65: $i,SV52: $i] :
( ( ~ ! [SY119: $i] :
~ ~ ( ~ ( member @ SY119 @ SV52 )
| ~ ( member @ SY119 @ SV65 ) )
| ( disjoint @ SV52 @ SV65 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[455]) ).
thf(476,plain,
! [SV66: $i,SV53: $i,SV72: $i] :
( ( ~ ( ~ ( member @ SV72 @ ( intersection @ SV53 @ SV66 ) )
| ~ ( ~ ( member @ SV72 @ SV53 )
| ~ ( member @ SV72 @ SV66 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[456]) ).
thf(477,plain,
! [SV66: $i,SV53: $i,SV72: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV72 @ SV53 )
| ~ ( member @ SV72 @ SV66 ) )
| ( member @ SV72 @ ( intersection @ SV53 @ SV66 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[456]) ).
thf(478,plain,
! [SV67: $i,SV55: $i] :
( ( ~ ( member @ ( ordered_pair @ SV55 @ SV67 ) @ element_relation )
| ~ ( ~ ( member @ SV67 @ universal_class )
| ~ ( member @ SV55 @ SV67 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[457]) ).
thf(479,plain,
! [SV55: $i,SV67: $i] :
( ( ~ ~ ( ~ ( member @ SV67 @ universal_class )
| ~ ( member @ SV55 @ SV67 ) )
| ( member @ ( ordered_pair @ SV55 @ SV67 ) @ element_relation ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[458]) ).
thf(480,plain,
! [SV68: $i,SV56: $i,SV73: $i] :
( ( ( member @ SV73 @ ( cross_product @ SV56 @ SV68 ) )
= $false )
| ( ( SV73
= ( ordered_pair @ ( first @ SV73 ) @ ( second @ SV73 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[459]) ).
thf(481,plain,
! [SV69: $i,SV58: $i,SV43: $i] :
( ( ~ ( member @ SV43 @ ( unordered_pair @ SV58 @ SV69 ) )
| ~ ( ~ ( member @ SV43 @ universal_class )
| ~ ( ( SV43 = SV58 )
| ( SV43 = SV69 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[460]) ).
thf(482,plain,
! [SV69: $i,SV58: $i,SV43: $i] :
( ( ~ ~ ( ~ ( member @ SV43 @ universal_class )
| ~ ( ( SV43 = SV58 )
| ( SV43 = SV69 ) ) )
| ( member @ SV43 @ ( unordered_pair @ SV58 @ SV69 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[461]) ).
thf(483,plain,
! [SV59: $i,SV44: $i,SV70: $i] :
( ( ~ ( member @ SV70 @ ( union @ SV44 @ SV59 ) )
| ( member @ SV70 @ SV44 )
| ( member @ SV70 @ SV59 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[462]) ).
thf(484,plain,
! [SV59: $i,SV44: $i,SV70: $i] :
( ( ~ ( ( member @ SV70 @ SV44 )
| ( member @ SV70 @ SV59 ) )
| ( member @ SV70 @ ( union @ SV44 @ SV59 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[463]) ).
thf(485,plain,
! [SV60: $i,SV45: $i] :
( ( ( ~ ( subclass @ SV45 @ SV60 ) )
= $true )
| ( ( ! [SY112: $i] :
( ~ ( member @ SY112 @ SV45 )
| ( member @ SY112 @ SV60 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[464]) ).
thf(486,plain,
! [SV60: $i,SV45: $i] :
( ( ( ~ ! [SY113: $i] :
( ~ ( member @ SY113 @ SV45 )
| ( member @ SY113 @ SV60 ) ) )
= $true )
| ( ( subclass @ SV45 @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[465]) ).
thf(487,plain,
! [SV46: $i,SV61: $i] :
( ( ( ~ ( member @ SV61 @ ( complement @ SV46 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ SV61 @ universal_class )
| ~ ~ ( member @ SV61 @ SV46 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[466]) ).
thf(488,plain,
! [SV46: $i,SV61: $i] :
( ( ( ~ ~ ( ~ ( member @ SV61 @ universal_class )
| ~ ~ ( member @ SV61 @ SV46 ) ) )
= $true )
| ( ( member @ SV61 @ ( complement @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[467]) ).
thf(489,plain,
! [SV62: $i,SV47: $i] :
( ( ( ~ ( member @ SV47 @ ( sum_class @ SV62 ) ) )
= $true )
| ( ( ~ ! [SY114: $i] :
~ ~ ( ~ ( member @ SV47 @ SY114 )
| ~ ( member @ SY114 @ SV62 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[468]) ).
thf(490,plain,
! [SV62: $i,SV47: $i] :
( ( ( ~ ~ ! [SY115: $i] :
~ ~ ( ~ ( member @ SV47 @ SY115 )
| ~ ( member @ SY115 @ SV62 ) ) )
= $true )
| ( ( member @ SV47 @ ( sum_class @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[469]) ).
thf(491,plain,
! [SV63: $i,SV48: $i] :
( ( ( ~ ( member @ SV48 @ universal_class ) )
= $true )
| ( ( ~ ( member @ SV63 @ universal_class ) )
= $true )
| ( ( ~ ( ( ( first @ ( ordered_pair @ SV48 @ SV63 ) )
!= SV48 )
| ( ( second @ ( ordered_pair @ SV48 @ SV63 ) )
!= SV63 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[470]) ).
thf(492,plain,
! [SV49: $i] :
( ( ( member @ SV49 @ identity_relation )
= $false )
| ( ( ~ ! [SY97: $i] :
~ ~ ( ~ ( member @ SY97 @ universal_class )
| ( SV49
!= ( ordered_pair @ SY97 @ SY97 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(493,plain,
! [SV49: $i] :
( ( ( ~ ! [SY98: $i] :
~ ~ ( ~ ( member @ SY98 @ universal_class )
| ( SV49
!= ( ordered_pair @ SY98 @ SY98 ) ) ) )
= $false )
| ( ( member @ SV49 @ identity_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[472]) ).
thf(494,plain,
! [SV74: $i,SV71: $i,SV64: $i,SV51: $i] :
( ( ~ ( ~ ( member @ ( ordered_pair @ SV51 @ SV64 ) @ ( cross_product @ SV71 @ SV74 ) )
| ~ ( ~ ( member @ SV51 @ SV71 )
| ~ ( member @ SV64 @ SV74 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[473]) ).
thf(495,plain,
! [SV74: $i,SV64: $i,SV71: $i,SV51: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV51 @ SV71 )
| ~ ( member @ SV64 @ SV74 ) )
| ( member @ ( ordered_pair @ SV51 @ SV64 ) @ ( cross_product @ SV71 @ SV74 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[473]) ).
thf(496,plain,
! [SV65: $i,SV52: $i] :
( ( ( ~ ( disjoint @ SV52 @ SV65 ) )
= $true )
| ( ( ! [SY118: $i] :
~ ~ ( ~ ( member @ SY118 @ SV52 )
| ~ ( member @ SY118 @ SV65 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[474]) ).
thf(497,plain,
! [SV65: $i,SV52: $i] :
( ( ( ~ ! [SY119: $i] :
~ ~ ( ~ ( member @ SY119 @ SV52 )
| ~ ( member @ SY119 @ SV65 ) ) )
= $true )
| ( ( disjoint @ SV52 @ SV65 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[475]) ).
thf(498,plain,
! [SV66: $i,SV53: $i,SV72: $i] :
( ( ~ ( member @ SV72 @ ( intersection @ SV53 @ SV66 ) )
| ~ ( ~ ( member @ SV72 @ SV53 )
| ~ ( member @ SV72 @ SV66 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[476]) ).
thf(499,plain,
! [SV66: $i,SV53: $i,SV72: $i] :
( ( ~ ~ ( ~ ( member @ SV72 @ SV53 )
| ~ ( member @ SV72 @ SV66 ) )
| ( member @ SV72 @ ( intersection @ SV53 @ SV66 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[477]) ).
thf(500,plain,
! [SV67: $i,SV55: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV55 @ SV67 ) @ element_relation ) )
= $true )
| ( ( ~ ( ~ ( member @ SV67 @ universal_class )
| ~ ( member @ SV55 @ SV67 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[478]) ).
thf(501,plain,
! [SV55: $i,SV67: $i] :
( ( ( ~ ~ ( ~ ( member @ SV67 @ universal_class )
| ~ ( member @ SV55 @ SV67 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ SV55 @ SV67 ) @ element_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[479]) ).
thf(502,plain,
! [SV69: $i,SV58: $i,SV43: $i] :
( ( ( ~ ( member @ SV43 @ ( unordered_pair @ SV58 @ SV69 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ SV43 @ universal_class )
| ~ ( ( SV43 = SV58 )
| ( SV43 = SV69 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[481]) ).
thf(503,plain,
! [SV69: $i,SV58: $i,SV43: $i] :
( ( ( ~ ~ ( ~ ( member @ SV43 @ universal_class )
| ~ ( ( SV43 = SV58 )
| ( SV43 = SV69 ) ) ) )
= $true )
| ( ( member @ SV43 @ ( unordered_pair @ SV58 @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[482]) ).
thf(504,plain,
! [SV59: $i,SV44: $i,SV70: $i] :
( ( ( ~ ( member @ SV70 @ ( union @ SV44 @ SV59 ) ) )
= $true )
| ( ( ( member @ SV70 @ SV44 )
| ( member @ SV70 @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[483]) ).
thf(505,plain,
! [SV59: $i,SV44: $i,SV70: $i] :
( ( ( ~ ( ( member @ SV70 @ SV44 )
| ( member @ SV70 @ SV59 ) ) )
= $true )
| ( ( member @ SV70 @ ( union @ SV44 @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[484]) ).
thf(506,plain,
! [SV60: $i,SV45: $i] :
( ( ( subclass @ SV45 @ SV60 )
= $false )
| ( ( ! [SY112: $i] :
( ~ ( member @ SY112 @ SV45 )
| ( member @ SY112 @ SV60 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[485]) ).
thf(507,plain,
! [SV60: $i,SV45: $i] :
( ( ( ! [SY113: $i] :
( ~ ( member @ SY113 @ SV45 )
| ( member @ SY113 @ SV60 ) ) )
= $false )
| ( ( subclass @ SV45 @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[486]) ).
thf(508,plain,
! [SV46: $i,SV61: $i] :
( ( ( member @ SV61 @ ( complement @ SV46 ) )
= $false )
| ( ( ~ ( ~ ( member @ SV61 @ universal_class )
| ~ ~ ( member @ SV61 @ SV46 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[487]) ).
thf(509,plain,
! [SV46: $i,SV61: $i] :
( ( ( ~ ( ~ ( member @ SV61 @ universal_class )
| ~ ~ ( member @ SV61 @ SV46 ) ) )
= $false )
| ( ( member @ SV61 @ ( complement @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[488]) ).
thf(510,plain,
! [SV62: $i,SV47: $i] :
( ( ( member @ SV47 @ ( sum_class @ SV62 ) )
= $false )
| ( ( ~ ! [SY114: $i] :
~ ~ ( ~ ( member @ SV47 @ SY114 )
| ~ ( member @ SY114 @ SV62 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[489]) ).
thf(511,plain,
! [SV62: $i,SV47: $i] :
( ( ( ~ ! [SY115: $i] :
~ ~ ( ~ ( member @ SV47 @ SY115 )
| ~ ( member @ SY115 @ SV62 ) ) )
= $false )
| ( ( member @ SV47 @ ( sum_class @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[490]) ).
thf(512,plain,
! [SV63: $i,SV48: $i] :
( ( ( member @ SV48 @ universal_class )
= $false )
| ( ( ~ ( member @ SV63 @ universal_class ) )
= $true )
| ( ( ~ ( ( ( first @ ( ordered_pair @ SV48 @ SV63 ) )
!= SV48 )
| ( ( second @ ( ordered_pair @ SV48 @ SV63 ) )
!= SV63 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[491]) ).
thf(513,plain,
! [SV49: $i] :
( ( ( ! [SY97: $i] :
~ ~ ( ~ ( member @ SY97 @ universal_class )
| ( SV49
!= ( ordered_pair @ SY97 @ SY97 ) ) ) )
= $false )
| ( ( member @ SV49 @ identity_relation )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[492]) ).
thf(514,plain,
! [SV49: $i] :
( ( ( ! [SY98: $i] :
~ ~ ( ~ ( member @ SY98 @ universal_class )
| ( SV49
!= ( ordered_pair @ SY98 @ SY98 ) ) ) )
= $true )
| ( ( member @ SV49 @ identity_relation )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[493]) ).
thf(515,plain,
! [SV74: $i,SV71: $i,SV64: $i,SV51: $i] :
( ( ~ ( member @ ( ordered_pair @ SV51 @ SV64 ) @ ( cross_product @ SV71 @ SV74 ) )
| ~ ( ~ ( member @ SV51 @ SV71 )
| ~ ( member @ SV64 @ SV74 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[494]) ).
thf(516,plain,
! [SV74: $i,SV64: $i,SV71: $i,SV51: $i] :
( ( ~ ~ ( ~ ( member @ SV51 @ SV71 )
| ~ ( member @ SV64 @ SV74 ) )
| ( member @ ( ordered_pair @ SV51 @ SV64 ) @ ( cross_product @ SV71 @ SV74 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[495]) ).
thf(517,plain,
! [SV65: $i,SV52: $i] :
( ( ( disjoint @ SV52 @ SV65 )
= $false )
| ( ( ! [SY118: $i] :
~ ~ ( ~ ( member @ SY118 @ SV52 )
| ~ ( member @ SY118 @ SV65 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(518,plain,
! [SV65: $i,SV52: $i] :
( ( ( ! [SY119: $i] :
~ ~ ( ~ ( member @ SY119 @ SV52 )
| ~ ( member @ SY119 @ SV65 ) ) )
= $false )
| ( ( disjoint @ SV52 @ SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(519,plain,
! [SV66: $i,SV53: $i,SV72: $i] :
( ( ( ~ ( member @ SV72 @ ( intersection @ SV53 @ SV66 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ SV72 @ SV53 )
| ~ ( member @ SV72 @ SV66 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[498]) ).
thf(520,plain,
! [SV66: $i,SV53: $i,SV72: $i] :
( ( ( ~ ~ ( ~ ( member @ SV72 @ SV53 )
| ~ ( member @ SV72 @ SV66 ) ) )
= $true )
| ( ( member @ SV72 @ ( intersection @ SV53 @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[499]) ).
thf(521,plain,
! [SV67: $i,SV55: $i] :
( ( ( member @ ( ordered_pair @ SV55 @ SV67 ) @ element_relation )
= $false )
| ( ( ~ ( ~ ( member @ SV67 @ universal_class )
| ~ ( member @ SV55 @ SV67 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(522,plain,
! [SV55: $i,SV67: $i] :
( ( ( ~ ( ~ ( member @ SV67 @ universal_class )
| ~ ( member @ SV55 @ SV67 ) ) )
= $false )
| ( ( member @ ( ordered_pair @ SV55 @ SV67 ) @ element_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(523,plain,
! [SV69: $i,SV58: $i,SV43: $i] :
( ( ( member @ SV43 @ ( unordered_pair @ SV58 @ SV69 ) )
= $false )
| ( ( ~ ( ~ ( member @ SV43 @ universal_class )
| ~ ( ( SV43 = SV58 )
| ( SV43 = SV69 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(524,plain,
! [SV69: $i,SV58: $i,SV43: $i] :
( ( ( ~ ( ~ ( member @ SV43 @ universal_class )
| ~ ( ( SV43 = SV58 )
| ( SV43 = SV69 ) ) ) )
= $false )
| ( ( member @ SV43 @ ( unordered_pair @ SV58 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(525,plain,
! [SV59: $i,SV44: $i,SV70: $i] :
( ( ( member @ SV70 @ ( union @ SV44 @ SV59 ) )
= $false )
| ( ( ( member @ SV70 @ SV44 )
| ( member @ SV70 @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(526,plain,
! [SV59: $i,SV44: $i,SV70: $i] :
( ( ( ( member @ SV70 @ SV44 )
| ( member @ SV70 @ SV59 ) )
= $false )
| ( ( member @ SV70 @ ( union @ SV44 @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[505]) ).
thf(527,plain,
! [SV60: $i,SV45: $i,SV75: $i] :
( ( ( ~ ( member @ SV75 @ SV45 )
| ( member @ SV75 @ SV60 ) )
= $true )
| ( ( subclass @ SV45 @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(528,plain,
! [SV45: $i,SV60: $i] :
( ( ( ~ ( member @ ( sK8_SY113 @ SV60 @ SV45 ) @ SV45 )
| ( member @ ( sK8_SY113 @ SV60 @ SV45 ) @ SV60 ) )
= $false )
| ( ( subclass @ SV45 @ SV60 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[507]) ).
thf(529,plain,
! [SV46: $i,SV61: $i] :
( ( ( ~ ( member @ SV61 @ universal_class )
| ~ ~ ( member @ SV61 @ SV46 ) )
= $false )
| ( ( member @ SV61 @ ( complement @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(530,plain,
! [SV46: $i,SV61: $i] :
( ( ( ~ ( member @ SV61 @ universal_class )
| ~ ~ ( member @ SV61 @ SV46 ) )
= $true )
| ( ( member @ SV61 @ ( complement @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[509]) ).
thf(531,plain,
! [SV62: $i,SV47: $i] :
( ( ( ! [SY114: $i] :
~ ~ ( ~ ( member @ SV47 @ SY114 )
| ~ ( member @ SY114 @ SV62 ) ) )
= $false )
| ( ( member @ SV47 @ ( sum_class @ SV62 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(532,plain,
! [SV62: $i,SV47: $i] :
( ( ( ! [SY115: $i] :
~ ~ ( ~ ( member @ SV47 @ SY115 )
| ~ ( member @ SY115 @ SV62 ) ) )
= $true )
| ( ( member @ SV47 @ ( sum_class @ SV62 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[511]) ).
thf(533,plain,
! [SV48: $i,SV63: $i] :
( ( ( member @ SV63 @ universal_class )
= $false )
| ( ( member @ SV48 @ universal_class )
= $false )
| ( ( ~ ( ( ( first @ ( ordered_pair @ SV48 @ SV63 ) )
!= SV48 )
| ( ( second @ ( ordered_pair @ SV48 @ SV63 ) )
!= SV63 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[512]) ).
thf(534,plain,
! [SV49: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK9_SY97 @ SV49 ) @ universal_class )
| ( SV49
!= ( ordered_pair @ ( sK9_SY97 @ SV49 ) @ ( sK9_SY97 @ SV49 ) ) ) ) )
= $false )
| ( ( member @ SV49 @ identity_relation )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[513]) ).
thf(535,plain,
! [SV49: $i,SV76: $i] :
( ( ( ~ ~ ( ~ ( member @ SV76 @ universal_class )
| ( SV49
!= ( ordered_pair @ SV76 @ SV76 ) ) ) )
= $true )
| ( ( member @ SV49 @ identity_relation )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(536,plain,
! [SV74: $i,SV71: $i,SV64: $i,SV51: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV51 @ SV64 ) @ ( cross_product @ SV71 @ SV74 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ SV51 @ SV71 )
| ~ ( member @ SV64 @ SV74 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[515]) ).
thf(537,plain,
! [SV74: $i,SV64: $i,SV71: $i,SV51: $i] :
( ( ( ~ ~ ( ~ ( member @ SV51 @ SV71 )
| ~ ( member @ SV64 @ SV74 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ SV51 @ SV64 ) @ ( cross_product @ SV71 @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[516]) ).
thf(538,plain,
! [SV65: $i,SV52: $i,SV77: $i] :
( ( ( ~ ~ ( ~ ( member @ SV77 @ SV52 )
| ~ ( member @ SV77 @ SV65 ) ) )
= $true )
| ( ( disjoint @ SV52 @ SV65 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(539,plain,
! [SV52: $i,SV65: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK10_SY119 @ SV65 @ SV52 ) @ SV52 )
| ~ ( member @ ( sK10_SY119 @ SV65 @ SV52 ) @ SV65 ) ) )
= $false )
| ( ( disjoint @ SV52 @ SV65 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[518]) ).
thf(540,plain,
! [SV66: $i,SV53: $i,SV72: $i] :
( ( ( member @ SV72 @ ( intersection @ SV53 @ SV66 ) )
= $false )
| ( ( ~ ( ~ ( member @ SV72 @ SV53 )
| ~ ( member @ SV72 @ SV66 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[519]) ).
thf(541,plain,
! [SV66: $i,SV53: $i,SV72: $i] :
( ( ( ~ ( ~ ( member @ SV72 @ SV53 )
| ~ ( member @ SV72 @ SV66 ) ) )
= $false )
| ( ( member @ SV72 @ ( intersection @ SV53 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[520]) ).
thf(542,plain,
! [SV55: $i,SV67: $i] :
( ( ( ~ ( member @ SV67 @ universal_class )
| ~ ( member @ SV55 @ SV67 ) )
= $false )
| ( ( member @ ( ordered_pair @ SV55 @ SV67 ) @ element_relation )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[521]) ).
thf(543,plain,
! [SV55: $i,SV67: $i] :
( ( ( ~ ( member @ SV67 @ universal_class )
| ~ ( member @ SV55 @ SV67 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV55 @ SV67 ) @ element_relation )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[522]) ).
thf(544,plain,
! [SV69: $i,SV58: $i,SV43: $i] :
( ( ( ~ ( member @ SV43 @ universal_class )
| ~ ( ( SV43 = SV58 )
| ( SV43 = SV69 ) ) )
= $false )
| ( ( member @ SV43 @ ( unordered_pair @ SV58 @ SV69 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[523]) ).
thf(545,plain,
! [SV69: $i,SV58: $i,SV43: $i] :
( ( ( ~ ( member @ SV43 @ universal_class )
| ~ ( ( SV43 = SV58 )
| ( SV43 = SV69 ) ) )
= $true )
| ( ( member @ SV43 @ ( unordered_pair @ SV58 @ SV69 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[524]) ).
thf(546,plain,
! [SV59: $i,SV44: $i,SV70: $i] :
( ( ( member @ SV70 @ SV44 )
= $true )
| ( ( member @ SV70 @ SV59 )
= $true )
| ( ( member @ SV70 @ ( union @ SV44 @ SV59 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[525]) ).
thf(547,plain,
! [SV59: $i,SV44: $i,SV70: $i] :
( ( ( member @ SV70 @ SV44 )
= $false )
| ( ( member @ SV70 @ ( union @ SV44 @ SV59 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[526]) ).
thf(548,plain,
! [SV44: $i,SV59: $i,SV70: $i] :
( ( ( member @ SV70 @ SV59 )
= $false )
| ( ( member @ SV70 @ ( union @ SV44 @ SV59 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[526]) ).
thf(549,plain,
! [SV60: $i,SV45: $i,SV75: $i] :
( ( ( ~ ( member @ SV75 @ SV45 ) )
= $true )
| ( ( member @ SV75 @ SV60 )
= $true )
| ( ( subclass @ SV45 @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[527]) ).
thf(550,plain,
! [SV45: $i,SV60: $i] :
( ( ( ~ ( member @ ( sK8_SY113 @ SV60 @ SV45 ) @ SV45 ) )
= $false )
| ( ( subclass @ SV45 @ SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[528]) ).
thf(551,plain,
! [SV45: $i,SV60: $i] :
( ( ( member @ ( sK8_SY113 @ SV60 @ SV45 ) @ SV60 )
= $false )
| ( ( subclass @ SV45 @ SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[528]) ).
thf(552,plain,
! [SV46: $i,SV61: $i] :
( ( ( ~ ( member @ SV61 @ universal_class ) )
= $false )
| ( ( member @ SV61 @ ( complement @ SV46 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[529]) ).
thf(553,plain,
! [SV46: $i,SV61: $i] :
( ( ( ~ ~ ( member @ SV61 @ SV46 ) )
= $false )
| ( ( member @ SV61 @ ( complement @ SV46 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[529]) ).
thf(554,plain,
! [SV46: $i,SV61: $i] :
( ( ( ~ ( member @ SV61 @ universal_class ) )
= $true )
| ( ( ~ ~ ( member @ SV61 @ SV46 ) )
= $true )
| ( ( member @ SV61 @ ( complement @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[530]) ).
thf(555,plain,
! [SV62: $i,SV47: $i] :
( ( ( ~ ~ ( ~ ( member @ SV47 @ ( sK11_SY114 @ SV62 @ SV47 ) )
| ~ ( member @ ( sK11_SY114 @ SV62 @ SV47 ) @ SV62 ) ) )
= $false )
| ( ( member @ SV47 @ ( sum_class @ SV62 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[531]) ).
thf(556,plain,
! [SV62: $i,SV78: $i,SV47: $i] :
( ( ( ~ ~ ( ~ ( member @ SV47 @ SV78 )
| ~ ( member @ SV78 @ SV62 ) ) )
= $true )
| ( ( member @ SV47 @ ( sum_class @ SV62 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(557,plain,
! [SV63: $i,SV48: $i] :
( ( ( ( ( first @ ( ordered_pair @ SV48 @ SV63 ) )
!= SV48 )
| ( ( second @ ( ordered_pair @ SV48 @ SV63 ) )
!= SV63 ) )
= $false )
| ( ( member @ SV48 @ universal_class )
= $false )
| ( ( member @ SV63 @ universal_class )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[533]) ).
thf(558,plain,
! [SV49: $i] :
( ( ( ~ ( ~ ( member @ ( sK9_SY97 @ SV49 ) @ universal_class )
| ( SV49
!= ( ordered_pair @ ( sK9_SY97 @ SV49 ) @ ( sK9_SY97 @ SV49 ) ) ) ) )
= $true )
| ( ( member @ SV49 @ identity_relation )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[534]) ).
thf(559,plain,
! [SV49: $i,SV76: $i] :
( ( ( ~ ( ~ ( member @ SV76 @ universal_class )
| ( SV49
!= ( ordered_pair @ SV76 @ SV76 ) ) ) )
= $false )
| ( ( member @ SV49 @ identity_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[535]) ).
thf(560,plain,
! [SV74: $i,SV71: $i,SV64: $i,SV51: $i] :
( ( ( member @ ( ordered_pair @ SV51 @ SV64 ) @ ( cross_product @ SV71 @ SV74 ) )
= $false )
| ( ( ~ ( ~ ( member @ SV51 @ SV71 )
| ~ ( member @ SV64 @ SV74 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[536]) ).
thf(561,plain,
! [SV74: $i,SV64: $i,SV71: $i,SV51: $i] :
( ( ( ~ ( ~ ( member @ SV51 @ SV71 )
| ~ ( member @ SV64 @ SV74 ) ) )
= $false )
| ( ( member @ ( ordered_pair @ SV51 @ SV64 ) @ ( cross_product @ SV71 @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[537]) ).
thf(562,plain,
! [SV65: $i,SV52: $i,SV77: $i] :
( ( ( ~ ( ~ ( member @ SV77 @ SV52 )
| ~ ( member @ SV77 @ SV65 ) ) )
= $false )
| ( ( disjoint @ SV52 @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[538]) ).
thf(563,plain,
! [SV52: $i,SV65: $i] :
( ( ( ~ ( ~ ( member @ ( sK10_SY119 @ SV65 @ SV52 ) @ SV52 )
| ~ ( member @ ( sK10_SY119 @ SV65 @ SV52 ) @ SV65 ) ) )
= $true )
| ( ( disjoint @ SV52 @ SV65 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[539]) ).
thf(564,plain,
! [SV66: $i,SV53: $i,SV72: $i] :
( ( ( ~ ( member @ SV72 @ SV53 )
| ~ ( member @ SV72 @ SV66 ) )
= $false )
| ( ( member @ SV72 @ ( intersection @ SV53 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[540]) ).
thf(565,plain,
! [SV66: $i,SV53: $i,SV72: $i] :
( ( ( ~ ( member @ SV72 @ SV53 )
| ~ ( member @ SV72 @ SV66 ) )
= $true )
| ( ( member @ SV72 @ ( intersection @ SV53 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[541]) ).
thf(566,plain,
! [SV55: $i,SV67: $i] :
( ( ( ~ ( member @ SV67 @ universal_class ) )
= $false )
| ( ( member @ ( ordered_pair @ SV55 @ SV67 ) @ element_relation )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[542]) ).
thf(567,plain,
! [SV67: $i,SV55: $i] :
( ( ( ~ ( member @ SV55 @ SV67 ) )
= $false )
| ( ( member @ ( ordered_pair @ SV55 @ SV67 ) @ element_relation )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[542]) ).
thf(568,plain,
! [SV55: $i,SV67: $i] :
( ( ( ~ ( member @ SV67 @ universal_class ) )
= $true )
| ( ( ~ ( member @ SV55 @ SV67 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV55 @ SV67 ) @ element_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[543]) ).
thf(569,plain,
! [SV69: $i,SV58: $i,SV43: $i] :
( ( ( ~ ( member @ SV43 @ universal_class ) )
= $false )
| ( ( member @ SV43 @ ( unordered_pair @ SV58 @ SV69 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[544]) ).
thf(570,plain,
! [SV69: $i,SV58: $i,SV43: $i] :
( ( ( ~ ( ( SV43 = SV58 )
| ( SV43 = SV69 ) ) )
= $false )
| ( ( member @ SV43 @ ( unordered_pair @ SV58 @ SV69 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[544]) ).
thf(571,plain,
! [SV69: $i,SV58: $i,SV43: $i] :
( ( ( ~ ( member @ SV43 @ universal_class ) )
= $true )
| ( ( ~ ( ( SV43 = SV58 )
| ( SV43 = SV69 ) ) )
= $true )
| ( ( member @ SV43 @ ( unordered_pair @ SV58 @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[545]) ).
thf(572,plain,
! [SV60: $i,SV45: $i,SV75: $i] :
( ( ( member @ SV75 @ SV45 )
= $false )
| ( ( member @ SV75 @ SV60 )
= $true )
| ( ( subclass @ SV45 @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[549]) ).
thf(573,plain,
! [SV45: $i,SV60: $i] :
( ( ( member @ ( sK8_SY113 @ SV60 @ SV45 ) @ SV45 )
= $true )
| ( ( subclass @ SV45 @ SV60 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[550]) ).
thf(574,plain,
! [SV46: $i,SV61: $i] :
( ( ( member @ SV61 @ universal_class )
= $true )
| ( ( member @ SV61 @ ( complement @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[552]) ).
thf(575,plain,
! [SV46: $i,SV61: $i] :
( ( ( ~ ( member @ SV61 @ SV46 ) )
= $true )
| ( ( member @ SV61 @ ( complement @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[553]) ).
thf(576,plain,
! [SV46: $i,SV61: $i] :
( ( ( member @ SV61 @ universal_class )
= $false )
| ( ( ~ ~ ( member @ SV61 @ SV46 ) )
= $true )
| ( ( member @ SV61 @ ( complement @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[554]) ).
thf(577,plain,
! [SV62: $i,SV47: $i] :
( ( ( ~ ( ~ ( member @ SV47 @ ( sK11_SY114 @ SV62 @ SV47 ) )
| ~ ( member @ ( sK11_SY114 @ SV62 @ SV47 ) @ SV62 ) ) )
= $true )
| ( ( member @ SV47 @ ( sum_class @ SV62 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[555]) ).
thf(578,plain,
! [SV62: $i,SV78: $i,SV47: $i] :
( ( ( ~ ( ~ ( member @ SV47 @ SV78 )
| ~ ( member @ SV78 @ SV62 ) ) )
= $false )
| ( ( member @ SV47 @ ( sum_class @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[556]) ).
thf(579,plain,
! [SV63: $i,SV48: $i] :
( ( ( ( first @ ( ordered_pair @ SV48 @ SV63 ) )
!= SV48 )
= $false )
| ( ( member @ SV48 @ universal_class )
= $false )
| ( ( member @ SV63 @ universal_class )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[557]) ).
thf(580,plain,
! [SV63: $i,SV48: $i] :
( ( ( ( second @ ( ordered_pair @ SV48 @ SV63 ) )
!= SV63 )
= $false )
| ( ( member @ SV48 @ universal_class )
= $false )
| ( ( member @ SV63 @ universal_class )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[557]) ).
thf(581,plain,
! [SV49: $i] :
( ( ( ~ ( member @ ( sK9_SY97 @ SV49 ) @ universal_class )
| ( SV49
!= ( ordered_pair @ ( sK9_SY97 @ SV49 ) @ ( sK9_SY97 @ SV49 ) ) ) )
= $false )
| ( ( member @ SV49 @ identity_relation )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[558]) ).
thf(582,plain,
! [SV49: $i,SV76: $i] :
( ( ( ~ ( member @ SV76 @ universal_class )
| ( SV49
!= ( ordered_pair @ SV76 @ SV76 ) ) )
= $true )
| ( ( member @ SV49 @ identity_relation )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[559]) ).
thf(583,plain,
! [SV74: $i,SV64: $i,SV71: $i,SV51: $i] :
( ( ( ~ ( member @ SV51 @ SV71 )
| ~ ( member @ SV64 @ SV74 ) )
= $false )
| ( ( member @ ( ordered_pair @ SV51 @ SV64 ) @ ( cross_product @ SV71 @ SV74 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[560]) ).
thf(584,plain,
! [SV74: $i,SV64: $i,SV71: $i,SV51: $i] :
( ( ( ~ ( member @ SV51 @ SV71 )
| ~ ( member @ SV64 @ SV74 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV51 @ SV64 ) @ ( cross_product @ SV71 @ SV74 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[561]) ).
thf(585,plain,
! [SV65: $i,SV52: $i,SV77: $i] :
( ( ( ~ ( member @ SV77 @ SV52 )
| ~ ( member @ SV77 @ SV65 ) )
= $true )
| ( ( disjoint @ SV52 @ SV65 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[562]) ).
thf(586,plain,
! [SV52: $i,SV65: $i] :
( ( ( ~ ( member @ ( sK10_SY119 @ SV65 @ SV52 ) @ SV52 )
| ~ ( member @ ( sK10_SY119 @ SV65 @ SV52 ) @ SV65 ) )
= $false )
| ( ( disjoint @ SV52 @ SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[563]) ).
thf(587,plain,
! [SV66: $i,SV53: $i,SV72: $i] :
( ( ( ~ ( member @ SV72 @ SV53 ) )
= $false )
| ( ( member @ SV72 @ ( intersection @ SV53 @ SV66 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[564]) ).
thf(588,plain,
! [SV53: $i,SV66: $i,SV72: $i] :
( ( ( ~ ( member @ SV72 @ SV66 ) )
= $false )
| ( ( member @ SV72 @ ( intersection @ SV53 @ SV66 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[564]) ).
thf(589,plain,
! [SV66: $i,SV53: $i,SV72: $i] :
( ( ( ~ ( member @ SV72 @ SV53 ) )
= $true )
| ( ( ~ ( member @ SV72 @ SV66 ) )
= $true )
| ( ( member @ SV72 @ ( intersection @ SV53 @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[565]) ).
thf(590,plain,
! [SV55: $i,SV67: $i] :
( ( ( member @ SV67 @ universal_class )
= $true )
| ( ( member @ ( ordered_pair @ SV55 @ SV67 ) @ element_relation )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[566]) ).
thf(591,plain,
! [SV67: $i,SV55: $i] :
( ( ( member @ SV55 @ SV67 )
= $true )
| ( ( member @ ( ordered_pair @ SV55 @ SV67 ) @ element_relation )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[567]) ).
thf(592,plain,
! [SV55: $i,SV67: $i] :
( ( ( member @ SV67 @ universal_class )
= $false )
| ( ( ~ ( member @ SV55 @ SV67 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV55 @ SV67 ) @ element_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[568]) ).
thf(593,plain,
! [SV69: $i,SV58: $i,SV43: $i] :
( ( ( member @ SV43 @ universal_class )
= $true )
| ( ( member @ SV43 @ ( unordered_pair @ SV58 @ SV69 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[569]) ).
thf(594,plain,
! [SV69: $i,SV58: $i,SV43: $i] :
( ( ( ( SV43 = SV58 )
| ( SV43 = SV69 ) )
= $true )
| ( ( member @ SV43 @ ( unordered_pair @ SV58 @ SV69 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[570]) ).
thf(595,plain,
! [SV69: $i,SV58: $i,SV43: $i] :
( ( ( member @ SV43 @ universal_class )
= $false )
| ( ( ~ ( ( SV43 = SV58 )
| ( SV43 = SV69 ) ) )
= $true )
| ( ( member @ SV43 @ ( unordered_pair @ SV58 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(596,plain,
! [SV46: $i,SV61: $i] :
( ( ( member @ SV61 @ SV46 )
= $false )
| ( ( member @ SV61 @ ( complement @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[575]) ).
thf(597,plain,
! [SV46: $i,SV61: $i] :
( ( ( ~ ( member @ SV61 @ SV46 ) )
= $false )
| ( ( member @ SV61 @ universal_class )
= $false )
| ( ( member @ SV61 @ ( complement @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(598,plain,
! [SV62: $i,SV47: $i] :
( ( ( ~ ( member @ SV47 @ ( sK11_SY114 @ SV62 @ SV47 ) )
| ~ ( member @ ( sK11_SY114 @ SV62 @ SV47 ) @ SV62 ) )
= $false )
| ( ( member @ SV47 @ ( sum_class @ SV62 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[577]) ).
thf(599,plain,
! [SV62: $i,SV78: $i,SV47: $i] :
( ( ( ~ ( member @ SV47 @ SV78 )
| ~ ( member @ SV78 @ SV62 ) )
= $true )
| ( ( member @ SV47 @ ( sum_class @ SV62 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[578]) ).
thf(600,plain,
! [SV63: $i,SV48: $i] :
( ( ( ( first @ ( ordered_pair @ SV48 @ SV63 ) )
= SV48 )
= $true )
| ( ( member @ SV48 @ universal_class )
= $false )
| ( ( member @ SV63 @ universal_class )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[579]) ).
thf(601,plain,
! [SV63: $i,SV48: $i] :
( ( ( ( second @ ( ordered_pair @ SV48 @ SV63 ) )
= SV63 )
= $true )
| ( ( member @ SV48 @ universal_class )
= $false )
| ( ( member @ SV63 @ universal_class )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[580]) ).
thf(602,plain,
! [SV49: $i] :
( ( ( ~ ( member @ ( sK9_SY97 @ SV49 ) @ universal_class ) )
= $false )
| ( ( member @ SV49 @ identity_relation )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[581]) ).
thf(603,plain,
! [SV49: $i] :
( ( ( SV49
!= ( ordered_pair @ ( sK9_SY97 @ SV49 ) @ ( sK9_SY97 @ SV49 ) ) )
= $false )
| ( ( member @ SV49 @ identity_relation )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[581]) ).
thf(604,plain,
! [SV49: $i,SV76: $i] :
( ( ( ~ ( member @ SV76 @ universal_class ) )
= $true )
| ( ( SV49
!= ( ordered_pair @ SV76 @ SV76 ) )
= $true )
| ( ( member @ SV49 @ identity_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[582]) ).
thf(605,plain,
! [SV74: $i,SV64: $i,SV71: $i,SV51: $i] :
( ( ( ~ ( member @ SV51 @ SV71 ) )
= $false )
| ( ( member @ ( ordered_pair @ SV51 @ SV64 ) @ ( cross_product @ SV71 @ SV74 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[583]) ).
thf(606,plain,
! [SV71: $i,SV51: $i,SV74: $i,SV64: $i] :
( ( ( ~ ( member @ SV64 @ SV74 ) )
= $false )
| ( ( member @ ( ordered_pair @ SV51 @ SV64 ) @ ( cross_product @ SV71 @ SV74 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[583]) ).
thf(607,plain,
! [SV74: $i,SV64: $i,SV71: $i,SV51: $i] :
( ( ( ~ ( member @ SV51 @ SV71 ) )
= $true )
| ( ( ~ ( member @ SV64 @ SV74 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV51 @ SV64 ) @ ( cross_product @ SV71 @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[584]) ).
thf(608,plain,
! [SV65: $i,SV52: $i,SV77: $i] :
( ( ( ~ ( member @ SV77 @ SV52 ) )
= $true )
| ( ( ~ ( member @ SV77 @ SV65 ) )
= $true )
| ( ( disjoint @ SV52 @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[585]) ).
thf(609,plain,
! [SV52: $i,SV65: $i] :
( ( ( ~ ( member @ ( sK10_SY119 @ SV65 @ SV52 ) @ SV52 ) )
= $false )
| ( ( disjoint @ SV52 @ SV65 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[586]) ).
thf(610,plain,
! [SV52: $i,SV65: $i] :
( ( ( ~ ( member @ ( sK10_SY119 @ SV65 @ SV52 ) @ SV65 ) )
= $false )
| ( ( disjoint @ SV52 @ SV65 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[586]) ).
thf(611,plain,
! [SV66: $i,SV53: $i,SV72: $i] :
( ( ( member @ SV72 @ SV53 )
= $true )
| ( ( member @ SV72 @ ( intersection @ SV53 @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[587]) ).
thf(612,plain,
! [SV53: $i,SV66: $i,SV72: $i] :
( ( ( member @ SV72 @ SV66 )
= $true )
| ( ( member @ SV72 @ ( intersection @ SV53 @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[588]) ).
thf(613,plain,
! [SV66: $i,SV53: $i,SV72: $i] :
( ( ( member @ SV72 @ SV53 )
= $false )
| ( ( ~ ( member @ SV72 @ SV66 ) )
= $true )
| ( ( member @ SV72 @ ( intersection @ SV53 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[589]) ).
thf(614,plain,
! [SV67: $i,SV55: $i] :
( ( ( member @ SV55 @ SV67 )
= $false )
| ( ( member @ SV67 @ universal_class )
= $false )
| ( ( member @ ( ordered_pair @ SV55 @ SV67 ) @ element_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[592]) ).
thf(615,plain,
! [SV69: $i,SV58: $i,SV43: $i] :
( ( ( SV43 = SV58 )
= $true )
| ( ( SV43 = SV69 )
= $true )
| ( ( member @ SV43 @ ( unordered_pair @ SV58 @ SV69 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[594]) ).
thf(616,plain,
! [SV69: $i,SV58: $i,SV43: $i] :
( ( ( ( SV43 = SV58 )
| ( SV43 = SV69 ) )
= $false )
| ( ( member @ SV43 @ universal_class )
= $false )
| ( ( member @ SV43 @ ( unordered_pair @ SV58 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[595]) ).
thf(617,plain,
! [SV46: $i,SV61: $i] :
( ( ( member @ SV61 @ SV46 )
= $true )
| ( ( member @ SV61 @ universal_class )
= $false )
| ( ( member @ SV61 @ ( complement @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[597]) ).
thf(618,plain,
! [SV62: $i,SV47: $i] :
( ( ( ~ ( member @ SV47 @ ( sK11_SY114 @ SV62 @ SV47 ) ) )
= $false )
| ( ( member @ SV47 @ ( sum_class @ SV62 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[598]) ).
thf(619,plain,
! [SV47: $i,SV62: $i] :
( ( ( ~ ( member @ ( sK11_SY114 @ SV62 @ SV47 ) @ SV62 ) )
= $false )
| ( ( member @ SV47 @ ( sum_class @ SV62 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[598]) ).
thf(620,plain,
! [SV62: $i,SV78: $i,SV47: $i] :
( ( ( ~ ( member @ SV47 @ SV78 ) )
= $true )
| ( ( ~ ( member @ SV78 @ SV62 ) )
= $true )
| ( ( member @ SV47 @ ( sum_class @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[599]) ).
thf(621,plain,
! [SV49: $i] :
( ( ( member @ ( sK9_SY97 @ SV49 ) @ universal_class )
= $true )
| ( ( member @ SV49 @ identity_relation )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[602]) ).
thf(622,plain,
! [SV49: $i] :
( ( ( SV49
= ( ordered_pair @ ( sK9_SY97 @ SV49 ) @ ( sK9_SY97 @ SV49 ) ) )
= $true )
| ( ( member @ SV49 @ identity_relation )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[603]) ).
thf(623,plain,
! [SV49: $i,SV76: $i] :
( ( ( member @ SV76 @ universal_class )
= $false )
| ( ( SV49
!= ( ordered_pair @ SV76 @ SV76 ) )
= $true )
| ( ( member @ SV49 @ identity_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(624,plain,
! [SV74: $i,SV64: $i,SV71: $i,SV51: $i] :
( ( ( member @ SV51 @ SV71 )
= $true )
| ( ( member @ ( ordered_pair @ SV51 @ SV64 ) @ ( cross_product @ SV71 @ SV74 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[605]) ).
thf(625,plain,
! [SV71: $i,SV51: $i,SV74: $i,SV64: $i] :
( ( ( member @ SV64 @ SV74 )
= $true )
| ( ( member @ ( ordered_pair @ SV51 @ SV64 ) @ ( cross_product @ SV71 @ SV74 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[606]) ).
thf(626,plain,
! [SV74: $i,SV64: $i,SV71: $i,SV51: $i] :
( ( ( member @ SV51 @ SV71 )
= $false )
| ( ( ~ ( member @ SV64 @ SV74 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV51 @ SV64 ) @ ( cross_product @ SV71 @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[607]) ).
thf(627,plain,
! [SV65: $i,SV52: $i,SV77: $i] :
( ( ( member @ SV77 @ SV52 )
= $false )
| ( ( ~ ( member @ SV77 @ SV65 ) )
= $true )
| ( ( disjoint @ SV52 @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[608]) ).
thf(628,plain,
! [SV52: $i,SV65: $i] :
( ( ( member @ ( sK10_SY119 @ SV65 @ SV52 ) @ SV52 )
= $true )
| ( ( disjoint @ SV52 @ SV65 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[609]) ).
thf(629,plain,
! [SV52: $i,SV65: $i] :
( ( ( member @ ( sK10_SY119 @ SV65 @ SV52 ) @ SV65 )
= $true )
| ( ( disjoint @ SV52 @ SV65 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[610]) ).
thf(630,plain,
! [SV53: $i,SV66: $i,SV72: $i] :
( ( ( member @ SV72 @ SV66 )
= $false )
| ( ( member @ SV72 @ SV53 )
= $false )
| ( ( member @ SV72 @ ( intersection @ SV53 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[613]) ).
thf(631,plain,
! [SV69: $i,SV58: $i,SV43: $i] :
( ( ( SV43 = SV58 )
= $false )
| ( ( member @ SV43 @ universal_class )
= $false )
| ( ( member @ SV43 @ ( unordered_pair @ SV58 @ SV69 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[616]) ).
thf(632,plain,
! [SV58: $i,SV69: $i,SV43: $i] :
( ( ( SV43 = SV69 )
= $false )
| ( ( member @ SV43 @ universal_class )
= $false )
| ( ( member @ SV43 @ ( unordered_pair @ SV58 @ SV69 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[616]) ).
thf(633,plain,
! [SV62: $i,SV47: $i] :
( ( ( member @ SV47 @ ( sK11_SY114 @ SV62 @ SV47 ) )
= $true )
| ( ( member @ SV47 @ ( sum_class @ SV62 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[618]) ).
thf(634,plain,
! [SV47: $i,SV62: $i] :
( ( ( member @ ( sK11_SY114 @ SV62 @ SV47 ) @ SV62 )
= $true )
| ( ( member @ SV47 @ ( sum_class @ SV62 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[619]) ).
thf(635,plain,
! [SV62: $i,SV78: $i,SV47: $i] :
( ( ( member @ SV47 @ SV78 )
= $false )
| ( ( ~ ( member @ SV78 @ SV62 ) )
= $true )
| ( ( member @ SV47 @ ( sum_class @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[620]) ).
thf(636,plain,
! [SV76: $i,SV49: $i] :
( ( ( SV49
= ( ordered_pair @ SV76 @ SV76 ) )
= $false )
| ( ( member @ SV76 @ universal_class )
= $false )
| ( ( member @ SV49 @ identity_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[623]) ).
thf(637,plain,
! [SV71: $i,SV51: $i,SV74: $i,SV64: $i] :
( ( ( member @ SV64 @ SV74 )
= $false )
| ( ( member @ SV51 @ SV71 )
= $false )
| ( ( member @ ( ordered_pair @ SV51 @ SV64 ) @ ( cross_product @ SV71 @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[626]) ).
thf(638,plain,
! [SV52: $i,SV65: $i,SV77: $i] :
( ( ( member @ SV77 @ SV65 )
= $false )
| ( ( member @ SV77 @ SV52 )
= $false )
| ( ( disjoint @ SV52 @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[627]) ).
thf(639,plain,
! [SV47: $i,SV62: $i,SV78: $i] :
( ( ( member @ SV78 @ SV62 )
= $false )
| ( ( member @ SV47 @ SV78 )
= $false )
| ( ( member @ SV47 @ ( sum_class @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[635]) ).
thf(640,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[375,639,638,637,636,634,633,632,631,630,629,628,625,624,622,621,617,615,614,612,611,601,600,596,593,591,590,574,573,572,551,548,547,546,480,439,435,412,411,396,393,377,376]) ).
thf(641,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[640,357]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET020+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.16 % Computer : n002.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Tue Oct 6 14:29:12 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.13/0.64
% 2.13/0.64 No.of.Axioms: 17
% 2.13/0.64
% 2.13/0.64 Length.of.Defs: 0
% 2.13/0.64
% 2.13/0.64 Contains.Choice.Funs: false
% 2.13/0.64 .................
% 2.13/0.64
% 2.13/0.64 ********************************
% 2.13/0.64 * All subproblems solved! *
% 2.13/0.64 ********************************
% 2.13/0.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:20,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:640,loop_count:0,foatp_calls:1,translation:fof_full)
% 2.13/0.64
% 2.13/0.64 %**** Beginning of derivation protocol ****
% 2.13/0.64 % SZS output start CNFRefutation
% See solution above
% 2.13/0.64
% 2.13/0.64 %**** End of derivation protocol ****
% 2.13/0.64 %**** no. of clauses in derivation: 615 ****
% 2.13/0.64 %**** clause counter: 640 ****
% 2.13/0.64
% 2.13/0.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:20,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:640,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------