%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET055-7 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:39:10 AM UTC 2026
% Result : Unsatisfiable 3.48s 0.70s
% Output : CNFRefutation 3.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 166
% Syntax : Number of formulae : 1254 ( 768 unt; 0 typ; 0 def)
% Number of atoms : 5910 (1538 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 13419 (1266 ~;1580 |; 0 &;10573 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 52 ( 49 usr; 11 con; 0-3 aty)
% Number of variables : 3345 ( 0 ^;3345 !; 0 ?;3345 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_apply,type,
apply: $i > $i > $i ).
thf(tp_cantor,type,
cantor: $i > $i ).
thf(tp_choice,type,
choice: $i ).
thf(tp_compatible,type,
compatible: $i > $i > $i > $o ).
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_diagonalise,type,
diagonalise: $i > $i ).
thf(tp_domain,type,
domain: $i > $i > $i > $i ).
thf(tp_domain_of,type,
domain_of: $i > $i ).
thf(tp_element_relation,type,
element_relation: $i ).
thf(tp_equalish,type,
equalish: $i > $i > $o ).
thf(tp_first,type,
first: $i > $i ).
thf(tp_flip,type,
flip: $i > $i ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_homomorphism,type,
homomorphism: $i > $i > $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_not_homomorphism1,type,
not_homomorphism1: $i > $i > $i > $i ).
thf(tp_not_homomorphism2,type,
not_homomorphism2: $i > $i > $i > $i ).
thf(tp_not_subclass_element,type,
not_subclass_element: $i > $i > $i ).
thf(tp_null_class,type,
null_class: $i ).
thf(tp_omega,type,
omega: $i ).
thf(tp_one_to_one,type,
one_to_one: $i > $o ).
thf(tp_operation,type,
operation: $i > $o ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_power_class,type,
power_class: $i > $i ).
thf(tp_range,type,
range: $i > $i > $i > $i ).
thf(tp_range_of,type,
range_of: $i > $i ).
thf(tp_regular,type,
regular: $i > $i ).
thf(tp_restrict,type,
restrict: $i > $i > $i > $i ).
thf(tp_rotate,type,
rotate: $i > $i ).
thf(tp_second,type,
second: $i > $i ).
thf(tp_single_valued_class,type,
single_valued_class: $i > $o ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subclass,type,
subclass: $i > $i > $o ).
thf(tp_subset_relation,type,
subset_relation: $i ).
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_symmetric_difference,type,
symmetric_difference: $i > $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(tp_x,type,
x: $i ).
thf(1,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( subclass @ X @ Y )
| ~ ( subclass @ Y @ Z )
| ( subclass @ X @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_subclass) ).
thf(2,axiom,
! [X: $i] : ( subclass @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_is_reflexive) ).
thf(3,axiom,
! [U: $i,V: $i,X: $i,Y: $i] :
( ~ ( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) )
| ( member @ V @ universal_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_2_to_cartesian_product) ).
thf(4,axiom,
! [U: $i,V: $i,X: $i,Y: $i] :
( ~ ( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) )
| ( member @ U @ universal_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_1_to_cartesian_product) ).
thf(5,axiom,
! [X: $i,Y: $i,U: $i,V: $i] :
( ~ ( member @ ( ordered_pair @ X @ Y ) @ ( cross_product @ U @ V ) )
| ( member @ Y @ ( unordered_pair @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_2_to_unordered_pair) ).
thf(6,axiom,
! [X: $i,Y: $i,U: $i,V: $i] :
( ~ ( member @ ( ordered_pair @ X @ Y ) @ ( cross_product @ U @ V ) )
| ( member @ X @ ( unordered_pair @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_1_to_unordered_pair) ).
thf(7,axiom,
! [Xf1: $i,Xf2: $i,Xh: $i] :
( ~ ( operation @ Xf1 )
| ~ ( operation @ Xf2 )
| ~ ( compatible @ Xh @ Xf1 @ Xf2 )
| ~ ( equalish @ ( apply @ Xf2 @ ( ordered_pair @ ( apply @ Xh @ ( not_homomorphism1 @ Xh @ Xf1 @ Xf2 ) ) @ ( apply @ Xh @ ( not_homomorphism2 @ Xh @ Xf1 @ Xf2 ) ) ) ) @ ( apply @ Xh @ ( apply @ Xf1 @ ( ordered_pair @ ( not_homomorphism1 @ Xh @ Xf1 @ Xf2 ) @ ( not_homomorphism2 @ Xh @ Xf1 @ Xf2 ) ) ) ) )
| ( homomorphism @ Xh @ Xf1 @ Xf2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism6) ).
thf(8,axiom,
! [Xf1: $i,Xf2: $i,Xh: $i] :
( ~ ( operation @ Xf1 )
| ~ ( operation @ Xf2 )
| ~ ( compatible @ Xh @ Xf1 @ Xf2 )
| ( member @ ( ordered_pair @ ( not_homomorphism1 @ Xh @ Xf1 @ Xf2 ) @ ( not_homomorphism2 @ Xh @ Xf1 @ Xf2 ) ) @ ( domain_of @ Xf1 ) )
| ( homomorphism @ Xh @ Xf1 @ Xf2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism5) ).
thf(9,axiom,
! [Xh: $i,Xf1: $i,Xf2: $i,X: $i,Y: $i] :
( ~ ( homomorphism @ Xh @ Xf1 @ Xf2 )
| ~ ( member @ ( ordered_pair @ X @ Y ) @ ( domain_of @ Xf1 ) )
| ( equalish @ ( apply @ Xf2 @ ( ordered_pair @ ( apply @ Xh @ X ) @ ( apply @ Xh @ Y ) ) ) @ ( apply @ Xh @ ( apply @ Xf1 @ ( ordered_pair @ X @ Y ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism4) ).
thf(10,axiom,
! [Xh: $i,Xf1: $i,Xf2: $i] :
( ~ ( homomorphism @ Xh @ Xf1 @ Xf2 )
| ( compatible @ Xh @ Xf1 @ Xf2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism3) ).
thf(11,axiom,
! [Xh: $i,Xf1: $i,Xf2: $i] :
( ~ ( homomorphism @ Xh @ Xf1 @ Xf2 )
| ( operation @ Xf2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism2) ).
thf(12,axiom,
! [Xh: $i,Xf1: $i,Xf2: $i] :
( ~ ( homomorphism @ Xh @ Xf1 @ Xf2 )
| ( operation @ Xf1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism1) ).
thf(13,axiom,
! [Xh: $i,Xf1: $i,Xf2: $i,Xh1: $i] :
( ~ ( function @ Xh )
| ~ ( equalish @ ( domain_of @ ( domain_of @ Xf1 ) ) @ ( domain_of @ Xh ) )
| ~ ( subclass @ ( range_of @ Xh ) @ ( domain_of @ ( domain_of @ Xf2 ) ) )
| ( compatible @ Xh1 @ Xf1 @ Xf2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible4) ).
thf(14,axiom,
! [Xh: $i,Xf1: $i,Xf2: $i] :
( ~ ( compatible @ Xh @ Xf1 @ Xf2 )
| ( subclass @ ( range_of @ Xh ) @ ( domain_of @ ( domain_of @ Xf2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible3) ).
thf(15,axiom,
! [Xh: $i,Xf1: $i,Xf2: $i] :
( ~ ( compatible @ Xh @ Xf1 @ Xf2 )
| ( equalish @ ( domain_of @ ( domain_of @ Xf1 ) ) @ ( domain_of @ Xh ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible2) ).
thf(16,axiom,
! [Xh: $i,Xf1: $i,Xf2: $i] :
( ~ ( compatible @ Xh @ Xf1 @ Xf2 )
| ( function @ Xh ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible1) ).
thf(17,axiom,
! [Xf: $i] :
( ~ ( function @ Xf )
| ~ ( equalish @ ( cross_product @ ( domain_of @ ( domain_of @ Xf ) ) @ ( domain_of @ ( domain_of @ Xf ) ) ) @ ( domain_of @ Xf ) )
| ~ ( subclass @ ( range_of @ Xf ) @ ( domain_of @ ( domain_of @ Xf ) ) )
| ( operation @ Xf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation4) ).
thf(18,axiom,
! [Xf: $i] :
( ~ ( operation @ Xf )
| ( subclass @ ( range_of @ Xf ) @ ( domain_of @ ( domain_of @ Xf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation3) ).
thf(19,axiom,
! [Xf: $i] :
( ~ ( operation @ Xf )
| ( equalish @ ( cross_product @ ( domain_of @ ( domain_of @ Xf ) ) @ ( domain_of @ ( domain_of @ Xf ) ) ) @ ( domain_of @ Xf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation2) ).
thf(20,axiom,
! [Xf: $i] :
( ~ ( operation @ Xf )
| ( function @ Xf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation1) ).
thf(21,axiom,
! [X: $i] : ( equalish @ ( intersection @ ( domain_of @ X ) @ ( diagonalise @ ( compose @ ( inverse @ element_relation ) @ X ) ) ) @ ( cantor @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cantor_class) ).
thf(22,axiom,
! [Xr: $i] : ( equalish @ ( complement @ ( domain_of @ ( intersection @ Xr @ identity_relation ) ) ) @ ( diagonalise @ Xr ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diagonalisation) ).
thf(23,axiom,
equalish @ ( intersection @ ( inverse @ subset_relation ) @ subset_relation ) @ identity_relation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_relation) ).
thf(24,axiom,
equalish @ ( intersection @ ( cross_product @ universal_class @ universal_class ) @ ( intersection @ ( cross_product @ universal_class @ universal_class ) @ ( complement @ ( compose @ ( complement @ element_relation ) @ ( inverse @ element_relation ) ) ) ) ) @ subset_relation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_relation) ).
thf(25,axiom,
! [Xf: $i] :
( ~ ( function @ ( inverse @ Xf ) )
| ~ ( function @ Xf )
| ( one_to_one @ Xf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one3) ).
thf(26,axiom,
! [Xf: $i] :
( ~ ( one_to_one @ Xf )
| ( function @ ( inverse @ Xf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one2) ).
thf(27,axiom,
! [Xf: $i] :
( ~ ( one_to_one @ Xf )
| ( function @ Xf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one1) ).
thf(28,axiom,
! [Y: $i] :
( ~ ( member @ Y @ universal_class )
| ( equalish @ Y @ null_class )
| ( member @ ( apply @ choice @ Y ) @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice2) ).
thf(29,axiom,
function @ choice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice1) ).
thf(30,axiom,
! [Xf: $i,Y: $i] : ( equalish @ ( sum_class @ ( image @ Xf @ ( singleton @ Y ) ) ) @ ( apply @ Xf @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply) ).
thf(31,axiom,
! [X: $i] :
( ( equalish @ X @ null_class )
| ( equalish @ ( intersection @ X @ ( regular @ X ) ) @ null_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity2) ).
thf(32,axiom,
! [X: $i] :
( ( equalish @ X @ null_class )
| ( member @ ( regular @ X ) @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity1) ).
thf(33,axiom,
! [Xf: $i,X: $i] :
( ~ ( function @ Xf )
| ~ ( member @ X @ universal_class )
| ( member @ ( image @ Xf @ X ) @ universal_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',replacement) ).
thf(34,axiom,
! [Xf: $i] :
( ~ ( subclass @ Xf @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ Xf @ ( inverse @ Xf ) ) @ identity_relation )
| ( function @ Xf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function3) ).
thf(35,axiom,
! [Xf: $i] :
( ~ ( function @ Xf )
| ( subclass @ ( compose @ Xf @ ( inverse @ Xf ) ) @ identity_relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function2) ).
thf(36,axiom,
! [Xf: $i] :
( ~ ( function @ Xf )
| ( subclass @ Xf @ ( cross_product @ universal_class @ universal_class ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function1) ).
thf(37,axiom,
! [X: $i] :
( ~ ( subclass @ ( compose @ X @ ( inverse @ X ) ) @ identity_relation )
| ( single_valued_class @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_valued_class2) ).
thf(38,axiom,
! [X: $i] :
( ~ ( single_valued_class @ X )
| ( subclass @ ( compose @ X @ ( inverse @ X ) ) @ identity_relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_valued_class1) ).
thf(39,axiom,
! [Z: $i,Yr: $i,Xr: $i,Y: $i] :
( ~ ( member @ Z @ ( image @ Yr @ ( image @ Xr @ ( singleton @ Y ) ) ) )
| ~ ( member @ ( ordered_pair @ Y @ Z ) @ ( cross_product @ universal_class @ universal_class ) )
| ( member @ ( ordered_pair @ Y @ Z ) @ ( compose @ Yr @ Xr ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose3) ).
thf(40,axiom,
! [Y: $i,Z: $i,Yr: $i,Xr: $i] :
( ~ ( member @ ( ordered_pair @ Y @ Z ) @ ( compose @ Yr @ Xr ) )
| ( member @ Z @ ( image @ Yr @ ( image @ Xr @ ( singleton @ Y ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose2) ).
thf(41,axiom,
! [Yr: $i,Xr: $i] : ( subclass @ ( compose @ Yr @ Xr ) @ ( cross_product @ universal_class @ universal_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose1) ).
thf(42,axiom,
! [U: $i] :
( ~ ( member @ U @ universal_class )
| ( member @ ( power_class @ U ) @ universal_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class2) ).
thf(43,axiom,
! [X: $i] : ( equalish @ ( complement @ ( image @ element_relation @ ( complement @ X ) ) ) @ ( power_class @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class_definition) ).
thf(44,axiom,
! [X: $i] :
( ~ ( member @ X @ universal_class )
| ( member @ ( sum_class @ X ) @ universal_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class2) ).
thf(45,axiom,
! [X: $i] : ( equalish @ ( domain_of @ ( restrict @ element_relation @ universal_class @ X ) ) @ ( sum_class @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class_definition) ).
thf(46,axiom,
member @ omega @ universal_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_in_universal) ).
thf(47,axiom,
! [Y: $i] :
( ~ ( inductive @ Y )
| ( subclass @ omega @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive2) ).
thf(48,axiom,
inductive @ omega,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive1) ).
thf(49,axiom,
! [X: $i] :
( ~ ( member @ null_class @ X )
| ~ ( subclass @ ( image @ successor_relation @ X ) @ X )
| ( inductive @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive3) ).
thf(50,axiom,
! [X: $i] :
( ~ ( inductive @ X )
| ( subclass @ ( image @ successor_relation @ X ) @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive2) ).
thf(51,axiom,
! [X: $i] :
( ~ ( inductive @ X )
| ( member @ null_class @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive1) ).
thf(52,axiom,
! [X: $i,Y: $i] :
( ~ ( equalish @ ( successor @ X ) @ Y )
| ~ ( member @ ( ordered_pair @ X @ Y ) @ ( cross_product @ universal_class @ universal_class ) )
| ( member @ ( ordered_pair @ X @ Y ) @ successor_relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation3) ).
thf(53,axiom,
! [X: $i,Y: $i] :
( ~ ( member @ ( ordered_pair @ X @ Y ) @ successor_relation )
| ( equalish @ ( successor @ X ) @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation2) ).
thf(54,axiom,
subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation1) ).
thf(55,axiom,
! [X: $i] : ( equalish @ ( union @ X @ ( singleton @ X ) ) @ ( successor @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor) ).
thf(56,axiom,
! [Xr: $i,X: $i] : ( equalish @ ( range_of @ ( restrict @ Xr @ X @ universal_class ) ) @ ( image @ Xr @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image) ).
thf(57,axiom,
! [Z: $i,X: $i,Y: $i] : ( equalish @ ( second @ ( not_subclass_element @ ( restrict @ Z @ ( singleton @ X ) @ Y ) @ null_class ) ) @ ( range @ Z @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range) ).
thf(58,axiom,
! [Z: $i,X: $i,Y: $i] : ( equalish @ ( first @ ( not_subclass_element @ ( restrict @ Z @ X @ ( singleton @ Y ) ) @ null_class ) ) @ ( domain @ Z @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain) ).
thf(59,axiom,
! [Z: $i] : ( equalish @ ( domain_of @ ( inverse @ Z ) ) @ ( range_of @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range_of) ).
thf(60,axiom,
! [Y: $i] : ( equalish @ ( domain_of @ ( flip @ ( cross_product @ Y @ universal_class ) ) ) @ ( inverse @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
thf(61,axiom,
! [V: $i,U: $i,W: $i,X: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ V @ U ) @ W ) @ X )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( flip @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip3) ).
thf(62,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( flip @ X ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ V @ U ) @ W ) @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip2) ).
thf(63,axiom,
! [X: $i] : ( subclass @ ( flip @ X ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip1) ).
thf(64,axiom,
! [V: $i,W: $i,U: $i,X: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ V @ W ) @ U ) @ X )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( rotate @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate3) ).
thf(65,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( rotate @ X ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ V @ W ) @ U ) @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate2) ).
thf(66,axiom,
! [X: $i] : ( subclass @ ( rotate @ X ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate1) ).
thf(67,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ universal_class )
| ( equalish @ ( restrict @ X @ ( singleton @ Z ) @ universal_class ) @ null_class )
| ( member @ Z @ ( domain_of @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).
thf(68,axiom,
! [X: $i,Z: $i] :
( ~ ( equalish @ ( restrict @ X @ ( singleton @ Z ) @ universal_class ) @ null_class )
| ~ ( member @ Z @ ( domain_of @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
thf(69,axiom,
! [X: $i,Y: $i,Xr: $i] : ( equalish @ ( intersection @ ( cross_product @ X @ Y ) @ Xr ) @ ( restrict @ Xr @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction2) ).
thf(70,axiom,
! [Xr: $i,X: $i,Y: $i] : ( equalish @ ( intersection @ Xr @ ( cross_product @ X @ Y ) ) @ ( restrict @ Xr @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction1) ).
thf(71,axiom,
! [X: $i,Y: $i] : ( equalish @ ( intersection @ ( complement @ ( intersection @ X @ Y ) ) @ ( complement @ ( intersection @ ( complement @ X ) @ ( complement @ Y ) ) ) ) @ ( symmetric_difference @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference) ).
thf(72,axiom,
! [X: $i,Y: $i] : ( equalish @ ( complement @ ( intersection @ ( complement @ X ) @ ( complement @ Y ) ) ) @ ( union @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
thf(73,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ universal_class )
| ( member @ Z @ ( complement @ X ) )
| ( member @ Z @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement2) ).
thf(74,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( complement @ X ) )
| ~ ( member @ Z @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).
thf(75,axiom,
! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ X )
| ~ ( member @ Z @ Y )
| ( member @ Z @ ( intersection @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection3) ).
thf(76,axiom,
! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( intersection @ X @ Y ) )
| ( member @ Z @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection2) ).
thf(77,axiom,
! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( intersection @ X @ Y ) )
| ( member @ Z @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).
thf(78,axiom,
! [X: $i,Y: $i] :
( ~ ( member @ ( ordered_pair @ X @ Y ) @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( member @ X @ Y )
| ( member @ ( ordered_pair @ X @ Y ) @ element_relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation3) ).
thf(79,axiom,
! [X: $i,Y: $i] :
( ~ ( member @ ( ordered_pair @ X @ Y ) @ element_relation )
| ( member @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation2) ).
thf(80,axiom,
subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation1) ).
thf(81,axiom,
! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( cross_product @ X @ Y ) )
| ( equalish @ ( ordered_pair @ ( first @ Z ) @ ( second @ Z ) ) @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product4) ).
thf(82,axiom,
! [U: $i,X: $i,V: $i,Y: $i] :
( ~ ( member @ U @ X )
| ~ ( member @ V @ Y )
| ( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product3) ).
thf(83,axiom,
! [U: $i,V: $i,X: $i,Y: $i] :
( ~ ( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) )
| ( member @ V @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product2) ).
thf(84,axiom,
! [U: $i,V: $i,X: $i,Y: $i] :
( ~ ( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) )
| ( member @ U @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product1) ).
thf(85,axiom,
! [X: $i,Y: $i] : ( equalish @ ( unordered_pair @ ( singleton @ X ) @ ( unordered_pair @ X @ ( singleton @ Y ) ) ) @ ( ordered_pair @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair) ).
thf(86,axiom,
! [X: $i] : ( equalish @ ( unordered_pair @ X @ X ) @ ( singleton @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set) ).
thf(87,axiom,
! [X: $i,Y: $i] : ( member @ ( unordered_pair @ X @ Y ) @ universal_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).
thf(88,axiom,
! [Y: $i,X: $i] :
( ~ ( member @ Y @ universal_class )
| ( member @ Y @ ( unordered_pair @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair3) ).
thf(89,axiom,
! [X: $i,Y: $i] :
( ~ ( member @ X @ universal_class )
| ( member @ X @ ( unordered_pair @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair2) ).
thf(90,axiom,
! [U: $i,X: $i,Y: $i] :
( ~ ( member @ U @ ( unordered_pair @ X @ Y ) )
| ( equalish @ U @ X )
| ( equalish @ U @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_member) ).
thf(91,axiom,
! [X: $i,Y: $i] :
( ~ ( subclass @ X @ Y )
| ~ ( subclass @ Y @ X )
| ( equalish @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_implies_equal) ).
thf(92,axiom,
! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ( subclass @ Y @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_implies_subclass2) ).
thf(93,axiom,
! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ( subclass @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_implies_subclass1) ).
thf(94,axiom,
! [X: $i] : ( subclass @ X @ universal_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).
thf(95,axiom,
! [X: $i,Y: $i] :
( ~ ( member @ ( not_subclass_element @ X @ Y ) @ Y )
| ( subclass @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members2) ).
thf(96,axiom,
! [X: $i,Y: $i] :
( ( member @ ( not_subclass_element @ X @ Y ) @ X )
| ( subclass @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members1) ).
thf(97,axiom,
! [X: $i,Y: $i,U: $i] :
( ~ ( subclass @ X @ Y )
| ~ ( member @ U @ X )
| ( member @ U @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_members) ).
thf(98,axiom,
! [O7: $i,P7: $i,Q7: $i] :
( ~ ( equalish @ O7 @ P7 )
| ~ ( subclass @ Q7 @ O7 )
| ( subclass @ Q7 @ P7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_substitution2) ).
thf(99,axiom,
! [L7: $i,M7: $i,N7: $i] :
( ~ ( equalish @ L7 @ M7 )
| ~ ( subclass @ L7 @ N7 )
| ( subclass @ M7 @ N7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_substitution1) ).
thf(100,axiom,
! [J7: $i,K7: $i] :
( ~ ( equalish @ J7 @ K7 )
| ~ ( single_valued_class @ J7 )
| ( single_valued_class @ K7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_valued_class_substitution1) ).
thf(101,axiom,
! [H7: $i,I7: $i] :
( ~ ( equalish @ H7 @ I7 )
| ~ ( operation @ H7 )
| ( operation @ I7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation_substitution1) ).
thf(102,axiom,
! [F7: $i,G7: $i] :
( ~ ( equalish @ F7 @ G7 )
| ~ ( one_to_one @ F7 )
| ( one_to_one @ G7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one_substitution1) ).
thf(103,axiom,
! [C7: $i,D7: $i,E7: $i] :
( ~ ( equalish @ C7 @ D7 )
| ~ ( member @ E7 @ C7 )
| ( member @ E7 @ D7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_substitution2) ).
thf(104,axiom,
! [Z6: $i,A7: $i,B7: $i] :
( ~ ( equalish @ Z6 @ A7 )
| ~ ( member @ Z6 @ B7 )
| ( member @ A7 @ B7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_substitution1) ).
thf(105,axiom,
! [X6: $i,Y6: $i] :
( ~ ( equalish @ X6 @ Y6 )
| ~ ( inductive @ X6 )
| ( inductive @ Y6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive_substitution1) ).
thf(106,axiom,
! [T6: $i,U6: $i,V6: $i,W6: $i] :
( ~ ( equalish @ T6 @ U6 )
| ~ ( homomorphism @ V6 @ W6 @ T6 )
| ( homomorphism @ V6 @ W6 @ U6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism_substitution3) ).
thf(107,axiom,
! [P6: $i,Q6: $i,R6: $i,S6: $i] :
( ~ ( equalish @ P6 @ Q6 )
| ~ ( homomorphism @ R6 @ P6 @ S6 )
| ( homomorphism @ R6 @ Q6 @ S6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism_substitution2) ).
thf(108,axiom,
! [L6: $i,M6: $i,N6: $i,O6: $i] :
( ~ ( equalish @ L6 @ M6 )
| ~ ( homomorphism @ L6 @ N6 @ O6 )
| ( homomorphism @ M6 @ N6 @ O6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism_substitution1) ).
thf(109,axiom,
! [J6: $i,K6: $i] :
( ~ ( equalish @ J6 @ K6 )
| ~ ( function @ J6 )
| ( function @ K6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function_substitution1) ).
thf(110,axiom,
! [F6: $i,G6: $i,H6: $i,I6: $i] :
( ~ ( equalish @ F6 @ G6 )
| ~ ( compatible @ H6 @ I6 @ F6 )
| ( compatible @ H6 @ I6 @ G6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible_substitution3) ).
thf(111,axiom,
! [B6: $i,C6: $i,D6: $i,E6: $i] :
( ~ ( equalish @ B6 @ C6 )
| ~ ( compatible @ D6 @ B6 @ E6 )
| ( compatible @ D6 @ C6 @ E6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible_substitution2) ).
thf(112,axiom,
! [X5: $i,Y5: $i,Z5: $i,A6: $i] :
( ~ ( equalish @ X5 @ Y5 )
| ~ ( compatible @ X5 @ Z5 @ A6 )
| ( compatible @ Y5 @ Z5 @ A6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible_substitution1) ).
thf(113,axiom,
! [U5: $i,V5: $i,W5: $i] :
( ~ ( equalish @ U5 @ V5 )
| ( equalish @ ( unordered_pair @ W5 @ U5 ) @ ( unordered_pair @ W5 @ V5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_substitution2) ).
thf(114,axiom,
! [R5: $i,S5: $i,T5: $i] :
( ~ ( equalish @ R5 @ S5 )
| ( equalish @ ( unordered_pair @ R5 @ T5 ) @ ( unordered_pair @ S5 @ T5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_substitution1) ).
thf(115,axiom,
! [O5: $i,P5: $i,Q5: $i] :
( ~ ( equalish @ O5 @ P5 )
| ( equalish @ ( union @ Q5 @ O5 ) @ ( union @ Q5 @ P5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_substitution2) ).
thf(116,axiom,
! [L5: $i,M5: $i,N5: $i] :
( ~ ( equalish @ L5 @ M5 )
| ( equalish @ ( union @ L5 @ N5 ) @ ( union @ M5 @ N5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_substitution1) ).
thf(117,axiom,
! [J5: $i,K5: $i] :
( ~ ( equalish @ J5 @ K5 )
| ( equalish @ ( sum_class @ J5 ) @ ( sum_class @ K5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class_substitution1) ).
thf(118,axiom,
! [H5: $i,I5: $i] :
( ~ ( equalish @ H5 @ I5 )
| ( equalish @ ( successor @ H5 ) @ ( successor @ I5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_substitution1) ).
thf(119,axiom,
! [F5: $i,G5: $i] :
( ~ ( equalish @ F5 @ G5 )
| ( equalish @ ( singleton @ F5 ) @ ( singleton @ G5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_substitution1) ).
thf(120,axiom,
! [D5: $i,E5: $i] :
( ~ ( equalish @ D5 @ E5 )
| ( equalish @ ( second @ D5 ) @ ( second @ E5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',second_substitution1) ).
thf(121,axiom,
! [B5: $i,C5: $i] :
( ~ ( equalish @ B5 @ C5 )
| ( equalish @ ( rotate @ B5 ) @ ( rotate @ C5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate_substitution1) ).
thf(122,axiom,
! [X4: $i,Y4: $i,Z4: $i,A5: $i] :
( ~ ( equalish @ X4 @ Y4 )
| ( equalish @ ( restrict @ Z4 @ A5 @ X4 ) @ ( restrict @ Z4 @ A5 @ Y4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restrict_substitution3) ).
thf(123,axiom,
! [T4: $i,U4: $i,V4: $i,W4: $i] :
( ~ ( equalish @ T4 @ U4 )
| ( equalish @ ( restrict @ V4 @ T4 @ W4 ) @ ( restrict @ V4 @ U4 @ W4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restrict_substitution2) ).
thf(124,axiom,
! [P4: $i,Q4: $i,R4: $i,S4: $i] :
( ~ ( equalish @ P4 @ Q4 )
| ( equalish @ ( restrict @ P4 @ R4 @ S4 ) @ ( restrict @ Q4 @ R4 @ S4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restrict_substitution1) ).
thf(125,axiom,
! [N4: $i,O4: $i] :
( ~ ( equalish @ N4 @ O4 )
| ( equalish @ ( regular @ N4 ) @ ( regular @ O4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regular_substitution1) ).
thf(126,axiom,
! [L4: $i,M4: $i] :
( ~ ( equalish @ L4 @ M4 )
| ( equalish @ ( range_of @ L4 ) @ ( range_of @ M4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range_of_substitution1) ).
thf(127,axiom,
! [H4: $i,I4: $i,J4: $i,K4: $i] :
( ~ ( equalish @ H4 @ I4 )
| ( equalish @ ( range @ J4 @ K4 @ H4 ) @ ( range @ J4 @ K4 @ I4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range_substitution3) ).
thf(128,axiom,
! [D4: $i,E4: $i,F4: $i,G4: $i] :
( ~ ( equalish @ D4 @ E4 )
| ( equalish @ ( range @ F4 @ D4 @ G4 ) @ ( range @ F4 @ E4 @ G4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range_substitution2) ).
thf(129,axiom,
! [Z3: $i,A4: $i,B4: $i,C4: $i] :
( ~ ( equalish @ Z3 @ A4 )
| ( equalish @ ( range @ Z3 @ B4 @ C4 ) @ ( range @ A4 @ B4 @ C4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range_substitution1) ).
thf(130,axiom,
! [X3: $i,Y3: $i] :
( ~ ( equalish @ X3 @ Y3 )
| ( equalish @ ( power_class @ X3 ) @ ( power_class @ Y3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class_substitution1) ).
thf(131,axiom,
! [U3: $i,V3: $i,W3: $i] :
( ~ ( equalish @ U3 @ V3 )
| ( equalish @ ( ordered_pair @ W3 @ U3 ) @ ( ordered_pair @ W3 @ V3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_substitution2) ).
thf(132,axiom,
! [R3: $i,S3: $i,T3: $i] :
( ~ ( equalish @ R3 @ S3 )
| ( equalish @ ( ordered_pair @ R3 @ T3 ) @ ( ordered_pair @ S3 @ T3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_substitution1) ).
thf(133,axiom,
! [O3: $i,P3: $i,Q3: $i] :
( ~ ( equalish @ O3 @ P3 )
| ( equalish @ ( not_subclass_element @ Q3 @ O3 ) @ ( not_subclass_element @ Q3 @ P3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_element_substitution2) ).
thf(134,axiom,
! [L3: $i,M3: $i,N3: $i] :
( ~ ( equalish @ L3 @ M3 )
| ( equalish @ ( not_subclass_element @ L3 @ N3 ) @ ( not_subclass_element @ M3 @ N3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_element_substitution1) ).
thf(135,axiom,
! [H3: $i,I3: $i,J3: $i,K3: $i] :
( ~ ( equalish @ H3 @ I3 )
| ( equalish @ ( not_homomorphism2 @ J3 @ K3 @ H3 ) @ ( not_homomorphism2 @ J3 @ K3 @ I3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_homomorphism2_substitution3) ).
thf(136,axiom,
! [D3: $i,E3: $i,F3: $i,G3: $i] :
( ~ ( equalish @ D3 @ E3 )
| ( equalish @ ( not_homomorphism2 @ F3 @ D3 @ G3 ) @ ( not_homomorphism2 @ F3 @ E3 @ G3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_homomorphism2_substitution2) ).
thf(137,axiom,
! [Z2: $i,A3: $i,B3: $i,C3: $i] :
( ~ ( equalish @ Z2 @ A3 )
| ( equalish @ ( not_homomorphism2 @ Z2 @ B3 @ C3 ) @ ( not_homomorphism2 @ A3 @ B3 @ C3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_homomorphism2_substitution1) ).
thf(138,axiom,
! [V2: $i,W2: $i,X2: $i,Y2: $i] :
( ~ ( equalish @ V2 @ W2 )
| ( equalish @ ( not_homomorphism1 @ X2 @ Y2 @ V2 ) @ ( not_homomorphism1 @ X2 @ Y2 @ W2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_homomorphism1_substitution3) ).
thf(139,axiom,
! [R2: $i,S2: $i,T2: $i,U2: $i] :
( ~ ( equalish @ R2 @ S2 )
| ( equalish @ ( not_homomorphism1 @ T2 @ R2 @ U2 ) @ ( not_homomorphism1 @ T2 @ S2 @ U2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_homomorphism1_substitution2) ).
thf(140,axiom,
! [N2: $i,O2: $i,P2: $i,Q2: $i] :
( ~ ( equalish @ N2 @ O2 )
| ( equalish @ ( not_homomorphism1 @ N2 @ P2 @ Q2 ) @ ( not_homomorphism1 @ O2 @ P2 @ Q2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_homomorphism1_substitution1) ).
thf(141,axiom,
! [L2: $i,M2: $i] :
( ~ ( equalish @ L2 @ M2 )
| ( equalish @ ( inverse @ L2 ) @ ( inverse @ M2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_substitution1) ).
thf(142,axiom,
! [I2: $i,J2: $i,K2: $i] :
( ~ ( equalish @ I2 @ J2 )
| ( equalish @ ( intersection @ K2 @ I2 ) @ ( intersection @ K2 @ J2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_substitution2) ).
thf(143,axiom,
! [F2: $i,G2: $i,H2: $i] :
( ~ ( equalish @ F2 @ G2 )
| ( equalish @ ( intersection @ F2 @ H2 ) @ ( intersection @ G2 @ H2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_substitution1) ).
thf(144,axiom,
! [C2: $i,D2: $i,E2: $i] :
( ~ ( equalish @ C2 @ D2 )
| ( equalish @ ( image @ E2 @ C2 ) @ ( image @ E2 @ D2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image_substitution2) ).
thf(145,axiom,
! [Z1: $i,A2: $i,B2: $i] :
( ~ ( equalish @ Z1 @ A2 )
| ( equalish @ ( image @ Z1 @ B2 ) @ ( image @ A2 @ B2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image_substitution1) ).
thf(146,axiom,
! [X1: $i,Y1: $i] :
( ~ ( equalish @ X1 @ Y1 )
| ( equalish @ ( flip @ X1 ) @ ( flip @ Y1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip_substitution1) ).
thf(147,axiom,
! [V1: $i,W1: $i] :
( ~ ( equalish @ V1 @ W1 )
| ( equalish @ ( first @ V1 ) @ ( first @ W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',first_substitution1) ).
thf(148,axiom,
! [T1: $i,U1: $i] :
( ~ ( equalish @ T1 @ U1 )
| ( equalish @ ( domain_of @ T1 ) @ ( domain_of @ U1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_of_substitution1) ).
thf(149,axiom,
! [P1: $i,Q1: $i,R1: $i,S1: $i] :
( ~ ( equalish @ P1 @ Q1 )
| ( equalish @ ( domain @ R1 @ S1 @ P1 ) @ ( domain @ R1 @ S1 @ Q1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_substitution3) ).
thf(150,axiom,
! [L1: $i,M1: $i,N1: $i,O1: $i] :
( ~ ( equalish @ L1 @ M1 )
| ( equalish @ ( domain @ N1 @ L1 @ O1 ) @ ( domain @ N1 @ M1 @ O1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_substitution2) ).
thf(151,axiom,
! [H1: $i,I1: $i,J1: $i,K1: $i] :
( ~ ( equalish @ H1 @ I1 )
| ( equalish @ ( domain @ H1 @ J1 @ K1 ) @ ( domain @ I1 @ J1 @ K1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_substitution1) ).
thf(152,axiom,
! [E1: $i,F1: $i,G1: $i] :
( ~ ( equalish @ E1 @ F1 )
| ( equalish @ ( symmetric_difference @ G1 @ E1 ) @ ( symmetric_difference @ G1 @ F1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference_substitution2) ).
thf(153,axiom,
! [B1: $i,C1: $i,D1: $i] :
( ~ ( equalish @ B1 @ C1 )
| ( equalish @ ( symmetric_difference @ B1 @ D1 ) @ ( symmetric_difference @ C1 @ D1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference_substitution1) ).
thf(154,axiom,
! [Z: $i,A1: $i] :
( ~ ( equalish @ Z @ A1 )
| ( equalish @ ( diagonalise @ Z ) @ ( diagonalise @ A1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diagonalise_substitution1) ).
thf(155,axiom,
! [W: $i,X: $i,Y: $i] :
( ~ ( equalish @ W @ X )
| ( equalish @ ( cross_product @ Y @ W ) @ ( cross_product @ Y @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cross_product_substitution2) ).
thf(156,axiom,
! [T: $i,U: $i,V: $i] :
( ~ ( equalish @ T @ U )
| ( equalish @ ( cross_product @ T @ V ) @ ( cross_product @ U @ V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cross_product_substitution1) ).
thf(157,axiom,
! [Q: $i,R: $i,S: $i] :
( ~ ( equalish @ Q @ R )
| ( equalish @ ( compose @ S @ Q ) @ ( compose @ S @ R ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_substitution2) ).
thf(158,axiom,
! [N: $i,O: $i,P: $i] :
( ~ ( equalish @ N @ O )
| ( equalish @ ( compose @ N @ P ) @ ( compose @ O @ P ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_substitution1) ).
thf(159,axiom,
! [L: $i,M: $i] :
( ~ ( equalish @ L @ M )
| ( equalish @ ( complement @ L ) @ ( complement @ M ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_substitution1) ).
thf(160,axiom,
! [J: $i,K: $i] :
( ~ ( equalish @ J @ K )
| ( equalish @ ( cantor @ J ) @ ( cantor @ K ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cantor_substitution1) ).
thf(161,axiom,
! [G: $i,H: $i,I: $i] :
( ~ ( equalish @ G @ H )
| ( equalish @ ( apply @ I @ G ) @ ( apply @ I @ H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply_substitution2) ).
thf(162,axiom,
! [D: $i,E: $i,F: $i] :
( ~ ( equalish @ D @ E )
| ( equalish @ ( apply @ D @ F ) @ ( apply @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply_substitution1) ).
thf(163,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( equalish @ Y @ Z )
| ( equalish @ X @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
thf(164,axiom,
! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ Y @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry) ).
thf(165,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(166,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[165]) ).
thf(167,negated_conjecture,
~ ( equalish @ x @ x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_reflexivity) ).
thf(168,plain,
$false = $false,
inference(unfold_def,[status(thm)],[166]) ).
thf(169,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( subclass @ X @ Y )
| ~ ( subclass @ Y @ Z )
| ( subclass @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(170,plain,
( ( ! [X: $i] : ( subclass @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(171,plain,
( ( ! [U: $i,V: $i,X: $i,Y: $i] :
( ~ ( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) )
| ( member @ V @ universal_class ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(172,plain,
( ( ! [U: $i,V: $i,X: $i,Y: $i] :
( ~ ( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) )
| ( member @ U @ universal_class ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(173,plain,
( ( ! [X: $i,Y: $i,U: $i,V: $i] :
( ~ ( member @ ( ordered_pair @ X @ Y ) @ ( cross_product @ U @ V ) )
| ( member @ Y @ ( unordered_pair @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(174,plain,
( ( ! [X: $i,Y: $i,U: $i,V: $i] :
( ~ ( member @ ( ordered_pair @ X @ Y ) @ ( cross_product @ U @ V ) )
| ( member @ X @ ( unordered_pair @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(175,plain,
( ( ! [Xf1: $i,Xf2: $i,Xh: $i] :
( ~ ( operation @ Xf1 )
| ~ ( operation @ Xf2 )
| ~ ( compatible @ Xh @ Xf1 @ Xf2 )
| ~ ( equalish @ ( apply @ Xf2 @ ( ordered_pair @ ( apply @ Xh @ ( not_homomorphism1 @ Xh @ Xf1 @ Xf2 ) ) @ ( apply @ Xh @ ( not_homomorphism2 @ Xh @ Xf1 @ Xf2 ) ) ) ) @ ( apply @ Xh @ ( apply @ Xf1 @ ( ordered_pair @ ( not_homomorphism1 @ Xh @ Xf1 @ Xf2 ) @ ( not_homomorphism2 @ Xh @ Xf1 @ Xf2 ) ) ) ) )
| ( homomorphism @ Xh @ Xf1 @ Xf2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(176,plain,
( ( ! [Xf1: $i,Xf2: $i,Xh: $i] :
( ~ ( operation @ Xf1 )
| ~ ( operation @ Xf2 )
| ~ ( compatible @ Xh @ Xf1 @ Xf2 )
| ( member @ ( ordered_pair @ ( not_homomorphism1 @ Xh @ Xf1 @ Xf2 ) @ ( not_homomorphism2 @ Xh @ Xf1 @ Xf2 ) ) @ ( domain_of @ Xf1 ) )
| ( homomorphism @ Xh @ Xf1 @ Xf2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(177,plain,
( ( ! [Xh: $i,Xf1: $i,Xf2: $i,X: $i,Y: $i] :
( ~ ( homomorphism @ Xh @ Xf1 @ Xf2 )
| ~ ( member @ ( ordered_pair @ X @ Y ) @ ( domain_of @ Xf1 ) )
| ( equalish @ ( apply @ Xf2 @ ( ordered_pair @ ( apply @ Xh @ X ) @ ( apply @ Xh @ Y ) ) ) @ ( apply @ Xh @ ( apply @ Xf1 @ ( ordered_pair @ X @ Y ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(178,plain,
( ( ! [Xh: $i,Xf1: $i,Xf2: $i] :
( ~ ( homomorphism @ Xh @ Xf1 @ Xf2 )
| ( compatible @ Xh @ Xf1 @ Xf2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(179,plain,
( ( ! [Xh: $i,Xf1: $i,Xf2: $i] :
( ~ ( homomorphism @ Xh @ Xf1 @ Xf2 )
| ( operation @ Xf2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(180,plain,
( ( ! [Xh: $i,Xf1: $i,Xf2: $i] :
( ~ ( homomorphism @ Xh @ Xf1 @ Xf2 )
| ( operation @ Xf1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(181,plain,
( ( ! [Xh: $i,Xf1: $i,Xf2: $i,Xh1: $i] :
( ~ ( function @ Xh )
| ~ ( equalish @ ( domain_of @ ( domain_of @ Xf1 ) ) @ ( domain_of @ Xh ) )
| ~ ( subclass @ ( range_of @ Xh ) @ ( domain_of @ ( domain_of @ Xf2 ) ) )
| ( compatible @ Xh1 @ Xf1 @ Xf2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(182,plain,
( ( ! [Xh: $i,Xf1: $i,Xf2: $i] :
( ~ ( compatible @ Xh @ Xf1 @ Xf2 )
| ( subclass @ ( range_of @ Xh ) @ ( domain_of @ ( domain_of @ Xf2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(183,plain,
( ( ! [Xh: $i,Xf1: $i,Xf2: $i] :
( ~ ( compatible @ Xh @ Xf1 @ Xf2 )
| ( equalish @ ( domain_of @ ( domain_of @ Xf1 ) ) @ ( domain_of @ Xh ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(184,plain,
( ( ! [Xh: $i,Xf1: $i,Xf2: $i] :
( ~ ( compatible @ Xh @ Xf1 @ Xf2 )
| ( function @ Xh ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(185,plain,
( ( ! [Xf: $i] :
( ~ ( function @ Xf )
| ~ ( equalish @ ( cross_product @ ( domain_of @ ( domain_of @ Xf ) ) @ ( domain_of @ ( domain_of @ Xf ) ) ) @ ( domain_of @ Xf ) )
| ~ ( subclass @ ( range_of @ Xf ) @ ( domain_of @ ( domain_of @ Xf ) ) )
| ( operation @ Xf ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(186,plain,
( ( ! [Xf: $i] :
( ~ ( operation @ Xf )
| ( subclass @ ( range_of @ Xf ) @ ( domain_of @ ( domain_of @ Xf ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(187,plain,
( ( ! [Xf: $i] :
( ~ ( operation @ Xf )
| ( equalish @ ( cross_product @ ( domain_of @ ( domain_of @ Xf ) ) @ ( domain_of @ ( domain_of @ Xf ) ) ) @ ( domain_of @ Xf ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(188,plain,
( ( ! [Xf: $i] :
( ~ ( operation @ Xf )
| ( function @ Xf ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(189,plain,
( ( ! [X: $i] : ( equalish @ ( intersection @ ( domain_of @ X ) @ ( diagonalise @ ( compose @ ( inverse @ element_relation ) @ X ) ) ) @ ( cantor @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(190,plain,
( ( ! [Xr: $i] : ( equalish @ ( complement @ ( domain_of @ ( intersection @ Xr @ identity_relation ) ) ) @ ( diagonalise @ Xr ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(191,plain,
( ( equalish @ ( intersection @ ( inverse @ subset_relation ) @ subset_relation ) @ identity_relation )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(192,plain,
( ( equalish @ ( intersection @ ( cross_product @ universal_class @ universal_class ) @ ( intersection @ ( cross_product @ universal_class @ universal_class ) @ ( complement @ ( compose @ ( complement @ element_relation ) @ ( inverse @ element_relation ) ) ) ) ) @ subset_relation )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(193,plain,
( ( ! [Xf: $i] :
( ~ ( function @ ( inverse @ Xf ) )
| ~ ( function @ Xf )
| ( one_to_one @ Xf ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(194,plain,
( ( ! [Xf: $i] :
( ~ ( one_to_one @ Xf )
| ( function @ ( inverse @ Xf ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(195,plain,
( ( ! [Xf: $i] :
( ~ ( one_to_one @ Xf )
| ( function @ Xf ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(196,plain,
( ( ! [Y: $i] :
( ~ ( member @ Y @ universal_class )
| ( equalish @ Y @ null_class )
| ( member @ ( apply @ choice @ Y ) @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(197,plain,
( ( function @ choice )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(198,plain,
( ( ! [Xf: $i,Y: $i] : ( equalish @ ( sum_class @ ( image @ Xf @ ( singleton @ Y ) ) ) @ ( apply @ Xf @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(199,plain,
( ( ! [X: $i] :
( ( equalish @ X @ null_class )
| ( equalish @ ( intersection @ X @ ( regular @ X ) ) @ null_class ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(200,plain,
( ( ! [X: $i] :
( ( equalish @ X @ null_class )
| ( member @ ( regular @ X ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(201,plain,
( ( ! [Xf: $i,X: $i] :
( ~ ( function @ Xf )
| ~ ( member @ X @ universal_class )
| ( member @ ( image @ Xf @ X ) @ universal_class ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(202,plain,
( ( ! [Xf: $i] :
( ~ ( subclass @ Xf @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ Xf @ ( inverse @ Xf ) ) @ identity_relation )
| ( function @ Xf ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(203,plain,
( ( ! [Xf: $i] :
( ~ ( function @ Xf )
| ( subclass @ ( compose @ Xf @ ( inverse @ Xf ) ) @ identity_relation ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(204,plain,
( ( ! [Xf: $i] :
( ~ ( function @ Xf )
| ( subclass @ Xf @ ( cross_product @ universal_class @ universal_class ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(205,plain,
( ( ! [X: $i] :
( ~ ( subclass @ ( compose @ X @ ( inverse @ X ) ) @ identity_relation )
| ( single_valued_class @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(206,plain,
( ( ! [X: $i] :
( ~ ( single_valued_class @ X )
| ( subclass @ ( compose @ X @ ( inverse @ X ) ) @ identity_relation ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(207,plain,
( ( ! [Z: $i,Yr: $i,Xr: $i,Y: $i] :
( ~ ( member @ Z @ ( image @ Yr @ ( image @ Xr @ ( singleton @ Y ) ) ) )
| ~ ( member @ ( ordered_pair @ Y @ Z ) @ ( cross_product @ universal_class @ universal_class ) )
| ( member @ ( ordered_pair @ Y @ Z ) @ ( compose @ Yr @ Xr ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(208,plain,
( ( ! [Y: $i,Z: $i,Yr: $i,Xr: $i] :
( ~ ( member @ ( ordered_pair @ Y @ Z ) @ ( compose @ Yr @ Xr ) )
| ( member @ Z @ ( image @ Yr @ ( image @ Xr @ ( singleton @ Y ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(209,plain,
( ( ! [Yr: $i,Xr: $i] : ( subclass @ ( compose @ Yr @ Xr ) @ ( cross_product @ universal_class @ universal_class ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(210,plain,
( ( ! [U: $i] :
( ~ ( member @ U @ universal_class )
| ( member @ ( power_class @ U ) @ universal_class ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(211,plain,
( ( ! [X: $i] : ( equalish @ ( complement @ ( image @ element_relation @ ( complement @ X ) ) ) @ ( power_class @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(212,plain,
( ( ! [X: $i] :
( ~ ( member @ X @ universal_class )
| ( member @ ( sum_class @ X ) @ universal_class ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(213,plain,
( ( ! [X: $i] : ( equalish @ ( domain_of @ ( restrict @ element_relation @ universal_class @ X ) ) @ ( sum_class @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(214,plain,
( ( member @ omega @ universal_class )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(215,plain,
( ( ! [Y: $i] :
( ~ ( inductive @ Y )
| ( subclass @ omega @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(216,plain,
( ( inductive @ omega )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(217,plain,
( ( ! [X: $i] :
( ~ ( member @ null_class @ X )
| ~ ( subclass @ ( image @ successor_relation @ X ) @ X )
| ( inductive @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(218,plain,
( ( ! [X: $i] :
( ~ ( inductive @ X )
| ( subclass @ ( image @ successor_relation @ X ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(219,plain,
( ( ! [X: $i] :
( ~ ( inductive @ X )
| ( member @ null_class @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(220,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ ( successor @ X ) @ Y )
| ~ ( member @ ( ordered_pair @ X @ Y ) @ ( cross_product @ universal_class @ universal_class ) )
| ( member @ ( ordered_pair @ X @ Y ) @ successor_relation ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(221,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( member @ ( ordered_pair @ X @ Y ) @ successor_relation )
| ( equalish @ ( successor @ X ) @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(222,plain,
( ( subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(223,plain,
( ( ! [X: $i] : ( equalish @ ( union @ X @ ( singleton @ X ) ) @ ( successor @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(224,plain,
( ( ! [Xr: $i,X: $i] : ( equalish @ ( range_of @ ( restrict @ Xr @ X @ universal_class ) ) @ ( image @ Xr @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(225,plain,
( ( ! [Z: $i,X: $i,Y: $i] : ( equalish @ ( second @ ( not_subclass_element @ ( restrict @ Z @ ( singleton @ X ) @ Y ) @ null_class ) ) @ ( range @ Z @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(226,plain,
( ( ! [Z: $i,X: $i,Y: $i] : ( equalish @ ( first @ ( not_subclass_element @ ( restrict @ Z @ X @ ( singleton @ Y ) ) @ null_class ) ) @ ( domain @ Z @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(227,plain,
( ( ! [Z: $i] : ( equalish @ ( domain_of @ ( inverse @ Z ) ) @ ( range_of @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(228,plain,
( ( ! [Y: $i] : ( equalish @ ( domain_of @ ( flip @ ( cross_product @ Y @ universal_class ) ) ) @ ( inverse @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(229,plain,
( ( ! [V: $i,U: $i,W: $i,X: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ V @ U ) @ W ) @ X )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( flip @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(230,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( flip @ X ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ V @ U ) @ W ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(231,plain,
( ( ! [X: $i] : ( subclass @ ( flip @ X ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(232,plain,
( ( ! [V: $i,W: $i,U: $i,X: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ V @ W ) @ U ) @ X )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( rotate @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(233,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( rotate @ X ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ V @ W ) @ U ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(234,plain,
( ( ! [X: $i] : ( subclass @ ( rotate @ X ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(235,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ universal_class )
| ( equalish @ ( restrict @ X @ ( singleton @ Z ) @ universal_class ) @ null_class )
| ( member @ Z @ ( domain_of @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(236,plain,
( ( ! [X: $i,Z: $i] :
( ~ ( equalish @ ( restrict @ X @ ( singleton @ Z ) @ universal_class ) @ null_class )
| ~ ( member @ Z @ ( domain_of @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(237,plain,
( ( ! [X: $i,Y: $i,Xr: $i] : ( equalish @ ( intersection @ ( cross_product @ X @ Y ) @ Xr ) @ ( restrict @ Xr @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(238,plain,
( ( ! [Xr: $i,X: $i,Y: $i] : ( equalish @ ( intersection @ Xr @ ( cross_product @ X @ Y ) ) @ ( restrict @ Xr @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(239,plain,
( ( ! [X: $i,Y: $i] : ( equalish @ ( intersection @ ( complement @ ( intersection @ X @ Y ) ) @ ( complement @ ( intersection @ ( complement @ X ) @ ( complement @ Y ) ) ) ) @ ( symmetric_difference @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(240,plain,
( ( ! [X: $i,Y: $i] : ( equalish @ ( complement @ ( intersection @ ( complement @ X ) @ ( complement @ Y ) ) ) @ ( union @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(241,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ universal_class )
| ( member @ Z @ ( complement @ X ) )
| ( member @ Z @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(242,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( complement @ X ) )
| ~ ( member @ Z @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(243,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ X )
| ~ ( member @ Z @ Y )
| ( member @ Z @ ( intersection @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(244,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( intersection @ X @ Y ) )
| ( member @ Z @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(245,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( intersection @ X @ Y ) )
| ( member @ Z @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(246,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( member @ ( ordered_pair @ X @ Y ) @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( member @ X @ Y )
| ( member @ ( ordered_pair @ X @ Y ) @ element_relation ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(247,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( member @ ( ordered_pair @ X @ Y ) @ element_relation )
| ( member @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(248,plain,
( ( subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(249,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( cross_product @ X @ Y ) )
| ( equalish @ ( ordered_pair @ ( first @ Z ) @ ( second @ Z ) ) @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(250,plain,
( ( ! [U: $i,X: $i,V: $i,Y: $i] :
( ~ ( member @ U @ X )
| ~ ( member @ V @ Y )
| ( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(251,plain,
( ( ! [U: $i,V: $i,X: $i,Y: $i] :
( ~ ( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) )
| ( member @ V @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(252,plain,
( ( ! [U: $i,V: $i,X: $i,Y: $i] :
( ~ ( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) )
| ( member @ U @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(253,plain,
( ( ! [X: $i,Y: $i] : ( equalish @ ( unordered_pair @ ( singleton @ X ) @ ( unordered_pair @ X @ ( singleton @ Y ) ) ) @ ( ordered_pair @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(254,plain,
( ( ! [X: $i] : ( equalish @ ( unordered_pair @ X @ X ) @ ( singleton @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(255,plain,
( ( ! [X: $i,Y: $i] : ( member @ ( unordered_pair @ X @ Y ) @ universal_class ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(256,plain,
( ( ! [Y: $i,X: $i] :
( ~ ( member @ Y @ universal_class )
| ( member @ Y @ ( unordered_pair @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(257,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( member @ X @ universal_class )
| ( member @ X @ ( unordered_pair @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(258,plain,
( ( ! [U: $i,X: $i,Y: $i] :
( ~ ( member @ U @ ( unordered_pair @ X @ Y ) )
| ( equalish @ U @ X )
| ( equalish @ U @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(259,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( subclass @ X @ Y )
| ~ ( subclass @ Y @ X )
| ( equalish @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(260,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ( subclass @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(261,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ( subclass @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(262,plain,
( ( ! [X: $i] : ( subclass @ X @ universal_class ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(263,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( member @ ( not_subclass_element @ X @ Y ) @ Y )
| ( subclass @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(264,plain,
( ( ! [X: $i,Y: $i] :
( ( member @ ( not_subclass_element @ X @ Y ) @ X )
| ( subclass @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(265,plain,
( ( ! [X: $i,Y: $i,U: $i] :
( ~ ( subclass @ X @ Y )
| ~ ( member @ U @ X )
| ( member @ U @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(266,plain,
( ( ! [O7: $i,P7: $i,Q7: $i] :
( ~ ( equalish @ O7 @ P7 )
| ~ ( subclass @ Q7 @ O7 )
| ( subclass @ Q7 @ P7 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(267,plain,
( ( ! [L7: $i,M7: $i,N7: $i] :
( ~ ( equalish @ L7 @ M7 )
| ~ ( subclass @ L7 @ N7 )
| ( subclass @ M7 @ N7 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(268,plain,
( ( ! [J7: $i,K7: $i] :
( ~ ( equalish @ J7 @ K7 )
| ~ ( single_valued_class @ J7 )
| ( single_valued_class @ K7 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(269,plain,
( ( ! [H7: $i,I7: $i] :
( ~ ( equalish @ H7 @ I7 )
| ~ ( operation @ H7 )
| ( operation @ I7 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(270,plain,
( ( ! [F7: $i,G7: $i] :
( ~ ( equalish @ F7 @ G7 )
| ~ ( one_to_one @ F7 )
| ( one_to_one @ G7 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(271,plain,
( ( ! [C7: $i,D7: $i,E7: $i] :
( ~ ( equalish @ C7 @ D7 )
| ~ ( member @ E7 @ C7 )
| ( member @ E7 @ D7 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(272,plain,
( ( ! [Z6: $i,A7: $i,B7: $i] :
( ~ ( equalish @ Z6 @ A7 )
| ~ ( member @ Z6 @ B7 )
| ( member @ A7 @ B7 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(273,plain,
( ( ! [X6: $i,Y6: $i] :
( ~ ( equalish @ X6 @ Y6 )
| ~ ( inductive @ X6 )
| ( inductive @ Y6 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(274,plain,
( ( ! [T6: $i,U6: $i,V6: $i,W6: $i] :
( ~ ( equalish @ T6 @ U6 )
| ~ ( homomorphism @ V6 @ W6 @ T6 )
| ( homomorphism @ V6 @ W6 @ U6 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(275,plain,
( ( ! [P6: $i,Q6: $i,R6: $i,S6: $i] :
( ~ ( equalish @ P6 @ Q6 )
| ~ ( homomorphism @ R6 @ P6 @ S6 )
| ( homomorphism @ R6 @ Q6 @ S6 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(276,plain,
( ( ! [L6: $i,M6: $i,N6: $i,O6: $i] :
( ~ ( equalish @ L6 @ M6 )
| ~ ( homomorphism @ L6 @ N6 @ O6 )
| ( homomorphism @ M6 @ N6 @ O6 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(277,plain,
( ( ! [J6: $i,K6: $i] :
( ~ ( equalish @ J6 @ K6 )
| ~ ( function @ J6 )
| ( function @ K6 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(278,plain,
( ( ! [F6: $i,G6: $i,H6: $i,I6: $i] :
( ~ ( equalish @ F6 @ G6 )
| ~ ( compatible @ H6 @ I6 @ F6 )
| ( compatible @ H6 @ I6 @ G6 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(279,plain,
( ( ! [B6: $i,C6: $i,D6: $i,E6: $i] :
( ~ ( equalish @ B6 @ C6 )
| ~ ( compatible @ D6 @ B6 @ E6 )
| ( compatible @ D6 @ C6 @ E6 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(280,plain,
( ( ! [X5: $i,Y5: $i,Z5: $i,A6: $i] :
( ~ ( equalish @ X5 @ Y5 )
| ~ ( compatible @ X5 @ Z5 @ A6 )
| ( compatible @ Y5 @ Z5 @ A6 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(281,plain,
( ( ! [U5: $i,V5: $i,W5: $i] :
( ~ ( equalish @ U5 @ V5 )
| ( equalish @ ( unordered_pair @ W5 @ U5 ) @ ( unordered_pair @ W5 @ V5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(282,plain,
( ( ! [R5: $i,S5: $i,T5: $i] :
( ~ ( equalish @ R5 @ S5 )
| ( equalish @ ( unordered_pair @ R5 @ T5 ) @ ( unordered_pair @ S5 @ T5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(283,plain,
( ( ! [O5: $i,P5: $i,Q5: $i] :
( ~ ( equalish @ O5 @ P5 )
| ( equalish @ ( union @ Q5 @ O5 ) @ ( union @ Q5 @ P5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(284,plain,
( ( ! [L5: $i,M5: $i,N5: $i] :
( ~ ( equalish @ L5 @ M5 )
| ( equalish @ ( union @ L5 @ N5 ) @ ( union @ M5 @ N5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(285,plain,
( ( ! [J5: $i,K5: $i] :
( ~ ( equalish @ J5 @ K5 )
| ( equalish @ ( sum_class @ J5 ) @ ( sum_class @ K5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(286,plain,
( ( ! [H5: $i,I5: $i] :
( ~ ( equalish @ H5 @ I5 )
| ( equalish @ ( successor @ H5 ) @ ( successor @ I5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(287,plain,
( ( ! [F5: $i,G5: $i] :
( ~ ( equalish @ F5 @ G5 )
| ( equalish @ ( singleton @ F5 ) @ ( singleton @ G5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(288,plain,
( ( ! [D5: $i,E5: $i] :
( ~ ( equalish @ D5 @ E5 )
| ( equalish @ ( second @ D5 ) @ ( second @ E5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(289,plain,
( ( ! [B5: $i,C5: $i] :
( ~ ( equalish @ B5 @ C5 )
| ( equalish @ ( rotate @ B5 ) @ ( rotate @ C5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(290,plain,
( ( ! [X4: $i,Y4: $i,Z4: $i,A5: $i] :
( ~ ( equalish @ X4 @ Y4 )
| ( equalish @ ( restrict @ Z4 @ A5 @ X4 ) @ ( restrict @ Z4 @ A5 @ Y4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(291,plain,
( ( ! [T4: $i,U4: $i,V4: $i,W4: $i] :
( ~ ( equalish @ T4 @ U4 )
| ( equalish @ ( restrict @ V4 @ T4 @ W4 ) @ ( restrict @ V4 @ U4 @ W4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(292,plain,
( ( ! [P4: $i,Q4: $i,R4: $i,S4: $i] :
( ~ ( equalish @ P4 @ Q4 )
| ( equalish @ ( restrict @ P4 @ R4 @ S4 ) @ ( restrict @ Q4 @ R4 @ S4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(293,plain,
( ( ! [N4: $i,O4: $i] :
( ~ ( equalish @ N4 @ O4 )
| ( equalish @ ( regular @ N4 ) @ ( regular @ O4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(294,plain,
( ( ! [L4: $i,M4: $i] :
( ~ ( equalish @ L4 @ M4 )
| ( equalish @ ( range_of @ L4 ) @ ( range_of @ M4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(295,plain,
( ( ! [H4: $i,I4: $i,J4: $i,K4: $i] :
( ~ ( equalish @ H4 @ I4 )
| ( equalish @ ( range @ J4 @ K4 @ H4 ) @ ( range @ J4 @ K4 @ I4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(296,plain,
( ( ! [D4: $i,E4: $i,F4: $i,G4: $i] :
( ~ ( equalish @ D4 @ E4 )
| ( equalish @ ( range @ F4 @ D4 @ G4 ) @ ( range @ F4 @ E4 @ G4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(297,plain,
( ( ! [Z3: $i,A4: $i,B4: $i,C4: $i] :
( ~ ( equalish @ Z3 @ A4 )
| ( equalish @ ( range @ Z3 @ B4 @ C4 ) @ ( range @ A4 @ B4 @ C4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(298,plain,
( ( ! [X3: $i,Y3: $i] :
( ~ ( equalish @ X3 @ Y3 )
| ( equalish @ ( power_class @ X3 ) @ ( power_class @ Y3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(299,plain,
( ( ! [U3: $i,V3: $i,W3: $i] :
( ~ ( equalish @ U3 @ V3 )
| ( equalish @ ( ordered_pair @ W3 @ U3 ) @ ( ordered_pair @ W3 @ V3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(300,plain,
( ( ! [R3: $i,S3: $i,T3: $i] :
( ~ ( equalish @ R3 @ S3 )
| ( equalish @ ( ordered_pair @ R3 @ T3 ) @ ( ordered_pair @ S3 @ T3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(301,plain,
( ( ! [O3: $i,P3: $i,Q3: $i] :
( ~ ( equalish @ O3 @ P3 )
| ( equalish @ ( not_subclass_element @ Q3 @ O3 ) @ ( not_subclass_element @ Q3 @ P3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(302,plain,
( ( ! [L3: $i,M3: $i,N3: $i] :
( ~ ( equalish @ L3 @ M3 )
| ( equalish @ ( not_subclass_element @ L3 @ N3 ) @ ( not_subclass_element @ M3 @ N3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(303,plain,
( ( ! [H3: $i,I3: $i,J3: $i,K3: $i] :
( ~ ( equalish @ H3 @ I3 )
| ( equalish @ ( not_homomorphism2 @ J3 @ K3 @ H3 ) @ ( not_homomorphism2 @ J3 @ K3 @ I3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(304,plain,
( ( ! [D3: $i,E3: $i,F3: $i,G3: $i] :
( ~ ( equalish @ D3 @ E3 )
| ( equalish @ ( not_homomorphism2 @ F3 @ D3 @ G3 ) @ ( not_homomorphism2 @ F3 @ E3 @ G3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(305,plain,
( ( ! [Z2: $i,A3: $i,B3: $i,C3: $i] :
( ~ ( equalish @ Z2 @ A3 )
| ( equalish @ ( not_homomorphism2 @ Z2 @ B3 @ C3 ) @ ( not_homomorphism2 @ A3 @ B3 @ C3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(306,plain,
( ( ! [V2: $i,W2: $i,X2: $i,Y2: $i] :
( ~ ( equalish @ V2 @ W2 )
| ( equalish @ ( not_homomorphism1 @ X2 @ Y2 @ V2 ) @ ( not_homomorphism1 @ X2 @ Y2 @ W2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(307,plain,
( ( ! [R2: $i,S2: $i,T2: $i,U2: $i] :
( ~ ( equalish @ R2 @ S2 )
| ( equalish @ ( not_homomorphism1 @ T2 @ R2 @ U2 ) @ ( not_homomorphism1 @ T2 @ S2 @ U2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(308,plain,
( ( ! [N2: $i,O2: $i,P2: $i,Q2: $i] :
( ~ ( equalish @ N2 @ O2 )
| ( equalish @ ( not_homomorphism1 @ N2 @ P2 @ Q2 ) @ ( not_homomorphism1 @ O2 @ P2 @ Q2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(309,plain,
( ( ! [L2: $i,M2: $i] :
( ~ ( equalish @ L2 @ M2 )
| ( equalish @ ( inverse @ L2 ) @ ( inverse @ M2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(310,plain,
( ( ! [I2: $i,J2: $i,K2: $i] :
( ~ ( equalish @ I2 @ J2 )
| ( equalish @ ( intersection @ K2 @ I2 ) @ ( intersection @ K2 @ J2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(311,plain,
( ( ! [F2: $i,G2: $i,H2: $i] :
( ~ ( equalish @ F2 @ G2 )
| ( equalish @ ( intersection @ F2 @ H2 ) @ ( intersection @ G2 @ H2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(312,plain,
( ( ! [C2: $i,D2: $i,E2: $i] :
( ~ ( equalish @ C2 @ D2 )
| ( equalish @ ( image @ E2 @ C2 ) @ ( image @ E2 @ D2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(313,plain,
( ( ! [Z1: $i,A2: $i,B2: $i] :
( ~ ( equalish @ Z1 @ A2 )
| ( equalish @ ( image @ Z1 @ B2 ) @ ( image @ A2 @ B2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(314,plain,
( ( ! [X1: $i,Y1: $i] :
( ~ ( equalish @ X1 @ Y1 )
| ( equalish @ ( flip @ X1 ) @ ( flip @ Y1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(315,plain,
( ( ! [V1: $i,W1: $i] :
( ~ ( equalish @ V1 @ W1 )
| ( equalish @ ( first @ V1 ) @ ( first @ W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(316,plain,
( ( ! [T1: $i,U1: $i] :
( ~ ( equalish @ T1 @ U1 )
| ( equalish @ ( domain_of @ T1 ) @ ( domain_of @ U1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(317,plain,
( ( ! [P1: $i,Q1: $i,R1: $i,S1: $i] :
( ~ ( equalish @ P1 @ Q1 )
| ( equalish @ ( domain @ R1 @ S1 @ P1 ) @ ( domain @ R1 @ S1 @ Q1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(318,plain,
( ( ! [L1: $i,M1: $i,N1: $i,O1: $i] :
( ~ ( equalish @ L1 @ M1 )
| ( equalish @ ( domain @ N1 @ L1 @ O1 ) @ ( domain @ N1 @ M1 @ O1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(319,plain,
( ( ! [H1: $i,I1: $i,J1: $i,K1: $i] :
( ~ ( equalish @ H1 @ I1 )
| ( equalish @ ( domain @ H1 @ J1 @ K1 ) @ ( domain @ I1 @ J1 @ K1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(320,plain,
( ( ! [E1: $i,F1: $i,G1: $i] :
( ~ ( equalish @ E1 @ F1 )
| ( equalish @ ( symmetric_difference @ G1 @ E1 ) @ ( symmetric_difference @ G1 @ F1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(321,plain,
( ( ! [B1: $i,C1: $i,D1: $i] :
( ~ ( equalish @ B1 @ C1 )
| ( equalish @ ( symmetric_difference @ B1 @ D1 ) @ ( symmetric_difference @ C1 @ D1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(322,plain,
( ( ! [Z: $i,A1: $i] :
( ~ ( equalish @ Z @ A1 )
| ( equalish @ ( diagonalise @ Z ) @ ( diagonalise @ A1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(323,plain,
( ( ! [W: $i,X: $i,Y: $i] :
( ~ ( equalish @ W @ X )
| ( equalish @ ( cross_product @ Y @ W ) @ ( cross_product @ Y @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(324,plain,
( ( ! [T: $i,U: $i,V: $i] :
( ~ ( equalish @ T @ U )
| ( equalish @ ( cross_product @ T @ V ) @ ( cross_product @ U @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(325,plain,
( ( ! [Q: $i,R: $i,S: $i] :
( ~ ( equalish @ Q @ R )
| ( equalish @ ( compose @ S @ Q ) @ ( compose @ S @ R ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(326,plain,
( ( ! [N: $i,O: $i,P: $i] :
( ~ ( equalish @ N @ O )
| ( equalish @ ( compose @ N @ P ) @ ( compose @ O @ P ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(327,plain,
( ( ! [L: $i,M: $i] :
( ~ ( equalish @ L @ M )
| ( equalish @ ( complement @ L ) @ ( complement @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(328,plain,
( ( ! [J: $i,K: $i] :
( ~ ( equalish @ J @ K )
| ( equalish @ ( cantor @ J ) @ ( cantor @ K ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(329,plain,
( ( ! [G: $i,H: $i,I: $i] :
( ~ ( equalish @ G @ H )
| ( equalish @ ( apply @ I @ G ) @ ( apply @ I @ H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(330,plain,
( ( ! [D: $i,E: $i,F: $i] :
( ~ ( equalish @ D @ E )
| ( equalish @ ( apply @ D @ F ) @ ( apply @ E @ F ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(331,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( equalish @ Y @ Z )
| ( equalish @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(332,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(333,plain,
( ( ~ ( equalish @ x @ x ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(334,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[168]) ).
thf(335,plain,
( ( ~ ( equalish @ x @ x ) )
= $true ),
inference(copy,[status(thm)],[333]) ).
thf(336,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[332]) ).
thf(337,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( equalish @ Y @ Z )
| ( equalish @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[331]) ).
thf(338,plain,
( ( ! [D: $i,E: $i,F: $i] :
( ~ ( equalish @ D @ E )
| ( equalish @ ( apply @ D @ F ) @ ( apply @ E @ F ) ) ) )
= $true ),
inference(copy,[status(thm)],[330]) ).
thf(339,plain,
( ( ! [G: $i,H: $i,I: $i] :
( ~ ( equalish @ G @ H )
| ( equalish @ ( apply @ I @ G ) @ ( apply @ I @ H ) ) ) )
= $true ),
inference(copy,[status(thm)],[329]) ).
thf(340,plain,
( ( ! [J: $i,K: $i] :
( ~ ( equalish @ J @ K )
| ( equalish @ ( cantor @ J ) @ ( cantor @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[328]) ).
thf(341,plain,
( ( ! [L: $i,M: $i] :
( ~ ( equalish @ L @ M )
| ( equalish @ ( complement @ L ) @ ( complement @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[327]) ).
thf(342,plain,
( ( ! [N: $i,O: $i,P: $i] :
( ~ ( equalish @ N @ O )
| ( equalish @ ( compose @ N @ P ) @ ( compose @ O @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[326]) ).
thf(343,plain,
( ( ! [Q: $i,R: $i,S: $i] :
( ~ ( equalish @ Q @ R )
| ( equalish @ ( compose @ S @ Q ) @ ( compose @ S @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[325]) ).
thf(344,plain,
( ( ! [T: $i,U: $i,V: $i] :
( ~ ( equalish @ T @ U )
| ( equalish @ ( cross_product @ T @ V ) @ ( cross_product @ U @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[324]) ).
thf(345,plain,
( ( ! [W: $i,X: $i,Y: $i] :
( ~ ( equalish @ W @ X )
| ( equalish @ ( cross_product @ Y @ W ) @ ( cross_product @ Y @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[323]) ).
thf(346,plain,
( ( ! [Z: $i,A1: $i] :
( ~ ( equalish @ Z @ A1 )
| ( equalish @ ( diagonalise @ Z ) @ ( diagonalise @ A1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[322]) ).
thf(347,plain,
( ( ! [B1: $i,C1: $i,D1: $i] :
( ~ ( equalish @ B1 @ C1 )
| ( equalish @ ( symmetric_difference @ B1 @ D1 ) @ ( symmetric_difference @ C1 @ D1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[321]) ).
thf(348,plain,
( ( ! [E1: $i,F1: $i,G1: $i] :
( ~ ( equalish @ E1 @ F1 )
| ( equalish @ ( symmetric_difference @ G1 @ E1 ) @ ( symmetric_difference @ G1 @ F1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[320]) ).
thf(349,plain,
( ( ! [H1: $i,I1: $i,J1: $i,K1: $i] :
( ~ ( equalish @ H1 @ I1 )
| ( equalish @ ( domain @ H1 @ J1 @ K1 ) @ ( domain @ I1 @ J1 @ K1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[319]) ).
thf(350,plain,
( ( ! [L1: $i,M1: $i,N1: $i,O1: $i] :
( ~ ( equalish @ L1 @ M1 )
| ( equalish @ ( domain @ N1 @ L1 @ O1 ) @ ( domain @ N1 @ M1 @ O1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[318]) ).
thf(351,plain,
( ( ! [P1: $i,Q1: $i,R1: $i,S1: $i] :
( ~ ( equalish @ P1 @ Q1 )
| ( equalish @ ( domain @ R1 @ S1 @ P1 ) @ ( domain @ R1 @ S1 @ Q1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[317]) ).
thf(352,plain,
( ( ! [T1: $i,U1: $i] :
( ~ ( equalish @ T1 @ U1 )
| ( equalish @ ( domain_of @ T1 ) @ ( domain_of @ U1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[316]) ).
thf(353,plain,
( ( ! [V1: $i,W1: $i] :
( ~ ( equalish @ V1 @ W1 )
| ( equalish @ ( first @ V1 ) @ ( first @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[315]) ).
thf(354,plain,
( ( ! [X1: $i,Y1: $i] :
( ~ ( equalish @ X1 @ Y1 )
| ( equalish @ ( flip @ X1 ) @ ( flip @ Y1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[314]) ).
thf(355,plain,
( ( ! [Z1: $i,A2: $i,B2: $i] :
( ~ ( equalish @ Z1 @ A2 )
| ( equalish @ ( image @ Z1 @ B2 ) @ ( image @ A2 @ B2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[313]) ).
thf(356,plain,
( ( ! [C2: $i,D2: $i,E2: $i] :
( ~ ( equalish @ C2 @ D2 )
| ( equalish @ ( image @ E2 @ C2 ) @ ( image @ E2 @ D2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[312]) ).
thf(357,plain,
( ( ! [F2: $i,G2: $i,H2: $i] :
( ~ ( equalish @ F2 @ G2 )
| ( equalish @ ( intersection @ F2 @ H2 ) @ ( intersection @ G2 @ H2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[311]) ).
thf(358,plain,
( ( ! [I2: $i,J2: $i,K2: $i] :
( ~ ( equalish @ I2 @ J2 )
| ( equalish @ ( intersection @ K2 @ I2 ) @ ( intersection @ K2 @ J2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[310]) ).
thf(359,plain,
( ( ! [L2: $i,M2: $i] :
( ~ ( equalish @ L2 @ M2 )
| ( equalish @ ( inverse @ L2 ) @ ( inverse @ M2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[309]) ).
thf(360,plain,
( ( ! [N2: $i,O2: $i,P2: $i,Q2: $i] :
( ~ ( equalish @ N2 @ O2 )
| ( equalish @ ( not_homomorphism1 @ N2 @ P2 @ Q2 ) @ ( not_homomorphism1 @ O2 @ P2 @ Q2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[308]) ).
thf(361,plain,
( ( ! [R2: $i,S2: $i,T2: $i,U2: $i] :
( ~ ( equalish @ R2 @ S2 )
| ( equalish @ ( not_homomorphism1 @ T2 @ R2 @ U2 ) @ ( not_homomorphism1 @ T2 @ S2 @ U2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[307]) ).
thf(362,plain,
( ( ! [V2: $i,W2: $i,X2: $i,Y2: $i] :
( ~ ( equalish @ V2 @ W2 )
| ( equalish @ ( not_homomorphism1 @ X2 @ Y2 @ V2 ) @ ( not_homomorphism1 @ X2 @ Y2 @ W2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[306]) ).
thf(363,plain,
( ( ! [Z2: $i,A3: $i,B3: $i,C3: $i] :
( ~ ( equalish @ Z2 @ A3 )
| ( equalish @ ( not_homomorphism2 @ Z2 @ B3 @ C3 ) @ ( not_homomorphism2 @ A3 @ B3 @ C3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[305]) ).
thf(364,plain,
( ( ! [D3: $i,E3: $i,F3: $i,G3: $i] :
( ~ ( equalish @ D3 @ E3 )
| ( equalish @ ( not_homomorphism2 @ F3 @ D3 @ G3 ) @ ( not_homomorphism2 @ F3 @ E3 @ G3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[304]) ).
thf(365,plain,
( ( ! [H3: $i,I3: $i,J3: $i,K3: $i] :
( ~ ( equalish @ H3 @ I3 )
| ( equalish @ ( not_homomorphism2 @ J3 @ K3 @ H3 ) @ ( not_homomorphism2 @ J3 @ K3 @ I3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[303]) ).
thf(366,plain,
( ( ! [L3: $i,M3: $i,N3: $i] :
( ~ ( equalish @ L3 @ M3 )
| ( equalish @ ( not_subclass_element @ L3 @ N3 ) @ ( not_subclass_element @ M3 @ N3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[302]) ).
thf(367,plain,
( ( ! [O3: $i,P3: $i,Q3: $i] :
( ~ ( equalish @ O3 @ P3 )
| ( equalish @ ( not_subclass_element @ Q3 @ O3 ) @ ( not_subclass_element @ Q3 @ P3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[301]) ).
thf(368,plain,
( ( ! [R3: $i,S3: $i,T3: $i] :
( ~ ( equalish @ R3 @ S3 )
| ( equalish @ ( ordered_pair @ R3 @ T3 ) @ ( ordered_pair @ S3 @ T3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[300]) ).
thf(369,plain,
( ( ! [U3: $i,V3: $i,W3: $i] :
( ~ ( equalish @ U3 @ V3 )
| ( equalish @ ( ordered_pair @ W3 @ U3 ) @ ( ordered_pair @ W3 @ V3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[299]) ).
thf(370,plain,
( ( ! [X3: $i,Y3: $i] :
( ~ ( equalish @ X3 @ Y3 )
| ( equalish @ ( power_class @ X3 ) @ ( power_class @ Y3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[298]) ).
thf(371,plain,
( ( ! [Z3: $i,A4: $i,B4: $i,C4: $i] :
( ~ ( equalish @ Z3 @ A4 )
| ( equalish @ ( range @ Z3 @ B4 @ C4 ) @ ( range @ A4 @ B4 @ C4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[297]) ).
thf(372,plain,
( ( ! [D4: $i,E4: $i,F4: $i,G4: $i] :
( ~ ( equalish @ D4 @ E4 )
| ( equalish @ ( range @ F4 @ D4 @ G4 ) @ ( range @ F4 @ E4 @ G4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[296]) ).
thf(373,plain,
( ( ! [H4: $i,I4: $i,J4: $i,K4: $i] :
( ~ ( equalish @ H4 @ I4 )
| ( equalish @ ( range @ J4 @ K4 @ H4 ) @ ( range @ J4 @ K4 @ I4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[295]) ).
thf(374,plain,
( ( ! [L4: $i,M4: $i] :
( ~ ( equalish @ L4 @ M4 )
| ( equalish @ ( range_of @ L4 ) @ ( range_of @ M4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[294]) ).
thf(375,plain,
( ( ! [N4: $i,O4: $i] :
( ~ ( equalish @ N4 @ O4 )
| ( equalish @ ( regular @ N4 ) @ ( regular @ O4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[293]) ).
thf(376,plain,
( ( ! [P4: $i,Q4: $i,R4: $i,S4: $i] :
( ~ ( equalish @ P4 @ Q4 )
| ( equalish @ ( restrict @ P4 @ R4 @ S4 ) @ ( restrict @ Q4 @ R4 @ S4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[292]) ).
thf(377,plain,
( ( ! [T4: $i,U4: $i,V4: $i,W4: $i] :
( ~ ( equalish @ T4 @ U4 )
| ( equalish @ ( restrict @ V4 @ T4 @ W4 ) @ ( restrict @ V4 @ U4 @ W4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[291]) ).
thf(378,plain,
( ( ! [X4: $i,Y4: $i,Z4: $i,A5: $i] :
( ~ ( equalish @ X4 @ Y4 )
| ( equalish @ ( restrict @ Z4 @ A5 @ X4 ) @ ( restrict @ Z4 @ A5 @ Y4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[290]) ).
thf(379,plain,
( ( ! [B5: $i,C5: $i] :
( ~ ( equalish @ B5 @ C5 )
| ( equalish @ ( rotate @ B5 ) @ ( rotate @ C5 ) ) ) )
= $true ),
inference(copy,[status(thm)],[289]) ).
thf(380,plain,
( ( ! [D5: $i,E5: $i] :
( ~ ( equalish @ D5 @ E5 )
| ( equalish @ ( second @ D5 ) @ ( second @ E5 ) ) ) )
= $true ),
inference(copy,[status(thm)],[288]) ).
thf(381,plain,
( ( ! [F5: $i,G5: $i] :
( ~ ( equalish @ F5 @ G5 )
| ( equalish @ ( singleton @ F5 ) @ ( singleton @ G5 ) ) ) )
= $true ),
inference(copy,[status(thm)],[287]) ).
thf(382,plain,
( ( ! [H5: $i,I5: $i] :
( ~ ( equalish @ H5 @ I5 )
| ( equalish @ ( successor @ H5 ) @ ( successor @ I5 ) ) ) )
= $true ),
inference(copy,[status(thm)],[286]) ).
thf(383,plain,
( ( ! [J5: $i,K5: $i] :
( ~ ( equalish @ J5 @ K5 )
| ( equalish @ ( sum_class @ J5 ) @ ( sum_class @ K5 ) ) ) )
= $true ),
inference(copy,[status(thm)],[285]) ).
thf(384,plain,
( ( ! [L5: $i,M5: $i,N5: $i] :
( ~ ( equalish @ L5 @ M5 )
| ( equalish @ ( union @ L5 @ N5 ) @ ( union @ M5 @ N5 ) ) ) )
= $true ),
inference(copy,[status(thm)],[284]) ).
thf(385,plain,
( ( ! [O5: $i,P5: $i,Q5: $i] :
( ~ ( equalish @ O5 @ P5 )
| ( equalish @ ( union @ Q5 @ O5 ) @ ( union @ Q5 @ P5 ) ) ) )
= $true ),
inference(copy,[status(thm)],[283]) ).
thf(386,plain,
( ( ! [R5: $i,S5: $i,T5: $i] :
( ~ ( equalish @ R5 @ S5 )
| ( equalish @ ( unordered_pair @ R5 @ T5 ) @ ( unordered_pair @ S5 @ T5 ) ) ) )
= $true ),
inference(copy,[status(thm)],[282]) ).
thf(387,plain,
( ( ! [U5: $i,V5: $i,W5: $i] :
( ~ ( equalish @ U5 @ V5 )
| ( equalish @ ( unordered_pair @ W5 @ U5 ) @ ( unordered_pair @ W5 @ V5 ) ) ) )
= $true ),
inference(copy,[status(thm)],[281]) ).
thf(388,plain,
( ( ! [X5: $i,Y5: $i,Z5: $i,A6: $i] :
( ~ ( equalish @ X5 @ Y5 )
| ~ ( compatible @ X5 @ Z5 @ A6 )
| ( compatible @ Y5 @ Z5 @ A6 ) ) )
= $true ),
inference(copy,[status(thm)],[280]) ).
thf(389,plain,
( ( ! [B6: $i,C6: $i,D6: $i,E6: $i] :
( ~ ( equalish @ B6 @ C6 )
| ~ ( compatible @ D6 @ B6 @ E6 )
| ( compatible @ D6 @ C6 @ E6 ) ) )
= $true ),
inference(copy,[status(thm)],[279]) ).
thf(390,plain,
( ( ! [F6: $i,G6: $i,H6: $i,I6: $i] :
( ~ ( equalish @ F6 @ G6 )
| ~ ( compatible @ H6 @ I6 @ F6 )
| ( compatible @ H6 @ I6 @ G6 ) ) )
= $true ),
inference(copy,[status(thm)],[278]) ).
thf(391,plain,
( ( ! [J6: $i,K6: $i] :
( ~ ( equalish @ J6 @ K6 )
| ~ ( function @ J6 )
| ( function @ K6 ) ) )
= $true ),
inference(copy,[status(thm)],[277]) ).
thf(392,plain,
( ( ! [L6: $i,M6: $i,N6: $i,O6: $i] :
( ~ ( equalish @ L6 @ M6 )
| ~ ( homomorphism @ L6 @ N6 @ O6 )
| ( homomorphism @ M6 @ N6 @ O6 ) ) )
= $true ),
inference(copy,[status(thm)],[276]) ).
thf(393,plain,
( ( ! [P6: $i,Q6: $i,R6: $i,S6: $i] :
( ~ ( equalish @ P6 @ Q6 )
| ~ ( homomorphism @ R6 @ P6 @ S6 )
| ( homomorphism @ R6 @ Q6 @ S6 ) ) )
= $true ),
inference(copy,[status(thm)],[275]) ).
thf(394,plain,
( ( ! [T6: $i,U6: $i,V6: $i,W6: $i] :
( ~ ( equalish @ T6 @ U6 )
| ~ ( homomorphism @ V6 @ W6 @ T6 )
| ( homomorphism @ V6 @ W6 @ U6 ) ) )
= $true ),
inference(copy,[status(thm)],[274]) ).
thf(395,plain,
( ( ! [X6: $i,Y6: $i] :
( ~ ( equalish @ X6 @ Y6 )
| ~ ( inductive @ X6 )
| ( inductive @ Y6 ) ) )
= $true ),
inference(copy,[status(thm)],[273]) ).
thf(396,plain,
( ( ! [Z6: $i,A7: $i,B7: $i] :
( ~ ( equalish @ Z6 @ A7 )
| ~ ( member @ Z6 @ B7 )
| ( member @ A7 @ B7 ) ) )
= $true ),
inference(copy,[status(thm)],[272]) ).
thf(397,plain,
( ( ! [C7: $i,D7: $i,E7: $i] :
( ~ ( equalish @ C7 @ D7 )
| ~ ( member @ E7 @ C7 )
| ( member @ E7 @ D7 ) ) )
= $true ),
inference(copy,[status(thm)],[271]) ).
thf(398,plain,
( ( ! [F7: $i,G7: $i] :
( ~ ( equalish @ F7 @ G7 )
| ~ ( one_to_one @ F7 )
| ( one_to_one @ G7 ) ) )
= $true ),
inference(copy,[status(thm)],[270]) ).
thf(399,plain,
( ( ! [H7: $i,I7: $i] :
( ~ ( equalish @ H7 @ I7 )
| ~ ( operation @ H7 )
| ( operation @ I7 ) ) )
= $true ),
inference(copy,[status(thm)],[269]) ).
thf(400,plain,
( ( ! [J7: $i,K7: $i] :
( ~ ( equalish @ J7 @ K7 )
| ~ ( single_valued_class @ J7 )
| ( single_valued_class @ K7 ) ) )
= $true ),
inference(copy,[status(thm)],[268]) ).
thf(401,plain,
( ( ! [L7: $i,M7: $i,N7: $i] :
( ~ ( equalish @ L7 @ M7 )
| ~ ( subclass @ L7 @ N7 )
| ( subclass @ M7 @ N7 ) ) )
= $true ),
inference(copy,[status(thm)],[267]) ).
thf(402,plain,
( ( ! [O7: $i,P7: $i,Q7: $i] :
( ~ ( equalish @ O7 @ P7 )
| ~ ( subclass @ Q7 @ O7 )
| ( subclass @ Q7 @ P7 ) ) )
= $true ),
inference(copy,[status(thm)],[266]) ).
thf(403,plain,
( ( ! [X: $i,Y: $i,U: $i] :
( ~ ( subclass @ X @ Y )
| ~ ( member @ U @ X )
| ( member @ U @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[265]) ).
thf(404,plain,
( ( ! [X: $i,Y: $i] :
( ( member @ ( not_subclass_element @ X @ Y ) @ X )
| ( subclass @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[264]) ).
thf(405,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( member @ ( not_subclass_element @ X @ Y ) @ Y )
| ( subclass @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[263]) ).
thf(406,plain,
( ( ! [X: $i] : ( subclass @ X @ universal_class ) )
= $true ),
inference(copy,[status(thm)],[262]) ).
thf(407,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ( subclass @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[261]) ).
thf(408,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ( subclass @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[260]) ).
thf(409,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( subclass @ X @ Y )
| ~ ( subclass @ Y @ X )
| ( equalish @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[259]) ).
thf(410,plain,
( ( ! [U: $i,X: $i,Y: $i] :
( ~ ( member @ U @ ( unordered_pair @ X @ Y ) )
| ( equalish @ U @ X )
| ( equalish @ U @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[258]) ).
thf(411,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( member @ X @ universal_class )
| ( member @ X @ ( unordered_pair @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[257]) ).
thf(412,plain,
( ( ! [Y: $i,X: $i] :
( ~ ( member @ Y @ universal_class )
| ( member @ Y @ ( unordered_pair @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[256]) ).
thf(413,plain,
( ( ! [X: $i,Y: $i] : ( member @ ( unordered_pair @ X @ Y ) @ universal_class ) )
= $true ),
inference(copy,[status(thm)],[255]) ).
thf(414,plain,
( ( ! [X: $i] : ( equalish @ ( unordered_pair @ X @ X ) @ ( singleton @ X ) ) )
= $true ),
inference(copy,[status(thm)],[254]) ).
thf(415,plain,
( ( ! [X: $i,Y: $i] : ( equalish @ ( unordered_pair @ ( singleton @ X ) @ ( unordered_pair @ X @ ( singleton @ Y ) ) ) @ ( ordered_pair @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[253]) ).
thf(416,plain,
( ( ! [U: $i,V: $i,X: $i,Y: $i] :
( ~ ( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) )
| ( member @ U @ X ) ) )
= $true ),
inference(copy,[status(thm)],[252]) ).
thf(417,plain,
( ( ! [U: $i,V: $i,X: $i,Y: $i] :
( ~ ( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) )
| ( member @ V @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[251]) ).
thf(418,plain,
( ( ! [U: $i,X: $i,V: $i,Y: $i] :
( ~ ( member @ U @ X )
| ~ ( member @ V @ Y )
| ( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[250]) ).
thf(419,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( cross_product @ X @ Y ) )
| ( equalish @ ( ordered_pair @ ( first @ Z ) @ ( second @ Z ) ) @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[249]) ).
thf(420,plain,
( ( subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ) )
= $true ),
inference(copy,[status(thm)],[248]) ).
thf(421,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( member @ ( ordered_pair @ X @ Y ) @ element_relation )
| ( member @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[247]) ).
thf(422,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( member @ ( ordered_pair @ X @ Y ) @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( member @ X @ Y )
| ( member @ ( ordered_pair @ X @ Y ) @ element_relation ) ) )
= $true ),
inference(copy,[status(thm)],[246]) ).
thf(423,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( intersection @ X @ Y ) )
| ( member @ Z @ X ) ) )
= $true ),
inference(copy,[status(thm)],[245]) ).
thf(424,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( intersection @ X @ Y ) )
| ( member @ Z @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[244]) ).
thf(425,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ X )
| ~ ( member @ Z @ Y )
| ( member @ Z @ ( intersection @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[243]) ).
thf(426,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( complement @ X ) )
| ~ ( member @ Z @ X ) ) )
= $true ),
inference(copy,[status(thm)],[242]) ).
thf(427,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ universal_class )
| ( member @ Z @ ( complement @ X ) )
| ( member @ Z @ X ) ) )
= $true ),
inference(copy,[status(thm)],[241]) ).
thf(428,plain,
( ( ! [X: $i,Y: $i] : ( equalish @ ( complement @ ( intersection @ ( complement @ X ) @ ( complement @ Y ) ) ) @ ( union @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[240]) ).
thf(429,plain,
( ( ! [X: $i,Y: $i] : ( equalish @ ( intersection @ ( complement @ ( intersection @ X @ Y ) ) @ ( complement @ ( intersection @ ( complement @ X ) @ ( complement @ Y ) ) ) ) @ ( symmetric_difference @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[239]) ).
thf(430,plain,
( ( ! [Xr: $i,X: $i,Y: $i] : ( equalish @ ( intersection @ Xr @ ( cross_product @ X @ Y ) ) @ ( restrict @ Xr @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[238]) ).
thf(431,plain,
( ( ! [X: $i,Y: $i,Xr: $i] : ( equalish @ ( intersection @ ( cross_product @ X @ Y ) @ Xr ) @ ( restrict @ Xr @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[237]) ).
thf(432,plain,
( ( ! [X: $i,Z: $i] :
( ~ ( equalish @ ( restrict @ X @ ( singleton @ Z ) @ universal_class ) @ null_class )
| ~ ( member @ Z @ ( domain_of @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[236]) ).
thf(433,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ universal_class )
| ( equalish @ ( restrict @ X @ ( singleton @ Z ) @ universal_class ) @ null_class )
| ( member @ Z @ ( domain_of @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[235]) ).
thf(434,plain,
( ( ! [X: $i] : ( subclass @ ( rotate @ X ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(435,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( rotate @ X ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ V @ W ) @ U ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(436,plain,
( ( ! [V: $i,W: $i,U: $i,X: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ V @ W ) @ U ) @ X )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( rotate @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[232]) ).
thf(437,plain,
( ( ! [X: $i] : ( subclass @ ( flip @ X ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[231]) ).
thf(438,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( flip @ X ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ V @ U ) @ W ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[230]) ).
thf(439,plain,
( ( ! [V: $i,U: $i,W: $i,X: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ V @ U ) @ W ) @ X )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( flip @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[229]) ).
thf(440,plain,
( ( ! [Y: $i] : ( equalish @ ( domain_of @ ( flip @ ( cross_product @ Y @ universal_class ) ) ) @ ( inverse @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[228]) ).
thf(441,plain,
( ( ! [Z: $i] : ( equalish @ ( domain_of @ ( inverse @ Z ) ) @ ( range_of @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[227]) ).
thf(442,plain,
( ( ! [Z: $i,X: $i,Y: $i] : ( equalish @ ( first @ ( not_subclass_element @ ( restrict @ Z @ X @ ( singleton @ Y ) ) @ null_class ) ) @ ( domain @ Z @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(443,plain,
( ( ! [Z: $i,X: $i,Y: $i] : ( equalish @ ( second @ ( not_subclass_element @ ( restrict @ Z @ ( singleton @ X ) @ Y ) @ null_class ) ) @ ( range @ Z @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[225]) ).
thf(444,plain,
( ( ! [Xr: $i,X: $i] : ( equalish @ ( range_of @ ( restrict @ Xr @ X @ universal_class ) ) @ ( image @ Xr @ X ) ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(445,plain,
( ( ! [X: $i] : ( equalish @ ( union @ X @ ( singleton @ X ) ) @ ( successor @ X ) ) )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(446,plain,
( ( subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ) )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(447,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( member @ ( ordered_pair @ X @ Y ) @ successor_relation )
| ( equalish @ ( successor @ X ) @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(448,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ ( successor @ X ) @ Y )
| ~ ( member @ ( ordered_pair @ X @ Y ) @ ( cross_product @ universal_class @ universal_class ) )
| ( member @ ( ordered_pair @ X @ Y ) @ successor_relation ) ) )
= $true ),
inference(copy,[status(thm)],[220]) ).
thf(449,plain,
( ( ! [X: $i] :
( ~ ( inductive @ X )
| ( member @ null_class @ X ) ) )
= $true ),
inference(copy,[status(thm)],[219]) ).
thf(450,plain,
( ( ! [X: $i] :
( ~ ( inductive @ X )
| ( subclass @ ( image @ successor_relation @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[218]) ).
thf(451,plain,
( ( ! [X: $i] :
( ~ ( member @ null_class @ X )
| ~ ( subclass @ ( image @ successor_relation @ X ) @ X )
| ( inductive @ X ) ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(452,plain,
( ( inductive @ omega )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(453,plain,
( ( ! [Y: $i] :
( ~ ( inductive @ Y )
| ( subclass @ omega @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[215]) ).
thf(454,plain,
( ( member @ omega @ universal_class )
= $true ),
inference(copy,[status(thm)],[214]) ).
thf(455,plain,
( ( ! [X: $i] : ( equalish @ ( domain_of @ ( restrict @ element_relation @ universal_class @ X ) ) @ ( sum_class @ X ) ) )
= $true ),
inference(copy,[status(thm)],[213]) ).
thf(456,plain,
( ( ! [X: $i] :
( ~ ( member @ X @ universal_class )
| ( member @ ( sum_class @ X ) @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[212]) ).
thf(457,plain,
( ( ! [X: $i] : ( equalish @ ( complement @ ( image @ element_relation @ ( complement @ X ) ) ) @ ( power_class @ X ) ) )
= $true ),
inference(copy,[status(thm)],[211]) ).
thf(458,plain,
( ( ! [U: $i] :
( ~ ( member @ U @ universal_class )
| ( member @ ( power_class @ U ) @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(459,plain,
( ( ! [Yr: $i,Xr: $i] : ( subclass @ ( compose @ Yr @ Xr ) @ ( cross_product @ universal_class @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(460,plain,
( ( ! [Y: $i,Z: $i,Yr: $i,Xr: $i] :
( ~ ( member @ ( ordered_pair @ Y @ Z ) @ ( compose @ Yr @ Xr ) )
| ( member @ Z @ ( image @ Yr @ ( image @ Xr @ ( singleton @ Y ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[208]) ).
thf(461,plain,
( ( ! [Z: $i,Yr: $i,Xr: $i,Y: $i] :
( ~ ( member @ Z @ ( image @ Yr @ ( image @ Xr @ ( singleton @ Y ) ) ) )
| ~ ( member @ ( ordered_pair @ Y @ Z ) @ ( cross_product @ universal_class @ universal_class ) )
| ( member @ ( ordered_pair @ Y @ Z ) @ ( compose @ Yr @ Xr ) ) ) )
= $true ),
inference(copy,[status(thm)],[207]) ).
thf(462,plain,
( ( ! [X: $i] :
( ~ ( single_valued_class @ X )
| ( subclass @ ( compose @ X @ ( inverse @ X ) ) @ identity_relation ) ) )
= $true ),
inference(copy,[status(thm)],[206]) ).
thf(463,plain,
( ( ! [X: $i] :
( ~ ( subclass @ ( compose @ X @ ( inverse @ X ) ) @ identity_relation )
| ( single_valued_class @ X ) ) )
= $true ),
inference(copy,[status(thm)],[205]) ).
thf(464,plain,
( ( ! [Xf: $i] :
( ~ ( function @ Xf )
| ( subclass @ Xf @ ( cross_product @ universal_class @ universal_class ) ) ) )
= $true ),
inference(copy,[status(thm)],[204]) ).
thf(465,plain,
( ( ! [Xf: $i] :
( ~ ( function @ Xf )
| ( subclass @ ( compose @ Xf @ ( inverse @ Xf ) ) @ identity_relation ) ) )
= $true ),
inference(copy,[status(thm)],[203]) ).
thf(466,plain,
( ( ! [Xf: $i] :
( ~ ( subclass @ Xf @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ Xf @ ( inverse @ Xf ) ) @ identity_relation )
| ( function @ Xf ) ) )
= $true ),
inference(copy,[status(thm)],[202]) ).
thf(467,plain,
( ( ! [Xf: $i,X: $i] :
( ~ ( function @ Xf )
| ~ ( member @ X @ universal_class )
| ( member @ ( image @ Xf @ X ) @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(468,plain,
( ( ! [X: $i] :
( ( equalish @ X @ null_class )
| ( member @ ( regular @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[200]) ).
thf(469,plain,
( ( ! [X: $i] :
( ( equalish @ X @ null_class )
| ( equalish @ ( intersection @ X @ ( regular @ X ) ) @ null_class ) ) )
= $true ),
inference(copy,[status(thm)],[199]) ).
thf(470,plain,
( ( ! [Xf: $i,Y: $i] : ( equalish @ ( sum_class @ ( image @ Xf @ ( singleton @ Y ) ) ) @ ( apply @ Xf @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[198]) ).
thf(471,plain,
( ( function @ choice )
= $true ),
inference(copy,[status(thm)],[197]) ).
thf(472,plain,
( ( ! [Y: $i] :
( ~ ( member @ Y @ universal_class )
| ( equalish @ Y @ null_class )
| ( member @ ( apply @ choice @ Y ) @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[196]) ).
thf(473,plain,
( ( ! [Xf: $i] :
( ~ ( one_to_one @ Xf )
| ( function @ Xf ) ) )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(474,plain,
( ( ! [Xf: $i] :
( ~ ( one_to_one @ Xf )
| ( function @ ( inverse @ Xf ) ) ) )
= $true ),
inference(copy,[status(thm)],[194]) ).
thf(475,plain,
( ( ! [Xf: $i] :
( ~ ( function @ ( inverse @ Xf ) )
| ~ ( function @ Xf )
| ( one_to_one @ Xf ) ) )
= $true ),
inference(copy,[status(thm)],[193]) ).
thf(476,plain,
( ( equalish @ ( intersection @ ( cross_product @ universal_class @ universal_class ) @ ( intersection @ ( cross_product @ universal_class @ universal_class ) @ ( complement @ ( compose @ ( complement @ element_relation ) @ ( inverse @ element_relation ) ) ) ) ) @ subset_relation )
= $true ),
inference(copy,[status(thm)],[192]) ).
thf(477,plain,
( ( equalish @ ( intersection @ ( inverse @ subset_relation ) @ subset_relation ) @ identity_relation )
= $true ),
inference(copy,[status(thm)],[191]) ).
thf(478,plain,
( ( ! [Xr: $i] : ( equalish @ ( complement @ ( domain_of @ ( intersection @ Xr @ identity_relation ) ) ) @ ( diagonalise @ Xr ) ) )
= $true ),
inference(copy,[status(thm)],[190]) ).
thf(479,plain,
( ( ! [X: $i] : ( equalish @ ( intersection @ ( domain_of @ X ) @ ( diagonalise @ ( compose @ ( inverse @ element_relation ) @ X ) ) ) @ ( cantor @ X ) ) )
= $true ),
inference(copy,[status(thm)],[189]) ).
thf(480,plain,
( ( ! [Xf: $i] :
( ~ ( operation @ Xf )
| ( function @ Xf ) ) )
= $true ),
inference(copy,[status(thm)],[188]) ).
thf(481,plain,
( ( ! [Xf: $i] :
( ~ ( operation @ Xf )
| ( equalish @ ( cross_product @ ( domain_of @ ( domain_of @ Xf ) ) @ ( domain_of @ ( domain_of @ Xf ) ) ) @ ( domain_of @ Xf ) ) ) )
= $true ),
inference(copy,[status(thm)],[187]) ).
thf(482,plain,
( ( ! [Xf: $i] :
( ~ ( operation @ Xf )
| ( subclass @ ( range_of @ Xf ) @ ( domain_of @ ( domain_of @ Xf ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[186]) ).
thf(483,plain,
( ( ! [Xf: $i] :
( ~ ( function @ Xf )
| ~ ( equalish @ ( cross_product @ ( domain_of @ ( domain_of @ Xf ) ) @ ( domain_of @ ( domain_of @ Xf ) ) ) @ ( domain_of @ Xf ) )
| ~ ( subclass @ ( range_of @ Xf ) @ ( domain_of @ ( domain_of @ Xf ) ) )
| ( operation @ Xf ) ) )
= $true ),
inference(copy,[status(thm)],[185]) ).
thf(484,plain,
( ( ! [Xh: $i,Xf1: $i,Xf2: $i] :
( ~ ( compatible @ Xh @ Xf1 @ Xf2 )
| ( function @ Xh ) ) )
= $true ),
inference(copy,[status(thm)],[184]) ).
thf(485,plain,
( ( ! [Xh: $i,Xf1: $i,Xf2: $i] :
( ~ ( compatible @ Xh @ Xf1 @ Xf2 )
| ( equalish @ ( domain_of @ ( domain_of @ Xf1 ) ) @ ( domain_of @ Xh ) ) ) )
= $true ),
inference(copy,[status(thm)],[183]) ).
thf(486,plain,
( ( ! [Xh: $i,Xf1: $i,Xf2: $i] :
( ~ ( compatible @ Xh @ Xf1 @ Xf2 )
| ( subclass @ ( range_of @ Xh ) @ ( domain_of @ ( domain_of @ Xf2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[182]) ).
thf(487,plain,
( ( ! [Xh: $i,Xf1: $i,Xf2: $i,Xh1: $i] :
( ~ ( function @ Xh )
| ~ ( equalish @ ( domain_of @ ( domain_of @ Xf1 ) ) @ ( domain_of @ Xh ) )
| ~ ( subclass @ ( range_of @ Xh ) @ ( domain_of @ ( domain_of @ Xf2 ) ) )
| ( compatible @ Xh1 @ Xf1 @ Xf2 ) ) )
= $true ),
inference(copy,[status(thm)],[181]) ).
thf(488,plain,
( ( ! [Xh: $i,Xf1: $i,Xf2: $i] :
( ~ ( homomorphism @ Xh @ Xf1 @ Xf2 )
| ( operation @ Xf1 ) ) )
= $true ),
inference(copy,[status(thm)],[180]) ).
thf(489,plain,
( ( ! [Xh: $i,Xf1: $i,Xf2: $i] :
( ~ ( homomorphism @ Xh @ Xf1 @ Xf2 )
| ( operation @ Xf2 ) ) )
= $true ),
inference(copy,[status(thm)],[179]) ).
thf(490,plain,
( ( ! [Xh: $i,Xf1: $i,Xf2: $i] :
( ~ ( homomorphism @ Xh @ Xf1 @ Xf2 )
| ( compatible @ Xh @ Xf1 @ Xf2 ) ) )
= $true ),
inference(copy,[status(thm)],[178]) ).
thf(491,plain,
( ( ! [Xh: $i,Xf1: $i,Xf2: $i,X: $i,Y: $i] :
( ~ ( homomorphism @ Xh @ Xf1 @ Xf2 )
| ~ ( member @ ( ordered_pair @ X @ Y ) @ ( domain_of @ Xf1 ) )
| ( equalish @ ( apply @ Xf2 @ ( ordered_pair @ ( apply @ Xh @ X ) @ ( apply @ Xh @ Y ) ) ) @ ( apply @ Xh @ ( apply @ Xf1 @ ( ordered_pair @ X @ Y ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[177]) ).
thf(492,plain,
( ( ! [Xf1: $i,Xf2: $i,Xh: $i] :
( ~ ( operation @ Xf1 )
| ~ ( operation @ Xf2 )
| ~ ( compatible @ Xh @ Xf1 @ Xf2 )
| ( member @ ( ordered_pair @ ( not_homomorphism1 @ Xh @ Xf1 @ Xf2 ) @ ( not_homomorphism2 @ Xh @ Xf1 @ Xf2 ) ) @ ( domain_of @ Xf1 ) )
| ( homomorphism @ Xh @ Xf1 @ Xf2 ) ) )
= $true ),
inference(copy,[status(thm)],[176]) ).
thf(493,plain,
( ( ! [Xf1: $i,Xf2: $i,Xh: $i] :
( ~ ( operation @ Xf1 )
| ~ ( operation @ Xf2 )
| ~ ( compatible @ Xh @ Xf1 @ Xf2 )
| ~ ( equalish @ ( apply @ Xf2 @ ( ordered_pair @ ( apply @ Xh @ ( not_homomorphism1 @ Xh @ Xf1 @ Xf2 ) ) @ ( apply @ Xh @ ( not_homomorphism2 @ Xh @ Xf1 @ Xf2 ) ) ) ) @ ( apply @ Xh @ ( apply @ Xf1 @ ( ordered_pair @ ( not_homomorphism1 @ Xh @ Xf1 @ Xf2 ) @ ( not_homomorphism2 @ Xh @ Xf1 @ Xf2 ) ) ) ) )
| ( homomorphism @ Xh @ Xf1 @ Xf2 ) ) )
= $true ),
inference(copy,[status(thm)],[175]) ).
thf(494,plain,
( ( ! [X: $i,Y: $i,U: $i,V: $i] :
( ~ ( member @ ( ordered_pair @ X @ Y ) @ ( cross_product @ U @ V ) )
| ( member @ X @ ( unordered_pair @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[174]) ).
thf(495,plain,
( ( ! [X: $i,Y: $i,U: $i,V: $i] :
( ~ ( member @ ( ordered_pair @ X @ Y ) @ ( cross_product @ U @ V ) )
| ( member @ Y @ ( unordered_pair @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[173]) ).
thf(496,plain,
( ( ! [U: $i,V: $i,X: $i,Y: $i] :
( ~ ( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) )
| ( member @ U @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[172]) ).
thf(497,plain,
( ( ! [U: $i,V: $i,X: $i,Y: $i] :
( ~ ( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) )
| ( member @ V @ universal_class ) ) )
= $true ),
inference(copy,[status(thm)],[171]) ).
thf(498,plain,
( ( ! [X: $i] : ( subclass @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[170]) ).
thf(499,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( subclass @ X @ Y )
| ~ ( subclass @ Y @ Z )
| ( subclass @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[169]) ).
thf(500,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[334]) ).
thf(501,plain,
( ( equalish @ x @ x )
= $false ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(502,plain,
! [SV1: $i] :
( ( ! [SY398: $i] :
( ~ ( equalish @ SV1 @ SY398 )
| ( equalish @ SY398 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(503,plain,
! [SV2: $i] :
( ( ! [SY399: $i,SY400: $i] :
( ~ ( equalish @ SV2 @ SY399 )
| ~ ( equalish @ SY399 @ SY400 )
| ( equalish @ SV2 @ SY400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(504,plain,
! [SV3: $i] :
( ( ! [SY401: $i,SY402: $i] :
( ~ ( equalish @ SV3 @ SY401 )
| ( equalish @ ( apply @ SV3 @ SY402 ) @ ( apply @ SY401 @ SY402 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(505,plain,
! [SV4: $i] :
( ( ! [SY403: $i,SY404: $i] :
( ~ ( equalish @ SV4 @ SY403 )
| ( equalish @ ( apply @ SY404 @ SV4 ) @ ( apply @ SY404 @ SY403 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(506,plain,
! [SV5: $i] :
( ( ! [SY405: $i] :
( ~ ( equalish @ SV5 @ SY405 )
| ( equalish @ ( cantor @ SV5 ) @ ( cantor @ SY405 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(507,plain,
! [SV6: $i] :
( ( ! [SY406: $i] :
( ~ ( equalish @ SV6 @ SY406 )
| ( equalish @ ( complement @ SV6 ) @ ( complement @ SY406 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(508,plain,
! [SV7: $i] :
( ( ! [SY407: $i,SY408: $i] :
( ~ ( equalish @ SV7 @ SY407 )
| ( equalish @ ( compose @ SV7 @ SY408 ) @ ( compose @ SY407 @ SY408 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(509,plain,
! [SV8: $i] :
( ( ! [SY409: $i,SY410: $i] :
( ~ ( equalish @ SV8 @ SY409 )
| ( equalish @ ( compose @ SY410 @ SV8 ) @ ( compose @ SY410 @ SY409 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(510,plain,
! [SV9: $i] :
( ( ! [SY411: $i,SY412: $i] :
( ~ ( equalish @ SV9 @ SY411 )
| ( equalish @ ( cross_product @ SV9 @ SY412 ) @ ( cross_product @ SY411 @ SY412 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(511,plain,
! [SV10: $i] :
( ( ! [SY413: $i,SY414: $i] :
( ~ ( equalish @ SV10 @ SY413 )
| ( equalish @ ( cross_product @ SY414 @ SV10 ) @ ( cross_product @ SY414 @ SY413 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(512,plain,
! [SV11: $i] :
( ( ! [SY415: $i] :
( ~ ( equalish @ SV11 @ SY415 )
| ( equalish @ ( diagonalise @ SV11 ) @ ( diagonalise @ SY415 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(513,plain,
! [SV12: $i] :
( ( ! [SY416: $i,SY417: $i] :
( ~ ( equalish @ SV12 @ SY416 )
| ( equalish @ ( symmetric_difference @ SV12 @ SY417 ) @ ( symmetric_difference @ SY416 @ SY417 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(514,plain,
! [SV13: $i] :
( ( ! [SY418: $i,SY419: $i] :
( ~ ( equalish @ SV13 @ SY418 )
| ( equalish @ ( symmetric_difference @ SY419 @ SV13 ) @ ( symmetric_difference @ SY419 @ SY418 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(515,plain,
! [SV14: $i] :
( ( ! [SY420: $i,SY421: $i,SY422: $i] :
( ~ ( equalish @ SV14 @ SY420 )
| ( equalish @ ( domain @ SV14 @ SY421 @ SY422 ) @ ( domain @ SY420 @ SY421 @ SY422 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(516,plain,
! [SV15: $i] :
( ( ! [SY423: $i,SY424: $i,SY425: $i] :
( ~ ( equalish @ SV15 @ SY423 )
| ( equalish @ ( domain @ SY424 @ SV15 @ SY425 ) @ ( domain @ SY424 @ SY423 @ SY425 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(517,plain,
! [SV16: $i] :
( ( ! [SY426: $i,SY427: $i,SY428: $i] :
( ~ ( equalish @ SV16 @ SY426 )
| ( equalish @ ( domain @ SY427 @ SY428 @ SV16 ) @ ( domain @ SY427 @ SY428 @ SY426 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(518,plain,
! [SV17: $i] :
( ( ! [SY429: $i] :
( ~ ( equalish @ SV17 @ SY429 )
| ( equalish @ ( domain_of @ SV17 ) @ ( domain_of @ SY429 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(519,plain,
! [SV18: $i] :
( ( ! [SY430: $i] :
( ~ ( equalish @ SV18 @ SY430 )
| ( equalish @ ( first @ SV18 ) @ ( first @ SY430 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(520,plain,
! [SV19: $i] :
( ( ! [SY431: $i] :
( ~ ( equalish @ SV19 @ SY431 )
| ( equalish @ ( flip @ SV19 ) @ ( flip @ SY431 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(521,plain,
! [SV20: $i] :
( ( ! [SY432: $i,SY433: $i] :
( ~ ( equalish @ SV20 @ SY432 )
| ( equalish @ ( image @ SV20 @ SY433 ) @ ( image @ SY432 @ SY433 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(522,plain,
! [SV21: $i] :
( ( ! [SY434: $i,SY435: $i] :
( ~ ( equalish @ SV21 @ SY434 )
| ( equalish @ ( image @ SY435 @ SV21 ) @ ( image @ SY435 @ SY434 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(523,plain,
! [SV22: $i] :
( ( ! [SY436: $i,SY437: $i] :
( ~ ( equalish @ SV22 @ SY436 )
| ( equalish @ ( intersection @ SV22 @ SY437 ) @ ( intersection @ SY436 @ SY437 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[357]) ).
thf(524,plain,
! [SV23: $i] :
( ( ! [SY438: $i,SY439: $i] :
( ~ ( equalish @ SV23 @ SY438 )
| ( equalish @ ( intersection @ SY439 @ SV23 ) @ ( intersection @ SY439 @ SY438 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(525,plain,
! [SV24: $i] :
( ( ! [SY440: $i] :
( ~ ( equalish @ SV24 @ SY440 )
| ( equalish @ ( inverse @ SV24 ) @ ( inverse @ SY440 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(526,plain,
! [SV25: $i] :
( ( ! [SY441: $i,SY442: $i,SY443: $i] :
( ~ ( equalish @ SV25 @ SY441 )
| ( equalish @ ( not_homomorphism1 @ SV25 @ SY442 @ SY443 ) @ ( not_homomorphism1 @ SY441 @ SY442 @ SY443 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(527,plain,
! [SV26: $i] :
( ( ! [SY444: $i,SY445: $i,SY446: $i] :
( ~ ( equalish @ SV26 @ SY444 )
| ( equalish @ ( not_homomorphism1 @ SY445 @ SV26 @ SY446 ) @ ( not_homomorphism1 @ SY445 @ SY444 @ SY446 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(528,plain,
! [SV27: $i] :
( ( ! [SY447: $i,SY448: $i,SY449: $i] :
( ~ ( equalish @ SV27 @ SY447 )
| ( equalish @ ( not_homomorphism1 @ SY448 @ SY449 @ SV27 ) @ ( not_homomorphism1 @ SY448 @ SY449 @ SY447 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(529,plain,
! [SV28: $i] :
( ( ! [SY450: $i,SY451: $i,SY452: $i] :
( ~ ( equalish @ SV28 @ SY450 )
| ( equalish @ ( not_homomorphism2 @ SV28 @ SY451 @ SY452 ) @ ( not_homomorphism2 @ SY450 @ SY451 @ SY452 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(530,plain,
! [SV29: $i] :
( ( ! [SY453: $i,SY454: $i,SY455: $i] :
( ~ ( equalish @ SV29 @ SY453 )
| ( equalish @ ( not_homomorphism2 @ SY454 @ SV29 @ SY455 ) @ ( not_homomorphism2 @ SY454 @ SY453 @ SY455 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(531,plain,
! [SV30: $i] :
( ( ! [SY456: $i,SY457: $i,SY458: $i] :
( ~ ( equalish @ SV30 @ SY456 )
| ( equalish @ ( not_homomorphism2 @ SY457 @ SY458 @ SV30 ) @ ( not_homomorphism2 @ SY457 @ SY458 @ SY456 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(532,plain,
! [SV31: $i] :
( ( ! [SY459: $i,SY460: $i] :
( ~ ( equalish @ SV31 @ SY459 )
| ( equalish @ ( not_subclass_element @ SV31 @ SY460 ) @ ( not_subclass_element @ SY459 @ SY460 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(533,plain,
! [SV32: $i] :
( ( ! [SY461: $i,SY462: $i] :
( ~ ( equalish @ SV32 @ SY461 )
| ( equalish @ ( not_subclass_element @ SY462 @ SV32 ) @ ( not_subclass_element @ SY462 @ SY461 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(534,plain,
! [SV33: $i] :
( ( ! [SY463: $i,SY464: $i] :
( ~ ( equalish @ SV33 @ SY463 )
| ( equalish @ ( ordered_pair @ SV33 @ SY464 ) @ ( ordered_pair @ SY463 @ SY464 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(535,plain,
! [SV34: $i] :
( ( ! [SY465: $i,SY466: $i] :
( ~ ( equalish @ SV34 @ SY465 )
| ( equalish @ ( ordered_pair @ SY466 @ SV34 ) @ ( ordered_pair @ SY466 @ SY465 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(536,plain,
! [SV35: $i] :
( ( ! [SY467: $i] :
( ~ ( equalish @ SV35 @ SY467 )
| ( equalish @ ( power_class @ SV35 ) @ ( power_class @ SY467 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(537,plain,
! [SV36: $i] :
( ( ! [SY468: $i,SY469: $i,SY470: $i] :
( ~ ( equalish @ SV36 @ SY468 )
| ( equalish @ ( range @ SV36 @ SY469 @ SY470 ) @ ( range @ SY468 @ SY469 @ SY470 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(538,plain,
! [SV37: $i] :
( ( ! [SY471: $i,SY472: $i,SY473: $i] :
( ~ ( equalish @ SV37 @ SY471 )
| ( equalish @ ( range @ SY472 @ SV37 @ SY473 ) @ ( range @ SY472 @ SY471 @ SY473 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(539,plain,
! [SV38: $i] :
( ( ! [SY474: $i,SY475: $i,SY476: $i] :
( ~ ( equalish @ SV38 @ SY474 )
| ( equalish @ ( range @ SY475 @ SY476 @ SV38 ) @ ( range @ SY475 @ SY476 @ SY474 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(540,plain,
! [SV39: $i] :
( ( ! [SY477: $i] :
( ~ ( equalish @ SV39 @ SY477 )
| ( equalish @ ( range_of @ SV39 ) @ ( range_of @ SY477 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(541,plain,
! [SV40: $i] :
( ( ! [SY478: $i] :
( ~ ( equalish @ SV40 @ SY478 )
| ( equalish @ ( regular @ SV40 ) @ ( regular @ SY478 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(542,plain,
! [SV41: $i] :
( ( ! [SY479: $i,SY480: $i,SY481: $i] :
( ~ ( equalish @ SV41 @ SY479 )
| ( equalish @ ( restrict @ SV41 @ SY480 @ SY481 ) @ ( restrict @ SY479 @ SY480 @ SY481 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(543,plain,
! [SV42: $i] :
( ( ! [SY482: $i,SY483: $i,SY484: $i] :
( ~ ( equalish @ SV42 @ SY482 )
| ( equalish @ ( restrict @ SY483 @ SV42 @ SY484 ) @ ( restrict @ SY483 @ SY482 @ SY484 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(544,plain,
! [SV43: $i] :
( ( ! [SY485: $i,SY486: $i,SY487: $i] :
( ~ ( equalish @ SV43 @ SY485 )
| ( equalish @ ( restrict @ SY486 @ SY487 @ SV43 ) @ ( restrict @ SY486 @ SY487 @ SY485 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(545,plain,
! [SV44: $i] :
( ( ! [SY488: $i] :
( ~ ( equalish @ SV44 @ SY488 )
| ( equalish @ ( rotate @ SV44 ) @ ( rotate @ SY488 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(546,plain,
! [SV45: $i] :
( ( ! [SY489: $i] :
( ~ ( equalish @ SV45 @ SY489 )
| ( equalish @ ( second @ SV45 ) @ ( second @ SY489 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(547,plain,
! [SV46: $i] :
( ( ! [SY490: $i] :
( ~ ( equalish @ SV46 @ SY490 )
| ( equalish @ ( singleton @ SV46 ) @ ( singleton @ SY490 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(548,plain,
! [SV47: $i] :
( ( ! [SY491: $i] :
( ~ ( equalish @ SV47 @ SY491 )
| ( equalish @ ( successor @ SV47 ) @ ( successor @ SY491 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(549,plain,
! [SV48: $i] :
( ( ! [SY492: $i] :
( ~ ( equalish @ SV48 @ SY492 )
| ( equalish @ ( sum_class @ SV48 ) @ ( sum_class @ SY492 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(550,plain,
! [SV49: $i] :
( ( ! [SY493: $i,SY494: $i] :
( ~ ( equalish @ SV49 @ SY493 )
| ( equalish @ ( union @ SV49 @ SY494 ) @ ( union @ SY493 @ SY494 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(551,plain,
! [SV50: $i] :
( ( ! [SY495: $i,SY496: $i] :
( ~ ( equalish @ SV50 @ SY495 )
| ( equalish @ ( union @ SY496 @ SV50 ) @ ( union @ SY496 @ SY495 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(552,plain,
! [SV51: $i] :
( ( ! [SY497: $i,SY498: $i] :
( ~ ( equalish @ SV51 @ SY497 )
| ( equalish @ ( unordered_pair @ SV51 @ SY498 ) @ ( unordered_pair @ SY497 @ SY498 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(553,plain,
! [SV52: $i] :
( ( ! [SY499: $i,SY500: $i] :
( ~ ( equalish @ SV52 @ SY499 )
| ( equalish @ ( unordered_pair @ SY500 @ SV52 ) @ ( unordered_pair @ SY500 @ SY499 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(554,plain,
! [SV53: $i] :
( ( ! [SY501: $i,SY502: $i,SY503: $i] :
( ~ ( equalish @ SV53 @ SY501 )
| ~ ( compatible @ SV53 @ SY502 @ SY503 )
| ( compatible @ SY501 @ SY502 @ SY503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(555,plain,
! [SV54: $i] :
( ( ! [SY504: $i,SY505: $i,SY506: $i] :
( ~ ( equalish @ SV54 @ SY504 )
| ~ ( compatible @ SY505 @ SV54 @ SY506 )
| ( compatible @ SY505 @ SY504 @ SY506 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(556,plain,
! [SV55: $i] :
( ( ! [SY507: $i,SY508: $i,SY509: $i] :
( ~ ( equalish @ SV55 @ SY507 )
| ~ ( compatible @ SY508 @ SY509 @ SV55 )
| ( compatible @ SY508 @ SY509 @ SY507 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(557,plain,
! [SV56: $i] :
( ( ! [SY510: $i] :
( ~ ( equalish @ SV56 @ SY510 )
| ~ ( function @ SV56 )
| ( function @ SY510 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(558,plain,
! [SV57: $i] :
( ( ! [SY511: $i,SY512: $i,SY513: $i] :
( ~ ( equalish @ SV57 @ SY511 )
| ~ ( homomorphism @ SV57 @ SY512 @ SY513 )
| ( homomorphism @ SY511 @ SY512 @ SY513 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(559,plain,
! [SV58: $i] :
( ( ! [SY514: $i,SY515: $i,SY516: $i] :
( ~ ( equalish @ SV58 @ SY514 )
| ~ ( homomorphism @ SY515 @ SV58 @ SY516 )
| ( homomorphism @ SY515 @ SY514 @ SY516 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(560,plain,
! [SV59: $i] :
( ( ! [SY517: $i,SY518: $i,SY519: $i] :
( ~ ( equalish @ SV59 @ SY517 )
| ~ ( homomorphism @ SY518 @ SY519 @ SV59 )
| ( homomorphism @ SY518 @ SY519 @ SY517 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(561,plain,
! [SV60: $i] :
( ( ! [SY520: $i] :
( ~ ( equalish @ SV60 @ SY520 )
| ~ ( inductive @ SV60 )
| ( inductive @ SY520 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(562,plain,
! [SV61: $i] :
( ( ! [SY521: $i,SY522: $i] :
( ~ ( equalish @ SV61 @ SY521 )
| ~ ( member @ SV61 @ SY522 )
| ( member @ SY521 @ SY522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(563,plain,
! [SV62: $i] :
( ( ! [SY523: $i,SY524: $i] :
( ~ ( equalish @ SV62 @ SY523 )
| ~ ( member @ SY524 @ SV62 )
| ( member @ SY524 @ SY523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(564,plain,
! [SV63: $i] :
( ( ! [SY525: $i] :
( ~ ( equalish @ SV63 @ SY525 )
| ~ ( one_to_one @ SV63 )
| ( one_to_one @ SY525 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(565,plain,
! [SV64: $i] :
( ( ! [SY526: $i] :
( ~ ( equalish @ SV64 @ SY526 )
| ~ ( operation @ SV64 )
| ( operation @ SY526 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(566,plain,
! [SV65: $i] :
( ( ! [SY527: $i] :
( ~ ( equalish @ SV65 @ SY527 )
| ~ ( single_valued_class @ SV65 )
| ( single_valued_class @ SY527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(567,plain,
! [SV66: $i] :
( ( ! [SY528: $i,SY529: $i] :
( ~ ( equalish @ SV66 @ SY528 )
| ~ ( subclass @ SV66 @ SY529 )
| ( subclass @ SY528 @ SY529 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(568,plain,
! [SV67: $i] :
( ( ! [SY530: $i,SY531: $i] :
( ~ ( equalish @ SV67 @ SY530 )
| ~ ( subclass @ SY531 @ SV67 )
| ( subclass @ SY531 @ SY530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(569,plain,
! [SV68: $i] :
( ( ! [SY532: $i,SY533: $i] :
( ~ ( subclass @ SV68 @ SY532 )
| ~ ( member @ SY533 @ SV68 )
| ( member @ SY533 @ SY532 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(570,plain,
! [SV69: $i] :
( ( ! [SY534: $i] :
( ( member @ ( not_subclass_element @ SV69 @ SY534 ) @ SV69 )
| ( subclass @ SV69 @ SY534 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(571,plain,
! [SV70: $i] :
( ( ! [SY535: $i] :
( ~ ( member @ ( not_subclass_element @ SV70 @ SY535 ) @ SY535 )
| ( subclass @ SV70 @ SY535 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(572,plain,
! [SV71: $i] :
( ( subclass @ SV71 @ universal_class )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(573,plain,
! [SV72: $i] :
( ( ! [SY536: $i] :
( ~ ( equalish @ SV72 @ SY536 )
| ( subclass @ SV72 @ SY536 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(574,plain,
! [SV73: $i] :
( ( ! [SY537: $i] :
( ~ ( equalish @ SV73 @ SY537 )
| ( subclass @ SY537 @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(575,plain,
! [SV74: $i] :
( ( ! [SY538: $i] :
( ~ ( subclass @ SV74 @ SY538 )
| ~ ( subclass @ SY538 @ SV74 )
| ( equalish @ SV74 @ SY538 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(576,plain,
! [SV75: $i] :
( ( ! [SY539: $i,SY540: $i] :
( ~ ( member @ SV75 @ ( unordered_pair @ SY539 @ SY540 ) )
| ( equalish @ SV75 @ SY539 )
| ( equalish @ SV75 @ SY540 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(577,plain,
! [SV76: $i] :
( ( ! [SY541: $i] :
( ~ ( member @ SV76 @ universal_class )
| ( member @ SV76 @ ( unordered_pair @ SV76 @ SY541 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(578,plain,
! [SV77: $i] :
( ( ! [SY542: $i] :
( ~ ( member @ SV77 @ universal_class )
| ( member @ SV77 @ ( unordered_pair @ SY542 @ SV77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(579,plain,
! [SV78: $i] :
( ( ! [SY543: $i] : ( member @ ( unordered_pair @ SV78 @ SY543 ) @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(580,plain,
! [SV79: $i] :
( ( equalish @ ( unordered_pair @ SV79 @ SV79 ) @ ( singleton @ SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(581,plain,
! [SV80: $i] :
( ( ! [SY544: $i] : ( equalish @ ( unordered_pair @ ( singleton @ SV80 ) @ ( unordered_pair @ SV80 @ ( singleton @ SY544 ) ) ) @ ( ordered_pair @ SV80 @ SY544 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(582,plain,
! [SV81: $i] :
( ( ! [SY545: $i,SY546: $i,SY547: $i] :
( ~ ( member @ ( ordered_pair @ SV81 @ SY545 ) @ ( cross_product @ SY546 @ SY547 ) )
| ( member @ SV81 @ SY546 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(583,plain,
! [SV82: $i] :
( ( ! [SY548: $i,SY549: $i,SY550: $i] :
( ~ ( member @ ( ordered_pair @ SV82 @ SY548 ) @ ( cross_product @ SY549 @ SY550 ) )
| ( member @ SY548 @ SY550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(584,plain,
! [SV83: $i] :
( ( ! [SY551: $i,SY552: $i,SY553: $i] :
( ~ ( member @ SV83 @ SY551 )
| ~ ( member @ SY552 @ SY553 )
| ( member @ ( ordered_pair @ SV83 @ SY552 ) @ ( cross_product @ SY551 @ SY553 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(585,plain,
! [SV84: $i] :
( ( ! [SY554: $i,SY555: $i] :
( ~ ( member @ SV84 @ ( cross_product @ SY554 @ SY555 ) )
| ( equalish @ ( ordered_pair @ ( first @ SV84 ) @ ( second @ SV84 ) ) @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(586,plain,
! [SV85: $i] :
( ( ! [SY556: $i] :
( ~ ( member @ ( ordered_pair @ SV85 @ SY556 ) @ element_relation )
| ( member @ SV85 @ SY556 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(587,plain,
! [SV86: $i] :
( ( ! [SY557: $i] :
( ~ ( member @ ( ordered_pair @ SV86 @ SY557 ) @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( member @ SV86 @ SY557 )
| ( member @ ( ordered_pair @ SV86 @ SY557 ) @ element_relation ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(588,plain,
! [SV87: $i] :
( ( ! [SY558: $i,SY559: $i] :
( ~ ( member @ SV87 @ ( intersection @ SY558 @ SY559 ) )
| ( member @ SV87 @ SY558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(589,plain,
! [SV88: $i] :
( ( ! [SY560: $i,SY561: $i] :
( ~ ( member @ SV88 @ ( intersection @ SY560 @ SY561 ) )
| ( member @ SV88 @ SY561 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(590,plain,
! [SV89: $i] :
( ( ! [SY562: $i,SY563: $i] :
( ~ ( member @ SV89 @ SY562 )
| ~ ( member @ SV89 @ SY563 )
| ( member @ SV89 @ ( intersection @ SY562 @ SY563 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(591,plain,
! [SV90: $i] :
( ( ! [SY564: $i] :
( ~ ( member @ SV90 @ ( complement @ SY564 ) )
| ~ ( member @ SV90 @ SY564 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(592,plain,
! [SV91: $i] :
( ( ! [SY565: $i] :
( ~ ( member @ SV91 @ universal_class )
| ( member @ SV91 @ ( complement @ SY565 ) )
| ( member @ SV91 @ SY565 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(593,plain,
! [SV92: $i] :
( ( ! [SY566: $i] : ( equalish @ ( complement @ ( intersection @ ( complement @ SV92 ) @ ( complement @ SY566 ) ) ) @ ( union @ SV92 @ SY566 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(594,plain,
! [SV93: $i] :
( ( ! [SY567: $i] : ( equalish @ ( intersection @ ( complement @ ( intersection @ SV93 @ SY567 ) ) @ ( complement @ ( intersection @ ( complement @ SV93 ) @ ( complement @ SY567 ) ) ) ) @ ( symmetric_difference @ SV93 @ SY567 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(595,plain,
! [SV94: $i] :
( ( ! [SY568: $i,SY569: $i] : ( equalish @ ( intersection @ SV94 @ ( cross_product @ SY568 @ SY569 ) ) @ ( restrict @ SV94 @ SY568 @ SY569 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(596,plain,
! [SV95: $i] :
( ( ! [SY570: $i,SY571: $i] : ( equalish @ ( intersection @ ( cross_product @ SV95 @ SY570 ) @ SY571 ) @ ( restrict @ SY571 @ SV95 @ SY570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(597,plain,
! [SV96: $i] :
( ( ! [SY572: $i] :
( ~ ( equalish @ ( restrict @ SV96 @ ( singleton @ SY572 ) @ universal_class ) @ null_class )
| ~ ( member @ SY572 @ ( domain_of @ SV96 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(598,plain,
! [SV97: $i] :
( ( ! [SY573: $i] :
( ~ ( member @ SV97 @ universal_class )
| ( equalish @ ( restrict @ SY573 @ ( singleton @ SV97 ) @ universal_class ) @ null_class )
| ( member @ SV97 @ ( domain_of @ SY573 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(599,plain,
! [SV98: $i] :
( ( subclass @ ( rotate @ SV98 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(600,plain,
! [SV99: $i] :
( ( ! [SY574: $i,SY575: $i,SY576: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV99 @ SY574 ) @ SY575 ) @ ( rotate @ SY576 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SY574 @ SY575 ) @ SV99 ) @ SY576 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(601,plain,
! [SV100: $i] :
( ( ! [SY577: $i,SY578: $i,SY579: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV100 @ SY577 ) @ SY578 ) @ SY579 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SY578 @ SV100 ) @ SY577 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SY578 @ SV100 ) @ SY577 ) @ ( rotate @ SY579 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(602,plain,
! [SV101: $i] :
( ( subclass @ ( flip @ SV101 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(603,plain,
! [SV102: $i] :
( ( ! [SY580: $i,SY581: $i,SY582: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV102 @ SY580 ) @ SY581 ) @ ( flip @ SY582 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SY580 @ SV102 ) @ SY581 ) @ SY582 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(604,plain,
! [SV103: $i] :
( ( ! [SY583: $i,SY584: $i,SY585: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV103 @ SY583 ) @ SY584 ) @ SY585 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SY583 @ SV103 ) @ SY584 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SY583 @ SV103 ) @ SY584 ) @ ( flip @ SY585 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(605,plain,
! [SV104: $i] :
( ( equalish @ ( domain_of @ ( flip @ ( cross_product @ SV104 @ universal_class ) ) ) @ ( inverse @ SV104 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(606,plain,
! [SV105: $i] :
( ( equalish @ ( domain_of @ ( inverse @ SV105 ) ) @ ( range_of @ SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(607,plain,
! [SV106: $i] :
( ( ! [SY586: $i,SY587: $i] : ( equalish @ ( first @ ( not_subclass_element @ ( restrict @ SV106 @ SY586 @ ( singleton @ SY587 ) ) @ null_class ) ) @ ( domain @ SV106 @ SY586 @ SY587 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(608,plain,
! [SV107: $i] :
( ( ! [SY588: $i,SY589: $i] : ( equalish @ ( second @ ( not_subclass_element @ ( restrict @ SV107 @ ( singleton @ SY588 ) @ SY589 ) @ null_class ) ) @ ( range @ SV107 @ SY588 @ SY589 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(609,plain,
! [SV108: $i] :
( ( ! [SY590: $i] : ( equalish @ ( range_of @ ( restrict @ SV108 @ SY590 @ universal_class ) ) @ ( image @ SV108 @ SY590 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(610,plain,
! [SV109: $i] :
( ( equalish @ ( union @ SV109 @ ( singleton @ SV109 ) ) @ ( successor @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(611,plain,
! [SV110: $i] :
( ( ! [SY591: $i] :
( ~ ( member @ ( ordered_pair @ SV110 @ SY591 ) @ successor_relation )
| ( equalish @ ( successor @ SV110 ) @ SY591 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(612,plain,
! [SV111: $i] :
( ( ! [SY592: $i] :
( ~ ( equalish @ ( successor @ SV111 ) @ SY592 )
| ~ ( member @ ( ordered_pair @ SV111 @ SY592 ) @ ( cross_product @ universal_class @ universal_class ) )
| ( member @ ( ordered_pair @ SV111 @ SY592 ) @ successor_relation ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(613,plain,
! [SV112: $i] :
( ( ~ ( inductive @ SV112 )
| ( member @ null_class @ SV112 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(614,plain,
! [SV113: $i] :
( ( ~ ( inductive @ SV113 )
| ( subclass @ ( image @ successor_relation @ SV113 ) @ SV113 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(615,plain,
! [SV114: $i] :
( ( ~ ( member @ null_class @ SV114 )
| ~ ( subclass @ ( image @ successor_relation @ SV114 ) @ SV114 )
| ( inductive @ SV114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(616,plain,
! [SV115: $i] :
( ( ~ ( inductive @ SV115 )
| ( subclass @ omega @ SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(617,plain,
! [SV116: $i] :
( ( equalish @ ( domain_of @ ( restrict @ element_relation @ universal_class @ SV116 ) ) @ ( sum_class @ SV116 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(618,plain,
! [SV117: $i] :
( ( ~ ( member @ SV117 @ universal_class )
| ( member @ ( sum_class @ SV117 ) @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(619,plain,
! [SV118: $i] :
( ( equalish @ ( complement @ ( image @ element_relation @ ( complement @ SV118 ) ) ) @ ( power_class @ SV118 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(620,plain,
! [SV119: $i] :
( ( ~ ( member @ SV119 @ universal_class )
| ( member @ ( power_class @ SV119 ) @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(621,plain,
! [SV120: $i] :
( ( ! [SY593: $i] : ( subclass @ ( compose @ SV120 @ SY593 ) @ ( cross_product @ universal_class @ universal_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(622,plain,
! [SV121: $i] :
( ( ! [SY594: $i,SY595: $i,SY596: $i] :
( ~ ( member @ ( ordered_pair @ SV121 @ SY594 ) @ ( compose @ SY595 @ SY596 ) )
| ( member @ SY594 @ ( image @ SY595 @ ( image @ SY596 @ ( singleton @ SV121 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(623,plain,
! [SV122: $i] :
( ( ! [SY597: $i,SY598: $i,SY599: $i] :
( ~ ( member @ SV122 @ ( image @ SY597 @ ( image @ SY598 @ ( singleton @ SY599 ) ) ) )
| ~ ( member @ ( ordered_pair @ SY599 @ SV122 ) @ ( cross_product @ universal_class @ universal_class ) )
| ( member @ ( ordered_pair @ SY599 @ SV122 ) @ ( compose @ SY597 @ SY598 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(624,plain,
! [SV123: $i] :
( ( ~ ( single_valued_class @ SV123 )
| ( subclass @ ( compose @ SV123 @ ( inverse @ SV123 ) ) @ identity_relation ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(625,plain,
! [SV124: $i] :
( ( ~ ( subclass @ ( compose @ SV124 @ ( inverse @ SV124 ) ) @ identity_relation )
| ( single_valued_class @ SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(626,plain,
! [SV125: $i] :
( ( ~ ( function @ SV125 )
| ( subclass @ SV125 @ ( cross_product @ universal_class @ universal_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(627,plain,
! [SV126: $i] :
( ( ~ ( function @ SV126 )
| ( subclass @ ( compose @ SV126 @ ( inverse @ SV126 ) ) @ identity_relation ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(628,plain,
! [SV127: $i] :
( ( ~ ( subclass @ SV127 @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ SV127 @ ( inverse @ SV127 ) ) @ identity_relation )
| ( function @ SV127 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(629,plain,
! [SV128: $i] :
( ( ! [SY600: $i] :
( ~ ( function @ SV128 )
| ~ ( member @ SY600 @ universal_class )
| ( member @ ( image @ SV128 @ SY600 ) @ universal_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(630,plain,
! [SV129: $i] :
( ( ( equalish @ SV129 @ null_class )
| ( member @ ( regular @ SV129 ) @ SV129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(631,plain,
! [SV130: $i] :
( ( ( equalish @ SV130 @ null_class )
| ( equalish @ ( intersection @ SV130 @ ( regular @ SV130 ) ) @ null_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(632,plain,
! [SV131: $i] :
( ( ! [SY601: $i] : ( equalish @ ( sum_class @ ( image @ SV131 @ ( singleton @ SY601 ) ) ) @ ( apply @ SV131 @ SY601 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(633,plain,
! [SV132: $i] :
( ( ~ ( member @ SV132 @ universal_class )
| ( equalish @ SV132 @ null_class )
| ( member @ ( apply @ choice @ SV132 ) @ SV132 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(634,plain,
! [SV133: $i] :
( ( ~ ( one_to_one @ SV133 )
| ( function @ SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(635,plain,
! [SV134: $i] :
( ( ~ ( one_to_one @ SV134 )
| ( function @ ( inverse @ SV134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(636,plain,
! [SV135: $i] :
( ( ~ ( function @ ( inverse @ SV135 ) )
| ~ ( function @ SV135 )
| ( one_to_one @ SV135 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(637,plain,
! [SV136: $i] :
( ( equalish @ ( complement @ ( domain_of @ ( intersection @ SV136 @ identity_relation ) ) ) @ ( diagonalise @ SV136 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(638,plain,
! [SV137: $i] :
( ( equalish @ ( intersection @ ( domain_of @ SV137 ) @ ( diagonalise @ ( compose @ ( inverse @ element_relation ) @ SV137 ) ) ) @ ( cantor @ SV137 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(639,plain,
! [SV138: $i] :
( ( ~ ( operation @ SV138 )
| ( function @ SV138 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(640,plain,
! [SV139: $i] :
( ( ~ ( operation @ SV139 )
| ( equalish @ ( cross_product @ ( domain_of @ ( domain_of @ SV139 ) ) @ ( domain_of @ ( domain_of @ SV139 ) ) ) @ ( domain_of @ SV139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(641,plain,
! [SV140: $i] :
( ( ~ ( operation @ SV140 )
| ( subclass @ ( range_of @ SV140 ) @ ( domain_of @ ( domain_of @ SV140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(642,plain,
! [SV141: $i] :
( ( ~ ( function @ SV141 )
| ~ ( equalish @ ( cross_product @ ( domain_of @ ( domain_of @ SV141 ) ) @ ( domain_of @ ( domain_of @ SV141 ) ) ) @ ( domain_of @ SV141 ) )
| ~ ( subclass @ ( range_of @ SV141 ) @ ( domain_of @ ( domain_of @ SV141 ) ) )
| ( operation @ SV141 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(643,plain,
! [SV142: $i] :
( ( ! [SY602: $i,SY603: $i] :
( ~ ( compatible @ SV142 @ SY602 @ SY603 )
| ( function @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(644,plain,
! [SV143: $i] :
( ( ! [SY604: $i,SY605: $i] :
( ~ ( compatible @ SV143 @ SY604 @ SY605 )
| ( equalish @ ( domain_of @ ( domain_of @ SY604 ) ) @ ( domain_of @ SV143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(645,plain,
! [SV144: $i] :
( ( ! [SY606: $i,SY607: $i] :
( ~ ( compatible @ SV144 @ SY606 @ SY607 )
| ( subclass @ ( range_of @ SV144 ) @ ( domain_of @ ( domain_of @ SY607 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(646,plain,
! [SV145: $i] :
( ( ! [SY608: $i,SY609: $i,SY610: $i] :
( ~ ( function @ SV145 )
| ~ ( equalish @ ( domain_of @ ( domain_of @ SY608 ) ) @ ( domain_of @ SV145 ) )
| ~ ( subclass @ ( range_of @ SV145 ) @ ( domain_of @ ( domain_of @ SY609 ) ) )
| ( compatible @ SY610 @ SY608 @ SY609 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(647,plain,
! [SV146: $i] :
( ( ! [SY611: $i,SY612: $i] :
( ~ ( homomorphism @ SV146 @ SY611 @ SY612 )
| ( operation @ SY611 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(648,plain,
! [SV147: $i] :
( ( ! [SY613: $i,SY614: $i] :
( ~ ( homomorphism @ SV147 @ SY613 @ SY614 )
| ( operation @ SY614 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(649,plain,
! [SV148: $i] :
( ( ! [SY615: $i,SY616: $i] :
( ~ ( homomorphism @ SV148 @ SY615 @ SY616 )
| ( compatible @ SV148 @ SY615 @ SY616 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(650,plain,
! [SV149: $i] :
( ( ! [SY617: $i,SY618: $i,SY619: $i,SY620: $i] :
( ~ ( homomorphism @ SV149 @ SY617 @ SY618 )
| ~ ( member @ ( ordered_pair @ SY619 @ SY620 ) @ ( domain_of @ SY617 ) )
| ( equalish @ ( apply @ SY618 @ ( ordered_pair @ ( apply @ SV149 @ SY619 ) @ ( apply @ SV149 @ SY620 ) ) ) @ ( apply @ SV149 @ ( apply @ SY617 @ ( ordered_pair @ SY619 @ SY620 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(651,plain,
! [SV150: $i] :
( ( ! [SY621: $i,SY622: $i] :
( ~ ( operation @ SV150 )
| ~ ( operation @ SY621 )
| ~ ( compatible @ SY622 @ SV150 @ SY621 )
| ( member @ ( ordered_pair @ ( not_homomorphism1 @ SY622 @ SV150 @ SY621 ) @ ( not_homomorphism2 @ SY622 @ SV150 @ SY621 ) ) @ ( domain_of @ SV150 ) )
| ( homomorphism @ SY622 @ SV150 @ SY621 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(652,plain,
! [SV151: $i] :
( ( ! [SY623: $i,SY624: $i] :
( ~ ( operation @ SV151 )
| ~ ( operation @ SY623 )
| ~ ( compatible @ SY624 @ SV151 @ SY623 )
| ~ ( equalish @ ( apply @ SY623 @ ( ordered_pair @ ( apply @ SY624 @ ( not_homomorphism1 @ SY624 @ SV151 @ SY623 ) ) @ ( apply @ SY624 @ ( not_homomorphism2 @ SY624 @ SV151 @ SY623 ) ) ) ) @ ( apply @ SY624 @ ( apply @ SV151 @ ( ordered_pair @ ( not_homomorphism1 @ SY624 @ SV151 @ SY623 ) @ ( not_homomorphism2 @ SY624 @ SV151 @ SY623 ) ) ) ) )
| ( homomorphism @ SY624 @ SV151 @ SY623 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(653,plain,
! [SV152: $i] :
( ( ! [SY625: $i,SY626: $i,SY627: $i] :
( ~ ( member @ ( ordered_pair @ SV152 @ SY625 ) @ ( cross_product @ SY626 @ SY627 ) )
| ( member @ SV152 @ ( unordered_pair @ SV152 @ SY625 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(654,plain,
! [SV153: $i] :
( ( ! [SY628: $i,SY629: $i,SY630: $i] :
( ~ ( member @ ( ordered_pair @ SV153 @ SY628 ) @ ( cross_product @ SY629 @ SY630 ) )
| ( member @ SY628 @ ( unordered_pair @ SV153 @ SY628 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(655,plain,
! [SV154: $i] :
( ( ! [SY631: $i,SY632: $i,SY633: $i] :
( ~ ( member @ ( ordered_pair @ SV154 @ SY631 ) @ ( cross_product @ SY632 @ SY633 ) )
| ( member @ SV154 @ universal_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(656,plain,
! [SV155: $i] :
( ( ! [SY634: $i,SY635: $i,SY636: $i] :
( ~ ( member @ ( ordered_pair @ SV155 @ SY634 ) @ ( cross_product @ SY635 @ SY636 ) )
| ( member @ SY634 @ universal_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(657,plain,
! [SV156: $i] :
( ( subclass @ SV156 @ SV156 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(658,plain,
! [SV157: $i] :
( ( ! [SY637: $i,SY638: $i] :
( ~ ( subclass @ SV157 @ SY637 )
| ~ ( subclass @ SY637 @ SY638 )
| ( subclass @ SV157 @ SY638 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(659,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(660,plain,
! [SV158: $i,SV1: $i] :
( ( ~ ( equalish @ SV1 @ SV158 )
| ( equalish @ SV158 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(661,plain,
! [SV159: $i,SV2: $i] :
( ( ! [SY639: $i] :
( ~ ( equalish @ SV2 @ SV159 )
| ~ ( equalish @ SV159 @ SY639 )
| ( equalish @ SV2 @ SY639 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(662,plain,
! [SV160: $i,SV3: $i] :
( ( ! [SY640: $i] :
( ~ ( equalish @ SV3 @ SV160 )
| ( equalish @ ( apply @ SV3 @ SY640 ) @ ( apply @ SV160 @ SY640 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(663,plain,
! [SV161: $i,SV4: $i] :
( ( ! [SY641: $i] :
( ~ ( equalish @ SV4 @ SV161 )
| ( equalish @ ( apply @ SY641 @ SV4 ) @ ( apply @ SY641 @ SV161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(664,plain,
! [SV162: $i,SV5: $i] :
( ( ~ ( equalish @ SV5 @ SV162 )
| ( equalish @ ( cantor @ SV5 ) @ ( cantor @ SV162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(665,plain,
! [SV163: $i,SV6: $i] :
( ( ~ ( equalish @ SV6 @ SV163 )
| ( equalish @ ( complement @ SV6 ) @ ( complement @ SV163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(666,plain,
! [SV164: $i,SV7: $i] :
( ( ! [SY642: $i] :
( ~ ( equalish @ SV7 @ SV164 )
| ( equalish @ ( compose @ SV7 @ SY642 ) @ ( compose @ SV164 @ SY642 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(667,plain,
! [SV165: $i,SV8: $i] :
( ( ! [SY643: $i] :
( ~ ( equalish @ SV8 @ SV165 )
| ( equalish @ ( compose @ SY643 @ SV8 ) @ ( compose @ SY643 @ SV165 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(668,plain,
! [SV166: $i,SV9: $i] :
( ( ! [SY644: $i] :
( ~ ( equalish @ SV9 @ SV166 )
| ( equalish @ ( cross_product @ SV9 @ SY644 ) @ ( cross_product @ SV166 @ SY644 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(669,plain,
! [SV167: $i,SV10: $i] :
( ( ! [SY645: $i] :
( ~ ( equalish @ SV10 @ SV167 )
| ( equalish @ ( cross_product @ SY645 @ SV10 ) @ ( cross_product @ SY645 @ SV167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(670,plain,
! [SV168: $i,SV11: $i] :
( ( ~ ( equalish @ SV11 @ SV168 )
| ( equalish @ ( diagonalise @ SV11 ) @ ( diagonalise @ SV168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(671,plain,
! [SV169: $i,SV12: $i] :
( ( ! [SY646: $i] :
( ~ ( equalish @ SV12 @ SV169 )
| ( equalish @ ( symmetric_difference @ SV12 @ SY646 ) @ ( symmetric_difference @ SV169 @ SY646 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(672,plain,
! [SV170: $i,SV13: $i] :
( ( ! [SY647: $i] :
( ~ ( equalish @ SV13 @ SV170 )
| ( equalish @ ( symmetric_difference @ SY647 @ SV13 ) @ ( symmetric_difference @ SY647 @ SV170 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(673,plain,
! [SV171: $i,SV14: $i] :
( ( ! [SY648: $i,SY649: $i] :
( ~ ( equalish @ SV14 @ SV171 )
| ( equalish @ ( domain @ SV14 @ SY648 @ SY649 ) @ ( domain @ SV171 @ SY648 @ SY649 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(674,plain,
! [SV172: $i,SV15: $i] :
( ( ! [SY650: $i,SY651: $i] :
( ~ ( equalish @ SV15 @ SV172 )
| ( equalish @ ( domain @ SY650 @ SV15 @ SY651 ) @ ( domain @ SY650 @ SV172 @ SY651 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(675,plain,
! [SV173: $i,SV16: $i] :
( ( ! [SY652: $i,SY653: $i] :
( ~ ( equalish @ SV16 @ SV173 )
| ( equalish @ ( domain @ SY652 @ SY653 @ SV16 ) @ ( domain @ SY652 @ SY653 @ SV173 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(676,plain,
! [SV174: $i,SV17: $i] :
( ( ~ ( equalish @ SV17 @ SV174 )
| ( equalish @ ( domain_of @ SV17 ) @ ( domain_of @ SV174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(677,plain,
! [SV175: $i,SV18: $i] :
( ( ~ ( equalish @ SV18 @ SV175 )
| ( equalish @ ( first @ SV18 ) @ ( first @ SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(678,plain,
! [SV176: $i,SV19: $i] :
( ( ~ ( equalish @ SV19 @ SV176 )
| ( equalish @ ( flip @ SV19 ) @ ( flip @ SV176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(679,plain,
! [SV177: $i,SV20: $i] :
( ( ! [SY654: $i] :
( ~ ( equalish @ SV20 @ SV177 )
| ( equalish @ ( image @ SV20 @ SY654 ) @ ( image @ SV177 @ SY654 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(680,plain,
! [SV178: $i,SV21: $i] :
( ( ! [SY655: $i] :
( ~ ( equalish @ SV21 @ SV178 )
| ( equalish @ ( image @ SY655 @ SV21 ) @ ( image @ SY655 @ SV178 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(681,plain,
! [SV179: $i,SV22: $i] :
( ( ! [SY656: $i] :
( ~ ( equalish @ SV22 @ SV179 )
| ( equalish @ ( intersection @ SV22 @ SY656 ) @ ( intersection @ SV179 @ SY656 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(682,plain,
! [SV180: $i,SV23: $i] :
( ( ! [SY657: $i] :
( ~ ( equalish @ SV23 @ SV180 )
| ( equalish @ ( intersection @ SY657 @ SV23 ) @ ( intersection @ SY657 @ SV180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(683,plain,
! [SV181: $i,SV24: $i] :
( ( ~ ( equalish @ SV24 @ SV181 )
| ( equalish @ ( inverse @ SV24 ) @ ( inverse @ SV181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(684,plain,
! [SV182: $i,SV25: $i] :
( ( ! [SY658: $i,SY659: $i] :
( ~ ( equalish @ SV25 @ SV182 )
| ( equalish @ ( not_homomorphism1 @ SV25 @ SY658 @ SY659 ) @ ( not_homomorphism1 @ SV182 @ SY658 @ SY659 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(685,plain,
! [SV183: $i,SV26: $i] :
( ( ! [SY660: $i,SY661: $i] :
( ~ ( equalish @ SV26 @ SV183 )
| ( equalish @ ( not_homomorphism1 @ SY660 @ SV26 @ SY661 ) @ ( not_homomorphism1 @ SY660 @ SV183 @ SY661 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(686,plain,
! [SV184: $i,SV27: $i] :
( ( ! [SY662: $i,SY663: $i] :
( ~ ( equalish @ SV27 @ SV184 )
| ( equalish @ ( not_homomorphism1 @ SY662 @ SY663 @ SV27 ) @ ( not_homomorphism1 @ SY662 @ SY663 @ SV184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(687,plain,
! [SV185: $i,SV28: $i] :
( ( ! [SY664: $i,SY665: $i] :
( ~ ( equalish @ SV28 @ SV185 )
| ( equalish @ ( not_homomorphism2 @ SV28 @ SY664 @ SY665 ) @ ( not_homomorphism2 @ SV185 @ SY664 @ SY665 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(688,plain,
! [SV186: $i,SV29: $i] :
( ( ! [SY666: $i,SY667: $i] :
( ~ ( equalish @ SV29 @ SV186 )
| ( equalish @ ( not_homomorphism2 @ SY666 @ SV29 @ SY667 ) @ ( not_homomorphism2 @ SY666 @ SV186 @ SY667 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(689,plain,
! [SV187: $i,SV30: $i] :
( ( ! [SY668: $i,SY669: $i] :
( ~ ( equalish @ SV30 @ SV187 )
| ( equalish @ ( not_homomorphism2 @ SY668 @ SY669 @ SV30 ) @ ( not_homomorphism2 @ SY668 @ SY669 @ SV187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(690,plain,
! [SV188: $i,SV31: $i] :
( ( ! [SY670: $i] :
( ~ ( equalish @ SV31 @ SV188 )
| ( equalish @ ( not_subclass_element @ SV31 @ SY670 ) @ ( not_subclass_element @ SV188 @ SY670 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(691,plain,
! [SV189: $i,SV32: $i] :
( ( ! [SY671: $i] :
( ~ ( equalish @ SV32 @ SV189 )
| ( equalish @ ( not_subclass_element @ SY671 @ SV32 ) @ ( not_subclass_element @ SY671 @ SV189 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(692,plain,
! [SV190: $i,SV33: $i] :
( ( ! [SY672: $i] :
( ~ ( equalish @ SV33 @ SV190 )
| ( equalish @ ( ordered_pair @ SV33 @ SY672 ) @ ( ordered_pair @ SV190 @ SY672 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(693,plain,
! [SV191: $i,SV34: $i] :
( ( ! [SY673: $i] :
( ~ ( equalish @ SV34 @ SV191 )
| ( equalish @ ( ordered_pair @ SY673 @ SV34 ) @ ( ordered_pair @ SY673 @ SV191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(694,plain,
! [SV192: $i,SV35: $i] :
( ( ~ ( equalish @ SV35 @ SV192 )
| ( equalish @ ( power_class @ SV35 ) @ ( power_class @ SV192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(695,plain,
! [SV193: $i,SV36: $i] :
( ( ! [SY674: $i,SY675: $i] :
( ~ ( equalish @ SV36 @ SV193 )
| ( equalish @ ( range @ SV36 @ SY674 @ SY675 ) @ ( range @ SV193 @ SY674 @ SY675 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(696,plain,
! [SV194: $i,SV37: $i] :
( ( ! [SY676: $i,SY677: $i] :
( ~ ( equalish @ SV37 @ SV194 )
| ( equalish @ ( range @ SY676 @ SV37 @ SY677 ) @ ( range @ SY676 @ SV194 @ SY677 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(697,plain,
! [SV195: $i,SV38: $i] :
( ( ! [SY678: $i,SY679: $i] :
( ~ ( equalish @ SV38 @ SV195 )
| ( equalish @ ( range @ SY678 @ SY679 @ SV38 ) @ ( range @ SY678 @ SY679 @ SV195 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(698,plain,
! [SV196: $i,SV39: $i] :
( ( ~ ( equalish @ SV39 @ SV196 )
| ( equalish @ ( range_of @ SV39 ) @ ( range_of @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(699,plain,
! [SV197: $i,SV40: $i] :
( ( ~ ( equalish @ SV40 @ SV197 )
| ( equalish @ ( regular @ SV40 ) @ ( regular @ SV197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(700,plain,
! [SV198: $i,SV41: $i] :
( ( ! [SY680: $i,SY681: $i] :
( ~ ( equalish @ SV41 @ SV198 )
| ( equalish @ ( restrict @ SV41 @ SY680 @ SY681 ) @ ( restrict @ SV198 @ SY680 @ SY681 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(701,plain,
! [SV199: $i,SV42: $i] :
( ( ! [SY682: $i,SY683: $i] :
( ~ ( equalish @ SV42 @ SV199 )
| ( equalish @ ( restrict @ SY682 @ SV42 @ SY683 ) @ ( restrict @ SY682 @ SV199 @ SY683 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(702,plain,
! [SV200: $i,SV43: $i] :
( ( ! [SY684: $i,SY685: $i] :
( ~ ( equalish @ SV43 @ SV200 )
| ( equalish @ ( restrict @ SY684 @ SY685 @ SV43 ) @ ( restrict @ SY684 @ SY685 @ SV200 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(703,plain,
! [SV201: $i,SV44: $i] :
( ( ~ ( equalish @ SV44 @ SV201 )
| ( equalish @ ( rotate @ SV44 ) @ ( rotate @ SV201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(704,plain,
! [SV202: $i,SV45: $i] :
( ( ~ ( equalish @ SV45 @ SV202 )
| ( equalish @ ( second @ SV45 ) @ ( second @ SV202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(705,plain,
! [SV203: $i,SV46: $i] :
( ( ~ ( equalish @ SV46 @ SV203 )
| ( equalish @ ( singleton @ SV46 ) @ ( singleton @ SV203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(706,plain,
! [SV204: $i,SV47: $i] :
( ( ~ ( equalish @ SV47 @ SV204 )
| ( equalish @ ( successor @ SV47 ) @ ( successor @ SV204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(707,plain,
! [SV205: $i,SV48: $i] :
( ( ~ ( equalish @ SV48 @ SV205 )
| ( equalish @ ( sum_class @ SV48 ) @ ( sum_class @ SV205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(708,plain,
! [SV206: $i,SV49: $i] :
( ( ! [SY686: $i] :
( ~ ( equalish @ SV49 @ SV206 )
| ( equalish @ ( union @ SV49 @ SY686 ) @ ( union @ SV206 @ SY686 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(709,plain,
! [SV207: $i,SV50: $i] :
( ( ! [SY687: $i] :
( ~ ( equalish @ SV50 @ SV207 )
| ( equalish @ ( union @ SY687 @ SV50 ) @ ( union @ SY687 @ SV207 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(710,plain,
! [SV208: $i,SV51: $i] :
( ( ! [SY688: $i] :
( ~ ( equalish @ SV51 @ SV208 )
| ( equalish @ ( unordered_pair @ SV51 @ SY688 ) @ ( unordered_pair @ SV208 @ SY688 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(711,plain,
! [SV209: $i,SV52: $i] :
( ( ! [SY689: $i] :
( ~ ( equalish @ SV52 @ SV209 )
| ( equalish @ ( unordered_pair @ SY689 @ SV52 ) @ ( unordered_pair @ SY689 @ SV209 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(712,plain,
! [SV210: $i,SV53: $i] :
( ( ! [SY690: $i,SY691: $i] :
( ~ ( equalish @ SV53 @ SV210 )
| ~ ( compatible @ SV53 @ SY690 @ SY691 )
| ( compatible @ SV210 @ SY690 @ SY691 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(713,plain,
! [SV211: $i,SV54: $i] :
( ( ! [SY692: $i,SY693: $i] :
( ~ ( equalish @ SV54 @ SV211 )
| ~ ( compatible @ SY692 @ SV54 @ SY693 )
| ( compatible @ SY692 @ SV211 @ SY693 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(714,plain,
! [SV212: $i,SV55: $i] :
( ( ! [SY694: $i,SY695: $i] :
( ~ ( equalish @ SV55 @ SV212 )
| ~ ( compatible @ SY694 @ SY695 @ SV55 )
| ( compatible @ SY694 @ SY695 @ SV212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(715,plain,
! [SV213: $i,SV56: $i] :
( ( ~ ( equalish @ SV56 @ SV213 )
| ~ ( function @ SV56 )
| ( function @ SV213 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(716,plain,
! [SV214: $i,SV57: $i] :
( ( ! [SY696: $i,SY697: $i] :
( ~ ( equalish @ SV57 @ SV214 )
| ~ ( homomorphism @ SV57 @ SY696 @ SY697 )
| ( homomorphism @ SV214 @ SY696 @ SY697 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(717,plain,
! [SV215: $i,SV58: $i] :
( ( ! [SY698: $i,SY699: $i] :
( ~ ( equalish @ SV58 @ SV215 )
| ~ ( homomorphism @ SY698 @ SV58 @ SY699 )
| ( homomorphism @ SY698 @ SV215 @ SY699 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(718,plain,
! [SV216: $i,SV59: $i] :
( ( ! [SY700: $i,SY701: $i] :
( ~ ( equalish @ SV59 @ SV216 )
| ~ ( homomorphism @ SY700 @ SY701 @ SV59 )
| ( homomorphism @ SY700 @ SY701 @ SV216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(719,plain,
! [SV217: $i,SV60: $i] :
( ( ~ ( equalish @ SV60 @ SV217 )
| ~ ( inductive @ SV60 )
| ( inductive @ SV217 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(720,plain,
! [SV218: $i,SV61: $i] :
( ( ! [SY702: $i] :
( ~ ( equalish @ SV61 @ SV218 )
| ~ ( member @ SV61 @ SY702 )
| ( member @ SV218 @ SY702 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(721,plain,
! [SV219: $i,SV62: $i] :
( ( ! [SY703: $i] :
( ~ ( equalish @ SV62 @ SV219 )
| ~ ( member @ SY703 @ SV62 )
| ( member @ SY703 @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(722,plain,
! [SV220: $i,SV63: $i] :
( ( ~ ( equalish @ SV63 @ SV220 )
| ~ ( one_to_one @ SV63 )
| ( one_to_one @ SV220 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(723,plain,
! [SV221: $i,SV64: $i] :
( ( ~ ( equalish @ SV64 @ SV221 )
| ~ ( operation @ SV64 )
| ( operation @ SV221 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(724,plain,
! [SV222: $i,SV65: $i] :
( ( ~ ( equalish @ SV65 @ SV222 )
| ~ ( single_valued_class @ SV65 )
| ( single_valued_class @ SV222 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(725,plain,
! [SV223: $i,SV66: $i] :
( ( ! [SY704: $i] :
( ~ ( equalish @ SV66 @ SV223 )
| ~ ( subclass @ SV66 @ SY704 )
| ( subclass @ SV223 @ SY704 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(726,plain,
! [SV224: $i,SV67: $i] :
( ( ! [SY705: $i] :
( ~ ( equalish @ SV67 @ SV224 )
| ~ ( subclass @ SY705 @ SV67 )
| ( subclass @ SY705 @ SV224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(727,plain,
! [SV225: $i,SV68: $i] :
( ( ! [SY706: $i] :
( ~ ( subclass @ SV68 @ SV225 )
| ~ ( member @ SY706 @ SV68 )
| ( member @ SY706 @ SV225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(728,plain,
! [SV226: $i,SV69: $i] :
( ( ( member @ ( not_subclass_element @ SV69 @ SV226 ) @ SV69 )
| ( subclass @ SV69 @ SV226 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(729,plain,
! [SV227: $i,SV70: $i] :
( ( ~ ( member @ ( not_subclass_element @ SV70 @ SV227 ) @ SV227 )
| ( subclass @ SV70 @ SV227 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(730,plain,
! [SV228: $i,SV72: $i] :
( ( ~ ( equalish @ SV72 @ SV228 )
| ( subclass @ SV72 @ SV228 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(731,plain,
! [SV229: $i,SV73: $i] :
( ( ~ ( equalish @ SV73 @ SV229 )
| ( subclass @ SV229 @ SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(732,plain,
! [SV230: $i,SV74: $i] :
( ( ~ ( subclass @ SV74 @ SV230 )
| ~ ( subclass @ SV230 @ SV74 )
| ( equalish @ SV74 @ SV230 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(733,plain,
! [SV231: $i,SV75: $i] :
( ( ! [SY707: $i] :
( ~ ( member @ SV75 @ ( unordered_pair @ SV231 @ SY707 ) )
| ( equalish @ SV75 @ SV231 )
| ( equalish @ SV75 @ SY707 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(734,plain,
! [SV232: $i,SV76: $i] :
( ( ~ ( member @ SV76 @ universal_class )
| ( member @ SV76 @ ( unordered_pair @ SV76 @ SV232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(735,plain,
! [SV233: $i,SV77: $i] :
( ( ~ ( member @ SV77 @ universal_class )
| ( member @ SV77 @ ( unordered_pair @ SV233 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(736,plain,
! [SV234: $i,SV78: $i] :
( ( member @ ( unordered_pair @ SV78 @ SV234 ) @ universal_class )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[579]) ).
thf(737,plain,
! [SV235: $i,SV80: $i] :
( ( equalish @ ( unordered_pair @ ( singleton @ SV80 ) @ ( unordered_pair @ SV80 @ ( singleton @ SV235 ) ) ) @ ( ordered_pair @ SV80 @ SV235 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(738,plain,
! [SV236: $i,SV81: $i] :
( ( ! [SY708: $i,SY709: $i] :
( ~ ( member @ ( ordered_pair @ SV81 @ SV236 ) @ ( cross_product @ SY708 @ SY709 ) )
| ( member @ SV81 @ SY708 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(739,plain,
! [SV237: $i,SV82: $i] :
( ( ! [SY710: $i,SY711: $i] :
( ~ ( member @ ( ordered_pair @ SV82 @ SV237 ) @ ( cross_product @ SY710 @ SY711 ) )
| ( member @ SV237 @ SY711 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(740,plain,
! [SV238: $i,SV83: $i] :
( ( ! [SY712: $i,SY713: $i] :
( ~ ( member @ SV83 @ SV238 )
| ~ ( member @ SY712 @ SY713 )
| ( member @ ( ordered_pair @ SV83 @ SY712 ) @ ( cross_product @ SV238 @ SY713 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(741,plain,
! [SV239: $i,SV84: $i] :
( ( ! [SY714: $i] :
( ~ ( member @ SV84 @ ( cross_product @ SV239 @ SY714 ) )
| ( equalish @ ( ordered_pair @ ( first @ SV84 ) @ ( second @ SV84 ) ) @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(742,plain,
! [SV240: $i,SV85: $i] :
( ( ~ ( member @ ( ordered_pair @ SV85 @ SV240 ) @ element_relation )
| ( member @ SV85 @ SV240 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[586]) ).
thf(743,plain,
! [SV241: $i,SV86: $i] :
( ( ~ ( member @ ( ordered_pair @ SV86 @ SV241 ) @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( member @ SV86 @ SV241 )
| ( member @ ( ordered_pair @ SV86 @ SV241 ) @ element_relation ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(744,plain,
! [SV242: $i,SV87: $i] :
( ( ! [SY715: $i] :
( ~ ( member @ SV87 @ ( intersection @ SV242 @ SY715 ) )
| ( member @ SV87 @ SV242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(745,plain,
! [SV243: $i,SV88: $i] :
( ( ! [SY716: $i] :
( ~ ( member @ SV88 @ ( intersection @ SV243 @ SY716 ) )
| ( member @ SV88 @ SY716 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(746,plain,
! [SV244: $i,SV89: $i] :
( ( ! [SY717: $i] :
( ~ ( member @ SV89 @ SV244 )
| ~ ( member @ SV89 @ SY717 )
| ( member @ SV89 @ ( intersection @ SV244 @ SY717 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(747,plain,
! [SV245: $i,SV90: $i] :
( ( ~ ( member @ SV90 @ ( complement @ SV245 ) )
| ~ ( member @ SV90 @ SV245 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(748,plain,
! [SV246: $i,SV91: $i] :
( ( ~ ( member @ SV91 @ universal_class )
| ( member @ SV91 @ ( complement @ SV246 ) )
| ( member @ SV91 @ SV246 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(749,plain,
! [SV247: $i,SV92: $i] :
( ( equalish @ ( complement @ ( intersection @ ( complement @ SV92 ) @ ( complement @ SV247 ) ) ) @ ( union @ SV92 @ SV247 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(750,plain,
! [SV248: $i,SV93: $i] :
( ( equalish @ ( intersection @ ( complement @ ( intersection @ SV93 @ SV248 ) ) @ ( complement @ ( intersection @ ( complement @ SV93 ) @ ( complement @ SV248 ) ) ) ) @ ( symmetric_difference @ SV93 @ SV248 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(751,plain,
! [SV249: $i,SV94: $i] :
( ( ! [SY718: $i] : ( equalish @ ( intersection @ SV94 @ ( cross_product @ SV249 @ SY718 ) ) @ ( restrict @ SV94 @ SV249 @ SY718 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(752,plain,
! [SV250: $i,SV95: $i] :
( ( ! [SY719: $i] : ( equalish @ ( intersection @ ( cross_product @ SV95 @ SV250 ) @ SY719 ) @ ( restrict @ SY719 @ SV95 @ SV250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(753,plain,
! [SV251: $i,SV96: $i] :
( ( ~ ( equalish @ ( restrict @ SV96 @ ( singleton @ SV251 ) @ universal_class ) @ null_class )
| ~ ( member @ SV251 @ ( domain_of @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(754,plain,
! [SV252: $i,SV97: $i] :
( ( ~ ( member @ SV97 @ universal_class )
| ( equalish @ ( restrict @ SV252 @ ( singleton @ SV97 ) @ universal_class ) @ null_class )
| ( member @ SV97 @ ( domain_of @ SV252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(755,plain,
! [SV253: $i,SV99: $i] :
( ( ! [SY720: $i,SY721: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV99 @ SV253 ) @ SY720 ) @ ( rotate @ SY721 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV253 @ SY720 ) @ SV99 ) @ SY721 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(756,plain,
! [SV254: $i,SV100: $i] :
( ( ! [SY722: $i,SY723: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV100 @ SV254 ) @ SY722 ) @ SY723 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SY722 @ SV100 ) @ SV254 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SY722 @ SV100 ) @ SV254 ) @ ( rotate @ SY723 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(757,plain,
! [SV255: $i,SV102: $i] :
( ( ! [SY724: $i,SY725: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV102 @ SV255 ) @ SY724 ) @ ( flip @ SY725 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV255 @ SV102 ) @ SY724 ) @ SY725 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(758,plain,
! [SV256: $i,SV103: $i] :
( ( ! [SY726: $i,SY727: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV103 @ SV256 ) @ SY726 ) @ SY727 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV256 @ SV103 ) @ SY726 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV256 @ SV103 ) @ SY726 ) @ ( flip @ SY727 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(759,plain,
! [SV257: $i,SV106: $i] :
( ( ! [SY728: $i] : ( equalish @ ( first @ ( not_subclass_element @ ( restrict @ SV106 @ SV257 @ ( singleton @ SY728 ) ) @ null_class ) ) @ ( domain @ SV106 @ SV257 @ SY728 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(760,plain,
! [SV258: $i,SV107: $i] :
( ( ! [SY729: $i] : ( equalish @ ( second @ ( not_subclass_element @ ( restrict @ SV107 @ ( singleton @ SV258 ) @ SY729 ) @ null_class ) ) @ ( range @ SV107 @ SV258 @ SY729 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(761,plain,
! [SV259: $i,SV108: $i] :
( ( equalish @ ( range_of @ ( restrict @ SV108 @ SV259 @ universal_class ) ) @ ( image @ SV108 @ SV259 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(762,plain,
! [SV260: $i,SV110: $i] :
( ( ~ ( member @ ( ordered_pair @ SV110 @ SV260 ) @ successor_relation )
| ( equalish @ ( successor @ SV110 ) @ SV260 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(763,plain,
! [SV261: $i,SV111: $i] :
( ( ~ ( equalish @ ( successor @ SV111 ) @ SV261 )
| ~ ( member @ ( ordered_pair @ SV111 @ SV261 ) @ ( cross_product @ universal_class @ universal_class ) )
| ( member @ ( ordered_pair @ SV111 @ SV261 ) @ successor_relation ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(764,plain,
! [SV112: $i] :
( ( ( ~ ( inductive @ SV112 ) )
= $true )
| ( ( member @ null_class @ SV112 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[613]) ).
thf(765,plain,
! [SV113: $i] :
( ( ( ~ ( inductive @ SV113 ) )
= $true )
| ( ( subclass @ ( image @ successor_relation @ SV113 ) @ SV113 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[614]) ).
thf(766,plain,
! [SV114: $i] :
( ( ( ~ ( member @ null_class @ SV114 ) )
= $true )
| ( ( ~ ( subclass @ ( image @ successor_relation @ SV114 ) @ SV114 )
| ( inductive @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[615]) ).
thf(767,plain,
! [SV115: $i] :
( ( ( ~ ( inductive @ SV115 ) )
= $true )
| ( ( subclass @ omega @ SV115 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[616]) ).
thf(768,plain,
! [SV117: $i] :
( ( ( ~ ( member @ SV117 @ universal_class ) )
= $true )
| ( ( member @ ( sum_class @ SV117 ) @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[618]) ).
thf(769,plain,
! [SV119: $i] :
( ( ( ~ ( member @ SV119 @ universal_class ) )
= $true )
| ( ( member @ ( power_class @ SV119 ) @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[620]) ).
thf(770,plain,
! [SV262: $i,SV120: $i] :
( ( subclass @ ( compose @ SV120 @ SV262 ) @ ( cross_product @ universal_class @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(771,plain,
! [SV263: $i,SV121: $i] :
( ( ! [SY730: $i,SY731: $i] :
( ~ ( member @ ( ordered_pair @ SV121 @ SV263 ) @ ( compose @ SY730 @ SY731 ) )
| ( member @ SV263 @ ( image @ SY730 @ ( image @ SY731 @ ( singleton @ SV121 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(772,plain,
! [SV264: $i,SV122: $i] :
( ( ! [SY732: $i,SY733: $i] :
( ~ ( member @ SV122 @ ( image @ SV264 @ ( image @ SY732 @ ( singleton @ SY733 ) ) ) )
| ~ ( member @ ( ordered_pair @ SY733 @ SV122 ) @ ( cross_product @ universal_class @ universal_class ) )
| ( member @ ( ordered_pair @ SY733 @ SV122 ) @ ( compose @ SV264 @ SY732 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(773,plain,
! [SV123: $i] :
( ( ( ~ ( single_valued_class @ SV123 ) )
= $true )
| ( ( subclass @ ( compose @ SV123 @ ( inverse @ SV123 ) ) @ identity_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[624]) ).
thf(774,plain,
! [SV124: $i] :
( ( ( ~ ( subclass @ ( compose @ SV124 @ ( inverse @ SV124 ) ) @ identity_relation ) )
= $true )
| ( ( single_valued_class @ SV124 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[625]) ).
thf(775,plain,
! [SV125: $i] :
( ( ( ~ ( function @ SV125 ) )
= $true )
| ( ( subclass @ SV125 @ ( cross_product @ universal_class @ universal_class ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[626]) ).
thf(776,plain,
! [SV126: $i] :
( ( ( ~ ( function @ SV126 ) )
= $true )
| ( ( subclass @ ( compose @ SV126 @ ( inverse @ SV126 ) ) @ identity_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[627]) ).
thf(777,plain,
! [SV127: $i] :
( ( ( ~ ( subclass @ SV127 @ ( cross_product @ universal_class @ universal_class ) ) )
= $true )
| ( ( ~ ( subclass @ ( compose @ SV127 @ ( inverse @ SV127 ) ) @ identity_relation )
| ( function @ SV127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[628]) ).
thf(778,plain,
! [SV265: $i,SV128: $i] :
( ( ~ ( function @ SV128 )
| ~ ( member @ SV265 @ universal_class )
| ( member @ ( image @ SV128 @ SV265 ) @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(779,plain,
! [SV129: $i] :
( ( ( equalish @ SV129 @ null_class )
= $true )
| ( ( member @ ( regular @ SV129 ) @ SV129 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[630]) ).
thf(780,plain,
! [SV130: $i] :
( ( ( equalish @ SV130 @ null_class )
= $true )
| ( ( equalish @ ( intersection @ SV130 @ ( regular @ SV130 ) ) @ null_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[631]) ).
thf(781,plain,
! [SV266: $i,SV131: $i] :
( ( equalish @ ( sum_class @ ( image @ SV131 @ ( singleton @ SV266 ) ) ) @ ( apply @ SV131 @ SV266 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(782,plain,
! [SV132: $i] :
( ( ( ~ ( member @ SV132 @ universal_class ) )
= $true )
| ( ( ( equalish @ SV132 @ null_class )
| ( member @ ( apply @ choice @ SV132 ) @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[633]) ).
thf(783,plain,
! [SV133: $i] :
( ( ( ~ ( one_to_one @ SV133 ) )
= $true )
| ( ( function @ SV133 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[634]) ).
thf(784,plain,
! [SV134: $i] :
( ( ( ~ ( one_to_one @ SV134 ) )
= $true )
| ( ( function @ ( inverse @ SV134 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[635]) ).
thf(785,plain,
! [SV135: $i] :
( ( ( ~ ( function @ ( inverse @ SV135 ) ) )
= $true )
| ( ( ~ ( function @ SV135 )
| ( one_to_one @ SV135 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[636]) ).
thf(786,plain,
! [SV138: $i] :
( ( ( ~ ( operation @ SV138 ) )
= $true )
| ( ( function @ SV138 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[639]) ).
thf(787,plain,
! [SV139: $i] :
( ( ( ~ ( operation @ SV139 ) )
= $true )
| ( ( equalish @ ( cross_product @ ( domain_of @ ( domain_of @ SV139 ) ) @ ( domain_of @ ( domain_of @ SV139 ) ) ) @ ( domain_of @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[640]) ).
thf(788,plain,
! [SV140: $i] :
( ( ( ~ ( operation @ SV140 ) )
= $true )
| ( ( subclass @ ( range_of @ SV140 ) @ ( domain_of @ ( domain_of @ SV140 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[641]) ).
thf(789,plain,
! [SV141: $i] :
( ( ( ~ ( function @ SV141 ) )
= $true )
| ( ( ~ ( equalish @ ( cross_product @ ( domain_of @ ( domain_of @ SV141 ) ) @ ( domain_of @ ( domain_of @ SV141 ) ) ) @ ( domain_of @ SV141 ) )
| ~ ( subclass @ ( range_of @ SV141 ) @ ( domain_of @ ( domain_of @ SV141 ) ) )
| ( operation @ SV141 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[642]) ).
thf(790,plain,
! [SV267: $i,SV142: $i] :
( ( ! [SY734: $i] :
( ~ ( compatible @ SV142 @ SV267 @ SY734 )
| ( function @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(791,plain,
! [SV268: $i,SV143: $i] :
( ( ! [SY735: $i] :
( ~ ( compatible @ SV143 @ SV268 @ SY735 )
| ( equalish @ ( domain_of @ ( domain_of @ SV268 ) ) @ ( domain_of @ SV143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(792,plain,
! [SV269: $i,SV144: $i] :
( ( ! [SY736: $i] :
( ~ ( compatible @ SV144 @ SV269 @ SY736 )
| ( subclass @ ( range_of @ SV144 ) @ ( domain_of @ ( domain_of @ SY736 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(793,plain,
! [SV270: $i,SV145: $i] :
( ( ! [SY737: $i,SY738: $i] :
( ~ ( function @ SV145 )
| ~ ( equalish @ ( domain_of @ ( domain_of @ SV270 ) ) @ ( domain_of @ SV145 ) )
| ~ ( subclass @ ( range_of @ SV145 ) @ ( domain_of @ ( domain_of @ SY737 ) ) )
| ( compatible @ SY738 @ SV270 @ SY737 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(794,plain,
! [SV271: $i,SV146: $i] :
( ( ! [SY739: $i] :
( ~ ( homomorphism @ SV146 @ SV271 @ SY739 )
| ( operation @ SV271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(795,plain,
! [SV272: $i,SV147: $i] :
( ( ! [SY740: $i] :
( ~ ( homomorphism @ SV147 @ SV272 @ SY740 )
| ( operation @ SY740 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(796,plain,
! [SV273: $i,SV148: $i] :
( ( ! [SY741: $i] :
( ~ ( homomorphism @ SV148 @ SV273 @ SY741 )
| ( compatible @ SV148 @ SV273 @ SY741 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(797,plain,
! [SV274: $i,SV149: $i] :
( ( ! [SY742: $i,SY743: $i,SY744: $i] :
( ~ ( homomorphism @ SV149 @ SV274 @ SY742 )
| ~ ( member @ ( ordered_pair @ SY743 @ SY744 ) @ ( domain_of @ SV274 ) )
| ( equalish @ ( apply @ SY742 @ ( ordered_pair @ ( apply @ SV149 @ SY743 ) @ ( apply @ SV149 @ SY744 ) ) ) @ ( apply @ SV149 @ ( apply @ SV274 @ ( ordered_pair @ SY743 @ SY744 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(798,plain,
! [SV275: $i,SV150: $i] :
( ( ! [SY745: $i] :
( ~ ( operation @ SV150 )
| ~ ( operation @ SV275 )
| ~ ( compatible @ SY745 @ SV150 @ SV275 )
| ( member @ ( ordered_pair @ ( not_homomorphism1 @ SY745 @ SV150 @ SV275 ) @ ( not_homomorphism2 @ SY745 @ SV150 @ SV275 ) ) @ ( domain_of @ SV150 ) )
| ( homomorphism @ SY745 @ SV150 @ SV275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(799,plain,
! [SV276: $i,SV151: $i] :
( ( ! [SY746: $i] :
( ~ ( operation @ SV151 )
| ~ ( operation @ SV276 )
| ~ ( compatible @ SY746 @ SV151 @ SV276 )
| ~ ( equalish @ ( apply @ SV276 @ ( ordered_pair @ ( apply @ SY746 @ ( not_homomorphism1 @ SY746 @ SV151 @ SV276 ) ) @ ( apply @ SY746 @ ( not_homomorphism2 @ SY746 @ SV151 @ SV276 ) ) ) ) @ ( apply @ SY746 @ ( apply @ SV151 @ ( ordered_pair @ ( not_homomorphism1 @ SY746 @ SV151 @ SV276 ) @ ( not_homomorphism2 @ SY746 @ SV151 @ SV276 ) ) ) ) )
| ( homomorphism @ SY746 @ SV151 @ SV276 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(800,plain,
! [SV277: $i,SV152: $i] :
( ( ! [SY747: $i,SY748: $i] :
( ~ ( member @ ( ordered_pair @ SV152 @ SV277 ) @ ( cross_product @ SY747 @ SY748 ) )
| ( member @ SV152 @ ( unordered_pair @ SV152 @ SV277 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(801,plain,
! [SV278: $i,SV153: $i] :
( ( ! [SY749: $i,SY750: $i] :
( ~ ( member @ ( ordered_pair @ SV153 @ SV278 ) @ ( cross_product @ SY749 @ SY750 ) )
| ( member @ SV278 @ ( unordered_pair @ SV153 @ SV278 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(802,plain,
! [SV279: $i,SV154: $i] :
( ( ! [SY751: $i,SY752: $i] :
( ~ ( member @ ( ordered_pair @ SV154 @ SV279 ) @ ( cross_product @ SY751 @ SY752 ) )
| ( member @ SV154 @ universal_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(803,plain,
! [SV280: $i,SV155: $i] :
( ( ! [SY753: $i,SY754: $i] :
( ~ ( member @ ( ordered_pair @ SV155 @ SV280 ) @ ( cross_product @ SY753 @ SY754 ) )
| ( member @ SV280 @ universal_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(804,plain,
! [SV281: $i,SV157: $i] :
( ( ! [SY755: $i] :
( ~ ( subclass @ SV157 @ SV281 )
| ~ ( subclass @ SV281 @ SY755 )
| ( subclass @ SV157 @ SY755 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(805,plain,
! [SV158: $i,SV1: $i] :
( ( ( ~ ( equalish @ SV1 @ SV158 ) )
= $true )
| ( ( equalish @ SV158 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[660]) ).
thf(806,plain,
! [SV282: $i,SV159: $i,SV2: $i] :
( ( ~ ( equalish @ SV2 @ SV159 )
| ~ ( equalish @ SV159 @ SV282 )
| ( equalish @ SV2 @ SV282 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(807,plain,
! [SV283: $i,SV160: $i,SV3: $i] :
( ( ~ ( equalish @ SV3 @ SV160 )
| ( equalish @ ( apply @ SV3 @ SV283 ) @ ( apply @ SV160 @ SV283 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(808,plain,
! [SV284: $i,SV161: $i,SV4: $i] :
( ( ~ ( equalish @ SV4 @ SV161 )
| ( equalish @ ( apply @ SV284 @ SV4 ) @ ( apply @ SV284 @ SV161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(809,plain,
! [SV162: $i,SV5: $i] :
( ( ( ~ ( equalish @ SV5 @ SV162 ) )
= $true )
| ( ( equalish @ ( cantor @ SV5 ) @ ( cantor @ SV162 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[664]) ).
thf(810,plain,
! [SV163: $i,SV6: $i] :
( ( ( ~ ( equalish @ SV6 @ SV163 ) )
= $true )
| ( ( equalish @ ( complement @ SV6 ) @ ( complement @ SV163 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[665]) ).
thf(811,plain,
! [SV285: $i,SV164: $i,SV7: $i] :
( ( ~ ( equalish @ SV7 @ SV164 )
| ( equalish @ ( compose @ SV7 @ SV285 ) @ ( compose @ SV164 @ SV285 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(812,plain,
! [SV286: $i,SV165: $i,SV8: $i] :
( ( ~ ( equalish @ SV8 @ SV165 )
| ( equalish @ ( compose @ SV286 @ SV8 ) @ ( compose @ SV286 @ SV165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(813,plain,
! [SV287: $i,SV166: $i,SV9: $i] :
( ( ~ ( equalish @ SV9 @ SV166 )
| ( equalish @ ( cross_product @ SV9 @ SV287 ) @ ( cross_product @ SV166 @ SV287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(814,plain,
! [SV288: $i,SV167: $i,SV10: $i] :
( ( ~ ( equalish @ SV10 @ SV167 )
| ( equalish @ ( cross_product @ SV288 @ SV10 ) @ ( cross_product @ SV288 @ SV167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(815,plain,
! [SV168: $i,SV11: $i] :
( ( ( ~ ( equalish @ SV11 @ SV168 ) )
= $true )
| ( ( equalish @ ( diagonalise @ SV11 ) @ ( diagonalise @ SV168 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[670]) ).
thf(816,plain,
! [SV289: $i,SV169: $i,SV12: $i] :
( ( ~ ( equalish @ SV12 @ SV169 )
| ( equalish @ ( symmetric_difference @ SV12 @ SV289 ) @ ( symmetric_difference @ SV169 @ SV289 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(817,plain,
! [SV290: $i,SV170: $i,SV13: $i] :
( ( ~ ( equalish @ SV13 @ SV170 )
| ( equalish @ ( symmetric_difference @ SV290 @ SV13 ) @ ( symmetric_difference @ SV290 @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(818,plain,
! [SV291: $i,SV171: $i,SV14: $i] :
( ( ! [SY756: $i] :
( ~ ( equalish @ SV14 @ SV171 )
| ( equalish @ ( domain @ SV14 @ SV291 @ SY756 ) @ ( domain @ SV171 @ SV291 @ SY756 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(819,plain,
! [SV292: $i,SV172: $i,SV15: $i] :
( ( ! [SY757: $i] :
( ~ ( equalish @ SV15 @ SV172 )
| ( equalish @ ( domain @ SV292 @ SV15 @ SY757 ) @ ( domain @ SV292 @ SV172 @ SY757 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(820,plain,
! [SV293: $i,SV173: $i,SV16: $i] :
( ( ! [SY758: $i] :
( ~ ( equalish @ SV16 @ SV173 )
| ( equalish @ ( domain @ SV293 @ SY758 @ SV16 ) @ ( domain @ SV293 @ SY758 @ SV173 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(821,plain,
! [SV174: $i,SV17: $i] :
( ( ( ~ ( equalish @ SV17 @ SV174 ) )
= $true )
| ( ( equalish @ ( domain_of @ SV17 ) @ ( domain_of @ SV174 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[676]) ).
thf(822,plain,
! [SV175: $i,SV18: $i] :
( ( ( ~ ( equalish @ SV18 @ SV175 ) )
= $true )
| ( ( equalish @ ( first @ SV18 ) @ ( first @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[677]) ).
thf(823,plain,
! [SV176: $i,SV19: $i] :
( ( ( ~ ( equalish @ SV19 @ SV176 ) )
= $true )
| ( ( equalish @ ( flip @ SV19 ) @ ( flip @ SV176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[678]) ).
thf(824,plain,
! [SV294: $i,SV177: $i,SV20: $i] :
( ( ~ ( equalish @ SV20 @ SV177 )
| ( equalish @ ( image @ SV20 @ SV294 ) @ ( image @ SV177 @ SV294 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(825,plain,
! [SV295: $i,SV178: $i,SV21: $i] :
( ( ~ ( equalish @ SV21 @ SV178 )
| ( equalish @ ( image @ SV295 @ SV21 ) @ ( image @ SV295 @ SV178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(826,plain,
! [SV296: $i,SV179: $i,SV22: $i] :
( ( ~ ( equalish @ SV22 @ SV179 )
| ( equalish @ ( intersection @ SV22 @ SV296 ) @ ( intersection @ SV179 @ SV296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(827,plain,
! [SV297: $i,SV180: $i,SV23: $i] :
( ( ~ ( equalish @ SV23 @ SV180 )
| ( equalish @ ( intersection @ SV297 @ SV23 ) @ ( intersection @ SV297 @ SV180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(828,plain,
! [SV181: $i,SV24: $i] :
( ( ( ~ ( equalish @ SV24 @ SV181 ) )
= $true )
| ( ( equalish @ ( inverse @ SV24 ) @ ( inverse @ SV181 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[683]) ).
thf(829,plain,
! [SV298: $i,SV182: $i,SV25: $i] :
( ( ! [SY759: $i] :
( ~ ( equalish @ SV25 @ SV182 )
| ( equalish @ ( not_homomorphism1 @ SV25 @ SV298 @ SY759 ) @ ( not_homomorphism1 @ SV182 @ SV298 @ SY759 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(830,plain,
! [SV299: $i,SV183: $i,SV26: $i] :
( ( ! [SY760: $i] :
( ~ ( equalish @ SV26 @ SV183 )
| ( equalish @ ( not_homomorphism1 @ SV299 @ SV26 @ SY760 ) @ ( not_homomorphism1 @ SV299 @ SV183 @ SY760 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(831,plain,
! [SV300: $i,SV184: $i,SV27: $i] :
( ( ! [SY761: $i] :
( ~ ( equalish @ SV27 @ SV184 )
| ( equalish @ ( not_homomorphism1 @ SV300 @ SY761 @ SV27 ) @ ( not_homomorphism1 @ SV300 @ SY761 @ SV184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(832,plain,
! [SV301: $i,SV185: $i,SV28: $i] :
( ( ! [SY762: $i] :
( ~ ( equalish @ SV28 @ SV185 )
| ( equalish @ ( not_homomorphism2 @ SV28 @ SV301 @ SY762 ) @ ( not_homomorphism2 @ SV185 @ SV301 @ SY762 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(833,plain,
! [SV302: $i,SV186: $i,SV29: $i] :
( ( ! [SY763: $i] :
( ~ ( equalish @ SV29 @ SV186 )
| ( equalish @ ( not_homomorphism2 @ SV302 @ SV29 @ SY763 ) @ ( not_homomorphism2 @ SV302 @ SV186 @ SY763 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(834,plain,
! [SV303: $i,SV187: $i,SV30: $i] :
( ( ! [SY764: $i] :
( ~ ( equalish @ SV30 @ SV187 )
| ( equalish @ ( not_homomorphism2 @ SV303 @ SY764 @ SV30 ) @ ( not_homomorphism2 @ SV303 @ SY764 @ SV187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(835,plain,
! [SV304: $i,SV188: $i,SV31: $i] :
( ( ~ ( equalish @ SV31 @ SV188 )
| ( equalish @ ( not_subclass_element @ SV31 @ SV304 ) @ ( not_subclass_element @ SV188 @ SV304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(836,plain,
! [SV305: $i,SV189: $i,SV32: $i] :
( ( ~ ( equalish @ SV32 @ SV189 )
| ( equalish @ ( not_subclass_element @ SV305 @ SV32 ) @ ( not_subclass_element @ SV305 @ SV189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(837,plain,
! [SV306: $i,SV190: $i,SV33: $i] :
( ( ~ ( equalish @ SV33 @ SV190 )
| ( equalish @ ( ordered_pair @ SV33 @ SV306 ) @ ( ordered_pair @ SV190 @ SV306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(838,plain,
! [SV307: $i,SV191: $i,SV34: $i] :
( ( ~ ( equalish @ SV34 @ SV191 )
| ( equalish @ ( ordered_pair @ SV307 @ SV34 ) @ ( ordered_pair @ SV307 @ SV191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(839,plain,
! [SV192: $i,SV35: $i] :
( ( ( ~ ( equalish @ SV35 @ SV192 ) )
= $true )
| ( ( equalish @ ( power_class @ SV35 ) @ ( power_class @ SV192 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[694]) ).
thf(840,plain,
! [SV308: $i,SV193: $i,SV36: $i] :
( ( ! [SY765: $i] :
( ~ ( equalish @ SV36 @ SV193 )
| ( equalish @ ( range @ SV36 @ SV308 @ SY765 ) @ ( range @ SV193 @ SV308 @ SY765 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(841,plain,
! [SV309: $i,SV194: $i,SV37: $i] :
( ( ! [SY766: $i] :
( ~ ( equalish @ SV37 @ SV194 )
| ( equalish @ ( range @ SV309 @ SV37 @ SY766 ) @ ( range @ SV309 @ SV194 @ SY766 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(842,plain,
! [SV310: $i,SV195: $i,SV38: $i] :
( ( ! [SY767: $i] :
( ~ ( equalish @ SV38 @ SV195 )
| ( equalish @ ( range @ SV310 @ SY767 @ SV38 ) @ ( range @ SV310 @ SY767 @ SV195 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(843,plain,
! [SV196: $i,SV39: $i] :
( ( ( ~ ( equalish @ SV39 @ SV196 ) )
= $true )
| ( ( equalish @ ( range_of @ SV39 ) @ ( range_of @ SV196 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[698]) ).
thf(844,plain,
! [SV197: $i,SV40: $i] :
( ( ( ~ ( equalish @ SV40 @ SV197 ) )
= $true )
| ( ( equalish @ ( regular @ SV40 ) @ ( regular @ SV197 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[699]) ).
thf(845,plain,
! [SV311: $i,SV198: $i,SV41: $i] :
( ( ! [SY768: $i] :
( ~ ( equalish @ SV41 @ SV198 )
| ( equalish @ ( restrict @ SV41 @ SV311 @ SY768 ) @ ( restrict @ SV198 @ SV311 @ SY768 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(846,plain,
! [SV312: $i,SV199: $i,SV42: $i] :
( ( ! [SY769: $i] :
( ~ ( equalish @ SV42 @ SV199 )
| ( equalish @ ( restrict @ SV312 @ SV42 @ SY769 ) @ ( restrict @ SV312 @ SV199 @ SY769 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(847,plain,
! [SV313: $i,SV200: $i,SV43: $i] :
( ( ! [SY770: $i] :
( ~ ( equalish @ SV43 @ SV200 )
| ( equalish @ ( restrict @ SV313 @ SY770 @ SV43 ) @ ( restrict @ SV313 @ SY770 @ SV200 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(848,plain,
! [SV201: $i,SV44: $i] :
( ( ( ~ ( equalish @ SV44 @ SV201 ) )
= $true )
| ( ( equalish @ ( rotate @ SV44 ) @ ( rotate @ SV201 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[703]) ).
thf(849,plain,
! [SV202: $i,SV45: $i] :
( ( ( ~ ( equalish @ SV45 @ SV202 ) )
= $true )
| ( ( equalish @ ( second @ SV45 ) @ ( second @ SV202 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[704]) ).
thf(850,plain,
! [SV203: $i,SV46: $i] :
( ( ( ~ ( equalish @ SV46 @ SV203 ) )
= $true )
| ( ( equalish @ ( singleton @ SV46 ) @ ( singleton @ SV203 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[705]) ).
thf(851,plain,
! [SV204: $i,SV47: $i] :
( ( ( ~ ( equalish @ SV47 @ SV204 ) )
= $true )
| ( ( equalish @ ( successor @ SV47 ) @ ( successor @ SV204 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[706]) ).
thf(852,plain,
! [SV205: $i,SV48: $i] :
( ( ( ~ ( equalish @ SV48 @ SV205 ) )
= $true )
| ( ( equalish @ ( sum_class @ SV48 ) @ ( sum_class @ SV205 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[707]) ).
thf(853,plain,
! [SV314: $i,SV206: $i,SV49: $i] :
( ( ~ ( equalish @ SV49 @ SV206 )
| ( equalish @ ( union @ SV49 @ SV314 ) @ ( union @ SV206 @ SV314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(854,plain,
! [SV315: $i,SV207: $i,SV50: $i] :
( ( ~ ( equalish @ SV50 @ SV207 )
| ( equalish @ ( union @ SV315 @ SV50 ) @ ( union @ SV315 @ SV207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(855,plain,
! [SV316: $i,SV208: $i,SV51: $i] :
( ( ~ ( equalish @ SV51 @ SV208 )
| ( equalish @ ( unordered_pair @ SV51 @ SV316 ) @ ( unordered_pair @ SV208 @ SV316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(856,plain,
! [SV317: $i,SV209: $i,SV52: $i] :
( ( ~ ( equalish @ SV52 @ SV209 )
| ( equalish @ ( unordered_pair @ SV317 @ SV52 ) @ ( unordered_pair @ SV317 @ SV209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(857,plain,
! [SV318: $i,SV210: $i,SV53: $i] :
( ( ! [SY771: $i] :
( ~ ( equalish @ SV53 @ SV210 )
| ~ ( compatible @ SV53 @ SV318 @ SY771 )
| ( compatible @ SV210 @ SV318 @ SY771 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(858,plain,
! [SV319: $i,SV211: $i,SV54: $i] :
( ( ! [SY772: $i] :
( ~ ( equalish @ SV54 @ SV211 )
| ~ ( compatible @ SV319 @ SV54 @ SY772 )
| ( compatible @ SV319 @ SV211 @ SY772 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(859,plain,
! [SV320: $i,SV212: $i,SV55: $i] :
( ( ! [SY773: $i] :
( ~ ( equalish @ SV55 @ SV212 )
| ~ ( compatible @ SV320 @ SY773 @ SV55 )
| ( compatible @ SV320 @ SY773 @ SV212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(860,plain,
! [SV213: $i,SV56: $i] :
( ( ( ~ ( equalish @ SV56 @ SV213 ) )
= $true )
| ( ( ~ ( function @ SV56 )
| ( function @ SV213 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[715]) ).
thf(861,plain,
! [SV321: $i,SV214: $i,SV57: $i] :
( ( ! [SY774: $i] :
( ~ ( equalish @ SV57 @ SV214 )
| ~ ( homomorphism @ SV57 @ SV321 @ SY774 )
| ( homomorphism @ SV214 @ SV321 @ SY774 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(862,plain,
! [SV322: $i,SV215: $i,SV58: $i] :
( ( ! [SY775: $i] :
( ~ ( equalish @ SV58 @ SV215 )
| ~ ( homomorphism @ SV322 @ SV58 @ SY775 )
| ( homomorphism @ SV322 @ SV215 @ SY775 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(863,plain,
! [SV323: $i,SV216: $i,SV59: $i] :
( ( ! [SY776: $i] :
( ~ ( equalish @ SV59 @ SV216 )
| ~ ( homomorphism @ SV323 @ SY776 @ SV59 )
| ( homomorphism @ SV323 @ SY776 @ SV216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(864,plain,
! [SV217: $i,SV60: $i] :
( ( ( ~ ( equalish @ SV60 @ SV217 ) )
= $true )
| ( ( ~ ( inductive @ SV60 )
| ( inductive @ SV217 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[719]) ).
thf(865,plain,
! [SV324: $i,SV218: $i,SV61: $i] :
( ( ~ ( equalish @ SV61 @ SV218 )
| ~ ( member @ SV61 @ SV324 )
| ( member @ SV218 @ SV324 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(866,plain,
! [SV325: $i,SV219: $i,SV62: $i] :
( ( ~ ( equalish @ SV62 @ SV219 )
| ~ ( member @ SV325 @ SV62 )
| ( member @ SV325 @ SV219 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(867,plain,
! [SV220: $i,SV63: $i] :
( ( ( ~ ( equalish @ SV63 @ SV220 ) )
= $true )
| ( ( ~ ( one_to_one @ SV63 )
| ( one_to_one @ SV220 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[722]) ).
thf(868,plain,
! [SV221: $i,SV64: $i] :
( ( ( ~ ( equalish @ SV64 @ SV221 ) )
= $true )
| ( ( ~ ( operation @ SV64 )
| ( operation @ SV221 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[723]) ).
thf(869,plain,
! [SV222: $i,SV65: $i] :
( ( ( ~ ( equalish @ SV65 @ SV222 ) )
= $true )
| ( ( ~ ( single_valued_class @ SV65 )
| ( single_valued_class @ SV222 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[724]) ).
thf(870,plain,
! [SV326: $i,SV223: $i,SV66: $i] :
( ( ~ ( equalish @ SV66 @ SV223 )
| ~ ( subclass @ SV66 @ SV326 )
| ( subclass @ SV223 @ SV326 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(871,plain,
! [SV327: $i,SV224: $i,SV67: $i] :
( ( ~ ( equalish @ SV67 @ SV224 )
| ~ ( subclass @ SV327 @ SV67 )
| ( subclass @ SV327 @ SV224 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(872,plain,
! [SV328: $i,SV225: $i,SV68: $i] :
( ( ~ ( subclass @ SV68 @ SV225 )
| ~ ( member @ SV328 @ SV68 )
| ( member @ SV328 @ SV225 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(873,plain,
! [SV226: $i,SV69: $i] :
( ( ( member @ ( not_subclass_element @ SV69 @ SV226 ) @ SV69 )
= $true )
| ( ( subclass @ SV69 @ SV226 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[728]) ).
thf(874,plain,
! [SV227: $i,SV70: $i] :
( ( ( ~ ( member @ ( not_subclass_element @ SV70 @ SV227 ) @ SV227 ) )
= $true )
| ( ( subclass @ SV70 @ SV227 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[729]) ).
thf(875,plain,
! [SV228: $i,SV72: $i] :
( ( ( ~ ( equalish @ SV72 @ SV228 ) )
= $true )
| ( ( subclass @ SV72 @ SV228 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[730]) ).
thf(876,plain,
! [SV229: $i,SV73: $i] :
( ( ( ~ ( equalish @ SV73 @ SV229 ) )
= $true )
| ( ( subclass @ SV229 @ SV73 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[731]) ).
thf(877,plain,
! [SV230: $i,SV74: $i] :
( ( ( ~ ( subclass @ SV74 @ SV230 ) )
= $true )
| ( ( ~ ( subclass @ SV230 @ SV74 )
| ( equalish @ SV74 @ SV230 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[732]) ).
thf(878,plain,
! [SV329: $i,SV231: $i,SV75: $i] :
( ( ~ ( member @ SV75 @ ( unordered_pair @ SV231 @ SV329 ) )
| ( equalish @ SV75 @ SV231 )
| ( equalish @ SV75 @ SV329 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(879,plain,
! [SV232: $i,SV76: $i] :
( ( ( ~ ( member @ SV76 @ universal_class ) )
= $true )
| ( ( member @ SV76 @ ( unordered_pair @ SV76 @ SV232 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[734]) ).
thf(880,plain,
! [SV233: $i,SV77: $i] :
( ( ( ~ ( member @ SV77 @ universal_class ) )
= $true )
| ( ( member @ SV77 @ ( unordered_pair @ SV233 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[735]) ).
thf(881,plain,
! [SV330: $i,SV236: $i,SV81: $i] :
( ( ! [SY777: $i] :
( ~ ( member @ ( ordered_pair @ SV81 @ SV236 ) @ ( cross_product @ SV330 @ SY777 ) )
| ( member @ SV81 @ SV330 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(882,plain,
! [SV331: $i,SV237: $i,SV82: $i] :
( ( ! [SY778: $i] :
( ~ ( member @ ( ordered_pair @ SV82 @ SV237 ) @ ( cross_product @ SV331 @ SY778 ) )
| ( member @ SV237 @ SY778 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(883,plain,
! [SV332: $i,SV238: $i,SV83: $i] :
( ( ! [SY779: $i] :
( ~ ( member @ SV83 @ SV238 )
| ~ ( member @ SV332 @ SY779 )
| ( member @ ( ordered_pair @ SV83 @ SV332 ) @ ( cross_product @ SV238 @ SY779 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(884,plain,
! [SV333: $i,SV239: $i,SV84: $i] :
( ( ~ ( member @ SV84 @ ( cross_product @ SV239 @ SV333 ) )
| ( equalish @ ( ordered_pair @ ( first @ SV84 ) @ ( second @ SV84 ) ) @ SV84 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(885,plain,
! [SV240: $i,SV85: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV85 @ SV240 ) @ element_relation ) )
= $true )
| ( ( member @ SV85 @ SV240 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[742]) ).
thf(886,plain,
! [SV241: $i,SV86: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV86 @ SV241 ) @ ( cross_product @ universal_class @ universal_class ) ) )
= $true )
| ( ( ~ ( member @ SV86 @ SV241 )
| ( member @ ( ordered_pair @ SV86 @ SV241 ) @ element_relation ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[743]) ).
thf(887,plain,
! [SV334: $i,SV242: $i,SV87: $i] :
( ( ~ ( member @ SV87 @ ( intersection @ SV242 @ SV334 ) )
| ( member @ SV87 @ SV242 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(888,plain,
! [SV335: $i,SV243: $i,SV88: $i] :
( ( ~ ( member @ SV88 @ ( intersection @ SV243 @ SV335 ) )
| ( member @ SV88 @ SV335 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(889,plain,
! [SV336: $i,SV244: $i,SV89: $i] :
( ( ~ ( member @ SV89 @ SV244 )
| ~ ( member @ SV89 @ SV336 )
| ( member @ SV89 @ ( intersection @ SV244 @ SV336 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(890,plain,
! [SV245: $i,SV90: $i] :
( ( ( ~ ( member @ SV90 @ ( complement @ SV245 ) ) )
= $true )
| ( ( ~ ( member @ SV90 @ SV245 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[747]) ).
thf(891,plain,
! [SV246: $i,SV91: $i] :
( ( ( ~ ( member @ SV91 @ universal_class ) )
= $true )
| ( ( ( member @ SV91 @ ( complement @ SV246 ) )
| ( member @ SV91 @ SV246 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[748]) ).
thf(892,plain,
! [SV337: $i,SV249: $i,SV94: $i] :
( ( equalish @ ( intersection @ SV94 @ ( cross_product @ SV249 @ SV337 ) ) @ ( restrict @ SV94 @ SV249 @ SV337 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(893,plain,
! [SV338: $i,SV250: $i,SV95: $i] :
( ( equalish @ ( intersection @ ( cross_product @ SV95 @ SV250 ) @ SV338 ) @ ( restrict @ SV338 @ SV95 @ SV250 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(894,plain,
! [SV251: $i,SV96: $i] :
( ( ( ~ ( equalish @ ( restrict @ SV96 @ ( singleton @ SV251 ) @ universal_class ) @ null_class ) )
= $true )
| ( ( ~ ( member @ SV251 @ ( domain_of @ SV96 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[753]) ).
thf(895,plain,
! [SV252: $i,SV97: $i] :
( ( ( ~ ( member @ SV97 @ universal_class ) )
= $true )
| ( ( ( equalish @ ( restrict @ SV252 @ ( singleton @ SV97 ) @ universal_class ) @ null_class )
| ( member @ SV97 @ ( domain_of @ SV252 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[754]) ).
thf(896,plain,
! [SV339: $i,SV253: $i,SV99: $i] :
( ( ! [SY780: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV99 @ SV253 ) @ SV339 ) @ ( rotate @ SY780 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV253 @ SV339 ) @ SV99 ) @ SY780 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(897,plain,
! [SV340: $i,SV254: $i,SV100: $i] :
( ( ! [SY781: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV100 @ SV254 ) @ SV340 ) @ SY781 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV340 @ SV100 ) @ SV254 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV340 @ SV100 ) @ SV254 ) @ ( rotate @ SY781 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(898,plain,
! [SV341: $i,SV255: $i,SV102: $i] :
( ( ! [SY782: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV102 @ SV255 ) @ SV341 ) @ ( flip @ SY782 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV255 @ SV102 ) @ SV341 ) @ SY782 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(899,plain,
! [SV342: $i,SV256: $i,SV103: $i] :
( ( ! [SY783: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV103 @ SV256 ) @ SV342 ) @ SY783 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV256 @ SV103 ) @ SV342 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV256 @ SV103 ) @ SV342 ) @ ( flip @ SY783 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(900,plain,
! [SV343: $i,SV257: $i,SV106: $i] :
( ( equalish @ ( first @ ( not_subclass_element @ ( restrict @ SV106 @ SV257 @ ( singleton @ SV343 ) ) @ null_class ) ) @ ( domain @ SV106 @ SV257 @ SV343 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(901,plain,
! [SV344: $i,SV258: $i,SV107: $i] :
( ( equalish @ ( second @ ( not_subclass_element @ ( restrict @ SV107 @ ( singleton @ SV258 ) @ SV344 ) @ null_class ) ) @ ( range @ SV107 @ SV258 @ SV344 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(902,plain,
! [SV260: $i,SV110: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV110 @ SV260 ) @ successor_relation ) )
= $true )
| ( ( equalish @ ( successor @ SV110 ) @ SV260 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[762]) ).
thf(903,plain,
! [SV261: $i,SV111: $i] :
( ( ( ~ ( equalish @ ( successor @ SV111 ) @ SV261 ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ SV111 @ SV261 ) @ ( cross_product @ universal_class @ universal_class ) )
| ( member @ ( ordered_pair @ SV111 @ SV261 ) @ successor_relation ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[763]) ).
thf(904,plain,
! [SV112: $i] :
( ( ( inductive @ SV112 )
= $false )
| ( ( member @ null_class @ SV112 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[764]) ).
thf(905,plain,
! [SV113: $i] :
( ( ( inductive @ SV113 )
= $false )
| ( ( subclass @ ( image @ successor_relation @ SV113 ) @ SV113 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[765]) ).
thf(906,plain,
! [SV114: $i] :
( ( ( member @ null_class @ SV114 )
= $false )
| ( ( ~ ( subclass @ ( image @ successor_relation @ SV114 ) @ SV114 )
| ( inductive @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[766]) ).
thf(907,plain,
! [SV115: $i] :
( ( ( inductive @ SV115 )
= $false )
| ( ( subclass @ omega @ SV115 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[767]) ).
thf(908,plain,
! [SV117: $i] :
( ( ( member @ SV117 @ universal_class )
= $false )
| ( ( member @ ( sum_class @ SV117 ) @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[768]) ).
thf(909,plain,
! [SV119: $i] :
( ( ( member @ SV119 @ universal_class )
= $false )
| ( ( member @ ( power_class @ SV119 ) @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[769]) ).
thf(910,plain,
! [SV345: $i,SV263: $i,SV121: $i] :
( ( ! [SY784: $i] :
( ~ ( member @ ( ordered_pair @ SV121 @ SV263 ) @ ( compose @ SV345 @ SY784 ) )
| ( member @ SV263 @ ( image @ SV345 @ ( image @ SY784 @ ( singleton @ SV121 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(911,plain,
! [SV346: $i,SV264: $i,SV122: $i] :
( ( ! [SY785: $i] :
( ~ ( member @ SV122 @ ( image @ SV264 @ ( image @ SV346 @ ( singleton @ SY785 ) ) ) )
| ~ ( member @ ( ordered_pair @ SY785 @ SV122 ) @ ( cross_product @ universal_class @ universal_class ) )
| ( member @ ( ordered_pair @ SY785 @ SV122 ) @ ( compose @ SV264 @ SV346 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(912,plain,
! [SV123: $i] :
( ( ( single_valued_class @ SV123 )
= $false )
| ( ( subclass @ ( compose @ SV123 @ ( inverse @ SV123 ) ) @ identity_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[773]) ).
thf(913,plain,
! [SV124: $i] :
( ( ( subclass @ ( compose @ SV124 @ ( inverse @ SV124 ) ) @ identity_relation )
= $false )
| ( ( single_valued_class @ SV124 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[774]) ).
thf(914,plain,
! [SV125: $i] :
( ( ( function @ SV125 )
= $false )
| ( ( subclass @ SV125 @ ( cross_product @ universal_class @ universal_class ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[775]) ).
thf(915,plain,
! [SV126: $i] :
( ( ( function @ SV126 )
= $false )
| ( ( subclass @ ( compose @ SV126 @ ( inverse @ SV126 ) ) @ identity_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[776]) ).
thf(916,plain,
! [SV127: $i] :
( ( ( subclass @ SV127 @ ( cross_product @ universal_class @ universal_class ) )
= $false )
| ( ( ~ ( subclass @ ( compose @ SV127 @ ( inverse @ SV127 ) ) @ identity_relation )
| ( function @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[777]) ).
thf(917,plain,
! [SV265: $i,SV128: $i] :
( ( ( ~ ( function @ SV128 ) )
= $true )
| ( ( ~ ( member @ SV265 @ universal_class )
| ( member @ ( image @ SV128 @ SV265 ) @ universal_class ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[778]) ).
thf(918,plain,
! [SV132: $i] :
( ( ( member @ SV132 @ universal_class )
= $false )
| ( ( ( equalish @ SV132 @ null_class )
| ( member @ ( apply @ choice @ SV132 ) @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[782]) ).
thf(919,plain,
! [SV133: $i] :
( ( ( one_to_one @ SV133 )
= $false )
| ( ( function @ SV133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[783]) ).
thf(920,plain,
! [SV134: $i] :
( ( ( one_to_one @ SV134 )
= $false )
| ( ( function @ ( inverse @ SV134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[784]) ).
thf(921,plain,
! [SV135: $i] :
( ( ( function @ ( inverse @ SV135 ) )
= $false )
| ( ( ~ ( function @ SV135 )
| ( one_to_one @ SV135 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[785]) ).
thf(922,plain,
! [SV138: $i] :
( ( ( operation @ SV138 )
= $false )
| ( ( function @ SV138 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[786]) ).
thf(923,plain,
! [SV139: $i] :
( ( ( operation @ SV139 )
= $false )
| ( ( equalish @ ( cross_product @ ( domain_of @ ( domain_of @ SV139 ) ) @ ( domain_of @ ( domain_of @ SV139 ) ) ) @ ( domain_of @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[787]) ).
thf(924,plain,
! [SV140: $i] :
( ( ( operation @ SV140 )
= $false )
| ( ( subclass @ ( range_of @ SV140 ) @ ( domain_of @ ( domain_of @ SV140 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[788]) ).
thf(925,plain,
! [SV141: $i] :
( ( ( function @ SV141 )
= $false )
| ( ( ~ ( equalish @ ( cross_product @ ( domain_of @ ( domain_of @ SV141 ) ) @ ( domain_of @ ( domain_of @ SV141 ) ) ) @ ( domain_of @ SV141 ) )
| ~ ( subclass @ ( range_of @ SV141 ) @ ( domain_of @ ( domain_of @ SV141 ) ) )
| ( operation @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[789]) ).
thf(926,plain,
! [SV347: $i,SV267: $i,SV142: $i] :
( ( ~ ( compatible @ SV142 @ SV267 @ SV347 )
| ( function @ SV142 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(927,plain,
! [SV348: $i,SV268: $i,SV143: $i] :
( ( ~ ( compatible @ SV143 @ SV268 @ SV348 )
| ( equalish @ ( domain_of @ ( domain_of @ SV268 ) ) @ ( domain_of @ SV143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(928,plain,
! [SV349: $i,SV269: $i,SV144: $i] :
( ( ~ ( compatible @ SV144 @ SV269 @ SV349 )
| ( subclass @ ( range_of @ SV144 ) @ ( domain_of @ ( domain_of @ SV349 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(929,plain,
! [SV350: $i,SV270: $i,SV145: $i] :
( ( ! [SY786: $i] :
( ~ ( function @ SV145 )
| ~ ( equalish @ ( domain_of @ ( domain_of @ SV270 ) ) @ ( domain_of @ SV145 ) )
| ~ ( subclass @ ( range_of @ SV145 ) @ ( domain_of @ ( domain_of @ SV350 ) ) )
| ( compatible @ SY786 @ SV270 @ SV350 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(930,plain,
! [SV351: $i,SV271: $i,SV146: $i] :
( ( ~ ( homomorphism @ SV146 @ SV271 @ SV351 )
| ( operation @ SV271 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(931,plain,
! [SV352: $i,SV272: $i,SV147: $i] :
( ( ~ ( homomorphism @ SV147 @ SV272 @ SV352 )
| ( operation @ SV352 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(932,plain,
! [SV353: $i,SV273: $i,SV148: $i] :
( ( ~ ( homomorphism @ SV148 @ SV273 @ SV353 )
| ( compatible @ SV148 @ SV273 @ SV353 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(933,plain,
! [SV354: $i,SV274: $i,SV149: $i] :
( ( ! [SY787: $i,SY788: $i] :
( ~ ( homomorphism @ SV149 @ SV274 @ SV354 )
| ~ ( member @ ( ordered_pair @ SY787 @ SY788 ) @ ( domain_of @ SV274 ) )
| ( equalish @ ( apply @ SV354 @ ( ordered_pair @ ( apply @ SV149 @ SY787 ) @ ( apply @ SV149 @ SY788 ) ) ) @ ( apply @ SV149 @ ( apply @ SV274 @ ( ordered_pair @ SY787 @ SY788 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(934,plain,
! [SV355: $i,SV275: $i,SV150: $i] :
( ( ~ ( operation @ SV150 )
| ~ ( operation @ SV275 )
| ~ ( compatible @ SV355 @ SV150 @ SV275 )
| ( member @ ( ordered_pair @ ( not_homomorphism1 @ SV355 @ SV150 @ SV275 ) @ ( not_homomorphism2 @ SV355 @ SV150 @ SV275 ) ) @ ( domain_of @ SV150 ) )
| ( homomorphism @ SV355 @ SV150 @ SV275 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(935,plain,
! [SV356: $i,SV276: $i,SV151: $i] :
( ( ~ ( operation @ SV151 )
| ~ ( operation @ SV276 )
| ~ ( compatible @ SV356 @ SV151 @ SV276 )
| ~ ( equalish @ ( apply @ SV276 @ ( ordered_pair @ ( apply @ SV356 @ ( not_homomorphism1 @ SV356 @ SV151 @ SV276 ) ) @ ( apply @ SV356 @ ( not_homomorphism2 @ SV356 @ SV151 @ SV276 ) ) ) ) @ ( apply @ SV356 @ ( apply @ SV151 @ ( ordered_pair @ ( not_homomorphism1 @ SV356 @ SV151 @ SV276 ) @ ( not_homomorphism2 @ SV356 @ SV151 @ SV276 ) ) ) ) )
| ( homomorphism @ SV356 @ SV151 @ SV276 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(936,plain,
! [SV357: $i,SV277: $i,SV152: $i] :
( ( ! [SY789: $i] :
( ~ ( member @ ( ordered_pair @ SV152 @ SV277 ) @ ( cross_product @ SV357 @ SY789 ) )
| ( member @ SV152 @ ( unordered_pair @ SV152 @ SV277 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(937,plain,
! [SV358: $i,SV278: $i,SV153: $i] :
( ( ! [SY790: $i] :
( ~ ( member @ ( ordered_pair @ SV153 @ SV278 ) @ ( cross_product @ SV358 @ SY790 ) )
| ( member @ SV278 @ ( unordered_pair @ SV153 @ SV278 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(938,plain,
! [SV359: $i,SV279: $i,SV154: $i] :
( ( ! [SY791: $i] :
( ~ ( member @ ( ordered_pair @ SV154 @ SV279 ) @ ( cross_product @ SV359 @ SY791 ) )
| ( member @ SV154 @ universal_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(939,plain,
! [SV360: $i,SV280: $i,SV155: $i] :
( ( ! [SY792: $i] :
( ~ ( member @ ( ordered_pair @ SV155 @ SV280 ) @ ( cross_product @ SV360 @ SY792 ) )
| ( member @ SV280 @ universal_class ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(940,plain,
! [SV361: $i,SV281: $i,SV157: $i] :
( ( ~ ( subclass @ SV157 @ SV281 )
| ~ ( subclass @ SV281 @ SV361 )
| ( subclass @ SV157 @ SV361 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(941,plain,
! [SV158: $i,SV1: $i] :
( ( ( equalish @ SV1 @ SV158 )
= $false )
| ( ( equalish @ SV158 @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[805]) ).
thf(942,plain,
! [SV282: $i,SV159: $i,SV2: $i] :
( ( ( ~ ( equalish @ SV2 @ SV159 ) )
= $true )
| ( ( ~ ( equalish @ SV159 @ SV282 )
| ( equalish @ SV2 @ SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[806]) ).
thf(943,plain,
! [SV283: $i,SV160: $i,SV3: $i] :
( ( ( ~ ( equalish @ SV3 @ SV160 ) )
= $true )
| ( ( equalish @ ( apply @ SV3 @ SV283 ) @ ( apply @ SV160 @ SV283 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[807]) ).
thf(944,plain,
! [SV284: $i,SV161: $i,SV4: $i] :
( ( ( ~ ( equalish @ SV4 @ SV161 ) )
= $true )
| ( ( equalish @ ( apply @ SV284 @ SV4 ) @ ( apply @ SV284 @ SV161 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[808]) ).
thf(945,plain,
! [SV162: $i,SV5: $i] :
( ( ( equalish @ SV5 @ SV162 )
= $false )
| ( ( equalish @ ( cantor @ SV5 ) @ ( cantor @ SV162 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[809]) ).
thf(946,plain,
! [SV163: $i,SV6: $i] :
( ( ( equalish @ SV6 @ SV163 )
= $false )
| ( ( equalish @ ( complement @ SV6 ) @ ( complement @ SV163 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[810]) ).
thf(947,plain,
! [SV285: $i,SV164: $i,SV7: $i] :
( ( ( ~ ( equalish @ SV7 @ SV164 ) )
= $true )
| ( ( equalish @ ( compose @ SV7 @ SV285 ) @ ( compose @ SV164 @ SV285 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[811]) ).
thf(948,plain,
! [SV286: $i,SV165: $i,SV8: $i] :
( ( ( ~ ( equalish @ SV8 @ SV165 ) )
= $true )
| ( ( equalish @ ( compose @ SV286 @ SV8 ) @ ( compose @ SV286 @ SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[812]) ).
thf(949,plain,
! [SV287: $i,SV166: $i,SV9: $i] :
( ( ( ~ ( equalish @ SV9 @ SV166 ) )
= $true )
| ( ( equalish @ ( cross_product @ SV9 @ SV287 ) @ ( cross_product @ SV166 @ SV287 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[813]) ).
thf(950,plain,
! [SV288: $i,SV167: $i,SV10: $i] :
( ( ( ~ ( equalish @ SV10 @ SV167 ) )
= $true )
| ( ( equalish @ ( cross_product @ SV288 @ SV10 ) @ ( cross_product @ SV288 @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[814]) ).
thf(951,plain,
! [SV168: $i,SV11: $i] :
( ( ( equalish @ SV11 @ SV168 )
= $false )
| ( ( equalish @ ( diagonalise @ SV11 ) @ ( diagonalise @ SV168 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[815]) ).
thf(952,plain,
! [SV289: $i,SV169: $i,SV12: $i] :
( ( ( ~ ( equalish @ SV12 @ SV169 ) )
= $true )
| ( ( equalish @ ( symmetric_difference @ SV12 @ SV289 ) @ ( symmetric_difference @ SV169 @ SV289 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[816]) ).
thf(953,plain,
! [SV290: $i,SV170: $i,SV13: $i] :
( ( ( ~ ( equalish @ SV13 @ SV170 ) )
= $true )
| ( ( equalish @ ( symmetric_difference @ SV290 @ SV13 ) @ ( symmetric_difference @ SV290 @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[817]) ).
thf(954,plain,
! [SV362: $i,SV291: $i,SV171: $i,SV14: $i] :
( ( ~ ( equalish @ SV14 @ SV171 )
| ( equalish @ ( domain @ SV14 @ SV291 @ SV362 ) @ ( domain @ SV171 @ SV291 @ SV362 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(955,plain,
! [SV363: $i,SV292: $i,SV172: $i,SV15: $i] :
( ( ~ ( equalish @ SV15 @ SV172 )
| ( equalish @ ( domain @ SV292 @ SV15 @ SV363 ) @ ( domain @ SV292 @ SV172 @ SV363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(956,plain,
! [SV364: $i,SV293: $i,SV173: $i,SV16: $i] :
( ( ~ ( equalish @ SV16 @ SV173 )
| ( equalish @ ( domain @ SV293 @ SV364 @ SV16 ) @ ( domain @ SV293 @ SV364 @ SV173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(957,plain,
! [SV174: $i,SV17: $i] :
( ( ( equalish @ SV17 @ SV174 )
= $false )
| ( ( equalish @ ( domain_of @ SV17 ) @ ( domain_of @ SV174 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[821]) ).
thf(958,plain,
! [SV175: $i,SV18: $i] :
( ( ( equalish @ SV18 @ SV175 )
= $false )
| ( ( equalish @ ( first @ SV18 ) @ ( first @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[822]) ).
thf(959,plain,
! [SV176: $i,SV19: $i] :
( ( ( equalish @ SV19 @ SV176 )
= $false )
| ( ( equalish @ ( flip @ SV19 ) @ ( flip @ SV176 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[823]) ).
thf(960,plain,
! [SV294: $i,SV177: $i,SV20: $i] :
( ( ( ~ ( equalish @ SV20 @ SV177 ) )
= $true )
| ( ( equalish @ ( image @ SV20 @ SV294 ) @ ( image @ SV177 @ SV294 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[824]) ).
thf(961,plain,
! [SV295: $i,SV178: $i,SV21: $i] :
( ( ( ~ ( equalish @ SV21 @ SV178 ) )
= $true )
| ( ( equalish @ ( image @ SV295 @ SV21 ) @ ( image @ SV295 @ SV178 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[825]) ).
thf(962,plain,
! [SV296: $i,SV179: $i,SV22: $i] :
( ( ( ~ ( equalish @ SV22 @ SV179 ) )
= $true )
| ( ( equalish @ ( intersection @ SV22 @ SV296 ) @ ( intersection @ SV179 @ SV296 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[826]) ).
thf(963,plain,
! [SV297: $i,SV180: $i,SV23: $i] :
( ( ( ~ ( equalish @ SV23 @ SV180 ) )
= $true )
| ( ( equalish @ ( intersection @ SV297 @ SV23 ) @ ( intersection @ SV297 @ SV180 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[827]) ).
thf(964,plain,
! [SV181: $i,SV24: $i] :
( ( ( equalish @ SV24 @ SV181 )
= $false )
| ( ( equalish @ ( inverse @ SV24 ) @ ( inverse @ SV181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[828]) ).
thf(965,plain,
! [SV365: $i,SV298: $i,SV182: $i,SV25: $i] :
( ( ~ ( equalish @ SV25 @ SV182 )
| ( equalish @ ( not_homomorphism1 @ SV25 @ SV298 @ SV365 ) @ ( not_homomorphism1 @ SV182 @ SV298 @ SV365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(966,plain,
! [SV366: $i,SV299: $i,SV183: $i,SV26: $i] :
( ( ~ ( equalish @ SV26 @ SV183 )
| ( equalish @ ( not_homomorphism1 @ SV299 @ SV26 @ SV366 ) @ ( not_homomorphism1 @ SV299 @ SV183 @ SV366 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(967,plain,
! [SV367: $i,SV300: $i,SV184: $i,SV27: $i] :
( ( ~ ( equalish @ SV27 @ SV184 )
| ( equalish @ ( not_homomorphism1 @ SV300 @ SV367 @ SV27 ) @ ( not_homomorphism1 @ SV300 @ SV367 @ SV184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(968,plain,
! [SV368: $i,SV301: $i,SV185: $i,SV28: $i] :
( ( ~ ( equalish @ SV28 @ SV185 )
| ( equalish @ ( not_homomorphism2 @ SV28 @ SV301 @ SV368 ) @ ( not_homomorphism2 @ SV185 @ SV301 @ SV368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(969,plain,
! [SV369: $i,SV302: $i,SV186: $i,SV29: $i] :
( ( ~ ( equalish @ SV29 @ SV186 )
| ( equalish @ ( not_homomorphism2 @ SV302 @ SV29 @ SV369 ) @ ( not_homomorphism2 @ SV302 @ SV186 @ SV369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(970,plain,
! [SV370: $i,SV303: $i,SV187: $i,SV30: $i] :
( ( ~ ( equalish @ SV30 @ SV187 )
| ( equalish @ ( not_homomorphism2 @ SV303 @ SV370 @ SV30 ) @ ( not_homomorphism2 @ SV303 @ SV370 @ SV187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(971,plain,
! [SV304: $i,SV188: $i,SV31: $i] :
( ( ( ~ ( equalish @ SV31 @ SV188 ) )
= $true )
| ( ( equalish @ ( not_subclass_element @ SV31 @ SV304 ) @ ( not_subclass_element @ SV188 @ SV304 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[835]) ).
thf(972,plain,
! [SV305: $i,SV189: $i,SV32: $i] :
( ( ( ~ ( equalish @ SV32 @ SV189 ) )
= $true )
| ( ( equalish @ ( not_subclass_element @ SV305 @ SV32 ) @ ( not_subclass_element @ SV305 @ SV189 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[836]) ).
thf(973,plain,
! [SV306: $i,SV190: $i,SV33: $i] :
( ( ( ~ ( equalish @ SV33 @ SV190 ) )
= $true )
| ( ( equalish @ ( ordered_pair @ SV33 @ SV306 ) @ ( ordered_pair @ SV190 @ SV306 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[837]) ).
thf(974,plain,
! [SV307: $i,SV191: $i,SV34: $i] :
( ( ( ~ ( equalish @ SV34 @ SV191 ) )
= $true )
| ( ( equalish @ ( ordered_pair @ SV307 @ SV34 ) @ ( ordered_pair @ SV307 @ SV191 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[838]) ).
thf(975,plain,
! [SV192: $i,SV35: $i] :
( ( ( equalish @ SV35 @ SV192 )
= $false )
| ( ( equalish @ ( power_class @ SV35 ) @ ( power_class @ SV192 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[839]) ).
thf(976,plain,
! [SV371: $i,SV308: $i,SV193: $i,SV36: $i] :
( ( ~ ( equalish @ SV36 @ SV193 )
| ( equalish @ ( range @ SV36 @ SV308 @ SV371 ) @ ( range @ SV193 @ SV308 @ SV371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(977,plain,
! [SV372: $i,SV309: $i,SV194: $i,SV37: $i] :
( ( ~ ( equalish @ SV37 @ SV194 )
| ( equalish @ ( range @ SV309 @ SV37 @ SV372 ) @ ( range @ SV309 @ SV194 @ SV372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(978,plain,
! [SV373: $i,SV310: $i,SV195: $i,SV38: $i] :
( ( ~ ( equalish @ SV38 @ SV195 )
| ( equalish @ ( range @ SV310 @ SV373 @ SV38 ) @ ( range @ SV310 @ SV373 @ SV195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(979,plain,
! [SV196: $i,SV39: $i] :
( ( ( equalish @ SV39 @ SV196 )
= $false )
| ( ( equalish @ ( range_of @ SV39 ) @ ( range_of @ SV196 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[843]) ).
thf(980,plain,
! [SV197: $i,SV40: $i] :
( ( ( equalish @ SV40 @ SV197 )
= $false )
| ( ( equalish @ ( regular @ SV40 ) @ ( regular @ SV197 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[844]) ).
thf(981,plain,
! [SV374: $i,SV311: $i,SV198: $i,SV41: $i] :
( ( ~ ( equalish @ SV41 @ SV198 )
| ( equalish @ ( restrict @ SV41 @ SV311 @ SV374 ) @ ( restrict @ SV198 @ SV311 @ SV374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(982,plain,
! [SV375: $i,SV312: $i,SV199: $i,SV42: $i] :
( ( ~ ( equalish @ SV42 @ SV199 )
| ( equalish @ ( restrict @ SV312 @ SV42 @ SV375 ) @ ( restrict @ SV312 @ SV199 @ SV375 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(983,plain,
! [SV376: $i,SV313: $i,SV200: $i,SV43: $i] :
( ( ~ ( equalish @ SV43 @ SV200 )
| ( equalish @ ( restrict @ SV313 @ SV376 @ SV43 ) @ ( restrict @ SV313 @ SV376 @ SV200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(984,plain,
! [SV201: $i,SV44: $i] :
( ( ( equalish @ SV44 @ SV201 )
= $false )
| ( ( equalish @ ( rotate @ SV44 ) @ ( rotate @ SV201 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[848]) ).
thf(985,plain,
! [SV202: $i,SV45: $i] :
( ( ( equalish @ SV45 @ SV202 )
= $false )
| ( ( equalish @ ( second @ SV45 ) @ ( second @ SV202 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[849]) ).
thf(986,plain,
! [SV203: $i,SV46: $i] :
( ( ( equalish @ SV46 @ SV203 )
= $false )
| ( ( equalish @ ( singleton @ SV46 ) @ ( singleton @ SV203 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[850]) ).
thf(987,plain,
! [SV204: $i,SV47: $i] :
( ( ( equalish @ SV47 @ SV204 )
= $false )
| ( ( equalish @ ( successor @ SV47 ) @ ( successor @ SV204 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[851]) ).
thf(988,plain,
! [SV205: $i,SV48: $i] :
( ( ( equalish @ SV48 @ SV205 )
= $false )
| ( ( equalish @ ( sum_class @ SV48 ) @ ( sum_class @ SV205 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[852]) ).
thf(989,plain,
! [SV314: $i,SV206: $i,SV49: $i] :
( ( ( ~ ( equalish @ SV49 @ SV206 ) )
= $true )
| ( ( equalish @ ( union @ SV49 @ SV314 ) @ ( union @ SV206 @ SV314 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[853]) ).
thf(990,plain,
! [SV315: $i,SV207: $i,SV50: $i] :
( ( ( ~ ( equalish @ SV50 @ SV207 ) )
= $true )
| ( ( equalish @ ( union @ SV315 @ SV50 ) @ ( union @ SV315 @ SV207 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[854]) ).
thf(991,plain,
! [SV316: $i,SV208: $i,SV51: $i] :
( ( ( ~ ( equalish @ SV51 @ SV208 ) )
= $true )
| ( ( equalish @ ( unordered_pair @ SV51 @ SV316 ) @ ( unordered_pair @ SV208 @ SV316 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[855]) ).
thf(992,plain,
! [SV317: $i,SV209: $i,SV52: $i] :
( ( ( ~ ( equalish @ SV52 @ SV209 ) )
= $true )
| ( ( equalish @ ( unordered_pair @ SV317 @ SV52 ) @ ( unordered_pair @ SV317 @ SV209 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[856]) ).
thf(993,plain,
! [SV377: $i,SV318: $i,SV210: $i,SV53: $i] :
( ( ~ ( equalish @ SV53 @ SV210 )
| ~ ( compatible @ SV53 @ SV318 @ SV377 )
| ( compatible @ SV210 @ SV318 @ SV377 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(994,plain,
! [SV378: $i,SV319: $i,SV211: $i,SV54: $i] :
( ( ~ ( equalish @ SV54 @ SV211 )
| ~ ( compatible @ SV319 @ SV54 @ SV378 )
| ( compatible @ SV319 @ SV211 @ SV378 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(995,plain,
! [SV379: $i,SV320: $i,SV212: $i,SV55: $i] :
( ( ~ ( equalish @ SV55 @ SV212 )
| ~ ( compatible @ SV320 @ SV379 @ SV55 )
| ( compatible @ SV320 @ SV379 @ SV212 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(996,plain,
! [SV213: $i,SV56: $i] :
( ( ( equalish @ SV56 @ SV213 )
= $false )
| ( ( ~ ( function @ SV56 )
| ( function @ SV213 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[860]) ).
thf(997,plain,
! [SV380: $i,SV321: $i,SV214: $i,SV57: $i] :
( ( ~ ( equalish @ SV57 @ SV214 )
| ~ ( homomorphism @ SV57 @ SV321 @ SV380 )
| ( homomorphism @ SV214 @ SV321 @ SV380 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(998,plain,
! [SV381: $i,SV322: $i,SV215: $i,SV58: $i] :
( ( ~ ( equalish @ SV58 @ SV215 )
| ~ ( homomorphism @ SV322 @ SV58 @ SV381 )
| ( homomorphism @ SV322 @ SV215 @ SV381 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(999,plain,
! [SV382: $i,SV323: $i,SV216: $i,SV59: $i] :
( ( ~ ( equalish @ SV59 @ SV216 )
| ~ ( homomorphism @ SV323 @ SV382 @ SV59 )
| ( homomorphism @ SV323 @ SV382 @ SV216 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[863]) ).
thf(1000,plain,
! [SV217: $i,SV60: $i] :
( ( ( equalish @ SV60 @ SV217 )
= $false )
| ( ( ~ ( inductive @ SV60 )
| ( inductive @ SV217 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[864]) ).
thf(1001,plain,
! [SV324: $i,SV218: $i,SV61: $i] :
( ( ( ~ ( equalish @ SV61 @ SV218 ) )
= $true )
| ( ( ~ ( member @ SV61 @ SV324 )
| ( member @ SV218 @ SV324 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[865]) ).
thf(1002,plain,
! [SV325: $i,SV219: $i,SV62: $i] :
( ( ( ~ ( equalish @ SV62 @ SV219 ) )
= $true )
| ( ( ~ ( member @ SV325 @ SV62 )
| ( member @ SV325 @ SV219 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[866]) ).
thf(1003,plain,
! [SV220: $i,SV63: $i] :
( ( ( equalish @ SV63 @ SV220 )
= $false )
| ( ( ~ ( one_to_one @ SV63 )
| ( one_to_one @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[867]) ).
thf(1004,plain,
! [SV221: $i,SV64: $i] :
( ( ( equalish @ SV64 @ SV221 )
= $false )
| ( ( ~ ( operation @ SV64 )
| ( operation @ SV221 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[868]) ).
thf(1005,plain,
! [SV222: $i,SV65: $i] :
( ( ( equalish @ SV65 @ SV222 )
= $false )
| ( ( ~ ( single_valued_class @ SV65 )
| ( single_valued_class @ SV222 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[869]) ).
thf(1006,plain,
! [SV326: $i,SV223: $i,SV66: $i] :
( ( ( ~ ( equalish @ SV66 @ SV223 ) )
= $true )
| ( ( ~ ( subclass @ SV66 @ SV326 )
| ( subclass @ SV223 @ SV326 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[870]) ).
thf(1007,plain,
! [SV327: $i,SV224: $i,SV67: $i] :
( ( ( ~ ( equalish @ SV67 @ SV224 ) )
= $true )
| ( ( ~ ( subclass @ SV327 @ SV67 )
| ( subclass @ SV327 @ SV224 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[871]) ).
thf(1008,plain,
! [SV328: $i,SV225: $i,SV68: $i] :
( ( ( ~ ( subclass @ SV68 @ SV225 ) )
= $true )
| ( ( ~ ( member @ SV328 @ SV68 )
| ( member @ SV328 @ SV225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[872]) ).
thf(1009,plain,
! [SV227: $i,SV70: $i] :
( ( ( member @ ( not_subclass_element @ SV70 @ SV227 ) @ SV227 )
= $false )
| ( ( subclass @ SV70 @ SV227 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[874]) ).
thf(1010,plain,
! [SV228: $i,SV72: $i] :
( ( ( equalish @ SV72 @ SV228 )
= $false )
| ( ( subclass @ SV72 @ SV228 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[875]) ).
thf(1011,plain,
! [SV229: $i,SV73: $i] :
( ( ( equalish @ SV73 @ SV229 )
= $false )
| ( ( subclass @ SV229 @ SV73 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[876]) ).
thf(1012,plain,
! [SV230: $i,SV74: $i] :
( ( ( subclass @ SV74 @ SV230 )
= $false )
| ( ( ~ ( subclass @ SV230 @ SV74 )
| ( equalish @ SV74 @ SV230 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[877]) ).
thf(1013,plain,
! [SV329: $i,SV231: $i,SV75: $i] :
( ( ( ~ ( member @ SV75 @ ( unordered_pair @ SV231 @ SV329 ) ) )
= $true )
| ( ( ( equalish @ SV75 @ SV231 )
| ( equalish @ SV75 @ SV329 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[878]) ).
thf(1014,plain,
! [SV232: $i,SV76: $i] :
( ( ( member @ SV76 @ universal_class )
= $false )
| ( ( member @ SV76 @ ( unordered_pair @ SV76 @ SV232 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[879]) ).
thf(1015,plain,
! [SV233: $i,SV77: $i] :
( ( ( member @ SV77 @ universal_class )
= $false )
| ( ( member @ SV77 @ ( unordered_pair @ SV233 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[880]) ).
thf(1016,plain,
! [SV383: $i,SV330: $i,SV236: $i,SV81: $i] :
( ( ~ ( member @ ( ordered_pair @ SV81 @ SV236 ) @ ( cross_product @ SV330 @ SV383 ) )
| ( member @ SV81 @ SV330 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[881]) ).
thf(1017,plain,
! [SV384: $i,SV331: $i,SV237: $i,SV82: $i] :
( ( ~ ( member @ ( ordered_pair @ SV82 @ SV237 ) @ ( cross_product @ SV331 @ SV384 ) )
| ( member @ SV237 @ SV384 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[882]) ).
thf(1018,plain,
! [SV385: $i,SV332: $i,SV238: $i,SV83: $i] :
( ( ~ ( member @ SV83 @ SV238 )
| ~ ( member @ SV332 @ SV385 )
| ( member @ ( ordered_pair @ SV83 @ SV332 ) @ ( cross_product @ SV238 @ SV385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(1019,plain,
! [SV333: $i,SV239: $i,SV84: $i] :
( ( ( ~ ( member @ SV84 @ ( cross_product @ SV239 @ SV333 ) ) )
= $true )
| ( ( equalish @ ( ordered_pair @ ( first @ SV84 ) @ ( second @ SV84 ) ) @ SV84 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[884]) ).
thf(1020,plain,
! [SV240: $i,SV85: $i] :
( ( ( member @ ( ordered_pair @ SV85 @ SV240 ) @ element_relation )
= $false )
| ( ( member @ SV85 @ SV240 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[885]) ).
thf(1021,plain,
! [SV241: $i,SV86: $i] :
( ( ( member @ ( ordered_pair @ SV86 @ SV241 ) @ ( cross_product @ universal_class @ universal_class ) )
= $false )
| ( ( ~ ( member @ SV86 @ SV241 )
| ( member @ ( ordered_pair @ SV86 @ SV241 ) @ element_relation ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[886]) ).
thf(1022,plain,
! [SV334: $i,SV242: $i,SV87: $i] :
( ( ( ~ ( member @ SV87 @ ( intersection @ SV242 @ SV334 ) ) )
= $true )
| ( ( member @ SV87 @ SV242 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[887]) ).
thf(1023,plain,
! [SV335: $i,SV243: $i,SV88: $i] :
( ( ( ~ ( member @ SV88 @ ( intersection @ SV243 @ SV335 ) ) )
= $true )
| ( ( member @ SV88 @ SV335 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[888]) ).
thf(1024,plain,
! [SV336: $i,SV244: $i,SV89: $i] :
( ( ( ~ ( member @ SV89 @ SV244 ) )
= $true )
| ( ( ~ ( member @ SV89 @ SV336 )
| ( member @ SV89 @ ( intersection @ SV244 @ SV336 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[889]) ).
thf(1025,plain,
! [SV245: $i,SV90: $i] :
( ( ( member @ SV90 @ ( complement @ SV245 ) )
= $false )
| ( ( ~ ( member @ SV90 @ SV245 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[890]) ).
thf(1026,plain,
! [SV246: $i,SV91: $i] :
( ( ( member @ SV91 @ universal_class )
= $false )
| ( ( ( member @ SV91 @ ( complement @ SV246 ) )
| ( member @ SV91 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[891]) ).
thf(1027,plain,
! [SV251: $i,SV96: $i] :
( ( ( equalish @ ( restrict @ SV96 @ ( singleton @ SV251 ) @ universal_class ) @ null_class )
= $false )
| ( ( ~ ( member @ SV251 @ ( domain_of @ SV96 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[894]) ).
thf(1028,plain,
! [SV252: $i,SV97: $i] :
( ( ( member @ SV97 @ universal_class )
= $false )
| ( ( ( equalish @ ( restrict @ SV252 @ ( singleton @ SV97 ) @ universal_class ) @ null_class )
| ( member @ SV97 @ ( domain_of @ SV252 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[895]) ).
thf(1029,plain,
! [SV386: $i,SV339: $i,SV253: $i,SV99: $i] :
( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV99 @ SV253 ) @ SV339 ) @ ( rotate @ SV386 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV253 @ SV339 ) @ SV99 ) @ SV386 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(1030,plain,
! [SV387: $i,SV340: $i,SV254: $i,SV100: $i] :
( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV100 @ SV254 ) @ SV340 ) @ SV387 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV340 @ SV100 ) @ SV254 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV340 @ SV100 ) @ SV254 ) @ ( rotate @ SV387 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(1031,plain,
! [SV388: $i,SV341: $i,SV255: $i,SV102: $i] :
( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV102 @ SV255 ) @ SV341 ) @ ( flip @ SV388 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV255 @ SV102 ) @ SV341 ) @ SV388 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[898]) ).
thf(1032,plain,
! [SV389: $i,SV342: $i,SV256: $i,SV103: $i] :
( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV103 @ SV256 ) @ SV342 ) @ SV389 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV256 @ SV103 ) @ SV342 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV256 @ SV103 ) @ SV342 ) @ ( flip @ SV389 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(1033,plain,
! [SV260: $i,SV110: $i] :
( ( ( member @ ( ordered_pair @ SV110 @ SV260 ) @ successor_relation )
= $false )
| ( ( equalish @ ( successor @ SV110 ) @ SV260 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(1034,plain,
! [SV261: $i,SV111: $i] :
( ( ( equalish @ ( successor @ SV111 ) @ SV261 )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ SV111 @ SV261 ) @ ( cross_product @ universal_class @ universal_class ) )
| ( member @ ( ordered_pair @ SV111 @ SV261 ) @ successor_relation ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[903]) ).
thf(1035,plain,
! [SV114: $i] :
( ( ( ~ ( subclass @ ( image @ successor_relation @ SV114 ) @ SV114 ) )
= $true )
| ( ( inductive @ SV114 )
= $true )
| ( ( member @ null_class @ SV114 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[906]) ).
thf(1036,plain,
! [SV390: $i,SV345: $i,SV263: $i,SV121: $i] :
( ( ~ ( member @ ( ordered_pair @ SV121 @ SV263 ) @ ( compose @ SV345 @ SV390 ) )
| ( member @ SV263 @ ( image @ SV345 @ ( image @ SV390 @ ( singleton @ SV121 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(1037,plain,
! [SV391: $i,SV346: $i,SV264: $i,SV122: $i] :
( ( ~ ( member @ SV122 @ ( image @ SV264 @ ( image @ SV346 @ ( singleton @ SV391 ) ) ) )
| ~ ( member @ ( ordered_pair @ SV391 @ SV122 ) @ ( cross_product @ universal_class @ universal_class ) )
| ( member @ ( ordered_pair @ SV391 @ SV122 ) @ ( compose @ SV264 @ SV346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(1038,plain,
! [SV127: $i] :
( ( ( ~ ( subclass @ ( compose @ SV127 @ ( inverse @ SV127 ) ) @ identity_relation ) )
= $true )
| ( ( function @ SV127 )
= $true )
| ( ( subclass @ SV127 @ ( cross_product @ universal_class @ universal_class ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[916]) ).
thf(1039,plain,
! [SV265: $i,SV128: $i] :
( ( ( function @ SV128 )
= $false )
| ( ( ~ ( member @ SV265 @ universal_class )
| ( member @ ( image @ SV128 @ SV265 ) @ universal_class ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[917]) ).
thf(1040,plain,
! [SV132: $i] :
( ( ( equalish @ SV132 @ null_class )
= $true )
| ( ( member @ ( apply @ choice @ SV132 ) @ SV132 )
= $true )
| ( ( member @ SV132 @ universal_class )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[918]) ).
thf(1041,plain,
! [SV135: $i] :
( ( ( ~ ( function @ SV135 ) )
= $true )
| ( ( one_to_one @ SV135 )
= $true )
| ( ( function @ ( inverse @ SV135 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[921]) ).
thf(1042,plain,
! [SV141: $i] :
( ( ( ~ ( equalish @ ( cross_product @ ( domain_of @ ( domain_of @ SV141 ) ) @ ( domain_of @ ( domain_of @ SV141 ) ) ) @ ( domain_of @ SV141 ) ) )
= $true )
| ( ( ~ ( subclass @ ( range_of @ SV141 ) @ ( domain_of @ ( domain_of @ SV141 ) ) )
| ( operation @ SV141 ) )
= $true )
| ( ( function @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[925]) ).
thf(1043,plain,
! [SV347: $i,SV267: $i,SV142: $i] :
( ( ( ~ ( compatible @ SV142 @ SV267 @ SV347 ) )
= $true )
| ( ( function @ SV142 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[926]) ).
thf(1044,plain,
! [SV348: $i,SV268: $i,SV143: $i] :
( ( ( ~ ( compatible @ SV143 @ SV268 @ SV348 ) )
= $true )
| ( ( equalish @ ( domain_of @ ( domain_of @ SV268 ) ) @ ( domain_of @ SV143 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[927]) ).
thf(1045,plain,
! [SV349: $i,SV269: $i,SV144: $i] :
( ( ( ~ ( compatible @ SV144 @ SV269 @ SV349 ) )
= $true )
| ( ( subclass @ ( range_of @ SV144 ) @ ( domain_of @ ( domain_of @ SV349 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[928]) ).
thf(1046,plain,
! [SV392: $i,SV350: $i,SV270: $i,SV145: $i] :
( ( ~ ( function @ SV145 )
| ~ ( equalish @ ( domain_of @ ( domain_of @ SV270 ) ) @ ( domain_of @ SV145 ) )
| ~ ( subclass @ ( range_of @ SV145 ) @ ( domain_of @ ( domain_of @ SV350 ) ) )
| ( compatible @ SV392 @ SV270 @ SV350 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(1047,plain,
! [SV351: $i,SV271: $i,SV146: $i] :
( ( ( ~ ( homomorphism @ SV146 @ SV271 @ SV351 ) )
= $true )
| ( ( operation @ SV271 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[930]) ).
thf(1048,plain,
! [SV352: $i,SV272: $i,SV147: $i] :
( ( ( ~ ( homomorphism @ SV147 @ SV272 @ SV352 ) )
= $true )
| ( ( operation @ SV352 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[931]) ).
thf(1049,plain,
! [SV353: $i,SV273: $i,SV148: $i] :
( ( ( ~ ( homomorphism @ SV148 @ SV273 @ SV353 ) )
= $true )
| ( ( compatible @ SV148 @ SV273 @ SV353 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[932]) ).
thf(1050,plain,
! [SV393: $i,SV354: $i,SV274: $i,SV149: $i] :
( ( ! [SY793: $i] :
( ~ ( homomorphism @ SV149 @ SV274 @ SV354 )
| ~ ( member @ ( ordered_pair @ SV393 @ SY793 ) @ ( domain_of @ SV274 ) )
| ( equalish @ ( apply @ SV354 @ ( ordered_pair @ ( apply @ SV149 @ SV393 ) @ ( apply @ SV149 @ SY793 ) ) ) @ ( apply @ SV149 @ ( apply @ SV274 @ ( ordered_pair @ SV393 @ SY793 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(1051,plain,
! [SV355: $i,SV275: $i,SV150: $i] :
( ( ( ~ ( operation @ SV150 ) )
= $true )
| ( ( ~ ( operation @ SV275 )
| ~ ( compatible @ SV355 @ SV150 @ SV275 )
| ( member @ ( ordered_pair @ ( not_homomorphism1 @ SV355 @ SV150 @ SV275 ) @ ( not_homomorphism2 @ SV355 @ SV150 @ SV275 ) ) @ ( domain_of @ SV150 ) )
| ( homomorphism @ SV355 @ SV150 @ SV275 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[934]) ).
thf(1052,plain,
! [SV356: $i,SV276: $i,SV151: $i] :
( ( ( ~ ( operation @ SV151 ) )
= $true )
| ( ( ~ ( operation @ SV276 )
| ~ ( compatible @ SV356 @ SV151 @ SV276 )
| ~ ( equalish @ ( apply @ SV276 @ ( ordered_pair @ ( apply @ SV356 @ ( not_homomorphism1 @ SV356 @ SV151 @ SV276 ) ) @ ( apply @ SV356 @ ( not_homomorphism2 @ SV356 @ SV151 @ SV276 ) ) ) ) @ ( apply @ SV356 @ ( apply @ SV151 @ ( ordered_pair @ ( not_homomorphism1 @ SV356 @ SV151 @ SV276 ) @ ( not_homomorphism2 @ SV356 @ SV151 @ SV276 ) ) ) ) )
| ( homomorphism @ SV356 @ SV151 @ SV276 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[935]) ).
thf(1053,plain,
! [SV394: $i,SV357: $i,SV277: $i,SV152: $i] :
( ( ~ ( member @ ( ordered_pair @ SV152 @ SV277 ) @ ( cross_product @ SV357 @ SV394 ) )
| ( member @ SV152 @ ( unordered_pair @ SV152 @ SV277 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1054,plain,
! [SV395: $i,SV358: $i,SV278: $i,SV153: $i] :
( ( ~ ( member @ ( ordered_pair @ SV153 @ SV278 ) @ ( cross_product @ SV358 @ SV395 ) )
| ( member @ SV278 @ ( unordered_pair @ SV153 @ SV278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[937]) ).
thf(1055,plain,
! [SV396: $i,SV359: $i,SV279: $i,SV154: $i] :
( ( ~ ( member @ ( ordered_pair @ SV154 @ SV279 ) @ ( cross_product @ SV359 @ SV396 ) )
| ( member @ SV154 @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[938]) ).
thf(1056,plain,
! [SV397: $i,SV360: $i,SV280: $i,SV155: $i] :
( ( ~ ( member @ ( ordered_pair @ SV155 @ SV280 ) @ ( cross_product @ SV360 @ SV397 ) )
| ( member @ SV280 @ universal_class ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(1057,plain,
! [SV361: $i,SV281: $i,SV157: $i] :
( ( ( ~ ( subclass @ SV157 @ SV281 ) )
= $true )
| ( ( ~ ( subclass @ SV281 @ SV361 )
| ( subclass @ SV157 @ SV361 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[940]) ).
thf(1058,plain,
! [SV282: $i,SV159: $i,SV2: $i] :
( ( ( equalish @ SV2 @ SV159 )
= $false )
| ( ( ~ ( equalish @ SV159 @ SV282 )
| ( equalish @ SV2 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[942]) ).
thf(1059,plain,
! [SV283: $i,SV160: $i,SV3: $i] :
( ( ( equalish @ SV3 @ SV160 )
= $false )
| ( ( equalish @ ( apply @ SV3 @ SV283 ) @ ( apply @ SV160 @ SV283 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[943]) ).
thf(1060,plain,
! [SV284: $i,SV161: $i,SV4: $i] :
( ( ( equalish @ SV4 @ SV161 )
= $false )
| ( ( equalish @ ( apply @ SV284 @ SV4 ) @ ( apply @ SV284 @ SV161 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[944]) ).
thf(1061,plain,
! [SV285: $i,SV164: $i,SV7: $i] :
( ( ( equalish @ SV7 @ SV164 )
= $false )
| ( ( equalish @ ( compose @ SV7 @ SV285 ) @ ( compose @ SV164 @ SV285 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[947]) ).
thf(1062,plain,
! [SV286: $i,SV165: $i,SV8: $i] :
( ( ( equalish @ SV8 @ SV165 )
= $false )
| ( ( equalish @ ( compose @ SV286 @ SV8 ) @ ( compose @ SV286 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[948]) ).
thf(1063,plain,
! [SV287: $i,SV166: $i,SV9: $i] :
( ( ( equalish @ SV9 @ SV166 )
= $false )
| ( ( equalish @ ( cross_product @ SV9 @ SV287 ) @ ( cross_product @ SV166 @ SV287 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[949]) ).
thf(1064,plain,
! [SV288: $i,SV167: $i,SV10: $i] :
( ( ( equalish @ SV10 @ SV167 )
= $false )
| ( ( equalish @ ( cross_product @ SV288 @ SV10 ) @ ( cross_product @ SV288 @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[950]) ).
thf(1065,plain,
! [SV289: $i,SV169: $i,SV12: $i] :
( ( ( equalish @ SV12 @ SV169 )
= $false )
| ( ( equalish @ ( symmetric_difference @ SV12 @ SV289 ) @ ( symmetric_difference @ SV169 @ SV289 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[952]) ).
thf(1066,plain,
! [SV290: $i,SV170: $i,SV13: $i] :
( ( ( equalish @ SV13 @ SV170 )
= $false )
| ( ( equalish @ ( symmetric_difference @ SV290 @ SV13 ) @ ( symmetric_difference @ SV290 @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[953]) ).
thf(1067,plain,
! [SV362: $i,SV291: $i,SV171: $i,SV14: $i] :
( ( ( ~ ( equalish @ SV14 @ SV171 ) )
= $true )
| ( ( equalish @ ( domain @ SV14 @ SV291 @ SV362 ) @ ( domain @ SV171 @ SV291 @ SV362 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[954]) ).
thf(1068,plain,
! [SV363: $i,SV292: $i,SV172: $i,SV15: $i] :
( ( ( ~ ( equalish @ SV15 @ SV172 ) )
= $true )
| ( ( equalish @ ( domain @ SV292 @ SV15 @ SV363 ) @ ( domain @ SV292 @ SV172 @ SV363 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[955]) ).
thf(1069,plain,
! [SV364: $i,SV293: $i,SV173: $i,SV16: $i] :
( ( ( ~ ( equalish @ SV16 @ SV173 ) )
= $true )
| ( ( equalish @ ( domain @ SV293 @ SV364 @ SV16 ) @ ( domain @ SV293 @ SV364 @ SV173 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[956]) ).
thf(1070,plain,
! [SV294: $i,SV177: $i,SV20: $i] :
( ( ( equalish @ SV20 @ SV177 )
= $false )
| ( ( equalish @ ( image @ SV20 @ SV294 ) @ ( image @ SV177 @ SV294 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[960]) ).
thf(1071,plain,
! [SV295: $i,SV178: $i,SV21: $i] :
( ( ( equalish @ SV21 @ SV178 )
= $false )
| ( ( equalish @ ( image @ SV295 @ SV21 ) @ ( image @ SV295 @ SV178 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[961]) ).
thf(1072,plain,
! [SV296: $i,SV179: $i,SV22: $i] :
( ( ( equalish @ SV22 @ SV179 )
= $false )
| ( ( equalish @ ( intersection @ SV22 @ SV296 ) @ ( intersection @ SV179 @ SV296 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[962]) ).
thf(1073,plain,
! [SV297: $i,SV180: $i,SV23: $i] :
( ( ( equalish @ SV23 @ SV180 )
= $false )
| ( ( equalish @ ( intersection @ SV297 @ SV23 ) @ ( intersection @ SV297 @ SV180 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[963]) ).
thf(1074,plain,
! [SV365: $i,SV298: $i,SV182: $i,SV25: $i] :
( ( ( ~ ( equalish @ SV25 @ SV182 ) )
= $true )
| ( ( equalish @ ( not_homomorphism1 @ SV25 @ SV298 @ SV365 ) @ ( not_homomorphism1 @ SV182 @ SV298 @ SV365 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[965]) ).
thf(1075,plain,
! [SV366: $i,SV299: $i,SV183: $i,SV26: $i] :
( ( ( ~ ( equalish @ SV26 @ SV183 ) )
= $true )
| ( ( equalish @ ( not_homomorphism1 @ SV299 @ SV26 @ SV366 ) @ ( not_homomorphism1 @ SV299 @ SV183 @ SV366 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[966]) ).
thf(1076,plain,
! [SV367: $i,SV300: $i,SV184: $i,SV27: $i] :
( ( ( ~ ( equalish @ SV27 @ SV184 ) )
= $true )
| ( ( equalish @ ( not_homomorphism1 @ SV300 @ SV367 @ SV27 ) @ ( not_homomorphism1 @ SV300 @ SV367 @ SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[967]) ).
thf(1077,plain,
! [SV368: $i,SV301: $i,SV185: $i,SV28: $i] :
( ( ( ~ ( equalish @ SV28 @ SV185 ) )
= $true )
| ( ( equalish @ ( not_homomorphism2 @ SV28 @ SV301 @ SV368 ) @ ( not_homomorphism2 @ SV185 @ SV301 @ SV368 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[968]) ).
thf(1078,plain,
! [SV369: $i,SV302: $i,SV186: $i,SV29: $i] :
( ( ( ~ ( equalish @ SV29 @ SV186 ) )
= $true )
| ( ( equalish @ ( not_homomorphism2 @ SV302 @ SV29 @ SV369 ) @ ( not_homomorphism2 @ SV302 @ SV186 @ SV369 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[969]) ).
thf(1079,plain,
! [SV370: $i,SV303: $i,SV187: $i,SV30: $i] :
( ( ( ~ ( equalish @ SV30 @ SV187 ) )
= $true )
| ( ( equalish @ ( not_homomorphism2 @ SV303 @ SV370 @ SV30 ) @ ( not_homomorphism2 @ SV303 @ SV370 @ SV187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[970]) ).
thf(1080,plain,
! [SV304: $i,SV188: $i,SV31: $i] :
( ( ( equalish @ SV31 @ SV188 )
= $false )
| ( ( equalish @ ( not_subclass_element @ SV31 @ SV304 ) @ ( not_subclass_element @ SV188 @ SV304 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[971]) ).
thf(1081,plain,
! [SV305: $i,SV189: $i,SV32: $i] :
( ( ( equalish @ SV32 @ SV189 )
= $false )
| ( ( equalish @ ( not_subclass_element @ SV305 @ SV32 ) @ ( not_subclass_element @ SV305 @ SV189 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[972]) ).
thf(1082,plain,
! [SV306: $i,SV190: $i,SV33: $i] :
( ( ( equalish @ SV33 @ SV190 )
= $false )
| ( ( equalish @ ( ordered_pair @ SV33 @ SV306 ) @ ( ordered_pair @ SV190 @ SV306 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[973]) ).
thf(1083,plain,
! [SV307: $i,SV191: $i,SV34: $i] :
( ( ( equalish @ SV34 @ SV191 )
= $false )
| ( ( equalish @ ( ordered_pair @ SV307 @ SV34 ) @ ( ordered_pair @ SV307 @ SV191 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[974]) ).
thf(1084,plain,
! [SV371: $i,SV308: $i,SV193: $i,SV36: $i] :
( ( ( ~ ( equalish @ SV36 @ SV193 ) )
= $true )
| ( ( equalish @ ( range @ SV36 @ SV308 @ SV371 ) @ ( range @ SV193 @ SV308 @ SV371 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[976]) ).
thf(1085,plain,
! [SV372: $i,SV309: $i,SV194: $i,SV37: $i] :
( ( ( ~ ( equalish @ SV37 @ SV194 ) )
= $true )
| ( ( equalish @ ( range @ SV309 @ SV37 @ SV372 ) @ ( range @ SV309 @ SV194 @ SV372 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[977]) ).
thf(1086,plain,
! [SV373: $i,SV310: $i,SV195: $i,SV38: $i] :
( ( ( ~ ( equalish @ SV38 @ SV195 ) )
= $true )
| ( ( equalish @ ( range @ SV310 @ SV373 @ SV38 ) @ ( range @ SV310 @ SV373 @ SV195 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[978]) ).
thf(1087,plain,
! [SV374: $i,SV311: $i,SV198: $i,SV41: $i] :
( ( ( ~ ( equalish @ SV41 @ SV198 ) )
= $true )
| ( ( equalish @ ( restrict @ SV41 @ SV311 @ SV374 ) @ ( restrict @ SV198 @ SV311 @ SV374 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[981]) ).
thf(1088,plain,
! [SV375: $i,SV312: $i,SV199: $i,SV42: $i] :
( ( ( ~ ( equalish @ SV42 @ SV199 ) )
= $true )
| ( ( equalish @ ( restrict @ SV312 @ SV42 @ SV375 ) @ ( restrict @ SV312 @ SV199 @ SV375 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[982]) ).
thf(1089,plain,
! [SV376: $i,SV313: $i,SV200: $i,SV43: $i] :
( ( ( ~ ( equalish @ SV43 @ SV200 ) )
= $true )
| ( ( equalish @ ( restrict @ SV313 @ SV376 @ SV43 ) @ ( restrict @ SV313 @ SV376 @ SV200 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[983]) ).
thf(1090,plain,
! [SV314: $i,SV206: $i,SV49: $i] :
( ( ( equalish @ SV49 @ SV206 )
= $false )
| ( ( equalish @ ( union @ SV49 @ SV314 ) @ ( union @ SV206 @ SV314 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[989]) ).
thf(1091,plain,
! [SV315: $i,SV207: $i,SV50: $i] :
( ( ( equalish @ SV50 @ SV207 )
= $false )
| ( ( equalish @ ( union @ SV315 @ SV50 ) @ ( union @ SV315 @ SV207 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[990]) ).
thf(1092,plain,
! [SV316: $i,SV208: $i,SV51: $i] :
( ( ( equalish @ SV51 @ SV208 )
= $false )
| ( ( equalish @ ( unordered_pair @ SV51 @ SV316 ) @ ( unordered_pair @ SV208 @ SV316 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[991]) ).
thf(1093,plain,
! [SV317: $i,SV209: $i,SV52: $i] :
( ( ( equalish @ SV52 @ SV209 )
= $false )
| ( ( equalish @ ( unordered_pair @ SV317 @ SV52 ) @ ( unordered_pair @ SV317 @ SV209 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[992]) ).
thf(1094,plain,
! [SV377: $i,SV318: $i,SV210: $i,SV53: $i] :
( ( ( ~ ( equalish @ SV53 @ SV210 ) )
= $true )
| ( ( ~ ( compatible @ SV53 @ SV318 @ SV377 )
| ( compatible @ SV210 @ SV318 @ SV377 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[993]) ).
thf(1095,plain,
! [SV378: $i,SV319: $i,SV211: $i,SV54: $i] :
( ( ( ~ ( equalish @ SV54 @ SV211 ) )
= $true )
| ( ( ~ ( compatible @ SV319 @ SV54 @ SV378 )
| ( compatible @ SV319 @ SV211 @ SV378 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[994]) ).
thf(1096,plain,
! [SV379: $i,SV320: $i,SV212: $i,SV55: $i] :
( ( ( ~ ( equalish @ SV55 @ SV212 ) )
= $true )
| ( ( ~ ( compatible @ SV320 @ SV379 @ SV55 )
| ( compatible @ SV320 @ SV379 @ SV212 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[995]) ).
thf(1097,plain,
! [SV213: $i,SV56: $i] :
( ( ( ~ ( function @ SV56 ) )
= $true )
| ( ( function @ SV213 )
= $true )
| ( ( equalish @ SV56 @ SV213 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[996]) ).
thf(1098,plain,
! [SV380: $i,SV321: $i,SV214: $i,SV57: $i] :
( ( ( ~ ( equalish @ SV57 @ SV214 ) )
= $true )
| ( ( ~ ( homomorphism @ SV57 @ SV321 @ SV380 )
| ( homomorphism @ SV214 @ SV321 @ SV380 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[997]) ).
thf(1099,plain,
! [SV381: $i,SV322: $i,SV215: $i,SV58: $i] :
( ( ( ~ ( equalish @ SV58 @ SV215 ) )
= $true )
| ( ( ~ ( homomorphism @ SV322 @ SV58 @ SV381 )
| ( homomorphism @ SV322 @ SV215 @ SV381 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[998]) ).
thf(1100,plain,
! [SV382: $i,SV323: $i,SV216: $i,SV59: $i] :
( ( ( ~ ( equalish @ SV59 @ SV216 ) )
= $true )
| ( ( ~ ( homomorphism @ SV323 @ SV382 @ SV59 )
| ( homomorphism @ SV323 @ SV382 @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[999]) ).
thf(1101,plain,
! [SV217: $i,SV60: $i] :
( ( ( ~ ( inductive @ SV60 ) )
= $true )
| ( ( inductive @ SV217 )
= $true )
| ( ( equalish @ SV60 @ SV217 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1000]) ).
thf(1102,plain,
! [SV324: $i,SV218: $i,SV61: $i] :
( ( ( equalish @ SV61 @ SV218 )
= $false )
| ( ( ~ ( member @ SV61 @ SV324 )
| ( member @ SV218 @ SV324 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1001]) ).
thf(1103,plain,
! [SV325: $i,SV219: $i,SV62: $i] :
( ( ( equalish @ SV62 @ SV219 )
= $false )
| ( ( ~ ( member @ SV325 @ SV62 )
| ( member @ SV325 @ SV219 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1002]) ).
thf(1104,plain,
! [SV220: $i,SV63: $i] :
( ( ( ~ ( one_to_one @ SV63 ) )
= $true )
| ( ( one_to_one @ SV220 )
= $true )
| ( ( equalish @ SV63 @ SV220 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1003]) ).
thf(1105,plain,
! [SV221: $i,SV64: $i] :
( ( ( ~ ( operation @ SV64 ) )
= $true )
| ( ( operation @ SV221 )
= $true )
| ( ( equalish @ SV64 @ SV221 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1004]) ).
thf(1106,plain,
! [SV222: $i,SV65: $i] :
( ( ( ~ ( single_valued_class @ SV65 ) )
= $true )
| ( ( single_valued_class @ SV222 )
= $true )
| ( ( equalish @ SV65 @ SV222 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1005]) ).
thf(1107,plain,
! [SV326: $i,SV223: $i,SV66: $i] :
( ( ( equalish @ SV66 @ SV223 )
= $false )
| ( ( ~ ( subclass @ SV66 @ SV326 )
| ( subclass @ SV223 @ SV326 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1006]) ).
thf(1108,plain,
! [SV327: $i,SV224: $i,SV67: $i] :
( ( ( equalish @ SV67 @ SV224 )
= $false )
| ( ( ~ ( subclass @ SV327 @ SV67 )
| ( subclass @ SV327 @ SV224 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1007]) ).
thf(1109,plain,
! [SV328: $i,SV225: $i,SV68: $i] :
( ( ( subclass @ SV68 @ SV225 )
= $false )
| ( ( ~ ( member @ SV328 @ SV68 )
| ( member @ SV328 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1008]) ).
thf(1110,plain,
! [SV74: $i,SV230: $i] :
( ( ( ~ ( subclass @ SV230 @ SV74 ) )
= $true )
| ( ( equalish @ SV74 @ SV230 )
= $true )
| ( ( subclass @ SV74 @ SV230 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1012]) ).
thf(1111,plain,
! [SV329: $i,SV231: $i,SV75: $i] :
( ( ( member @ SV75 @ ( unordered_pair @ SV231 @ SV329 ) )
= $false )
| ( ( ( equalish @ SV75 @ SV231 )
| ( equalish @ SV75 @ SV329 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1013]) ).
thf(1112,plain,
! [SV383: $i,SV330: $i,SV236: $i,SV81: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV81 @ SV236 ) @ ( cross_product @ SV330 @ SV383 ) ) )
= $true )
| ( ( member @ SV81 @ SV330 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1016]) ).
thf(1113,plain,
! [SV384: $i,SV331: $i,SV237: $i,SV82: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV82 @ SV237 ) @ ( cross_product @ SV331 @ SV384 ) ) )
= $true )
| ( ( member @ SV237 @ SV384 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1017]) ).
thf(1114,plain,
! [SV385: $i,SV332: $i,SV238: $i,SV83: $i] :
( ( ( ~ ( member @ SV83 @ SV238 ) )
= $true )
| ( ( ~ ( member @ SV332 @ SV385 )
| ( member @ ( ordered_pair @ SV83 @ SV332 ) @ ( cross_product @ SV238 @ SV385 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1018]) ).
thf(1115,plain,
! [SV333: $i,SV239: $i,SV84: $i] :
( ( ( member @ SV84 @ ( cross_product @ SV239 @ SV333 ) )
= $false )
| ( ( equalish @ ( ordered_pair @ ( first @ SV84 ) @ ( second @ SV84 ) ) @ SV84 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1019]) ).
thf(1116,plain,
! [SV241: $i,SV86: $i] :
( ( ( ~ ( member @ SV86 @ SV241 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV86 @ SV241 ) @ element_relation )
= $true )
| ( ( member @ ( ordered_pair @ SV86 @ SV241 ) @ ( cross_product @ universal_class @ universal_class ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1021]) ).
thf(1117,plain,
! [SV334: $i,SV242: $i,SV87: $i] :
( ( ( member @ SV87 @ ( intersection @ SV242 @ SV334 ) )
= $false )
| ( ( member @ SV87 @ SV242 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1022]) ).
thf(1118,plain,
! [SV335: $i,SV243: $i,SV88: $i] :
( ( ( member @ SV88 @ ( intersection @ SV243 @ SV335 ) )
= $false )
| ( ( member @ SV88 @ SV335 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1023]) ).
thf(1119,plain,
! [SV336: $i,SV244: $i,SV89: $i] :
( ( ( member @ SV89 @ SV244 )
= $false )
| ( ( ~ ( member @ SV89 @ SV336 )
| ( member @ SV89 @ ( intersection @ SV244 @ SV336 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1024]) ).
thf(1120,plain,
! [SV245: $i,SV90: $i] :
( ( ( member @ SV90 @ SV245 )
= $false )
| ( ( member @ SV90 @ ( complement @ SV245 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1025]) ).
thf(1121,plain,
! [SV246: $i,SV91: $i] :
( ( ( member @ SV91 @ ( complement @ SV246 ) )
= $true )
| ( ( member @ SV91 @ SV246 )
= $true )
| ( ( member @ SV91 @ universal_class )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1026]) ).
thf(1122,plain,
! [SV96: $i,SV251: $i] :
( ( ( member @ SV251 @ ( domain_of @ SV96 ) )
= $false )
| ( ( equalish @ ( restrict @ SV96 @ ( singleton @ SV251 ) @ universal_class ) @ null_class )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1027]) ).
thf(1123,plain,
! [SV97: $i,SV252: $i] :
( ( ( equalish @ ( restrict @ SV252 @ ( singleton @ SV97 ) @ universal_class ) @ null_class )
= $true )
| ( ( member @ SV97 @ ( domain_of @ SV252 ) )
= $true )
| ( ( member @ SV97 @ universal_class )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1028]) ).
thf(1124,plain,
! [SV386: $i,SV339: $i,SV253: $i,SV99: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV99 @ SV253 ) @ SV339 ) @ ( rotate @ SV386 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV253 @ SV339 ) @ SV99 ) @ SV386 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1029]) ).
thf(1125,plain,
! [SV387: $i,SV340: $i,SV254: $i,SV100: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV100 @ SV254 ) @ SV340 ) @ SV387 ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV340 @ SV100 ) @ SV254 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV340 @ SV100 ) @ SV254 ) @ ( rotate @ SV387 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1030]) ).
thf(1126,plain,
! [SV388: $i,SV341: $i,SV255: $i,SV102: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV102 @ SV255 ) @ SV341 ) @ ( flip @ SV388 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV255 @ SV102 ) @ SV341 ) @ SV388 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1031]) ).
thf(1127,plain,
! [SV389: $i,SV342: $i,SV256: $i,SV103: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV103 @ SV256 ) @ SV342 ) @ SV389 ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV256 @ SV103 ) @ SV342 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV256 @ SV103 ) @ SV342 ) @ ( flip @ SV389 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1032]) ).
thf(1128,plain,
! [SV261: $i,SV111: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV111 @ SV261 ) @ ( cross_product @ universal_class @ universal_class ) ) )
= $true )
| ( ( member @ ( ordered_pair @ SV111 @ SV261 ) @ successor_relation )
= $true )
| ( ( equalish @ ( successor @ SV111 ) @ SV261 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1034]) ).
thf(1129,plain,
! [SV114: $i] :
( ( ( subclass @ ( image @ successor_relation @ SV114 ) @ SV114 )
= $false )
| ( ( inductive @ SV114 )
= $true )
| ( ( member @ null_class @ SV114 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1035]) ).
thf(1130,plain,
! [SV390: $i,SV345: $i,SV263: $i,SV121: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV121 @ SV263 ) @ ( compose @ SV345 @ SV390 ) ) )
= $true )
| ( ( member @ SV263 @ ( image @ SV345 @ ( image @ SV390 @ ( singleton @ SV121 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1036]) ).
thf(1131,plain,
! [SV391: $i,SV346: $i,SV264: $i,SV122: $i] :
( ( ( ~ ( member @ SV122 @ ( image @ SV264 @ ( image @ SV346 @ ( singleton @ SV391 ) ) ) ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ SV391 @ SV122 ) @ ( cross_product @ universal_class @ universal_class ) )
| ( member @ ( ordered_pair @ SV391 @ SV122 ) @ ( compose @ SV264 @ SV346 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1037]) ).
thf(1132,plain,
! [SV127: $i] :
( ( ( subclass @ ( compose @ SV127 @ ( inverse @ SV127 ) ) @ identity_relation )
= $false )
| ( ( function @ SV127 )
= $true )
| ( ( subclass @ SV127 @ ( cross_product @ universal_class @ universal_class ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1038]) ).
thf(1133,plain,
! [SV128: $i,SV265: $i] :
( ( ( ~ ( member @ SV265 @ universal_class ) )
= $true )
| ( ( member @ ( image @ SV128 @ SV265 ) @ universal_class )
= $true )
| ( ( function @ SV128 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1039]) ).
thf(1134,plain,
! [SV135: $i] :
( ( ( function @ SV135 )
= $false )
| ( ( one_to_one @ SV135 )
= $true )
| ( ( function @ ( inverse @ SV135 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1041]) ).
thf(1135,plain,
! [SV141: $i] :
( ( ( equalish @ ( cross_product @ ( domain_of @ ( domain_of @ SV141 ) ) @ ( domain_of @ ( domain_of @ SV141 ) ) ) @ ( domain_of @ SV141 ) )
= $false )
| ( ( ~ ( subclass @ ( range_of @ SV141 ) @ ( domain_of @ ( domain_of @ SV141 ) ) )
| ( operation @ SV141 ) )
= $true )
| ( ( function @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1042]) ).
thf(1136,plain,
! [SV347: $i,SV267: $i,SV142: $i] :
( ( ( compatible @ SV142 @ SV267 @ SV347 )
= $false )
| ( ( function @ SV142 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1043]) ).
thf(1137,plain,
! [SV348: $i,SV268: $i,SV143: $i] :
( ( ( compatible @ SV143 @ SV268 @ SV348 )
= $false )
| ( ( equalish @ ( domain_of @ ( domain_of @ SV268 ) ) @ ( domain_of @ SV143 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1044]) ).
thf(1138,plain,
! [SV349: $i,SV269: $i,SV144: $i] :
( ( ( compatible @ SV144 @ SV269 @ SV349 )
= $false )
| ( ( subclass @ ( range_of @ SV144 ) @ ( domain_of @ ( domain_of @ SV349 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1045]) ).
thf(1139,plain,
! [SV392: $i,SV350: $i,SV270: $i,SV145: $i] :
( ( ( ~ ( function @ SV145 ) )
= $true )
| ( ( ~ ( equalish @ ( domain_of @ ( domain_of @ SV270 ) ) @ ( domain_of @ SV145 ) )
| ~ ( subclass @ ( range_of @ SV145 ) @ ( domain_of @ ( domain_of @ SV350 ) ) )
| ( compatible @ SV392 @ SV270 @ SV350 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1046]) ).
thf(1140,plain,
! [SV351: $i,SV271: $i,SV146: $i] :
( ( ( homomorphism @ SV146 @ SV271 @ SV351 )
= $false )
| ( ( operation @ SV271 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1047]) ).
thf(1141,plain,
! [SV352: $i,SV272: $i,SV147: $i] :
( ( ( homomorphism @ SV147 @ SV272 @ SV352 )
= $false )
| ( ( operation @ SV352 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1048]) ).
thf(1142,plain,
! [SV353: $i,SV273: $i,SV148: $i] :
( ( ( homomorphism @ SV148 @ SV273 @ SV353 )
= $false )
| ( ( compatible @ SV148 @ SV273 @ SV353 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1049]) ).
thf(1143,plain,
! [SV398: $i,SV393: $i,SV354: $i,SV274: $i,SV149: $i] :
( ( ~ ( homomorphism @ SV149 @ SV274 @ SV354 )
| ~ ( member @ ( ordered_pair @ SV393 @ SV398 ) @ ( domain_of @ SV274 ) )
| ( equalish @ ( apply @ SV354 @ ( ordered_pair @ ( apply @ SV149 @ SV393 ) @ ( apply @ SV149 @ SV398 ) ) ) @ ( apply @ SV149 @ ( apply @ SV274 @ ( ordered_pair @ SV393 @ SV398 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1144,plain,
! [SV355: $i,SV275: $i,SV150: $i] :
( ( ( operation @ SV150 )
= $false )
| ( ( ~ ( operation @ SV275 )
| ~ ( compatible @ SV355 @ SV150 @ SV275 )
| ( member @ ( ordered_pair @ ( not_homomorphism1 @ SV355 @ SV150 @ SV275 ) @ ( not_homomorphism2 @ SV355 @ SV150 @ SV275 ) ) @ ( domain_of @ SV150 ) )
| ( homomorphism @ SV355 @ SV150 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1051]) ).
thf(1145,plain,
! [SV356: $i,SV276: $i,SV151: $i] :
( ( ( operation @ SV151 )
= $false )
| ( ( ~ ( operation @ SV276 )
| ~ ( compatible @ SV356 @ SV151 @ SV276 )
| ~ ( equalish @ ( apply @ SV276 @ ( ordered_pair @ ( apply @ SV356 @ ( not_homomorphism1 @ SV356 @ SV151 @ SV276 ) ) @ ( apply @ SV356 @ ( not_homomorphism2 @ SV356 @ SV151 @ SV276 ) ) ) ) @ ( apply @ SV356 @ ( apply @ SV151 @ ( ordered_pair @ ( not_homomorphism1 @ SV356 @ SV151 @ SV276 ) @ ( not_homomorphism2 @ SV356 @ SV151 @ SV276 ) ) ) ) )
| ( homomorphism @ SV356 @ SV151 @ SV276 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1052]) ).
thf(1146,plain,
! [SV394: $i,SV357: $i,SV277: $i,SV152: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV152 @ SV277 ) @ ( cross_product @ SV357 @ SV394 ) ) )
= $true )
| ( ( member @ SV152 @ ( unordered_pair @ SV152 @ SV277 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1053]) ).
thf(1147,plain,
! [SV395: $i,SV358: $i,SV278: $i,SV153: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV153 @ SV278 ) @ ( cross_product @ SV358 @ SV395 ) ) )
= $true )
| ( ( member @ SV278 @ ( unordered_pair @ SV153 @ SV278 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1054]) ).
thf(1148,plain,
! [SV396: $i,SV359: $i,SV279: $i,SV154: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV154 @ SV279 ) @ ( cross_product @ SV359 @ SV396 ) ) )
= $true )
| ( ( member @ SV154 @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1055]) ).
thf(1149,plain,
! [SV397: $i,SV360: $i,SV280: $i,SV155: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV155 @ SV280 ) @ ( cross_product @ SV360 @ SV397 ) ) )
= $true )
| ( ( member @ SV280 @ universal_class )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1056]) ).
thf(1150,plain,
! [SV361: $i,SV281: $i,SV157: $i] :
( ( ( subclass @ SV157 @ SV281 )
= $false )
| ( ( ~ ( subclass @ SV281 @ SV361 )
| ( subclass @ SV157 @ SV361 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1057]) ).
thf(1151,plain,
! [SV2: $i,SV282: $i,SV159: $i] :
( ( ( ~ ( equalish @ SV159 @ SV282 ) )
= $true )
| ( ( equalish @ SV2 @ SV282 )
= $true )
| ( ( equalish @ SV2 @ SV159 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1058]) ).
thf(1152,plain,
! [SV362: $i,SV291: $i,SV171: $i,SV14: $i] :
( ( ( equalish @ SV14 @ SV171 )
= $false )
| ( ( equalish @ ( domain @ SV14 @ SV291 @ SV362 ) @ ( domain @ SV171 @ SV291 @ SV362 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1067]) ).
thf(1153,plain,
! [SV363: $i,SV292: $i,SV172: $i,SV15: $i] :
( ( ( equalish @ SV15 @ SV172 )
= $false )
| ( ( equalish @ ( domain @ SV292 @ SV15 @ SV363 ) @ ( domain @ SV292 @ SV172 @ SV363 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1068]) ).
thf(1154,plain,
! [SV364: $i,SV293: $i,SV173: $i,SV16: $i] :
( ( ( equalish @ SV16 @ SV173 )
= $false )
| ( ( equalish @ ( domain @ SV293 @ SV364 @ SV16 ) @ ( domain @ SV293 @ SV364 @ SV173 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1069]) ).
thf(1155,plain,
! [SV365: $i,SV298: $i,SV182: $i,SV25: $i] :
( ( ( equalish @ SV25 @ SV182 )
= $false )
| ( ( equalish @ ( not_homomorphism1 @ SV25 @ SV298 @ SV365 ) @ ( not_homomorphism1 @ SV182 @ SV298 @ SV365 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1074]) ).
thf(1156,plain,
! [SV366: $i,SV299: $i,SV183: $i,SV26: $i] :
( ( ( equalish @ SV26 @ SV183 )
= $false )
| ( ( equalish @ ( not_homomorphism1 @ SV299 @ SV26 @ SV366 ) @ ( not_homomorphism1 @ SV299 @ SV183 @ SV366 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1075]) ).
thf(1157,plain,
! [SV367: $i,SV300: $i,SV184: $i,SV27: $i] :
( ( ( equalish @ SV27 @ SV184 )
= $false )
| ( ( equalish @ ( not_homomorphism1 @ SV300 @ SV367 @ SV27 ) @ ( not_homomorphism1 @ SV300 @ SV367 @ SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1076]) ).
thf(1158,plain,
! [SV368: $i,SV301: $i,SV185: $i,SV28: $i] :
( ( ( equalish @ SV28 @ SV185 )
= $false )
| ( ( equalish @ ( not_homomorphism2 @ SV28 @ SV301 @ SV368 ) @ ( not_homomorphism2 @ SV185 @ SV301 @ SV368 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1077]) ).
thf(1159,plain,
! [SV369: $i,SV302: $i,SV186: $i,SV29: $i] :
( ( ( equalish @ SV29 @ SV186 )
= $false )
| ( ( equalish @ ( not_homomorphism2 @ SV302 @ SV29 @ SV369 ) @ ( not_homomorphism2 @ SV302 @ SV186 @ SV369 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1078]) ).
thf(1160,plain,
! [SV370: $i,SV303: $i,SV187: $i,SV30: $i] :
( ( ( equalish @ SV30 @ SV187 )
= $false )
| ( ( equalish @ ( not_homomorphism2 @ SV303 @ SV370 @ SV30 ) @ ( not_homomorphism2 @ SV303 @ SV370 @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1079]) ).
thf(1161,plain,
! [SV371: $i,SV308: $i,SV193: $i,SV36: $i] :
( ( ( equalish @ SV36 @ SV193 )
= $false )
| ( ( equalish @ ( range @ SV36 @ SV308 @ SV371 ) @ ( range @ SV193 @ SV308 @ SV371 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1084]) ).
thf(1162,plain,
! [SV372: $i,SV309: $i,SV194: $i,SV37: $i] :
( ( ( equalish @ SV37 @ SV194 )
= $false )
| ( ( equalish @ ( range @ SV309 @ SV37 @ SV372 ) @ ( range @ SV309 @ SV194 @ SV372 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1085]) ).
thf(1163,plain,
! [SV373: $i,SV310: $i,SV195: $i,SV38: $i] :
( ( ( equalish @ SV38 @ SV195 )
= $false )
| ( ( equalish @ ( range @ SV310 @ SV373 @ SV38 ) @ ( range @ SV310 @ SV373 @ SV195 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1086]) ).
thf(1164,plain,
! [SV374: $i,SV311: $i,SV198: $i,SV41: $i] :
( ( ( equalish @ SV41 @ SV198 )
= $false )
| ( ( equalish @ ( restrict @ SV41 @ SV311 @ SV374 ) @ ( restrict @ SV198 @ SV311 @ SV374 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1087]) ).
thf(1165,plain,
! [SV375: $i,SV312: $i,SV199: $i,SV42: $i] :
( ( ( equalish @ SV42 @ SV199 )
= $false )
| ( ( equalish @ ( restrict @ SV312 @ SV42 @ SV375 ) @ ( restrict @ SV312 @ SV199 @ SV375 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1088]) ).
thf(1166,plain,
! [SV376: $i,SV313: $i,SV200: $i,SV43: $i] :
( ( ( equalish @ SV43 @ SV200 )
= $false )
| ( ( equalish @ ( restrict @ SV313 @ SV376 @ SV43 ) @ ( restrict @ SV313 @ SV376 @ SV200 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1089]) ).
thf(1167,plain,
! [SV377: $i,SV318: $i,SV210: $i,SV53: $i] :
( ( ( equalish @ SV53 @ SV210 )
= $false )
| ( ( ~ ( compatible @ SV53 @ SV318 @ SV377 )
| ( compatible @ SV210 @ SV318 @ SV377 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1094]) ).
thf(1168,plain,
! [SV378: $i,SV319: $i,SV211: $i,SV54: $i] :
( ( ( equalish @ SV54 @ SV211 )
= $false )
| ( ( ~ ( compatible @ SV319 @ SV54 @ SV378 )
| ( compatible @ SV319 @ SV211 @ SV378 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1095]) ).
thf(1169,plain,
! [SV379: $i,SV320: $i,SV212: $i,SV55: $i] :
( ( ( equalish @ SV55 @ SV212 )
= $false )
| ( ( ~ ( compatible @ SV320 @ SV379 @ SV55 )
| ( compatible @ SV320 @ SV379 @ SV212 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1096]) ).
thf(1170,plain,
! [SV213: $i,SV56: $i] :
( ( ( function @ SV56 )
= $false )
| ( ( function @ SV213 )
= $true )
| ( ( equalish @ SV56 @ SV213 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1097]) ).
thf(1171,plain,
! [SV380: $i,SV321: $i,SV214: $i,SV57: $i] :
( ( ( equalish @ SV57 @ SV214 )
= $false )
| ( ( ~ ( homomorphism @ SV57 @ SV321 @ SV380 )
| ( homomorphism @ SV214 @ SV321 @ SV380 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1098]) ).
thf(1172,plain,
! [SV381: $i,SV322: $i,SV215: $i,SV58: $i] :
( ( ( equalish @ SV58 @ SV215 )
= $false )
| ( ( ~ ( homomorphism @ SV322 @ SV58 @ SV381 )
| ( homomorphism @ SV322 @ SV215 @ SV381 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1099]) ).
thf(1173,plain,
! [SV382: $i,SV323: $i,SV216: $i,SV59: $i] :
( ( ( equalish @ SV59 @ SV216 )
= $false )
| ( ( ~ ( homomorphism @ SV323 @ SV382 @ SV59 )
| ( homomorphism @ SV323 @ SV382 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1100]) ).
thf(1174,plain,
! [SV217: $i,SV60: $i] :
( ( ( inductive @ SV60 )
= $false )
| ( ( inductive @ SV217 )
= $true )
| ( ( equalish @ SV60 @ SV217 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1101]) ).
thf(1175,plain,
! [SV218: $i,SV324: $i,SV61: $i] :
( ( ( ~ ( member @ SV61 @ SV324 ) )
= $true )
| ( ( member @ SV218 @ SV324 )
= $true )
| ( ( equalish @ SV61 @ SV218 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1102]) ).
thf(1176,plain,
! [SV219: $i,SV62: $i,SV325: $i] :
( ( ( ~ ( member @ SV325 @ SV62 ) )
= $true )
| ( ( member @ SV325 @ SV219 )
= $true )
| ( ( equalish @ SV62 @ SV219 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1103]) ).
thf(1177,plain,
! [SV220: $i,SV63: $i] :
( ( ( one_to_one @ SV63 )
= $false )
| ( ( one_to_one @ SV220 )
= $true )
| ( ( equalish @ SV63 @ SV220 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1104]) ).
thf(1178,plain,
! [SV221: $i,SV64: $i] :
( ( ( operation @ SV64 )
= $false )
| ( ( operation @ SV221 )
= $true )
| ( ( equalish @ SV64 @ SV221 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1105]) ).
thf(1179,plain,
! [SV222: $i,SV65: $i] :
( ( ( single_valued_class @ SV65 )
= $false )
| ( ( single_valued_class @ SV222 )
= $true )
| ( ( equalish @ SV65 @ SV222 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1106]) ).
thf(1180,plain,
! [SV223: $i,SV326: $i,SV66: $i] :
( ( ( ~ ( subclass @ SV66 @ SV326 ) )
= $true )
| ( ( subclass @ SV223 @ SV326 )
= $true )
| ( ( equalish @ SV66 @ SV223 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1107]) ).
thf(1181,plain,
! [SV224: $i,SV67: $i,SV327: $i] :
( ( ( ~ ( subclass @ SV327 @ SV67 ) )
= $true )
| ( ( subclass @ SV327 @ SV224 )
= $true )
| ( ( equalish @ SV67 @ SV224 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1108]) ).
thf(1182,plain,
! [SV225: $i,SV68: $i,SV328: $i] :
( ( ( ~ ( member @ SV328 @ SV68 ) )
= $true )
| ( ( member @ SV328 @ SV225 )
= $true )
| ( ( subclass @ SV68 @ SV225 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1109]) ).
thf(1183,plain,
! [SV74: $i,SV230: $i] :
( ( ( subclass @ SV230 @ SV74 )
= $false )
| ( ( equalish @ SV74 @ SV230 )
= $true )
| ( ( subclass @ SV74 @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1110]) ).
thf(1184,plain,
! [SV329: $i,SV231: $i,SV75: $i] :
( ( ( equalish @ SV75 @ SV231 )
= $true )
| ( ( equalish @ SV75 @ SV329 )
= $true )
| ( ( member @ SV75 @ ( unordered_pair @ SV231 @ SV329 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1111]) ).
thf(1185,plain,
! [SV383: $i,SV330: $i,SV236: $i,SV81: $i] :
( ( ( member @ ( ordered_pair @ SV81 @ SV236 ) @ ( cross_product @ SV330 @ SV383 ) )
= $false )
| ( ( member @ SV81 @ SV330 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1112]) ).
thf(1186,plain,
! [SV384: $i,SV331: $i,SV237: $i,SV82: $i] :
( ( ( member @ ( ordered_pair @ SV82 @ SV237 ) @ ( cross_product @ SV331 @ SV384 ) )
= $false )
| ( ( member @ SV237 @ SV384 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1113]) ).
thf(1187,plain,
! [SV385: $i,SV332: $i,SV238: $i,SV83: $i] :
( ( ( member @ SV83 @ SV238 )
= $false )
| ( ( ~ ( member @ SV332 @ SV385 )
| ( member @ ( ordered_pair @ SV83 @ SV332 ) @ ( cross_product @ SV238 @ SV385 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1114]) ).
thf(1188,plain,
! [SV241: $i,SV86: $i] :
( ( ( member @ SV86 @ SV241 )
= $false )
| ( ( member @ ( ordered_pair @ SV86 @ SV241 ) @ element_relation )
= $true )
| ( ( member @ ( ordered_pair @ SV86 @ SV241 ) @ ( cross_product @ universal_class @ universal_class ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1116]) ).
thf(1189,plain,
! [SV244: $i,SV336: $i,SV89: $i] :
( ( ( ~ ( member @ SV89 @ SV336 ) )
= $true )
| ( ( member @ SV89 @ ( intersection @ SV244 @ SV336 ) )
= $true )
| ( ( member @ SV89 @ SV244 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1119]) ).
thf(1190,plain,
! [SV386: $i,SV339: $i,SV253: $i,SV99: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ SV99 @ SV253 ) @ SV339 ) @ ( rotate @ SV386 ) )
= $false )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV253 @ SV339 ) @ SV99 ) @ SV386 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1124]) ).
thf(1191,plain,
! [SV387: $i,SV340: $i,SV254: $i,SV100: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ SV100 @ SV254 ) @ SV340 ) @ SV387 )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV340 @ SV100 ) @ SV254 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV340 @ SV100 ) @ SV254 ) @ ( rotate @ SV387 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1125]) ).
thf(1192,plain,
! [SV388: $i,SV341: $i,SV255: $i,SV102: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ SV102 @ SV255 ) @ SV341 ) @ ( flip @ SV388 ) )
= $false )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV255 @ SV102 ) @ SV341 ) @ SV388 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1126]) ).
thf(1193,plain,
! [SV389: $i,SV342: $i,SV256: $i,SV103: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ SV103 @ SV256 ) @ SV342 ) @ SV389 )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV256 @ SV103 ) @ SV342 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ SV256 @ SV103 ) @ SV342 ) @ ( flip @ SV389 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1127]) ).
thf(1194,plain,
! [SV261: $i,SV111: $i] :
( ( ( member @ ( ordered_pair @ SV111 @ SV261 ) @ ( cross_product @ universal_class @ universal_class ) )
= $false )
| ( ( member @ ( ordered_pair @ SV111 @ SV261 ) @ successor_relation )
= $true )
| ( ( equalish @ ( successor @ SV111 ) @ SV261 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1128]) ).
thf(1195,plain,
! [SV390: $i,SV345: $i,SV263: $i,SV121: $i] :
( ( ( member @ ( ordered_pair @ SV121 @ SV263 ) @ ( compose @ SV345 @ SV390 ) )
= $false )
| ( ( member @ SV263 @ ( image @ SV345 @ ( image @ SV390 @ ( singleton @ SV121 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1130]) ).
thf(1196,plain,
! [SV391: $i,SV346: $i,SV264: $i,SV122: $i] :
( ( ( member @ SV122 @ ( image @ SV264 @ ( image @ SV346 @ ( singleton @ SV391 ) ) ) )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ SV391 @ SV122 ) @ ( cross_product @ universal_class @ universal_class ) )
| ( member @ ( ordered_pair @ SV391 @ SV122 ) @ ( compose @ SV264 @ SV346 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1131]) ).
thf(1197,plain,
! [SV128: $i,SV265: $i] :
( ( ( member @ SV265 @ universal_class )
= $false )
| ( ( member @ ( image @ SV128 @ SV265 ) @ universal_class )
= $true )
| ( ( function @ SV128 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1133]) ).
thf(1198,plain,
! [SV141: $i] :
( ( ( ~ ( subclass @ ( range_of @ SV141 ) @ ( domain_of @ ( domain_of @ SV141 ) ) ) )
= $true )
| ( ( operation @ SV141 )
= $true )
| ( ( equalish @ ( cross_product @ ( domain_of @ ( domain_of @ SV141 ) ) @ ( domain_of @ ( domain_of @ SV141 ) ) ) @ ( domain_of @ SV141 ) )
= $false )
| ( ( function @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1135]) ).
thf(1199,plain,
! [SV392: $i,SV350: $i,SV270: $i,SV145: $i] :
( ( ( function @ SV145 )
= $false )
| ( ( ~ ( equalish @ ( domain_of @ ( domain_of @ SV270 ) ) @ ( domain_of @ SV145 ) )
| ~ ( subclass @ ( range_of @ SV145 ) @ ( domain_of @ ( domain_of @ SV350 ) ) )
| ( compatible @ SV392 @ SV270 @ SV350 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1139]) ).
thf(1200,plain,
! [SV398: $i,SV393: $i,SV354: $i,SV274: $i,SV149: $i] :
( ( ( ~ ( homomorphism @ SV149 @ SV274 @ SV354 ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ SV393 @ SV398 ) @ ( domain_of @ SV274 ) )
| ( equalish @ ( apply @ SV354 @ ( ordered_pair @ ( apply @ SV149 @ SV393 ) @ ( apply @ SV149 @ SV398 ) ) ) @ ( apply @ SV149 @ ( apply @ SV274 @ ( ordered_pair @ SV393 @ SV398 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1143]) ).
thf(1201,plain,
! [SV150: $i,SV355: $i,SV275: $i] :
( ( ( ~ ( operation @ SV275 ) )
= $true )
| ( ( ~ ( compatible @ SV355 @ SV150 @ SV275 )
| ( member @ ( ordered_pair @ ( not_homomorphism1 @ SV355 @ SV150 @ SV275 ) @ ( not_homomorphism2 @ SV355 @ SV150 @ SV275 ) ) @ ( domain_of @ SV150 ) )
| ( homomorphism @ SV355 @ SV150 @ SV275 ) )
= $true )
| ( ( operation @ SV150 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1144]) ).
thf(1202,plain,
! [SV151: $i,SV356: $i,SV276: $i] :
( ( ( ~ ( operation @ SV276 ) )
= $true )
| ( ( ~ ( compatible @ SV356 @ SV151 @ SV276 )
| ~ ( equalish @ ( apply @ SV276 @ ( ordered_pair @ ( apply @ SV356 @ ( not_homomorphism1 @ SV356 @ SV151 @ SV276 ) ) @ ( apply @ SV356 @ ( not_homomorphism2 @ SV356 @ SV151 @ SV276 ) ) ) ) @ ( apply @ SV356 @ ( apply @ SV151 @ ( ordered_pair @ ( not_homomorphism1 @ SV356 @ SV151 @ SV276 ) @ ( not_homomorphism2 @ SV356 @ SV151 @ SV276 ) ) ) ) )
| ( homomorphism @ SV356 @ SV151 @ SV276 ) )
= $true )
| ( ( operation @ SV151 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1145]) ).
thf(1203,plain,
! [SV394: $i,SV357: $i,SV277: $i,SV152: $i] :
( ( ( member @ ( ordered_pair @ SV152 @ SV277 ) @ ( cross_product @ SV357 @ SV394 ) )
= $false )
| ( ( member @ SV152 @ ( unordered_pair @ SV152 @ SV277 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1146]) ).
thf(1204,plain,
! [SV395: $i,SV358: $i,SV278: $i,SV153: $i] :
( ( ( member @ ( ordered_pair @ SV153 @ SV278 ) @ ( cross_product @ SV358 @ SV395 ) )
= $false )
| ( ( member @ SV278 @ ( unordered_pair @ SV153 @ SV278 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1147]) ).
thf(1205,plain,
! [SV396: $i,SV359: $i,SV279: $i,SV154: $i] :
( ( ( member @ ( ordered_pair @ SV154 @ SV279 ) @ ( cross_product @ SV359 @ SV396 ) )
= $false )
| ( ( member @ SV154 @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1148]) ).
thf(1206,plain,
! [SV397: $i,SV360: $i,SV280: $i,SV155: $i] :
( ( ( member @ ( ordered_pair @ SV155 @ SV280 ) @ ( cross_product @ SV360 @ SV397 ) )
= $false )
| ( ( member @ SV280 @ universal_class )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1149]) ).
thf(1207,plain,
! [SV157: $i,SV361: $i,SV281: $i] :
( ( ( ~ ( subclass @ SV281 @ SV361 ) )
= $true )
| ( ( subclass @ SV157 @ SV361 )
= $true )
| ( ( subclass @ SV157 @ SV281 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1150]) ).
thf(1208,plain,
! [SV2: $i,SV282: $i,SV159: $i] :
( ( ( equalish @ SV159 @ SV282 )
= $false )
| ( ( equalish @ SV2 @ SV282 )
= $true )
| ( ( equalish @ SV2 @ SV159 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1151]) ).
thf(1209,plain,
! [SV210: $i,SV377: $i,SV318: $i,SV53: $i] :
( ( ( ~ ( compatible @ SV53 @ SV318 @ SV377 ) )
= $true )
| ( ( compatible @ SV210 @ SV318 @ SV377 )
= $true )
| ( ( equalish @ SV53 @ SV210 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1167]) ).
thf(1210,plain,
! [SV211: $i,SV378: $i,SV54: $i,SV319: $i] :
( ( ( ~ ( compatible @ SV319 @ SV54 @ SV378 ) )
= $true )
| ( ( compatible @ SV319 @ SV211 @ SV378 )
= $true )
| ( ( equalish @ SV54 @ SV211 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1168]) ).
thf(1211,plain,
! [SV212: $i,SV55: $i,SV379: $i,SV320: $i] :
( ( ( ~ ( compatible @ SV320 @ SV379 @ SV55 ) )
= $true )
| ( ( compatible @ SV320 @ SV379 @ SV212 )
= $true )
| ( ( equalish @ SV55 @ SV212 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1169]) ).
thf(1212,plain,
! [SV214: $i,SV380: $i,SV321: $i,SV57: $i] :
( ( ( ~ ( homomorphism @ SV57 @ SV321 @ SV380 ) )
= $true )
| ( ( homomorphism @ SV214 @ SV321 @ SV380 )
= $true )
| ( ( equalish @ SV57 @ SV214 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1171]) ).
thf(1213,plain,
! [SV215: $i,SV381: $i,SV58: $i,SV322: $i] :
( ( ( ~ ( homomorphism @ SV322 @ SV58 @ SV381 ) )
= $true )
| ( ( homomorphism @ SV322 @ SV215 @ SV381 )
= $true )
| ( ( equalish @ SV58 @ SV215 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1172]) ).
thf(1214,plain,
! [SV216: $i,SV59: $i,SV382: $i,SV323: $i] :
( ( ( ~ ( homomorphism @ SV323 @ SV382 @ SV59 ) )
= $true )
| ( ( homomorphism @ SV323 @ SV382 @ SV216 )
= $true )
| ( ( equalish @ SV59 @ SV216 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1173]) ).
thf(1215,plain,
! [SV218: $i,SV324: $i,SV61: $i] :
( ( ( member @ SV61 @ SV324 )
= $false )
| ( ( member @ SV218 @ SV324 )
= $true )
| ( ( equalish @ SV61 @ SV218 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1175]) ).
thf(1216,plain,
! [SV219: $i,SV62: $i,SV325: $i] :
( ( ( member @ SV325 @ SV62 )
= $false )
| ( ( member @ SV325 @ SV219 )
= $true )
| ( ( equalish @ SV62 @ SV219 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1176]) ).
thf(1217,plain,
! [SV223: $i,SV326: $i,SV66: $i] :
( ( ( subclass @ SV66 @ SV326 )
= $false )
| ( ( subclass @ SV223 @ SV326 )
= $true )
| ( ( equalish @ SV66 @ SV223 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1180]) ).
thf(1218,plain,
! [SV224: $i,SV67: $i,SV327: $i] :
( ( ( subclass @ SV327 @ SV67 )
= $false )
| ( ( subclass @ SV327 @ SV224 )
= $true )
| ( ( equalish @ SV67 @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1181]) ).
thf(1219,plain,
! [SV225: $i,SV68: $i,SV328: $i] :
( ( ( member @ SV328 @ SV68 )
= $false )
| ( ( member @ SV328 @ SV225 )
= $true )
| ( ( subclass @ SV68 @ SV225 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1182]) ).
thf(1220,plain,
! [SV238: $i,SV83: $i,SV385: $i,SV332: $i] :
( ( ( ~ ( member @ SV332 @ SV385 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV83 @ SV332 ) @ ( cross_product @ SV238 @ SV385 ) )
= $true )
| ( ( member @ SV83 @ SV238 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1187]) ).
thf(1221,plain,
! [SV244: $i,SV336: $i,SV89: $i] :
( ( ( member @ SV89 @ SV336 )
= $false )
| ( ( member @ SV89 @ ( intersection @ SV244 @ SV336 ) )
= $true )
| ( ( member @ SV89 @ SV244 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1189]) ).
thf(1222,plain,
! [SV387: $i,SV254: $i,SV100: $i,SV340: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV340 @ SV100 ) @ SV254 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV340 @ SV100 ) @ SV254 ) @ ( rotate @ SV387 ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV100 @ SV254 ) @ SV340 ) @ SV387 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1191]) ).
thf(1223,plain,
! [SV389: $i,SV342: $i,SV103: $i,SV256: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV256 @ SV103 ) @ SV342 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV256 @ SV103 ) @ SV342 ) @ ( flip @ SV389 ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV103 @ SV256 ) @ SV342 ) @ SV389 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1193]) ).
thf(1224,plain,
! [SV346: $i,SV264: $i,SV122: $i,SV391: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV391 @ SV122 ) @ ( cross_product @ universal_class @ universal_class ) ) )
= $true )
| ( ( member @ ( ordered_pair @ SV391 @ SV122 ) @ ( compose @ SV264 @ SV346 ) )
= $true )
| ( ( member @ SV122 @ ( image @ SV264 @ ( image @ SV346 @ ( singleton @ SV391 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1196]) ).
thf(1225,plain,
! [SV141: $i] :
( ( ( subclass @ ( range_of @ SV141 ) @ ( domain_of @ ( domain_of @ SV141 ) ) )
= $false )
| ( ( operation @ SV141 )
= $true )
| ( ( equalish @ ( cross_product @ ( domain_of @ ( domain_of @ SV141 ) ) @ ( domain_of @ ( domain_of @ SV141 ) ) ) @ ( domain_of @ SV141 ) )
= $false )
| ( ( function @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1198]) ).
thf(1226,plain,
! [SV392: $i,SV350: $i,SV145: $i,SV270: $i] :
( ( ( ~ ( equalish @ ( domain_of @ ( domain_of @ SV270 ) ) @ ( domain_of @ SV145 ) ) )
= $true )
| ( ( ~ ( subclass @ ( range_of @ SV145 ) @ ( domain_of @ ( domain_of @ SV350 ) ) )
| ( compatible @ SV392 @ SV270 @ SV350 ) )
= $true )
| ( ( function @ SV145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1199]) ).
thf(1227,plain,
! [SV398: $i,SV393: $i,SV354: $i,SV274: $i,SV149: $i] :
( ( ( homomorphism @ SV149 @ SV274 @ SV354 )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ SV393 @ SV398 ) @ ( domain_of @ SV274 ) )
| ( equalish @ ( apply @ SV354 @ ( ordered_pair @ ( apply @ SV149 @ SV393 ) @ ( apply @ SV149 @ SV398 ) ) ) @ ( apply @ SV149 @ ( apply @ SV274 @ ( ordered_pair @ SV393 @ SV398 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1200]) ).
thf(1228,plain,
! [SV150: $i,SV355: $i,SV275: $i] :
( ( ( operation @ SV275 )
= $false )
| ( ( ~ ( compatible @ SV355 @ SV150 @ SV275 )
| ( member @ ( ordered_pair @ ( not_homomorphism1 @ SV355 @ SV150 @ SV275 ) @ ( not_homomorphism2 @ SV355 @ SV150 @ SV275 ) ) @ ( domain_of @ SV150 ) )
| ( homomorphism @ SV355 @ SV150 @ SV275 ) )
= $true )
| ( ( operation @ SV150 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1201]) ).
thf(1229,plain,
! [SV151: $i,SV356: $i,SV276: $i] :
( ( ( operation @ SV276 )
= $false )
| ( ( ~ ( compatible @ SV356 @ SV151 @ SV276 )
| ~ ( equalish @ ( apply @ SV276 @ ( ordered_pair @ ( apply @ SV356 @ ( not_homomorphism1 @ SV356 @ SV151 @ SV276 ) ) @ ( apply @ SV356 @ ( not_homomorphism2 @ SV356 @ SV151 @ SV276 ) ) ) ) @ ( apply @ SV356 @ ( apply @ SV151 @ ( ordered_pair @ ( not_homomorphism1 @ SV356 @ SV151 @ SV276 ) @ ( not_homomorphism2 @ SV356 @ SV151 @ SV276 ) ) ) ) )
| ( homomorphism @ SV356 @ SV151 @ SV276 ) )
= $true )
| ( ( operation @ SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1202]) ).
thf(1230,plain,
! [SV157: $i,SV361: $i,SV281: $i] :
( ( ( subclass @ SV281 @ SV361 )
= $false )
| ( ( subclass @ SV157 @ SV361 )
= $true )
| ( ( subclass @ SV157 @ SV281 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1207]) ).
thf(1231,plain,
! [SV210: $i,SV377: $i,SV318: $i,SV53: $i] :
( ( ( compatible @ SV53 @ SV318 @ SV377 )
= $false )
| ( ( compatible @ SV210 @ SV318 @ SV377 )
= $true )
| ( ( equalish @ SV53 @ SV210 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1209]) ).
thf(1232,plain,
! [SV211: $i,SV378: $i,SV54: $i,SV319: $i] :
( ( ( compatible @ SV319 @ SV54 @ SV378 )
= $false )
| ( ( compatible @ SV319 @ SV211 @ SV378 )
= $true )
| ( ( equalish @ SV54 @ SV211 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1210]) ).
thf(1233,plain,
! [SV212: $i,SV55: $i,SV379: $i,SV320: $i] :
( ( ( compatible @ SV320 @ SV379 @ SV55 )
= $false )
| ( ( compatible @ SV320 @ SV379 @ SV212 )
= $true )
| ( ( equalish @ SV55 @ SV212 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1211]) ).
thf(1234,plain,
! [SV214: $i,SV380: $i,SV321: $i,SV57: $i] :
( ( ( homomorphism @ SV57 @ SV321 @ SV380 )
= $false )
| ( ( homomorphism @ SV214 @ SV321 @ SV380 )
= $true )
| ( ( equalish @ SV57 @ SV214 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1212]) ).
thf(1235,plain,
! [SV215: $i,SV381: $i,SV58: $i,SV322: $i] :
( ( ( homomorphism @ SV322 @ SV58 @ SV381 )
= $false )
| ( ( homomorphism @ SV322 @ SV215 @ SV381 )
= $true )
| ( ( equalish @ SV58 @ SV215 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1213]) ).
thf(1236,plain,
! [SV216: $i,SV59: $i,SV382: $i,SV323: $i] :
( ( ( homomorphism @ SV323 @ SV382 @ SV59 )
= $false )
| ( ( homomorphism @ SV323 @ SV382 @ SV216 )
= $true )
| ( ( equalish @ SV59 @ SV216 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1214]) ).
thf(1237,plain,
! [SV238: $i,SV83: $i,SV385: $i,SV332: $i] :
( ( ( member @ SV332 @ SV385 )
= $false )
| ( ( member @ ( ordered_pair @ SV83 @ SV332 ) @ ( cross_product @ SV238 @ SV385 ) )
= $true )
| ( ( member @ SV83 @ SV238 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1220]) ).
thf(1238,plain,
! [SV387: $i,SV254: $i,SV100: $i,SV340: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ SV340 @ SV100 ) @ SV254 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
= $false )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV340 @ SV100 ) @ SV254 ) @ ( rotate @ SV387 ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV100 @ SV254 ) @ SV340 ) @ SV387 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1222]) ).
thf(1239,plain,
! [SV389: $i,SV342: $i,SV103: $i,SV256: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ SV256 @ SV103 ) @ SV342 ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
= $false )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV256 @ SV103 ) @ SV342 ) @ ( flip @ SV389 ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ SV103 @ SV256 ) @ SV342 ) @ SV389 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1223]) ).
thf(1240,plain,
! [SV346: $i,SV264: $i,SV122: $i,SV391: $i] :
( ( ( member @ ( ordered_pair @ SV391 @ SV122 ) @ ( cross_product @ universal_class @ universal_class ) )
= $false )
| ( ( member @ ( ordered_pair @ SV391 @ SV122 ) @ ( compose @ SV264 @ SV346 ) )
= $true )
| ( ( member @ SV122 @ ( image @ SV264 @ ( image @ SV346 @ ( singleton @ SV391 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1224]) ).
thf(1241,plain,
! [SV392: $i,SV350: $i,SV145: $i,SV270: $i] :
( ( ( equalish @ ( domain_of @ ( domain_of @ SV270 ) ) @ ( domain_of @ SV145 ) )
= $false )
| ( ( ~ ( subclass @ ( range_of @ SV145 ) @ ( domain_of @ ( domain_of @ SV350 ) ) )
| ( compatible @ SV392 @ SV270 @ SV350 ) )
= $true )
| ( ( function @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1226]) ).
thf(1242,plain,
! [SV149: $i,SV354: $i,SV274: $i,SV398: $i,SV393: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV393 @ SV398 ) @ ( domain_of @ SV274 ) ) )
= $true )
| ( ( equalish @ ( apply @ SV354 @ ( ordered_pair @ ( apply @ SV149 @ SV393 ) @ ( apply @ SV149 @ SV398 ) ) ) @ ( apply @ SV149 @ ( apply @ SV274 @ ( ordered_pair @ SV393 @ SV398 ) ) ) )
= $true )
| ( ( homomorphism @ SV149 @ SV274 @ SV354 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1227]) ).
thf(1243,plain,
! [SV275: $i,SV150: $i,SV355: $i] :
( ( ( ~ ( compatible @ SV355 @ SV150 @ SV275 ) )
= $true )
| ( ( ( member @ ( ordered_pair @ ( not_homomorphism1 @ SV355 @ SV150 @ SV275 ) @ ( not_homomorphism2 @ SV355 @ SV150 @ SV275 ) ) @ ( domain_of @ SV150 ) )
| ( homomorphism @ SV355 @ SV150 @ SV275 ) )
= $true )
| ( ( operation @ SV275 )
= $false )
| ( ( operation @ SV150 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1228]) ).
thf(1244,plain,
! [SV276: $i,SV151: $i,SV356: $i] :
( ( ( ~ ( compatible @ SV356 @ SV151 @ SV276 ) )
= $true )
| ( ( ~ ( equalish @ ( apply @ SV276 @ ( ordered_pair @ ( apply @ SV356 @ ( not_homomorphism1 @ SV356 @ SV151 @ SV276 ) ) @ ( apply @ SV356 @ ( not_homomorphism2 @ SV356 @ SV151 @ SV276 ) ) ) ) @ ( apply @ SV356 @ ( apply @ SV151 @ ( ordered_pair @ ( not_homomorphism1 @ SV356 @ SV151 @ SV276 ) @ ( not_homomorphism2 @ SV356 @ SV151 @ SV276 ) ) ) ) )
| ( homomorphism @ SV356 @ SV151 @ SV276 ) )
= $true )
| ( ( operation @ SV276 )
= $false )
| ( ( operation @ SV151 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1229]) ).
thf(1245,plain,
! [SV270: $i,SV392: $i,SV350: $i,SV145: $i] :
( ( ( ~ ( subclass @ ( range_of @ SV145 ) @ ( domain_of @ ( domain_of @ SV350 ) ) ) )
= $true )
| ( ( compatible @ SV392 @ SV270 @ SV350 )
= $true )
| ( ( equalish @ ( domain_of @ ( domain_of @ SV270 ) ) @ ( domain_of @ SV145 ) )
= $false )
| ( ( function @ SV145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1241]) ).
thf(1246,plain,
! [SV149: $i,SV354: $i,SV274: $i,SV398: $i,SV393: $i] :
( ( ( member @ ( ordered_pair @ SV393 @ SV398 ) @ ( domain_of @ SV274 ) )
= $false )
| ( ( equalish @ ( apply @ SV354 @ ( ordered_pair @ ( apply @ SV149 @ SV393 ) @ ( apply @ SV149 @ SV398 ) ) ) @ ( apply @ SV149 @ ( apply @ SV274 @ ( ordered_pair @ SV393 @ SV398 ) ) ) )
= $true )
| ( ( homomorphism @ SV149 @ SV274 @ SV354 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1242]) ).
thf(1247,plain,
! [SV275: $i,SV150: $i,SV355: $i] :
( ( ( compatible @ SV355 @ SV150 @ SV275 )
= $false )
| ( ( ( member @ ( ordered_pair @ ( not_homomorphism1 @ SV355 @ SV150 @ SV275 ) @ ( not_homomorphism2 @ SV355 @ SV150 @ SV275 ) ) @ ( domain_of @ SV150 ) )
| ( homomorphism @ SV355 @ SV150 @ SV275 ) )
= $true )
| ( ( operation @ SV275 )
= $false )
| ( ( operation @ SV150 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1243]) ).
thf(1248,plain,
! [SV276: $i,SV151: $i,SV356: $i] :
( ( ( compatible @ SV356 @ SV151 @ SV276 )
= $false )
| ( ( ~ ( equalish @ ( apply @ SV276 @ ( ordered_pair @ ( apply @ SV356 @ ( not_homomorphism1 @ SV356 @ SV151 @ SV276 ) ) @ ( apply @ SV356 @ ( not_homomorphism2 @ SV356 @ SV151 @ SV276 ) ) ) ) @ ( apply @ SV356 @ ( apply @ SV151 @ ( ordered_pair @ ( not_homomorphism1 @ SV356 @ SV151 @ SV276 ) @ ( not_homomorphism2 @ SV356 @ SV151 @ SV276 ) ) ) ) )
| ( homomorphism @ SV356 @ SV151 @ SV276 ) )
= $true )
| ( ( operation @ SV276 )
= $false )
| ( ( operation @ SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1244]) ).
thf(1249,plain,
! [SV270: $i,SV392: $i,SV350: $i,SV145: $i] :
( ( ( subclass @ ( range_of @ SV145 ) @ ( domain_of @ ( domain_of @ SV350 ) ) )
= $false )
| ( ( compatible @ SV392 @ SV270 @ SV350 )
= $true )
| ( ( equalish @ ( domain_of @ ( domain_of @ SV270 ) ) @ ( domain_of @ SV145 ) )
= $false )
| ( ( function @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1245]) ).
thf(1250,plain,
! [SV275: $i,SV150: $i,SV355: $i] :
( ( ( member @ ( ordered_pair @ ( not_homomorphism1 @ SV355 @ SV150 @ SV275 ) @ ( not_homomorphism2 @ SV355 @ SV150 @ SV275 ) ) @ ( domain_of @ SV150 ) )
= $true )
| ( ( homomorphism @ SV355 @ SV150 @ SV275 )
= $true )
| ( ( compatible @ SV355 @ SV150 @ SV275 )
= $false )
| ( ( operation @ SV275 )
= $false )
| ( ( operation @ SV150 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1247]) ).
thf(1251,plain,
! [SV151: $i,SV356: $i,SV276: $i] :
( ( ( ~ ( equalish @ ( apply @ SV276 @ ( ordered_pair @ ( apply @ SV356 @ ( not_homomorphism1 @ SV356 @ SV151 @ SV276 ) ) @ ( apply @ SV356 @ ( not_homomorphism2 @ SV356 @ SV151 @ SV276 ) ) ) ) @ ( apply @ SV356 @ ( apply @ SV151 @ ( ordered_pair @ ( not_homomorphism1 @ SV356 @ SV151 @ SV276 ) @ ( not_homomorphism2 @ SV356 @ SV151 @ SV276 ) ) ) ) ) )
= $true )
| ( ( homomorphism @ SV356 @ SV151 @ SV276 )
= $true )
| ( ( compatible @ SV356 @ SV151 @ SV276 )
= $false )
| ( ( operation @ SV276 )
= $false )
| ( ( operation @ SV151 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1248]) ).
thf(1252,plain,
! [SV151: $i,SV356: $i,SV276: $i] :
( ( ( equalish @ ( apply @ SV276 @ ( ordered_pair @ ( apply @ SV356 @ ( not_homomorphism1 @ SV356 @ SV151 @ SV276 ) ) @ ( apply @ SV356 @ ( not_homomorphism2 @ SV356 @ SV151 @ SV276 ) ) ) ) @ ( apply @ SV356 @ ( apply @ SV151 @ ( ordered_pair @ ( not_homomorphism1 @ SV356 @ SV151 @ SV276 ) @ ( not_homomorphism2 @ SV356 @ SV151 @ SV276 ) ) ) ) )
= $false )
| ( ( homomorphism @ SV356 @ SV151 @ SV276 )
= $true )
| ( ( compatible @ SV356 @ SV151 @ SV276 )
= $false )
| ( ( operation @ SV276 )
= $false )
| ( ( operation @ SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1251]) ).
thf(1253,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[420,1252,1250,1249,1246,1240,1239,1238,1237,1236,1235,1234,1233,1232,1231,1230,1225,1221,1219,1218,1217,1216,1215,1208,1206,1205,1204,1203,1197,1195,1194,1192,1190,1188,1186,1185,1184,1183,1179,1178,1177,1174,1170,1166,1165,1164,1163,1162,1161,1160,1159,1158,1157,1156,1155,1154,1153,1152,1142,1141,1140,1138,1137,1136,1134,1132,1129,1123,1122,1121,1120,1118,1117,1115,1093,1092,1091,1090,1083,1082,1081,1080,1073,1072,1071,1070,1066,1065,1064,1063,1062,1061,1060,1059,1040,1033,1020,1015,1014,1011,1010,1009,988,987,986,985,984,980,979,975,964,959,958,957,951,946,945,941,924,923,922,920,919,915,914,913,912,909,908,907,905,904,901,900,893,892,873,781,780,779,770,761,750,749,737,736,659,657,638,637,619,617,610,606,605,602,599,580,572,501,477,476,471,454,452,446]) ).
thf(1254,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1253]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET055-7 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Oct 6 14:28:46 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.48/0.70 .
% 3.48/0.70
% 3.48/0.70 No.of.Axioms: 165
% 3.48/0.70
% 3.48/0.70 Length.of.Defs: 0
% 3.48/0.70
% 3.48/0.70 Contains.Choice.Funs: false
% 3.48/0.70 .............................
% 3.48/0.70
% 3.48/0.70 ********************************
% 3.48/0.70 * All subproblems solved! *
% 3.48/0.70 ********************************
% 3.48/0.70 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:165,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1253,loop_count:0,foatp_calls:1,translation:fof_full)
% 3.48/0.70
% 3.48/0.70 %**** Beginning of derivation protocol ****
% 3.48/0.70 % SZS output start CNFRefutation
% See solution above
% 3.48/0.71
% 3.48/0.71 %**** End of derivation protocol ****
% 3.48/0.71 %**** no. of clauses in derivation: 1254 ****
% 3.48/0.71 %**** clause counter: 1253 ****
% 3.48/0.71
% 3.48/0.71 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:165,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1253,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------