%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET025-4 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 10:39:01 AM UTC 2026
% Result : Unsatisfiable 5.03s 1.05s
% Output : CNFRefutation 5.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 143
% Syntax : Number of formulae : 1209 ( 630 unt; 0 typ; 0 def)
% Number of atoms : 7508 (2415 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 14218 (1822 ~;2431 |; 0 &;9965 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 77 ( 74 usr; 10 con; 0-5 aty)
% Number of variables : 3211 ( 0 ^;3211 !; 0 ?;3211 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_apply,type,
apply: $i > $i > $i ).
thf(tp_apply_to_two_arguments,type,
apply_to_two_arguments: $i > $i > $i > $i ).
thf(tp_b,type,
b: $i ).
thf(tp_closed,type,
closed: $i > $i > $o ).
thf(tp_complement,type,
complement: $i > $i ).
thf(tp_compose,type,
compose: $i > $i > $i ).
thf(tp_converse,type,
converse: $i > $i ).
thf(tp_cross_product,type,
cross_product: $i > $i > $i ).
thf(tp_disjoint,type,
disjoint: $i > $i > $o ).
thf(tp_domain_of,type,
domain_of: $i > $i ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_estin,type,
estin: $i ).
thf(tp_f1,type,
f1: $i > $i > $i ).
thf(tp_f10,type,
f10: $i > $i > $i ).
thf(tp_f11,type,
f11: $i > $i > $i ).
thf(tp_f12,type,
f12: $i > $i > $i ).
thf(tp_f13,type,
f13: $i > $i > $i ).
thf(tp_f14,type,
f14: $i > $i > $i ).
thf(tp_f16,type,
f16: $i > $i > $i ).
thf(tp_f17,type,
f17: $i > $i > $i ).
thf(tp_f18,type,
f18: $i > $i ).
thf(tp_f19,type,
f19: $i > $i ).
thf(tp_f2,type,
f2: $i > $i ).
thf(tp_f20,type,
f20: $i > $i ).
thf(tp_f21,type,
f21: $i > $i ).
thf(tp_f22,type,
f22: $i > $i > $i > $i ).
thf(tp_f23,type,
f23: $i > $i > $i ).
thf(tp_f24,type,
f24: $i > $i ).
thf(tp_f25,type,
f25: $i ).
thf(tp_f26,type,
f26: $i > $i ).
thf(tp_f27,type,
f27: $i > $i > $i ).
thf(tp_f28,type,
f28: $i > $i > $i > $i ).
thf(tp_f29,type,
f29: $i > $i > $i > $i ).
thf(tp_f3,type,
f3: $i > $i ).
thf(tp_f30,type,
f30: $i > $i > $i > $i ).
thf(tp_f31,type,
f31: $i > $i > $i > $i ).
thf(tp_f32,type,
f32: $i > $i > $i > $i > $i > $i ).
thf(tp_f33,type,
f33: $i > $i > $i > $i > $i > $i ).
thf(tp_f4,type,
f4: $i > $i > $i ).
thf(tp_f5,type,
f5: $i > $i > $i ).
thf(tp_f6,type,
f6: $i > $i > $i ).
thf(tp_f7,type,
f7: $i > $i > $i ).
thf(tp_f8,type,
f8: $i > $i > $i ).
thf(tp_f9,type,
f9: $i > $i > $i ).
thf(tp_first,type,
first: $i > $i ).
thf(tp_flip_range_of,type,
flip_range_of: $i > $i ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_homomorphism,type,
homomorphism: $i > $i > $i > $i > $i > $o ).
thf(tp_identity_relation,type,
identity_relation: $i ).
thf(tp_image,type,
image: $i > $i > $i ).
thf(tp_infinity,type,
infinity: $i ).
thf(tp_intersection,type,
intersection: $i > $i > $i ).
thf(tp_little_set,type,
little_set: $i > $o ).
thf(tp_maps,type,
maps: $i > $i > $i > $o ).
thf(tp_member,type,
member: $i > $i > $o ).
thf(tp_non_ordered_pair,type,
non_ordered_pair: $i > $i > $i ).
thf(tp_one_to_one_function,type,
one_to_one_function: $i > $o ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_ordered_pair_predicate,type,
ordered_pair_predicate: $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_proper_subset,type,
proper_subset: $i > $i > $o ).
thf(tp_range_of,type,
range_of: $i > $i ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_restrict,type,
restrict: $i > $i > $i ).
thf(tp_rotate_right,type,
rotate_right: $i > $i ).
thf(tp_second,type,
second: $i > $i ).
thf(tp_sigma,type,
sigma: $i > $i ).
thf(tp_single_valued_set,type,
single_valued_set: $i > $o ).
thf(tp_singleton_set,type,
singleton_set: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_successor,type,
successor: $i > $i ).
thf(tp_union,type,
union: $i > $i > $i ).
thf(tp_universal_set,type,
universal_set: $i ).
thf(1,axiom,
! [Xh: $i,Xs1: $i,Xf1: $i,Xs2: $i,Xf2: $i] :
( ( homomorphism @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 )
| ~ ( closed @ Xs1 @ Xf1 )
| ~ ( closed @ Xs2 @ Xf2 )
| ~ ( maps @ Xh @ Xs1 @ Xs2 )
| ( ( apply @ Xh @ ( apply_to_two_arguments @ Xf1 @ ( f32 @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 ) @ ( f33 @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 ) ) )
!= ( apply_to_two_arguments @ Xf2 @ ( apply @ Xh @ ( f32 @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 ) ) @ ( apply @ Xh @ ( f33 @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism7) ).
thf(2,axiom,
! [Xh: $i,Xs1: $i,Xf1: $i,Xs2: $i,Xf2: $i] :
( ( homomorphism @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 )
| ~ ( closed @ Xs1 @ Xf1 )
| ~ ( closed @ Xs2 @ Xf2 )
| ~ ( maps @ Xh @ Xs1 @ Xs2 )
| ( member @ ( f33 @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 ) @ Xs1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism6) ).
thf(3,axiom,
! [Xh: $i,Xs1: $i,Xf1: $i,Xs2: $i,Xf2: $i] :
( ( homomorphism @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 )
| ~ ( closed @ Xs1 @ Xf1 )
| ~ ( closed @ Xs2 @ Xf2 )
| ~ ( maps @ Xh @ Xs1 @ Xs2 )
| ( member @ ( f32 @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 ) @ Xs1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism5) ).
thf(4,axiom,
! [Xh: $i,Xs1: $i,Xf1: $i,Xs2: $i,Xf2: $i,X: $i,Y: $i] :
( ~ ( homomorphism @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 )
| ~ ( member @ X @ Xs1 )
| ~ ( member @ Y @ Xs1 )
| ( ( apply @ Xh @ ( apply_to_two_arguments @ Xf1 @ X @ Y ) )
= ( apply_to_two_arguments @ Xf2 @ ( apply @ Xh @ X ) @ ( apply @ Xh @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism4) ).
thf(5,axiom,
! [Xh: $i,Xs1: $i,Xf1: $i,Xs2: $i,Xf2: $i] :
( ~ ( homomorphism @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 )
| ( maps @ Xh @ Xs1 @ Xs2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism3) ).
thf(6,axiom,
! [Xh: $i,Xs1: $i,Xf1: $i,Xs2: $i,Xf2: $i] :
( ~ ( homomorphism @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 )
| ( closed @ Xs2 @ Xf2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism2) ).
thf(7,axiom,
! [Xh: $i,Xs1: $i,Xf1: $i,Xs2: $i,Xf2: $i] :
( ~ ( homomorphism @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 )
| ( closed @ Xs1 @ Xf1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism1) ).
thf(8,axiom,
! [Z: $i,Xf: $i,Xg: $i,X: $i,Y: $i,W: $i] :
( ( member @ Z @ ( compose @ Xf @ Xg ) )
| ~ ( little_set @ Z )
| ~ ( little_set @ X )
| ~ ( little_set @ Y )
| ~ ( little_set @ W )
| ( Z
!= ( ordered_pair @ X @ Y ) )
| ~ ( member @ ( ordered_pair @ X @ W ) @ Xf )
| ~ ( member @ ( ordered_pair @ W @ Y ) @ Xg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose7) ).
thf(9,axiom,
! [Z: $i,Xf: $i,Xg: $i] :
( ~ ( member @ Z @ ( compose @ Xf @ Xg ) )
| ( member @ ( ordered_pair @ ( f31 @ Z @ Xf @ Xg ) @ ( f30 @ Z @ Xf @ Xg ) ) @ Xg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose6) ).
thf(10,axiom,
! [Z: $i,Xf: $i,Xg: $i] :
( ~ ( member @ Z @ ( compose @ Xf @ Xg ) )
| ( member @ ( ordered_pair @ ( f29 @ Z @ Xf @ Xg ) @ ( f31 @ Z @ Xf @ Xg ) ) @ Xf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose5) ).
thf(11,axiom,
! [Z: $i,Xf: $i,Xg: $i] :
( ~ ( member @ Z @ ( compose @ Xf @ Xg ) )
| ( Z
= ( ordered_pair @ ( f29 @ Z @ Xf @ Xg ) @ ( f30 @ Z @ Xf @ Xg ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose4) ).
thf(12,axiom,
! [Z: $i,Xf: $i,Xg: $i] :
( ~ ( member @ Z @ ( compose @ Xf @ Xg ) )
| ( little_set @ ( f31 @ Z @ Xf @ Xg ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose3) ).
thf(13,axiom,
! [Z: $i,Xf: $i,Xg: $i] :
( ~ ( member @ Z @ ( compose @ Xf @ Xg ) )
| ( little_set @ ( f30 @ Z @ Xf @ Xg ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose2) ).
thf(14,axiom,
! [Z: $i,Xf: $i,Xg: $i] :
( ~ ( member @ Z @ ( compose @ Xf @ Xg ) )
| ( little_set @ ( f29 @ Z @ Xf @ Xg ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose1) ).
thf(15,axiom,
! [Xs: $i,Xf: $i] :
( ( closed @ Xs @ Xf )
| ~ ( little_set @ Xs )
| ~ ( little_set @ Xf )
| ~ ( maps @ Xf @ ( cross_product @ Xs @ Xs ) @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closed4) ).
thf(16,axiom,
! [Xs: $i,Xf: $i] :
( ~ ( closed @ Xs @ Xf )
| ( maps @ Xf @ ( cross_product @ Xs @ Xs ) @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closed3) ).
thf(17,axiom,
! [Xs: $i,Xf: $i] :
( ~ ( closed @ Xs @ Xf )
| ( little_set @ Xf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closed2) ).
thf(18,axiom,
! [Xs: $i,Xf: $i] :
( ~ ( closed @ Xs @ Xf )
| ( little_set @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closed1) ).
thf(19,axiom,
! [Xf: $i,X: $i,Y: $i] :
( ( maps @ Xf @ X @ Y )
| ~ ( function @ Xf )
| ( ( domain_of @ Xf )
!= X )
| ~ ( subset @ ( range_of @ Xf ) @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps4) ).
thf(20,axiom,
! [Xf: $i,X: $i,Y: $i] :
( ~ ( maps @ Xf @ X @ Y )
| ( subset @ ( range_of @ Xf ) @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps3) ).
thf(21,axiom,
! [Xf: $i,X: $i,Y: $i] :
( ~ ( maps @ Xf @ X @ Y )
| ( ( domain_of @ Xf )
= X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps2) ).
thf(22,axiom,
! [Xf: $i,X: $i,Y: $i] :
( ~ ( maps @ Xf @ X @ Y )
| ( function @ Xf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps1) ).
thf(23,axiom,
! [Xf: $i,X: $i,Y: $i] :
( ( apply_to_two_arguments @ Xf @ X @ Y )
= ( apply @ Xf @ ( ordered_pair @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply_to_two_arguments) ).
thf(24,axiom,
! [Z: $i,Xf: $i,Y: $i,W: $i] :
( ( member @ Z @ ( apply @ Xf @ Y ) )
| ~ ( ordered_pair_predicate @ W )
| ~ ( member @ W @ Xf )
| ( ( first @ W )
!= Y )
| ~ ( member @ Z @ ( second @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply5) ).
thf(25,axiom,
! [Z: $i,Xf: $i,Y: $i] :
( ~ ( member @ Z @ ( apply @ Xf @ Y ) )
| ( member @ Z @ ( second @ ( f28 @ Z @ Xf @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply4) ).
thf(26,axiom,
! [Z: $i,Xf: $i,Y: $i] :
( ~ ( member @ Z @ ( apply @ Xf @ Y ) )
| ( ( first @ ( f28 @ Z @ Xf @ Y ) )
= Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply3) ).
thf(27,axiom,
! [Z: $i,Xf: $i,Y: $i] :
( ~ ( member @ Z @ ( apply @ Xf @ Y ) )
| ( member @ ( f28 @ Z @ Xf @ Y ) @ Xf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply2) ).
thf(28,axiom,
! [Z: $i,Xf: $i,Y: $i] :
( ~ ( member @ Z @ ( apply @ Xf @ Y ) )
| ( ordered_pair_predicate @ ( f28 @ Z @ Xf @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply1) ).
thf(29,axiom,
! [Xf: $i] :
( ( one_to_one_function @ Xf )
| ~ ( function @ Xf )
| ~ ( function @ ( converse @ Xf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one_function3) ).
thf(30,axiom,
! [Xf: $i] :
( ~ ( one_to_one_function @ Xf )
| ( function @ ( converse @ Xf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one_function2) ).
thf(31,axiom,
! [Xf: $i] :
( ~ ( one_to_one_function @ Xf )
| ( function @ Xf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one_function1) ).
thf(32,axiom,
! [X: $i,Y: $i] :
( ( restrict @ X @ Y )
= ( intersection @ X @ ( cross_product @ Y @ universal_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',restrict) ).
thf(33,axiom,
! [Z: $i] :
( ( member @ Z @ identity_relation )
| ~ ( little_set @ Z )
| ~ ( ordered_pair_predicate @ Z )
| ( ( first @ Z )
!= ( second @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_relation3) ).
thf(34,axiom,
! [Z: $i] :
( ~ ( member @ Z @ identity_relation )
| ( ( first @ Z )
= ( second @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_relation2) ).
thf(35,axiom,
! [Z: $i] :
( ~ ( member @ Z @ identity_relation )
| ( ordered_pair_predicate @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_relation1) ).
thf(36,axiom,
! [Z: $i,X: $i,Xp: $i] :
( ( member @ Z @ ( range_of @ X ) )
| ~ ( little_set @ Z )
| ~ ( ordered_pair_predicate @ Xp )
| ~ ( member @ Xp @ X )
| ( Z
!= ( second @ Xp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',range_of4) ).
thf(37,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( range_of @ X ) )
| ( Z
= ( second @ ( f27 @ Z @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',range_of3) ).
thf(38,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( range_of @ X ) )
| ( member @ ( f27 @ Z @ X ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',range_of2) ).
thf(39,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( range_of @ X ) )
| ( ordered_pair_predicate @ ( f27 @ Z @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',range_of1) ).
thf(40,axiom,
! [X: $i] :
( ~ ( little_set @ X )
| ( X = empty_set )
| ( member @ ( ordered_pair @ X @ ( f26 @ X ) ) @ f25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice3) ).
thf(41,axiom,
! [X: $i] :
( ~ ( little_set @ X )
| ( X = empty_set )
| ( member @ ( f26 @ X ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice2) ).
thf(42,axiom,
function @ f25,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice1) ).
thf(43,axiom,
! [X: $i] :
( ( X = empty_set )
| ( disjoint @ ( f24 @ X ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity2) ).
thf(44,axiom,
! [X: $i] :
( ( X = empty_set )
| ( member @ ( f24 @ X ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity1) ).
thf(45,axiom,
! [X: $i,Y: $i] :
( ( disjoint @ X @ Y )
| ( member @ ( f23 @ X @ Y ) @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint3) ).
thf(46,axiom,
! [X: $i,Y: $i] :
( ( disjoint @ X @ Y )
| ( member @ ( f23 @ X @ Y ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint2) ).
thf(47,axiom,
! [X: $i,Y: $i,U: $i] :
( ~ ( disjoint @ X @ Y )
| ~ ( member @ U @ X )
| ~ ( member @ U @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint1) ).
thf(48,axiom,
! [X: $i,Xf: $i] :
( ~ ( little_set @ X )
| ~ ( function @ Xf )
| ( little_set @ ( image @ X @ Xf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image_and_substitution6) ).
thf(49,axiom,
! [Z: $i,X: $i,Xf: $i,Y: $i] :
( ( member @ Z @ ( image @ X @ Xf ) )
| ~ ( little_set @ Z )
| ~ ( ordered_pair_predicate @ Y )
| ~ ( member @ Y @ Xf )
| ~ ( member @ ( first @ Y ) @ X )
| ( ( second @ Y )
!= Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image_and_substitution5) ).
thf(50,axiom,
! [Z: $i,X: $i,Xf: $i] :
( ~ ( member @ Z @ ( image @ X @ Xf ) )
| ( ( second @ ( f22 @ Z @ X @ Xf ) )
= Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image_and_substitution4) ).
thf(51,axiom,
! [Z: $i,X: $i,Xf: $i] :
( ~ ( member @ Z @ ( image @ X @ Xf ) )
| ( member @ ( first @ ( f22 @ Z @ X @ Xf ) ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image_and_substitution3) ).
thf(52,axiom,
! [Z: $i,X: $i,Xf: $i] :
( ~ ( member @ Z @ ( image @ X @ Xf ) )
| ( member @ ( f22 @ Z @ X @ Xf ) @ Xf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image_and_substitution2) ).
thf(53,axiom,
! [Z: $i,X: $i,Xf: $i] :
( ~ ( member @ Z @ ( image @ X @ Xf ) )
| ( ordered_pair_predicate @ ( f22 @ Z @ X @ Xf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image_and_substitution1) ).
thf(54,axiom,
! [Xf: $i] :
( ( function @ Xf )
| ~ ( relation @ Xf )
| ~ ( single_valued_set @ Xf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function3) ).
thf(55,axiom,
! [Xf: $i] :
( ~ ( function @ Xf )
| ( single_valued_set @ Xf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function2) ).
thf(56,axiom,
! [Xf: $i] :
( ~ ( function @ Xf )
| ( relation @ Xf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function1) ).
thf(57,axiom,
! [X: $i] :
( ( single_valued_set @ X )
| ( ( f20 @ X )
!= ( f21 @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_set7) ).
thf(58,axiom,
! [X: $i] :
( ( single_valued_set @ X )
| ( member @ ( ordered_pair @ ( f19 @ X ) @ ( f21 @ X ) ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_set6) ).
thf(59,axiom,
! [X: $i] :
( ( single_valued_set @ X )
| ( member @ ( ordered_pair @ ( f19 @ X ) @ ( f20 @ X ) ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_set5) ).
thf(60,axiom,
! [X: $i] :
( ( single_valued_set @ X )
| ( little_set @ ( f21 @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_set4) ).
thf(61,axiom,
! [X: $i] :
( ( single_valued_set @ X )
| ( little_set @ ( f20 @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_set3) ).
thf(62,axiom,
! [X: $i] :
( ( single_valued_set @ X )
| ( little_set @ ( f19 @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_set2) ).
thf(63,axiom,
! [X: $i,U: $i,V: $i,W: $i] :
( ~ ( single_valued_set @ X )
| ~ ( little_set @ U )
| ~ ( little_set @ V )
| ~ ( little_set @ W )
| ~ ( member @ ( ordered_pair @ U @ V ) @ X )
| ~ ( member @ ( ordered_pair @ U @ W ) @ X )
| ( V = W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_set1) ).
thf(64,axiom,
! [Z: $i] :
( ( relation @ Z )
| ~ ( ordered_pair_predicate @ ( f18 @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',relation3) ).
thf(65,axiom,
! [Z: $i] :
( ( relation @ Z )
| ( member @ ( f18 @ Z ) @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',relation2) ).
thf(66,axiom,
! [Z: $i,X: $i] :
( ~ ( relation @ Z )
| ~ ( member @ X @ Z )
| ( ordered_pair_predicate @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',relation1) ).
thf(67,axiom,
! [U: $i] :
( ~ ( little_set @ U )
| ( little_set @ ( powerset @ U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset3) ).
thf(68,axiom,
! [Z: $i,X: $i] :
( ( member @ Z @ ( powerset @ X ) )
| ~ ( little_set @ Z )
| ~ ( subset @ Z @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset2) ).
thf(69,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( powerset @ X ) )
| ( subset @ Z @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset1) ).
thf(70,axiom,
! [X: $i,Y: $i] :
( ( proper_subset @ X @ Y )
| ~ ( subset @ X @ Y )
| ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',proper_subset3) ).
thf(71,axiom,
! [X: $i,Y: $i] :
( ~ ( proper_subset @ X @ Y )
| ( X != Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',proper_subset2) ).
thf(72,axiom,
! [X: $i,Y: $i] :
( ~ ( proper_subset @ X @ Y )
| ( subset @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',proper_subset1) ).
thf(73,axiom,
! [X: $i,Y: $i] :
( ( subset @ X @ Y )
| ~ ( member @ ( f17 @ X @ Y ) @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset3) ).
thf(74,axiom,
! [X: $i,Y: $i] :
( ( subset @ X @ Y )
| ( member @ ( f17 @ X @ Y ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2) ).
thf(75,axiom,
! [X: $i,Y: $i,U: $i] :
( ~ ( subset @ X @ Y )
| ~ ( member @ U @ X )
| ( member @ U @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset1) ).
thf(76,axiom,
! [U: $i] :
( ~ ( little_set @ U )
| ( little_set @ ( sigma @ U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sigma4) ).
thf(77,axiom,
! [Z: $i,X: $i,Y: $i] :
( ( member @ Z @ ( sigma @ X ) )
| ~ ( member @ Y @ X )
| ~ ( member @ Z @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sigma3) ).
thf(78,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( sigma @ X ) )
| ( member @ Z @ ( f16 @ Z @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sigma2) ).
thf(79,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( sigma @ X ) )
| ( member @ ( f16 @ Z @ X ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sigma1) ).
thf(80,axiom,
! [X: $i] :
( ~ ( member @ X @ infinity )
| ( member @ ( successor @ X ) @ infinity ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infinity3) ).
thf(81,axiom,
member @ empty_set @ infinity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infinity2) ).
thf(82,axiom,
little_set @ infinity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infinity1) ).
thf(83,axiom,
! [Z: $i] :
( ( member @ Z @ universal_set )
| ~ ( little_set @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',universal_set) ).
thf(84,axiom,
! [Z: $i] :
~ ( member @ Z @ empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).
thf(85,axiom,
! [X: $i] :
( ( successor @ X )
= ( union @ X @ ( singleton_set @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor) ).
thf(86,axiom,
! [Z: $i,X: $i,U: $i,V: $i,W: $i] :
( ( member @ Z @ ( flip_range_of @ X ) )
| ~ ( little_set @ Z )
| ~ ( little_set @ U )
| ~ ( little_set @ V )
| ~ ( little_set @ W )
| ( Z
!= ( ordered_pair @ U @ ( ordered_pair @ V @ W ) ) )
| ~ ( member @ ( ordered_pair @ U @ ( ordered_pair @ W @ V ) ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip_range6) ).
thf(87,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( flip_range_of @ X ) )
| ( member @ ( ordered_pair @ ( f12 @ Z @ X ) @ ( ordered_pair @ ( f14 @ Z @ X ) @ ( f13 @ Z @ X ) ) ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip_range5) ).
thf(88,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( flip_range_of @ X ) )
| ( Z
= ( ordered_pair @ ( f12 @ Z @ X ) @ ( ordered_pair @ ( f13 @ Z @ X ) @ ( f14 @ Z @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip_range4) ).
thf(89,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( flip_range_of @ X ) )
| ( little_set @ ( f14 @ Z @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip_range3) ).
thf(90,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( flip_range_of @ X ) )
| ( little_set @ ( f13 @ Z @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip_range2) ).
thf(91,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( flip_range_of @ X ) )
| ( little_set @ ( f12 @ Z @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip_range1) ).
thf(92,axiom,
! [Z: $i,X: $i,U: $i,V: $i,W: $i] :
( ( member @ Z @ ( rotate_right @ X ) )
| ~ ( little_set @ Z )
| ~ ( little_set @ U )
| ~ ( little_set @ V )
| ~ ( little_set @ W )
| ( Z
!= ( ordered_pair @ U @ ( ordered_pair @ V @ W ) ) )
| ~ ( member @ ( ordered_pair @ V @ ( ordered_pair @ W @ U ) ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate_right6) ).
thf(93,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( rotate_right @ X ) )
| ( member @ ( ordered_pair @ ( f10 @ Z @ X ) @ ( ordered_pair @ ( f11 @ Z @ X ) @ ( f9 @ Z @ X ) ) ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate_right5) ).
thf(94,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( rotate_right @ X ) )
| ( Z
= ( ordered_pair @ ( f9 @ Z @ X ) @ ( ordered_pair @ ( f10 @ Z @ X ) @ ( f11 @ Z @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate_right4) ).
thf(95,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( rotate_right @ X ) )
| ( little_set @ ( f11 @ Z @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate_right3) ).
thf(96,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( rotate_right @ X ) )
| ( little_set @ ( f10 @ Z @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate_right2) ).
thf(97,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( rotate_right @ X ) )
| ( little_set @ ( f9 @ Z @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate_right1) ).
thf(98,axiom,
! [Z: $i,X: $i] :
( ( member @ Z @ ( converse @ X ) )
| ~ ( little_set @ Z )
| ~ ( ordered_pair_predicate @ Z )
| ~ ( member @ ( ordered_pair @ ( second @ Z ) @ ( first @ Z ) ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse3) ).
thf(99,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( converse @ X ) )
| ( member @ ( ordered_pair @ ( second @ Z ) @ ( first @ Z ) ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse2) ).
thf(100,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( converse @ X ) )
| ( ordered_pair_predicate @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse1) ).
thf(101,axiom,
! [Z: $i,X: $i,Y: $i] :
( ( member @ Z @ ( cross_product @ X @ Y ) )
| ~ ( little_set @ Z )
| ~ ( ordered_pair_predicate @ Z )
| ~ ( member @ ( first @ Z ) @ X )
| ~ ( member @ ( second @ Z ) @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cross_product4) ).
thf(102,axiom,
! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( cross_product @ X @ Y ) )
| ( member @ ( second @ Z ) @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cross_product3) ).
thf(103,axiom,
! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( cross_product @ X @ Y ) )
| ( member @ ( first @ Z ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cross_product2) ).
thf(104,axiom,
! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( cross_product @ X @ Y ) )
| ( ordered_pair_predicate @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cross_product1) ).
thf(105,axiom,
! [Z: $i,X: $i,Xp: $i] :
( ( member @ Z @ ( domain_of @ X ) )
| ~ ( little_set @ Z )
| ~ ( ordered_pair_predicate @ Xp )
| ~ ( member @ Xp @ X )
| ( Z
!= ( first @ Xp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain4) ).
thf(106,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( domain_of @ X ) )
| ( Z
= ( first @ ( f8 @ Z @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain3) ).
thf(107,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( domain_of @ X ) )
| ( member @ ( f8 @ Z @ X ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain2) ).
thf(108,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( domain_of @ X ) )
| ( ordered_pair_predicate @ ( f8 @ Z @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
thf(109,axiom,
! [X: $i,Y: $i] :
( ( union @ X @ Y )
= ( complement @ ( intersection @ ( complement @ X ) @ ( complement @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
thf(110,axiom,
! [Z: $i,X: $i] :
( ( member @ Z @ ( complement @ X ) )
| ~ ( little_set @ Z )
| ( member @ Z @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).
thf(111,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( complement @ X ) )
| ~ ( member @ Z @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
thf(112,axiom,
! [Z: $i,X: $i,Y: $i] :
( ( member @ Z @ ( intersection @ X @ Y ) )
| ~ ( member @ Z @ X )
| ~ ( member @ Z @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection3) ).
thf(113,axiom,
! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( intersection @ X @ Y ) )
| ( member @ Z @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).
thf(114,axiom,
! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( intersection @ X @ Y ) )
| ( member @ Z @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
thf(115,axiom,
! [Z: $i] :
( ( member @ Z @ estin )
| ~ ( little_set @ Z )
| ~ ( ordered_pair_predicate @ Z )
| ~ ( member @ ( first @ Z ) @ ( second @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation3) ).
thf(116,axiom,
! [Z: $i] :
( ~ ( member @ Z @ estin )
| ( member @ ( first @ Z ) @ ( second @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation2) ).
thf(117,axiom,
! [Z: $i] :
( ~ ( member @ Z @ estin )
| ( ordered_pair_predicate @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation1) ).
thf(118,axiom,
! [Z: $i,X: $i,U: $i,V: $i] :
( ( member @ Z @ ( second @ X ) )
| ~ ( little_set @ U )
| ~ ( little_set @ V )
| ( X
!= ( ordered_pair @ U @ V ) )
| ~ ( member @ Z @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',second5) ).
thf(119,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( second @ X ) )
| ( member @ Z @ ( f7 @ Z @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',second4) ).
thf(120,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( second @ X ) )
| ( X
= ( ordered_pair @ ( f6 @ Z @ X ) @ ( f7 @ Z @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',second3) ).
thf(121,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( second @ X ) )
| ( little_set @ ( f7 @ Z @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',second2) ).
thf(122,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( second @ X ) )
| ( little_set @ ( f6 @ Z @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',second1) ).
thf(123,axiom,
! [Z: $i,X: $i,U: $i,V: $i] :
( ( member @ Z @ ( first @ X ) )
| ~ ( little_set @ U )
| ~ ( little_set @ V )
| ( X
!= ( ordered_pair @ U @ V ) )
| ~ ( member @ Z @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first5) ).
thf(124,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( first @ X ) )
| ( member @ Z @ ( f4 @ Z @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first4) ).
thf(125,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( first @ X ) )
| ( X
= ( ordered_pair @ ( f4 @ Z @ X ) @ ( f5 @ Z @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first3) ).
thf(126,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( first @ X ) )
| ( little_set @ ( f5 @ Z @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first2) ).
thf(127,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( first @ X ) )
| ( little_set @ ( f4 @ Z @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first1) ).
thf(128,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( ordered_pair_predicate @ X )
| ~ ( little_set @ Y )
| ~ ( little_set @ Z )
| ( X
!= ( ordered_pair @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_predicate4) ).
thf(129,axiom,
! [X: $i] :
( ~ ( ordered_pair_predicate @ X )
| ( X
= ( ordered_pair @ ( f2 @ X ) @ ( f3 @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_predicate3) ).
thf(130,axiom,
! [X: $i] :
( ~ ( ordered_pair_predicate @ X )
| ( little_set @ ( f3 @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_predicate2) ).
thf(131,axiom,
! [X: $i] :
( ~ ( ordered_pair_predicate @ X )
| ( little_set @ ( f2 @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_predicate1) ).
thf(132,axiom,
! [X: $i,Y: $i] :
( ( ordered_pair @ X @ Y )
= ( non_ordered_pair @ ( singleton_set @ X ) @ ( non_ordered_pair @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair) ).
thf(133,axiom,
! [X: $i] :
( ( singleton_set @ X )
= ( non_ordered_pair @ X @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
thf(134,axiom,
! [X: $i,Y: $i] : ( little_set @ ( non_ordered_pair @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',non_ordered_pair4) ).
thf(135,axiom,
! [U: $i,X: $i,Y: $i] :
( ( member @ U @ ( non_ordered_pair @ X @ Y ) )
| ~ ( little_set @ U )
| ( U != Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',non_ordered_pair3) ).
thf(136,axiom,
! [U: $i,X: $i,Y: $i] :
( ( member @ U @ ( non_ordered_pair @ X @ Y ) )
| ~ ( little_set @ U )
| ( U != X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',non_ordered_pair2) ).
thf(137,axiom,
! [U: $i,X: $i,Y: $i] :
( ~ ( member @ U @ ( non_ordered_pair @ X @ Y ) )
| ( U = X )
| ( U = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',non_ordered_pair1) ).
thf(138,axiom,
! [X: $i,Y: $i] :
( ~ ( member @ ( f1 @ X @ Y ) @ X )
| ~ ( member @ ( f1 @ X @ Y ) @ Y )
| ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality3) ).
thf(139,axiom,
! [X: $i,Y: $i] :
( ( member @ ( f1 @ X @ Y ) @ X )
| ( member @ ( f1 @ X @ Y ) @ Y )
| ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality2) ).
thf(140,axiom,
! [X: $i,Y: $i] :
( ( little_set @ ( f1 @ X @ Y ) )
| ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality1) ).
thf(141,axiom,
! [X: $i,Y: $i] :
( ~ ( member @ X @ Y )
| ( little_set @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
thf(142,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(143,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[142]) ).
thf(144,negated_conjecture,
~ ( little_set @ ( ordered_pair @ a @ b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ordered_pairs_are_small) ).
thf(145,plain,
$false = $false,
inference(unfold_def,[status(thm)],[143]) ).
thf(146,plain,
( ( ! [Xh: $i,Xs1: $i,Xf1: $i,Xs2: $i,Xf2: $i] :
( ( homomorphism @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 )
| ~ ( closed @ Xs1 @ Xf1 )
| ~ ( closed @ Xs2 @ Xf2 )
| ~ ( maps @ Xh @ Xs1 @ Xs2 )
| ( ( apply @ Xh @ ( apply_to_two_arguments @ Xf1 @ ( f32 @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 ) @ ( f33 @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 ) ) )
!= ( apply_to_two_arguments @ Xf2 @ ( apply @ Xh @ ( f32 @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 ) ) @ ( apply @ Xh @ ( f33 @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(147,plain,
( ( ! [Xh: $i,Xs1: $i,Xf1: $i,Xs2: $i,Xf2: $i] :
( ( homomorphism @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 )
| ~ ( closed @ Xs1 @ Xf1 )
| ~ ( closed @ Xs2 @ Xf2 )
| ~ ( maps @ Xh @ Xs1 @ Xs2 )
| ( member @ ( f33 @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 ) @ Xs1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(148,plain,
( ( ! [Xh: $i,Xs1: $i,Xf1: $i,Xs2: $i,Xf2: $i] :
( ( homomorphism @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 )
| ~ ( closed @ Xs1 @ Xf1 )
| ~ ( closed @ Xs2 @ Xf2 )
| ~ ( maps @ Xh @ Xs1 @ Xs2 )
| ( member @ ( f32 @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 ) @ Xs1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(149,plain,
( ( ! [Xh: $i,Xs1: $i,Xf1: $i,Xs2: $i,Xf2: $i,X: $i,Y: $i] :
( ~ ( homomorphism @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 )
| ~ ( member @ X @ Xs1 )
| ~ ( member @ Y @ Xs1 )
| ( ( apply @ Xh @ ( apply_to_two_arguments @ Xf1 @ X @ Y ) )
= ( apply_to_two_arguments @ Xf2 @ ( apply @ Xh @ X ) @ ( apply @ Xh @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(150,plain,
( ( ! [Xh: $i,Xs1: $i,Xf1: $i,Xs2: $i,Xf2: $i] :
( ~ ( homomorphism @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 )
| ( maps @ Xh @ Xs1 @ Xs2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(151,plain,
( ( ! [Xh: $i,Xs1: $i,Xf1: $i,Xs2: $i,Xf2: $i] :
( ~ ( homomorphism @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 )
| ( closed @ Xs2 @ Xf2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(152,plain,
( ( ! [Xh: $i,Xs1: $i,Xf1: $i,Xs2: $i,Xf2: $i] :
( ~ ( homomorphism @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 )
| ( closed @ Xs1 @ Xf1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(153,plain,
( ( ! [Z: $i,Xf: $i,Xg: $i,X: $i,Y: $i,W: $i] :
( ( member @ Z @ ( compose @ Xf @ Xg ) )
| ~ ( little_set @ Z )
| ~ ( little_set @ X )
| ~ ( little_set @ Y )
| ~ ( little_set @ W )
| ( Z
!= ( ordered_pair @ X @ Y ) )
| ~ ( member @ ( ordered_pair @ X @ W ) @ Xf )
| ~ ( member @ ( ordered_pair @ W @ Y ) @ Xg ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(154,plain,
( ( ! [Z: $i,Xf: $i,Xg: $i] :
( ~ ( member @ Z @ ( compose @ Xf @ Xg ) )
| ( member @ ( ordered_pair @ ( f31 @ Z @ Xf @ Xg ) @ ( f30 @ Z @ Xf @ Xg ) ) @ Xg ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(155,plain,
( ( ! [Z: $i,Xf: $i,Xg: $i] :
( ~ ( member @ Z @ ( compose @ Xf @ Xg ) )
| ( member @ ( ordered_pair @ ( f29 @ Z @ Xf @ Xg ) @ ( f31 @ Z @ Xf @ Xg ) ) @ Xf ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(156,plain,
( ( ! [Z: $i,Xf: $i,Xg: $i] :
( ~ ( member @ Z @ ( compose @ Xf @ Xg ) )
| ( Z
= ( ordered_pair @ ( f29 @ Z @ Xf @ Xg ) @ ( f30 @ Z @ Xf @ Xg ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(157,plain,
( ( ! [Z: $i,Xf: $i,Xg: $i] :
( ~ ( member @ Z @ ( compose @ Xf @ Xg ) )
| ( little_set @ ( f31 @ Z @ Xf @ Xg ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(158,plain,
( ( ! [Z: $i,Xf: $i,Xg: $i] :
( ~ ( member @ Z @ ( compose @ Xf @ Xg ) )
| ( little_set @ ( f30 @ Z @ Xf @ Xg ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(159,plain,
( ( ! [Z: $i,Xf: $i,Xg: $i] :
( ~ ( member @ Z @ ( compose @ Xf @ Xg ) )
| ( little_set @ ( f29 @ Z @ Xf @ Xg ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(160,plain,
( ( ! [Xs: $i,Xf: $i] :
( ( closed @ Xs @ Xf )
| ~ ( little_set @ Xs )
| ~ ( little_set @ Xf )
| ~ ( maps @ Xf @ ( cross_product @ Xs @ Xs ) @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(161,plain,
( ( ! [Xs: $i,Xf: $i] :
( ~ ( closed @ Xs @ Xf )
| ( maps @ Xf @ ( cross_product @ Xs @ Xs ) @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(162,plain,
( ( ! [Xs: $i,Xf: $i] :
( ~ ( closed @ Xs @ Xf )
| ( little_set @ Xf ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(163,plain,
( ( ! [Xs: $i,Xf: $i] :
( ~ ( closed @ Xs @ Xf )
| ( little_set @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(164,plain,
( ( ! [Xf: $i,X: $i,Y: $i] :
( ( maps @ Xf @ X @ Y )
| ~ ( function @ Xf )
| ( ( domain_of @ Xf )
!= X )
| ~ ( subset @ ( range_of @ Xf ) @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(165,plain,
( ( ! [Xf: $i,X: $i,Y: $i] :
( ~ ( maps @ Xf @ X @ Y )
| ( subset @ ( range_of @ Xf ) @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(166,plain,
( ( ! [Xf: $i,X: $i,Y: $i] :
( ~ ( maps @ Xf @ X @ Y )
| ( ( domain_of @ Xf )
= X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(167,plain,
( ( ! [Xf: $i,X: $i,Y: $i] :
( ~ ( maps @ Xf @ X @ Y )
| ( function @ Xf ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(168,plain,
( ( ! [Xf: $i,X: $i,Y: $i] :
( ( apply_to_two_arguments @ Xf @ X @ Y )
= ( apply @ Xf @ ( ordered_pair @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(169,plain,
( ( ! [Z: $i,Xf: $i,Y: $i,W: $i] :
( ( member @ Z @ ( apply @ Xf @ Y ) )
| ~ ( ordered_pair_predicate @ W )
| ~ ( member @ W @ Xf )
| ( ( first @ W )
!= Y )
| ~ ( member @ Z @ ( second @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(170,plain,
( ( ! [Z: $i,Xf: $i,Y: $i] :
( ~ ( member @ Z @ ( apply @ Xf @ Y ) )
| ( member @ Z @ ( second @ ( f28 @ Z @ Xf @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(171,plain,
( ( ! [Z: $i,Xf: $i,Y: $i] :
( ~ ( member @ Z @ ( apply @ Xf @ Y ) )
| ( ( first @ ( f28 @ Z @ Xf @ Y ) )
= Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(172,plain,
( ( ! [Z: $i,Xf: $i,Y: $i] :
( ~ ( member @ Z @ ( apply @ Xf @ Y ) )
| ( member @ ( f28 @ Z @ Xf @ Y ) @ Xf ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(173,plain,
( ( ! [Z: $i,Xf: $i,Y: $i] :
( ~ ( member @ Z @ ( apply @ Xf @ Y ) )
| ( ordered_pair_predicate @ ( f28 @ Z @ Xf @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(174,plain,
( ( ! [Xf: $i] :
( ( one_to_one_function @ Xf )
| ~ ( function @ Xf )
| ~ ( function @ ( converse @ Xf ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(175,plain,
( ( ! [Xf: $i] :
( ~ ( one_to_one_function @ Xf )
| ( function @ ( converse @ Xf ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(176,plain,
( ( ! [Xf: $i] :
( ~ ( one_to_one_function @ Xf )
| ( function @ Xf ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(177,plain,
( ( ! [X: $i,Y: $i] :
( ( restrict @ X @ Y )
= ( intersection @ X @ ( cross_product @ Y @ universal_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(178,plain,
( ( ! [Z: $i] :
( ( member @ Z @ identity_relation )
| ~ ( little_set @ Z )
| ~ ( ordered_pair_predicate @ Z )
| ( ( first @ Z )
!= ( second @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(179,plain,
( ( ! [Z: $i] :
( ~ ( member @ Z @ identity_relation )
| ( ( first @ Z )
= ( second @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(180,plain,
( ( ! [Z: $i] :
( ~ ( member @ Z @ identity_relation )
| ( ordered_pair_predicate @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(181,plain,
( ( ! [Z: $i,X: $i,Xp: $i] :
( ( member @ Z @ ( range_of @ X ) )
| ~ ( little_set @ Z )
| ~ ( ordered_pair_predicate @ Xp )
| ~ ( member @ Xp @ X )
| ( Z
!= ( second @ Xp ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(182,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( range_of @ X ) )
| ( Z
= ( second @ ( f27 @ Z @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(183,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( range_of @ X ) )
| ( member @ ( f27 @ Z @ X ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(184,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( range_of @ X ) )
| ( ordered_pair_predicate @ ( f27 @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(185,plain,
( ( ! [X: $i] :
( ~ ( little_set @ X )
| ( X = empty_set )
| ( member @ ( ordered_pair @ X @ ( f26 @ X ) ) @ f25 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(186,plain,
( ( ! [X: $i] :
( ~ ( little_set @ X )
| ( X = empty_set )
| ( member @ ( f26 @ X ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(187,plain,
( ( function @ f25 )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(188,plain,
( ( ! [X: $i] :
( ( X = empty_set )
| ( disjoint @ ( f24 @ X ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(189,plain,
( ( ! [X: $i] :
( ( X = empty_set )
| ( member @ ( f24 @ X ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(190,plain,
( ( ! [X: $i,Y: $i] :
( ( disjoint @ X @ Y )
| ( member @ ( f23 @ X @ Y ) @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(191,plain,
( ( ! [X: $i,Y: $i] :
( ( disjoint @ X @ Y )
| ( member @ ( f23 @ X @ Y ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(192,plain,
( ( ! [X: $i,Y: $i,U: $i] :
( ~ ( disjoint @ X @ Y )
| ~ ( member @ U @ X )
| ~ ( member @ U @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(193,plain,
( ( ! [X: $i,Xf: $i] :
( ~ ( little_set @ X )
| ~ ( function @ Xf )
| ( little_set @ ( image @ X @ Xf ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(194,plain,
( ( ! [Z: $i,X: $i,Xf: $i,Y: $i] :
( ( member @ Z @ ( image @ X @ Xf ) )
| ~ ( little_set @ Z )
| ~ ( ordered_pair_predicate @ Y )
| ~ ( member @ Y @ Xf )
| ~ ( member @ ( first @ Y ) @ X )
| ( ( second @ Y )
!= Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(195,plain,
( ( ! [Z: $i,X: $i,Xf: $i] :
( ~ ( member @ Z @ ( image @ X @ Xf ) )
| ( ( second @ ( f22 @ Z @ X @ Xf ) )
= Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(196,plain,
( ( ! [Z: $i,X: $i,Xf: $i] :
( ~ ( member @ Z @ ( image @ X @ Xf ) )
| ( member @ ( first @ ( f22 @ Z @ X @ Xf ) ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(197,plain,
( ( ! [Z: $i,X: $i,Xf: $i] :
( ~ ( member @ Z @ ( image @ X @ Xf ) )
| ( member @ ( f22 @ Z @ X @ Xf ) @ Xf ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(198,plain,
( ( ! [Z: $i,X: $i,Xf: $i] :
( ~ ( member @ Z @ ( image @ X @ Xf ) )
| ( ordered_pair_predicate @ ( f22 @ Z @ X @ Xf ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(199,plain,
( ( ! [Xf: $i] :
( ( function @ Xf )
| ~ ( relation @ Xf )
| ~ ( single_valued_set @ Xf ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(200,plain,
( ( ! [Xf: $i] :
( ~ ( function @ Xf )
| ( single_valued_set @ Xf ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(201,plain,
( ( ! [Xf: $i] :
( ~ ( function @ Xf )
| ( relation @ Xf ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(202,plain,
( ( ! [X: $i] :
( ( single_valued_set @ X )
| ( ( f20 @ X )
!= ( f21 @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(203,plain,
( ( ! [X: $i] :
( ( single_valued_set @ X )
| ( member @ ( ordered_pair @ ( f19 @ X ) @ ( f21 @ X ) ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(204,plain,
( ( ! [X: $i] :
( ( single_valued_set @ X )
| ( member @ ( ordered_pair @ ( f19 @ X ) @ ( f20 @ X ) ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(205,plain,
( ( ! [X: $i] :
( ( single_valued_set @ X )
| ( little_set @ ( f21 @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(206,plain,
( ( ! [X: $i] :
( ( single_valued_set @ X )
| ( little_set @ ( f20 @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(207,plain,
( ( ! [X: $i] :
( ( single_valued_set @ X )
| ( little_set @ ( f19 @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(208,plain,
( ( ! [X: $i,U: $i,V: $i,W: $i] :
( ~ ( single_valued_set @ X )
| ~ ( little_set @ U )
| ~ ( little_set @ V )
| ~ ( little_set @ W )
| ~ ( member @ ( ordered_pair @ U @ V ) @ X )
| ~ ( member @ ( ordered_pair @ U @ W ) @ X )
| ( V = W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(209,plain,
( ( ! [Z: $i] :
( ( relation @ Z )
| ~ ( ordered_pair_predicate @ ( f18 @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(210,plain,
( ( ! [Z: $i] :
( ( relation @ Z )
| ( member @ ( f18 @ Z ) @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(211,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( relation @ Z )
| ~ ( member @ X @ Z )
| ( ordered_pair_predicate @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(212,plain,
( ( ! [U: $i] :
( ~ ( little_set @ U )
| ( little_set @ ( powerset @ U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(213,plain,
( ( ! [Z: $i,X: $i] :
( ( member @ Z @ ( powerset @ X ) )
| ~ ( little_set @ Z )
| ~ ( subset @ Z @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(214,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( powerset @ X ) )
| ( subset @ Z @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(215,plain,
( ( ! [X: $i,Y: $i] :
( ( proper_subset @ X @ Y )
| ~ ( subset @ X @ Y )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(216,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( proper_subset @ X @ Y )
| ( X != Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(217,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( proper_subset @ X @ Y )
| ( subset @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(218,plain,
( ( ! [X: $i,Y: $i] :
( ( subset @ X @ Y )
| ~ ( member @ ( f17 @ X @ Y ) @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(219,plain,
( ( ! [X: $i,Y: $i] :
( ( subset @ X @ Y )
| ( member @ ( f17 @ X @ Y ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(220,plain,
( ( ! [X: $i,Y: $i,U: $i] :
( ~ ( subset @ X @ Y )
| ~ ( member @ U @ X )
| ( member @ U @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(221,plain,
( ( ! [U: $i] :
( ~ ( little_set @ U )
| ( little_set @ ( sigma @ U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(222,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ( member @ Z @ ( sigma @ X ) )
| ~ ( member @ Y @ X )
| ~ ( member @ Z @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(223,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( sigma @ X ) )
| ( member @ Z @ ( f16 @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(224,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( sigma @ X ) )
| ( member @ ( f16 @ Z @ X ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(225,plain,
( ( ! [X: $i] :
( ~ ( member @ X @ infinity )
| ( member @ ( successor @ X ) @ infinity ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(226,plain,
( ( member @ empty_set @ infinity )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(227,plain,
( ( little_set @ infinity )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(228,plain,
( ( ! [Z: $i] :
( ( member @ Z @ universal_set )
| ~ ( little_set @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(229,plain,
( ( ! [Z: $i] :
~ ( member @ Z @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(230,plain,
( ( ! [X: $i] :
( ( successor @ X )
= ( union @ X @ ( singleton_set @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(231,plain,
( ( ! [Z: $i,X: $i,U: $i,V: $i,W: $i] :
( ( member @ Z @ ( flip_range_of @ X ) )
| ~ ( little_set @ Z )
| ~ ( little_set @ U )
| ~ ( little_set @ V )
| ~ ( little_set @ W )
| ( Z
!= ( ordered_pair @ U @ ( ordered_pair @ V @ W ) ) )
| ~ ( member @ ( ordered_pair @ U @ ( ordered_pair @ W @ V ) ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(232,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( flip_range_of @ X ) )
| ( member @ ( ordered_pair @ ( f12 @ Z @ X ) @ ( ordered_pair @ ( f14 @ Z @ X ) @ ( f13 @ Z @ X ) ) ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(233,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( flip_range_of @ X ) )
| ( Z
= ( ordered_pair @ ( f12 @ Z @ X ) @ ( ordered_pair @ ( f13 @ Z @ X ) @ ( f14 @ Z @ X ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(234,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( flip_range_of @ X ) )
| ( little_set @ ( f14 @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(235,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( flip_range_of @ X ) )
| ( little_set @ ( f13 @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(236,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( flip_range_of @ X ) )
| ( little_set @ ( f12 @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(237,plain,
( ( ! [Z: $i,X: $i,U: $i,V: $i,W: $i] :
( ( member @ Z @ ( rotate_right @ X ) )
| ~ ( little_set @ Z )
| ~ ( little_set @ U )
| ~ ( little_set @ V )
| ~ ( little_set @ W )
| ( Z
!= ( ordered_pair @ U @ ( ordered_pair @ V @ W ) ) )
| ~ ( member @ ( ordered_pair @ V @ ( ordered_pair @ W @ U ) ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(238,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( rotate_right @ X ) )
| ( member @ ( ordered_pair @ ( f10 @ Z @ X ) @ ( ordered_pair @ ( f11 @ Z @ X ) @ ( f9 @ Z @ X ) ) ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(239,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( rotate_right @ X ) )
| ( Z
= ( ordered_pair @ ( f9 @ Z @ X ) @ ( ordered_pair @ ( f10 @ Z @ X ) @ ( f11 @ Z @ X ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(240,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( rotate_right @ X ) )
| ( little_set @ ( f11 @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(241,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( rotate_right @ X ) )
| ( little_set @ ( f10 @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(242,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( rotate_right @ X ) )
| ( little_set @ ( f9 @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(243,plain,
( ( ! [Z: $i,X: $i] :
( ( member @ Z @ ( converse @ X ) )
| ~ ( little_set @ Z )
| ~ ( ordered_pair_predicate @ Z )
| ~ ( member @ ( ordered_pair @ ( second @ Z ) @ ( first @ Z ) ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(244,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( converse @ X ) )
| ( member @ ( ordered_pair @ ( second @ Z ) @ ( first @ Z ) ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(245,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( converse @ X ) )
| ( ordered_pair_predicate @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(246,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ( member @ Z @ ( cross_product @ X @ Y ) )
| ~ ( little_set @ Z )
| ~ ( ordered_pair_predicate @ Z )
| ~ ( member @ ( first @ Z ) @ X )
| ~ ( member @ ( second @ Z ) @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(247,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( cross_product @ X @ Y ) )
| ( member @ ( second @ Z ) @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(248,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( cross_product @ X @ Y ) )
| ( member @ ( first @ Z ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(249,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( cross_product @ X @ Y ) )
| ( ordered_pair_predicate @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(250,plain,
( ( ! [Z: $i,X: $i,Xp: $i] :
( ( member @ Z @ ( domain_of @ X ) )
| ~ ( little_set @ Z )
| ~ ( ordered_pair_predicate @ Xp )
| ~ ( member @ Xp @ X )
| ( Z
!= ( first @ Xp ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(251,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( domain_of @ X ) )
| ( Z
= ( first @ ( f8 @ Z @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(252,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( domain_of @ X ) )
| ( member @ ( f8 @ Z @ X ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(253,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( domain_of @ X ) )
| ( ordered_pair_predicate @ ( f8 @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(254,plain,
( ( ! [X: $i,Y: $i] :
( ( union @ X @ Y )
= ( complement @ ( intersection @ ( complement @ X ) @ ( complement @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(255,plain,
( ( ! [Z: $i,X: $i] :
( ( member @ Z @ ( complement @ X ) )
| ~ ( little_set @ Z )
| ( member @ Z @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(256,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( complement @ X ) )
| ~ ( member @ Z @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(257,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ( member @ Z @ ( intersection @ X @ Y ) )
| ~ ( member @ Z @ X )
| ~ ( member @ Z @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(258,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( intersection @ X @ Y ) )
| ( member @ Z @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(259,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( intersection @ X @ Y ) )
| ( member @ Z @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(260,plain,
( ( ! [Z: $i] :
( ( member @ Z @ estin )
| ~ ( little_set @ Z )
| ~ ( ordered_pair_predicate @ Z )
| ~ ( member @ ( first @ Z ) @ ( second @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(261,plain,
( ( ! [Z: $i] :
( ~ ( member @ Z @ estin )
| ( member @ ( first @ Z ) @ ( second @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(262,plain,
( ( ! [Z: $i] :
( ~ ( member @ Z @ estin )
| ( ordered_pair_predicate @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(263,plain,
( ( ! [Z: $i,X: $i,U: $i,V: $i] :
( ( member @ Z @ ( second @ X ) )
| ~ ( little_set @ U )
| ~ ( little_set @ V )
| ( X
!= ( ordered_pair @ U @ V ) )
| ~ ( member @ Z @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(264,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( second @ X ) )
| ( member @ Z @ ( f7 @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(265,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( second @ X ) )
| ( X
= ( ordered_pair @ ( f6 @ Z @ X ) @ ( f7 @ Z @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(266,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( second @ X ) )
| ( little_set @ ( f7 @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(267,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( second @ X ) )
| ( little_set @ ( f6 @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(268,plain,
( ( ! [Z: $i,X: $i,U: $i,V: $i] :
( ( member @ Z @ ( first @ X ) )
| ~ ( little_set @ U )
| ~ ( little_set @ V )
| ( X
!= ( ordered_pair @ U @ V ) )
| ~ ( member @ Z @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(269,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( first @ X ) )
| ( member @ Z @ ( f4 @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(270,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( first @ X ) )
| ( X
= ( ordered_pair @ ( f4 @ Z @ X ) @ ( f5 @ Z @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(271,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( first @ X ) )
| ( little_set @ ( f5 @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(272,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( first @ X ) )
| ( little_set @ ( f4 @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(273,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ordered_pair_predicate @ X )
| ~ ( little_set @ Y )
| ~ ( little_set @ Z )
| ( X
!= ( ordered_pair @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(274,plain,
( ( ! [X: $i] :
( ~ ( ordered_pair_predicate @ X )
| ( X
= ( ordered_pair @ ( f2 @ X ) @ ( f3 @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(275,plain,
( ( ! [X: $i] :
( ~ ( ordered_pair_predicate @ X )
| ( little_set @ ( f3 @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(276,plain,
( ( ! [X: $i] :
( ~ ( ordered_pair_predicate @ X )
| ( little_set @ ( f2 @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(277,plain,
( ( ! [X: $i,Y: $i] :
( ( ordered_pair @ X @ Y )
= ( non_ordered_pair @ ( singleton_set @ X ) @ ( non_ordered_pair @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(278,plain,
( ( ! [X: $i] :
( ( singleton_set @ X )
= ( non_ordered_pair @ X @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(279,plain,
( ( ! [X: $i,Y: $i] : ( little_set @ ( non_ordered_pair @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(280,plain,
( ( ! [U: $i,X: $i,Y: $i] :
( ( member @ U @ ( non_ordered_pair @ X @ Y ) )
| ~ ( little_set @ U )
| ( U != Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(281,plain,
( ( ! [U: $i,X: $i,Y: $i] :
( ( member @ U @ ( non_ordered_pair @ X @ Y ) )
| ~ ( little_set @ U )
| ( U != X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(282,plain,
( ( ! [U: $i,X: $i,Y: $i] :
( ~ ( member @ U @ ( non_ordered_pair @ X @ Y ) )
| ( U = X )
| ( U = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(283,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( member @ ( f1 @ X @ Y ) @ X )
| ~ ( member @ ( f1 @ X @ Y ) @ Y )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(284,plain,
( ( ! [X: $i,Y: $i] :
( ( member @ ( f1 @ X @ Y ) @ X )
| ( member @ ( f1 @ X @ Y ) @ Y )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(285,plain,
( ( ! [X: $i,Y: $i] :
( ( little_set @ ( f1 @ X @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(286,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( member @ X @ Y )
| ( little_set @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(287,plain,
( ( ~ ( little_set @ ( ordered_pair @ a @ b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(288,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[145]) ).
thf(289,plain,
( ( ! [Xh: $i,Xs1: $i,Xf1: $i,Xs2: $i,Xf2: $i] :
( ( homomorphism @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 )
| ~ ( closed @ Xs1 @ Xf1 )
| ~ ( closed @ Xs2 @ Xf2 )
| ~ ( maps @ Xh @ Xs1 @ Xs2 )
| ( ( apply @ Xh @ ( apply_to_two_arguments @ Xf1 @ ( f32 @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 ) @ ( f33 @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 ) ) )
!= ( apply_to_two_arguments @ Xf2 @ ( apply @ Xh @ ( f32 @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 ) ) @ ( apply @ Xh @ ( f33 @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[146]) ).
thf(290,plain,
( ( ! [Xh: $i,Xs1: $i,Xf1: $i,Xs2: $i,Xf2: $i] :
( ~ ( homomorphism @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 )
| ! [X: $i] :
( ~ ( member @ X @ Xs1 )
| ! [Y: $i] :
( ~ ( member @ Y @ Xs1 )
| ( ( apply @ Xh @ ( apply_to_two_arguments @ Xf1 @ X @ Y ) )
= ( apply_to_two_arguments @ Xf2 @ ( apply @ Xh @ X ) @ ( apply @ Xh @ Y ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[149]) ).
thf(291,plain,
( ( ! [Xh: $i,Xs1: $i,Xf1: $i,Xs2: $i] :
( ! [Xf2: $i] :
~ ( homomorphism @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 )
| ( maps @ Xh @ Xs1 @ Xs2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[150]) ).
thf(292,plain,
( ( ! [Xh: $i,Xs1: $i,Xf1: $i] :
( ! [Xs2: $i,Xf2: $i] :
~ ( homomorphism @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 )
| ( closed @ Xs1 @ Xf1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[152]) ).
thf(293,plain,
( ( ! [Z: $i,Xf: $i,Xg: $i,X: $i] :
( ( member @ Z @ ( compose @ Xf @ Xg ) )
| ~ ( little_set @ Z )
| ~ ( little_set @ X )
| ! [Y: $i] :
( ~ ( little_set @ Y )
| ! [W: $i] :
( ~ ( little_set @ W )
| ( Z
!= ( ordered_pair @ X @ Y ) )
| ~ ( member @ ( ordered_pair @ X @ W ) @ Xf )
| ~ ( member @ ( ordered_pair @ W @ Y ) @ Xg ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[153]) ).
thf(294,plain,
( ( ! [Xs: $i] :
( ! [Xf: $i] :
~ ( closed @ Xs @ Xf )
| ( little_set @ Xs ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[163]) ).
thf(295,plain,
( ( ! [Xf: $i,X: $i,Y: $i] :
( ( maps @ Xf @ X @ Y )
| ~ ( function @ Xf )
| ( ( domain_of @ Xf )
!= X )
| ~ ( subset @ ( range_of @ Xf ) @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[164]) ).
thf(296,plain,
( ( ! [Xf: $i,X: $i] :
( ! [Y: $i] :
~ ( maps @ Xf @ X @ Y )
| ( ( domain_of @ Xf )
= X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[166]) ).
thf(297,plain,
( ( ! [Xf: $i] :
( ! [X: $i,Y: $i] :
~ ( maps @ Xf @ X @ Y )
| ( function @ Xf ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[167]) ).
thf(298,plain,
( ( ! [Z: $i,Xf: $i,Y: $i] :
( ( member @ Z @ ( apply @ Xf @ Y ) )
| ! [W: $i] :
( ~ ( ordered_pair_predicate @ W )
| ~ ( member @ W @ Xf )
| ( ( first @ W )
!= Y )
| ~ ( member @ Z @ ( second @ W ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[169]) ).
thf(299,plain,
( ( ! [Z: $i] :
( ( member @ Z @ identity_relation )
| ~ ( little_set @ Z )
| ~ ( ordered_pair_predicate @ Z )
| ( ( first @ Z )
!= ( second @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[178]) ).
thf(300,plain,
( ( ! [Z: $i,X: $i] :
( ( member @ Z @ ( range_of @ X ) )
| ~ ( little_set @ Z )
| ! [Xp: $i] :
( ~ ( ordered_pair_predicate @ Xp )
| ~ ( member @ Xp @ X )
| ( Z
!= ( second @ Xp ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[181]) ).
thf(301,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( disjoint @ X @ Y )
| ! [U: $i] :
( ~ ( member @ U @ X )
| ~ ( member @ U @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[192]) ).
thf(302,plain,
( ( ! [X: $i] :
( ~ ( little_set @ X )
| ! [Xf: $i] :
( ~ ( function @ Xf )
| ( little_set @ ( image @ X @ Xf ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[193]) ).
thf(303,plain,
( ( ! [Z: $i,X: $i,Xf: $i] :
( ( member @ Z @ ( image @ X @ Xf ) )
| ~ ( little_set @ Z )
| ! [Y: $i] :
( ~ ( ordered_pair_predicate @ Y )
| ~ ( member @ Y @ Xf )
| ~ ( member @ ( first @ Y ) @ X )
| ( ( second @ Y )
!= Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[194]) ).
thf(304,plain,
( ( ! [X: $i] :
( ( ( f20 @ X )
!= ( f21 @ X ) )
| ( single_valued_set @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[202]) ).
thf(305,plain,
( ( ! [X: $i] :
( ( member @ ( ordered_pair @ ( f19 @ X ) @ ( f21 @ X ) ) @ X )
| ( single_valued_set @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[203]) ).
thf(306,plain,
( ( ! [X: $i] :
( ( member @ ( ordered_pair @ ( f19 @ X ) @ ( f20 @ X ) ) @ X )
| ( single_valued_set @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[204]) ).
thf(307,plain,
( ( ! [X: $i] :
( ( little_set @ ( f21 @ X ) )
| ( single_valued_set @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[205]) ).
thf(308,plain,
( ( ! [X: $i] :
( ( little_set @ ( f20 @ X ) )
| ( single_valued_set @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[206]) ).
thf(309,plain,
( ( ! [X: $i] :
( ( little_set @ ( f19 @ X ) )
| ( single_valued_set @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[207]) ).
thf(310,plain,
( ( ! [X: $i,U: $i] :
( ~ ( single_valued_set @ X )
| ~ ( little_set @ U )
| ! [V: $i] :
( ~ ( little_set @ V )
| ! [W: $i] :
( ~ ( little_set @ W )
| ~ ( member @ ( ordered_pair @ U @ V ) @ X )
| ~ ( member @ ( ordered_pair @ U @ W ) @ X )
| ( V = W ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[208]) ).
thf(311,plain,
( ( ! [Z: $i] :
( ( member @ ( f18 @ Z ) @ Z )
| ( relation @ Z ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[210]) ).
thf(312,plain,
( ( ! [Z: $i] :
( ~ ( relation @ Z )
| ! [X: $i] :
( ~ ( member @ X @ Z )
| ( ordered_pair_predicate @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[211]) ).
thf(313,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( proper_subset @ X @ Y )
| ( X != Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[216]) ).
thf(314,plain,
( ( ! [X: $i,Y: $i] :
( ( member @ ( f17 @ X @ Y ) @ X )
| ( subset @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[219]) ).
thf(315,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( subset @ X @ Y )
| ! [U: $i] :
( ~ ( member @ U @ X )
| ( member @ U @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[220]) ).
thf(316,plain,
( ( ! [Z: $i,X: $i] :
( ( member @ Z @ ( sigma @ X ) )
| ! [Y: $i] :
( ~ ( member @ Y @ X )
| ~ ( member @ Z @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[222]) ).
thf(317,plain,
( ( ! [Z: $i,X: $i,U: $i] :
( ( member @ Z @ ( flip_range_of @ X ) )
| ~ ( little_set @ Z )
| ~ ( little_set @ U )
| ! [V: $i] :
( ~ ( little_set @ V )
| ! [W: $i] :
( ~ ( little_set @ W )
| ( Z
!= ( ordered_pair @ U @ ( ordered_pair @ V @ W ) ) )
| ~ ( member @ ( ordered_pair @ U @ ( ordered_pair @ W @ V ) ) @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[231]) ).
thf(318,plain,
( ( ! [Z: $i,X: $i,U: $i] :
( ( member @ Z @ ( rotate_right @ X ) )
| ~ ( little_set @ Z )
| ~ ( little_set @ U )
| ! [V: $i] :
( ~ ( little_set @ V )
| ! [W: $i] :
( ~ ( little_set @ W )
| ( Z
!= ( ordered_pair @ U @ ( ordered_pair @ V @ W ) ) )
| ~ ( member @ ( ordered_pair @ V @ ( ordered_pair @ W @ U ) ) @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[237]) ).
thf(319,plain,
( ( ! [Z: $i] :
( ! [X: $i] :
~ ( member @ Z @ ( converse @ X ) )
| ( ordered_pair_predicate @ Z ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[245]) ).
thf(320,plain,
( ( ! [Z: $i,X: $i] :
( ! [Y: $i] :
~ ( member @ Z @ ( cross_product @ X @ Y ) )
| ( member @ ( first @ Z ) @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[248]) ).
thf(321,plain,
( ( ! [Z: $i] :
( ! [X: $i,Y: $i] :
~ ( member @ Z @ ( cross_product @ X @ Y ) )
| ( ordered_pair_predicate @ Z ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[249]) ).
thf(322,plain,
( ( ! [Z: $i,X: $i] :
( ( member @ Z @ ( domain_of @ X ) )
| ~ ( little_set @ Z )
| ! [Xp: $i] :
( ~ ( ordered_pair_predicate @ Xp )
| ~ ( member @ Xp @ X )
| ( Z
!= ( first @ Xp ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[250]) ).
thf(323,plain,
( ( ! [Z: $i,X: $i] :
( ! [Y: $i] :
~ ( member @ Z @ ( intersection @ X @ Y ) )
| ( member @ Z @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[259]) ).
thf(324,plain,
( ( ! [Z: $i,X: $i] :
( ( member @ Z @ ( second @ X ) )
| ! [U: $i] :
( ~ ( little_set @ U )
| ! [V: $i] :
( ~ ( little_set @ V )
| ( X
!= ( ordered_pair @ U @ V ) )
| ~ ( member @ Z @ V ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[263]) ).
thf(325,plain,
( ( ! [Z: $i,X: $i] :
( ( member @ Z @ ( first @ X ) )
| ! [U: $i] :
( ~ ( little_set @ U )
| ! [V: $i] :
( ~ ( little_set @ V )
| ( X
!= ( ordered_pair @ U @ V ) )
| ~ ( member @ Z @ U ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[268]) ).
thf(326,plain,
( ( ! [X: $i] :
( ( ordered_pair_predicate @ X )
| ! [Y: $i] :
( ~ ( little_set @ Y )
| ! [Z: $i] :
( ~ ( little_set @ Z )
| ( X
!= ( ordered_pair @ Y @ Z ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[273]) ).
thf(327,plain,
( ( ! [U: $i,X: $i,Y: $i] :
( ( member @ U @ ( non_ordered_pair @ X @ Y ) )
| ~ ( little_set @ U )
| ( U != Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[280]) ).
thf(328,plain,
( ( ! [U: $i,X: $i] :
( ! [Y: $i] : ( member @ U @ ( non_ordered_pair @ X @ Y ) )
| ~ ( little_set @ U )
| ( U != X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[281]) ).
thf(329,plain,
( ( ! [X: $i,Y: $i] :
( ( member @ ( f1 @ X @ Y ) @ X )
| ( X = Y )
| ( member @ ( f1 @ X @ Y ) @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[284]) ).
thf(330,plain,
( ( ! [X: $i,Y: $i] :
( ( X = Y )
| ( little_set @ ( f1 @ X @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[285]) ).
thf(331,plain,
( ( ! [X: $i] :
( ! [Y: $i] :
~ ( member @ X @ Y )
| ( little_set @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[286]) ).
thf(332,plain,
( ( ~ ( little_set @ ( ordered_pair @ a @ b ) ) )
= $true ),
inference(copy,[status(thm)],[287]) ).
thf(333,plain,
( ( ! [X: $i] :
( ! [Y: $i] :
~ ( member @ X @ Y )
| ( little_set @ X ) ) )
= $true ),
inference(copy,[status(thm)],[331]) ).
thf(334,plain,
( ( ! [X: $i,Y: $i] :
( ( X = Y )
| ( little_set @ ( f1 @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[330]) ).
thf(335,plain,
( ( ! [X: $i,Y: $i] :
( ( member @ ( f1 @ X @ Y ) @ X )
| ( X = Y )
| ( member @ ( f1 @ X @ Y ) @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[329]) ).
thf(336,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( member @ ( f1 @ X @ Y ) @ X )
| ~ ( member @ ( f1 @ X @ Y ) @ Y )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[283]) ).
thf(337,plain,
( ( ! [U: $i,X: $i,Y: $i] :
( ~ ( member @ U @ ( non_ordered_pair @ X @ Y ) )
| ( U = X )
| ( U = Y ) ) )
= $true ),
inference(copy,[status(thm)],[282]) ).
thf(338,plain,
( ( ! [U: $i,X: $i] :
( ! [Y: $i] : ( member @ U @ ( non_ordered_pair @ X @ Y ) )
| ~ ( little_set @ U )
| ( U != X ) ) )
= $true ),
inference(copy,[status(thm)],[328]) ).
thf(339,plain,
( ( ! [U: $i,X: $i,Y: $i] :
( ( member @ U @ ( non_ordered_pair @ X @ Y ) )
| ~ ( little_set @ U )
| ( U != Y ) ) )
= $true ),
inference(copy,[status(thm)],[327]) ).
thf(340,plain,
( ( ! [X: $i,Y: $i] : ( little_set @ ( non_ordered_pair @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[279]) ).
thf(341,plain,
( ( ! [X: $i] :
( ( singleton_set @ X )
= ( non_ordered_pair @ X @ X ) ) )
= $true ),
inference(copy,[status(thm)],[278]) ).
thf(342,plain,
( ( ! [X: $i,Y: $i] :
( ( ordered_pair @ X @ Y )
= ( non_ordered_pair @ ( singleton_set @ X ) @ ( non_ordered_pair @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[277]) ).
thf(343,plain,
( ( ! [X: $i] :
( ~ ( ordered_pair_predicate @ X )
| ( little_set @ ( f2 @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[276]) ).
thf(344,plain,
( ( ! [X: $i] :
( ~ ( ordered_pair_predicate @ X )
| ( little_set @ ( f3 @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[275]) ).
thf(345,plain,
( ( ! [X: $i] :
( ~ ( ordered_pair_predicate @ X )
| ( X
= ( ordered_pair @ ( f2 @ X ) @ ( f3 @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[274]) ).
thf(346,plain,
( ( ! [X: $i] :
( ( ordered_pair_predicate @ X )
| ! [Y: $i] :
( ~ ( little_set @ Y )
| ! [Z: $i] :
( ~ ( little_set @ Z )
| ( X
!= ( ordered_pair @ Y @ Z ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[326]) ).
thf(347,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( first @ X ) )
| ( little_set @ ( f4 @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[272]) ).
thf(348,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( first @ X ) )
| ( little_set @ ( f5 @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[271]) ).
thf(349,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( first @ X ) )
| ( X
= ( ordered_pair @ ( f4 @ Z @ X ) @ ( f5 @ Z @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[270]) ).
thf(350,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( first @ X ) )
| ( member @ Z @ ( f4 @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[269]) ).
thf(351,plain,
( ( ! [Z: $i,X: $i] :
( ( member @ Z @ ( first @ X ) )
| ! [U: $i] :
( ~ ( little_set @ U )
| ! [V: $i] :
( ~ ( little_set @ V )
| ( X
!= ( ordered_pair @ U @ V ) )
| ~ ( member @ Z @ U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[325]) ).
thf(352,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( second @ X ) )
| ( little_set @ ( f6 @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[267]) ).
thf(353,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( second @ X ) )
| ( little_set @ ( f7 @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[266]) ).
thf(354,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( second @ X ) )
| ( X
= ( ordered_pair @ ( f6 @ Z @ X ) @ ( f7 @ Z @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[265]) ).
thf(355,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( second @ X ) )
| ( member @ Z @ ( f7 @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[264]) ).
thf(356,plain,
( ( ! [Z: $i,X: $i] :
( ( member @ Z @ ( second @ X ) )
| ! [U: $i] :
( ~ ( little_set @ U )
| ! [V: $i] :
( ~ ( little_set @ V )
| ( X
!= ( ordered_pair @ U @ V ) )
| ~ ( member @ Z @ V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[324]) ).
thf(357,plain,
( ( ! [Z: $i] :
( ~ ( member @ Z @ estin )
| ( ordered_pair_predicate @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[262]) ).
thf(358,plain,
( ( ! [Z: $i] :
( ~ ( member @ Z @ estin )
| ( member @ ( first @ Z ) @ ( second @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[261]) ).
thf(359,plain,
( ( ! [Z: $i] :
( ( member @ Z @ estin )
| ~ ( little_set @ Z )
| ~ ( ordered_pair_predicate @ Z )
| ~ ( member @ ( first @ Z ) @ ( second @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[260]) ).
thf(360,plain,
( ( ! [Z: $i,X: $i] :
( ! [Y: $i] :
~ ( member @ Z @ ( intersection @ X @ Y ) )
| ( member @ Z @ X ) ) )
= $true ),
inference(copy,[status(thm)],[323]) ).
thf(361,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( intersection @ X @ Y ) )
| ( member @ Z @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[258]) ).
thf(362,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ( member @ Z @ ( intersection @ X @ Y ) )
| ~ ( member @ Z @ X )
| ~ ( member @ Z @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[257]) ).
thf(363,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( complement @ X ) )
| ~ ( member @ Z @ X ) ) )
= $true ),
inference(copy,[status(thm)],[256]) ).
thf(364,plain,
( ( ! [Z: $i,X: $i] :
( ( member @ Z @ ( complement @ X ) )
| ~ ( little_set @ Z )
| ( member @ Z @ X ) ) )
= $true ),
inference(copy,[status(thm)],[255]) ).
thf(365,plain,
( ( ! [X: $i,Y: $i] :
( ( union @ X @ Y )
= ( complement @ ( intersection @ ( complement @ X ) @ ( complement @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[254]) ).
thf(366,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( domain_of @ X ) )
| ( ordered_pair_predicate @ ( f8 @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[253]) ).
thf(367,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( domain_of @ X ) )
| ( member @ ( f8 @ Z @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[252]) ).
thf(368,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( domain_of @ X ) )
| ( Z
= ( first @ ( f8 @ Z @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[251]) ).
thf(369,plain,
( ( ! [Z: $i,X: $i] :
( ( member @ Z @ ( domain_of @ X ) )
| ~ ( little_set @ Z )
| ! [Xp: $i] :
( ~ ( ordered_pair_predicate @ Xp )
| ~ ( member @ Xp @ X )
| ( Z
!= ( first @ Xp ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[322]) ).
thf(370,plain,
( ( ! [Z: $i] :
( ! [X: $i,Y: $i] :
~ ( member @ Z @ ( cross_product @ X @ Y ) )
| ( ordered_pair_predicate @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[321]) ).
thf(371,plain,
( ( ! [Z: $i,X: $i] :
( ! [Y: $i] :
~ ( member @ Z @ ( cross_product @ X @ Y ) )
| ( member @ ( first @ Z ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[320]) ).
thf(372,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( cross_product @ X @ Y ) )
| ( member @ ( second @ Z ) @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[247]) ).
thf(373,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ( member @ Z @ ( cross_product @ X @ Y ) )
| ~ ( little_set @ Z )
| ~ ( ordered_pair_predicate @ Z )
| ~ ( member @ ( first @ Z ) @ X )
| ~ ( member @ ( second @ Z ) @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[246]) ).
thf(374,plain,
( ( ! [Z: $i] :
( ! [X: $i] :
~ ( member @ Z @ ( converse @ X ) )
| ( ordered_pair_predicate @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[319]) ).
thf(375,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( converse @ X ) )
| ( member @ ( ordered_pair @ ( second @ Z ) @ ( first @ Z ) ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[244]) ).
thf(376,plain,
( ( ! [Z: $i,X: $i] :
( ( member @ Z @ ( converse @ X ) )
| ~ ( little_set @ Z )
| ~ ( ordered_pair_predicate @ Z )
| ~ ( member @ ( ordered_pair @ ( second @ Z ) @ ( first @ Z ) ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[243]) ).
thf(377,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( rotate_right @ X ) )
| ( little_set @ ( f9 @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[242]) ).
thf(378,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( rotate_right @ X ) )
| ( little_set @ ( f10 @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[241]) ).
thf(379,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( rotate_right @ X ) )
| ( little_set @ ( f11 @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[240]) ).
thf(380,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( rotate_right @ X ) )
| ( Z
= ( ordered_pair @ ( f9 @ Z @ X ) @ ( ordered_pair @ ( f10 @ Z @ X ) @ ( f11 @ Z @ X ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[239]) ).
thf(381,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( rotate_right @ X ) )
| ( member @ ( ordered_pair @ ( f10 @ Z @ X ) @ ( ordered_pair @ ( f11 @ Z @ X ) @ ( f9 @ Z @ X ) ) ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[238]) ).
thf(382,plain,
( ( ! [Z: $i,X: $i,U: $i] :
( ( member @ Z @ ( rotate_right @ X ) )
| ~ ( little_set @ Z )
| ~ ( little_set @ U )
| ! [V: $i] :
( ~ ( little_set @ V )
| ! [W: $i] :
( ~ ( little_set @ W )
| ( Z
!= ( ordered_pair @ U @ ( ordered_pair @ V @ W ) ) )
| ~ ( member @ ( ordered_pair @ V @ ( ordered_pair @ W @ U ) ) @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[318]) ).
thf(383,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( flip_range_of @ X ) )
| ( little_set @ ( f12 @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[236]) ).
thf(384,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( flip_range_of @ X ) )
| ( little_set @ ( f13 @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[235]) ).
thf(385,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( flip_range_of @ X ) )
| ( little_set @ ( f14 @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(386,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( flip_range_of @ X ) )
| ( Z
= ( ordered_pair @ ( f12 @ Z @ X ) @ ( ordered_pair @ ( f13 @ Z @ X ) @ ( f14 @ Z @ X ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(387,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( flip_range_of @ X ) )
| ( member @ ( ordered_pair @ ( f12 @ Z @ X ) @ ( ordered_pair @ ( f14 @ Z @ X ) @ ( f13 @ Z @ X ) ) ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[232]) ).
thf(388,plain,
( ( ! [Z: $i,X: $i,U: $i] :
( ( member @ Z @ ( flip_range_of @ X ) )
| ~ ( little_set @ Z )
| ~ ( little_set @ U )
| ! [V: $i] :
( ~ ( little_set @ V )
| ! [W: $i] :
( ~ ( little_set @ W )
| ( Z
!= ( ordered_pair @ U @ ( ordered_pair @ V @ W ) ) )
| ~ ( member @ ( ordered_pair @ U @ ( ordered_pair @ W @ V ) ) @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[317]) ).
thf(389,plain,
( ( ! [X: $i] :
( ( successor @ X )
= ( union @ X @ ( singleton_set @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[230]) ).
thf(390,plain,
( ( ! [Z: $i] :
~ ( member @ Z @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[229]) ).
thf(391,plain,
( ( ! [Z: $i] :
( ( member @ Z @ universal_set )
| ~ ( little_set @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[228]) ).
thf(392,plain,
( ( little_set @ infinity )
= $true ),
inference(copy,[status(thm)],[227]) ).
thf(393,plain,
( ( member @ empty_set @ infinity )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(394,plain,
( ( ! [X: $i] :
( ~ ( member @ X @ infinity )
| ( member @ ( successor @ X ) @ infinity ) ) )
= $true ),
inference(copy,[status(thm)],[225]) ).
thf(395,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( sigma @ X ) )
| ( member @ ( f16 @ Z @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(396,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( sigma @ X ) )
| ( member @ Z @ ( f16 @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(397,plain,
( ( ! [Z: $i,X: $i] :
( ( member @ Z @ ( sigma @ X ) )
| ! [Y: $i] :
( ~ ( member @ Y @ X )
| ~ ( member @ Z @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[316]) ).
thf(398,plain,
( ( ! [U: $i] :
( ~ ( little_set @ U )
| ( little_set @ ( sigma @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(399,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( subset @ X @ Y )
| ! [U: $i] :
( ~ ( member @ U @ X )
| ( member @ U @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[315]) ).
thf(400,plain,
( ( ! [X: $i,Y: $i] :
( ( member @ ( f17 @ X @ Y ) @ X )
| ( subset @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[314]) ).
thf(401,plain,
( ( ! [X: $i,Y: $i] :
( ( subset @ X @ Y )
| ~ ( member @ ( f17 @ X @ Y ) @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[218]) ).
thf(402,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( proper_subset @ X @ Y )
| ( subset @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(403,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( proper_subset @ X @ Y )
| ( X != Y ) ) )
= $true ),
inference(copy,[status(thm)],[313]) ).
thf(404,plain,
( ( ! [X: $i,Y: $i] :
( ( proper_subset @ X @ Y )
| ~ ( subset @ X @ Y )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[215]) ).
thf(405,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( powerset @ X ) )
| ( subset @ Z @ X ) ) )
= $true ),
inference(copy,[status(thm)],[214]) ).
thf(406,plain,
( ( ! [Z: $i,X: $i] :
( ( member @ Z @ ( powerset @ X ) )
| ~ ( little_set @ Z )
| ~ ( subset @ Z @ X ) ) )
= $true ),
inference(copy,[status(thm)],[213]) ).
thf(407,plain,
( ( ! [U: $i] :
( ~ ( little_set @ U )
| ( little_set @ ( powerset @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[212]) ).
thf(408,plain,
( ( ! [Z: $i] :
( ~ ( relation @ Z )
| ! [X: $i] :
( ~ ( member @ X @ Z )
| ( ordered_pair_predicate @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[312]) ).
thf(409,plain,
( ( ! [Z: $i] :
( ( member @ ( f18 @ Z ) @ Z )
| ( relation @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[311]) ).
thf(410,plain,
( ( ! [Z: $i] :
( ( relation @ Z )
| ~ ( ordered_pair_predicate @ ( f18 @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(411,plain,
( ( ! [X: $i,U: $i] :
( ~ ( single_valued_set @ X )
| ~ ( little_set @ U )
| ! [V: $i] :
( ~ ( little_set @ V )
| ! [W: $i] :
( ~ ( little_set @ W )
| ~ ( member @ ( ordered_pair @ U @ V ) @ X )
| ~ ( member @ ( ordered_pair @ U @ W ) @ X )
| ( V = W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[310]) ).
thf(412,plain,
( ( ! [X: $i] :
( ( little_set @ ( f19 @ X ) )
| ( single_valued_set @ X ) ) )
= $true ),
inference(copy,[status(thm)],[309]) ).
thf(413,plain,
( ( ! [X: $i] :
( ( little_set @ ( f20 @ X ) )
| ( single_valued_set @ X ) ) )
= $true ),
inference(copy,[status(thm)],[308]) ).
thf(414,plain,
( ( ! [X: $i] :
( ( little_set @ ( f21 @ X ) )
| ( single_valued_set @ X ) ) )
= $true ),
inference(copy,[status(thm)],[307]) ).
thf(415,plain,
( ( ! [X: $i] :
( ( member @ ( ordered_pair @ ( f19 @ X ) @ ( f20 @ X ) ) @ X )
| ( single_valued_set @ X ) ) )
= $true ),
inference(copy,[status(thm)],[306]) ).
thf(416,plain,
( ( ! [X: $i] :
( ( member @ ( ordered_pair @ ( f19 @ X ) @ ( f21 @ X ) ) @ X )
| ( single_valued_set @ X ) ) )
= $true ),
inference(copy,[status(thm)],[305]) ).
thf(417,plain,
( ( ! [X: $i] :
( ( ( f20 @ X )
!= ( f21 @ X ) )
| ( single_valued_set @ X ) ) )
= $true ),
inference(copy,[status(thm)],[304]) ).
thf(418,plain,
( ( ! [Xf: $i] :
( ~ ( function @ Xf )
| ( relation @ Xf ) ) )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(419,plain,
( ( ! [Xf: $i] :
( ~ ( function @ Xf )
| ( single_valued_set @ Xf ) ) )
= $true ),
inference(copy,[status(thm)],[200]) ).
thf(420,plain,
( ( ! [Xf: $i] :
( ( function @ Xf )
| ~ ( relation @ Xf )
| ~ ( single_valued_set @ Xf ) ) )
= $true ),
inference(copy,[status(thm)],[199]) ).
thf(421,plain,
( ( ! [Z: $i,X: $i,Xf: $i] :
( ~ ( member @ Z @ ( image @ X @ Xf ) )
| ( ordered_pair_predicate @ ( f22 @ Z @ X @ Xf ) ) ) )
= $true ),
inference(copy,[status(thm)],[198]) ).
thf(422,plain,
( ( ! [Z: $i,X: $i,Xf: $i] :
( ~ ( member @ Z @ ( image @ X @ Xf ) )
| ( member @ ( f22 @ Z @ X @ Xf ) @ Xf ) ) )
= $true ),
inference(copy,[status(thm)],[197]) ).
thf(423,plain,
( ( ! [Z: $i,X: $i,Xf: $i] :
( ~ ( member @ Z @ ( image @ X @ Xf ) )
| ( member @ ( first @ ( f22 @ Z @ X @ Xf ) ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[196]) ).
thf(424,plain,
( ( ! [Z: $i,X: $i,Xf: $i] :
( ~ ( member @ Z @ ( image @ X @ Xf ) )
| ( ( second @ ( f22 @ Z @ X @ Xf ) )
= Z ) ) )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(425,plain,
( ( ! [Z: $i,X: $i,Xf: $i] :
( ( member @ Z @ ( image @ X @ Xf ) )
| ~ ( little_set @ Z )
| ! [Y: $i] :
( ~ ( ordered_pair_predicate @ Y )
| ~ ( member @ Y @ Xf )
| ~ ( member @ ( first @ Y ) @ X )
| ( ( second @ Y )
!= Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[303]) ).
thf(426,plain,
( ( ! [X: $i] :
( ~ ( little_set @ X )
| ! [Xf: $i] :
( ~ ( function @ Xf )
| ( little_set @ ( image @ X @ Xf ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[302]) ).
thf(427,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( disjoint @ X @ Y )
| ! [U: $i] :
( ~ ( member @ U @ X )
| ~ ( member @ U @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[301]) ).
thf(428,plain,
( ( ! [X: $i,Y: $i] :
( ( disjoint @ X @ Y )
| ( member @ ( f23 @ X @ Y ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[191]) ).
thf(429,plain,
( ( ! [X: $i,Y: $i] :
( ( disjoint @ X @ Y )
| ( member @ ( f23 @ X @ Y ) @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[190]) ).
thf(430,plain,
( ( ! [X: $i] :
( ( X = empty_set )
| ( member @ ( f24 @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[189]) ).
thf(431,plain,
( ( ! [X: $i] :
( ( X = empty_set )
| ( disjoint @ ( f24 @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[188]) ).
thf(432,plain,
( ( function @ f25 )
= $true ),
inference(copy,[status(thm)],[187]) ).
thf(433,plain,
( ( ! [X: $i] :
( ~ ( little_set @ X )
| ( X = empty_set )
| ( member @ ( f26 @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[186]) ).
thf(434,plain,
( ( ! [X: $i] :
( ~ ( little_set @ X )
| ( X = empty_set )
| ( member @ ( ordered_pair @ X @ ( f26 @ X ) ) @ f25 ) ) )
= $true ),
inference(copy,[status(thm)],[185]) ).
thf(435,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( range_of @ X ) )
| ( ordered_pair_predicate @ ( f27 @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[184]) ).
thf(436,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( range_of @ X ) )
| ( member @ ( f27 @ Z @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[183]) ).
thf(437,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( range_of @ X ) )
| ( Z
= ( second @ ( f27 @ Z @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[182]) ).
thf(438,plain,
( ( ! [Z: $i,X: $i] :
( ( member @ Z @ ( range_of @ X ) )
| ~ ( little_set @ Z )
| ! [Xp: $i] :
( ~ ( ordered_pair_predicate @ Xp )
| ~ ( member @ Xp @ X )
| ( Z
!= ( second @ Xp ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[300]) ).
thf(439,plain,
( ( ! [Z: $i] :
( ~ ( member @ Z @ identity_relation )
| ( ordered_pair_predicate @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[180]) ).
thf(440,plain,
( ( ! [Z: $i] :
( ~ ( member @ Z @ identity_relation )
| ( ( first @ Z )
= ( second @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[179]) ).
thf(441,plain,
( ( ! [Z: $i] :
( ( member @ Z @ identity_relation )
| ~ ( little_set @ Z )
| ~ ( ordered_pair_predicate @ Z )
| ( ( first @ Z )
!= ( second @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[299]) ).
thf(442,plain,
( ( ! [X: $i,Y: $i] :
( ( restrict @ X @ Y )
= ( intersection @ X @ ( cross_product @ Y @ universal_set ) ) ) )
= $true ),
inference(copy,[status(thm)],[177]) ).
thf(443,plain,
( ( ! [Xf: $i] :
( ~ ( one_to_one_function @ Xf )
| ( function @ Xf ) ) )
= $true ),
inference(copy,[status(thm)],[176]) ).
thf(444,plain,
( ( ! [Xf: $i] :
( ~ ( one_to_one_function @ Xf )
| ( function @ ( converse @ Xf ) ) ) )
= $true ),
inference(copy,[status(thm)],[175]) ).
thf(445,plain,
( ( ! [Xf: $i] :
( ( one_to_one_function @ Xf )
| ~ ( function @ Xf )
| ~ ( function @ ( converse @ Xf ) ) ) )
= $true ),
inference(copy,[status(thm)],[174]) ).
thf(446,plain,
( ( ! [Z: $i,Xf: $i,Y: $i] :
( ~ ( member @ Z @ ( apply @ Xf @ Y ) )
| ( ordered_pair_predicate @ ( f28 @ Z @ Xf @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[173]) ).
thf(447,plain,
( ( ! [Z: $i,Xf: $i,Y: $i] :
( ~ ( member @ Z @ ( apply @ Xf @ Y ) )
| ( member @ ( f28 @ Z @ Xf @ Y ) @ Xf ) ) )
= $true ),
inference(copy,[status(thm)],[172]) ).
thf(448,plain,
( ( ! [Z: $i,Xf: $i,Y: $i] :
( ~ ( member @ Z @ ( apply @ Xf @ Y ) )
| ( ( first @ ( f28 @ Z @ Xf @ Y ) )
= Y ) ) )
= $true ),
inference(copy,[status(thm)],[171]) ).
thf(449,plain,
( ( ! [Z: $i,Xf: $i,Y: $i] :
( ~ ( member @ Z @ ( apply @ Xf @ Y ) )
| ( member @ Z @ ( second @ ( f28 @ Z @ Xf @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[170]) ).
thf(450,plain,
( ( ! [Z: $i,Xf: $i,Y: $i] :
( ( member @ Z @ ( apply @ Xf @ Y ) )
| ! [W: $i] :
( ~ ( ordered_pair_predicate @ W )
| ~ ( member @ W @ Xf )
| ( ( first @ W )
!= Y )
| ~ ( member @ Z @ ( second @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[298]) ).
thf(451,plain,
( ( ! [Xf: $i,X: $i,Y: $i] :
( ( apply_to_two_arguments @ Xf @ X @ Y )
= ( apply @ Xf @ ( ordered_pair @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[168]) ).
thf(452,plain,
( ( ! [Xf: $i] :
( ! [X: $i,Y: $i] :
~ ( maps @ Xf @ X @ Y )
| ( function @ Xf ) ) )
= $true ),
inference(copy,[status(thm)],[297]) ).
thf(453,plain,
( ( ! [Xf: $i,X: $i] :
( ! [Y: $i] :
~ ( maps @ Xf @ X @ Y )
| ( ( domain_of @ Xf )
= X ) ) )
= $true ),
inference(copy,[status(thm)],[296]) ).
thf(454,plain,
( ( ! [Xf: $i,X: $i,Y: $i] :
( ~ ( maps @ Xf @ X @ Y )
| ( subset @ ( range_of @ Xf ) @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[165]) ).
thf(455,plain,
( ( ! [Xf: $i,X: $i,Y: $i] :
( ( maps @ Xf @ X @ Y )
| ~ ( function @ Xf )
| ( ( domain_of @ Xf )
!= X )
| ~ ( subset @ ( range_of @ Xf ) @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[295]) ).
thf(456,plain,
( ( ! [Xs: $i] :
( ! [Xf: $i] :
~ ( closed @ Xs @ Xf )
| ( little_set @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[294]) ).
thf(457,plain,
( ( ! [Xs: $i,Xf: $i] :
( ~ ( closed @ Xs @ Xf )
| ( little_set @ Xf ) ) )
= $true ),
inference(copy,[status(thm)],[162]) ).
thf(458,plain,
( ( ! [Xs: $i,Xf: $i] :
( ~ ( closed @ Xs @ Xf )
| ( maps @ Xf @ ( cross_product @ Xs @ Xs ) @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[161]) ).
thf(459,plain,
( ( ! [Xs: $i,Xf: $i] :
( ( closed @ Xs @ Xf )
| ~ ( little_set @ Xs )
| ~ ( little_set @ Xf )
| ~ ( maps @ Xf @ ( cross_product @ Xs @ Xs ) @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[160]) ).
thf(460,plain,
( ( ! [Z: $i,Xf: $i,Xg: $i] :
( ~ ( member @ Z @ ( compose @ Xf @ Xg ) )
| ( little_set @ ( f29 @ Z @ Xf @ Xg ) ) ) )
= $true ),
inference(copy,[status(thm)],[159]) ).
thf(461,plain,
( ( ! [Z: $i,Xf: $i,Xg: $i] :
( ~ ( member @ Z @ ( compose @ Xf @ Xg ) )
| ( little_set @ ( f30 @ Z @ Xf @ Xg ) ) ) )
= $true ),
inference(copy,[status(thm)],[158]) ).
thf(462,plain,
( ( ! [Z: $i,Xf: $i,Xg: $i] :
( ~ ( member @ Z @ ( compose @ Xf @ Xg ) )
| ( little_set @ ( f31 @ Z @ Xf @ Xg ) ) ) )
= $true ),
inference(copy,[status(thm)],[157]) ).
thf(463,plain,
( ( ! [Z: $i,Xf: $i,Xg: $i] :
( ~ ( member @ Z @ ( compose @ Xf @ Xg ) )
| ( Z
= ( ordered_pair @ ( f29 @ Z @ Xf @ Xg ) @ ( f30 @ Z @ Xf @ Xg ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[156]) ).
thf(464,plain,
( ( ! [Z: $i,Xf: $i,Xg: $i] :
( ~ ( member @ Z @ ( compose @ Xf @ Xg ) )
| ( member @ ( ordered_pair @ ( f29 @ Z @ Xf @ Xg ) @ ( f31 @ Z @ Xf @ Xg ) ) @ Xf ) ) )
= $true ),
inference(copy,[status(thm)],[155]) ).
thf(465,plain,
( ( ! [Z: $i,Xf: $i,Xg: $i] :
( ~ ( member @ Z @ ( compose @ Xf @ Xg ) )
| ( member @ ( ordered_pair @ ( f31 @ Z @ Xf @ Xg ) @ ( f30 @ Z @ Xf @ Xg ) ) @ Xg ) ) )
= $true ),
inference(copy,[status(thm)],[154]) ).
thf(466,plain,
( ( ! [Z: $i,Xf: $i,Xg: $i,X: $i] :
( ( member @ Z @ ( compose @ Xf @ Xg ) )
| ~ ( little_set @ Z )
| ~ ( little_set @ X )
| ! [Y: $i] :
( ~ ( little_set @ Y )
| ! [W: $i] :
( ~ ( little_set @ W )
| ( Z
!= ( ordered_pair @ X @ Y ) )
| ~ ( member @ ( ordered_pair @ X @ W ) @ Xf )
| ~ ( member @ ( ordered_pair @ W @ Y ) @ Xg ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[293]) ).
thf(467,plain,
( ( ! [Xh: $i,Xs1: $i,Xf1: $i] :
( ! [Xs2: $i,Xf2: $i] :
~ ( homomorphism @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 )
| ( closed @ Xs1 @ Xf1 ) ) )
= $true ),
inference(copy,[status(thm)],[292]) ).
thf(468,plain,
( ( ! [Xh: $i,Xs1: $i,Xf1: $i,Xs2: $i,Xf2: $i] :
( ~ ( homomorphism @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 )
| ( closed @ Xs2 @ Xf2 ) ) )
= $true ),
inference(copy,[status(thm)],[151]) ).
thf(469,plain,
( ( ! [Xh: $i,Xs1: $i,Xf1: $i,Xs2: $i] :
( ! [Xf2: $i] :
~ ( homomorphism @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 )
| ( maps @ Xh @ Xs1 @ Xs2 ) ) )
= $true ),
inference(copy,[status(thm)],[291]) ).
thf(470,plain,
( ( ! [Xh: $i,Xs1: $i,Xf1: $i,Xs2: $i,Xf2: $i] :
( ~ ( homomorphism @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 )
| ! [X: $i] :
( ~ ( member @ X @ Xs1 )
| ! [Y: $i] :
( ~ ( member @ Y @ Xs1 )
| ( ( apply @ Xh @ ( apply_to_two_arguments @ Xf1 @ X @ Y ) )
= ( apply_to_two_arguments @ Xf2 @ ( apply @ Xh @ X ) @ ( apply @ Xh @ Y ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[290]) ).
thf(471,plain,
( ( ! [Xh: $i,Xs1: $i,Xf1: $i,Xs2: $i,Xf2: $i] :
( ( homomorphism @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 )
| ~ ( closed @ Xs1 @ Xf1 )
| ~ ( closed @ Xs2 @ Xf2 )
| ~ ( maps @ Xh @ Xs1 @ Xs2 )
| ( member @ ( f32 @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 ) @ Xs1 ) ) )
= $true ),
inference(copy,[status(thm)],[148]) ).
thf(472,plain,
( ( ! [Xh: $i,Xs1: $i,Xf1: $i,Xs2: $i,Xf2: $i] :
( ( homomorphism @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 )
| ~ ( closed @ Xs1 @ Xf1 )
| ~ ( closed @ Xs2 @ Xf2 )
| ~ ( maps @ Xh @ Xs1 @ Xs2 )
| ( member @ ( f33 @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 ) @ Xs1 ) ) )
= $true ),
inference(copy,[status(thm)],[147]) ).
thf(473,plain,
( ( ! [Xh: $i,Xs1: $i,Xf1: $i,Xs2: $i,Xf2: $i] :
( ( homomorphism @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 )
| ~ ( closed @ Xs1 @ Xf1 )
| ~ ( closed @ Xs2 @ Xf2 )
| ~ ( maps @ Xh @ Xs1 @ Xs2 )
| ( ( apply @ Xh @ ( apply_to_two_arguments @ Xf1 @ ( f32 @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 ) @ ( f33 @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 ) ) )
!= ( apply_to_two_arguments @ Xf2 @ ( apply @ Xh @ ( f32 @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 ) ) @ ( apply @ Xh @ ( f33 @ Xh @ Xs1 @ Xf1 @ Xs2 @ Xf2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[289]) ).
thf(474,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[288]) ).
thf(475,plain,
( ( little_set @ ( ordered_pair @ a @ b ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(476,plain,
! [SV1: $i] :
( ( ! [SY320: $i] :
~ ( member @ SV1 @ SY320 )
| ( little_set @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(477,plain,
! [SV2: $i] :
( ( ! [SY321: $i] :
( ( SV2 = SY321 )
| ( little_set @ ( f1 @ SV2 @ SY321 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(478,plain,
! [SV3: $i] :
( ( ! [SY322: $i] :
( ( member @ ( f1 @ SV3 @ SY322 ) @ SV3 )
| ( SV3 = SY322 )
| ( member @ ( f1 @ SV3 @ SY322 ) @ SY322 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[335]) ).
thf(479,plain,
! [SV4: $i] :
( ( ! [SY323: $i] :
( ~ ( member @ ( f1 @ SV4 @ SY323 ) @ SV4 )
| ~ ( member @ ( f1 @ SV4 @ SY323 ) @ SY323 )
| ( SV4 = SY323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(480,plain,
! [SV5: $i] :
( ( ! [SY324: $i,SY325: $i] :
( ~ ( member @ SV5 @ ( non_ordered_pair @ SY324 @ SY325 ) )
| ( SV5 = SY324 )
| ( SV5 = SY325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(481,plain,
! [SV6: $i] :
( ( ! [SY326: $i] :
( ! [SY327: $i] : ( member @ SV6 @ ( non_ordered_pair @ SY326 @ SY327 ) )
| ~ ( little_set @ SV6 )
| ( SV6 != SY326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(482,plain,
! [SV7: $i] :
( ( ! [SY328: $i,SY329: $i] :
( ( member @ SV7 @ ( non_ordered_pair @ SY328 @ SY329 ) )
| ~ ( little_set @ SV7 )
| ( SV7 != SY329 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(483,plain,
! [SV8: $i] :
( ( ! [SY330: $i] : ( little_set @ ( non_ordered_pair @ SV8 @ SY330 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(484,plain,
! [SV9: $i] :
( ( ( singleton_set @ SV9 )
= ( non_ordered_pair @ SV9 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(485,plain,
! [SV10: $i] :
( ( ! [SY331: $i] :
( ( ordered_pair @ SV10 @ SY331 )
= ( non_ordered_pair @ ( singleton_set @ SV10 ) @ ( non_ordered_pair @ SV10 @ SY331 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(486,plain,
! [SV11: $i] :
( ( ~ ( ordered_pair_predicate @ SV11 )
| ( little_set @ ( f2 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(487,plain,
! [SV12: $i] :
( ( ~ ( ordered_pair_predicate @ SV12 )
| ( little_set @ ( f3 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(488,plain,
! [SV13: $i] :
( ( ~ ( ordered_pair_predicate @ SV13 )
| ( SV13
= ( ordered_pair @ ( f2 @ SV13 ) @ ( f3 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(489,plain,
! [SV14: $i] :
( ( ( ordered_pair_predicate @ SV14 )
| ! [SY332: $i] :
( ~ ( little_set @ SY332 )
| ! [SY333: $i] :
( ~ ( little_set @ SY333 )
| ( SV14
!= ( ordered_pair @ SY332 @ SY333 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(490,plain,
! [SV15: $i] :
( ( ! [SY334: $i] :
( ~ ( member @ SV15 @ ( first @ SY334 ) )
| ( little_set @ ( f4 @ SV15 @ SY334 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(491,plain,
! [SV16: $i] :
( ( ! [SY335: $i] :
( ~ ( member @ SV16 @ ( first @ SY335 ) )
| ( little_set @ ( f5 @ SV16 @ SY335 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(492,plain,
! [SV17: $i] :
( ( ! [SY336: $i] :
( ~ ( member @ SV17 @ ( first @ SY336 ) )
| ( SY336
= ( ordered_pair @ ( f4 @ SV17 @ SY336 ) @ ( f5 @ SV17 @ SY336 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(493,plain,
! [SV18: $i] :
( ( ! [SY337: $i] :
( ~ ( member @ SV18 @ ( first @ SY337 ) )
| ( member @ SV18 @ ( f4 @ SV18 @ SY337 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(494,plain,
! [SV19: $i] :
( ( ! [SY338: $i] :
( ( member @ SV19 @ ( first @ SY338 ) )
| ! [SY339: $i] :
( ~ ( little_set @ SY339 )
| ! [SY340: $i] :
( ~ ( little_set @ SY340 )
| ( SY338
!= ( ordered_pair @ SY339 @ SY340 ) )
| ~ ( member @ SV19 @ SY339 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(495,plain,
! [SV20: $i] :
( ( ! [SY341: $i] :
( ~ ( member @ SV20 @ ( second @ SY341 ) )
| ( little_set @ ( f6 @ SV20 @ SY341 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(496,plain,
! [SV21: $i] :
( ( ! [SY342: $i] :
( ~ ( member @ SV21 @ ( second @ SY342 ) )
| ( little_set @ ( f7 @ SV21 @ SY342 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(497,plain,
! [SV22: $i] :
( ( ! [SY343: $i] :
( ~ ( member @ SV22 @ ( second @ SY343 ) )
| ( SY343
= ( ordered_pair @ ( f6 @ SV22 @ SY343 ) @ ( f7 @ SV22 @ SY343 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(498,plain,
! [SV23: $i] :
( ( ! [SY344: $i] :
( ~ ( member @ SV23 @ ( second @ SY344 ) )
| ( member @ SV23 @ ( f7 @ SV23 @ SY344 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(499,plain,
! [SV24: $i] :
( ( ! [SY345: $i] :
( ( member @ SV24 @ ( second @ SY345 ) )
| ! [SY346: $i] :
( ~ ( little_set @ SY346 )
| ! [SY347: $i] :
( ~ ( little_set @ SY347 )
| ( SY345
!= ( ordered_pair @ SY346 @ SY347 ) )
| ~ ( member @ SV24 @ SY347 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(500,plain,
! [SV25: $i] :
( ( ~ ( member @ SV25 @ estin )
| ( ordered_pair_predicate @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[357]) ).
thf(501,plain,
! [SV26: $i] :
( ( ~ ( member @ SV26 @ estin )
| ( member @ ( first @ SV26 ) @ ( second @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(502,plain,
! [SV27: $i] :
( ( ( member @ SV27 @ estin )
| ~ ( little_set @ SV27 )
| ~ ( ordered_pair_predicate @ SV27 )
| ~ ( member @ ( first @ SV27 ) @ ( second @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(503,plain,
! [SV28: $i] :
( ( ! [SY348: $i] :
( ! [SY349: $i] :
~ ( member @ SV28 @ ( intersection @ SY348 @ SY349 ) )
| ( member @ SV28 @ SY348 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(504,plain,
! [SV29: $i] :
( ( ! [SY350: $i,SY351: $i] :
( ~ ( member @ SV29 @ ( intersection @ SY350 @ SY351 ) )
| ( member @ SV29 @ SY351 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(505,plain,
! [SV30: $i] :
( ( ! [SY352: $i,SY353: $i] :
( ( member @ SV30 @ ( intersection @ SY352 @ SY353 ) )
| ~ ( member @ SV30 @ SY352 )
| ~ ( member @ SV30 @ SY353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(506,plain,
! [SV31: $i] :
( ( ! [SY354: $i] :
( ~ ( member @ SV31 @ ( complement @ SY354 ) )
| ~ ( member @ SV31 @ SY354 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(507,plain,
! [SV32: $i] :
( ( ! [SY355: $i] :
( ( member @ SV32 @ ( complement @ SY355 ) )
| ~ ( little_set @ SV32 )
| ( member @ SV32 @ SY355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(508,plain,
! [SV33: $i] :
( ( ! [SY356: $i] :
( ( union @ SV33 @ SY356 )
= ( complement @ ( intersection @ ( complement @ SV33 ) @ ( complement @ SY356 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(509,plain,
! [SV34: $i] :
( ( ! [SY357: $i] :
( ~ ( member @ SV34 @ ( domain_of @ SY357 ) )
| ( ordered_pair_predicate @ ( f8 @ SV34 @ SY357 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(510,plain,
! [SV35: $i] :
( ( ! [SY358: $i] :
( ~ ( member @ SV35 @ ( domain_of @ SY358 ) )
| ( member @ ( f8 @ SV35 @ SY358 ) @ SY358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(511,plain,
! [SV36: $i] :
( ( ! [SY359: $i] :
( ~ ( member @ SV36 @ ( domain_of @ SY359 ) )
| ( SV36
= ( first @ ( f8 @ SV36 @ SY359 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(512,plain,
! [SV37: $i] :
( ( ! [SY360: $i] :
( ( member @ SV37 @ ( domain_of @ SY360 ) )
| ~ ( little_set @ SV37 )
| ! [SY361: $i] :
( ~ ( ordered_pair_predicate @ SY361 )
| ~ ( member @ SY361 @ SY360 )
| ( SV37
!= ( first @ SY361 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(513,plain,
! [SV38: $i] :
( ( ! [SY362: $i,SY363: $i] :
~ ( member @ SV38 @ ( cross_product @ SY362 @ SY363 ) )
| ( ordered_pair_predicate @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(514,plain,
! [SV39: $i] :
( ( ! [SY364: $i] :
( ! [SY365: $i] :
~ ( member @ SV39 @ ( cross_product @ SY364 @ SY365 ) )
| ( member @ ( first @ SV39 ) @ SY364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(515,plain,
! [SV40: $i] :
( ( ! [SY366: $i,SY367: $i] :
( ~ ( member @ SV40 @ ( cross_product @ SY366 @ SY367 ) )
| ( member @ ( second @ SV40 ) @ SY367 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(516,plain,
! [SV41: $i] :
( ( ! [SY368: $i,SY369: $i] :
( ( member @ SV41 @ ( cross_product @ SY368 @ SY369 ) )
| ~ ( little_set @ SV41 )
| ~ ( ordered_pair_predicate @ SV41 )
| ~ ( member @ ( first @ SV41 ) @ SY368 )
| ~ ( member @ ( second @ SV41 ) @ SY369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(517,plain,
! [SV42: $i] :
( ( ! [SY370: $i] :
~ ( member @ SV42 @ ( converse @ SY370 ) )
| ( ordered_pair_predicate @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(518,plain,
! [SV43: $i] :
( ( ! [SY371: $i] :
( ~ ( member @ SV43 @ ( converse @ SY371 ) )
| ( member @ ( ordered_pair @ ( second @ SV43 ) @ ( first @ SV43 ) ) @ SY371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(519,plain,
! [SV44: $i] :
( ( ! [SY372: $i] :
( ( member @ SV44 @ ( converse @ SY372 ) )
| ~ ( little_set @ SV44 )
| ~ ( ordered_pair_predicate @ SV44 )
| ~ ( member @ ( ordered_pair @ ( second @ SV44 ) @ ( first @ SV44 ) ) @ SY372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(520,plain,
! [SV45: $i] :
( ( ! [SY373: $i] :
( ~ ( member @ SV45 @ ( rotate_right @ SY373 ) )
| ( little_set @ ( f9 @ SV45 @ SY373 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(521,plain,
! [SV46: $i] :
( ( ! [SY374: $i] :
( ~ ( member @ SV46 @ ( rotate_right @ SY374 ) )
| ( little_set @ ( f10 @ SV46 @ SY374 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(522,plain,
! [SV47: $i] :
( ( ! [SY375: $i] :
( ~ ( member @ SV47 @ ( rotate_right @ SY375 ) )
| ( little_set @ ( f11 @ SV47 @ SY375 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(523,plain,
! [SV48: $i] :
( ( ! [SY376: $i] :
( ~ ( member @ SV48 @ ( rotate_right @ SY376 ) )
| ( SV48
= ( ordered_pair @ ( f9 @ SV48 @ SY376 ) @ ( ordered_pair @ ( f10 @ SV48 @ SY376 ) @ ( f11 @ SV48 @ SY376 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(524,plain,
! [SV49: $i] :
( ( ! [SY377: $i] :
( ~ ( member @ SV49 @ ( rotate_right @ SY377 ) )
| ( member @ ( ordered_pair @ ( f10 @ SV49 @ SY377 ) @ ( ordered_pair @ ( f11 @ SV49 @ SY377 ) @ ( f9 @ SV49 @ SY377 ) ) ) @ SY377 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(525,plain,
! [SV50: $i] :
( ( ! [SY378: $i,SY379: $i] :
( ( member @ SV50 @ ( rotate_right @ SY378 ) )
| ~ ( little_set @ SV50 )
| ~ ( little_set @ SY379 )
| ! [SY380: $i] :
( ~ ( little_set @ SY380 )
| ! [SY381: $i] :
( ~ ( little_set @ SY381 )
| ( SV50
!= ( ordered_pair @ SY379 @ ( ordered_pair @ SY380 @ SY381 ) ) )
| ~ ( member @ ( ordered_pair @ SY380 @ ( ordered_pair @ SY381 @ SY379 ) ) @ SY378 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(526,plain,
! [SV51: $i] :
( ( ! [SY382: $i] :
( ~ ( member @ SV51 @ ( flip_range_of @ SY382 ) )
| ( little_set @ ( f12 @ SV51 @ SY382 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(527,plain,
! [SV52: $i] :
( ( ! [SY383: $i] :
( ~ ( member @ SV52 @ ( flip_range_of @ SY383 ) )
| ( little_set @ ( f13 @ SV52 @ SY383 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(528,plain,
! [SV53: $i] :
( ( ! [SY384: $i] :
( ~ ( member @ SV53 @ ( flip_range_of @ SY384 ) )
| ( little_set @ ( f14 @ SV53 @ SY384 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(529,plain,
! [SV54: $i] :
( ( ! [SY385: $i] :
( ~ ( member @ SV54 @ ( flip_range_of @ SY385 ) )
| ( SV54
= ( ordered_pair @ ( f12 @ SV54 @ SY385 ) @ ( ordered_pair @ ( f13 @ SV54 @ SY385 ) @ ( f14 @ SV54 @ SY385 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(530,plain,
! [SV55: $i] :
( ( ! [SY386: $i] :
( ~ ( member @ SV55 @ ( flip_range_of @ SY386 ) )
| ( member @ ( ordered_pair @ ( f12 @ SV55 @ SY386 ) @ ( ordered_pair @ ( f14 @ SV55 @ SY386 ) @ ( f13 @ SV55 @ SY386 ) ) ) @ SY386 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(531,plain,
! [SV56: $i] :
( ( ! [SY387: $i,SY388: $i] :
( ( member @ SV56 @ ( flip_range_of @ SY387 ) )
| ~ ( little_set @ SV56 )
| ~ ( little_set @ SY388 )
| ! [SY389: $i] :
( ~ ( little_set @ SY389 )
| ! [SY390: $i] :
( ~ ( little_set @ SY390 )
| ( SV56
!= ( ordered_pair @ SY388 @ ( ordered_pair @ SY389 @ SY390 ) ) )
| ~ ( member @ ( ordered_pair @ SY388 @ ( ordered_pair @ SY390 @ SY389 ) ) @ SY387 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(532,plain,
! [SV57: $i] :
( ( ( successor @ SV57 )
= ( union @ SV57 @ ( singleton_set @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(533,plain,
! [SV58: $i] :
( ( ~ ( member @ SV58 @ empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(534,plain,
! [SV59: $i] :
( ( ( member @ SV59 @ universal_set )
| ~ ( little_set @ SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(535,plain,
! [SV60: $i] :
( ( ~ ( member @ SV60 @ infinity )
| ( member @ ( successor @ SV60 ) @ infinity ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(536,plain,
! [SV61: $i] :
( ( ! [SY391: $i] :
( ~ ( member @ SV61 @ ( sigma @ SY391 ) )
| ( member @ ( f16 @ SV61 @ SY391 ) @ SY391 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(537,plain,
! [SV62: $i] :
( ( ! [SY392: $i] :
( ~ ( member @ SV62 @ ( sigma @ SY392 ) )
| ( member @ SV62 @ ( f16 @ SV62 @ SY392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(538,plain,
! [SV63: $i] :
( ( ! [SY393: $i] :
( ( member @ SV63 @ ( sigma @ SY393 ) )
| ! [SY394: $i] :
( ~ ( member @ SY394 @ SY393 )
| ~ ( member @ SV63 @ SY394 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(539,plain,
! [SV64: $i] :
( ( ~ ( little_set @ SV64 )
| ( little_set @ ( sigma @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(540,plain,
! [SV65: $i] :
( ( ! [SY395: $i] :
( ~ ( subset @ SV65 @ SY395 )
| ! [SY396: $i] :
( ~ ( member @ SY396 @ SV65 )
| ( member @ SY396 @ SY395 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(541,plain,
! [SV66: $i] :
( ( ! [SY397: $i] :
( ( member @ ( f17 @ SV66 @ SY397 ) @ SV66 )
| ( subset @ SV66 @ SY397 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(542,plain,
! [SV67: $i] :
( ( ! [SY398: $i] :
( ( subset @ SV67 @ SY398 )
| ~ ( member @ ( f17 @ SV67 @ SY398 ) @ SY398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(543,plain,
! [SV68: $i] :
( ( ! [SY399: $i] :
( ~ ( proper_subset @ SV68 @ SY399 )
| ( subset @ SV68 @ SY399 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(544,plain,
! [SV69: $i] :
( ( ! [SY400: $i] :
( ~ ( proper_subset @ SV69 @ SY400 )
| ( SV69 != SY400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(545,plain,
! [SV70: $i] :
( ( ! [SY401: $i] :
( ( proper_subset @ SV70 @ SY401 )
| ~ ( subset @ SV70 @ SY401 )
| ( SV70 = SY401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(546,plain,
! [SV71: $i] :
( ( ! [SY402: $i] :
( ~ ( member @ SV71 @ ( powerset @ SY402 ) )
| ( subset @ SV71 @ SY402 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(547,plain,
! [SV72: $i] :
( ( ! [SY403: $i] :
( ( member @ SV72 @ ( powerset @ SY403 ) )
| ~ ( little_set @ SV72 )
| ~ ( subset @ SV72 @ SY403 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(548,plain,
! [SV73: $i] :
( ( ~ ( little_set @ SV73 )
| ( little_set @ ( powerset @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(549,plain,
! [SV74: $i] :
( ( ~ ( relation @ SV74 )
| ! [SY404: $i] :
( ~ ( member @ SY404 @ SV74 )
| ( ordered_pair_predicate @ SY404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(550,plain,
! [SV75: $i] :
( ( ( member @ ( f18 @ SV75 ) @ SV75 )
| ( relation @ SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(551,plain,
! [SV76: $i] :
( ( ( relation @ SV76 )
| ~ ( ordered_pair_predicate @ ( f18 @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(552,plain,
! [SV77: $i] :
( ( ! [SY405: $i] :
( ~ ( single_valued_set @ SV77 )
| ~ ( little_set @ SY405 )
| ! [SY406: $i] :
( ~ ( little_set @ SY406 )
| ! [SY407: $i] :
( ~ ( little_set @ SY407 )
| ~ ( member @ ( ordered_pair @ SY405 @ SY406 ) @ SV77 )
| ~ ( member @ ( ordered_pair @ SY405 @ SY407 ) @ SV77 )
| ( SY406 = SY407 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(553,plain,
! [SV78: $i] :
( ( ( little_set @ ( f19 @ SV78 ) )
| ( single_valued_set @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(554,plain,
! [SV79: $i] :
( ( ( little_set @ ( f20 @ SV79 ) )
| ( single_valued_set @ SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(555,plain,
! [SV80: $i] :
( ( ( little_set @ ( f21 @ SV80 ) )
| ( single_valued_set @ SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(556,plain,
! [SV81: $i] :
( ( ( member @ ( ordered_pair @ ( f19 @ SV81 ) @ ( f20 @ SV81 ) ) @ SV81 )
| ( single_valued_set @ SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(557,plain,
! [SV82: $i] :
( ( ( member @ ( ordered_pair @ ( f19 @ SV82 ) @ ( f21 @ SV82 ) ) @ SV82 )
| ( single_valued_set @ SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(558,plain,
! [SV83: $i] :
( ( ( ( f20 @ SV83 )
!= ( f21 @ SV83 ) )
| ( single_valued_set @ SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(559,plain,
! [SV84: $i] :
( ( ~ ( function @ SV84 )
| ( relation @ SV84 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(560,plain,
! [SV85: $i] :
( ( ~ ( function @ SV85 )
| ( single_valued_set @ SV85 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(561,plain,
! [SV86: $i] :
( ( ( function @ SV86 )
| ~ ( relation @ SV86 )
| ~ ( single_valued_set @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(562,plain,
! [SV87: $i] :
( ( ! [SY408: $i,SY409: $i] :
( ~ ( member @ SV87 @ ( image @ SY408 @ SY409 ) )
| ( ordered_pair_predicate @ ( f22 @ SV87 @ SY408 @ SY409 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(563,plain,
! [SV88: $i] :
( ( ! [SY410: $i,SY411: $i] :
( ~ ( member @ SV88 @ ( image @ SY410 @ SY411 ) )
| ( member @ ( f22 @ SV88 @ SY410 @ SY411 ) @ SY411 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(564,plain,
! [SV89: $i] :
( ( ! [SY412: $i,SY413: $i] :
( ~ ( member @ SV89 @ ( image @ SY412 @ SY413 ) )
| ( member @ ( first @ ( f22 @ SV89 @ SY412 @ SY413 ) ) @ SY412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(565,plain,
! [SV90: $i] :
( ( ! [SY414: $i,SY415: $i] :
( ~ ( member @ SV90 @ ( image @ SY414 @ SY415 ) )
| ( ( second @ ( f22 @ SV90 @ SY414 @ SY415 ) )
= SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(566,plain,
! [SV91: $i] :
( ( ! [SY416: $i,SY417: $i] :
( ( member @ SV91 @ ( image @ SY416 @ SY417 ) )
| ~ ( little_set @ SV91 )
| ! [SY418: $i] :
( ~ ( ordered_pair_predicate @ SY418 )
| ~ ( member @ SY418 @ SY417 )
| ~ ( member @ ( first @ SY418 ) @ SY416 )
| ( ( second @ SY418 )
!= SV91 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(567,plain,
! [SV92: $i] :
( ( ~ ( little_set @ SV92 )
| ! [SY419: $i] :
( ~ ( function @ SY419 )
| ( little_set @ ( image @ SV92 @ SY419 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(568,plain,
! [SV93: $i] :
( ( ! [SY420: $i] :
( ~ ( disjoint @ SV93 @ SY420 )
| ! [SY421: $i] :
( ~ ( member @ SY421 @ SV93 )
| ~ ( member @ SY421 @ SY420 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(569,plain,
! [SV94: $i] :
( ( ! [SY422: $i] :
( ( disjoint @ SV94 @ SY422 )
| ( member @ ( f23 @ SV94 @ SY422 ) @ SV94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(570,plain,
! [SV95: $i] :
( ( ! [SY423: $i] :
( ( disjoint @ SV95 @ SY423 )
| ( member @ ( f23 @ SV95 @ SY423 ) @ SY423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(571,plain,
! [SV96: $i] :
( ( ( SV96 = empty_set )
| ( member @ ( f24 @ SV96 ) @ SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(572,plain,
! [SV97: $i] :
( ( ( SV97 = empty_set )
| ( disjoint @ ( f24 @ SV97 ) @ SV97 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(573,plain,
! [SV98: $i] :
( ( ~ ( little_set @ SV98 )
| ( SV98 = empty_set )
| ( member @ ( f26 @ SV98 ) @ SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(574,plain,
! [SV99: $i] :
( ( ~ ( little_set @ SV99 )
| ( SV99 = empty_set )
| ( member @ ( ordered_pair @ SV99 @ ( f26 @ SV99 ) ) @ f25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(575,plain,
! [SV100: $i] :
( ( ! [SY424: $i] :
( ~ ( member @ SV100 @ ( range_of @ SY424 ) )
| ( ordered_pair_predicate @ ( f27 @ SV100 @ SY424 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(576,plain,
! [SV101: $i] :
( ( ! [SY425: $i] :
( ~ ( member @ SV101 @ ( range_of @ SY425 ) )
| ( member @ ( f27 @ SV101 @ SY425 ) @ SY425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(577,plain,
! [SV102: $i] :
( ( ! [SY426: $i] :
( ~ ( member @ SV102 @ ( range_of @ SY426 ) )
| ( SV102
= ( second @ ( f27 @ SV102 @ SY426 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(578,plain,
! [SV103: $i] :
( ( ! [SY427: $i] :
( ( member @ SV103 @ ( range_of @ SY427 ) )
| ~ ( little_set @ SV103 )
| ! [SY428: $i] :
( ~ ( ordered_pair_predicate @ SY428 )
| ~ ( member @ SY428 @ SY427 )
| ( SV103
!= ( second @ SY428 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(579,plain,
! [SV104: $i] :
( ( ~ ( member @ SV104 @ identity_relation )
| ( ordered_pair_predicate @ SV104 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(580,plain,
! [SV105: $i] :
( ( ~ ( member @ SV105 @ identity_relation )
| ( ( first @ SV105 )
= ( second @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(581,plain,
! [SV106: $i] :
( ( ( member @ SV106 @ identity_relation )
| ~ ( little_set @ SV106 )
| ~ ( ordered_pair_predicate @ SV106 )
| ( ( first @ SV106 )
!= ( second @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(582,plain,
! [SV107: $i] :
( ( ! [SY429: $i] :
( ( restrict @ SV107 @ SY429 )
= ( intersection @ SV107 @ ( cross_product @ SY429 @ universal_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(583,plain,
! [SV108: $i] :
( ( ~ ( one_to_one_function @ SV108 )
| ( function @ SV108 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(584,plain,
! [SV109: $i] :
( ( ~ ( one_to_one_function @ SV109 )
| ( function @ ( converse @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(585,plain,
! [SV110: $i] :
( ( ( one_to_one_function @ SV110 )
| ~ ( function @ SV110 )
| ~ ( function @ ( converse @ SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(586,plain,
! [SV111: $i] :
( ( ! [SY430: $i,SY431: $i] :
( ~ ( member @ SV111 @ ( apply @ SY430 @ SY431 ) )
| ( ordered_pair_predicate @ ( f28 @ SV111 @ SY430 @ SY431 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(587,plain,
! [SV112: $i] :
( ( ! [SY432: $i,SY433: $i] :
( ~ ( member @ SV112 @ ( apply @ SY432 @ SY433 ) )
| ( member @ ( f28 @ SV112 @ SY432 @ SY433 ) @ SY432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(588,plain,
! [SV113: $i] :
( ( ! [SY434: $i,SY435: $i] :
( ~ ( member @ SV113 @ ( apply @ SY434 @ SY435 ) )
| ( ( first @ ( f28 @ SV113 @ SY434 @ SY435 ) )
= SY435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(589,plain,
! [SV114: $i] :
( ( ! [SY436: $i,SY437: $i] :
( ~ ( member @ SV114 @ ( apply @ SY436 @ SY437 ) )
| ( member @ SV114 @ ( second @ ( f28 @ SV114 @ SY436 @ SY437 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(590,plain,
! [SV115: $i] :
( ( ! [SY438: $i,SY439: $i] :
( ( member @ SV115 @ ( apply @ SY438 @ SY439 ) )
| ! [SY440: $i] :
( ~ ( ordered_pair_predicate @ SY440 )
| ~ ( member @ SY440 @ SY438 )
| ( ( first @ SY440 )
!= SY439 )
| ~ ( member @ SV115 @ ( second @ SY440 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(591,plain,
! [SV116: $i] :
( ( ! [SY441: $i,SY442: $i] :
( ( apply_to_two_arguments @ SV116 @ SY441 @ SY442 )
= ( apply @ SV116 @ ( ordered_pair @ SY441 @ SY442 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(592,plain,
! [SV117: $i] :
( ( ! [SY443: $i,SY444: $i] :
~ ( maps @ SV117 @ SY443 @ SY444 )
| ( function @ SV117 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(593,plain,
! [SV118: $i] :
( ( ! [SY445: $i] :
( ! [SY446: $i] :
~ ( maps @ SV118 @ SY445 @ SY446 )
| ( ( domain_of @ SV118 )
= SY445 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(594,plain,
! [SV119: $i] :
( ( ! [SY447: $i,SY448: $i] :
( ~ ( maps @ SV119 @ SY447 @ SY448 )
| ( subset @ ( range_of @ SV119 ) @ SY448 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(595,plain,
! [SV120: $i] :
( ( ! [SY449: $i,SY450: $i] :
( ( maps @ SV120 @ SY449 @ SY450 )
| ~ ( function @ SV120 )
| ( ( domain_of @ SV120 )
!= SY449 )
| ~ ( subset @ ( range_of @ SV120 ) @ SY450 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(596,plain,
! [SV121: $i] :
( ( ! [SY451: $i] :
~ ( closed @ SV121 @ SY451 )
| ( little_set @ SV121 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(597,plain,
! [SV122: $i] :
( ( ! [SY452: $i] :
( ~ ( closed @ SV122 @ SY452 )
| ( little_set @ SY452 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(598,plain,
! [SV123: $i] :
( ( ! [SY453: $i] :
( ~ ( closed @ SV123 @ SY453 )
| ( maps @ SY453 @ ( cross_product @ SV123 @ SV123 ) @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(599,plain,
! [SV124: $i] :
( ( ! [SY454: $i] :
( ( closed @ SV124 @ SY454 )
| ~ ( little_set @ SV124 )
| ~ ( little_set @ SY454 )
| ~ ( maps @ SY454 @ ( cross_product @ SV124 @ SV124 ) @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(600,plain,
! [SV125: $i] :
( ( ! [SY455: $i,SY456: $i] :
( ~ ( member @ SV125 @ ( compose @ SY455 @ SY456 ) )
| ( little_set @ ( f29 @ SV125 @ SY455 @ SY456 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(601,plain,
! [SV126: $i] :
( ( ! [SY457: $i,SY458: $i] :
( ~ ( member @ SV126 @ ( compose @ SY457 @ SY458 ) )
| ( little_set @ ( f30 @ SV126 @ SY457 @ SY458 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(602,plain,
! [SV127: $i] :
( ( ! [SY459: $i,SY460: $i] :
( ~ ( member @ SV127 @ ( compose @ SY459 @ SY460 ) )
| ( little_set @ ( f31 @ SV127 @ SY459 @ SY460 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(603,plain,
! [SV128: $i] :
( ( ! [SY461: $i,SY462: $i] :
( ~ ( member @ SV128 @ ( compose @ SY461 @ SY462 ) )
| ( SV128
= ( ordered_pair @ ( f29 @ SV128 @ SY461 @ SY462 ) @ ( f30 @ SV128 @ SY461 @ SY462 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(604,plain,
! [SV129: $i] :
( ( ! [SY463: $i,SY464: $i] :
( ~ ( member @ SV129 @ ( compose @ SY463 @ SY464 ) )
| ( member @ ( ordered_pair @ ( f29 @ SV129 @ SY463 @ SY464 ) @ ( f31 @ SV129 @ SY463 @ SY464 ) ) @ SY463 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(605,plain,
! [SV130: $i] :
( ( ! [SY465: $i,SY466: $i] :
( ~ ( member @ SV130 @ ( compose @ SY465 @ SY466 ) )
| ( member @ ( ordered_pair @ ( f31 @ SV130 @ SY465 @ SY466 ) @ ( f30 @ SV130 @ SY465 @ SY466 ) ) @ SY466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(606,plain,
! [SV131: $i] :
( ( ! [SY467: $i,SY468: $i,SY469: $i] :
( ( member @ SV131 @ ( compose @ SY467 @ SY468 ) )
| ~ ( little_set @ SV131 )
| ~ ( little_set @ SY469 )
| ! [SY470: $i] :
( ~ ( little_set @ SY470 )
| ! [SY471: $i] :
( ~ ( little_set @ SY471 )
| ( SV131
!= ( ordered_pair @ SY469 @ SY470 ) )
| ~ ( member @ ( ordered_pair @ SY469 @ SY471 ) @ SY467 )
| ~ ( member @ ( ordered_pair @ SY471 @ SY470 ) @ SY468 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(607,plain,
! [SV132: $i] :
( ( ! [SY472: $i,SY473: $i] :
( ! [SY474: $i,SY475: $i] :
~ ( homomorphism @ SV132 @ SY472 @ SY473 @ SY474 @ SY475 )
| ( closed @ SY472 @ SY473 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(608,plain,
! [SV133: $i] :
( ( ! [SY476: $i,SY477: $i,SY478: $i,SY479: $i] :
( ~ ( homomorphism @ SV133 @ SY476 @ SY477 @ SY478 @ SY479 )
| ( closed @ SY478 @ SY479 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(609,plain,
! [SV134: $i] :
( ( ! [SY480: $i,SY481: $i,SY482: $i] :
( ! [SY483: $i] :
~ ( homomorphism @ SV134 @ SY480 @ SY481 @ SY482 @ SY483 )
| ( maps @ SV134 @ SY480 @ SY482 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(610,plain,
! [SV135: $i] :
( ( ! [SY484: $i,SY485: $i,SY486: $i,SY487: $i] :
( ~ ( homomorphism @ SV135 @ SY484 @ SY485 @ SY486 @ SY487 )
| ! [SY488: $i] :
( ~ ( member @ SY488 @ SY484 )
| ! [SY489: $i] :
( ~ ( member @ SY489 @ SY484 )
| ( ( apply @ SV135 @ ( apply_to_two_arguments @ SY485 @ SY488 @ SY489 ) )
= ( apply_to_two_arguments @ SY487 @ ( apply @ SV135 @ SY488 ) @ ( apply @ SV135 @ SY489 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(611,plain,
! [SV136: $i] :
( ( ! [SY490: $i,SY491: $i,SY492: $i,SY493: $i] :
( ( homomorphism @ SV136 @ SY490 @ SY491 @ SY492 @ SY493 )
| ~ ( closed @ SY490 @ SY491 )
| ~ ( closed @ SY492 @ SY493 )
| ~ ( maps @ SV136 @ SY490 @ SY492 )
| ( member @ ( f32 @ SV136 @ SY490 @ SY491 @ SY492 @ SY493 ) @ SY490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(612,plain,
! [SV137: $i] :
( ( ! [SY494: $i,SY495: $i,SY496: $i,SY497: $i] :
( ( homomorphism @ SV137 @ SY494 @ SY495 @ SY496 @ SY497 )
| ~ ( closed @ SY494 @ SY495 )
| ~ ( closed @ SY496 @ SY497 )
| ~ ( maps @ SV137 @ SY494 @ SY496 )
| ( member @ ( f33 @ SV137 @ SY494 @ SY495 @ SY496 @ SY497 ) @ SY494 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(613,plain,
! [SV138: $i] :
( ( ! [SY498: $i,SY499: $i,SY500: $i,SY501: $i] :
( ( homomorphism @ SV138 @ SY498 @ SY499 @ SY500 @ SY501 )
| ~ ( closed @ SY498 @ SY499 )
| ~ ( closed @ SY500 @ SY501 )
| ~ ( maps @ SV138 @ SY498 @ SY500 )
| ( ( apply @ SV138 @ ( apply_to_two_arguments @ SY499 @ ( f32 @ SV138 @ SY498 @ SY499 @ SY500 @ SY501 ) @ ( f33 @ SV138 @ SY498 @ SY499 @ SY500 @ SY501 ) ) )
!= ( apply_to_two_arguments @ SY501 @ ( apply @ SV138 @ ( f32 @ SV138 @ SY498 @ SY499 @ SY500 @ SY501 ) ) @ ( apply @ SV138 @ ( f33 @ SV138 @ SY498 @ SY499 @ SY500 @ SY501 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(614,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[474]) ).
thf(615,plain,
! [SV1: $i] :
( ( ( ! [SY320: $i] :
~ ( member @ SV1 @ SY320 ) )
= $true )
| ( ( little_set @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[476]) ).
thf(616,plain,
! [SV139: $i,SV2: $i] :
( ( ( SV2 = SV139 )
| ( little_set @ ( f1 @ SV2 @ SV139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(617,plain,
! [SV140: $i,SV3: $i] :
( ( ( member @ ( f1 @ SV3 @ SV140 ) @ SV3 )
| ( SV3 = SV140 )
| ( member @ ( f1 @ SV3 @ SV140 ) @ SV140 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(618,plain,
! [SV141: $i,SV4: $i] :
( ( ~ ( member @ ( f1 @ SV4 @ SV141 ) @ SV4 )
| ~ ( member @ ( f1 @ SV4 @ SV141 ) @ SV141 )
| ( SV4 = SV141 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(619,plain,
! [SV142: $i,SV5: $i] :
( ( ! [SY502: $i] :
( ~ ( member @ SV5 @ ( non_ordered_pair @ SV142 @ SY502 ) )
| ( SV5 = SV142 )
| ( SV5 = SY502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(620,plain,
! [SV143: $i,SV6: $i] :
( ( ! [SY503: $i] : ( member @ SV6 @ ( non_ordered_pair @ SV143 @ SY503 ) )
| ~ ( little_set @ SV6 )
| ( SV6 != SV143 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(621,plain,
! [SV144: $i,SV7: $i] :
( ( ! [SY504: $i] :
( ( member @ SV7 @ ( non_ordered_pair @ SV144 @ SY504 ) )
| ~ ( little_set @ SV7 )
| ( SV7 != SY504 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(622,plain,
! [SV145: $i,SV8: $i] :
( ( little_set @ ( non_ordered_pair @ SV8 @ SV145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(623,plain,
! [SV146: $i,SV10: $i] :
( ( ( ordered_pair @ SV10 @ SV146 )
= ( non_ordered_pair @ ( singleton_set @ SV10 ) @ ( non_ordered_pair @ SV10 @ SV146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(624,plain,
! [SV11: $i] :
( ( ( ~ ( ordered_pair_predicate @ SV11 ) )
= $true )
| ( ( little_set @ ( f2 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[486]) ).
thf(625,plain,
! [SV12: $i] :
( ( ( ~ ( ordered_pair_predicate @ SV12 ) )
= $true )
| ( ( little_set @ ( f3 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[487]) ).
thf(626,plain,
! [SV13: $i] :
( ( ( ~ ( ordered_pair_predicate @ SV13 ) )
= $true )
| ( ( SV13
= ( ordered_pair @ ( f2 @ SV13 ) @ ( f3 @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[488]) ).
thf(627,plain,
! [SV14: $i] :
( ( ( ordered_pair_predicate @ SV14 )
= $true )
| ( ( ! [SY332: $i] :
( ~ ( little_set @ SY332 )
| ! [SY333: $i] :
( ~ ( little_set @ SY333 )
| ( SV14
!= ( ordered_pair @ SY332 @ SY333 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[489]) ).
thf(628,plain,
! [SV147: $i,SV15: $i] :
( ( ~ ( member @ SV15 @ ( first @ SV147 ) )
| ( little_set @ ( f4 @ SV15 @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(629,plain,
! [SV148: $i,SV16: $i] :
( ( ~ ( member @ SV16 @ ( first @ SV148 ) )
| ( little_set @ ( f5 @ SV16 @ SV148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(630,plain,
! [SV149: $i,SV17: $i] :
( ( ~ ( member @ SV17 @ ( first @ SV149 ) )
| ( SV149
= ( ordered_pair @ ( f4 @ SV17 @ SV149 ) @ ( f5 @ SV17 @ SV149 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(631,plain,
! [SV150: $i,SV18: $i] :
( ( ~ ( member @ SV18 @ ( first @ SV150 ) )
| ( member @ SV18 @ ( f4 @ SV18 @ SV150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(632,plain,
! [SV151: $i,SV19: $i] :
( ( ( member @ SV19 @ ( first @ SV151 ) )
| ! [SY505: $i] :
( ~ ( little_set @ SY505 )
| ! [SY506: $i] :
( ~ ( little_set @ SY506 )
| ( SV151
!= ( ordered_pair @ SY505 @ SY506 ) )
| ~ ( member @ SV19 @ SY505 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(633,plain,
! [SV152: $i,SV20: $i] :
( ( ~ ( member @ SV20 @ ( second @ SV152 ) )
| ( little_set @ ( f6 @ SV20 @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(634,plain,
! [SV153: $i,SV21: $i] :
( ( ~ ( member @ SV21 @ ( second @ SV153 ) )
| ( little_set @ ( f7 @ SV21 @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(635,plain,
! [SV154: $i,SV22: $i] :
( ( ~ ( member @ SV22 @ ( second @ SV154 ) )
| ( SV154
= ( ordered_pair @ ( f6 @ SV22 @ SV154 ) @ ( f7 @ SV22 @ SV154 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(636,plain,
! [SV155: $i,SV23: $i] :
( ( ~ ( member @ SV23 @ ( second @ SV155 ) )
| ( member @ SV23 @ ( f7 @ SV23 @ SV155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(637,plain,
! [SV156: $i,SV24: $i] :
( ( ( member @ SV24 @ ( second @ SV156 ) )
| ! [SY507: $i] :
( ~ ( little_set @ SY507 )
| ! [SY508: $i] :
( ~ ( little_set @ SY508 )
| ( SV156
!= ( ordered_pair @ SY507 @ SY508 ) )
| ~ ( member @ SV24 @ SY508 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(638,plain,
! [SV25: $i] :
( ( ( ~ ( member @ SV25 @ estin ) )
= $true )
| ( ( ordered_pair_predicate @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[500]) ).
thf(639,plain,
! [SV26: $i] :
( ( ( ~ ( member @ SV26 @ estin ) )
= $true )
| ( ( member @ ( first @ SV26 ) @ ( second @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[501]) ).
thf(640,plain,
! [SV27: $i] :
( ( ( member @ SV27 @ estin )
= $true )
| ( ( ~ ( little_set @ SV27 )
| ~ ( ordered_pair_predicate @ SV27 )
| ~ ( member @ ( first @ SV27 ) @ ( second @ SV27 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[502]) ).
thf(641,plain,
! [SV157: $i,SV28: $i] :
( ( ! [SY509: $i] :
~ ( member @ SV28 @ ( intersection @ SV157 @ SY509 ) )
| ( member @ SV28 @ SV157 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(642,plain,
! [SV158: $i,SV29: $i] :
( ( ! [SY510: $i] :
( ~ ( member @ SV29 @ ( intersection @ SV158 @ SY510 ) )
| ( member @ SV29 @ SY510 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(643,plain,
! [SV159: $i,SV30: $i] :
( ( ! [SY511: $i] :
( ( member @ SV30 @ ( intersection @ SV159 @ SY511 ) )
| ~ ( member @ SV30 @ SV159 )
| ~ ( member @ SV30 @ SY511 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(644,plain,
! [SV160: $i,SV31: $i] :
( ( ~ ( member @ SV31 @ ( complement @ SV160 ) )
| ~ ( member @ SV31 @ SV160 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(645,plain,
! [SV161: $i,SV32: $i] :
( ( ( member @ SV32 @ ( complement @ SV161 ) )
| ~ ( little_set @ SV32 )
| ( member @ SV32 @ SV161 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(646,plain,
! [SV162: $i,SV33: $i] :
( ( ( union @ SV33 @ SV162 )
= ( complement @ ( intersection @ ( complement @ SV33 ) @ ( complement @ SV162 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(647,plain,
! [SV163: $i,SV34: $i] :
( ( ~ ( member @ SV34 @ ( domain_of @ SV163 ) )
| ( ordered_pair_predicate @ ( f8 @ SV34 @ SV163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(648,plain,
! [SV164: $i,SV35: $i] :
( ( ~ ( member @ SV35 @ ( domain_of @ SV164 ) )
| ( member @ ( f8 @ SV35 @ SV164 ) @ SV164 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(649,plain,
! [SV165: $i,SV36: $i] :
( ( ~ ( member @ SV36 @ ( domain_of @ SV165 ) )
| ( SV36
= ( first @ ( f8 @ SV36 @ SV165 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(650,plain,
! [SV166: $i,SV37: $i] :
( ( ( member @ SV37 @ ( domain_of @ SV166 ) )
| ~ ( little_set @ SV37 )
| ! [SY512: $i] :
( ~ ( ordered_pair_predicate @ SY512 )
| ~ ( member @ SY512 @ SV166 )
| ( SV37
!= ( first @ SY512 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(651,plain,
! [SV38: $i] :
( ( ( ! [SY362: $i,SY363: $i] :
~ ( member @ SV38 @ ( cross_product @ SY362 @ SY363 ) ) )
= $true )
| ( ( ordered_pair_predicate @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[513]) ).
thf(652,plain,
! [SV167: $i,SV39: $i] :
( ( ! [SY513: $i] :
~ ( member @ SV39 @ ( cross_product @ SV167 @ SY513 ) )
| ( member @ ( first @ SV39 ) @ SV167 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(653,plain,
! [SV168: $i,SV40: $i] :
( ( ! [SY514: $i] :
( ~ ( member @ SV40 @ ( cross_product @ SV168 @ SY514 ) )
| ( member @ ( second @ SV40 ) @ SY514 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(654,plain,
! [SV169: $i,SV41: $i] :
( ( ! [SY515: $i] :
( ( member @ SV41 @ ( cross_product @ SV169 @ SY515 ) )
| ~ ( little_set @ SV41 )
| ~ ( ordered_pair_predicate @ SV41 )
| ~ ( member @ ( first @ SV41 ) @ SV169 )
| ~ ( member @ ( second @ SV41 ) @ SY515 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(655,plain,
! [SV42: $i] :
( ( ( ! [SY370: $i] :
~ ( member @ SV42 @ ( converse @ SY370 ) ) )
= $true )
| ( ( ordered_pair_predicate @ SV42 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[517]) ).
thf(656,plain,
! [SV170: $i,SV43: $i] :
( ( ~ ( member @ SV43 @ ( converse @ SV170 ) )
| ( member @ ( ordered_pair @ ( second @ SV43 ) @ ( first @ SV43 ) ) @ SV170 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(657,plain,
! [SV171: $i,SV44: $i] :
( ( ( member @ SV44 @ ( converse @ SV171 ) )
| ~ ( little_set @ SV44 )
| ~ ( ordered_pair_predicate @ SV44 )
| ~ ( member @ ( ordered_pair @ ( second @ SV44 ) @ ( first @ SV44 ) ) @ SV171 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(658,plain,
! [SV172: $i,SV45: $i] :
( ( ~ ( member @ SV45 @ ( rotate_right @ SV172 ) )
| ( little_set @ ( f9 @ SV45 @ SV172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(659,plain,
! [SV173: $i,SV46: $i] :
( ( ~ ( member @ SV46 @ ( rotate_right @ SV173 ) )
| ( little_set @ ( f10 @ SV46 @ SV173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(660,plain,
! [SV174: $i,SV47: $i] :
( ( ~ ( member @ SV47 @ ( rotate_right @ SV174 ) )
| ( little_set @ ( f11 @ SV47 @ SV174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(661,plain,
! [SV175: $i,SV48: $i] :
( ( ~ ( member @ SV48 @ ( rotate_right @ SV175 ) )
| ( SV48
= ( ordered_pair @ ( f9 @ SV48 @ SV175 ) @ ( ordered_pair @ ( f10 @ SV48 @ SV175 ) @ ( f11 @ SV48 @ SV175 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(662,plain,
! [SV176: $i,SV49: $i] :
( ( ~ ( member @ SV49 @ ( rotate_right @ SV176 ) )
| ( member @ ( ordered_pair @ ( f10 @ SV49 @ SV176 ) @ ( ordered_pair @ ( f11 @ SV49 @ SV176 ) @ ( f9 @ SV49 @ SV176 ) ) ) @ SV176 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(663,plain,
! [SV177: $i,SV50: $i] :
( ( ! [SY516: $i] :
( ( member @ SV50 @ ( rotate_right @ SV177 ) )
| ~ ( little_set @ SV50 )
| ~ ( little_set @ SY516 )
| ! [SY517: $i] :
( ~ ( little_set @ SY517 )
| ! [SY518: $i] :
( ~ ( little_set @ SY518 )
| ( SV50
!= ( ordered_pair @ SY516 @ ( ordered_pair @ SY517 @ SY518 ) ) )
| ~ ( member @ ( ordered_pair @ SY517 @ ( ordered_pair @ SY518 @ SY516 ) ) @ SV177 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(664,plain,
! [SV178: $i,SV51: $i] :
( ( ~ ( member @ SV51 @ ( flip_range_of @ SV178 ) )
| ( little_set @ ( f12 @ SV51 @ SV178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(665,plain,
! [SV179: $i,SV52: $i] :
( ( ~ ( member @ SV52 @ ( flip_range_of @ SV179 ) )
| ( little_set @ ( f13 @ SV52 @ SV179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(666,plain,
! [SV180: $i,SV53: $i] :
( ( ~ ( member @ SV53 @ ( flip_range_of @ SV180 ) )
| ( little_set @ ( f14 @ SV53 @ SV180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(667,plain,
! [SV181: $i,SV54: $i] :
( ( ~ ( member @ SV54 @ ( flip_range_of @ SV181 ) )
| ( SV54
= ( ordered_pair @ ( f12 @ SV54 @ SV181 ) @ ( ordered_pair @ ( f13 @ SV54 @ SV181 ) @ ( f14 @ SV54 @ SV181 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(668,plain,
! [SV182: $i,SV55: $i] :
( ( ~ ( member @ SV55 @ ( flip_range_of @ SV182 ) )
| ( member @ ( ordered_pair @ ( f12 @ SV55 @ SV182 ) @ ( ordered_pair @ ( f14 @ SV55 @ SV182 ) @ ( f13 @ SV55 @ SV182 ) ) ) @ SV182 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(669,plain,
! [SV183: $i,SV56: $i] :
( ( ! [SY519: $i] :
( ( member @ SV56 @ ( flip_range_of @ SV183 ) )
| ~ ( little_set @ SV56 )
| ~ ( little_set @ SY519 )
| ! [SY520: $i] :
( ~ ( little_set @ SY520 )
| ! [SY521: $i] :
( ~ ( little_set @ SY521 )
| ( SV56
!= ( ordered_pair @ SY519 @ ( ordered_pair @ SY520 @ SY521 ) ) )
| ~ ( member @ ( ordered_pair @ SY519 @ ( ordered_pair @ SY521 @ SY520 ) ) @ SV183 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(670,plain,
! [SV58: $i] :
( ( member @ SV58 @ empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[533]) ).
thf(671,plain,
! [SV59: $i] :
( ( ( member @ SV59 @ universal_set )
= $true )
| ( ( ~ ( little_set @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[534]) ).
thf(672,plain,
! [SV60: $i] :
( ( ( ~ ( member @ SV60 @ infinity ) )
= $true )
| ( ( member @ ( successor @ SV60 ) @ infinity )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[535]) ).
thf(673,plain,
! [SV184: $i,SV61: $i] :
( ( ~ ( member @ SV61 @ ( sigma @ SV184 ) )
| ( member @ ( f16 @ SV61 @ SV184 ) @ SV184 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(674,plain,
! [SV185: $i,SV62: $i] :
( ( ~ ( member @ SV62 @ ( sigma @ SV185 ) )
| ( member @ SV62 @ ( f16 @ SV62 @ SV185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(675,plain,
! [SV186: $i,SV63: $i] :
( ( ( member @ SV63 @ ( sigma @ SV186 ) )
| ! [SY522: $i] :
( ~ ( member @ SY522 @ SV186 )
| ~ ( member @ SV63 @ SY522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(676,plain,
! [SV64: $i] :
( ( ( ~ ( little_set @ SV64 ) )
= $true )
| ( ( little_set @ ( sigma @ SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[539]) ).
thf(677,plain,
! [SV187: $i,SV65: $i] :
( ( ~ ( subset @ SV65 @ SV187 )
| ! [SY523: $i] :
( ~ ( member @ SY523 @ SV65 )
| ( member @ SY523 @ SV187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(678,plain,
! [SV188: $i,SV66: $i] :
( ( ( member @ ( f17 @ SV66 @ SV188 ) @ SV66 )
| ( subset @ SV66 @ SV188 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(679,plain,
! [SV189: $i,SV67: $i] :
( ( ( subset @ SV67 @ SV189 )
| ~ ( member @ ( f17 @ SV67 @ SV189 ) @ SV189 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(680,plain,
! [SV190: $i,SV68: $i] :
( ( ~ ( proper_subset @ SV68 @ SV190 )
| ( subset @ SV68 @ SV190 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(681,plain,
! [SV191: $i,SV69: $i] :
( ( ~ ( proper_subset @ SV69 @ SV191 )
| ( SV69 != SV191 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(682,plain,
! [SV192: $i,SV70: $i] :
( ( ( proper_subset @ SV70 @ SV192 )
| ~ ( subset @ SV70 @ SV192 )
| ( SV70 = SV192 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(683,plain,
! [SV193: $i,SV71: $i] :
( ( ~ ( member @ SV71 @ ( powerset @ SV193 ) )
| ( subset @ SV71 @ SV193 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(684,plain,
! [SV194: $i,SV72: $i] :
( ( ( member @ SV72 @ ( powerset @ SV194 ) )
| ~ ( little_set @ SV72 )
| ~ ( subset @ SV72 @ SV194 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(685,plain,
! [SV73: $i] :
( ( ( ~ ( little_set @ SV73 ) )
= $true )
| ( ( little_set @ ( powerset @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[548]) ).
thf(686,plain,
! [SV74: $i] :
( ( ( ~ ( relation @ SV74 ) )
= $true )
| ( ( ! [SY404: $i] :
( ~ ( member @ SY404 @ SV74 )
| ( ordered_pair_predicate @ SY404 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[549]) ).
thf(687,plain,
! [SV75: $i] :
( ( ( member @ ( f18 @ SV75 ) @ SV75 )
= $true )
| ( ( relation @ SV75 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[550]) ).
thf(688,plain,
! [SV76: $i] :
( ( ( relation @ SV76 )
= $true )
| ( ( ~ ( ordered_pair_predicate @ ( f18 @ SV76 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[551]) ).
thf(689,plain,
! [SV195: $i,SV77: $i] :
( ( ~ ( single_valued_set @ SV77 )
| ~ ( little_set @ SV195 )
| ! [SY524: $i] :
( ~ ( little_set @ SY524 )
| ! [SY525: $i] :
( ~ ( little_set @ SY525 )
| ~ ( member @ ( ordered_pair @ SV195 @ SY524 ) @ SV77 )
| ~ ( member @ ( ordered_pair @ SV195 @ SY525 ) @ SV77 )
| ( SY524 = SY525 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(690,plain,
! [SV78: $i] :
( ( ( little_set @ ( f19 @ SV78 ) )
= $true )
| ( ( single_valued_set @ SV78 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[553]) ).
thf(691,plain,
! [SV79: $i] :
( ( ( little_set @ ( f20 @ SV79 ) )
= $true )
| ( ( single_valued_set @ SV79 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[554]) ).
thf(692,plain,
! [SV80: $i] :
( ( ( little_set @ ( f21 @ SV80 ) )
= $true )
| ( ( single_valued_set @ SV80 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[555]) ).
thf(693,plain,
! [SV81: $i] :
( ( ( member @ ( ordered_pair @ ( f19 @ SV81 ) @ ( f20 @ SV81 ) ) @ SV81 )
= $true )
| ( ( single_valued_set @ SV81 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[556]) ).
thf(694,plain,
! [SV82: $i] :
( ( ( member @ ( ordered_pair @ ( f19 @ SV82 ) @ ( f21 @ SV82 ) ) @ SV82 )
= $true )
| ( ( single_valued_set @ SV82 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[557]) ).
thf(695,plain,
! [SV83: $i] :
( ( ( ( f20 @ SV83 )
!= ( f21 @ SV83 ) )
= $true )
| ( ( single_valued_set @ SV83 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[558]) ).
thf(696,plain,
! [SV84: $i] :
( ( ( ~ ( function @ SV84 ) )
= $true )
| ( ( relation @ SV84 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[559]) ).
thf(697,plain,
! [SV85: $i] :
( ( ( ~ ( function @ SV85 ) )
= $true )
| ( ( single_valued_set @ SV85 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[560]) ).
thf(698,plain,
! [SV86: $i] :
( ( ( function @ SV86 )
= $true )
| ( ( ~ ( relation @ SV86 )
| ~ ( single_valued_set @ SV86 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[561]) ).
thf(699,plain,
! [SV196: $i,SV87: $i] :
( ( ! [SY526: $i] :
( ~ ( member @ SV87 @ ( image @ SV196 @ SY526 ) )
| ( ordered_pair_predicate @ ( f22 @ SV87 @ SV196 @ SY526 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(700,plain,
! [SV197: $i,SV88: $i] :
( ( ! [SY527: $i] :
( ~ ( member @ SV88 @ ( image @ SV197 @ SY527 ) )
| ( member @ ( f22 @ SV88 @ SV197 @ SY527 ) @ SY527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(701,plain,
! [SV198: $i,SV89: $i] :
( ( ! [SY528: $i] :
( ~ ( member @ SV89 @ ( image @ SV198 @ SY528 ) )
| ( member @ ( first @ ( f22 @ SV89 @ SV198 @ SY528 ) ) @ SV198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(702,plain,
! [SV199: $i,SV90: $i] :
( ( ! [SY529: $i] :
( ~ ( member @ SV90 @ ( image @ SV199 @ SY529 ) )
| ( ( second @ ( f22 @ SV90 @ SV199 @ SY529 ) )
= SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(703,plain,
! [SV200: $i,SV91: $i] :
( ( ! [SY530: $i] :
( ( member @ SV91 @ ( image @ SV200 @ SY530 ) )
| ~ ( little_set @ SV91 )
| ! [SY531: $i] :
( ~ ( ordered_pair_predicate @ SY531 )
| ~ ( member @ SY531 @ SY530 )
| ~ ( member @ ( first @ SY531 ) @ SV200 )
| ( ( second @ SY531 )
!= SV91 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(704,plain,
! [SV92: $i] :
( ( ( ~ ( little_set @ SV92 ) )
= $true )
| ( ( ! [SY419: $i] :
( ~ ( function @ SY419 )
| ( little_set @ ( image @ SV92 @ SY419 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[567]) ).
thf(705,plain,
! [SV201: $i,SV93: $i] :
( ( ~ ( disjoint @ SV93 @ SV201 )
| ! [SY532: $i] :
( ~ ( member @ SY532 @ SV93 )
| ~ ( member @ SY532 @ SV201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(706,plain,
! [SV202: $i,SV94: $i] :
( ( ( disjoint @ SV94 @ SV202 )
| ( member @ ( f23 @ SV94 @ SV202 ) @ SV94 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(707,plain,
! [SV203: $i,SV95: $i] :
( ( ( disjoint @ SV95 @ SV203 )
| ( member @ ( f23 @ SV95 @ SV203 ) @ SV203 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(708,plain,
! [SV96: $i] :
( ( ( SV96 = empty_set )
= $true )
| ( ( member @ ( f24 @ SV96 ) @ SV96 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[571]) ).
thf(709,plain,
! [SV97: $i] :
( ( ( SV97 = empty_set )
= $true )
| ( ( disjoint @ ( f24 @ SV97 ) @ SV97 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[572]) ).
thf(710,plain,
! [SV98: $i] :
( ( ( ~ ( little_set @ SV98 ) )
= $true )
| ( ( ( SV98 = empty_set )
| ( member @ ( f26 @ SV98 ) @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[573]) ).
thf(711,plain,
! [SV99: $i] :
( ( ( ~ ( little_set @ SV99 ) )
= $true )
| ( ( ( SV99 = empty_set )
| ( member @ ( ordered_pair @ SV99 @ ( f26 @ SV99 ) ) @ f25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[574]) ).
thf(712,plain,
! [SV204: $i,SV100: $i] :
( ( ~ ( member @ SV100 @ ( range_of @ SV204 ) )
| ( ordered_pair_predicate @ ( f27 @ SV100 @ SV204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(713,plain,
! [SV205: $i,SV101: $i] :
( ( ~ ( member @ SV101 @ ( range_of @ SV205 ) )
| ( member @ ( f27 @ SV101 @ SV205 ) @ SV205 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(714,plain,
! [SV206: $i,SV102: $i] :
( ( ~ ( member @ SV102 @ ( range_of @ SV206 ) )
| ( SV102
= ( second @ ( f27 @ SV102 @ SV206 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(715,plain,
! [SV207: $i,SV103: $i] :
( ( ( member @ SV103 @ ( range_of @ SV207 ) )
| ~ ( little_set @ SV103 )
| ! [SY533: $i] :
( ~ ( ordered_pair_predicate @ SY533 )
| ~ ( member @ SY533 @ SV207 )
| ( SV103
!= ( second @ SY533 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(716,plain,
! [SV104: $i] :
( ( ( ~ ( member @ SV104 @ identity_relation ) )
= $true )
| ( ( ordered_pair_predicate @ SV104 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[579]) ).
thf(717,plain,
! [SV105: $i] :
( ( ( ~ ( member @ SV105 @ identity_relation ) )
= $true )
| ( ( ( first @ SV105 )
= ( second @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[580]) ).
thf(718,plain,
! [SV106: $i] :
( ( ( member @ SV106 @ identity_relation )
= $true )
| ( ( ~ ( little_set @ SV106 )
| ~ ( ordered_pair_predicate @ SV106 )
| ( ( first @ SV106 )
!= ( second @ SV106 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[581]) ).
thf(719,plain,
! [SV208: $i,SV107: $i] :
( ( ( restrict @ SV107 @ SV208 )
= ( intersection @ SV107 @ ( cross_product @ SV208 @ universal_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(720,plain,
! [SV108: $i] :
( ( ( ~ ( one_to_one_function @ SV108 ) )
= $true )
| ( ( function @ SV108 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[583]) ).
thf(721,plain,
! [SV109: $i] :
( ( ( ~ ( one_to_one_function @ SV109 ) )
= $true )
| ( ( function @ ( converse @ SV109 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[584]) ).
thf(722,plain,
! [SV110: $i] :
( ( ( one_to_one_function @ SV110 )
= $true )
| ( ( ~ ( function @ SV110 )
| ~ ( function @ ( converse @ SV110 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[585]) ).
thf(723,plain,
! [SV209: $i,SV111: $i] :
( ( ! [SY534: $i] :
( ~ ( member @ SV111 @ ( apply @ SV209 @ SY534 ) )
| ( ordered_pair_predicate @ ( f28 @ SV111 @ SV209 @ SY534 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[586]) ).
thf(724,plain,
! [SV210: $i,SV112: $i] :
( ( ! [SY535: $i] :
( ~ ( member @ SV112 @ ( apply @ SV210 @ SY535 ) )
| ( member @ ( f28 @ SV112 @ SV210 @ SY535 ) @ SV210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(725,plain,
! [SV211: $i,SV113: $i] :
( ( ! [SY536: $i] :
( ~ ( member @ SV113 @ ( apply @ SV211 @ SY536 ) )
| ( ( first @ ( f28 @ SV113 @ SV211 @ SY536 ) )
= SY536 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(726,plain,
! [SV212: $i,SV114: $i] :
( ( ! [SY537: $i] :
( ~ ( member @ SV114 @ ( apply @ SV212 @ SY537 ) )
| ( member @ SV114 @ ( second @ ( f28 @ SV114 @ SV212 @ SY537 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(727,plain,
! [SV213: $i,SV115: $i] :
( ( ! [SY538: $i] :
( ( member @ SV115 @ ( apply @ SV213 @ SY538 ) )
| ! [SY539: $i] :
( ~ ( ordered_pair_predicate @ SY539 )
| ~ ( member @ SY539 @ SV213 )
| ( ( first @ SY539 )
!= SY538 )
| ~ ( member @ SV115 @ ( second @ SY539 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(728,plain,
! [SV214: $i,SV116: $i] :
( ( ! [SY540: $i] :
( ( apply_to_two_arguments @ SV116 @ SV214 @ SY540 )
= ( apply @ SV116 @ ( ordered_pair @ SV214 @ SY540 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(729,plain,
! [SV117: $i] :
( ( ( ! [SY443: $i,SY444: $i] :
~ ( maps @ SV117 @ SY443 @ SY444 ) )
= $true )
| ( ( function @ SV117 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[592]) ).
thf(730,plain,
! [SV215: $i,SV118: $i] :
( ( ! [SY541: $i] :
~ ( maps @ SV118 @ SV215 @ SY541 )
| ( ( domain_of @ SV118 )
= SV215 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(731,plain,
! [SV216: $i,SV119: $i] :
( ( ! [SY542: $i] :
( ~ ( maps @ SV119 @ SV216 @ SY542 )
| ( subset @ ( range_of @ SV119 ) @ SY542 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(732,plain,
! [SV217: $i,SV120: $i] :
( ( ! [SY543: $i] :
( ( maps @ SV120 @ SV217 @ SY543 )
| ~ ( function @ SV120 )
| ( ( domain_of @ SV120 )
!= SV217 )
| ~ ( subset @ ( range_of @ SV120 ) @ SY543 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(733,plain,
! [SV121: $i] :
( ( ( ! [SY451: $i] :
~ ( closed @ SV121 @ SY451 ) )
= $true )
| ( ( little_set @ SV121 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[596]) ).
thf(734,plain,
! [SV218: $i,SV122: $i] :
( ( ~ ( closed @ SV122 @ SV218 )
| ( little_set @ SV218 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(735,plain,
! [SV219: $i,SV123: $i] :
( ( ~ ( closed @ SV123 @ SV219 )
| ( maps @ SV219 @ ( cross_product @ SV123 @ SV123 ) @ SV123 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(736,plain,
! [SV220: $i,SV124: $i] :
( ( ( closed @ SV124 @ SV220 )
| ~ ( little_set @ SV124 )
| ~ ( little_set @ SV220 )
| ~ ( maps @ SV220 @ ( cross_product @ SV124 @ SV124 ) @ SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(737,plain,
! [SV221: $i,SV125: $i] :
( ( ! [SY544: $i] :
( ~ ( member @ SV125 @ ( compose @ SV221 @ SY544 ) )
| ( little_set @ ( f29 @ SV125 @ SV221 @ SY544 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(738,plain,
! [SV222: $i,SV126: $i] :
( ( ! [SY545: $i] :
( ~ ( member @ SV126 @ ( compose @ SV222 @ SY545 ) )
| ( little_set @ ( f30 @ SV126 @ SV222 @ SY545 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(739,plain,
! [SV223: $i,SV127: $i] :
( ( ! [SY546: $i] :
( ~ ( member @ SV127 @ ( compose @ SV223 @ SY546 ) )
| ( little_set @ ( f31 @ SV127 @ SV223 @ SY546 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(740,plain,
! [SV224: $i,SV128: $i] :
( ( ! [SY547: $i] :
( ~ ( member @ SV128 @ ( compose @ SV224 @ SY547 ) )
| ( SV128
= ( ordered_pair @ ( f29 @ SV128 @ SV224 @ SY547 ) @ ( f30 @ SV128 @ SV224 @ SY547 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(741,plain,
! [SV225: $i,SV129: $i] :
( ( ! [SY548: $i] :
( ~ ( member @ SV129 @ ( compose @ SV225 @ SY548 ) )
| ( member @ ( ordered_pair @ ( f29 @ SV129 @ SV225 @ SY548 ) @ ( f31 @ SV129 @ SV225 @ SY548 ) ) @ SV225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(742,plain,
! [SV226: $i,SV130: $i] :
( ( ! [SY549: $i] :
( ~ ( member @ SV130 @ ( compose @ SV226 @ SY549 ) )
| ( member @ ( ordered_pair @ ( f31 @ SV130 @ SV226 @ SY549 ) @ ( f30 @ SV130 @ SV226 @ SY549 ) ) @ SY549 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[605]) ).
thf(743,plain,
! [SV227: $i,SV131: $i] :
( ( ! [SY550: $i,SY551: $i] :
( ( member @ SV131 @ ( compose @ SV227 @ SY550 ) )
| ~ ( little_set @ SV131 )
| ~ ( little_set @ SY551 )
| ! [SY552: $i] :
( ~ ( little_set @ SY552 )
| ! [SY553: $i] :
( ~ ( little_set @ SY553 )
| ( SV131
!= ( ordered_pair @ SY551 @ SY552 ) )
| ~ ( member @ ( ordered_pair @ SY551 @ SY553 ) @ SV227 )
| ~ ( member @ ( ordered_pair @ SY553 @ SY552 ) @ SY550 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(744,plain,
! [SV228: $i,SV132: $i] :
( ( ! [SY554: $i] :
( ! [SY555: $i,SY556: $i] :
~ ( homomorphism @ SV132 @ SV228 @ SY554 @ SY555 @ SY556 )
| ( closed @ SV228 @ SY554 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(745,plain,
! [SV229: $i,SV133: $i] :
( ( ! [SY557: $i,SY558: $i,SY559: $i] :
( ~ ( homomorphism @ SV133 @ SV229 @ SY557 @ SY558 @ SY559 )
| ( closed @ SY558 @ SY559 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(746,plain,
! [SV230: $i,SV134: $i] :
( ( ! [SY560: $i,SY561: $i] :
( ! [SY562: $i] :
~ ( homomorphism @ SV134 @ SV230 @ SY560 @ SY561 @ SY562 )
| ( maps @ SV134 @ SV230 @ SY561 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(747,plain,
! [SV231: $i,SV135: $i] :
( ( ! [SY563: $i,SY564: $i,SY565: $i] :
( ~ ( homomorphism @ SV135 @ SV231 @ SY563 @ SY564 @ SY565 )
| ! [SY566: $i] :
( ~ ( member @ SY566 @ SV231 )
| ! [SY567: $i] :
( ~ ( member @ SY567 @ SV231 )
| ( ( apply @ SV135 @ ( apply_to_two_arguments @ SY563 @ SY566 @ SY567 ) )
= ( apply_to_two_arguments @ SY565 @ ( apply @ SV135 @ SY566 ) @ ( apply @ SV135 @ SY567 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(748,plain,
! [SV232: $i,SV136: $i] :
( ( ! [SY568: $i,SY569: $i,SY570: $i] :
( ( homomorphism @ SV136 @ SV232 @ SY568 @ SY569 @ SY570 )
| ~ ( closed @ SV232 @ SY568 )
| ~ ( closed @ SY569 @ SY570 )
| ~ ( maps @ SV136 @ SV232 @ SY569 )
| ( member @ ( f32 @ SV136 @ SV232 @ SY568 @ SY569 @ SY570 ) @ SV232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(749,plain,
! [SV233: $i,SV137: $i] :
( ( ! [SY571: $i,SY572: $i,SY573: $i] :
( ( homomorphism @ SV137 @ SV233 @ SY571 @ SY572 @ SY573 )
| ~ ( closed @ SV233 @ SY571 )
| ~ ( closed @ SY572 @ SY573 )
| ~ ( maps @ SV137 @ SV233 @ SY572 )
| ( member @ ( f33 @ SV137 @ SV233 @ SY571 @ SY572 @ SY573 ) @ SV233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(750,plain,
! [SV234: $i,SV138: $i] :
( ( ! [SY574: $i,SY575: $i,SY576: $i] :
( ( homomorphism @ SV138 @ SV234 @ SY574 @ SY575 @ SY576 )
| ~ ( closed @ SV234 @ SY574 )
| ~ ( closed @ SY575 @ SY576 )
| ~ ( maps @ SV138 @ SV234 @ SY575 )
| ( ( apply @ SV138 @ ( apply_to_two_arguments @ SY574 @ ( f32 @ SV138 @ SV234 @ SY574 @ SY575 @ SY576 ) @ ( f33 @ SV138 @ SV234 @ SY574 @ SY575 @ SY576 ) ) )
!= ( apply_to_two_arguments @ SY576 @ ( apply @ SV138 @ ( f32 @ SV138 @ SV234 @ SY574 @ SY575 @ SY576 ) ) @ ( apply @ SV138 @ ( f33 @ SV138 @ SV234 @ SY574 @ SY575 @ SY576 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(751,plain,
! [SV235: $i,SV1: $i] :
( ( ( ~ ( member @ SV1 @ SV235 ) )
= $true )
| ( ( little_set @ SV1 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(752,plain,
! [SV139: $i,SV2: $i] :
( ( ( SV2 = SV139 )
= $true )
| ( ( little_set @ ( f1 @ SV2 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[616]) ).
thf(753,plain,
! [SV140: $i,SV3: $i] :
( ( ( member @ ( f1 @ SV3 @ SV140 ) @ SV3 )
= $true )
| ( ( ( SV3 = SV140 )
| ( member @ ( f1 @ SV3 @ SV140 ) @ SV140 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[617]) ).
thf(754,plain,
! [SV141: $i,SV4: $i] :
( ( ( ~ ( member @ ( f1 @ SV4 @ SV141 ) @ SV4 ) )
= $true )
| ( ( ~ ( member @ ( f1 @ SV4 @ SV141 ) @ SV141 )
| ( SV4 = SV141 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[618]) ).
thf(755,plain,
! [SV236: $i,SV142: $i,SV5: $i] :
( ( ~ ( member @ SV5 @ ( non_ordered_pair @ SV142 @ SV236 ) )
| ( SV5 = SV142 )
| ( SV5 = SV236 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(756,plain,
! [SV143: $i,SV6: $i] :
( ( ( ! [SY503: $i] : ( member @ SV6 @ ( non_ordered_pair @ SV143 @ SY503 ) ) )
= $true )
| ( ( ~ ( little_set @ SV6 )
| ( SV6 != SV143 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[620]) ).
thf(757,plain,
! [SV237: $i,SV144: $i,SV7: $i] :
( ( ( member @ SV7 @ ( non_ordered_pair @ SV144 @ SV237 ) )
| ~ ( little_set @ SV7 )
| ( SV7 != SV237 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(758,plain,
! [SV11: $i] :
( ( ( ordered_pair_predicate @ SV11 )
= $false )
| ( ( little_set @ ( f2 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[624]) ).
thf(759,plain,
! [SV12: $i] :
( ( ( ordered_pair_predicate @ SV12 )
= $false )
| ( ( little_set @ ( f3 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[625]) ).
thf(760,plain,
! [SV13: $i] :
( ( ( ordered_pair_predicate @ SV13 )
= $false )
| ( ( SV13
= ( ordered_pair @ ( f2 @ SV13 ) @ ( f3 @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[626]) ).
thf(761,plain,
! [SV14: $i,SV238: $i] :
( ( ( ~ ( little_set @ SV238 )
| ! [SY577: $i] :
( ~ ( little_set @ SY577 )
| ( SV14
!= ( ordered_pair @ SV238 @ SY577 ) ) ) )
= $true )
| ( ( ordered_pair_predicate @ SV14 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(762,plain,
! [SV147: $i,SV15: $i] :
( ( ( ~ ( member @ SV15 @ ( first @ SV147 ) ) )
= $true )
| ( ( little_set @ ( f4 @ SV15 @ SV147 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[628]) ).
thf(763,plain,
! [SV148: $i,SV16: $i] :
( ( ( ~ ( member @ SV16 @ ( first @ SV148 ) ) )
= $true )
| ( ( little_set @ ( f5 @ SV16 @ SV148 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[629]) ).
thf(764,plain,
! [SV149: $i,SV17: $i] :
( ( ( ~ ( member @ SV17 @ ( first @ SV149 ) ) )
= $true )
| ( ( SV149
= ( ordered_pair @ ( f4 @ SV17 @ SV149 ) @ ( f5 @ SV17 @ SV149 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[630]) ).
thf(765,plain,
! [SV150: $i,SV18: $i] :
( ( ( ~ ( member @ SV18 @ ( first @ SV150 ) ) )
= $true )
| ( ( member @ SV18 @ ( f4 @ SV18 @ SV150 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[631]) ).
thf(766,plain,
! [SV151: $i,SV19: $i] :
( ( ( member @ SV19 @ ( first @ SV151 ) )
= $true )
| ( ( ! [SY505: $i] :
( ~ ( little_set @ SY505 )
| ! [SY506: $i] :
( ~ ( little_set @ SY506 )
| ( SV151
!= ( ordered_pair @ SY505 @ SY506 ) )
| ~ ( member @ SV19 @ SY505 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[632]) ).
thf(767,plain,
! [SV152: $i,SV20: $i] :
( ( ( ~ ( member @ SV20 @ ( second @ SV152 ) ) )
= $true )
| ( ( little_set @ ( f6 @ SV20 @ SV152 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[633]) ).
thf(768,plain,
! [SV153: $i,SV21: $i] :
( ( ( ~ ( member @ SV21 @ ( second @ SV153 ) ) )
= $true )
| ( ( little_set @ ( f7 @ SV21 @ SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[634]) ).
thf(769,plain,
! [SV154: $i,SV22: $i] :
( ( ( ~ ( member @ SV22 @ ( second @ SV154 ) ) )
= $true )
| ( ( SV154
= ( ordered_pair @ ( f6 @ SV22 @ SV154 ) @ ( f7 @ SV22 @ SV154 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[635]) ).
thf(770,plain,
! [SV155: $i,SV23: $i] :
( ( ( ~ ( member @ SV23 @ ( second @ SV155 ) ) )
= $true )
| ( ( member @ SV23 @ ( f7 @ SV23 @ SV155 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[636]) ).
thf(771,plain,
! [SV156: $i,SV24: $i] :
( ( ( member @ SV24 @ ( second @ SV156 ) )
= $true )
| ( ( ! [SY507: $i] :
( ~ ( little_set @ SY507 )
| ! [SY508: $i] :
( ~ ( little_set @ SY508 )
| ( SV156
!= ( ordered_pair @ SY507 @ SY508 ) )
| ~ ( member @ SV24 @ SY508 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[637]) ).
thf(772,plain,
! [SV25: $i] :
( ( ( member @ SV25 @ estin )
= $false )
| ( ( ordered_pair_predicate @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[638]) ).
thf(773,plain,
! [SV26: $i] :
( ( ( member @ SV26 @ estin )
= $false )
| ( ( member @ ( first @ SV26 ) @ ( second @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[639]) ).
thf(774,plain,
! [SV27: $i] :
( ( ( ~ ( little_set @ SV27 ) )
= $true )
| ( ( ~ ( ordered_pair_predicate @ SV27 )
| ~ ( member @ ( first @ SV27 ) @ ( second @ SV27 ) ) )
= $true )
| ( ( member @ SV27 @ estin )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[640]) ).
thf(775,plain,
! [SV157: $i,SV28: $i] :
( ( ( ! [SY509: $i] :
~ ( member @ SV28 @ ( intersection @ SV157 @ SY509 ) ) )
= $true )
| ( ( member @ SV28 @ SV157 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[641]) ).
thf(776,plain,
! [SV239: $i,SV158: $i,SV29: $i] :
( ( ~ ( member @ SV29 @ ( intersection @ SV158 @ SV239 ) )
| ( member @ SV29 @ SV239 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(777,plain,
! [SV240: $i,SV159: $i,SV30: $i] :
( ( ( member @ SV30 @ ( intersection @ SV159 @ SV240 ) )
| ~ ( member @ SV30 @ SV159 )
| ~ ( member @ SV30 @ SV240 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(778,plain,
! [SV160: $i,SV31: $i] :
( ( ( ~ ( member @ SV31 @ ( complement @ SV160 ) ) )
= $true )
| ( ( ~ ( member @ SV31 @ SV160 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[644]) ).
thf(779,plain,
! [SV161: $i,SV32: $i] :
( ( ( member @ SV32 @ ( complement @ SV161 ) )
= $true )
| ( ( ~ ( little_set @ SV32 )
| ( member @ SV32 @ SV161 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[645]) ).
thf(780,plain,
! [SV163: $i,SV34: $i] :
( ( ( ~ ( member @ SV34 @ ( domain_of @ SV163 ) ) )
= $true )
| ( ( ordered_pair_predicate @ ( f8 @ SV34 @ SV163 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[647]) ).
thf(781,plain,
! [SV164: $i,SV35: $i] :
( ( ( ~ ( member @ SV35 @ ( domain_of @ SV164 ) ) )
= $true )
| ( ( member @ ( f8 @ SV35 @ SV164 ) @ SV164 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[648]) ).
thf(782,plain,
! [SV165: $i,SV36: $i] :
( ( ( ~ ( member @ SV36 @ ( domain_of @ SV165 ) ) )
= $true )
| ( ( SV36
= ( first @ ( f8 @ SV36 @ SV165 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[649]) ).
thf(783,plain,
! [SV166: $i,SV37: $i] :
( ( ( member @ SV37 @ ( domain_of @ SV166 ) )
= $true )
| ( ( ~ ( little_set @ SV37 )
| ! [SY512: $i] :
( ~ ( ordered_pair_predicate @ SY512 )
| ~ ( member @ SY512 @ SV166 )
| ( SV37
!= ( first @ SY512 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[650]) ).
thf(784,plain,
! [SV241: $i,SV38: $i] :
( ( ( ! [SY578: $i] :
~ ( member @ SV38 @ ( cross_product @ SV241 @ SY578 ) ) )
= $true )
| ( ( ordered_pair_predicate @ SV38 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(785,plain,
! [SV167: $i,SV39: $i] :
( ( ( ! [SY513: $i] :
~ ( member @ SV39 @ ( cross_product @ SV167 @ SY513 ) ) )
= $true )
| ( ( member @ ( first @ SV39 ) @ SV167 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[652]) ).
thf(786,plain,
! [SV242: $i,SV168: $i,SV40: $i] :
( ( ~ ( member @ SV40 @ ( cross_product @ SV168 @ SV242 ) )
| ( member @ ( second @ SV40 ) @ SV242 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(787,plain,
! [SV243: $i,SV169: $i,SV41: $i] :
( ( ( member @ SV41 @ ( cross_product @ SV169 @ SV243 ) )
| ~ ( little_set @ SV41 )
| ~ ( ordered_pair_predicate @ SV41 )
| ~ ( member @ ( first @ SV41 ) @ SV169 )
| ~ ( member @ ( second @ SV41 ) @ SV243 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(788,plain,
! [SV244: $i,SV42: $i] :
( ( ( ~ ( member @ SV42 @ ( converse @ SV244 ) ) )
= $true )
| ( ( ordered_pair_predicate @ SV42 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(789,plain,
! [SV170: $i,SV43: $i] :
( ( ( ~ ( member @ SV43 @ ( converse @ SV170 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ ( second @ SV43 ) @ ( first @ SV43 ) ) @ SV170 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[656]) ).
thf(790,plain,
! [SV171: $i,SV44: $i] :
( ( ( member @ SV44 @ ( converse @ SV171 ) )
= $true )
| ( ( ~ ( little_set @ SV44 )
| ~ ( ordered_pair_predicate @ SV44 )
| ~ ( member @ ( ordered_pair @ ( second @ SV44 ) @ ( first @ SV44 ) ) @ SV171 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[657]) ).
thf(791,plain,
! [SV172: $i,SV45: $i] :
( ( ( ~ ( member @ SV45 @ ( rotate_right @ SV172 ) ) )
= $true )
| ( ( little_set @ ( f9 @ SV45 @ SV172 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[658]) ).
thf(792,plain,
! [SV173: $i,SV46: $i] :
( ( ( ~ ( member @ SV46 @ ( rotate_right @ SV173 ) ) )
= $true )
| ( ( little_set @ ( f10 @ SV46 @ SV173 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[659]) ).
thf(793,plain,
! [SV174: $i,SV47: $i] :
( ( ( ~ ( member @ SV47 @ ( rotate_right @ SV174 ) ) )
= $true )
| ( ( little_set @ ( f11 @ SV47 @ SV174 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[660]) ).
thf(794,plain,
! [SV175: $i,SV48: $i] :
( ( ( ~ ( member @ SV48 @ ( rotate_right @ SV175 ) ) )
= $true )
| ( ( SV48
= ( ordered_pair @ ( f9 @ SV48 @ SV175 ) @ ( ordered_pair @ ( f10 @ SV48 @ SV175 ) @ ( f11 @ SV48 @ SV175 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[661]) ).
thf(795,plain,
! [SV176: $i,SV49: $i] :
( ( ( ~ ( member @ SV49 @ ( rotate_right @ SV176 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ ( f10 @ SV49 @ SV176 ) @ ( ordered_pair @ ( f11 @ SV49 @ SV176 ) @ ( f9 @ SV49 @ SV176 ) ) ) @ SV176 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[662]) ).
thf(796,plain,
! [SV245: $i,SV177: $i,SV50: $i] :
( ( ( member @ SV50 @ ( rotate_right @ SV177 ) )
| ~ ( little_set @ SV50 )
| ~ ( little_set @ SV245 )
| ! [SY579: $i] :
( ~ ( little_set @ SY579 )
| ! [SY580: $i] :
( ~ ( little_set @ SY580 )
| ( SV50
!= ( ordered_pair @ SV245 @ ( ordered_pair @ SY579 @ SY580 ) ) )
| ~ ( member @ ( ordered_pair @ SY579 @ ( ordered_pair @ SY580 @ SV245 ) ) @ SV177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(797,plain,
! [SV178: $i,SV51: $i] :
( ( ( ~ ( member @ SV51 @ ( flip_range_of @ SV178 ) ) )
= $true )
| ( ( little_set @ ( f12 @ SV51 @ SV178 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[664]) ).
thf(798,plain,
! [SV179: $i,SV52: $i] :
( ( ( ~ ( member @ SV52 @ ( flip_range_of @ SV179 ) ) )
= $true )
| ( ( little_set @ ( f13 @ SV52 @ SV179 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[665]) ).
thf(799,plain,
! [SV180: $i,SV53: $i] :
( ( ( ~ ( member @ SV53 @ ( flip_range_of @ SV180 ) ) )
= $true )
| ( ( little_set @ ( f14 @ SV53 @ SV180 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[666]) ).
thf(800,plain,
! [SV181: $i,SV54: $i] :
( ( ( ~ ( member @ SV54 @ ( flip_range_of @ SV181 ) ) )
= $true )
| ( ( SV54
= ( ordered_pair @ ( f12 @ SV54 @ SV181 ) @ ( ordered_pair @ ( f13 @ SV54 @ SV181 ) @ ( f14 @ SV54 @ SV181 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[667]) ).
thf(801,plain,
! [SV182: $i,SV55: $i] :
( ( ( ~ ( member @ SV55 @ ( flip_range_of @ SV182 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ ( f12 @ SV55 @ SV182 ) @ ( ordered_pair @ ( f14 @ SV55 @ SV182 ) @ ( f13 @ SV55 @ SV182 ) ) ) @ SV182 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[668]) ).
thf(802,plain,
! [SV246: $i,SV183: $i,SV56: $i] :
( ( ( member @ SV56 @ ( flip_range_of @ SV183 ) )
| ~ ( little_set @ SV56 )
| ~ ( little_set @ SV246 )
| ! [SY581: $i] :
( ~ ( little_set @ SY581 )
| ! [SY582: $i] :
( ~ ( little_set @ SY582 )
| ( SV56
!= ( ordered_pair @ SV246 @ ( ordered_pair @ SY581 @ SY582 ) ) )
| ~ ( member @ ( ordered_pair @ SV246 @ ( ordered_pair @ SY582 @ SY581 ) ) @ SV183 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(803,plain,
! [SV59: $i] :
( ( ( little_set @ SV59 )
= $false )
| ( ( member @ SV59 @ universal_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[671]) ).
thf(804,plain,
! [SV60: $i] :
( ( ( member @ SV60 @ infinity )
= $false )
| ( ( member @ ( successor @ SV60 ) @ infinity )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[672]) ).
thf(805,plain,
! [SV184: $i,SV61: $i] :
( ( ( ~ ( member @ SV61 @ ( sigma @ SV184 ) ) )
= $true )
| ( ( member @ ( f16 @ SV61 @ SV184 ) @ SV184 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[673]) ).
thf(806,plain,
! [SV185: $i,SV62: $i] :
( ( ( ~ ( member @ SV62 @ ( sigma @ SV185 ) ) )
= $true )
| ( ( member @ SV62 @ ( f16 @ SV62 @ SV185 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[674]) ).
thf(807,plain,
! [SV186: $i,SV63: $i] :
( ( ( member @ SV63 @ ( sigma @ SV186 ) )
= $true )
| ( ( ! [SY522: $i] :
( ~ ( member @ SY522 @ SV186 )
| ~ ( member @ SV63 @ SY522 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[675]) ).
thf(808,plain,
! [SV64: $i] :
( ( ( little_set @ SV64 )
= $false )
| ( ( little_set @ ( sigma @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[676]) ).
thf(809,plain,
! [SV187: $i,SV65: $i] :
( ( ( ~ ( subset @ SV65 @ SV187 ) )
= $true )
| ( ( ! [SY523: $i] :
( ~ ( member @ SY523 @ SV65 )
| ( member @ SY523 @ SV187 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[677]) ).
thf(810,plain,
! [SV188: $i,SV66: $i] :
( ( ( member @ ( f17 @ SV66 @ SV188 ) @ SV66 )
= $true )
| ( ( subset @ SV66 @ SV188 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[678]) ).
thf(811,plain,
! [SV189: $i,SV67: $i] :
( ( ( subset @ SV67 @ SV189 )
= $true )
| ( ( ~ ( member @ ( f17 @ SV67 @ SV189 ) @ SV189 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[679]) ).
thf(812,plain,
! [SV190: $i,SV68: $i] :
( ( ( ~ ( proper_subset @ SV68 @ SV190 ) )
= $true )
| ( ( subset @ SV68 @ SV190 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[680]) ).
thf(813,plain,
! [SV191: $i,SV69: $i] :
( ( ( ~ ( proper_subset @ SV69 @ SV191 ) )
= $true )
| ( ( SV69 != SV191 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[681]) ).
thf(814,plain,
! [SV192: $i,SV70: $i] :
( ( ( proper_subset @ SV70 @ SV192 )
= $true )
| ( ( ~ ( subset @ SV70 @ SV192 )
| ( SV70 = SV192 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[682]) ).
thf(815,plain,
! [SV193: $i,SV71: $i] :
( ( ( ~ ( member @ SV71 @ ( powerset @ SV193 ) ) )
= $true )
| ( ( subset @ SV71 @ SV193 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[683]) ).
thf(816,plain,
! [SV194: $i,SV72: $i] :
( ( ( member @ SV72 @ ( powerset @ SV194 ) )
= $true )
| ( ( ~ ( little_set @ SV72 )
| ~ ( subset @ SV72 @ SV194 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[684]) ).
thf(817,plain,
! [SV73: $i] :
( ( ( little_set @ SV73 )
= $false )
| ( ( little_set @ ( powerset @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[685]) ).
thf(818,plain,
! [SV74: $i] :
( ( ( relation @ SV74 )
= $false )
| ( ( ! [SY404: $i] :
( ~ ( member @ SY404 @ SV74 )
| ( ordered_pair_predicate @ SY404 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[686]) ).
thf(819,plain,
! [SV76: $i] :
( ( ( ordered_pair_predicate @ ( f18 @ SV76 ) )
= $false )
| ( ( relation @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[688]) ).
thf(820,plain,
! [SV195: $i,SV77: $i] :
( ( ( ~ ( single_valued_set @ SV77 ) )
= $true )
| ( ( ~ ( little_set @ SV195 )
| ! [SY524: $i] :
( ~ ( little_set @ SY524 )
| ! [SY525: $i] :
( ~ ( little_set @ SY525 )
| ~ ( member @ ( ordered_pair @ SV195 @ SY524 ) @ SV77 )
| ~ ( member @ ( ordered_pair @ SV195 @ SY525 ) @ SV77 )
| ( SY524 = SY525 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[689]) ).
thf(821,plain,
! [SV83: $i] :
( ( ( ( f20 @ SV83 )
= ( f21 @ SV83 ) )
= $false )
| ( ( single_valued_set @ SV83 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[695]) ).
thf(822,plain,
! [SV84: $i] :
( ( ( function @ SV84 )
= $false )
| ( ( relation @ SV84 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[696]) ).
thf(823,plain,
! [SV85: $i] :
( ( ( function @ SV85 )
= $false )
| ( ( single_valued_set @ SV85 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[697]) ).
thf(824,plain,
! [SV86: $i] :
( ( ( ~ ( relation @ SV86 ) )
= $true )
| ( ( ~ ( single_valued_set @ SV86 ) )
= $true )
| ( ( function @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[698]) ).
thf(825,plain,
! [SV247: $i,SV196: $i,SV87: $i] :
( ( ~ ( member @ SV87 @ ( image @ SV196 @ SV247 ) )
| ( ordered_pair_predicate @ ( f22 @ SV87 @ SV196 @ SV247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(826,plain,
! [SV248: $i,SV197: $i,SV88: $i] :
( ( ~ ( member @ SV88 @ ( image @ SV197 @ SV248 ) )
| ( member @ ( f22 @ SV88 @ SV197 @ SV248 ) @ SV248 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(827,plain,
! [SV249: $i,SV198: $i,SV89: $i] :
( ( ~ ( member @ SV89 @ ( image @ SV198 @ SV249 ) )
| ( member @ ( first @ ( f22 @ SV89 @ SV198 @ SV249 ) ) @ SV198 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(828,plain,
! [SV250: $i,SV199: $i,SV90: $i] :
( ( ~ ( member @ SV90 @ ( image @ SV199 @ SV250 ) )
| ( ( second @ ( f22 @ SV90 @ SV199 @ SV250 ) )
= SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(829,plain,
! [SV251: $i,SV200: $i,SV91: $i] :
( ( ( member @ SV91 @ ( image @ SV200 @ SV251 ) )
| ~ ( little_set @ SV91 )
| ! [SY583: $i] :
( ~ ( ordered_pair_predicate @ SY583 )
| ~ ( member @ SY583 @ SV251 )
| ~ ( member @ ( first @ SY583 ) @ SV200 )
| ( ( second @ SY583 )
!= SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(830,plain,
! [SV92: $i] :
( ( ( little_set @ SV92 )
= $false )
| ( ( ! [SY419: $i] :
( ~ ( function @ SY419 )
| ( little_set @ ( image @ SV92 @ SY419 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[704]) ).
thf(831,plain,
! [SV201: $i,SV93: $i] :
( ( ( ~ ( disjoint @ SV93 @ SV201 ) )
= $true )
| ( ( ! [SY532: $i] :
( ~ ( member @ SY532 @ SV93 )
| ~ ( member @ SY532 @ SV201 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[705]) ).
thf(832,plain,
! [SV202: $i,SV94: $i] :
( ( ( disjoint @ SV94 @ SV202 )
= $true )
| ( ( member @ ( f23 @ SV94 @ SV202 ) @ SV94 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[706]) ).
thf(833,plain,
! [SV203: $i,SV95: $i] :
( ( ( disjoint @ SV95 @ SV203 )
= $true )
| ( ( member @ ( f23 @ SV95 @ SV203 ) @ SV203 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[707]) ).
thf(834,plain,
! [SV98: $i] :
( ( ( little_set @ SV98 )
= $false )
| ( ( ( SV98 = empty_set )
| ( member @ ( f26 @ SV98 ) @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[710]) ).
thf(835,plain,
! [SV99: $i] :
( ( ( little_set @ SV99 )
= $false )
| ( ( ( SV99 = empty_set )
| ( member @ ( ordered_pair @ SV99 @ ( f26 @ SV99 ) ) @ f25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[711]) ).
thf(836,plain,
! [SV204: $i,SV100: $i] :
( ( ( ~ ( member @ SV100 @ ( range_of @ SV204 ) ) )
= $true )
| ( ( ordered_pair_predicate @ ( f27 @ SV100 @ SV204 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[712]) ).
thf(837,plain,
! [SV205: $i,SV101: $i] :
( ( ( ~ ( member @ SV101 @ ( range_of @ SV205 ) ) )
= $true )
| ( ( member @ ( f27 @ SV101 @ SV205 ) @ SV205 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[713]) ).
thf(838,plain,
! [SV206: $i,SV102: $i] :
( ( ( ~ ( member @ SV102 @ ( range_of @ SV206 ) ) )
= $true )
| ( ( SV102
= ( second @ ( f27 @ SV102 @ SV206 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[714]) ).
thf(839,plain,
! [SV207: $i,SV103: $i] :
( ( ( member @ SV103 @ ( range_of @ SV207 ) )
= $true )
| ( ( ~ ( little_set @ SV103 )
| ! [SY533: $i] :
( ~ ( ordered_pair_predicate @ SY533 )
| ~ ( member @ SY533 @ SV207 )
| ( SV103
!= ( second @ SY533 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[715]) ).
thf(840,plain,
! [SV104: $i] :
( ( ( member @ SV104 @ identity_relation )
= $false )
| ( ( ordered_pair_predicate @ SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[716]) ).
thf(841,plain,
! [SV105: $i] :
( ( ( member @ SV105 @ identity_relation )
= $false )
| ( ( ( first @ SV105 )
= ( second @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[717]) ).
thf(842,plain,
! [SV106: $i] :
( ( ( ~ ( little_set @ SV106 ) )
= $true )
| ( ( ~ ( ordered_pair_predicate @ SV106 )
| ( ( first @ SV106 )
!= ( second @ SV106 ) ) )
= $true )
| ( ( member @ SV106 @ identity_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[718]) ).
thf(843,plain,
! [SV108: $i] :
( ( ( one_to_one_function @ SV108 )
= $false )
| ( ( function @ SV108 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[720]) ).
thf(844,plain,
! [SV109: $i] :
( ( ( one_to_one_function @ SV109 )
= $false )
| ( ( function @ ( converse @ SV109 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[721]) ).
thf(845,plain,
! [SV110: $i] :
( ( ( ~ ( function @ SV110 ) )
= $true )
| ( ( ~ ( function @ ( converse @ SV110 ) ) )
= $true )
| ( ( one_to_one_function @ SV110 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[722]) ).
thf(846,plain,
! [SV252: $i,SV209: $i,SV111: $i] :
( ( ~ ( member @ SV111 @ ( apply @ SV209 @ SV252 ) )
| ( ordered_pair_predicate @ ( f28 @ SV111 @ SV209 @ SV252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(847,plain,
! [SV253: $i,SV210: $i,SV112: $i] :
( ( ~ ( member @ SV112 @ ( apply @ SV210 @ SV253 ) )
| ( member @ ( f28 @ SV112 @ SV210 @ SV253 ) @ SV210 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(848,plain,
! [SV254: $i,SV211: $i,SV113: $i] :
( ( ~ ( member @ SV113 @ ( apply @ SV211 @ SV254 ) )
| ( ( first @ ( f28 @ SV113 @ SV211 @ SV254 ) )
= SV254 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(849,plain,
! [SV255: $i,SV212: $i,SV114: $i] :
( ( ~ ( member @ SV114 @ ( apply @ SV212 @ SV255 ) )
| ( member @ SV114 @ ( second @ ( f28 @ SV114 @ SV212 @ SV255 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(850,plain,
! [SV256: $i,SV213: $i,SV115: $i] :
( ( ( member @ SV115 @ ( apply @ SV213 @ SV256 ) )
| ! [SY584: $i] :
( ~ ( ordered_pair_predicate @ SY584 )
| ~ ( member @ SY584 @ SV213 )
| ( ( first @ SY584 )
!= SV256 )
| ~ ( member @ SV115 @ ( second @ SY584 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(851,plain,
! [SV257: $i,SV214: $i,SV116: $i] :
( ( ( apply_to_two_arguments @ SV116 @ SV214 @ SV257 )
= ( apply @ SV116 @ ( ordered_pair @ SV214 @ SV257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(852,plain,
! [SV258: $i,SV117: $i] :
( ( ( ! [SY585: $i] :
~ ( maps @ SV117 @ SV258 @ SY585 ) )
= $true )
| ( ( function @ SV117 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(853,plain,
! [SV215: $i,SV118: $i] :
( ( ( ! [SY541: $i] :
~ ( maps @ SV118 @ SV215 @ SY541 ) )
= $true )
| ( ( ( domain_of @ SV118 )
= SV215 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[730]) ).
thf(854,plain,
! [SV259: $i,SV216: $i,SV119: $i] :
( ( ~ ( maps @ SV119 @ SV216 @ SV259 )
| ( subset @ ( range_of @ SV119 ) @ SV259 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(855,plain,
! [SV260: $i,SV217: $i,SV120: $i] :
( ( ( maps @ SV120 @ SV217 @ SV260 )
| ~ ( function @ SV120 )
| ( ( domain_of @ SV120 )
!= SV217 )
| ~ ( subset @ ( range_of @ SV120 ) @ SV260 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(856,plain,
! [SV261: $i,SV121: $i] :
( ( ( ~ ( closed @ SV121 @ SV261 ) )
= $true )
| ( ( little_set @ SV121 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(857,plain,
! [SV218: $i,SV122: $i] :
( ( ( ~ ( closed @ SV122 @ SV218 ) )
= $true )
| ( ( little_set @ SV218 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[734]) ).
thf(858,plain,
! [SV219: $i,SV123: $i] :
( ( ( ~ ( closed @ SV123 @ SV219 ) )
= $true )
| ( ( maps @ SV219 @ ( cross_product @ SV123 @ SV123 ) @ SV123 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[735]) ).
thf(859,plain,
! [SV220: $i,SV124: $i] :
( ( ( closed @ SV124 @ SV220 )
= $true )
| ( ( ~ ( little_set @ SV124 )
| ~ ( little_set @ SV220 )
| ~ ( maps @ SV220 @ ( cross_product @ SV124 @ SV124 ) @ SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[736]) ).
thf(860,plain,
! [SV262: $i,SV221: $i,SV125: $i] :
( ( ~ ( member @ SV125 @ ( compose @ SV221 @ SV262 ) )
| ( little_set @ ( f29 @ SV125 @ SV221 @ SV262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(861,plain,
! [SV263: $i,SV222: $i,SV126: $i] :
( ( ~ ( member @ SV126 @ ( compose @ SV222 @ SV263 ) )
| ( little_set @ ( f30 @ SV126 @ SV222 @ SV263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(862,plain,
! [SV264: $i,SV223: $i,SV127: $i] :
( ( ~ ( member @ SV127 @ ( compose @ SV223 @ SV264 ) )
| ( little_set @ ( f31 @ SV127 @ SV223 @ SV264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(863,plain,
! [SV265: $i,SV224: $i,SV128: $i] :
( ( ~ ( member @ SV128 @ ( compose @ SV224 @ SV265 ) )
| ( SV128
= ( ordered_pair @ ( f29 @ SV128 @ SV224 @ SV265 ) @ ( f30 @ SV128 @ SV224 @ SV265 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(864,plain,
! [SV266: $i,SV225: $i,SV129: $i] :
( ( ~ ( member @ SV129 @ ( compose @ SV225 @ SV266 ) )
| ( member @ ( ordered_pair @ ( f29 @ SV129 @ SV225 @ SV266 ) @ ( f31 @ SV129 @ SV225 @ SV266 ) ) @ SV225 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(865,plain,
! [SV267: $i,SV226: $i,SV130: $i] :
( ( ~ ( member @ SV130 @ ( compose @ SV226 @ SV267 ) )
| ( member @ ( ordered_pair @ ( f31 @ SV130 @ SV226 @ SV267 ) @ ( f30 @ SV130 @ SV226 @ SV267 ) ) @ SV267 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(866,plain,
! [SV268: $i,SV227: $i,SV131: $i] :
( ( ! [SY586: $i] :
( ( member @ SV131 @ ( compose @ SV227 @ SV268 ) )
| ~ ( little_set @ SV131 )
| ~ ( little_set @ SY586 )
| ! [SY587: $i] :
( ~ ( little_set @ SY587 )
| ! [SY588: $i] :
( ~ ( little_set @ SY588 )
| ( SV131
!= ( ordered_pair @ SY586 @ SY587 ) )
| ~ ( member @ ( ordered_pair @ SY586 @ SY588 ) @ SV227 )
| ~ ( member @ ( ordered_pair @ SY588 @ SY587 ) @ SV268 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(867,plain,
! [SV269: $i,SV228: $i,SV132: $i] :
( ( ! [SY589: $i,SY590: $i] :
~ ( homomorphism @ SV132 @ SV228 @ SV269 @ SY589 @ SY590 )
| ( closed @ SV228 @ SV269 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(868,plain,
! [SV270: $i,SV229: $i,SV133: $i] :
( ( ! [SY591: $i,SY592: $i] :
( ~ ( homomorphism @ SV133 @ SV229 @ SV270 @ SY591 @ SY592 )
| ( closed @ SY591 @ SY592 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(869,plain,
! [SV271: $i,SV230: $i,SV134: $i] :
( ( ! [SY593: $i] :
( ! [SY594: $i] :
~ ( homomorphism @ SV134 @ SV230 @ SV271 @ SY593 @ SY594 )
| ( maps @ SV134 @ SV230 @ SY593 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(870,plain,
! [SV272: $i,SV231: $i,SV135: $i] :
( ( ! [SY595: $i,SY596: $i] :
( ~ ( homomorphism @ SV135 @ SV231 @ SV272 @ SY595 @ SY596 )
| ! [SY597: $i] :
( ~ ( member @ SY597 @ SV231 )
| ! [SY598: $i] :
( ~ ( member @ SY598 @ SV231 )
| ( ( apply @ SV135 @ ( apply_to_two_arguments @ SV272 @ SY597 @ SY598 ) )
= ( apply_to_two_arguments @ SY596 @ ( apply @ SV135 @ SY597 ) @ ( apply @ SV135 @ SY598 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(871,plain,
! [SV273: $i,SV232: $i,SV136: $i] :
( ( ! [SY599: $i,SY600: $i] :
( ( homomorphism @ SV136 @ SV232 @ SV273 @ SY599 @ SY600 )
| ~ ( closed @ SV232 @ SV273 )
| ~ ( closed @ SY599 @ SY600 )
| ~ ( maps @ SV136 @ SV232 @ SY599 )
| ( member @ ( f32 @ SV136 @ SV232 @ SV273 @ SY599 @ SY600 ) @ SV232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(872,plain,
! [SV274: $i,SV233: $i,SV137: $i] :
( ( ! [SY601: $i,SY602: $i] :
( ( homomorphism @ SV137 @ SV233 @ SV274 @ SY601 @ SY602 )
| ~ ( closed @ SV233 @ SV274 )
| ~ ( closed @ SY601 @ SY602 )
| ~ ( maps @ SV137 @ SV233 @ SY601 )
| ( member @ ( f33 @ SV137 @ SV233 @ SV274 @ SY601 @ SY602 ) @ SV233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(873,plain,
! [SV275: $i,SV234: $i,SV138: $i] :
( ( ! [SY603: $i,SY604: $i] :
( ( homomorphism @ SV138 @ SV234 @ SV275 @ SY603 @ SY604 )
| ~ ( closed @ SV234 @ SV275 )
| ~ ( closed @ SY603 @ SY604 )
| ~ ( maps @ SV138 @ SV234 @ SY603 )
| ( ( apply @ SV138 @ ( apply_to_two_arguments @ SV275 @ ( f32 @ SV138 @ SV234 @ SV275 @ SY603 @ SY604 ) @ ( f33 @ SV138 @ SV234 @ SV275 @ SY603 @ SY604 ) ) )
!= ( apply_to_two_arguments @ SY604 @ ( apply @ SV138 @ ( f32 @ SV138 @ SV234 @ SV275 @ SY603 @ SY604 ) ) @ ( apply @ SV138 @ ( f33 @ SV138 @ SV234 @ SV275 @ SY603 @ SY604 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(874,plain,
! [SV235: $i,SV1: $i] :
( ( ( member @ SV1 @ SV235 )
= $false )
| ( ( little_set @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[751]) ).
thf(875,plain,
! [SV140: $i,SV3: $i] :
( ( ( SV3 = SV140 )
= $true )
| ( ( member @ ( f1 @ SV3 @ SV140 ) @ SV140 )
= $true )
| ( ( member @ ( f1 @ SV3 @ SV140 ) @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[753]) ).
thf(876,plain,
! [SV141: $i,SV4: $i] :
( ( ( member @ ( f1 @ SV4 @ SV141 ) @ SV4 )
= $false )
| ( ( ~ ( member @ ( f1 @ SV4 @ SV141 ) @ SV141 )
| ( SV4 = SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[754]) ).
thf(877,plain,
! [SV236: $i,SV142: $i,SV5: $i] :
( ( ( ~ ( member @ SV5 @ ( non_ordered_pair @ SV142 @ SV236 ) ) )
= $true )
| ( ( ( SV5 = SV142 )
| ( SV5 = SV236 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[755]) ).
thf(878,plain,
! [SV276: $i,SV143: $i,SV6: $i] :
( ( ( member @ SV6 @ ( non_ordered_pair @ SV143 @ SV276 ) )
= $true )
| ( ( ~ ( little_set @ SV6 )
| ( SV6 != SV143 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(879,plain,
! [SV237: $i,SV144: $i,SV7: $i] :
( ( ( member @ SV7 @ ( non_ordered_pair @ SV144 @ SV237 ) )
= $true )
| ( ( ~ ( little_set @ SV7 )
| ( SV7 != SV237 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[757]) ).
thf(880,plain,
! [SV14: $i,SV238: $i] :
( ( ( ~ ( little_set @ SV238 ) )
= $true )
| ( ( ! [SY577: $i] :
( ~ ( little_set @ SY577 )
| ( SV14
!= ( ordered_pair @ SV238 @ SY577 ) ) ) )
= $true )
| ( ( ordered_pair_predicate @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[761]) ).
thf(881,plain,
! [SV147: $i,SV15: $i] :
( ( ( member @ SV15 @ ( first @ SV147 ) )
= $false )
| ( ( little_set @ ( f4 @ SV15 @ SV147 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[762]) ).
thf(882,plain,
! [SV148: $i,SV16: $i] :
( ( ( member @ SV16 @ ( first @ SV148 ) )
= $false )
| ( ( little_set @ ( f5 @ SV16 @ SV148 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[763]) ).
thf(883,plain,
! [SV149: $i,SV17: $i] :
( ( ( member @ SV17 @ ( first @ SV149 ) )
= $false )
| ( ( SV149
= ( ordered_pair @ ( f4 @ SV17 @ SV149 ) @ ( f5 @ SV17 @ SV149 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[764]) ).
thf(884,plain,
! [SV150: $i,SV18: $i] :
( ( ( member @ SV18 @ ( first @ SV150 ) )
= $false )
| ( ( member @ SV18 @ ( f4 @ SV18 @ SV150 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[765]) ).
thf(885,plain,
! [SV19: $i,SV151: $i,SV277: $i] :
( ( ( ~ ( little_set @ SV277 )
| ! [SY605: $i] :
( ~ ( little_set @ SY605 )
| ( SV151
!= ( ordered_pair @ SV277 @ SY605 ) )
| ~ ( member @ SV19 @ SV277 ) ) )
= $true )
| ( ( member @ SV19 @ ( first @ SV151 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(886,plain,
! [SV152: $i,SV20: $i] :
( ( ( member @ SV20 @ ( second @ SV152 ) )
= $false )
| ( ( little_set @ ( f6 @ SV20 @ SV152 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[767]) ).
thf(887,plain,
! [SV153: $i,SV21: $i] :
( ( ( member @ SV21 @ ( second @ SV153 ) )
= $false )
| ( ( little_set @ ( f7 @ SV21 @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[768]) ).
thf(888,plain,
! [SV154: $i,SV22: $i] :
( ( ( member @ SV22 @ ( second @ SV154 ) )
= $false )
| ( ( SV154
= ( ordered_pair @ ( f6 @ SV22 @ SV154 ) @ ( f7 @ SV22 @ SV154 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[769]) ).
thf(889,plain,
! [SV155: $i,SV23: $i] :
( ( ( member @ SV23 @ ( second @ SV155 ) )
= $false )
| ( ( member @ SV23 @ ( f7 @ SV23 @ SV155 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[770]) ).
thf(890,plain,
! [SV24: $i,SV156: $i,SV278: $i] :
( ( ( ~ ( little_set @ SV278 )
| ! [SY606: $i] :
( ~ ( little_set @ SY606 )
| ( SV156
!= ( ordered_pair @ SV278 @ SY606 ) )
| ~ ( member @ SV24 @ SY606 ) ) )
= $true )
| ( ( member @ SV24 @ ( second @ SV156 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(891,plain,
! [SV27: $i] :
( ( ( little_set @ SV27 )
= $false )
| ( ( ~ ( ordered_pair_predicate @ SV27 )
| ~ ( member @ ( first @ SV27 ) @ ( second @ SV27 ) ) )
= $true )
| ( ( member @ SV27 @ estin )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[774]) ).
thf(892,plain,
! [SV279: $i,SV157: $i,SV28: $i] :
( ( ( ~ ( member @ SV28 @ ( intersection @ SV157 @ SV279 ) ) )
= $true )
| ( ( member @ SV28 @ SV157 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(893,plain,
! [SV239: $i,SV158: $i,SV29: $i] :
( ( ( ~ ( member @ SV29 @ ( intersection @ SV158 @ SV239 ) ) )
= $true )
| ( ( member @ SV29 @ SV239 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[776]) ).
thf(894,plain,
! [SV240: $i,SV159: $i,SV30: $i] :
( ( ( member @ SV30 @ ( intersection @ SV159 @ SV240 ) )
= $true )
| ( ( ~ ( member @ SV30 @ SV159 )
| ~ ( member @ SV30 @ SV240 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[777]) ).
thf(895,plain,
! [SV160: $i,SV31: $i] :
( ( ( member @ SV31 @ ( complement @ SV160 ) )
= $false )
| ( ( ~ ( member @ SV31 @ SV160 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[778]) ).
thf(896,plain,
! [SV161: $i,SV32: $i] :
( ( ( ~ ( little_set @ SV32 ) )
= $true )
| ( ( member @ SV32 @ SV161 )
= $true )
| ( ( member @ SV32 @ ( complement @ SV161 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[779]) ).
thf(897,plain,
! [SV163: $i,SV34: $i] :
( ( ( member @ SV34 @ ( domain_of @ SV163 ) )
= $false )
| ( ( ordered_pair_predicate @ ( f8 @ SV34 @ SV163 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[780]) ).
thf(898,plain,
! [SV164: $i,SV35: $i] :
( ( ( member @ SV35 @ ( domain_of @ SV164 ) )
= $false )
| ( ( member @ ( f8 @ SV35 @ SV164 ) @ SV164 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[781]) ).
thf(899,plain,
! [SV165: $i,SV36: $i] :
( ( ( member @ SV36 @ ( domain_of @ SV165 ) )
= $false )
| ( ( SV36
= ( first @ ( f8 @ SV36 @ SV165 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[782]) ).
thf(900,plain,
! [SV166: $i,SV37: $i] :
( ( ( ~ ( little_set @ SV37 ) )
= $true )
| ( ( ! [SY512: $i] :
( ~ ( ordered_pair_predicate @ SY512 )
| ~ ( member @ SY512 @ SV166 )
| ( SV37
!= ( first @ SY512 ) ) ) )
= $true )
| ( ( member @ SV37 @ ( domain_of @ SV166 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[783]) ).
thf(901,plain,
! [SV280: $i,SV241: $i,SV38: $i] :
( ( ( ~ ( member @ SV38 @ ( cross_product @ SV241 @ SV280 ) ) )
= $true )
| ( ( ordered_pair_predicate @ SV38 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(902,plain,
! [SV281: $i,SV167: $i,SV39: $i] :
( ( ( ~ ( member @ SV39 @ ( cross_product @ SV167 @ SV281 ) ) )
= $true )
| ( ( member @ ( first @ SV39 ) @ SV167 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(903,plain,
! [SV242: $i,SV168: $i,SV40: $i] :
( ( ( ~ ( member @ SV40 @ ( cross_product @ SV168 @ SV242 ) ) )
= $true )
| ( ( member @ ( second @ SV40 ) @ SV242 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[786]) ).
thf(904,plain,
! [SV243: $i,SV169: $i,SV41: $i] :
( ( ( member @ SV41 @ ( cross_product @ SV169 @ SV243 ) )
= $true )
| ( ( ~ ( little_set @ SV41 )
| ~ ( ordered_pair_predicate @ SV41 )
| ~ ( member @ ( first @ SV41 ) @ SV169 )
| ~ ( member @ ( second @ SV41 ) @ SV243 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[787]) ).
thf(905,plain,
! [SV244: $i,SV42: $i] :
( ( ( member @ SV42 @ ( converse @ SV244 ) )
= $false )
| ( ( ordered_pair_predicate @ SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[788]) ).
thf(906,plain,
! [SV170: $i,SV43: $i] :
( ( ( member @ SV43 @ ( converse @ SV170 ) )
= $false )
| ( ( member @ ( ordered_pair @ ( second @ SV43 ) @ ( first @ SV43 ) ) @ SV170 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[789]) ).
thf(907,plain,
! [SV171: $i,SV44: $i] :
( ( ( ~ ( little_set @ SV44 ) )
= $true )
| ( ( ~ ( ordered_pair_predicate @ SV44 )
| ~ ( member @ ( ordered_pair @ ( second @ SV44 ) @ ( first @ SV44 ) ) @ SV171 ) )
= $true )
| ( ( member @ SV44 @ ( converse @ SV171 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[790]) ).
thf(908,plain,
! [SV172: $i,SV45: $i] :
( ( ( member @ SV45 @ ( rotate_right @ SV172 ) )
= $false )
| ( ( little_set @ ( f9 @ SV45 @ SV172 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[791]) ).
thf(909,plain,
! [SV173: $i,SV46: $i] :
( ( ( member @ SV46 @ ( rotate_right @ SV173 ) )
= $false )
| ( ( little_set @ ( f10 @ SV46 @ SV173 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[792]) ).
thf(910,plain,
! [SV174: $i,SV47: $i] :
( ( ( member @ SV47 @ ( rotate_right @ SV174 ) )
= $false )
| ( ( little_set @ ( f11 @ SV47 @ SV174 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[793]) ).
thf(911,plain,
! [SV175: $i,SV48: $i] :
( ( ( member @ SV48 @ ( rotate_right @ SV175 ) )
= $false )
| ( ( SV48
= ( ordered_pair @ ( f9 @ SV48 @ SV175 ) @ ( ordered_pair @ ( f10 @ SV48 @ SV175 ) @ ( f11 @ SV48 @ SV175 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[794]) ).
thf(912,plain,
! [SV176: $i,SV49: $i] :
( ( ( member @ SV49 @ ( rotate_right @ SV176 ) )
= $false )
| ( ( member @ ( ordered_pair @ ( f10 @ SV49 @ SV176 ) @ ( ordered_pair @ ( f11 @ SV49 @ SV176 ) @ ( f9 @ SV49 @ SV176 ) ) ) @ SV176 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[795]) ).
thf(913,plain,
! [SV245: $i,SV177: $i,SV50: $i] :
( ( ( member @ SV50 @ ( rotate_right @ SV177 ) )
= $true )
| ( ( ~ ( little_set @ SV50 )
| ~ ( little_set @ SV245 )
| ! [SY579: $i] :
( ~ ( little_set @ SY579 )
| ! [SY580: $i] :
( ~ ( little_set @ SY580 )
| ( SV50
!= ( ordered_pair @ SV245 @ ( ordered_pair @ SY579 @ SY580 ) ) )
| ~ ( member @ ( ordered_pair @ SY579 @ ( ordered_pair @ SY580 @ SV245 ) ) @ SV177 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[796]) ).
thf(914,plain,
! [SV178: $i,SV51: $i] :
( ( ( member @ SV51 @ ( flip_range_of @ SV178 ) )
= $false )
| ( ( little_set @ ( f12 @ SV51 @ SV178 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[797]) ).
thf(915,plain,
! [SV179: $i,SV52: $i] :
( ( ( member @ SV52 @ ( flip_range_of @ SV179 ) )
= $false )
| ( ( little_set @ ( f13 @ SV52 @ SV179 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[798]) ).
thf(916,plain,
! [SV180: $i,SV53: $i] :
( ( ( member @ SV53 @ ( flip_range_of @ SV180 ) )
= $false )
| ( ( little_set @ ( f14 @ SV53 @ SV180 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[799]) ).
thf(917,plain,
! [SV181: $i,SV54: $i] :
( ( ( member @ SV54 @ ( flip_range_of @ SV181 ) )
= $false )
| ( ( SV54
= ( ordered_pair @ ( f12 @ SV54 @ SV181 ) @ ( ordered_pair @ ( f13 @ SV54 @ SV181 ) @ ( f14 @ SV54 @ SV181 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[800]) ).
thf(918,plain,
! [SV182: $i,SV55: $i] :
( ( ( member @ SV55 @ ( flip_range_of @ SV182 ) )
= $false )
| ( ( member @ ( ordered_pair @ ( f12 @ SV55 @ SV182 ) @ ( ordered_pair @ ( f14 @ SV55 @ SV182 ) @ ( f13 @ SV55 @ SV182 ) ) ) @ SV182 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[801]) ).
thf(919,plain,
! [SV246: $i,SV183: $i,SV56: $i] :
( ( ( member @ SV56 @ ( flip_range_of @ SV183 ) )
= $true )
| ( ( ~ ( little_set @ SV56 )
| ~ ( little_set @ SV246 )
| ! [SY581: $i] :
( ~ ( little_set @ SY581 )
| ! [SY582: $i] :
( ~ ( little_set @ SY582 )
| ( SV56
!= ( ordered_pair @ SV246 @ ( ordered_pair @ SY581 @ SY582 ) ) )
| ~ ( member @ ( ordered_pair @ SV246 @ ( ordered_pair @ SY582 @ SY581 ) ) @ SV183 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[802]) ).
thf(920,plain,
! [SV184: $i,SV61: $i] :
( ( ( member @ SV61 @ ( sigma @ SV184 ) )
= $false )
| ( ( member @ ( f16 @ SV61 @ SV184 ) @ SV184 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[805]) ).
thf(921,plain,
! [SV185: $i,SV62: $i] :
( ( ( member @ SV62 @ ( sigma @ SV185 ) )
= $false )
| ( ( member @ SV62 @ ( f16 @ SV62 @ SV185 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[806]) ).
thf(922,plain,
! [SV63: $i,SV186: $i,SV282: $i] :
( ( ( ~ ( member @ SV282 @ SV186 )
| ~ ( member @ SV63 @ SV282 ) )
= $true )
| ( ( member @ SV63 @ ( sigma @ SV186 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(923,plain,
! [SV187: $i,SV65: $i] :
( ( ( subset @ SV65 @ SV187 )
= $false )
| ( ( ! [SY523: $i] :
( ~ ( member @ SY523 @ SV65 )
| ( member @ SY523 @ SV187 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[809]) ).
thf(924,plain,
! [SV189: $i,SV67: $i] :
( ( ( member @ ( f17 @ SV67 @ SV189 ) @ SV189 )
= $false )
| ( ( subset @ SV67 @ SV189 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[811]) ).
thf(925,plain,
! [SV190: $i,SV68: $i] :
( ( ( proper_subset @ SV68 @ SV190 )
= $false )
| ( ( subset @ SV68 @ SV190 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[812]) ).
thf(926,plain,
! [SV191: $i,SV69: $i] :
( ( ( proper_subset @ SV69 @ SV191 )
= $false )
| ( ( SV69 != SV191 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[813]) ).
thf(927,plain,
! [SV192: $i,SV70: $i] :
( ( ( ~ ( subset @ SV70 @ SV192 ) )
= $true )
| ( ( SV70 = SV192 )
= $true )
| ( ( proper_subset @ SV70 @ SV192 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[814]) ).
thf(928,plain,
! [SV193: $i,SV71: $i] :
( ( ( member @ SV71 @ ( powerset @ SV193 ) )
= $false )
| ( ( subset @ SV71 @ SV193 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[815]) ).
thf(929,plain,
! [SV194: $i,SV72: $i] :
( ( ( ~ ( little_set @ SV72 ) )
= $true )
| ( ( ~ ( subset @ SV72 @ SV194 ) )
= $true )
| ( ( member @ SV72 @ ( powerset @ SV194 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[816]) ).
thf(930,plain,
! [SV74: $i,SV283: $i] :
( ( ( ~ ( member @ SV283 @ SV74 )
| ( ordered_pair_predicate @ SV283 ) )
= $true )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(931,plain,
! [SV195: $i,SV77: $i] :
( ( ( single_valued_set @ SV77 )
= $false )
| ( ( ~ ( little_set @ SV195 )
| ! [SY524: $i] :
( ~ ( little_set @ SY524 )
| ! [SY525: $i] :
( ~ ( little_set @ SY525 )
| ~ ( member @ ( ordered_pair @ SV195 @ SY524 ) @ SV77 )
| ~ ( member @ ( ordered_pair @ SV195 @ SY525 ) @ SV77 )
| ( SY524 = SY525 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[820]) ).
thf(932,plain,
! [SV86: $i] :
( ( ( relation @ SV86 )
= $false )
| ( ( ~ ( single_valued_set @ SV86 ) )
= $true )
| ( ( function @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[824]) ).
thf(933,plain,
! [SV247: $i,SV196: $i,SV87: $i] :
( ( ( ~ ( member @ SV87 @ ( image @ SV196 @ SV247 ) ) )
= $true )
| ( ( ordered_pair_predicate @ ( f22 @ SV87 @ SV196 @ SV247 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[825]) ).
thf(934,plain,
! [SV248: $i,SV197: $i,SV88: $i] :
( ( ( ~ ( member @ SV88 @ ( image @ SV197 @ SV248 ) ) )
= $true )
| ( ( member @ ( f22 @ SV88 @ SV197 @ SV248 ) @ SV248 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[826]) ).
thf(935,plain,
! [SV249: $i,SV198: $i,SV89: $i] :
( ( ( ~ ( member @ SV89 @ ( image @ SV198 @ SV249 ) ) )
= $true )
| ( ( member @ ( first @ ( f22 @ SV89 @ SV198 @ SV249 ) ) @ SV198 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[827]) ).
thf(936,plain,
! [SV250: $i,SV199: $i,SV90: $i] :
( ( ( ~ ( member @ SV90 @ ( image @ SV199 @ SV250 ) ) )
= $true )
| ( ( ( second @ ( f22 @ SV90 @ SV199 @ SV250 ) )
= SV90 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[828]) ).
thf(937,plain,
! [SV251: $i,SV200: $i,SV91: $i] :
( ( ( member @ SV91 @ ( image @ SV200 @ SV251 ) )
= $true )
| ( ( ~ ( little_set @ SV91 )
| ! [SY583: $i] :
( ~ ( ordered_pair_predicate @ SY583 )
| ~ ( member @ SY583 @ SV251 )
| ~ ( member @ ( first @ SY583 ) @ SV200 )
| ( ( second @ SY583 )
!= SV91 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[829]) ).
thf(938,plain,
! [SV92: $i,SV284: $i] :
( ( ( ~ ( function @ SV284 )
| ( little_set @ ( image @ SV92 @ SV284 ) ) )
= $true )
| ( ( little_set @ SV92 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(939,plain,
! [SV201: $i,SV93: $i] :
( ( ( disjoint @ SV93 @ SV201 )
= $false )
| ( ( ! [SY532: $i] :
( ~ ( member @ SY532 @ SV93 )
| ~ ( member @ SY532 @ SV201 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[831]) ).
thf(940,plain,
! [SV98: $i] :
( ( ( SV98 = empty_set )
= $true )
| ( ( member @ ( f26 @ SV98 ) @ SV98 )
= $true )
| ( ( little_set @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[834]) ).
thf(941,plain,
! [SV99: $i] :
( ( ( SV99 = empty_set )
= $true )
| ( ( member @ ( ordered_pair @ SV99 @ ( f26 @ SV99 ) ) @ f25 )
= $true )
| ( ( little_set @ SV99 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[835]) ).
thf(942,plain,
! [SV204: $i,SV100: $i] :
( ( ( member @ SV100 @ ( range_of @ SV204 ) )
= $false )
| ( ( ordered_pair_predicate @ ( f27 @ SV100 @ SV204 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[836]) ).
thf(943,plain,
! [SV205: $i,SV101: $i] :
( ( ( member @ SV101 @ ( range_of @ SV205 ) )
= $false )
| ( ( member @ ( f27 @ SV101 @ SV205 ) @ SV205 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[837]) ).
thf(944,plain,
! [SV206: $i,SV102: $i] :
( ( ( member @ SV102 @ ( range_of @ SV206 ) )
= $false )
| ( ( SV102
= ( second @ ( f27 @ SV102 @ SV206 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[838]) ).
thf(945,plain,
! [SV207: $i,SV103: $i] :
( ( ( ~ ( little_set @ SV103 ) )
= $true )
| ( ( ! [SY533: $i] :
( ~ ( ordered_pair_predicate @ SY533 )
| ~ ( member @ SY533 @ SV207 )
| ( SV103
!= ( second @ SY533 ) ) ) )
= $true )
| ( ( member @ SV103 @ ( range_of @ SV207 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[839]) ).
thf(946,plain,
! [SV106: $i] :
( ( ( little_set @ SV106 )
= $false )
| ( ( ~ ( ordered_pair_predicate @ SV106 )
| ( ( first @ SV106 )
!= ( second @ SV106 ) ) )
= $true )
| ( ( member @ SV106 @ identity_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[842]) ).
thf(947,plain,
! [SV110: $i] :
( ( ( function @ SV110 )
= $false )
| ( ( ~ ( function @ ( converse @ SV110 ) ) )
= $true )
| ( ( one_to_one_function @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[845]) ).
thf(948,plain,
! [SV252: $i,SV209: $i,SV111: $i] :
( ( ( ~ ( member @ SV111 @ ( apply @ SV209 @ SV252 ) ) )
= $true )
| ( ( ordered_pair_predicate @ ( f28 @ SV111 @ SV209 @ SV252 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[846]) ).
thf(949,plain,
! [SV253: $i,SV210: $i,SV112: $i] :
( ( ( ~ ( member @ SV112 @ ( apply @ SV210 @ SV253 ) ) )
= $true )
| ( ( member @ ( f28 @ SV112 @ SV210 @ SV253 ) @ SV210 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[847]) ).
thf(950,plain,
! [SV254: $i,SV211: $i,SV113: $i] :
( ( ( ~ ( member @ SV113 @ ( apply @ SV211 @ SV254 ) ) )
= $true )
| ( ( ( first @ ( f28 @ SV113 @ SV211 @ SV254 ) )
= SV254 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[848]) ).
thf(951,plain,
! [SV255: $i,SV212: $i,SV114: $i] :
( ( ( ~ ( member @ SV114 @ ( apply @ SV212 @ SV255 ) ) )
= $true )
| ( ( member @ SV114 @ ( second @ ( f28 @ SV114 @ SV212 @ SV255 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[849]) ).
thf(952,plain,
! [SV256: $i,SV213: $i,SV115: $i] :
( ( ( member @ SV115 @ ( apply @ SV213 @ SV256 ) )
= $true )
| ( ( ! [SY584: $i] :
( ~ ( ordered_pair_predicate @ SY584 )
| ~ ( member @ SY584 @ SV213 )
| ( ( first @ SY584 )
!= SV256 )
| ~ ( member @ SV115 @ ( second @ SY584 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[850]) ).
thf(953,plain,
! [SV285: $i,SV258: $i,SV117: $i] :
( ( ( ~ ( maps @ SV117 @ SV258 @ SV285 ) )
= $true )
| ( ( function @ SV117 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(954,plain,
! [SV286: $i,SV215: $i,SV118: $i] :
( ( ( ~ ( maps @ SV118 @ SV215 @ SV286 ) )
= $true )
| ( ( ( domain_of @ SV118 )
= SV215 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(955,plain,
! [SV259: $i,SV216: $i,SV119: $i] :
( ( ( ~ ( maps @ SV119 @ SV216 @ SV259 ) )
= $true )
| ( ( subset @ ( range_of @ SV119 ) @ SV259 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[854]) ).
thf(956,plain,
! [SV260: $i,SV217: $i,SV120: $i] :
( ( ( maps @ SV120 @ SV217 @ SV260 )
= $true )
| ( ( ~ ( function @ SV120 )
| ( ( domain_of @ SV120 )
!= SV217 )
| ~ ( subset @ ( range_of @ SV120 ) @ SV260 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[855]) ).
thf(957,plain,
! [SV261: $i,SV121: $i] :
( ( ( closed @ SV121 @ SV261 )
= $false )
| ( ( little_set @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[856]) ).
thf(958,plain,
! [SV218: $i,SV122: $i] :
( ( ( closed @ SV122 @ SV218 )
= $false )
| ( ( little_set @ SV218 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[857]) ).
thf(959,plain,
! [SV219: $i,SV123: $i] :
( ( ( closed @ SV123 @ SV219 )
= $false )
| ( ( maps @ SV219 @ ( cross_product @ SV123 @ SV123 ) @ SV123 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[858]) ).
thf(960,plain,
! [SV220: $i,SV124: $i] :
( ( ( ~ ( little_set @ SV124 ) )
= $true )
| ( ( ~ ( little_set @ SV220 )
| ~ ( maps @ SV220 @ ( cross_product @ SV124 @ SV124 ) @ SV124 ) )
= $true )
| ( ( closed @ SV124 @ SV220 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[859]) ).
thf(961,plain,
! [SV262: $i,SV221: $i,SV125: $i] :
( ( ( ~ ( member @ SV125 @ ( compose @ SV221 @ SV262 ) ) )
= $true )
| ( ( little_set @ ( f29 @ SV125 @ SV221 @ SV262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[860]) ).
thf(962,plain,
! [SV263: $i,SV222: $i,SV126: $i] :
( ( ( ~ ( member @ SV126 @ ( compose @ SV222 @ SV263 ) ) )
= $true )
| ( ( little_set @ ( f30 @ SV126 @ SV222 @ SV263 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[861]) ).
thf(963,plain,
! [SV264: $i,SV223: $i,SV127: $i] :
( ( ( ~ ( member @ SV127 @ ( compose @ SV223 @ SV264 ) ) )
= $true )
| ( ( little_set @ ( f31 @ SV127 @ SV223 @ SV264 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[862]) ).
thf(964,plain,
! [SV265: $i,SV224: $i,SV128: $i] :
( ( ( ~ ( member @ SV128 @ ( compose @ SV224 @ SV265 ) ) )
= $true )
| ( ( SV128
= ( ordered_pair @ ( f29 @ SV128 @ SV224 @ SV265 ) @ ( f30 @ SV128 @ SV224 @ SV265 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[863]) ).
thf(965,plain,
! [SV266: $i,SV225: $i,SV129: $i] :
( ( ( ~ ( member @ SV129 @ ( compose @ SV225 @ SV266 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ ( f29 @ SV129 @ SV225 @ SV266 ) @ ( f31 @ SV129 @ SV225 @ SV266 ) ) @ SV225 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[864]) ).
thf(966,plain,
! [SV267: $i,SV226: $i,SV130: $i] :
( ( ( ~ ( member @ SV130 @ ( compose @ SV226 @ SV267 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ ( f31 @ SV130 @ SV226 @ SV267 ) @ ( f30 @ SV130 @ SV226 @ SV267 ) ) @ SV267 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[865]) ).
thf(967,plain,
! [SV287: $i,SV268: $i,SV227: $i,SV131: $i] :
( ( ( member @ SV131 @ ( compose @ SV227 @ SV268 ) )
| ~ ( little_set @ SV131 )
| ~ ( little_set @ SV287 )
| ! [SY607: $i] :
( ~ ( little_set @ SY607 )
| ! [SY608: $i] :
( ~ ( little_set @ SY608 )
| ( SV131
!= ( ordered_pair @ SV287 @ SY607 ) )
| ~ ( member @ ( ordered_pair @ SV287 @ SY608 ) @ SV227 )
| ~ ( member @ ( ordered_pair @ SY608 @ SY607 ) @ SV268 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(968,plain,
! [SV269: $i,SV228: $i,SV132: $i] :
( ( ( ! [SY589: $i,SY590: $i] :
~ ( homomorphism @ SV132 @ SV228 @ SV269 @ SY589 @ SY590 ) )
= $true )
| ( ( closed @ SV228 @ SV269 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[867]) ).
thf(969,plain,
! [SV288: $i,SV270: $i,SV229: $i,SV133: $i] :
( ( ! [SY609: $i] :
( ~ ( homomorphism @ SV133 @ SV229 @ SV270 @ SV288 @ SY609 )
| ( closed @ SV288 @ SY609 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(970,plain,
! [SV289: $i,SV271: $i,SV230: $i,SV134: $i] :
( ( ! [SY610: $i] :
~ ( homomorphism @ SV134 @ SV230 @ SV271 @ SV289 @ SY610 )
| ( maps @ SV134 @ SV230 @ SV289 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(971,plain,
! [SV290: $i,SV272: $i,SV231: $i,SV135: $i] :
( ( ! [SY611: $i] :
( ~ ( homomorphism @ SV135 @ SV231 @ SV272 @ SV290 @ SY611 )
| ! [SY597: $i] :
( ~ ( member @ SY597 @ SV231 )
| ! [SY598: $i] :
( ~ ( member @ SY598 @ SV231 )
| ( ( apply @ SV135 @ ( apply_to_two_arguments @ SV272 @ SY597 @ SY598 ) )
= ( apply_to_two_arguments @ SY611 @ ( apply @ SV135 @ SY597 ) @ ( apply @ SV135 @ SY598 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[870]) ).
thf(972,plain,
! [SV291: $i,SV273: $i,SV232: $i,SV136: $i] :
( ( ! [SY614: $i] :
( ( homomorphism @ SV136 @ SV232 @ SV273 @ SV291 @ SY614 )
| ~ ( closed @ SV232 @ SV273 )
| ~ ( closed @ SV291 @ SY614 )
| ~ ( maps @ SV136 @ SV232 @ SV291 )
| ( member @ ( f32 @ SV136 @ SV232 @ SV273 @ SV291 @ SY614 ) @ SV232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[871]) ).
thf(973,plain,
! [SV292: $i,SV274: $i,SV233: $i,SV137: $i] :
( ( ! [SY615: $i] :
( ( homomorphism @ SV137 @ SV233 @ SV274 @ SV292 @ SY615 )
| ~ ( closed @ SV233 @ SV274 )
| ~ ( closed @ SV292 @ SY615 )
| ~ ( maps @ SV137 @ SV233 @ SV292 )
| ( member @ ( f33 @ SV137 @ SV233 @ SV274 @ SV292 @ SY615 ) @ SV233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[872]) ).
thf(974,plain,
! [SV293: $i,SV275: $i,SV234: $i,SV138: $i] :
( ( ! [SY616: $i] :
( ( homomorphism @ SV138 @ SV234 @ SV275 @ SV293 @ SY616 )
| ~ ( closed @ SV234 @ SV275 )
| ~ ( closed @ SV293 @ SY616 )
| ~ ( maps @ SV138 @ SV234 @ SV293 )
| ( ( apply @ SV138 @ ( apply_to_two_arguments @ SV275 @ ( f32 @ SV138 @ SV234 @ SV275 @ SV293 @ SY616 ) @ ( f33 @ SV138 @ SV234 @ SV275 @ SV293 @ SY616 ) ) )
!= ( apply_to_two_arguments @ SY616 @ ( apply @ SV138 @ ( f32 @ SV138 @ SV234 @ SV275 @ SV293 @ SY616 ) ) @ ( apply @ SV138 @ ( f33 @ SV138 @ SV234 @ SV275 @ SV293 @ SY616 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[873]) ).
thf(975,plain,
! [SV141: $i,SV4: $i] :
( ( ( ~ ( member @ ( f1 @ SV4 @ SV141 ) @ SV141 ) )
= $true )
| ( ( SV4 = SV141 )
= $true )
| ( ( member @ ( f1 @ SV4 @ SV141 ) @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[876]) ).
thf(976,plain,
! [SV236: $i,SV142: $i,SV5: $i] :
( ( ( member @ SV5 @ ( non_ordered_pair @ SV142 @ SV236 ) )
= $false )
| ( ( ( SV5 = SV142 )
| ( SV5 = SV236 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[877]) ).
thf(977,plain,
! [SV276: $i,SV143: $i,SV6: $i] :
( ( ( ~ ( little_set @ SV6 ) )
= $true )
| ( ( SV6 != SV143 )
= $true )
| ( ( member @ SV6 @ ( non_ordered_pair @ SV143 @ SV276 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[878]) ).
thf(978,plain,
! [SV144: $i,SV237: $i,SV7: $i] :
( ( ( ~ ( little_set @ SV7 ) )
= $true )
| ( ( SV7 != SV237 )
= $true )
| ( ( member @ SV7 @ ( non_ordered_pair @ SV144 @ SV237 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[879]) ).
thf(979,plain,
! [SV14: $i,SV238: $i] :
( ( ( little_set @ SV238 )
= $false )
| ( ( ! [SY577: $i] :
( ~ ( little_set @ SY577 )
| ( SV14
!= ( ordered_pair @ SV238 @ SY577 ) ) ) )
= $true )
| ( ( ordered_pair_predicate @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[880]) ).
thf(980,plain,
! [SV19: $i,SV151: $i,SV277: $i] :
( ( ( ~ ( little_set @ SV277 ) )
= $true )
| ( ( ! [SY605: $i] :
( ~ ( little_set @ SY605 )
| ( SV151
!= ( ordered_pair @ SV277 @ SY605 ) )
| ~ ( member @ SV19 @ SV277 ) ) )
= $true )
| ( ( member @ SV19 @ ( first @ SV151 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[885]) ).
thf(981,plain,
! [SV24: $i,SV156: $i,SV278: $i] :
( ( ( ~ ( little_set @ SV278 ) )
= $true )
| ( ( ! [SY606: $i] :
( ~ ( little_set @ SY606 )
| ( SV156
!= ( ordered_pair @ SV278 @ SY606 ) )
| ~ ( member @ SV24 @ SY606 ) ) )
= $true )
| ( ( member @ SV24 @ ( second @ SV156 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[890]) ).
thf(982,plain,
! [SV27: $i] :
( ( ( ~ ( ordered_pair_predicate @ SV27 ) )
= $true )
| ( ( ~ ( member @ ( first @ SV27 ) @ ( second @ SV27 ) ) )
= $true )
| ( ( little_set @ SV27 )
= $false )
| ( ( member @ SV27 @ estin )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[891]) ).
thf(983,plain,
! [SV279: $i,SV157: $i,SV28: $i] :
( ( ( member @ SV28 @ ( intersection @ SV157 @ SV279 ) )
= $false )
| ( ( member @ SV28 @ SV157 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[892]) ).
thf(984,plain,
! [SV239: $i,SV158: $i,SV29: $i] :
( ( ( member @ SV29 @ ( intersection @ SV158 @ SV239 ) )
= $false )
| ( ( member @ SV29 @ SV239 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[893]) ).
thf(985,plain,
! [SV240: $i,SV159: $i,SV30: $i] :
( ( ( ~ ( member @ SV30 @ SV159 ) )
= $true )
| ( ( ~ ( member @ SV30 @ SV240 ) )
= $true )
| ( ( member @ SV30 @ ( intersection @ SV159 @ SV240 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[894]) ).
thf(986,plain,
! [SV160: $i,SV31: $i] :
( ( ( member @ SV31 @ SV160 )
= $false )
| ( ( member @ SV31 @ ( complement @ SV160 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[895]) ).
thf(987,plain,
! [SV161: $i,SV32: $i] :
( ( ( little_set @ SV32 )
= $false )
| ( ( member @ SV32 @ SV161 )
= $true )
| ( ( member @ SV32 @ ( complement @ SV161 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[896]) ).
thf(988,plain,
! [SV166: $i,SV37: $i] :
( ( ( little_set @ SV37 )
= $false )
| ( ( ! [SY512: $i] :
( ~ ( ordered_pair_predicate @ SY512 )
| ~ ( member @ SY512 @ SV166 )
| ( SV37
!= ( first @ SY512 ) ) ) )
= $true )
| ( ( member @ SV37 @ ( domain_of @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[900]) ).
thf(989,plain,
! [SV280: $i,SV241: $i,SV38: $i] :
( ( ( member @ SV38 @ ( cross_product @ SV241 @ SV280 ) )
= $false )
| ( ( ordered_pair_predicate @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[901]) ).
thf(990,plain,
! [SV281: $i,SV167: $i,SV39: $i] :
( ( ( member @ SV39 @ ( cross_product @ SV167 @ SV281 ) )
= $false )
| ( ( member @ ( first @ SV39 ) @ SV167 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(991,plain,
! [SV242: $i,SV168: $i,SV40: $i] :
( ( ( member @ SV40 @ ( cross_product @ SV168 @ SV242 ) )
= $false )
| ( ( member @ ( second @ SV40 ) @ SV242 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[903]) ).
thf(992,plain,
! [SV243: $i,SV169: $i,SV41: $i] :
( ( ( ~ ( little_set @ SV41 ) )
= $true )
| ( ( ~ ( ordered_pair_predicate @ SV41 )
| ~ ( member @ ( first @ SV41 ) @ SV169 )
| ~ ( member @ ( second @ SV41 ) @ SV243 ) )
= $true )
| ( ( member @ SV41 @ ( cross_product @ SV169 @ SV243 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[904]) ).
thf(993,plain,
! [SV171: $i,SV44: $i] :
( ( ( little_set @ SV44 )
= $false )
| ( ( ~ ( ordered_pair_predicate @ SV44 )
| ~ ( member @ ( ordered_pair @ ( second @ SV44 ) @ ( first @ SV44 ) ) @ SV171 ) )
= $true )
| ( ( member @ SV44 @ ( converse @ SV171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[907]) ).
thf(994,plain,
! [SV177: $i,SV245: $i,SV50: $i] :
( ( ( ~ ( little_set @ SV50 ) )
= $true )
| ( ( ~ ( little_set @ SV245 )
| ! [SY579: $i] :
( ~ ( little_set @ SY579 )
| ! [SY580: $i] :
( ~ ( little_set @ SY580 )
| ( SV50
!= ( ordered_pair @ SV245 @ ( ordered_pair @ SY579 @ SY580 ) ) )
| ~ ( member @ ( ordered_pair @ SY579 @ ( ordered_pair @ SY580 @ SV245 ) ) @ SV177 ) ) ) )
= $true )
| ( ( member @ SV50 @ ( rotate_right @ SV177 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[913]) ).
thf(995,plain,
! [SV183: $i,SV246: $i,SV56: $i] :
( ( ( ~ ( little_set @ SV56 ) )
= $true )
| ( ( ~ ( little_set @ SV246 )
| ! [SY581: $i] :
( ~ ( little_set @ SY581 )
| ! [SY582: $i] :
( ~ ( little_set @ SY582 )
| ( SV56
!= ( ordered_pair @ SV246 @ ( ordered_pair @ SY581 @ SY582 ) ) )
| ~ ( member @ ( ordered_pair @ SV246 @ ( ordered_pair @ SY582 @ SY581 ) ) @ SV183 ) ) ) )
= $true )
| ( ( member @ SV56 @ ( flip_range_of @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[919]) ).
thf(996,plain,
! [SV63: $i,SV186: $i,SV282: $i] :
( ( ( ~ ( member @ SV282 @ SV186 ) )
= $true )
| ( ( ~ ( member @ SV63 @ SV282 ) )
= $true )
| ( ( member @ SV63 @ ( sigma @ SV186 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[922]) ).
thf(997,plain,
! [SV187: $i,SV65: $i,SV294: $i] :
( ( ( ~ ( member @ SV294 @ SV65 )
| ( member @ SV294 @ SV187 ) )
= $true )
| ( ( subset @ SV65 @ SV187 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[923]) ).
thf(998,plain,
! [SV191: $i,SV69: $i] :
( ( ( SV69 = SV191 )
= $false )
| ( ( proper_subset @ SV69 @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[926]) ).
thf(999,plain,
! [SV192: $i,SV70: $i] :
( ( ( subset @ SV70 @ SV192 )
= $false )
| ( ( SV70 = SV192 )
= $true )
| ( ( proper_subset @ SV70 @ SV192 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[927]) ).
thf(1000,plain,
! [SV194: $i,SV72: $i] :
( ( ( little_set @ SV72 )
= $false )
| ( ( ~ ( subset @ SV72 @ SV194 ) )
= $true )
| ( ( member @ SV72 @ ( powerset @ SV194 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[929]) ).
thf(1001,plain,
! [SV74: $i,SV283: $i] :
( ( ( ~ ( member @ SV283 @ SV74 ) )
= $true )
| ( ( ordered_pair_predicate @ SV283 )
= $true )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[930]) ).
thf(1002,plain,
! [SV77: $i,SV195: $i] :
( ( ( ~ ( little_set @ SV195 ) )
= $true )
| ( ( ! [SY524: $i] :
( ~ ( little_set @ SY524 )
| ! [SY525: $i] :
( ~ ( little_set @ SY525 )
| ~ ( member @ ( ordered_pair @ SV195 @ SY524 ) @ SV77 )
| ~ ( member @ ( ordered_pair @ SV195 @ SY525 ) @ SV77 )
| ( SY524 = SY525 ) ) ) )
= $true )
| ( ( single_valued_set @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[931]) ).
thf(1003,plain,
! [SV86: $i] :
( ( ( single_valued_set @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false )
| ( ( function @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[932]) ).
thf(1004,plain,
! [SV247: $i,SV196: $i,SV87: $i] :
( ( ( member @ SV87 @ ( image @ SV196 @ SV247 ) )
= $false )
| ( ( ordered_pair_predicate @ ( f22 @ SV87 @ SV196 @ SV247 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[933]) ).
thf(1005,plain,
! [SV248: $i,SV197: $i,SV88: $i] :
( ( ( member @ SV88 @ ( image @ SV197 @ SV248 ) )
= $false )
| ( ( member @ ( f22 @ SV88 @ SV197 @ SV248 ) @ SV248 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[934]) ).
thf(1006,plain,
! [SV249: $i,SV198: $i,SV89: $i] :
( ( ( member @ SV89 @ ( image @ SV198 @ SV249 ) )
= $false )
| ( ( member @ ( first @ ( f22 @ SV89 @ SV198 @ SV249 ) ) @ SV198 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[935]) ).
thf(1007,plain,
! [SV250: $i,SV199: $i,SV90: $i] :
( ( ( member @ SV90 @ ( image @ SV199 @ SV250 ) )
= $false )
| ( ( ( second @ ( f22 @ SV90 @ SV199 @ SV250 ) )
= SV90 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[936]) ).
thf(1008,plain,
! [SV200: $i,SV251: $i,SV91: $i] :
( ( ( ~ ( little_set @ SV91 ) )
= $true )
| ( ( ! [SY583: $i] :
( ~ ( ordered_pair_predicate @ SY583 )
| ~ ( member @ SY583 @ SV251 )
| ~ ( member @ ( first @ SY583 ) @ SV200 )
| ( ( second @ SY583 )
!= SV91 ) ) )
= $true )
| ( ( member @ SV91 @ ( image @ SV200 @ SV251 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[937]) ).
thf(1009,plain,
! [SV92: $i,SV284: $i] :
( ( ( ~ ( function @ SV284 ) )
= $true )
| ( ( little_set @ ( image @ SV92 @ SV284 ) )
= $true )
| ( ( little_set @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[938]) ).
thf(1010,plain,
! [SV201: $i,SV93: $i,SV295: $i] :
( ( ( ~ ( member @ SV295 @ SV93 )
| ~ ( member @ SV295 @ SV201 ) )
= $true )
| ( ( disjoint @ SV93 @ SV201 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(1011,plain,
! [SV207: $i,SV103: $i] :
( ( ( little_set @ SV103 )
= $false )
| ( ( ! [SY533: $i] :
( ~ ( ordered_pair_predicate @ SY533 )
| ~ ( member @ SY533 @ SV207 )
| ( SV103
!= ( second @ SY533 ) ) ) )
= $true )
| ( ( member @ SV103 @ ( range_of @ SV207 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[945]) ).
thf(1012,plain,
! [SV106: $i] :
( ( ( ~ ( ordered_pair_predicate @ SV106 ) )
= $true )
| ( ( ( first @ SV106 )
!= ( second @ SV106 ) )
= $true )
| ( ( little_set @ SV106 )
= $false )
| ( ( member @ SV106 @ identity_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[946]) ).
thf(1013,plain,
! [SV110: $i] :
( ( ( function @ ( converse @ SV110 ) )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( one_to_one_function @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[947]) ).
thf(1014,plain,
! [SV252: $i,SV209: $i,SV111: $i] :
( ( ( member @ SV111 @ ( apply @ SV209 @ SV252 ) )
= $false )
| ( ( ordered_pair_predicate @ ( f28 @ SV111 @ SV209 @ SV252 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[948]) ).
thf(1015,plain,
! [SV253: $i,SV210: $i,SV112: $i] :
( ( ( member @ SV112 @ ( apply @ SV210 @ SV253 ) )
= $false )
| ( ( member @ ( f28 @ SV112 @ SV210 @ SV253 ) @ SV210 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[949]) ).
thf(1016,plain,
! [SV254: $i,SV211: $i,SV113: $i] :
( ( ( member @ SV113 @ ( apply @ SV211 @ SV254 ) )
= $false )
| ( ( ( first @ ( f28 @ SV113 @ SV211 @ SV254 ) )
= SV254 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[950]) ).
thf(1017,plain,
! [SV255: $i,SV212: $i,SV114: $i] :
( ( ( member @ SV114 @ ( apply @ SV212 @ SV255 ) )
= $false )
| ( ( member @ SV114 @ ( second @ ( f28 @ SV114 @ SV212 @ SV255 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[951]) ).
thf(1018,plain,
! [SV115: $i,SV256: $i,SV213: $i,SV296: $i] :
( ( ( ~ ( ordered_pair_predicate @ SV296 )
| ~ ( member @ SV296 @ SV213 )
| ( ( first @ SV296 )
!= SV256 )
| ~ ( member @ SV115 @ ( second @ SV296 ) ) )
= $true )
| ( ( member @ SV115 @ ( apply @ SV213 @ SV256 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1019,plain,
! [SV285: $i,SV258: $i,SV117: $i] :
( ( ( maps @ SV117 @ SV258 @ SV285 )
= $false )
| ( ( function @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[953]) ).
thf(1020,plain,
! [SV286: $i,SV215: $i,SV118: $i] :
( ( ( maps @ SV118 @ SV215 @ SV286 )
= $false )
| ( ( ( domain_of @ SV118 )
= SV215 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[954]) ).
thf(1021,plain,
! [SV259: $i,SV216: $i,SV119: $i] :
( ( ( maps @ SV119 @ SV216 @ SV259 )
= $false )
| ( ( subset @ ( range_of @ SV119 ) @ SV259 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[955]) ).
thf(1022,plain,
! [SV260: $i,SV217: $i,SV120: $i] :
( ( ( ~ ( function @ SV120 ) )
= $true )
| ( ( ( ( domain_of @ SV120 )
!= SV217 )
| ~ ( subset @ ( range_of @ SV120 ) @ SV260 ) )
= $true )
| ( ( maps @ SV120 @ SV217 @ SV260 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[956]) ).
thf(1023,plain,
! [SV220: $i,SV124: $i] :
( ( ( little_set @ SV124 )
= $false )
| ( ( ~ ( little_set @ SV220 )
| ~ ( maps @ SV220 @ ( cross_product @ SV124 @ SV124 ) @ SV124 ) )
= $true )
| ( ( closed @ SV124 @ SV220 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[960]) ).
thf(1024,plain,
! [SV262: $i,SV221: $i,SV125: $i] :
( ( ( member @ SV125 @ ( compose @ SV221 @ SV262 ) )
= $false )
| ( ( little_set @ ( f29 @ SV125 @ SV221 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[961]) ).
thf(1025,plain,
! [SV263: $i,SV222: $i,SV126: $i] :
( ( ( member @ SV126 @ ( compose @ SV222 @ SV263 ) )
= $false )
| ( ( little_set @ ( f30 @ SV126 @ SV222 @ SV263 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[962]) ).
thf(1026,plain,
! [SV264: $i,SV223: $i,SV127: $i] :
( ( ( member @ SV127 @ ( compose @ SV223 @ SV264 ) )
= $false )
| ( ( little_set @ ( f31 @ SV127 @ SV223 @ SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[963]) ).
thf(1027,plain,
! [SV265: $i,SV224: $i,SV128: $i] :
( ( ( member @ SV128 @ ( compose @ SV224 @ SV265 ) )
= $false )
| ( ( SV128
= ( ordered_pair @ ( f29 @ SV128 @ SV224 @ SV265 ) @ ( f30 @ SV128 @ SV224 @ SV265 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[964]) ).
thf(1028,plain,
! [SV266: $i,SV225: $i,SV129: $i] :
( ( ( member @ SV129 @ ( compose @ SV225 @ SV266 ) )
= $false )
| ( ( member @ ( ordered_pair @ ( f29 @ SV129 @ SV225 @ SV266 ) @ ( f31 @ SV129 @ SV225 @ SV266 ) ) @ SV225 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[965]) ).
thf(1029,plain,
! [SV267: $i,SV226: $i,SV130: $i] :
( ( ( member @ SV130 @ ( compose @ SV226 @ SV267 ) )
= $false )
| ( ( member @ ( ordered_pair @ ( f31 @ SV130 @ SV226 @ SV267 ) @ ( f30 @ SV130 @ SV226 @ SV267 ) ) @ SV267 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[966]) ).
thf(1030,plain,
! [SV287: $i,SV268: $i,SV227: $i,SV131: $i] :
( ( ( member @ SV131 @ ( compose @ SV227 @ SV268 ) )
= $true )
| ( ( ~ ( little_set @ SV131 )
| ~ ( little_set @ SV287 )
| ! [SY607: $i] :
( ~ ( little_set @ SY607 )
| ! [SY608: $i] :
( ~ ( little_set @ SY608 )
| ( SV131
!= ( ordered_pair @ SV287 @ SY607 ) )
| ~ ( member @ ( ordered_pair @ SV287 @ SY608 ) @ SV227 )
| ~ ( member @ ( ordered_pair @ SY608 @ SY607 ) @ SV268 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[967]) ).
thf(1031,plain,
! [SV297: $i,SV269: $i,SV228: $i,SV132: $i] :
( ( ( ! [SY617: $i] :
~ ( homomorphism @ SV132 @ SV228 @ SV269 @ SV297 @ SY617 ) )
= $true )
| ( ( closed @ SV228 @ SV269 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1032,plain,
! [SV298: $i,SV288: $i,SV270: $i,SV229: $i,SV133: $i] :
( ( ~ ( homomorphism @ SV133 @ SV229 @ SV270 @ SV288 @ SV298 )
| ( closed @ SV288 @ SV298 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1033,plain,
! [SV289: $i,SV271: $i,SV230: $i,SV134: $i] :
( ( ( ! [SY610: $i] :
~ ( homomorphism @ SV134 @ SV230 @ SV271 @ SV289 @ SY610 ) )
= $true )
| ( ( maps @ SV134 @ SV230 @ SV289 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[970]) ).
thf(1034,plain,
! [SV299: $i,SV290: $i,SV272: $i,SV231: $i,SV135: $i] :
( ( ~ ( homomorphism @ SV135 @ SV231 @ SV272 @ SV290 @ SV299 )
| ! [SY618: $i] :
( ~ ( member @ SY618 @ SV231 )
| ! [SY619: $i] :
( ~ ( member @ SY619 @ SV231 )
| ( ( apply @ SV135 @ ( apply_to_two_arguments @ SV272 @ SY618 @ SY619 ) )
= ( apply_to_two_arguments @ SV299 @ ( apply @ SV135 @ SY618 ) @ ( apply @ SV135 @ SY619 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1035,plain,
! [SV300: $i,SV291: $i,SV273: $i,SV232: $i,SV136: $i] :
( ( ( homomorphism @ SV136 @ SV232 @ SV273 @ SV291 @ SV300 )
| ~ ( closed @ SV232 @ SV273 )
| ~ ( closed @ SV291 @ SV300 )
| ~ ( maps @ SV136 @ SV232 @ SV291 )
| ( member @ ( f32 @ SV136 @ SV232 @ SV273 @ SV291 @ SV300 ) @ SV232 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1036,plain,
! [SV301: $i,SV292: $i,SV274: $i,SV233: $i,SV137: $i] :
( ( ( homomorphism @ SV137 @ SV233 @ SV274 @ SV292 @ SV301 )
| ~ ( closed @ SV233 @ SV274 )
| ~ ( closed @ SV292 @ SV301 )
| ~ ( maps @ SV137 @ SV233 @ SV292 )
| ( member @ ( f33 @ SV137 @ SV233 @ SV274 @ SV292 @ SV301 ) @ SV233 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1037,plain,
! [SV302: $i,SV293: $i,SV275: $i,SV234: $i,SV138: $i] :
( ( ( homomorphism @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 )
| ~ ( closed @ SV234 @ SV275 )
| ~ ( closed @ SV293 @ SV302 )
| ~ ( maps @ SV138 @ SV234 @ SV293 )
| ( ( apply @ SV138 @ ( apply_to_two_arguments @ SV275 @ ( f32 @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 ) @ ( f33 @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 ) ) )
!= ( apply_to_two_arguments @ SV302 @ ( apply @ SV138 @ ( f32 @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 ) ) @ ( apply @ SV138 @ ( f33 @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1038,plain,
! [SV141: $i,SV4: $i] :
( ( ( member @ ( f1 @ SV4 @ SV141 ) @ SV141 )
= $false )
| ( ( SV4 = SV141 )
= $true )
| ( ( member @ ( f1 @ SV4 @ SV141 ) @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[975]) ).
thf(1039,plain,
! [SV236: $i,SV142: $i,SV5: $i] :
( ( ( SV5 = SV142 )
= $true )
| ( ( SV5 = SV236 )
= $true )
| ( ( member @ SV5 @ ( non_ordered_pair @ SV142 @ SV236 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[976]) ).
thf(1040,plain,
! [SV276: $i,SV143: $i,SV6: $i] :
( ( ( little_set @ SV6 )
= $false )
| ( ( SV6 != SV143 )
= $true )
| ( ( member @ SV6 @ ( non_ordered_pair @ SV143 @ SV276 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[977]) ).
thf(1041,plain,
! [SV144: $i,SV237: $i,SV7: $i] :
( ( ( little_set @ SV7 )
= $false )
| ( ( SV7 != SV237 )
= $true )
| ( ( member @ SV7 @ ( non_ordered_pair @ SV144 @ SV237 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[978]) ).
thf(1042,plain,
! [SV238: $i,SV14: $i,SV303: $i] :
( ( ( ~ ( little_set @ SV303 )
| ( SV14
!= ( ordered_pair @ SV238 @ SV303 ) ) )
= $true )
| ( ( little_set @ SV238 )
= $false )
| ( ( ordered_pair_predicate @ SV14 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(1043,plain,
! [SV19: $i,SV151: $i,SV277: $i] :
( ( ( little_set @ SV277 )
= $false )
| ( ( ! [SY605: $i] :
( ~ ( little_set @ SY605 )
| ( SV151
!= ( ordered_pair @ SV277 @ SY605 ) )
| ~ ( member @ SV19 @ SV277 ) ) )
= $true )
| ( ( member @ SV19 @ ( first @ SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[980]) ).
thf(1044,plain,
! [SV24: $i,SV156: $i,SV278: $i] :
( ( ( little_set @ SV278 )
= $false )
| ( ( ! [SY606: $i] :
( ~ ( little_set @ SY606 )
| ( SV156
!= ( ordered_pair @ SV278 @ SY606 ) )
| ~ ( member @ SV24 @ SY606 ) ) )
= $true )
| ( ( member @ SV24 @ ( second @ SV156 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[981]) ).
thf(1045,plain,
! [SV27: $i] :
( ( ( ordered_pair_predicate @ SV27 )
= $false )
| ( ( ~ ( member @ ( first @ SV27 ) @ ( second @ SV27 ) ) )
= $true )
| ( ( little_set @ SV27 )
= $false )
| ( ( member @ SV27 @ estin )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(1046,plain,
! [SV240: $i,SV159: $i,SV30: $i] :
( ( ( member @ SV30 @ SV159 )
= $false )
| ( ( ~ ( member @ SV30 @ SV240 ) )
= $true )
| ( ( member @ SV30 @ ( intersection @ SV159 @ SV240 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[985]) ).
thf(1047,plain,
! [SV37: $i,SV166: $i,SV304: $i] :
( ( ( ~ ( ordered_pair_predicate @ SV304 )
| ~ ( member @ SV304 @ SV166 )
| ( SV37
!= ( first @ SV304 ) ) )
= $true )
| ( ( little_set @ SV37 )
= $false )
| ( ( member @ SV37 @ ( domain_of @ SV166 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1048,plain,
! [SV243: $i,SV169: $i,SV41: $i] :
( ( ( little_set @ SV41 )
= $false )
| ( ( ~ ( ordered_pair_predicate @ SV41 )
| ~ ( member @ ( first @ SV41 ) @ SV169 )
| ~ ( member @ ( second @ SV41 ) @ SV243 ) )
= $true )
| ( ( member @ SV41 @ ( cross_product @ SV169 @ SV243 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[992]) ).
thf(1049,plain,
! [SV171: $i,SV44: $i] :
( ( ( ~ ( ordered_pair_predicate @ SV44 ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ ( second @ SV44 ) @ ( first @ SV44 ) ) @ SV171 ) )
= $true )
| ( ( little_set @ SV44 )
= $false )
| ( ( member @ SV44 @ ( converse @ SV171 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[993]) ).
thf(1050,plain,
! [SV177: $i,SV245: $i,SV50: $i] :
( ( ( little_set @ SV50 )
= $false )
| ( ( ~ ( little_set @ SV245 )
| ! [SY579: $i] :
( ~ ( little_set @ SY579 )
| ! [SY580: $i] :
( ~ ( little_set @ SY580 )
| ( SV50
!= ( ordered_pair @ SV245 @ ( ordered_pair @ SY579 @ SY580 ) ) )
| ~ ( member @ ( ordered_pair @ SY579 @ ( ordered_pair @ SY580 @ SV245 ) ) @ SV177 ) ) ) )
= $true )
| ( ( member @ SV50 @ ( rotate_right @ SV177 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[994]) ).
thf(1051,plain,
! [SV183: $i,SV246: $i,SV56: $i] :
( ( ( little_set @ SV56 )
= $false )
| ( ( ~ ( little_set @ SV246 )
| ! [SY581: $i] :
( ~ ( little_set @ SY581 )
| ! [SY582: $i] :
( ~ ( little_set @ SY582 )
| ( SV56
!= ( ordered_pair @ SV246 @ ( ordered_pair @ SY581 @ SY582 ) ) )
| ~ ( member @ ( ordered_pair @ SV246 @ ( ordered_pair @ SY582 @ SY581 ) ) @ SV183 ) ) ) )
= $true )
| ( ( member @ SV56 @ ( flip_range_of @ SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[995]) ).
thf(1052,plain,
! [SV63: $i,SV186: $i,SV282: $i] :
( ( ( member @ SV282 @ SV186 )
= $false )
| ( ( ~ ( member @ SV63 @ SV282 ) )
= $true )
| ( ( member @ SV63 @ ( sigma @ SV186 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[996]) ).
thf(1053,plain,
! [SV187: $i,SV65: $i,SV294: $i] :
( ( ( ~ ( member @ SV294 @ SV65 ) )
= $true )
| ( ( member @ SV294 @ SV187 )
= $true )
| ( ( subset @ SV65 @ SV187 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[997]) ).
thf(1054,plain,
! [SV194: $i,SV72: $i] :
( ( ( subset @ SV72 @ SV194 )
= $false )
| ( ( little_set @ SV72 )
= $false )
| ( ( member @ SV72 @ ( powerset @ SV194 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1000]) ).
thf(1055,plain,
! [SV74: $i,SV283: $i] :
( ( ( member @ SV283 @ SV74 )
= $false )
| ( ( ordered_pair_predicate @ SV283 )
= $true )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1001]) ).
thf(1056,plain,
! [SV77: $i,SV195: $i] :
( ( ( little_set @ SV195 )
= $false )
| ( ( ! [SY524: $i] :
( ~ ( little_set @ SY524 )
| ! [SY525: $i] :
( ~ ( little_set @ SY525 )
| ~ ( member @ ( ordered_pair @ SV195 @ SY524 ) @ SV77 )
| ~ ( member @ ( ordered_pair @ SV195 @ SY525 ) @ SV77 )
| ( SY524 = SY525 ) ) ) )
= $true )
| ( ( single_valued_set @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1002]) ).
thf(1057,plain,
! [SV200: $i,SV251: $i,SV91: $i] :
( ( ( little_set @ SV91 )
= $false )
| ( ( ! [SY583: $i] :
( ~ ( ordered_pair_predicate @ SY583 )
| ~ ( member @ SY583 @ SV251 )
| ~ ( member @ ( first @ SY583 ) @ SV200 )
| ( ( second @ SY583 )
!= SV91 ) ) )
= $true )
| ( ( member @ SV91 @ ( image @ SV200 @ SV251 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1008]) ).
thf(1058,plain,
! [SV92: $i,SV284: $i] :
( ( ( function @ SV284 )
= $false )
| ( ( little_set @ ( image @ SV92 @ SV284 ) )
= $true )
| ( ( little_set @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1009]) ).
thf(1059,plain,
! [SV201: $i,SV93: $i,SV295: $i] :
( ( ( ~ ( member @ SV295 @ SV93 ) )
= $true )
| ( ( ~ ( member @ SV295 @ SV201 ) )
= $true )
| ( ( disjoint @ SV93 @ SV201 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1010]) ).
thf(1060,plain,
! [SV103: $i,SV207: $i,SV305: $i] :
( ( ( ~ ( ordered_pair_predicate @ SV305 )
| ~ ( member @ SV305 @ SV207 )
| ( SV103
!= ( second @ SV305 ) ) )
= $true )
| ( ( little_set @ SV103 )
= $false )
| ( ( member @ SV103 @ ( range_of @ SV207 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1061,plain,
! [SV106: $i] :
( ( ( ordered_pair_predicate @ SV106 )
= $false )
| ( ( ( first @ SV106 )
!= ( second @ SV106 ) )
= $true )
| ( ( little_set @ SV106 )
= $false )
| ( ( member @ SV106 @ identity_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1012]) ).
thf(1062,plain,
! [SV115: $i,SV256: $i,SV213: $i,SV296: $i] :
( ( ( ~ ( ordered_pair_predicate @ SV296 ) )
= $true )
| ( ( ~ ( member @ SV296 @ SV213 )
| ( ( first @ SV296 )
!= SV256 )
| ~ ( member @ SV115 @ ( second @ SV296 ) ) )
= $true )
| ( ( member @ SV115 @ ( apply @ SV213 @ SV256 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1018]) ).
thf(1063,plain,
! [SV260: $i,SV217: $i,SV120: $i] :
( ( ( function @ SV120 )
= $false )
| ( ( ( ( domain_of @ SV120 )
!= SV217 )
| ~ ( subset @ ( range_of @ SV120 ) @ SV260 ) )
= $true )
| ( ( maps @ SV120 @ SV217 @ SV260 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1022]) ).
thf(1064,plain,
! [SV124: $i,SV220: $i] :
( ( ( ~ ( little_set @ SV220 ) )
= $true )
| ( ( ~ ( maps @ SV220 @ ( cross_product @ SV124 @ SV124 ) @ SV124 ) )
= $true )
| ( ( little_set @ SV124 )
= $false )
| ( ( closed @ SV124 @ SV220 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1023]) ).
thf(1065,plain,
! [SV268: $i,SV227: $i,SV287: $i,SV131: $i] :
( ( ( ~ ( little_set @ SV131 ) )
= $true )
| ( ( ~ ( little_set @ SV287 )
| ! [SY607: $i] :
( ~ ( little_set @ SY607 )
| ! [SY608: $i] :
( ~ ( little_set @ SY608 )
| ( SV131
!= ( ordered_pair @ SV287 @ SY607 ) )
| ~ ( member @ ( ordered_pair @ SV287 @ SY608 ) @ SV227 )
| ~ ( member @ ( ordered_pair @ SY608 @ SY607 ) @ SV268 ) ) ) )
= $true )
| ( ( member @ SV131 @ ( compose @ SV227 @ SV268 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1030]) ).
thf(1066,plain,
! [SV306: $i,SV297: $i,SV269: $i,SV228: $i,SV132: $i] :
( ( ( ~ ( homomorphism @ SV132 @ SV228 @ SV269 @ SV297 @ SV306 ) )
= $true )
| ( ( closed @ SV228 @ SV269 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1067,plain,
! [SV298: $i,SV288: $i,SV270: $i,SV229: $i,SV133: $i] :
( ( ( ~ ( homomorphism @ SV133 @ SV229 @ SV270 @ SV288 @ SV298 ) )
= $true )
| ( ( closed @ SV288 @ SV298 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1032]) ).
thf(1068,plain,
! [SV307: $i,SV289: $i,SV271: $i,SV230: $i,SV134: $i] :
( ( ( ~ ( homomorphism @ SV134 @ SV230 @ SV271 @ SV289 @ SV307 ) )
= $true )
| ( ( maps @ SV134 @ SV230 @ SV289 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1069,plain,
! [SV299: $i,SV290: $i,SV272: $i,SV231: $i,SV135: $i] :
( ( ( ~ ( homomorphism @ SV135 @ SV231 @ SV272 @ SV290 @ SV299 ) )
= $true )
| ( ( ! [SY618: $i] :
( ~ ( member @ SY618 @ SV231 )
| ! [SY619: $i] :
( ~ ( member @ SY619 @ SV231 )
| ( ( apply @ SV135 @ ( apply_to_two_arguments @ SV272 @ SY618 @ SY619 ) )
= ( apply_to_two_arguments @ SV299 @ ( apply @ SV135 @ SY618 ) @ ( apply @ SV135 @ SY619 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1034]) ).
thf(1070,plain,
! [SV300: $i,SV291: $i,SV273: $i,SV232: $i,SV136: $i] :
( ( ( homomorphism @ SV136 @ SV232 @ SV273 @ SV291 @ SV300 )
= $true )
| ( ( ~ ( closed @ SV232 @ SV273 )
| ~ ( closed @ SV291 @ SV300 )
| ~ ( maps @ SV136 @ SV232 @ SV291 )
| ( member @ ( f32 @ SV136 @ SV232 @ SV273 @ SV291 @ SV300 ) @ SV232 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1035]) ).
thf(1071,plain,
! [SV301: $i,SV292: $i,SV274: $i,SV233: $i,SV137: $i] :
( ( ( homomorphism @ SV137 @ SV233 @ SV274 @ SV292 @ SV301 )
= $true )
| ( ( ~ ( closed @ SV233 @ SV274 )
| ~ ( closed @ SV292 @ SV301 )
| ~ ( maps @ SV137 @ SV233 @ SV292 )
| ( member @ ( f33 @ SV137 @ SV233 @ SV274 @ SV292 @ SV301 ) @ SV233 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1036]) ).
thf(1072,plain,
! [SV302: $i,SV293: $i,SV275: $i,SV234: $i,SV138: $i] :
( ( ( homomorphism @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 )
= $true )
| ( ( ~ ( closed @ SV234 @ SV275 )
| ~ ( closed @ SV293 @ SV302 )
| ~ ( maps @ SV138 @ SV234 @ SV293 )
| ( ( apply @ SV138 @ ( apply_to_two_arguments @ SV275 @ ( f32 @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 ) @ ( f33 @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 ) ) )
!= ( apply_to_two_arguments @ SV302 @ ( apply @ SV138 @ ( f32 @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 ) ) @ ( apply @ SV138 @ ( f33 @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1037]) ).
thf(1073,plain,
! [SV276: $i,SV143: $i,SV6: $i] :
( ( ( SV6 = SV143 )
= $false )
| ( ( little_set @ SV6 )
= $false )
| ( ( member @ SV6 @ ( non_ordered_pair @ SV143 @ SV276 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1040]) ).
thf(1074,plain,
! [SV144: $i,SV237: $i,SV7: $i] :
( ( ( SV7 = SV237 )
= $false )
| ( ( little_set @ SV7 )
= $false )
| ( ( member @ SV7 @ ( non_ordered_pair @ SV144 @ SV237 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1041]) ).
thf(1075,plain,
! [SV238: $i,SV14: $i,SV303: $i] :
( ( ( ~ ( little_set @ SV303 ) )
= $true )
| ( ( SV14
!= ( ordered_pair @ SV238 @ SV303 ) )
= $true )
| ( ( little_set @ SV238 )
= $false )
| ( ( ordered_pair_predicate @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1042]) ).
thf(1076,plain,
! [SV19: $i,SV277: $i,SV151: $i,SV308: $i] :
( ( ( ~ ( little_set @ SV308 )
| ( SV151
!= ( ordered_pair @ SV277 @ SV308 ) )
| ~ ( member @ SV19 @ SV277 ) )
= $true )
| ( ( little_set @ SV277 )
= $false )
| ( ( member @ SV19 @ ( first @ SV151 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1077,plain,
! [SV24: $i,SV278: $i,SV156: $i,SV309: $i] :
( ( ( ~ ( little_set @ SV309 )
| ( SV156
!= ( ordered_pair @ SV278 @ SV309 ) )
| ~ ( member @ SV24 @ SV309 ) )
= $true )
| ( ( little_set @ SV278 )
= $false )
| ( ( member @ SV24 @ ( second @ SV156 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1078,plain,
! [SV27: $i] :
( ( ( member @ ( first @ SV27 ) @ ( second @ SV27 ) )
= $false )
| ( ( ordered_pair_predicate @ SV27 )
= $false )
| ( ( little_set @ SV27 )
= $false )
| ( ( member @ SV27 @ estin )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1045]) ).
thf(1079,plain,
! [SV159: $i,SV240: $i,SV30: $i] :
( ( ( member @ SV30 @ SV240 )
= $false )
| ( ( member @ SV30 @ SV159 )
= $false )
| ( ( member @ SV30 @ ( intersection @ SV159 @ SV240 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1046]) ).
thf(1080,plain,
! [SV37: $i,SV166: $i,SV304: $i] :
( ( ( ~ ( ordered_pair_predicate @ SV304 ) )
= $true )
| ( ( ~ ( member @ SV304 @ SV166 )
| ( SV37
!= ( first @ SV304 ) ) )
= $true )
| ( ( little_set @ SV37 )
= $false )
| ( ( member @ SV37 @ ( domain_of @ SV166 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1047]) ).
thf(1081,plain,
! [SV243: $i,SV169: $i,SV41: $i] :
( ( ( ~ ( ordered_pair_predicate @ SV41 ) )
= $true )
| ( ( ~ ( member @ ( first @ SV41 ) @ SV169 )
| ~ ( member @ ( second @ SV41 ) @ SV243 ) )
= $true )
| ( ( little_set @ SV41 )
= $false )
| ( ( member @ SV41 @ ( cross_product @ SV169 @ SV243 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1048]) ).
thf(1082,plain,
! [SV171: $i,SV44: $i] :
( ( ( ordered_pair_predicate @ SV44 )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ ( second @ SV44 ) @ ( first @ SV44 ) ) @ SV171 ) )
= $true )
| ( ( little_set @ SV44 )
= $false )
| ( ( member @ SV44 @ ( converse @ SV171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1049]) ).
thf(1083,plain,
! [SV177: $i,SV50: $i,SV245: $i] :
( ( ( ~ ( little_set @ SV245 ) )
= $true )
| ( ( ! [SY579: $i] :
( ~ ( little_set @ SY579 )
| ! [SY580: $i] :
( ~ ( little_set @ SY580 )
| ( SV50
!= ( ordered_pair @ SV245 @ ( ordered_pair @ SY579 @ SY580 ) ) )
| ~ ( member @ ( ordered_pair @ SY579 @ ( ordered_pair @ SY580 @ SV245 ) ) @ SV177 ) ) ) )
= $true )
| ( ( little_set @ SV50 )
= $false )
| ( ( member @ SV50 @ ( rotate_right @ SV177 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1050]) ).
thf(1084,plain,
! [SV183: $i,SV56: $i,SV246: $i] :
( ( ( ~ ( little_set @ SV246 ) )
= $true )
| ( ( ! [SY581: $i] :
( ~ ( little_set @ SY581 )
| ! [SY582: $i] :
( ~ ( little_set @ SY582 )
| ( SV56
!= ( ordered_pair @ SV246 @ ( ordered_pair @ SY581 @ SY582 ) ) )
| ~ ( member @ ( ordered_pair @ SV246 @ ( ordered_pair @ SY582 @ SY581 ) ) @ SV183 ) ) ) )
= $true )
| ( ( little_set @ SV56 )
= $false )
| ( ( member @ SV56 @ ( flip_range_of @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1051]) ).
thf(1085,plain,
! [SV186: $i,SV282: $i,SV63: $i] :
( ( ( member @ SV63 @ SV282 )
= $false )
| ( ( member @ SV282 @ SV186 )
= $false )
| ( ( member @ SV63 @ ( sigma @ SV186 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1052]) ).
thf(1086,plain,
! [SV187: $i,SV65: $i,SV294: $i] :
( ( ( member @ SV294 @ SV65 )
= $false )
| ( ( member @ SV294 @ SV187 )
= $true )
| ( ( subset @ SV65 @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1053]) ).
thf(1087,plain,
! [SV77: $i,SV195: $i,SV310: $i] :
( ( ( ~ ( little_set @ SV310 )
| ! [SY620: $i] :
( ~ ( little_set @ SY620 )
| ~ ( member @ ( ordered_pair @ SV195 @ SV310 ) @ SV77 )
| ~ ( member @ ( ordered_pair @ SV195 @ SY620 ) @ SV77 )
| ( SV310 = SY620 ) ) )
= $true )
| ( ( little_set @ SV195 )
= $false )
| ( ( single_valued_set @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1088,plain,
! [SV91: $i,SV200: $i,SV251: $i,SV311: $i] :
( ( ( ~ ( ordered_pair_predicate @ SV311 )
| ~ ( member @ SV311 @ SV251 )
| ~ ( member @ ( first @ SV311 ) @ SV200 )
| ( ( second @ SV311 )
!= SV91 ) )
= $true )
| ( ( little_set @ SV91 )
= $false )
| ( ( member @ SV91 @ ( image @ SV200 @ SV251 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1057]) ).
thf(1089,plain,
! [SV201: $i,SV93: $i,SV295: $i] :
( ( ( member @ SV295 @ SV93 )
= $false )
| ( ( ~ ( member @ SV295 @ SV201 ) )
= $true )
| ( ( disjoint @ SV93 @ SV201 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1059]) ).
thf(1090,plain,
! [SV103: $i,SV207: $i,SV305: $i] :
( ( ( ~ ( ordered_pair_predicate @ SV305 ) )
= $true )
| ( ( ~ ( member @ SV305 @ SV207 )
| ( SV103
!= ( second @ SV305 ) ) )
= $true )
| ( ( little_set @ SV103 )
= $false )
| ( ( member @ SV103 @ ( range_of @ SV207 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1060]) ).
thf(1091,plain,
! [SV106: $i] :
( ( ( ( first @ SV106 )
= ( second @ SV106 ) )
= $false )
| ( ( ordered_pair_predicate @ SV106 )
= $false )
| ( ( little_set @ SV106 )
= $false )
| ( ( member @ SV106 @ identity_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1061]) ).
thf(1092,plain,
! [SV115: $i,SV256: $i,SV213: $i,SV296: $i] :
( ( ( ordered_pair_predicate @ SV296 )
= $false )
| ( ( ~ ( member @ SV296 @ SV213 )
| ( ( first @ SV296 )
!= SV256 )
| ~ ( member @ SV115 @ ( second @ SV296 ) ) )
= $true )
| ( ( member @ SV115 @ ( apply @ SV213 @ SV256 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1062]) ).
thf(1093,plain,
! [SV260: $i,SV217: $i,SV120: $i] :
( ( ( ( domain_of @ SV120 )
!= SV217 )
= $true )
| ( ( ~ ( subset @ ( range_of @ SV120 ) @ SV260 ) )
= $true )
| ( ( function @ SV120 )
= $false )
| ( ( maps @ SV120 @ SV217 @ SV260 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1063]) ).
thf(1094,plain,
! [SV124: $i,SV220: $i] :
( ( ( little_set @ SV220 )
= $false )
| ( ( ~ ( maps @ SV220 @ ( cross_product @ SV124 @ SV124 ) @ SV124 ) )
= $true )
| ( ( little_set @ SV124 )
= $false )
| ( ( closed @ SV124 @ SV220 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1064]) ).
thf(1095,plain,
! [SV268: $i,SV227: $i,SV287: $i,SV131: $i] :
( ( ( little_set @ SV131 )
= $false )
| ( ( ~ ( little_set @ SV287 )
| ! [SY607: $i] :
( ~ ( little_set @ SY607 )
| ! [SY608: $i] :
( ~ ( little_set @ SY608 )
| ( SV131
!= ( ordered_pair @ SV287 @ SY607 ) )
| ~ ( member @ ( ordered_pair @ SV287 @ SY608 ) @ SV227 )
| ~ ( member @ ( ordered_pair @ SY608 @ SY607 ) @ SV268 ) ) ) )
= $true )
| ( ( member @ SV131 @ ( compose @ SV227 @ SV268 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1065]) ).
thf(1096,plain,
! [SV306: $i,SV297: $i,SV269: $i,SV228: $i,SV132: $i] :
( ( ( homomorphism @ SV132 @ SV228 @ SV269 @ SV297 @ SV306 )
= $false )
| ( ( closed @ SV228 @ SV269 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1066]) ).
thf(1097,plain,
! [SV298: $i,SV288: $i,SV270: $i,SV229: $i,SV133: $i] :
( ( ( homomorphism @ SV133 @ SV229 @ SV270 @ SV288 @ SV298 )
= $false )
| ( ( closed @ SV288 @ SV298 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1067]) ).
thf(1098,plain,
! [SV307: $i,SV289: $i,SV271: $i,SV230: $i,SV134: $i] :
( ( ( homomorphism @ SV134 @ SV230 @ SV271 @ SV289 @ SV307 )
= $false )
| ( ( maps @ SV134 @ SV230 @ SV289 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1068]) ).
thf(1099,plain,
! [SV299: $i,SV290: $i,SV272: $i,SV231: $i,SV135: $i] :
( ( ( homomorphism @ SV135 @ SV231 @ SV272 @ SV290 @ SV299 )
= $false )
| ( ( ! [SY618: $i] :
( ~ ( member @ SY618 @ SV231 )
| ! [SY619: $i] :
( ~ ( member @ SY619 @ SV231 )
| ( ( apply @ SV135 @ ( apply_to_two_arguments @ SV272 @ SY618 @ SY619 ) )
= ( apply_to_two_arguments @ SV299 @ ( apply @ SV135 @ SY618 ) @ ( apply @ SV135 @ SY619 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1069]) ).
thf(1100,plain,
! [SV136: $i,SV300: $i,SV291: $i,SV273: $i,SV232: $i] :
( ( ( ~ ( closed @ SV232 @ SV273 ) )
= $true )
| ( ( ~ ( closed @ SV291 @ SV300 )
| ~ ( maps @ SV136 @ SV232 @ SV291 )
| ( member @ ( f32 @ SV136 @ SV232 @ SV273 @ SV291 @ SV300 ) @ SV232 ) )
= $true )
| ( ( homomorphism @ SV136 @ SV232 @ SV273 @ SV291 @ SV300 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1070]) ).
thf(1101,plain,
! [SV137: $i,SV301: $i,SV292: $i,SV274: $i,SV233: $i] :
( ( ( ~ ( closed @ SV233 @ SV274 ) )
= $true )
| ( ( ~ ( closed @ SV292 @ SV301 )
| ~ ( maps @ SV137 @ SV233 @ SV292 )
| ( member @ ( f33 @ SV137 @ SV233 @ SV274 @ SV292 @ SV301 ) @ SV233 ) )
= $true )
| ( ( homomorphism @ SV137 @ SV233 @ SV274 @ SV292 @ SV301 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1071]) ).
thf(1102,plain,
! [SV138: $i,SV302: $i,SV293: $i,SV275: $i,SV234: $i] :
( ( ( ~ ( closed @ SV234 @ SV275 ) )
= $true )
| ( ( ~ ( closed @ SV293 @ SV302 )
| ~ ( maps @ SV138 @ SV234 @ SV293 )
| ( ( apply @ SV138 @ ( apply_to_two_arguments @ SV275 @ ( f32 @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 ) @ ( f33 @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 ) ) )
!= ( apply_to_two_arguments @ SV302 @ ( apply @ SV138 @ ( f32 @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 ) ) @ ( apply @ SV138 @ ( f33 @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 ) ) ) ) )
= $true )
| ( ( homomorphism @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1072]) ).
thf(1103,plain,
! [SV238: $i,SV14: $i,SV303: $i] :
( ( ( little_set @ SV303 )
= $false )
| ( ( SV14
!= ( ordered_pair @ SV238 @ SV303 ) )
= $true )
| ( ( little_set @ SV238 )
= $false )
| ( ( ordered_pair_predicate @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1075]) ).
thf(1104,plain,
! [SV19: $i,SV277: $i,SV151: $i,SV308: $i] :
( ( ( ~ ( little_set @ SV308 ) )
= $true )
| ( ( ( SV151
!= ( ordered_pair @ SV277 @ SV308 ) )
| ~ ( member @ SV19 @ SV277 ) )
= $true )
| ( ( little_set @ SV277 )
= $false )
| ( ( member @ SV19 @ ( first @ SV151 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1076]) ).
thf(1105,plain,
! [SV24: $i,SV278: $i,SV156: $i,SV309: $i] :
( ( ( ~ ( little_set @ SV309 ) )
= $true )
| ( ( ( SV156
!= ( ordered_pair @ SV278 @ SV309 ) )
| ~ ( member @ SV24 @ SV309 ) )
= $true )
| ( ( little_set @ SV278 )
= $false )
| ( ( member @ SV24 @ ( second @ SV156 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1077]) ).
thf(1106,plain,
! [SV37: $i,SV166: $i,SV304: $i] :
( ( ( ordered_pair_predicate @ SV304 )
= $false )
| ( ( ~ ( member @ SV304 @ SV166 )
| ( SV37
!= ( first @ SV304 ) ) )
= $true )
| ( ( little_set @ SV37 )
= $false )
| ( ( member @ SV37 @ ( domain_of @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1080]) ).
thf(1107,plain,
! [SV243: $i,SV169: $i,SV41: $i] :
( ( ( ordered_pair_predicate @ SV41 )
= $false )
| ( ( ~ ( member @ ( first @ SV41 ) @ SV169 )
| ~ ( member @ ( second @ SV41 ) @ SV243 ) )
= $true )
| ( ( little_set @ SV41 )
= $false )
| ( ( member @ SV41 @ ( cross_product @ SV169 @ SV243 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1081]) ).
thf(1108,plain,
! [SV171: $i,SV44: $i] :
( ( ( member @ ( ordered_pair @ ( second @ SV44 ) @ ( first @ SV44 ) ) @ SV171 )
= $false )
| ( ( ordered_pair_predicate @ SV44 )
= $false )
| ( ( little_set @ SV44 )
= $false )
| ( ( member @ SV44 @ ( converse @ SV171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1082]) ).
thf(1109,plain,
! [SV177: $i,SV50: $i,SV245: $i] :
( ( ( little_set @ SV245 )
= $false )
| ( ( ! [SY579: $i] :
( ~ ( little_set @ SY579 )
| ! [SY580: $i] :
( ~ ( little_set @ SY580 )
| ( SV50
!= ( ordered_pair @ SV245 @ ( ordered_pair @ SY579 @ SY580 ) ) )
| ~ ( member @ ( ordered_pair @ SY579 @ ( ordered_pair @ SY580 @ SV245 ) ) @ SV177 ) ) ) )
= $true )
| ( ( little_set @ SV50 )
= $false )
| ( ( member @ SV50 @ ( rotate_right @ SV177 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1083]) ).
thf(1110,plain,
! [SV183: $i,SV56: $i,SV246: $i] :
( ( ( little_set @ SV246 )
= $false )
| ( ( ! [SY581: $i] :
( ~ ( little_set @ SY581 )
| ! [SY582: $i] :
( ~ ( little_set @ SY582 )
| ( SV56
!= ( ordered_pair @ SV246 @ ( ordered_pair @ SY581 @ SY582 ) ) )
| ~ ( member @ ( ordered_pair @ SV246 @ ( ordered_pair @ SY582 @ SY581 ) ) @ SV183 ) ) ) )
= $true )
| ( ( little_set @ SV56 )
= $false )
| ( ( member @ SV56 @ ( flip_range_of @ SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1084]) ).
thf(1111,plain,
! [SV77: $i,SV195: $i,SV310: $i] :
( ( ( ~ ( little_set @ SV310 ) )
= $true )
| ( ( ! [SY620: $i] :
( ~ ( little_set @ SY620 )
| ~ ( member @ ( ordered_pair @ SV195 @ SV310 ) @ SV77 )
| ~ ( member @ ( ordered_pair @ SV195 @ SY620 ) @ SV77 )
| ( SV310 = SY620 ) ) )
= $true )
| ( ( little_set @ SV195 )
= $false )
| ( ( single_valued_set @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1087]) ).
thf(1112,plain,
! [SV91: $i,SV200: $i,SV251: $i,SV311: $i] :
( ( ( ~ ( ordered_pair_predicate @ SV311 ) )
= $true )
| ( ( ~ ( member @ SV311 @ SV251 )
| ~ ( member @ ( first @ SV311 ) @ SV200 )
| ( ( second @ SV311 )
!= SV91 ) )
= $true )
| ( ( little_set @ SV91 )
= $false )
| ( ( member @ SV91 @ ( image @ SV200 @ SV251 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1088]) ).
thf(1113,plain,
! [SV93: $i,SV201: $i,SV295: $i] :
( ( ( member @ SV295 @ SV201 )
= $false )
| ( ( member @ SV295 @ SV93 )
= $false )
| ( ( disjoint @ SV93 @ SV201 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1089]) ).
thf(1114,plain,
! [SV103: $i,SV207: $i,SV305: $i] :
( ( ( ordered_pair_predicate @ SV305 )
= $false )
| ( ( ~ ( member @ SV305 @ SV207 )
| ( SV103
!= ( second @ SV305 ) ) )
= $true )
| ( ( little_set @ SV103 )
= $false )
| ( ( member @ SV103 @ ( range_of @ SV207 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1090]) ).
thf(1115,plain,
! [SV115: $i,SV256: $i,SV213: $i,SV296: $i] :
( ( ( ~ ( member @ SV296 @ SV213 ) )
= $true )
| ( ( ( ( first @ SV296 )
!= SV256 )
| ~ ( member @ SV115 @ ( second @ SV296 ) ) )
= $true )
| ( ( ordered_pair_predicate @ SV296 )
= $false )
| ( ( member @ SV115 @ ( apply @ SV213 @ SV256 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1092]) ).
thf(1116,plain,
! [SV260: $i,SV217: $i,SV120: $i] :
( ( ( ( domain_of @ SV120 )
= SV217 )
= $false )
| ( ( ~ ( subset @ ( range_of @ SV120 ) @ SV260 ) )
= $true )
| ( ( function @ SV120 )
= $false )
| ( ( maps @ SV120 @ SV217 @ SV260 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1093]) ).
thf(1117,plain,
! [SV124: $i,SV220: $i] :
( ( ( maps @ SV220 @ ( cross_product @ SV124 @ SV124 ) @ SV124 )
= $false )
| ( ( little_set @ SV220 )
= $false )
| ( ( little_set @ SV124 )
= $false )
| ( ( closed @ SV124 @ SV220 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1094]) ).
thf(1118,plain,
! [SV268: $i,SV227: $i,SV131: $i,SV287: $i] :
( ( ( ~ ( little_set @ SV287 ) )
= $true )
| ( ( ! [SY607: $i] :
( ~ ( little_set @ SY607 )
| ! [SY608: $i] :
( ~ ( little_set @ SY608 )
| ( SV131
!= ( ordered_pair @ SV287 @ SY607 ) )
| ~ ( member @ ( ordered_pair @ SV287 @ SY608 ) @ SV227 )
| ~ ( member @ ( ordered_pair @ SY608 @ SY607 ) @ SV268 ) ) ) )
= $true )
| ( ( little_set @ SV131 )
= $false )
| ( ( member @ SV131 @ ( compose @ SV227 @ SV268 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1095]) ).
thf(1119,plain,
! [SV290: $i,SV299: $i,SV272: $i,SV135: $i,SV231: $i,SV312: $i] :
( ( ( ~ ( member @ SV312 @ SV231 )
| ! [SY621: $i] :
( ~ ( member @ SY621 @ SV231 )
| ( ( apply @ SV135 @ ( apply_to_two_arguments @ SV272 @ SV312 @ SY621 ) )
= ( apply_to_two_arguments @ SV299 @ ( apply @ SV135 @ SV312 ) @ ( apply @ SV135 @ SY621 ) ) ) ) )
= $true )
| ( ( homomorphism @ SV135 @ SV231 @ SV272 @ SV290 @ SV299 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1099]) ).
thf(1120,plain,
! [SV136: $i,SV300: $i,SV291: $i,SV273: $i,SV232: $i] :
( ( ( closed @ SV232 @ SV273 )
= $false )
| ( ( ~ ( closed @ SV291 @ SV300 )
| ~ ( maps @ SV136 @ SV232 @ SV291 )
| ( member @ ( f32 @ SV136 @ SV232 @ SV273 @ SV291 @ SV300 ) @ SV232 ) )
= $true )
| ( ( homomorphism @ SV136 @ SV232 @ SV273 @ SV291 @ SV300 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1100]) ).
thf(1121,plain,
! [SV137: $i,SV301: $i,SV292: $i,SV274: $i,SV233: $i] :
( ( ( closed @ SV233 @ SV274 )
= $false )
| ( ( ~ ( closed @ SV292 @ SV301 )
| ~ ( maps @ SV137 @ SV233 @ SV292 )
| ( member @ ( f33 @ SV137 @ SV233 @ SV274 @ SV292 @ SV301 ) @ SV233 ) )
= $true )
| ( ( homomorphism @ SV137 @ SV233 @ SV274 @ SV292 @ SV301 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1101]) ).
thf(1122,plain,
! [SV138: $i,SV302: $i,SV293: $i,SV275: $i,SV234: $i] :
( ( ( closed @ SV234 @ SV275 )
= $false )
| ( ( ~ ( closed @ SV293 @ SV302 )
| ~ ( maps @ SV138 @ SV234 @ SV293 )
| ( ( apply @ SV138 @ ( apply_to_two_arguments @ SV275 @ ( f32 @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 ) @ ( f33 @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 ) ) )
!= ( apply_to_two_arguments @ SV302 @ ( apply @ SV138 @ ( f32 @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 ) ) @ ( apply @ SV138 @ ( f33 @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 ) ) ) ) )
= $true )
| ( ( homomorphism @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1102]) ).
thf(1123,plain,
! [SV303: $i,SV238: $i,SV14: $i] :
( ( ( SV14
= ( ordered_pair @ SV238 @ SV303 ) )
= $false )
| ( ( little_set @ SV303 )
= $false )
| ( ( little_set @ SV238 )
= $false )
| ( ( ordered_pair_predicate @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1103]) ).
thf(1124,plain,
! [SV19: $i,SV277: $i,SV151: $i,SV308: $i] :
( ( ( little_set @ SV308 )
= $false )
| ( ( ( SV151
!= ( ordered_pair @ SV277 @ SV308 ) )
| ~ ( member @ SV19 @ SV277 ) )
= $true )
| ( ( little_set @ SV277 )
= $false )
| ( ( member @ SV19 @ ( first @ SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1104]) ).
thf(1125,plain,
! [SV24: $i,SV278: $i,SV156: $i,SV309: $i] :
( ( ( little_set @ SV309 )
= $false )
| ( ( ( SV156
!= ( ordered_pair @ SV278 @ SV309 ) )
| ~ ( member @ SV24 @ SV309 ) )
= $true )
| ( ( little_set @ SV278 )
= $false )
| ( ( member @ SV24 @ ( second @ SV156 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1105]) ).
thf(1126,plain,
! [SV37: $i,SV166: $i,SV304: $i] :
( ( ( ~ ( member @ SV304 @ SV166 ) )
= $true )
| ( ( SV37
!= ( first @ SV304 ) )
= $true )
| ( ( ordered_pair_predicate @ SV304 )
= $false )
| ( ( little_set @ SV37 )
= $false )
| ( ( member @ SV37 @ ( domain_of @ SV166 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1106]) ).
thf(1127,plain,
! [SV243: $i,SV169: $i,SV41: $i] :
( ( ( ~ ( member @ ( first @ SV41 ) @ SV169 ) )
= $true )
| ( ( ~ ( member @ ( second @ SV41 ) @ SV243 ) )
= $true )
| ( ( ordered_pair_predicate @ SV41 )
= $false )
| ( ( little_set @ SV41 )
= $false )
| ( ( member @ SV41 @ ( cross_product @ SV169 @ SV243 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1107]) ).
thf(1128,plain,
! [SV177: $i,SV245: $i,SV50: $i,SV313: $i] :
( ( ( ~ ( little_set @ SV313 )
| ! [SY622: $i] :
( ~ ( little_set @ SY622 )
| ( SV50
!= ( ordered_pair @ SV245 @ ( ordered_pair @ SV313 @ SY622 ) ) )
| ~ ( member @ ( ordered_pair @ SV313 @ ( ordered_pair @ SY622 @ SV245 ) ) @ SV177 ) ) )
= $true )
| ( ( little_set @ SV245 )
= $false )
| ( ( little_set @ SV50 )
= $false )
| ( ( member @ SV50 @ ( rotate_right @ SV177 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1109]) ).
thf(1129,plain,
! [SV183: $i,SV246: $i,SV56: $i,SV314: $i] :
( ( ( ~ ( little_set @ SV314 )
| ! [SY623: $i] :
( ~ ( little_set @ SY623 )
| ( SV56
!= ( ordered_pair @ SV246 @ ( ordered_pair @ SV314 @ SY623 ) ) )
| ~ ( member @ ( ordered_pair @ SV246 @ ( ordered_pair @ SY623 @ SV314 ) ) @ SV183 ) ) )
= $true )
| ( ( little_set @ SV246 )
= $false )
| ( ( little_set @ SV56 )
= $false )
| ( ( member @ SV56 @ ( flip_range_of @ SV183 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1110]) ).
thf(1130,plain,
! [SV77: $i,SV195: $i,SV310: $i] :
( ( ( little_set @ SV310 )
= $false )
| ( ( ! [SY620: $i] :
( ~ ( little_set @ SY620 )
| ~ ( member @ ( ordered_pair @ SV195 @ SV310 ) @ SV77 )
| ~ ( member @ ( ordered_pair @ SV195 @ SY620 ) @ SV77 )
| ( SV310 = SY620 ) ) )
= $true )
| ( ( little_set @ SV195 )
= $false )
| ( ( single_valued_set @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1111]) ).
thf(1131,plain,
! [SV91: $i,SV200: $i,SV251: $i,SV311: $i] :
( ( ( ordered_pair_predicate @ SV311 )
= $false )
| ( ( ~ ( member @ SV311 @ SV251 )
| ~ ( member @ ( first @ SV311 ) @ SV200 )
| ( ( second @ SV311 )
!= SV91 ) )
= $true )
| ( ( little_set @ SV91 )
= $false )
| ( ( member @ SV91 @ ( image @ SV200 @ SV251 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1112]) ).
thf(1132,plain,
! [SV103: $i,SV207: $i,SV305: $i] :
( ( ( ~ ( member @ SV305 @ SV207 ) )
= $true )
| ( ( SV103
!= ( second @ SV305 ) )
= $true )
| ( ( ordered_pair_predicate @ SV305 )
= $false )
| ( ( little_set @ SV103 )
= $false )
| ( ( member @ SV103 @ ( range_of @ SV207 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1114]) ).
thf(1133,plain,
! [SV115: $i,SV256: $i,SV213: $i,SV296: $i] :
( ( ( member @ SV296 @ SV213 )
= $false )
| ( ( ( ( first @ SV296 )
!= SV256 )
| ~ ( member @ SV115 @ ( second @ SV296 ) ) )
= $true )
| ( ( ordered_pair_predicate @ SV296 )
= $false )
| ( ( member @ SV115 @ ( apply @ SV213 @ SV256 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1115]) ).
thf(1134,plain,
! [SV217: $i,SV260: $i,SV120: $i] :
( ( ( subset @ ( range_of @ SV120 ) @ SV260 )
= $false )
| ( ( ( domain_of @ SV120 )
= SV217 )
= $false )
| ( ( function @ SV120 )
= $false )
| ( ( maps @ SV120 @ SV217 @ SV260 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1116]) ).
thf(1135,plain,
! [SV268: $i,SV227: $i,SV131: $i,SV287: $i] :
( ( ( little_set @ SV287 )
= $false )
| ( ( ! [SY607: $i] :
( ~ ( little_set @ SY607 )
| ! [SY608: $i] :
( ~ ( little_set @ SY608 )
| ( SV131
!= ( ordered_pair @ SV287 @ SY607 ) )
| ~ ( member @ ( ordered_pair @ SV287 @ SY608 ) @ SV227 )
| ~ ( member @ ( ordered_pair @ SY608 @ SY607 ) @ SV268 ) ) ) )
= $true )
| ( ( little_set @ SV131 )
= $false )
| ( ( member @ SV131 @ ( compose @ SV227 @ SV268 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1118]) ).
thf(1136,plain,
! [SV290: $i,SV299: $i,SV272: $i,SV135: $i,SV231: $i,SV312: $i] :
( ( ( ~ ( member @ SV312 @ SV231 ) )
= $true )
| ( ( ! [SY621: $i] :
( ~ ( member @ SY621 @ SV231 )
| ( ( apply @ SV135 @ ( apply_to_two_arguments @ SV272 @ SV312 @ SY621 ) )
= ( apply_to_two_arguments @ SV299 @ ( apply @ SV135 @ SV312 ) @ ( apply @ SV135 @ SY621 ) ) ) ) )
= $true )
| ( ( homomorphism @ SV135 @ SV231 @ SV272 @ SV290 @ SV299 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1119]) ).
thf(1137,plain,
! [SV273: $i,SV232: $i,SV136: $i,SV300: $i,SV291: $i] :
( ( ( ~ ( closed @ SV291 @ SV300 ) )
= $true )
| ( ( ~ ( maps @ SV136 @ SV232 @ SV291 )
| ( member @ ( f32 @ SV136 @ SV232 @ SV273 @ SV291 @ SV300 ) @ SV232 ) )
= $true )
| ( ( closed @ SV232 @ SV273 )
= $false )
| ( ( homomorphism @ SV136 @ SV232 @ SV273 @ SV291 @ SV300 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1120]) ).
thf(1138,plain,
! [SV274: $i,SV233: $i,SV137: $i,SV301: $i,SV292: $i] :
( ( ( ~ ( closed @ SV292 @ SV301 ) )
= $true )
| ( ( ~ ( maps @ SV137 @ SV233 @ SV292 )
| ( member @ ( f33 @ SV137 @ SV233 @ SV274 @ SV292 @ SV301 ) @ SV233 ) )
= $true )
| ( ( closed @ SV233 @ SV274 )
= $false )
| ( ( homomorphism @ SV137 @ SV233 @ SV274 @ SV292 @ SV301 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1121]) ).
thf(1139,plain,
! [SV275: $i,SV234: $i,SV138: $i,SV302: $i,SV293: $i] :
( ( ( ~ ( closed @ SV293 @ SV302 ) )
= $true )
| ( ( ~ ( maps @ SV138 @ SV234 @ SV293 )
| ( ( apply @ SV138 @ ( apply_to_two_arguments @ SV275 @ ( f32 @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 ) @ ( f33 @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 ) ) )
!= ( apply_to_two_arguments @ SV302 @ ( apply @ SV138 @ ( f32 @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 ) ) @ ( apply @ SV138 @ ( f33 @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 ) ) ) ) )
= $true )
| ( ( closed @ SV234 @ SV275 )
= $false )
| ( ( homomorphism @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1122]) ).
thf(1140,plain,
! [SV19: $i,SV308: $i,SV277: $i,SV151: $i] :
( ( ( SV151
!= ( ordered_pair @ SV277 @ SV308 ) )
= $true )
| ( ( ~ ( member @ SV19 @ SV277 ) )
= $true )
| ( ( little_set @ SV308 )
= $false )
| ( ( little_set @ SV277 )
= $false )
| ( ( member @ SV19 @ ( first @ SV151 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1124]) ).
thf(1141,plain,
! [SV24: $i,SV309: $i,SV278: $i,SV156: $i] :
( ( ( SV156
!= ( ordered_pair @ SV278 @ SV309 ) )
= $true )
| ( ( ~ ( member @ SV24 @ SV309 ) )
= $true )
| ( ( little_set @ SV309 )
= $false )
| ( ( little_set @ SV278 )
= $false )
| ( ( member @ SV24 @ ( second @ SV156 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1125]) ).
thf(1142,plain,
! [SV37: $i,SV166: $i,SV304: $i] :
( ( ( member @ SV304 @ SV166 )
= $false )
| ( ( SV37
!= ( first @ SV304 ) )
= $true )
| ( ( ordered_pair_predicate @ SV304 )
= $false )
| ( ( little_set @ SV37 )
= $false )
| ( ( member @ SV37 @ ( domain_of @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1126]) ).
thf(1143,plain,
! [SV243: $i,SV169: $i,SV41: $i] :
( ( ( member @ ( first @ SV41 ) @ SV169 )
= $false )
| ( ( ~ ( member @ ( second @ SV41 ) @ SV243 ) )
= $true )
| ( ( ordered_pair_predicate @ SV41 )
= $false )
| ( ( little_set @ SV41 )
= $false )
| ( ( member @ SV41 @ ( cross_product @ SV169 @ SV243 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1127]) ).
thf(1144,plain,
! [SV177: $i,SV245: $i,SV50: $i,SV313: $i] :
( ( ( ~ ( little_set @ SV313 ) )
= $true )
| ( ( ! [SY622: $i] :
( ~ ( little_set @ SY622 )
| ( SV50
!= ( ordered_pair @ SV245 @ ( ordered_pair @ SV313 @ SY622 ) ) )
| ~ ( member @ ( ordered_pair @ SV313 @ ( ordered_pair @ SY622 @ SV245 ) ) @ SV177 ) ) )
= $true )
| ( ( little_set @ SV245 )
= $false )
| ( ( little_set @ SV50 )
= $false )
| ( ( member @ SV50 @ ( rotate_right @ SV177 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1128]) ).
thf(1145,plain,
! [SV183: $i,SV246: $i,SV56: $i,SV314: $i] :
( ( ( ~ ( little_set @ SV314 ) )
= $true )
| ( ( ! [SY623: $i] :
( ~ ( little_set @ SY623 )
| ( SV56
!= ( ordered_pair @ SV246 @ ( ordered_pair @ SV314 @ SY623 ) ) )
| ~ ( member @ ( ordered_pair @ SV246 @ ( ordered_pair @ SY623 @ SV314 ) ) @ SV183 ) ) )
= $true )
| ( ( little_set @ SV246 )
= $false )
| ( ( little_set @ SV56 )
= $false )
| ( ( member @ SV56 @ ( flip_range_of @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1129]) ).
thf(1146,plain,
! [SV77: $i,SV310: $i,SV195: $i,SV315: $i] :
( ( ( ~ ( little_set @ SV315 )
| ~ ( member @ ( ordered_pair @ SV195 @ SV310 ) @ SV77 )
| ~ ( member @ ( ordered_pair @ SV195 @ SV315 ) @ SV77 )
| ( SV310 = SV315 ) )
= $true )
| ( ( little_set @ SV310 )
= $false )
| ( ( little_set @ SV195 )
= $false )
| ( ( single_valued_set @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1147,plain,
! [SV91: $i,SV200: $i,SV251: $i,SV311: $i] :
( ( ( ~ ( member @ SV311 @ SV251 ) )
= $true )
| ( ( ~ ( member @ ( first @ SV311 ) @ SV200 )
| ( ( second @ SV311 )
!= SV91 ) )
= $true )
| ( ( ordered_pair_predicate @ SV311 )
= $false )
| ( ( little_set @ SV91 )
= $false )
| ( ( member @ SV91 @ ( image @ SV200 @ SV251 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1131]) ).
thf(1148,plain,
! [SV103: $i,SV207: $i,SV305: $i] :
( ( ( member @ SV305 @ SV207 )
= $false )
| ( ( SV103
!= ( second @ SV305 ) )
= $true )
| ( ( ordered_pair_predicate @ SV305 )
= $false )
| ( ( little_set @ SV103 )
= $false )
| ( ( member @ SV103 @ ( range_of @ SV207 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1132]) ).
thf(1149,plain,
! [SV213: $i,SV115: $i,SV256: $i,SV296: $i] :
( ( ( ( first @ SV296 )
!= SV256 )
= $true )
| ( ( ~ ( member @ SV115 @ ( second @ SV296 ) ) )
= $true )
| ( ( member @ SV296 @ SV213 )
= $false )
| ( ( ordered_pair_predicate @ SV296 )
= $false )
| ( ( member @ SV115 @ ( apply @ SV213 @ SV256 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1133]) ).
thf(1150,plain,
! [SV268: $i,SV227: $i,SV287: $i,SV131: $i,SV316: $i] :
( ( ( ~ ( little_set @ SV316 )
| ! [SY624: $i] :
( ~ ( little_set @ SY624 )
| ( SV131
!= ( ordered_pair @ SV287 @ SV316 ) )
| ~ ( member @ ( ordered_pair @ SV287 @ SY624 ) @ SV227 )
| ~ ( member @ ( ordered_pair @ SY624 @ SV316 ) @ SV268 ) ) )
= $true )
| ( ( little_set @ SV287 )
= $false )
| ( ( little_set @ SV131 )
= $false )
| ( ( member @ SV131 @ ( compose @ SV227 @ SV268 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1135]) ).
thf(1151,plain,
! [SV290: $i,SV299: $i,SV272: $i,SV135: $i,SV231: $i,SV312: $i] :
( ( ( member @ SV312 @ SV231 )
= $false )
| ( ( ! [SY621: $i] :
( ~ ( member @ SY621 @ SV231 )
| ( ( apply @ SV135 @ ( apply_to_two_arguments @ SV272 @ SV312 @ SY621 ) )
= ( apply_to_two_arguments @ SV299 @ ( apply @ SV135 @ SV312 ) @ ( apply @ SV135 @ SY621 ) ) ) ) )
= $true )
| ( ( homomorphism @ SV135 @ SV231 @ SV272 @ SV290 @ SV299 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1136]) ).
thf(1152,plain,
! [SV273: $i,SV232: $i,SV136: $i,SV300: $i,SV291: $i] :
( ( ( closed @ SV291 @ SV300 )
= $false )
| ( ( ~ ( maps @ SV136 @ SV232 @ SV291 )
| ( member @ ( f32 @ SV136 @ SV232 @ SV273 @ SV291 @ SV300 ) @ SV232 ) )
= $true )
| ( ( closed @ SV232 @ SV273 )
= $false )
| ( ( homomorphism @ SV136 @ SV232 @ SV273 @ SV291 @ SV300 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1137]) ).
thf(1153,plain,
! [SV274: $i,SV233: $i,SV137: $i,SV301: $i,SV292: $i] :
( ( ( closed @ SV292 @ SV301 )
= $false )
| ( ( ~ ( maps @ SV137 @ SV233 @ SV292 )
| ( member @ ( f33 @ SV137 @ SV233 @ SV274 @ SV292 @ SV301 ) @ SV233 ) )
= $true )
| ( ( closed @ SV233 @ SV274 )
= $false )
| ( ( homomorphism @ SV137 @ SV233 @ SV274 @ SV292 @ SV301 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1138]) ).
thf(1154,plain,
! [SV275: $i,SV234: $i,SV138: $i,SV302: $i,SV293: $i] :
( ( ( closed @ SV293 @ SV302 )
= $false )
| ( ( ~ ( maps @ SV138 @ SV234 @ SV293 )
| ( ( apply @ SV138 @ ( apply_to_two_arguments @ SV275 @ ( f32 @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 ) @ ( f33 @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 ) ) )
!= ( apply_to_two_arguments @ SV302 @ ( apply @ SV138 @ ( f32 @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 ) ) @ ( apply @ SV138 @ ( f33 @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 ) ) ) ) )
= $true )
| ( ( closed @ SV234 @ SV275 )
= $false )
| ( ( homomorphism @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1139]) ).
thf(1155,plain,
! [SV19: $i,SV308: $i,SV277: $i,SV151: $i] :
( ( ( SV151
= ( ordered_pair @ SV277 @ SV308 ) )
= $false )
| ( ( ~ ( member @ SV19 @ SV277 ) )
= $true )
| ( ( little_set @ SV308 )
= $false )
| ( ( little_set @ SV277 )
= $false )
| ( ( member @ SV19 @ ( first @ SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1140]) ).
thf(1156,plain,
! [SV24: $i,SV309: $i,SV278: $i,SV156: $i] :
( ( ( SV156
= ( ordered_pair @ SV278 @ SV309 ) )
= $false )
| ( ( ~ ( member @ SV24 @ SV309 ) )
= $true )
| ( ( little_set @ SV309 )
= $false )
| ( ( little_set @ SV278 )
= $false )
| ( ( member @ SV24 @ ( second @ SV156 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1141]) ).
thf(1157,plain,
! [SV166: $i,SV304: $i,SV37: $i] :
( ( ( SV37
= ( first @ SV304 ) )
= $false )
| ( ( member @ SV304 @ SV166 )
= $false )
| ( ( ordered_pair_predicate @ SV304 )
= $false )
| ( ( little_set @ SV37 )
= $false )
| ( ( member @ SV37 @ ( domain_of @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1142]) ).
thf(1158,plain,
! [SV169: $i,SV243: $i,SV41: $i] :
( ( ( member @ ( second @ SV41 ) @ SV243 )
= $false )
| ( ( member @ ( first @ SV41 ) @ SV169 )
= $false )
| ( ( ordered_pair_predicate @ SV41 )
= $false )
| ( ( little_set @ SV41 )
= $false )
| ( ( member @ SV41 @ ( cross_product @ SV169 @ SV243 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1143]) ).
thf(1159,plain,
! [SV177: $i,SV245: $i,SV50: $i,SV313: $i] :
( ( ( little_set @ SV313 )
= $false )
| ( ( ! [SY622: $i] :
( ~ ( little_set @ SY622 )
| ( SV50
!= ( ordered_pair @ SV245 @ ( ordered_pair @ SV313 @ SY622 ) ) )
| ~ ( member @ ( ordered_pair @ SV313 @ ( ordered_pair @ SY622 @ SV245 ) ) @ SV177 ) ) )
= $true )
| ( ( little_set @ SV245 )
= $false )
| ( ( little_set @ SV50 )
= $false )
| ( ( member @ SV50 @ ( rotate_right @ SV177 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1144]) ).
thf(1160,plain,
! [SV183: $i,SV246: $i,SV56: $i,SV314: $i] :
( ( ( little_set @ SV314 )
= $false )
| ( ( ! [SY623: $i] :
( ~ ( little_set @ SY623 )
| ( SV56
!= ( ordered_pair @ SV246 @ ( ordered_pair @ SV314 @ SY623 ) ) )
| ~ ( member @ ( ordered_pair @ SV246 @ ( ordered_pair @ SY623 @ SV314 ) ) @ SV183 ) ) )
= $true )
| ( ( little_set @ SV246 )
= $false )
| ( ( little_set @ SV56 )
= $false )
| ( ( member @ SV56 @ ( flip_range_of @ SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1145]) ).
thf(1161,plain,
! [SV77: $i,SV310: $i,SV195: $i,SV315: $i] :
( ( ( ~ ( little_set @ SV315 ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ SV195 @ SV310 ) @ SV77 )
| ~ ( member @ ( ordered_pair @ SV195 @ SV315 ) @ SV77 )
| ( SV310 = SV315 ) )
= $true )
| ( ( little_set @ SV310 )
= $false )
| ( ( little_set @ SV195 )
= $false )
| ( ( single_valued_set @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1146]) ).
thf(1162,plain,
! [SV91: $i,SV200: $i,SV251: $i,SV311: $i] :
( ( ( member @ SV311 @ SV251 )
= $false )
| ( ( ~ ( member @ ( first @ SV311 ) @ SV200 )
| ( ( second @ SV311 )
!= SV91 ) )
= $true )
| ( ( ordered_pair_predicate @ SV311 )
= $false )
| ( ( little_set @ SV91 )
= $false )
| ( ( member @ SV91 @ ( image @ SV200 @ SV251 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1147]) ).
thf(1163,plain,
! [SV207: $i,SV305: $i,SV103: $i] :
( ( ( SV103
= ( second @ SV305 ) )
= $false )
| ( ( member @ SV305 @ SV207 )
= $false )
| ( ( ordered_pair_predicate @ SV305 )
= $false )
| ( ( little_set @ SV103 )
= $false )
| ( ( member @ SV103 @ ( range_of @ SV207 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1148]) ).
thf(1164,plain,
! [SV213: $i,SV115: $i,SV256: $i,SV296: $i] :
( ( ( ( first @ SV296 )
= SV256 )
= $false )
| ( ( ~ ( member @ SV115 @ ( second @ SV296 ) ) )
= $true )
| ( ( member @ SV296 @ SV213 )
= $false )
| ( ( ordered_pair_predicate @ SV296 )
= $false )
| ( ( member @ SV115 @ ( apply @ SV213 @ SV256 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1149]) ).
thf(1165,plain,
! [SV268: $i,SV227: $i,SV287: $i,SV131: $i,SV316: $i] :
( ( ( ~ ( little_set @ SV316 ) )
= $true )
| ( ( ! [SY624: $i] :
( ~ ( little_set @ SY624 )
| ( SV131
!= ( ordered_pair @ SV287 @ SV316 ) )
| ~ ( member @ ( ordered_pair @ SV287 @ SY624 ) @ SV227 )
| ~ ( member @ ( ordered_pair @ SY624 @ SV316 ) @ SV268 ) ) )
= $true )
| ( ( little_set @ SV287 )
= $false )
| ( ( little_set @ SV131 )
= $false )
| ( ( member @ SV131 @ ( compose @ SV227 @ SV268 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1150]) ).
thf(1166,plain,
! [SV290: $i,SV299: $i,SV312: $i,SV272: $i,SV135: $i,SV231: $i,SV317: $i] :
( ( ( ~ ( member @ SV317 @ SV231 )
| ( ( apply @ SV135 @ ( apply_to_two_arguments @ SV272 @ SV312 @ SV317 ) )
= ( apply_to_two_arguments @ SV299 @ ( apply @ SV135 @ SV312 ) @ ( apply @ SV135 @ SV317 ) ) ) )
= $true )
| ( ( member @ SV312 @ SV231 )
= $false )
| ( ( homomorphism @ SV135 @ SV231 @ SV272 @ SV290 @ SV299 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1151]) ).
thf(1167,plain,
! [SV300: $i,SV273: $i,SV291: $i,SV232: $i,SV136: $i] :
( ( ( ~ ( maps @ SV136 @ SV232 @ SV291 ) )
= $true )
| ( ( member @ ( f32 @ SV136 @ SV232 @ SV273 @ SV291 @ SV300 ) @ SV232 )
= $true )
| ( ( closed @ SV291 @ SV300 )
= $false )
| ( ( closed @ SV232 @ SV273 )
= $false )
| ( ( homomorphism @ SV136 @ SV232 @ SV273 @ SV291 @ SV300 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1152]) ).
thf(1168,plain,
! [SV301: $i,SV274: $i,SV292: $i,SV233: $i,SV137: $i] :
( ( ( ~ ( maps @ SV137 @ SV233 @ SV292 ) )
= $true )
| ( ( member @ ( f33 @ SV137 @ SV233 @ SV274 @ SV292 @ SV301 ) @ SV233 )
= $true )
| ( ( closed @ SV292 @ SV301 )
= $false )
| ( ( closed @ SV233 @ SV274 )
= $false )
| ( ( homomorphism @ SV137 @ SV233 @ SV274 @ SV292 @ SV301 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1153]) ).
thf(1169,plain,
! [SV302: $i,SV275: $i,SV293: $i,SV234: $i,SV138: $i] :
( ( ( ~ ( maps @ SV138 @ SV234 @ SV293 ) )
= $true )
| ( ( ( apply @ SV138 @ ( apply_to_two_arguments @ SV275 @ ( f32 @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 ) @ ( f33 @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 ) ) )
!= ( apply_to_two_arguments @ SV302 @ ( apply @ SV138 @ ( f32 @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 ) ) @ ( apply @ SV138 @ ( f33 @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 ) ) ) )
= $true )
| ( ( closed @ SV293 @ SV302 )
= $false )
| ( ( closed @ SV234 @ SV275 )
= $false )
| ( ( homomorphism @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1154]) ).
thf(1170,plain,
! [SV308: $i,SV151: $i,SV277: $i,SV19: $i] :
( ( ( member @ SV19 @ SV277 )
= $false )
| ( ( SV151
= ( ordered_pair @ SV277 @ SV308 ) )
= $false )
| ( ( little_set @ SV308 )
= $false )
| ( ( little_set @ SV277 )
= $false )
| ( ( member @ SV19 @ ( first @ SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1155]) ).
thf(1171,plain,
! [SV278: $i,SV156: $i,SV309: $i,SV24: $i] :
( ( ( member @ SV24 @ SV309 )
= $false )
| ( ( SV156
= ( ordered_pair @ SV278 @ SV309 ) )
= $false )
| ( ( little_set @ SV309 )
= $false )
| ( ( little_set @ SV278 )
= $false )
| ( ( member @ SV24 @ ( second @ SV156 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1156]) ).
thf(1172,plain,
! [SV177: $i,SV313: $i,SV245: $i,SV50: $i,SV318: $i] :
( ( ( ~ ( little_set @ SV318 )
| ( SV50
!= ( ordered_pair @ SV245 @ ( ordered_pair @ SV313 @ SV318 ) ) )
| ~ ( member @ ( ordered_pair @ SV313 @ ( ordered_pair @ SV318 @ SV245 ) ) @ SV177 ) )
= $true )
| ( ( little_set @ SV313 )
= $false )
| ( ( little_set @ SV245 )
= $false )
| ( ( little_set @ SV50 )
= $false )
| ( ( member @ SV50 @ ( rotate_right @ SV177 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1159]) ).
thf(1173,plain,
! [SV183: $i,SV314: $i,SV246: $i,SV56: $i,SV319: $i] :
( ( ( ~ ( little_set @ SV319 )
| ( SV56
!= ( ordered_pair @ SV246 @ ( ordered_pair @ SV314 @ SV319 ) ) )
| ~ ( member @ ( ordered_pair @ SV246 @ ( ordered_pair @ SV319 @ SV314 ) ) @ SV183 ) )
= $true )
| ( ( little_set @ SV314 )
= $false )
| ( ( little_set @ SV246 )
= $false )
| ( ( little_set @ SV56 )
= $false )
| ( ( member @ SV56 @ ( flip_range_of @ SV183 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1160]) ).
thf(1174,plain,
! [SV77: $i,SV310: $i,SV195: $i,SV315: $i] :
( ( ( little_set @ SV315 )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ SV195 @ SV310 ) @ SV77 )
| ~ ( member @ ( ordered_pair @ SV195 @ SV315 ) @ SV77 )
| ( SV310 = SV315 ) )
= $true )
| ( ( little_set @ SV310 )
= $false )
| ( ( little_set @ SV195 )
= $false )
| ( ( single_valued_set @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1161]) ).
thf(1175,plain,
! [SV251: $i,SV91: $i,SV200: $i,SV311: $i] :
( ( ( ~ ( member @ ( first @ SV311 ) @ SV200 ) )
= $true )
| ( ( ( second @ SV311 )
!= SV91 )
= $true )
| ( ( member @ SV311 @ SV251 )
= $false )
| ( ( ordered_pair_predicate @ SV311 )
= $false )
| ( ( little_set @ SV91 )
= $false )
| ( ( member @ SV91 @ ( image @ SV200 @ SV251 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1162]) ).
thf(1176,plain,
! [SV213: $i,SV256: $i,SV296: $i,SV115: $i] :
( ( ( member @ SV115 @ ( second @ SV296 ) )
= $false )
| ( ( ( first @ SV296 )
= SV256 )
= $false )
| ( ( member @ SV296 @ SV213 )
= $false )
| ( ( ordered_pair_predicate @ SV296 )
= $false )
| ( ( member @ SV115 @ ( apply @ SV213 @ SV256 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1164]) ).
thf(1177,plain,
! [SV268: $i,SV227: $i,SV287: $i,SV131: $i,SV316: $i] :
( ( ( little_set @ SV316 )
= $false )
| ( ( ! [SY624: $i] :
( ~ ( little_set @ SY624 )
| ( SV131
!= ( ordered_pair @ SV287 @ SV316 ) )
| ~ ( member @ ( ordered_pair @ SV287 @ SY624 ) @ SV227 )
| ~ ( member @ ( ordered_pair @ SY624 @ SV316 ) @ SV268 ) ) )
= $true )
| ( ( little_set @ SV287 )
= $false )
| ( ( little_set @ SV131 )
= $false )
| ( ( member @ SV131 @ ( compose @ SV227 @ SV268 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1165]) ).
thf(1178,plain,
! [SV290: $i,SV299: $i,SV312: $i,SV272: $i,SV135: $i,SV231: $i,SV317: $i] :
( ( ( ~ ( member @ SV317 @ SV231 ) )
= $true )
| ( ( ( apply @ SV135 @ ( apply_to_two_arguments @ SV272 @ SV312 @ SV317 ) )
= ( apply_to_two_arguments @ SV299 @ ( apply @ SV135 @ SV312 ) @ ( apply @ SV135 @ SV317 ) ) )
= $true )
| ( ( member @ SV312 @ SV231 )
= $false )
| ( ( homomorphism @ SV135 @ SV231 @ SV272 @ SV290 @ SV299 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1166]) ).
thf(1179,plain,
! [SV300: $i,SV273: $i,SV291: $i,SV232: $i,SV136: $i] :
( ( ( maps @ SV136 @ SV232 @ SV291 )
= $false )
| ( ( member @ ( f32 @ SV136 @ SV232 @ SV273 @ SV291 @ SV300 ) @ SV232 )
= $true )
| ( ( closed @ SV291 @ SV300 )
= $false )
| ( ( closed @ SV232 @ SV273 )
= $false )
| ( ( homomorphism @ SV136 @ SV232 @ SV273 @ SV291 @ SV300 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1167]) ).
thf(1180,plain,
! [SV301: $i,SV274: $i,SV292: $i,SV233: $i,SV137: $i] :
( ( ( maps @ SV137 @ SV233 @ SV292 )
= $false )
| ( ( member @ ( f33 @ SV137 @ SV233 @ SV274 @ SV292 @ SV301 ) @ SV233 )
= $true )
| ( ( closed @ SV292 @ SV301 )
= $false )
| ( ( closed @ SV233 @ SV274 )
= $false )
| ( ( homomorphism @ SV137 @ SV233 @ SV274 @ SV292 @ SV301 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1168]) ).
thf(1181,plain,
! [SV302: $i,SV275: $i,SV293: $i,SV234: $i,SV138: $i] :
( ( ( maps @ SV138 @ SV234 @ SV293 )
= $false )
| ( ( ( apply @ SV138 @ ( apply_to_two_arguments @ SV275 @ ( f32 @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 ) @ ( f33 @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 ) ) )
!= ( apply_to_two_arguments @ SV302 @ ( apply @ SV138 @ ( f32 @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 ) ) @ ( apply @ SV138 @ ( f33 @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 ) ) ) )
= $true )
| ( ( closed @ SV293 @ SV302 )
= $false )
| ( ( closed @ SV234 @ SV275 )
= $false )
| ( ( homomorphism @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1169]) ).
thf(1182,plain,
! [SV177: $i,SV313: $i,SV245: $i,SV50: $i,SV318: $i] :
( ( ( ~ ( little_set @ SV318 ) )
= $true )
| ( ( ( SV50
!= ( ordered_pair @ SV245 @ ( ordered_pair @ SV313 @ SV318 ) ) )
| ~ ( member @ ( ordered_pair @ SV313 @ ( ordered_pair @ SV318 @ SV245 ) ) @ SV177 ) )
= $true )
| ( ( little_set @ SV313 )
= $false )
| ( ( little_set @ SV245 )
= $false )
| ( ( little_set @ SV50 )
= $false )
| ( ( member @ SV50 @ ( rotate_right @ SV177 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1172]) ).
thf(1183,plain,
! [SV183: $i,SV314: $i,SV246: $i,SV56: $i,SV319: $i] :
( ( ( ~ ( little_set @ SV319 ) )
= $true )
| ( ( ( SV56
!= ( ordered_pair @ SV246 @ ( ordered_pair @ SV314 @ SV319 ) ) )
| ~ ( member @ ( ordered_pair @ SV246 @ ( ordered_pair @ SV319 @ SV314 ) ) @ SV183 ) )
= $true )
| ( ( little_set @ SV314 )
= $false )
| ( ( little_set @ SV246 )
= $false )
| ( ( little_set @ SV56 )
= $false )
| ( ( member @ SV56 @ ( flip_range_of @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1173]) ).
thf(1184,plain,
! [SV315: $i,SV77: $i,SV310: $i,SV195: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV195 @ SV310 ) @ SV77 ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ SV195 @ SV315 ) @ SV77 )
| ( SV310 = SV315 ) )
= $true )
| ( ( little_set @ SV315 )
= $false )
| ( ( little_set @ SV310 )
= $false )
| ( ( little_set @ SV195 )
= $false )
| ( ( single_valued_set @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1174]) ).
thf(1185,plain,
! [SV251: $i,SV91: $i,SV200: $i,SV311: $i] :
( ( ( member @ ( first @ SV311 ) @ SV200 )
= $false )
| ( ( ( second @ SV311 )
!= SV91 )
= $true )
| ( ( member @ SV311 @ SV251 )
= $false )
| ( ( ordered_pair_predicate @ SV311 )
= $false )
| ( ( little_set @ SV91 )
= $false )
| ( ( member @ SV91 @ ( image @ SV200 @ SV251 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1175]) ).
thf(1186,plain,
! [SV268: $i,SV227: $i,SV316: $i,SV287: $i,SV131: $i,SV320: $i] :
( ( ( ~ ( little_set @ SV320 )
| ( SV131
!= ( ordered_pair @ SV287 @ SV316 ) )
| ~ ( member @ ( ordered_pair @ SV287 @ SV320 ) @ SV227 )
| ~ ( member @ ( ordered_pair @ SV320 @ SV316 ) @ SV268 ) )
= $true )
| ( ( little_set @ SV316 )
= $false )
| ( ( little_set @ SV287 )
= $false )
| ( ( little_set @ SV131 )
= $false )
| ( ( member @ SV131 @ ( compose @ SV227 @ SV268 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1177]) ).
thf(1187,plain,
! [SV290: $i,SV299: $i,SV312: $i,SV272: $i,SV135: $i,SV231: $i,SV317: $i] :
( ( ( member @ SV317 @ SV231 )
= $false )
| ( ( ( apply @ SV135 @ ( apply_to_two_arguments @ SV272 @ SV312 @ SV317 ) )
= ( apply_to_two_arguments @ SV299 @ ( apply @ SV135 @ SV312 ) @ ( apply @ SV135 @ SV317 ) ) )
= $true )
| ( ( member @ SV312 @ SV231 )
= $false )
| ( ( homomorphism @ SV135 @ SV231 @ SV272 @ SV290 @ SV299 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1178]) ).
thf(1188,plain,
! [SV302: $i,SV293: $i,SV234: $i,SV275: $i,SV138: $i] :
( ( ( ( apply @ SV138 @ ( apply_to_two_arguments @ SV275 @ ( f32 @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 ) @ ( f33 @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 ) ) )
= ( apply_to_two_arguments @ SV302 @ ( apply @ SV138 @ ( f32 @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 ) ) @ ( apply @ SV138 @ ( f33 @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 ) ) ) )
= $false )
| ( ( maps @ SV138 @ SV234 @ SV293 )
= $false )
| ( ( closed @ SV293 @ SV302 )
= $false )
| ( ( closed @ SV234 @ SV275 )
= $false )
| ( ( homomorphism @ SV138 @ SV234 @ SV275 @ SV293 @ SV302 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1181]) ).
thf(1189,plain,
! [SV177: $i,SV313: $i,SV245: $i,SV50: $i,SV318: $i] :
( ( ( little_set @ SV318 )
= $false )
| ( ( ( SV50
!= ( ordered_pair @ SV245 @ ( ordered_pair @ SV313 @ SV318 ) ) )
| ~ ( member @ ( ordered_pair @ SV313 @ ( ordered_pair @ SV318 @ SV245 ) ) @ SV177 ) )
= $true )
| ( ( little_set @ SV313 )
= $false )
| ( ( little_set @ SV245 )
= $false )
| ( ( little_set @ SV50 )
= $false )
| ( ( member @ SV50 @ ( rotate_right @ SV177 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1182]) ).
thf(1190,plain,
! [SV183: $i,SV314: $i,SV246: $i,SV56: $i,SV319: $i] :
( ( ( little_set @ SV319 )
= $false )
| ( ( ( SV56
!= ( ordered_pair @ SV246 @ ( ordered_pair @ SV314 @ SV319 ) ) )
| ~ ( member @ ( ordered_pair @ SV246 @ ( ordered_pair @ SV319 @ SV314 ) ) @ SV183 ) )
= $true )
| ( ( little_set @ SV314 )
= $false )
| ( ( little_set @ SV246 )
= $false )
| ( ( little_set @ SV56 )
= $false )
| ( ( member @ SV56 @ ( flip_range_of @ SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1183]) ).
thf(1191,plain,
! [SV315: $i,SV77: $i,SV310: $i,SV195: $i] :
( ( ( member @ ( ordered_pair @ SV195 @ SV310 ) @ SV77 )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ SV195 @ SV315 ) @ SV77 )
| ( SV310 = SV315 ) )
= $true )
| ( ( little_set @ SV315 )
= $false )
| ( ( little_set @ SV310 )
= $false )
| ( ( little_set @ SV195 )
= $false )
| ( ( single_valued_set @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1184]) ).
thf(1192,plain,
! [SV251: $i,SV200: $i,SV91: $i,SV311: $i] :
( ( ( ( second @ SV311 )
= SV91 )
= $false )
| ( ( member @ ( first @ SV311 ) @ SV200 )
= $false )
| ( ( member @ SV311 @ SV251 )
= $false )
| ( ( ordered_pair_predicate @ SV311 )
= $false )
| ( ( little_set @ SV91 )
= $false )
| ( ( member @ SV91 @ ( image @ SV200 @ SV251 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1185]) ).
thf(1193,plain,
! [SV268: $i,SV227: $i,SV316: $i,SV287: $i,SV131: $i,SV320: $i] :
( ( ( ~ ( little_set @ SV320 ) )
= $true )
| ( ( ( SV131
!= ( ordered_pair @ SV287 @ SV316 ) )
| ~ ( member @ ( ordered_pair @ SV287 @ SV320 ) @ SV227 )
| ~ ( member @ ( ordered_pair @ SV320 @ SV316 ) @ SV268 ) )
= $true )
| ( ( little_set @ SV316 )
= $false )
| ( ( little_set @ SV287 )
= $false )
| ( ( little_set @ SV131 )
= $false )
| ( ( member @ SV131 @ ( compose @ SV227 @ SV268 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1186]) ).
thf(1194,plain,
! [SV177: $i,SV318: $i,SV313: $i,SV245: $i,SV50: $i] :
( ( ( SV50
!= ( ordered_pair @ SV245 @ ( ordered_pair @ SV313 @ SV318 ) ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ SV313 @ ( ordered_pair @ SV318 @ SV245 ) ) @ SV177 ) )
= $true )
| ( ( little_set @ SV318 )
= $false )
| ( ( little_set @ SV313 )
= $false )
| ( ( little_set @ SV245 )
= $false )
| ( ( little_set @ SV50 )
= $false )
| ( ( member @ SV50 @ ( rotate_right @ SV177 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1189]) ).
thf(1195,plain,
! [SV183: $i,SV319: $i,SV314: $i,SV246: $i,SV56: $i] :
( ( ( SV56
!= ( ordered_pair @ SV246 @ ( ordered_pair @ SV314 @ SV319 ) ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ SV246 @ ( ordered_pair @ SV319 @ SV314 ) ) @ SV183 ) )
= $true )
| ( ( little_set @ SV319 )
= $false )
| ( ( little_set @ SV314 )
= $false )
| ( ( little_set @ SV246 )
= $false )
| ( ( little_set @ SV56 )
= $false )
| ( ( member @ SV56 @ ( flip_range_of @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1190]) ).
thf(1196,plain,
! [SV310: $i,SV77: $i,SV315: $i,SV195: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV195 @ SV315 ) @ SV77 ) )
= $true )
| ( ( SV310 = SV315 )
= $true )
| ( ( member @ ( ordered_pair @ SV195 @ SV310 ) @ SV77 )
= $false )
| ( ( little_set @ SV315 )
= $false )
| ( ( little_set @ SV310 )
= $false )
| ( ( little_set @ SV195 )
= $false )
| ( ( single_valued_set @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1191]) ).
thf(1197,plain,
! [SV268: $i,SV227: $i,SV316: $i,SV287: $i,SV131: $i,SV320: $i] :
( ( ( little_set @ SV320 )
= $false )
| ( ( ( SV131
!= ( ordered_pair @ SV287 @ SV316 ) )
| ~ ( member @ ( ordered_pair @ SV287 @ SV320 ) @ SV227 )
| ~ ( member @ ( ordered_pair @ SV320 @ SV316 ) @ SV268 ) )
= $true )
| ( ( little_set @ SV316 )
= $false )
| ( ( little_set @ SV287 )
= $false )
| ( ( little_set @ SV131 )
= $false )
| ( ( member @ SV131 @ ( compose @ SV227 @ SV268 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1193]) ).
thf(1198,plain,
! [SV177: $i,SV318: $i,SV313: $i,SV245: $i,SV50: $i] :
( ( ( SV50
= ( ordered_pair @ SV245 @ ( ordered_pair @ SV313 @ SV318 ) ) )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ SV313 @ ( ordered_pair @ SV318 @ SV245 ) ) @ SV177 ) )
= $true )
| ( ( little_set @ SV318 )
= $false )
| ( ( little_set @ SV313 )
= $false )
| ( ( little_set @ SV245 )
= $false )
| ( ( little_set @ SV50 )
= $false )
| ( ( member @ SV50 @ ( rotate_right @ SV177 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1194]) ).
thf(1199,plain,
! [SV183: $i,SV319: $i,SV314: $i,SV246: $i,SV56: $i] :
( ( ( SV56
= ( ordered_pair @ SV246 @ ( ordered_pair @ SV314 @ SV319 ) ) )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ SV246 @ ( ordered_pair @ SV319 @ SV314 ) ) @ SV183 ) )
= $true )
| ( ( little_set @ SV319 )
= $false )
| ( ( little_set @ SV314 )
= $false )
| ( ( little_set @ SV246 )
= $false )
| ( ( little_set @ SV56 )
= $false )
| ( ( member @ SV56 @ ( flip_range_of @ SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1195]) ).
thf(1200,plain,
! [SV310: $i,SV77: $i,SV315: $i,SV195: $i] :
( ( ( member @ ( ordered_pair @ SV195 @ SV315 ) @ SV77 )
= $false )
| ( ( SV310 = SV315 )
= $true )
| ( ( member @ ( ordered_pair @ SV195 @ SV310 ) @ SV77 )
= $false )
| ( ( little_set @ SV315 )
= $false )
| ( ( little_set @ SV310 )
= $false )
| ( ( little_set @ SV195 )
= $false )
| ( ( single_valued_set @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1196]) ).
thf(1201,plain,
! [SV268: $i,SV227: $i,SV320: $i,SV316: $i,SV287: $i,SV131: $i] :
( ( ( SV131
!= ( ordered_pair @ SV287 @ SV316 ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ SV287 @ SV320 ) @ SV227 )
| ~ ( member @ ( ordered_pair @ SV320 @ SV316 ) @ SV268 ) )
= $true )
| ( ( little_set @ SV320 )
= $false )
| ( ( little_set @ SV316 )
= $false )
| ( ( little_set @ SV287 )
= $false )
| ( ( little_set @ SV131 )
= $false )
| ( ( member @ SV131 @ ( compose @ SV227 @ SV268 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1197]) ).
thf(1202,plain,
! [SV50: $i,SV177: $i,SV245: $i,SV318: $i,SV313: $i] :
( ( ( member @ ( ordered_pair @ SV313 @ ( ordered_pair @ SV318 @ SV245 ) ) @ SV177 )
= $false )
| ( ( SV50
= ( ordered_pair @ SV245 @ ( ordered_pair @ SV313 @ SV318 ) ) )
= $false )
| ( ( little_set @ SV318 )
= $false )
| ( ( little_set @ SV313 )
= $false )
| ( ( little_set @ SV245 )
= $false )
| ( ( little_set @ SV50 )
= $false )
| ( ( member @ SV50 @ ( rotate_right @ SV177 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1198]) ).
thf(1203,plain,
! [SV56: $i,SV183: $i,SV314: $i,SV319: $i,SV246: $i] :
( ( ( member @ ( ordered_pair @ SV246 @ ( ordered_pair @ SV319 @ SV314 ) ) @ SV183 )
= $false )
| ( ( SV56
= ( ordered_pair @ SV246 @ ( ordered_pair @ SV314 @ SV319 ) ) )
= $false )
| ( ( little_set @ SV319 )
= $false )
| ( ( little_set @ SV314 )
= $false )
| ( ( little_set @ SV246 )
= $false )
| ( ( little_set @ SV56 )
= $false )
| ( ( member @ SV56 @ ( flip_range_of @ SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1199]) ).
thf(1204,plain,
! [SV268: $i,SV227: $i,SV320: $i,SV316: $i,SV287: $i,SV131: $i] :
( ( ( SV131
= ( ordered_pair @ SV287 @ SV316 ) )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ SV287 @ SV320 ) @ SV227 )
| ~ ( member @ ( ordered_pair @ SV320 @ SV316 ) @ SV268 ) )
= $true )
| ( ( little_set @ SV320 )
= $false )
| ( ( little_set @ SV316 )
= $false )
| ( ( little_set @ SV287 )
= $false )
| ( ( little_set @ SV131 )
= $false )
| ( ( member @ SV131 @ ( compose @ SV227 @ SV268 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1201]) ).
thf(1205,plain,
! [SV131: $i,SV268: $i,SV316: $i,SV227: $i,SV320: $i,SV287: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV287 @ SV320 ) @ SV227 ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ SV320 @ SV316 ) @ SV268 ) )
= $true )
| ( ( SV131
= ( ordered_pair @ SV287 @ SV316 ) )
= $false )
| ( ( little_set @ SV320 )
= $false )
| ( ( little_set @ SV316 )
= $false )
| ( ( little_set @ SV287 )
= $false )
| ( ( little_set @ SV131 )
= $false )
| ( ( member @ SV131 @ ( compose @ SV227 @ SV268 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1204]) ).
thf(1206,plain,
! [SV131: $i,SV268: $i,SV316: $i,SV227: $i,SV320: $i,SV287: $i] :
( ( ( member @ ( ordered_pair @ SV287 @ SV320 ) @ SV227 )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ SV320 @ SV316 ) @ SV268 ) )
= $true )
| ( ( SV131
= ( ordered_pair @ SV287 @ SV316 ) )
= $false )
| ( ( little_set @ SV320 )
= $false )
| ( ( little_set @ SV316 )
= $false )
| ( ( little_set @ SV287 )
= $false )
| ( ( little_set @ SV131 )
= $false )
| ( ( member @ SV131 @ ( compose @ SV227 @ SV268 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1205]) ).
thf(1207,plain,
! [SV131: $i,SV227: $i,SV287: $i,SV268: $i,SV316: $i,SV320: $i] :
( ( ( member @ ( ordered_pair @ SV320 @ SV316 ) @ SV268 )
= $false )
| ( ( member @ ( ordered_pair @ SV287 @ SV320 ) @ SV227 )
= $false )
| ( ( SV131
= ( ordered_pair @ SV287 @ SV316 ) )
= $false )
| ( ( little_set @ SV320 )
= $false )
| ( ( little_set @ SV316 )
= $false )
| ( ( little_set @ SV287 )
= $false )
| ( ( little_set @ SV131 )
= $false )
| ( ( member @ SV131 @ ( compose @ SV227 @ SV268 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1206]) ).
thf(1208,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[392,1207,1203,1202,1200,1192,1188,1187,1180,1179,1176,1171,1170,1163,1158,1157,1134,1123,1117,1113,1108,1098,1097,1096,1091,1086,1085,1079,1078,1074,1073,1058,1055,1054,1039,1038,1029,1028,1027,1026,1025,1024,1021,1020,1019,1017,1016,1015,1014,1013,1007,1006,1005,1004,1003,999,998,991,990,989,987,986,984,983,959,958,957,944,943,942,941,940,928,925,924,921,920,918,917,916,915,914,912,911,910,909,908,906,905,899,898,897,889,888,887,886,884,883,882,881,875,874,851,844,843,841,840,833,832,823,822,821,819,817,810,808,804,803,773,772,760,759,758,752,719,709,708,694,693,692,691,690,687,670,646,623,622,614,532,484,475,432,393]) ).
thf(1209,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1208]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET025-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.19 % Computer : n008.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Oct 6 14:27:54 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.03/1.05 .
% 5.03/1.05
% 5.03/1.05 No.of.Axioms: 142
% 5.03/1.05
% 5.03/1.05 Length.of.Defs: 0
% 5.03/1.05
% 5.03/1.05 Contains.Choice.Funs: false
% 5.03/1.05 ........................................................
% 5.03/1.05
% 5.03/1.05 ********************************
% 5.03/1.05 * All subproblems solved! *
% 5.03/1.05 ********************************
% 5.03/1.05 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:142,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1208,loop_count:0,foatp_calls:1,translation:fof_full)
% 5.03/1.05
% 5.03/1.05 %**** Beginning of derivation protocol ****
% 5.03/1.05 % SZS output start CNFRefutation
% See solution above
% 5.03/1.05
% 5.03/1.05 %**** End of derivation protocol ****
% 5.03/1.05 %**** no. of clauses in derivation: 1209 ****
% 5.03/1.05 %**** clause counter: 1208 ****
% 5.03/1.05
% 5.03/1.05 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:142,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1208,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------