%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM009-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 : n003.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 10:32:47 AM UTC 2026
% Result : Unsatisfiable 15.67s 2.81s
% Output : CNFRefutation 15.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 221
% Syntax : Number of formulae : 1944 ( 972 unt; 0 typ; 0 def)
% Number of atoms : 13193 (4064 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 28051 (3108 ~;4669 |; 0 &;20274 @)
% ( 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 : 113 ( 110 usr; 14 con; 0-5 aty)
% Number of variables : 4917 ( 0 ^;4917 !; 0 ?;4917 :)
% Comments :
%------------------------------------------------------------------------------
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_associative,type,
associative: $i > $i > $o ).
thf(tp_closed,type,
closed: $i > $i > $o ).
thf(tp_commutes,type,
commutes: $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_even_numbers,type,
even_numbers: $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_f34,type,
f34: $i > $i > $i ).
thf(tp_f35,type,
f35: $i > $i > $i ).
thf(tp_f36,type,
f36: $i > $i > $i ).
thf(tp_f37,type,
f37: $i > $i > $i > $i ).
thf(tp_f38,type,
f38: $i > $i > $i > $i > $i ).
thf(tp_f39,type,
f39: $i > $i > $i ).
thf(tp_f4,type,
f4: $i > $i > $i ).
thf(tp_f40,type,
f40: $i > $i > $i ).
thf(tp_f41,type,
f41: $i > $i > $i ).
thf(tp_f42,type,
f42: $i > $i > $i ).
thf(tp_f43,type,
f43: $i > $i > $i ).
thf(tp_f44,type,
f44: $i > $i ).
thf(tp_f45,type,
f45: $i > $i > $i ).
thf(tp_f46,type,
f46: $i > $i > $i ).
thf(tp_f47,type,
f47: $i > $i > $i ).
thf(tp_f48,type,
f48: $i > $i > $i ).
thf(tp_f49,type,
f49: $i > $i ).
thf(tp_f5,type,
f5: $i > $i > $i ).
thf(tp_f50,type,
f50: $i > $i > $i ).
thf(tp_f51,type,
f51: $i > $i > $i ).
thf(tp_f52,type,
f52: $i > $i > $i ).
thf(tp_f53,type,
f53: $i > $i > $i ).
thf(tp_f54,type,
f54: $i > $i ).
thf(tp_f55,type,
f55: $i > $i ).
thf(tp_f56,type,
f56: $i > $i ).
thf(tp_f57,type,
f57: $i > $i ).
thf(tp_f58,type,
f58: $i > $i ).
thf(tp_f59,type,
f59: $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_finite,type,
finite: $i > $o ).
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_group,type,
group: $i > $i > $o ).
thf(tp_homomorphism,type,
homomorphism: $i > $i > $i > $i > $i > $o ).
thf(tp_identity,type,
identity: $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_inverse,type,
inverse: $i > $i > $i > $i > $o ).
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_natural_numbers,type,
natural_numbers: $i ).
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_plus,type,
plus: $i ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_prime_numbers,type,
prime_numbers: $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_times,type,
times: $i ).
thf(tp_twin_prime_numbers,type,
twin_prime_numbers: $i ).
thf(tp_union,type,
union: $i > $i > $i ).
thf(tp_universal_set,type,
universal_set: $i ).
thf(1,axiom,
! [Z: $i,X: $i] :
( ( member @ Z @ even_numbers )
| ~ ( member @ Z @ natural_numbers )
| ~ ( member @ X @ natural_numbers )
| ( ( apply_to_two_arguments @ plus @ X @ X )
!= Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',even_numbers4) ).
thf(2,axiom,
! [Z: $i] :
( ~ ( member @ Z @ even_numbers )
| ( ( apply_to_two_arguments @ plus @ ( f59 @ Z ) @ ( f59 @ Z ) )
= Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',even_numbers3) ).
thf(3,axiom,
! [Z: $i] :
( ~ ( member @ Z @ even_numbers )
| ( member @ ( f59 @ Z ) @ natural_numbers ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',even_numbers2) ).
thf(4,axiom,
! [Z: $i] :
( ~ ( member @ Z @ even_numbers )
| ( member @ Z @ natural_numbers ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',even_numbers1) ).
thf(5,axiom,
! [Z: $i] :
( ( member @ Z @ twin_prime_numbers )
| ~ ( member @ Z @ prime_numbers )
| ~ ( member @ ( successor @ ( successor @ Z ) ) @ prime_numbers ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',twin_primes3) ).
thf(6,axiom,
! [Z: $i] :
( ~ ( member @ Z @ twin_prime_numbers )
| ( member @ ( successor @ ( successor @ Z ) ) @ prime_numbers ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',twin_primes2) ).
thf(7,axiom,
! [Z: $i] :
( ~ ( member @ Z @ twin_prime_numbers )
| ( member @ Z @ prime_numbers ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',twin_primes1) ).
thf(8,axiom,
! [X: $i,Xn: $i,Xf: $i] :
( ( finite @ X )
| ~ ( member @ Xn @ natural_numbers )
| ~ ( maps @ Xf @ Xn @ X )
| ( ( range_of @ Xf )
!= X )
| ~ ( one_to_one_function @ Xf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite5) ).
thf(9,axiom,
! [X: $i] :
( ~ ( finite @ X )
| ( one_to_one_function @ ( f58 @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite4) ).
thf(10,axiom,
! [X: $i] :
( ~ ( finite @ X )
| ( ( range_of @ ( f58 @ X ) )
= X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite3) ).
thf(11,axiom,
! [X: $i] :
( ~ ( finite @ X )
| ( maps @ ( f58 @ X ) @ ( f57 @ X ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite2) ).
thf(12,axiom,
! [X: $i] :
( ~ ( finite @ X )
| ( member @ ( f57 @ X ) @ natural_numbers ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite1) ).
thf(13,axiom,
! [Z: $i] :
( ( member @ Z @ prime_numbers )
| ~ ( member @ Z @ natural_numbers )
| ( Z = empty_set )
| ( Z
= ( successor @ empty_set ) )
| ~ ( member @ ( f55 @ Z ) @ ( non_ordered_pair @ ( successor @ empty_set ) @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prime_numbers8) ).
thf(14,axiom,
! [Z: $i] :
( ( member @ Z @ prime_numbers )
| ~ ( member @ Z @ natural_numbers )
| ( Z = empty_set )
| ( Z
= ( successor @ empty_set ) )
| ( ( apply_to_two_arguments @ times @ ( f55 @ Z ) @ ( f56 @ Z ) )
= Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prime_numbers7) ).
thf(15,axiom,
! [Z: $i] :
( ( member @ Z @ prime_numbers )
| ~ ( member @ Z @ natural_numbers )
| ( Z = empty_set )
| ( Z
= ( successor @ empty_set ) )
| ( member @ ( f56 @ Z ) @ natural_numbers ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prime_numbers6) ).
thf(16,axiom,
! [Z: $i] :
( ( member @ Z @ prime_numbers )
| ~ ( member @ Z @ natural_numbers )
| ( Z = empty_set )
| ( Z
= ( successor @ empty_set ) )
| ( member @ ( f55 @ Z ) @ natural_numbers ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prime_numbers5) ).
thf(17,axiom,
! [Z: $i,U: $i,V: $i] :
( ~ ( member @ Z @ prime_numbers )
| ~ ( member @ U @ natural_numbers )
| ~ ( member @ V @ natural_numbers )
| ( ( apply_to_two_arguments @ times @ U @ V )
!= Z )
| ( member @ U @ ( non_ordered_pair @ ( successor @ empty_set ) @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prime_numbers4) ).
thf(18,axiom,
! [Z: $i] :
( ~ ( member @ Z @ prime_numbers )
| ( Z
!= ( successor @ empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prime_numbers3) ).
thf(19,axiom,
! [Z: $i] :
( ~ ( member @ Z @ prime_numbers )
| ( Z != empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prime_numbers2) ).
thf(20,axiom,
! [Z: $i] :
( ~ ( member @ Z @ prime_numbers )
| ( member @ Z @ natural_numbers ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prime_numbers1) ).
thf(21,axiom,
! [Z: $i] :
( ( member @ Z @ times )
| ~ ( member @ Z @ ( f54 @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times14) ).
thf(22,axiom,
! [Z: $i,Uu2: $i,Xj: $i,Xk: $i] :
( ( member @ Z @ times )
| ~ ( little_set @ Z )
| ~ ( member @ Uu2 @ natural_numbers )
| ~ ( member @ Xj @ natural_numbers )
| ~ ( member @ Xk @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ Uu2 @ Xj ) @ Xk ) @ ( f54 @ Z ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ Uu2 ) @ Xj ) @ ( apply_to_two_arguments @ plus @ Xk @ Xj ) ) @ ( f54 @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times13) ).
thf(23,axiom,
! [Z: $i,Xi: $i] :
( ( member @ Z @ times )
| ~ ( little_set @ Z )
| ~ ( member @ Xi @ natural_numbers )
| ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ Xi ) @ empty_set ) @ ( f54 @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times12) ).
thf(24,axiom,
! [Z: $i] :
( ( member @ Z @ times )
| ~ ( little_set @ Z )
| ( little_set @ ( f54 @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times11) ).
thf(25,axiom,
! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ times )
| ~ ( little_set @ Xs )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ Z @ Xs ) ) @ empty_set ) @ Xs )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f51 @ Z @ Xs ) ) @ ( f52 @ Z @ Xs ) ) @ ( apply_to_two_arguments @ plus @ ( f53 @ Z @ Xs ) @ ( f52 @ Z @ Xs ) ) ) @ Xs )
| ( member @ Z @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times10) ).
thf(26,axiom,
! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ times )
| ~ ( little_set @ Xs )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ Z @ Xs ) ) @ empty_set ) @ Xs )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( f51 @ Z @ Xs ) @ ( f52 @ Z @ Xs ) ) @ ( f53 @ Z @ Xs ) ) @ Xs )
| ( member @ Z @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times9) ).
thf(27,axiom,
! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ times )
| ~ ( little_set @ Xs )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ Z @ Xs ) ) @ empty_set ) @ Xs )
| ( member @ ( f53 @ Z @ Xs ) @ natural_numbers )
| ( member @ Z @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times8) ).
thf(28,axiom,
! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ times )
| ~ ( little_set @ Xs )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ Z @ Xs ) ) @ empty_set ) @ Xs )
| ( member @ ( f52 @ Z @ Xs ) @ natural_numbers )
| ( member @ Z @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times7) ).
thf(29,axiom,
! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ times )
| ~ ( little_set @ Xs )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ Z @ Xs ) ) @ empty_set ) @ Xs )
| ( member @ ( f51 @ Z @ Xs ) @ natural_numbers )
| ( member @ Z @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times6) ).
thf(30,axiom,
! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ times )
| ~ ( little_set @ Xs )
| ( member @ ( f50 @ Z @ Xs ) @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f51 @ Z @ Xs ) ) @ ( f52 @ Z @ Xs ) ) @ ( apply_to_two_arguments @ plus @ ( f53 @ Z @ Xs ) @ ( f52 @ Z @ Xs ) ) ) @ Xs )
| ( member @ Z @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times5) ).
thf(31,axiom,
! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ times )
| ~ ( little_set @ Xs )
| ( member @ ( f50 @ Z @ Xs ) @ natural_numbers )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( f51 @ Z @ Xs ) @ ( f52 @ Z @ Xs ) ) @ ( f53 @ Z @ Xs ) ) @ Xs )
| ( member @ Z @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times4) ).
thf(32,axiom,
! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ times )
| ~ ( little_set @ Xs )
| ( member @ ( f50 @ Z @ Xs ) @ natural_numbers )
| ( member @ ( f53 @ Z @ Xs ) @ natural_numbers )
| ( member @ Z @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times3) ).
thf(33,axiom,
! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ times )
| ~ ( little_set @ Xs )
| ( member @ ( f50 @ Z @ Xs ) @ natural_numbers )
| ( member @ ( f52 @ Z @ Xs ) @ natural_numbers )
| ( member @ Z @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times2) ).
thf(34,axiom,
! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ times )
| ~ ( little_set @ Xs )
| ( member @ ( f50 @ Z @ Xs ) @ natural_numbers )
| ( member @ ( f51 @ Z @ Xs ) @ natural_numbers )
| ( member @ Z @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times1) ).
thf(35,axiom,
! [Z: $i] :
( ( member @ Z @ plus )
| ~ ( member @ Z @ ( f49 @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus14) ).
thf(36,axiom,
! [Z: $i,Uu1: $i,Xj: $i,Xk: $i] :
( ( member @ Z @ plus )
| ~ ( little_set @ Z )
| ~ ( member @ Uu1 @ natural_numbers )
| ~ ( member @ Xj @ natural_numbers )
| ~ ( member @ Xk @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ Uu1 @ Xj ) @ Xk ) @ ( f49 @ Z ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ Uu1 ) @ Xj ) @ ( successor @ Xk ) ) @ ( f49 @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus13) ).
thf(37,axiom,
! [Z: $i,Xi: $i] :
( ( member @ Z @ plus )
| ~ ( little_set @ Z )
| ~ ( member @ Xi @ natural_numbers )
| ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ Xi ) @ Xi ) @ ( f49 @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus12) ).
thf(38,axiom,
! [Z: $i] :
( ( member @ Z @ plus )
| ~ ( little_set @ Z )
| ( little_set @ ( f49 @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus11) ).
thf(39,axiom,
! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ plus )
| ~ ( little_set @ Xs )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ Z @ Xs ) ) @ ( f45 @ Z @ Xs ) ) @ Xs )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f46 @ Z @ Xs ) ) @ ( f47 @ Z @ Xs ) ) @ ( successor @ ( f48 @ Z @ Xs ) ) ) @ Xs )
| ( member @ Z @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus10) ).
thf(40,axiom,
! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ plus )
| ~ ( little_set @ Xs )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ Z @ Xs ) ) @ ( f45 @ Z @ Xs ) ) @ Xs )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( f46 @ Z @ Xs ) @ ( f47 @ Z @ Xs ) ) @ ( f48 @ Z @ Xs ) ) @ Xs )
| ( member @ Z @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus9) ).
thf(41,axiom,
! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ plus )
| ~ ( little_set @ Xs )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ Z @ Xs ) ) @ ( f45 @ Z @ Xs ) ) @ Xs )
| ( member @ ( f48 @ Z @ Xs ) @ natural_numbers )
| ( member @ Z @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus8) ).
thf(42,axiom,
! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ plus )
| ~ ( little_set @ Xs )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ Z @ Xs ) ) @ ( f45 @ Z @ Xs ) ) @ Xs )
| ( member @ ( f47 @ Z @ Xs ) @ natural_numbers )
| ( member @ Z @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus7) ).
thf(43,axiom,
! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ plus )
| ~ ( little_set @ Xs )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ Z @ Xs ) ) @ ( f45 @ Z @ Xs ) ) @ Xs )
| ( member @ ( f46 @ Z @ Xs ) @ natural_numbers )
| ( member @ Z @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus6) ).
thf(44,axiom,
! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ plus )
| ~ ( little_set @ Xs )
| ( member @ ( f45 @ Z @ Xs ) @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f46 @ Z @ Xs ) ) @ ( f47 @ Z @ Xs ) ) @ ( successor @ ( f48 @ Z @ Xs ) ) ) @ Xs )
| ( member @ Z @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus5) ).
thf(45,axiom,
! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ plus )
| ~ ( little_set @ Xs )
| ( member @ ( f45 @ Z @ Xs ) @ natural_numbers )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( f46 @ Z @ Xs ) @ ( f47 @ Z @ Xs ) ) @ ( f48 @ Z @ Xs ) ) @ Xs )
| ( member @ Z @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus4) ).
thf(46,axiom,
! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ plus )
| ~ ( little_set @ Xs )
| ( member @ ( f45 @ Z @ Xs ) @ natural_numbers )
| ( member @ ( f48 @ Z @ Xs ) @ natural_numbers )
| ( member @ Z @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus3) ).
thf(47,axiom,
! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ plus )
| ~ ( little_set @ Xs )
| ( member @ ( f45 @ Z @ Xs ) @ natural_numbers )
| ( member @ ( f47 @ Z @ Xs ) @ natural_numbers )
| ( member @ Z @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus2) ).
thf(48,axiom,
! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ plus )
| ~ ( little_set @ Xs )
| ( member @ ( f45 @ Z @ Xs ) @ natural_numbers )
| ( member @ ( f46 @ Z @ Xs ) @ natural_numbers )
| ( member @ Z @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus1) ).
thf(49,axiom,
! [Z: $i] :
( ( member @ Z @ natural_numbers )
| ~ ( member @ Z @ ( f44 @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',natural_numbers6) ).
thf(50,axiom,
! [Z: $i,Xk: $i] :
( ( member @ Z @ natural_numbers )
| ~ ( little_set @ Z )
| ~ ( member @ Xk @ ( f44 @ Z ) )
| ( member @ ( successor @ Xk ) @ ( f44 @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',natural_numbers5) ).
thf(51,axiom,
! [Z: $i] :
( ( member @ Z @ natural_numbers )
| ~ ( little_set @ Z )
| ( member @ empty_set @ ( f44 @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',natural_numbers4) ).
thf(52,axiom,
! [Z: $i] :
( ( member @ Z @ natural_numbers )
| ~ ( little_set @ Z )
| ( little_set @ ( f44 @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',natural_numbers3) ).
thf(53,axiom,
! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ natural_numbers )
| ~ ( little_set @ Xs )
| ~ ( member @ empty_set @ Xs )
| ~ ( member @ ( successor @ ( f43 @ Z @ Xs ) ) @ Xs )
| ( member @ Z @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',natural_numbers2) ).
thf(54,axiom,
! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ natural_numbers )
| ~ ( little_set @ Xs )
| ~ ( member @ empty_set @ Xs )
| ( member @ ( f43 @ Z @ Xs ) @ Xs )
| ( member @ Z @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',natural_numbers1) ).
thf(55,axiom,
! [Xs: $i,Xf: $i] :
( ( commutes @ Xs @ Xf )
| ( ( apply_to_two_arguments @ Xf @ ( f41 @ Xs @ Xf ) @ ( f42 @ Xs @ Xf ) )
!= ( apply_to_two_arguments @ Xf @ ( f42 @ Xs @ Xf ) @ ( f41 @ Xs @ Xf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutes4) ).
thf(56,axiom,
! [Xs: $i,Xf: $i] :
( ( commutes @ Xs @ Xf )
| ( member @ ( f42 @ Xs @ Xf ) @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutes3) ).
thf(57,axiom,
! [Xs: $i,Xf: $i] :
( ( commutes @ Xs @ Xf )
| ( member @ ( f41 @ Xs @ Xf ) @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutes2) ).
thf(58,axiom,
! [Xs: $i,Xf: $i,X: $i,Y: $i] :
( ~ ( commutes @ Xs @ Xf )
| ~ ( member @ X @ Xs )
| ~ ( member @ Y @ Xs )
| ( ( apply_to_two_arguments @ Xf @ X @ Y )
= ( apply_to_two_arguments @ Xf @ Y @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutes1) ).
thf(59,axiom,
! [Xs: $i,Xf: $i,Xe: $i,Xg: $i] :
( ( group @ Xs @ Xf )
| ~ ( closed @ Xs @ Xf )
| ~ ( associative @ Xs @ Xf )
| ~ ( identity @ Xs @ Xf @ Xe )
| ~ ( inverse @ Xs @ Xf @ Xe @ Xg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',group5) ).
thf(60,axiom,
! [Xs: $i,Xf: $i] :
( ~ ( group @ Xs @ Xf )
| ( inverse @ Xs @ Xf @ ( f39 @ Xs @ Xf ) @ ( f40 @ Xs @ Xf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',group4) ).
thf(61,axiom,
! [Xs: $i,Xf: $i] :
( ~ ( group @ Xs @ Xf )
| ( identity @ Xs @ Xf @ ( f39 @ Xs @ Xf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',group3) ).
thf(62,axiom,
! [Xs: $i,Xf: $i] :
( ~ ( group @ Xs @ Xf )
| ( associative @ Xs @ Xf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',group2) ).
thf(63,axiom,
! [Xs: $i,Xf: $i] :
( ~ ( group @ Xs @ Xf )
| ( closed @ Xs @ Xf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',group1) ).
thf(64,axiom,
! [Xs: $i,Xf: $i,Xe: $i,Xg: $i] :
( ( inverse @ Xs @ Xf @ Xe @ Xg )
| ~ ( maps @ Xg @ Xs @ Xs )
| ( ( apply_to_two_arguments @ Xf @ ( apply @ Xg @ ( f38 @ Xs @ Xf @ Xe @ Xg ) ) @ ( f38 @ Xs @ Xf @ Xe @ Xg ) )
!= Xe )
| ( ( apply_to_two_arguments @ Xf @ ( f38 @ Xs @ Xf @ Xe @ Xg ) @ ( apply @ Xg @ ( f38 @ Xs @ Xf @ Xe @ Xg ) ) )
!= Xe ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse5) ).
thf(65,axiom,
! [Xs: $i,Xf: $i,Xe: $i,Xg: $i] :
( ( inverse @ Xs @ Xf @ Xe @ Xg )
| ~ ( maps @ Xg @ Xs @ Xs )
| ( member @ ( f38 @ Xs @ Xf @ Xe @ Xg ) @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse4) ).
thf(66,axiom,
! [Xs: $i,Xf: $i,Xe: $i,Xg: $i,X: $i] :
( ~ ( inverse @ Xs @ Xf @ Xe @ Xg )
| ~ ( member @ X @ Xs )
| ( ( apply_to_two_arguments @ Xf @ X @ ( apply @ Xg @ X ) )
= Xe ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse3) ).
thf(67,axiom,
! [Xs: $i,Xf: $i,Xe: $i,Xg: $i,X: $i] :
( ~ ( inverse @ Xs @ Xf @ Xe @ Xg )
| ~ ( member @ X @ Xs )
| ( ( apply_to_two_arguments @ Xf @ ( apply @ Xg @ X ) @ X )
= Xe ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse2) ).
thf(68,axiom,
! [Xs: $i,Xf: $i,Xe: $i,Xg: $i] :
( ~ ( inverse @ Xs @ Xf @ Xe @ Xg )
| ( maps @ Xg @ Xs @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse1) ).
thf(69,axiom,
! [Xs: $i,Xf: $i,Xe: $i] :
( ( identity @ Xs @ Xf @ Xe )
| ~ ( member @ Xe @ Xs )
| ( ( apply_to_two_arguments @ Xf @ Xe @ ( f37 @ Xs @ Xf @ Xe ) )
!= ( f37 @ Xs @ Xf @ Xe ) )
| ( ( apply_to_two_arguments @ Xf @ ( f37 @ Xs @ Xf @ Xe ) @ Xe )
!= ( f37 @ Xs @ Xf @ Xe ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity5) ).
thf(70,axiom,
! [Xs: $i,Xf: $i,Xe: $i] :
( ( identity @ Xs @ Xf @ Xe )
| ~ ( member @ Xe @ Xs )
| ( member @ ( f37 @ Xs @ Xf @ Xe ) @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity4) ).
thf(71,axiom,
! [Xs: $i,Xf: $i,Xe: $i,X: $i] :
( ~ ( identity @ Xs @ Xf @ Xe )
| ~ ( member @ X @ Xs )
| ( ( apply_to_two_arguments @ Xf @ X @ Xe )
= X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity3) ).
thf(72,axiom,
! [Xs: $i,Xf: $i,Xe: $i,X: $i] :
( ~ ( identity @ Xs @ Xf @ Xe )
| ~ ( member @ X @ Xs )
| ( ( apply_to_two_arguments @ Xf @ Xe @ X )
= X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity2) ).
thf(73,axiom,
! [Xs: $i,Xf: $i,Xe: $i] :
( ~ ( identity @ Xs @ Xf @ Xe )
| ( member @ Xe @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity1) ).
thf(74,axiom,
! [Xs: $i,Xf: $i] :
( ( associative @ Xs @ Xf )
| ( ( apply_to_two_arguments @ Xf @ ( apply_to_two_arguments @ Xf @ ( f34 @ Xs @ Xf ) @ ( f35 @ Xs @ Xf ) ) @ ( f36 @ Xs @ Xf ) )
!= ( apply_to_two_arguments @ Xf @ ( f34 @ Xs @ Xf ) @ ( apply_to_two_arguments @ Xf @ ( f35 @ Xs @ Xf ) @ ( f36 @ Xs @ Xf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associative_system5) ).
thf(75,axiom,
! [Xs: $i,Xf: $i] :
( ( associative @ Xs @ Xf )
| ( member @ ( f36 @ Xs @ Xf ) @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associative_system4) ).
thf(76,axiom,
! [Xs: $i,Xf: $i] :
( ( associative @ Xs @ Xf )
| ( member @ ( f35 @ Xs @ Xf ) @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associative_system3) ).
thf(77,axiom,
! [Xs: $i,Xf: $i] :
( ( associative @ Xs @ Xf )
| ( member @ ( f34 @ Xs @ Xf ) @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associative_system2) ).
thf(78,axiom,
! [Xs: $i,Xf: $i,X: $i,Y: $i,Z: $i] :
( ~ ( associative @ Xs @ Xf )
| ~ ( member @ X @ Xs )
| ~ ( member @ Y @ Xs )
| ~ ( member @ Z @ Xs )
| ( ( apply_to_two_arguments @ Xf @ ( apply_to_two_arguments @ Xf @ X @ Y ) @ Z )
= ( apply_to_two_arguments @ Xf @ X @ ( apply_to_two_arguments @ Xf @ Y @ Z ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associative_system1) ).
thf(79,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(80,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(81,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(82,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(83,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(84,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(85,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(86,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(87,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(88,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(89,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(90,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(91,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(92,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(93,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(94,axiom,
! [Xs: $i,Xf: $i] :
( ~ ( closed @ Xs @ Xf )
| ( maps @ Xf @ ( cross_product @ Xs @ Xs ) @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closed3) ).
thf(95,axiom,
! [Xs: $i,Xf: $i] :
( ~ ( closed @ Xs @ Xf )
| ( little_set @ Xf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closed2) ).
thf(96,axiom,
! [Xs: $i,Xf: $i] :
( ~ ( closed @ Xs @ Xf )
| ( little_set @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closed1) ).
thf(97,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(98,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(99,axiom,
! [Xf: $i,X: $i,Y: $i] :
( ~ ( maps @ Xf @ X @ Y )
| ( ( domain_of @ Xf )
= X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps2) ).
thf(100,axiom,
! [Xf: $i,X: $i,Y: $i] :
( ~ ( maps @ Xf @ X @ Y )
| ( function @ Xf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps1) ).
thf(101,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(102,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(103,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(104,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(105,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(106,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(107,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(108,axiom,
! [Xf: $i] :
( ~ ( one_to_one_function @ Xf )
| ( function @ ( converse @ Xf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one_function2) ).
thf(109,axiom,
! [Xf: $i] :
( ~ ( one_to_one_function @ Xf )
| ( function @ Xf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one_function1) ).
thf(110,axiom,
! [X: $i,Y: $i] :
( ( restrict @ X @ Y )
= ( intersection @ X @ ( cross_product @ Y @ universal_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',restrict) ).
thf(111,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(112,axiom,
! [Z: $i] :
( ~ ( member @ Z @ identity_relation )
| ( ( first @ Z )
= ( second @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_relation2) ).
thf(113,axiom,
! [Z: $i] :
( ~ ( member @ Z @ identity_relation )
| ( ordered_pair_predicate @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_relation1) ).
thf(114,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(115,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(116,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(117,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(118,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(119,axiom,
! [X: $i] :
( ~ ( little_set @ X )
| ( X = empty_set )
| ( member @ ( f26 @ X ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice2) ).
thf(120,axiom,
function @ f25,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice1) ).
thf(121,axiom,
! [X: $i] :
( ( X = empty_set )
| ( disjoint @ ( f24 @ X ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity2) ).
thf(122,axiom,
! [X: $i] :
( ( X = empty_set )
| ( member @ ( f24 @ X ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity1) ).
thf(123,axiom,
! [X: $i,Y: $i] :
( ( disjoint @ X @ Y )
| ( member @ ( f23 @ X @ Y ) @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint3) ).
thf(124,axiom,
! [X: $i,Y: $i] :
( ( disjoint @ X @ Y )
| ( member @ ( f23 @ X @ Y ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint2) ).
thf(125,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(126,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(127,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(128,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(129,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(130,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(131,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(132,axiom,
! [Xf: $i] :
( ( function @ Xf )
| ~ ( relation @ Xf )
| ~ ( single_valued_set @ Xf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function3) ).
thf(133,axiom,
! [Xf: $i] :
( ~ ( function @ Xf )
| ( single_valued_set @ Xf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function2) ).
thf(134,axiom,
! [Xf: $i] :
( ~ ( function @ Xf )
| ( relation @ Xf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function1) ).
thf(135,axiom,
! [X: $i] :
( ( single_valued_set @ X )
| ( ( f20 @ X )
!= ( f21 @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_set7) ).
thf(136,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(137,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(138,axiom,
! [X: $i] :
( ( single_valued_set @ X )
| ( little_set @ ( f21 @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_set4) ).
thf(139,axiom,
! [X: $i] :
( ( single_valued_set @ X )
| ( little_set @ ( f20 @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_set3) ).
thf(140,axiom,
! [X: $i] :
( ( single_valued_set @ X )
| ( little_set @ ( f19 @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_set2) ).
thf(141,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(142,axiom,
! [Z: $i] :
( ( relation @ Z )
| ~ ( ordered_pair_predicate @ ( f18 @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',relation3) ).
thf(143,axiom,
! [Z: $i] :
( ( relation @ Z )
| ( member @ ( f18 @ Z ) @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',relation2) ).
thf(144,axiom,
! [Z: $i,X: $i] :
( ~ ( relation @ Z )
| ~ ( member @ X @ Z )
| ( ordered_pair_predicate @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',relation1) ).
thf(145,axiom,
! [U: $i] :
( ~ ( little_set @ U )
| ( little_set @ ( powerset @ U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset3) ).
thf(146,axiom,
! [Z: $i,X: $i] :
( ( member @ Z @ ( powerset @ X ) )
| ~ ( little_set @ Z )
| ~ ( subset @ Z @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset2) ).
thf(147,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( powerset @ X ) )
| ( subset @ Z @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset1) ).
thf(148,axiom,
! [X: $i,Y: $i] :
( ( proper_subset @ X @ Y )
| ~ ( subset @ X @ Y )
| ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',proper_subset3) ).
thf(149,axiom,
! [X: $i,Y: $i] :
( ~ ( proper_subset @ X @ Y )
| ( X != Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',proper_subset2) ).
thf(150,axiom,
! [X: $i,Y: $i] :
( ~ ( proper_subset @ X @ Y )
| ( subset @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',proper_subset1) ).
thf(151,axiom,
! [X: $i,Y: $i] :
( ( subset @ X @ Y )
| ~ ( member @ ( f17 @ X @ Y ) @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset3) ).
thf(152,axiom,
! [X: $i,Y: $i] :
( ( subset @ X @ Y )
| ( member @ ( f17 @ X @ Y ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2) ).
thf(153,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(154,axiom,
! [U: $i] :
( ~ ( little_set @ U )
| ( little_set @ ( sigma @ U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sigma4) ).
thf(155,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(156,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( sigma @ X ) )
| ( member @ Z @ ( f16 @ Z @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sigma2) ).
thf(157,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( sigma @ X ) )
| ( member @ ( f16 @ Z @ X ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sigma1) ).
thf(158,axiom,
! [X: $i] :
( ~ ( member @ X @ infinity )
| ( member @ ( successor @ X ) @ infinity ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infinity3) ).
thf(159,axiom,
member @ empty_set @ infinity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infinity2) ).
thf(160,axiom,
little_set @ infinity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infinity1) ).
thf(161,axiom,
! [Z: $i] :
( ( member @ Z @ universal_set )
| ~ ( little_set @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',universal_set) ).
thf(162,axiom,
! [Z: $i] :
~ ( member @ Z @ empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).
thf(163,axiom,
! [X: $i] :
( ( successor @ X )
= ( union @ X @ ( singleton_set @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor) ).
thf(164,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(165,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(166,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(167,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(168,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(169,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(170,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(171,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(172,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(173,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(174,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(175,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(176,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(177,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(178,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( converse @ X ) )
| ( ordered_pair_predicate @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse1) ).
thf(179,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(180,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(181,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(182,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(183,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(184,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( domain_of @ X ) )
| ( Z
= ( first @ ( f8 @ Z @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain3) ).
thf(185,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( domain_of @ X ) )
| ( member @ ( f8 @ Z @ X ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain2) ).
thf(186,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(187,axiom,
! [X: $i,Y: $i] :
( ( union @ X @ Y )
= ( complement @ ( intersection @ ( complement @ X ) @ ( complement @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
thf(188,axiom,
! [Z: $i,X: $i] :
( ( member @ Z @ ( complement @ X ) )
| ~ ( little_set @ Z )
| ( member @ Z @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).
thf(189,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( complement @ X ) )
| ~ ( member @ Z @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
thf(190,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(191,axiom,
! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( intersection @ X @ Y ) )
| ( member @ Z @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).
thf(192,axiom,
! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( intersection @ X @ Y ) )
| ( member @ Z @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
thf(193,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(194,axiom,
! [Z: $i] :
( ~ ( member @ Z @ estin )
| ( member @ ( first @ Z ) @ ( second @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation2) ).
thf(195,axiom,
! [Z: $i] :
( ~ ( member @ Z @ estin )
| ( ordered_pair_predicate @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation1) ).
thf(196,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(197,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( second @ X ) )
| ( member @ Z @ ( f7 @ Z @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',second4) ).
thf(198,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(199,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( second @ X ) )
| ( little_set @ ( f7 @ Z @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',second2) ).
thf(200,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( second @ X ) )
| ( little_set @ ( f6 @ Z @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',second1) ).
thf(201,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(202,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( first @ X ) )
| ( member @ Z @ ( f4 @ Z @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first4) ).
thf(203,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(204,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( first @ X ) )
| ( little_set @ ( f5 @ Z @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first2) ).
thf(205,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( first @ X ) )
| ( little_set @ ( f4 @ Z @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first1) ).
thf(206,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(207,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(208,axiom,
! [X: $i] :
( ~ ( ordered_pair_predicate @ X )
| ( little_set @ ( f3 @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_predicate2) ).
thf(209,axiom,
! [X: $i] :
( ~ ( ordered_pair_predicate @ X )
| ( little_set @ ( f2 @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_predicate1) ).
thf(210,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(211,axiom,
! [X: $i] :
( ( singleton_set @ X )
= ( non_ordered_pair @ X @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
thf(212,axiom,
! [X: $i,Y: $i] : ( little_set @ ( non_ordered_pair @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',non_ordered_pair4) ).
thf(213,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(214,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(215,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(216,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(217,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(218,axiom,
! [X: $i,Y: $i] :
( ( little_set @ ( f1 @ X @ Y ) )
| ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality1) ).
thf(219,axiom,
! [X: $i,Y: $i] :
( ~ ( member @ X @ Y )
| ( little_set @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
thf(220,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(221,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[220]) ).
thf(222,negated_conjecture,
~ ( member @ empty_set @ natural_numbers ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_zero_is_a_natural) ).
thf(223,plain,
$false = $false,
inference(unfold_def,[status(thm)],[221]) ).
thf(224,plain,
( ( ! [Z: $i,X: $i] :
( ( member @ Z @ even_numbers )
| ~ ( member @ Z @ natural_numbers )
| ~ ( member @ X @ natural_numbers )
| ( ( apply_to_two_arguments @ plus @ X @ X )
!= Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(225,plain,
( ( ! [Z: $i] :
( ~ ( member @ Z @ even_numbers )
| ( ( apply_to_two_arguments @ plus @ ( f59 @ Z ) @ ( f59 @ Z ) )
= Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(226,plain,
( ( ! [Z: $i] :
( ~ ( member @ Z @ even_numbers )
| ( member @ ( f59 @ Z ) @ natural_numbers ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(227,plain,
( ( ! [Z: $i] :
( ~ ( member @ Z @ even_numbers )
| ( member @ Z @ natural_numbers ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(228,plain,
( ( ! [Z: $i] :
( ( member @ Z @ twin_prime_numbers )
| ~ ( member @ Z @ prime_numbers )
| ~ ( member @ ( successor @ ( successor @ Z ) ) @ prime_numbers ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(229,plain,
( ( ! [Z: $i] :
( ~ ( member @ Z @ twin_prime_numbers )
| ( member @ ( successor @ ( successor @ Z ) ) @ prime_numbers ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(230,plain,
( ( ! [Z: $i] :
( ~ ( member @ Z @ twin_prime_numbers )
| ( member @ Z @ prime_numbers ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(231,plain,
( ( ! [X: $i,Xn: $i,Xf: $i] :
( ( finite @ X )
| ~ ( member @ Xn @ natural_numbers )
| ~ ( maps @ Xf @ Xn @ X )
| ( ( range_of @ Xf )
!= X )
| ~ ( one_to_one_function @ Xf ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(232,plain,
( ( ! [X: $i] :
( ~ ( finite @ X )
| ( one_to_one_function @ ( f58 @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(233,plain,
( ( ! [X: $i] :
( ~ ( finite @ X )
| ( ( range_of @ ( f58 @ X ) )
= X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(234,plain,
( ( ! [X: $i] :
( ~ ( finite @ X )
| ( maps @ ( f58 @ X ) @ ( f57 @ X ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(235,plain,
( ( ! [X: $i] :
( ~ ( finite @ X )
| ( member @ ( f57 @ X ) @ natural_numbers ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(236,plain,
( ( ! [Z: $i] :
( ( member @ Z @ prime_numbers )
| ~ ( member @ Z @ natural_numbers )
| ( Z = empty_set )
| ( Z
= ( successor @ empty_set ) )
| ~ ( member @ ( f55 @ Z ) @ ( non_ordered_pair @ ( successor @ empty_set ) @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(237,plain,
( ( ! [Z: $i] :
( ( member @ Z @ prime_numbers )
| ~ ( member @ Z @ natural_numbers )
| ( Z = empty_set )
| ( Z
= ( successor @ empty_set ) )
| ( ( apply_to_two_arguments @ times @ ( f55 @ Z ) @ ( f56 @ Z ) )
= Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(238,plain,
( ( ! [Z: $i] :
( ( member @ Z @ prime_numbers )
| ~ ( member @ Z @ natural_numbers )
| ( Z = empty_set )
| ( Z
= ( successor @ empty_set ) )
| ( member @ ( f56 @ Z ) @ natural_numbers ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(239,plain,
( ( ! [Z: $i] :
( ( member @ Z @ prime_numbers )
| ~ ( member @ Z @ natural_numbers )
| ( Z = empty_set )
| ( Z
= ( successor @ empty_set ) )
| ( member @ ( f55 @ Z ) @ natural_numbers ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(240,plain,
( ( ! [Z: $i,U: $i,V: $i] :
( ~ ( member @ Z @ prime_numbers )
| ~ ( member @ U @ natural_numbers )
| ~ ( member @ V @ natural_numbers )
| ( ( apply_to_two_arguments @ times @ U @ V )
!= Z )
| ( member @ U @ ( non_ordered_pair @ ( successor @ empty_set ) @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(241,plain,
( ( ! [Z: $i] :
( ~ ( member @ Z @ prime_numbers )
| ( Z
!= ( successor @ empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(242,plain,
( ( ! [Z: $i] :
( ~ ( member @ Z @ prime_numbers )
| ( Z != empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(243,plain,
( ( ! [Z: $i] :
( ~ ( member @ Z @ prime_numbers )
| ( member @ Z @ natural_numbers ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(244,plain,
( ( ! [Z: $i] :
( ( member @ Z @ times )
| ~ ( member @ Z @ ( f54 @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(245,plain,
( ( ! [Z: $i,Uu2: $i,Xj: $i,Xk: $i] :
( ( member @ Z @ times )
| ~ ( little_set @ Z )
| ~ ( member @ Uu2 @ natural_numbers )
| ~ ( member @ Xj @ natural_numbers )
| ~ ( member @ Xk @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ Uu2 @ Xj ) @ Xk ) @ ( f54 @ Z ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ Uu2 ) @ Xj ) @ ( apply_to_two_arguments @ plus @ Xk @ Xj ) ) @ ( f54 @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(246,plain,
( ( ! [Z: $i,Xi: $i] :
( ( member @ Z @ times )
| ~ ( little_set @ Z )
| ~ ( member @ Xi @ natural_numbers )
| ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ Xi ) @ empty_set ) @ ( f54 @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(247,plain,
( ( ! [Z: $i] :
( ( member @ Z @ times )
| ~ ( little_set @ Z )
| ( little_set @ ( f54 @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(248,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ times )
| ~ ( little_set @ Xs )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ Z @ Xs ) ) @ empty_set ) @ Xs )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f51 @ Z @ Xs ) ) @ ( f52 @ Z @ Xs ) ) @ ( apply_to_two_arguments @ plus @ ( f53 @ Z @ Xs ) @ ( f52 @ Z @ Xs ) ) ) @ Xs )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(249,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ times )
| ~ ( little_set @ Xs )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ Z @ Xs ) ) @ empty_set ) @ Xs )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( f51 @ Z @ Xs ) @ ( f52 @ Z @ Xs ) ) @ ( f53 @ Z @ Xs ) ) @ Xs )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(250,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ times )
| ~ ( little_set @ Xs )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ Z @ Xs ) ) @ empty_set ) @ Xs )
| ( member @ ( f53 @ Z @ Xs ) @ natural_numbers )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(251,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ times )
| ~ ( little_set @ Xs )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ Z @ Xs ) ) @ empty_set ) @ Xs )
| ( member @ ( f52 @ Z @ Xs ) @ natural_numbers )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(252,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ times )
| ~ ( little_set @ Xs )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ Z @ Xs ) ) @ empty_set ) @ Xs )
| ( member @ ( f51 @ Z @ Xs ) @ natural_numbers )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(253,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ times )
| ~ ( little_set @ Xs )
| ( member @ ( f50 @ Z @ Xs ) @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f51 @ Z @ Xs ) ) @ ( f52 @ Z @ Xs ) ) @ ( apply_to_two_arguments @ plus @ ( f53 @ Z @ Xs ) @ ( f52 @ Z @ Xs ) ) ) @ Xs )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(254,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ times )
| ~ ( little_set @ Xs )
| ( member @ ( f50 @ Z @ Xs ) @ natural_numbers )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( f51 @ Z @ Xs ) @ ( f52 @ Z @ Xs ) ) @ ( f53 @ Z @ Xs ) ) @ Xs )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(255,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ times )
| ~ ( little_set @ Xs )
| ( member @ ( f50 @ Z @ Xs ) @ natural_numbers )
| ( member @ ( f53 @ Z @ Xs ) @ natural_numbers )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(256,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ times )
| ~ ( little_set @ Xs )
| ( member @ ( f50 @ Z @ Xs ) @ natural_numbers )
| ( member @ ( f52 @ Z @ Xs ) @ natural_numbers )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(257,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ times )
| ~ ( little_set @ Xs )
| ( member @ ( f50 @ Z @ Xs ) @ natural_numbers )
| ( member @ ( f51 @ Z @ Xs ) @ natural_numbers )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(258,plain,
( ( ! [Z: $i] :
( ( member @ Z @ plus )
| ~ ( member @ Z @ ( f49 @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(259,plain,
( ( ! [Z: $i,Uu1: $i,Xj: $i,Xk: $i] :
( ( member @ Z @ plus )
| ~ ( little_set @ Z )
| ~ ( member @ Uu1 @ natural_numbers )
| ~ ( member @ Xj @ natural_numbers )
| ~ ( member @ Xk @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ Uu1 @ Xj ) @ Xk ) @ ( f49 @ Z ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ Uu1 ) @ Xj ) @ ( successor @ Xk ) ) @ ( f49 @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(260,plain,
( ( ! [Z: $i,Xi: $i] :
( ( member @ Z @ plus )
| ~ ( little_set @ Z )
| ~ ( member @ Xi @ natural_numbers )
| ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ Xi ) @ Xi ) @ ( f49 @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(261,plain,
( ( ! [Z: $i] :
( ( member @ Z @ plus )
| ~ ( little_set @ Z )
| ( little_set @ ( f49 @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(262,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ plus )
| ~ ( little_set @ Xs )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ Z @ Xs ) ) @ ( f45 @ Z @ Xs ) ) @ Xs )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f46 @ Z @ Xs ) ) @ ( f47 @ Z @ Xs ) ) @ ( successor @ ( f48 @ Z @ Xs ) ) ) @ Xs )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(263,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ plus )
| ~ ( little_set @ Xs )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ Z @ Xs ) ) @ ( f45 @ Z @ Xs ) ) @ Xs )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( f46 @ Z @ Xs ) @ ( f47 @ Z @ Xs ) ) @ ( f48 @ Z @ Xs ) ) @ Xs )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(264,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ plus )
| ~ ( little_set @ Xs )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ Z @ Xs ) ) @ ( f45 @ Z @ Xs ) ) @ Xs )
| ( member @ ( f48 @ Z @ Xs ) @ natural_numbers )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(265,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ plus )
| ~ ( little_set @ Xs )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ Z @ Xs ) ) @ ( f45 @ Z @ Xs ) ) @ Xs )
| ( member @ ( f47 @ Z @ Xs ) @ natural_numbers )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(266,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ plus )
| ~ ( little_set @ Xs )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ Z @ Xs ) ) @ ( f45 @ Z @ Xs ) ) @ Xs )
| ( member @ ( f46 @ Z @ Xs ) @ natural_numbers )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(267,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ plus )
| ~ ( little_set @ Xs )
| ( member @ ( f45 @ Z @ Xs ) @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f46 @ Z @ Xs ) ) @ ( f47 @ Z @ Xs ) ) @ ( successor @ ( f48 @ Z @ Xs ) ) ) @ Xs )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(268,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ plus )
| ~ ( little_set @ Xs )
| ( member @ ( f45 @ Z @ Xs ) @ natural_numbers )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( f46 @ Z @ Xs ) @ ( f47 @ Z @ Xs ) ) @ ( f48 @ Z @ Xs ) ) @ Xs )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(269,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ plus )
| ~ ( little_set @ Xs )
| ( member @ ( f45 @ Z @ Xs ) @ natural_numbers )
| ( member @ ( f48 @ Z @ Xs ) @ natural_numbers )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(270,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ plus )
| ~ ( little_set @ Xs )
| ( member @ ( f45 @ Z @ Xs ) @ natural_numbers )
| ( member @ ( f47 @ Z @ Xs ) @ natural_numbers )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(271,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ plus )
| ~ ( little_set @ Xs )
| ( member @ ( f45 @ Z @ Xs ) @ natural_numbers )
| ( member @ ( f46 @ Z @ Xs ) @ natural_numbers )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(272,plain,
( ( ! [Z: $i] :
( ( member @ Z @ natural_numbers )
| ~ ( member @ Z @ ( f44 @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(273,plain,
( ( ! [Z: $i,Xk: $i] :
( ( member @ Z @ natural_numbers )
| ~ ( little_set @ Z )
| ~ ( member @ Xk @ ( f44 @ Z ) )
| ( member @ ( successor @ Xk ) @ ( f44 @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(274,plain,
( ( ! [Z: $i] :
( ( member @ Z @ natural_numbers )
| ~ ( little_set @ Z )
| ( member @ empty_set @ ( f44 @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(275,plain,
( ( ! [Z: $i] :
( ( member @ Z @ natural_numbers )
| ~ ( little_set @ Z )
| ( little_set @ ( f44 @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(276,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ natural_numbers )
| ~ ( little_set @ Xs )
| ~ ( member @ empty_set @ Xs )
| ~ ( member @ ( successor @ ( f43 @ Z @ Xs ) ) @ Xs )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(277,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ natural_numbers )
| ~ ( little_set @ Xs )
| ~ ( member @ empty_set @ Xs )
| ( member @ ( f43 @ Z @ Xs ) @ Xs )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(278,plain,
( ( ! [Xs: $i,Xf: $i] :
( ( commutes @ Xs @ Xf )
| ( ( apply_to_two_arguments @ Xf @ ( f41 @ Xs @ Xf ) @ ( f42 @ Xs @ Xf ) )
!= ( apply_to_two_arguments @ Xf @ ( f42 @ Xs @ Xf ) @ ( f41 @ Xs @ Xf ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(279,plain,
( ( ! [Xs: $i,Xf: $i] :
( ( commutes @ Xs @ Xf )
| ( member @ ( f42 @ Xs @ Xf ) @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(280,plain,
( ( ! [Xs: $i,Xf: $i] :
( ( commutes @ Xs @ Xf )
| ( member @ ( f41 @ Xs @ Xf ) @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(281,plain,
( ( ! [Xs: $i,Xf: $i,X: $i,Y: $i] :
( ~ ( commutes @ Xs @ Xf )
| ~ ( member @ X @ Xs )
| ~ ( member @ Y @ Xs )
| ( ( apply_to_two_arguments @ Xf @ X @ Y )
= ( apply_to_two_arguments @ Xf @ Y @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(282,plain,
( ( ! [Xs: $i,Xf: $i,Xe: $i,Xg: $i] :
( ( group @ Xs @ Xf )
| ~ ( closed @ Xs @ Xf )
| ~ ( associative @ Xs @ Xf )
| ~ ( identity @ Xs @ Xf @ Xe )
| ~ ( inverse @ Xs @ Xf @ Xe @ Xg ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(283,plain,
( ( ! [Xs: $i,Xf: $i] :
( ~ ( group @ Xs @ Xf )
| ( inverse @ Xs @ Xf @ ( f39 @ Xs @ Xf ) @ ( f40 @ Xs @ Xf ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(284,plain,
( ( ! [Xs: $i,Xf: $i] :
( ~ ( group @ Xs @ Xf )
| ( identity @ Xs @ Xf @ ( f39 @ Xs @ Xf ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(285,plain,
( ( ! [Xs: $i,Xf: $i] :
( ~ ( group @ Xs @ Xf )
| ( associative @ Xs @ Xf ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(286,plain,
( ( ! [Xs: $i,Xf: $i] :
( ~ ( group @ Xs @ Xf )
| ( closed @ Xs @ Xf ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(287,plain,
( ( ! [Xs: $i,Xf: $i,Xe: $i,Xg: $i] :
( ( inverse @ Xs @ Xf @ Xe @ Xg )
| ~ ( maps @ Xg @ Xs @ Xs )
| ( ( apply_to_two_arguments @ Xf @ ( apply @ Xg @ ( f38 @ Xs @ Xf @ Xe @ Xg ) ) @ ( f38 @ Xs @ Xf @ Xe @ Xg ) )
!= Xe )
| ( ( apply_to_two_arguments @ Xf @ ( f38 @ Xs @ Xf @ Xe @ Xg ) @ ( apply @ Xg @ ( f38 @ Xs @ Xf @ Xe @ Xg ) ) )
!= Xe ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(288,plain,
( ( ! [Xs: $i,Xf: $i,Xe: $i,Xg: $i] :
( ( inverse @ Xs @ Xf @ Xe @ Xg )
| ~ ( maps @ Xg @ Xs @ Xs )
| ( member @ ( f38 @ Xs @ Xf @ Xe @ Xg ) @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(289,plain,
( ( ! [Xs: $i,Xf: $i,Xe: $i,Xg: $i,X: $i] :
( ~ ( inverse @ Xs @ Xf @ Xe @ Xg )
| ~ ( member @ X @ Xs )
| ( ( apply_to_two_arguments @ Xf @ X @ ( apply @ Xg @ X ) )
= Xe ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(290,plain,
( ( ! [Xs: $i,Xf: $i,Xe: $i,Xg: $i,X: $i] :
( ~ ( inverse @ Xs @ Xf @ Xe @ Xg )
| ~ ( member @ X @ Xs )
| ( ( apply_to_two_arguments @ Xf @ ( apply @ Xg @ X ) @ X )
= Xe ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(291,plain,
( ( ! [Xs: $i,Xf: $i,Xe: $i,Xg: $i] :
( ~ ( inverse @ Xs @ Xf @ Xe @ Xg )
| ( maps @ Xg @ Xs @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(292,plain,
( ( ! [Xs: $i,Xf: $i,Xe: $i] :
( ( identity @ Xs @ Xf @ Xe )
| ~ ( member @ Xe @ Xs )
| ( ( apply_to_two_arguments @ Xf @ Xe @ ( f37 @ Xs @ Xf @ Xe ) )
!= ( f37 @ Xs @ Xf @ Xe ) )
| ( ( apply_to_two_arguments @ Xf @ ( f37 @ Xs @ Xf @ Xe ) @ Xe )
!= ( f37 @ Xs @ Xf @ Xe ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(293,plain,
( ( ! [Xs: $i,Xf: $i,Xe: $i] :
( ( identity @ Xs @ Xf @ Xe )
| ~ ( member @ Xe @ Xs )
| ( member @ ( f37 @ Xs @ Xf @ Xe ) @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(294,plain,
( ( ! [Xs: $i,Xf: $i,Xe: $i,X: $i] :
( ~ ( identity @ Xs @ Xf @ Xe )
| ~ ( member @ X @ Xs )
| ( ( apply_to_two_arguments @ Xf @ X @ Xe )
= X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(295,plain,
( ( ! [Xs: $i,Xf: $i,Xe: $i,X: $i] :
( ~ ( identity @ Xs @ Xf @ Xe )
| ~ ( member @ X @ Xs )
| ( ( apply_to_two_arguments @ Xf @ Xe @ X )
= X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(296,plain,
( ( ! [Xs: $i,Xf: $i,Xe: $i] :
( ~ ( identity @ Xs @ Xf @ Xe )
| ( member @ Xe @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(297,plain,
( ( ! [Xs: $i,Xf: $i] :
( ( associative @ Xs @ Xf )
| ( ( apply_to_two_arguments @ Xf @ ( apply_to_two_arguments @ Xf @ ( f34 @ Xs @ Xf ) @ ( f35 @ Xs @ Xf ) ) @ ( f36 @ Xs @ Xf ) )
!= ( apply_to_two_arguments @ Xf @ ( f34 @ Xs @ Xf ) @ ( apply_to_two_arguments @ Xf @ ( f35 @ Xs @ Xf ) @ ( f36 @ Xs @ Xf ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(298,plain,
( ( ! [Xs: $i,Xf: $i] :
( ( associative @ Xs @ Xf )
| ( member @ ( f36 @ Xs @ Xf ) @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(299,plain,
( ( ! [Xs: $i,Xf: $i] :
( ( associative @ Xs @ Xf )
| ( member @ ( f35 @ Xs @ Xf ) @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(300,plain,
( ( ! [Xs: $i,Xf: $i] :
( ( associative @ Xs @ Xf )
| ( member @ ( f34 @ Xs @ Xf ) @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(301,plain,
( ( ! [Xs: $i,Xf: $i,X: $i,Y: $i,Z: $i] :
( ~ ( associative @ Xs @ Xf )
| ~ ( member @ X @ Xs )
| ~ ( member @ Y @ Xs )
| ~ ( member @ Z @ Xs )
| ( ( apply_to_two_arguments @ Xf @ ( apply_to_two_arguments @ Xf @ X @ Y ) @ Z )
= ( apply_to_two_arguments @ Xf @ X @ ( apply_to_two_arguments @ Xf @ Y @ Z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(302,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)],[79]) ).
thf(303,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)],[80]) ).
thf(304,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)],[81]) ).
thf(305,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)],[82]) ).
thf(306,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)],[83]) ).
thf(307,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)],[84]) ).
thf(308,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)],[85]) ).
thf(309,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)],[86]) ).
thf(310,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)],[87]) ).
thf(311,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)],[88]) ).
thf(312,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)],[89]) ).
thf(313,plain,
( ( ! [Z: $i,Xf: $i,Xg: $i] :
( ~ ( member @ Z @ ( compose @ Xf @ Xg ) )
| ( little_set @ ( f31 @ Z @ Xf @ Xg ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(314,plain,
( ( ! [Z: $i,Xf: $i,Xg: $i] :
( ~ ( member @ Z @ ( compose @ Xf @ Xg ) )
| ( little_set @ ( f30 @ Z @ Xf @ Xg ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(315,plain,
( ( ! [Z: $i,Xf: $i,Xg: $i] :
( ~ ( member @ Z @ ( compose @ Xf @ Xg ) )
| ( little_set @ ( f29 @ Z @ Xf @ Xg ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(316,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)],[93]) ).
thf(317,plain,
( ( ! [Xs: $i,Xf: $i] :
( ~ ( closed @ Xs @ Xf )
| ( maps @ Xf @ ( cross_product @ Xs @ Xs ) @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(318,plain,
( ( ! [Xs: $i,Xf: $i] :
( ~ ( closed @ Xs @ Xf )
| ( little_set @ Xf ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(319,plain,
( ( ! [Xs: $i,Xf: $i] :
( ~ ( closed @ Xs @ Xf )
| ( little_set @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(320,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)],[97]) ).
thf(321,plain,
( ( ! [Xf: $i,X: $i,Y: $i] :
( ~ ( maps @ Xf @ X @ Y )
| ( subset @ ( range_of @ Xf ) @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(322,plain,
( ( ! [Xf: $i,X: $i,Y: $i] :
( ~ ( maps @ Xf @ X @ Y )
| ( ( domain_of @ Xf )
= X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(323,plain,
( ( ! [Xf: $i,X: $i,Y: $i] :
( ~ ( maps @ Xf @ X @ Y )
| ( function @ Xf ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(324,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)],[101]) ).
thf(325,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)],[102]) ).
thf(326,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)],[103]) ).
thf(327,plain,
( ( ! [Z: $i,Xf: $i,Y: $i] :
( ~ ( member @ Z @ ( apply @ Xf @ Y ) )
| ( ( first @ ( f28 @ Z @ Xf @ Y ) )
= Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(328,plain,
( ( ! [Z: $i,Xf: $i,Y: $i] :
( ~ ( member @ Z @ ( apply @ Xf @ Y ) )
| ( member @ ( f28 @ Z @ Xf @ Y ) @ Xf ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(329,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)],[106]) ).
thf(330,plain,
( ( ! [Xf: $i] :
( ( one_to_one_function @ Xf )
| ~ ( function @ Xf )
| ~ ( function @ ( converse @ Xf ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(331,plain,
( ( ! [Xf: $i] :
( ~ ( one_to_one_function @ Xf )
| ( function @ ( converse @ Xf ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(332,plain,
( ( ! [Xf: $i] :
( ~ ( one_to_one_function @ Xf )
| ( function @ Xf ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(333,plain,
( ( ! [X: $i,Y: $i] :
( ( restrict @ X @ Y )
= ( intersection @ X @ ( cross_product @ Y @ universal_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(334,plain,
( ( ! [Z: $i] :
( ( member @ Z @ identity_relation )
| ~ ( little_set @ Z )
| ~ ( ordered_pair_predicate @ Z )
| ( ( first @ Z )
!= ( second @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(335,plain,
( ( ! [Z: $i] :
( ~ ( member @ Z @ identity_relation )
| ( ( first @ Z )
= ( second @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(336,plain,
( ( ! [Z: $i] :
( ~ ( member @ Z @ identity_relation )
| ( ordered_pair_predicate @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(337,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)],[114]) ).
thf(338,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( range_of @ X ) )
| ( Z
= ( second @ ( f27 @ Z @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(339,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( range_of @ X ) )
| ( member @ ( f27 @ Z @ X ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(340,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( range_of @ X ) )
| ( ordered_pair_predicate @ ( f27 @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(341,plain,
( ( ! [X: $i] :
( ~ ( little_set @ X )
| ( X = empty_set )
| ( member @ ( ordered_pair @ X @ ( f26 @ X ) ) @ f25 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(342,plain,
( ( ! [X: $i] :
( ~ ( little_set @ X )
| ( X = empty_set )
| ( member @ ( f26 @ X ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(343,plain,
( ( function @ f25 )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(344,plain,
( ( ! [X: $i] :
( ( X = empty_set )
| ( disjoint @ ( f24 @ X ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(345,plain,
( ( ! [X: $i] :
( ( X = empty_set )
| ( member @ ( f24 @ X ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(346,plain,
( ( ! [X: $i,Y: $i] :
( ( disjoint @ X @ Y )
| ( member @ ( f23 @ X @ Y ) @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(347,plain,
( ( ! [X: $i,Y: $i] :
( ( disjoint @ X @ Y )
| ( member @ ( f23 @ X @ Y ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(348,plain,
( ( ! [X: $i,Y: $i,U: $i] :
( ~ ( disjoint @ X @ Y )
| ~ ( member @ U @ X )
| ~ ( member @ U @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(349,plain,
( ( ! [X: $i,Xf: $i] :
( ~ ( little_set @ X )
| ~ ( function @ Xf )
| ( little_set @ ( image @ X @ Xf ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(350,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)],[127]) ).
thf(351,plain,
( ( ! [Z: $i,X: $i,Xf: $i] :
( ~ ( member @ Z @ ( image @ X @ Xf ) )
| ( ( second @ ( f22 @ Z @ X @ Xf ) )
= Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(352,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)],[129]) ).
thf(353,plain,
( ( ! [Z: $i,X: $i,Xf: $i] :
( ~ ( member @ Z @ ( image @ X @ Xf ) )
| ( member @ ( f22 @ Z @ X @ Xf ) @ Xf ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(354,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)],[131]) ).
thf(355,plain,
( ( ! [Xf: $i] :
( ( function @ Xf )
| ~ ( relation @ Xf )
| ~ ( single_valued_set @ Xf ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(356,plain,
( ( ! [Xf: $i] :
( ~ ( function @ Xf )
| ( single_valued_set @ Xf ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(357,plain,
( ( ! [Xf: $i] :
( ~ ( function @ Xf )
| ( relation @ Xf ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(358,plain,
( ( ! [X: $i] :
( ( single_valued_set @ X )
| ( ( f20 @ X )
!= ( f21 @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(359,plain,
( ( ! [X: $i] :
( ( single_valued_set @ X )
| ( member @ ( ordered_pair @ ( f19 @ X ) @ ( f21 @ X ) ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(360,plain,
( ( ! [X: $i] :
( ( single_valued_set @ X )
| ( member @ ( ordered_pair @ ( f19 @ X ) @ ( f20 @ X ) ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(361,plain,
( ( ! [X: $i] :
( ( single_valued_set @ X )
| ( little_set @ ( f21 @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(362,plain,
( ( ! [X: $i] :
( ( single_valued_set @ X )
| ( little_set @ ( f20 @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(363,plain,
( ( ! [X: $i] :
( ( single_valued_set @ X )
| ( little_set @ ( f19 @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(364,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)],[141]) ).
thf(365,plain,
( ( ! [Z: $i] :
( ( relation @ Z )
| ~ ( ordered_pair_predicate @ ( f18 @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(366,plain,
( ( ! [Z: $i] :
( ( relation @ Z )
| ( member @ ( f18 @ Z ) @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(367,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( relation @ Z )
| ~ ( member @ X @ Z )
| ( ordered_pair_predicate @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(368,plain,
( ( ! [U: $i] :
( ~ ( little_set @ U )
| ( little_set @ ( powerset @ U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(369,plain,
( ( ! [Z: $i,X: $i] :
( ( member @ Z @ ( powerset @ X ) )
| ~ ( little_set @ Z )
| ~ ( subset @ Z @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(370,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( powerset @ X ) )
| ( subset @ Z @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(371,plain,
( ( ! [X: $i,Y: $i] :
( ( proper_subset @ X @ Y )
| ~ ( subset @ X @ Y )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(372,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( proper_subset @ X @ Y )
| ( X != Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(373,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( proper_subset @ X @ Y )
| ( subset @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(374,plain,
( ( ! [X: $i,Y: $i] :
( ( subset @ X @ Y )
| ~ ( member @ ( f17 @ X @ Y ) @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(375,plain,
( ( ! [X: $i,Y: $i] :
( ( subset @ X @ Y )
| ( member @ ( f17 @ X @ Y ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(376,plain,
( ( ! [X: $i,Y: $i,U: $i] :
( ~ ( subset @ X @ Y )
| ~ ( member @ U @ X )
| ( member @ U @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(377,plain,
( ( ! [U: $i] :
( ~ ( little_set @ U )
| ( little_set @ ( sigma @ U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(378,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ( member @ Z @ ( sigma @ X ) )
| ~ ( member @ Y @ X )
| ~ ( member @ Z @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(379,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( sigma @ X ) )
| ( member @ Z @ ( f16 @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(380,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( sigma @ X ) )
| ( member @ ( f16 @ Z @ X ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(381,plain,
( ( ! [X: $i] :
( ~ ( member @ X @ infinity )
| ( member @ ( successor @ X ) @ infinity ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(382,plain,
( ( member @ empty_set @ infinity )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(383,plain,
( ( little_set @ infinity )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(384,plain,
( ( ! [Z: $i] :
( ( member @ Z @ universal_set )
| ~ ( little_set @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(385,plain,
( ( ! [Z: $i] :
~ ( member @ Z @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(386,plain,
( ( ! [X: $i] :
( ( successor @ X )
= ( union @ X @ ( singleton_set @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(387,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)],[164]) ).
thf(388,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)],[165]) ).
thf(389,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)],[166]) ).
thf(390,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( flip_range_of @ X ) )
| ( little_set @ ( f14 @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(391,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( flip_range_of @ X ) )
| ( little_set @ ( f13 @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(392,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( flip_range_of @ X ) )
| ( little_set @ ( f12 @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(393,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)],[170]) ).
thf(394,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)],[171]) ).
thf(395,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)],[172]) ).
thf(396,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( rotate_right @ X ) )
| ( little_set @ ( f11 @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(397,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( rotate_right @ X ) )
| ( little_set @ ( f10 @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(398,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( rotate_right @ X ) )
| ( little_set @ ( f9 @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(399,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)],[176]) ).
thf(400,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( converse @ X ) )
| ( member @ ( ordered_pair @ ( second @ Z ) @ ( first @ Z ) ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(401,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( converse @ X ) )
| ( ordered_pair_predicate @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(402,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)],[179]) ).
thf(403,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( cross_product @ X @ Y ) )
| ( member @ ( second @ Z ) @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(404,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( cross_product @ X @ Y ) )
| ( member @ ( first @ Z ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(405,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( cross_product @ X @ Y ) )
| ( ordered_pair_predicate @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(406,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)],[183]) ).
thf(407,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( domain_of @ X ) )
| ( Z
= ( first @ ( f8 @ Z @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(408,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( domain_of @ X ) )
| ( member @ ( f8 @ Z @ X ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(409,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( domain_of @ X ) )
| ( ordered_pair_predicate @ ( f8 @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(410,plain,
( ( ! [X: $i,Y: $i] :
( ( union @ X @ Y )
= ( complement @ ( intersection @ ( complement @ X ) @ ( complement @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(411,plain,
( ( ! [Z: $i,X: $i] :
( ( member @ Z @ ( complement @ X ) )
| ~ ( little_set @ Z )
| ( member @ Z @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(412,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( complement @ X ) )
| ~ ( member @ Z @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[189]) ).
thf(413,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ( member @ Z @ ( intersection @ X @ Y ) )
| ~ ( member @ Z @ X )
| ~ ( member @ Z @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(414,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( intersection @ X @ Y ) )
| ( member @ Z @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(415,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( intersection @ X @ Y ) )
| ( member @ Z @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(416,plain,
( ( ! [Z: $i] :
( ( member @ Z @ estin )
| ~ ( little_set @ Z )
| ~ ( ordered_pair_predicate @ Z )
| ~ ( member @ ( first @ Z ) @ ( second @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(417,plain,
( ( ! [Z: $i] :
( ~ ( member @ Z @ estin )
| ( member @ ( first @ Z ) @ ( second @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(418,plain,
( ( ! [Z: $i] :
( ~ ( member @ Z @ estin )
| ( ordered_pair_predicate @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[195]) ).
thf(419,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)],[196]) ).
thf(420,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( second @ X ) )
| ( member @ Z @ ( f7 @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[197]) ).
thf(421,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( second @ X ) )
| ( X
= ( ordered_pair @ ( f6 @ Z @ X ) @ ( f7 @ Z @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[198]) ).
thf(422,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( second @ X ) )
| ( little_set @ ( f7 @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(423,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( second @ X ) )
| ( little_set @ ( f6 @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(424,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)],[201]) ).
thf(425,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( first @ X ) )
| ( member @ Z @ ( f4 @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[202]) ).
thf(426,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( first @ X ) )
| ( X
= ( ordered_pair @ ( f4 @ Z @ X ) @ ( f5 @ Z @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(427,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( first @ X ) )
| ( little_set @ ( f5 @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[204]) ).
thf(428,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( first @ X ) )
| ( little_set @ ( f4 @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[205]) ).
thf(429,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)],[206]) ).
thf(430,plain,
( ( ! [X: $i] :
( ~ ( ordered_pair_predicate @ X )
| ( X
= ( ordered_pair @ ( f2 @ X ) @ ( f3 @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(431,plain,
( ( ! [X: $i] :
( ~ ( ordered_pair_predicate @ X )
| ( little_set @ ( f3 @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[208]) ).
thf(432,plain,
( ( ! [X: $i] :
( ~ ( ordered_pair_predicate @ X )
| ( little_set @ ( f2 @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(433,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)],[210]) ).
thf(434,plain,
( ( ! [X: $i] :
( ( singleton_set @ X )
= ( non_ordered_pair @ X @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[211]) ).
thf(435,plain,
( ( ! [X: $i,Y: $i] : ( little_set @ ( non_ordered_pair @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(436,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)],[213]) ).
thf(437,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)],[214]) ).
thf(438,plain,
( ( ! [U: $i,X: $i,Y: $i] :
( ~ ( member @ U @ ( non_ordered_pair @ X @ Y ) )
| ( U = X )
| ( U = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(439,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( member @ ( f1 @ X @ Y ) @ X )
| ~ ( member @ ( f1 @ X @ Y ) @ Y )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[216]) ).
thf(440,plain,
( ( ! [X: $i,Y: $i] :
( ( member @ ( f1 @ X @ Y ) @ X )
| ( member @ ( f1 @ X @ Y ) @ Y )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[217]) ).
thf(441,plain,
( ( ! [X: $i,Y: $i] :
( ( little_set @ ( f1 @ X @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(442,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( member @ X @ Y )
| ( little_set @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[219]) ).
thf(443,plain,
( ( ~ ( member @ empty_set @ natural_numbers ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(444,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[223]) ).
thf(445,plain,
( ( ~ ( member @ empty_set @ natural_numbers ) )
= $true ),
inference(copy,[status(thm)],[443]) ).
thf(446,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( member @ X @ Y )
| ( little_set @ X ) ) )
= $true ),
inference(copy,[status(thm)],[442]) ).
thf(447,plain,
( ( ! [X: $i,Y: $i] :
( ( little_set @ ( f1 @ X @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[441]) ).
thf(448,plain,
( ( ! [X: $i,Y: $i] :
( ( member @ ( f1 @ X @ Y ) @ X )
| ( member @ ( f1 @ X @ Y ) @ Y )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[440]) ).
thf(449,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( member @ ( f1 @ X @ Y ) @ X )
| ~ ( member @ ( f1 @ X @ Y ) @ Y )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[439]) ).
thf(450,plain,
( ( ! [U: $i,X: $i,Y: $i] :
( ~ ( member @ U @ ( non_ordered_pair @ X @ Y ) )
| ( U = X )
| ( U = Y ) ) )
= $true ),
inference(copy,[status(thm)],[438]) ).
thf(451,plain,
( ( ! [U: $i,X: $i,Y: $i] :
( ( member @ U @ ( non_ordered_pair @ X @ Y ) )
| ~ ( little_set @ U )
| ( U != X ) ) )
= $true ),
inference(copy,[status(thm)],[437]) ).
thf(452,plain,
( ( ! [U: $i,X: $i,Y: $i] :
( ( member @ U @ ( non_ordered_pair @ X @ Y ) )
| ~ ( little_set @ U )
| ( U != Y ) ) )
= $true ),
inference(copy,[status(thm)],[436]) ).
thf(453,plain,
( ( ! [X: $i,Y: $i] : ( little_set @ ( non_ordered_pair @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[435]) ).
thf(454,plain,
( ( ! [X: $i] :
( ( singleton_set @ X )
= ( non_ordered_pair @ X @ X ) ) )
= $true ),
inference(copy,[status(thm)],[434]) ).
thf(455,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)],[433]) ).
thf(456,plain,
( ( ! [X: $i] :
( ~ ( ordered_pair_predicate @ X )
| ( little_set @ ( f2 @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[432]) ).
thf(457,plain,
( ( ! [X: $i] :
( ~ ( ordered_pair_predicate @ X )
| ( little_set @ ( f3 @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[431]) ).
thf(458,plain,
( ( ! [X: $i] :
( ~ ( ordered_pair_predicate @ X )
| ( X
= ( ordered_pair @ ( f2 @ X ) @ ( f3 @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[430]) ).
thf(459,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ordered_pair_predicate @ X )
| ~ ( little_set @ Y )
| ~ ( little_set @ Z )
| ( X
!= ( ordered_pair @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[429]) ).
thf(460,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( first @ X ) )
| ( little_set @ ( f4 @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[428]) ).
thf(461,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( first @ X ) )
| ( little_set @ ( f5 @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[427]) ).
thf(462,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( first @ X ) )
| ( X
= ( ordered_pair @ ( f4 @ Z @ X ) @ ( f5 @ Z @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[426]) ).
thf(463,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( first @ X ) )
| ( member @ Z @ ( f4 @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[425]) ).
thf(464,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(copy,[status(thm)],[424]) ).
thf(465,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( second @ X ) )
| ( little_set @ ( f6 @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[423]) ).
thf(466,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( second @ X ) )
| ( little_set @ ( f7 @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[422]) ).
thf(467,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( second @ X ) )
| ( X
= ( ordered_pair @ ( f6 @ Z @ X ) @ ( f7 @ Z @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[421]) ).
thf(468,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( second @ X ) )
| ( member @ Z @ ( f7 @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[420]) ).
thf(469,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(copy,[status(thm)],[419]) ).
thf(470,plain,
( ( ! [Z: $i] :
( ~ ( member @ Z @ estin )
| ( ordered_pair_predicate @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[418]) ).
thf(471,plain,
( ( ! [Z: $i] :
( ~ ( member @ Z @ estin )
| ( member @ ( first @ Z ) @ ( second @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[417]) ).
thf(472,plain,
( ( ! [Z: $i] :
( ( member @ Z @ estin )
| ~ ( little_set @ Z )
| ~ ( ordered_pair_predicate @ Z )
| ~ ( member @ ( first @ Z ) @ ( second @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[416]) ).
thf(473,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( intersection @ X @ Y ) )
| ( member @ Z @ X ) ) )
= $true ),
inference(copy,[status(thm)],[415]) ).
thf(474,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( intersection @ X @ Y ) )
| ( member @ Z @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[414]) ).
thf(475,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ( member @ Z @ ( intersection @ X @ Y ) )
| ~ ( member @ Z @ X )
| ~ ( member @ Z @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[413]) ).
thf(476,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( complement @ X ) )
| ~ ( member @ Z @ X ) ) )
= $true ),
inference(copy,[status(thm)],[412]) ).
thf(477,plain,
( ( ! [Z: $i,X: $i] :
( ( member @ Z @ ( complement @ X ) )
| ~ ( little_set @ Z )
| ( member @ Z @ X ) ) )
= $true ),
inference(copy,[status(thm)],[411]) ).
thf(478,plain,
( ( ! [X: $i,Y: $i] :
( ( union @ X @ Y )
= ( complement @ ( intersection @ ( complement @ X ) @ ( complement @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[410]) ).
thf(479,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( domain_of @ X ) )
| ( ordered_pair_predicate @ ( f8 @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[409]) ).
thf(480,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( domain_of @ X ) )
| ( member @ ( f8 @ Z @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[408]) ).
thf(481,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( domain_of @ X ) )
| ( Z
= ( first @ ( f8 @ Z @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[407]) ).
thf(482,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(copy,[status(thm)],[406]) ).
thf(483,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( cross_product @ X @ Y ) )
| ( ordered_pair_predicate @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[405]) ).
thf(484,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( cross_product @ X @ Y ) )
| ( member @ ( first @ Z ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[404]) ).
thf(485,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( cross_product @ X @ Y ) )
| ( member @ ( second @ Z ) @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(486,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)],[402]) ).
thf(487,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( converse @ X ) )
| ( ordered_pair_predicate @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[401]) ).
thf(488,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( converse @ X ) )
| ( member @ ( ordered_pair @ ( second @ Z ) @ ( first @ Z ) ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[400]) ).
thf(489,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)],[399]) ).
thf(490,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( rotate_right @ X ) )
| ( little_set @ ( f9 @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[398]) ).
thf(491,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( rotate_right @ X ) )
| ( little_set @ ( f10 @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[397]) ).
thf(492,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( rotate_right @ X ) )
| ( little_set @ ( f11 @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[396]) ).
thf(493,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)],[395]) ).
thf(494,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)],[394]) ).
thf(495,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(copy,[status(thm)],[393]) ).
thf(496,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( flip_range_of @ X ) )
| ( little_set @ ( f12 @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[392]) ).
thf(497,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( flip_range_of @ X ) )
| ( little_set @ ( f13 @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[391]) ).
thf(498,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( flip_range_of @ X ) )
| ( little_set @ ( f14 @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[390]) ).
thf(499,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)],[389]) ).
thf(500,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)],[388]) ).
thf(501,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(copy,[status(thm)],[387]) ).
thf(502,plain,
( ( ! [X: $i] :
( ( successor @ X )
= ( union @ X @ ( singleton_set @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[386]) ).
thf(503,plain,
( ( ! [Z: $i] :
~ ( member @ Z @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[385]) ).
thf(504,plain,
( ( ! [Z: $i] :
( ( member @ Z @ universal_set )
| ~ ( little_set @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[384]) ).
thf(505,plain,
( ( little_set @ infinity )
= $true ),
inference(copy,[status(thm)],[383]) ).
thf(506,plain,
( ( member @ empty_set @ infinity )
= $true ),
inference(copy,[status(thm)],[382]) ).
thf(507,plain,
( ( ! [X: $i] :
( ~ ( member @ X @ infinity )
| ( member @ ( successor @ X ) @ infinity ) ) )
= $true ),
inference(copy,[status(thm)],[381]) ).
thf(508,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( sigma @ X ) )
| ( member @ ( f16 @ Z @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[380]) ).
thf(509,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( sigma @ X ) )
| ( member @ Z @ ( f16 @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[379]) ).
thf(510,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ( member @ Z @ ( sigma @ X ) )
| ~ ( member @ Y @ X )
| ~ ( member @ Z @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[378]) ).
thf(511,plain,
( ( ! [U: $i] :
( ~ ( little_set @ U )
| ( little_set @ ( sigma @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(512,plain,
( ( ! [X: $i,Y: $i,U: $i] :
( ~ ( subset @ X @ Y )
| ~ ( member @ U @ X )
| ( member @ U @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[376]) ).
thf(513,plain,
( ( ! [X: $i,Y: $i] :
( ( subset @ X @ Y )
| ( member @ ( f17 @ X @ Y ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[375]) ).
thf(514,plain,
( ( ! [X: $i,Y: $i] :
( ( subset @ X @ Y )
| ~ ( member @ ( f17 @ X @ Y ) @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[374]) ).
thf(515,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( proper_subset @ X @ Y )
| ( subset @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(516,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( proper_subset @ X @ Y )
| ( X != Y ) ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(517,plain,
( ( ! [X: $i,Y: $i] :
( ( proper_subset @ X @ Y )
| ~ ( subset @ X @ Y )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(518,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( powerset @ X ) )
| ( subset @ Z @ X ) ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(519,plain,
( ( ! [Z: $i,X: $i] :
( ( member @ Z @ ( powerset @ X ) )
| ~ ( little_set @ Z )
| ~ ( subset @ Z @ X ) ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(520,plain,
( ( ! [U: $i] :
( ~ ( little_set @ U )
| ( little_set @ ( powerset @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(521,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( relation @ Z )
| ~ ( member @ X @ Z )
| ( ordered_pair_predicate @ X ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(522,plain,
( ( ! [Z: $i] :
( ( relation @ Z )
| ( member @ ( f18 @ Z ) @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(523,plain,
( ( ! [Z: $i] :
( ( relation @ Z )
| ~ ( ordered_pair_predicate @ ( f18 @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[365]) ).
thf(524,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(copy,[status(thm)],[364]) ).
thf(525,plain,
( ( ! [X: $i] :
( ( single_valued_set @ X )
| ( little_set @ ( f19 @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(526,plain,
( ( ! [X: $i] :
( ( single_valued_set @ X )
| ( little_set @ ( f20 @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[362]) ).
thf(527,plain,
( ( ! [X: $i] :
( ( single_valued_set @ X )
| ( little_set @ ( f21 @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[361]) ).
thf(528,plain,
( ( ! [X: $i] :
( ( single_valued_set @ X )
| ( member @ ( ordered_pair @ ( f19 @ X ) @ ( f20 @ X ) ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(529,plain,
( ( ! [X: $i] :
( ( single_valued_set @ X )
| ( member @ ( ordered_pair @ ( f19 @ X ) @ ( f21 @ X ) ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(530,plain,
( ( ! [X: $i] :
( ( single_valued_set @ X )
| ( ( f20 @ X )
!= ( f21 @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[358]) ).
thf(531,plain,
( ( ! [Xf: $i] :
( ~ ( function @ Xf )
| ( relation @ Xf ) ) )
= $true ),
inference(copy,[status(thm)],[357]) ).
thf(532,plain,
( ( ! [Xf: $i] :
( ~ ( function @ Xf )
| ( single_valued_set @ Xf ) ) )
= $true ),
inference(copy,[status(thm)],[356]) ).
thf(533,plain,
( ( ! [Xf: $i] :
( ( function @ Xf )
| ~ ( relation @ Xf )
| ~ ( single_valued_set @ Xf ) ) )
= $true ),
inference(copy,[status(thm)],[355]) ).
thf(534,plain,
( ( ! [Z: $i,X: $i,Xf: $i] :
( ~ ( member @ Z @ ( image @ X @ Xf ) )
| ( ordered_pair_predicate @ ( f22 @ Z @ X @ Xf ) ) ) )
= $true ),
inference(copy,[status(thm)],[354]) ).
thf(535,plain,
( ( ! [Z: $i,X: $i,Xf: $i] :
( ~ ( member @ Z @ ( image @ X @ Xf ) )
| ( member @ ( f22 @ Z @ X @ Xf ) @ Xf ) ) )
= $true ),
inference(copy,[status(thm)],[353]) ).
thf(536,plain,
( ( ! [Z: $i,X: $i,Xf: $i] :
( ~ ( member @ Z @ ( image @ X @ Xf ) )
| ( member @ ( first @ ( f22 @ Z @ X @ Xf ) ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[352]) ).
thf(537,plain,
( ( ! [Z: $i,X: $i,Xf: $i] :
( ~ ( member @ Z @ ( image @ X @ Xf ) )
| ( ( second @ ( f22 @ Z @ X @ Xf ) )
= Z ) ) )
= $true ),
inference(copy,[status(thm)],[351]) ).
thf(538,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(copy,[status(thm)],[350]) ).
thf(539,plain,
( ( ! [X: $i,Xf: $i] :
( ~ ( little_set @ X )
| ~ ( function @ Xf )
| ( little_set @ ( image @ X @ Xf ) ) ) )
= $true ),
inference(copy,[status(thm)],[349]) ).
thf(540,plain,
( ( ! [X: $i,Y: $i,U: $i] :
( ~ ( disjoint @ X @ Y )
| ~ ( member @ U @ X )
| ~ ( member @ U @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[348]) ).
thf(541,plain,
( ( ! [X: $i,Y: $i] :
( ( disjoint @ X @ Y )
| ( member @ ( f23 @ X @ Y ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[347]) ).
thf(542,plain,
( ( ! [X: $i,Y: $i] :
( ( disjoint @ X @ Y )
| ( member @ ( f23 @ X @ Y ) @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[346]) ).
thf(543,plain,
( ( ! [X: $i] :
( ( X = empty_set )
| ( member @ ( f24 @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[345]) ).
thf(544,plain,
( ( ! [X: $i] :
( ( X = empty_set )
| ( disjoint @ ( f24 @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[344]) ).
thf(545,plain,
( ( function @ f25 )
= $true ),
inference(copy,[status(thm)],[343]) ).
thf(546,plain,
( ( ! [X: $i] :
( ~ ( little_set @ X )
| ( X = empty_set )
| ( member @ ( f26 @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[342]) ).
thf(547,plain,
( ( ! [X: $i] :
( ~ ( little_set @ X )
| ( X = empty_set )
| ( member @ ( ordered_pair @ X @ ( f26 @ X ) ) @ f25 ) ) )
= $true ),
inference(copy,[status(thm)],[341]) ).
thf(548,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( range_of @ X ) )
| ( ordered_pair_predicate @ ( f27 @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[340]) ).
thf(549,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( range_of @ X ) )
| ( member @ ( f27 @ Z @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[339]) ).
thf(550,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( range_of @ X ) )
| ( Z
= ( second @ ( f27 @ Z @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[338]) ).
thf(551,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(copy,[status(thm)],[337]) ).
thf(552,plain,
( ( ! [Z: $i] :
( ~ ( member @ Z @ identity_relation )
| ( ordered_pair_predicate @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[336]) ).
thf(553,plain,
( ( ! [Z: $i] :
( ~ ( member @ Z @ identity_relation )
| ( ( first @ Z )
= ( second @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[335]) ).
thf(554,plain,
( ( ! [Z: $i] :
( ( member @ Z @ identity_relation )
| ~ ( little_set @ Z )
| ~ ( ordered_pair_predicate @ Z )
| ( ( first @ Z )
!= ( second @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[334]) ).
thf(555,plain,
( ( ! [X: $i,Y: $i] :
( ( restrict @ X @ Y )
= ( intersection @ X @ ( cross_product @ Y @ universal_set ) ) ) )
= $true ),
inference(copy,[status(thm)],[333]) ).
thf(556,plain,
( ( ! [Xf: $i] :
( ~ ( one_to_one_function @ Xf )
| ( function @ Xf ) ) )
= $true ),
inference(copy,[status(thm)],[332]) ).
thf(557,plain,
( ( ! [Xf: $i] :
( ~ ( one_to_one_function @ Xf )
| ( function @ ( converse @ Xf ) ) ) )
= $true ),
inference(copy,[status(thm)],[331]) ).
thf(558,plain,
( ( ! [Xf: $i] :
( ( one_to_one_function @ Xf )
| ~ ( function @ Xf )
| ~ ( function @ ( converse @ Xf ) ) ) )
= $true ),
inference(copy,[status(thm)],[330]) ).
thf(559,plain,
( ( ! [Z: $i,Xf: $i,Y: $i] :
( ~ ( member @ Z @ ( apply @ Xf @ Y ) )
| ( ordered_pair_predicate @ ( f28 @ Z @ Xf @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[329]) ).
thf(560,plain,
( ( ! [Z: $i,Xf: $i,Y: $i] :
( ~ ( member @ Z @ ( apply @ Xf @ Y ) )
| ( member @ ( f28 @ Z @ Xf @ Y ) @ Xf ) ) )
= $true ),
inference(copy,[status(thm)],[328]) ).
thf(561,plain,
( ( ! [Z: $i,Xf: $i,Y: $i] :
( ~ ( member @ Z @ ( apply @ Xf @ Y ) )
| ( ( first @ ( f28 @ Z @ Xf @ Y ) )
= Y ) ) )
= $true ),
inference(copy,[status(thm)],[327]) ).
thf(562,plain,
( ( ! [Z: $i,Xf: $i,Y: $i] :
( ~ ( member @ Z @ ( apply @ Xf @ Y ) )
| ( member @ Z @ ( second @ ( f28 @ Z @ Xf @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[326]) ).
thf(563,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(copy,[status(thm)],[325]) ).
thf(564,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)],[324]) ).
thf(565,plain,
( ( ! [Xf: $i,X: $i,Y: $i] :
( ~ ( maps @ Xf @ X @ Y )
| ( function @ Xf ) ) )
= $true ),
inference(copy,[status(thm)],[323]) ).
thf(566,plain,
( ( ! [Xf: $i,X: $i,Y: $i] :
( ~ ( maps @ Xf @ X @ Y )
| ( ( domain_of @ Xf )
= X ) ) )
= $true ),
inference(copy,[status(thm)],[322]) ).
thf(567,plain,
( ( ! [Xf: $i,X: $i,Y: $i] :
( ~ ( maps @ Xf @ X @ Y )
| ( subset @ ( range_of @ Xf ) @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[321]) ).
thf(568,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)],[320]) ).
thf(569,plain,
( ( ! [Xs: $i,Xf: $i] :
( ~ ( closed @ Xs @ Xf )
| ( little_set @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[319]) ).
thf(570,plain,
( ( ! [Xs: $i,Xf: $i] :
( ~ ( closed @ Xs @ Xf )
| ( little_set @ Xf ) ) )
= $true ),
inference(copy,[status(thm)],[318]) ).
thf(571,plain,
( ( ! [Xs: $i,Xf: $i] :
( ~ ( closed @ Xs @ Xf )
| ( maps @ Xf @ ( cross_product @ Xs @ Xs ) @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[317]) ).
thf(572,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)],[316]) ).
thf(573,plain,
( ( ! [Z: $i,Xf: $i,Xg: $i] :
( ~ ( member @ Z @ ( compose @ Xf @ Xg ) )
| ( little_set @ ( f29 @ Z @ Xf @ Xg ) ) ) )
= $true ),
inference(copy,[status(thm)],[315]) ).
thf(574,plain,
( ( ! [Z: $i,Xf: $i,Xg: $i] :
( ~ ( member @ Z @ ( compose @ Xf @ Xg ) )
| ( little_set @ ( f30 @ Z @ Xf @ Xg ) ) ) )
= $true ),
inference(copy,[status(thm)],[314]) ).
thf(575,plain,
( ( ! [Z: $i,Xf: $i,Xg: $i] :
( ~ ( member @ Z @ ( compose @ Xf @ Xg ) )
| ( little_set @ ( f31 @ Z @ Xf @ Xg ) ) ) )
= $true ),
inference(copy,[status(thm)],[313]) ).
thf(576,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)],[312]) ).
thf(577,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)],[311]) ).
thf(578,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)],[310]) ).
thf(579,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(copy,[status(thm)],[309]) ).
thf(580,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)],[308]) ).
thf(581,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)],[307]) ).
thf(582,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)],[306]) ).
thf(583,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(copy,[status(thm)],[305]) ).
thf(584,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)],[304]) ).
thf(585,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)],[303]) ).
thf(586,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)],[302]) ).
thf(587,plain,
( ( ! [Xs: $i,Xf: $i,X: $i,Y: $i,Z: $i] :
( ~ ( associative @ Xs @ Xf )
| ~ ( member @ X @ Xs )
| ~ ( member @ Y @ Xs )
| ~ ( member @ Z @ Xs )
| ( ( apply_to_two_arguments @ Xf @ ( apply_to_two_arguments @ Xf @ X @ Y ) @ Z )
= ( apply_to_two_arguments @ Xf @ X @ ( apply_to_two_arguments @ Xf @ Y @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[301]) ).
thf(588,plain,
( ( ! [Xs: $i,Xf: $i] :
( ( associative @ Xs @ Xf )
| ( member @ ( f34 @ Xs @ Xf ) @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[300]) ).
thf(589,plain,
( ( ! [Xs: $i,Xf: $i] :
( ( associative @ Xs @ Xf )
| ( member @ ( f35 @ Xs @ Xf ) @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[299]) ).
thf(590,plain,
( ( ! [Xs: $i,Xf: $i] :
( ( associative @ Xs @ Xf )
| ( member @ ( f36 @ Xs @ Xf ) @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[298]) ).
thf(591,plain,
( ( ! [Xs: $i,Xf: $i] :
( ( associative @ Xs @ Xf )
| ( ( apply_to_two_arguments @ Xf @ ( apply_to_two_arguments @ Xf @ ( f34 @ Xs @ Xf ) @ ( f35 @ Xs @ Xf ) ) @ ( f36 @ Xs @ Xf ) )
!= ( apply_to_two_arguments @ Xf @ ( f34 @ Xs @ Xf ) @ ( apply_to_two_arguments @ Xf @ ( f35 @ Xs @ Xf ) @ ( f36 @ Xs @ Xf ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[297]) ).
thf(592,plain,
( ( ! [Xs: $i,Xf: $i,Xe: $i] :
( ~ ( identity @ Xs @ Xf @ Xe )
| ( member @ Xe @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[296]) ).
thf(593,plain,
( ( ! [Xs: $i,Xf: $i,Xe: $i,X: $i] :
( ~ ( identity @ Xs @ Xf @ Xe )
| ~ ( member @ X @ Xs )
| ( ( apply_to_two_arguments @ Xf @ Xe @ X )
= X ) ) )
= $true ),
inference(copy,[status(thm)],[295]) ).
thf(594,plain,
( ( ! [Xs: $i,Xf: $i,Xe: $i,X: $i] :
( ~ ( identity @ Xs @ Xf @ Xe )
| ~ ( member @ X @ Xs )
| ( ( apply_to_two_arguments @ Xf @ X @ Xe )
= X ) ) )
= $true ),
inference(copy,[status(thm)],[294]) ).
thf(595,plain,
( ( ! [Xs: $i,Xf: $i,Xe: $i] :
( ( identity @ Xs @ Xf @ Xe )
| ~ ( member @ Xe @ Xs )
| ( member @ ( f37 @ Xs @ Xf @ Xe ) @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[293]) ).
thf(596,plain,
( ( ! [Xs: $i,Xf: $i,Xe: $i] :
( ( identity @ Xs @ Xf @ Xe )
| ~ ( member @ Xe @ Xs )
| ( ( apply_to_two_arguments @ Xf @ Xe @ ( f37 @ Xs @ Xf @ Xe ) )
!= ( f37 @ Xs @ Xf @ Xe ) )
| ( ( apply_to_two_arguments @ Xf @ ( f37 @ Xs @ Xf @ Xe ) @ Xe )
!= ( f37 @ Xs @ Xf @ Xe ) ) ) )
= $true ),
inference(copy,[status(thm)],[292]) ).
thf(597,plain,
( ( ! [Xs: $i,Xf: $i,Xe: $i,Xg: $i] :
( ~ ( inverse @ Xs @ Xf @ Xe @ Xg )
| ( maps @ Xg @ Xs @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[291]) ).
thf(598,plain,
( ( ! [Xs: $i,Xf: $i,Xe: $i,Xg: $i,X: $i] :
( ~ ( inverse @ Xs @ Xf @ Xe @ Xg )
| ~ ( member @ X @ Xs )
| ( ( apply_to_two_arguments @ Xf @ ( apply @ Xg @ X ) @ X )
= Xe ) ) )
= $true ),
inference(copy,[status(thm)],[290]) ).
thf(599,plain,
( ( ! [Xs: $i,Xf: $i,Xe: $i,Xg: $i,X: $i] :
( ~ ( inverse @ Xs @ Xf @ Xe @ Xg )
| ~ ( member @ X @ Xs )
| ( ( apply_to_two_arguments @ Xf @ X @ ( apply @ Xg @ X ) )
= Xe ) ) )
= $true ),
inference(copy,[status(thm)],[289]) ).
thf(600,plain,
( ( ! [Xs: $i,Xf: $i,Xe: $i,Xg: $i] :
( ( inverse @ Xs @ Xf @ Xe @ Xg )
| ~ ( maps @ Xg @ Xs @ Xs )
| ( member @ ( f38 @ Xs @ Xf @ Xe @ Xg ) @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[288]) ).
thf(601,plain,
( ( ! [Xs: $i,Xf: $i,Xe: $i,Xg: $i] :
( ( inverse @ Xs @ Xf @ Xe @ Xg )
| ~ ( maps @ Xg @ Xs @ Xs )
| ( ( apply_to_two_arguments @ Xf @ ( apply @ Xg @ ( f38 @ Xs @ Xf @ Xe @ Xg ) ) @ ( f38 @ Xs @ Xf @ Xe @ Xg ) )
!= Xe )
| ( ( apply_to_two_arguments @ Xf @ ( f38 @ Xs @ Xf @ Xe @ Xg ) @ ( apply @ Xg @ ( f38 @ Xs @ Xf @ Xe @ Xg ) ) )
!= Xe ) ) )
= $true ),
inference(copy,[status(thm)],[287]) ).
thf(602,plain,
( ( ! [Xs: $i,Xf: $i] :
( ~ ( group @ Xs @ Xf )
| ( closed @ Xs @ Xf ) ) )
= $true ),
inference(copy,[status(thm)],[286]) ).
thf(603,plain,
( ( ! [Xs: $i,Xf: $i] :
( ~ ( group @ Xs @ Xf )
| ( associative @ Xs @ Xf ) ) )
= $true ),
inference(copy,[status(thm)],[285]) ).
thf(604,plain,
( ( ! [Xs: $i,Xf: $i] :
( ~ ( group @ Xs @ Xf )
| ( identity @ Xs @ Xf @ ( f39 @ Xs @ Xf ) ) ) )
= $true ),
inference(copy,[status(thm)],[284]) ).
thf(605,plain,
( ( ! [Xs: $i,Xf: $i] :
( ~ ( group @ Xs @ Xf )
| ( inverse @ Xs @ Xf @ ( f39 @ Xs @ Xf ) @ ( f40 @ Xs @ Xf ) ) ) )
= $true ),
inference(copy,[status(thm)],[283]) ).
thf(606,plain,
( ( ! [Xs: $i,Xf: $i,Xe: $i,Xg: $i] :
( ( group @ Xs @ Xf )
| ~ ( closed @ Xs @ Xf )
| ~ ( associative @ Xs @ Xf )
| ~ ( identity @ Xs @ Xf @ Xe )
| ~ ( inverse @ Xs @ Xf @ Xe @ Xg ) ) )
= $true ),
inference(copy,[status(thm)],[282]) ).
thf(607,plain,
( ( ! [Xs: $i,Xf: $i,X: $i,Y: $i] :
( ~ ( commutes @ Xs @ Xf )
| ~ ( member @ X @ Xs )
| ~ ( member @ Y @ Xs )
| ( ( apply_to_two_arguments @ Xf @ X @ Y )
= ( apply_to_two_arguments @ Xf @ Y @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[281]) ).
thf(608,plain,
( ( ! [Xs: $i,Xf: $i] :
( ( commutes @ Xs @ Xf )
| ( member @ ( f41 @ Xs @ Xf ) @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[280]) ).
thf(609,plain,
( ( ! [Xs: $i,Xf: $i] :
( ( commutes @ Xs @ Xf )
| ( member @ ( f42 @ Xs @ Xf ) @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[279]) ).
thf(610,plain,
( ( ! [Xs: $i,Xf: $i] :
( ( commutes @ Xs @ Xf )
| ( ( apply_to_two_arguments @ Xf @ ( f41 @ Xs @ Xf ) @ ( f42 @ Xs @ Xf ) )
!= ( apply_to_two_arguments @ Xf @ ( f42 @ Xs @ Xf ) @ ( f41 @ Xs @ Xf ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[278]) ).
thf(611,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ natural_numbers )
| ~ ( little_set @ Xs )
| ~ ( member @ empty_set @ Xs )
| ( member @ ( f43 @ Z @ Xs ) @ Xs )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[277]) ).
thf(612,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ natural_numbers )
| ~ ( little_set @ Xs )
| ~ ( member @ empty_set @ Xs )
| ~ ( member @ ( successor @ ( f43 @ Z @ Xs ) ) @ Xs )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[276]) ).
thf(613,plain,
( ( ! [Z: $i] :
( ( member @ Z @ natural_numbers )
| ~ ( little_set @ Z )
| ( little_set @ ( f44 @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[275]) ).
thf(614,plain,
( ( ! [Z: $i] :
( ( member @ Z @ natural_numbers )
| ~ ( little_set @ Z )
| ( member @ empty_set @ ( f44 @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[274]) ).
thf(615,plain,
( ( ! [Z: $i,Xk: $i] :
( ( member @ Z @ natural_numbers )
| ~ ( little_set @ Z )
| ~ ( member @ Xk @ ( f44 @ Z ) )
| ( member @ ( successor @ Xk ) @ ( f44 @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[273]) ).
thf(616,plain,
( ( ! [Z: $i] :
( ( member @ Z @ natural_numbers )
| ~ ( member @ Z @ ( f44 @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[272]) ).
thf(617,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ plus )
| ~ ( little_set @ Xs )
| ( member @ ( f45 @ Z @ Xs ) @ natural_numbers )
| ( member @ ( f46 @ Z @ Xs ) @ natural_numbers )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[271]) ).
thf(618,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ plus )
| ~ ( little_set @ Xs )
| ( member @ ( f45 @ Z @ Xs ) @ natural_numbers )
| ( member @ ( f47 @ Z @ Xs ) @ natural_numbers )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[270]) ).
thf(619,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ plus )
| ~ ( little_set @ Xs )
| ( member @ ( f45 @ Z @ Xs ) @ natural_numbers )
| ( member @ ( f48 @ Z @ Xs ) @ natural_numbers )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[269]) ).
thf(620,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ plus )
| ~ ( little_set @ Xs )
| ( member @ ( f45 @ Z @ Xs ) @ natural_numbers )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( f46 @ Z @ Xs ) @ ( f47 @ Z @ Xs ) ) @ ( f48 @ Z @ Xs ) ) @ Xs )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[268]) ).
thf(621,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ plus )
| ~ ( little_set @ Xs )
| ( member @ ( f45 @ Z @ Xs ) @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f46 @ Z @ Xs ) ) @ ( f47 @ Z @ Xs ) ) @ ( successor @ ( f48 @ Z @ Xs ) ) ) @ Xs )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[267]) ).
thf(622,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ plus )
| ~ ( little_set @ Xs )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ Z @ Xs ) ) @ ( f45 @ Z @ Xs ) ) @ Xs )
| ( member @ ( f46 @ Z @ Xs ) @ natural_numbers )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[266]) ).
thf(623,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ plus )
| ~ ( little_set @ Xs )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ Z @ Xs ) ) @ ( f45 @ Z @ Xs ) ) @ Xs )
| ( member @ ( f47 @ Z @ Xs ) @ natural_numbers )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[265]) ).
thf(624,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ plus )
| ~ ( little_set @ Xs )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ Z @ Xs ) ) @ ( f45 @ Z @ Xs ) ) @ Xs )
| ( member @ ( f48 @ Z @ Xs ) @ natural_numbers )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[264]) ).
thf(625,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ plus )
| ~ ( little_set @ Xs )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ Z @ Xs ) ) @ ( f45 @ Z @ Xs ) ) @ Xs )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( f46 @ Z @ Xs ) @ ( f47 @ Z @ Xs ) ) @ ( f48 @ Z @ Xs ) ) @ Xs )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[263]) ).
thf(626,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ plus )
| ~ ( little_set @ Xs )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ Z @ Xs ) ) @ ( f45 @ Z @ Xs ) ) @ Xs )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f46 @ Z @ Xs ) ) @ ( f47 @ Z @ Xs ) ) @ ( successor @ ( f48 @ Z @ Xs ) ) ) @ Xs )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[262]) ).
thf(627,plain,
( ( ! [Z: $i] :
( ( member @ Z @ plus )
| ~ ( little_set @ Z )
| ( little_set @ ( f49 @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[261]) ).
thf(628,plain,
( ( ! [Z: $i,Xi: $i] :
( ( member @ Z @ plus )
| ~ ( little_set @ Z )
| ~ ( member @ Xi @ natural_numbers )
| ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ Xi ) @ Xi ) @ ( f49 @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[260]) ).
thf(629,plain,
( ( ! [Z: $i,Uu1: $i,Xj: $i,Xk: $i] :
( ( member @ Z @ plus )
| ~ ( little_set @ Z )
| ~ ( member @ Uu1 @ natural_numbers )
| ~ ( member @ Xj @ natural_numbers )
| ~ ( member @ Xk @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ Uu1 @ Xj ) @ Xk ) @ ( f49 @ Z ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ Uu1 ) @ Xj ) @ ( successor @ Xk ) ) @ ( f49 @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[259]) ).
thf(630,plain,
( ( ! [Z: $i] :
( ( member @ Z @ plus )
| ~ ( member @ Z @ ( f49 @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[258]) ).
thf(631,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ times )
| ~ ( little_set @ Xs )
| ( member @ ( f50 @ Z @ Xs ) @ natural_numbers )
| ( member @ ( f51 @ Z @ Xs ) @ natural_numbers )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[257]) ).
thf(632,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ times )
| ~ ( little_set @ Xs )
| ( member @ ( f50 @ Z @ Xs ) @ natural_numbers )
| ( member @ ( f52 @ Z @ Xs ) @ natural_numbers )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[256]) ).
thf(633,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ times )
| ~ ( little_set @ Xs )
| ( member @ ( f50 @ Z @ Xs ) @ natural_numbers )
| ( member @ ( f53 @ Z @ Xs ) @ natural_numbers )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[255]) ).
thf(634,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ times )
| ~ ( little_set @ Xs )
| ( member @ ( f50 @ Z @ Xs ) @ natural_numbers )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( f51 @ Z @ Xs ) @ ( f52 @ Z @ Xs ) ) @ ( f53 @ Z @ Xs ) ) @ Xs )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[254]) ).
thf(635,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ times )
| ~ ( little_set @ Xs )
| ( member @ ( f50 @ Z @ Xs ) @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f51 @ Z @ Xs ) ) @ ( f52 @ Z @ Xs ) ) @ ( apply_to_two_arguments @ plus @ ( f53 @ Z @ Xs ) @ ( f52 @ Z @ Xs ) ) ) @ Xs )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[253]) ).
thf(636,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ times )
| ~ ( little_set @ Xs )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ Z @ Xs ) ) @ empty_set ) @ Xs )
| ( member @ ( f51 @ Z @ Xs ) @ natural_numbers )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[252]) ).
thf(637,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ times )
| ~ ( little_set @ Xs )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ Z @ Xs ) ) @ empty_set ) @ Xs )
| ( member @ ( f52 @ Z @ Xs ) @ natural_numbers )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[251]) ).
thf(638,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ times )
| ~ ( little_set @ Xs )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ Z @ Xs ) ) @ empty_set ) @ Xs )
| ( member @ ( f53 @ Z @ Xs ) @ natural_numbers )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[250]) ).
thf(639,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ times )
| ~ ( little_set @ Xs )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ Z @ Xs ) ) @ empty_set ) @ Xs )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( f51 @ Z @ Xs ) @ ( f52 @ Z @ Xs ) ) @ ( f53 @ Z @ Xs ) ) @ Xs )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[249]) ).
thf(640,plain,
( ( ! [Z: $i,Xs: $i] :
( ~ ( member @ Z @ times )
| ~ ( little_set @ Xs )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ Z @ Xs ) ) @ empty_set ) @ Xs )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f51 @ Z @ Xs ) ) @ ( f52 @ Z @ Xs ) ) @ ( apply_to_two_arguments @ plus @ ( f53 @ Z @ Xs ) @ ( f52 @ Z @ Xs ) ) ) @ Xs )
| ( member @ Z @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[248]) ).
thf(641,plain,
( ( ! [Z: $i] :
( ( member @ Z @ times )
| ~ ( little_set @ Z )
| ( little_set @ ( f54 @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[247]) ).
thf(642,plain,
( ( ! [Z: $i,Xi: $i] :
( ( member @ Z @ times )
| ~ ( little_set @ Z )
| ~ ( member @ Xi @ natural_numbers )
| ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ Xi ) @ empty_set ) @ ( f54 @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[246]) ).
thf(643,plain,
( ( ! [Z: $i,Uu2: $i,Xj: $i,Xk: $i] :
( ( member @ Z @ times )
| ~ ( little_set @ Z )
| ~ ( member @ Uu2 @ natural_numbers )
| ~ ( member @ Xj @ natural_numbers )
| ~ ( member @ Xk @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ Uu2 @ Xj ) @ Xk ) @ ( f54 @ Z ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ Uu2 ) @ Xj ) @ ( apply_to_two_arguments @ plus @ Xk @ Xj ) ) @ ( f54 @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[245]) ).
thf(644,plain,
( ( ! [Z: $i] :
( ( member @ Z @ times )
| ~ ( member @ Z @ ( f54 @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[244]) ).
thf(645,plain,
( ( ! [Z: $i] :
( ~ ( member @ Z @ prime_numbers )
| ( member @ Z @ natural_numbers ) ) )
= $true ),
inference(copy,[status(thm)],[243]) ).
thf(646,plain,
( ( ! [Z: $i] :
( ~ ( member @ Z @ prime_numbers )
| ( Z != empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[242]) ).
thf(647,plain,
( ( ! [Z: $i] :
( ~ ( member @ Z @ prime_numbers )
| ( Z
!= ( successor @ empty_set ) ) ) )
= $true ),
inference(copy,[status(thm)],[241]) ).
thf(648,plain,
( ( ! [Z: $i,U: $i,V: $i] :
( ~ ( member @ Z @ prime_numbers )
| ~ ( member @ U @ natural_numbers )
| ~ ( member @ V @ natural_numbers )
| ( ( apply_to_two_arguments @ times @ U @ V )
!= Z )
| ( member @ U @ ( non_ordered_pair @ ( successor @ empty_set ) @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[240]) ).
thf(649,plain,
( ( ! [Z: $i] :
( ( member @ Z @ prime_numbers )
| ~ ( member @ Z @ natural_numbers )
| ( Z = empty_set )
| ( Z
= ( successor @ empty_set ) )
| ( member @ ( f55 @ Z ) @ natural_numbers ) ) )
= $true ),
inference(copy,[status(thm)],[239]) ).
thf(650,plain,
( ( ! [Z: $i] :
( ( member @ Z @ prime_numbers )
| ~ ( member @ Z @ natural_numbers )
| ( Z = empty_set )
| ( Z
= ( successor @ empty_set ) )
| ( member @ ( f56 @ Z ) @ natural_numbers ) ) )
= $true ),
inference(copy,[status(thm)],[238]) ).
thf(651,plain,
( ( ! [Z: $i] :
( ( member @ Z @ prime_numbers )
| ~ ( member @ Z @ natural_numbers )
| ( Z = empty_set )
| ( Z
= ( successor @ empty_set ) )
| ( ( apply_to_two_arguments @ times @ ( f55 @ Z ) @ ( f56 @ Z ) )
= Z ) ) )
= $true ),
inference(copy,[status(thm)],[237]) ).
thf(652,plain,
( ( ! [Z: $i] :
( ( member @ Z @ prime_numbers )
| ~ ( member @ Z @ natural_numbers )
| ( Z = empty_set )
| ( Z
= ( successor @ empty_set ) )
| ~ ( member @ ( f55 @ Z ) @ ( non_ordered_pair @ ( successor @ empty_set ) @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[236]) ).
thf(653,plain,
( ( ! [X: $i] :
( ~ ( finite @ X )
| ( member @ ( f57 @ X ) @ natural_numbers ) ) )
= $true ),
inference(copy,[status(thm)],[235]) ).
thf(654,plain,
( ( ! [X: $i] :
( ~ ( finite @ X )
| ( maps @ ( f58 @ X ) @ ( f57 @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(655,plain,
( ( ! [X: $i] :
( ~ ( finite @ X )
| ( ( range_of @ ( f58 @ X ) )
= X ) ) )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(656,plain,
( ( ! [X: $i] :
( ~ ( finite @ X )
| ( one_to_one_function @ ( f58 @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[232]) ).
thf(657,plain,
( ( ! [X: $i,Xn: $i,Xf: $i] :
( ( finite @ X )
| ~ ( member @ Xn @ natural_numbers )
| ~ ( maps @ Xf @ Xn @ X )
| ( ( range_of @ Xf )
!= X )
| ~ ( one_to_one_function @ Xf ) ) )
= $true ),
inference(copy,[status(thm)],[231]) ).
thf(658,plain,
( ( ! [Z: $i] :
( ~ ( member @ Z @ twin_prime_numbers )
| ( member @ Z @ prime_numbers ) ) )
= $true ),
inference(copy,[status(thm)],[230]) ).
thf(659,plain,
( ( ! [Z: $i] :
( ~ ( member @ Z @ twin_prime_numbers )
| ( member @ ( successor @ ( successor @ Z ) ) @ prime_numbers ) ) )
= $true ),
inference(copy,[status(thm)],[229]) ).
thf(660,plain,
( ( ! [Z: $i] :
( ( member @ Z @ twin_prime_numbers )
| ~ ( member @ Z @ prime_numbers )
| ~ ( member @ ( successor @ ( successor @ Z ) ) @ prime_numbers ) ) )
= $true ),
inference(copy,[status(thm)],[228]) ).
thf(661,plain,
( ( ! [Z: $i] :
( ~ ( member @ Z @ even_numbers )
| ( member @ Z @ natural_numbers ) ) )
= $true ),
inference(copy,[status(thm)],[227]) ).
thf(662,plain,
( ( ! [Z: $i] :
( ~ ( member @ Z @ even_numbers )
| ( member @ ( f59 @ Z ) @ natural_numbers ) ) )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(663,plain,
( ( ! [Z: $i] :
( ~ ( member @ Z @ even_numbers )
| ( ( apply_to_two_arguments @ plus @ ( f59 @ Z ) @ ( f59 @ Z ) )
= Z ) ) )
= $true ),
inference(copy,[status(thm)],[225]) ).
thf(664,plain,
( ( ! [Z: $i,X: $i] :
( ( member @ Z @ even_numbers )
| ~ ( member @ Z @ natural_numbers )
| ~ ( member @ X @ natural_numbers )
| ( ( apply_to_two_arguments @ plus @ X @ X )
!= Z ) ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(665,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[444]) ).
thf(666,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( member @ SX0 @ ( second @ SX1 ) )
| ~ ( little_set @ SX2 )
| ~ ( little_set @ SX3 )
| ( SX1
!= ( ordered_pair @ SX2 @ SX3 ) )
| ~ ( member @ SX0 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[469]) ).
thf(667,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( inverse @ SX0 @ SX1 @ SX2 @ SX3 )
| ~ ( maps @ SX3 @ SX0 @ SX0 )
| ( ( apply_to_two_arguments @ SX1 @ ( apply @ SX3 @ ( f38 @ SX0 @ SX1 @ SX2 @ SX3 ) ) @ ( f38 @ SX0 @ SX1 @ SX2 @ SX3 ) )
!= SX2 )
| ( ( apply_to_two_arguments @ SX1 @ ( f38 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( apply @ SX3 @ ( f38 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
!= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[601]) ).
thf(668,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ prime_numbers )
| ~ ( member @ SX1 @ natural_numbers )
| ~ ( member @ SX2 @ natural_numbers )
| ( ( apply_to_two_arguments @ times @ SX1 @ SX2 )
!= SX0 )
| ( member @ SX1 @ ( non_ordered_pair @ ( successor @ empty_set ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[648]) ).
thf(669,plain,
( ( ! [SX0: $i] :
( ~ ( member @ SX0 @ prime_numbers )
| ( SX0 != empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[646]) ).
thf(670,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( member @ SX0 @ ( flip_range_of @ SX1 ) )
| ~ ( little_set @ SX0 )
| ~ ( little_set @ SX2 )
| ~ ( little_set @ SX3 )
| ~ ( little_set @ SX4 )
| ( SX0
!= ( ordered_pair @ SX2 @ ( ordered_pair @ SX3 @ SX4 ) ) )
| ~ ( member @ ( ordered_pair @ SX2 @ ( ordered_pair @ SX4 @ SX3 ) ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[501]) ).
thf(671,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( member @ SX0 @ ( non_ordered_pair @ SX1 @ SX2 ) )
| ~ ( little_set @ SX0 )
| ( SX0 != SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[452]) ).
thf(672,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( member @ SX0 @ ( first @ SX1 ) )
| ~ ( little_set @ SX2 )
| ~ ( little_set @ SX3 )
| ( SX1
!= ( ordered_pair @ SX2 @ SX3 ) )
| ~ ( member @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[464]) ).
thf(673,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( member @ SX0 @ ( image @ SX1 @ SX2 ) )
| ~ ( little_set @ SX0 )
| ~ ( ordered_pair_predicate @ SX3 )
| ~ ( member @ SX3 @ SX2 )
| ~ ( member @ ( first @ SX3 ) @ SX1 )
| ( ( second @ SX3 )
!= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[538]) ).
thf(674,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( member @ SX0 @ ( rotate_right @ SX1 ) )
| ~ ( little_set @ SX0 )
| ~ ( little_set @ SX2 )
| ~ ( little_set @ SX3 )
| ~ ( little_set @ SX4 )
| ( SX0
!= ( ordered_pair @ SX2 @ ( ordered_pair @ SX3 @ SX4 ) ) )
| ~ ( member @ ( ordered_pair @ SX3 @ ( ordered_pair @ SX4 @ SX2 ) ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[495]) ).
thf(675,plain,
( ( ! [SX0: $i] :
( ( single_valued_set @ SX0 )
| ( ( f20 @ SX0 )
!= ( f21 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[530]) ).
thf(676,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( member @ SX0 @ ( compose @ SX1 @ SX2 ) )
| ~ ( little_set @ SX0 )
| ~ ( little_set @ SX3 )
| ~ ( little_set @ SX4 )
| ~ ( little_set @ SX5 )
| ( SX0
!= ( ordered_pair @ SX3 @ SX4 ) )
| ~ ( member @ ( ordered_pair @ SX3 @ SX5 ) @ SX1 )
| ~ ( member @ ( ordered_pair @ SX5 @ SX4 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[579]) ).
thf(677,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ordered_pair_predicate @ SX0 )
| ~ ( little_set @ SX1 )
| ~ ( little_set @ SX2 )
| ( SX0
!= ( ordered_pair @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[459]) ).
thf(678,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( member @ SX0 @ ( non_ordered_pair @ SX1 @ SX2 ) )
| ~ ( little_set @ SX0 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[451]) ).
thf(679,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( member @ SX0 @ even_numbers )
| ~ ( member @ SX0 @ natural_numbers )
| ~ ( member @ SX1 @ natural_numbers )
| ( ( apply_to_two_arguments @ plus @ SX1 @ SX1 )
!= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[664]) ).
thf(680,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[516]) ).
thf(681,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( homomorphism @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 )
| ~ ( closed @ SX1 @ SX2 )
| ~ ( closed @ SX3 @ SX4 )
| ~ ( maps @ SX0 @ SX1 @ SX3 )
| ( ( apply @ SX0 @ ( apply_to_two_arguments @ SX2 @ ( f32 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) @ ( f33 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) ) )
!= ( apply_to_two_arguments @ SX4 @ ( apply @ SX0 @ ( f32 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) ) @ ( apply @ SX0 @ ( f33 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[586]) ).
thf(682,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( finite @ SX0 )
| ~ ( member @ SX1 @ natural_numbers )
| ~ ( maps @ SX2 @ SX1 @ SX0 )
| ( ( range_of @ SX2 )
!= SX0 )
| ~ ( one_to_one_function @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[657]) ).
thf(683,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( maps @ SX0 @ SX1 @ SX2 )
| ~ ( function @ SX0 )
| ( ( domain_of @ SX0 )
!= SX1 )
| ~ ( subset @ ( range_of @ SX0 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[568]) ).
thf(684,plain,
( ( ! [SX0: $i] :
( ~ ( member @ SX0 @ prime_numbers )
| ( SX0
!= ( successor @ empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[647]) ).
thf(685,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( commutes @ SX0 @ SX1 )
| ( ( apply_to_two_arguments @ SX1 @ ( f41 @ SX0 @ SX1 ) @ ( f42 @ SX0 @ SX1 ) )
!= ( apply_to_two_arguments @ SX1 @ ( f42 @ SX0 @ SX1 ) @ ( f41 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[610]) ).
thf(686,plain,
( ( ! [SX0: $i] :
( ( member @ SX0 @ identity_relation )
| ~ ( little_set @ SX0 )
| ~ ( ordered_pair_predicate @ SX0 )
| ( ( first @ SX0 )
!= ( second @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[554]) ).
thf(687,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( member @ SX0 @ ( range_of @ SX1 ) )
| ~ ( little_set @ SX0 )
| ~ ( ordered_pair_predicate @ SX2 )
| ~ ( member @ SX2 @ SX1 )
| ( SX0
!= ( second @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[551]) ).
thf(688,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( associative @ SX0 @ SX1 )
| ( ( apply_to_two_arguments @ SX1 @ ( apply_to_two_arguments @ SX1 @ ( f34 @ SX0 @ SX1 ) @ ( f35 @ SX0 @ SX1 ) ) @ ( f36 @ SX0 @ SX1 ) )
!= ( apply_to_two_arguments @ SX1 @ ( f34 @ SX0 @ SX1 ) @ ( apply_to_two_arguments @ SX1 @ ( f35 @ SX0 @ SX1 ) @ ( f36 @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[591]) ).
thf(689,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( identity @ SX0 @ SX1 @ SX2 )
| ~ ( member @ SX2 @ SX0 )
| ( ( apply_to_two_arguments @ SX1 @ SX2 @ ( f37 @ SX0 @ SX1 @ SX2 ) )
!= ( f37 @ SX0 @ SX1 @ SX2 ) )
| ( ( apply_to_two_arguments @ SX1 @ ( f37 @ SX0 @ SX1 @ SX2 ) @ SX2 )
!= ( f37 @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[596]) ).
thf(690,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( member @ SX0 @ ( domain_of @ SX1 ) )
| ~ ( little_set @ SX0 )
| ~ ( ordered_pair_predicate @ SX2 )
| ~ ( member @ SX2 @ SX1 )
| ( SX0
!= ( first @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[482]) ).
thf(691,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( member @ SX0 @ ( apply @ SX1 @ SX2 ) )
| ~ ( ordered_pair_predicate @ SX3 )
| ~ ( member @ SX3 @ SX1 )
| ( ( first @ SX3 )
!= SX2 )
| ~ ( member @ SX0 @ ( second @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[563]) ).
thf(692,plain,
( ( member @ empty_set @ natural_numbers )
= $false ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(693,plain,
! [SV1: $i] :
( ( ! [SY484: $i] :
( ~ ( member @ SV1 @ SY484 )
| ( little_set @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(694,plain,
! [SV2: $i] :
( ( ! [SY485: $i] :
( ( little_set @ ( f1 @ SV2 @ SY485 ) )
| ( SV2 = SY485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(695,plain,
! [SV3: $i] :
( ( ! [SY486: $i] :
( ( member @ ( f1 @ SV3 @ SY486 ) @ SV3 )
| ( member @ ( f1 @ SV3 @ SY486 ) @ SY486 )
| ( SV3 = SY486 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(696,plain,
! [SV4: $i] :
( ( ! [SY487: $i] :
( ~ ( member @ ( f1 @ SV4 @ SY487 ) @ SV4 )
| ~ ( member @ ( f1 @ SV4 @ SY487 ) @ SY487 )
| ( SV4 = SY487 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(697,plain,
! [SV5: $i] :
( ( ! [SY488: $i,SY489: $i] :
( ~ ( member @ SV5 @ ( non_ordered_pair @ SY488 @ SY489 ) )
| ( SV5 = SY488 )
| ( SV5 = SY489 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(698,plain,
! [SV6: $i] :
( ( ! [SY490: $i] : ( little_set @ ( non_ordered_pair @ SV6 @ SY490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(699,plain,
! [SV7: $i] :
( ( ( singleton_set @ SV7 )
= ( non_ordered_pair @ SV7 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(700,plain,
! [SV8: $i] :
( ( ! [SY491: $i] :
( ( ordered_pair @ SV8 @ SY491 )
= ( non_ordered_pair @ ( singleton_set @ SV8 ) @ ( non_ordered_pair @ SV8 @ SY491 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(701,plain,
! [SV9: $i] :
( ( ~ ( ordered_pair_predicate @ SV9 )
| ( little_set @ ( f2 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(702,plain,
! [SV10: $i] :
( ( ~ ( ordered_pair_predicate @ SV10 )
| ( little_set @ ( f3 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(703,plain,
! [SV11: $i] :
( ( ~ ( ordered_pair_predicate @ SV11 )
| ( SV11
= ( ordered_pair @ ( f2 @ SV11 ) @ ( f3 @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(704,plain,
! [SV12: $i] :
( ( ! [SY492: $i] :
( ~ ( member @ SV12 @ ( first @ SY492 ) )
| ( little_set @ ( f4 @ SV12 @ SY492 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(705,plain,
! [SV13: $i] :
( ( ! [SY493: $i] :
( ~ ( member @ SV13 @ ( first @ SY493 ) )
| ( little_set @ ( f5 @ SV13 @ SY493 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(706,plain,
! [SV14: $i] :
( ( ! [SY494: $i] :
( ~ ( member @ SV14 @ ( first @ SY494 ) )
| ( SY494
= ( ordered_pair @ ( f4 @ SV14 @ SY494 ) @ ( f5 @ SV14 @ SY494 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(707,plain,
! [SV15: $i] :
( ( ! [SY495: $i] :
( ~ ( member @ SV15 @ ( first @ SY495 ) )
| ( member @ SV15 @ ( f4 @ SV15 @ SY495 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(708,plain,
! [SV16: $i] :
( ( ! [SY496: $i] :
( ~ ( member @ SV16 @ ( second @ SY496 ) )
| ( little_set @ ( f6 @ SV16 @ SY496 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(709,plain,
! [SV17: $i] :
( ( ! [SY497: $i] :
( ~ ( member @ SV17 @ ( second @ SY497 ) )
| ( little_set @ ( f7 @ SV17 @ SY497 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(710,plain,
! [SV18: $i] :
( ( ! [SY498: $i] :
( ~ ( member @ SV18 @ ( second @ SY498 ) )
| ( SY498
= ( ordered_pair @ ( f6 @ SV18 @ SY498 ) @ ( f7 @ SV18 @ SY498 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(711,plain,
! [SV19: $i] :
( ( ! [SY499: $i] :
( ~ ( member @ SV19 @ ( second @ SY499 ) )
| ( member @ SV19 @ ( f7 @ SV19 @ SY499 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(712,plain,
! [SV20: $i] :
( ( ~ ( member @ SV20 @ estin )
| ( ordered_pair_predicate @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(713,plain,
! [SV21: $i] :
( ( ~ ( member @ SV21 @ estin )
| ( member @ ( first @ SV21 ) @ ( second @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(714,plain,
! [SV22: $i] :
( ( ( member @ SV22 @ estin )
| ~ ( little_set @ SV22 )
| ~ ( ordered_pair_predicate @ SV22 )
| ~ ( member @ ( first @ SV22 ) @ ( second @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(715,plain,
! [SV23: $i] :
( ( ! [SY500: $i,SY501: $i] :
( ~ ( member @ SV23 @ ( intersection @ SY500 @ SY501 ) )
| ( member @ SV23 @ SY500 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(716,plain,
! [SV24: $i] :
( ( ! [SY502: $i,SY503: $i] :
( ~ ( member @ SV24 @ ( intersection @ SY502 @ SY503 ) )
| ( member @ SV24 @ SY503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(717,plain,
! [SV25: $i] :
( ( ! [SY504: $i,SY505: $i] :
( ( member @ SV25 @ ( intersection @ SY504 @ SY505 ) )
| ~ ( member @ SV25 @ SY504 )
| ~ ( member @ SV25 @ SY505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(718,plain,
! [SV26: $i] :
( ( ! [SY506: $i] :
( ~ ( member @ SV26 @ ( complement @ SY506 ) )
| ~ ( member @ SV26 @ SY506 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(719,plain,
! [SV27: $i] :
( ( ! [SY507: $i] :
( ( member @ SV27 @ ( complement @ SY507 ) )
| ~ ( little_set @ SV27 )
| ( member @ SV27 @ SY507 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(720,plain,
! [SV28: $i] :
( ( ! [SY508: $i] :
( ( union @ SV28 @ SY508 )
= ( complement @ ( intersection @ ( complement @ SV28 ) @ ( complement @ SY508 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(721,plain,
! [SV29: $i] :
( ( ! [SY509: $i] :
( ~ ( member @ SV29 @ ( domain_of @ SY509 ) )
| ( ordered_pair_predicate @ ( f8 @ SV29 @ SY509 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(722,plain,
! [SV30: $i] :
( ( ! [SY510: $i] :
( ~ ( member @ SV30 @ ( domain_of @ SY510 ) )
| ( member @ ( f8 @ SV30 @ SY510 ) @ SY510 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(723,plain,
! [SV31: $i] :
( ( ! [SY511: $i] :
( ~ ( member @ SV31 @ ( domain_of @ SY511 ) )
| ( SV31
= ( first @ ( f8 @ SV31 @ SY511 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(724,plain,
! [SV32: $i] :
( ( ! [SY512: $i,SY513: $i] :
( ~ ( member @ SV32 @ ( cross_product @ SY512 @ SY513 ) )
| ( ordered_pair_predicate @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(725,plain,
! [SV33: $i] :
( ( ! [SY514: $i,SY515: $i] :
( ~ ( member @ SV33 @ ( cross_product @ SY514 @ SY515 ) )
| ( member @ ( first @ SV33 ) @ SY514 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(726,plain,
! [SV34: $i] :
( ( ! [SY516: $i,SY517: $i] :
( ~ ( member @ SV34 @ ( cross_product @ SY516 @ SY517 ) )
| ( member @ ( second @ SV34 ) @ SY517 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(727,plain,
! [SV35: $i] :
( ( ! [SY518: $i,SY519: $i] :
( ( member @ SV35 @ ( cross_product @ SY518 @ SY519 ) )
| ~ ( little_set @ SV35 )
| ~ ( ordered_pair_predicate @ SV35 )
| ~ ( member @ ( first @ SV35 ) @ SY518 )
| ~ ( member @ ( second @ SV35 ) @ SY519 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(728,plain,
! [SV36: $i] :
( ( ! [SY520: $i] :
( ~ ( member @ SV36 @ ( converse @ SY520 ) )
| ( ordered_pair_predicate @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(729,plain,
! [SV37: $i] :
( ( ! [SY521: $i] :
( ~ ( member @ SV37 @ ( converse @ SY521 ) )
| ( member @ ( ordered_pair @ ( second @ SV37 ) @ ( first @ SV37 ) ) @ SY521 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(730,plain,
! [SV38: $i] :
( ( ! [SY522: $i] :
( ( member @ SV38 @ ( converse @ SY522 ) )
| ~ ( little_set @ SV38 )
| ~ ( ordered_pair_predicate @ SV38 )
| ~ ( member @ ( ordered_pair @ ( second @ SV38 ) @ ( first @ SV38 ) ) @ SY522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(731,plain,
! [SV39: $i] :
( ( ! [SY523: $i] :
( ~ ( member @ SV39 @ ( rotate_right @ SY523 ) )
| ( little_set @ ( f9 @ SV39 @ SY523 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(732,plain,
! [SV40: $i] :
( ( ! [SY524: $i] :
( ~ ( member @ SV40 @ ( rotate_right @ SY524 ) )
| ( little_set @ ( f10 @ SV40 @ SY524 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(733,plain,
! [SV41: $i] :
( ( ! [SY525: $i] :
( ~ ( member @ SV41 @ ( rotate_right @ SY525 ) )
| ( little_set @ ( f11 @ SV41 @ SY525 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(734,plain,
! [SV42: $i] :
( ( ! [SY526: $i] :
( ~ ( member @ SV42 @ ( rotate_right @ SY526 ) )
| ( SV42
= ( ordered_pair @ ( f9 @ SV42 @ SY526 ) @ ( ordered_pair @ ( f10 @ SV42 @ SY526 ) @ ( f11 @ SV42 @ SY526 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(735,plain,
! [SV43: $i] :
( ( ! [SY527: $i] :
( ~ ( member @ SV43 @ ( rotate_right @ SY527 ) )
| ( member @ ( ordered_pair @ ( f10 @ SV43 @ SY527 ) @ ( ordered_pair @ ( f11 @ SV43 @ SY527 ) @ ( f9 @ SV43 @ SY527 ) ) ) @ SY527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(736,plain,
! [SV44: $i] :
( ( ! [SY528: $i] :
( ~ ( member @ SV44 @ ( flip_range_of @ SY528 ) )
| ( little_set @ ( f12 @ SV44 @ SY528 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(737,plain,
! [SV45: $i] :
( ( ! [SY529: $i] :
( ~ ( member @ SV45 @ ( flip_range_of @ SY529 ) )
| ( little_set @ ( f13 @ SV45 @ SY529 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(738,plain,
! [SV46: $i] :
( ( ! [SY530: $i] :
( ~ ( member @ SV46 @ ( flip_range_of @ SY530 ) )
| ( little_set @ ( f14 @ SV46 @ SY530 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(739,plain,
! [SV47: $i] :
( ( ! [SY531: $i] :
( ~ ( member @ SV47 @ ( flip_range_of @ SY531 ) )
| ( SV47
= ( ordered_pair @ ( f12 @ SV47 @ SY531 ) @ ( ordered_pair @ ( f13 @ SV47 @ SY531 ) @ ( f14 @ SV47 @ SY531 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(740,plain,
! [SV48: $i] :
( ( ! [SY532: $i] :
( ~ ( member @ SV48 @ ( flip_range_of @ SY532 ) )
| ( member @ ( ordered_pair @ ( f12 @ SV48 @ SY532 ) @ ( ordered_pair @ ( f14 @ SV48 @ SY532 ) @ ( f13 @ SV48 @ SY532 ) ) ) @ SY532 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(741,plain,
! [SV49: $i] :
( ( ( successor @ SV49 )
= ( union @ SV49 @ ( singleton_set @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(742,plain,
! [SV50: $i] :
( ( ~ ( member @ SV50 @ empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(743,plain,
! [SV51: $i] :
( ( ( member @ SV51 @ universal_set )
| ~ ( little_set @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(744,plain,
! [SV52: $i] :
( ( ~ ( member @ SV52 @ infinity )
| ( member @ ( successor @ SV52 ) @ infinity ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(745,plain,
! [SV53: $i] :
( ( ! [SY533: $i] :
( ~ ( member @ SV53 @ ( sigma @ SY533 ) )
| ( member @ ( f16 @ SV53 @ SY533 ) @ SY533 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(746,plain,
! [SV54: $i] :
( ( ! [SY534: $i] :
( ~ ( member @ SV54 @ ( sigma @ SY534 ) )
| ( member @ SV54 @ ( f16 @ SV54 @ SY534 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(747,plain,
! [SV55: $i] :
( ( ! [SY535: $i,SY536: $i] :
( ( member @ SV55 @ ( sigma @ SY535 ) )
| ~ ( member @ SY536 @ SY535 )
| ~ ( member @ SV55 @ SY536 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(748,plain,
! [SV56: $i] :
( ( ~ ( little_set @ SV56 )
| ( little_set @ ( sigma @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(749,plain,
! [SV57: $i] :
( ( ! [SY537: $i,SY538: $i] :
( ~ ( subset @ SV57 @ SY537 )
| ~ ( member @ SY538 @ SV57 )
| ( member @ SY538 @ SY537 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(750,plain,
! [SV58: $i] :
( ( ! [SY539: $i] :
( ( subset @ SV58 @ SY539 )
| ( member @ ( f17 @ SV58 @ SY539 ) @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(751,plain,
! [SV59: $i] :
( ( ! [SY540: $i] :
( ( subset @ SV59 @ SY540 )
| ~ ( member @ ( f17 @ SV59 @ SY540 ) @ SY540 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(752,plain,
! [SV60: $i] :
( ( ! [SY541: $i] :
( ~ ( proper_subset @ SV60 @ SY541 )
| ( subset @ SV60 @ SY541 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(753,plain,
! [SV61: $i] :
( ( ! [SY542: $i] :
( ( proper_subset @ SV61 @ SY542 )
| ~ ( subset @ SV61 @ SY542 )
| ( SV61 = SY542 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(754,plain,
! [SV62: $i] :
( ( ! [SY543: $i] :
( ~ ( member @ SV62 @ ( powerset @ SY543 ) )
| ( subset @ SV62 @ SY543 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(755,plain,
! [SV63: $i] :
( ( ! [SY544: $i] :
( ( member @ SV63 @ ( powerset @ SY544 ) )
| ~ ( little_set @ SV63 )
| ~ ( subset @ SV63 @ SY544 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(756,plain,
! [SV64: $i] :
( ( ~ ( little_set @ SV64 )
| ( little_set @ ( powerset @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(757,plain,
! [SV65: $i] :
( ( ! [SY545: $i] :
( ~ ( relation @ SV65 )
| ~ ( member @ SY545 @ SV65 )
| ( ordered_pair_predicate @ SY545 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(758,plain,
! [SV66: $i] :
( ( ( relation @ SV66 )
| ( member @ ( f18 @ SV66 ) @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(759,plain,
! [SV67: $i] :
( ( ( relation @ SV67 )
| ~ ( ordered_pair_predicate @ ( f18 @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(760,plain,
! [SV68: $i] :
( ( ! [SY546: $i,SY547: $i,SY548: $i] :
( ~ ( single_valued_set @ SV68 )
| ~ ( little_set @ SY546 )
| ~ ( little_set @ SY547 )
| ~ ( little_set @ SY548 )
| ~ ( member @ ( ordered_pair @ SY546 @ SY547 ) @ SV68 )
| ~ ( member @ ( ordered_pair @ SY546 @ SY548 ) @ SV68 )
| ( SY547 = SY548 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(761,plain,
! [SV69: $i] :
( ( ( single_valued_set @ SV69 )
| ( little_set @ ( f19 @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(762,plain,
! [SV70: $i] :
( ( ( single_valued_set @ SV70 )
| ( little_set @ ( f20 @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(763,plain,
! [SV71: $i] :
( ( ( single_valued_set @ SV71 )
| ( little_set @ ( f21 @ SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(764,plain,
! [SV72: $i] :
( ( ( single_valued_set @ SV72 )
| ( member @ ( ordered_pair @ ( f19 @ SV72 ) @ ( f20 @ SV72 ) ) @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(765,plain,
! [SV73: $i] :
( ( ( single_valued_set @ SV73 )
| ( member @ ( ordered_pair @ ( f19 @ SV73 ) @ ( f21 @ SV73 ) ) @ SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(766,plain,
! [SV74: $i] :
( ( ~ ( function @ SV74 )
| ( relation @ SV74 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(767,plain,
! [SV75: $i] :
( ( ~ ( function @ SV75 )
| ( single_valued_set @ SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(768,plain,
! [SV76: $i] :
( ( ( function @ SV76 )
| ~ ( relation @ SV76 )
| ~ ( single_valued_set @ SV76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(769,plain,
! [SV77: $i] :
( ( ! [SY549: $i,SY550: $i] :
( ~ ( member @ SV77 @ ( image @ SY549 @ SY550 ) )
| ( ordered_pair_predicate @ ( f22 @ SV77 @ SY549 @ SY550 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(770,plain,
! [SV78: $i] :
( ( ! [SY551: $i,SY552: $i] :
( ~ ( member @ SV78 @ ( image @ SY551 @ SY552 ) )
| ( member @ ( f22 @ SV78 @ SY551 @ SY552 ) @ SY552 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(771,plain,
! [SV79: $i] :
( ( ! [SY553: $i,SY554: $i] :
( ~ ( member @ SV79 @ ( image @ SY553 @ SY554 ) )
| ( member @ ( first @ ( f22 @ SV79 @ SY553 @ SY554 ) ) @ SY553 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(772,plain,
! [SV80: $i] :
( ( ! [SY555: $i,SY556: $i] :
( ~ ( member @ SV80 @ ( image @ SY555 @ SY556 ) )
| ( ( second @ ( f22 @ SV80 @ SY555 @ SY556 ) )
= SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(773,plain,
! [SV81: $i] :
( ( ! [SY557: $i] :
( ~ ( little_set @ SV81 )
| ~ ( function @ SY557 )
| ( little_set @ ( image @ SV81 @ SY557 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(774,plain,
! [SV82: $i] :
( ( ! [SY558: $i,SY559: $i] :
( ~ ( disjoint @ SV82 @ SY558 )
| ~ ( member @ SY559 @ SV82 )
| ~ ( member @ SY559 @ SY558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(775,plain,
! [SV83: $i] :
( ( ! [SY560: $i] :
( ( disjoint @ SV83 @ SY560 )
| ( member @ ( f23 @ SV83 @ SY560 ) @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(776,plain,
! [SV84: $i] :
( ( ! [SY561: $i] :
( ( disjoint @ SV84 @ SY561 )
| ( member @ ( f23 @ SV84 @ SY561 ) @ SY561 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(777,plain,
! [SV85: $i] :
( ( ( SV85 = empty_set )
| ( member @ ( f24 @ SV85 ) @ SV85 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(778,plain,
! [SV86: $i] :
( ( ( SV86 = empty_set )
| ( disjoint @ ( f24 @ SV86 ) @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(779,plain,
! [SV87: $i] :
( ( ~ ( little_set @ SV87 )
| ( SV87 = empty_set )
| ( member @ ( f26 @ SV87 ) @ SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(780,plain,
! [SV88: $i] :
( ( ~ ( little_set @ SV88 )
| ( SV88 = empty_set )
| ( member @ ( ordered_pair @ SV88 @ ( f26 @ SV88 ) ) @ f25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(781,plain,
! [SV89: $i] :
( ( ! [SY562: $i] :
( ~ ( member @ SV89 @ ( range_of @ SY562 ) )
| ( ordered_pair_predicate @ ( f27 @ SV89 @ SY562 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(782,plain,
! [SV90: $i] :
( ( ! [SY563: $i] :
( ~ ( member @ SV90 @ ( range_of @ SY563 ) )
| ( member @ ( f27 @ SV90 @ SY563 ) @ SY563 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(783,plain,
! [SV91: $i] :
( ( ! [SY564: $i] :
( ~ ( member @ SV91 @ ( range_of @ SY564 ) )
| ( SV91
= ( second @ ( f27 @ SV91 @ SY564 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(784,plain,
! [SV92: $i] :
( ( ~ ( member @ SV92 @ identity_relation )
| ( ordered_pair_predicate @ SV92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(785,plain,
! [SV93: $i] :
( ( ~ ( member @ SV93 @ identity_relation )
| ( ( first @ SV93 )
= ( second @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(786,plain,
! [SV94: $i] :
( ( ! [SY565: $i] :
( ( restrict @ SV94 @ SY565 )
= ( intersection @ SV94 @ ( cross_product @ SY565 @ universal_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(787,plain,
! [SV95: $i] :
( ( ~ ( one_to_one_function @ SV95 )
| ( function @ SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(788,plain,
! [SV96: $i] :
( ( ~ ( one_to_one_function @ SV96 )
| ( function @ ( converse @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(789,plain,
! [SV97: $i] :
( ( ( one_to_one_function @ SV97 )
| ~ ( function @ SV97 )
| ~ ( function @ ( converse @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(790,plain,
! [SV98: $i] :
( ( ! [SY566: $i,SY567: $i] :
( ~ ( member @ SV98 @ ( apply @ SY566 @ SY567 ) )
| ( ordered_pair_predicate @ ( f28 @ SV98 @ SY566 @ SY567 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(791,plain,
! [SV99: $i] :
( ( ! [SY568: $i,SY569: $i] :
( ~ ( member @ SV99 @ ( apply @ SY568 @ SY569 ) )
| ( member @ ( f28 @ SV99 @ SY568 @ SY569 ) @ SY568 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(792,plain,
! [SV100: $i] :
( ( ! [SY570: $i,SY571: $i] :
( ~ ( member @ SV100 @ ( apply @ SY570 @ SY571 ) )
| ( ( first @ ( f28 @ SV100 @ SY570 @ SY571 ) )
= SY571 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(793,plain,
! [SV101: $i] :
( ( ! [SY572: $i,SY573: $i] :
( ~ ( member @ SV101 @ ( apply @ SY572 @ SY573 ) )
| ( member @ SV101 @ ( second @ ( f28 @ SV101 @ SY572 @ SY573 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(794,plain,
! [SV102: $i] :
( ( ! [SY574: $i,SY575: $i] :
( ( apply_to_two_arguments @ SV102 @ SY574 @ SY575 )
= ( apply @ SV102 @ ( ordered_pair @ SY574 @ SY575 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(795,plain,
! [SV103: $i] :
( ( ! [SY576: $i,SY577: $i] :
( ~ ( maps @ SV103 @ SY576 @ SY577 )
| ( function @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(796,plain,
! [SV104: $i] :
( ( ! [SY578: $i,SY579: $i] :
( ~ ( maps @ SV104 @ SY578 @ SY579 )
| ( ( domain_of @ SV104 )
= SY578 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(797,plain,
! [SV105: $i] :
( ( ! [SY580: $i,SY581: $i] :
( ~ ( maps @ SV105 @ SY580 @ SY581 )
| ( subset @ ( range_of @ SV105 ) @ SY581 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(798,plain,
! [SV106: $i] :
( ( ! [SY582: $i] :
( ~ ( closed @ SV106 @ SY582 )
| ( little_set @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(799,plain,
! [SV107: $i] :
( ( ! [SY583: $i] :
( ~ ( closed @ SV107 @ SY583 )
| ( little_set @ SY583 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(800,plain,
! [SV108: $i] :
( ( ! [SY584: $i] :
( ~ ( closed @ SV108 @ SY584 )
| ( maps @ SY584 @ ( cross_product @ SV108 @ SV108 ) @ SV108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(801,plain,
! [SV109: $i] :
( ( ! [SY585: $i] :
( ( closed @ SV109 @ SY585 )
| ~ ( little_set @ SV109 )
| ~ ( little_set @ SY585 )
| ~ ( maps @ SY585 @ ( cross_product @ SV109 @ SV109 ) @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(802,plain,
! [SV110: $i] :
( ( ! [SY586: $i,SY587: $i] :
( ~ ( member @ SV110 @ ( compose @ SY586 @ SY587 ) )
| ( little_set @ ( f29 @ SV110 @ SY586 @ SY587 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(803,plain,
! [SV111: $i] :
( ( ! [SY588: $i,SY589: $i] :
( ~ ( member @ SV111 @ ( compose @ SY588 @ SY589 ) )
| ( little_set @ ( f30 @ SV111 @ SY588 @ SY589 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(804,plain,
! [SV112: $i] :
( ( ! [SY590: $i,SY591: $i] :
( ~ ( member @ SV112 @ ( compose @ SY590 @ SY591 ) )
| ( little_set @ ( f31 @ SV112 @ SY590 @ SY591 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(805,plain,
! [SV113: $i] :
( ( ! [SY592: $i,SY593: $i] :
( ~ ( member @ SV113 @ ( compose @ SY592 @ SY593 ) )
| ( SV113
= ( ordered_pair @ ( f29 @ SV113 @ SY592 @ SY593 ) @ ( f30 @ SV113 @ SY592 @ SY593 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(806,plain,
! [SV114: $i] :
( ( ! [SY594: $i,SY595: $i] :
( ~ ( member @ SV114 @ ( compose @ SY594 @ SY595 ) )
| ( member @ ( ordered_pair @ ( f29 @ SV114 @ SY594 @ SY595 ) @ ( f31 @ SV114 @ SY594 @ SY595 ) ) @ SY594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(807,plain,
! [SV115: $i] :
( ( ! [SY596: $i,SY597: $i] :
( ~ ( member @ SV115 @ ( compose @ SY596 @ SY597 ) )
| ( member @ ( ordered_pair @ ( f31 @ SV115 @ SY596 @ SY597 ) @ ( f30 @ SV115 @ SY596 @ SY597 ) ) @ SY597 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(808,plain,
! [SV116: $i] :
( ( ! [SY598: $i,SY599: $i,SY600: $i,SY601: $i] :
( ~ ( homomorphism @ SV116 @ SY598 @ SY599 @ SY600 @ SY601 )
| ( closed @ SY598 @ SY599 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(809,plain,
! [SV117: $i] :
( ( ! [SY602: $i,SY603: $i,SY604: $i,SY605: $i] :
( ~ ( homomorphism @ SV117 @ SY602 @ SY603 @ SY604 @ SY605 )
| ( closed @ SY604 @ SY605 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(810,plain,
! [SV118: $i] :
( ( ! [SY606: $i,SY607: $i,SY608: $i,SY609: $i] :
( ~ ( homomorphism @ SV118 @ SY606 @ SY607 @ SY608 @ SY609 )
| ( maps @ SV118 @ SY606 @ SY608 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(811,plain,
! [SV119: $i] :
( ( ! [SY610: $i,SY611: $i,SY612: $i,SY613: $i,SY614: $i,SY615: $i] :
( ~ ( homomorphism @ SV119 @ SY610 @ SY611 @ SY612 @ SY613 )
| ~ ( member @ SY614 @ SY610 )
| ~ ( member @ SY615 @ SY610 )
| ( ( apply @ SV119 @ ( apply_to_two_arguments @ SY611 @ SY614 @ SY615 ) )
= ( apply_to_two_arguments @ SY613 @ ( apply @ SV119 @ SY614 ) @ ( apply @ SV119 @ SY615 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(812,plain,
! [SV120: $i] :
( ( ! [SY616: $i,SY617: $i,SY618: $i,SY619: $i] :
( ( homomorphism @ SV120 @ SY616 @ SY617 @ SY618 @ SY619 )
| ~ ( closed @ SY616 @ SY617 )
| ~ ( closed @ SY618 @ SY619 )
| ~ ( maps @ SV120 @ SY616 @ SY618 )
| ( member @ ( f32 @ SV120 @ SY616 @ SY617 @ SY618 @ SY619 ) @ SY616 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(813,plain,
! [SV121: $i] :
( ( ! [SY620: $i,SY621: $i,SY622: $i,SY623: $i] :
( ( homomorphism @ SV121 @ SY620 @ SY621 @ SY622 @ SY623 )
| ~ ( closed @ SY620 @ SY621 )
| ~ ( closed @ SY622 @ SY623 )
| ~ ( maps @ SV121 @ SY620 @ SY622 )
| ( member @ ( f33 @ SV121 @ SY620 @ SY621 @ SY622 @ SY623 ) @ SY620 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(814,plain,
! [SV122: $i] :
( ( ! [SY624: $i,SY625: $i,SY626: $i,SY627: $i] :
( ~ ( associative @ SV122 @ SY624 )
| ~ ( member @ SY625 @ SV122 )
| ~ ( member @ SY626 @ SV122 )
| ~ ( member @ SY627 @ SV122 )
| ( ( apply_to_two_arguments @ SY624 @ ( apply_to_two_arguments @ SY624 @ SY625 @ SY626 ) @ SY627 )
= ( apply_to_two_arguments @ SY624 @ SY625 @ ( apply_to_two_arguments @ SY624 @ SY626 @ SY627 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(815,plain,
! [SV123: $i] :
( ( ! [SY628: $i] :
( ( associative @ SV123 @ SY628 )
| ( member @ ( f34 @ SV123 @ SY628 ) @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(816,plain,
! [SV124: $i] :
( ( ! [SY629: $i] :
( ( associative @ SV124 @ SY629 )
| ( member @ ( f35 @ SV124 @ SY629 ) @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(817,plain,
! [SV125: $i] :
( ( ! [SY630: $i] :
( ( associative @ SV125 @ SY630 )
| ( member @ ( f36 @ SV125 @ SY630 ) @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(818,plain,
! [SV126: $i] :
( ( ! [SY631: $i,SY632: $i] :
( ~ ( identity @ SV126 @ SY631 @ SY632 )
| ( member @ SY632 @ SV126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(819,plain,
! [SV127: $i] :
( ( ! [SY633: $i,SY634: $i,SY635: $i] :
( ~ ( identity @ SV127 @ SY633 @ SY634 )
| ~ ( member @ SY635 @ SV127 )
| ( ( apply_to_two_arguments @ SY633 @ SY634 @ SY635 )
= SY635 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(820,plain,
! [SV128: $i] :
( ( ! [SY636: $i,SY637: $i,SY638: $i] :
( ~ ( identity @ SV128 @ SY636 @ SY637 )
| ~ ( member @ SY638 @ SV128 )
| ( ( apply_to_two_arguments @ SY636 @ SY638 @ SY637 )
= SY638 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(821,plain,
! [SV129: $i] :
( ( ! [SY639: $i,SY640: $i] :
( ( identity @ SV129 @ SY639 @ SY640 )
| ~ ( member @ SY640 @ SV129 )
| ( member @ ( f37 @ SV129 @ SY639 @ SY640 ) @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(822,plain,
! [SV130: $i] :
( ( ! [SY641: $i,SY642: $i,SY643: $i] :
( ~ ( inverse @ SV130 @ SY641 @ SY642 @ SY643 )
| ( maps @ SY643 @ SV130 @ SV130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(823,plain,
! [SV131: $i] :
( ( ! [SY644: $i,SY645: $i,SY646: $i,SY647: $i] :
( ~ ( inverse @ SV131 @ SY644 @ SY645 @ SY646 )
| ~ ( member @ SY647 @ SV131 )
| ( ( apply_to_two_arguments @ SY644 @ ( apply @ SY646 @ SY647 ) @ SY647 )
= SY645 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(824,plain,
! [SV132: $i] :
( ( ! [SY648: $i,SY649: $i,SY650: $i,SY651: $i] :
( ~ ( inverse @ SV132 @ SY648 @ SY649 @ SY650 )
| ~ ( member @ SY651 @ SV132 )
| ( ( apply_to_two_arguments @ SY648 @ SY651 @ ( apply @ SY650 @ SY651 ) )
= SY649 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(825,plain,
! [SV133: $i] :
( ( ! [SY652: $i,SY653: $i,SY654: $i] :
( ( inverse @ SV133 @ SY652 @ SY653 @ SY654 )
| ~ ( maps @ SY654 @ SV133 @ SV133 )
| ( member @ ( f38 @ SV133 @ SY652 @ SY653 @ SY654 ) @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(826,plain,
! [SV134: $i] :
( ( ! [SY655: $i] :
( ~ ( group @ SV134 @ SY655 )
| ( closed @ SV134 @ SY655 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(827,plain,
! [SV135: $i] :
( ( ! [SY656: $i] :
( ~ ( group @ SV135 @ SY656 )
| ( associative @ SV135 @ SY656 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(828,plain,
! [SV136: $i] :
( ( ! [SY657: $i] :
( ~ ( group @ SV136 @ SY657 )
| ( identity @ SV136 @ SY657 @ ( f39 @ SV136 @ SY657 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(829,plain,
! [SV137: $i] :
( ( ! [SY658: $i] :
( ~ ( group @ SV137 @ SY658 )
| ( inverse @ SV137 @ SY658 @ ( f39 @ SV137 @ SY658 ) @ ( f40 @ SV137 @ SY658 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[605]) ).
thf(830,plain,
! [SV138: $i] :
( ( ! [SY659: $i,SY660: $i,SY661: $i] :
( ( group @ SV138 @ SY659 )
| ~ ( closed @ SV138 @ SY659 )
| ~ ( associative @ SV138 @ SY659 )
| ~ ( identity @ SV138 @ SY659 @ SY660 )
| ~ ( inverse @ SV138 @ SY659 @ SY660 @ SY661 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(831,plain,
! [SV139: $i] :
( ( ! [SY662: $i,SY663: $i,SY664: $i] :
( ~ ( commutes @ SV139 @ SY662 )
| ~ ( member @ SY663 @ SV139 )
| ~ ( member @ SY664 @ SV139 )
| ( ( apply_to_two_arguments @ SY662 @ SY663 @ SY664 )
= ( apply_to_two_arguments @ SY662 @ SY664 @ SY663 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(832,plain,
! [SV140: $i] :
( ( ! [SY665: $i] :
( ( commutes @ SV140 @ SY665 )
| ( member @ ( f41 @ SV140 @ SY665 ) @ SV140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(833,plain,
! [SV141: $i] :
( ( ! [SY666: $i] :
( ( commutes @ SV141 @ SY666 )
| ( member @ ( f42 @ SV141 @ SY666 ) @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(834,plain,
! [SV142: $i] :
( ( ! [SY667: $i] :
( ~ ( member @ SV142 @ natural_numbers )
| ~ ( little_set @ SY667 )
| ~ ( member @ empty_set @ SY667 )
| ( member @ ( f43 @ SV142 @ SY667 ) @ SY667 )
| ( member @ SV142 @ SY667 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(835,plain,
! [SV143: $i] :
( ( ! [SY668: $i] :
( ~ ( member @ SV143 @ natural_numbers )
| ~ ( little_set @ SY668 )
| ~ ( member @ empty_set @ SY668 )
| ~ ( member @ ( successor @ ( f43 @ SV143 @ SY668 ) ) @ SY668 )
| ( member @ SV143 @ SY668 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(836,plain,
! [SV144: $i] :
( ( ( member @ SV144 @ natural_numbers )
| ~ ( little_set @ SV144 )
| ( little_set @ ( f44 @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(837,plain,
! [SV145: $i] :
( ( ( member @ SV145 @ natural_numbers )
| ~ ( little_set @ SV145 )
| ( member @ empty_set @ ( f44 @ SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(838,plain,
! [SV146: $i] :
( ( ! [SY669: $i] :
( ( member @ SV146 @ natural_numbers )
| ~ ( little_set @ SV146 )
| ~ ( member @ SY669 @ ( f44 @ SV146 ) )
| ( member @ ( successor @ SY669 ) @ ( f44 @ SV146 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(839,plain,
! [SV147: $i] :
( ( ( member @ SV147 @ natural_numbers )
| ~ ( member @ SV147 @ ( f44 @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(840,plain,
! [SV148: $i] :
( ( ! [SY670: $i] :
( ~ ( member @ SV148 @ plus )
| ~ ( little_set @ SY670 )
| ( member @ ( f45 @ SV148 @ SY670 ) @ natural_numbers )
| ( member @ ( f46 @ SV148 @ SY670 ) @ natural_numbers )
| ( member @ SV148 @ SY670 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(841,plain,
! [SV149: $i] :
( ( ! [SY671: $i] :
( ~ ( member @ SV149 @ plus )
| ~ ( little_set @ SY671 )
| ( member @ ( f45 @ SV149 @ SY671 ) @ natural_numbers )
| ( member @ ( f47 @ SV149 @ SY671 ) @ natural_numbers )
| ( member @ SV149 @ SY671 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(842,plain,
! [SV150: $i] :
( ( ! [SY672: $i] :
( ~ ( member @ SV150 @ plus )
| ~ ( little_set @ SY672 )
| ( member @ ( f45 @ SV150 @ SY672 ) @ natural_numbers )
| ( member @ ( f48 @ SV150 @ SY672 ) @ natural_numbers )
| ( member @ SV150 @ SY672 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(843,plain,
! [SV151: $i] :
( ( ! [SY673: $i] :
( ~ ( member @ SV151 @ plus )
| ~ ( little_set @ SY673 )
| ( member @ ( f45 @ SV151 @ SY673 ) @ natural_numbers )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( f46 @ SV151 @ SY673 ) @ ( f47 @ SV151 @ SY673 ) ) @ ( f48 @ SV151 @ SY673 ) ) @ SY673 )
| ( member @ SV151 @ SY673 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(844,plain,
! [SV152: $i] :
( ( ! [SY674: $i] :
( ~ ( member @ SV152 @ plus )
| ~ ( little_set @ SY674 )
| ( member @ ( f45 @ SV152 @ SY674 ) @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f46 @ SV152 @ SY674 ) ) @ ( f47 @ SV152 @ SY674 ) ) @ ( successor @ ( f48 @ SV152 @ SY674 ) ) ) @ SY674 )
| ( member @ SV152 @ SY674 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(845,plain,
! [SV153: $i] :
( ( ! [SY675: $i] :
( ~ ( member @ SV153 @ plus )
| ~ ( little_set @ SY675 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV153 @ SY675 ) ) @ ( f45 @ SV153 @ SY675 ) ) @ SY675 )
| ( member @ ( f46 @ SV153 @ SY675 ) @ natural_numbers )
| ( member @ SV153 @ SY675 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(846,plain,
! [SV154: $i] :
( ( ! [SY676: $i] :
( ~ ( member @ SV154 @ plus )
| ~ ( little_set @ SY676 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV154 @ SY676 ) ) @ ( f45 @ SV154 @ SY676 ) ) @ SY676 )
| ( member @ ( f47 @ SV154 @ SY676 ) @ natural_numbers )
| ( member @ SV154 @ SY676 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(847,plain,
! [SV155: $i] :
( ( ! [SY677: $i] :
( ~ ( member @ SV155 @ plus )
| ~ ( little_set @ SY677 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV155 @ SY677 ) ) @ ( f45 @ SV155 @ SY677 ) ) @ SY677 )
| ( member @ ( f48 @ SV155 @ SY677 ) @ natural_numbers )
| ( member @ SV155 @ SY677 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(848,plain,
! [SV156: $i] :
( ( ! [SY678: $i] :
( ~ ( member @ SV156 @ plus )
| ~ ( little_set @ SY678 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV156 @ SY678 ) ) @ ( f45 @ SV156 @ SY678 ) ) @ SY678 )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( f46 @ SV156 @ SY678 ) @ ( f47 @ SV156 @ SY678 ) ) @ ( f48 @ SV156 @ SY678 ) ) @ SY678 )
| ( member @ SV156 @ SY678 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(849,plain,
! [SV157: $i] :
( ( ! [SY679: $i] :
( ~ ( member @ SV157 @ plus )
| ~ ( little_set @ SY679 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV157 @ SY679 ) ) @ ( f45 @ SV157 @ SY679 ) ) @ SY679 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f46 @ SV157 @ SY679 ) ) @ ( f47 @ SV157 @ SY679 ) ) @ ( successor @ ( f48 @ SV157 @ SY679 ) ) ) @ SY679 )
| ( member @ SV157 @ SY679 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(850,plain,
! [SV158: $i] :
( ( ( member @ SV158 @ plus )
| ~ ( little_set @ SV158 )
| ( little_set @ ( f49 @ SV158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(851,plain,
! [SV159: $i] :
( ( ! [SY680: $i] :
( ( member @ SV159 @ plus )
| ~ ( little_set @ SV159 )
| ~ ( member @ SY680 @ natural_numbers )
| ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ SY680 ) @ SY680 ) @ ( f49 @ SV159 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(852,plain,
! [SV160: $i] :
( ( ! [SY681: $i,SY682: $i,SY683: $i] :
( ( member @ SV160 @ plus )
| ~ ( little_set @ SV160 )
| ~ ( member @ SY681 @ natural_numbers )
| ~ ( member @ SY682 @ natural_numbers )
| ~ ( member @ SY683 @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SY681 @ SY682 ) @ SY683 ) @ ( f49 @ SV160 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ SY681 ) @ SY682 ) @ ( successor @ SY683 ) ) @ ( f49 @ SV160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(853,plain,
! [SV161: $i] :
( ( ( member @ SV161 @ plus )
| ~ ( member @ SV161 @ ( f49 @ SV161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(854,plain,
! [SV162: $i] :
( ( ! [SY684: $i] :
( ~ ( member @ SV162 @ times )
| ~ ( little_set @ SY684 )
| ( member @ ( f50 @ SV162 @ SY684 ) @ natural_numbers )
| ( member @ ( f51 @ SV162 @ SY684 ) @ natural_numbers )
| ( member @ SV162 @ SY684 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(855,plain,
! [SV163: $i] :
( ( ! [SY685: $i] :
( ~ ( member @ SV163 @ times )
| ~ ( little_set @ SY685 )
| ( member @ ( f50 @ SV163 @ SY685 ) @ natural_numbers )
| ( member @ ( f52 @ SV163 @ SY685 ) @ natural_numbers )
| ( member @ SV163 @ SY685 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(856,plain,
! [SV164: $i] :
( ( ! [SY686: $i] :
( ~ ( member @ SV164 @ times )
| ~ ( little_set @ SY686 )
| ( member @ ( f50 @ SV164 @ SY686 ) @ natural_numbers )
| ( member @ ( f53 @ SV164 @ SY686 ) @ natural_numbers )
| ( member @ SV164 @ SY686 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(857,plain,
! [SV165: $i] :
( ( ! [SY687: $i] :
( ~ ( member @ SV165 @ times )
| ~ ( little_set @ SY687 )
| ( member @ ( f50 @ SV165 @ SY687 ) @ natural_numbers )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( f51 @ SV165 @ SY687 ) @ ( f52 @ SV165 @ SY687 ) ) @ ( f53 @ SV165 @ SY687 ) ) @ SY687 )
| ( member @ SV165 @ SY687 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(858,plain,
! [SV166: $i] :
( ( ! [SY688: $i] :
( ~ ( member @ SV166 @ times )
| ~ ( little_set @ SY688 )
| ( member @ ( f50 @ SV166 @ SY688 ) @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f51 @ SV166 @ SY688 ) ) @ ( f52 @ SV166 @ SY688 ) ) @ ( apply_to_two_arguments @ plus @ ( f53 @ SV166 @ SY688 ) @ ( f52 @ SV166 @ SY688 ) ) ) @ SY688 )
| ( member @ SV166 @ SY688 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(859,plain,
! [SV167: $i] :
( ( ! [SY689: $i] :
( ~ ( member @ SV167 @ times )
| ~ ( little_set @ SY689 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV167 @ SY689 ) ) @ empty_set ) @ SY689 )
| ( member @ ( f51 @ SV167 @ SY689 ) @ natural_numbers )
| ( member @ SV167 @ SY689 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(860,plain,
! [SV168: $i] :
( ( ! [SY690: $i] :
( ~ ( member @ SV168 @ times )
| ~ ( little_set @ SY690 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV168 @ SY690 ) ) @ empty_set ) @ SY690 )
| ( member @ ( f52 @ SV168 @ SY690 ) @ natural_numbers )
| ( member @ SV168 @ SY690 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(861,plain,
! [SV169: $i] :
( ( ! [SY691: $i] :
( ~ ( member @ SV169 @ times )
| ~ ( little_set @ SY691 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV169 @ SY691 ) ) @ empty_set ) @ SY691 )
| ( member @ ( f53 @ SV169 @ SY691 ) @ natural_numbers )
| ( member @ SV169 @ SY691 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(862,plain,
! [SV170: $i] :
( ( ! [SY692: $i] :
( ~ ( member @ SV170 @ times )
| ~ ( little_set @ SY692 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV170 @ SY692 ) ) @ empty_set ) @ SY692 )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( f51 @ SV170 @ SY692 ) @ ( f52 @ SV170 @ SY692 ) ) @ ( f53 @ SV170 @ SY692 ) ) @ SY692 )
| ( member @ SV170 @ SY692 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(863,plain,
! [SV171: $i] :
( ( ! [SY693: $i] :
( ~ ( member @ SV171 @ times )
| ~ ( little_set @ SY693 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV171 @ SY693 ) ) @ empty_set ) @ SY693 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f51 @ SV171 @ SY693 ) ) @ ( f52 @ SV171 @ SY693 ) ) @ ( apply_to_two_arguments @ plus @ ( f53 @ SV171 @ SY693 ) @ ( f52 @ SV171 @ SY693 ) ) ) @ SY693 )
| ( member @ SV171 @ SY693 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(864,plain,
! [SV172: $i] :
( ( ( member @ SV172 @ times )
| ~ ( little_set @ SV172 )
| ( little_set @ ( f54 @ SV172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(865,plain,
! [SV173: $i] :
( ( ! [SY694: $i] :
( ( member @ SV173 @ times )
| ~ ( little_set @ SV173 )
| ~ ( member @ SY694 @ natural_numbers )
| ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ SY694 ) @ empty_set ) @ ( f54 @ SV173 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(866,plain,
! [SV174: $i] :
( ( ! [SY695: $i,SY696: $i,SY697: $i] :
( ( member @ SV174 @ times )
| ~ ( little_set @ SV174 )
| ~ ( member @ SY695 @ natural_numbers )
| ~ ( member @ SY696 @ natural_numbers )
| ~ ( member @ SY697 @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SY695 @ SY696 ) @ SY697 ) @ ( f54 @ SV174 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ SY695 ) @ SY696 ) @ ( apply_to_two_arguments @ plus @ SY697 @ SY696 ) ) @ ( f54 @ SV174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(867,plain,
! [SV175: $i] :
( ( ( member @ SV175 @ times )
| ~ ( member @ SV175 @ ( f54 @ SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(868,plain,
! [SV176: $i] :
( ( ~ ( member @ SV176 @ prime_numbers )
| ( member @ SV176 @ natural_numbers ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(869,plain,
! [SV177: $i] :
( ( ( member @ SV177 @ prime_numbers )
| ~ ( member @ SV177 @ natural_numbers )
| ( SV177 = empty_set )
| ( SV177
= ( successor @ empty_set ) )
| ( member @ ( f55 @ SV177 ) @ natural_numbers ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(870,plain,
! [SV178: $i] :
( ( ( member @ SV178 @ prime_numbers )
| ~ ( member @ SV178 @ natural_numbers )
| ( SV178 = empty_set )
| ( SV178
= ( successor @ empty_set ) )
| ( member @ ( f56 @ SV178 ) @ natural_numbers ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(871,plain,
! [SV179: $i] :
( ( ( member @ SV179 @ prime_numbers )
| ~ ( member @ SV179 @ natural_numbers )
| ( SV179 = empty_set )
| ( SV179
= ( successor @ empty_set ) )
| ( ( apply_to_two_arguments @ times @ ( f55 @ SV179 ) @ ( f56 @ SV179 ) )
= SV179 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(872,plain,
! [SV180: $i] :
( ( ( member @ SV180 @ prime_numbers )
| ~ ( member @ SV180 @ natural_numbers )
| ( SV180 = empty_set )
| ( SV180
= ( successor @ empty_set ) )
| ~ ( member @ ( f55 @ SV180 ) @ ( non_ordered_pair @ ( successor @ empty_set ) @ SV180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(873,plain,
! [SV181: $i] :
( ( ~ ( finite @ SV181 )
| ( member @ ( f57 @ SV181 ) @ natural_numbers ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(874,plain,
! [SV182: $i] :
( ( ~ ( finite @ SV182 )
| ( maps @ ( f58 @ SV182 ) @ ( f57 @ SV182 ) @ SV182 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(875,plain,
! [SV183: $i] :
( ( ~ ( finite @ SV183 )
| ( ( range_of @ ( f58 @ SV183 ) )
= SV183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(876,plain,
! [SV184: $i] :
( ( ~ ( finite @ SV184 )
| ( one_to_one_function @ ( f58 @ SV184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(877,plain,
! [SV185: $i] :
( ( ~ ( member @ SV185 @ twin_prime_numbers )
| ( member @ SV185 @ prime_numbers ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(878,plain,
! [SV186: $i] :
( ( ~ ( member @ SV186 @ twin_prime_numbers )
| ( member @ ( successor @ ( successor @ SV186 ) ) @ prime_numbers ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(879,plain,
! [SV187: $i] :
( ( ( member @ SV187 @ twin_prime_numbers )
| ~ ( member @ SV187 @ prime_numbers )
| ~ ( member @ ( successor @ ( successor @ SV187 ) ) @ prime_numbers ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(880,plain,
! [SV188: $i] :
( ( ~ ( member @ SV188 @ even_numbers )
| ( member @ SV188 @ natural_numbers ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(881,plain,
! [SV189: $i] :
( ( ~ ( member @ SV189 @ even_numbers )
| ( member @ ( f59 @ SV189 ) @ natural_numbers ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(882,plain,
! [SV190: $i] :
( ( ~ ( member @ SV190 @ even_numbers )
| ( ( apply_to_two_arguments @ plus @ ( f59 @ SV190 ) @ ( f59 @ SV190 ) )
= SV190 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(883,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[665]) ).
thf(884,plain,
! [SV191: $i] :
( ( ! [SY698: $i,SY699: $i,SY700: $i] :
( ( member @ SV191 @ ( second @ SY698 ) )
| ~ ( little_set @ SY699 )
| ~ ( little_set @ SY700 )
| ( SY698
!= ( ordered_pair @ SY699 @ SY700 ) )
| ~ ( member @ SV191 @ SY700 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(885,plain,
! [SV192: $i] :
( ( ! [SY701: $i,SY702: $i,SY703: $i] :
( ( inverse @ SV192 @ SY701 @ SY702 @ SY703 )
| ~ ( maps @ SY703 @ SV192 @ SV192 )
| ( ( apply_to_two_arguments @ SY701 @ ( apply @ SY703 @ ( f38 @ SV192 @ SY701 @ SY702 @ SY703 ) ) @ ( f38 @ SV192 @ SY701 @ SY702 @ SY703 ) )
!= SY702 )
| ( ( apply_to_two_arguments @ SY701 @ ( f38 @ SV192 @ SY701 @ SY702 @ SY703 ) @ ( apply @ SY703 @ ( f38 @ SV192 @ SY701 @ SY702 @ SY703 ) ) )
!= SY702 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(886,plain,
! [SV193: $i] :
( ( ! [SY704: $i,SY705: $i] :
( ~ ( member @ SV193 @ prime_numbers )
| ~ ( member @ SY704 @ natural_numbers )
| ~ ( member @ SY705 @ natural_numbers )
| ( ( apply_to_two_arguments @ times @ SY704 @ SY705 )
!= SV193 )
| ( member @ SY704 @ ( non_ordered_pair @ ( successor @ empty_set ) @ SV193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(887,plain,
! [SV194: $i] :
( ( ~ ( member @ SV194 @ prime_numbers )
| ( SV194 != empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(888,plain,
! [SV195: $i] :
( ( ! [SY706: $i,SY707: $i,SY708: $i,SY709: $i] :
( ( member @ SV195 @ ( flip_range_of @ SY706 ) )
| ~ ( little_set @ SV195 )
| ~ ( little_set @ SY707 )
| ~ ( little_set @ SY708 )
| ~ ( little_set @ SY709 )
| ( SV195
!= ( ordered_pair @ SY707 @ ( ordered_pair @ SY708 @ SY709 ) ) )
| ~ ( member @ ( ordered_pair @ SY707 @ ( ordered_pair @ SY709 @ SY708 ) ) @ SY706 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(889,plain,
! [SV196: $i] :
( ( ! [SY710: $i,SY711: $i] :
( ( member @ SV196 @ ( non_ordered_pair @ SY710 @ SY711 ) )
| ~ ( little_set @ SV196 )
| ( SV196 != SY711 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(890,plain,
! [SV197: $i] :
( ( ! [SY712: $i,SY713: $i,SY714: $i] :
( ( member @ SV197 @ ( first @ SY712 ) )
| ~ ( little_set @ SY713 )
| ~ ( little_set @ SY714 )
| ( SY712
!= ( ordered_pair @ SY713 @ SY714 ) )
| ~ ( member @ SV197 @ SY713 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(891,plain,
! [SV198: $i] :
( ( ! [SY715: $i,SY716: $i,SY717: $i] :
( ( member @ SV198 @ ( image @ SY715 @ SY716 ) )
| ~ ( little_set @ SV198 )
| ~ ( ordered_pair_predicate @ SY717 )
| ~ ( member @ SY717 @ SY716 )
| ~ ( member @ ( first @ SY717 ) @ SY715 )
| ( ( second @ SY717 )
!= SV198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(892,plain,
! [SV199: $i] :
( ( ! [SY718: $i,SY719: $i,SY720: $i,SY721: $i] :
( ( member @ SV199 @ ( rotate_right @ SY718 ) )
| ~ ( little_set @ SV199 )
| ~ ( little_set @ SY719 )
| ~ ( little_set @ SY720 )
| ~ ( little_set @ SY721 )
| ( SV199
!= ( ordered_pair @ SY719 @ ( ordered_pair @ SY720 @ SY721 ) ) )
| ~ ( member @ ( ordered_pair @ SY720 @ ( ordered_pair @ SY721 @ SY719 ) ) @ SY718 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(893,plain,
! [SV200: $i] :
( ( ( single_valued_set @ SV200 )
| ( ( f20 @ SV200 )
!= ( f21 @ SV200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(894,plain,
! [SV201: $i] :
( ( ! [SY722: $i,SY723: $i,SY724: $i,SY725: $i,SY726: $i] :
( ( member @ SV201 @ ( compose @ SY722 @ SY723 ) )
| ~ ( little_set @ SV201 )
| ~ ( little_set @ SY724 )
| ~ ( little_set @ SY725 )
| ~ ( little_set @ SY726 )
| ( SV201
!= ( ordered_pair @ SY724 @ SY725 ) )
| ~ ( member @ ( ordered_pair @ SY724 @ SY726 ) @ SY722 )
| ~ ( member @ ( ordered_pair @ SY726 @ SY725 ) @ SY723 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(895,plain,
! [SV202: $i] :
( ( ! [SY727: $i,SY728: $i] :
( ( ordered_pair_predicate @ SV202 )
| ~ ( little_set @ SY727 )
| ~ ( little_set @ SY728 )
| ( SV202
!= ( ordered_pair @ SY727 @ SY728 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(896,plain,
! [SV203: $i] :
( ( ! [SY729: $i,SY730: $i] :
( ( member @ SV203 @ ( non_ordered_pair @ SY729 @ SY730 ) )
| ~ ( little_set @ SV203 )
| ( SV203 != SY729 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(897,plain,
! [SV204: $i] :
( ( ! [SY731: $i] :
( ( member @ SV204 @ even_numbers )
| ~ ( member @ SV204 @ natural_numbers )
| ~ ( member @ SY731 @ natural_numbers )
| ( ( apply_to_two_arguments @ plus @ SY731 @ SY731 )
!= SV204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(898,plain,
! [SV205: $i] :
( ( ! [SY732: $i] :
( ~ ( proper_subset @ SV205 @ SY732 )
| ( SV205 != SY732 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(899,plain,
! [SV206: $i] :
( ( ! [SY733: $i,SY734: $i,SY735: $i,SY736: $i] :
( ( homomorphism @ SV206 @ SY733 @ SY734 @ SY735 @ SY736 )
| ~ ( closed @ SY733 @ SY734 )
| ~ ( closed @ SY735 @ SY736 )
| ~ ( maps @ SV206 @ SY733 @ SY735 )
| ( ( apply @ SV206 @ ( apply_to_two_arguments @ SY734 @ ( f32 @ SV206 @ SY733 @ SY734 @ SY735 @ SY736 ) @ ( f33 @ SV206 @ SY733 @ SY734 @ SY735 @ SY736 ) ) )
!= ( apply_to_two_arguments @ SY736 @ ( apply @ SV206 @ ( f32 @ SV206 @ SY733 @ SY734 @ SY735 @ SY736 ) ) @ ( apply @ SV206 @ ( f33 @ SV206 @ SY733 @ SY734 @ SY735 @ SY736 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(900,plain,
! [SV207: $i] :
( ( ! [SY737: $i,SY738: $i] :
( ( finite @ SV207 )
| ~ ( member @ SY737 @ natural_numbers )
| ~ ( maps @ SY738 @ SY737 @ SV207 )
| ( ( range_of @ SY738 )
!= SV207 )
| ~ ( one_to_one_function @ SY738 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(901,plain,
! [SV208: $i] :
( ( ! [SY739: $i,SY740: $i] :
( ( maps @ SV208 @ SY739 @ SY740 )
| ~ ( function @ SV208 )
| ( ( domain_of @ SV208 )
!= SY739 )
| ~ ( subset @ ( range_of @ SV208 ) @ SY740 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(902,plain,
! [SV209: $i] :
( ( ~ ( member @ SV209 @ prime_numbers )
| ( SV209
!= ( successor @ empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(903,plain,
! [SV210: $i] :
( ( ! [SY741: $i] :
( ( commutes @ SV210 @ SY741 )
| ( ( apply_to_two_arguments @ SY741 @ ( f41 @ SV210 @ SY741 ) @ ( f42 @ SV210 @ SY741 ) )
!= ( apply_to_two_arguments @ SY741 @ ( f42 @ SV210 @ SY741 ) @ ( f41 @ SV210 @ SY741 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(904,plain,
! [SV211: $i] :
( ( ( member @ SV211 @ identity_relation )
| ~ ( little_set @ SV211 )
| ~ ( ordered_pair_predicate @ SV211 )
| ( ( first @ SV211 )
!= ( second @ SV211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(905,plain,
! [SV212: $i] :
( ( ! [SY742: $i,SY743: $i] :
( ( member @ SV212 @ ( range_of @ SY742 ) )
| ~ ( little_set @ SV212 )
| ~ ( ordered_pair_predicate @ SY743 )
| ~ ( member @ SY743 @ SY742 )
| ( SV212
!= ( second @ SY743 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(906,plain,
! [SV213: $i] :
( ( ! [SY744: $i] :
( ( associative @ SV213 @ SY744 )
| ( ( apply_to_two_arguments @ SY744 @ ( apply_to_two_arguments @ SY744 @ ( f34 @ SV213 @ SY744 ) @ ( f35 @ SV213 @ SY744 ) ) @ ( f36 @ SV213 @ SY744 ) )
!= ( apply_to_two_arguments @ SY744 @ ( f34 @ SV213 @ SY744 ) @ ( apply_to_two_arguments @ SY744 @ ( f35 @ SV213 @ SY744 ) @ ( f36 @ SV213 @ SY744 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(907,plain,
! [SV214: $i] :
( ( ! [SY745: $i,SY746: $i] :
( ( identity @ SV214 @ SY745 @ SY746 )
| ~ ( member @ SY746 @ SV214 )
| ( ( apply_to_two_arguments @ SY745 @ SY746 @ ( f37 @ SV214 @ SY745 @ SY746 ) )
!= ( f37 @ SV214 @ SY745 @ SY746 ) )
| ( ( apply_to_two_arguments @ SY745 @ ( f37 @ SV214 @ SY745 @ SY746 ) @ SY746 )
!= ( f37 @ SV214 @ SY745 @ SY746 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(908,plain,
! [SV215: $i] :
( ( ! [SY747: $i,SY748: $i] :
( ( member @ SV215 @ ( domain_of @ SY747 ) )
| ~ ( little_set @ SV215 )
| ~ ( ordered_pair_predicate @ SY748 )
| ~ ( member @ SY748 @ SY747 )
| ( SV215
!= ( first @ SY748 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(909,plain,
! [SV216: $i] :
( ( ! [SY749: $i,SY750: $i,SY751: $i] :
( ( member @ SV216 @ ( apply @ SY749 @ SY750 ) )
| ~ ( ordered_pair_predicate @ SY751 )
| ~ ( member @ SY751 @ SY749 )
| ( ( first @ SY751 )
!= SY750 )
| ~ ( member @ SV216 @ ( second @ SY751 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(910,plain,
! [SV217: $i,SV1: $i] :
( ( ~ ( member @ SV1 @ SV217 )
| ( little_set @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(911,plain,
! [SV218: $i,SV2: $i] :
( ( ( little_set @ ( f1 @ SV2 @ SV218 ) )
| ( SV2 = SV218 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(912,plain,
! [SV219: $i,SV3: $i] :
( ( ( member @ ( f1 @ SV3 @ SV219 ) @ SV3 )
| ( member @ ( f1 @ SV3 @ SV219 ) @ SV219 )
| ( SV3 = SV219 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(913,plain,
! [SV220: $i,SV4: $i] :
( ( ~ ( member @ ( f1 @ SV4 @ SV220 ) @ SV4 )
| ~ ( member @ ( f1 @ SV4 @ SV220 ) @ SV220 )
| ( SV4 = SV220 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(914,plain,
! [SV221: $i,SV5: $i] :
( ( ! [SY752: $i] :
( ~ ( member @ SV5 @ ( non_ordered_pair @ SV221 @ SY752 ) )
| ( SV5 = SV221 )
| ( SV5 = SY752 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(915,plain,
! [SV222: $i,SV6: $i] :
( ( little_set @ ( non_ordered_pair @ SV6 @ SV222 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(916,plain,
! [SV223: $i,SV8: $i] :
( ( ( ordered_pair @ SV8 @ SV223 )
= ( non_ordered_pair @ ( singleton_set @ SV8 ) @ ( non_ordered_pair @ SV8 @ SV223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(917,plain,
! [SV9: $i] :
( ( ( ~ ( ordered_pair_predicate @ SV9 ) )
= $true )
| ( ( little_set @ ( f2 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[701]) ).
thf(918,plain,
! [SV10: $i] :
( ( ( ~ ( ordered_pair_predicate @ SV10 ) )
= $true )
| ( ( little_set @ ( f3 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[702]) ).
thf(919,plain,
! [SV11: $i] :
( ( ( ~ ( ordered_pair_predicate @ SV11 ) )
= $true )
| ( ( SV11
= ( ordered_pair @ ( f2 @ SV11 ) @ ( f3 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[703]) ).
thf(920,plain,
! [SV224: $i,SV12: $i] :
( ( ~ ( member @ SV12 @ ( first @ SV224 ) )
| ( little_set @ ( f4 @ SV12 @ SV224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(921,plain,
! [SV225: $i,SV13: $i] :
( ( ~ ( member @ SV13 @ ( first @ SV225 ) )
| ( little_set @ ( f5 @ SV13 @ SV225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(922,plain,
! [SV226: $i,SV14: $i] :
( ( ~ ( member @ SV14 @ ( first @ SV226 ) )
| ( SV226
= ( ordered_pair @ ( f4 @ SV14 @ SV226 ) @ ( f5 @ SV14 @ SV226 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(923,plain,
! [SV227: $i,SV15: $i] :
( ( ~ ( member @ SV15 @ ( first @ SV227 ) )
| ( member @ SV15 @ ( f4 @ SV15 @ SV227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(924,plain,
! [SV228: $i,SV16: $i] :
( ( ~ ( member @ SV16 @ ( second @ SV228 ) )
| ( little_set @ ( f6 @ SV16 @ SV228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(925,plain,
! [SV229: $i,SV17: $i] :
( ( ~ ( member @ SV17 @ ( second @ SV229 ) )
| ( little_set @ ( f7 @ SV17 @ SV229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(926,plain,
! [SV230: $i,SV18: $i] :
( ( ~ ( member @ SV18 @ ( second @ SV230 ) )
| ( SV230
= ( ordered_pair @ ( f6 @ SV18 @ SV230 ) @ ( f7 @ SV18 @ SV230 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(927,plain,
! [SV231: $i,SV19: $i] :
( ( ~ ( member @ SV19 @ ( second @ SV231 ) )
| ( member @ SV19 @ ( f7 @ SV19 @ SV231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(928,plain,
! [SV20: $i] :
( ( ( ~ ( member @ SV20 @ estin ) )
= $true )
| ( ( ordered_pair_predicate @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[712]) ).
thf(929,plain,
! [SV21: $i] :
( ( ( ~ ( member @ SV21 @ estin ) )
= $true )
| ( ( member @ ( first @ SV21 ) @ ( second @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[713]) ).
thf(930,plain,
! [SV22: $i] :
( ( ( member @ SV22 @ estin )
= $true )
| ( ( ~ ( little_set @ SV22 )
| ~ ( ordered_pair_predicate @ SV22 )
| ~ ( member @ ( first @ SV22 ) @ ( second @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[714]) ).
thf(931,plain,
! [SV232: $i,SV23: $i] :
( ( ! [SY753: $i] :
( ~ ( member @ SV23 @ ( intersection @ SV232 @ SY753 ) )
| ( member @ SV23 @ SV232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(932,plain,
! [SV233: $i,SV24: $i] :
( ( ! [SY754: $i] :
( ~ ( member @ SV24 @ ( intersection @ SV233 @ SY754 ) )
| ( member @ SV24 @ SY754 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(933,plain,
! [SV234: $i,SV25: $i] :
( ( ! [SY755: $i] :
( ( member @ SV25 @ ( intersection @ SV234 @ SY755 ) )
| ~ ( member @ SV25 @ SV234 )
| ~ ( member @ SV25 @ SY755 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(934,plain,
! [SV235: $i,SV26: $i] :
( ( ~ ( member @ SV26 @ ( complement @ SV235 ) )
| ~ ( member @ SV26 @ SV235 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(935,plain,
! [SV236: $i,SV27: $i] :
( ( ( member @ SV27 @ ( complement @ SV236 ) )
| ~ ( little_set @ SV27 )
| ( member @ SV27 @ SV236 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(936,plain,
! [SV237: $i,SV28: $i] :
( ( ( union @ SV28 @ SV237 )
= ( complement @ ( intersection @ ( complement @ SV28 ) @ ( complement @ SV237 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(937,plain,
! [SV238: $i,SV29: $i] :
( ( ~ ( member @ SV29 @ ( domain_of @ SV238 ) )
| ( ordered_pair_predicate @ ( f8 @ SV29 @ SV238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(938,plain,
! [SV239: $i,SV30: $i] :
( ( ~ ( member @ SV30 @ ( domain_of @ SV239 ) )
| ( member @ ( f8 @ SV30 @ SV239 ) @ SV239 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(939,plain,
! [SV240: $i,SV31: $i] :
( ( ~ ( member @ SV31 @ ( domain_of @ SV240 ) )
| ( SV31
= ( first @ ( f8 @ SV31 @ SV240 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(940,plain,
! [SV241: $i,SV32: $i] :
( ( ! [SY756: $i] :
( ~ ( member @ SV32 @ ( cross_product @ SV241 @ SY756 ) )
| ( ordered_pair_predicate @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(941,plain,
! [SV242: $i,SV33: $i] :
( ( ! [SY757: $i] :
( ~ ( member @ SV33 @ ( cross_product @ SV242 @ SY757 ) )
| ( member @ ( first @ SV33 ) @ SV242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(942,plain,
! [SV243: $i,SV34: $i] :
( ( ! [SY758: $i] :
( ~ ( member @ SV34 @ ( cross_product @ SV243 @ SY758 ) )
| ( member @ ( second @ SV34 ) @ SY758 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(943,plain,
! [SV244: $i,SV35: $i] :
( ( ! [SY759: $i] :
( ( member @ SV35 @ ( cross_product @ SV244 @ SY759 ) )
| ~ ( little_set @ SV35 )
| ~ ( ordered_pair_predicate @ SV35 )
| ~ ( member @ ( first @ SV35 ) @ SV244 )
| ~ ( member @ ( second @ SV35 ) @ SY759 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(944,plain,
! [SV245: $i,SV36: $i] :
( ( ~ ( member @ SV36 @ ( converse @ SV245 ) )
| ( ordered_pair_predicate @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(945,plain,
! [SV246: $i,SV37: $i] :
( ( ~ ( member @ SV37 @ ( converse @ SV246 ) )
| ( member @ ( ordered_pair @ ( second @ SV37 ) @ ( first @ SV37 ) ) @ SV246 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(946,plain,
! [SV247: $i,SV38: $i] :
( ( ( member @ SV38 @ ( converse @ SV247 ) )
| ~ ( little_set @ SV38 )
| ~ ( ordered_pair_predicate @ SV38 )
| ~ ( member @ ( ordered_pair @ ( second @ SV38 ) @ ( first @ SV38 ) ) @ SV247 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(947,plain,
! [SV248: $i,SV39: $i] :
( ( ~ ( member @ SV39 @ ( rotate_right @ SV248 ) )
| ( little_set @ ( f9 @ SV39 @ SV248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(948,plain,
! [SV249: $i,SV40: $i] :
( ( ~ ( member @ SV40 @ ( rotate_right @ SV249 ) )
| ( little_set @ ( f10 @ SV40 @ SV249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(949,plain,
! [SV250: $i,SV41: $i] :
( ( ~ ( member @ SV41 @ ( rotate_right @ SV250 ) )
| ( little_set @ ( f11 @ SV41 @ SV250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(950,plain,
! [SV251: $i,SV42: $i] :
( ( ~ ( member @ SV42 @ ( rotate_right @ SV251 ) )
| ( SV42
= ( ordered_pair @ ( f9 @ SV42 @ SV251 ) @ ( ordered_pair @ ( f10 @ SV42 @ SV251 ) @ ( f11 @ SV42 @ SV251 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(951,plain,
! [SV252: $i,SV43: $i] :
( ( ~ ( member @ SV43 @ ( rotate_right @ SV252 ) )
| ( member @ ( ordered_pair @ ( f10 @ SV43 @ SV252 ) @ ( ordered_pair @ ( f11 @ SV43 @ SV252 ) @ ( f9 @ SV43 @ SV252 ) ) ) @ SV252 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(952,plain,
! [SV253: $i,SV44: $i] :
( ( ~ ( member @ SV44 @ ( flip_range_of @ SV253 ) )
| ( little_set @ ( f12 @ SV44 @ SV253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(953,plain,
! [SV254: $i,SV45: $i] :
( ( ~ ( member @ SV45 @ ( flip_range_of @ SV254 ) )
| ( little_set @ ( f13 @ SV45 @ SV254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(954,plain,
! [SV255: $i,SV46: $i] :
( ( ~ ( member @ SV46 @ ( flip_range_of @ SV255 ) )
| ( little_set @ ( f14 @ SV46 @ SV255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(955,plain,
! [SV256: $i,SV47: $i] :
( ( ~ ( member @ SV47 @ ( flip_range_of @ SV256 ) )
| ( SV47
= ( ordered_pair @ ( f12 @ SV47 @ SV256 ) @ ( ordered_pair @ ( f13 @ SV47 @ SV256 ) @ ( f14 @ SV47 @ SV256 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(956,plain,
! [SV257: $i,SV48: $i] :
( ( ~ ( member @ SV48 @ ( flip_range_of @ SV257 ) )
| ( member @ ( ordered_pair @ ( f12 @ SV48 @ SV257 ) @ ( ordered_pair @ ( f14 @ SV48 @ SV257 ) @ ( f13 @ SV48 @ SV257 ) ) ) @ SV257 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(957,plain,
! [SV50: $i] :
( ( member @ SV50 @ empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[742]) ).
thf(958,plain,
! [SV51: $i] :
( ( ( member @ SV51 @ universal_set )
= $true )
| ( ( ~ ( little_set @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[743]) ).
thf(959,plain,
! [SV52: $i] :
( ( ( ~ ( member @ SV52 @ infinity ) )
= $true )
| ( ( member @ ( successor @ SV52 ) @ infinity )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[744]) ).
thf(960,plain,
! [SV258: $i,SV53: $i] :
( ( ~ ( member @ SV53 @ ( sigma @ SV258 ) )
| ( member @ ( f16 @ SV53 @ SV258 ) @ SV258 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(961,plain,
! [SV259: $i,SV54: $i] :
( ( ~ ( member @ SV54 @ ( sigma @ SV259 ) )
| ( member @ SV54 @ ( f16 @ SV54 @ SV259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(962,plain,
! [SV260: $i,SV55: $i] :
( ( ! [SY760: $i] :
( ( member @ SV55 @ ( sigma @ SV260 ) )
| ~ ( member @ SY760 @ SV260 )
| ~ ( member @ SV55 @ SY760 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(963,plain,
! [SV56: $i] :
( ( ( ~ ( little_set @ SV56 ) )
= $true )
| ( ( little_set @ ( sigma @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[748]) ).
thf(964,plain,
! [SV261: $i,SV57: $i] :
( ( ! [SY761: $i] :
( ~ ( subset @ SV57 @ SV261 )
| ~ ( member @ SY761 @ SV57 )
| ( member @ SY761 @ SV261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(965,plain,
! [SV262: $i,SV58: $i] :
( ( ( subset @ SV58 @ SV262 )
| ( member @ ( f17 @ SV58 @ SV262 ) @ SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(966,plain,
! [SV263: $i,SV59: $i] :
( ( ( subset @ SV59 @ SV263 )
| ~ ( member @ ( f17 @ SV59 @ SV263 ) @ SV263 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(967,plain,
! [SV264: $i,SV60: $i] :
( ( ~ ( proper_subset @ SV60 @ SV264 )
| ( subset @ SV60 @ SV264 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(968,plain,
! [SV265: $i,SV61: $i] :
( ( ( proper_subset @ SV61 @ SV265 )
| ~ ( subset @ SV61 @ SV265 )
| ( SV61 = SV265 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(969,plain,
! [SV266: $i,SV62: $i] :
( ( ~ ( member @ SV62 @ ( powerset @ SV266 ) )
| ( subset @ SV62 @ SV266 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(970,plain,
! [SV267: $i,SV63: $i] :
( ( ( member @ SV63 @ ( powerset @ SV267 ) )
| ~ ( little_set @ SV63 )
| ~ ( subset @ SV63 @ SV267 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(971,plain,
! [SV64: $i] :
( ( ( ~ ( little_set @ SV64 ) )
= $true )
| ( ( little_set @ ( powerset @ SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[756]) ).
thf(972,plain,
! [SV268: $i,SV65: $i] :
( ( ~ ( relation @ SV65 )
| ~ ( member @ SV268 @ SV65 )
| ( ordered_pair_predicate @ SV268 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(973,plain,
! [SV66: $i] :
( ( ( relation @ SV66 )
= $true )
| ( ( member @ ( f18 @ SV66 ) @ SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[758]) ).
thf(974,plain,
! [SV67: $i] :
( ( ( relation @ SV67 )
= $true )
| ( ( ~ ( ordered_pair_predicate @ ( f18 @ SV67 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[759]) ).
thf(975,plain,
! [SV269: $i,SV68: $i] :
( ( ! [SY762: $i,SY763: $i] :
( ~ ( single_valued_set @ SV68 )
| ~ ( little_set @ SV269 )
| ~ ( little_set @ SY762 )
| ~ ( little_set @ SY763 )
| ~ ( member @ ( ordered_pair @ SV269 @ SY762 ) @ SV68 )
| ~ ( member @ ( ordered_pair @ SV269 @ SY763 ) @ SV68 )
| ( SY762 = SY763 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(976,plain,
! [SV69: $i] :
( ( ( single_valued_set @ SV69 )
= $true )
| ( ( little_set @ ( f19 @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[761]) ).
thf(977,plain,
! [SV70: $i] :
( ( ( single_valued_set @ SV70 )
= $true )
| ( ( little_set @ ( f20 @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[762]) ).
thf(978,plain,
! [SV71: $i] :
( ( ( single_valued_set @ SV71 )
= $true )
| ( ( little_set @ ( f21 @ SV71 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[763]) ).
thf(979,plain,
! [SV72: $i] :
( ( ( single_valued_set @ SV72 )
= $true )
| ( ( member @ ( ordered_pair @ ( f19 @ SV72 ) @ ( f20 @ SV72 ) ) @ SV72 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[764]) ).
thf(980,plain,
! [SV73: $i] :
( ( ( single_valued_set @ SV73 )
= $true )
| ( ( member @ ( ordered_pair @ ( f19 @ SV73 ) @ ( f21 @ SV73 ) ) @ SV73 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[765]) ).
thf(981,plain,
! [SV74: $i] :
( ( ( ~ ( function @ SV74 ) )
= $true )
| ( ( relation @ SV74 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[766]) ).
thf(982,plain,
! [SV75: $i] :
( ( ( ~ ( function @ SV75 ) )
= $true )
| ( ( single_valued_set @ SV75 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[767]) ).
thf(983,plain,
! [SV76: $i] :
( ( ( function @ SV76 )
= $true )
| ( ( ~ ( relation @ SV76 )
| ~ ( single_valued_set @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[768]) ).
thf(984,plain,
! [SV270: $i,SV77: $i] :
( ( ! [SY764: $i] :
( ~ ( member @ SV77 @ ( image @ SV270 @ SY764 ) )
| ( ordered_pair_predicate @ ( f22 @ SV77 @ SV270 @ SY764 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(985,plain,
! [SV271: $i,SV78: $i] :
( ( ! [SY765: $i] :
( ~ ( member @ SV78 @ ( image @ SV271 @ SY765 ) )
| ( member @ ( f22 @ SV78 @ SV271 @ SY765 ) @ SY765 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(986,plain,
! [SV272: $i,SV79: $i] :
( ( ! [SY766: $i] :
( ~ ( member @ SV79 @ ( image @ SV272 @ SY766 ) )
| ( member @ ( first @ ( f22 @ SV79 @ SV272 @ SY766 ) ) @ SV272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(987,plain,
! [SV273: $i,SV80: $i] :
( ( ! [SY767: $i] :
( ~ ( member @ SV80 @ ( image @ SV273 @ SY767 ) )
| ( ( second @ ( f22 @ SV80 @ SV273 @ SY767 ) )
= SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(988,plain,
! [SV274: $i,SV81: $i] :
( ( ~ ( little_set @ SV81 )
| ~ ( function @ SV274 )
| ( little_set @ ( image @ SV81 @ SV274 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(989,plain,
! [SV275: $i,SV82: $i] :
( ( ! [SY768: $i] :
( ~ ( disjoint @ SV82 @ SV275 )
| ~ ( member @ SY768 @ SV82 )
| ~ ( member @ SY768 @ SV275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(990,plain,
! [SV276: $i,SV83: $i] :
( ( ( disjoint @ SV83 @ SV276 )
| ( member @ ( f23 @ SV83 @ SV276 ) @ SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(991,plain,
! [SV277: $i,SV84: $i] :
( ( ( disjoint @ SV84 @ SV277 )
| ( member @ ( f23 @ SV84 @ SV277 ) @ SV277 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(992,plain,
! [SV85: $i] :
( ( ( SV85 = empty_set )
= $true )
| ( ( member @ ( f24 @ SV85 ) @ SV85 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[777]) ).
thf(993,plain,
! [SV86: $i] :
( ( ( SV86 = empty_set )
= $true )
| ( ( disjoint @ ( f24 @ SV86 ) @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[778]) ).
thf(994,plain,
! [SV87: $i] :
( ( ( ~ ( little_set @ SV87 ) )
= $true )
| ( ( ( SV87 = empty_set )
| ( member @ ( f26 @ SV87 ) @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[779]) ).
thf(995,plain,
! [SV88: $i] :
( ( ( ~ ( little_set @ SV88 ) )
= $true )
| ( ( ( SV88 = empty_set )
| ( member @ ( ordered_pair @ SV88 @ ( f26 @ SV88 ) ) @ f25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[780]) ).
thf(996,plain,
! [SV278: $i,SV89: $i] :
( ( ~ ( member @ SV89 @ ( range_of @ SV278 ) )
| ( ordered_pair_predicate @ ( f27 @ SV89 @ SV278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(997,plain,
! [SV279: $i,SV90: $i] :
( ( ~ ( member @ SV90 @ ( range_of @ SV279 ) )
| ( member @ ( f27 @ SV90 @ SV279 ) @ SV279 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[782]) ).
thf(998,plain,
! [SV280: $i,SV91: $i] :
( ( ~ ( member @ SV91 @ ( range_of @ SV280 ) )
| ( SV91
= ( second @ ( f27 @ SV91 @ SV280 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(999,plain,
! [SV92: $i] :
( ( ( ~ ( member @ SV92 @ identity_relation ) )
= $true )
| ( ( ordered_pair_predicate @ SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[784]) ).
thf(1000,plain,
! [SV93: $i] :
( ( ( ~ ( member @ SV93 @ identity_relation ) )
= $true )
| ( ( ( first @ SV93 )
= ( second @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[785]) ).
thf(1001,plain,
! [SV281: $i,SV94: $i] :
( ( ( restrict @ SV94 @ SV281 )
= ( intersection @ SV94 @ ( cross_product @ SV281 @ universal_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(1002,plain,
! [SV95: $i] :
( ( ( ~ ( one_to_one_function @ SV95 ) )
= $true )
| ( ( function @ SV95 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[787]) ).
thf(1003,plain,
! [SV96: $i] :
( ( ( ~ ( one_to_one_function @ SV96 ) )
= $true )
| ( ( function @ ( converse @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[788]) ).
thf(1004,plain,
! [SV97: $i] :
( ( ( one_to_one_function @ SV97 )
= $true )
| ( ( ~ ( function @ SV97 )
| ~ ( function @ ( converse @ SV97 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[789]) ).
thf(1005,plain,
! [SV282: $i,SV98: $i] :
( ( ! [SY769: $i] :
( ~ ( member @ SV98 @ ( apply @ SV282 @ SY769 ) )
| ( ordered_pair_predicate @ ( f28 @ SV98 @ SV282 @ SY769 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(1006,plain,
! [SV283: $i,SV99: $i] :
( ( ! [SY770: $i] :
( ~ ( member @ SV99 @ ( apply @ SV283 @ SY770 ) )
| ( member @ ( f28 @ SV99 @ SV283 @ SY770 ) @ SV283 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(1007,plain,
! [SV284: $i,SV100: $i] :
( ( ! [SY771: $i] :
( ~ ( member @ SV100 @ ( apply @ SV284 @ SY771 ) )
| ( ( first @ ( f28 @ SV100 @ SV284 @ SY771 ) )
= SY771 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(1008,plain,
! [SV285: $i,SV101: $i] :
( ( ! [SY772: $i] :
( ~ ( member @ SV101 @ ( apply @ SV285 @ SY772 ) )
| ( member @ SV101 @ ( second @ ( f28 @ SV101 @ SV285 @ SY772 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(1009,plain,
! [SV286: $i,SV102: $i] :
( ( ! [SY773: $i] :
( ( apply_to_two_arguments @ SV102 @ SV286 @ SY773 )
= ( apply @ SV102 @ ( ordered_pair @ SV286 @ SY773 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(1010,plain,
! [SV287: $i,SV103: $i] :
( ( ! [SY774: $i] :
( ~ ( maps @ SV103 @ SV287 @ SY774 )
| ( function @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(1011,plain,
! [SV288: $i,SV104: $i] :
( ( ! [SY775: $i] :
( ~ ( maps @ SV104 @ SV288 @ SY775 )
| ( ( domain_of @ SV104 )
= SV288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(1012,plain,
! [SV289: $i,SV105: $i] :
( ( ! [SY776: $i] :
( ~ ( maps @ SV105 @ SV289 @ SY776 )
| ( subset @ ( range_of @ SV105 ) @ SY776 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(1013,plain,
! [SV290: $i,SV106: $i] :
( ( ~ ( closed @ SV106 @ SV290 )
| ( little_set @ SV106 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(1014,plain,
! [SV291: $i,SV107: $i] :
( ( ~ ( closed @ SV107 @ SV291 )
| ( little_set @ SV291 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(1015,plain,
! [SV292: $i,SV108: $i] :
( ( ~ ( closed @ SV108 @ SV292 )
| ( maps @ SV292 @ ( cross_product @ SV108 @ SV108 ) @ SV108 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(1016,plain,
! [SV293: $i,SV109: $i] :
( ( ( closed @ SV109 @ SV293 )
| ~ ( little_set @ SV109 )
| ~ ( little_set @ SV293 )
| ~ ( maps @ SV293 @ ( cross_product @ SV109 @ SV109 ) @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(1017,plain,
! [SV294: $i,SV110: $i] :
( ( ! [SY777: $i] :
( ~ ( member @ SV110 @ ( compose @ SV294 @ SY777 ) )
| ( little_set @ ( f29 @ SV110 @ SV294 @ SY777 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(1018,plain,
! [SV295: $i,SV111: $i] :
( ( ! [SY778: $i] :
( ~ ( member @ SV111 @ ( compose @ SV295 @ SY778 ) )
| ( little_set @ ( f30 @ SV111 @ SV295 @ SY778 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(1019,plain,
! [SV296: $i,SV112: $i] :
( ( ! [SY779: $i] :
( ~ ( member @ SV112 @ ( compose @ SV296 @ SY779 ) )
| ( little_set @ ( f31 @ SV112 @ SV296 @ SY779 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(1020,plain,
! [SV297: $i,SV113: $i] :
( ( ! [SY780: $i] :
( ~ ( member @ SV113 @ ( compose @ SV297 @ SY780 ) )
| ( SV113
= ( ordered_pair @ ( f29 @ SV113 @ SV297 @ SY780 ) @ ( f30 @ SV113 @ SV297 @ SY780 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(1021,plain,
! [SV298: $i,SV114: $i] :
( ( ! [SY781: $i] :
( ~ ( member @ SV114 @ ( compose @ SV298 @ SY781 ) )
| ( member @ ( ordered_pair @ ( f29 @ SV114 @ SV298 @ SY781 ) @ ( f31 @ SV114 @ SV298 @ SY781 ) ) @ SV298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(1022,plain,
! [SV299: $i,SV115: $i] :
( ( ! [SY782: $i] :
( ~ ( member @ SV115 @ ( compose @ SV299 @ SY782 ) )
| ( member @ ( ordered_pair @ ( f31 @ SV115 @ SV299 @ SY782 ) @ ( f30 @ SV115 @ SV299 @ SY782 ) ) @ SY782 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(1023,plain,
! [SV300: $i,SV116: $i] :
( ( ! [SY783: $i,SY784: $i,SY785: $i] :
( ~ ( homomorphism @ SV116 @ SV300 @ SY783 @ SY784 @ SY785 )
| ( closed @ SV300 @ SY783 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(1024,plain,
! [SV301: $i,SV117: $i] :
( ( ! [SY786: $i,SY787: $i,SY788: $i] :
( ~ ( homomorphism @ SV117 @ SV301 @ SY786 @ SY787 @ SY788 )
| ( closed @ SY787 @ SY788 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(1025,plain,
! [SV302: $i,SV118: $i] :
( ( ! [SY789: $i,SY790: $i,SY791: $i] :
( ~ ( homomorphism @ SV118 @ SV302 @ SY789 @ SY790 @ SY791 )
| ( maps @ SV118 @ SV302 @ SY790 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(1026,plain,
! [SV303: $i,SV119: $i] :
( ( ! [SY792: $i,SY793: $i,SY794: $i,SY795: $i,SY796: $i] :
( ~ ( homomorphism @ SV119 @ SV303 @ SY792 @ SY793 @ SY794 )
| ~ ( member @ SY795 @ SV303 )
| ~ ( member @ SY796 @ SV303 )
| ( ( apply @ SV119 @ ( apply_to_two_arguments @ SY792 @ SY795 @ SY796 ) )
= ( apply_to_two_arguments @ SY794 @ ( apply @ SV119 @ SY795 ) @ ( apply @ SV119 @ SY796 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(1027,plain,
! [SV304: $i,SV120: $i] :
( ( ! [SY797: $i,SY798: $i,SY799: $i] :
( ( homomorphism @ SV120 @ SV304 @ SY797 @ SY798 @ SY799 )
| ~ ( closed @ SV304 @ SY797 )
| ~ ( closed @ SY798 @ SY799 )
| ~ ( maps @ SV120 @ SV304 @ SY798 )
| ( member @ ( f32 @ SV120 @ SV304 @ SY797 @ SY798 @ SY799 ) @ SV304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(1028,plain,
! [SV305: $i,SV121: $i] :
( ( ! [SY800: $i,SY801: $i,SY802: $i] :
( ( homomorphism @ SV121 @ SV305 @ SY800 @ SY801 @ SY802 )
| ~ ( closed @ SV305 @ SY800 )
| ~ ( closed @ SY801 @ SY802 )
| ~ ( maps @ SV121 @ SV305 @ SY801 )
| ( member @ ( f33 @ SV121 @ SV305 @ SY800 @ SY801 @ SY802 ) @ SV305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(1029,plain,
! [SV306: $i,SV122: $i] :
( ( ! [SY803: $i,SY804: $i,SY805: $i] :
( ~ ( associative @ SV122 @ SV306 )
| ~ ( member @ SY803 @ SV122 )
| ~ ( member @ SY804 @ SV122 )
| ~ ( member @ SY805 @ SV122 )
| ( ( apply_to_two_arguments @ SV306 @ ( apply_to_two_arguments @ SV306 @ SY803 @ SY804 ) @ SY805 )
= ( apply_to_two_arguments @ SV306 @ SY803 @ ( apply_to_two_arguments @ SV306 @ SY804 @ SY805 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(1030,plain,
! [SV307: $i,SV123: $i] :
( ( ( associative @ SV123 @ SV307 )
| ( member @ ( f34 @ SV123 @ SV307 ) @ SV123 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(1031,plain,
! [SV308: $i,SV124: $i] :
( ( ( associative @ SV124 @ SV308 )
| ( member @ ( f35 @ SV124 @ SV308 ) @ SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(1032,plain,
! [SV309: $i,SV125: $i] :
( ( ( associative @ SV125 @ SV309 )
| ( member @ ( f36 @ SV125 @ SV309 ) @ SV125 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(1033,plain,
! [SV310: $i,SV126: $i] :
( ( ! [SY806: $i] :
( ~ ( identity @ SV126 @ SV310 @ SY806 )
| ( member @ SY806 @ SV126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(1034,plain,
! [SV311: $i,SV127: $i] :
( ( ! [SY807: $i,SY808: $i] :
( ~ ( identity @ SV127 @ SV311 @ SY807 )
| ~ ( member @ SY808 @ SV127 )
| ( ( apply_to_two_arguments @ SV311 @ SY807 @ SY808 )
= SY808 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(1035,plain,
! [SV312: $i,SV128: $i] :
( ( ! [SY809: $i,SY810: $i] :
( ~ ( identity @ SV128 @ SV312 @ SY809 )
| ~ ( member @ SY810 @ SV128 )
| ( ( apply_to_two_arguments @ SV312 @ SY810 @ SY809 )
= SY810 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(1036,plain,
! [SV313: $i,SV129: $i] :
( ( ! [SY811: $i] :
( ( identity @ SV129 @ SV313 @ SY811 )
| ~ ( member @ SY811 @ SV129 )
| ( member @ ( f37 @ SV129 @ SV313 @ SY811 ) @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(1037,plain,
! [SV314: $i,SV130: $i] :
( ( ! [SY812: $i,SY813: $i] :
( ~ ( inverse @ SV130 @ SV314 @ SY812 @ SY813 )
| ( maps @ SY813 @ SV130 @ SV130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(1038,plain,
! [SV315: $i,SV131: $i] :
( ( ! [SY814: $i,SY815: $i,SY816: $i] :
( ~ ( inverse @ SV131 @ SV315 @ SY814 @ SY815 )
| ~ ( member @ SY816 @ SV131 )
| ( ( apply_to_two_arguments @ SV315 @ ( apply @ SY815 @ SY816 ) @ SY816 )
= SY814 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(1039,plain,
! [SV316: $i,SV132: $i] :
( ( ! [SY817: $i,SY818: $i,SY819: $i] :
( ~ ( inverse @ SV132 @ SV316 @ SY817 @ SY818 )
| ~ ( member @ SY819 @ SV132 )
| ( ( apply_to_two_arguments @ SV316 @ SY819 @ ( apply @ SY818 @ SY819 ) )
= SY817 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(1040,plain,
! [SV317: $i,SV133: $i] :
( ( ! [SY820: $i,SY821: $i] :
( ( inverse @ SV133 @ SV317 @ SY820 @ SY821 )
| ~ ( maps @ SY821 @ SV133 @ SV133 )
| ( member @ ( f38 @ SV133 @ SV317 @ SY820 @ SY821 ) @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(1041,plain,
! [SV318: $i,SV134: $i] :
( ( ~ ( group @ SV134 @ SV318 )
| ( closed @ SV134 @ SV318 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(1042,plain,
! [SV319: $i,SV135: $i] :
( ( ~ ( group @ SV135 @ SV319 )
| ( associative @ SV135 @ SV319 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(1043,plain,
! [SV320: $i,SV136: $i] :
( ( ~ ( group @ SV136 @ SV320 )
| ( identity @ SV136 @ SV320 @ ( f39 @ SV136 @ SV320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(1044,plain,
! [SV321: $i,SV137: $i] :
( ( ~ ( group @ SV137 @ SV321 )
| ( inverse @ SV137 @ SV321 @ ( f39 @ SV137 @ SV321 ) @ ( f40 @ SV137 @ SV321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(1045,plain,
! [SV322: $i,SV138: $i] :
( ( ! [SY822: $i,SY823: $i] :
( ( group @ SV138 @ SV322 )
| ~ ( closed @ SV138 @ SV322 )
| ~ ( associative @ SV138 @ SV322 )
| ~ ( identity @ SV138 @ SV322 @ SY822 )
| ~ ( inverse @ SV138 @ SV322 @ SY822 @ SY823 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(1046,plain,
! [SV323: $i,SV139: $i] :
( ( ! [SY824: $i,SY825: $i] :
( ~ ( commutes @ SV139 @ SV323 )
| ~ ( member @ SY824 @ SV139 )
| ~ ( member @ SY825 @ SV139 )
| ( ( apply_to_two_arguments @ SV323 @ SY824 @ SY825 )
= ( apply_to_two_arguments @ SV323 @ SY825 @ SY824 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(1047,plain,
! [SV324: $i,SV140: $i] :
( ( ( commutes @ SV140 @ SV324 )
| ( member @ ( f41 @ SV140 @ SV324 ) @ SV140 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(1048,plain,
! [SV325: $i,SV141: $i] :
( ( ( commutes @ SV141 @ SV325 )
| ( member @ ( f42 @ SV141 @ SV325 ) @ SV141 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(1049,plain,
! [SV326: $i,SV142: $i] :
( ( ~ ( member @ SV142 @ natural_numbers )
| ~ ( little_set @ SV326 )
| ~ ( member @ empty_set @ SV326 )
| ( member @ ( f43 @ SV142 @ SV326 ) @ SV326 )
| ( member @ SV142 @ SV326 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(1050,plain,
! [SV327: $i,SV143: $i] :
( ( ~ ( member @ SV143 @ natural_numbers )
| ~ ( little_set @ SV327 )
| ~ ( member @ empty_set @ SV327 )
| ~ ( member @ ( successor @ ( f43 @ SV143 @ SV327 ) ) @ SV327 )
| ( member @ SV143 @ SV327 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(1051,plain,
! [SV144: $i] :
( ( ( member @ SV144 @ natural_numbers )
= $true )
| ( ( ~ ( little_set @ SV144 )
| ( little_set @ ( f44 @ SV144 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[836]) ).
thf(1052,plain,
! [SV145: $i] :
( ( ( member @ SV145 @ natural_numbers )
= $true )
| ( ( ~ ( little_set @ SV145 )
| ( member @ empty_set @ ( f44 @ SV145 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[837]) ).
thf(1053,plain,
! [SV328: $i,SV146: $i] :
( ( ( member @ SV146 @ natural_numbers )
| ~ ( little_set @ SV146 )
| ~ ( member @ SV328 @ ( f44 @ SV146 ) )
| ( member @ ( successor @ SV328 ) @ ( f44 @ SV146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(1054,plain,
! [SV147: $i] :
( ( ( member @ SV147 @ natural_numbers )
= $true )
| ( ( ~ ( member @ SV147 @ ( f44 @ SV147 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[839]) ).
thf(1055,plain,
! [SV329: $i,SV148: $i] :
( ( ~ ( member @ SV148 @ plus )
| ~ ( little_set @ SV329 )
| ( member @ ( f45 @ SV148 @ SV329 ) @ natural_numbers )
| ( member @ ( f46 @ SV148 @ SV329 ) @ natural_numbers )
| ( member @ SV148 @ SV329 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(1056,plain,
! [SV330: $i,SV149: $i] :
( ( ~ ( member @ SV149 @ plus )
| ~ ( little_set @ SV330 )
| ( member @ ( f45 @ SV149 @ SV330 ) @ natural_numbers )
| ( member @ ( f47 @ SV149 @ SV330 ) @ natural_numbers )
| ( member @ SV149 @ SV330 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(1057,plain,
! [SV331: $i,SV150: $i] :
( ( ~ ( member @ SV150 @ plus )
| ~ ( little_set @ SV331 )
| ( member @ ( f45 @ SV150 @ SV331 ) @ natural_numbers )
| ( member @ ( f48 @ SV150 @ SV331 ) @ natural_numbers )
| ( member @ SV150 @ SV331 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(1058,plain,
! [SV332: $i,SV151: $i] :
( ( ~ ( member @ SV151 @ plus )
| ~ ( little_set @ SV332 )
| ( member @ ( f45 @ SV151 @ SV332 ) @ natural_numbers )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( f46 @ SV151 @ SV332 ) @ ( f47 @ SV151 @ SV332 ) ) @ ( f48 @ SV151 @ SV332 ) ) @ SV332 )
| ( member @ SV151 @ SV332 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(1059,plain,
! [SV333: $i,SV152: $i] :
( ( ~ ( member @ SV152 @ plus )
| ~ ( little_set @ SV333 )
| ( member @ ( f45 @ SV152 @ SV333 ) @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f46 @ SV152 @ SV333 ) ) @ ( f47 @ SV152 @ SV333 ) ) @ ( successor @ ( f48 @ SV152 @ SV333 ) ) ) @ SV333 )
| ( member @ SV152 @ SV333 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(1060,plain,
! [SV334: $i,SV153: $i] :
( ( ~ ( member @ SV153 @ plus )
| ~ ( little_set @ SV334 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV153 @ SV334 ) ) @ ( f45 @ SV153 @ SV334 ) ) @ SV334 )
| ( member @ ( f46 @ SV153 @ SV334 ) @ natural_numbers )
| ( member @ SV153 @ SV334 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(1061,plain,
! [SV335: $i,SV154: $i] :
( ( ~ ( member @ SV154 @ plus )
| ~ ( little_set @ SV335 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV154 @ SV335 ) ) @ ( f45 @ SV154 @ SV335 ) ) @ SV335 )
| ( member @ ( f47 @ SV154 @ SV335 ) @ natural_numbers )
| ( member @ SV154 @ SV335 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(1062,plain,
! [SV336: $i,SV155: $i] :
( ( ~ ( member @ SV155 @ plus )
| ~ ( little_set @ SV336 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV155 @ SV336 ) ) @ ( f45 @ SV155 @ SV336 ) ) @ SV336 )
| ( member @ ( f48 @ SV155 @ SV336 ) @ natural_numbers )
| ( member @ SV155 @ SV336 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(1063,plain,
! [SV337: $i,SV156: $i] :
( ( ~ ( member @ SV156 @ plus )
| ~ ( little_set @ SV337 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV156 @ SV337 ) ) @ ( f45 @ SV156 @ SV337 ) ) @ SV337 )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( f46 @ SV156 @ SV337 ) @ ( f47 @ SV156 @ SV337 ) ) @ ( f48 @ SV156 @ SV337 ) ) @ SV337 )
| ( member @ SV156 @ SV337 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[848]) ).
thf(1064,plain,
! [SV338: $i,SV157: $i] :
( ( ~ ( member @ SV157 @ plus )
| ~ ( little_set @ SV338 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV157 @ SV338 ) ) @ ( f45 @ SV157 @ SV338 ) ) @ SV338 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f46 @ SV157 @ SV338 ) ) @ ( f47 @ SV157 @ SV338 ) ) @ ( successor @ ( f48 @ SV157 @ SV338 ) ) ) @ SV338 )
| ( member @ SV157 @ SV338 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(1065,plain,
! [SV158: $i] :
( ( ( member @ SV158 @ plus )
= $true )
| ( ( ~ ( little_set @ SV158 )
| ( little_set @ ( f49 @ SV158 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[850]) ).
thf(1066,plain,
! [SV339: $i,SV159: $i] :
( ( ( member @ SV159 @ plus )
| ~ ( little_set @ SV159 )
| ~ ( member @ SV339 @ natural_numbers )
| ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ SV339 ) @ SV339 ) @ ( f49 @ SV159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[851]) ).
thf(1067,plain,
! [SV340: $i,SV160: $i] :
( ( ! [SY826: $i,SY827: $i] :
( ( member @ SV160 @ plus )
| ~ ( little_set @ SV160 )
| ~ ( member @ SV340 @ natural_numbers )
| ~ ( member @ SY826 @ natural_numbers )
| ~ ( member @ SY827 @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV340 @ SY826 ) @ SY827 ) @ ( f49 @ SV160 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ SV340 ) @ SY826 ) @ ( successor @ SY827 ) ) @ ( f49 @ SV160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(1068,plain,
! [SV161: $i] :
( ( ( member @ SV161 @ plus )
= $true )
| ( ( ~ ( member @ SV161 @ ( f49 @ SV161 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[853]) ).
thf(1069,plain,
! [SV341: $i,SV162: $i] :
( ( ~ ( member @ SV162 @ times )
| ~ ( little_set @ SV341 )
| ( member @ ( f50 @ SV162 @ SV341 ) @ natural_numbers )
| ( member @ ( f51 @ SV162 @ SV341 ) @ natural_numbers )
| ( member @ SV162 @ SV341 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(1070,plain,
! [SV342: $i,SV163: $i] :
( ( ~ ( member @ SV163 @ times )
| ~ ( little_set @ SV342 )
| ( member @ ( f50 @ SV163 @ SV342 ) @ natural_numbers )
| ( member @ ( f52 @ SV163 @ SV342 ) @ natural_numbers )
| ( member @ SV163 @ SV342 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(1071,plain,
! [SV343: $i,SV164: $i] :
( ( ~ ( member @ SV164 @ times )
| ~ ( little_set @ SV343 )
| ( member @ ( f50 @ SV164 @ SV343 ) @ natural_numbers )
| ( member @ ( f53 @ SV164 @ SV343 ) @ natural_numbers )
| ( member @ SV164 @ SV343 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(1072,plain,
! [SV344: $i,SV165: $i] :
( ( ~ ( member @ SV165 @ times )
| ~ ( little_set @ SV344 )
| ( member @ ( f50 @ SV165 @ SV344 ) @ natural_numbers )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( f51 @ SV165 @ SV344 ) @ ( f52 @ SV165 @ SV344 ) ) @ ( f53 @ SV165 @ SV344 ) ) @ SV344 )
| ( member @ SV165 @ SV344 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(1073,plain,
! [SV345: $i,SV166: $i] :
( ( ~ ( member @ SV166 @ times )
| ~ ( little_set @ SV345 )
| ( member @ ( f50 @ SV166 @ SV345 ) @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f51 @ SV166 @ SV345 ) ) @ ( f52 @ SV166 @ SV345 ) ) @ ( apply_to_two_arguments @ plus @ ( f53 @ SV166 @ SV345 ) @ ( f52 @ SV166 @ SV345 ) ) ) @ SV345 )
| ( member @ SV166 @ SV345 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(1074,plain,
! [SV346: $i,SV167: $i] :
( ( ~ ( member @ SV167 @ times )
| ~ ( little_set @ SV346 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV167 @ SV346 ) ) @ empty_set ) @ SV346 )
| ( member @ ( f51 @ SV167 @ SV346 ) @ natural_numbers )
| ( member @ SV167 @ SV346 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(1075,plain,
! [SV347: $i,SV168: $i] :
( ( ~ ( member @ SV168 @ times )
| ~ ( little_set @ SV347 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV168 @ SV347 ) ) @ empty_set ) @ SV347 )
| ( member @ ( f52 @ SV168 @ SV347 ) @ natural_numbers )
| ( member @ SV168 @ SV347 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(1076,plain,
! [SV348: $i,SV169: $i] :
( ( ~ ( member @ SV169 @ times )
| ~ ( little_set @ SV348 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV169 @ SV348 ) ) @ empty_set ) @ SV348 )
| ( member @ ( f53 @ SV169 @ SV348 ) @ natural_numbers )
| ( member @ SV169 @ SV348 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(1077,plain,
! [SV349: $i,SV170: $i] :
( ( ~ ( member @ SV170 @ times )
| ~ ( little_set @ SV349 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV170 @ SV349 ) ) @ empty_set ) @ SV349 )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( f51 @ SV170 @ SV349 ) @ ( f52 @ SV170 @ SV349 ) ) @ ( f53 @ SV170 @ SV349 ) ) @ SV349 )
| ( member @ SV170 @ SV349 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(1078,plain,
! [SV350: $i,SV171: $i] :
( ( ~ ( member @ SV171 @ times )
| ~ ( little_set @ SV350 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV171 @ SV350 ) ) @ empty_set ) @ SV350 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f51 @ SV171 @ SV350 ) ) @ ( f52 @ SV171 @ SV350 ) ) @ ( apply_to_two_arguments @ plus @ ( f53 @ SV171 @ SV350 ) @ ( f52 @ SV171 @ SV350 ) ) ) @ SV350 )
| ( member @ SV171 @ SV350 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[863]) ).
thf(1079,plain,
! [SV172: $i] :
( ( ( member @ SV172 @ times )
= $true )
| ( ( ~ ( little_set @ SV172 )
| ( little_set @ ( f54 @ SV172 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[864]) ).
thf(1080,plain,
! [SV351: $i,SV173: $i] :
( ( ( member @ SV173 @ times )
| ~ ( little_set @ SV173 )
| ~ ( member @ SV351 @ natural_numbers )
| ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ SV351 ) @ empty_set ) @ ( f54 @ SV173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(1081,plain,
! [SV352: $i,SV174: $i] :
( ( ! [SY828: $i,SY829: $i] :
( ( member @ SV174 @ times )
| ~ ( little_set @ SV174 )
| ~ ( member @ SV352 @ natural_numbers )
| ~ ( member @ SY828 @ natural_numbers )
| ~ ( member @ SY829 @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV352 @ SY828 ) @ SY829 ) @ ( f54 @ SV174 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ SV352 ) @ SY828 ) @ ( apply_to_two_arguments @ plus @ SY829 @ SY828 ) ) @ ( f54 @ SV174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(1082,plain,
! [SV175: $i] :
( ( ( member @ SV175 @ times )
= $true )
| ( ( ~ ( member @ SV175 @ ( f54 @ SV175 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[867]) ).
thf(1083,plain,
! [SV176: $i] :
( ( ( ~ ( member @ SV176 @ prime_numbers ) )
= $true )
| ( ( member @ SV176 @ natural_numbers )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[868]) ).
thf(1084,plain,
! [SV177: $i] :
( ( ( member @ SV177 @ prime_numbers )
= $true )
| ( ( ~ ( member @ SV177 @ natural_numbers )
| ( SV177 = empty_set )
| ( SV177
= ( successor @ empty_set ) )
| ( member @ ( f55 @ SV177 ) @ natural_numbers ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[869]) ).
thf(1085,plain,
! [SV178: $i] :
( ( ( member @ SV178 @ prime_numbers )
= $true )
| ( ( ~ ( member @ SV178 @ natural_numbers )
| ( SV178 = empty_set )
| ( SV178
= ( successor @ empty_set ) )
| ( member @ ( f56 @ SV178 ) @ natural_numbers ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[870]) ).
thf(1086,plain,
! [SV179: $i] :
( ( ( member @ SV179 @ prime_numbers )
= $true )
| ( ( ~ ( member @ SV179 @ natural_numbers )
| ( SV179 = empty_set )
| ( SV179
= ( successor @ empty_set ) )
| ( ( apply_to_two_arguments @ times @ ( f55 @ SV179 ) @ ( f56 @ SV179 ) )
= SV179 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[871]) ).
thf(1087,plain,
! [SV180: $i] :
( ( ( member @ SV180 @ prime_numbers )
= $true )
| ( ( ~ ( member @ SV180 @ natural_numbers )
| ( SV180 = empty_set )
| ( SV180
= ( successor @ empty_set ) )
| ~ ( member @ ( f55 @ SV180 ) @ ( non_ordered_pair @ ( successor @ empty_set ) @ SV180 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[872]) ).
thf(1088,plain,
! [SV181: $i] :
( ( ( ~ ( finite @ SV181 ) )
= $true )
| ( ( member @ ( f57 @ SV181 ) @ natural_numbers )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[873]) ).
thf(1089,plain,
! [SV182: $i] :
( ( ( ~ ( finite @ SV182 ) )
= $true )
| ( ( maps @ ( f58 @ SV182 ) @ ( f57 @ SV182 ) @ SV182 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[874]) ).
thf(1090,plain,
! [SV183: $i] :
( ( ( ~ ( finite @ SV183 ) )
= $true )
| ( ( ( range_of @ ( f58 @ SV183 ) )
= SV183 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[875]) ).
thf(1091,plain,
! [SV184: $i] :
( ( ( ~ ( finite @ SV184 ) )
= $true )
| ( ( one_to_one_function @ ( f58 @ SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[876]) ).
thf(1092,plain,
! [SV185: $i] :
( ( ( ~ ( member @ SV185 @ twin_prime_numbers ) )
= $true )
| ( ( member @ SV185 @ prime_numbers )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[877]) ).
thf(1093,plain,
! [SV186: $i] :
( ( ( ~ ( member @ SV186 @ twin_prime_numbers ) )
= $true )
| ( ( member @ ( successor @ ( successor @ SV186 ) ) @ prime_numbers )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[878]) ).
thf(1094,plain,
! [SV187: $i] :
( ( ( member @ SV187 @ twin_prime_numbers )
= $true )
| ( ( ~ ( member @ SV187 @ prime_numbers )
| ~ ( member @ ( successor @ ( successor @ SV187 ) ) @ prime_numbers ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[879]) ).
thf(1095,plain,
! [SV188: $i] :
( ( ( ~ ( member @ SV188 @ even_numbers ) )
= $true )
| ( ( member @ SV188 @ natural_numbers )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[880]) ).
thf(1096,plain,
! [SV189: $i] :
( ( ( ~ ( member @ SV189 @ even_numbers ) )
= $true )
| ( ( member @ ( f59 @ SV189 ) @ natural_numbers )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[881]) ).
thf(1097,plain,
! [SV190: $i] :
( ( ( ~ ( member @ SV190 @ even_numbers ) )
= $true )
| ( ( ( apply_to_two_arguments @ plus @ ( f59 @ SV190 ) @ ( f59 @ SV190 ) )
= SV190 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[882]) ).
thf(1098,plain,
! [SV353: $i,SV191: $i] :
( ( ! [SY830: $i,SY831: $i] :
( ( member @ SV191 @ ( second @ SV353 ) )
| ~ ( little_set @ SY830 )
| ~ ( little_set @ SY831 )
| ( SV353
!= ( ordered_pair @ SY830 @ SY831 ) )
| ~ ( member @ SV191 @ SY831 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[884]) ).
thf(1099,plain,
! [SV354: $i,SV192: $i] :
( ( ! [SY832: $i,SY833: $i] :
( ( inverse @ SV192 @ SV354 @ SY832 @ SY833 )
| ~ ( maps @ SY833 @ SV192 @ SV192 )
| ( ( apply_to_two_arguments @ SV354 @ ( apply @ SY833 @ ( f38 @ SV192 @ SV354 @ SY832 @ SY833 ) ) @ ( f38 @ SV192 @ SV354 @ SY832 @ SY833 ) )
!= SY832 )
| ( ( apply_to_two_arguments @ SV354 @ ( f38 @ SV192 @ SV354 @ SY832 @ SY833 ) @ ( apply @ SY833 @ ( f38 @ SV192 @ SV354 @ SY832 @ SY833 ) ) )
!= SY832 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[885]) ).
thf(1100,plain,
! [SV355: $i,SV193: $i] :
( ( ! [SY834: $i] :
( ~ ( member @ SV193 @ prime_numbers )
| ~ ( member @ SV355 @ natural_numbers )
| ~ ( member @ SY834 @ natural_numbers )
| ( ( apply_to_two_arguments @ times @ SV355 @ SY834 )
!= SV193 )
| ( member @ SV355 @ ( non_ordered_pair @ ( successor @ empty_set ) @ SV193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[886]) ).
thf(1101,plain,
! [SV194: $i] :
( ( ( ~ ( member @ SV194 @ prime_numbers ) )
= $true )
| ( ( SV194 != empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[887]) ).
thf(1102,plain,
! [SV356: $i,SV195: $i] :
( ( ! [SY835: $i,SY836: $i,SY837: $i] :
( ( member @ SV195 @ ( flip_range_of @ SV356 ) )
| ~ ( little_set @ SV195 )
| ~ ( little_set @ SY835 )
| ~ ( little_set @ SY836 )
| ~ ( little_set @ SY837 )
| ( SV195
!= ( ordered_pair @ SY835 @ ( ordered_pair @ SY836 @ SY837 ) ) )
| ~ ( member @ ( ordered_pair @ SY835 @ ( ordered_pair @ SY837 @ SY836 ) ) @ SV356 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[888]) ).
thf(1103,plain,
! [SV357: $i,SV196: $i] :
( ( ! [SY838: $i] :
( ( member @ SV196 @ ( non_ordered_pair @ SV357 @ SY838 ) )
| ~ ( little_set @ SV196 )
| ( SV196 != SY838 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(1104,plain,
! [SV358: $i,SV197: $i] :
( ( ! [SY839: $i,SY840: $i] :
( ( member @ SV197 @ ( first @ SV358 ) )
| ~ ( little_set @ SY839 )
| ~ ( little_set @ SY840 )
| ( SV358
!= ( ordered_pair @ SY839 @ SY840 ) )
| ~ ( member @ SV197 @ SY839 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(1105,plain,
! [SV359: $i,SV198: $i] :
( ( ! [SY841: $i,SY842: $i] :
( ( member @ SV198 @ ( image @ SV359 @ SY841 ) )
| ~ ( little_set @ SV198 )
| ~ ( ordered_pair_predicate @ SY842 )
| ~ ( member @ SY842 @ SY841 )
| ~ ( member @ ( first @ SY842 ) @ SV359 )
| ( ( second @ SY842 )
!= SV198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(1106,plain,
! [SV360: $i,SV199: $i] :
( ( ! [SY843: $i,SY844: $i,SY845: $i] :
( ( member @ SV199 @ ( rotate_right @ SV360 ) )
| ~ ( little_set @ SV199 )
| ~ ( little_set @ SY843 )
| ~ ( little_set @ SY844 )
| ~ ( little_set @ SY845 )
| ( SV199
!= ( ordered_pair @ SY843 @ ( ordered_pair @ SY844 @ SY845 ) ) )
| ~ ( member @ ( ordered_pair @ SY844 @ ( ordered_pair @ SY845 @ SY843 ) ) @ SV360 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[892]) ).
thf(1107,plain,
! [SV200: $i] :
( ( ( single_valued_set @ SV200 )
= $true )
| ( ( ( f20 @ SV200 )
!= ( f21 @ SV200 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[893]) ).
thf(1108,plain,
! [SV361: $i,SV201: $i] :
( ( ! [SY846: $i,SY847: $i,SY848: $i,SY849: $i] :
( ( member @ SV201 @ ( compose @ SV361 @ SY846 ) )
| ~ ( little_set @ SV201 )
| ~ ( little_set @ SY847 )
| ~ ( little_set @ SY848 )
| ~ ( little_set @ SY849 )
| ( SV201
!= ( ordered_pair @ SY847 @ SY848 ) )
| ~ ( member @ ( ordered_pair @ SY847 @ SY849 ) @ SV361 )
| ~ ( member @ ( ordered_pair @ SY849 @ SY848 ) @ SY846 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(1109,plain,
! [SV362: $i,SV202: $i] :
( ( ! [SY850: $i] :
( ( ordered_pair_predicate @ SV202 )
| ~ ( little_set @ SV362 )
| ~ ( little_set @ SY850 )
| ( SV202
!= ( ordered_pair @ SV362 @ SY850 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[895]) ).
thf(1110,plain,
! [SV363: $i,SV203: $i] :
( ( ! [SY851: $i] :
( ( member @ SV203 @ ( non_ordered_pair @ SV363 @ SY851 ) )
| ~ ( little_set @ SV203 )
| ( SV203 != SV363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(1111,plain,
! [SV364: $i,SV204: $i] :
( ( ( member @ SV204 @ even_numbers )
| ~ ( member @ SV204 @ natural_numbers )
| ~ ( member @ SV364 @ natural_numbers )
| ( ( apply_to_two_arguments @ plus @ SV364 @ SV364 )
!= SV204 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(1112,plain,
! [SV365: $i,SV205: $i] :
( ( ~ ( proper_subset @ SV205 @ SV365 )
| ( SV205 != SV365 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[898]) ).
thf(1113,plain,
! [SV366: $i,SV206: $i] :
( ( ! [SY852: $i,SY853: $i,SY854: $i] :
( ( homomorphism @ SV206 @ SV366 @ SY852 @ SY853 @ SY854 )
| ~ ( closed @ SV366 @ SY852 )
| ~ ( closed @ SY853 @ SY854 )
| ~ ( maps @ SV206 @ SV366 @ SY853 )
| ( ( apply @ SV206 @ ( apply_to_two_arguments @ SY852 @ ( f32 @ SV206 @ SV366 @ SY852 @ SY853 @ SY854 ) @ ( f33 @ SV206 @ SV366 @ SY852 @ SY853 @ SY854 ) ) )
!= ( apply_to_two_arguments @ SY854 @ ( apply @ SV206 @ ( f32 @ SV206 @ SV366 @ SY852 @ SY853 @ SY854 ) ) @ ( apply @ SV206 @ ( f33 @ SV206 @ SV366 @ SY852 @ SY853 @ SY854 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(1114,plain,
! [SV367: $i,SV207: $i] :
( ( ! [SY855: $i] :
( ( finite @ SV207 )
| ~ ( member @ SV367 @ natural_numbers )
| ~ ( maps @ SY855 @ SV367 @ SV207 )
| ( ( range_of @ SY855 )
!= SV207 )
| ~ ( one_to_one_function @ SY855 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(1115,plain,
! [SV368: $i,SV208: $i] :
( ( ! [SY856: $i] :
( ( maps @ SV208 @ SV368 @ SY856 )
| ~ ( function @ SV208 )
| ( ( domain_of @ SV208 )
!= SV368 )
| ~ ( subset @ ( range_of @ SV208 ) @ SY856 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(1116,plain,
! [SV209: $i] :
( ( ( ~ ( member @ SV209 @ prime_numbers ) )
= $true )
| ( ( SV209
!= ( successor @ empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[902]) ).
thf(1117,plain,
! [SV369: $i,SV210: $i] :
( ( ( commutes @ SV210 @ SV369 )
| ( ( apply_to_two_arguments @ SV369 @ ( f41 @ SV210 @ SV369 ) @ ( f42 @ SV210 @ SV369 ) )
!= ( apply_to_two_arguments @ SV369 @ ( f42 @ SV210 @ SV369 ) @ ( f41 @ SV210 @ SV369 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(1118,plain,
! [SV211: $i] :
( ( ( member @ SV211 @ identity_relation )
= $true )
| ( ( ~ ( little_set @ SV211 )
| ~ ( ordered_pair_predicate @ SV211 )
| ( ( first @ SV211 )
!= ( second @ SV211 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[904]) ).
thf(1119,plain,
! [SV370: $i,SV212: $i] :
( ( ! [SY857: $i] :
( ( member @ SV212 @ ( range_of @ SV370 ) )
| ~ ( little_set @ SV212 )
| ~ ( ordered_pair_predicate @ SY857 )
| ~ ( member @ SY857 @ SV370 )
| ( SV212
!= ( second @ SY857 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(1120,plain,
! [SV371: $i,SV213: $i] :
( ( ( associative @ SV213 @ SV371 )
| ( ( apply_to_two_arguments @ SV371 @ ( apply_to_two_arguments @ SV371 @ ( f34 @ SV213 @ SV371 ) @ ( f35 @ SV213 @ SV371 ) ) @ ( f36 @ SV213 @ SV371 ) )
!= ( apply_to_two_arguments @ SV371 @ ( f34 @ SV213 @ SV371 ) @ ( apply_to_two_arguments @ SV371 @ ( f35 @ SV213 @ SV371 ) @ ( f36 @ SV213 @ SV371 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[906]) ).
thf(1121,plain,
! [SV372: $i,SV214: $i] :
( ( ! [SY858: $i] :
( ( identity @ SV214 @ SV372 @ SY858 )
| ~ ( member @ SY858 @ SV214 )
| ( ( apply_to_two_arguments @ SV372 @ SY858 @ ( f37 @ SV214 @ SV372 @ SY858 ) )
!= ( f37 @ SV214 @ SV372 @ SY858 ) )
| ( ( apply_to_two_arguments @ SV372 @ ( f37 @ SV214 @ SV372 @ SY858 ) @ SY858 )
!= ( f37 @ SV214 @ SV372 @ SY858 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(1122,plain,
! [SV373: $i,SV215: $i] :
( ( ! [SY859: $i] :
( ( member @ SV215 @ ( domain_of @ SV373 ) )
| ~ ( little_set @ SV215 )
| ~ ( ordered_pair_predicate @ SY859 )
| ~ ( member @ SY859 @ SV373 )
| ( SV215
!= ( first @ SY859 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[908]) ).
thf(1123,plain,
! [SV374: $i,SV216: $i] :
( ( ! [SY860: $i,SY861: $i] :
( ( member @ SV216 @ ( apply @ SV374 @ SY860 ) )
| ~ ( ordered_pair_predicate @ SY861 )
| ~ ( member @ SY861 @ SV374 )
| ( ( first @ SY861 )
!= SY860 )
| ~ ( member @ SV216 @ ( second @ SY861 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[909]) ).
thf(1124,plain,
! [SV217: $i,SV1: $i] :
( ( ( ~ ( member @ SV1 @ SV217 ) )
= $true )
| ( ( little_set @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[910]) ).
thf(1125,plain,
! [SV218: $i,SV2: $i] :
( ( ( little_set @ ( f1 @ SV2 @ SV218 ) )
= $true )
| ( ( SV2 = SV218 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[911]) ).
thf(1126,plain,
! [SV219: $i,SV3: $i] :
( ( ( member @ ( f1 @ SV3 @ SV219 ) @ SV3 )
= $true )
| ( ( ( member @ ( f1 @ SV3 @ SV219 ) @ SV219 )
| ( SV3 = SV219 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[912]) ).
thf(1127,plain,
! [SV220: $i,SV4: $i] :
( ( ( ~ ( member @ ( f1 @ SV4 @ SV220 ) @ SV4 ) )
= $true )
| ( ( ~ ( member @ ( f1 @ SV4 @ SV220 ) @ SV220 )
| ( SV4 = SV220 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[913]) ).
thf(1128,plain,
! [SV375: $i,SV221: $i,SV5: $i] :
( ( ~ ( member @ SV5 @ ( non_ordered_pair @ SV221 @ SV375 ) )
| ( SV5 = SV221 )
| ( SV5 = SV375 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(1129,plain,
! [SV9: $i] :
( ( ( ordered_pair_predicate @ SV9 )
= $false )
| ( ( little_set @ ( f2 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[917]) ).
thf(1130,plain,
! [SV10: $i] :
( ( ( ordered_pair_predicate @ SV10 )
= $false )
| ( ( little_set @ ( f3 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[918]) ).
thf(1131,plain,
! [SV11: $i] :
( ( ( ordered_pair_predicate @ SV11 )
= $false )
| ( ( SV11
= ( ordered_pair @ ( f2 @ SV11 ) @ ( f3 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[919]) ).
thf(1132,plain,
! [SV224: $i,SV12: $i] :
( ( ( ~ ( member @ SV12 @ ( first @ SV224 ) ) )
= $true )
| ( ( little_set @ ( f4 @ SV12 @ SV224 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[920]) ).
thf(1133,plain,
! [SV225: $i,SV13: $i] :
( ( ( ~ ( member @ SV13 @ ( first @ SV225 ) ) )
= $true )
| ( ( little_set @ ( f5 @ SV13 @ SV225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[921]) ).
thf(1134,plain,
! [SV226: $i,SV14: $i] :
( ( ( ~ ( member @ SV14 @ ( first @ SV226 ) ) )
= $true )
| ( ( SV226
= ( ordered_pair @ ( f4 @ SV14 @ SV226 ) @ ( f5 @ SV14 @ SV226 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[922]) ).
thf(1135,plain,
! [SV227: $i,SV15: $i] :
( ( ( ~ ( member @ SV15 @ ( first @ SV227 ) ) )
= $true )
| ( ( member @ SV15 @ ( f4 @ SV15 @ SV227 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[923]) ).
thf(1136,plain,
! [SV228: $i,SV16: $i] :
( ( ( ~ ( member @ SV16 @ ( second @ SV228 ) ) )
= $true )
| ( ( little_set @ ( f6 @ SV16 @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[924]) ).
thf(1137,plain,
! [SV229: $i,SV17: $i] :
( ( ( ~ ( member @ SV17 @ ( second @ SV229 ) ) )
= $true )
| ( ( little_set @ ( f7 @ SV17 @ SV229 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[925]) ).
thf(1138,plain,
! [SV230: $i,SV18: $i] :
( ( ( ~ ( member @ SV18 @ ( second @ SV230 ) ) )
= $true )
| ( ( SV230
= ( ordered_pair @ ( f6 @ SV18 @ SV230 ) @ ( f7 @ SV18 @ SV230 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[926]) ).
thf(1139,plain,
! [SV231: $i,SV19: $i] :
( ( ( ~ ( member @ SV19 @ ( second @ SV231 ) ) )
= $true )
| ( ( member @ SV19 @ ( f7 @ SV19 @ SV231 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[927]) ).
thf(1140,plain,
! [SV20: $i] :
( ( ( member @ SV20 @ estin )
= $false )
| ( ( ordered_pair_predicate @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[928]) ).
thf(1141,plain,
! [SV21: $i] :
( ( ( member @ SV21 @ estin )
= $false )
| ( ( member @ ( first @ SV21 ) @ ( second @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[929]) ).
thf(1142,plain,
! [SV22: $i] :
( ( ( ~ ( little_set @ SV22 ) )
= $true )
| ( ( ~ ( ordered_pair_predicate @ SV22 )
| ~ ( member @ ( first @ SV22 ) @ ( second @ SV22 ) ) )
= $true )
| ( ( member @ SV22 @ estin )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[930]) ).
thf(1143,plain,
! [SV376: $i,SV232: $i,SV23: $i] :
( ( ~ ( member @ SV23 @ ( intersection @ SV232 @ SV376 ) )
| ( member @ SV23 @ SV232 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(1144,plain,
! [SV377: $i,SV233: $i,SV24: $i] :
( ( ~ ( member @ SV24 @ ( intersection @ SV233 @ SV377 ) )
| ( member @ SV24 @ SV377 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(1145,plain,
! [SV378: $i,SV234: $i,SV25: $i] :
( ( ( member @ SV25 @ ( intersection @ SV234 @ SV378 ) )
| ~ ( member @ SV25 @ SV234 )
| ~ ( member @ SV25 @ SV378 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(1146,plain,
! [SV235: $i,SV26: $i] :
( ( ( ~ ( member @ SV26 @ ( complement @ SV235 ) ) )
= $true )
| ( ( ~ ( member @ SV26 @ SV235 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[934]) ).
thf(1147,plain,
! [SV236: $i,SV27: $i] :
( ( ( member @ SV27 @ ( complement @ SV236 ) )
= $true )
| ( ( ~ ( little_set @ SV27 )
| ( member @ SV27 @ SV236 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[935]) ).
thf(1148,plain,
! [SV238: $i,SV29: $i] :
( ( ( ~ ( member @ SV29 @ ( domain_of @ SV238 ) ) )
= $true )
| ( ( ordered_pair_predicate @ ( f8 @ SV29 @ SV238 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[937]) ).
thf(1149,plain,
! [SV239: $i,SV30: $i] :
( ( ( ~ ( member @ SV30 @ ( domain_of @ SV239 ) ) )
= $true )
| ( ( member @ ( f8 @ SV30 @ SV239 ) @ SV239 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[938]) ).
thf(1150,plain,
! [SV240: $i,SV31: $i] :
( ( ( ~ ( member @ SV31 @ ( domain_of @ SV240 ) ) )
= $true )
| ( ( SV31
= ( first @ ( f8 @ SV31 @ SV240 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[939]) ).
thf(1151,plain,
! [SV379: $i,SV241: $i,SV32: $i] :
( ( ~ ( member @ SV32 @ ( cross_product @ SV241 @ SV379 ) )
| ( ordered_pair_predicate @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[940]) ).
thf(1152,plain,
! [SV380: $i,SV242: $i,SV33: $i] :
( ( ~ ( member @ SV33 @ ( cross_product @ SV242 @ SV380 ) )
| ( member @ ( first @ SV33 ) @ SV242 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[941]) ).
thf(1153,plain,
! [SV381: $i,SV243: $i,SV34: $i] :
( ( ~ ( member @ SV34 @ ( cross_product @ SV243 @ SV381 ) )
| ( member @ ( second @ SV34 ) @ SV381 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[942]) ).
thf(1154,plain,
! [SV382: $i,SV244: $i,SV35: $i] :
( ( ( member @ SV35 @ ( cross_product @ SV244 @ SV382 ) )
| ~ ( little_set @ SV35 )
| ~ ( ordered_pair_predicate @ SV35 )
| ~ ( member @ ( first @ SV35 ) @ SV244 )
| ~ ( member @ ( second @ SV35 ) @ SV382 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(1155,plain,
! [SV245: $i,SV36: $i] :
( ( ( ~ ( member @ SV36 @ ( converse @ SV245 ) ) )
= $true )
| ( ( ordered_pair_predicate @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[944]) ).
thf(1156,plain,
! [SV246: $i,SV37: $i] :
( ( ( ~ ( member @ SV37 @ ( converse @ SV246 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ ( second @ SV37 ) @ ( first @ SV37 ) ) @ SV246 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[945]) ).
thf(1157,plain,
! [SV247: $i,SV38: $i] :
( ( ( member @ SV38 @ ( converse @ SV247 ) )
= $true )
| ( ( ~ ( little_set @ SV38 )
| ~ ( ordered_pair_predicate @ SV38 )
| ~ ( member @ ( ordered_pair @ ( second @ SV38 ) @ ( first @ SV38 ) ) @ SV247 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[946]) ).
thf(1158,plain,
! [SV248: $i,SV39: $i] :
( ( ( ~ ( member @ SV39 @ ( rotate_right @ SV248 ) ) )
= $true )
| ( ( little_set @ ( f9 @ SV39 @ SV248 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[947]) ).
thf(1159,plain,
! [SV249: $i,SV40: $i] :
( ( ( ~ ( member @ SV40 @ ( rotate_right @ SV249 ) ) )
= $true )
| ( ( little_set @ ( f10 @ SV40 @ SV249 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[948]) ).
thf(1160,plain,
! [SV250: $i,SV41: $i] :
( ( ( ~ ( member @ SV41 @ ( rotate_right @ SV250 ) ) )
= $true )
| ( ( little_set @ ( f11 @ SV41 @ SV250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[949]) ).
thf(1161,plain,
! [SV251: $i,SV42: $i] :
( ( ( ~ ( member @ SV42 @ ( rotate_right @ SV251 ) ) )
= $true )
| ( ( SV42
= ( ordered_pair @ ( f9 @ SV42 @ SV251 ) @ ( ordered_pair @ ( f10 @ SV42 @ SV251 ) @ ( f11 @ SV42 @ SV251 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[950]) ).
thf(1162,plain,
! [SV252: $i,SV43: $i] :
( ( ( ~ ( member @ SV43 @ ( rotate_right @ SV252 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ ( f10 @ SV43 @ SV252 ) @ ( ordered_pair @ ( f11 @ SV43 @ SV252 ) @ ( f9 @ SV43 @ SV252 ) ) ) @ SV252 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[951]) ).
thf(1163,plain,
! [SV253: $i,SV44: $i] :
( ( ( ~ ( member @ SV44 @ ( flip_range_of @ SV253 ) ) )
= $true )
| ( ( little_set @ ( f12 @ SV44 @ SV253 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[952]) ).
thf(1164,plain,
! [SV254: $i,SV45: $i] :
( ( ( ~ ( member @ SV45 @ ( flip_range_of @ SV254 ) ) )
= $true )
| ( ( little_set @ ( f13 @ SV45 @ SV254 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[953]) ).
thf(1165,plain,
! [SV255: $i,SV46: $i] :
( ( ( ~ ( member @ SV46 @ ( flip_range_of @ SV255 ) ) )
= $true )
| ( ( little_set @ ( f14 @ SV46 @ SV255 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[954]) ).
thf(1166,plain,
! [SV256: $i,SV47: $i] :
( ( ( ~ ( member @ SV47 @ ( flip_range_of @ SV256 ) ) )
= $true )
| ( ( SV47
= ( ordered_pair @ ( f12 @ SV47 @ SV256 ) @ ( ordered_pair @ ( f13 @ SV47 @ SV256 ) @ ( f14 @ SV47 @ SV256 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[955]) ).
thf(1167,plain,
! [SV257: $i,SV48: $i] :
( ( ( ~ ( member @ SV48 @ ( flip_range_of @ SV257 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ ( f12 @ SV48 @ SV257 ) @ ( ordered_pair @ ( f14 @ SV48 @ SV257 ) @ ( f13 @ SV48 @ SV257 ) ) ) @ SV257 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[956]) ).
thf(1168,plain,
! [SV51: $i] :
( ( ( little_set @ SV51 )
= $false )
| ( ( member @ SV51 @ universal_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[958]) ).
thf(1169,plain,
! [SV52: $i] :
( ( ( member @ SV52 @ infinity )
= $false )
| ( ( member @ ( successor @ SV52 ) @ infinity )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[959]) ).
thf(1170,plain,
! [SV258: $i,SV53: $i] :
( ( ( ~ ( member @ SV53 @ ( sigma @ SV258 ) ) )
= $true )
| ( ( member @ ( f16 @ SV53 @ SV258 ) @ SV258 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[960]) ).
thf(1171,plain,
! [SV259: $i,SV54: $i] :
( ( ( ~ ( member @ SV54 @ ( sigma @ SV259 ) ) )
= $true )
| ( ( member @ SV54 @ ( f16 @ SV54 @ SV259 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[961]) ).
thf(1172,plain,
! [SV383: $i,SV260: $i,SV55: $i] :
( ( ( member @ SV55 @ ( sigma @ SV260 ) )
| ~ ( member @ SV383 @ SV260 )
| ~ ( member @ SV55 @ SV383 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1173,plain,
! [SV56: $i] :
( ( ( little_set @ SV56 )
= $false )
| ( ( little_set @ ( sigma @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[963]) ).
thf(1174,plain,
! [SV384: $i,SV261: $i,SV57: $i] :
( ( ~ ( subset @ SV57 @ SV261 )
| ~ ( member @ SV384 @ SV57 )
| ( member @ SV384 @ SV261 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[964]) ).
thf(1175,plain,
! [SV262: $i,SV58: $i] :
( ( ( subset @ SV58 @ SV262 )
= $true )
| ( ( member @ ( f17 @ SV58 @ SV262 ) @ SV58 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[965]) ).
thf(1176,plain,
! [SV263: $i,SV59: $i] :
( ( ( subset @ SV59 @ SV263 )
= $true )
| ( ( ~ ( member @ ( f17 @ SV59 @ SV263 ) @ SV263 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[966]) ).
thf(1177,plain,
! [SV264: $i,SV60: $i] :
( ( ( ~ ( proper_subset @ SV60 @ SV264 ) )
= $true )
| ( ( subset @ SV60 @ SV264 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[967]) ).
thf(1178,plain,
! [SV265: $i,SV61: $i] :
( ( ( proper_subset @ SV61 @ SV265 )
= $true )
| ( ( ~ ( subset @ SV61 @ SV265 )
| ( SV61 = SV265 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[968]) ).
thf(1179,plain,
! [SV266: $i,SV62: $i] :
( ( ( ~ ( member @ SV62 @ ( powerset @ SV266 ) ) )
= $true )
| ( ( subset @ SV62 @ SV266 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[969]) ).
thf(1180,plain,
! [SV267: $i,SV63: $i] :
( ( ( member @ SV63 @ ( powerset @ SV267 ) )
= $true )
| ( ( ~ ( little_set @ SV63 )
| ~ ( subset @ SV63 @ SV267 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[970]) ).
thf(1181,plain,
! [SV64: $i] :
( ( ( little_set @ SV64 )
= $false )
| ( ( little_set @ ( powerset @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[971]) ).
thf(1182,plain,
! [SV268: $i,SV65: $i] :
( ( ( ~ ( relation @ SV65 ) )
= $true )
| ( ( ~ ( member @ SV268 @ SV65 )
| ( ordered_pair_predicate @ SV268 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[972]) ).
thf(1183,plain,
! [SV67: $i] :
( ( ( ordered_pair_predicate @ ( f18 @ SV67 ) )
= $false )
| ( ( relation @ SV67 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[974]) ).
thf(1184,plain,
! [SV385: $i,SV269: $i,SV68: $i] :
( ( ! [SY862: $i] :
( ~ ( single_valued_set @ SV68 )
| ~ ( little_set @ SV269 )
| ~ ( little_set @ SV385 )
| ~ ( little_set @ SY862 )
| ~ ( member @ ( ordered_pair @ SV269 @ SV385 ) @ SV68 )
| ~ ( member @ ( ordered_pair @ SV269 @ SY862 ) @ SV68 )
| ( SV385 = SY862 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1185,plain,
! [SV74: $i] :
( ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[981]) ).
thf(1186,plain,
! [SV75: $i] :
( ( ( function @ SV75 )
= $false )
| ( ( single_valued_set @ SV75 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(1187,plain,
! [SV76: $i] :
( ( ( ~ ( relation @ SV76 ) )
= $true )
| ( ( ~ ( single_valued_set @ SV76 ) )
= $true )
| ( ( function @ SV76 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[983]) ).
thf(1188,plain,
! [SV386: $i,SV270: $i,SV77: $i] :
( ( ~ ( member @ SV77 @ ( image @ SV270 @ SV386 ) )
| ( ordered_pair_predicate @ ( f22 @ SV77 @ SV270 @ SV386 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(1189,plain,
! [SV387: $i,SV271: $i,SV78: $i] :
( ( ~ ( member @ SV78 @ ( image @ SV271 @ SV387 ) )
| ( member @ ( f22 @ SV78 @ SV271 @ SV387 ) @ SV387 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1190,plain,
! [SV388: $i,SV272: $i,SV79: $i] :
( ( ~ ( member @ SV79 @ ( image @ SV272 @ SV388 ) )
| ( member @ ( first @ ( f22 @ SV79 @ SV272 @ SV388 ) ) @ SV272 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1191,plain,
! [SV389: $i,SV273: $i,SV80: $i] :
( ( ~ ( member @ SV80 @ ( image @ SV273 @ SV389 ) )
| ( ( second @ ( f22 @ SV80 @ SV273 @ SV389 ) )
= SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(1192,plain,
! [SV274: $i,SV81: $i] :
( ( ( ~ ( little_set @ SV81 ) )
= $true )
| ( ( ~ ( function @ SV274 )
| ( little_set @ ( image @ SV81 @ SV274 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[988]) ).
thf(1193,plain,
! [SV390: $i,SV275: $i,SV82: $i] :
( ( ~ ( disjoint @ SV82 @ SV275 )
| ~ ( member @ SV390 @ SV82 )
| ~ ( member @ SV390 @ SV275 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[989]) ).
thf(1194,plain,
! [SV276: $i,SV83: $i] :
( ( ( disjoint @ SV83 @ SV276 )
= $true )
| ( ( member @ ( f23 @ SV83 @ SV276 ) @ SV83 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[990]) ).
thf(1195,plain,
! [SV277: $i,SV84: $i] :
( ( ( disjoint @ SV84 @ SV277 )
= $true )
| ( ( member @ ( f23 @ SV84 @ SV277 ) @ SV277 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[991]) ).
thf(1196,plain,
! [SV87: $i] :
( ( ( little_set @ SV87 )
= $false )
| ( ( ( SV87 = empty_set )
| ( member @ ( f26 @ SV87 ) @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[994]) ).
thf(1197,plain,
! [SV88: $i] :
( ( ( little_set @ SV88 )
= $false )
| ( ( ( SV88 = empty_set )
| ( member @ ( ordered_pair @ SV88 @ ( f26 @ SV88 ) ) @ f25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[995]) ).
thf(1198,plain,
! [SV278: $i,SV89: $i] :
( ( ( ~ ( member @ SV89 @ ( range_of @ SV278 ) ) )
= $true )
| ( ( ordered_pair_predicate @ ( f27 @ SV89 @ SV278 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[996]) ).
thf(1199,plain,
! [SV279: $i,SV90: $i] :
( ( ( ~ ( member @ SV90 @ ( range_of @ SV279 ) ) )
= $true )
| ( ( member @ ( f27 @ SV90 @ SV279 ) @ SV279 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[997]) ).
thf(1200,plain,
! [SV280: $i,SV91: $i] :
( ( ( ~ ( member @ SV91 @ ( range_of @ SV280 ) ) )
= $true )
| ( ( SV91
= ( second @ ( f27 @ SV91 @ SV280 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[998]) ).
thf(1201,plain,
! [SV92: $i] :
( ( ( member @ SV92 @ identity_relation )
= $false )
| ( ( ordered_pair_predicate @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[999]) ).
thf(1202,plain,
! [SV93: $i] :
( ( ( member @ SV93 @ identity_relation )
= $false )
| ( ( ( first @ SV93 )
= ( second @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1000]) ).
thf(1203,plain,
! [SV95: $i] :
( ( ( one_to_one_function @ SV95 )
= $false )
| ( ( function @ SV95 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1002]) ).
thf(1204,plain,
! [SV96: $i] :
( ( ( one_to_one_function @ SV96 )
= $false )
| ( ( function @ ( converse @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1003]) ).
thf(1205,plain,
! [SV97: $i] :
( ( ( ~ ( function @ SV97 ) )
= $true )
| ( ( ~ ( function @ ( converse @ SV97 ) ) )
= $true )
| ( ( one_to_one_function @ SV97 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1004]) ).
thf(1206,plain,
! [SV391: $i,SV282: $i,SV98: $i] :
( ( ~ ( member @ SV98 @ ( apply @ SV282 @ SV391 ) )
| ( ordered_pair_predicate @ ( f28 @ SV98 @ SV282 @ SV391 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1207,plain,
! [SV392: $i,SV283: $i,SV99: $i] :
( ( ~ ( member @ SV99 @ ( apply @ SV283 @ SV392 ) )
| ( member @ ( f28 @ SV99 @ SV283 @ SV392 ) @ SV283 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1208,plain,
! [SV393: $i,SV284: $i,SV100: $i] :
( ( ~ ( member @ SV100 @ ( apply @ SV284 @ SV393 ) )
| ( ( first @ ( f28 @ SV100 @ SV284 @ SV393 ) )
= SV393 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1007]) ).
thf(1209,plain,
! [SV394: $i,SV285: $i,SV101: $i] :
( ( ~ ( member @ SV101 @ ( apply @ SV285 @ SV394 ) )
| ( member @ SV101 @ ( second @ ( f28 @ SV101 @ SV285 @ SV394 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1210,plain,
! [SV395: $i,SV286: $i,SV102: $i] :
( ( ( apply_to_two_arguments @ SV102 @ SV286 @ SV395 )
= ( apply @ SV102 @ ( ordered_pair @ SV286 @ SV395 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1009]) ).
thf(1211,plain,
! [SV396: $i,SV287: $i,SV103: $i] :
( ( ~ ( maps @ SV103 @ SV287 @ SV396 )
| ( function @ SV103 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1212,plain,
! [SV397: $i,SV288: $i,SV104: $i] :
( ( ~ ( maps @ SV104 @ SV288 @ SV397 )
| ( ( domain_of @ SV104 )
= SV288 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1213,plain,
! [SV398: $i,SV289: $i,SV105: $i] :
( ( ~ ( maps @ SV105 @ SV289 @ SV398 )
| ( subset @ ( range_of @ SV105 ) @ SV398 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1214,plain,
! [SV290: $i,SV106: $i] :
( ( ( ~ ( closed @ SV106 @ SV290 ) )
= $true )
| ( ( little_set @ SV106 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1013]) ).
thf(1215,plain,
! [SV291: $i,SV107: $i] :
( ( ( ~ ( closed @ SV107 @ SV291 ) )
= $true )
| ( ( little_set @ SV291 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1014]) ).
thf(1216,plain,
! [SV292: $i,SV108: $i] :
( ( ( ~ ( closed @ SV108 @ SV292 ) )
= $true )
| ( ( maps @ SV292 @ ( cross_product @ SV108 @ SV108 ) @ SV108 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1015]) ).
thf(1217,plain,
! [SV293: $i,SV109: $i] :
( ( ( closed @ SV109 @ SV293 )
= $true )
| ( ( ~ ( little_set @ SV109 )
| ~ ( little_set @ SV293 )
| ~ ( maps @ SV293 @ ( cross_product @ SV109 @ SV109 ) @ SV109 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1016]) ).
thf(1218,plain,
! [SV399: $i,SV294: $i,SV110: $i] :
( ( ~ ( member @ SV110 @ ( compose @ SV294 @ SV399 ) )
| ( little_set @ ( f29 @ SV110 @ SV294 @ SV399 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1219,plain,
! [SV400: $i,SV295: $i,SV111: $i] :
( ( ~ ( member @ SV111 @ ( compose @ SV295 @ SV400 ) )
| ( little_set @ ( f30 @ SV111 @ SV295 @ SV400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1220,plain,
! [SV401: $i,SV296: $i,SV112: $i] :
( ( ~ ( member @ SV112 @ ( compose @ SV296 @ SV401 ) )
| ( little_set @ ( f31 @ SV112 @ SV296 @ SV401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1019]) ).
thf(1221,plain,
! [SV402: $i,SV297: $i,SV113: $i] :
( ( ~ ( member @ SV113 @ ( compose @ SV297 @ SV402 ) )
| ( SV113
= ( ordered_pair @ ( f29 @ SV113 @ SV297 @ SV402 ) @ ( f30 @ SV113 @ SV297 @ SV402 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1222,plain,
! [SV403: $i,SV298: $i,SV114: $i] :
( ( ~ ( member @ SV114 @ ( compose @ SV298 @ SV403 ) )
| ( member @ ( ordered_pair @ ( f29 @ SV114 @ SV298 @ SV403 ) @ ( f31 @ SV114 @ SV298 @ SV403 ) ) @ SV298 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1223,plain,
! [SV404: $i,SV299: $i,SV115: $i] :
( ( ~ ( member @ SV115 @ ( compose @ SV299 @ SV404 ) )
| ( member @ ( ordered_pair @ ( f31 @ SV115 @ SV299 @ SV404 ) @ ( f30 @ SV115 @ SV299 @ SV404 ) ) @ SV404 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1224,plain,
! [SV405: $i,SV300: $i,SV116: $i] :
( ( ! [SY863: $i,SY864: $i] :
( ~ ( homomorphism @ SV116 @ SV300 @ SV405 @ SY863 @ SY864 )
| ( closed @ SV300 @ SV405 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1023]) ).
thf(1225,plain,
! [SV406: $i,SV301: $i,SV117: $i] :
( ( ! [SY865: $i,SY866: $i] :
( ~ ( homomorphism @ SV117 @ SV301 @ SV406 @ SY865 @ SY866 )
| ( closed @ SY865 @ SY866 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1226,plain,
! [SV407: $i,SV302: $i,SV118: $i] :
( ( ! [SY867: $i,SY868: $i] :
( ~ ( homomorphism @ SV118 @ SV302 @ SV407 @ SY867 @ SY868 )
| ( maps @ SV118 @ SV302 @ SY867 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1227,plain,
! [SV408: $i,SV303: $i,SV119: $i] :
( ( ! [SY869: $i,SY870: $i,SY871: $i,SY872: $i] :
( ~ ( homomorphism @ SV119 @ SV303 @ SV408 @ SY869 @ SY870 )
| ~ ( member @ SY871 @ SV303 )
| ~ ( member @ SY872 @ SV303 )
| ( ( apply @ SV119 @ ( apply_to_two_arguments @ SV408 @ SY871 @ SY872 ) )
= ( apply_to_two_arguments @ SY870 @ ( apply @ SV119 @ SY871 ) @ ( apply @ SV119 @ SY872 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1228,plain,
! [SV409: $i,SV304: $i,SV120: $i] :
( ( ! [SY873: $i,SY874: $i] :
( ( homomorphism @ SV120 @ SV304 @ SV409 @ SY873 @ SY874 )
| ~ ( closed @ SV304 @ SV409 )
| ~ ( closed @ SY873 @ SY874 )
| ~ ( maps @ SV120 @ SV304 @ SY873 )
| ( member @ ( f32 @ SV120 @ SV304 @ SV409 @ SY873 @ SY874 ) @ SV304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1027]) ).
thf(1229,plain,
! [SV410: $i,SV305: $i,SV121: $i] :
( ( ! [SY875: $i,SY876: $i] :
( ( homomorphism @ SV121 @ SV305 @ SV410 @ SY875 @ SY876 )
| ~ ( closed @ SV305 @ SV410 )
| ~ ( closed @ SY875 @ SY876 )
| ~ ( maps @ SV121 @ SV305 @ SY875 )
| ( member @ ( f33 @ SV121 @ SV305 @ SV410 @ SY875 @ SY876 ) @ SV305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1230,plain,
! [SV411: $i,SV306: $i,SV122: $i] :
( ( ! [SY877: $i,SY878: $i] :
( ~ ( associative @ SV122 @ SV306 )
| ~ ( member @ SV411 @ SV122 )
| ~ ( member @ SY877 @ SV122 )
| ~ ( member @ SY878 @ SV122 )
| ( ( apply_to_two_arguments @ SV306 @ ( apply_to_two_arguments @ SV306 @ SV411 @ SY877 ) @ SY878 )
= ( apply_to_two_arguments @ SV306 @ SV411 @ ( apply_to_two_arguments @ SV306 @ SY877 @ SY878 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1029]) ).
thf(1231,plain,
! [SV307: $i,SV123: $i] :
( ( ( associative @ SV123 @ SV307 )
= $true )
| ( ( member @ ( f34 @ SV123 @ SV307 ) @ SV123 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1030]) ).
thf(1232,plain,
! [SV308: $i,SV124: $i] :
( ( ( associative @ SV124 @ SV308 )
= $true )
| ( ( member @ ( f35 @ SV124 @ SV308 ) @ SV124 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1031]) ).
thf(1233,plain,
! [SV309: $i,SV125: $i] :
( ( ( associative @ SV125 @ SV309 )
= $true )
| ( ( member @ ( f36 @ SV125 @ SV309 ) @ SV125 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1032]) ).
thf(1234,plain,
! [SV412: $i,SV310: $i,SV126: $i] :
( ( ~ ( identity @ SV126 @ SV310 @ SV412 )
| ( member @ SV412 @ SV126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1235,plain,
! [SV413: $i,SV311: $i,SV127: $i] :
( ( ! [SY879: $i] :
( ~ ( identity @ SV127 @ SV311 @ SV413 )
| ~ ( member @ SY879 @ SV127 )
| ( ( apply_to_two_arguments @ SV311 @ SV413 @ SY879 )
= SY879 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1034]) ).
thf(1236,plain,
! [SV414: $i,SV312: $i,SV128: $i] :
( ( ! [SY880: $i] :
( ~ ( identity @ SV128 @ SV312 @ SV414 )
| ~ ( member @ SY880 @ SV128 )
| ( ( apply_to_two_arguments @ SV312 @ SY880 @ SV414 )
= SY880 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1237,plain,
! [SV415: $i,SV313: $i,SV129: $i] :
( ( ( identity @ SV129 @ SV313 @ SV415 )
| ~ ( member @ SV415 @ SV129 )
| ( member @ ( f37 @ SV129 @ SV313 @ SV415 ) @ SV129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1036]) ).
thf(1238,plain,
! [SV416: $i,SV314: $i,SV130: $i] :
( ( ! [SY881: $i] :
( ~ ( inverse @ SV130 @ SV314 @ SV416 @ SY881 )
| ( maps @ SY881 @ SV130 @ SV130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1037]) ).
thf(1239,plain,
! [SV417: $i,SV315: $i,SV131: $i] :
( ( ! [SY882: $i,SY883: $i] :
( ~ ( inverse @ SV131 @ SV315 @ SV417 @ SY882 )
| ~ ( member @ SY883 @ SV131 )
| ( ( apply_to_two_arguments @ SV315 @ ( apply @ SY882 @ SY883 ) @ SY883 )
= SV417 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1240,plain,
! [SV418: $i,SV316: $i,SV132: $i] :
( ( ! [SY884: $i,SY885: $i] :
( ~ ( inverse @ SV132 @ SV316 @ SV418 @ SY884 )
| ~ ( member @ SY885 @ SV132 )
| ( ( apply_to_two_arguments @ SV316 @ SY885 @ ( apply @ SY884 @ SY885 ) )
= SV418 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1241,plain,
! [SV419: $i,SV317: $i,SV133: $i] :
( ( ! [SY886: $i] :
( ( inverse @ SV133 @ SV317 @ SV419 @ SY886 )
| ~ ( maps @ SY886 @ SV133 @ SV133 )
| ( member @ ( f38 @ SV133 @ SV317 @ SV419 @ SY886 ) @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1040]) ).
thf(1242,plain,
! [SV318: $i,SV134: $i] :
( ( ( ~ ( group @ SV134 @ SV318 ) )
= $true )
| ( ( closed @ SV134 @ SV318 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1041]) ).
thf(1243,plain,
! [SV319: $i,SV135: $i] :
( ( ( ~ ( group @ SV135 @ SV319 ) )
= $true )
| ( ( associative @ SV135 @ SV319 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1042]) ).
thf(1244,plain,
! [SV320: $i,SV136: $i] :
( ( ( ~ ( group @ SV136 @ SV320 ) )
= $true )
| ( ( identity @ SV136 @ SV320 @ ( f39 @ SV136 @ SV320 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1043]) ).
thf(1245,plain,
! [SV321: $i,SV137: $i] :
( ( ( ~ ( group @ SV137 @ SV321 ) )
= $true )
| ( ( inverse @ SV137 @ SV321 @ ( f39 @ SV137 @ SV321 ) @ ( f40 @ SV137 @ SV321 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1044]) ).
thf(1246,plain,
! [SV420: $i,SV322: $i,SV138: $i] :
( ( ! [SY887: $i] :
( ( group @ SV138 @ SV322 )
| ~ ( closed @ SV138 @ SV322 )
| ~ ( associative @ SV138 @ SV322 )
| ~ ( identity @ SV138 @ SV322 @ SV420 )
| ~ ( inverse @ SV138 @ SV322 @ SV420 @ SY887 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1247,plain,
! [SV421: $i,SV323: $i,SV139: $i] :
( ( ! [SY888: $i] :
( ~ ( commutes @ SV139 @ SV323 )
| ~ ( member @ SV421 @ SV139 )
| ~ ( member @ SY888 @ SV139 )
| ( ( apply_to_two_arguments @ SV323 @ SV421 @ SY888 )
= ( apply_to_two_arguments @ SV323 @ SY888 @ SV421 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1248,plain,
! [SV324: $i,SV140: $i] :
( ( ( commutes @ SV140 @ SV324 )
= $true )
| ( ( member @ ( f41 @ SV140 @ SV324 ) @ SV140 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1047]) ).
thf(1249,plain,
! [SV325: $i,SV141: $i] :
( ( ( commutes @ SV141 @ SV325 )
= $true )
| ( ( member @ ( f42 @ SV141 @ SV325 ) @ SV141 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1048]) ).
thf(1250,plain,
! [SV326: $i,SV142: $i] :
( ( ( ~ ( member @ SV142 @ natural_numbers ) )
= $true )
| ( ( ~ ( little_set @ SV326 )
| ~ ( member @ empty_set @ SV326 )
| ( member @ ( f43 @ SV142 @ SV326 ) @ SV326 )
| ( member @ SV142 @ SV326 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1049]) ).
thf(1251,plain,
! [SV327: $i,SV143: $i] :
( ( ( ~ ( member @ SV143 @ natural_numbers ) )
= $true )
| ( ( ~ ( little_set @ SV327 )
| ~ ( member @ empty_set @ SV327 )
| ~ ( member @ ( successor @ ( f43 @ SV143 @ SV327 ) ) @ SV327 )
| ( member @ SV143 @ SV327 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1050]) ).
thf(1252,plain,
! [SV144: $i] :
( ( ( ~ ( little_set @ SV144 ) )
= $true )
| ( ( little_set @ ( f44 @ SV144 ) )
= $true )
| ( ( member @ SV144 @ natural_numbers )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1051]) ).
thf(1253,plain,
! [SV145: $i] :
( ( ( ~ ( little_set @ SV145 ) )
= $true )
| ( ( member @ empty_set @ ( f44 @ SV145 ) )
= $true )
| ( ( member @ SV145 @ natural_numbers )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1052]) ).
thf(1254,plain,
! [SV328: $i,SV146: $i] :
( ( ( member @ SV146 @ natural_numbers )
= $true )
| ( ( ~ ( little_set @ SV146 )
| ~ ( member @ SV328 @ ( f44 @ SV146 ) )
| ( member @ ( successor @ SV328 ) @ ( f44 @ SV146 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1053]) ).
thf(1255,plain,
! [SV147: $i] :
( ( ( member @ SV147 @ ( f44 @ SV147 ) )
= $false )
| ( ( member @ SV147 @ natural_numbers )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1054]) ).
thf(1256,plain,
! [SV329: $i,SV148: $i] :
( ( ( ~ ( member @ SV148 @ plus ) )
= $true )
| ( ( ~ ( little_set @ SV329 )
| ( member @ ( f45 @ SV148 @ SV329 ) @ natural_numbers )
| ( member @ ( f46 @ SV148 @ SV329 ) @ natural_numbers )
| ( member @ SV148 @ SV329 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1055]) ).
thf(1257,plain,
! [SV330: $i,SV149: $i] :
( ( ( ~ ( member @ SV149 @ plus ) )
= $true )
| ( ( ~ ( little_set @ SV330 )
| ( member @ ( f45 @ SV149 @ SV330 ) @ natural_numbers )
| ( member @ ( f47 @ SV149 @ SV330 ) @ natural_numbers )
| ( member @ SV149 @ SV330 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1056]) ).
thf(1258,plain,
! [SV331: $i,SV150: $i] :
( ( ( ~ ( member @ SV150 @ plus ) )
= $true )
| ( ( ~ ( little_set @ SV331 )
| ( member @ ( f45 @ SV150 @ SV331 ) @ natural_numbers )
| ( member @ ( f48 @ SV150 @ SV331 ) @ natural_numbers )
| ( member @ SV150 @ SV331 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1057]) ).
thf(1259,plain,
! [SV332: $i,SV151: $i] :
( ( ( ~ ( member @ SV151 @ plus ) )
= $true )
| ( ( ~ ( little_set @ SV332 )
| ( member @ ( f45 @ SV151 @ SV332 ) @ natural_numbers )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( f46 @ SV151 @ SV332 ) @ ( f47 @ SV151 @ SV332 ) ) @ ( f48 @ SV151 @ SV332 ) ) @ SV332 )
| ( member @ SV151 @ SV332 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1058]) ).
thf(1260,plain,
! [SV333: $i,SV152: $i] :
( ( ( ~ ( member @ SV152 @ plus ) )
= $true )
| ( ( ~ ( little_set @ SV333 )
| ( member @ ( f45 @ SV152 @ SV333 ) @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f46 @ SV152 @ SV333 ) ) @ ( f47 @ SV152 @ SV333 ) ) @ ( successor @ ( f48 @ SV152 @ SV333 ) ) ) @ SV333 )
| ( member @ SV152 @ SV333 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1059]) ).
thf(1261,plain,
! [SV334: $i,SV153: $i] :
( ( ( ~ ( member @ SV153 @ plus ) )
= $true )
| ( ( ~ ( little_set @ SV334 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV153 @ SV334 ) ) @ ( f45 @ SV153 @ SV334 ) ) @ SV334 )
| ( member @ ( f46 @ SV153 @ SV334 ) @ natural_numbers )
| ( member @ SV153 @ SV334 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1060]) ).
thf(1262,plain,
! [SV335: $i,SV154: $i] :
( ( ( ~ ( member @ SV154 @ plus ) )
= $true )
| ( ( ~ ( little_set @ SV335 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV154 @ SV335 ) ) @ ( f45 @ SV154 @ SV335 ) ) @ SV335 )
| ( member @ ( f47 @ SV154 @ SV335 ) @ natural_numbers )
| ( member @ SV154 @ SV335 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1061]) ).
thf(1263,plain,
! [SV336: $i,SV155: $i] :
( ( ( ~ ( member @ SV155 @ plus ) )
= $true )
| ( ( ~ ( little_set @ SV336 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV155 @ SV336 ) ) @ ( f45 @ SV155 @ SV336 ) ) @ SV336 )
| ( member @ ( f48 @ SV155 @ SV336 ) @ natural_numbers )
| ( member @ SV155 @ SV336 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1062]) ).
thf(1264,plain,
! [SV337: $i,SV156: $i] :
( ( ( ~ ( member @ SV156 @ plus ) )
= $true )
| ( ( ~ ( little_set @ SV337 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV156 @ SV337 ) ) @ ( f45 @ SV156 @ SV337 ) ) @ SV337 )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( f46 @ SV156 @ SV337 ) @ ( f47 @ SV156 @ SV337 ) ) @ ( f48 @ SV156 @ SV337 ) ) @ SV337 )
| ( member @ SV156 @ SV337 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1063]) ).
thf(1265,plain,
! [SV338: $i,SV157: $i] :
( ( ( ~ ( member @ SV157 @ plus ) )
= $true )
| ( ( ~ ( little_set @ SV338 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV157 @ SV338 ) ) @ ( f45 @ SV157 @ SV338 ) ) @ SV338 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f46 @ SV157 @ SV338 ) ) @ ( f47 @ SV157 @ SV338 ) ) @ ( successor @ ( f48 @ SV157 @ SV338 ) ) ) @ SV338 )
| ( member @ SV157 @ SV338 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1064]) ).
thf(1266,plain,
! [SV158: $i] :
( ( ( ~ ( little_set @ SV158 ) )
= $true )
| ( ( little_set @ ( f49 @ SV158 ) )
= $true )
| ( ( member @ SV158 @ plus )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1065]) ).
thf(1267,plain,
! [SV339: $i,SV159: $i] :
( ( ( member @ SV159 @ plus )
= $true )
| ( ( ~ ( little_set @ SV159 )
| ~ ( member @ SV339 @ natural_numbers )
| ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ SV339 ) @ SV339 ) @ ( f49 @ SV159 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1066]) ).
thf(1268,plain,
! [SV422: $i,SV340: $i,SV160: $i] :
( ( ! [SY889: $i] :
( ( member @ SV160 @ plus )
| ~ ( little_set @ SV160 )
| ~ ( member @ SV340 @ natural_numbers )
| ~ ( member @ SV422 @ natural_numbers )
| ~ ( member @ SY889 @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV340 @ SV422 ) @ SY889 ) @ ( f49 @ SV160 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ SV340 ) @ SV422 ) @ ( successor @ SY889 ) ) @ ( f49 @ SV160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1269,plain,
! [SV161: $i] :
( ( ( member @ SV161 @ ( f49 @ SV161 ) )
= $false )
| ( ( member @ SV161 @ plus )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1068]) ).
thf(1270,plain,
! [SV341: $i,SV162: $i] :
( ( ( ~ ( member @ SV162 @ times ) )
= $true )
| ( ( ~ ( little_set @ SV341 )
| ( member @ ( f50 @ SV162 @ SV341 ) @ natural_numbers )
| ( member @ ( f51 @ SV162 @ SV341 ) @ natural_numbers )
| ( member @ SV162 @ SV341 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1069]) ).
thf(1271,plain,
! [SV342: $i,SV163: $i] :
( ( ( ~ ( member @ SV163 @ times ) )
= $true )
| ( ( ~ ( little_set @ SV342 )
| ( member @ ( f50 @ SV163 @ SV342 ) @ natural_numbers )
| ( member @ ( f52 @ SV163 @ SV342 ) @ natural_numbers )
| ( member @ SV163 @ SV342 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1070]) ).
thf(1272,plain,
! [SV343: $i,SV164: $i] :
( ( ( ~ ( member @ SV164 @ times ) )
= $true )
| ( ( ~ ( little_set @ SV343 )
| ( member @ ( f50 @ SV164 @ SV343 ) @ natural_numbers )
| ( member @ ( f53 @ SV164 @ SV343 ) @ natural_numbers )
| ( member @ SV164 @ SV343 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1071]) ).
thf(1273,plain,
! [SV344: $i,SV165: $i] :
( ( ( ~ ( member @ SV165 @ times ) )
= $true )
| ( ( ~ ( little_set @ SV344 )
| ( member @ ( f50 @ SV165 @ SV344 ) @ natural_numbers )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( f51 @ SV165 @ SV344 ) @ ( f52 @ SV165 @ SV344 ) ) @ ( f53 @ SV165 @ SV344 ) ) @ SV344 )
| ( member @ SV165 @ SV344 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1072]) ).
thf(1274,plain,
! [SV345: $i,SV166: $i] :
( ( ( ~ ( member @ SV166 @ times ) )
= $true )
| ( ( ~ ( little_set @ SV345 )
| ( member @ ( f50 @ SV166 @ SV345 ) @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f51 @ SV166 @ SV345 ) ) @ ( f52 @ SV166 @ SV345 ) ) @ ( apply_to_two_arguments @ plus @ ( f53 @ SV166 @ SV345 ) @ ( f52 @ SV166 @ SV345 ) ) ) @ SV345 )
| ( member @ SV166 @ SV345 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1073]) ).
thf(1275,plain,
! [SV346: $i,SV167: $i] :
( ( ( ~ ( member @ SV167 @ times ) )
= $true )
| ( ( ~ ( little_set @ SV346 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV167 @ SV346 ) ) @ empty_set ) @ SV346 )
| ( member @ ( f51 @ SV167 @ SV346 ) @ natural_numbers )
| ( member @ SV167 @ SV346 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1074]) ).
thf(1276,plain,
! [SV347: $i,SV168: $i] :
( ( ( ~ ( member @ SV168 @ times ) )
= $true )
| ( ( ~ ( little_set @ SV347 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV168 @ SV347 ) ) @ empty_set ) @ SV347 )
| ( member @ ( f52 @ SV168 @ SV347 ) @ natural_numbers )
| ( member @ SV168 @ SV347 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1075]) ).
thf(1277,plain,
! [SV348: $i,SV169: $i] :
( ( ( ~ ( member @ SV169 @ times ) )
= $true )
| ( ( ~ ( little_set @ SV348 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV169 @ SV348 ) ) @ empty_set ) @ SV348 )
| ( member @ ( f53 @ SV169 @ SV348 ) @ natural_numbers )
| ( member @ SV169 @ SV348 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1076]) ).
thf(1278,plain,
! [SV349: $i,SV170: $i] :
( ( ( ~ ( member @ SV170 @ times ) )
= $true )
| ( ( ~ ( little_set @ SV349 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV170 @ SV349 ) ) @ empty_set ) @ SV349 )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( f51 @ SV170 @ SV349 ) @ ( f52 @ SV170 @ SV349 ) ) @ ( f53 @ SV170 @ SV349 ) ) @ SV349 )
| ( member @ SV170 @ SV349 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1077]) ).
thf(1279,plain,
! [SV350: $i,SV171: $i] :
( ( ( ~ ( member @ SV171 @ times ) )
= $true )
| ( ( ~ ( little_set @ SV350 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV171 @ SV350 ) ) @ empty_set ) @ SV350 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f51 @ SV171 @ SV350 ) ) @ ( f52 @ SV171 @ SV350 ) ) @ ( apply_to_two_arguments @ plus @ ( f53 @ SV171 @ SV350 ) @ ( f52 @ SV171 @ SV350 ) ) ) @ SV350 )
| ( member @ SV171 @ SV350 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1078]) ).
thf(1280,plain,
! [SV172: $i] :
( ( ( ~ ( little_set @ SV172 ) )
= $true )
| ( ( little_set @ ( f54 @ SV172 ) )
= $true )
| ( ( member @ SV172 @ times )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1079]) ).
thf(1281,plain,
! [SV351: $i,SV173: $i] :
( ( ( member @ SV173 @ times )
= $true )
| ( ( ~ ( little_set @ SV173 )
| ~ ( member @ SV351 @ natural_numbers )
| ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ SV351 ) @ empty_set ) @ ( f54 @ SV173 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1080]) ).
thf(1282,plain,
! [SV423: $i,SV352: $i,SV174: $i] :
( ( ! [SY890: $i] :
( ( member @ SV174 @ times )
| ~ ( little_set @ SV174 )
| ~ ( member @ SV352 @ natural_numbers )
| ~ ( member @ SV423 @ natural_numbers )
| ~ ( member @ SY890 @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV352 @ SV423 ) @ SY890 ) @ ( f54 @ SV174 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ SV352 ) @ SV423 ) @ ( apply_to_two_arguments @ plus @ SY890 @ SV423 ) ) @ ( f54 @ SV174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1081]) ).
thf(1283,plain,
! [SV175: $i] :
( ( ( member @ SV175 @ ( f54 @ SV175 ) )
= $false )
| ( ( member @ SV175 @ times )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1082]) ).
thf(1284,plain,
! [SV176: $i] :
( ( ( member @ SV176 @ prime_numbers )
= $false )
| ( ( member @ SV176 @ natural_numbers )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1083]) ).
thf(1285,plain,
! [SV177: $i] :
( ( ( ~ ( member @ SV177 @ natural_numbers ) )
= $true )
| ( ( ( SV177 = empty_set )
| ( SV177
= ( successor @ empty_set ) )
| ( member @ ( f55 @ SV177 ) @ natural_numbers ) )
= $true )
| ( ( member @ SV177 @ prime_numbers )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1084]) ).
thf(1286,plain,
! [SV178: $i] :
( ( ( ~ ( member @ SV178 @ natural_numbers ) )
= $true )
| ( ( ( SV178 = empty_set )
| ( SV178
= ( successor @ empty_set ) )
| ( member @ ( f56 @ SV178 ) @ natural_numbers ) )
= $true )
| ( ( member @ SV178 @ prime_numbers )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1085]) ).
thf(1287,plain,
! [SV179: $i] :
( ( ( ~ ( member @ SV179 @ natural_numbers ) )
= $true )
| ( ( ( SV179 = empty_set )
| ( SV179
= ( successor @ empty_set ) )
| ( ( apply_to_two_arguments @ times @ ( f55 @ SV179 ) @ ( f56 @ SV179 ) )
= SV179 ) )
= $true )
| ( ( member @ SV179 @ prime_numbers )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1086]) ).
thf(1288,plain,
! [SV180: $i] :
( ( ( ~ ( member @ SV180 @ natural_numbers ) )
= $true )
| ( ( ( SV180 = empty_set )
| ( SV180
= ( successor @ empty_set ) )
| ~ ( member @ ( f55 @ SV180 ) @ ( non_ordered_pair @ ( successor @ empty_set ) @ SV180 ) ) )
= $true )
| ( ( member @ SV180 @ prime_numbers )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1087]) ).
thf(1289,plain,
! [SV181: $i] :
( ( ( finite @ SV181 )
= $false )
| ( ( member @ ( f57 @ SV181 ) @ natural_numbers )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1088]) ).
thf(1290,plain,
! [SV182: $i] :
( ( ( finite @ SV182 )
= $false )
| ( ( maps @ ( f58 @ SV182 ) @ ( f57 @ SV182 ) @ SV182 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1089]) ).
thf(1291,plain,
! [SV183: $i] :
( ( ( finite @ SV183 )
= $false )
| ( ( ( range_of @ ( f58 @ SV183 ) )
= SV183 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1090]) ).
thf(1292,plain,
! [SV184: $i] :
( ( ( finite @ SV184 )
= $false )
| ( ( one_to_one_function @ ( f58 @ SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1091]) ).
thf(1293,plain,
! [SV185: $i] :
( ( ( member @ SV185 @ twin_prime_numbers )
= $false )
| ( ( member @ SV185 @ prime_numbers )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1092]) ).
thf(1294,plain,
! [SV186: $i] :
( ( ( member @ SV186 @ twin_prime_numbers )
= $false )
| ( ( member @ ( successor @ ( successor @ SV186 ) ) @ prime_numbers )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1093]) ).
thf(1295,plain,
! [SV187: $i] :
( ( ( ~ ( member @ SV187 @ prime_numbers ) )
= $true )
| ( ( ~ ( member @ ( successor @ ( successor @ SV187 ) ) @ prime_numbers ) )
= $true )
| ( ( member @ SV187 @ twin_prime_numbers )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1094]) ).
thf(1296,plain,
! [SV188: $i] :
( ( ( member @ SV188 @ even_numbers )
= $false )
| ( ( member @ SV188 @ natural_numbers )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1095]) ).
thf(1297,plain,
! [SV189: $i] :
( ( ( member @ SV189 @ even_numbers )
= $false )
| ( ( member @ ( f59 @ SV189 ) @ natural_numbers )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1096]) ).
thf(1298,plain,
! [SV190: $i] :
( ( ( member @ SV190 @ even_numbers )
= $false )
| ( ( ( apply_to_two_arguments @ plus @ ( f59 @ SV190 ) @ ( f59 @ SV190 ) )
= SV190 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1097]) ).
thf(1299,plain,
! [SV424: $i,SV353: $i,SV191: $i] :
( ( ! [SY891: $i] :
( ( member @ SV191 @ ( second @ SV353 ) )
| ~ ( little_set @ SV424 )
| ~ ( little_set @ SY891 )
| ( SV353
!= ( ordered_pair @ SV424 @ SY891 ) )
| ~ ( member @ SV191 @ SY891 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1098]) ).
thf(1300,plain,
! [SV425: $i,SV354: $i,SV192: $i] :
( ( ! [SY892: $i] :
( ( inverse @ SV192 @ SV354 @ SV425 @ SY892 )
| ~ ( maps @ SY892 @ SV192 @ SV192 )
| ( ( apply_to_two_arguments @ SV354 @ ( apply @ SY892 @ ( f38 @ SV192 @ SV354 @ SV425 @ SY892 ) ) @ ( f38 @ SV192 @ SV354 @ SV425 @ SY892 ) )
!= SV425 )
| ( ( apply_to_two_arguments @ SV354 @ ( f38 @ SV192 @ SV354 @ SV425 @ SY892 ) @ ( apply @ SY892 @ ( f38 @ SV192 @ SV354 @ SV425 @ SY892 ) ) )
!= SV425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1099]) ).
thf(1301,plain,
! [SV426: $i,SV355: $i,SV193: $i] :
( ( ~ ( member @ SV193 @ prime_numbers )
| ~ ( member @ SV355 @ natural_numbers )
| ~ ( member @ SV426 @ natural_numbers )
| ( ( apply_to_two_arguments @ times @ SV355 @ SV426 )
!= SV193 )
| ( member @ SV355 @ ( non_ordered_pair @ ( successor @ empty_set ) @ SV193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1100]) ).
thf(1302,plain,
! [SV194: $i] :
( ( ( member @ SV194 @ prime_numbers )
= $false )
| ( ( SV194 != empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1101]) ).
thf(1303,plain,
! [SV427: $i,SV356: $i,SV195: $i] :
( ( ! [SY893: $i,SY894: $i] :
( ( member @ SV195 @ ( flip_range_of @ SV356 ) )
| ~ ( little_set @ SV195 )
| ~ ( little_set @ SV427 )
| ~ ( little_set @ SY893 )
| ~ ( little_set @ SY894 )
| ( SV195
!= ( ordered_pair @ SV427 @ ( ordered_pair @ SY893 @ SY894 ) ) )
| ~ ( member @ ( ordered_pair @ SV427 @ ( ordered_pair @ SY894 @ SY893 ) ) @ SV356 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1102]) ).
thf(1304,plain,
! [SV428: $i,SV357: $i,SV196: $i] :
( ( ( member @ SV196 @ ( non_ordered_pair @ SV357 @ SV428 ) )
| ~ ( little_set @ SV196 )
| ( SV196 != SV428 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1103]) ).
thf(1305,plain,
! [SV429: $i,SV358: $i,SV197: $i] :
( ( ! [SY895: $i] :
( ( member @ SV197 @ ( first @ SV358 ) )
| ~ ( little_set @ SV429 )
| ~ ( little_set @ SY895 )
| ( SV358
!= ( ordered_pair @ SV429 @ SY895 ) )
| ~ ( member @ SV197 @ SV429 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1306,plain,
! [SV430: $i,SV359: $i,SV198: $i] :
( ( ! [SY896: $i] :
( ( member @ SV198 @ ( image @ SV359 @ SV430 ) )
| ~ ( little_set @ SV198 )
| ~ ( ordered_pair_predicate @ SY896 )
| ~ ( member @ SY896 @ SV430 )
| ~ ( member @ ( first @ SY896 ) @ SV359 )
| ( ( second @ SY896 )
!= SV198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1105]) ).
thf(1307,plain,
! [SV431: $i,SV360: $i,SV199: $i] :
( ( ! [SY897: $i,SY898: $i] :
( ( member @ SV199 @ ( rotate_right @ SV360 ) )
| ~ ( little_set @ SV199 )
| ~ ( little_set @ SV431 )
| ~ ( little_set @ SY897 )
| ~ ( little_set @ SY898 )
| ( SV199
!= ( ordered_pair @ SV431 @ ( ordered_pair @ SY897 @ SY898 ) ) )
| ~ ( member @ ( ordered_pair @ SY897 @ ( ordered_pair @ SY898 @ SV431 ) ) @ SV360 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1106]) ).
thf(1308,plain,
! [SV200: $i] :
( ( ( ( f20 @ SV200 )
= ( f21 @ SV200 ) )
= $false )
| ( ( single_valued_set @ SV200 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1107]) ).
thf(1309,plain,
! [SV432: $i,SV361: $i,SV201: $i] :
( ( ! [SY899: $i,SY900: $i,SY901: $i] :
( ( member @ SV201 @ ( compose @ SV361 @ SV432 ) )
| ~ ( little_set @ SV201 )
| ~ ( little_set @ SY899 )
| ~ ( little_set @ SY900 )
| ~ ( little_set @ SY901 )
| ( SV201
!= ( ordered_pair @ SY899 @ SY900 ) )
| ~ ( member @ ( ordered_pair @ SY899 @ SY901 ) @ SV361 )
| ~ ( member @ ( ordered_pair @ SY901 @ SY900 ) @ SV432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1310,plain,
! [SV433: $i,SV362: $i,SV202: $i] :
( ( ( ordered_pair_predicate @ SV202 )
| ~ ( little_set @ SV362 )
| ~ ( little_set @ SV433 )
| ( SV202
!= ( ordered_pair @ SV362 @ SV433 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1109]) ).
thf(1311,plain,
! [SV434: $i,SV363: $i,SV203: $i] :
( ( ( member @ SV203 @ ( non_ordered_pair @ SV363 @ SV434 ) )
| ~ ( little_set @ SV203 )
| ( SV203 != SV363 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1110]) ).
thf(1312,plain,
! [SV364: $i,SV204: $i] :
( ( ( member @ SV204 @ even_numbers )
= $true )
| ( ( ~ ( member @ SV204 @ natural_numbers )
| ~ ( member @ SV364 @ natural_numbers )
| ( ( apply_to_two_arguments @ plus @ SV364 @ SV364 )
!= SV204 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1111]) ).
thf(1313,plain,
! [SV365: $i,SV205: $i] :
( ( ( ~ ( proper_subset @ SV205 @ SV365 ) )
= $true )
| ( ( SV205 != SV365 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1112]) ).
thf(1314,plain,
! [SV435: $i,SV366: $i,SV206: $i] :
( ( ! [SY902: $i,SY903: $i] :
( ( homomorphism @ SV206 @ SV366 @ SV435 @ SY902 @ SY903 )
| ~ ( closed @ SV366 @ SV435 )
| ~ ( closed @ SY902 @ SY903 )
| ~ ( maps @ SV206 @ SV366 @ SY902 )
| ( ( apply @ SV206 @ ( apply_to_two_arguments @ SV435 @ ( f32 @ SV206 @ SV366 @ SV435 @ SY902 @ SY903 ) @ ( f33 @ SV206 @ SV366 @ SV435 @ SY902 @ SY903 ) ) )
!= ( apply_to_two_arguments @ SY903 @ ( apply @ SV206 @ ( f32 @ SV206 @ SV366 @ SV435 @ SY902 @ SY903 ) ) @ ( apply @ SV206 @ ( f33 @ SV206 @ SV366 @ SV435 @ SY902 @ SY903 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1113]) ).
thf(1315,plain,
! [SV436: $i,SV367: $i,SV207: $i] :
( ( ( finite @ SV207 )
| ~ ( member @ SV367 @ natural_numbers )
| ~ ( maps @ SV436 @ SV367 @ SV207 )
| ( ( range_of @ SV436 )
!= SV207 )
| ~ ( one_to_one_function @ SV436 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1114]) ).
thf(1316,plain,
! [SV437: $i,SV368: $i,SV208: $i] :
( ( ( maps @ SV208 @ SV368 @ SV437 )
| ~ ( function @ SV208 )
| ( ( domain_of @ SV208 )
!= SV368 )
| ~ ( subset @ ( range_of @ SV208 ) @ SV437 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1317,plain,
! [SV209: $i] :
( ( ( member @ SV209 @ prime_numbers )
= $false )
| ( ( SV209
!= ( successor @ empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1116]) ).
thf(1318,plain,
! [SV369: $i,SV210: $i] :
( ( ( commutes @ SV210 @ SV369 )
= $true )
| ( ( ( apply_to_two_arguments @ SV369 @ ( f41 @ SV210 @ SV369 ) @ ( f42 @ SV210 @ SV369 ) )
!= ( apply_to_two_arguments @ SV369 @ ( f42 @ SV210 @ SV369 ) @ ( f41 @ SV210 @ SV369 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1117]) ).
thf(1319,plain,
! [SV211: $i] :
( ( ( ~ ( little_set @ SV211 ) )
= $true )
| ( ( ~ ( ordered_pair_predicate @ SV211 )
| ( ( first @ SV211 )
!= ( second @ SV211 ) ) )
= $true )
| ( ( member @ SV211 @ identity_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1118]) ).
thf(1320,plain,
! [SV438: $i,SV370: $i,SV212: $i] :
( ( ( member @ SV212 @ ( range_of @ SV370 ) )
| ~ ( little_set @ SV212 )
| ~ ( ordered_pair_predicate @ SV438 )
| ~ ( member @ SV438 @ SV370 )
| ( SV212
!= ( second @ SV438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1119]) ).
thf(1321,plain,
! [SV371: $i,SV213: $i] :
( ( ( associative @ SV213 @ SV371 )
= $true )
| ( ( ( apply_to_two_arguments @ SV371 @ ( apply_to_two_arguments @ SV371 @ ( f34 @ SV213 @ SV371 ) @ ( f35 @ SV213 @ SV371 ) ) @ ( f36 @ SV213 @ SV371 ) )
!= ( apply_to_two_arguments @ SV371 @ ( f34 @ SV213 @ SV371 ) @ ( apply_to_two_arguments @ SV371 @ ( f35 @ SV213 @ SV371 ) @ ( f36 @ SV213 @ SV371 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1120]) ).
thf(1322,plain,
! [SV439: $i,SV372: $i,SV214: $i] :
( ( ( identity @ SV214 @ SV372 @ SV439 )
| ~ ( member @ SV439 @ SV214 )
| ( ( apply_to_two_arguments @ SV372 @ SV439 @ ( f37 @ SV214 @ SV372 @ SV439 ) )
!= ( f37 @ SV214 @ SV372 @ SV439 ) )
| ( ( apply_to_two_arguments @ SV372 @ ( f37 @ SV214 @ SV372 @ SV439 ) @ SV439 )
!= ( f37 @ SV214 @ SV372 @ SV439 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1323,plain,
! [SV440: $i,SV373: $i,SV215: $i] :
( ( ( member @ SV215 @ ( domain_of @ SV373 ) )
| ~ ( little_set @ SV215 )
| ~ ( ordered_pair_predicate @ SV440 )
| ~ ( member @ SV440 @ SV373 )
| ( SV215
!= ( first @ SV440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1324,plain,
! [SV441: $i,SV374: $i,SV216: $i] :
( ( ! [SY904: $i] :
( ( member @ SV216 @ ( apply @ SV374 @ SV441 ) )
| ~ ( ordered_pair_predicate @ SY904 )
| ~ ( member @ SY904 @ SV374 )
| ( ( first @ SY904 )
!= SV441 )
| ~ ( member @ SV216 @ ( second @ SY904 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1123]) ).
thf(1325,plain,
! [SV217: $i,SV1: $i] :
( ( ( member @ SV1 @ SV217 )
= $false )
| ( ( little_set @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1124]) ).
thf(1326,plain,
! [SV219: $i,SV3: $i] :
( ( ( member @ ( f1 @ SV3 @ SV219 ) @ SV219 )
= $true )
| ( ( SV3 = SV219 )
= $true )
| ( ( member @ ( f1 @ SV3 @ SV219 ) @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1126]) ).
thf(1327,plain,
! [SV220: $i,SV4: $i] :
( ( ( member @ ( f1 @ SV4 @ SV220 ) @ SV4 )
= $false )
| ( ( ~ ( member @ ( f1 @ SV4 @ SV220 ) @ SV220 )
| ( SV4 = SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1127]) ).
thf(1328,plain,
! [SV375: $i,SV221: $i,SV5: $i] :
( ( ( ~ ( member @ SV5 @ ( non_ordered_pair @ SV221 @ SV375 ) ) )
= $true )
| ( ( ( SV5 = SV221 )
| ( SV5 = SV375 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1128]) ).
thf(1329,plain,
! [SV224: $i,SV12: $i] :
( ( ( member @ SV12 @ ( first @ SV224 ) )
= $false )
| ( ( little_set @ ( f4 @ SV12 @ SV224 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1132]) ).
thf(1330,plain,
! [SV225: $i,SV13: $i] :
( ( ( member @ SV13 @ ( first @ SV225 ) )
= $false )
| ( ( little_set @ ( f5 @ SV13 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1133]) ).
thf(1331,plain,
! [SV226: $i,SV14: $i] :
( ( ( member @ SV14 @ ( first @ SV226 ) )
= $false )
| ( ( SV226
= ( ordered_pair @ ( f4 @ SV14 @ SV226 ) @ ( f5 @ SV14 @ SV226 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1134]) ).
thf(1332,plain,
! [SV227: $i,SV15: $i] :
( ( ( member @ SV15 @ ( first @ SV227 ) )
= $false )
| ( ( member @ SV15 @ ( f4 @ SV15 @ SV227 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1135]) ).
thf(1333,plain,
! [SV228: $i,SV16: $i] :
( ( ( member @ SV16 @ ( second @ SV228 ) )
= $false )
| ( ( little_set @ ( f6 @ SV16 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1136]) ).
thf(1334,plain,
! [SV229: $i,SV17: $i] :
( ( ( member @ SV17 @ ( second @ SV229 ) )
= $false )
| ( ( little_set @ ( f7 @ SV17 @ SV229 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1137]) ).
thf(1335,plain,
! [SV230: $i,SV18: $i] :
( ( ( member @ SV18 @ ( second @ SV230 ) )
= $false )
| ( ( SV230
= ( ordered_pair @ ( f6 @ SV18 @ SV230 ) @ ( f7 @ SV18 @ SV230 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1138]) ).
thf(1336,plain,
! [SV231: $i,SV19: $i] :
( ( ( member @ SV19 @ ( second @ SV231 ) )
= $false )
| ( ( member @ SV19 @ ( f7 @ SV19 @ SV231 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1139]) ).
thf(1337,plain,
! [SV22: $i] :
( ( ( little_set @ SV22 )
= $false )
| ( ( ~ ( ordered_pair_predicate @ SV22 )
| ~ ( member @ ( first @ SV22 ) @ ( second @ SV22 ) ) )
= $true )
| ( ( member @ SV22 @ estin )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1142]) ).
thf(1338,plain,
! [SV376: $i,SV232: $i,SV23: $i] :
( ( ( ~ ( member @ SV23 @ ( intersection @ SV232 @ SV376 ) ) )
= $true )
| ( ( member @ SV23 @ SV232 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1143]) ).
thf(1339,plain,
! [SV377: $i,SV233: $i,SV24: $i] :
( ( ( ~ ( member @ SV24 @ ( intersection @ SV233 @ SV377 ) ) )
= $true )
| ( ( member @ SV24 @ SV377 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1144]) ).
thf(1340,plain,
! [SV378: $i,SV234: $i,SV25: $i] :
( ( ( member @ SV25 @ ( intersection @ SV234 @ SV378 ) )
= $true )
| ( ( ~ ( member @ SV25 @ SV234 )
| ~ ( member @ SV25 @ SV378 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1145]) ).
thf(1341,plain,
! [SV235: $i,SV26: $i] :
( ( ( member @ SV26 @ ( complement @ SV235 ) )
= $false )
| ( ( ~ ( member @ SV26 @ SV235 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1146]) ).
thf(1342,plain,
! [SV236: $i,SV27: $i] :
( ( ( ~ ( little_set @ SV27 ) )
= $true )
| ( ( member @ SV27 @ SV236 )
= $true )
| ( ( member @ SV27 @ ( complement @ SV236 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1147]) ).
thf(1343,plain,
! [SV238: $i,SV29: $i] :
( ( ( member @ SV29 @ ( domain_of @ SV238 ) )
= $false )
| ( ( ordered_pair_predicate @ ( f8 @ SV29 @ SV238 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1148]) ).
thf(1344,plain,
! [SV239: $i,SV30: $i] :
( ( ( member @ SV30 @ ( domain_of @ SV239 ) )
= $false )
| ( ( member @ ( f8 @ SV30 @ SV239 ) @ SV239 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1149]) ).
thf(1345,plain,
! [SV240: $i,SV31: $i] :
( ( ( member @ SV31 @ ( domain_of @ SV240 ) )
= $false )
| ( ( SV31
= ( first @ ( f8 @ SV31 @ SV240 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1150]) ).
thf(1346,plain,
! [SV379: $i,SV241: $i,SV32: $i] :
( ( ( ~ ( member @ SV32 @ ( cross_product @ SV241 @ SV379 ) ) )
= $true )
| ( ( ordered_pair_predicate @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1151]) ).
thf(1347,plain,
! [SV380: $i,SV242: $i,SV33: $i] :
( ( ( ~ ( member @ SV33 @ ( cross_product @ SV242 @ SV380 ) ) )
= $true )
| ( ( member @ ( first @ SV33 ) @ SV242 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1152]) ).
thf(1348,plain,
! [SV381: $i,SV243: $i,SV34: $i] :
( ( ( ~ ( member @ SV34 @ ( cross_product @ SV243 @ SV381 ) ) )
= $true )
| ( ( member @ ( second @ SV34 ) @ SV381 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1153]) ).
thf(1349,plain,
! [SV382: $i,SV244: $i,SV35: $i] :
( ( ( member @ SV35 @ ( cross_product @ SV244 @ SV382 ) )
= $true )
| ( ( ~ ( little_set @ SV35 )
| ~ ( ordered_pair_predicate @ SV35 )
| ~ ( member @ ( first @ SV35 ) @ SV244 )
| ~ ( member @ ( second @ SV35 ) @ SV382 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1154]) ).
thf(1350,plain,
! [SV245: $i,SV36: $i] :
( ( ( member @ SV36 @ ( converse @ SV245 ) )
= $false )
| ( ( ordered_pair_predicate @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1155]) ).
thf(1351,plain,
! [SV246: $i,SV37: $i] :
( ( ( member @ SV37 @ ( converse @ SV246 ) )
= $false )
| ( ( member @ ( ordered_pair @ ( second @ SV37 ) @ ( first @ SV37 ) ) @ SV246 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1156]) ).
thf(1352,plain,
! [SV247: $i,SV38: $i] :
( ( ( ~ ( little_set @ SV38 ) )
= $true )
| ( ( ~ ( ordered_pair_predicate @ SV38 )
| ~ ( member @ ( ordered_pair @ ( second @ SV38 ) @ ( first @ SV38 ) ) @ SV247 ) )
= $true )
| ( ( member @ SV38 @ ( converse @ SV247 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1157]) ).
thf(1353,plain,
! [SV248: $i,SV39: $i] :
( ( ( member @ SV39 @ ( rotate_right @ SV248 ) )
= $false )
| ( ( little_set @ ( f9 @ SV39 @ SV248 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1158]) ).
thf(1354,plain,
! [SV249: $i,SV40: $i] :
( ( ( member @ SV40 @ ( rotate_right @ SV249 ) )
= $false )
| ( ( little_set @ ( f10 @ SV40 @ SV249 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1159]) ).
thf(1355,plain,
! [SV250: $i,SV41: $i] :
( ( ( member @ SV41 @ ( rotate_right @ SV250 ) )
= $false )
| ( ( little_set @ ( f11 @ SV41 @ SV250 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1160]) ).
thf(1356,plain,
! [SV251: $i,SV42: $i] :
( ( ( member @ SV42 @ ( rotate_right @ SV251 ) )
= $false )
| ( ( SV42
= ( ordered_pair @ ( f9 @ SV42 @ SV251 ) @ ( ordered_pair @ ( f10 @ SV42 @ SV251 ) @ ( f11 @ SV42 @ SV251 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1161]) ).
thf(1357,plain,
! [SV252: $i,SV43: $i] :
( ( ( member @ SV43 @ ( rotate_right @ SV252 ) )
= $false )
| ( ( member @ ( ordered_pair @ ( f10 @ SV43 @ SV252 ) @ ( ordered_pair @ ( f11 @ SV43 @ SV252 ) @ ( f9 @ SV43 @ SV252 ) ) ) @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1162]) ).
thf(1358,plain,
! [SV253: $i,SV44: $i] :
( ( ( member @ SV44 @ ( flip_range_of @ SV253 ) )
= $false )
| ( ( little_set @ ( f12 @ SV44 @ SV253 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1163]) ).
thf(1359,plain,
! [SV254: $i,SV45: $i] :
( ( ( member @ SV45 @ ( flip_range_of @ SV254 ) )
= $false )
| ( ( little_set @ ( f13 @ SV45 @ SV254 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1164]) ).
thf(1360,plain,
! [SV255: $i,SV46: $i] :
( ( ( member @ SV46 @ ( flip_range_of @ SV255 ) )
= $false )
| ( ( little_set @ ( f14 @ SV46 @ SV255 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1165]) ).
thf(1361,plain,
! [SV256: $i,SV47: $i] :
( ( ( member @ SV47 @ ( flip_range_of @ SV256 ) )
= $false )
| ( ( SV47
= ( ordered_pair @ ( f12 @ SV47 @ SV256 ) @ ( ordered_pair @ ( f13 @ SV47 @ SV256 ) @ ( f14 @ SV47 @ SV256 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1166]) ).
thf(1362,plain,
! [SV257: $i,SV48: $i] :
( ( ( member @ SV48 @ ( flip_range_of @ SV257 ) )
= $false )
| ( ( member @ ( ordered_pair @ ( f12 @ SV48 @ SV257 ) @ ( ordered_pair @ ( f14 @ SV48 @ SV257 ) @ ( f13 @ SV48 @ SV257 ) ) ) @ SV257 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1167]) ).
thf(1363,plain,
! [SV258: $i,SV53: $i] :
( ( ( member @ SV53 @ ( sigma @ SV258 ) )
= $false )
| ( ( member @ ( f16 @ SV53 @ SV258 ) @ SV258 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1170]) ).
thf(1364,plain,
! [SV259: $i,SV54: $i] :
( ( ( member @ SV54 @ ( sigma @ SV259 ) )
= $false )
| ( ( member @ SV54 @ ( f16 @ SV54 @ SV259 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1171]) ).
thf(1365,plain,
! [SV383: $i,SV260: $i,SV55: $i] :
( ( ( member @ SV55 @ ( sigma @ SV260 ) )
= $true )
| ( ( ~ ( member @ SV383 @ SV260 )
| ~ ( member @ SV55 @ SV383 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1172]) ).
thf(1366,plain,
! [SV384: $i,SV261: $i,SV57: $i] :
( ( ( ~ ( subset @ SV57 @ SV261 ) )
= $true )
| ( ( ~ ( member @ SV384 @ SV57 )
| ( member @ SV384 @ SV261 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1174]) ).
thf(1367,plain,
! [SV263: $i,SV59: $i] :
( ( ( member @ ( f17 @ SV59 @ SV263 ) @ SV263 )
= $false )
| ( ( subset @ SV59 @ SV263 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1176]) ).
thf(1368,plain,
! [SV264: $i,SV60: $i] :
( ( ( proper_subset @ SV60 @ SV264 )
= $false )
| ( ( subset @ SV60 @ SV264 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1177]) ).
thf(1369,plain,
! [SV265: $i,SV61: $i] :
( ( ( ~ ( subset @ SV61 @ SV265 ) )
= $true )
| ( ( SV61 = SV265 )
= $true )
| ( ( proper_subset @ SV61 @ SV265 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1178]) ).
thf(1370,plain,
! [SV266: $i,SV62: $i] :
( ( ( member @ SV62 @ ( powerset @ SV266 ) )
= $false )
| ( ( subset @ SV62 @ SV266 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1179]) ).
thf(1371,plain,
! [SV267: $i,SV63: $i] :
( ( ( ~ ( little_set @ SV63 ) )
= $true )
| ( ( ~ ( subset @ SV63 @ SV267 ) )
= $true )
| ( ( member @ SV63 @ ( powerset @ SV267 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1180]) ).
thf(1372,plain,
! [SV268: $i,SV65: $i] :
( ( ( relation @ SV65 )
= $false )
| ( ( ~ ( member @ SV268 @ SV65 )
| ( ordered_pair_predicate @ SV268 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1182]) ).
thf(1373,plain,
! [SV442: $i,SV385: $i,SV269: $i,SV68: $i] :
( ( ~ ( single_valued_set @ SV68 )
| ~ ( little_set @ SV269 )
| ~ ( little_set @ SV385 )
| ~ ( little_set @ SV442 )
| ~ ( member @ ( ordered_pair @ SV269 @ SV385 ) @ SV68 )
| ~ ( member @ ( ordered_pair @ SV269 @ SV442 ) @ SV68 )
| ( SV385 = SV442 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1184]) ).
thf(1374,plain,
! [SV76: $i] :
( ( ( relation @ SV76 )
= $false )
| ( ( ~ ( single_valued_set @ SV76 ) )
= $true )
| ( ( function @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1187]) ).
thf(1375,plain,
! [SV386: $i,SV270: $i,SV77: $i] :
( ( ( ~ ( member @ SV77 @ ( image @ SV270 @ SV386 ) ) )
= $true )
| ( ( ordered_pair_predicate @ ( f22 @ SV77 @ SV270 @ SV386 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1188]) ).
thf(1376,plain,
! [SV387: $i,SV271: $i,SV78: $i] :
( ( ( ~ ( member @ SV78 @ ( image @ SV271 @ SV387 ) ) )
= $true )
| ( ( member @ ( f22 @ SV78 @ SV271 @ SV387 ) @ SV387 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1189]) ).
thf(1377,plain,
! [SV388: $i,SV272: $i,SV79: $i] :
( ( ( ~ ( member @ SV79 @ ( image @ SV272 @ SV388 ) ) )
= $true )
| ( ( member @ ( first @ ( f22 @ SV79 @ SV272 @ SV388 ) ) @ SV272 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1190]) ).
thf(1378,plain,
! [SV389: $i,SV273: $i,SV80: $i] :
( ( ( ~ ( member @ SV80 @ ( image @ SV273 @ SV389 ) ) )
= $true )
| ( ( ( second @ ( f22 @ SV80 @ SV273 @ SV389 ) )
= SV80 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1191]) ).
thf(1379,plain,
! [SV274: $i,SV81: $i] :
( ( ( little_set @ SV81 )
= $false )
| ( ( ~ ( function @ SV274 )
| ( little_set @ ( image @ SV81 @ SV274 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1192]) ).
thf(1380,plain,
! [SV390: $i,SV275: $i,SV82: $i] :
( ( ( ~ ( disjoint @ SV82 @ SV275 ) )
= $true )
| ( ( ~ ( member @ SV390 @ SV82 )
| ~ ( member @ SV390 @ SV275 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1193]) ).
thf(1381,plain,
! [SV87: $i] :
( ( ( SV87 = empty_set )
= $true )
| ( ( member @ ( f26 @ SV87 ) @ SV87 )
= $true )
| ( ( little_set @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1196]) ).
thf(1382,plain,
! [SV88: $i] :
( ( ( SV88 = empty_set )
= $true )
| ( ( member @ ( ordered_pair @ SV88 @ ( f26 @ SV88 ) ) @ f25 )
= $true )
| ( ( little_set @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1197]) ).
thf(1383,plain,
! [SV278: $i,SV89: $i] :
( ( ( member @ SV89 @ ( range_of @ SV278 ) )
= $false )
| ( ( ordered_pair_predicate @ ( f27 @ SV89 @ SV278 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1198]) ).
thf(1384,plain,
! [SV279: $i,SV90: $i] :
( ( ( member @ SV90 @ ( range_of @ SV279 ) )
= $false )
| ( ( member @ ( f27 @ SV90 @ SV279 ) @ SV279 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1199]) ).
thf(1385,plain,
! [SV280: $i,SV91: $i] :
( ( ( member @ SV91 @ ( range_of @ SV280 ) )
= $false )
| ( ( SV91
= ( second @ ( f27 @ SV91 @ SV280 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1200]) ).
thf(1386,plain,
! [SV97: $i] :
( ( ( function @ SV97 )
= $false )
| ( ( ~ ( function @ ( converse @ SV97 ) ) )
= $true )
| ( ( one_to_one_function @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1205]) ).
thf(1387,plain,
! [SV391: $i,SV282: $i,SV98: $i] :
( ( ( ~ ( member @ SV98 @ ( apply @ SV282 @ SV391 ) ) )
= $true )
| ( ( ordered_pair_predicate @ ( f28 @ SV98 @ SV282 @ SV391 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1206]) ).
thf(1388,plain,
! [SV392: $i,SV283: $i,SV99: $i] :
( ( ( ~ ( member @ SV99 @ ( apply @ SV283 @ SV392 ) ) )
= $true )
| ( ( member @ ( f28 @ SV99 @ SV283 @ SV392 ) @ SV283 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1207]) ).
thf(1389,plain,
! [SV393: $i,SV284: $i,SV100: $i] :
( ( ( ~ ( member @ SV100 @ ( apply @ SV284 @ SV393 ) ) )
= $true )
| ( ( ( first @ ( f28 @ SV100 @ SV284 @ SV393 ) )
= SV393 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1208]) ).
thf(1390,plain,
! [SV394: $i,SV285: $i,SV101: $i] :
( ( ( ~ ( member @ SV101 @ ( apply @ SV285 @ SV394 ) ) )
= $true )
| ( ( member @ SV101 @ ( second @ ( f28 @ SV101 @ SV285 @ SV394 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1209]) ).
thf(1391,plain,
! [SV396: $i,SV287: $i,SV103: $i] :
( ( ( ~ ( maps @ SV103 @ SV287 @ SV396 ) )
= $true )
| ( ( function @ SV103 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1211]) ).
thf(1392,plain,
! [SV397: $i,SV288: $i,SV104: $i] :
( ( ( ~ ( maps @ SV104 @ SV288 @ SV397 ) )
= $true )
| ( ( ( domain_of @ SV104 )
= SV288 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1212]) ).
thf(1393,plain,
! [SV398: $i,SV289: $i,SV105: $i] :
( ( ( ~ ( maps @ SV105 @ SV289 @ SV398 ) )
= $true )
| ( ( subset @ ( range_of @ SV105 ) @ SV398 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1213]) ).
thf(1394,plain,
! [SV290: $i,SV106: $i] :
( ( ( closed @ SV106 @ SV290 )
= $false )
| ( ( little_set @ SV106 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1214]) ).
thf(1395,plain,
! [SV291: $i,SV107: $i] :
( ( ( closed @ SV107 @ SV291 )
= $false )
| ( ( little_set @ SV291 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1215]) ).
thf(1396,plain,
! [SV292: $i,SV108: $i] :
( ( ( closed @ SV108 @ SV292 )
= $false )
| ( ( maps @ SV292 @ ( cross_product @ SV108 @ SV108 ) @ SV108 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1216]) ).
thf(1397,plain,
! [SV293: $i,SV109: $i] :
( ( ( ~ ( little_set @ SV109 ) )
= $true )
| ( ( ~ ( little_set @ SV293 )
| ~ ( maps @ SV293 @ ( cross_product @ SV109 @ SV109 ) @ SV109 ) )
= $true )
| ( ( closed @ SV109 @ SV293 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1217]) ).
thf(1398,plain,
! [SV399: $i,SV294: $i,SV110: $i] :
( ( ( ~ ( member @ SV110 @ ( compose @ SV294 @ SV399 ) ) )
= $true )
| ( ( little_set @ ( f29 @ SV110 @ SV294 @ SV399 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1218]) ).
thf(1399,plain,
! [SV400: $i,SV295: $i,SV111: $i] :
( ( ( ~ ( member @ SV111 @ ( compose @ SV295 @ SV400 ) ) )
= $true )
| ( ( little_set @ ( f30 @ SV111 @ SV295 @ SV400 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1219]) ).
thf(1400,plain,
! [SV401: $i,SV296: $i,SV112: $i] :
( ( ( ~ ( member @ SV112 @ ( compose @ SV296 @ SV401 ) ) )
= $true )
| ( ( little_set @ ( f31 @ SV112 @ SV296 @ SV401 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1220]) ).
thf(1401,plain,
! [SV402: $i,SV297: $i,SV113: $i] :
( ( ( ~ ( member @ SV113 @ ( compose @ SV297 @ SV402 ) ) )
= $true )
| ( ( SV113
= ( ordered_pair @ ( f29 @ SV113 @ SV297 @ SV402 ) @ ( f30 @ SV113 @ SV297 @ SV402 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1221]) ).
thf(1402,plain,
! [SV403: $i,SV298: $i,SV114: $i] :
( ( ( ~ ( member @ SV114 @ ( compose @ SV298 @ SV403 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ ( f29 @ SV114 @ SV298 @ SV403 ) @ ( f31 @ SV114 @ SV298 @ SV403 ) ) @ SV298 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1222]) ).
thf(1403,plain,
! [SV404: $i,SV299: $i,SV115: $i] :
( ( ( ~ ( member @ SV115 @ ( compose @ SV299 @ SV404 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ ( f31 @ SV115 @ SV299 @ SV404 ) @ ( f30 @ SV115 @ SV299 @ SV404 ) ) @ SV404 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1223]) ).
thf(1404,plain,
! [SV443: $i,SV405: $i,SV300: $i,SV116: $i] :
( ( ! [SY905: $i] :
( ~ ( homomorphism @ SV116 @ SV300 @ SV405 @ SV443 @ SY905 )
| ( closed @ SV300 @ SV405 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1224]) ).
thf(1405,plain,
! [SV444: $i,SV406: $i,SV301: $i,SV117: $i] :
( ( ! [SY906: $i] :
( ~ ( homomorphism @ SV117 @ SV301 @ SV406 @ SV444 @ SY906 )
| ( closed @ SV444 @ SY906 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1406,plain,
! [SV445: $i,SV407: $i,SV302: $i,SV118: $i] :
( ( ! [SY907: $i] :
( ~ ( homomorphism @ SV118 @ SV302 @ SV407 @ SV445 @ SY907 )
| ( maps @ SV118 @ SV302 @ SV445 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1226]) ).
thf(1407,plain,
! [SV446: $i,SV408: $i,SV303: $i,SV119: $i] :
( ( ! [SY908: $i,SY909: $i,SY910: $i] :
( ~ ( homomorphism @ SV119 @ SV303 @ SV408 @ SV446 @ SY908 )
| ~ ( member @ SY909 @ SV303 )
| ~ ( member @ SY910 @ SV303 )
| ( ( apply @ SV119 @ ( apply_to_two_arguments @ SV408 @ SY909 @ SY910 ) )
= ( apply_to_two_arguments @ SY908 @ ( apply @ SV119 @ SY909 ) @ ( apply @ SV119 @ SY910 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1227]) ).
thf(1408,plain,
! [SV447: $i,SV409: $i,SV304: $i,SV120: $i] :
( ( ! [SY911: $i] :
( ( homomorphism @ SV120 @ SV304 @ SV409 @ SV447 @ SY911 )
| ~ ( closed @ SV304 @ SV409 )
| ~ ( closed @ SV447 @ SY911 )
| ~ ( maps @ SV120 @ SV304 @ SV447 )
| ( member @ ( f32 @ SV120 @ SV304 @ SV409 @ SV447 @ SY911 ) @ SV304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1228]) ).
thf(1409,plain,
! [SV448: $i,SV410: $i,SV305: $i,SV121: $i] :
( ( ! [SY912: $i] :
( ( homomorphism @ SV121 @ SV305 @ SV410 @ SV448 @ SY912 )
| ~ ( closed @ SV305 @ SV410 )
| ~ ( closed @ SV448 @ SY912 )
| ~ ( maps @ SV121 @ SV305 @ SV448 )
| ( member @ ( f33 @ SV121 @ SV305 @ SV410 @ SV448 @ SY912 ) @ SV305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1229]) ).
thf(1410,plain,
! [SV449: $i,SV411: $i,SV306: $i,SV122: $i] :
( ( ! [SY913: $i] :
( ~ ( associative @ SV122 @ SV306 )
| ~ ( member @ SV411 @ SV122 )
| ~ ( member @ SV449 @ SV122 )
| ~ ( member @ SY913 @ SV122 )
| ( ( apply_to_two_arguments @ SV306 @ ( apply_to_two_arguments @ SV306 @ SV411 @ SV449 ) @ SY913 )
= ( apply_to_two_arguments @ SV306 @ SV411 @ ( apply_to_two_arguments @ SV306 @ SV449 @ SY913 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1230]) ).
thf(1411,plain,
! [SV412: $i,SV310: $i,SV126: $i] :
( ( ( ~ ( identity @ SV126 @ SV310 @ SV412 ) )
= $true )
| ( ( member @ SV412 @ SV126 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1234]) ).
thf(1412,plain,
! [SV450: $i,SV413: $i,SV311: $i,SV127: $i] :
( ( ~ ( identity @ SV127 @ SV311 @ SV413 )
| ~ ( member @ SV450 @ SV127 )
| ( ( apply_to_two_arguments @ SV311 @ SV413 @ SV450 )
= SV450 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1235]) ).
thf(1413,plain,
! [SV451: $i,SV414: $i,SV312: $i,SV128: $i] :
( ( ~ ( identity @ SV128 @ SV312 @ SV414 )
| ~ ( member @ SV451 @ SV128 )
| ( ( apply_to_two_arguments @ SV312 @ SV451 @ SV414 )
= SV451 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1236]) ).
thf(1414,plain,
! [SV415: $i,SV313: $i,SV129: $i] :
( ( ( identity @ SV129 @ SV313 @ SV415 )
= $true )
| ( ( ~ ( member @ SV415 @ SV129 )
| ( member @ ( f37 @ SV129 @ SV313 @ SV415 ) @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1237]) ).
thf(1415,plain,
! [SV452: $i,SV416: $i,SV314: $i,SV130: $i] :
( ( ~ ( inverse @ SV130 @ SV314 @ SV416 @ SV452 )
| ( maps @ SV452 @ SV130 @ SV130 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1238]) ).
thf(1416,plain,
! [SV453: $i,SV417: $i,SV315: $i,SV131: $i] :
( ( ! [SY914: $i] :
( ~ ( inverse @ SV131 @ SV315 @ SV417 @ SV453 )
| ~ ( member @ SY914 @ SV131 )
| ( ( apply_to_two_arguments @ SV315 @ ( apply @ SV453 @ SY914 ) @ SY914 )
= SV417 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1239]) ).
thf(1417,plain,
! [SV454: $i,SV418: $i,SV316: $i,SV132: $i] :
( ( ! [SY915: $i] :
( ~ ( inverse @ SV132 @ SV316 @ SV418 @ SV454 )
| ~ ( member @ SY915 @ SV132 )
| ( ( apply_to_two_arguments @ SV316 @ SY915 @ ( apply @ SV454 @ SY915 ) )
= SV418 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1240]) ).
thf(1418,plain,
! [SV455: $i,SV419: $i,SV317: $i,SV133: $i] :
( ( ( inverse @ SV133 @ SV317 @ SV419 @ SV455 )
| ~ ( maps @ SV455 @ SV133 @ SV133 )
| ( member @ ( f38 @ SV133 @ SV317 @ SV419 @ SV455 ) @ SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1241]) ).
thf(1419,plain,
! [SV318: $i,SV134: $i] :
( ( ( group @ SV134 @ SV318 )
= $false )
| ( ( closed @ SV134 @ SV318 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1242]) ).
thf(1420,plain,
! [SV319: $i,SV135: $i] :
( ( ( group @ SV135 @ SV319 )
= $false )
| ( ( associative @ SV135 @ SV319 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1243]) ).
thf(1421,plain,
! [SV320: $i,SV136: $i] :
( ( ( group @ SV136 @ SV320 )
= $false )
| ( ( identity @ SV136 @ SV320 @ ( f39 @ SV136 @ SV320 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1244]) ).
thf(1422,plain,
! [SV321: $i,SV137: $i] :
( ( ( group @ SV137 @ SV321 )
= $false )
| ( ( inverse @ SV137 @ SV321 @ ( f39 @ SV137 @ SV321 ) @ ( f40 @ SV137 @ SV321 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1245]) ).
thf(1423,plain,
! [SV456: $i,SV420: $i,SV322: $i,SV138: $i] :
( ( ( group @ SV138 @ SV322 )
| ~ ( closed @ SV138 @ SV322 )
| ~ ( associative @ SV138 @ SV322 )
| ~ ( identity @ SV138 @ SV322 @ SV420 )
| ~ ( inverse @ SV138 @ SV322 @ SV420 @ SV456 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1246]) ).
thf(1424,plain,
! [SV457: $i,SV421: $i,SV323: $i,SV139: $i] :
( ( ~ ( commutes @ SV139 @ SV323 )
| ~ ( member @ SV421 @ SV139 )
| ~ ( member @ SV457 @ SV139 )
| ( ( apply_to_two_arguments @ SV323 @ SV421 @ SV457 )
= ( apply_to_two_arguments @ SV323 @ SV457 @ SV421 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1247]) ).
thf(1425,plain,
! [SV326: $i,SV142: $i] :
( ( ( member @ SV142 @ natural_numbers )
= $false )
| ( ( ~ ( little_set @ SV326 )
| ~ ( member @ empty_set @ SV326 )
| ( member @ ( f43 @ SV142 @ SV326 ) @ SV326 )
| ( member @ SV142 @ SV326 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1250]) ).
thf(1426,plain,
! [SV327: $i,SV143: $i] :
( ( ( member @ SV143 @ natural_numbers )
= $false )
| ( ( ~ ( little_set @ SV327 )
| ~ ( member @ empty_set @ SV327 )
| ~ ( member @ ( successor @ ( f43 @ SV143 @ SV327 ) ) @ SV327 )
| ( member @ SV143 @ SV327 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1251]) ).
thf(1427,plain,
! [SV144: $i] :
( ( ( little_set @ SV144 )
= $false )
| ( ( little_set @ ( f44 @ SV144 ) )
= $true )
| ( ( member @ SV144 @ natural_numbers )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1252]) ).
thf(1428,plain,
! [SV145: $i] :
( ( ( little_set @ SV145 )
= $false )
| ( ( member @ empty_set @ ( f44 @ SV145 ) )
= $true )
| ( ( member @ SV145 @ natural_numbers )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1253]) ).
thf(1429,plain,
! [SV328: $i,SV146: $i] :
( ( ( ~ ( little_set @ SV146 ) )
= $true )
| ( ( ~ ( member @ SV328 @ ( f44 @ SV146 ) )
| ( member @ ( successor @ SV328 ) @ ( f44 @ SV146 ) ) )
= $true )
| ( ( member @ SV146 @ natural_numbers )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1254]) ).
thf(1430,plain,
! [SV329: $i,SV148: $i] :
( ( ( member @ SV148 @ plus )
= $false )
| ( ( ~ ( little_set @ SV329 )
| ( member @ ( f45 @ SV148 @ SV329 ) @ natural_numbers )
| ( member @ ( f46 @ SV148 @ SV329 ) @ natural_numbers )
| ( member @ SV148 @ SV329 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1256]) ).
thf(1431,plain,
! [SV330: $i,SV149: $i] :
( ( ( member @ SV149 @ plus )
= $false )
| ( ( ~ ( little_set @ SV330 )
| ( member @ ( f45 @ SV149 @ SV330 ) @ natural_numbers )
| ( member @ ( f47 @ SV149 @ SV330 ) @ natural_numbers )
| ( member @ SV149 @ SV330 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1257]) ).
thf(1432,plain,
! [SV331: $i,SV150: $i] :
( ( ( member @ SV150 @ plus )
= $false )
| ( ( ~ ( little_set @ SV331 )
| ( member @ ( f45 @ SV150 @ SV331 ) @ natural_numbers )
| ( member @ ( f48 @ SV150 @ SV331 ) @ natural_numbers )
| ( member @ SV150 @ SV331 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1258]) ).
thf(1433,plain,
! [SV332: $i,SV151: $i] :
( ( ( member @ SV151 @ plus )
= $false )
| ( ( ~ ( little_set @ SV332 )
| ( member @ ( f45 @ SV151 @ SV332 ) @ natural_numbers )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( f46 @ SV151 @ SV332 ) @ ( f47 @ SV151 @ SV332 ) ) @ ( f48 @ SV151 @ SV332 ) ) @ SV332 )
| ( member @ SV151 @ SV332 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1259]) ).
thf(1434,plain,
! [SV333: $i,SV152: $i] :
( ( ( member @ SV152 @ plus )
= $false )
| ( ( ~ ( little_set @ SV333 )
| ( member @ ( f45 @ SV152 @ SV333 ) @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f46 @ SV152 @ SV333 ) ) @ ( f47 @ SV152 @ SV333 ) ) @ ( successor @ ( f48 @ SV152 @ SV333 ) ) ) @ SV333 )
| ( member @ SV152 @ SV333 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1260]) ).
thf(1435,plain,
! [SV334: $i,SV153: $i] :
( ( ( member @ SV153 @ plus )
= $false )
| ( ( ~ ( little_set @ SV334 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV153 @ SV334 ) ) @ ( f45 @ SV153 @ SV334 ) ) @ SV334 )
| ( member @ ( f46 @ SV153 @ SV334 ) @ natural_numbers )
| ( member @ SV153 @ SV334 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1261]) ).
thf(1436,plain,
! [SV335: $i,SV154: $i] :
( ( ( member @ SV154 @ plus )
= $false )
| ( ( ~ ( little_set @ SV335 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV154 @ SV335 ) ) @ ( f45 @ SV154 @ SV335 ) ) @ SV335 )
| ( member @ ( f47 @ SV154 @ SV335 ) @ natural_numbers )
| ( member @ SV154 @ SV335 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1262]) ).
thf(1437,plain,
! [SV336: $i,SV155: $i] :
( ( ( member @ SV155 @ plus )
= $false )
| ( ( ~ ( little_set @ SV336 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV155 @ SV336 ) ) @ ( f45 @ SV155 @ SV336 ) ) @ SV336 )
| ( member @ ( f48 @ SV155 @ SV336 ) @ natural_numbers )
| ( member @ SV155 @ SV336 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1263]) ).
thf(1438,plain,
! [SV337: $i,SV156: $i] :
( ( ( member @ SV156 @ plus )
= $false )
| ( ( ~ ( little_set @ SV337 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV156 @ SV337 ) ) @ ( f45 @ SV156 @ SV337 ) ) @ SV337 )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( f46 @ SV156 @ SV337 ) @ ( f47 @ SV156 @ SV337 ) ) @ ( f48 @ SV156 @ SV337 ) ) @ SV337 )
| ( member @ SV156 @ SV337 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1264]) ).
thf(1439,plain,
! [SV338: $i,SV157: $i] :
( ( ( member @ SV157 @ plus )
= $false )
| ( ( ~ ( little_set @ SV338 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV157 @ SV338 ) ) @ ( f45 @ SV157 @ SV338 ) ) @ SV338 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f46 @ SV157 @ SV338 ) ) @ ( f47 @ SV157 @ SV338 ) ) @ ( successor @ ( f48 @ SV157 @ SV338 ) ) ) @ SV338 )
| ( member @ SV157 @ SV338 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1265]) ).
thf(1440,plain,
! [SV158: $i] :
( ( ( little_set @ SV158 )
= $false )
| ( ( little_set @ ( f49 @ SV158 ) )
= $true )
| ( ( member @ SV158 @ plus )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1266]) ).
thf(1441,plain,
! [SV339: $i,SV159: $i] :
( ( ( ~ ( little_set @ SV159 ) )
= $true )
| ( ( ~ ( member @ SV339 @ natural_numbers )
| ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ SV339 ) @ SV339 ) @ ( f49 @ SV159 ) ) )
= $true )
| ( ( member @ SV159 @ plus )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1267]) ).
thf(1442,plain,
! [SV458: $i,SV422: $i,SV340: $i,SV160: $i] :
( ( ( member @ SV160 @ plus )
| ~ ( little_set @ SV160 )
| ~ ( member @ SV340 @ natural_numbers )
| ~ ( member @ SV422 @ natural_numbers )
| ~ ( member @ SV458 @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV340 @ SV422 ) @ SV458 ) @ ( f49 @ SV160 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ SV340 ) @ SV422 ) @ ( successor @ SV458 ) ) @ ( f49 @ SV160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1268]) ).
thf(1443,plain,
! [SV341: $i,SV162: $i] :
( ( ( member @ SV162 @ times )
= $false )
| ( ( ~ ( little_set @ SV341 )
| ( member @ ( f50 @ SV162 @ SV341 ) @ natural_numbers )
| ( member @ ( f51 @ SV162 @ SV341 ) @ natural_numbers )
| ( member @ SV162 @ SV341 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1270]) ).
thf(1444,plain,
! [SV342: $i,SV163: $i] :
( ( ( member @ SV163 @ times )
= $false )
| ( ( ~ ( little_set @ SV342 )
| ( member @ ( f50 @ SV163 @ SV342 ) @ natural_numbers )
| ( member @ ( f52 @ SV163 @ SV342 ) @ natural_numbers )
| ( member @ SV163 @ SV342 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1271]) ).
thf(1445,plain,
! [SV343: $i,SV164: $i] :
( ( ( member @ SV164 @ times )
= $false )
| ( ( ~ ( little_set @ SV343 )
| ( member @ ( f50 @ SV164 @ SV343 ) @ natural_numbers )
| ( member @ ( f53 @ SV164 @ SV343 ) @ natural_numbers )
| ( member @ SV164 @ SV343 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1272]) ).
thf(1446,plain,
! [SV344: $i,SV165: $i] :
( ( ( member @ SV165 @ times )
= $false )
| ( ( ~ ( little_set @ SV344 )
| ( member @ ( f50 @ SV165 @ SV344 ) @ natural_numbers )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( f51 @ SV165 @ SV344 ) @ ( f52 @ SV165 @ SV344 ) ) @ ( f53 @ SV165 @ SV344 ) ) @ SV344 )
| ( member @ SV165 @ SV344 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1273]) ).
thf(1447,plain,
! [SV345: $i,SV166: $i] :
( ( ( member @ SV166 @ times )
= $false )
| ( ( ~ ( little_set @ SV345 )
| ( member @ ( f50 @ SV166 @ SV345 ) @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f51 @ SV166 @ SV345 ) ) @ ( f52 @ SV166 @ SV345 ) ) @ ( apply_to_two_arguments @ plus @ ( f53 @ SV166 @ SV345 ) @ ( f52 @ SV166 @ SV345 ) ) ) @ SV345 )
| ( member @ SV166 @ SV345 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1274]) ).
thf(1448,plain,
! [SV346: $i,SV167: $i] :
( ( ( member @ SV167 @ times )
= $false )
| ( ( ~ ( little_set @ SV346 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV167 @ SV346 ) ) @ empty_set ) @ SV346 )
| ( member @ ( f51 @ SV167 @ SV346 ) @ natural_numbers )
| ( member @ SV167 @ SV346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1275]) ).
thf(1449,plain,
! [SV347: $i,SV168: $i] :
( ( ( member @ SV168 @ times )
= $false )
| ( ( ~ ( little_set @ SV347 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV168 @ SV347 ) ) @ empty_set ) @ SV347 )
| ( member @ ( f52 @ SV168 @ SV347 ) @ natural_numbers )
| ( member @ SV168 @ SV347 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1276]) ).
thf(1450,plain,
! [SV348: $i,SV169: $i] :
( ( ( member @ SV169 @ times )
= $false )
| ( ( ~ ( little_set @ SV348 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV169 @ SV348 ) ) @ empty_set ) @ SV348 )
| ( member @ ( f53 @ SV169 @ SV348 ) @ natural_numbers )
| ( member @ SV169 @ SV348 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1277]) ).
thf(1451,plain,
! [SV349: $i,SV170: $i] :
( ( ( member @ SV170 @ times )
= $false )
| ( ( ~ ( little_set @ SV349 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV170 @ SV349 ) ) @ empty_set ) @ SV349 )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( f51 @ SV170 @ SV349 ) @ ( f52 @ SV170 @ SV349 ) ) @ ( f53 @ SV170 @ SV349 ) ) @ SV349 )
| ( member @ SV170 @ SV349 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1278]) ).
thf(1452,plain,
! [SV350: $i,SV171: $i] :
( ( ( member @ SV171 @ times )
= $false )
| ( ( ~ ( little_set @ SV350 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV171 @ SV350 ) ) @ empty_set ) @ SV350 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f51 @ SV171 @ SV350 ) ) @ ( f52 @ SV171 @ SV350 ) ) @ ( apply_to_two_arguments @ plus @ ( f53 @ SV171 @ SV350 ) @ ( f52 @ SV171 @ SV350 ) ) ) @ SV350 )
| ( member @ SV171 @ SV350 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1279]) ).
thf(1453,plain,
! [SV172: $i] :
( ( ( little_set @ SV172 )
= $false )
| ( ( little_set @ ( f54 @ SV172 ) )
= $true )
| ( ( member @ SV172 @ times )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1280]) ).
thf(1454,plain,
! [SV351: $i,SV173: $i] :
( ( ( ~ ( little_set @ SV173 ) )
= $true )
| ( ( ~ ( member @ SV351 @ natural_numbers )
| ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ SV351 ) @ empty_set ) @ ( f54 @ SV173 ) ) )
= $true )
| ( ( member @ SV173 @ times )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1281]) ).
thf(1455,plain,
! [SV459: $i,SV423: $i,SV352: $i,SV174: $i] :
( ( ( member @ SV174 @ times )
| ~ ( little_set @ SV174 )
| ~ ( member @ SV352 @ natural_numbers )
| ~ ( member @ SV423 @ natural_numbers )
| ~ ( member @ SV459 @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV352 @ SV423 ) @ SV459 ) @ ( f54 @ SV174 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ SV352 ) @ SV423 ) @ ( apply_to_two_arguments @ plus @ SV459 @ SV423 ) ) @ ( f54 @ SV174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1282]) ).
thf(1456,plain,
! [SV177: $i] :
( ( ( member @ SV177 @ natural_numbers )
= $false )
| ( ( ( SV177 = empty_set )
| ( SV177
= ( successor @ empty_set ) )
| ( member @ ( f55 @ SV177 ) @ natural_numbers ) )
= $true )
| ( ( member @ SV177 @ prime_numbers )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1285]) ).
thf(1457,plain,
! [SV178: $i] :
( ( ( member @ SV178 @ natural_numbers )
= $false )
| ( ( ( SV178 = empty_set )
| ( SV178
= ( successor @ empty_set ) )
| ( member @ ( f56 @ SV178 ) @ natural_numbers ) )
= $true )
| ( ( member @ SV178 @ prime_numbers )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1286]) ).
thf(1458,plain,
! [SV179: $i] :
( ( ( member @ SV179 @ natural_numbers )
= $false )
| ( ( ( SV179 = empty_set )
| ( SV179
= ( successor @ empty_set ) )
| ( ( apply_to_two_arguments @ times @ ( f55 @ SV179 ) @ ( f56 @ SV179 ) )
= SV179 ) )
= $true )
| ( ( member @ SV179 @ prime_numbers )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1287]) ).
thf(1459,plain,
! [SV180: $i] :
( ( ( member @ SV180 @ natural_numbers )
= $false )
| ( ( ( SV180 = empty_set )
| ( SV180
= ( successor @ empty_set ) )
| ~ ( member @ ( f55 @ SV180 ) @ ( non_ordered_pair @ ( successor @ empty_set ) @ SV180 ) ) )
= $true )
| ( ( member @ SV180 @ prime_numbers )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1288]) ).
thf(1460,plain,
! [SV187: $i] :
( ( ( member @ SV187 @ prime_numbers )
= $false )
| ( ( ~ ( member @ ( successor @ ( successor @ SV187 ) ) @ prime_numbers ) )
= $true )
| ( ( member @ SV187 @ twin_prime_numbers )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1295]) ).
thf(1461,plain,
! [SV460: $i,SV424: $i,SV353: $i,SV191: $i] :
( ( ( member @ SV191 @ ( second @ SV353 ) )
| ~ ( little_set @ SV424 )
| ~ ( little_set @ SV460 )
| ( SV353
!= ( ordered_pair @ SV424 @ SV460 ) )
| ~ ( member @ SV191 @ SV460 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1299]) ).
thf(1462,plain,
! [SV461: $i,SV425: $i,SV354: $i,SV192: $i] :
( ( ( inverse @ SV192 @ SV354 @ SV425 @ SV461 )
| ~ ( maps @ SV461 @ SV192 @ SV192 )
| ( ( apply_to_two_arguments @ SV354 @ ( apply @ SV461 @ ( f38 @ SV192 @ SV354 @ SV425 @ SV461 ) ) @ ( f38 @ SV192 @ SV354 @ SV425 @ SV461 ) )
!= SV425 )
| ( ( apply_to_two_arguments @ SV354 @ ( f38 @ SV192 @ SV354 @ SV425 @ SV461 ) @ ( apply @ SV461 @ ( f38 @ SV192 @ SV354 @ SV425 @ SV461 ) ) )
!= SV425 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1300]) ).
thf(1463,plain,
! [SV426: $i,SV355: $i,SV193: $i] :
( ( ( ~ ( member @ SV193 @ prime_numbers ) )
= $true )
| ( ( ~ ( member @ SV355 @ natural_numbers )
| ~ ( member @ SV426 @ natural_numbers )
| ( ( apply_to_two_arguments @ times @ SV355 @ SV426 )
!= SV193 )
| ( member @ SV355 @ ( non_ordered_pair @ ( successor @ empty_set ) @ SV193 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1301]) ).
thf(1464,plain,
! [SV194: $i] :
( ( ( SV194 = empty_set )
= $false )
| ( ( member @ SV194 @ prime_numbers )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1302]) ).
thf(1465,plain,
! [SV462: $i,SV427: $i,SV356: $i,SV195: $i] :
( ( ! [SY916: $i] :
( ( member @ SV195 @ ( flip_range_of @ SV356 ) )
| ~ ( little_set @ SV195 )
| ~ ( little_set @ SV427 )
| ~ ( little_set @ SV462 )
| ~ ( little_set @ SY916 )
| ( SV195
!= ( ordered_pair @ SV427 @ ( ordered_pair @ SV462 @ SY916 ) ) )
| ~ ( member @ ( ordered_pair @ SV427 @ ( ordered_pair @ SY916 @ SV462 ) ) @ SV356 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1303]) ).
thf(1466,plain,
! [SV428: $i,SV357: $i,SV196: $i] :
( ( ( member @ SV196 @ ( non_ordered_pair @ SV357 @ SV428 ) )
= $true )
| ( ( ~ ( little_set @ SV196 )
| ( SV196 != SV428 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1304]) ).
thf(1467,plain,
! [SV463: $i,SV429: $i,SV358: $i,SV197: $i] :
( ( ( member @ SV197 @ ( first @ SV358 ) )
| ~ ( little_set @ SV429 )
| ~ ( little_set @ SV463 )
| ( SV358
!= ( ordered_pair @ SV429 @ SV463 ) )
| ~ ( member @ SV197 @ SV429 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1305]) ).
thf(1468,plain,
! [SV464: $i,SV430: $i,SV359: $i,SV198: $i] :
( ( ( member @ SV198 @ ( image @ SV359 @ SV430 ) )
| ~ ( little_set @ SV198 )
| ~ ( ordered_pair_predicate @ SV464 )
| ~ ( member @ SV464 @ SV430 )
| ~ ( member @ ( first @ SV464 ) @ SV359 )
| ( ( second @ SV464 )
!= SV198 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1306]) ).
thf(1469,plain,
! [SV465: $i,SV431: $i,SV360: $i,SV199: $i] :
( ( ! [SY917: $i] :
( ( member @ SV199 @ ( rotate_right @ SV360 ) )
| ~ ( little_set @ SV199 )
| ~ ( little_set @ SV431 )
| ~ ( little_set @ SV465 )
| ~ ( little_set @ SY917 )
| ( SV199
!= ( ordered_pair @ SV431 @ ( ordered_pair @ SV465 @ SY917 ) ) )
| ~ ( member @ ( ordered_pair @ SV465 @ ( ordered_pair @ SY917 @ SV431 ) ) @ SV360 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1307]) ).
thf(1470,plain,
! [SV466: $i,SV432: $i,SV361: $i,SV201: $i] :
( ( ! [SY918: $i,SY919: $i] :
( ( member @ SV201 @ ( compose @ SV361 @ SV432 ) )
| ~ ( little_set @ SV201 )
| ~ ( little_set @ SV466 )
| ~ ( little_set @ SY918 )
| ~ ( little_set @ SY919 )
| ( SV201
!= ( ordered_pair @ SV466 @ SY918 ) )
| ~ ( member @ ( ordered_pair @ SV466 @ SY919 ) @ SV361 )
| ~ ( member @ ( ordered_pair @ SY919 @ SY918 ) @ SV432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1309]) ).
thf(1471,plain,
! [SV433: $i,SV362: $i,SV202: $i] :
( ( ( ordered_pair_predicate @ SV202 )
= $true )
| ( ( ~ ( little_set @ SV362 )
| ~ ( little_set @ SV433 )
| ( SV202
!= ( ordered_pair @ SV362 @ SV433 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1310]) ).
thf(1472,plain,
! [SV434: $i,SV363: $i,SV203: $i] :
( ( ( member @ SV203 @ ( non_ordered_pair @ SV363 @ SV434 ) )
= $true )
| ( ( ~ ( little_set @ SV203 )
| ( SV203 != SV363 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1311]) ).
thf(1473,plain,
! [SV364: $i,SV204: $i] :
( ( ( ~ ( member @ SV204 @ natural_numbers ) )
= $true )
| ( ( ~ ( member @ SV364 @ natural_numbers )
| ( ( apply_to_two_arguments @ plus @ SV364 @ SV364 )
!= SV204 ) )
= $true )
| ( ( member @ SV204 @ even_numbers )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1312]) ).
thf(1474,plain,
! [SV365: $i,SV205: $i] :
( ( ( proper_subset @ SV205 @ SV365 )
= $false )
| ( ( SV205 != SV365 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1313]) ).
thf(1475,plain,
! [SV467: $i,SV435: $i,SV366: $i,SV206: $i] :
( ( ! [SY920: $i] :
( ( homomorphism @ SV206 @ SV366 @ SV435 @ SV467 @ SY920 )
| ~ ( closed @ SV366 @ SV435 )
| ~ ( closed @ SV467 @ SY920 )
| ~ ( maps @ SV206 @ SV366 @ SV467 )
| ( ( apply @ SV206 @ ( apply_to_two_arguments @ SV435 @ ( f32 @ SV206 @ SV366 @ SV435 @ SV467 @ SY920 ) @ ( f33 @ SV206 @ SV366 @ SV435 @ SV467 @ SY920 ) ) )
!= ( apply_to_two_arguments @ SY920 @ ( apply @ SV206 @ ( f32 @ SV206 @ SV366 @ SV435 @ SV467 @ SY920 ) ) @ ( apply @ SV206 @ ( f33 @ SV206 @ SV366 @ SV435 @ SV467 @ SY920 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1314]) ).
thf(1476,plain,
! [SV436: $i,SV367: $i,SV207: $i] :
( ( ( finite @ SV207 )
= $true )
| ( ( ~ ( member @ SV367 @ natural_numbers )
| ~ ( maps @ SV436 @ SV367 @ SV207 )
| ( ( range_of @ SV436 )
!= SV207 )
| ~ ( one_to_one_function @ SV436 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1315]) ).
thf(1477,plain,
! [SV437: $i,SV368: $i,SV208: $i] :
( ( ( maps @ SV208 @ SV368 @ SV437 )
= $true )
| ( ( ~ ( function @ SV208 )
| ( ( domain_of @ SV208 )
!= SV368 )
| ~ ( subset @ ( range_of @ SV208 ) @ SV437 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1316]) ).
thf(1478,plain,
! [SV209: $i] :
( ( ( SV209
= ( successor @ empty_set ) )
= $false )
| ( ( member @ SV209 @ prime_numbers )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1317]) ).
thf(1479,plain,
! [SV210: $i,SV369: $i] :
( ( ( ( apply_to_two_arguments @ SV369 @ ( f41 @ SV210 @ SV369 ) @ ( f42 @ SV210 @ SV369 ) )
= ( apply_to_two_arguments @ SV369 @ ( f42 @ SV210 @ SV369 ) @ ( f41 @ SV210 @ SV369 ) ) )
= $false )
| ( ( commutes @ SV210 @ SV369 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1318]) ).
thf(1480,plain,
! [SV211: $i] :
( ( ( little_set @ SV211 )
= $false )
| ( ( ~ ( ordered_pair_predicate @ SV211 )
| ( ( first @ SV211 )
!= ( second @ SV211 ) ) )
= $true )
| ( ( member @ SV211 @ identity_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1319]) ).
thf(1481,plain,
! [SV438: $i,SV370: $i,SV212: $i] :
( ( ( member @ SV212 @ ( range_of @ SV370 ) )
= $true )
| ( ( ~ ( little_set @ SV212 )
| ~ ( ordered_pair_predicate @ SV438 )
| ~ ( member @ SV438 @ SV370 )
| ( SV212
!= ( second @ SV438 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1320]) ).
thf(1482,plain,
! [SV213: $i,SV371: $i] :
( ( ( ( apply_to_two_arguments @ SV371 @ ( apply_to_two_arguments @ SV371 @ ( f34 @ SV213 @ SV371 ) @ ( f35 @ SV213 @ SV371 ) ) @ ( f36 @ SV213 @ SV371 ) )
= ( apply_to_two_arguments @ SV371 @ ( f34 @ SV213 @ SV371 ) @ ( apply_to_two_arguments @ SV371 @ ( f35 @ SV213 @ SV371 ) @ ( f36 @ SV213 @ SV371 ) ) ) )
= $false )
| ( ( associative @ SV213 @ SV371 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1321]) ).
thf(1483,plain,
! [SV439: $i,SV372: $i,SV214: $i] :
( ( ( identity @ SV214 @ SV372 @ SV439 )
= $true )
| ( ( ~ ( member @ SV439 @ SV214 )
| ( ( apply_to_two_arguments @ SV372 @ SV439 @ ( f37 @ SV214 @ SV372 @ SV439 ) )
!= ( f37 @ SV214 @ SV372 @ SV439 ) )
| ( ( apply_to_two_arguments @ SV372 @ ( f37 @ SV214 @ SV372 @ SV439 ) @ SV439 )
!= ( f37 @ SV214 @ SV372 @ SV439 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1322]) ).
thf(1484,plain,
! [SV440: $i,SV373: $i,SV215: $i] :
( ( ( member @ SV215 @ ( domain_of @ SV373 ) )
= $true )
| ( ( ~ ( little_set @ SV215 )
| ~ ( ordered_pair_predicate @ SV440 )
| ~ ( member @ SV440 @ SV373 )
| ( SV215
!= ( first @ SV440 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1323]) ).
thf(1485,plain,
! [SV468: $i,SV441: $i,SV374: $i,SV216: $i] :
( ( ( member @ SV216 @ ( apply @ SV374 @ SV441 ) )
| ~ ( ordered_pair_predicate @ SV468 )
| ~ ( member @ SV468 @ SV374 )
| ( ( first @ SV468 )
!= SV441 )
| ~ ( member @ SV216 @ ( second @ SV468 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1324]) ).
thf(1486,plain,
! [SV220: $i,SV4: $i] :
( ( ( ~ ( member @ ( f1 @ SV4 @ SV220 ) @ SV220 ) )
= $true )
| ( ( SV4 = SV220 )
= $true )
| ( ( member @ ( f1 @ SV4 @ SV220 ) @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1327]) ).
thf(1487,plain,
! [SV375: $i,SV221: $i,SV5: $i] :
( ( ( member @ SV5 @ ( non_ordered_pair @ SV221 @ SV375 ) )
= $false )
| ( ( ( SV5 = SV221 )
| ( SV5 = SV375 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1328]) ).
thf(1488,plain,
! [SV22: $i] :
( ( ( ~ ( ordered_pair_predicate @ SV22 ) )
= $true )
| ( ( ~ ( member @ ( first @ SV22 ) @ ( second @ SV22 ) ) )
= $true )
| ( ( little_set @ SV22 )
= $false )
| ( ( member @ SV22 @ estin )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1337]) ).
thf(1489,plain,
! [SV376: $i,SV232: $i,SV23: $i] :
( ( ( member @ SV23 @ ( intersection @ SV232 @ SV376 ) )
= $false )
| ( ( member @ SV23 @ SV232 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1338]) ).
thf(1490,plain,
! [SV377: $i,SV233: $i,SV24: $i] :
( ( ( member @ SV24 @ ( intersection @ SV233 @ SV377 ) )
= $false )
| ( ( member @ SV24 @ SV377 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1339]) ).
thf(1491,plain,
! [SV378: $i,SV234: $i,SV25: $i] :
( ( ( ~ ( member @ SV25 @ SV234 ) )
= $true )
| ( ( ~ ( member @ SV25 @ SV378 ) )
= $true )
| ( ( member @ SV25 @ ( intersection @ SV234 @ SV378 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1340]) ).
thf(1492,plain,
! [SV235: $i,SV26: $i] :
( ( ( member @ SV26 @ SV235 )
= $false )
| ( ( member @ SV26 @ ( complement @ SV235 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1341]) ).
thf(1493,plain,
! [SV236: $i,SV27: $i] :
( ( ( little_set @ SV27 )
= $false )
| ( ( member @ SV27 @ SV236 )
= $true )
| ( ( member @ SV27 @ ( complement @ SV236 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1342]) ).
thf(1494,plain,
! [SV379: $i,SV241: $i,SV32: $i] :
( ( ( member @ SV32 @ ( cross_product @ SV241 @ SV379 ) )
= $false )
| ( ( ordered_pair_predicate @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1346]) ).
thf(1495,plain,
! [SV380: $i,SV242: $i,SV33: $i] :
( ( ( member @ SV33 @ ( cross_product @ SV242 @ SV380 ) )
= $false )
| ( ( member @ ( first @ SV33 ) @ SV242 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1347]) ).
thf(1496,plain,
! [SV381: $i,SV243: $i,SV34: $i] :
( ( ( member @ SV34 @ ( cross_product @ SV243 @ SV381 ) )
= $false )
| ( ( member @ ( second @ SV34 ) @ SV381 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1348]) ).
thf(1497,plain,
! [SV382: $i,SV244: $i,SV35: $i] :
( ( ( ~ ( little_set @ SV35 ) )
= $true )
| ( ( ~ ( ordered_pair_predicate @ SV35 )
| ~ ( member @ ( first @ SV35 ) @ SV244 )
| ~ ( member @ ( second @ SV35 ) @ SV382 ) )
= $true )
| ( ( member @ SV35 @ ( cross_product @ SV244 @ SV382 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1349]) ).
thf(1498,plain,
! [SV247: $i,SV38: $i] :
( ( ( little_set @ SV38 )
= $false )
| ( ( ~ ( ordered_pair_predicate @ SV38 )
| ~ ( member @ ( ordered_pair @ ( second @ SV38 ) @ ( first @ SV38 ) ) @ SV247 ) )
= $true )
| ( ( member @ SV38 @ ( converse @ SV247 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1352]) ).
thf(1499,plain,
! [SV55: $i,SV260: $i,SV383: $i] :
( ( ( ~ ( member @ SV383 @ SV260 ) )
= $true )
| ( ( ~ ( member @ SV55 @ SV383 ) )
= $true )
| ( ( member @ SV55 @ ( sigma @ SV260 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1365]) ).
thf(1500,plain,
! [SV384: $i,SV261: $i,SV57: $i] :
( ( ( subset @ SV57 @ SV261 )
= $false )
| ( ( ~ ( member @ SV384 @ SV57 )
| ( member @ SV384 @ SV261 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1366]) ).
thf(1501,plain,
! [SV265: $i,SV61: $i] :
( ( ( subset @ SV61 @ SV265 )
= $false )
| ( ( SV61 = SV265 )
= $true )
| ( ( proper_subset @ SV61 @ SV265 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1369]) ).
thf(1502,plain,
! [SV267: $i,SV63: $i] :
( ( ( little_set @ SV63 )
= $false )
| ( ( ~ ( subset @ SV63 @ SV267 ) )
= $true )
| ( ( member @ SV63 @ ( powerset @ SV267 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1371]) ).
thf(1503,plain,
! [SV65: $i,SV268: $i] :
( ( ( ~ ( member @ SV268 @ SV65 ) )
= $true )
| ( ( ordered_pair_predicate @ SV268 )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1372]) ).
thf(1504,plain,
! [SV442: $i,SV385: $i,SV269: $i,SV68: $i] :
( ( ( ~ ( single_valued_set @ SV68 ) )
= $true )
| ( ( ~ ( little_set @ SV269 )
| ~ ( little_set @ SV385 )
| ~ ( little_set @ SV442 )
| ~ ( member @ ( ordered_pair @ SV269 @ SV385 ) @ SV68 )
| ~ ( member @ ( ordered_pair @ SV269 @ SV442 ) @ SV68 )
| ( SV385 = SV442 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1373]) ).
thf(1505,plain,
! [SV76: $i] :
( ( ( single_valued_set @ SV76 )
= $false )
| ( ( relation @ SV76 )
= $false )
| ( ( function @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1374]) ).
thf(1506,plain,
! [SV386: $i,SV270: $i,SV77: $i] :
( ( ( member @ SV77 @ ( image @ SV270 @ SV386 ) )
= $false )
| ( ( ordered_pair_predicate @ ( f22 @ SV77 @ SV270 @ SV386 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1375]) ).
thf(1507,plain,
! [SV387: $i,SV271: $i,SV78: $i] :
( ( ( member @ SV78 @ ( image @ SV271 @ SV387 ) )
= $false )
| ( ( member @ ( f22 @ SV78 @ SV271 @ SV387 ) @ SV387 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1376]) ).
thf(1508,plain,
! [SV388: $i,SV272: $i,SV79: $i] :
( ( ( member @ SV79 @ ( image @ SV272 @ SV388 ) )
= $false )
| ( ( member @ ( first @ ( f22 @ SV79 @ SV272 @ SV388 ) ) @ SV272 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1377]) ).
thf(1509,plain,
! [SV389: $i,SV273: $i,SV80: $i] :
( ( ( member @ SV80 @ ( image @ SV273 @ SV389 ) )
= $false )
| ( ( ( second @ ( f22 @ SV80 @ SV273 @ SV389 ) )
= SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1378]) ).
thf(1510,plain,
! [SV81: $i,SV274: $i] :
( ( ( ~ ( function @ SV274 ) )
= $true )
| ( ( little_set @ ( image @ SV81 @ SV274 ) )
= $true )
| ( ( little_set @ SV81 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1379]) ).
thf(1511,plain,
! [SV390: $i,SV275: $i,SV82: $i] :
( ( ( disjoint @ SV82 @ SV275 )
= $false )
| ( ( ~ ( member @ SV390 @ SV82 )
| ~ ( member @ SV390 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1380]) ).
thf(1512,plain,
! [SV97: $i] :
( ( ( function @ ( converse @ SV97 ) )
= $false )
| ( ( function @ SV97 )
= $false )
| ( ( one_to_one_function @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1386]) ).
thf(1513,plain,
! [SV391: $i,SV282: $i,SV98: $i] :
( ( ( member @ SV98 @ ( apply @ SV282 @ SV391 ) )
= $false )
| ( ( ordered_pair_predicate @ ( f28 @ SV98 @ SV282 @ SV391 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1387]) ).
thf(1514,plain,
! [SV392: $i,SV283: $i,SV99: $i] :
( ( ( member @ SV99 @ ( apply @ SV283 @ SV392 ) )
= $false )
| ( ( member @ ( f28 @ SV99 @ SV283 @ SV392 ) @ SV283 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1388]) ).
thf(1515,plain,
! [SV393: $i,SV284: $i,SV100: $i] :
( ( ( member @ SV100 @ ( apply @ SV284 @ SV393 ) )
= $false )
| ( ( ( first @ ( f28 @ SV100 @ SV284 @ SV393 ) )
= SV393 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1389]) ).
thf(1516,plain,
! [SV394: $i,SV285: $i,SV101: $i] :
( ( ( member @ SV101 @ ( apply @ SV285 @ SV394 ) )
= $false )
| ( ( member @ SV101 @ ( second @ ( f28 @ SV101 @ SV285 @ SV394 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1390]) ).
thf(1517,plain,
! [SV396: $i,SV287: $i,SV103: $i] :
( ( ( maps @ SV103 @ SV287 @ SV396 )
= $false )
| ( ( function @ SV103 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1391]) ).
thf(1518,plain,
! [SV397: $i,SV288: $i,SV104: $i] :
( ( ( maps @ SV104 @ SV288 @ SV397 )
= $false )
| ( ( ( domain_of @ SV104 )
= SV288 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1392]) ).
thf(1519,plain,
! [SV398: $i,SV289: $i,SV105: $i] :
( ( ( maps @ SV105 @ SV289 @ SV398 )
= $false )
| ( ( subset @ ( range_of @ SV105 ) @ SV398 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1393]) ).
thf(1520,plain,
! [SV293: $i,SV109: $i] :
( ( ( little_set @ SV109 )
= $false )
| ( ( ~ ( little_set @ SV293 )
| ~ ( maps @ SV293 @ ( cross_product @ SV109 @ SV109 ) @ SV109 ) )
= $true )
| ( ( closed @ SV109 @ SV293 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1397]) ).
thf(1521,plain,
! [SV399: $i,SV294: $i,SV110: $i] :
( ( ( member @ SV110 @ ( compose @ SV294 @ SV399 ) )
= $false )
| ( ( little_set @ ( f29 @ SV110 @ SV294 @ SV399 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1398]) ).
thf(1522,plain,
! [SV400: $i,SV295: $i,SV111: $i] :
( ( ( member @ SV111 @ ( compose @ SV295 @ SV400 ) )
= $false )
| ( ( little_set @ ( f30 @ SV111 @ SV295 @ SV400 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1399]) ).
thf(1523,plain,
! [SV401: $i,SV296: $i,SV112: $i] :
( ( ( member @ SV112 @ ( compose @ SV296 @ SV401 ) )
= $false )
| ( ( little_set @ ( f31 @ SV112 @ SV296 @ SV401 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1400]) ).
thf(1524,plain,
! [SV402: $i,SV297: $i,SV113: $i] :
( ( ( member @ SV113 @ ( compose @ SV297 @ SV402 ) )
= $false )
| ( ( SV113
= ( ordered_pair @ ( f29 @ SV113 @ SV297 @ SV402 ) @ ( f30 @ SV113 @ SV297 @ SV402 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1401]) ).
thf(1525,plain,
! [SV403: $i,SV298: $i,SV114: $i] :
( ( ( member @ SV114 @ ( compose @ SV298 @ SV403 ) )
= $false )
| ( ( member @ ( ordered_pair @ ( f29 @ SV114 @ SV298 @ SV403 ) @ ( f31 @ SV114 @ SV298 @ SV403 ) ) @ SV298 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1402]) ).
thf(1526,plain,
! [SV404: $i,SV299: $i,SV115: $i] :
( ( ( member @ SV115 @ ( compose @ SV299 @ SV404 ) )
= $false )
| ( ( member @ ( ordered_pair @ ( f31 @ SV115 @ SV299 @ SV404 ) @ ( f30 @ SV115 @ SV299 @ SV404 ) ) @ SV404 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1403]) ).
thf(1527,plain,
! [SV469: $i,SV443: $i,SV405: $i,SV300: $i,SV116: $i] :
( ( ~ ( homomorphism @ SV116 @ SV300 @ SV405 @ SV443 @ SV469 )
| ( closed @ SV300 @ SV405 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1404]) ).
thf(1528,plain,
! [SV470: $i,SV444: $i,SV406: $i,SV301: $i,SV117: $i] :
( ( ~ ( homomorphism @ SV117 @ SV301 @ SV406 @ SV444 @ SV470 )
| ( closed @ SV444 @ SV470 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1405]) ).
thf(1529,plain,
! [SV471: $i,SV445: $i,SV407: $i,SV302: $i,SV118: $i] :
( ( ~ ( homomorphism @ SV118 @ SV302 @ SV407 @ SV445 @ SV471 )
| ( maps @ SV118 @ SV302 @ SV445 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1406]) ).
thf(1530,plain,
! [SV472: $i,SV446: $i,SV408: $i,SV303: $i,SV119: $i] :
( ( ! [SY921: $i,SY922: $i] :
( ~ ( homomorphism @ SV119 @ SV303 @ SV408 @ SV446 @ SV472 )
| ~ ( member @ SY921 @ SV303 )
| ~ ( member @ SY922 @ SV303 )
| ( ( apply @ SV119 @ ( apply_to_two_arguments @ SV408 @ SY921 @ SY922 ) )
= ( apply_to_two_arguments @ SV472 @ ( apply @ SV119 @ SY921 ) @ ( apply @ SV119 @ SY922 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1407]) ).
thf(1531,plain,
! [SV473: $i,SV447: $i,SV409: $i,SV304: $i,SV120: $i] :
( ( ( homomorphism @ SV120 @ SV304 @ SV409 @ SV447 @ SV473 )
| ~ ( closed @ SV304 @ SV409 )
| ~ ( closed @ SV447 @ SV473 )
| ~ ( maps @ SV120 @ SV304 @ SV447 )
| ( member @ ( f32 @ SV120 @ SV304 @ SV409 @ SV447 @ SV473 ) @ SV304 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1408]) ).
thf(1532,plain,
! [SV474: $i,SV448: $i,SV410: $i,SV305: $i,SV121: $i] :
( ( ( homomorphism @ SV121 @ SV305 @ SV410 @ SV448 @ SV474 )
| ~ ( closed @ SV305 @ SV410 )
| ~ ( closed @ SV448 @ SV474 )
| ~ ( maps @ SV121 @ SV305 @ SV448 )
| ( member @ ( f33 @ SV121 @ SV305 @ SV410 @ SV448 @ SV474 ) @ SV305 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1409]) ).
thf(1533,plain,
! [SV475: $i,SV449: $i,SV411: $i,SV306: $i,SV122: $i] :
( ( ~ ( associative @ SV122 @ SV306 )
| ~ ( member @ SV411 @ SV122 )
| ~ ( member @ SV449 @ SV122 )
| ~ ( member @ SV475 @ SV122 )
| ( ( apply_to_two_arguments @ SV306 @ ( apply_to_two_arguments @ SV306 @ SV411 @ SV449 ) @ SV475 )
= ( apply_to_two_arguments @ SV306 @ SV411 @ ( apply_to_two_arguments @ SV306 @ SV449 @ SV475 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1410]) ).
thf(1534,plain,
! [SV412: $i,SV310: $i,SV126: $i] :
( ( ( identity @ SV126 @ SV310 @ SV412 )
= $false )
| ( ( member @ SV412 @ SV126 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1411]) ).
thf(1535,plain,
! [SV450: $i,SV413: $i,SV311: $i,SV127: $i] :
( ( ( ~ ( identity @ SV127 @ SV311 @ SV413 ) )
= $true )
| ( ( ~ ( member @ SV450 @ SV127 )
| ( ( apply_to_two_arguments @ SV311 @ SV413 @ SV450 )
= SV450 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1412]) ).
thf(1536,plain,
! [SV451: $i,SV414: $i,SV312: $i,SV128: $i] :
( ( ( ~ ( identity @ SV128 @ SV312 @ SV414 ) )
= $true )
| ( ( ~ ( member @ SV451 @ SV128 )
| ( ( apply_to_two_arguments @ SV312 @ SV451 @ SV414 )
= SV451 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1413]) ).
thf(1537,plain,
! [SV313: $i,SV129: $i,SV415: $i] :
( ( ( ~ ( member @ SV415 @ SV129 ) )
= $true )
| ( ( member @ ( f37 @ SV129 @ SV313 @ SV415 ) @ SV129 )
= $true )
| ( ( identity @ SV129 @ SV313 @ SV415 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1414]) ).
thf(1538,plain,
! [SV452: $i,SV416: $i,SV314: $i,SV130: $i] :
( ( ( ~ ( inverse @ SV130 @ SV314 @ SV416 @ SV452 ) )
= $true )
| ( ( maps @ SV452 @ SV130 @ SV130 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1415]) ).
thf(1539,plain,
! [SV476: $i,SV453: $i,SV417: $i,SV315: $i,SV131: $i] :
( ( ~ ( inverse @ SV131 @ SV315 @ SV417 @ SV453 )
| ~ ( member @ SV476 @ SV131 )
| ( ( apply_to_two_arguments @ SV315 @ ( apply @ SV453 @ SV476 ) @ SV476 )
= SV417 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1416]) ).
thf(1540,plain,
! [SV477: $i,SV454: $i,SV418: $i,SV316: $i,SV132: $i] :
( ( ~ ( inverse @ SV132 @ SV316 @ SV418 @ SV454 )
| ~ ( member @ SV477 @ SV132 )
| ( ( apply_to_two_arguments @ SV316 @ SV477 @ ( apply @ SV454 @ SV477 ) )
= SV418 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1417]) ).
thf(1541,plain,
! [SV455: $i,SV419: $i,SV317: $i,SV133: $i] :
( ( ( inverse @ SV133 @ SV317 @ SV419 @ SV455 )
= $true )
| ( ( ~ ( maps @ SV455 @ SV133 @ SV133 )
| ( member @ ( f38 @ SV133 @ SV317 @ SV419 @ SV455 ) @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1418]) ).
thf(1542,plain,
! [SV456: $i,SV420: $i,SV322: $i,SV138: $i] :
( ( ( group @ SV138 @ SV322 )
= $true )
| ( ( ~ ( closed @ SV138 @ SV322 )
| ~ ( associative @ SV138 @ SV322 )
| ~ ( identity @ SV138 @ SV322 @ SV420 )
| ~ ( inverse @ SV138 @ SV322 @ SV420 @ SV456 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1423]) ).
thf(1543,plain,
! [SV457: $i,SV421: $i,SV323: $i,SV139: $i] :
( ( ( ~ ( commutes @ SV139 @ SV323 ) )
= $true )
| ( ( ~ ( member @ SV421 @ SV139 )
| ~ ( member @ SV457 @ SV139 )
| ( ( apply_to_two_arguments @ SV323 @ SV421 @ SV457 )
= ( apply_to_two_arguments @ SV323 @ SV457 @ SV421 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1424]) ).
thf(1544,plain,
! [SV142: $i,SV326: $i] :
( ( ( ~ ( little_set @ SV326 ) )
= $true )
| ( ( ~ ( member @ empty_set @ SV326 )
| ( member @ ( f43 @ SV142 @ SV326 ) @ SV326 )
| ( member @ SV142 @ SV326 ) )
= $true )
| ( ( member @ SV142 @ natural_numbers )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1425]) ).
thf(1545,plain,
! [SV143: $i,SV327: $i] :
( ( ( ~ ( little_set @ SV327 ) )
= $true )
| ( ( ~ ( member @ empty_set @ SV327 )
| ~ ( member @ ( successor @ ( f43 @ SV143 @ SV327 ) ) @ SV327 )
| ( member @ SV143 @ SV327 ) )
= $true )
| ( ( member @ SV143 @ natural_numbers )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1426]) ).
thf(1546,plain,
! [SV328: $i,SV146: $i] :
( ( ( little_set @ SV146 )
= $false )
| ( ( ~ ( member @ SV328 @ ( f44 @ SV146 ) )
| ( member @ ( successor @ SV328 ) @ ( f44 @ SV146 ) ) )
= $true )
| ( ( member @ SV146 @ natural_numbers )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1429]) ).
thf(1547,plain,
! [SV148: $i,SV329: $i] :
( ( ( ~ ( little_set @ SV329 ) )
= $true )
| ( ( ( member @ ( f45 @ SV148 @ SV329 ) @ natural_numbers )
| ( member @ ( f46 @ SV148 @ SV329 ) @ natural_numbers )
| ( member @ SV148 @ SV329 ) )
= $true )
| ( ( member @ SV148 @ plus )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1430]) ).
thf(1548,plain,
! [SV149: $i,SV330: $i] :
( ( ( ~ ( little_set @ SV330 ) )
= $true )
| ( ( ( member @ ( f45 @ SV149 @ SV330 ) @ natural_numbers )
| ( member @ ( f47 @ SV149 @ SV330 ) @ natural_numbers )
| ( member @ SV149 @ SV330 ) )
= $true )
| ( ( member @ SV149 @ plus )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1431]) ).
thf(1549,plain,
! [SV150: $i,SV331: $i] :
( ( ( ~ ( little_set @ SV331 ) )
= $true )
| ( ( ( member @ ( f45 @ SV150 @ SV331 ) @ natural_numbers )
| ( member @ ( f48 @ SV150 @ SV331 ) @ natural_numbers )
| ( member @ SV150 @ SV331 ) )
= $true )
| ( ( member @ SV150 @ plus )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1432]) ).
thf(1550,plain,
! [SV151: $i,SV332: $i] :
( ( ( ~ ( little_set @ SV332 ) )
= $true )
| ( ( ( member @ ( f45 @ SV151 @ SV332 ) @ natural_numbers )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( f46 @ SV151 @ SV332 ) @ ( f47 @ SV151 @ SV332 ) ) @ ( f48 @ SV151 @ SV332 ) ) @ SV332 )
| ( member @ SV151 @ SV332 ) )
= $true )
| ( ( member @ SV151 @ plus )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1433]) ).
thf(1551,plain,
! [SV152: $i,SV333: $i] :
( ( ( ~ ( little_set @ SV333 ) )
= $true )
| ( ( ( member @ ( f45 @ SV152 @ SV333 ) @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f46 @ SV152 @ SV333 ) ) @ ( f47 @ SV152 @ SV333 ) ) @ ( successor @ ( f48 @ SV152 @ SV333 ) ) ) @ SV333 )
| ( member @ SV152 @ SV333 ) )
= $true )
| ( ( member @ SV152 @ plus )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1434]) ).
thf(1552,plain,
! [SV153: $i,SV334: $i] :
( ( ( ~ ( little_set @ SV334 ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV153 @ SV334 ) ) @ ( f45 @ SV153 @ SV334 ) ) @ SV334 )
| ( member @ ( f46 @ SV153 @ SV334 ) @ natural_numbers )
| ( member @ SV153 @ SV334 ) )
= $true )
| ( ( member @ SV153 @ plus )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1435]) ).
thf(1553,plain,
! [SV154: $i,SV335: $i] :
( ( ( ~ ( little_set @ SV335 ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV154 @ SV335 ) ) @ ( f45 @ SV154 @ SV335 ) ) @ SV335 )
| ( member @ ( f47 @ SV154 @ SV335 ) @ natural_numbers )
| ( member @ SV154 @ SV335 ) )
= $true )
| ( ( member @ SV154 @ plus )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1436]) ).
thf(1554,plain,
! [SV155: $i,SV336: $i] :
( ( ( ~ ( little_set @ SV336 ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV155 @ SV336 ) ) @ ( f45 @ SV155 @ SV336 ) ) @ SV336 )
| ( member @ ( f48 @ SV155 @ SV336 ) @ natural_numbers )
| ( member @ SV155 @ SV336 ) )
= $true )
| ( ( member @ SV155 @ plus )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1437]) ).
thf(1555,plain,
! [SV156: $i,SV337: $i] :
( ( ( ~ ( little_set @ SV337 ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV156 @ SV337 ) ) @ ( f45 @ SV156 @ SV337 ) ) @ SV337 )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( f46 @ SV156 @ SV337 ) @ ( f47 @ SV156 @ SV337 ) ) @ ( f48 @ SV156 @ SV337 ) ) @ SV337 )
| ( member @ SV156 @ SV337 ) )
= $true )
| ( ( member @ SV156 @ plus )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1438]) ).
thf(1556,plain,
! [SV157: $i,SV338: $i] :
( ( ( ~ ( little_set @ SV338 ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV157 @ SV338 ) ) @ ( f45 @ SV157 @ SV338 ) ) @ SV338 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f46 @ SV157 @ SV338 ) ) @ ( f47 @ SV157 @ SV338 ) ) @ ( successor @ ( f48 @ SV157 @ SV338 ) ) ) @ SV338 )
| ( member @ SV157 @ SV338 ) )
= $true )
| ( ( member @ SV157 @ plus )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1439]) ).
thf(1557,plain,
! [SV339: $i,SV159: $i] :
( ( ( little_set @ SV159 )
= $false )
| ( ( ~ ( member @ SV339 @ natural_numbers )
| ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ SV339 ) @ SV339 ) @ ( f49 @ SV159 ) ) )
= $true )
| ( ( member @ SV159 @ plus )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1441]) ).
thf(1558,plain,
! [SV458: $i,SV422: $i,SV340: $i,SV160: $i] :
( ( ( member @ SV160 @ plus )
= $true )
| ( ( ~ ( little_set @ SV160 )
| ~ ( member @ SV340 @ natural_numbers )
| ~ ( member @ SV422 @ natural_numbers )
| ~ ( member @ SV458 @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV340 @ SV422 ) @ SV458 ) @ ( f49 @ SV160 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ SV340 ) @ SV422 ) @ ( successor @ SV458 ) ) @ ( f49 @ SV160 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1442]) ).
thf(1559,plain,
! [SV162: $i,SV341: $i] :
( ( ( ~ ( little_set @ SV341 ) )
= $true )
| ( ( ( member @ ( f50 @ SV162 @ SV341 ) @ natural_numbers )
| ( member @ ( f51 @ SV162 @ SV341 ) @ natural_numbers )
| ( member @ SV162 @ SV341 ) )
= $true )
| ( ( member @ SV162 @ times )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1443]) ).
thf(1560,plain,
! [SV163: $i,SV342: $i] :
( ( ( ~ ( little_set @ SV342 ) )
= $true )
| ( ( ( member @ ( f50 @ SV163 @ SV342 ) @ natural_numbers )
| ( member @ ( f52 @ SV163 @ SV342 ) @ natural_numbers )
| ( member @ SV163 @ SV342 ) )
= $true )
| ( ( member @ SV163 @ times )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1444]) ).
thf(1561,plain,
! [SV164: $i,SV343: $i] :
( ( ( ~ ( little_set @ SV343 ) )
= $true )
| ( ( ( member @ ( f50 @ SV164 @ SV343 ) @ natural_numbers )
| ( member @ ( f53 @ SV164 @ SV343 ) @ natural_numbers )
| ( member @ SV164 @ SV343 ) )
= $true )
| ( ( member @ SV164 @ times )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1445]) ).
thf(1562,plain,
! [SV165: $i,SV344: $i] :
( ( ( ~ ( little_set @ SV344 ) )
= $true )
| ( ( ( member @ ( f50 @ SV165 @ SV344 ) @ natural_numbers )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( f51 @ SV165 @ SV344 ) @ ( f52 @ SV165 @ SV344 ) ) @ ( f53 @ SV165 @ SV344 ) ) @ SV344 )
| ( member @ SV165 @ SV344 ) )
= $true )
| ( ( member @ SV165 @ times )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1446]) ).
thf(1563,plain,
! [SV166: $i,SV345: $i] :
( ( ( ~ ( little_set @ SV345 ) )
= $true )
| ( ( ( member @ ( f50 @ SV166 @ SV345 ) @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f51 @ SV166 @ SV345 ) ) @ ( f52 @ SV166 @ SV345 ) ) @ ( apply_to_two_arguments @ plus @ ( f53 @ SV166 @ SV345 ) @ ( f52 @ SV166 @ SV345 ) ) ) @ SV345 )
| ( member @ SV166 @ SV345 ) )
= $true )
| ( ( member @ SV166 @ times )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1447]) ).
thf(1564,plain,
! [SV167: $i,SV346: $i] :
( ( ( ~ ( little_set @ SV346 ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV167 @ SV346 ) ) @ empty_set ) @ SV346 )
| ( member @ ( f51 @ SV167 @ SV346 ) @ natural_numbers )
| ( member @ SV167 @ SV346 ) )
= $true )
| ( ( member @ SV167 @ times )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1448]) ).
thf(1565,plain,
! [SV168: $i,SV347: $i] :
( ( ( ~ ( little_set @ SV347 ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV168 @ SV347 ) ) @ empty_set ) @ SV347 )
| ( member @ ( f52 @ SV168 @ SV347 ) @ natural_numbers )
| ( member @ SV168 @ SV347 ) )
= $true )
| ( ( member @ SV168 @ times )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1449]) ).
thf(1566,plain,
! [SV169: $i,SV348: $i] :
( ( ( ~ ( little_set @ SV348 ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV169 @ SV348 ) ) @ empty_set ) @ SV348 )
| ( member @ ( f53 @ SV169 @ SV348 ) @ natural_numbers )
| ( member @ SV169 @ SV348 ) )
= $true )
| ( ( member @ SV169 @ times )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1450]) ).
thf(1567,plain,
! [SV170: $i,SV349: $i] :
( ( ( ~ ( little_set @ SV349 ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV170 @ SV349 ) ) @ empty_set ) @ SV349 )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( f51 @ SV170 @ SV349 ) @ ( f52 @ SV170 @ SV349 ) ) @ ( f53 @ SV170 @ SV349 ) ) @ SV349 )
| ( member @ SV170 @ SV349 ) )
= $true )
| ( ( member @ SV170 @ times )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1451]) ).
thf(1568,plain,
! [SV171: $i,SV350: $i] :
( ( ( ~ ( little_set @ SV350 ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV171 @ SV350 ) ) @ empty_set ) @ SV350 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f51 @ SV171 @ SV350 ) ) @ ( f52 @ SV171 @ SV350 ) ) @ ( apply_to_two_arguments @ plus @ ( f53 @ SV171 @ SV350 ) @ ( f52 @ SV171 @ SV350 ) ) ) @ SV350 )
| ( member @ SV171 @ SV350 ) )
= $true )
| ( ( member @ SV171 @ times )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1452]) ).
thf(1569,plain,
! [SV351: $i,SV173: $i] :
( ( ( little_set @ SV173 )
= $false )
| ( ( ~ ( member @ SV351 @ natural_numbers )
| ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ SV351 ) @ empty_set ) @ ( f54 @ SV173 ) ) )
= $true )
| ( ( member @ SV173 @ times )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1454]) ).
thf(1570,plain,
! [SV459: $i,SV423: $i,SV352: $i,SV174: $i] :
( ( ( member @ SV174 @ times )
= $true )
| ( ( ~ ( little_set @ SV174 )
| ~ ( member @ SV352 @ natural_numbers )
| ~ ( member @ SV423 @ natural_numbers )
| ~ ( member @ SV459 @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV352 @ SV423 ) @ SV459 ) @ ( f54 @ SV174 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ SV352 ) @ SV423 ) @ ( apply_to_two_arguments @ plus @ SV459 @ SV423 ) ) @ ( f54 @ SV174 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1455]) ).
thf(1571,plain,
! [SV177: $i] :
( ( ( SV177 = empty_set )
= $true )
| ( ( ( SV177
= ( successor @ empty_set ) )
| ( member @ ( f55 @ SV177 ) @ natural_numbers ) )
= $true )
| ( ( member @ SV177 @ natural_numbers )
= $false )
| ( ( member @ SV177 @ prime_numbers )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1456]) ).
thf(1572,plain,
! [SV178: $i] :
( ( ( SV178 = empty_set )
= $true )
| ( ( ( SV178
= ( successor @ empty_set ) )
| ( member @ ( f56 @ SV178 ) @ natural_numbers ) )
= $true )
| ( ( member @ SV178 @ natural_numbers )
= $false )
| ( ( member @ SV178 @ prime_numbers )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1457]) ).
thf(1573,plain,
! [SV179: $i] :
( ( ( SV179 = empty_set )
= $true )
| ( ( ( SV179
= ( successor @ empty_set ) )
| ( ( apply_to_two_arguments @ times @ ( f55 @ SV179 ) @ ( f56 @ SV179 ) )
= SV179 ) )
= $true )
| ( ( member @ SV179 @ natural_numbers )
= $false )
| ( ( member @ SV179 @ prime_numbers )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1458]) ).
thf(1574,plain,
! [SV180: $i] :
( ( ( SV180 = empty_set )
= $true )
| ( ( ( SV180
= ( successor @ empty_set ) )
| ~ ( member @ ( f55 @ SV180 ) @ ( non_ordered_pair @ ( successor @ empty_set ) @ SV180 ) ) )
= $true )
| ( ( member @ SV180 @ natural_numbers )
= $false )
| ( ( member @ SV180 @ prime_numbers )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1459]) ).
thf(1575,plain,
! [SV187: $i] :
( ( ( member @ ( successor @ ( successor @ SV187 ) ) @ prime_numbers )
= $false )
| ( ( member @ SV187 @ prime_numbers )
= $false )
| ( ( member @ SV187 @ twin_prime_numbers )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1460]) ).
thf(1576,plain,
! [SV460: $i,SV424: $i,SV353: $i,SV191: $i] :
( ( ( member @ SV191 @ ( second @ SV353 ) )
= $true )
| ( ( ~ ( little_set @ SV424 )
| ~ ( little_set @ SV460 )
| ( SV353
!= ( ordered_pair @ SV424 @ SV460 ) )
| ~ ( member @ SV191 @ SV460 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1461]) ).
thf(1577,plain,
! [SV461: $i,SV425: $i,SV354: $i,SV192: $i] :
( ( ( inverse @ SV192 @ SV354 @ SV425 @ SV461 )
= $true )
| ( ( ~ ( maps @ SV461 @ SV192 @ SV192 )
| ( ( apply_to_two_arguments @ SV354 @ ( apply @ SV461 @ ( f38 @ SV192 @ SV354 @ SV425 @ SV461 ) ) @ ( f38 @ SV192 @ SV354 @ SV425 @ SV461 ) )
!= SV425 )
| ( ( apply_to_two_arguments @ SV354 @ ( f38 @ SV192 @ SV354 @ SV425 @ SV461 ) @ ( apply @ SV461 @ ( f38 @ SV192 @ SV354 @ SV425 @ SV461 ) ) )
!= SV425 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1462]) ).
thf(1578,plain,
! [SV426: $i,SV355: $i,SV193: $i] :
( ( ( member @ SV193 @ prime_numbers )
= $false )
| ( ( ~ ( member @ SV355 @ natural_numbers )
| ~ ( member @ SV426 @ natural_numbers )
| ( ( apply_to_two_arguments @ times @ SV355 @ SV426 )
!= SV193 )
| ( member @ SV355 @ ( non_ordered_pair @ ( successor @ empty_set ) @ SV193 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1463]) ).
thf(1579,plain,
! [SV478: $i,SV462: $i,SV427: $i,SV356: $i,SV195: $i] :
( ( ( member @ SV195 @ ( flip_range_of @ SV356 ) )
| ~ ( little_set @ SV195 )
| ~ ( little_set @ SV427 )
| ~ ( little_set @ SV462 )
| ~ ( little_set @ SV478 )
| ( SV195
!= ( ordered_pair @ SV427 @ ( ordered_pair @ SV462 @ SV478 ) ) )
| ~ ( member @ ( ordered_pair @ SV427 @ ( ordered_pair @ SV478 @ SV462 ) ) @ SV356 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1465]) ).
thf(1580,plain,
! [SV357: $i,SV428: $i,SV196: $i] :
( ( ( ~ ( little_set @ SV196 ) )
= $true )
| ( ( SV196 != SV428 )
= $true )
| ( ( member @ SV196 @ ( non_ordered_pair @ SV357 @ SV428 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1466]) ).
thf(1581,plain,
! [SV463: $i,SV429: $i,SV358: $i,SV197: $i] :
( ( ( member @ SV197 @ ( first @ SV358 ) )
= $true )
| ( ( ~ ( little_set @ SV429 )
| ~ ( little_set @ SV463 )
| ( SV358
!= ( ordered_pair @ SV429 @ SV463 ) )
| ~ ( member @ SV197 @ SV429 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1467]) ).
thf(1582,plain,
! [SV464: $i,SV430: $i,SV359: $i,SV198: $i] :
( ( ( member @ SV198 @ ( image @ SV359 @ SV430 ) )
= $true )
| ( ( ~ ( little_set @ SV198 )
| ~ ( ordered_pair_predicate @ SV464 )
| ~ ( member @ SV464 @ SV430 )
| ~ ( member @ ( first @ SV464 ) @ SV359 )
| ( ( second @ SV464 )
!= SV198 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1468]) ).
thf(1583,plain,
! [SV479: $i,SV465: $i,SV431: $i,SV360: $i,SV199: $i] :
( ( ( member @ SV199 @ ( rotate_right @ SV360 ) )
| ~ ( little_set @ SV199 )
| ~ ( little_set @ SV431 )
| ~ ( little_set @ SV465 )
| ~ ( little_set @ SV479 )
| ( SV199
!= ( ordered_pair @ SV431 @ ( ordered_pair @ SV465 @ SV479 ) ) )
| ~ ( member @ ( ordered_pair @ SV465 @ ( ordered_pair @ SV479 @ SV431 ) ) @ SV360 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1469]) ).
thf(1584,plain,
! [SV480: $i,SV466: $i,SV432: $i,SV361: $i,SV201: $i] :
( ( ! [SY923: $i] :
( ( member @ SV201 @ ( compose @ SV361 @ SV432 ) )
| ~ ( little_set @ SV201 )
| ~ ( little_set @ SV466 )
| ~ ( little_set @ SV480 )
| ~ ( little_set @ SY923 )
| ( SV201
!= ( ordered_pair @ SV466 @ SV480 ) )
| ~ ( member @ ( ordered_pair @ SV466 @ SY923 ) @ SV361 )
| ~ ( member @ ( ordered_pair @ SY923 @ SV480 ) @ SV432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1470]) ).
thf(1585,plain,
! [SV202: $i,SV433: $i,SV362: $i] :
( ( ( ~ ( little_set @ SV362 ) )
= $true )
| ( ( ~ ( little_set @ SV433 )
| ( SV202
!= ( ordered_pair @ SV362 @ SV433 ) ) )
= $true )
| ( ( ordered_pair_predicate @ SV202 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1471]) ).
thf(1586,plain,
! [SV434: $i,SV363: $i,SV203: $i] :
( ( ( ~ ( little_set @ SV203 ) )
= $true )
| ( ( SV203 != SV363 )
= $true )
| ( ( member @ SV203 @ ( non_ordered_pair @ SV363 @ SV434 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1472]) ).
thf(1587,plain,
! [SV364: $i,SV204: $i] :
( ( ( member @ SV204 @ natural_numbers )
= $false )
| ( ( ~ ( member @ SV364 @ natural_numbers )
| ( ( apply_to_two_arguments @ plus @ SV364 @ SV364 )
!= SV204 ) )
= $true )
| ( ( member @ SV204 @ even_numbers )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1473]) ).
thf(1588,plain,
! [SV365: $i,SV205: $i] :
( ( ( SV205 = SV365 )
= $false )
| ( ( proper_subset @ SV205 @ SV365 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1474]) ).
thf(1589,plain,
! [SV481: $i,SV467: $i,SV435: $i,SV366: $i,SV206: $i] :
( ( ( homomorphism @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 )
| ~ ( closed @ SV366 @ SV435 )
| ~ ( closed @ SV467 @ SV481 )
| ~ ( maps @ SV206 @ SV366 @ SV467 )
| ( ( apply @ SV206 @ ( apply_to_two_arguments @ SV435 @ ( f32 @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 ) @ ( f33 @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 ) ) )
!= ( apply_to_two_arguments @ SV481 @ ( apply @ SV206 @ ( f32 @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 ) ) @ ( apply @ SV206 @ ( f33 @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1475]) ).
thf(1590,plain,
! [SV207: $i,SV436: $i,SV367: $i] :
( ( ( ~ ( member @ SV367 @ natural_numbers ) )
= $true )
| ( ( ~ ( maps @ SV436 @ SV367 @ SV207 )
| ( ( range_of @ SV436 )
!= SV207 )
| ~ ( one_to_one_function @ SV436 ) )
= $true )
| ( ( finite @ SV207 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1476]) ).
thf(1591,plain,
! [SV437: $i,SV368: $i,SV208: $i] :
( ( ( ~ ( function @ SV208 ) )
= $true )
| ( ( ( ( domain_of @ SV208 )
!= SV368 )
| ~ ( subset @ ( range_of @ SV208 ) @ SV437 ) )
= $true )
| ( ( maps @ SV208 @ SV368 @ SV437 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1477]) ).
thf(1592,plain,
! [SV211: $i] :
( ( ( ~ ( ordered_pair_predicate @ SV211 ) )
= $true )
| ( ( ( first @ SV211 )
!= ( second @ SV211 ) )
= $true )
| ( ( little_set @ SV211 )
= $false )
| ( ( member @ SV211 @ identity_relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1480]) ).
thf(1593,plain,
! [SV370: $i,SV438: $i,SV212: $i] :
( ( ( ~ ( little_set @ SV212 ) )
= $true )
| ( ( ~ ( ordered_pair_predicate @ SV438 )
| ~ ( member @ SV438 @ SV370 )
| ( SV212
!= ( second @ SV438 ) ) )
= $true )
| ( ( member @ SV212 @ ( range_of @ SV370 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1481]) ).
thf(1594,plain,
! [SV372: $i,SV214: $i,SV439: $i] :
( ( ( ~ ( member @ SV439 @ SV214 ) )
= $true )
| ( ( ( ( apply_to_two_arguments @ SV372 @ SV439 @ ( f37 @ SV214 @ SV372 @ SV439 ) )
!= ( f37 @ SV214 @ SV372 @ SV439 ) )
| ( ( apply_to_two_arguments @ SV372 @ ( f37 @ SV214 @ SV372 @ SV439 ) @ SV439 )
!= ( f37 @ SV214 @ SV372 @ SV439 ) ) )
= $true )
| ( ( identity @ SV214 @ SV372 @ SV439 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1483]) ).
thf(1595,plain,
! [SV373: $i,SV440: $i,SV215: $i] :
( ( ( ~ ( little_set @ SV215 ) )
= $true )
| ( ( ~ ( ordered_pair_predicate @ SV440 )
| ~ ( member @ SV440 @ SV373 )
| ( SV215
!= ( first @ SV440 ) ) )
= $true )
| ( ( member @ SV215 @ ( domain_of @ SV373 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1484]) ).
thf(1596,plain,
! [SV468: $i,SV441: $i,SV374: $i,SV216: $i] :
( ( ( member @ SV216 @ ( apply @ SV374 @ SV441 ) )
= $true )
| ( ( ~ ( ordered_pair_predicate @ SV468 )
| ~ ( member @ SV468 @ SV374 )
| ( ( first @ SV468 )
!= SV441 )
| ~ ( member @ SV216 @ ( second @ SV468 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1485]) ).
thf(1597,plain,
! [SV220: $i,SV4: $i] :
( ( ( member @ ( f1 @ SV4 @ SV220 ) @ SV220 )
= $false )
| ( ( SV4 = SV220 )
= $true )
| ( ( member @ ( f1 @ SV4 @ SV220 ) @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1486]) ).
thf(1598,plain,
! [SV375: $i,SV221: $i,SV5: $i] :
( ( ( SV5 = SV221 )
= $true )
| ( ( SV5 = SV375 )
= $true )
| ( ( member @ SV5 @ ( non_ordered_pair @ SV221 @ SV375 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1487]) ).
thf(1599,plain,
! [SV22: $i] :
( ( ( ordered_pair_predicate @ SV22 )
= $false )
| ( ( ~ ( member @ ( first @ SV22 ) @ ( second @ SV22 ) ) )
= $true )
| ( ( little_set @ SV22 )
= $false )
| ( ( member @ SV22 @ estin )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1488]) ).
thf(1600,plain,
! [SV378: $i,SV234: $i,SV25: $i] :
( ( ( member @ SV25 @ SV234 )
= $false )
| ( ( ~ ( member @ SV25 @ SV378 ) )
= $true )
| ( ( member @ SV25 @ ( intersection @ SV234 @ SV378 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1491]) ).
thf(1601,plain,
! [SV382: $i,SV244: $i,SV35: $i] :
( ( ( little_set @ SV35 )
= $false )
| ( ( ~ ( ordered_pair_predicate @ SV35 )
| ~ ( member @ ( first @ SV35 ) @ SV244 )
| ~ ( member @ ( second @ SV35 ) @ SV382 ) )
= $true )
| ( ( member @ SV35 @ ( cross_product @ SV244 @ SV382 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1497]) ).
thf(1602,plain,
! [SV247: $i,SV38: $i] :
( ( ( ~ ( ordered_pair_predicate @ SV38 ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ ( second @ SV38 ) @ ( first @ SV38 ) ) @ SV247 ) )
= $true )
| ( ( little_set @ SV38 )
= $false )
| ( ( member @ SV38 @ ( converse @ SV247 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1498]) ).
thf(1603,plain,
! [SV55: $i,SV260: $i,SV383: $i] :
( ( ( member @ SV383 @ SV260 )
= $false )
| ( ( ~ ( member @ SV55 @ SV383 ) )
= $true )
| ( ( member @ SV55 @ ( sigma @ SV260 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1499]) ).
thf(1604,plain,
! [SV261: $i,SV57: $i,SV384: $i] :
( ( ( ~ ( member @ SV384 @ SV57 ) )
= $true )
| ( ( member @ SV384 @ SV261 )
= $true )
| ( ( subset @ SV57 @ SV261 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1500]) ).
thf(1605,plain,
! [SV267: $i,SV63: $i] :
( ( ( subset @ SV63 @ SV267 )
= $false )
| ( ( little_set @ SV63 )
= $false )
| ( ( member @ SV63 @ ( powerset @ SV267 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1502]) ).
thf(1606,plain,
! [SV65: $i,SV268: $i] :
( ( ( member @ SV268 @ SV65 )
= $false )
| ( ( ordered_pair_predicate @ SV268 )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1503]) ).
thf(1607,plain,
! [SV442: $i,SV385: $i,SV269: $i,SV68: $i] :
( ( ( single_valued_set @ SV68 )
= $false )
| ( ( ~ ( little_set @ SV269 )
| ~ ( little_set @ SV385 )
| ~ ( little_set @ SV442 )
| ~ ( member @ ( ordered_pair @ SV269 @ SV385 ) @ SV68 )
| ~ ( member @ ( ordered_pair @ SV269 @ SV442 ) @ SV68 )
| ( SV385 = SV442 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1504]) ).
thf(1608,plain,
! [SV81: $i,SV274: $i] :
( ( ( function @ SV274 )
= $false )
| ( ( little_set @ ( image @ SV81 @ SV274 ) )
= $true )
| ( ( little_set @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1510]) ).
thf(1609,plain,
! [SV275: $i,SV82: $i,SV390: $i] :
( ( ( ~ ( member @ SV390 @ SV82 ) )
= $true )
| ( ( ~ ( member @ SV390 @ SV275 ) )
= $true )
| ( ( disjoint @ SV82 @ SV275 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1511]) ).
thf(1610,plain,
! [SV109: $i,SV293: $i] :
( ( ( ~ ( little_set @ SV293 ) )
= $true )
| ( ( ~ ( maps @ SV293 @ ( cross_product @ SV109 @ SV109 ) @ SV109 ) )
= $true )
| ( ( little_set @ SV109 )
= $false )
| ( ( closed @ SV109 @ SV293 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1520]) ).
thf(1611,plain,
! [SV469: $i,SV443: $i,SV405: $i,SV300: $i,SV116: $i] :
( ( ( ~ ( homomorphism @ SV116 @ SV300 @ SV405 @ SV443 @ SV469 ) )
= $true )
| ( ( closed @ SV300 @ SV405 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1527]) ).
thf(1612,plain,
! [SV470: $i,SV444: $i,SV406: $i,SV301: $i,SV117: $i] :
( ( ( ~ ( homomorphism @ SV117 @ SV301 @ SV406 @ SV444 @ SV470 ) )
= $true )
| ( ( closed @ SV444 @ SV470 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1528]) ).
thf(1613,plain,
! [SV471: $i,SV445: $i,SV407: $i,SV302: $i,SV118: $i] :
( ( ( ~ ( homomorphism @ SV118 @ SV302 @ SV407 @ SV445 @ SV471 ) )
= $true )
| ( ( maps @ SV118 @ SV302 @ SV445 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1529]) ).
thf(1614,plain,
! [SV482: $i,SV472: $i,SV446: $i,SV408: $i,SV303: $i,SV119: $i] :
( ( ! [SY924: $i] :
( ~ ( homomorphism @ SV119 @ SV303 @ SV408 @ SV446 @ SV472 )
| ~ ( member @ SV482 @ SV303 )
| ~ ( member @ SY924 @ SV303 )
| ( ( apply @ SV119 @ ( apply_to_two_arguments @ SV408 @ SV482 @ SY924 ) )
= ( apply_to_two_arguments @ SV472 @ ( apply @ SV119 @ SV482 ) @ ( apply @ SV119 @ SY924 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1530]) ).
thf(1615,plain,
! [SV473: $i,SV447: $i,SV409: $i,SV304: $i,SV120: $i] :
( ( ( homomorphism @ SV120 @ SV304 @ SV409 @ SV447 @ SV473 )
= $true )
| ( ( ~ ( closed @ SV304 @ SV409 )
| ~ ( closed @ SV447 @ SV473 )
| ~ ( maps @ SV120 @ SV304 @ SV447 )
| ( member @ ( f32 @ SV120 @ SV304 @ SV409 @ SV447 @ SV473 ) @ SV304 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1531]) ).
thf(1616,plain,
! [SV474: $i,SV448: $i,SV410: $i,SV305: $i,SV121: $i] :
( ( ( homomorphism @ SV121 @ SV305 @ SV410 @ SV448 @ SV474 )
= $true )
| ( ( ~ ( closed @ SV305 @ SV410 )
| ~ ( closed @ SV448 @ SV474 )
| ~ ( maps @ SV121 @ SV305 @ SV448 )
| ( member @ ( f33 @ SV121 @ SV305 @ SV410 @ SV448 @ SV474 ) @ SV305 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1532]) ).
thf(1617,plain,
! [SV475: $i,SV449: $i,SV411: $i,SV306: $i,SV122: $i] :
( ( ( ~ ( associative @ SV122 @ SV306 ) )
= $true )
| ( ( ~ ( member @ SV411 @ SV122 )
| ~ ( member @ SV449 @ SV122 )
| ~ ( member @ SV475 @ SV122 )
| ( ( apply_to_two_arguments @ SV306 @ ( apply_to_two_arguments @ SV306 @ SV411 @ SV449 ) @ SV475 )
= ( apply_to_two_arguments @ SV306 @ SV411 @ ( apply_to_two_arguments @ SV306 @ SV449 @ SV475 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1533]) ).
thf(1618,plain,
! [SV450: $i,SV413: $i,SV311: $i,SV127: $i] :
( ( ( identity @ SV127 @ SV311 @ SV413 )
= $false )
| ( ( ~ ( member @ SV450 @ SV127 )
| ( ( apply_to_two_arguments @ SV311 @ SV413 @ SV450 )
= SV450 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1535]) ).
thf(1619,plain,
! [SV451: $i,SV414: $i,SV312: $i,SV128: $i] :
( ( ( identity @ SV128 @ SV312 @ SV414 )
= $false )
| ( ( ~ ( member @ SV451 @ SV128 )
| ( ( apply_to_two_arguments @ SV312 @ SV451 @ SV414 )
= SV451 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1536]) ).
thf(1620,plain,
! [SV313: $i,SV129: $i,SV415: $i] :
( ( ( member @ SV415 @ SV129 )
= $false )
| ( ( member @ ( f37 @ SV129 @ SV313 @ SV415 ) @ SV129 )
= $true )
| ( ( identity @ SV129 @ SV313 @ SV415 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1537]) ).
thf(1621,plain,
! [SV452: $i,SV416: $i,SV314: $i,SV130: $i] :
( ( ( inverse @ SV130 @ SV314 @ SV416 @ SV452 )
= $false )
| ( ( maps @ SV452 @ SV130 @ SV130 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1538]) ).
thf(1622,plain,
! [SV476: $i,SV453: $i,SV417: $i,SV315: $i,SV131: $i] :
( ( ( ~ ( inverse @ SV131 @ SV315 @ SV417 @ SV453 ) )
= $true )
| ( ( ~ ( member @ SV476 @ SV131 )
| ( ( apply_to_two_arguments @ SV315 @ ( apply @ SV453 @ SV476 ) @ SV476 )
= SV417 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1539]) ).
thf(1623,plain,
! [SV477: $i,SV454: $i,SV418: $i,SV316: $i,SV132: $i] :
( ( ( ~ ( inverse @ SV132 @ SV316 @ SV418 @ SV454 ) )
= $true )
| ( ( ~ ( member @ SV477 @ SV132 )
| ( ( apply_to_two_arguments @ SV316 @ SV477 @ ( apply @ SV454 @ SV477 ) )
= SV418 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1540]) ).
thf(1624,plain,
! [SV419: $i,SV317: $i,SV133: $i,SV455: $i] :
( ( ( ~ ( maps @ SV455 @ SV133 @ SV133 ) )
= $true )
| ( ( member @ ( f38 @ SV133 @ SV317 @ SV419 @ SV455 ) @ SV133 )
= $true )
| ( ( inverse @ SV133 @ SV317 @ SV419 @ SV455 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1541]) ).
thf(1625,plain,
! [SV456: $i,SV420: $i,SV322: $i,SV138: $i] :
( ( ( ~ ( closed @ SV138 @ SV322 ) )
= $true )
| ( ( ~ ( associative @ SV138 @ SV322 )
| ~ ( identity @ SV138 @ SV322 @ SV420 )
| ~ ( inverse @ SV138 @ SV322 @ SV420 @ SV456 ) )
= $true )
| ( ( group @ SV138 @ SV322 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1542]) ).
thf(1626,plain,
! [SV457: $i,SV421: $i,SV323: $i,SV139: $i] :
( ( ( commutes @ SV139 @ SV323 )
= $false )
| ( ( ~ ( member @ SV421 @ SV139 )
| ~ ( member @ SV457 @ SV139 )
| ( ( apply_to_two_arguments @ SV323 @ SV421 @ SV457 )
= ( apply_to_two_arguments @ SV323 @ SV457 @ SV421 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1543]) ).
thf(1627,plain,
! [SV142: $i,SV326: $i] :
( ( ( little_set @ SV326 )
= $false )
| ( ( ~ ( member @ empty_set @ SV326 )
| ( member @ ( f43 @ SV142 @ SV326 ) @ SV326 )
| ( member @ SV142 @ SV326 ) )
= $true )
| ( ( member @ SV142 @ natural_numbers )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1544]) ).
thf(1628,plain,
! [SV143: $i,SV327: $i] :
( ( ( little_set @ SV327 )
= $false )
| ( ( ~ ( member @ empty_set @ SV327 )
| ~ ( member @ ( successor @ ( f43 @ SV143 @ SV327 ) ) @ SV327 )
| ( member @ SV143 @ SV327 ) )
= $true )
| ( ( member @ SV143 @ natural_numbers )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1545]) ).
thf(1629,plain,
! [SV146: $i,SV328: $i] :
( ( ( ~ ( member @ SV328 @ ( f44 @ SV146 ) ) )
= $true )
| ( ( member @ ( successor @ SV328 ) @ ( f44 @ SV146 ) )
= $true )
| ( ( little_set @ SV146 )
= $false )
| ( ( member @ SV146 @ natural_numbers )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1546]) ).
thf(1630,plain,
! [SV148: $i,SV329: $i] :
( ( ( little_set @ SV329 )
= $false )
| ( ( ( member @ ( f45 @ SV148 @ SV329 ) @ natural_numbers )
| ( member @ ( f46 @ SV148 @ SV329 ) @ natural_numbers )
| ( member @ SV148 @ SV329 ) )
= $true )
| ( ( member @ SV148 @ plus )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1547]) ).
thf(1631,plain,
! [SV149: $i,SV330: $i] :
( ( ( little_set @ SV330 )
= $false )
| ( ( ( member @ ( f45 @ SV149 @ SV330 ) @ natural_numbers )
| ( member @ ( f47 @ SV149 @ SV330 ) @ natural_numbers )
| ( member @ SV149 @ SV330 ) )
= $true )
| ( ( member @ SV149 @ plus )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1548]) ).
thf(1632,plain,
! [SV150: $i,SV331: $i] :
( ( ( little_set @ SV331 )
= $false )
| ( ( ( member @ ( f45 @ SV150 @ SV331 ) @ natural_numbers )
| ( member @ ( f48 @ SV150 @ SV331 ) @ natural_numbers )
| ( member @ SV150 @ SV331 ) )
= $true )
| ( ( member @ SV150 @ plus )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1549]) ).
thf(1633,plain,
! [SV151: $i,SV332: $i] :
( ( ( little_set @ SV332 )
= $false )
| ( ( ( member @ ( f45 @ SV151 @ SV332 ) @ natural_numbers )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( f46 @ SV151 @ SV332 ) @ ( f47 @ SV151 @ SV332 ) ) @ ( f48 @ SV151 @ SV332 ) ) @ SV332 )
| ( member @ SV151 @ SV332 ) )
= $true )
| ( ( member @ SV151 @ plus )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1550]) ).
thf(1634,plain,
! [SV152: $i,SV333: $i] :
( ( ( little_set @ SV333 )
= $false )
| ( ( ( member @ ( f45 @ SV152 @ SV333 ) @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f46 @ SV152 @ SV333 ) ) @ ( f47 @ SV152 @ SV333 ) ) @ ( successor @ ( f48 @ SV152 @ SV333 ) ) ) @ SV333 )
| ( member @ SV152 @ SV333 ) )
= $true )
| ( ( member @ SV152 @ plus )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1551]) ).
thf(1635,plain,
! [SV153: $i,SV334: $i] :
( ( ( little_set @ SV334 )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV153 @ SV334 ) ) @ ( f45 @ SV153 @ SV334 ) ) @ SV334 )
| ( member @ ( f46 @ SV153 @ SV334 ) @ natural_numbers )
| ( member @ SV153 @ SV334 ) )
= $true )
| ( ( member @ SV153 @ plus )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1552]) ).
thf(1636,plain,
! [SV154: $i,SV335: $i] :
( ( ( little_set @ SV335 )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV154 @ SV335 ) ) @ ( f45 @ SV154 @ SV335 ) ) @ SV335 )
| ( member @ ( f47 @ SV154 @ SV335 ) @ natural_numbers )
| ( member @ SV154 @ SV335 ) )
= $true )
| ( ( member @ SV154 @ plus )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1553]) ).
thf(1637,plain,
! [SV155: $i,SV336: $i] :
( ( ( little_set @ SV336 )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV155 @ SV336 ) ) @ ( f45 @ SV155 @ SV336 ) ) @ SV336 )
| ( member @ ( f48 @ SV155 @ SV336 ) @ natural_numbers )
| ( member @ SV155 @ SV336 ) )
= $true )
| ( ( member @ SV155 @ plus )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1554]) ).
thf(1638,plain,
! [SV156: $i,SV337: $i] :
( ( ( little_set @ SV337 )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV156 @ SV337 ) ) @ ( f45 @ SV156 @ SV337 ) ) @ SV337 )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( f46 @ SV156 @ SV337 ) @ ( f47 @ SV156 @ SV337 ) ) @ ( f48 @ SV156 @ SV337 ) ) @ SV337 )
| ( member @ SV156 @ SV337 ) )
= $true )
| ( ( member @ SV156 @ plus )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1555]) ).
thf(1639,plain,
! [SV157: $i,SV338: $i] :
( ( ( little_set @ SV338 )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV157 @ SV338 ) ) @ ( f45 @ SV157 @ SV338 ) ) @ SV338 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f46 @ SV157 @ SV338 ) ) @ ( f47 @ SV157 @ SV338 ) ) @ ( successor @ ( f48 @ SV157 @ SV338 ) ) ) @ SV338 )
| ( member @ SV157 @ SV338 ) )
= $true )
| ( ( member @ SV157 @ plus )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1556]) ).
thf(1640,plain,
! [SV159: $i,SV339: $i] :
( ( ( ~ ( member @ SV339 @ natural_numbers ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ SV339 ) @ SV339 ) @ ( f49 @ SV159 ) )
= $true )
| ( ( little_set @ SV159 )
= $false )
| ( ( member @ SV159 @ plus )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1557]) ).
thf(1641,plain,
! [SV458: $i,SV422: $i,SV340: $i,SV160: $i] :
( ( ( ~ ( little_set @ SV160 ) )
= $true )
| ( ( ~ ( member @ SV340 @ natural_numbers )
| ~ ( member @ SV422 @ natural_numbers )
| ~ ( member @ SV458 @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV340 @ SV422 ) @ SV458 ) @ ( f49 @ SV160 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ SV340 ) @ SV422 ) @ ( successor @ SV458 ) ) @ ( f49 @ SV160 ) ) )
= $true )
| ( ( member @ SV160 @ plus )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1558]) ).
thf(1642,plain,
! [SV162: $i,SV341: $i] :
( ( ( little_set @ SV341 )
= $false )
| ( ( ( member @ ( f50 @ SV162 @ SV341 ) @ natural_numbers )
| ( member @ ( f51 @ SV162 @ SV341 ) @ natural_numbers )
| ( member @ SV162 @ SV341 ) )
= $true )
| ( ( member @ SV162 @ times )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1559]) ).
thf(1643,plain,
! [SV163: $i,SV342: $i] :
( ( ( little_set @ SV342 )
= $false )
| ( ( ( member @ ( f50 @ SV163 @ SV342 ) @ natural_numbers )
| ( member @ ( f52 @ SV163 @ SV342 ) @ natural_numbers )
| ( member @ SV163 @ SV342 ) )
= $true )
| ( ( member @ SV163 @ times )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1560]) ).
thf(1644,plain,
! [SV164: $i,SV343: $i] :
( ( ( little_set @ SV343 )
= $false )
| ( ( ( member @ ( f50 @ SV164 @ SV343 ) @ natural_numbers )
| ( member @ ( f53 @ SV164 @ SV343 ) @ natural_numbers )
| ( member @ SV164 @ SV343 ) )
= $true )
| ( ( member @ SV164 @ times )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1561]) ).
thf(1645,plain,
! [SV165: $i,SV344: $i] :
( ( ( little_set @ SV344 )
= $false )
| ( ( ( member @ ( f50 @ SV165 @ SV344 ) @ natural_numbers )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( f51 @ SV165 @ SV344 ) @ ( f52 @ SV165 @ SV344 ) ) @ ( f53 @ SV165 @ SV344 ) ) @ SV344 )
| ( member @ SV165 @ SV344 ) )
= $true )
| ( ( member @ SV165 @ times )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1562]) ).
thf(1646,plain,
! [SV166: $i,SV345: $i] :
( ( ( little_set @ SV345 )
= $false )
| ( ( ( member @ ( f50 @ SV166 @ SV345 ) @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f51 @ SV166 @ SV345 ) ) @ ( f52 @ SV166 @ SV345 ) ) @ ( apply_to_two_arguments @ plus @ ( f53 @ SV166 @ SV345 ) @ ( f52 @ SV166 @ SV345 ) ) ) @ SV345 )
| ( member @ SV166 @ SV345 ) )
= $true )
| ( ( member @ SV166 @ times )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1563]) ).
thf(1647,plain,
! [SV167: $i,SV346: $i] :
( ( ( little_set @ SV346 )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV167 @ SV346 ) ) @ empty_set ) @ SV346 )
| ( member @ ( f51 @ SV167 @ SV346 ) @ natural_numbers )
| ( member @ SV167 @ SV346 ) )
= $true )
| ( ( member @ SV167 @ times )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1564]) ).
thf(1648,plain,
! [SV168: $i,SV347: $i] :
( ( ( little_set @ SV347 )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV168 @ SV347 ) ) @ empty_set ) @ SV347 )
| ( member @ ( f52 @ SV168 @ SV347 ) @ natural_numbers )
| ( member @ SV168 @ SV347 ) )
= $true )
| ( ( member @ SV168 @ times )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1565]) ).
thf(1649,plain,
! [SV169: $i,SV348: $i] :
( ( ( little_set @ SV348 )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV169 @ SV348 ) ) @ empty_set ) @ SV348 )
| ( member @ ( f53 @ SV169 @ SV348 ) @ natural_numbers )
| ( member @ SV169 @ SV348 ) )
= $true )
| ( ( member @ SV169 @ times )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1566]) ).
thf(1650,plain,
! [SV170: $i,SV349: $i] :
( ( ( little_set @ SV349 )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV170 @ SV349 ) ) @ empty_set ) @ SV349 )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( f51 @ SV170 @ SV349 ) @ ( f52 @ SV170 @ SV349 ) ) @ ( f53 @ SV170 @ SV349 ) ) @ SV349 )
| ( member @ SV170 @ SV349 ) )
= $true )
| ( ( member @ SV170 @ times )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1567]) ).
thf(1651,plain,
! [SV171: $i,SV350: $i] :
( ( ( little_set @ SV350 )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV171 @ SV350 ) ) @ empty_set ) @ SV350 )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f51 @ SV171 @ SV350 ) ) @ ( f52 @ SV171 @ SV350 ) ) @ ( apply_to_two_arguments @ plus @ ( f53 @ SV171 @ SV350 ) @ ( f52 @ SV171 @ SV350 ) ) ) @ SV350 )
| ( member @ SV171 @ SV350 ) )
= $true )
| ( ( member @ SV171 @ times )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1568]) ).
thf(1652,plain,
! [SV173: $i,SV351: $i] :
( ( ( ~ ( member @ SV351 @ natural_numbers ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ SV351 ) @ empty_set ) @ ( f54 @ SV173 ) )
= $true )
| ( ( little_set @ SV173 )
= $false )
| ( ( member @ SV173 @ times )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1569]) ).
thf(1653,plain,
! [SV459: $i,SV423: $i,SV352: $i,SV174: $i] :
( ( ( ~ ( little_set @ SV174 ) )
= $true )
| ( ( ~ ( member @ SV352 @ natural_numbers )
| ~ ( member @ SV423 @ natural_numbers )
| ~ ( member @ SV459 @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV352 @ SV423 ) @ SV459 ) @ ( f54 @ SV174 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ SV352 ) @ SV423 ) @ ( apply_to_two_arguments @ plus @ SV459 @ SV423 ) ) @ ( f54 @ SV174 ) ) )
= $true )
| ( ( member @ SV174 @ times )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1570]) ).
thf(1654,plain,
! [SV177: $i] :
( ( ( SV177
= ( successor @ empty_set ) )
= $true )
| ( ( member @ ( f55 @ SV177 ) @ natural_numbers )
= $true )
| ( ( SV177 = empty_set )
= $true )
| ( ( member @ SV177 @ natural_numbers )
= $false )
| ( ( member @ SV177 @ prime_numbers )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1571]) ).
thf(1655,plain,
! [SV178: $i] :
( ( ( SV178
= ( successor @ empty_set ) )
= $true )
| ( ( member @ ( f56 @ SV178 ) @ natural_numbers )
= $true )
| ( ( SV178 = empty_set )
= $true )
| ( ( member @ SV178 @ natural_numbers )
= $false )
| ( ( member @ SV178 @ prime_numbers )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1572]) ).
thf(1656,plain,
! [SV179: $i] :
( ( ( SV179
= ( successor @ empty_set ) )
= $true )
| ( ( ( apply_to_two_arguments @ times @ ( f55 @ SV179 ) @ ( f56 @ SV179 ) )
= SV179 )
= $true )
| ( ( SV179 = empty_set )
= $true )
| ( ( member @ SV179 @ natural_numbers )
= $false )
| ( ( member @ SV179 @ prime_numbers )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1573]) ).
thf(1657,plain,
! [SV180: $i] :
( ( ( SV180
= ( successor @ empty_set ) )
= $true )
| ( ( ~ ( member @ ( f55 @ SV180 ) @ ( non_ordered_pair @ ( successor @ empty_set ) @ SV180 ) ) )
= $true )
| ( ( SV180 = empty_set )
= $true )
| ( ( member @ SV180 @ natural_numbers )
= $false )
| ( ( member @ SV180 @ prime_numbers )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1574]) ).
thf(1658,plain,
! [SV191: $i,SV353: $i,SV460: $i,SV424: $i] :
( ( ( ~ ( little_set @ SV424 ) )
= $true )
| ( ( ~ ( little_set @ SV460 )
| ( SV353
!= ( ordered_pair @ SV424 @ SV460 ) )
| ~ ( member @ SV191 @ SV460 ) )
= $true )
| ( ( member @ SV191 @ ( second @ SV353 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1576]) ).
thf(1659,plain,
! [SV425: $i,SV354: $i,SV192: $i,SV461: $i] :
( ( ( ~ ( maps @ SV461 @ SV192 @ SV192 ) )
= $true )
| ( ( ( ( apply_to_two_arguments @ SV354 @ ( apply @ SV461 @ ( f38 @ SV192 @ SV354 @ SV425 @ SV461 ) ) @ ( f38 @ SV192 @ SV354 @ SV425 @ SV461 ) )
!= SV425 )
| ( ( apply_to_two_arguments @ SV354 @ ( f38 @ SV192 @ SV354 @ SV425 @ SV461 ) @ ( apply @ SV461 @ ( f38 @ SV192 @ SV354 @ SV425 @ SV461 ) ) )
!= SV425 ) )
= $true )
| ( ( inverse @ SV192 @ SV354 @ SV425 @ SV461 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1577]) ).
thf(1660,plain,
! [SV193: $i,SV426: $i,SV355: $i] :
( ( ( ~ ( member @ SV355 @ natural_numbers ) )
= $true )
| ( ( ~ ( member @ SV426 @ natural_numbers )
| ( ( apply_to_two_arguments @ times @ SV355 @ SV426 )
!= SV193 )
| ( member @ SV355 @ ( non_ordered_pair @ ( successor @ empty_set ) @ SV193 ) ) )
= $true )
| ( ( member @ SV193 @ prime_numbers )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1578]) ).
thf(1661,plain,
! [SV478: $i,SV462: $i,SV427: $i,SV356: $i,SV195: $i] :
( ( ( member @ SV195 @ ( flip_range_of @ SV356 ) )
= $true )
| ( ( ~ ( little_set @ SV195 )
| ~ ( little_set @ SV427 )
| ~ ( little_set @ SV462 )
| ~ ( little_set @ SV478 )
| ( SV195
!= ( ordered_pair @ SV427 @ ( ordered_pair @ SV462 @ SV478 ) ) )
| ~ ( member @ ( ordered_pair @ SV427 @ ( ordered_pair @ SV478 @ SV462 ) ) @ SV356 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1579]) ).
thf(1662,plain,
! [SV357: $i,SV428: $i,SV196: $i] :
( ( ( little_set @ SV196 )
= $false )
| ( ( SV196 != SV428 )
= $true )
| ( ( member @ SV196 @ ( non_ordered_pair @ SV357 @ SV428 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1580]) ).
thf(1663,plain,
! [SV197: $i,SV358: $i,SV463: $i,SV429: $i] :
( ( ( ~ ( little_set @ SV429 ) )
= $true )
| ( ( ~ ( little_set @ SV463 )
| ( SV358
!= ( ordered_pair @ SV429 @ SV463 ) )
| ~ ( member @ SV197 @ SV429 ) )
= $true )
| ( ( member @ SV197 @ ( first @ SV358 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1581]) ).
thf(1664,plain,
! [SV359: $i,SV430: $i,SV464: $i,SV198: $i] :
( ( ( ~ ( little_set @ SV198 ) )
= $true )
| ( ( ~ ( ordered_pair_predicate @ SV464 )
| ~ ( member @ SV464 @ SV430 )
| ~ ( member @ ( first @ SV464 ) @ SV359 )
| ( ( second @ SV464 )
!= SV198 ) )
= $true )
| ( ( member @ SV198 @ ( image @ SV359 @ SV430 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1582]) ).
thf(1665,plain,
! [SV479: $i,SV465: $i,SV431: $i,SV360: $i,SV199: $i] :
( ( ( member @ SV199 @ ( rotate_right @ SV360 ) )
= $true )
| ( ( ~ ( little_set @ SV199 )
| ~ ( little_set @ SV431 )
| ~ ( little_set @ SV465 )
| ~ ( little_set @ SV479 )
| ( SV199
!= ( ordered_pair @ SV431 @ ( ordered_pair @ SV465 @ SV479 ) ) )
| ~ ( member @ ( ordered_pair @ SV465 @ ( ordered_pair @ SV479 @ SV431 ) ) @ SV360 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1583]) ).
thf(1666,plain,
! [SV483: $i,SV480: $i,SV466: $i,SV432: $i,SV361: $i,SV201: $i] :
( ( ( member @ SV201 @ ( compose @ SV361 @ SV432 ) )
| ~ ( little_set @ SV201 )
| ~ ( little_set @ SV466 )
| ~ ( little_set @ SV480 )
| ~ ( little_set @ SV483 )
| ( SV201
!= ( ordered_pair @ SV466 @ SV480 ) )
| ~ ( member @ ( ordered_pair @ SV466 @ SV483 ) @ SV361 )
| ~ ( member @ ( ordered_pair @ SV483 @ SV480 ) @ SV432 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1584]) ).
thf(1667,plain,
! [SV202: $i,SV433: $i,SV362: $i] :
( ( ( little_set @ SV362 )
= $false )
| ( ( ~ ( little_set @ SV433 )
| ( SV202
!= ( ordered_pair @ SV362 @ SV433 ) ) )
= $true )
| ( ( ordered_pair_predicate @ SV202 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1585]) ).
thf(1668,plain,
! [SV434: $i,SV363: $i,SV203: $i] :
( ( ( little_set @ SV203 )
= $false )
| ( ( SV203 != SV363 )
= $true )
| ( ( member @ SV203 @ ( non_ordered_pair @ SV363 @ SV434 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1586]) ).
thf(1669,plain,
! [SV204: $i,SV364: $i] :
( ( ( ~ ( member @ SV364 @ natural_numbers ) )
= $true )
| ( ( ( apply_to_two_arguments @ plus @ SV364 @ SV364 )
!= SV204 )
= $true )
| ( ( member @ SV204 @ natural_numbers )
= $false )
| ( ( member @ SV204 @ even_numbers )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1587]) ).
thf(1670,plain,
! [SV481: $i,SV467: $i,SV435: $i,SV366: $i,SV206: $i] :
( ( ( homomorphism @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 )
= $true )
| ( ( ~ ( closed @ SV366 @ SV435 )
| ~ ( closed @ SV467 @ SV481 )
| ~ ( maps @ SV206 @ SV366 @ SV467 )
| ( ( apply @ SV206 @ ( apply_to_two_arguments @ SV435 @ ( f32 @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 ) @ ( f33 @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 ) ) )
!= ( apply_to_two_arguments @ SV481 @ ( apply @ SV206 @ ( f32 @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 ) ) @ ( apply @ SV206 @ ( f33 @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1589]) ).
thf(1671,plain,
! [SV207: $i,SV436: $i,SV367: $i] :
( ( ( member @ SV367 @ natural_numbers )
= $false )
| ( ( ~ ( maps @ SV436 @ SV367 @ SV207 )
| ( ( range_of @ SV436 )
!= SV207 )
| ~ ( one_to_one_function @ SV436 ) )
= $true )
| ( ( finite @ SV207 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1590]) ).
thf(1672,plain,
! [SV437: $i,SV368: $i,SV208: $i] :
( ( ( function @ SV208 )
= $false )
| ( ( ( ( domain_of @ SV208 )
!= SV368 )
| ~ ( subset @ ( range_of @ SV208 ) @ SV437 ) )
= $true )
| ( ( maps @ SV208 @ SV368 @ SV437 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1591]) ).
thf(1673,plain,
! [SV211: $i] :
( ( ( ordered_pair_predicate @ SV211 )
= $false )
| ( ( ( first @ SV211 )
!= ( second @ SV211 ) )
= $true )
| ( ( little_set @ SV211 )
= $false )
| ( ( member @ SV211 @ identity_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1592]) ).
thf(1674,plain,
! [SV370: $i,SV438: $i,SV212: $i] :
( ( ( little_set @ SV212 )
= $false )
| ( ( ~ ( ordered_pair_predicate @ SV438 )
| ~ ( member @ SV438 @ SV370 )
| ( SV212
!= ( second @ SV438 ) ) )
= $true )
| ( ( member @ SV212 @ ( range_of @ SV370 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1593]) ).
thf(1675,plain,
! [SV372: $i,SV214: $i,SV439: $i] :
( ( ( member @ SV439 @ SV214 )
= $false )
| ( ( ( ( apply_to_two_arguments @ SV372 @ SV439 @ ( f37 @ SV214 @ SV372 @ SV439 ) )
!= ( f37 @ SV214 @ SV372 @ SV439 ) )
| ( ( apply_to_two_arguments @ SV372 @ ( f37 @ SV214 @ SV372 @ SV439 ) @ SV439 )
!= ( f37 @ SV214 @ SV372 @ SV439 ) ) )
= $true )
| ( ( identity @ SV214 @ SV372 @ SV439 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1594]) ).
thf(1676,plain,
! [SV373: $i,SV440: $i,SV215: $i] :
( ( ( little_set @ SV215 )
= $false )
| ( ( ~ ( ordered_pair_predicate @ SV440 )
| ~ ( member @ SV440 @ SV373 )
| ( SV215
!= ( first @ SV440 ) ) )
= $true )
| ( ( member @ SV215 @ ( domain_of @ SV373 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1595]) ).
thf(1677,plain,
! [SV216: $i,SV441: $i,SV374: $i,SV468: $i] :
( ( ( ~ ( ordered_pair_predicate @ SV468 ) )
= $true )
| ( ( ~ ( member @ SV468 @ SV374 )
| ( ( first @ SV468 )
!= SV441 )
| ~ ( member @ SV216 @ ( second @ SV468 ) ) )
= $true )
| ( ( member @ SV216 @ ( apply @ SV374 @ SV441 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1596]) ).
thf(1678,plain,
! [SV22: $i] :
( ( ( member @ ( first @ SV22 ) @ ( second @ SV22 ) )
= $false )
| ( ( ordered_pair_predicate @ SV22 )
= $false )
| ( ( little_set @ SV22 )
= $false )
| ( ( member @ SV22 @ estin )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1599]) ).
thf(1679,plain,
! [SV234: $i,SV378: $i,SV25: $i] :
( ( ( member @ SV25 @ SV378 )
= $false )
| ( ( member @ SV25 @ SV234 )
= $false )
| ( ( member @ SV25 @ ( intersection @ SV234 @ SV378 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1600]) ).
thf(1680,plain,
! [SV382: $i,SV244: $i,SV35: $i] :
( ( ( ~ ( ordered_pair_predicate @ SV35 ) )
= $true )
| ( ( ~ ( member @ ( first @ SV35 ) @ SV244 )
| ~ ( member @ ( second @ SV35 ) @ SV382 ) )
= $true )
| ( ( little_set @ SV35 )
= $false )
| ( ( member @ SV35 @ ( cross_product @ SV244 @ SV382 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1601]) ).
thf(1681,plain,
! [SV247: $i,SV38: $i] :
( ( ( ordered_pair_predicate @ SV38 )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ ( second @ SV38 ) @ ( first @ SV38 ) ) @ SV247 ) )
= $true )
| ( ( little_set @ SV38 )
= $false )
| ( ( member @ SV38 @ ( converse @ SV247 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1602]) ).
thf(1682,plain,
! [SV260: $i,SV383: $i,SV55: $i] :
( ( ( member @ SV55 @ SV383 )
= $false )
| ( ( member @ SV383 @ SV260 )
= $false )
| ( ( member @ SV55 @ ( sigma @ SV260 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1603]) ).
thf(1683,plain,
! [SV261: $i,SV57: $i,SV384: $i] :
( ( ( member @ SV384 @ SV57 )
= $false )
| ( ( member @ SV384 @ SV261 )
= $true )
| ( ( subset @ SV57 @ SV261 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1604]) ).
thf(1684,plain,
! [SV68: $i,SV442: $i,SV385: $i,SV269: $i] :
( ( ( ~ ( little_set @ SV269 ) )
= $true )
| ( ( ~ ( little_set @ SV385 )
| ~ ( little_set @ SV442 )
| ~ ( member @ ( ordered_pair @ SV269 @ SV385 ) @ SV68 )
| ~ ( member @ ( ordered_pair @ SV269 @ SV442 ) @ SV68 )
| ( SV385 = SV442 ) )
= $true )
| ( ( single_valued_set @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1607]) ).
thf(1685,plain,
! [SV275: $i,SV82: $i,SV390: $i] :
( ( ( member @ SV390 @ SV82 )
= $false )
| ( ( ~ ( member @ SV390 @ SV275 ) )
= $true )
| ( ( disjoint @ SV82 @ SV275 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1609]) ).
thf(1686,plain,
! [SV109: $i,SV293: $i] :
( ( ( little_set @ SV293 )
= $false )
| ( ( ~ ( maps @ SV293 @ ( cross_product @ SV109 @ SV109 ) @ SV109 ) )
= $true )
| ( ( little_set @ SV109 )
= $false )
| ( ( closed @ SV109 @ SV293 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1610]) ).
thf(1687,plain,
! [SV469: $i,SV443: $i,SV405: $i,SV300: $i,SV116: $i] :
( ( ( homomorphism @ SV116 @ SV300 @ SV405 @ SV443 @ SV469 )
= $false )
| ( ( closed @ SV300 @ SV405 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1611]) ).
thf(1688,plain,
! [SV470: $i,SV444: $i,SV406: $i,SV301: $i,SV117: $i] :
( ( ( homomorphism @ SV117 @ SV301 @ SV406 @ SV444 @ SV470 )
= $false )
| ( ( closed @ SV444 @ SV470 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1612]) ).
thf(1689,plain,
! [SV471: $i,SV445: $i,SV407: $i,SV302: $i,SV118: $i] :
( ( ( homomorphism @ SV118 @ SV302 @ SV407 @ SV445 @ SV471 )
= $false )
| ( ( maps @ SV118 @ SV302 @ SV445 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1613]) ).
thf(1690,plain,
! [SV484: $i,SV482: $i,SV472: $i,SV446: $i,SV408: $i,SV303: $i,SV119: $i] :
( ( ~ ( homomorphism @ SV119 @ SV303 @ SV408 @ SV446 @ SV472 )
| ~ ( member @ SV482 @ SV303 )
| ~ ( member @ SV484 @ SV303 )
| ( ( apply @ SV119 @ ( apply_to_two_arguments @ SV408 @ SV482 @ SV484 ) )
= ( apply_to_two_arguments @ SV472 @ ( apply @ SV119 @ SV482 ) @ ( apply @ SV119 @ SV484 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1614]) ).
thf(1691,plain,
! [SV120: $i,SV473: $i,SV447: $i,SV409: $i,SV304: $i] :
( ( ( ~ ( closed @ SV304 @ SV409 ) )
= $true )
| ( ( ~ ( closed @ SV447 @ SV473 )
| ~ ( maps @ SV120 @ SV304 @ SV447 )
| ( member @ ( f32 @ SV120 @ SV304 @ SV409 @ SV447 @ SV473 ) @ SV304 ) )
= $true )
| ( ( homomorphism @ SV120 @ SV304 @ SV409 @ SV447 @ SV473 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1615]) ).
thf(1692,plain,
! [SV121: $i,SV474: $i,SV448: $i,SV410: $i,SV305: $i] :
( ( ( ~ ( closed @ SV305 @ SV410 ) )
= $true )
| ( ( ~ ( closed @ SV448 @ SV474 )
| ~ ( maps @ SV121 @ SV305 @ SV448 )
| ( member @ ( f33 @ SV121 @ SV305 @ SV410 @ SV448 @ SV474 ) @ SV305 ) )
= $true )
| ( ( homomorphism @ SV121 @ SV305 @ SV410 @ SV448 @ SV474 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1616]) ).
thf(1693,plain,
! [SV475: $i,SV449: $i,SV411: $i,SV306: $i,SV122: $i] :
( ( ( associative @ SV122 @ SV306 )
= $false )
| ( ( ~ ( member @ SV411 @ SV122 )
| ~ ( member @ SV449 @ SV122 )
| ~ ( member @ SV475 @ SV122 )
| ( ( apply_to_two_arguments @ SV306 @ ( apply_to_two_arguments @ SV306 @ SV411 @ SV449 ) @ SV475 )
= ( apply_to_two_arguments @ SV306 @ SV411 @ ( apply_to_two_arguments @ SV306 @ SV449 @ SV475 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1617]) ).
thf(1694,plain,
! [SV413: $i,SV311: $i,SV127: $i,SV450: $i] :
( ( ( ~ ( member @ SV450 @ SV127 ) )
= $true )
| ( ( ( apply_to_two_arguments @ SV311 @ SV413 @ SV450 )
= SV450 )
= $true )
| ( ( identity @ SV127 @ SV311 @ SV413 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1618]) ).
thf(1695,plain,
! [SV414: $i,SV312: $i,SV128: $i,SV451: $i] :
( ( ( ~ ( member @ SV451 @ SV128 ) )
= $true )
| ( ( ( apply_to_two_arguments @ SV312 @ SV451 @ SV414 )
= SV451 )
= $true )
| ( ( identity @ SV128 @ SV312 @ SV414 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1619]) ).
thf(1696,plain,
! [SV476: $i,SV453: $i,SV417: $i,SV315: $i,SV131: $i] :
( ( ( inverse @ SV131 @ SV315 @ SV417 @ SV453 )
= $false )
| ( ( ~ ( member @ SV476 @ SV131 )
| ( ( apply_to_two_arguments @ SV315 @ ( apply @ SV453 @ SV476 ) @ SV476 )
= SV417 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1622]) ).
thf(1697,plain,
! [SV477: $i,SV454: $i,SV418: $i,SV316: $i,SV132: $i] :
( ( ( inverse @ SV132 @ SV316 @ SV418 @ SV454 )
= $false )
| ( ( ~ ( member @ SV477 @ SV132 )
| ( ( apply_to_two_arguments @ SV316 @ SV477 @ ( apply @ SV454 @ SV477 ) )
= SV418 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1623]) ).
thf(1698,plain,
! [SV419: $i,SV317: $i,SV133: $i,SV455: $i] :
( ( ( maps @ SV455 @ SV133 @ SV133 )
= $false )
| ( ( member @ ( f38 @ SV133 @ SV317 @ SV419 @ SV455 ) @ SV133 )
= $true )
| ( ( inverse @ SV133 @ SV317 @ SV419 @ SV455 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1624]) ).
thf(1699,plain,
! [SV456: $i,SV420: $i,SV322: $i,SV138: $i] :
( ( ( closed @ SV138 @ SV322 )
= $false )
| ( ( ~ ( associative @ SV138 @ SV322 )
| ~ ( identity @ SV138 @ SV322 @ SV420 )
| ~ ( inverse @ SV138 @ SV322 @ SV420 @ SV456 ) )
= $true )
| ( ( group @ SV138 @ SV322 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1625]) ).
thf(1700,plain,
! [SV323: $i,SV457: $i,SV139: $i,SV421: $i] :
( ( ( ~ ( member @ SV421 @ SV139 ) )
= $true )
| ( ( ~ ( member @ SV457 @ SV139 )
| ( ( apply_to_two_arguments @ SV323 @ SV421 @ SV457 )
= ( apply_to_two_arguments @ SV323 @ SV457 @ SV421 ) ) )
= $true )
| ( ( commutes @ SV139 @ SV323 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1626]) ).
thf(1701,plain,
! [SV142: $i,SV326: $i] :
( ( ( ~ ( member @ empty_set @ SV326 ) )
= $true )
| ( ( ( member @ ( f43 @ SV142 @ SV326 ) @ SV326 )
| ( member @ SV142 @ SV326 ) )
= $true )
| ( ( little_set @ SV326 )
= $false )
| ( ( member @ SV142 @ natural_numbers )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1627]) ).
thf(1702,plain,
! [SV143: $i,SV327: $i] :
( ( ( ~ ( member @ empty_set @ SV327 ) )
= $true )
| ( ( ~ ( member @ ( successor @ ( f43 @ SV143 @ SV327 ) ) @ SV327 )
| ( member @ SV143 @ SV327 ) )
= $true )
| ( ( little_set @ SV327 )
= $false )
| ( ( member @ SV143 @ natural_numbers )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1628]) ).
thf(1703,plain,
! [SV146: $i,SV328: $i] :
( ( ( member @ SV328 @ ( f44 @ SV146 ) )
= $false )
| ( ( member @ ( successor @ SV328 ) @ ( f44 @ SV146 ) )
= $true )
| ( ( little_set @ SV146 )
= $false )
| ( ( member @ SV146 @ natural_numbers )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1629]) ).
thf(1704,plain,
! [SV329: $i,SV148: $i] :
( ( ( member @ ( f45 @ SV148 @ SV329 ) @ natural_numbers )
= $true )
| ( ( ( member @ ( f46 @ SV148 @ SV329 ) @ natural_numbers )
| ( member @ SV148 @ SV329 ) )
= $true )
| ( ( little_set @ SV329 )
= $false )
| ( ( member @ SV148 @ plus )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1630]) ).
thf(1705,plain,
! [SV330: $i,SV149: $i] :
( ( ( member @ ( f45 @ SV149 @ SV330 ) @ natural_numbers )
= $true )
| ( ( ( member @ ( f47 @ SV149 @ SV330 ) @ natural_numbers )
| ( member @ SV149 @ SV330 ) )
= $true )
| ( ( little_set @ SV330 )
= $false )
| ( ( member @ SV149 @ plus )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1631]) ).
thf(1706,plain,
! [SV331: $i,SV150: $i] :
( ( ( member @ ( f45 @ SV150 @ SV331 ) @ natural_numbers )
= $true )
| ( ( ( member @ ( f48 @ SV150 @ SV331 ) @ natural_numbers )
| ( member @ SV150 @ SV331 ) )
= $true )
| ( ( little_set @ SV331 )
= $false )
| ( ( member @ SV150 @ plus )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1632]) ).
thf(1707,plain,
! [SV332: $i,SV151: $i] :
( ( ( member @ ( f45 @ SV151 @ SV332 ) @ natural_numbers )
= $true )
| ( ( ( member @ ( ordered_pair @ ( ordered_pair @ ( f46 @ SV151 @ SV332 ) @ ( f47 @ SV151 @ SV332 ) ) @ ( f48 @ SV151 @ SV332 ) ) @ SV332 )
| ( member @ SV151 @ SV332 ) )
= $true )
| ( ( little_set @ SV332 )
= $false )
| ( ( member @ SV151 @ plus )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1633]) ).
thf(1708,plain,
! [SV333: $i,SV152: $i] :
( ( ( member @ ( f45 @ SV152 @ SV333 ) @ natural_numbers )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f46 @ SV152 @ SV333 ) ) @ ( f47 @ SV152 @ SV333 ) ) @ ( successor @ ( f48 @ SV152 @ SV333 ) ) ) @ SV333 )
| ( member @ SV152 @ SV333 ) )
= $true )
| ( ( little_set @ SV333 )
= $false )
| ( ( member @ SV152 @ plus )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1634]) ).
thf(1709,plain,
! [SV334: $i,SV153: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV153 @ SV334 ) ) @ ( f45 @ SV153 @ SV334 ) ) @ SV334 ) )
= $true )
| ( ( ( member @ ( f46 @ SV153 @ SV334 ) @ natural_numbers )
| ( member @ SV153 @ SV334 ) )
= $true )
| ( ( little_set @ SV334 )
= $false )
| ( ( member @ SV153 @ plus )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1635]) ).
thf(1710,plain,
! [SV335: $i,SV154: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV154 @ SV335 ) ) @ ( f45 @ SV154 @ SV335 ) ) @ SV335 ) )
= $true )
| ( ( ( member @ ( f47 @ SV154 @ SV335 ) @ natural_numbers )
| ( member @ SV154 @ SV335 ) )
= $true )
| ( ( little_set @ SV335 )
= $false )
| ( ( member @ SV154 @ plus )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1636]) ).
thf(1711,plain,
! [SV336: $i,SV155: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV155 @ SV336 ) ) @ ( f45 @ SV155 @ SV336 ) ) @ SV336 ) )
= $true )
| ( ( ( member @ ( f48 @ SV155 @ SV336 ) @ natural_numbers )
| ( member @ SV155 @ SV336 ) )
= $true )
| ( ( little_set @ SV336 )
= $false )
| ( ( member @ SV155 @ plus )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1637]) ).
thf(1712,plain,
! [SV337: $i,SV156: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV156 @ SV337 ) ) @ ( f45 @ SV156 @ SV337 ) ) @ SV337 ) )
= $true )
| ( ( ( member @ ( ordered_pair @ ( ordered_pair @ ( f46 @ SV156 @ SV337 ) @ ( f47 @ SV156 @ SV337 ) ) @ ( f48 @ SV156 @ SV337 ) ) @ SV337 )
| ( member @ SV156 @ SV337 ) )
= $true )
| ( ( little_set @ SV337 )
= $false )
| ( ( member @ SV156 @ plus )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1638]) ).
thf(1713,plain,
! [SV338: $i,SV157: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV157 @ SV338 ) ) @ ( f45 @ SV157 @ SV338 ) ) @ SV338 ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f46 @ SV157 @ SV338 ) ) @ ( f47 @ SV157 @ SV338 ) ) @ ( successor @ ( f48 @ SV157 @ SV338 ) ) ) @ SV338 )
| ( member @ SV157 @ SV338 ) )
= $true )
| ( ( little_set @ SV338 )
= $false )
| ( ( member @ SV157 @ plus )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1639]) ).
thf(1714,plain,
! [SV159: $i,SV339: $i] :
( ( ( member @ SV339 @ natural_numbers )
= $false )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ SV339 ) @ SV339 ) @ ( f49 @ SV159 ) )
= $true )
| ( ( little_set @ SV159 )
= $false )
| ( ( member @ SV159 @ plus )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1640]) ).
thf(1715,plain,
! [SV458: $i,SV422: $i,SV340: $i,SV160: $i] :
( ( ( little_set @ SV160 )
= $false )
| ( ( ~ ( member @ SV340 @ natural_numbers )
| ~ ( member @ SV422 @ natural_numbers )
| ~ ( member @ SV458 @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV340 @ SV422 ) @ SV458 ) @ ( f49 @ SV160 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ SV340 ) @ SV422 ) @ ( successor @ SV458 ) ) @ ( f49 @ SV160 ) ) )
= $true )
| ( ( member @ SV160 @ plus )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1641]) ).
thf(1716,plain,
! [SV341: $i,SV162: $i] :
( ( ( member @ ( f50 @ SV162 @ SV341 ) @ natural_numbers )
= $true )
| ( ( ( member @ ( f51 @ SV162 @ SV341 ) @ natural_numbers )
| ( member @ SV162 @ SV341 ) )
= $true )
| ( ( little_set @ SV341 )
= $false )
| ( ( member @ SV162 @ times )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1642]) ).
thf(1717,plain,
! [SV342: $i,SV163: $i] :
( ( ( member @ ( f50 @ SV163 @ SV342 ) @ natural_numbers )
= $true )
| ( ( ( member @ ( f52 @ SV163 @ SV342 ) @ natural_numbers )
| ( member @ SV163 @ SV342 ) )
= $true )
| ( ( little_set @ SV342 )
= $false )
| ( ( member @ SV163 @ times )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1643]) ).
thf(1718,plain,
! [SV343: $i,SV164: $i] :
( ( ( member @ ( f50 @ SV164 @ SV343 ) @ natural_numbers )
= $true )
| ( ( ( member @ ( f53 @ SV164 @ SV343 ) @ natural_numbers )
| ( member @ SV164 @ SV343 ) )
= $true )
| ( ( little_set @ SV343 )
= $false )
| ( ( member @ SV164 @ times )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1644]) ).
thf(1719,plain,
! [SV344: $i,SV165: $i] :
( ( ( member @ ( f50 @ SV165 @ SV344 ) @ natural_numbers )
= $true )
| ( ( ( member @ ( ordered_pair @ ( ordered_pair @ ( f51 @ SV165 @ SV344 ) @ ( f52 @ SV165 @ SV344 ) ) @ ( f53 @ SV165 @ SV344 ) ) @ SV344 )
| ( member @ SV165 @ SV344 ) )
= $true )
| ( ( little_set @ SV344 )
= $false )
| ( ( member @ SV165 @ times )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1645]) ).
thf(1720,plain,
! [SV345: $i,SV166: $i] :
( ( ( member @ ( f50 @ SV166 @ SV345 ) @ natural_numbers )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f51 @ SV166 @ SV345 ) ) @ ( f52 @ SV166 @ SV345 ) ) @ ( apply_to_two_arguments @ plus @ ( f53 @ SV166 @ SV345 ) @ ( f52 @ SV166 @ SV345 ) ) ) @ SV345 )
| ( member @ SV166 @ SV345 ) )
= $true )
| ( ( little_set @ SV345 )
= $false )
| ( ( member @ SV166 @ times )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1646]) ).
thf(1721,plain,
! [SV346: $i,SV167: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV167 @ SV346 ) ) @ empty_set ) @ SV346 ) )
= $true )
| ( ( ( member @ ( f51 @ SV167 @ SV346 ) @ natural_numbers )
| ( member @ SV167 @ SV346 ) )
= $true )
| ( ( little_set @ SV346 )
= $false )
| ( ( member @ SV167 @ times )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1647]) ).
thf(1722,plain,
! [SV347: $i,SV168: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV168 @ SV347 ) ) @ empty_set ) @ SV347 ) )
= $true )
| ( ( ( member @ ( f52 @ SV168 @ SV347 ) @ natural_numbers )
| ( member @ SV168 @ SV347 ) )
= $true )
| ( ( little_set @ SV347 )
= $false )
| ( ( member @ SV168 @ times )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1648]) ).
thf(1723,plain,
! [SV348: $i,SV169: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV169 @ SV348 ) ) @ empty_set ) @ SV348 ) )
= $true )
| ( ( ( member @ ( f53 @ SV169 @ SV348 ) @ natural_numbers )
| ( member @ SV169 @ SV348 ) )
= $true )
| ( ( little_set @ SV348 )
= $false )
| ( ( member @ SV169 @ times )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1649]) ).
thf(1724,plain,
! [SV349: $i,SV170: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV170 @ SV349 ) ) @ empty_set ) @ SV349 ) )
= $true )
| ( ( ( member @ ( ordered_pair @ ( ordered_pair @ ( f51 @ SV170 @ SV349 ) @ ( f52 @ SV170 @ SV349 ) ) @ ( f53 @ SV170 @ SV349 ) ) @ SV349 )
| ( member @ SV170 @ SV349 ) )
= $true )
| ( ( little_set @ SV349 )
= $false )
| ( ( member @ SV170 @ times )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1650]) ).
thf(1725,plain,
! [SV350: $i,SV171: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV171 @ SV350 ) ) @ empty_set ) @ SV350 ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f51 @ SV171 @ SV350 ) ) @ ( f52 @ SV171 @ SV350 ) ) @ ( apply_to_two_arguments @ plus @ ( f53 @ SV171 @ SV350 ) @ ( f52 @ SV171 @ SV350 ) ) ) @ SV350 )
| ( member @ SV171 @ SV350 ) )
= $true )
| ( ( little_set @ SV350 )
= $false )
| ( ( member @ SV171 @ times )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1651]) ).
thf(1726,plain,
! [SV173: $i,SV351: $i] :
( ( ( member @ SV351 @ natural_numbers )
= $false )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ SV351 ) @ empty_set ) @ ( f54 @ SV173 ) )
= $true )
| ( ( little_set @ SV173 )
= $false )
| ( ( member @ SV173 @ times )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1652]) ).
thf(1727,plain,
! [SV459: $i,SV423: $i,SV352: $i,SV174: $i] :
( ( ( little_set @ SV174 )
= $false )
| ( ( ~ ( member @ SV352 @ natural_numbers )
| ~ ( member @ SV423 @ natural_numbers )
| ~ ( member @ SV459 @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV352 @ SV423 ) @ SV459 ) @ ( f54 @ SV174 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ SV352 ) @ SV423 ) @ ( apply_to_two_arguments @ plus @ SV459 @ SV423 ) ) @ ( f54 @ SV174 ) ) )
= $true )
| ( ( member @ SV174 @ times )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1653]) ).
thf(1728,plain,
! [SV180: $i] :
( ( ( member @ ( f55 @ SV180 ) @ ( non_ordered_pair @ ( successor @ empty_set ) @ SV180 ) )
= $false )
| ( ( SV180
= ( successor @ empty_set ) )
= $true )
| ( ( SV180 = empty_set )
= $true )
| ( ( member @ SV180 @ natural_numbers )
= $false )
| ( ( member @ SV180 @ prime_numbers )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1657]) ).
thf(1729,plain,
! [SV191: $i,SV353: $i,SV460: $i,SV424: $i] :
( ( ( little_set @ SV424 )
= $false )
| ( ( ~ ( little_set @ SV460 )
| ( SV353
!= ( ordered_pair @ SV424 @ SV460 ) )
| ~ ( member @ SV191 @ SV460 ) )
= $true )
| ( ( member @ SV191 @ ( second @ SV353 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1658]) ).
thf(1730,plain,
! [SV425: $i,SV354: $i,SV192: $i,SV461: $i] :
( ( ( maps @ SV461 @ SV192 @ SV192 )
= $false )
| ( ( ( ( apply_to_two_arguments @ SV354 @ ( apply @ SV461 @ ( f38 @ SV192 @ SV354 @ SV425 @ SV461 ) ) @ ( f38 @ SV192 @ SV354 @ SV425 @ SV461 ) )
!= SV425 )
| ( ( apply_to_two_arguments @ SV354 @ ( f38 @ SV192 @ SV354 @ SV425 @ SV461 ) @ ( apply @ SV461 @ ( f38 @ SV192 @ SV354 @ SV425 @ SV461 ) ) )
!= SV425 ) )
= $true )
| ( ( inverse @ SV192 @ SV354 @ SV425 @ SV461 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1659]) ).
thf(1731,plain,
! [SV193: $i,SV426: $i,SV355: $i] :
( ( ( member @ SV355 @ natural_numbers )
= $false )
| ( ( ~ ( member @ SV426 @ natural_numbers )
| ( ( apply_to_two_arguments @ times @ SV355 @ SV426 )
!= SV193 )
| ( member @ SV355 @ ( non_ordered_pair @ ( successor @ empty_set ) @ SV193 ) ) )
= $true )
| ( ( member @ SV193 @ prime_numbers )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1660]) ).
thf(1732,plain,
! [SV356: $i,SV478: $i,SV462: $i,SV427: $i,SV195: $i] :
( ( ( ~ ( little_set @ SV195 ) )
= $true )
| ( ( ~ ( little_set @ SV427 )
| ~ ( little_set @ SV462 )
| ~ ( little_set @ SV478 )
| ( SV195
!= ( ordered_pair @ SV427 @ ( ordered_pair @ SV462 @ SV478 ) ) )
| ~ ( member @ ( ordered_pair @ SV427 @ ( ordered_pair @ SV478 @ SV462 ) ) @ SV356 ) )
= $true )
| ( ( member @ SV195 @ ( flip_range_of @ SV356 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1661]) ).
thf(1733,plain,
! [SV357: $i,SV428: $i,SV196: $i] :
( ( ( SV196 = SV428 )
= $false )
| ( ( little_set @ SV196 )
= $false )
| ( ( member @ SV196 @ ( non_ordered_pair @ SV357 @ SV428 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1662]) ).
thf(1734,plain,
! [SV197: $i,SV358: $i,SV463: $i,SV429: $i] :
( ( ( little_set @ SV429 )
= $false )
| ( ( ~ ( little_set @ SV463 )
| ( SV358
!= ( ordered_pair @ SV429 @ SV463 ) )
| ~ ( member @ SV197 @ SV429 ) )
= $true )
| ( ( member @ SV197 @ ( first @ SV358 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1663]) ).
thf(1735,plain,
! [SV359: $i,SV430: $i,SV464: $i,SV198: $i] :
( ( ( little_set @ SV198 )
= $false )
| ( ( ~ ( ordered_pair_predicate @ SV464 )
| ~ ( member @ SV464 @ SV430 )
| ~ ( member @ ( first @ SV464 ) @ SV359 )
| ( ( second @ SV464 )
!= SV198 ) )
= $true )
| ( ( member @ SV198 @ ( image @ SV359 @ SV430 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1664]) ).
thf(1736,plain,
! [SV360: $i,SV479: $i,SV465: $i,SV431: $i,SV199: $i] :
( ( ( ~ ( little_set @ SV199 ) )
= $true )
| ( ( ~ ( little_set @ SV431 )
| ~ ( little_set @ SV465 )
| ~ ( little_set @ SV479 )
| ( SV199
!= ( ordered_pair @ SV431 @ ( ordered_pair @ SV465 @ SV479 ) ) )
| ~ ( member @ ( ordered_pair @ SV465 @ ( ordered_pair @ SV479 @ SV431 ) ) @ SV360 ) )
= $true )
| ( ( member @ SV199 @ ( rotate_right @ SV360 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1665]) ).
thf(1737,plain,
! [SV483: $i,SV480: $i,SV466: $i,SV432: $i,SV361: $i,SV201: $i] :
( ( ( member @ SV201 @ ( compose @ SV361 @ SV432 ) )
= $true )
| ( ( ~ ( little_set @ SV201 )
| ~ ( little_set @ SV466 )
| ~ ( little_set @ SV480 )
| ~ ( little_set @ SV483 )
| ( SV201
!= ( ordered_pair @ SV466 @ SV480 ) )
| ~ ( member @ ( ordered_pair @ SV466 @ SV483 ) @ SV361 )
| ~ ( member @ ( ordered_pair @ SV483 @ SV480 ) @ SV432 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1666]) ).
thf(1738,plain,
! [SV362: $i,SV202: $i,SV433: $i] :
( ( ( ~ ( little_set @ SV433 ) )
= $true )
| ( ( SV202
!= ( ordered_pair @ SV362 @ SV433 ) )
= $true )
| ( ( little_set @ SV362 )
= $false )
| ( ( ordered_pair_predicate @ SV202 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1667]) ).
thf(1739,plain,
! [SV434: $i,SV363: $i,SV203: $i] :
( ( ( SV203 = SV363 )
= $false )
| ( ( little_set @ SV203 )
= $false )
| ( ( member @ SV203 @ ( non_ordered_pair @ SV363 @ SV434 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1668]) ).
thf(1740,plain,
! [SV204: $i,SV364: $i] :
( ( ( member @ SV364 @ natural_numbers )
= $false )
| ( ( ( apply_to_two_arguments @ plus @ SV364 @ SV364 )
!= SV204 )
= $true )
| ( ( member @ SV204 @ natural_numbers )
= $false )
| ( ( member @ SV204 @ even_numbers )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1669]) ).
thf(1741,plain,
! [SV206: $i,SV481: $i,SV467: $i,SV435: $i,SV366: $i] :
( ( ( ~ ( closed @ SV366 @ SV435 ) )
= $true )
| ( ( ~ ( closed @ SV467 @ SV481 )
| ~ ( maps @ SV206 @ SV366 @ SV467 )
| ( ( apply @ SV206 @ ( apply_to_two_arguments @ SV435 @ ( f32 @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 ) @ ( f33 @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 ) ) )
!= ( apply_to_two_arguments @ SV481 @ ( apply @ SV206 @ ( f32 @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 ) ) @ ( apply @ SV206 @ ( f33 @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 ) ) ) ) )
= $true )
| ( ( homomorphism @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1670]) ).
thf(1742,plain,
! [SV207: $i,SV367: $i,SV436: $i] :
( ( ( ~ ( maps @ SV436 @ SV367 @ SV207 ) )
= $true )
| ( ( ( ( range_of @ SV436 )
!= SV207 )
| ~ ( one_to_one_function @ SV436 ) )
= $true )
| ( ( member @ SV367 @ natural_numbers )
= $false )
| ( ( finite @ SV207 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1671]) ).
thf(1743,plain,
! [SV437: $i,SV368: $i,SV208: $i] :
( ( ( ( domain_of @ SV208 )
!= SV368 )
= $true )
| ( ( ~ ( subset @ ( range_of @ SV208 ) @ SV437 ) )
= $true )
| ( ( function @ SV208 )
= $false )
| ( ( maps @ SV208 @ SV368 @ SV437 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1672]) ).
thf(1744,plain,
! [SV211: $i] :
( ( ( ( first @ SV211 )
= ( second @ SV211 ) )
= $false )
| ( ( ordered_pair_predicate @ SV211 )
= $false )
| ( ( little_set @ SV211 )
= $false )
| ( ( member @ SV211 @ identity_relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1673]) ).
thf(1745,plain,
! [SV212: $i,SV370: $i,SV438: $i] :
( ( ( ~ ( ordered_pair_predicate @ SV438 ) )
= $true )
| ( ( ~ ( member @ SV438 @ SV370 )
| ( SV212
!= ( second @ SV438 ) ) )
= $true )
| ( ( little_set @ SV212 )
= $false )
| ( ( member @ SV212 @ ( range_of @ SV370 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1674]) ).
thf(1746,plain,
! [SV214: $i,SV439: $i,SV372: $i] :
( ( ( ( apply_to_two_arguments @ SV372 @ SV439 @ ( f37 @ SV214 @ SV372 @ SV439 ) )
!= ( f37 @ SV214 @ SV372 @ SV439 ) )
= $true )
| ( ( ( apply_to_two_arguments @ SV372 @ ( f37 @ SV214 @ SV372 @ SV439 ) @ SV439 )
!= ( f37 @ SV214 @ SV372 @ SV439 ) )
= $true )
| ( ( member @ SV439 @ SV214 )
= $false )
| ( ( identity @ SV214 @ SV372 @ SV439 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1675]) ).
thf(1747,plain,
! [SV215: $i,SV373: $i,SV440: $i] :
( ( ( ~ ( ordered_pair_predicate @ SV440 ) )
= $true )
| ( ( ~ ( member @ SV440 @ SV373 )
| ( SV215
!= ( first @ SV440 ) ) )
= $true )
| ( ( little_set @ SV215 )
= $false )
| ( ( member @ SV215 @ ( domain_of @ SV373 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1676]) ).
thf(1748,plain,
! [SV216: $i,SV441: $i,SV374: $i,SV468: $i] :
( ( ( ordered_pair_predicate @ SV468 )
= $false )
| ( ( ~ ( member @ SV468 @ SV374 )
| ( ( first @ SV468 )
!= SV441 )
| ~ ( member @ SV216 @ ( second @ SV468 ) ) )
= $true )
| ( ( member @ SV216 @ ( apply @ SV374 @ SV441 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1677]) ).
thf(1749,plain,
! [SV382: $i,SV244: $i,SV35: $i] :
( ( ( ordered_pair_predicate @ SV35 )
= $false )
| ( ( ~ ( member @ ( first @ SV35 ) @ SV244 )
| ~ ( member @ ( second @ SV35 ) @ SV382 ) )
= $true )
| ( ( little_set @ SV35 )
= $false )
| ( ( member @ SV35 @ ( cross_product @ SV244 @ SV382 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1680]) ).
thf(1750,plain,
! [SV247: $i,SV38: $i] :
( ( ( member @ ( ordered_pair @ ( second @ SV38 ) @ ( first @ SV38 ) ) @ SV247 )
= $false )
| ( ( ordered_pair_predicate @ SV38 )
= $false )
| ( ( little_set @ SV38 )
= $false )
| ( ( member @ SV38 @ ( converse @ SV247 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1681]) ).
thf(1751,plain,
! [SV68: $i,SV442: $i,SV385: $i,SV269: $i] :
( ( ( little_set @ SV269 )
= $false )
| ( ( ~ ( little_set @ SV385 )
| ~ ( little_set @ SV442 )
| ~ ( member @ ( ordered_pair @ SV269 @ SV385 ) @ SV68 )
| ~ ( member @ ( ordered_pair @ SV269 @ SV442 ) @ SV68 )
| ( SV385 = SV442 ) )
= $true )
| ( ( single_valued_set @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1684]) ).
thf(1752,plain,
! [SV82: $i,SV275: $i,SV390: $i] :
( ( ( member @ SV390 @ SV275 )
= $false )
| ( ( member @ SV390 @ SV82 )
= $false )
| ( ( disjoint @ SV82 @ SV275 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1685]) ).
thf(1753,plain,
! [SV109: $i,SV293: $i] :
( ( ( maps @ SV293 @ ( cross_product @ SV109 @ SV109 ) @ SV109 )
= $false )
| ( ( little_set @ SV293 )
= $false )
| ( ( little_set @ SV109 )
= $false )
| ( ( closed @ SV109 @ SV293 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1686]) ).
thf(1754,plain,
! [SV484: $i,SV482: $i,SV472: $i,SV446: $i,SV408: $i,SV303: $i,SV119: $i] :
( ( ( ~ ( homomorphism @ SV119 @ SV303 @ SV408 @ SV446 @ SV472 ) )
= $true )
| ( ( ~ ( member @ SV482 @ SV303 )
| ~ ( member @ SV484 @ SV303 )
| ( ( apply @ SV119 @ ( apply_to_two_arguments @ SV408 @ SV482 @ SV484 ) )
= ( apply_to_two_arguments @ SV472 @ ( apply @ SV119 @ SV482 ) @ ( apply @ SV119 @ SV484 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1690]) ).
thf(1755,plain,
! [SV120: $i,SV473: $i,SV447: $i,SV409: $i,SV304: $i] :
( ( ( closed @ SV304 @ SV409 )
= $false )
| ( ( ~ ( closed @ SV447 @ SV473 )
| ~ ( maps @ SV120 @ SV304 @ SV447 )
| ( member @ ( f32 @ SV120 @ SV304 @ SV409 @ SV447 @ SV473 ) @ SV304 ) )
= $true )
| ( ( homomorphism @ SV120 @ SV304 @ SV409 @ SV447 @ SV473 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1691]) ).
thf(1756,plain,
! [SV121: $i,SV474: $i,SV448: $i,SV410: $i,SV305: $i] :
( ( ( closed @ SV305 @ SV410 )
= $false )
| ( ( ~ ( closed @ SV448 @ SV474 )
| ~ ( maps @ SV121 @ SV305 @ SV448 )
| ( member @ ( f33 @ SV121 @ SV305 @ SV410 @ SV448 @ SV474 ) @ SV305 ) )
= $true )
| ( ( homomorphism @ SV121 @ SV305 @ SV410 @ SV448 @ SV474 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1692]) ).
thf(1757,plain,
! [SV306: $i,SV475: $i,SV449: $i,SV122: $i,SV411: $i] :
( ( ( ~ ( member @ SV411 @ SV122 ) )
= $true )
| ( ( ~ ( member @ SV449 @ SV122 )
| ~ ( member @ SV475 @ SV122 )
| ( ( apply_to_two_arguments @ SV306 @ ( apply_to_two_arguments @ SV306 @ SV411 @ SV449 ) @ SV475 )
= ( apply_to_two_arguments @ SV306 @ SV411 @ ( apply_to_two_arguments @ SV306 @ SV449 @ SV475 ) ) ) )
= $true )
| ( ( associative @ SV122 @ SV306 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1693]) ).
thf(1758,plain,
! [SV413: $i,SV311: $i,SV127: $i,SV450: $i] :
( ( ( member @ SV450 @ SV127 )
= $false )
| ( ( ( apply_to_two_arguments @ SV311 @ SV413 @ SV450 )
= SV450 )
= $true )
| ( ( identity @ SV127 @ SV311 @ SV413 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1694]) ).
thf(1759,plain,
! [SV414: $i,SV312: $i,SV128: $i,SV451: $i] :
( ( ( member @ SV451 @ SV128 )
= $false )
| ( ( ( apply_to_two_arguments @ SV312 @ SV451 @ SV414 )
= SV451 )
= $true )
| ( ( identity @ SV128 @ SV312 @ SV414 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1695]) ).
thf(1760,plain,
! [SV417: $i,SV453: $i,SV315: $i,SV131: $i,SV476: $i] :
( ( ( ~ ( member @ SV476 @ SV131 ) )
= $true )
| ( ( ( apply_to_two_arguments @ SV315 @ ( apply @ SV453 @ SV476 ) @ SV476 )
= SV417 )
= $true )
| ( ( inverse @ SV131 @ SV315 @ SV417 @ SV453 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1696]) ).
thf(1761,plain,
! [SV418: $i,SV454: $i,SV316: $i,SV132: $i,SV477: $i] :
( ( ( ~ ( member @ SV477 @ SV132 ) )
= $true )
| ( ( ( apply_to_two_arguments @ SV316 @ SV477 @ ( apply @ SV454 @ SV477 ) )
= SV418 )
= $true )
| ( ( inverse @ SV132 @ SV316 @ SV418 @ SV454 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1697]) ).
thf(1762,plain,
! [SV456: $i,SV420: $i,SV322: $i,SV138: $i] :
( ( ( ~ ( associative @ SV138 @ SV322 ) )
= $true )
| ( ( ~ ( identity @ SV138 @ SV322 @ SV420 )
| ~ ( inverse @ SV138 @ SV322 @ SV420 @ SV456 ) )
= $true )
| ( ( closed @ SV138 @ SV322 )
= $false )
| ( ( group @ SV138 @ SV322 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1699]) ).
thf(1763,plain,
! [SV323: $i,SV457: $i,SV139: $i,SV421: $i] :
( ( ( member @ SV421 @ SV139 )
= $false )
| ( ( ~ ( member @ SV457 @ SV139 )
| ( ( apply_to_two_arguments @ SV323 @ SV421 @ SV457 )
= ( apply_to_two_arguments @ SV323 @ SV457 @ SV421 ) ) )
= $true )
| ( ( commutes @ SV139 @ SV323 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1700]) ).
thf(1764,plain,
! [SV142: $i,SV326: $i] :
( ( ( member @ empty_set @ SV326 )
= $false )
| ( ( ( member @ ( f43 @ SV142 @ SV326 ) @ SV326 )
| ( member @ SV142 @ SV326 ) )
= $true )
| ( ( little_set @ SV326 )
= $false )
| ( ( member @ SV142 @ natural_numbers )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1701]) ).
thf(1765,plain,
! [SV143: $i,SV327: $i] :
( ( ( member @ empty_set @ SV327 )
= $false )
| ( ( ~ ( member @ ( successor @ ( f43 @ SV143 @ SV327 ) ) @ SV327 )
| ( member @ SV143 @ SV327 ) )
= $true )
| ( ( little_set @ SV327 )
= $false )
| ( ( member @ SV143 @ natural_numbers )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1702]) ).
thf(1766,plain,
! [SV329: $i,SV148: $i] :
( ( ( member @ ( f46 @ SV148 @ SV329 ) @ natural_numbers )
= $true )
| ( ( member @ SV148 @ SV329 )
= $true )
| ( ( member @ ( f45 @ SV148 @ SV329 ) @ natural_numbers )
= $true )
| ( ( little_set @ SV329 )
= $false )
| ( ( member @ SV148 @ plus )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1704]) ).
thf(1767,plain,
! [SV330: $i,SV149: $i] :
( ( ( member @ ( f47 @ SV149 @ SV330 ) @ natural_numbers )
= $true )
| ( ( member @ SV149 @ SV330 )
= $true )
| ( ( member @ ( f45 @ SV149 @ SV330 ) @ natural_numbers )
= $true )
| ( ( little_set @ SV330 )
= $false )
| ( ( member @ SV149 @ plus )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1705]) ).
thf(1768,plain,
! [SV331: $i,SV150: $i] :
( ( ( member @ ( f48 @ SV150 @ SV331 ) @ natural_numbers )
= $true )
| ( ( member @ SV150 @ SV331 )
= $true )
| ( ( member @ ( f45 @ SV150 @ SV331 ) @ natural_numbers )
= $true )
| ( ( little_set @ SV331 )
= $false )
| ( ( member @ SV150 @ plus )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1706]) ).
thf(1769,plain,
! [SV332: $i,SV151: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ ( f46 @ SV151 @ SV332 ) @ ( f47 @ SV151 @ SV332 ) ) @ ( f48 @ SV151 @ SV332 ) ) @ SV332 )
= $true )
| ( ( member @ SV151 @ SV332 )
= $true )
| ( ( member @ ( f45 @ SV151 @ SV332 ) @ natural_numbers )
= $true )
| ( ( little_set @ SV332 )
= $false )
| ( ( member @ SV151 @ plus )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1707]) ).
thf(1770,plain,
! [SV333: $i,SV152: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f46 @ SV152 @ SV333 ) ) @ ( f47 @ SV152 @ SV333 ) ) @ ( successor @ ( f48 @ SV152 @ SV333 ) ) ) @ SV333 ) )
= $true )
| ( ( member @ SV152 @ SV333 )
= $true )
| ( ( member @ ( f45 @ SV152 @ SV333 ) @ natural_numbers )
= $true )
| ( ( little_set @ SV333 )
= $false )
| ( ( member @ SV152 @ plus )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1708]) ).
thf(1771,plain,
! [SV334: $i,SV153: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV153 @ SV334 ) ) @ ( f45 @ SV153 @ SV334 ) ) @ SV334 )
= $false )
| ( ( ( member @ ( f46 @ SV153 @ SV334 ) @ natural_numbers )
| ( member @ SV153 @ SV334 ) )
= $true )
| ( ( little_set @ SV334 )
= $false )
| ( ( member @ SV153 @ plus )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1709]) ).
thf(1772,plain,
! [SV335: $i,SV154: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV154 @ SV335 ) ) @ ( f45 @ SV154 @ SV335 ) ) @ SV335 )
= $false )
| ( ( ( member @ ( f47 @ SV154 @ SV335 ) @ natural_numbers )
| ( member @ SV154 @ SV335 ) )
= $true )
| ( ( little_set @ SV335 )
= $false )
| ( ( member @ SV154 @ plus )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1710]) ).
thf(1773,plain,
! [SV336: $i,SV155: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV155 @ SV336 ) ) @ ( f45 @ SV155 @ SV336 ) ) @ SV336 )
= $false )
| ( ( ( member @ ( f48 @ SV155 @ SV336 ) @ natural_numbers )
| ( member @ SV155 @ SV336 ) )
= $true )
| ( ( little_set @ SV336 )
= $false )
| ( ( member @ SV155 @ plus )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1711]) ).
thf(1774,plain,
! [SV337: $i,SV156: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV156 @ SV337 ) ) @ ( f45 @ SV156 @ SV337 ) ) @ SV337 )
= $false )
| ( ( ( member @ ( ordered_pair @ ( ordered_pair @ ( f46 @ SV156 @ SV337 ) @ ( f47 @ SV156 @ SV337 ) ) @ ( f48 @ SV156 @ SV337 ) ) @ SV337 )
| ( member @ SV156 @ SV337 ) )
= $true )
| ( ( little_set @ SV337 )
= $false )
| ( ( member @ SV156 @ plus )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1712]) ).
thf(1775,plain,
! [SV338: $i,SV157: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV157 @ SV338 ) ) @ ( f45 @ SV157 @ SV338 ) ) @ SV338 )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f46 @ SV157 @ SV338 ) ) @ ( f47 @ SV157 @ SV338 ) ) @ ( successor @ ( f48 @ SV157 @ SV338 ) ) ) @ SV338 )
| ( member @ SV157 @ SV338 ) )
= $true )
| ( ( little_set @ SV338 )
= $false )
| ( ( member @ SV157 @ plus )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1713]) ).
thf(1776,plain,
! [SV160: $i,SV458: $i,SV422: $i,SV340: $i] :
( ( ( ~ ( member @ SV340 @ natural_numbers ) )
= $true )
| ( ( ~ ( member @ SV422 @ natural_numbers )
| ~ ( member @ SV458 @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV340 @ SV422 ) @ SV458 ) @ ( f49 @ SV160 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ SV340 ) @ SV422 ) @ ( successor @ SV458 ) ) @ ( f49 @ SV160 ) ) )
= $true )
| ( ( little_set @ SV160 )
= $false )
| ( ( member @ SV160 @ plus )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1715]) ).
thf(1777,plain,
! [SV341: $i,SV162: $i] :
( ( ( member @ ( f51 @ SV162 @ SV341 ) @ natural_numbers )
= $true )
| ( ( member @ SV162 @ SV341 )
= $true )
| ( ( member @ ( f50 @ SV162 @ SV341 ) @ natural_numbers )
= $true )
| ( ( little_set @ SV341 )
= $false )
| ( ( member @ SV162 @ times )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1716]) ).
thf(1778,plain,
! [SV342: $i,SV163: $i] :
( ( ( member @ ( f52 @ SV163 @ SV342 ) @ natural_numbers )
= $true )
| ( ( member @ SV163 @ SV342 )
= $true )
| ( ( member @ ( f50 @ SV163 @ SV342 ) @ natural_numbers )
= $true )
| ( ( little_set @ SV342 )
= $false )
| ( ( member @ SV163 @ times )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1717]) ).
thf(1779,plain,
! [SV343: $i,SV164: $i] :
( ( ( member @ ( f53 @ SV164 @ SV343 ) @ natural_numbers )
= $true )
| ( ( member @ SV164 @ SV343 )
= $true )
| ( ( member @ ( f50 @ SV164 @ SV343 ) @ natural_numbers )
= $true )
| ( ( little_set @ SV343 )
= $false )
| ( ( member @ SV164 @ times )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1718]) ).
thf(1780,plain,
! [SV344: $i,SV165: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ ( f51 @ SV165 @ SV344 ) @ ( f52 @ SV165 @ SV344 ) ) @ ( f53 @ SV165 @ SV344 ) ) @ SV344 )
= $true )
| ( ( member @ SV165 @ SV344 )
= $true )
| ( ( member @ ( f50 @ SV165 @ SV344 ) @ natural_numbers )
= $true )
| ( ( little_set @ SV344 )
= $false )
| ( ( member @ SV165 @ times )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1719]) ).
thf(1781,plain,
! [SV345: $i,SV166: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f51 @ SV166 @ SV345 ) ) @ ( f52 @ SV166 @ SV345 ) ) @ ( apply_to_two_arguments @ plus @ ( f53 @ SV166 @ SV345 ) @ ( f52 @ SV166 @ SV345 ) ) ) @ SV345 ) )
= $true )
| ( ( member @ SV166 @ SV345 )
= $true )
| ( ( member @ ( f50 @ SV166 @ SV345 ) @ natural_numbers )
= $true )
| ( ( little_set @ SV345 )
= $false )
| ( ( member @ SV166 @ times )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1720]) ).
thf(1782,plain,
! [SV346: $i,SV167: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV167 @ SV346 ) ) @ empty_set ) @ SV346 )
= $false )
| ( ( ( member @ ( f51 @ SV167 @ SV346 ) @ natural_numbers )
| ( member @ SV167 @ SV346 ) )
= $true )
| ( ( little_set @ SV346 )
= $false )
| ( ( member @ SV167 @ times )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1721]) ).
thf(1783,plain,
! [SV347: $i,SV168: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV168 @ SV347 ) ) @ empty_set ) @ SV347 )
= $false )
| ( ( ( member @ ( f52 @ SV168 @ SV347 ) @ natural_numbers )
| ( member @ SV168 @ SV347 ) )
= $true )
| ( ( little_set @ SV347 )
= $false )
| ( ( member @ SV168 @ times )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1722]) ).
thf(1784,plain,
! [SV348: $i,SV169: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV169 @ SV348 ) ) @ empty_set ) @ SV348 )
= $false )
| ( ( ( member @ ( f53 @ SV169 @ SV348 ) @ natural_numbers )
| ( member @ SV169 @ SV348 ) )
= $true )
| ( ( little_set @ SV348 )
= $false )
| ( ( member @ SV169 @ times )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1723]) ).
thf(1785,plain,
! [SV349: $i,SV170: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV170 @ SV349 ) ) @ empty_set ) @ SV349 )
= $false )
| ( ( ( member @ ( ordered_pair @ ( ordered_pair @ ( f51 @ SV170 @ SV349 ) @ ( f52 @ SV170 @ SV349 ) ) @ ( f53 @ SV170 @ SV349 ) ) @ SV349 )
| ( member @ SV170 @ SV349 ) )
= $true )
| ( ( little_set @ SV349 )
= $false )
| ( ( member @ SV170 @ times )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1724]) ).
thf(1786,plain,
! [SV350: $i,SV171: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV171 @ SV350 ) ) @ empty_set ) @ SV350 )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f51 @ SV171 @ SV350 ) ) @ ( f52 @ SV171 @ SV350 ) ) @ ( apply_to_two_arguments @ plus @ ( f53 @ SV171 @ SV350 ) @ ( f52 @ SV171 @ SV350 ) ) ) @ SV350 )
| ( member @ SV171 @ SV350 ) )
= $true )
| ( ( little_set @ SV350 )
= $false )
| ( ( member @ SV171 @ times )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1725]) ).
thf(1787,plain,
! [SV174: $i,SV459: $i,SV423: $i,SV352: $i] :
( ( ( ~ ( member @ SV352 @ natural_numbers ) )
= $true )
| ( ( ~ ( member @ SV423 @ natural_numbers )
| ~ ( member @ SV459 @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV352 @ SV423 ) @ SV459 ) @ ( f54 @ SV174 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ SV352 ) @ SV423 ) @ ( apply_to_two_arguments @ plus @ SV459 @ SV423 ) ) @ ( f54 @ SV174 ) ) )
= $true )
| ( ( little_set @ SV174 )
= $false )
| ( ( member @ SV174 @ times )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1727]) ).
thf(1788,plain,
! [SV191: $i,SV424: $i,SV353: $i,SV460: $i] :
( ( ( ~ ( little_set @ SV460 ) )
= $true )
| ( ( ( SV353
!= ( ordered_pair @ SV424 @ SV460 ) )
| ~ ( member @ SV191 @ SV460 ) )
= $true )
| ( ( little_set @ SV424 )
= $false )
| ( ( member @ SV191 @ ( second @ SV353 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1729]) ).
thf(1789,plain,
! [SV425: $i,SV192: $i,SV461: $i,SV354: $i] :
( ( ( ( apply_to_two_arguments @ SV354 @ ( apply @ SV461 @ ( f38 @ SV192 @ SV354 @ SV425 @ SV461 ) ) @ ( f38 @ SV192 @ SV354 @ SV425 @ SV461 ) )
!= SV425 )
= $true )
| ( ( ( apply_to_two_arguments @ SV354 @ ( f38 @ SV192 @ SV354 @ SV425 @ SV461 ) @ ( apply @ SV461 @ ( f38 @ SV192 @ SV354 @ SV425 @ SV461 ) ) )
!= SV425 )
= $true )
| ( ( maps @ SV461 @ SV192 @ SV192 )
= $false )
| ( ( inverse @ SV192 @ SV354 @ SV425 @ SV461 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1730]) ).
thf(1790,plain,
! [SV193: $i,SV355: $i,SV426: $i] :
( ( ( ~ ( member @ SV426 @ natural_numbers ) )
= $true )
| ( ( ( ( apply_to_two_arguments @ times @ SV355 @ SV426 )
!= SV193 )
| ( member @ SV355 @ ( non_ordered_pair @ ( successor @ empty_set ) @ SV193 ) ) )
= $true )
| ( ( member @ SV355 @ natural_numbers )
= $false )
| ( ( member @ SV193 @ prime_numbers )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1731]) ).
thf(1791,plain,
! [SV356: $i,SV478: $i,SV462: $i,SV427: $i,SV195: $i] :
( ( ( little_set @ SV195 )
= $false )
| ( ( ~ ( little_set @ SV427 )
| ~ ( little_set @ SV462 )
| ~ ( little_set @ SV478 )
| ( SV195
!= ( ordered_pair @ SV427 @ ( ordered_pair @ SV462 @ SV478 ) ) )
| ~ ( member @ ( ordered_pair @ SV427 @ ( ordered_pair @ SV478 @ SV462 ) ) @ SV356 ) )
= $true )
| ( ( member @ SV195 @ ( flip_range_of @ SV356 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1732]) ).
thf(1792,plain,
! [SV197: $i,SV429: $i,SV358: $i,SV463: $i] :
( ( ( ~ ( little_set @ SV463 ) )
= $true )
| ( ( ( SV358
!= ( ordered_pair @ SV429 @ SV463 ) )
| ~ ( member @ SV197 @ SV429 ) )
= $true )
| ( ( little_set @ SV429 )
= $false )
| ( ( member @ SV197 @ ( first @ SV358 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1734]) ).
thf(1793,plain,
! [SV198: $i,SV359: $i,SV430: $i,SV464: $i] :
( ( ( ~ ( ordered_pair_predicate @ SV464 ) )
= $true )
| ( ( ~ ( member @ SV464 @ SV430 )
| ~ ( member @ ( first @ SV464 ) @ SV359 )
| ( ( second @ SV464 )
!= SV198 ) )
= $true )
| ( ( little_set @ SV198 )
= $false )
| ( ( member @ SV198 @ ( image @ SV359 @ SV430 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1735]) ).
thf(1794,plain,
! [SV360: $i,SV479: $i,SV465: $i,SV431: $i,SV199: $i] :
( ( ( little_set @ SV199 )
= $false )
| ( ( ~ ( little_set @ SV431 )
| ~ ( little_set @ SV465 )
| ~ ( little_set @ SV479 )
| ( SV199
!= ( ordered_pair @ SV431 @ ( ordered_pair @ SV465 @ SV479 ) ) )
| ~ ( member @ ( ordered_pair @ SV465 @ ( ordered_pair @ SV479 @ SV431 ) ) @ SV360 ) )
= $true )
| ( ( member @ SV199 @ ( rotate_right @ SV360 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1736]) ).
thf(1795,plain,
! [SV432: $i,SV361: $i,SV483: $i,SV480: $i,SV466: $i,SV201: $i] :
( ( ( ~ ( little_set @ SV201 ) )
= $true )
| ( ( ~ ( little_set @ SV466 )
| ~ ( little_set @ SV480 )
| ~ ( little_set @ SV483 )
| ( SV201
!= ( ordered_pair @ SV466 @ SV480 ) )
| ~ ( member @ ( ordered_pair @ SV466 @ SV483 ) @ SV361 )
| ~ ( member @ ( ordered_pair @ SV483 @ SV480 ) @ SV432 ) )
= $true )
| ( ( member @ SV201 @ ( compose @ SV361 @ SV432 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1737]) ).
thf(1796,plain,
! [SV362: $i,SV202: $i,SV433: $i] :
( ( ( little_set @ SV433 )
= $false )
| ( ( SV202
!= ( ordered_pair @ SV362 @ SV433 ) )
= $true )
| ( ( little_set @ SV362 )
= $false )
| ( ( ordered_pair_predicate @ SV202 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1738]) ).
thf(1797,plain,
! [SV204: $i,SV364: $i] :
( ( ( ( apply_to_two_arguments @ plus @ SV364 @ SV364 )
= SV204 )
= $false )
| ( ( member @ SV364 @ natural_numbers )
= $false )
| ( ( member @ SV204 @ natural_numbers )
= $false )
| ( ( member @ SV204 @ even_numbers )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1740]) ).
thf(1798,plain,
! [SV206: $i,SV481: $i,SV467: $i,SV435: $i,SV366: $i] :
( ( ( closed @ SV366 @ SV435 )
= $false )
| ( ( ~ ( closed @ SV467 @ SV481 )
| ~ ( maps @ SV206 @ SV366 @ SV467 )
| ( ( apply @ SV206 @ ( apply_to_two_arguments @ SV435 @ ( f32 @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 ) @ ( f33 @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 ) ) )
!= ( apply_to_two_arguments @ SV481 @ ( apply @ SV206 @ ( f32 @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 ) ) @ ( apply @ SV206 @ ( f33 @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 ) ) ) ) )
= $true )
| ( ( homomorphism @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1741]) ).
thf(1799,plain,
! [SV207: $i,SV367: $i,SV436: $i] :
( ( ( maps @ SV436 @ SV367 @ SV207 )
= $false )
| ( ( ( ( range_of @ SV436 )
!= SV207 )
| ~ ( one_to_one_function @ SV436 ) )
= $true )
| ( ( member @ SV367 @ natural_numbers )
= $false )
| ( ( finite @ SV207 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1742]) ).
thf(1800,plain,
! [SV437: $i,SV368: $i,SV208: $i] :
( ( ( ( domain_of @ SV208 )
= SV368 )
= $false )
| ( ( ~ ( subset @ ( range_of @ SV208 ) @ SV437 ) )
= $true )
| ( ( function @ SV208 )
= $false )
| ( ( maps @ SV208 @ SV368 @ SV437 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1743]) ).
thf(1801,plain,
! [SV212: $i,SV370: $i,SV438: $i] :
( ( ( ordered_pair_predicate @ SV438 )
= $false )
| ( ( ~ ( member @ SV438 @ SV370 )
| ( SV212
!= ( second @ SV438 ) ) )
= $true )
| ( ( little_set @ SV212 )
= $false )
| ( ( member @ SV212 @ ( range_of @ SV370 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1745]) ).
thf(1802,plain,
! [SV214: $i,SV439: $i,SV372: $i] :
( ( ( ( apply_to_two_arguments @ SV372 @ SV439 @ ( f37 @ SV214 @ SV372 @ SV439 ) )
= ( f37 @ SV214 @ SV372 @ SV439 ) )
= $false )
| ( ( ( apply_to_two_arguments @ SV372 @ ( f37 @ SV214 @ SV372 @ SV439 ) @ SV439 )
!= ( f37 @ SV214 @ SV372 @ SV439 ) )
= $true )
| ( ( member @ SV439 @ SV214 )
= $false )
| ( ( identity @ SV214 @ SV372 @ SV439 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1746]) ).
thf(1803,plain,
! [SV215: $i,SV373: $i,SV440: $i] :
( ( ( ordered_pair_predicate @ SV440 )
= $false )
| ( ( ~ ( member @ SV440 @ SV373 )
| ( SV215
!= ( first @ SV440 ) ) )
= $true )
| ( ( little_set @ SV215 )
= $false )
| ( ( member @ SV215 @ ( domain_of @ SV373 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1747]) ).
thf(1804,plain,
! [SV216: $i,SV441: $i,SV374: $i,SV468: $i] :
( ( ( ~ ( member @ SV468 @ SV374 ) )
= $true )
| ( ( ( ( first @ SV468 )
!= SV441 )
| ~ ( member @ SV216 @ ( second @ SV468 ) ) )
= $true )
| ( ( ordered_pair_predicate @ SV468 )
= $false )
| ( ( member @ SV216 @ ( apply @ SV374 @ SV441 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1748]) ).
thf(1805,plain,
! [SV382: $i,SV244: $i,SV35: $i] :
( ( ( ~ ( member @ ( first @ SV35 ) @ SV244 ) )
= $true )
| ( ( ~ ( member @ ( second @ SV35 ) @ SV382 ) )
= $true )
| ( ( ordered_pair_predicate @ SV35 )
= $false )
| ( ( little_set @ SV35 )
= $false )
| ( ( member @ SV35 @ ( cross_product @ SV244 @ SV382 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1749]) ).
thf(1806,plain,
! [SV68: $i,SV269: $i,SV442: $i,SV385: $i] :
( ( ( ~ ( little_set @ SV385 ) )
= $true )
| ( ( ~ ( little_set @ SV442 )
| ~ ( member @ ( ordered_pair @ SV269 @ SV385 ) @ SV68 )
| ~ ( member @ ( ordered_pair @ SV269 @ SV442 ) @ SV68 )
| ( SV385 = SV442 ) )
= $true )
| ( ( little_set @ SV269 )
= $false )
| ( ( single_valued_set @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1751]) ).
thf(1807,plain,
! [SV484: $i,SV482: $i,SV472: $i,SV446: $i,SV408: $i,SV303: $i,SV119: $i] :
( ( ( homomorphism @ SV119 @ SV303 @ SV408 @ SV446 @ SV472 )
= $false )
| ( ( ~ ( member @ SV482 @ SV303 )
| ~ ( member @ SV484 @ SV303 )
| ( ( apply @ SV119 @ ( apply_to_two_arguments @ SV408 @ SV482 @ SV484 ) )
= ( apply_to_two_arguments @ SV472 @ ( apply @ SV119 @ SV482 ) @ ( apply @ SV119 @ SV484 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1754]) ).
thf(1808,plain,
! [SV409: $i,SV304: $i,SV120: $i,SV473: $i,SV447: $i] :
( ( ( ~ ( closed @ SV447 @ SV473 ) )
= $true )
| ( ( ~ ( maps @ SV120 @ SV304 @ SV447 )
| ( member @ ( f32 @ SV120 @ SV304 @ SV409 @ SV447 @ SV473 ) @ SV304 ) )
= $true )
| ( ( closed @ SV304 @ SV409 )
= $false )
| ( ( homomorphism @ SV120 @ SV304 @ SV409 @ SV447 @ SV473 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1755]) ).
thf(1809,plain,
! [SV410: $i,SV305: $i,SV121: $i,SV474: $i,SV448: $i] :
( ( ( ~ ( closed @ SV448 @ SV474 ) )
= $true )
| ( ( ~ ( maps @ SV121 @ SV305 @ SV448 )
| ( member @ ( f33 @ SV121 @ SV305 @ SV410 @ SV448 @ SV474 ) @ SV305 ) )
= $true )
| ( ( closed @ SV305 @ SV410 )
= $false )
| ( ( homomorphism @ SV121 @ SV305 @ SV410 @ SV448 @ SV474 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1756]) ).
thf(1810,plain,
! [SV306: $i,SV475: $i,SV449: $i,SV122: $i,SV411: $i] :
( ( ( member @ SV411 @ SV122 )
= $false )
| ( ( ~ ( member @ SV449 @ SV122 )
| ~ ( member @ SV475 @ SV122 )
| ( ( apply_to_two_arguments @ SV306 @ ( apply_to_two_arguments @ SV306 @ SV411 @ SV449 ) @ SV475 )
= ( apply_to_two_arguments @ SV306 @ SV411 @ ( apply_to_two_arguments @ SV306 @ SV449 @ SV475 ) ) ) )
= $true )
| ( ( associative @ SV122 @ SV306 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1757]) ).
thf(1811,plain,
! [SV417: $i,SV453: $i,SV315: $i,SV131: $i,SV476: $i] :
( ( ( member @ SV476 @ SV131 )
= $false )
| ( ( ( apply_to_two_arguments @ SV315 @ ( apply @ SV453 @ SV476 ) @ SV476 )
= SV417 )
= $true )
| ( ( inverse @ SV131 @ SV315 @ SV417 @ SV453 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1760]) ).
thf(1812,plain,
! [SV418: $i,SV454: $i,SV316: $i,SV132: $i,SV477: $i] :
( ( ( member @ SV477 @ SV132 )
= $false )
| ( ( ( apply_to_two_arguments @ SV316 @ SV477 @ ( apply @ SV454 @ SV477 ) )
= SV418 )
= $true )
| ( ( inverse @ SV132 @ SV316 @ SV418 @ SV454 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1761]) ).
thf(1813,plain,
! [SV456: $i,SV420: $i,SV322: $i,SV138: $i] :
( ( ( associative @ SV138 @ SV322 )
= $false )
| ( ( ~ ( identity @ SV138 @ SV322 @ SV420 )
| ~ ( inverse @ SV138 @ SV322 @ SV420 @ SV456 ) )
= $true )
| ( ( closed @ SV138 @ SV322 )
= $false )
| ( ( group @ SV138 @ SV322 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1762]) ).
thf(1814,plain,
! [SV421: $i,SV323: $i,SV139: $i,SV457: $i] :
( ( ( ~ ( member @ SV457 @ SV139 ) )
= $true )
| ( ( ( apply_to_two_arguments @ SV323 @ SV421 @ SV457 )
= ( apply_to_two_arguments @ SV323 @ SV457 @ SV421 ) )
= $true )
| ( ( member @ SV421 @ SV139 )
= $false )
| ( ( commutes @ SV139 @ SV323 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1763]) ).
thf(1815,plain,
! [SV326: $i,SV142: $i] :
( ( ( member @ ( f43 @ SV142 @ SV326 ) @ SV326 )
= $true )
| ( ( member @ SV142 @ SV326 )
= $true )
| ( ( member @ empty_set @ SV326 )
= $false )
| ( ( little_set @ SV326 )
= $false )
| ( ( member @ SV142 @ natural_numbers )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1764]) ).
thf(1816,plain,
! [SV327: $i,SV143: $i] :
( ( ( ~ ( member @ ( successor @ ( f43 @ SV143 @ SV327 ) ) @ SV327 ) )
= $true )
| ( ( member @ SV143 @ SV327 )
= $true )
| ( ( member @ empty_set @ SV327 )
= $false )
| ( ( little_set @ SV327 )
= $false )
| ( ( member @ SV143 @ natural_numbers )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1765]) ).
thf(1817,plain,
! [SV333: $i,SV152: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f46 @ SV152 @ SV333 ) ) @ ( f47 @ SV152 @ SV333 ) ) @ ( successor @ ( f48 @ SV152 @ SV333 ) ) ) @ SV333 )
= $false )
| ( ( member @ SV152 @ SV333 )
= $true )
| ( ( member @ ( f45 @ SV152 @ SV333 ) @ natural_numbers )
= $true )
| ( ( little_set @ SV333 )
= $false )
| ( ( member @ SV152 @ plus )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1770]) ).
thf(1818,plain,
! [SV334: $i,SV153: $i] :
( ( ( member @ ( f46 @ SV153 @ SV334 ) @ natural_numbers )
= $true )
| ( ( member @ SV153 @ SV334 )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV153 @ SV334 ) ) @ ( f45 @ SV153 @ SV334 ) ) @ SV334 )
= $false )
| ( ( little_set @ SV334 )
= $false )
| ( ( member @ SV153 @ plus )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1771]) ).
thf(1819,plain,
! [SV335: $i,SV154: $i] :
( ( ( member @ ( f47 @ SV154 @ SV335 ) @ natural_numbers )
= $true )
| ( ( member @ SV154 @ SV335 )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV154 @ SV335 ) ) @ ( f45 @ SV154 @ SV335 ) ) @ SV335 )
= $false )
| ( ( little_set @ SV335 )
= $false )
| ( ( member @ SV154 @ plus )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1772]) ).
thf(1820,plain,
! [SV336: $i,SV155: $i] :
( ( ( member @ ( f48 @ SV155 @ SV336 ) @ natural_numbers )
= $true )
| ( ( member @ SV155 @ SV336 )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV155 @ SV336 ) ) @ ( f45 @ SV155 @ SV336 ) ) @ SV336 )
= $false )
| ( ( little_set @ SV336 )
= $false )
| ( ( member @ SV155 @ plus )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1773]) ).
thf(1821,plain,
! [SV337: $i,SV156: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ ( f46 @ SV156 @ SV337 ) @ ( f47 @ SV156 @ SV337 ) ) @ ( f48 @ SV156 @ SV337 ) ) @ SV337 )
= $true )
| ( ( member @ SV156 @ SV337 )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV156 @ SV337 ) ) @ ( f45 @ SV156 @ SV337 ) ) @ SV337 )
= $false )
| ( ( little_set @ SV337 )
= $false )
| ( ( member @ SV156 @ plus )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1774]) ).
thf(1822,plain,
! [SV338: $i,SV157: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f46 @ SV157 @ SV338 ) ) @ ( f47 @ SV157 @ SV338 ) ) @ ( successor @ ( f48 @ SV157 @ SV338 ) ) ) @ SV338 ) )
= $true )
| ( ( member @ SV157 @ SV338 )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV157 @ SV338 ) ) @ ( f45 @ SV157 @ SV338 ) ) @ SV338 )
= $false )
| ( ( little_set @ SV338 )
= $false )
| ( ( member @ SV157 @ plus )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1775]) ).
thf(1823,plain,
! [SV160: $i,SV458: $i,SV422: $i,SV340: $i] :
( ( ( member @ SV340 @ natural_numbers )
= $false )
| ( ( ~ ( member @ SV422 @ natural_numbers )
| ~ ( member @ SV458 @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV340 @ SV422 ) @ SV458 ) @ ( f49 @ SV160 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ SV340 ) @ SV422 ) @ ( successor @ SV458 ) ) @ ( f49 @ SV160 ) ) )
= $true )
| ( ( little_set @ SV160 )
= $false )
| ( ( member @ SV160 @ plus )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1776]) ).
thf(1824,plain,
! [SV345: $i,SV166: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f51 @ SV166 @ SV345 ) ) @ ( f52 @ SV166 @ SV345 ) ) @ ( apply_to_two_arguments @ plus @ ( f53 @ SV166 @ SV345 ) @ ( f52 @ SV166 @ SV345 ) ) ) @ SV345 )
= $false )
| ( ( member @ SV166 @ SV345 )
= $true )
| ( ( member @ ( f50 @ SV166 @ SV345 ) @ natural_numbers )
= $true )
| ( ( little_set @ SV345 )
= $false )
| ( ( member @ SV166 @ times )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1781]) ).
thf(1825,plain,
! [SV346: $i,SV167: $i] :
( ( ( member @ ( f51 @ SV167 @ SV346 ) @ natural_numbers )
= $true )
| ( ( member @ SV167 @ SV346 )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV167 @ SV346 ) ) @ empty_set ) @ SV346 )
= $false )
| ( ( little_set @ SV346 )
= $false )
| ( ( member @ SV167 @ times )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1782]) ).
thf(1826,plain,
! [SV347: $i,SV168: $i] :
( ( ( member @ ( f52 @ SV168 @ SV347 ) @ natural_numbers )
= $true )
| ( ( member @ SV168 @ SV347 )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV168 @ SV347 ) ) @ empty_set ) @ SV347 )
= $false )
| ( ( little_set @ SV347 )
= $false )
| ( ( member @ SV168 @ times )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1783]) ).
thf(1827,plain,
! [SV348: $i,SV169: $i] :
( ( ( member @ ( f53 @ SV169 @ SV348 ) @ natural_numbers )
= $true )
| ( ( member @ SV169 @ SV348 )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV169 @ SV348 ) ) @ empty_set ) @ SV348 )
= $false )
| ( ( little_set @ SV348 )
= $false )
| ( ( member @ SV169 @ times )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1784]) ).
thf(1828,plain,
! [SV349: $i,SV170: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ ( f51 @ SV170 @ SV349 ) @ ( f52 @ SV170 @ SV349 ) ) @ ( f53 @ SV170 @ SV349 ) ) @ SV349 )
= $true )
| ( ( member @ SV170 @ SV349 )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV170 @ SV349 ) ) @ empty_set ) @ SV349 )
= $false )
| ( ( little_set @ SV349 )
= $false )
| ( ( member @ SV170 @ times )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1785]) ).
thf(1829,plain,
! [SV350: $i,SV171: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f51 @ SV171 @ SV350 ) ) @ ( f52 @ SV171 @ SV350 ) ) @ ( apply_to_two_arguments @ plus @ ( f53 @ SV171 @ SV350 ) @ ( f52 @ SV171 @ SV350 ) ) ) @ SV350 ) )
= $true )
| ( ( member @ SV171 @ SV350 )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV171 @ SV350 ) ) @ empty_set ) @ SV350 )
= $false )
| ( ( little_set @ SV350 )
= $false )
| ( ( member @ SV171 @ times )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1786]) ).
thf(1830,plain,
! [SV174: $i,SV459: $i,SV423: $i,SV352: $i] :
( ( ( member @ SV352 @ natural_numbers )
= $false )
| ( ( ~ ( member @ SV423 @ natural_numbers )
| ~ ( member @ SV459 @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV352 @ SV423 ) @ SV459 ) @ ( f54 @ SV174 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ SV352 ) @ SV423 ) @ ( apply_to_two_arguments @ plus @ SV459 @ SV423 ) ) @ ( f54 @ SV174 ) ) )
= $true )
| ( ( little_set @ SV174 )
= $false )
| ( ( member @ SV174 @ times )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1787]) ).
thf(1831,plain,
! [SV191: $i,SV424: $i,SV353: $i,SV460: $i] :
( ( ( little_set @ SV460 )
= $false )
| ( ( ( SV353
!= ( ordered_pair @ SV424 @ SV460 ) )
| ~ ( member @ SV191 @ SV460 ) )
= $true )
| ( ( little_set @ SV424 )
= $false )
| ( ( member @ SV191 @ ( second @ SV353 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1788]) ).
thf(1832,plain,
! [SV425: $i,SV192: $i,SV461: $i,SV354: $i] :
( ( ( ( apply_to_two_arguments @ SV354 @ ( apply @ SV461 @ ( f38 @ SV192 @ SV354 @ SV425 @ SV461 ) ) @ ( f38 @ SV192 @ SV354 @ SV425 @ SV461 ) )
= SV425 )
= $false )
| ( ( ( apply_to_two_arguments @ SV354 @ ( f38 @ SV192 @ SV354 @ SV425 @ SV461 ) @ ( apply @ SV461 @ ( f38 @ SV192 @ SV354 @ SV425 @ SV461 ) ) )
!= SV425 )
= $true )
| ( ( maps @ SV461 @ SV192 @ SV192 )
= $false )
| ( ( inverse @ SV192 @ SV354 @ SV425 @ SV461 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1789]) ).
thf(1833,plain,
! [SV193: $i,SV355: $i,SV426: $i] :
( ( ( member @ SV426 @ natural_numbers )
= $false )
| ( ( ( ( apply_to_two_arguments @ times @ SV355 @ SV426 )
!= SV193 )
| ( member @ SV355 @ ( non_ordered_pair @ ( successor @ empty_set ) @ SV193 ) ) )
= $true )
| ( ( member @ SV355 @ natural_numbers )
= $false )
| ( ( member @ SV193 @ prime_numbers )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1790]) ).
thf(1834,plain,
! [SV356: $i,SV195: $i,SV478: $i,SV462: $i,SV427: $i] :
( ( ( ~ ( little_set @ SV427 ) )
= $true )
| ( ( ~ ( little_set @ SV462 )
| ~ ( little_set @ SV478 )
| ( SV195
!= ( ordered_pair @ SV427 @ ( ordered_pair @ SV462 @ SV478 ) ) )
| ~ ( member @ ( ordered_pair @ SV427 @ ( ordered_pair @ SV478 @ SV462 ) ) @ SV356 ) )
= $true )
| ( ( little_set @ SV195 )
= $false )
| ( ( member @ SV195 @ ( flip_range_of @ SV356 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1791]) ).
thf(1835,plain,
! [SV197: $i,SV429: $i,SV358: $i,SV463: $i] :
( ( ( little_set @ SV463 )
= $false )
| ( ( ( SV358
!= ( ordered_pair @ SV429 @ SV463 ) )
| ~ ( member @ SV197 @ SV429 ) )
= $true )
| ( ( little_set @ SV429 )
= $false )
| ( ( member @ SV197 @ ( first @ SV358 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1792]) ).
thf(1836,plain,
! [SV198: $i,SV359: $i,SV430: $i,SV464: $i] :
( ( ( ordered_pair_predicate @ SV464 )
= $false )
| ( ( ~ ( member @ SV464 @ SV430 )
| ~ ( member @ ( first @ SV464 ) @ SV359 )
| ( ( second @ SV464 )
!= SV198 ) )
= $true )
| ( ( little_set @ SV198 )
= $false )
| ( ( member @ SV198 @ ( image @ SV359 @ SV430 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1793]) ).
thf(1837,plain,
! [SV360: $i,SV199: $i,SV479: $i,SV465: $i,SV431: $i] :
( ( ( ~ ( little_set @ SV431 ) )
= $true )
| ( ( ~ ( little_set @ SV465 )
| ~ ( little_set @ SV479 )
| ( SV199
!= ( ordered_pair @ SV431 @ ( ordered_pair @ SV465 @ SV479 ) ) )
| ~ ( member @ ( ordered_pair @ SV465 @ ( ordered_pair @ SV479 @ SV431 ) ) @ SV360 ) )
= $true )
| ( ( little_set @ SV199 )
= $false )
| ( ( member @ SV199 @ ( rotate_right @ SV360 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1794]) ).
thf(1838,plain,
! [SV432: $i,SV361: $i,SV483: $i,SV480: $i,SV466: $i,SV201: $i] :
( ( ( little_set @ SV201 )
= $false )
| ( ( ~ ( little_set @ SV466 )
| ~ ( little_set @ SV480 )
| ~ ( little_set @ SV483 )
| ( SV201
!= ( ordered_pair @ SV466 @ SV480 ) )
| ~ ( member @ ( ordered_pair @ SV466 @ SV483 ) @ SV361 )
| ~ ( member @ ( ordered_pair @ SV483 @ SV480 ) @ SV432 ) )
= $true )
| ( ( member @ SV201 @ ( compose @ SV361 @ SV432 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1795]) ).
thf(1839,plain,
! [SV433: $i,SV362: $i,SV202: $i] :
( ( ( SV202
= ( ordered_pair @ SV362 @ SV433 ) )
= $false )
| ( ( little_set @ SV433 )
= $false )
| ( ( little_set @ SV362 )
= $false )
| ( ( ordered_pair_predicate @ SV202 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1796]) ).
thf(1840,plain,
! [SV435: $i,SV366: $i,SV206: $i,SV481: $i,SV467: $i] :
( ( ( ~ ( closed @ SV467 @ SV481 ) )
= $true )
| ( ( ~ ( maps @ SV206 @ SV366 @ SV467 )
| ( ( apply @ SV206 @ ( apply_to_two_arguments @ SV435 @ ( f32 @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 ) @ ( f33 @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 ) ) )
!= ( apply_to_two_arguments @ SV481 @ ( apply @ SV206 @ ( f32 @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 ) ) @ ( apply @ SV206 @ ( f33 @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 ) ) ) ) )
= $true )
| ( ( closed @ SV366 @ SV435 )
= $false )
| ( ( homomorphism @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1798]) ).
thf(1841,plain,
! [SV367: $i,SV207: $i,SV436: $i] :
( ( ( ( range_of @ SV436 )
!= SV207 )
= $true )
| ( ( ~ ( one_to_one_function @ SV436 ) )
= $true )
| ( ( maps @ SV436 @ SV367 @ SV207 )
= $false )
| ( ( member @ SV367 @ natural_numbers )
= $false )
| ( ( finite @ SV207 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1799]) ).
thf(1842,plain,
! [SV368: $i,SV437: $i,SV208: $i] :
( ( ( subset @ ( range_of @ SV208 ) @ SV437 )
= $false )
| ( ( ( domain_of @ SV208 )
= SV368 )
= $false )
| ( ( function @ SV208 )
= $false )
| ( ( maps @ SV208 @ SV368 @ SV437 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1800]) ).
thf(1843,plain,
! [SV212: $i,SV370: $i,SV438: $i] :
( ( ( ~ ( member @ SV438 @ SV370 ) )
= $true )
| ( ( SV212
!= ( second @ SV438 ) )
= $true )
| ( ( ordered_pair_predicate @ SV438 )
= $false )
| ( ( little_set @ SV212 )
= $false )
| ( ( member @ SV212 @ ( range_of @ SV370 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1801]) ).
thf(1844,plain,
! [SV439: $i,SV214: $i,SV372: $i] :
( ( ( ( apply_to_two_arguments @ SV372 @ ( f37 @ SV214 @ SV372 @ SV439 ) @ SV439 )
= ( f37 @ SV214 @ SV372 @ SV439 ) )
= $false )
| ( ( ( apply_to_two_arguments @ SV372 @ SV439 @ ( f37 @ SV214 @ SV372 @ SV439 ) )
= ( f37 @ SV214 @ SV372 @ SV439 ) )
= $false )
| ( ( member @ SV439 @ SV214 )
= $false )
| ( ( identity @ SV214 @ SV372 @ SV439 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1802]) ).
thf(1845,plain,
! [SV215: $i,SV373: $i,SV440: $i] :
( ( ( ~ ( member @ SV440 @ SV373 ) )
= $true )
| ( ( SV215
!= ( first @ SV440 ) )
= $true )
| ( ( ordered_pair_predicate @ SV440 )
= $false )
| ( ( little_set @ SV215 )
= $false )
| ( ( member @ SV215 @ ( domain_of @ SV373 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1803]) ).
thf(1846,plain,
! [SV216: $i,SV441: $i,SV374: $i,SV468: $i] :
( ( ( member @ SV468 @ SV374 )
= $false )
| ( ( ( ( first @ SV468 )
!= SV441 )
| ~ ( member @ SV216 @ ( second @ SV468 ) ) )
= $true )
| ( ( ordered_pair_predicate @ SV468 )
= $false )
| ( ( member @ SV216 @ ( apply @ SV374 @ SV441 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1804]) ).
thf(1847,plain,
! [SV382: $i,SV244: $i,SV35: $i] :
( ( ( member @ ( first @ SV35 ) @ SV244 )
= $false )
| ( ( ~ ( member @ ( second @ SV35 ) @ SV382 ) )
= $true )
| ( ( ordered_pair_predicate @ SV35 )
= $false )
| ( ( little_set @ SV35 )
= $false )
| ( ( member @ SV35 @ ( cross_product @ SV244 @ SV382 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1805]) ).
thf(1848,plain,
! [SV68: $i,SV269: $i,SV442: $i,SV385: $i] :
( ( ( little_set @ SV385 )
= $false )
| ( ( ~ ( little_set @ SV442 )
| ~ ( member @ ( ordered_pair @ SV269 @ SV385 ) @ SV68 )
| ~ ( member @ ( ordered_pair @ SV269 @ SV442 ) @ SV68 )
| ( SV385 = SV442 ) )
= $true )
| ( ( little_set @ SV269 )
= $false )
| ( ( single_valued_set @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1806]) ).
thf(1849,plain,
! [SV446: $i,SV472: $i,SV408: $i,SV119: $i,SV484: $i,SV303: $i,SV482: $i] :
( ( ( ~ ( member @ SV482 @ SV303 ) )
= $true )
| ( ( ~ ( member @ SV484 @ SV303 )
| ( ( apply @ SV119 @ ( apply_to_two_arguments @ SV408 @ SV482 @ SV484 ) )
= ( apply_to_two_arguments @ SV472 @ ( apply @ SV119 @ SV482 ) @ ( apply @ SV119 @ SV484 ) ) ) )
= $true )
| ( ( homomorphism @ SV119 @ SV303 @ SV408 @ SV446 @ SV472 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1807]) ).
thf(1850,plain,
! [SV409: $i,SV304: $i,SV120: $i,SV473: $i,SV447: $i] :
( ( ( closed @ SV447 @ SV473 )
= $false )
| ( ( ~ ( maps @ SV120 @ SV304 @ SV447 )
| ( member @ ( f32 @ SV120 @ SV304 @ SV409 @ SV447 @ SV473 ) @ SV304 ) )
= $true )
| ( ( closed @ SV304 @ SV409 )
= $false )
| ( ( homomorphism @ SV120 @ SV304 @ SV409 @ SV447 @ SV473 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1808]) ).
thf(1851,plain,
! [SV410: $i,SV305: $i,SV121: $i,SV474: $i,SV448: $i] :
( ( ( closed @ SV448 @ SV474 )
= $false )
| ( ( ~ ( maps @ SV121 @ SV305 @ SV448 )
| ( member @ ( f33 @ SV121 @ SV305 @ SV410 @ SV448 @ SV474 ) @ SV305 ) )
= $true )
| ( ( closed @ SV305 @ SV410 )
= $false )
| ( ( homomorphism @ SV121 @ SV305 @ SV410 @ SV448 @ SV474 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1809]) ).
thf(1852,plain,
! [SV411: $i,SV306: $i,SV475: $i,SV122: $i,SV449: $i] :
( ( ( ~ ( member @ SV449 @ SV122 ) )
= $true )
| ( ( ~ ( member @ SV475 @ SV122 )
| ( ( apply_to_two_arguments @ SV306 @ ( apply_to_two_arguments @ SV306 @ SV411 @ SV449 ) @ SV475 )
= ( apply_to_two_arguments @ SV306 @ SV411 @ ( apply_to_two_arguments @ SV306 @ SV449 @ SV475 ) ) ) )
= $true )
| ( ( member @ SV411 @ SV122 )
= $false )
| ( ( associative @ SV122 @ SV306 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1810]) ).
thf(1853,plain,
! [SV456: $i,SV420: $i,SV322: $i,SV138: $i] :
( ( ( ~ ( identity @ SV138 @ SV322 @ SV420 ) )
= $true )
| ( ( ~ ( inverse @ SV138 @ SV322 @ SV420 @ SV456 ) )
= $true )
| ( ( associative @ SV138 @ SV322 )
= $false )
| ( ( closed @ SV138 @ SV322 )
= $false )
| ( ( group @ SV138 @ SV322 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1813]) ).
thf(1854,plain,
! [SV421: $i,SV323: $i,SV139: $i,SV457: $i] :
( ( ( member @ SV457 @ SV139 )
= $false )
| ( ( ( apply_to_two_arguments @ SV323 @ SV421 @ SV457 )
= ( apply_to_two_arguments @ SV323 @ SV457 @ SV421 ) )
= $true )
| ( ( member @ SV421 @ SV139 )
= $false )
| ( ( commutes @ SV139 @ SV323 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1814]) ).
thf(1855,plain,
! [SV327: $i,SV143: $i] :
( ( ( member @ ( successor @ ( f43 @ SV143 @ SV327 ) ) @ SV327 )
= $false )
| ( ( member @ SV143 @ SV327 )
= $true )
| ( ( member @ empty_set @ SV327 )
= $false )
| ( ( little_set @ SV327 )
= $false )
| ( ( member @ SV143 @ natural_numbers )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1816]) ).
thf(1856,plain,
! [SV338: $i,SV157: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f46 @ SV157 @ SV338 ) ) @ ( f47 @ SV157 @ SV338 ) ) @ ( successor @ ( f48 @ SV157 @ SV338 ) ) ) @ SV338 )
= $false )
| ( ( member @ SV157 @ SV338 )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f45 @ SV157 @ SV338 ) ) @ ( f45 @ SV157 @ SV338 ) ) @ SV338 )
= $false )
| ( ( little_set @ SV338 )
= $false )
| ( ( member @ SV157 @ plus )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1822]) ).
thf(1857,plain,
! [SV160: $i,SV340: $i,SV458: $i,SV422: $i] :
( ( ( ~ ( member @ SV422 @ natural_numbers ) )
= $true )
| ( ( ~ ( member @ SV458 @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV340 @ SV422 ) @ SV458 ) @ ( f49 @ SV160 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ SV340 ) @ SV422 ) @ ( successor @ SV458 ) ) @ ( f49 @ SV160 ) ) )
= $true )
| ( ( member @ SV340 @ natural_numbers )
= $false )
| ( ( little_set @ SV160 )
= $false )
| ( ( member @ SV160 @ plus )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1823]) ).
thf(1858,plain,
! [SV350: $i,SV171: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ ( f51 @ SV171 @ SV350 ) ) @ ( f52 @ SV171 @ SV350 ) ) @ ( apply_to_two_arguments @ plus @ ( f53 @ SV171 @ SV350 ) @ ( f52 @ SV171 @ SV350 ) ) ) @ SV350 )
= $false )
| ( ( member @ SV171 @ SV350 )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ empty_set @ ( f50 @ SV171 @ SV350 ) ) @ empty_set ) @ SV350 )
= $false )
| ( ( little_set @ SV350 )
= $false )
| ( ( member @ SV171 @ times )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1829]) ).
thf(1859,plain,
! [SV174: $i,SV352: $i,SV459: $i,SV423: $i] :
( ( ( ~ ( member @ SV423 @ natural_numbers ) )
= $true )
| ( ( ~ ( member @ SV459 @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV352 @ SV423 ) @ SV459 ) @ ( f54 @ SV174 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ SV352 ) @ SV423 ) @ ( apply_to_two_arguments @ plus @ SV459 @ SV423 ) ) @ ( f54 @ SV174 ) ) )
= $true )
| ( ( member @ SV352 @ natural_numbers )
= $false )
| ( ( little_set @ SV174 )
= $false )
| ( ( member @ SV174 @ times )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1830]) ).
thf(1860,plain,
! [SV191: $i,SV460: $i,SV424: $i,SV353: $i] :
( ( ( SV353
!= ( ordered_pair @ SV424 @ SV460 ) )
= $true )
| ( ( ~ ( member @ SV191 @ SV460 ) )
= $true )
| ( ( little_set @ SV460 )
= $false )
| ( ( little_set @ SV424 )
= $false )
| ( ( member @ SV191 @ ( second @ SV353 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1831]) ).
thf(1861,plain,
! [SV461: $i,SV425: $i,SV192: $i,SV354: $i] :
( ( ( ( apply_to_two_arguments @ SV354 @ ( f38 @ SV192 @ SV354 @ SV425 @ SV461 ) @ ( apply @ SV461 @ ( f38 @ SV192 @ SV354 @ SV425 @ SV461 ) ) )
= SV425 )
= $false )
| ( ( ( apply_to_two_arguments @ SV354 @ ( apply @ SV461 @ ( f38 @ SV192 @ SV354 @ SV425 @ SV461 ) ) @ ( f38 @ SV192 @ SV354 @ SV425 @ SV461 ) )
= SV425 )
= $false )
| ( ( maps @ SV461 @ SV192 @ SV192 )
= $false )
| ( ( inverse @ SV192 @ SV354 @ SV425 @ SV461 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1832]) ).
thf(1862,plain,
! [SV193: $i,SV426: $i,SV355: $i] :
( ( ( ( apply_to_two_arguments @ times @ SV355 @ SV426 )
!= SV193 )
= $true )
| ( ( member @ SV355 @ ( non_ordered_pair @ ( successor @ empty_set ) @ SV193 ) )
= $true )
| ( ( member @ SV426 @ natural_numbers )
= $false )
| ( ( member @ SV355 @ natural_numbers )
= $false )
| ( ( member @ SV193 @ prime_numbers )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1833]) ).
thf(1863,plain,
! [SV356: $i,SV195: $i,SV478: $i,SV462: $i,SV427: $i] :
( ( ( little_set @ SV427 )
= $false )
| ( ( ~ ( little_set @ SV462 )
| ~ ( little_set @ SV478 )
| ( SV195
!= ( ordered_pair @ SV427 @ ( ordered_pair @ SV462 @ SV478 ) ) )
| ~ ( member @ ( ordered_pair @ SV427 @ ( ordered_pair @ SV478 @ SV462 ) ) @ SV356 ) )
= $true )
| ( ( little_set @ SV195 )
= $false )
| ( ( member @ SV195 @ ( flip_range_of @ SV356 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1834]) ).
thf(1864,plain,
! [SV197: $i,SV463: $i,SV429: $i,SV358: $i] :
( ( ( SV358
!= ( ordered_pair @ SV429 @ SV463 ) )
= $true )
| ( ( ~ ( member @ SV197 @ SV429 ) )
= $true )
| ( ( little_set @ SV463 )
= $false )
| ( ( little_set @ SV429 )
= $false )
| ( ( member @ SV197 @ ( first @ SV358 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1835]) ).
thf(1865,plain,
! [SV198: $i,SV359: $i,SV430: $i,SV464: $i] :
( ( ( ~ ( member @ SV464 @ SV430 ) )
= $true )
| ( ( ~ ( member @ ( first @ SV464 ) @ SV359 )
| ( ( second @ SV464 )
!= SV198 ) )
= $true )
| ( ( ordered_pair_predicate @ SV464 )
= $false )
| ( ( little_set @ SV198 )
= $false )
| ( ( member @ SV198 @ ( image @ SV359 @ SV430 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1836]) ).
thf(1866,plain,
! [SV360: $i,SV199: $i,SV479: $i,SV465: $i,SV431: $i] :
( ( ( little_set @ SV431 )
= $false )
| ( ( ~ ( little_set @ SV465 )
| ~ ( little_set @ SV479 )
| ( SV199
!= ( ordered_pair @ SV431 @ ( ordered_pair @ SV465 @ SV479 ) ) )
| ~ ( member @ ( ordered_pair @ SV465 @ ( ordered_pair @ SV479 @ SV431 ) ) @ SV360 ) )
= $true )
| ( ( little_set @ SV199 )
= $false )
| ( ( member @ SV199 @ ( rotate_right @ SV360 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1837]) ).
thf(1867,plain,
! [SV432: $i,SV361: $i,SV201: $i,SV483: $i,SV480: $i,SV466: $i] :
( ( ( ~ ( little_set @ SV466 ) )
= $true )
| ( ( ~ ( little_set @ SV480 )
| ~ ( little_set @ SV483 )
| ( SV201
!= ( ordered_pair @ SV466 @ SV480 ) )
| ~ ( member @ ( ordered_pair @ SV466 @ SV483 ) @ SV361 )
| ~ ( member @ ( ordered_pair @ SV483 @ SV480 ) @ SV432 ) )
= $true )
| ( ( little_set @ SV201 )
= $false )
| ( ( member @ SV201 @ ( compose @ SV361 @ SV432 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1838]) ).
thf(1868,plain,
! [SV435: $i,SV366: $i,SV206: $i,SV481: $i,SV467: $i] :
( ( ( closed @ SV467 @ SV481 )
= $false )
| ( ( ~ ( maps @ SV206 @ SV366 @ SV467 )
| ( ( apply @ SV206 @ ( apply_to_two_arguments @ SV435 @ ( f32 @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 ) @ ( f33 @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 ) ) )
!= ( apply_to_two_arguments @ SV481 @ ( apply @ SV206 @ ( f32 @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 ) ) @ ( apply @ SV206 @ ( f33 @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 ) ) ) ) )
= $true )
| ( ( closed @ SV366 @ SV435 )
= $false )
| ( ( homomorphism @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1840]) ).
thf(1869,plain,
! [SV367: $i,SV207: $i,SV436: $i] :
( ( ( ( range_of @ SV436 )
= SV207 )
= $false )
| ( ( ~ ( one_to_one_function @ SV436 ) )
= $true )
| ( ( maps @ SV436 @ SV367 @ SV207 )
= $false )
| ( ( member @ SV367 @ natural_numbers )
= $false )
| ( ( finite @ SV207 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1841]) ).
thf(1870,plain,
! [SV212: $i,SV370: $i,SV438: $i] :
( ( ( member @ SV438 @ SV370 )
= $false )
| ( ( SV212
!= ( second @ SV438 ) )
= $true )
| ( ( ordered_pair_predicate @ SV438 )
= $false )
| ( ( little_set @ SV212 )
= $false )
| ( ( member @ SV212 @ ( range_of @ SV370 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1843]) ).
thf(1871,plain,
! [SV215: $i,SV373: $i,SV440: $i] :
( ( ( member @ SV440 @ SV373 )
= $false )
| ( ( SV215
!= ( first @ SV440 ) )
= $true )
| ( ( ordered_pair_predicate @ SV440 )
= $false )
| ( ( little_set @ SV215 )
= $false )
| ( ( member @ SV215 @ ( domain_of @ SV373 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1845]) ).
thf(1872,plain,
! [SV374: $i,SV216: $i,SV441: $i,SV468: $i] :
( ( ( ( first @ SV468 )
!= SV441 )
= $true )
| ( ( ~ ( member @ SV216 @ ( second @ SV468 ) ) )
= $true )
| ( ( member @ SV468 @ SV374 )
= $false )
| ( ( ordered_pair_predicate @ SV468 )
= $false )
| ( ( member @ SV216 @ ( apply @ SV374 @ SV441 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1846]) ).
thf(1873,plain,
! [SV244: $i,SV382: $i,SV35: $i] :
( ( ( member @ ( second @ SV35 ) @ SV382 )
= $false )
| ( ( member @ ( first @ SV35 ) @ SV244 )
= $false )
| ( ( ordered_pair_predicate @ SV35 )
= $false )
| ( ( little_set @ SV35 )
= $false )
| ( ( member @ SV35 @ ( cross_product @ SV244 @ SV382 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1847]) ).
thf(1874,plain,
! [SV68: $i,SV385: $i,SV269: $i,SV442: $i] :
( ( ( ~ ( little_set @ SV442 ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ SV269 @ SV385 ) @ SV68 )
| ~ ( member @ ( ordered_pair @ SV269 @ SV442 ) @ SV68 )
| ( SV385 = SV442 ) )
= $true )
| ( ( little_set @ SV385 )
= $false )
| ( ( little_set @ SV269 )
= $false )
| ( ( single_valued_set @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1848]) ).
thf(1875,plain,
! [SV446: $i,SV472: $i,SV408: $i,SV119: $i,SV484: $i,SV303: $i,SV482: $i] :
( ( ( member @ SV482 @ SV303 )
= $false )
| ( ( ~ ( member @ SV484 @ SV303 )
| ( ( apply @ SV119 @ ( apply_to_two_arguments @ SV408 @ SV482 @ SV484 ) )
= ( apply_to_two_arguments @ SV472 @ ( apply @ SV119 @ SV482 ) @ ( apply @ SV119 @ SV484 ) ) ) )
= $true )
| ( ( homomorphism @ SV119 @ SV303 @ SV408 @ SV446 @ SV472 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1849]) ).
thf(1876,plain,
! [SV473: $i,SV409: $i,SV447: $i,SV304: $i,SV120: $i] :
( ( ( ~ ( maps @ SV120 @ SV304 @ SV447 ) )
= $true )
| ( ( member @ ( f32 @ SV120 @ SV304 @ SV409 @ SV447 @ SV473 ) @ SV304 )
= $true )
| ( ( closed @ SV447 @ SV473 )
= $false )
| ( ( closed @ SV304 @ SV409 )
= $false )
| ( ( homomorphism @ SV120 @ SV304 @ SV409 @ SV447 @ SV473 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1850]) ).
thf(1877,plain,
! [SV474: $i,SV410: $i,SV448: $i,SV305: $i,SV121: $i] :
( ( ( ~ ( maps @ SV121 @ SV305 @ SV448 ) )
= $true )
| ( ( member @ ( f33 @ SV121 @ SV305 @ SV410 @ SV448 @ SV474 ) @ SV305 )
= $true )
| ( ( closed @ SV448 @ SV474 )
= $false )
| ( ( closed @ SV305 @ SV410 )
= $false )
| ( ( homomorphism @ SV121 @ SV305 @ SV410 @ SV448 @ SV474 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1851]) ).
thf(1878,plain,
! [SV411: $i,SV306: $i,SV475: $i,SV122: $i,SV449: $i] :
( ( ( member @ SV449 @ SV122 )
= $false )
| ( ( ~ ( member @ SV475 @ SV122 )
| ( ( apply_to_two_arguments @ SV306 @ ( apply_to_two_arguments @ SV306 @ SV411 @ SV449 ) @ SV475 )
= ( apply_to_two_arguments @ SV306 @ SV411 @ ( apply_to_two_arguments @ SV306 @ SV449 @ SV475 ) ) ) )
= $true )
| ( ( member @ SV411 @ SV122 )
= $false )
| ( ( associative @ SV122 @ SV306 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1852]) ).
thf(1879,plain,
! [SV456: $i,SV420: $i,SV322: $i,SV138: $i] :
( ( ( identity @ SV138 @ SV322 @ SV420 )
= $false )
| ( ( ~ ( inverse @ SV138 @ SV322 @ SV420 @ SV456 ) )
= $true )
| ( ( associative @ SV138 @ SV322 )
= $false )
| ( ( closed @ SV138 @ SV322 )
= $false )
| ( ( group @ SV138 @ SV322 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1853]) ).
thf(1880,plain,
! [SV160: $i,SV340: $i,SV458: $i,SV422: $i] :
( ( ( member @ SV422 @ natural_numbers )
= $false )
| ( ( ~ ( member @ SV458 @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV340 @ SV422 ) @ SV458 ) @ ( f49 @ SV160 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ SV340 ) @ SV422 ) @ ( successor @ SV458 ) ) @ ( f49 @ SV160 ) ) )
= $true )
| ( ( member @ SV340 @ natural_numbers )
= $false )
| ( ( little_set @ SV160 )
= $false )
| ( ( member @ SV160 @ plus )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1857]) ).
thf(1881,plain,
! [SV174: $i,SV352: $i,SV459: $i,SV423: $i] :
( ( ( member @ SV423 @ natural_numbers )
= $false )
| ( ( ~ ( member @ SV459 @ natural_numbers )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV352 @ SV423 ) @ SV459 ) @ ( f54 @ SV174 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ SV352 ) @ SV423 ) @ ( apply_to_two_arguments @ plus @ SV459 @ SV423 ) ) @ ( f54 @ SV174 ) ) )
= $true )
| ( ( member @ SV352 @ natural_numbers )
= $false )
| ( ( little_set @ SV174 )
= $false )
| ( ( member @ SV174 @ times )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1859]) ).
thf(1882,plain,
! [SV191: $i,SV460: $i,SV424: $i,SV353: $i] :
( ( ( SV353
= ( ordered_pair @ SV424 @ SV460 ) )
= $false )
| ( ( ~ ( member @ SV191 @ SV460 ) )
= $true )
| ( ( little_set @ SV460 )
= $false )
| ( ( little_set @ SV424 )
= $false )
| ( ( member @ SV191 @ ( second @ SV353 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1860]) ).
thf(1883,plain,
! [SV193: $i,SV426: $i,SV355: $i] :
( ( ( ( apply_to_two_arguments @ times @ SV355 @ SV426 )
= SV193 )
= $false )
| ( ( member @ SV355 @ ( non_ordered_pair @ ( successor @ empty_set ) @ SV193 ) )
= $true )
| ( ( member @ SV426 @ natural_numbers )
= $false )
| ( ( member @ SV355 @ natural_numbers )
= $false )
| ( ( member @ SV193 @ prime_numbers )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1862]) ).
thf(1884,plain,
! [SV356: $i,SV427: $i,SV195: $i,SV478: $i,SV462: $i] :
( ( ( ~ ( little_set @ SV462 ) )
= $true )
| ( ( ~ ( little_set @ SV478 )
| ( SV195
!= ( ordered_pair @ SV427 @ ( ordered_pair @ SV462 @ SV478 ) ) )
| ~ ( member @ ( ordered_pair @ SV427 @ ( ordered_pair @ SV478 @ SV462 ) ) @ SV356 ) )
= $true )
| ( ( little_set @ SV427 )
= $false )
| ( ( little_set @ SV195 )
= $false )
| ( ( member @ SV195 @ ( flip_range_of @ SV356 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1863]) ).
thf(1885,plain,
! [SV197: $i,SV463: $i,SV429: $i,SV358: $i] :
( ( ( SV358
= ( ordered_pair @ SV429 @ SV463 ) )
= $false )
| ( ( ~ ( member @ SV197 @ SV429 ) )
= $true )
| ( ( little_set @ SV463 )
= $false )
| ( ( little_set @ SV429 )
= $false )
| ( ( member @ SV197 @ ( first @ SV358 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1864]) ).
thf(1886,plain,
! [SV198: $i,SV359: $i,SV430: $i,SV464: $i] :
( ( ( member @ SV464 @ SV430 )
= $false )
| ( ( ~ ( member @ ( first @ SV464 ) @ SV359 )
| ( ( second @ SV464 )
!= SV198 ) )
= $true )
| ( ( ordered_pair_predicate @ SV464 )
= $false )
| ( ( little_set @ SV198 )
= $false )
| ( ( member @ SV198 @ ( image @ SV359 @ SV430 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1865]) ).
thf(1887,plain,
! [SV360: $i,SV431: $i,SV199: $i,SV479: $i,SV465: $i] :
( ( ( ~ ( little_set @ SV465 ) )
= $true )
| ( ( ~ ( little_set @ SV479 )
| ( SV199
!= ( ordered_pair @ SV431 @ ( ordered_pair @ SV465 @ SV479 ) ) )
| ~ ( member @ ( ordered_pair @ SV465 @ ( ordered_pair @ SV479 @ SV431 ) ) @ SV360 ) )
= $true )
| ( ( little_set @ SV431 )
= $false )
| ( ( little_set @ SV199 )
= $false )
| ( ( member @ SV199 @ ( rotate_right @ SV360 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1866]) ).
thf(1888,plain,
! [SV432: $i,SV361: $i,SV201: $i,SV483: $i,SV480: $i,SV466: $i] :
( ( ( little_set @ SV466 )
= $false )
| ( ( ~ ( little_set @ SV480 )
| ~ ( little_set @ SV483 )
| ( SV201
!= ( ordered_pair @ SV466 @ SV480 ) )
| ~ ( member @ ( ordered_pair @ SV466 @ SV483 ) @ SV361 )
| ~ ( member @ ( ordered_pair @ SV483 @ SV480 ) @ SV432 ) )
= $true )
| ( ( little_set @ SV201 )
= $false )
| ( ( member @ SV201 @ ( compose @ SV361 @ SV432 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1867]) ).
thf(1889,plain,
! [SV481: $i,SV435: $i,SV467: $i,SV366: $i,SV206: $i] :
( ( ( ~ ( maps @ SV206 @ SV366 @ SV467 ) )
= $true )
| ( ( ( apply @ SV206 @ ( apply_to_two_arguments @ SV435 @ ( f32 @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 ) @ ( f33 @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 ) ) )
!= ( apply_to_two_arguments @ SV481 @ ( apply @ SV206 @ ( f32 @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 ) ) @ ( apply @ SV206 @ ( f33 @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 ) ) ) )
= $true )
| ( ( closed @ SV467 @ SV481 )
= $false )
| ( ( closed @ SV366 @ SV435 )
= $false )
| ( ( homomorphism @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1868]) ).
thf(1890,plain,
! [SV367: $i,SV207: $i,SV436: $i] :
( ( ( one_to_one_function @ SV436 )
= $false )
| ( ( ( range_of @ SV436 )
= SV207 )
= $false )
| ( ( maps @ SV436 @ SV367 @ SV207 )
= $false )
| ( ( member @ SV367 @ natural_numbers )
= $false )
| ( ( finite @ SV207 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1869]) ).
thf(1891,plain,
! [SV370: $i,SV438: $i,SV212: $i] :
( ( ( SV212
= ( second @ SV438 ) )
= $false )
| ( ( member @ SV438 @ SV370 )
= $false )
| ( ( ordered_pair_predicate @ SV438 )
= $false )
| ( ( little_set @ SV212 )
= $false )
| ( ( member @ SV212 @ ( range_of @ SV370 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1870]) ).
thf(1892,plain,
! [SV373: $i,SV440: $i,SV215: $i] :
( ( ( SV215
= ( first @ SV440 ) )
= $false )
| ( ( member @ SV440 @ SV373 )
= $false )
| ( ( ordered_pair_predicate @ SV440 )
= $false )
| ( ( little_set @ SV215 )
= $false )
| ( ( member @ SV215 @ ( domain_of @ SV373 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1871]) ).
thf(1893,plain,
! [SV374: $i,SV216: $i,SV441: $i,SV468: $i] :
( ( ( ( first @ SV468 )
= SV441 )
= $false )
| ( ( ~ ( member @ SV216 @ ( second @ SV468 ) ) )
= $true )
| ( ( member @ SV468 @ SV374 )
= $false )
| ( ( ordered_pair_predicate @ SV468 )
= $false )
| ( ( member @ SV216 @ ( apply @ SV374 @ SV441 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1872]) ).
thf(1894,plain,
! [SV68: $i,SV385: $i,SV269: $i,SV442: $i] :
( ( ( little_set @ SV442 )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ SV269 @ SV385 ) @ SV68 )
| ~ ( member @ ( ordered_pair @ SV269 @ SV442 ) @ SV68 )
| ( SV385 = SV442 ) )
= $true )
| ( ( little_set @ SV385 )
= $false )
| ( ( little_set @ SV269 )
= $false )
| ( ( single_valued_set @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1874]) ).
thf(1895,plain,
! [SV446: $i,SV472: $i,SV482: $i,SV408: $i,SV119: $i,SV303: $i,SV484: $i] :
( ( ( ~ ( member @ SV484 @ SV303 ) )
= $true )
| ( ( ( apply @ SV119 @ ( apply_to_two_arguments @ SV408 @ SV482 @ SV484 ) )
= ( apply_to_two_arguments @ SV472 @ ( apply @ SV119 @ SV482 ) @ ( apply @ SV119 @ SV484 ) ) )
= $true )
| ( ( member @ SV482 @ SV303 )
= $false )
| ( ( homomorphism @ SV119 @ SV303 @ SV408 @ SV446 @ SV472 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1875]) ).
thf(1896,plain,
! [SV473: $i,SV409: $i,SV447: $i,SV304: $i,SV120: $i] :
( ( ( maps @ SV120 @ SV304 @ SV447 )
= $false )
| ( ( member @ ( f32 @ SV120 @ SV304 @ SV409 @ SV447 @ SV473 ) @ SV304 )
= $true )
| ( ( closed @ SV447 @ SV473 )
= $false )
| ( ( closed @ SV304 @ SV409 )
= $false )
| ( ( homomorphism @ SV120 @ SV304 @ SV409 @ SV447 @ SV473 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1876]) ).
thf(1897,plain,
! [SV474: $i,SV410: $i,SV448: $i,SV305: $i,SV121: $i] :
( ( ( maps @ SV121 @ SV305 @ SV448 )
= $false )
| ( ( member @ ( f33 @ SV121 @ SV305 @ SV410 @ SV448 @ SV474 ) @ SV305 )
= $true )
| ( ( closed @ SV448 @ SV474 )
= $false )
| ( ( closed @ SV305 @ SV410 )
= $false )
| ( ( homomorphism @ SV121 @ SV305 @ SV410 @ SV448 @ SV474 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1877]) ).
thf(1898,plain,
! [SV449: $i,SV411: $i,SV306: $i,SV122: $i,SV475: $i] :
( ( ( ~ ( member @ SV475 @ SV122 ) )
= $true )
| ( ( ( apply_to_two_arguments @ SV306 @ ( apply_to_two_arguments @ SV306 @ SV411 @ SV449 ) @ SV475 )
= ( apply_to_two_arguments @ SV306 @ SV411 @ ( apply_to_two_arguments @ SV306 @ SV449 @ SV475 ) ) )
= $true )
| ( ( member @ SV449 @ SV122 )
= $false )
| ( ( member @ SV411 @ SV122 )
= $false )
| ( ( associative @ SV122 @ SV306 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1878]) ).
thf(1899,plain,
! [SV456: $i,SV420: $i,SV322: $i,SV138: $i] :
( ( ( inverse @ SV138 @ SV322 @ SV420 @ SV456 )
= $false )
| ( ( identity @ SV138 @ SV322 @ SV420 )
= $false )
| ( ( associative @ SV138 @ SV322 )
= $false )
| ( ( closed @ SV138 @ SV322 )
= $false )
| ( ( group @ SV138 @ SV322 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1879]) ).
thf(1900,plain,
! [SV160: $i,SV422: $i,SV340: $i,SV458: $i] :
( ( ( ~ ( member @ SV458 @ natural_numbers ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV340 @ SV422 ) @ SV458 ) @ ( f49 @ SV160 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ SV340 ) @ SV422 ) @ ( successor @ SV458 ) ) @ ( f49 @ SV160 ) ) )
= $true )
| ( ( member @ SV422 @ natural_numbers )
= $false )
| ( ( member @ SV340 @ natural_numbers )
= $false )
| ( ( little_set @ SV160 )
= $false )
| ( ( member @ SV160 @ plus )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1880]) ).
thf(1901,plain,
! [SV174: $i,SV423: $i,SV352: $i,SV459: $i] :
( ( ( ~ ( member @ SV459 @ natural_numbers ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV352 @ SV423 ) @ SV459 ) @ ( f54 @ SV174 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ SV352 ) @ SV423 ) @ ( apply_to_two_arguments @ plus @ SV459 @ SV423 ) ) @ ( f54 @ SV174 ) ) )
= $true )
| ( ( member @ SV423 @ natural_numbers )
= $false )
| ( ( member @ SV352 @ natural_numbers )
= $false )
| ( ( little_set @ SV174 )
= $false )
| ( ( member @ SV174 @ times )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1881]) ).
thf(1902,plain,
! [SV424: $i,SV353: $i,SV460: $i,SV191: $i] :
( ( ( member @ SV191 @ SV460 )
= $false )
| ( ( SV353
= ( ordered_pair @ SV424 @ SV460 ) )
= $false )
| ( ( little_set @ SV460 )
= $false )
| ( ( little_set @ SV424 )
= $false )
| ( ( member @ SV191 @ ( second @ SV353 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1882]) ).
thf(1903,plain,
! [SV356: $i,SV427: $i,SV195: $i,SV478: $i,SV462: $i] :
( ( ( little_set @ SV462 )
= $false )
| ( ( ~ ( little_set @ SV478 )
| ( SV195
!= ( ordered_pair @ SV427 @ ( ordered_pair @ SV462 @ SV478 ) ) )
| ~ ( member @ ( ordered_pair @ SV427 @ ( ordered_pair @ SV478 @ SV462 ) ) @ SV356 ) )
= $true )
| ( ( little_set @ SV427 )
= $false )
| ( ( little_set @ SV195 )
= $false )
| ( ( member @ SV195 @ ( flip_range_of @ SV356 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1884]) ).
thf(1904,plain,
! [SV463: $i,SV358: $i,SV429: $i,SV197: $i] :
( ( ( member @ SV197 @ SV429 )
= $false )
| ( ( SV358
= ( ordered_pair @ SV429 @ SV463 ) )
= $false )
| ( ( little_set @ SV463 )
= $false )
| ( ( little_set @ SV429 )
= $false )
| ( ( member @ SV197 @ ( first @ SV358 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1885]) ).
thf(1905,plain,
! [SV430: $i,SV198: $i,SV359: $i,SV464: $i] :
( ( ( ~ ( member @ ( first @ SV464 ) @ SV359 ) )
= $true )
| ( ( ( second @ SV464 )
!= SV198 )
= $true )
| ( ( member @ SV464 @ SV430 )
= $false )
| ( ( ordered_pair_predicate @ SV464 )
= $false )
| ( ( little_set @ SV198 )
= $false )
| ( ( member @ SV198 @ ( image @ SV359 @ SV430 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1886]) ).
thf(1906,plain,
! [SV360: $i,SV431: $i,SV199: $i,SV479: $i,SV465: $i] :
( ( ( little_set @ SV465 )
= $false )
| ( ( ~ ( little_set @ SV479 )
| ( SV199
!= ( ordered_pair @ SV431 @ ( ordered_pair @ SV465 @ SV479 ) ) )
| ~ ( member @ ( ordered_pair @ SV465 @ ( ordered_pair @ SV479 @ SV431 ) ) @ SV360 ) )
= $true )
| ( ( little_set @ SV431 )
= $false )
| ( ( little_set @ SV199 )
= $false )
| ( ( member @ SV199 @ ( rotate_right @ SV360 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1887]) ).
thf(1907,plain,
! [SV432: $i,SV361: $i,SV466: $i,SV201: $i,SV483: $i,SV480: $i] :
( ( ( ~ ( little_set @ SV480 ) )
= $true )
| ( ( ~ ( little_set @ SV483 )
| ( SV201
!= ( ordered_pair @ SV466 @ SV480 ) )
| ~ ( member @ ( ordered_pair @ SV466 @ SV483 ) @ SV361 )
| ~ ( member @ ( ordered_pair @ SV483 @ SV480 ) @ SV432 ) )
= $true )
| ( ( little_set @ SV466 )
= $false )
| ( ( little_set @ SV201 )
= $false )
| ( ( member @ SV201 @ ( compose @ SV361 @ SV432 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1888]) ).
thf(1908,plain,
! [SV481: $i,SV435: $i,SV467: $i,SV366: $i,SV206: $i] :
( ( ( maps @ SV206 @ SV366 @ SV467 )
= $false )
| ( ( ( apply @ SV206 @ ( apply_to_two_arguments @ SV435 @ ( f32 @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 ) @ ( f33 @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 ) ) )
!= ( apply_to_two_arguments @ SV481 @ ( apply @ SV206 @ ( f32 @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 ) ) @ ( apply @ SV206 @ ( f33 @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 ) ) ) )
= $true )
| ( ( closed @ SV467 @ SV481 )
= $false )
| ( ( closed @ SV366 @ SV435 )
= $false )
| ( ( homomorphism @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1889]) ).
thf(1909,plain,
! [SV374: $i,SV441: $i,SV468: $i,SV216: $i] :
( ( ( member @ SV216 @ ( second @ SV468 ) )
= $false )
| ( ( ( first @ SV468 )
= SV441 )
= $false )
| ( ( member @ SV468 @ SV374 )
= $false )
| ( ( ordered_pair_predicate @ SV468 )
= $false )
| ( ( member @ SV216 @ ( apply @ SV374 @ SV441 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1893]) ).
thf(1910,plain,
! [SV442: $i,SV68: $i,SV385: $i,SV269: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV269 @ SV385 ) @ SV68 ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ SV269 @ SV442 ) @ SV68 )
| ( SV385 = SV442 ) )
= $true )
| ( ( little_set @ SV442 )
= $false )
| ( ( little_set @ SV385 )
= $false )
| ( ( little_set @ SV269 )
= $false )
| ( ( single_valued_set @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1894]) ).
thf(1911,plain,
! [SV446: $i,SV472: $i,SV482: $i,SV408: $i,SV119: $i,SV303: $i,SV484: $i] :
( ( ( member @ SV484 @ SV303 )
= $false )
| ( ( ( apply @ SV119 @ ( apply_to_two_arguments @ SV408 @ SV482 @ SV484 ) )
= ( apply_to_two_arguments @ SV472 @ ( apply @ SV119 @ SV482 ) @ ( apply @ SV119 @ SV484 ) ) )
= $true )
| ( ( member @ SV482 @ SV303 )
= $false )
| ( ( homomorphism @ SV119 @ SV303 @ SV408 @ SV446 @ SV472 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1895]) ).
thf(1912,plain,
! [SV449: $i,SV411: $i,SV306: $i,SV122: $i,SV475: $i] :
( ( ( member @ SV475 @ SV122 )
= $false )
| ( ( ( apply_to_two_arguments @ SV306 @ ( apply_to_two_arguments @ SV306 @ SV411 @ SV449 ) @ SV475 )
= ( apply_to_two_arguments @ SV306 @ SV411 @ ( apply_to_two_arguments @ SV306 @ SV449 @ SV475 ) ) )
= $true )
| ( ( member @ SV449 @ SV122 )
= $false )
| ( ( member @ SV411 @ SV122 )
= $false )
| ( ( associative @ SV122 @ SV306 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1898]) ).
thf(1913,plain,
! [SV160: $i,SV422: $i,SV340: $i,SV458: $i] :
( ( ( member @ SV458 @ natural_numbers )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV340 @ SV422 ) @ SV458 ) @ ( f49 @ SV160 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ SV340 ) @ SV422 ) @ ( successor @ SV458 ) ) @ ( f49 @ SV160 ) ) )
= $true )
| ( ( member @ SV422 @ natural_numbers )
= $false )
| ( ( member @ SV340 @ natural_numbers )
= $false )
| ( ( little_set @ SV160 )
= $false )
| ( ( member @ SV160 @ plus )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1900]) ).
thf(1914,plain,
! [SV174: $i,SV423: $i,SV352: $i,SV459: $i] :
( ( ( member @ SV459 @ natural_numbers )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV352 @ SV423 ) @ SV459 ) @ ( f54 @ SV174 ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ SV352 ) @ SV423 ) @ ( apply_to_two_arguments @ plus @ SV459 @ SV423 ) ) @ ( f54 @ SV174 ) ) )
= $true )
| ( ( member @ SV423 @ natural_numbers )
= $false )
| ( ( member @ SV352 @ natural_numbers )
= $false )
| ( ( little_set @ SV174 )
= $false )
| ( ( member @ SV174 @ times )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1901]) ).
thf(1915,plain,
! [SV356: $i,SV462: $i,SV427: $i,SV195: $i,SV478: $i] :
( ( ( ~ ( little_set @ SV478 ) )
= $true )
| ( ( ( SV195
!= ( ordered_pair @ SV427 @ ( ordered_pair @ SV462 @ SV478 ) ) )
| ~ ( member @ ( ordered_pair @ SV427 @ ( ordered_pair @ SV478 @ SV462 ) ) @ SV356 ) )
= $true )
| ( ( little_set @ SV462 )
= $false )
| ( ( little_set @ SV427 )
= $false )
| ( ( little_set @ SV195 )
= $false )
| ( ( member @ SV195 @ ( flip_range_of @ SV356 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1903]) ).
thf(1916,plain,
! [SV430: $i,SV198: $i,SV359: $i,SV464: $i] :
( ( ( member @ ( first @ SV464 ) @ SV359 )
= $false )
| ( ( ( second @ SV464 )
!= SV198 )
= $true )
| ( ( member @ SV464 @ SV430 )
= $false )
| ( ( ordered_pair_predicate @ SV464 )
= $false )
| ( ( little_set @ SV198 )
= $false )
| ( ( member @ SV198 @ ( image @ SV359 @ SV430 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1905]) ).
thf(1917,plain,
! [SV360: $i,SV465: $i,SV431: $i,SV199: $i,SV479: $i] :
( ( ( ~ ( little_set @ SV479 ) )
= $true )
| ( ( ( SV199
!= ( ordered_pair @ SV431 @ ( ordered_pair @ SV465 @ SV479 ) ) )
| ~ ( member @ ( ordered_pair @ SV465 @ ( ordered_pair @ SV479 @ SV431 ) ) @ SV360 ) )
= $true )
| ( ( little_set @ SV465 )
= $false )
| ( ( little_set @ SV431 )
= $false )
| ( ( little_set @ SV199 )
= $false )
| ( ( member @ SV199 @ ( rotate_right @ SV360 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1906]) ).
thf(1918,plain,
! [SV432: $i,SV361: $i,SV466: $i,SV201: $i,SV483: $i,SV480: $i] :
( ( ( little_set @ SV480 )
= $false )
| ( ( ~ ( little_set @ SV483 )
| ( SV201
!= ( ordered_pair @ SV466 @ SV480 ) )
| ~ ( member @ ( ordered_pair @ SV466 @ SV483 ) @ SV361 )
| ~ ( member @ ( ordered_pair @ SV483 @ SV480 ) @ SV432 ) )
= $true )
| ( ( little_set @ SV466 )
= $false )
| ( ( little_set @ SV201 )
= $false )
| ( ( member @ SV201 @ ( compose @ SV361 @ SV432 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1907]) ).
thf(1919,plain,
! [SV481: $i,SV467: $i,SV366: $i,SV435: $i,SV206: $i] :
( ( ( ( apply @ SV206 @ ( apply_to_two_arguments @ SV435 @ ( f32 @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 ) @ ( f33 @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 ) ) )
= ( apply_to_two_arguments @ SV481 @ ( apply @ SV206 @ ( f32 @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 ) ) @ ( apply @ SV206 @ ( f33 @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 ) ) ) )
= $false )
| ( ( maps @ SV206 @ SV366 @ SV467 )
= $false )
| ( ( closed @ SV467 @ SV481 )
= $false )
| ( ( closed @ SV366 @ SV435 )
= $false )
| ( ( homomorphism @ SV206 @ SV366 @ SV435 @ SV467 @ SV481 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1908]) ).
thf(1920,plain,
! [SV442: $i,SV68: $i,SV385: $i,SV269: $i] :
( ( ( member @ ( ordered_pair @ SV269 @ SV385 ) @ SV68 )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ SV269 @ SV442 ) @ SV68 )
| ( SV385 = SV442 ) )
= $true )
| ( ( little_set @ SV442 )
= $false )
| ( ( little_set @ SV385 )
= $false )
| ( ( little_set @ SV269 )
= $false )
| ( ( single_valued_set @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1910]) ).
thf(1921,plain,
! [SV160: $i,SV458: $i,SV422: $i,SV340: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV340 @ SV422 ) @ SV458 ) @ ( f49 @ SV160 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ SV340 ) @ SV422 ) @ ( successor @ SV458 ) ) @ ( f49 @ SV160 ) )
= $true )
| ( ( member @ SV458 @ natural_numbers )
= $false )
| ( ( member @ SV422 @ natural_numbers )
= $false )
| ( ( member @ SV340 @ natural_numbers )
= $false )
| ( ( little_set @ SV160 )
= $false )
| ( ( member @ SV160 @ plus )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1913]) ).
thf(1922,plain,
! [SV174: $i,SV459: $i,SV423: $i,SV352: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( ordered_pair @ SV352 @ SV423 ) @ SV459 ) @ ( f54 @ SV174 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ SV352 ) @ SV423 ) @ ( apply_to_two_arguments @ plus @ SV459 @ SV423 ) ) @ ( f54 @ SV174 ) )
= $true )
| ( ( member @ SV459 @ natural_numbers )
= $false )
| ( ( member @ SV423 @ natural_numbers )
= $false )
| ( ( member @ SV352 @ natural_numbers )
= $false )
| ( ( little_set @ SV174 )
= $false )
| ( ( member @ SV174 @ times )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1914]) ).
thf(1923,plain,
! [SV356: $i,SV462: $i,SV427: $i,SV195: $i,SV478: $i] :
( ( ( little_set @ SV478 )
= $false )
| ( ( ( SV195
!= ( ordered_pair @ SV427 @ ( ordered_pair @ SV462 @ SV478 ) ) )
| ~ ( member @ ( ordered_pair @ SV427 @ ( ordered_pair @ SV478 @ SV462 ) ) @ SV356 ) )
= $true )
| ( ( little_set @ SV462 )
= $false )
| ( ( little_set @ SV427 )
= $false )
| ( ( little_set @ SV195 )
= $false )
| ( ( member @ SV195 @ ( flip_range_of @ SV356 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1915]) ).
thf(1924,plain,
! [SV430: $i,SV359: $i,SV198: $i,SV464: $i] :
( ( ( ( second @ SV464 )
= SV198 )
= $false )
| ( ( member @ ( first @ SV464 ) @ SV359 )
= $false )
| ( ( member @ SV464 @ SV430 )
= $false )
| ( ( ordered_pair_predicate @ SV464 )
= $false )
| ( ( little_set @ SV198 )
= $false )
| ( ( member @ SV198 @ ( image @ SV359 @ SV430 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1916]) ).
thf(1925,plain,
! [SV360: $i,SV465: $i,SV431: $i,SV199: $i,SV479: $i] :
( ( ( little_set @ SV479 )
= $false )
| ( ( ( SV199
!= ( ordered_pair @ SV431 @ ( ordered_pair @ SV465 @ SV479 ) ) )
| ~ ( member @ ( ordered_pair @ SV465 @ ( ordered_pair @ SV479 @ SV431 ) ) @ SV360 ) )
= $true )
| ( ( little_set @ SV465 )
= $false )
| ( ( little_set @ SV431 )
= $false )
| ( ( little_set @ SV199 )
= $false )
| ( ( member @ SV199 @ ( rotate_right @ SV360 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1917]) ).
thf(1926,plain,
! [SV432: $i,SV361: $i,SV480: $i,SV466: $i,SV201: $i,SV483: $i] :
( ( ( ~ ( little_set @ SV483 ) )
= $true )
| ( ( ( SV201
!= ( ordered_pair @ SV466 @ SV480 ) )
| ~ ( member @ ( ordered_pair @ SV466 @ SV483 ) @ SV361 )
| ~ ( member @ ( ordered_pair @ SV483 @ SV480 ) @ SV432 ) )
= $true )
| ( ( little_set @ SV480 )
= $false )
| ( ( little_set @ SV466 )
= $false )
| ( ( little_set @ SV201 )
= $false )
| ( ( member @ SV201 @ ( compose @ SV361 @ SV432 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1918]) ).
thf(1927,plain,
! [SV385: $i,SV68: $i,SV442: $i,SV269: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV269 @ SV442 ) @ SV68 ) )
= $true )
| ( ( SV385 = SV442 )
= $true )
| ( ( member @ ( ordered_pair @ SV269 @ SV385 ) @ SV68 )
= $false )
| ( ( little_set @ SV442 )
= $false )
| ( ( little_set @ SV385 )
= $false )
| ( ( little_set @ SV269 )
= $false )
| ( ( single_valued_set @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1920]) ).
thf(1928,plain,
! [SV160: $i,SV458: $i,SV422: $i,SV340: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ SV340 @ SV422 ) @ SV458 ) @ ( f49 @ SV160 ) )
= $false )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ SV340 ) @ SV422 ) @ ( successor @ SV458 ) ) @ ( f49 @ SV160 ) )
= $true )
| ( ( member @ SV458 @ natural_numbers )
= $false )
| ( ( member @ SV422 @ natural_numbers )
= $false )
| ( ( member @ SV340 @ natural_numbers )
= $false )
| ( ( little_set @ SV160 )
= $false )
| ( ( member @ SV160 @ plus )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1921]) ).
thf(1929,plain,
! [SV174: $i,SV459: $i,SV423: $i,SV352: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ SV352 @ SV423 ) @ SV459 ) @ ( f54 @ SV174 ) )
= $false )
| ( ( member @ ( ordered_pair @ ( ordered_pair @ ( successor @ SV352 ) @ SV423 ) @ ( apply_to_two_arguments @ plus @ SV459 @ SV423 ) ) @ ( f54 @ SV174 ) )
= $true )
| ( ( member @ SV459 @ natural_numbers )
= $false )
| ( ( member @ SV423 @ natural_numbers )
= $false )
| ( ( member @ SV352 @ natural_numbers )
= $false )
| ( ( little_set @ SV174 )
= $false )
| ( ( member @ SV174 @ times )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1922]) ).
thf(1930,plain,
! [SV356: $i,SV478: $i,SV462: $i,SV427: $i,SV195: $i] :
( ( ( SV195
!= ( ordered_pair @ SV427 @ ( ordered_pair @ SV462 @ SV478 ) ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ SV427 @ ( ordered_pair @ SV478 @ SV462 ) ) @ SV356 ) )
= $true )
| ( ( little_set @ SV478 )
= $false )
| ( ( little_set @ SV462 )
= $false )
| ( ( little_set @ SV427 )
= $false )
| ( ( little_set @ SV195 )
= $false )
| ( ( member @ SV195 @ ( flip_range_of @ SV356 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1923]) ).
thf(1931,plain,
! [SV360: $i,SV479: $i,SV465: $i,SV431: $i,SV199: $i] :
( ( ( SV199
!= ( ordered_pair @ SV431 @ ( ordered_pair @ SV465 @ SV479 ) ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ SV465 @ ( ordered_pair @ SV479 @ SV431 ) ) @ SV360 ) )
= $true )
| ( ( little_set @ SV479 )
= $false )
| ( ( little_set @ SV465 )
= $false )
| ( ( little_set @ SV431 )
= $false )
| ( ( little_set @ SV199 )
= $false )
| ( ( member @ SV199 @ ( rotate_right @ SV360 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1925]) ).
thf(1932,plain,
! [SV432: $i,SV361: $i,SV480: $i,SV466: $i,SV201: $i,SV483: $i] :
( ( ( little_set @ SV483 )
= $false )
| ( ( ( SV201
!= ( ordered_pair @ SV466 @ SV480 ) )
| ~ ( member @ ( ordered_pair @ SV466 @ SV483 ) @ SV361 )
| ~ ( member @ ( ordered_pair @ SV483 @ SV480 ) @ SV432 ) )
= $true )
| ( ( little_set @ SV480 )
= $false )
| ( ( little_set @ SV466 )
= $false )
| ( ( little_set @ SV201 )
= $false )
| ( ( member @ SV201 @ ( compose @ SV361 @ SV432 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1926]) ).
thf(1933,plain,
! [SV385: $i,SV68: $i,SV442: $i,SV269: $i] :
( ( ( member @ ( ordered_pair @ SV269 @ SV442 ) @ SV68 )
= $false )
| ( ( SV385 = SV442 )
= $true )
| ( ( member @ ( ordered_pair @ SV269 @ SV385 ) @ SV68 )
= $false )
| ( ( little_set @ SV442 )
= $false )
| ( ( little_set @ SV385 )
= $false )
| ( ( little_set @ SV269 )
= $false )
| ( ( single_valued_set @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1927]) ).
thf(1934,plain,
! [SV356: $i,SV478: $i,SV462: $i,SV427: $i,SV195: $i] :
( ( ( SV195
= ( ordered_pair @ SV427 @ ( ordered_pair @ SV462 @ SV478 ) ) )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ SV427 @ ( ordered_pair @ SV478 @ SV462 ) ) @ SV356 ) )
= $true )
| ( ( little_set @ SV478 )
= $false )
| ( ( little_set @ SV462 )
= $false )
| ( ( little_set @ SV427 )
= $false )
| ( ( little_set @ SV195 )
= $false )
| ( ( member @ SV195 @ ( flip_range_of @ SV356 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1930]) ).
thf(1935,plain,
! [SV360: $i,SV479: $i,SV465: $i,SV431: $i,SV199: $i] :
( ( ( SV199
= ( ordered_pair @ SV431 @ ( ordered_pair @ SV465 @ SV479 ) ) )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ SV465 @ ( ordered_pair @ SV479 @ SV431 ) ) @ SV360 ) )
= $true )
| ( ( little_set @ SV479 )
= $false )
| ( ( little_set @ SV465 )
= $false )
| ( ( little_set @ SV431 )
= $false )
| ( ( little_set @ SV199 )
= $false )
| ( ( member @ SV199 @ ( rotate_right @ SV360 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1931]) ).
thf(1936,plain,
! [SV432: $i,SV361: $i,SV483: $i,SV480: $i,SV466: $i,SV201: $i] :
( ( ( SV201
!= ( ordered_pair @ SV466 @ SV480 ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ SV466 @ SV483 ) @ SV361 )
| ~ ( member @ ( ordered_pair @ SV483 @ SV480 ) @ SV432 ) )
= $true )
| ( ( little_set @ SV483 )
= $false )
| ( ( little_set @ SV480 )
= $false )
| ( ( little_set @ SV466 )
= $false )
| ( ( little_set @ SV201 )
= $false )
| ( ( member @ SV201 @ ( compose @ SV361 @ SV432 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1932]) ).
thf(1937,plain,
! [SV195: $i,SV356: $i,SV462: $i,SV478: $i,SV427: $i] :
( ( ( member @ ( ordered_pair @ SV427 @ ( ordered_pair @ SV478 @ SV462 ) ) @ SV356 )
= $false )
| ( ( SV195
= ( ordered_pair @ SV427 @ ( ordered_pair @ SV462 @ SV478 ) ) )
= $false )
| ( ( little_set @ SV478 )
= $false )
| ( ( little_set @ SV462 )
= $false )
| ( ( little_set @ SV427 )
= $false )
| ( ( little_set @ SV195 )
= $false )
| ( ( member @ SV195 @ ( flip_range_of @ SV356 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1934]) ).
thf(1938,plain,
! [SV199: $i,SV360: $i,SV431: $i,SV479: $i,SV465: $i] :
( ( ( member @ ( ordered_pair @ SV465 @ ( ordered_pair @ SV479 @ SV431 ) ) @ SV360 )
= $false )
| ( ( SV199
= ( ordered_pair @ SV431 @ ( ordered_pair @ SV465 @ SV479 ) ) )
= $false )
| ( ( little_set @ SV479 )
= $false )
| ( ( little_set @ SV465 )
= $false )
| ( ( little_set @ SV431 )
= $false )
| ( ( little_set @ SV199 )
= $false )
| ( ( member @ SV199 @ ( rotate_right @ SV360 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1935]) ).
thf(1939,plain,
! [SV432: $i,SV361: $i,SV483: $i,SV480: $i,SV466: $i,SV201: $i] :
( ( ( SV201
= ( ordered_pair @ SV466 @ SV480 ) )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ SV466 @ SV483 ) @ SV361 )
| ~ ( member @ ( ordered_pair @ SV483 @ SV480 ) @ SV432 ) )
= $true )
| ( ( little_set @ SV483 )
= $false )
| ( ( little_set @ SV480 )
= $false )
| ( ( little_set @ SV466 )
= $false )
| ( ( little_set @ SV201 )
= $false )
| ( ( member @ SV201 @ ( compose @ SV361 @ SV432 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1936]) ).
thf(1940,plain,
! [SV201: $i,SV432: $i,SV480: $i,SV361: $i,SV483: $i,SV466: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV466 @ SV483 ) @ SV361 ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ SV483 @ SV480 ) @ SV432 ) )
= $true )
| ( ( SV201
= ( ordered_pair @ SV466 @ SV480 ) )
= $false )
| ( ( little_set @ SV483 )
= $false )
| ( ( little_set @ SV480 )
= $false )
| ( ( little_set @ SV466 )
= $false )
| ( ( little_set @ SV201 )
= $false )
| ( ( member @ SV201 @ ( compose @ SV361 @ SV432 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1939]) ).
thf(1941,plain,
! [SV201: $i,SV432: $i,SV480: $i,SV361: $i,SV483: $i,SV466: $i] :
( ( ( member @ ( ordered_pair @ SV466 @ SV483 ) @ SV361 )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ SV483 @ SV480 ) @ SV432 ) )
= $true )
| ( ( SV201
= ( ordered_pair @ SV466 @ SV480 ) )
= $false )
| ( ( little_set @ SV483 )
= $false )
| ( ( little_set @ SV480 )
= $false )
| ( ( little_set @ SV466 )
= $false )
| ( ( little_set @ SV201 )
= $false )
| ( ( member @ SV201 @ ( compose @ SV361 @ SV432 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1940]) ).
thf(1942,plain,
! [SV201: $i,SV361: $i,SV466: $i,SV432: $i,SV480: $i,SV483: $i] :
( ( ( member @ ( ordered_pair @ SV483 @ SV480 ) @ SV432 )
= $false )
| ( ( member @ ( ordered_pair @ SV466 @ SV483 ) @ SV361 )
= $false )
| ( ( SV201
= ( ordered_pair @ SV466 @ SV480 ) )
= $false )
| ( ( little_set @ SV483 )
= $false )
| ( ( little_set @ SV480 )
= $false )
| ( ( little_set @ SV466 )
= $false )
| ( ( little_set @ SV201 )
= $false )
| ( ( member @ SV201 @ ( compose @ SV361 @ SV432 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1941]) ).
thf(1943,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[505,1942,1938,1937,1933,1929,1928,1924,1919,1912,1911,1909,1904,1902,1899,1897,1896,1892,1891,1890,1883,1873,1861,1858,1856,1855,1854,1844,1842,1839,1828,1827,1826,1825,1824,1821,1820,1819,1818,1817,1815,1812,1811,1797,1780,1779,1778,1777,1769,1768,1767,1766,1759,1758,1753,1752,1750,1744,1739,1733,1728,1726,1714,1703,1698,1689,1688,1687,1683,1682,1679,1678,1656,1655,1654,1621,1620,1608,1606,1605,1598,1597,1588,1575,1534,1526,1525,1524,1523,1522,1521,1519,1518,1517,1516,1515,1514,1513,1512,1509,1508,1507,1506,1505,1501,1496,1495,1494,1493,1492,1490,1489,1482,1479,1478,1464,1453,1440,1428,1427,1422,1421,1420,1419,1396,1395,1394,1385,1384,1383,1382,1381,1370,1368,1367,1364,1363,1362,1361,1360,1359,1358,1357,1356,1355,1354,1353,1351,1350,1345,1344,1343,1336,1335,1334,1333,1332,1331,1330,1329,1326,1325,1308,1298,1297,1296,1294,1293,1292,1291,1290,1289,1284,1283,1269,1255,1249,1248,1233,1232,1231,1210,1204,1203,1202,1201,1195,1194,1186,1185,1183,1181,1175,1173,1169,1168,1141,1140,1131,1130,1129,1125,1001,993,992,980,979,978,977,976,973,957,936,916,915,883,741,699,692,545,506]) ).
thf(1944,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1943]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM009-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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
% 0.07/0.18 % Computer : n003.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 13:02:09 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.67/2.81 .
% 15.67/2.81
% 15.67/2.81 No.of.Axioms: 220
% 15.67/2.81
% 15.67/2.81 Length.of.Defs: 0
% 15.67/2.81
% 15.67/2.81 Contains.Choice.Funs: false
% 15.67/2.81 .......................................................
% 15.67/2.81
% 15.67/2.81 ********************************
% 15.67/2.81 * All subproblems solved! *
% 15.67/2.81 ********************************
% 15.67/2.81 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:220,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1943,loop_count:0,foatp_calls:1,translation:fof_full)
% 15.67/2.81
% 15.67/2.81 %**** Beginning of derivation protocol ****
% 15.67/2.81 % SZS output start CNFRefutation
% See solution above
% 15.67/2.84
% 15.67/2.84 %**** End of derivation protocol ****
% 15.67/2.84 %**** no. of clauses in derivation: 1944 ****
% 15.67/2.84 %**** clause counter: 1943 ****
% 15.67/2.84
% 15.67/2.84 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:220,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1943,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------