TSTP Solution File: SEU098+1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU098+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 12:06:39 EDT 2022
% Result : Theorem 1.88s 2.06s
% Output : CNFRefutation 3.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 142
% Syntax : Number of formulae : 2186 (1536 unt; 62 typ; 0 def)
% Number of atoms : 12007 (2977 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 19534 (5769 ~;3456 |; 522 &;9684 @)
% ( 9 <=>; 94 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 56 ( 56 >; 0 *; 0 +; 0 <<)
% Number of symbols : 65 ( 62 usr; 26 con; 0-4 aty)
% Number of variables : 2409 ( 0 ^2351 !; 58 ?;2409 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_being_limit_ordinal,type,
being_limit_ordinal: $i > $o ).
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_epsilon_connected,type,
epsilon_connected: $i > $o ).
thf(tp_epsilon_transitive,type,
epsilon_transitive: $i > $o ).
thf(tp_finite,type,
finite: $i > $o ).
thf(tp_first_projection,type,
first_projection: $i > $i > $i ).
thf(tp_first_projection_as_func_of,type,
first_projection_as_func_of: $i > $i > $i ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_function_image,type,
function_image: $i > $i > $i > $i > $i ).
thf(tp_function_yielding,type,
function_yielding: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_natural,type,
natural: $i > $o ).
thf(tp_one_to_one,type,
one_to_one: $i > $o ).
thf(tp_ordinal,type,
ordinal: $i > $o ).
thf(tp_ordinal_yielding,type,
ordinal_yielding: $i > $o ).
thf(tp_positive_rationals,type,
positive_rationals: $i ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_quasi_total,type,
quasi_total: $i > $i > $i > $o ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_dom,type,
relation_dom: $i > $i ).
thf(tp_relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
thf(tp_relation_image,type,
relation_image: $i > $i > $i ).
thf(tp_relation_non_empty,type,
relation_non_empty: $i > $o ).
thf(tp_relation_of2,type,
relation_of2: $i > $i > $i > $o ).
thf(tp_relation_of2_as_subset,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(tp_relation_rng,type,
relation_rng: $i > $i ).
thf(tp_sK10_A,type,
sK10_A: $i ).
thf(tp_sK11_A,type,
sK11_A: $i ).
thf(tp_sK12_B,type,
sK12_B: $i > $i ).
thf(tp_sK13_A,type,
sK13_A: $i ).
thf(tp_sK14_A,type,
sK14_A: $i ).
thf(tp_sK15_A,type,
sK15_A: $i ).
thf(tp_sK16_A,type,
sK16_A: $i ).
thf(tp_sK17_B,type,
sK17_B: $i > $i ).
thf(tp_sK18_A,type,
sK18_A: $i ).
thf(tp_sK19_A,type,
sK19_A: $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_B,type,
sK20_B: $i > $i ).
thf(tp_sK21_A,type,
sK21_A: $i ).
thf(tp_sK22_A,type,
sK22_A: $i ).
thf(tp_sK23_A,type,
sK23_A: $i ).
thf(tp_sK24_A,type,
sK24_A: $i ).
thf(tp_sK25_A,type,
sK25_A: $i ).
thf(tp_sK26_A,type,
sK26_A: $i ).
thf(tp_sK27_A,type,
sK27_A: $i ).
thf(tp_sK28_C,type,
sK28_C: $i > $i > $i ).
thf(tp_sK29_B,type,
sK29_B: $i > $i ).
thf(tp_sK2_A,type,
sK2_A: $i ).
thf(tp_sK30_C,type,
sK30_C: $i > $i > $i ).
thf(tp_sK3_A,type,
sK3_A: $i ).
thf(tp_sK4_A,type,
sK4_A: $i ).
thf(tp_sK5_B,type,
sK5_B: $i > $i ).
thf(tp_sK6_A,type,
sK6_A: $i ).
thf(tp_sK7_A,type,
sK7_A: $i ).
thf(tp_sK8_A,type,
sK8_A: $i ).
thf(tp_sK9_B,type,
sK9_B: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_transfinite_sequence,type,
transfinite_sequence: $i > $o ).
thf(tp_with_non_empty_elements,type,
with_non_empty_elements: $i > $o ).
thf(1,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(3,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(8,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( finite @ ( relation_dom @ A ) )
=> ( finite @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_finset_1) ).
thf(9,axiom,
! [A: $i] :
( ( relation @ A )
=> ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relat_1) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( cartesian_product2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_finset_1) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( finite @ A )
=> ( finite @ ( relation_image @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_finset_1) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( ( subset @ A @ B )
& ( finite @ B ) )
=> ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_finset_1) ).
thf(14,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( function_image @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) @ ( relation_dom @ A ) @ ( first_projection_as_func_of @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) @ A )
= ( relation_dom @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_funct_3) ).
thf(15,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
<=> ( relation_of2 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( first_projection_as_func_of @ A @ B )
= ( first_projection @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k9_funct_3) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( function @ C )
& ( quasi_total @ C @ A @ B )
& ( relation_of2 @ C @ A @ B ) )
=> ( ( function_image @ A @ B @ C @ D )
= ( relation_image @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_funct_2) ).
thf(19,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_non_empty @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_funct_1) ).
thf(20,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( transfinite_sequence @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_ordinal1) ).
thf(21,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_funct_1) ).
thf(22,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(23,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(24,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_ordinal1) ).
thf(25,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(26,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(27,axiom,
? [A: $i] :
( ( element @ A @ positive_rationals )
& ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A )
& ( natural @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_arytm_3) ).
thf(28,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(29,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(30,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(31,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( transfinite_sequence @ A )
& ( ordinal_yielding @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_ordinal2) ).
thf(32,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A )
& ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_ordinal1) ).
thf(33,axiom,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(34,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B )
& ( relation @ B )
& ( function @ B )
& ( one_to_one @ B )
& ( epsilon_transitive @ B )
& ( epsilon_connected @ B )
& ( ordinal @ B )
& ( natural @ B )
& ( finite @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_finset_1) ).
thf(35,axiom,
? [A: $i] :
( ( element @ A @ positive_rationals )
& ~ ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_arytm_3) ).
thf(36,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(37,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(38,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(39,axiom,
? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A )
& ( being_limit_ordinal @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_ordinal2) ).
thf(40,axiom,
? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_ordinal1) ).
thf(41,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(42,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( function_yielding @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funcop_1) ).
thf(43,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(44,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A )
& ( natural @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_arytm_3) ).
thf(45,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(46,axiom,
~ ( empty @ positive_rationals ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_arytm_3) ).
thf(47,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(48,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(49,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( relation_non_empty @ A )
& ( function @ A ) )
=> ( with_non_empty_elements @ ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_funct_1) ).
thf(50,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(51,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( transfinite_sequence @ A ) )
=> ( ( epsilon_transitive @ ( relation_dom @ A ) )
& ( epsilon_connected @ ( relation_dom @ A ) )
& ( ordinal @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_ordinal1) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(53,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(54,axiom,
( ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set )
& ( function @ empty_set )
& ( one_to_one @ empty_set )
& ( empty @ empty_set )
& ( epsilon_transitive @ empty_set )
& ( epsilon_connected @ empty_set )
& ( ordinal @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_ordinal1) ).
thf(55,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(56,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(57,axiom,
! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( cartesian_product2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc14_finset_1) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( finite @ B ) )
=> ( finite @ ( relation_image @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc13_finset_1) ).
thf(59,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(60,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(61,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(62,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2 @ C @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(64,axiom,
! [A: $i,B: $i] :
( ( function @ ( first_projection_as_func_of @ A @ B ) )
& ( quasi_total @ ( first_projection_as_func_of @ A @ B ) @ ( cartesian_product2 @ A @ B ) @ A )
& ( relation_of2_as_subset @ ( first_projection_as_func_of @ A @ B ) @ ( cartesian_product2 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_funct_3) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( relation @ ( first_projection @ A @ B ) )
& ( function @ ( first_projection @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_funct_3) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( function @ C )
& ( quasi_total @ C @ A @ B )
& ( relation_of2 @ C @ A @ B ) )
=> ( element @ ( function_image @ A @ B @ C @ D ) @ ( powerset @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_2) ).
thf(67,axiom,
! [A: $i] :
( ( element @ A @ positive_rationals )
=> ( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A )
& ( natural @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_arytm_3) ).
thf(68,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_ordinal1) ).
thf(69,axiom,
! [A: $i] :
( ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) )
=> ( ordinal @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_ordinal1) ).
thf(70,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(71,axiom,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(72,axiom,
! [A: $i] :
( ( ( empty @ A )
& ( ordinal @ A ) )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A )
& ( natural @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_arytm_3) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(74,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(75,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).
thf(76,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(77,axiom,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(78,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( ( epsilon_transitive @ B )
& ( epsilon_connected @ B )
& ( ordinal @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_arytm_3) ).
thf(79,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(80,conjecture,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( finite @ ( relation_dom @ A ) )
<=> ( finite @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_finset_1) ).
thf(81,negated_conjecture,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( finite @ ( relation_dom @ A ) )
<=> ( finite @ A ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[80]) ).
thf(82,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( finite @ ( relation_dom @ A ) )
<=> ( finite @ A ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[81]) ).
thf(83,plain,
( ( ! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(84,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(85,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(86,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(87,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(88,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(89,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(90,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( finite @ ( relation_dom @ A ) )
=> ( finite @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(91,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(92,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(93,plain,
( ( ! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(94,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( finite @ A )
=> ( finite @ ( relation_image @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(95,plain,
( ( ! [A: $i,B: $i] :
( ( ( subset @ A @ B )
& ( finite @ B ) )
=> ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(96,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( function_image @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) @ ( relation_dom @ A ) @ ( first_projection_as_func_of @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) @ A )
= ( relation_dom @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(97,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(98,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
<=> ( relation_of2 @ C @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(99,plain,
( ( ! [A: $i,B: $i] :
( ( first_projection_as_func_of @ A @ B )
= ( first_projection @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(100,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( function @ C )
& ( quasi_total @ C @ A @ B )
& ( relation_of2 @ C @ A @ B ) )
=> ( ( function_image @ A @ B @ C @ D )
= ( relation_image @ C @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(101,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_non_empty @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(102,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( transfinite_sequence @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(103,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(104,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(105,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(106,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(107,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(108,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(109,plain,
( ( ? [A: $i] :
( ( element @ A @ positive_rationals )
& ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A )
& ( natural @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(110,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(111,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(112,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(113,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( transfinite_sequence @ A )
& ( ordinal_yielding @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(114,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A )
& ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(115,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(116,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B )
& ( relation @ B )
& ( function @ B )
& ( one_to_one @ B )
& ( epsilon_transitive @ B )
& ( epsilon_connected @ B )
& ( ordinal @ B )
& ( natural @ B )
& ( finite @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(117,plain,
( ( ? [A: $i] :
( ( element @ A @ positive_rationals )
& ~ ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(118,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(119,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(120,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(121,plain,
( ( ? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A )
& ( being_limit_ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(122,plain,
( ( ? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(123,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(124,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( function_yielding @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(125,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(126,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A )
& ( natural @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(127,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(128,plain,
( ( ~ ( empty @ positive_rationals ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(129,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(130,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(131,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( relation_non_empty @ A )
& ( function @ A ) )
=> ( with_non_empty_elements @ ( relation_rng @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(132,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(133,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( transfinite_sequence @ A ) )
=> ( ( epsilon_transitive @ ( relation_dom @ A ) )
& ( epsilon_connected @ ( relation_dom @ A ) )
& ( ordinal @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(134,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(135,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(136,plain,
( ( ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set )
& ( function @ empty_set )
& ( one_to_one @ empty_set )
& ( empty @ empty_set )
& ( epsilon_transitive @ empty_set )
& ( epsilon_connected @ empty_set )
& ( ordinal @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(137,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(138,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(139,plain,
( ( ! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(140,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( finite @ B ) )
=> ( finite @ ( relation_image @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(141,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(142,plain,
( ( ! [A: $i,B: $i] :
? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(143,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(144,plain,
( ( ! [A: $i,B: $i] :
? [C: $i] : ( relation_of2 @ C @ A @ B ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(145,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(146,plain,
( ( ! [A: $i,B: $i] :
( ( function @ ( first_projection_as_func_of @ A @ B ) )
& ( quasi_total @ ( first_projection_as_func_of @ A @ B ) @ ( cartesian_product2 @ A @ B ) @ A )
& ( relation_of2_as_subset @ ( first_projection_as_func_of @ A @ B ) @ ( cartesian_product2 @ A @ B ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(147,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ ( first_projection @ A @ B ) )
& ( function @ ( first_projection @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(148,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( function @ C )
& ( quasi_total @ C @ A @ B )
& ( relation_of2 @ C @ A @ B ) )
=> ( element @ ( function_image @ A @ B @ C @ D ) @ ( powerset @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(149,plain,
( ( ! [A: $i] :
( ( element @ A @ positive_rationals )
=> ( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A )
& ( natural @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(150,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(151,plain,
( ( ! [A: $i] :
( ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) )
=> ( ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(152,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(153,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(154,plain,
( ( ! [A: $i] :
( ( ( empty @ A )
& ( ordinal @ A ) )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A )
& ( natural @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(155,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(156,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(157,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(158,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(159,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(160,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( ( epsilon_transitive @ B )
& ( epsilon_connected @ B )
& ( ordinal @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(161,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(162,plain,
( ( ( ( relation @ sK1_A )
& ( function @ sK1_A ) )
=> ( ( finite @ ( relation_dom @ sK1_A ) )
<=> ( finite @ sK1_A ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[82]) ).
thf(163,plain,
( ( relation @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[162]) ).
thf(164,plain,
( ( function @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[162]) ).
thf(165,plain,
( ( ( finite @ ( relation_dom @ sK1_A ) )
<=> ( finite @ sK1_A ) )
= $false ),
inference(standard_cnf,[status(thm)],[162]) ).
thf(166,plain,
( ( ( finite @ ( relation_dom @ sK1_A ) )
=> ( finite @ sK1_A ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[165]) ).
thf(167,plain,
( ( ( finite @ sK1_A )
=> ( finite @ ( relation_dom @ sK1_A ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[165]) ).
thf(168,plain,
( ( ~ ( ( finite @ ( relation_dom @ sK1_A ) )
=> ( finite @ sK1_A ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[166]) ).
thf(169,plain,
( ( ~ ( ( finite @ sK1_A )
=> ( finite @ ( relation_dom @ sK1_A ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[167]) ).
thf(170,plain,
( ( ( finite @ ( relation_dom @ sK1_A ) )
& ~ ( finite @ sK1_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[168]) ).
thf(171,plain,
( ( ( finite @ sK1_A )
& ~ ( finite @ ( relation_dom @ sK1_A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[169]) ).
thf(172,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[83]) ).
thf(173,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[84]) ).
thf(174,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[85]) ).
thf(175,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[86]) ).
thf(176,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[87]) ).
thf(177,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[88]) ).
thf(178,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[89]) ).
thf(179,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( finite @ ( relation_dom @ A ) )
| ( finite @ ( relation_rng @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[90]) ).
thf(180,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[91]) ).
thf(181,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[92]) ).
thf(182,plain,
( ( ! [A: $i,B: $i] :
( ~ ( finite @ A )
| ~ ( finite @ B )
| ( finite @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[93]) ).
thf(183,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ~ ( finite @ A )
| ( finite @ ( relation_image @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[94]) ).
thf(184,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ~ ( finite @ B )
| ~ ( subset @ A @ B ) )
| ( finite @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[95]) ).
thf(185,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ( function_image @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) @ ( relation_dom @ A ) @ ( first_projection_as_func_of @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) @ A )
= ( relation_dom @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[96]) ).
thf(186,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[97]) ).
thf(187,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( relation_of2_as_subset @ C @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( relation_of2 @ C @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[98]) ).
thf(188,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( quasi_total @ C @ A @ B )
| ~ ( relation_of2 @ C @ A @ B )
| ! [D: $i] :
( ( function_image @ A @ B @ C @ D )
= ( relation_image @ C @ D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[100]) ).
thf(189,plain,
( ( ( relation @ sK2_A )
& ( relation_non_empty @ sK2_A )
& ( function @ sK2_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[101]) ).
thf(190,plain,
( ( ( function @ sK3_A )
& ( relation @ sK3_A )
& ( transfinite_sequence @ sK3_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[102]) ).
thf(191,plain,
( ( ( relation @ sK4_A )
& ( relation_empty_yielding @ sK4_A )
& ( function @ sK4_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[103]) ).
thf(192,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK5_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK5_B @ A ) )
& ( finite @ ( sK5_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[104]) ).
thf(193,plain,
( ( ( relation @ sK6_A )
& ( relation_empty_yielding @ sK6_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[105]) ).
thf(194,plain,
( ( ~ ( empty @ sK7_A )
& ( epsilon_transitive @ sK7_A )
& ( epsilon_connected @ sK7_A )
& ( ordinal @ sK7_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[106]) ).
thf(195,plain,
( ( ( function @ sK8_A )
& ( relation @ sK8_A )
& ( one_to_one @ sK8_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[107]) ).
thf(196,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK9_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK9_B @ A ) )
& ( finite @ ( sK9_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[108]) ).
thf(197,plain,
( ( ( element @ sK10_A @ positive_rationals )
& ( empty @ sK10_A )
& ( epsilon_transitive @ sK10_A )
& ( epsilon_connected @ sK10_A )
& ( ordinal @ sK10_A )
& ( natural @ sK10_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[109]) ).
thf(198,plain,
( ( ~ ( empty @ sK11_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[110]) ).
thf(199,plain,
( ( ! [A: $i] :
( ( element @ ( sK12_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK12_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[111]) ).
thf(200,plain,
( ( ~ ( empty @ sK13_A )
& ( relation @ sK13_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[112]) ).
thf(201,plain,
( ( ( function @ sK14_A )
& ( relation @ sK14_A )
& ( transfinite_sequence @ sK14_A )
& ( ordinal_yielding @ sK14_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[113]) ).
thf(202,plain,
( ( ( function @ sK15_A )
& ( relation @ sK15_A )
& ( one_to_one @ sK15_A )
& ( empty @ sK15_A )
& ( epsilon_transitive @ sK15_A )
& ( epsilon_connected @ sK15_A )
& ( ordinal @ sK15_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[114]) ).
thf(203,plain,
( ( ( empty @ sK16_A )
& ( relation @ sK16_A )
& ( function @ sK16_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[115]) ).
thf(204,plain,
( ( ! [A: $i] :
( ( element @ ( sK17_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK17_B @ A ) )
& ( relation @ ( sK17_B @ A ) )
& ( function @ ( sK17_B @ A ) )
& ( one_to_one @ ( sK17_B @ A ) )
& ( epsilon_transitive @ ( sK17_B @ A ) )
& ( epsilon_connected @ ( sK17_B @ A ) )
& ( ordinal @ ( sK17_B @ A ) )
& ( natural @ ( sK17_B @ A ) )
& ( finite @ ( sK17_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[116]) ).
thf(205,plain,
( ( ( element @ sK18_A @ positive_rationals )
& ~ ( empty @ sK18_A )
& ( epsilon_transitive @ sK18_A )
& ( epsilon_connected @ sK18_A )
& ( ordinal @ sK18_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[117]) ).
thf(206,plain,
( ( empty @ sK19_A )
= $true ),
inference(extcnf_combined,[status(esa)],[118]) ).
thf(207,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK20_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK20_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[119]) ).
thf(208,plain,
( ( ( empty @ sK21_A )
& ( relation @ sK21_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[120]) ).
thf(209,plain,
( ( ( epsilon_connected @ sK22_A )
& ( epsilon_transitive @ sK22_A )
& ( ordinal @ sK22_A )
& ( being_limit_ordinal @ sK22_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[121]) ).
thf(210,plain,
( ( ( epsilon_connected @ sK23_A )
& ( epsilon_transitive @ sK23_A )
& ( ordinal @ sK23_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[122]) ).
thf(211,plain,
( ( ( function @ sK24_A )
& ( relation @ sK24_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[123]) ).
thf(212,plain,
( ( ( function @ sK25_A )
& ( relation @ sK25_A )
& ( function_yielding @ sK25_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[124]) ).
thf(213,plain,
( ( ~ ( empty @ sK26_A )
& ( finite @ sK26_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[125]) ).
thf(214,plain,
( ( ~ ( empty @ sK27_A )
& ( epsilon_transitive @ sK27_A )
& ( epsilon_connected @ sK27_A )
& ( ordinal @ sK27_A )
& ( natural @ sK27_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[126]) ).
thf(215,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_rng @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_rng @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[127]) ).
thf(216,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[129]) ).
thf(217,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[130]) ).
thf(218,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ~ ( relation_non_empty @ A )
| ~ ( function @ A )
| ( with_non_empty_elements @ ( relation_rng @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[131]) ).
thf(219,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[132]) ).
thf(220,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( transfinite_sequence @ A )
| ( epsilon_connected @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( transfinite_sequence @ A )
| ( epsilon_transitive @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( transfinite_sequence @ A )
| ( ordinal @ ( relation_dom @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[133]) ).
thf(221,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[134]) ).
thf(222,plain,
( ( ! [A: $i,B: $i] :
( ~ ( finite @ A )
| ~ ( finite @ B )
| ( finite @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[139]) ).
thf(223,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( finite @ B )
| ( finite @ ( relation_image @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[140]) ).
thf(224,plain,
( ( ! [A: $i,B: $i] : ( relation_of2_as_subset @ ( sK28_C @ B @ A ) @ A @ B ) )
= $true ),
inference(extcnf_combined,[status(esa)],[142]) ).
thf(225,plain,
( ( ! [A: $i] : ( element @ ( sK29_B @ A ) @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[143]) ).
thf(226,plain,
( ( ! [A: $i,B: $i] : ( relation_of2 @ ( sK30_C @ B @ A ) @ A @ B ) )
= $true ),
inference(extcnf_combined,[status(esa)],[144]) ).
thf(227,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[145]) ).
thf(228,plain,
( ( ! [A: $i,B: $i] : ( function @ ( first_projection_as_func_of @ A @ B ) )
& ! [A: $i,B: $i] : ( quasi_total @ ( first_projection_as_func_of @ A @ B ) @ ( cartesian_product2 @ A @ B ) @ A )
& ! [A: $i,B: $i] : ( relation_of2_as_subset @ ( first_projection_as_func_of @ A @ B ) @ ( cartesian_product2 @ A @ B ) @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[146]) ).
thf(229,plain,
( ( ! [A: $i,B: $i] : ( function @ ( first_projection @ A @ B ) )
& ! [A: $i,B: $i] : ( relation @ ( first_projection @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[147]) ).
thf(230,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( quasi_total @ C @ A @ B )
| ~ ( relation_of2 @ C @ A @ B )
| ! [D: $i] : ( element @ ( function_image @ A @ B @ C @ D ) @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[148]) ).
thf(231,plain,
( ( ! [A: $i] :
( ~ ( element @ A @ positive_rationals )
| ~ ( ordinal @ A )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( element @ A @ positive_rationals )
| ~ ( ordinal @ A )
| ( epsilon_transitive @ A ) )
& ! [A: $i] :
( ~ ( element @ A @ positive_rationals )
| ~ ( ordinal @ A )
| ( ordinal @ A ) )
& ! [A: $i] :
( ~ ( element @ A @ positive_rationals )
| ~ ( ordinal @ A )
| ( natural @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[149]) ).
thf(232,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( epsilon_transitive @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( ordinal @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[150]) ).
thf(233,plain,
( ( ! [A: $i] :
( ~ ( epsilon_connected @ A )
| ~ ( epsilon_transitive @ A )
| ( ordinal @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[151]) ).
thf(234,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( function @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( one_to_one @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[152]) ).
thf(235,plain,
( ( ! [A: $i] :
( ~ ( finite @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( finite @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[153]) ).
thf(236,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ~ ( ordinal @ A )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ~ ( ordinal @ A )
| ( epsilon_transitive @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ~ ( ordinal @ A )
| ( ordinal @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ~ ( ordinal @ A )
| ( natural @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[154]) ).
thf(237,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
| ( relation @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[155]) ).
thf(238,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[156]) ).
thf(239,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_transitive @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[157]) ).
thf(240,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[158]) ).
thf(241,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( finite @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[159]) ).
thf(242,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ( ! [B: $i] :
( ~ ( element @ B @ A )
| ( epsilon_connected @ B ) )
& ! [B: $i] :
( ~ ( element @ B @ A )
| ( epsilon_transitive @ B ) )
& ! [B: $i] :
( ~ ( element @ B @ A )
| ( ordinal @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[160]) ).
thf(243,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[161]) ).
thf(244,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[243]) ).
thf(245,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ( ! [B: $i] :
( ~ ( element @ B @ A )
| ( epsilon_connected @ B ) )
& ! [B: $i] :
( ~ ( element @ B @ A )
| ( epsilon_transitive @ B ) )
& ! [B: $i] :
( ~ ( element @ B @ A )
| ( ordinal @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[242]) ).
thf(246,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[241]) ).
thf(247,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[240]) ).
thf(248,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_transitive @ A ) ) )
= $true ),
inference(copy,[status(thm)],[239]) ).
thf(249,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[238]) ).
thf(250,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
| ( relation @ C ) ) )
= $true ),
inference(copy,[status(thm)],[237]) ).
thf(251,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ~ ( ordinal @ A )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ~ ( ordinal @ A )
| ( epsilon_transitive @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ~ ( ordinal @ A )
| ( ordinal @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ~ ( ordinal @ A )
| ( natural @ A ) ) )
= $true ),
inference(copy,[status(thm)],[236]) ).
thf(252,plain,
( ( ! [A: $i] :
( ~ ( finite @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[235]) ).
thf(253,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( function @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( one_to_one @ A ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(254,plain,
( ( ! [A: $i] :
( ~ ( epsilon_connected @ A )
| ~ ( epsilon_transitive @ A )
| ( ordinal @ A ) ) )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(255,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( epsilon_transitive @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( ordinal @ A ) ) )
= $true ),
inference(copy,[status(thm)],[232]) ).
thf(256,plain,
( ( ! [A: $i] :
( ~ ( element @ A @ positive_rationals )
| ~ ( ordinal @ A )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( element @ A @ positive_rationals )
| ~ ( ordinal @ A )
| ( epsilon_transitive @ A ) )
& ! [A: $i] :
( ~ ( element @ A @ positive_rationals )
| ~ ( ordinal @ A )
| ( ordinal @ A ) )
& ! [A: $i] :
( ~ ( element @ A @ positive_rationals )
| ~ ( ordinal @ A )
| ( natural @ A ) ) )
= $true ),
inference(copy,[status(thm)],[231]) ).
thf(257,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( quasi_total @ C @ A @ B )
| ~ ( relation_of2 @ C @ A @ B )
| ! [D: $i] : ( element @ ( function_image @ A @ B @ C @ D ) @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[230]) ).
thf(258,plain,
( ( ! [A: $i,B: $i] : ( function @ ( first_projection @ A @ B ) )
& ! [A: $i,B: $i] : ( relation @ ( first_projection @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[229]) ).
thf(259,plain,
( ( ! [A: $i,B: $i] : ( function @ ( first_projection_as_func_of @ A @ B ) )
& ! [A: $i,B: $i] : ( quasi_total @ ( first_projection_as_func_of @ A @ B ) @ ( cartesian_product2 @ A @ B ) @ A )
& ! [A: $i,B: $i] : ( relation_of2_as_subset @ ( first_projection_as_func_of @ A @ B ) @ ( cartesian_product2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[228]) ).
thf(260,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[227]) ).
thf(261,plain,
( ( ! [A: $i,B: $i] : ( relation_of2 @ ( sK30_C @ B @ A ) @ A @ B ) )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(262,plain,
( ( ! [A: $i] : ( element @ ( sK29_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[225]) ).
thf(263,plain,
( ( ! [A: $i,B: $i] : ( relation_of2_as_subset @ ( sK28_C @ B @ A ) @ A @ B ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(264,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(265,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( finite @ B )
| ( finite @ ( relation_image @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(266,plain,
( ( ! [A: $i,B: $i] :
( ~ ( finite @ A )
| ~ ( finite @ B )
| ( finite @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(267,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(268,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(269,plain,
( ( ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set )
& ( function @ empty_set )
& ( one_to_one @ empty_set )
& ( empty @ empty_set )
& ( epsilon_transitive @ empty_set )
& ( epsilon_connected @ empty_set )
& ( ordinal @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(270,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(271,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(272,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( transfinite_sequence @ A )
| ( epsilon_connected @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( transfinite_sequence @ A )
| ( epsilon_transitive @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( transfinite_sequence @ A )
| ( ordinal @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[220]) ).
thf(273,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[219]) ).
thf(274,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ~ ( relation_non_empty @ A )
| ~ ( function @ A )
| ( with_non_empty_elements @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[218]) ).
thf(275,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(276,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(277,plain,
( ( ~ ( empty @ positive_rationals ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(278,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_rng @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[215]) ).
thf(279,plain,
( ( ~ ( empty @ sK27_A )
& ( epsilon_transitive @ sK27_A )
& ( epsilon_connected @ sK27_A )
& ( ordinal @ sK27_A )
& ( natural @ sK27_A ) )
= $true ),
inference(copy,[status(thm)],[214]) ).
thf(280,plain,
( ( ~ ( empty @ sK26_A )
& ( finite @ sK26_A ) )
= $true ),
inference(copy,[status(thm)],[213]) ).
thf(281,plain,
( ( ( function @ sK25_A )
& ( relation @ sK25_A )
& ( function_yielding @ sK25_A ) )
= $true ),
inference(copy,[status(thm)],[212]) ).
thf(282,plain,
( ( ( function @ sK24_A )
& ( relation @ sK24_A ) )
= $true ),
inference(copy,[status(thm)],[211]) ).
thf(283,plain,
( ( ( epsilon_connected @ sK23_A )
& ( epsilon_transitive @ sK23_A )
& ( ordinal @ sK23_A ) )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(284,plain,
( ( ( epsilon_connected @ sK22_A )
& ( epsilon_transitive @ sK22_A )
& ( ordinal @ sK22_A )
& ( being_limit_ordinal @ sK22_A ) )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(285,plain,
( ( ( empty @ sK21_A )
& ( relation @ sK21_A ) )
= $true ),
inference(copy,[status(thm)],[208]) ).
thf(286,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK20_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK20_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[207]) ).
thf(287,plain,
( ( empty @ sK19_A )
= $true ),
inference(copy,[status(thm)],[206]) ).
thf(288,plain,
( ( ( element @ sK18_A @ positive_rationals )
& ~ ( empty @ sK18_A )
& ( epsilon_transitive @ sK18_A )
& ( epsilon_connected @ sK18_A )
& ( ordinal @ sK18_A ) )
= $true ),
inference(copy,[status(thm)],[205]) ).
thf(289,plain,
( ( ! [A: $i] :
( ( element @ ( sK17_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK17_B @ A ) )
& ( relation @ ( sK17_B @ A ) )
& ( function @ ( sK17_B @ A ) )
& ( one_to_one @ ( sK17_B @ A ) )
& ( epsilon_transitive @ ( sK17_B @ A ) )
& ( epsilon_connected @ ( sK17_B @ A ) )
& ( ordinal @ ( sK17_B @ A ) )
& ( natural @ ( sK17_B @ A ) )
& ( finite @ ( sK17_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[204]) ).
thf(290,plain,
( ( ( empty @ sK16_A )
& ( relation @ sK16_A )
& ( function @ sK16_A ) )
= $true ),
inference(copy,[status(thm)],[203]) ).
thf(291,plain,
( ( ( function @ sK15_A )
& ( relation @ sK15_A )
& ( one_to_one @ sK15_A )
& ( empty @ sK15_A )
& ( epsilon_transitive @ sK15_A )
& ( epsilon_connected @ sK15_A )
& ( ordinal @ sK15_A ) )
= $true ),
inference(copy,[status(thm)],[202]) ).
thf(292,plain,
( ( ( function @ sK14_A )
& ( relation @ sK14_A )
& ( transfinite_sequence @ sK14_A )
& ( ordinal_yielding @ sK14_A ) )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(293,plain,
( ( ~ ( empty @ sK13_A )
& ( relation @ sK13_A ) )
= $true ),
inference(copy,[status(thm)],[200]) ).
thf(294,plain,
( ( ! [A: $i] :
( ( element @ ( sK12_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK12_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[199]) ).
thf(295,plain,
( ( ~ ( empty @ sK11_A ) )
= $true ),
inference(copy,[status(thm)],[198]) ).
thf(296,plain,
( ( ( element @ sK10_A @ positive_rationals )
& ( empty @ sK10_A )
& ( epsilon_transitive @ sK10_A )
& ( epsilon_connected @ sK10_A )
& ( ordinal @ sK10_A )
& ( natural @ sK10_A ) )
= $true ),
inference(copy,[status(thm)],[197]) ).
thf(297,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK9_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK9_B @ A ) )
& ( finite @ ( sK9_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[196]) ).
thf(298,plain,
( ( ( function @ sK8_A )
& ( relation @ sK8_A )
& ( one_to_one @ sK8_A ) )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(299,plain,
( ( ~ ( empty @ sK7_A )
& ( epsilon_transitive @ sK7_A )
& ( epsilon_connected @ sK7_A )
& ( ordinal @ sK7_A ) )
= $true ),
inference(copy,[status(thm)],[194]) ).
thf(300,plain,
( ( ( relation @ sK6_A )
& ( relation_empty_yielding @ sK6_A ) )
= $true ),
inference(copy,[status(thm)],[193]) ).
thf(301,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK5_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK5_B @ A ) )
& ( finite @ ( sK5_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[192]) ).
thf(302,plain,
( ( ( relation @ sK4_A )
& ( relation_empty_yielding @ sK4_A )
& ( function @ sK4_A ) )
= $true ),
inference(copy,[status(thm)],[191]) ).
thf(303,plain,
( ( ( function @ sK3_A )
& ( relation @ sK3_A )
& ( transfinite_sequence @ sK3_A ) )
= $true ),
inference(copy,[status(thm)],[190]) ).
thf(304,plain,
( ( ( relation @ sK2_A )
& ( relation_non_empty @ sK2_A )
& ( function @ sK2_A ) )
= $true ),
inference(copy,[status(thm)],[189]) ).
thf(305,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( quasi_total @ C @ A @ B )
| ~ ( relation_of2 @ C @ A @ B )
| ! [D: $i] :
( ( function_image @ A @ B @ C @ D )
= ( relation_image @ C @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[188]) ).
thf(306,plain,
( ( ! [A: $i,B: $i] :
( ( first_projection_as_func_of @ A @ B )
= ( first_projection @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(307,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( relation_of2_as_subset @ C @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( relation_of2 @ C @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[187]) ).
thf(308,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[186]) ).
thf(309,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ( function_image @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) @ ( relation_dom @ A ) @ ( first_projection_as_func_of @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) @ A )
= ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[185]) ).
thf(310,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ~ ( finite @ B )
| ~ ( subset @ A @ B ) )
| ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[184]) ).
thf(311,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ~ ( finite @ A )
| ( finite @ ( relation_image @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[183]) ).
thf(312,plain,
( ( ! [A: $i,B: $i] :
( ~ ( finite @ A )
| ~ ( finite @ B )
| ( finite @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[182]) ).
thf(313,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[181]) ).
thf(314,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[180]) ).
thf(315,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( finite @ ( relation_dom @ A ) )
| ( finite @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[179]) ).
thf(316,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[178]) ).
thf(317,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[177]) ).
thf(318,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[176]) ).
thf(319,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[175]) ).
thf(320,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[174]) ).
thf(321,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[173]) ).
thf(322,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[172]) ).
thf(323,plain,
( ( function @ sK1_A )
= $true ),
inference(copy,[status(thm)],[164]) ).
thf(324,plain,
( ( relation @ sK1_A )
= $true ),
inference(copy,[status(thm)],[163]) ).
thf(325,plain,
( ( ( finite @ ( relation_dom @ sK1_A ) )
& ~ ( finite @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[170]) ).
thf(326,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ sK16_A )
| ~ ( relation @ sK16_A ) )
| ~ ( function @ sK16_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(327,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(328,plain,
( ( ~ ( ~ ( function @ sK24_A )
| ~ ( relation @ sK24_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(329,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( ordinal @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255]) ).
thf(330,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[278]) ).
thf(331,plain,
( ( ~ ( ~ ( relation @ sK6_A )
| ~ ( relation_empty_yielding @ sK6_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(332,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ sK2_A )
| ~ ( relation_non_empty @ sK2_A ) )
| ~ ( function @ sK2_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[304]) ).
thf(333,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK7_A )
| ~ ( epsilon_transitive @ sK7_A ) )
| ~ ( epsilon_connected @ sK7_A ) )
| ~ ( ordinal @ sK7_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(334,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ sK18_A @ positive_rationals )
| ~ ~ ( empty @ sK18_A ) )
| ~ ( epsilon_transitive @ sK18_A ) )
| ~ ( epsilon_connected @ sK18_A ) )
| ~ ( ordinal @ sK18_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(335,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( epsilon_connected @ sK22_A )
| ~ ( epsilon_transitive @ sK22_A ) )
| ~ ( ordinal @ sK22_A ) )
| ~ ( being_limit_ordinal @ sK22_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(336,plain,
( ( ~ ( ~ ( finite @ ( relation_dom @ sK1_A ) )
| ~ ~ ( finite @ sK1_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[325]) ).
thf(337,plain,
( ( ~ ( ~ ~ ( ~ ( function @ sK8_A )
| ~ ( relation @ sK8_A ) )
| ~ ( one_to_one @ sK8_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(338,plain,
( ( ~ ( ~ ~ ( ~ ( function @ sK25_A )
| ~ ( relation @ sK25_A ) )
| ~ ( function_yielding @ sK25_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[281]) ).
thf(339,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) )
| ~ ( epsilon_transitive @ empty_set ) )
| ~ ( epsilon_connected @ empty_set ) )
| ~ ( ordinal @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[269]) ).
thf(340,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] : ( function @ ( first_projection_as_func_of @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] : ( quasi_total @ ( first_projection_as_func_of @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX0 @ SX1 ) @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] : ( relation_of2_as_subset @ ( first_projection_as_func_of @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX0 @ SX1 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259]) ).
thf(341,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2 @ SX2 @ SX0 @ SX1 )
| ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( relation_of2 @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(342,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ sK10_A @ positive_rationals )
| ~ ( empty @ sK10_A ) )
| ~ ( epsilon_transitive @ sK10_A ) )
| ~ ( epsilon_connected @ sK10_A ) )
| ~ ( ordinal @ sK10_A ) )
| ~ ( natural @ sK10_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(343,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] : ( function @ ( first_projection @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] : ( relation @ ( first_projection @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(344,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ~ ( ~ ( element @ ( sK5_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK5_B @ SX0 ) ) )
| ~ ( finite @ ( sK5_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(345,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(346,plain,
( ( ~ ( ~ ~ ( ~ ( epsilon_connected @ sK23_A )
| ~ ( epsilon_transitive @ sK23_A ) )
| ~ ( ordinal @ sK23_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(347,plain,
( ( ~ ( ~ ~ ( empty @ sK13_A )
| ~ ( relation @ sK13_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(348,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( ordinal @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( natural @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[256]) ).
thf(349,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ~ ~ ( ~ ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( epsilon_connected @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( epsilon_transitive @ SX1 ) ) )
| ~ ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( ordinal @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(350,plain,
( ( ~ ( ~ ( empty @ sK21_A )
| ~ ( relation @ sK21_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[285]) ).
thf(351,plain,
( ( ~ ( ~ ~ ( ~ ( function @ sK3_A )
| ~ ( relation @ sK3_A ) )
| ~ ( transfinite_sequence @ sK3_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(352,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[270]) ).
thf(353,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK15_A )
| ~ ( relation @ sK15_A ) )
| ~ ( one_to_one @ sK15_A ) )
| ~ ( empty @ sK15_A ) )
| ~ ( epsilon_transitive @ sK15_A ) )
| ~ ( epsilon_connected @ sK15_A ) )
| ~ ( ordinal @ sK15_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(354,plain,
( ( ! [SX0: $i] :
~ ( ~ ( element @ ( sK12_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ( empty @ ( sK12_B @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(355,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[276]) ).
thf(356,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK14_A )
| ~ ( relation @ sK14_A ) )
| ~ ( transfinite_sequence @ sK14_A ) )
| ~ ( ordinal_yielding @ sK14_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(357,plain,
( ( ~ ( ~ ~ ( empty @ sK26_A )
| ~ ( finite @ sK26_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[280]) ).
thf(358,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ( element @ ( sK20_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK20_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286]) ).
thf(359,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317]) ).
thf(360,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( ordinal @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( natural @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(361,plain,
( ( ! [SX0: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ( empty @ ( sK17_B @ SX0 ) ) )
| ~ ( relation @ ( sK17_B @ SX0 ) ) )
| ~ ( function @ ( sK17_B @ SX0 ) ) )
| ~ ( one_to_one @ ( sK17_B @ SX0 ) ) )
| ~ ( epsilon_transitive @ ( sK17_B @ SX0 ) ) )
| ~ ( epsilon_connected @ ( sK17_B @ SX0 ) ) )
| ~ ( ordinal @ ( sK17_B @ SX0 ) ) )
| ~ ( natural @ ( sK17_B @ SX0 ) ) )
| ~ ( finite @ ( sK17_B @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(362,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(363,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ~ ( ~ ( element @ ( sK9_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK9_B @ SX0 ) ) )
| ~ ( finite @ ( sK9_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(364,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK27_A )
| ~ ( epsilon_transitive @ sK27_A ) )
| ~ ( epsilon_connected @ sK27_A ) )
| ~ ( ordinal @ sK27_A ) )
| ~ ( natural @ sK27_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[279]) ).
thf(365,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( transfinite_sequence @ SX0 )
| ( epsilon_connected @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( transfinite_sequence @ SX0 )
| ( epsilon_transitive @ ( relation_dom @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( transfinite_sequence @ SX0 )
| ( ordinal @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[272]) ).
thf(366,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ sK4_A )
| ~ ( relation_empty_yielding @ sK4_A ) )
| ~ ( function @ sK4_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(367,plain,
! [SV1: $i] :
( ( ! [SY119: $i] :
( ~ ( in @ SV1 @ SY119 )
| ~ ( in @ SY119 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(368,plain,
! [SV2: $i] :
( ( ~ ( empty @ SV2 )
| ( finite @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(369,plain,
! [SV3: $i] :
( ( ~ ( empty @ SV3 )
| ( function @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(370,plain,
! [SV4: $i] :
( ( ~ ( empty @ SV4 )
| ( relation @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(371,plain,
! [SV5: $i] :
( ( ! [SY120: $i,SY121: $i] :
( ~ ( element @ SY121 @ ( powerset @ ( cartesian_product2 @ SV5 @ SY120 ) ) )
| ( relation @ SY121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(372,plain,
! [SV6: $i] :
( ( ~ ( finite @ SV6 )
| ! [SY122: $i] :
( ~ ( element @ SY122 @ ( powerset @ SV6 ) )
| ( finite @ SY122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(373,plain,
! [SV7: $i] :
( ( ~ ( epsilon_connected @ SV7 )
| ~ ( epsilon_transitive @ SV7 )
| ( ordinal @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(374,plain,
! [SV8: $i] :
( ( ! [SY123: $i,SY124: $i] :
( ~ ( function @ SY124 )
| ~ ( quasi_total @ SY124 @ SV8 @ SY123 )
| ~ ( relation_of2 @ SY124 @ SV8 @ SY123 )
| ! [SY125: $i] : ( element @ ( function_image @ SV8 @ SY123 @ SY124 @ SY125 ) @ ( powerset @ SY123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(375,plain,
! [SV9: $i] :
( ( ! [SY126: $i,SY127: $i] :
( ~ ( relation_of2_as_subset @ SY127 @ SV9 @ SY126 )
| ( element @ SY127 @ ( powerset @ ( cartesian_product2 @ SV9 @ SY126 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(376,plain,
! [SV10: $i] :
( ( ! [SY128: $i] : ( relation_of2 @ ( sK30_C @ SY128 @ SV10 ) @ SV10 @ SY128 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(377,plain,
! [SV11: $i] :
( ( element @ ( sK29_B @ SV11 ) @ SV11 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(378,plain,
! [SV12: $i] :
( ( ! [SY129: $i] : ( relation_of2_as_subset @ ( sK28_C @ SY129 @ SV12 ) @ SV12 @ SY129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(379,plain,
! [SV13: $i] :
( ( ! [SY130: $i] :
( ~ ( function @ SV13 )
| ~ ( relation @ SV13 )
| ~ ( finite @ SY130 )
| ( finite @ ( relation_image @ SV13 @ SY130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(380,plain,
! [SV14: $i] :
( ( ! [SY131: $i] :
( ~ ( finite @ SV14 )
| ~ ( finite @ SY131 )
| ( finite @ ( cartesian_product2 @ SV14 @ SY131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(381,plain,
! [SV15: $i] :
( ( ~ ( empty @ ( powerset @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(382,plain,
! [SV16: $i] :
( ( ! [SY132: $i] :
( ( empty @ SV16 )
| ( empty @ SY132 )
| ~ ( empty @ ( cartesian_product2 @ SV16 @ SY132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(383,plain,
! [SV17: $i] :
( ( ( empty @ SV17 )
| ~ ( relation @ SV17 )
| ~ ( empty @ ( relation_dom @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(384,plain,
! [SV18: $i] :
( ( ~ ( relation @ SV18 )
| ~ ( relation_non_empty @ SV18 )
| ~ ( function @ SV18 )
| ( with_non_empty_elements @ ( relation_rng @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(385,plain,
! [SV19: $i] :
( ( ( empty @ SV19 )
| ~ ( relation @ SV19 )
| ~ ( empty @ ( relation_rng @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(386,plain,
( ( empty @ positive_rationals )
= $false ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(387,plain,
( ( empty @ sK11_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(388,plain,
! [SV20: $i] :
( ( ! [SY133: $i,SY134: $i] :
( ~ ( function @ SY134 )
| ~ ( quasi_total @ SY134 @ SV20 @ SY133 )
| ~ ( relation_of2 @ SY134 @ SV20 @ SY133 )
| ! [SY135: $i] :
( ( function_image @ SV20 @ SY133 @ SY134 @ SY135 )
= ( relation_image @ SY134 @ SY135 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(389,plain,
! [SV21: $i] :
( ( ! [SY136: $i] :
( ( first_projection_as_func_of @ SV21 @ SY136 )
= ( first_projection @ SV21 @ SY136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(390,plain,
! [SV22: $i] :
( ( subset @ SV22 @ SV22 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(391,plain,
! [SV23: $i] :
( ( ~ ( function @ SV23 )
| ~ ( relation @ SV23 )
| ( ( function_image @ ( cartesian_product2 @ ( relation_dom @ SV23 ) @ ( relation_rng @ SV23 ) ) @ ( relation_dom @ SV23 ) @ ( first_projection_as_func_of @ ( relation_dom @ SV23 ) @ ( relation_rng @ SV23 ) ) @ SV23 )
= ( relation_dom @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(392,plain,
! [SV24: $i] :
( ( ! [SY137: $i] :
( ~ ( finite @ SY137 )
| ~ ( subset @ SV24 @ SY137 ) )
| ( finite @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(393,plain,
! [SV25: $i] :
( ( ! [SY138: $i] :
( ~ ( function @ SY138 )
| ~ ( relation @ SY138 )
| ~ ( finite @ SV25 )
| ( finite @ ( relation_image @ SY138 @ SV25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(394,plain,
! [SV26: $i] :
( ( ! [SY139: $i] :
( ~ ( finite @ SV26 )
| ~ ( finite @ SY139 )
| ( finite @ ( cartesian_product2 @ SV26 @ SY139 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(395,plain,
! [SV27: $i] :
( ( ! [SY140: $i] :
( ~ ( in @ SV27 @ SY140 )
| ( element @ SV27 @ SY140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(396,plain,
! [SV28: $i] :
( ( ~ ( relation @ SV28 )
| ( subset @ SV28 @ ( cartesian_product2 @ ( relation_dom @ SV28 ) @ ( relation_rng @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(397,plain,
! [SV29: $i] :
( ( ~ ( function @ SV29 )
| ~ ( relation @ SV29 )
| ~ ( finite @ ( relation_dom @ SV29 ) )
| ( finite @ ( relation_rng @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(398,plain,
! [SV30: $i] :
( ( ! [SY141: $i] :
( ~ ( element @ SV30 @ SY141 )
| ( empty @ SY141 )
| ( in @ SV30 @ SY141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(399,plain,
! [SV31: $i] :
( ( ! [SY142: $i,SY143: $i] :
( ~ ( element @ SY142 @ ( powerset @ SY143 ) )
| ~ ( in @ SV31 @ SY142 )
| ( element @ SV31 @ SY143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(400,plain,
! [SV32: $i] :
( ( ! [SY144: $i,SY145: $i] :
( ~ ( element @ SY144 @ ( powerset @ SY145 ) )
| ~ ( in @ SV32 @ SY144 )
| ~ ( empty @ SY145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(401,plain,
! [SV33: $i] :
( ( ~ ( empty @ SV33 )
| ( SV33 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(402,plain,
! [SV34: $i] :
( ( ! [SY146: $i] :
( ~ ( empty @ SY146 )
| ~ ( in @ SV34 @ SY146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(403,plain,
! [SV35: $i] :
( ( ! [SY147: $i] :
( ( SV35 = SY147 )
| ~ ( empty @ SV35 )
| ~ ( empty @ SY147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(404,plain,
( ( ~ ~ ( ~ ( empty @ sK16_A )
| ~ ( relation @ sK16_A ) )
| ~ ( function @ sK16_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(405,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(406,plain,
( ( ~ ( function @ sK24_A )
| ~ ( relation @ sK24_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(407,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( ordinal @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(408,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(409,plain,
( ( ~ ( relation @ sK6_A )
| ~ ( relation_empty_yielding @ sK6_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(410,plain,
( ( ~ ~ ( ~ ( relation @ sK2_A )
| ~ ( relation_non_empty @ sK2_A ) )
| ~ ( function @ sK2_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(411,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK7_A )
| ~ ( epsilon_transitive @ sK7_A ) )
| ~ ( epsilon_connected @ sK7_A ) )
| ~ ( ordinal @ sK7_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(412,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ sK18_A @ positive_rationals )
| ~ ~ ( empty @ sK18_A ) )
| ~ ( epsilon_transitive @ sK18_A ) )
| ~ ( epsilon_connected @ sK18_A ) )
| ~ ( ordinal @ sK18_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(413,plain,
( ( ~ ~ ( ~ ~ ( ~ ( epsilon_connected @ sK22_A )
| ~ ( epsilon_transitive @ sK22_A ) )
| ~ ( ordinal @ sK22_A ) )
| ~ ( being_limit_ordinal @ sK22_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(414,plain,
( ( ~ ( finite @ ( relation_dom @ sK1_A ) )
| ~ ~ ( finite @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(415,plain,
( ( ~ ~ ( ~ ( function @ sK8_A )
| ~ ( relation @ sK8_A ) )
| ~ ( one_to_one @ sK8_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(416,plain,
( ( ~ ~ ( ~ ( function @ sK25_A )
| ~ ( relation @ sK25_A ) )
| ~ ( function_yielding @ sK25_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(417,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) )
| ~ ( epsilon_transitive @ empty_set ) )
| ~ ( epsilon_connected @ empty_set ) )
| ~ ( ordinal @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(418,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] : ( function @ ( first_projection_as_func_of @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] : ( quasi_total @ ( first_projection_as_func_of @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX0 @ SX1 ) @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] : ( relation_of2_as_subset @ ( first_projection_as_func_of @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX0 @ SX1 ) @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(419,plain,
! [SV36: $i] :
( ( ~ ( ~ ! [SY148: $i,SY149: $i] :
( ~ ( relation_of2 @ SY149 @ SV36 @ SY148 )
| ( relation_of2_as_subset @ SY149 @ SV36 @ SY148 ) )
| ~ ! [SY150: $i,SY151: $i] :
( ~ ( relation_of2_as_subset @ SY151 @ SV36 @ SY150 )
| ( relation_of2 @ SY151 @ SV36 @ SY150 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(420,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ sK10_A @ positive_rationals )
| ~ ( empty @ sK10_A ) )
| ~ ( epsilon_transitive @ sK10_A ) )
| ~ ( epsilon_connected @ sK10_A ) )
| ~ ( ordinal @ sK10_A ) )
| ~ ( natural @ sK10_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(421,plain,
( ( ~ ! [SX0: $i,SX1: $i] : ( function @ ( first_projection @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] : ( relation @ ( first_projection @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(422,plain,
! [SV37: $i] :
( ( ( empty @ SV37 )
| ~ ( ~ ~ ( ~ ( element @ ( sK5_B @ SV37 ) @ ( powerset @ SV37 ) )
| ~ ~ ( empty @ ( sK5_B @ SV37 ) ) )
| ~ ( finite @ ( sK5_B @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(423,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(424,plain,
( ( ~ ~ ( ~ ( epsilon_connected @ sK23_A )
| ~ ( epsilon_transitive @ sK23_A ) )
| ~ ( ordinal @ sK23_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(425,plain,
( ( ~ ~ ( empty @ sK13_A )
| ~ ( relation @ sK13_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(426,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( ordinal @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( natural @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[348]) ).
thf(427,plain,
! [SV38: $i] :
( ( ~ ( ordinal @ SV38 )
| ~ ( ~ ~ ( ~ ! [SY152: $i] :
( ~ ( element @ SY152 @ SV38 )
| ( epsilon_connected @ SY152 ) )
| ~ ! [SY153: $i] :
( ~ ( element @ SY153 @ SV38 )
| ( epsilon_transitive @ SY153 ) ) )
| ~ ! [SY154: $i] :
( ~ ( element @ SY154 @ SV38 )
| ( ordinal @ SY154 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(428,plain,
( ( ~ ( empty @ sK21_A )
| ~ ( relation @ sK21_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(429,plain,
( ( ~ ~ ( ~ ( function @ sK3_A )
| ~ ( relation @ sK3_A ) )
| ~ ( transfinite_sequence @ sK3_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(430,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(431,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK15_A )
| ~ ( relation @ sK15_A ) )
| ~ ( one_to_one @ sK15_A ) )
| ~ ( empty @ sK15_A ) )
| ~ ( epsilon_transitive @ sK15_A ) )
| ~ ( epsilon_connected @ sK15_A ) )
| ~ ( ordinal @ sK15_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(432,plain,
! [SV39: $i] :
( ( ~ ( ~ ( element @ ( sK12_B @ SV39 ) @ ( powerset @ SV39 ) )
| ~ ( empty @ ( sK12_B @ SV39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(433,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(434,plain,
( ( ~ ~ ( ~ ~ ( ~ ( function @ sK14_A )
| ~ ( relation @ sK14_A ) )
| ~ ( transfinite_sequence @ sK14_A ) )
| ~ ( ordinal_yielding @ sK14_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(435,plain,
( ( ~ ~ ( empty @ sK26_A )
| ~ ( finite @ sK26_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(436,plain,
! [SV40: $i] :
( ( ( empty @ SV40 )
| ~ ( ~ ( element @ ( sK20_B @ SV40 ) @ ( powerset @ SV40 ) )
| ~ ~ ( empty @ ( sK20_B @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(437,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(438,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( ordinal @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( natural @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(439,plain,
! [SV41: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV41 ) @ ( powerset @ SV41 ) )
| ~ ( empty @ ( sK17_B @ SV41 ) ) )
| ~ ( relation @ ( sK17_B @ SV41 ) ) )
| ~ ( function @ ( sK17_B @ SV41 ) ) )
| ~ ( one_to_one @ ( sK17_B @ SV41 ) ) )
| ~ ( epsilon_transitive @ ( sK17_B @ SV41 ) ) )
| ~ ( epsilon_connected @ ( sK17_B @ SV41 ) ) )
| ~ ( ordinal @ ( sK17_B @ SV41 ) ) )
| ~ ( natural @ ( sK17_B @ SV41 ) ) )
| ~ ( finite @ ( sK17_B @ SV41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(440,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(441,plain,
! [SV42: $i] :
( ( ( empty @ SV42 )
| ~ ( ~ ~ ( ~ ( element @ ( sK9_B @ SV42 ) @ ( powerset @ SV42 ) )
| ~ ~ ( empty @ ( sK9_B @ SV42 ) ) )
| ~ ( finite @ ( sK9_B @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(442,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK27_A )
| ~ ( epsilon_transitive @ sK27_A ) )
| ~ ( epsilon_connected @ sK27_A ) )
| ~ ( ordinal @ sK27_A ) )
| ~ ( natural @ sK27_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(443,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( transfinite_sequence @ SX0 )
| ( epsilon_connected @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( transfinite_sequence @ SX0 )
| ( epsilon_transitive @ ( relation_dom @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( transfinite_sequence @ SX0 )
| ( ordinal @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[365]) ).
thf(444,plain,
( ( ~ ~ ( ~ ( relation @ sK4_A )
| ~ ( relation_empty_yielding @ sK4_A ) )
| ~ ( function @ sK4_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(445,plain,
! [SV43: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV43 )
| ~ ( in @ SV43 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(446,plain,
! [SV2: $i] :
( ( ( ~ ( empty @ SV2 ) )
= $true )
| ( ( finite @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[368]) ).
thf(447,plain,
! [SV3: $i] :
( ( ( ~ ( empty @ SV3 ) )
= $true )
| ( ( function @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[369]) ).
thf(448,plain,
! [SV4: $i] :
( ( ( ~ ( empty @ SV4 ) )
= $true )
| ( ( relation @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[370]) ).
thf(449,plain,
! [SV44: $i,SV5: $i] :
( ( ! [SY155: $i] :
( ~ ( element @ SY155 @ ( powerset @ ( cartesian_product2 @ SV5 @ SV44 ) ) )
| ( relation @ SY155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(450,plain,
! [SV6: $i] :
( ( ( ~ ( finite @ SV6 ) )
= $true )
| ( ( ! [SY122: $i] :
( ~ ( element @ SY122 @ ( powerset @ SV6 ) )
| ( finite @ SY122 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[372]) ).
thf(451,plain,
! [SV7: $i] :
( ( ( ~ ( epsilon_connected @ SV7 )
| ~ ( epsilon_transitive @ SV7 ) )
= $true )
| ( ( ordinal @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[373]) ).
thf(452,plain,
! [SV45: $i,SV8: $i] :
( ( ! [SY156: $i] :
( ~ ( function @ SY156 )
| ~ ( quasi_total @ SY156 @ SV8 @ SV45 )
| ~ ( relation_of2 @ SY156 @ SV8 @ SV45 )
| ! [SY157: $i] : ( element @ ( function_image @ SV8 @ SV45 @ SY156 @ SY157 ) @ ( powerset @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(453,plain,
! [SV46: $i,SV9: $i] :
( ( ! [SY158: $i] :
( ~ ( relation_of2_as_subset @ SY158 @ SV9 @ SV46 )
| ( element @ SY158 @ ( powerset @ ( cartesian_product2 @ SV9 @ SV46 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(454,plain,
! [SV10: $i,SV47: $i] :
( ( relation_of2 @ ( sK30_C @ SV47 @ SV10 ) @ SV10 @ SV47 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(455,plain,
! [SV12: $i,SV48: $i] :
( ( relation_of2_as_subset @ ( sK28_C @ SV48 @ SV12 ) @ SV12 @ SV48 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(456,plain,
! [SV49: $i,SV13: $i] :
( ( ~ ( function @ SV13 )
| ~ ( relation @ SV13 )
| ~ ( finite @ SV49 )
| ( finite @ ( relation_image @ SV13 @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(457,plain,
! [SV50: $i,SV14: $i] :
( ( ~ ( finite @ SV14 )
| ~ ( finite @ SV50 )
| ( finite @ ( cartesian_product2 @ SV14 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(458,plain,
! [SV15: $i] :
( ( empty @ ( powerset @ SV15 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(459,plain,
! [SV51: $i,SV16: $i] :
( ( ( empty @ SV16 )
| ( empty @ SV51 )
| ~ ( empty @ ( cartesian_product2 @ SV16 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(460,plain,
! [SV17: $i] :
( ( ( ( empty @ SV17 )
| ~ ( relation @ SV17 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV17 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[383]) ).
thf(461,plain,
! [SV18: $i] :
( ( ( ~ ( relation @ SV18 )
| ~ ( relation_non_empty @ SV18 )
| ~ ( function @ SV18 ) )
= $true )
| ( ( with_non_empty_elements @ ( relation_rng @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[384]) ).
thf(462,plain,
! [SV19: $i] :
( ( ( ( empty @ SV19 )
| ~ ( relation @ SV19 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV19 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[385]) ).
thf(463,plain,
! [SV52: $i,SV20: $i] :
( ( ! [SY159: $i] :
( ~ ( function @ SY159 )
| ~ ( quasi_total @ SY159 @ SV20 @ SV52 )
| ~ ( relation_of2 @ SY159 @ SV20 @ SV52 )
| ! [SY160: $i] :
( ( function_image @ SV20 @ SV52 @ SY159 @ SY160 )
= ( relation_image @ SY159 @ SY160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(464,plain,
! [SV53: $i,SV21: $i] :
( ( ( first_projection_as_func_of @ SV21 @ SV53 )
= ( first_projection @ SV21 @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(465,plain,
! [SV23: $i] :
( ( ( ~ ( function @ SV23 )
| ~ ( relation @ SV23 ) )
= $true )
| ( ( ( function_image @ ( cartesian_product2 @ ( relation_dom @ SV23 ) @ ( relation_rng @ SV23 ) ) @ ( relation_dom @ SV23 ) @ ( first_projection_as_func_of @ ( relation_dom @ SV23 ) @ ( relation_rng @ SV23 ) ) @ SV23 )
= ( relation_dom @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[391]) ).
thf(466,plain,
! [SV24: $i] :
( ( ( ! [SY137: $i] :
( ~ ( finite @ SY137 )
| ~ ( subset @ SV24 @ SY137 ) ) )
= $true )
| ( ( finite @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[392]) ).
thf(467,plain,
! [SV25: $i,SV54: $i] :
( ( ~ ( function @ SV54 )
| ~ ( relation @ SV54 )
| ~ ( finite @ SV25 )
| ( finite @ ( relation_image @ SV54 @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(468,plain,
! [SV55: $i,SV26: $i] :
( ( ~ ( finite @ SV26 )
| ~ ( finite @ SV55 )
| ( finite @ ( cartesian_product2 @ SV26 @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(469,plain,
! [SV56: $i,SV27: $i] :
( ( ~ ( in @ SV27 @ SV56 )
| ( element @ SV27 @ SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(470,plain,
! [SV28: $i] :
( ( ( ~ ( relation @ SV28 ) )
= $true )
| ( ( subset @ SV28 @ ( cartesian_product2 @ ( relation_dom @ SV28 ) @ ( relation_rng @ SV28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[396]) ).
thf(471,plain,
! [SV29: $i] :
( ( ( ~ ( function @ SV29 )
| ~ ( relation @ SV29 ) )
= $true )
| ( ( ~ ( finite @ ( relation_dom @ SV29 ) )
| ( finite @ ( relation_rng @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[397]) ).
thf(472,plain,
! [SV57: $i,SV30: $i] :
( ( ~ ( element @ SV30 @ SV57 )
| ( empty @ SV57 )
| ( in @ SV30 @ SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(473,plain,
! [SV31: $i,SV58: $i] :
( ( ! [SY161: $i] :
( ~ ( element @ SV58 @ ( powerset @ SY161 ) )
| ~ ( in @ SV31 @ SV58 )
| ( element @ SV31 @ SY161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(474,plain,
! [SV32: $i,SV59: $i] :
( ( ! [SY162: $i] :
( ~ ( element @ SV59 @ ( powerset @ SY162 ) )
| ~ ( in @ SV32 @ SV59 )
| ~ ( empty @ SY162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(475,plain,
! [SV33: $i] :
( ( ( ~ ( empty @ SV33 ) )
= $true )
| ( ( SV33 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[401]) ).
thf(476,plain,
! [SV34: $i,SV60: $i] :
( ( ~ ( empty @ SV60 )
| ~ ( in @ SV34 @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(477,plain,
! [SV61: $i,SV35: $i] :
( ( ( SV35 = SV61 )
| ~ ( empty @ SV35 )
| ~ ( empty @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(478,plain,
( ( ~ ~ ( ~ ( empty @ sK16_A )
| ~ ( relation @ sK16_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[404]) ).
thf(479,plain,
( ( ~ ( function @ sK16_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[404]) ).
thf(480,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[405]) ).
thf(481,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[405]) ).
thf(482,plain,
( ( ~ ( function @ sK24_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[406]) ).
thf(483,plain,
( ( ~ ( relation @ sK24_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[406]) ).
thf(484,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_transitive @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[407]) ).
thf(485,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( ordinal @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[407]) ).
thf(486,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[408]) ).
thf(487,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[408]) ).
thf(488,plain,
( ( ~ ( relation @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[409]) ).
thf(489,plain,
( ( ~ ( relation_empty_yielding @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[409]) ).
thf(490,plain,
( ( ~ ~ ( ~ ( relation @ sK2_A )
| ~ ( relation_non_empty @ sK2_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[410]) ).
thf(491,plain,
( ( ~ ( function @ sK2_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[410]) ).
thf(492,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK7_A )
| ~ ( epsilon_transitive @ sK7_A ) )
| ~ ( epsilon_connected @ sK7_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[411]) ).
thf(493,plain,
( ( ~ ( ordinal @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[411]) ).
thf(494,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ sK18_A @ positive_rationals )
| ~ ~ ( empty @ sK18_A ) )
| ~ ( epsilon_transitive @ sK18_A ) )
| ~ ( epsilon_connected @ sK18_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[412]) ).
thf(495,plain,
( ( ~ ( ordinal @ sK18_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[412]) ).
thf(496,plain,
( ( ~ ~ ( ~ ~ ( ~ ( epsilon_connected @ sK22_A )
| ~ ( epsilon_transitive @ sK22_A ) )
| ~ ( ordinal @ sK22_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[413]) ).
thf(497,plain,
( ( ~ ( being_limit_ordinal @ sK22_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[413]) ).
thf(498,plain,
( ( ~ ( finite @ ( relation_dom @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[414]) ).
thf(499,plain,
( ( ~ ~ ( finite @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[414]) ).
thf(500,plain,
( ( ~ ~ ( ~ ( function @ sK8_A )
| ~ ( relation @ sK8_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[415]) ).
thf(501,plain,
( ( ~ ( one_to_one @ sK8_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[415]) ).
thf(502,plain,
( ( ~ ~ ( ~ ( function @ sK25_A )
| ~ ( relation @ sK25_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[416]) ).
thf(503,plain,
( ( ~ ( function_yielding @ sK25_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[416]) ).
thf(504,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) )
| ~ ( epsilon_transitive @ empty_set ) )
| ~ ( epsilon_connected @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[417]) ).
thf(505,plain,
( ( ~ ( ordinal @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[417]) ).
thf(506,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] : ( function @ ( first_projection_as_func_of @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] : ( quasi_total @ ( first_projection_as_func_of @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX0 @ SX1 ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[418]) ).
thf(507,plain,
( ( ~ ! [SX0: $i,SX1: $i] : ( relation_of2_as_subset @ ( first_projection_as_func_of @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX0 @ SX1 ) @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[418]) ).
thf(508,plain,
! [SV36: $i] :
( ( ~ ! [SY148: $i,SY149: $i] :
( ~ ( relation_of2 @ SY149 @ SV36 @ SY148 )
| ( relation_of2_as_subset @ SY149 @ SV36 @ SY148 ) )
| ~ ! [SY150: $i,SY151: $i] :
( ~ ( relation_of2_as_subset @ SY151 @ SV36 @ SY150 )
| ( relation_of2 @ SY151 @ SV36 @ SY150 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(509,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ sK10_A @ positive_rationals )
| ~ ( empty @ sK10_A ) )
| ~ ( epsilon_transitive @ sK10_A ) )
| ~ ( epsilon_connected @ sK10_A ) )
| ~ ( ordinal @ sK10_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[420]) ).
thf(510,plain,
( ( ~ ( natural @ sK10_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[420]) ).
thf(511,plain,
( ( ~ ! [SX0: $i,SX1: $i] : ( function @ ( first_projection @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[421]) ).
thf(512,plain,
( ( ~ ! [SX0: $i,SX1: $i] : ( relation @ ( first_projection @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[421]) ).
thf(513,plain,
! [SV37: $i] :
( ( ( empty @ SV37 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( element @ ( sK5_B @ SV37 ) @ ( powerset @ SV37 ) )
| ~ ~ ( empty @ ( sK5_B @ SV37 ) ) )
| ~ ( finite @ ( sK5_B @ SV37 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[422]) ).
thf(514,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[423]) ).
thf(515,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[423]) ).
thf(516,plain,
( ( ~ ~ ( ~ ( epsilon_connected @ sK23_A )
| ~ ( epsilon_transitive @ sK23_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[424]) ).
thf(517,plain,
( ( ~ ( ordinal @ sK23_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[424]) ).
thf(518,plain,
( ( ~ ~ ( empty @ sK13_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[425]) ).
thf(519,plain,
( ( ~ ( relation @ sK13_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[425]) ).
thf(520,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( ordinal @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[426]) ).
thf(521,plain,
( ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( natural @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[426]) ).
thf(522,plain,
! [SV38: $i] :
( ( ( ~ ( ordinal @ SV38 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY152: $i] :
( ~ ( element @ SY152 @ SV38 )
| ( epsilon_connected @ SY152 ) )
| ~ ! [SY153: $i] :
( ~ ( element @ SY153 @ SV38 )
| ( epsilon_transitive @ SY153 ) ) )
| ~ ! [SY154: $i] :
( ~ ( element @ SY154 @ SV38 )
| ( ordinal @ SY154 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[427]) ).
thf(523,plain,
( ( ~ ( empty @ sK21_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[428]) ).
thf(524,plain,
( ( ~ ( relation @ sK21_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[428]) ).
thf(525,plain,
( ( ~ ~ ( ~ ( function @ sK3_A )
| ~ ( relation @ sK3_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[429]) ).
thf(526,plain,
( ( ~ ( transfinite_sequence @ sK3_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[429]) ).
thf(527,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[430]) ).
thf(528,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[430]) ).
thf(529,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK15_A )
| ~ ( relation @ sK15_A ) )
| ~ ( one_to_one @ sK15_A ) )
| ~ ( empty @ sK15_A ) )
| ~ ( epsilon_transitive @ sK15_A ) )
| ~ ( epsilon_connected @ sK15_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[431]) ).
thf(530,plain,
( ( ~ ( ordinal @ sK15_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[431]) ).
thf(531,plain,
! [SV39: $i] :
( ( ~ ( element @ ( sK12_B @ SV39 ) @ ( powerset @ SV39 ) )
| ~ ( empty @ ( sK12_B @ SV39 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(532,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(533,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(534,plain,
( ( ~ ~ ( ~ ~ ( ~ ( function @ sK14_A )
| ~ ( relation @ sK14_A ) )
| ~ ( transfinite_sequence @ sK14_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[434]) ).
thf(535,plain,
( ( ~ ( ordinal_yielding @ sK14_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[434]) ).
thf(536,plain,
( ( ~ ~ ( empty @ sK26_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[435]) ).
thf(537,plain,
( ( ~ ( finite @ sK26_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[435]) ).
thf(538,plain,
! [SV40: $i] :
( ( ( empty @ SV40 )
= $true )
| ( ( ~ ( ~ ( element @ ( sK20_B @ SV40 ) @ ( powerset @ SV40 ) )
| ~ ~ ( empty @ ( sK20_B @ SV40 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[436]) ).
thf(539,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[437]) ).
thf(540,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[437]) ).
thf(541,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( ordinal @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[438]) ).
thf(542,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( natural @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[438]) ).
thf(543,plain,
! [SV41: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV41 ) @ ( powerset @ SV41 ) )
| ~ ( empty @ ( sK17_B @ SV41 ) ) )
| ~ ( relation @ ( sK17_B @ SV41 ) ) )
| ~ ( function @ ( sK17_B @ SV41 ) ) )
| ~ ( one_to_one @ ( sK17_B @ SV41 ) ) )
| ~ ( epsilon_transitive @ ( sK17_B @ SV41 ) ) )
| ~ ( epsilon_connected @ ( sK17_B @ SV41 ) ) )
| ~ ( ordinal @ ( sK17_B @ SV41 ) ) )
| ~ ( natural @ ( sK17_B @ SV41 ) ) )
| ~ ( finite @ ( sK17_B @ SV41 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(544,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[440]) ).
thf(545,plain,
( ( ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[440]) ).
thf(546,plain,
! [SV42: $i] :
( ( ( empty @ SV42 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( element @ ( sK9_B @ SV42 ) @ ( powerset @ SV42 ) )
| ~ ~ ( empty @ ( sK9_B @ SV42 ) ) )
| ~ ( finite @ ( sK9_B @ SV42 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[441]) ).
thf(547,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK27_A )
| ~ ( epsilon_transitive @ sK27_A ) )
| ~ ( epsilon_connected @ sK27_A ) )
| ~ ( ordinal @ sK27_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[442]) ).
thf(548,plain,
( ( ~ ( natural @ sK27_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[442]) ).
thf(549,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( transfinite_sequence @ SX0 )
| ( epsilon_connected @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( transfinite_sequence @ SX0 )
| ( epsilon_transitive @ ( relation_dom @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[443]) ).
thf(550,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( transfinite_sequence @ SX0 )
| ( ordinal @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[443]) ).
thf(551,plain,
( ( ~ ~ ( ~ ( relation @ sK4_A )
| ~ ( relation_empty_yielding @ sK4_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[444]) ).
thf(552,plain,
( ( ~ ( function @ sK4_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[444]) ).
thf(553,plain,
! [SV43: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV43 ) )
= $true )
| ( ( ~ ( in @ SV43 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[445]) ).
thf(554,plain,
! [SV2: $i] :
( ( ( empty @ SV2 )
= $false )
| ( ( finite @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(555,plain,
! [SV3: $i] :
( ( ( empty @ SV3 )
= $false )
| ( ( function @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(556,plain,
! [SV4: $i] :
( ( ( empty @ SV4 )
= $false )
| ( ( relation @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(557,plain,
! [SV44: $i,SV5: $i,SV62: $i] :
( ( ~ ( element @ SV62 @ ( powerset @ ( cartesian_product2 @ SV5 @ SV44 ) ) )
| ( relation @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(558,plain,
! [SV6: $i] :
( ( ( finite @ SV6 )
= $false )
| ( ( ! [SY122: $i] :
( ~ ( element @ SY122 @ ( powerset @ SV6 ) )
| ( finite @ SY122 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(559,plain,
! [SV7: $i] :
( ( ( ~ ( epsilon_connected @ SV7 ) )
= $true )
| ( ( ~ ( epsilon_transitive @ SV7 ) )
= $true )
| ( ( ordinal @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[451]) ).
thf(560,plain,
! [SV45: $i,SV8: $i,SV63: $i] :
( ( ~ ( function @ SV63 )
| ~ ( quasi_total @ SV63 @ SV8 @ SV45 )
| ~ ( relation_of2 @ SV63 @ SV8 @ SV45 )
| ! [SY163: $i] : ( element @ ( function_image @ SV8 @ SV45 @ SV63 @ SY163 ) @ ( powerset @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(561,plain,
! [SV46: $i,SV9: $i,SV64: $i] :
( ( ~ ( relation_of2_as_subset @ SV64 @ SV9 @ SV46 )
| ( element @ SV64 @ ( powerset @ ( cartesian_product2 @ SV9 @ SV46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(562,plain,
! [SV49: $i,SV13: $i] :
( ( ( ~ ( function @ SV13 )
| ~ ( relation @ SV13 )
| ~ ( finite @ SV49 ) )
= $true )
| ( ( finite @ ( relation_image @ SV13 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[456]) ).
thf(563,plain,
! [SV50: $i,SV14: $i] :
( ( ( ~ ( finite @ SV14 )
| ~ ( finite @ SV50 ) )
= $true )
| ( ( finite @ ( cartesian_product2 @ SV14 @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[457]) ).
thf(564,plain,
! [SV51: $i,SV16: $i] :
( ( ( ( empty @ SV16 )
| ( empty @ SV51 ) )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV16 @ SV51 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[459]) ).
thf(565,plain,
! [SV17: $i] :
( ( ( empty @ SV17 )
= $true )
| ( ( ~ ( relation @ SV17 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV17 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[460]) ).
thf(566,plain,
! [SV18: $i] :
( ( ( ~ ( relation @ SV18 )
| ~ ( relation_non_empty @ SV18 ) )
= $true )
| ( ( ~ ( function @ SV18 ) )
= $true )
| ( ( with_non_empty_elements @ ( relation_rng @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(567,plain,
! [SV19: $i] :
( ( ( empty @ SV19 )
= $true )
| ( ( ~ ( relation @ SV19 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV19 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[462]) ).
thf(568,plain,
! [SV52: $i,SV20: $i,SV65: $i] :
( ( ~ ( function @ SV65 )
| ~ ( quasi_total @ SV65 @ SV20 @ SV52 )
| ~ ( relation_of2 @ SV65 @ SV20 @ SV52 )
| ! [SY164: $i] :
( ( function_image @ SV20 @ SV52 @ SV65 @ SY164 )
= ( relation_image @ SV65 @ SY164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(569,plain,
! [SV23: $i] :
( ( ( ~ ( function @ SV23 ) )
= $true )
| ( ( ~ ( relation @ SV23 ) )
= $true )
| ( ( ( function_image @ ( cartesian_product2 @ ( relation_dom @ SV23 ) @ ( relation_rng @ SV23 ) ) @ ( relation_dom @ SV23 ) @ ( first_projection_as_func_of @ ( relation_dom @ SV23 ) @ ( relation_rng @ SV23 ) ) @ SV23 )
= ( relation_dom @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[465]) ).
thf(570,plain,
! [SV24: $i,SV66: $i] :
( ( ( ~ ( finite @ SV66 )
| ~ ( subset @ SV24 @ SV66 ) )
= $true )
| ( ( finite @ SV24 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(571,plain,
! [SV25: $i,SV54: $i] :
( ( ( ~ ( function @ SV54 )
| ~ ( relation @ SV54 ) )
= $true )
| ( ( ~ ( finite @ SV25 )
| ( finite @ ( relation_image @ SV54 @ SV25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[467]) ).
thf(572,plain,
! [SV55: $i,SV26: $i] :
( ( ( ~ ( finite @ SV26 )
| ~ ( finite @ SV55 ) )
= $true )
| ( ( finite @ ( cartesian_product2 @ SV26 @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[468]) ).
thf(573,plain,
! [SV56: $i,SV27: $i] :
( ( ( ~ ( in @ SV27 @ SV56 ) )
= $true )
| ( ( element @ SV27 @ SV56 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[469]) ).
thf(574,plain,
! [SV28: $i] :
( ( ( relation @ SV28 )
= $false )
| ( ( subset @ SV28 @ ( cartesian_product2 @ ( relation_dom @ SV28 ) @ ( relation_rng @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[470]) ).
thf(575,plain,
! [SV29: $i] :
( ( ( ~ ( function @ SV29 ) )
= $true )
| ( ( ~ ( relation @ SV29 ) )
= $true )
| ( ( ~ ( finite @ ( relation_dom @ SV29 ) )
| ( finite @ ( relation_rng @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[471]) ).
thf(576,plain,
! [SV57: $i,SV30: $i] :
( ( ( ~ ( element @ SV30 @ SV57 ) )
= $true )
| ( ( ( empty @ SV57 )
| ( in @ SV30 @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[472]) ).
thf(577,plain,
! [SV31: $i,SV67: $i,SV58: $i] :
( ( ~ ( element @ SV58 @ ( powerset @ SV67 ) )
| ~ ( in @ SV31 @ SV58 )
| ( element @ SV31 @ SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(578,plain,
! [SV32: $i,SV68: $i,SV59: $i] :
( ( ~ ( element @ SV59 @ ( powerset @ SV68 ) )
| ~ ( in @ SV32 @ SV59 )
| ~ ( empty @ SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(579,plain,
! [SV33: $i] :
( ( ( empty @ SV33 )
= $false )
| ( ( SV33 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(580,plain,
! [SV34: $i,SV60: $i] :
( ( ( ~ ( empty @ SV60 ) )
= $true )
| ( ( ~ ( in @ SV34 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[476]) ).
thf(581,plain,
! [SV61: $i,SV35: $i] :
( ( ( ( SV35 = SV61 )
| ~ ( empty @ SV35 ) )
= $true )
| ( ( ~ ( empty @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[477]) ).
thf(582,plain,
( ( ~ ( ~ ( empty @ sK16_A )
| ~ ( relation @ sK16_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[478]) ).
thf(583,plain,
( ( function @ sK16_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[479]) ).
thf(584,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[480]) ).
thf(585,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[481]) ).
thf(586,plain,
( ( function @ sK24_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[482]) ).
thf(587,plain,
( ( relation @ sK24_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[483]) ).
thf(588,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_transitive @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[484]) ).
thf(589,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( ordinal @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[485]) ).
thf(590,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[486]) ).
thf(591,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[487]) ).
thf(592,plain,
( ( relation @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[488]) ).
thf(593,plain,
( ( relation_empty_yielding @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[489]) ).
thf(594,plain,
( ( ~ ( ~ ( relation @ sK2_A )
| ~ ( relation_non_empty @ sK2_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[490]) ).
thf(595,plain,
( ( function @ sK2_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[491]) ).
thf(596,plain,
( ( ~ ( ~ ~ ( ~ ~ ( empty @ sK7_A )
| ~ ( epsilon_transitive @ sK7_A ) )
| ~ ( epsilon_connected @ sK7_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[492]) ).
thf(597,plain,
( ( ordinal @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[493]) ).
thf(598,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ sK18_A @ positive_rationals )
| ~ ~ ( empty @ sK18_A ) )
| ~ ( epsilon_transitive @ sK18_A ) )
| ~ ( epsilon_connected @ sK18_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[494]) ).
thf(599,plain,
( ( ordinal @ sK18_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[495]) ).
thf(600,plain,
( ( ~ ( ~ ~ ( ~ ( epsilon_connected @ sK22_A )
| ~ ( epsilon_transitive @ sK22_A ) )
| ~ ( ordinal @ sK22_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[496]) ).
thf(601,plain,
( ( being_limit_ordinal @ sK22_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[497]) ).
thf(602,plain,
( ( finite @ ( relation_dom @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[498]) ).
thf(603,plain,
( ( ~ ( finite @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[499]) ).
thf(604,plain,
( ( ~ ( ~ ( function @ sK8_A )
| ~ ( relation @ sK8_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[500]) ).
thf(605,plain,
( ( one_to_one @ sK8_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[501]) ).
thf(606,plain,
( ( ~ ( ~ ( function @ sK25_A )
| ~ ( relation @ sK25_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[502]) ).
thf(607,plain,
( ( function_yielding @ sK25_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[503]) ).
thf(608,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) )
| ~ ( epsilon_transitive @ empty_set ) )
| ~ ( epsilon_connected @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[504]) ).
thf(609,plain,
( ( ordinal @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[505]) ).
thf(610,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] : ( function @ ( first_projection_as_func_of @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] : ( quasi_total @ ( first_projection_as_func_of @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX0 @ SX1 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[506]) ).
thf(611,plain,
( ( ! [SX0: $i,SX1: $i] : ( relation_of2_as_subset @ ( first_projection_as_func_of @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX0 @ SX1 ) @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[507]) ).
thf(612,plain,
! [SV36: $i] :
( ( ~ ! [SY148: $i,SY149: $i] :
( ~ ( relation_of2 @ SY149 @ SV36 @ SY148 )
| ( relation_of2_as_subset @ SY149 @ SV36 @ SY148 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[508]) ).
thf(613,plain,
! [SV36: $i] :
( ( ~ ! [SY150: $i,SY151: $i] :
( ~ ( relation_of2_as_subset @ SY151 @ SV36 @ SY150 )
| ( relation_of2 @ SY151 @ SV36 @ SY150 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[508]) ).
thf(614,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ sK10_A @ positive_rationals )
| ~ ( empty @ sK10_A ) )
| ~ ( epsilon_transitive @ sK10_A ) )
| ~ ( epsilon_connected @ sK10_A ) )
| ~ ( ordinal @ sK10_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[509]) ).
thf(615,plain,
( ( natural @ sK10_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[510]) ).
thf(616,plain,
( ( ! [SX0: $i,SX1: $i] : ( function @ ( first_projection @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[511]) ).
thf(617,plain,
( ( ! [SX0: $i,SX1: $i] : ( relation @ ( first_projection @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[512]) ).
thf(618,plain,
! [SV37: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK5_B @ SV37 ) @ ( powerset @ SV37 ) )
| ~ ~ ( empty @ ( sK5_B @ SV37 ) ) )
| ~ ( finite @ ( sK5_B @ SV37 ) ) )
= $false )
| ( ( empty @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[513]) ).
thf(619,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[514]) ).
thf(620,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[515]) ).
thf(621,plain,
( ( ~ ( ~ ( epsilon_connected @ sK23_A )
| ~ ( epsilon_transitive @ sK23_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[516]) ).
thf(622,plain,
( ( ordinal @ sK23_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[517]) ).
thf(623,plain,
( ( ~ ( empty @ sK13_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[518]) ).
thf(624,plain,
( ( relation @ sK13_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[519]) ).
thf(625,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( ordinal @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[520]) ).
thf(626,plain,
( ( ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( natural @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[521]) ).
thf(627,plain,
! [SV38: $i] :
( ( ( ordinal @ SV38 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY152: $i] :
( ~ ( element @ SY152 @ SV38 )
| ( epsilon_connected @ SY152 ) )
| ~ ! [SY153: $i] :
( ~ ( element @ SY153 @ SV38 )
| ( epsilon_transitive @ SY153 ) ) )
| ~ ! [SY154: $i] :
( ~ ( element @ SY154 @ SV38 )
| ( ordinal @ SY154 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[522]) ).
thf(628,plain,
( ( empty @ sK21_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[523]) ).
thf(629,plain,
( ( relation @ sK21_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[524]) ).
thf(630,plain,
( ( ~ ( ~ ( function @ sK3_A )
| ~ ( relation @ sK3_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[525]) ).
thf(631,plain,
( ( transfinite_sequence @ sK3_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[526]) ).
thf(632,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[527]) ).
thf(633,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[528]) ).
thf(634,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK15_A )
| ~ ( relation @ sK15_A ) )
| ~ ( one_to_one @ sK15_A ) )
| ~ ( empty @ sK15_A ) )
| ~ ( epsilon_transitive @ sK15_A ) )
| ~ ( epsilon_connected @ sK15_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[529]) ).
thf(635,plain,
( ( ordinal @ sK15_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[530]) ).
thf(636,plain,
! [SV39: $i] :
( ( ~ ( element @ ( sK12_B @ SV39 ) @ ( powerset @ SV39 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[531]) ).
thf(637,plain,
! [SV39: $i] :
( ( ~ ( empty @ ( sK12_B @ SV39 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[531]) ).
thf(638,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[532]) ).
thf(639,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[533]) ).
thf(640,plain,
( ( ~ ( ~ ~ ( ~ ( function @ sK14_A )
| ~ ( relation @ sK14_A ) )
| ~ ( transfinite_sequence @ sK14_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[534]) ).
thf(641,plain,
( ( ordinal_yielding @ sK14_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[535]) ).
thf(642,plain,
( ( ~ ( empty @ sK26_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[536]) ).
thf(643,plain,
( ( finite @ sK26_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[537]) ).
thf(644,plain,
! [SV40: $i] :
( ( ( ~ ( element @ ( sK20_B @ SV40 ) @ ( powerset @ SV40 ) )
| ~ ~ ( empty @ ( sK20_B @ SV40 ) ) )
= $false )
| ( ( empty @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[538]) ).
thf(645,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[539]) ).
thf(646,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[540]) ).
thf(647,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( ordinal @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[541]) ).
thf(648,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( natural @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[542]) ).
thf(649,plain,
! [SV41: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV41 ) @ ( powerset @ SV41 ) )
| ~ ( empty @ ( sK17_B @ SV41 ) ) )
| ~ ( relation @ ( sK17_B @ SV41 ) ) )
| ~ ( function @ ( sK17_B @ SV41 ) ) )
| ~ ( one_to_one @ ( sK17_B @ SV41 ) ) )
| ~ ( epsilon_transitive @ ( sK17_B @ SV41 ) ) )
| ~ ( epsilon_connected @ ( sK17_B @ SV41 ) ) )
| ~ ( ordinal @ ( sK17_B @ SV41 ) ) )
| ~ ( natural @ ( sK17_B @ SV41 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[543]) ).
thf(650,plain,
! [SV41: $i] :
( ( ~ ( finite @ ( sK17_B @ SV41 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[543]) ).
thf(651,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[544]) ).
thf(652,plain,
( ( relation_empty_yielding @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[545]) ).
thf(653,plain,
! [SV42: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK9_B @ SV42 ) @ ( powerset @ SV42 ) )
| ~ ~ ( empty @ ( sK9_B @ SV42 ) ) )
| ~ ( finite @ ( sK9_B @ SV42 ) ) )
= $false )
| ( ( empty @ SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[546]) ).
thf(654,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK27_A )
| ~ ( epsilon_transitive @ sK27_A ) )
| ~ ( epsilon_connected @ sK27_A ) )
| ~ ( ordinal @ sK27_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[547]) ).
thf(655,plain,
( ( natural @ sK27_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[548]) ).
thf(656,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( transfinite_sequence @ SX0 )
| ( epsilon_connected @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( transfinite_sequence @ SX0 )
| ( epsilon_transitive @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[549]) ).
thf(657,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( transfinite_sequence @ SX0 )
| ( ordinal @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[550]) ).
thf(658,plain,
( ( ~ ( ~ ( relation @ sK4_A )
| ~ ( relation_empty_yielding @ sK4_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[551]) ).
thf(659,plain,
( ( function @ sK4_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[552]) ).
thf(660,plain,
! [SV43: $i,SV1: $i] :
( ( ( in @ SV1 @ SV43 )
= $false )
| ( ( ~ ( in @ SV43 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(661,plain,
! [SV44: $i,SV5: $i,SV62: $i] :
( ( ( ~ ( element @ SV62 @ ( powerset @ ( cartesian_product2 @ SV5 @ SV44 ) ) ) )
= $true )
| ( ( relation @ SV62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[557]) ).
thf(662,plain,
! [SV6: $i,SV69: $i] :
( ( ( ~ ( element @ SV69 @ ( powerset @ SV6 ) )
| ( finite @ SV69 ) )
= $true )
| ( ( finite @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(663,plain,
! [SV7: $i] :
( ( ( epsilon_connected @ SV7 )
= $false )
| ( ( ~ ( epsilon_transitive @ SV7 ) )
= $true )
| ( ( ordinal @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[559]) ).
thf(664,plain,
! [SV45: $i,SV8: $i,SV63: $i] :
( ( ( ~ ( function @ SV63 )
| ~ ( quasi_total @ SV63 @ SV8 @ SV45 )
| ~ ( relation_of2 @ SV63 @ SV8 @ SV45 ) )
= $true )
| ( ( ! [SY163: $i] : ( element @ ( function_image @ SV8 @ SV45 @ SV63 @ SY163 ) @ ( powerset @ SV45 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[560]) ).
thf(665,plain,
! [SV46: $i,SV9: $i,SV64: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV64 @ SV9 @ SV46 ) )
= $true )
| ( ( element @ SV64 @ ( powerset @ ( cartesian_product2 @ SV9 @ SV46 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[561]) ).
thf(666,plain,
! [SV49: $i,SV13: $i] :
( ( ( ~ ( function @ SV13 )
| ~ ( relation @ SV13 ) )
= $true )
| ( ( ~ ( finite @ SV49 ) )
= $true )
| ( ( finite @ ( relation_image @ SV13 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[562]) ).
thf(667,plain,
! [SV50: $i,SV14: $i] :
( ( ( ~ ( finite @ SV14 ) )
= $true )
| ( ( ~ ( finite @ SV50 ) )
= $true )
| ( ( finite @ ( cartesian_product2 @ SV14 @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[563]) ).
thf(668,plain,
! [SV51: $i,SV16: $i] :
( ( ( empty @ SV16 )
= $true )
| ( ( empty @ SV51 )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV16 @ SV51 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[564]) ).
thf(669,plain,
! [SV17: $i] :
( ( ( relation @ SV17 )
= $false )
| ( ( empty @ SV17 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV17 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[565]) ).
thf(670,plain,
! [SV18: $i] :
( ( ( ~ ( relation @ SV18 ) )
= $true )
| ( ( ~ ( relation_non_empty @ SV18 ) )
= $true )
| ( ( ~ ( function @ SV18 ) )
= $true )
| ( ( with_non_empty_elements @ ( relation_rng @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[566]) ).
thf(671,plain,
! [SV19: $i] :
( ( ( relation @ SV19 )
= $false )
| ( ( empty @ SV19 )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV19 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[567]) ).
thf(672,plain,
! [SV52: $i,SV20: $i,SV65: $i] :
( ( ( ~ ( function @ SV65 )
| ~ ( quasi_total @ SV65 @ SV20 @ SV52 )
| ~ ( relation_of2 @ SV65 @ SV20 @ SV52 ) )
= $true )
| ( ( ! [SY164: $i] :
( ( function_image @ SV20 @ SV52 @ SV65 @ SY164 )
= ( relation_image @ SV65 @ SY164 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[568]) ).
thf(673,plain,
! [SV23: $i] :
( ( ( function @ SV23 )
= $false )
| ( ( ~ ( relation @ SV23 ) )
= $true )
| ( ( ( function_image @ ( cartesian_product2 @ ( relation_dom @ SV23 ) @ ( relation_rng @ SV23 ) ) @ ( relation_dom @ SV23 ) @ ( first_projection_as_func_of @ ( relation_dom @ SV23 ) @ ( relation_rng @ SV23 ) ) @ SV23 )
= ( relation_dom @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[569]) ).
thf(674,plain,
! [SV24: $i,SV66: $i] :
( ( ( ~ ( finite @ SV66 ) )
= $true )
| ( ( ~ ( subset @ SV24 @ SV66 ) )
= $true )
| ( ( finite @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[570]) ).
thf(675,plain,
! [SV25: $i,SV54: $i] :
( ( ( ~ ( function @ SV54 ) )
= $true )
| ( ( ~ ( relation @ SV54 ) )
= $true )
| ( ( ~ ( finite @ SV25 )
| ( finite @ ( relation_image @ SV54 @ SV25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[571]) ).
thf(676,plain,
! [SV55: $i,SV26: $i] :
( ( ( ~ ( finite @ SV26 ) )
= $true )
| ( ( ~ ( finite @ SV55 ) )
= $true )
| ( ( finite @ ( cartesian_product2 @ SV26 @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[572]) ).
thf(677,plain,
! [SV56: $i,SV27: $i] :
( ( ( in @ SV27 @ SV56 )
= $false )
| ( ( element @ SV27 @ SV56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[573]) ).
thf(678,plain,
! [SV29: $i] :
( ( ( function @ SV29 )
= $false )
| ( ( ~ ( relation @ SV29 ) )
= $true )
| ( ( ~ ( finite @ ( relation_dom @ SV29 ) )
| ( finite @ ( relation_rng @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[575]) ).
thf(679,plain,
! [SV57: $i,SV30: $i] :
( ( ( element @ SV30 @ SV57 )
= $false )
| ( ( ( empty @ SV57 )
| ( in @ SV30 @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(680,plain,
! [SV31: $i,SV67: $i,SV58: $i] :
( ( ( ~ ( element @ SV58 @ ( powerset @ SV67 ) )
| ~ ( in @ SV31 @ SV58 ) )
= $true )
| ( ( element @ SV31 @ SV67 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[577]) ).
thf(681,plain,
! [SV32: $i,SV68: $i,SV59: $i] :
( ( ( ~ ( element @ SV59 @ ( powerset @ SV68 ) )
| ~ ( in @ SV32 @ SV59 ) )
= $true )
| ( ( ~ ( empty @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[578]) ).
thf(682,plain,
! [SV34: $i,SV60: $i] :
( ( ( empty @ SV60 )
= $false )
| ( ( ~ ( in @ SV34 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[580]) ).
thf(683,plain,
! [SV61: $i,SV35: $i] :
( ( ( SV35 = SV61 )
= $true )
| ( ( ~ ( empty @ SV35 ) )
= $true )
| ( ( ~ ( empty @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[581]) ).
thf(684,plain,
( ( ~ ( empty @ sK16_A )
| ~ ( relation @ sK16_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[582]) ).
thf(685,plain,
! [SV70: $i] :
( ( ~ ( ordinal @ SV70 )
| ( epsilon_connected @ SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(686,plain,
! [SV71: $i] :
( ( ~ ( ordinal @ SV71 )
| ( epsilon_transitive @ SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(687,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[588]) ).
thf(688,plain,
! [SV72: $i] :
( ( ~ ( empty @ SV72 )
| ( ordinal @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(689,plain,
! [SV73: $i] :
( ( ~ ( empty @ SV73 )
| ( empty @ ( relation_rng @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(690,plain,
! [SV74: $i] :
( ( ~ ( empty @ SV74 )
| ( relation @ ( relation_rng @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(691,plain,
( ( ~ ( relation @ sK2_A )
| ~ ( relation_non_empty @ sK2_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[594]) ).
thf(692,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK7_A )
| ~ ( epsilon_transitive @ sK7_A ) )
| ~ ( epsilon_connected @ sK7_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[596]) ).
thf(693,plain,
( ( ~ ~ ( ~ ~ ( ~ ( element @ sK18_A @ positive_rationals )
| ~ ~ ( empty @ sK18_A ) )
| ~ ( epsilon_transitive @ sK18_A ) )
| ~ ( epsilon_connected @ sK18_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[598]) ).
thf(694,plain,
( ( ~ ~ ( ~ ( epsilon_connected @ sK22_A )
| ~ ( epsilon_transitive @ sK22_A ) )
| ~ ( ordinal @ sK22_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[600]) ).
thf(695,plain,
( ( finite @ sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[603]) ).
thf(696,plain,
( ( ~ ( function @ sK8_A )
| ~ ( relation @ sK8_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(697,plain,
( ( ~ ( function @ sK25_A )
| ~ ( relation @ sK25_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[606]) ).
thf(698,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) )
| ~ ( epsilon_transitive @ empty_set ) )
| ~ ( epsilon_connected @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[608]) ).
thf(699,plain,
( ( ~ ! [SX0: $i,SX1: $i] : ( function @ ( first_projection_as_func_of @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] : ( quasi_total @ ( first_projection_as_func_of @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX0 @ SX1 ) @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[610]) ).
thf(700,plain,
! [SV75: $i] :
( ( ! [SY165: $i] : ( relation_of2_as_subset @ ( first_projection_as_func_of @ SV75 @ SY165 ) @ ( cartesian_product2 @ SV75 @ SY165 ) @ SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(701,plain,
! [SV36: $i] :
( ( ! [SY148: $i,SY149: $i] :
( ~ ( relation_of2 @ SY149 @ SV36 @ SY148 )
| ( relation_of2_as_subset @ SY149 @ SV36 @ SY148 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[612]) ).
thf(702,plain,
! [SV36: $i] :
( ( ! [SY150: $i,SY151: $i] :
( ~ ( relation_of2_as_subset @ SY151 @ SV36 @ SY150 )
| ( relation_of2 @ SY151 @ SV36 @ SY150 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[613]) ).
thf(703,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ sK10_A @ positive_rationals )
| ~ ( empty @ sK10_A ) )
| ~ ( epsilon_transitive @ sK10_A ) )
| ~ ( epsilon_connected @ sK10_A ) )
| ~ ( ordinal @ sK10_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[614]) ).
thf(704,plain,
! [SV76: $i] :
( ( ! [SY166: $i] : ( function @ ( first_projection @ SV76 @ SY166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(705,plain,
! [SV77: $i] :
( ( ! [SY167: $i] : ( relation @ ( first_projection @ SV77 @ SY167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(706,plain,
! [SV37: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK5_B @ SV37 ) @ ( powerset @ SV37 ) )
| ~ ~ ( empty @ ( sK5_B @ SV37 ) ) ) )
= $false )
| ( ( empty @ SV37 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[618]) ).
thf(707,plain,
! [SV37: $i] :
( ( ( ~ ( finite @ ( sK5_B @ SV37 ) ) )
= $false )
| ( ( empty @ SV37 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[618]) ).
thf(708,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[619]) ).
thf(709,plain,
! [SV78: $i] :
( ( ~ ( empty @ SV78 )
| ~ ( relation @ SV78 )
| ~ ( function @ SV78 )
| ( one_to_one @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(710,plain,
( ( ~ ( epsilon_connected @ sK23_A )
| ~ ( epsilon_transitive @ sK23_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[621]) ).
thf(711,plain,
( ( empty @ sK13_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[623]) ).
thf(712,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( ordinal @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[625]) ).
thf(713,plain,
! [SV79: $i] :
( ( ~ ( element @ SV79 @ positive_rationals )
| ~ ( ordinal @ SV79 )
| ( natural @ SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(714,plain,
! [SV38: $i] :
( ( ( ~ ~ ( ~ ! [SY152: $i] :
( ~ ( element @ SY152 @ SV38 )
| ( epsilon_connected @ SY152 ) )
| ~ ! [SY153: $i] :
( ~ ( element @ SY153 @ SV38 )
| ( epsilon_transitive @ SY153 ) ) )
| ~ ! [SY154: $i] :
( ~ ( element @ SY154 @ SV38 )
| ( ordinal @ SY154 ) ) )
= $false )
| ( ( ordinal @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[627]) ).
thf(715,plain,
( ( ~ ( function @ sK3_A )
| ~ ( relation @ sK3_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[630]) ).
thf(716,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK15_A )
| ~ ( relation @ sK15_A ) )
| ~ ( one_to_one @ sK15_A ) )
| ~ ( empty @ sK15_A ) )
| ~ ( epsilon_transitive @ sK15_A ) )
| ~ ( epsilon_connected @ sK15_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[634]) ).
thf(717,plain,
! [SV39: $i] :
( ( element @ ( sK12_B @ SV39 ) @ ( powerset @ SV39 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[636]) ).
thf(718,plain,
! [SV39: $i] :
( ( empty @ ( sK12_B @ SV39 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[637]) ).
thf(719,plain,
! [SV80: $i] :
( ( ~ ( empty @ SV80 )
| ( empty @ ( relation_dom @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(720,plain,
! [SV81: $i] :
( ( ~ ( empty @ SV81 )
| ( relation @ ( relation_dom @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(721,plain,
( ( ~ ~ ( ~ ( function @ sK14_A )
| ~ ( relation @ sK14_A ) )
| ~ ( transfinite_sequence @ sK14_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[640]) ).
thf(722,plain,
( ( empty @ sK26_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[642]) ).
thf(723,plain,
! [SV40: $i] :
( ( ( ~ ( element @ ( sK20_B @ SV40 ) @ ( powerset @ SV40 ) ) )
= $false )
| ( ( empty @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[644]) ).
thf(724,plain,
! [SV40: $i] :
( ( ( ~ ~ ( empty @ ( sK20_B @ SV40 ) ) )
= $false )
| ( ( empty @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[644]) ).
thf(725,plain,
! [SV82: $i] :
( ( ! [SY168: $i] :
( ~ ( element @ SV82 @ ( powerset @ SY168 ) )
| ( subset @ SV82 @ SY168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(726,plain,
! [SV83: $i] :
( ( ! [SY169: $i] :
( ~ ( subset @ SV83 @ SY169 )
| ( element @ SV83 @ ( powerset @ SY169 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(727,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( ordinal @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[647]) ).
thf(728,plain,
! [SV84: $i] :
( ( ~ ( empty @ SV84 )
| ~ ( ordinal @ SV84 )
| ( natural @ SV84 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(729,plain,
! [SV41: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV41 ) @ ( powerset @ SV41 ) )
| ~ ( empty @ ( sK17_B @ SV41 ) ) )
| ~ ( relation @ ( sK17_B @ SV41 ) ) )
| ~ ( function @ ( sK17_B @ SV41 ) ) )
| ~ ( one_to_one @ ( sK17_B @ SV41 ) ) )
| ~ ( epsilon_transitive @ ( sK17_B @ SV41 ) ) )
| ~ ( epsilon_connected @ ( sK17_B @ SV41 ) ) )
| ~ ( ordinal @ ( sK17_B @ SV41 ) ) )
| ~ ( natural @ ( sK17_B @ SV41 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[649]) ).
thf(730,plain,
! [SV41: $i] :
( ( finite @ ( sK17_B @ SV41 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[650]) ).
thf(731,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[651]) ).
thf(732,plain,
! [SV42: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK9_B @ SV42 ) @ ( powerset @ SV42 ) )
| ~ ~ ( empty @ ( sK9_B @ SV42 ) ) ) )
= $false )
| ( ( empty @ SV42 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[653]) ).
thf(733,plain,
! [SV42: $i] :
( ( ( ~ ( finite @ ( sK9_B @ SV42 ) ) )
= $false )
| ( ( empty @ SV42 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[653]) ).
thf(734,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK27_A )
| ~ ( epsilon_transitive @ sK27_A ) )
| ~ ( epsilon_connected @ sK27_A ) )
| ~ ( ordinal @ sK27_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[654]) ).
thf(735,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( transfinite_sequence @ SX0 )
| ( epsilon_connected @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( transfinite_sequence @ SX0 )
| ( epsilon_transitive @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[656]) ).
thf(736,plain,
! [SV85: $i] :
( ( ~ ( function @ SV85 )
| ~ ( relation @ SV85 )
| ~ ( transfinite_sequence @ SV85 )
| ( ordinal @ ( relation_dom @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(737,plain,
( ( ~ ( relation @ sK4_A )
| ~ ( relation_empty_yielding @ sK4_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[658]) ).
thf(738,plain,
! [SV1: $i,SV43: $i] :
( ( ( in @ SV43 @ SV1 )
= $false )
| ( ( in @ SV1 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[660]) ).
thf(739,plain,
! [SV44: $i,SV5: $i,SV62: $i] :
( ( ( element @ SV62 @ ( powerset @ ( cartesian_product2 @ SV5 @ SV44 ) ) )
= $false )
| ( ( relation @ SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[661]) ).
thf(740,plain,
! [SV6: $i,SV69: $i] :
( ( ( ~ ( element @ SV69 @ ( powerset @ SV6 ) ) )
= $true )
| ( ( finite @ SV69 )
= $true )
| ( ( finite @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[662]) ).
thf(741,plain,
! [SV7: $i] :
( ( ( epsilon_transitive @ SV7 )
= $false )
| ( ( epsilon_connected @ SV7 )
= $false )
| ( ( ordinal @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[663]) ).
thf(742,plain,
! [SV45: $i,SV8: $i,SV63: $i] :
( ( ( ~ ( function @ SV63 )
| ~ ( quasi_total @ SV63 @ SV8 @ SV45 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV63 @ SV8 @ SV45 ) )
= $true )
| ( ( ! [SY163: $i] : ( element @ ( function_image @ SV8 @ SV45 @ SV63 @ SY163 ) @ ( powerset @ SV45 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[664]) ).
thf(743,plain,
! [SV46: $i,SV9: $i,SV64: $i] :
( ( ( relation_of2_as_subset @ SV64 @ SV9 @ SV46 )
= $false )
| ( ( element @ SV64 @ ( powerset @ ( cartesian_product2 @ SV9 @ SV46 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[665]) ).
thf(744,plain,
! [SV49: $i,SV13: $i] :
( ( ( ~ ( function @ SV13 ) )
= $true )
| ( ( ~ ( relation @ SV13 ) )
= $true )
| ( ( ~ ( finite @ SV49 ) )
= $true )
| ( ( finite @ ( relation_image @ SV13 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[666]) ).
thf(745,plain,
! [SV50: $i,SV14: $i] :
( ( ( finite @ SV14 )
= $false )
| ( ( ~ ( finite @ SV50 ) )
= $true )
| ( ( finite @ ( cartesian_product2 @ SV14 @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[667]) ).
thf(746,plain,
! [SV51: $i,SV16: $i] :
( ( ( empty @ ( cartesian_product2 @ SV16 @ SV51 ) )
= $false )
| ( ( empty @ SV51 )
= $true )
| ( ( empty @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[668]) ).
thf(747,plain,
! [SV17: $i] :
( ( ( empty @ ( relation_dom @ SV17 ) )
= $false )
| ( ( empty @ SV17 )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[669]) ).
thf(748,plain,
! [SV18: $i] :
( ( ( relation @ SV18 )
= $false )
| ( ( ~ ( relation_non_empty @ SV18 ) )
= $true )
| ( ( ~ ( function @ SV18 ) )
= $true )
| ( ( with_non_empty_elements @ ( relation_rng @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[670]) ).
thf(749,plain,
! [SV19: $i] :
( ( ( empty @ ( relation_rng @ SV19 ) )
= $false )
| ( ( empty @ SV19 )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[671]) ).
thf(750,plain,
! [SV52: $i,SV20: $i,SV65: $i] :
( ( ( ~ ( function @ SV65 )
| ~ ( quasi_total @ SV65 @ SV20 @ SV52 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV65 @ SV20 @ SV52 ) )
= $true )
| ( ( ! [SY164: $i] :
( ( function_image @ SV20 @ SV52 @ SV65 @ SY164 )
= ( relation_image @ SV65 @ SY164 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[672]) ).
thf(751,plain,
! [SV23: $i] :
( ( ( relation @ SV23 )
= $false )
| ( ( function @ SV23 )
= $false )
| ( ( ( function_image @ ( cartesian_product2 @ ( relation_dom @ SV23 ) @ ( relation_rng @ SV23 ) ) @ ( relation_dom @ SV23 ) @ ( first_projection_as_func_of @ ( relation_dom @ SV23 ) @ ( relation_rng @ SV23 ) ) @ SV23 )
= ( relation_dom @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[673]) ).
thf(752,plain,
! [SV24: $i,SV66: $i] :
( ( ( finite @ SV66 )
= $false )
| ( ( ~ ( subset @ SV24 @ SV66 ) )
= $true )
| ( ( finite @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[674]) ).
thf(753,plain,
! [SV25: $i,SV54: $i] :
( ( ( function @ SV54 )
= $false )
| ( ( ~ ( relation @ SV54 ) )
= $true )
| ( ( ~ ( finite @ SV25 )
| ( finite @ ( relation_image @ SV54 @ SV25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[675]) ).
thf(754,plain,
! [SV55: $i,SV26: $i] :
( ( ( finite @ SV26 )
= $false )
| ( ( ~ ( finite @ SV55 ) )
= $true )
| ( ( finite @ ( cartesian_product2 @ SV26 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[676]) ).
thf(755,plain,
! [SV29: $i] :
( ( ( relation @ SV29 )
= $false )
| ( ( function @ SV29 )
= $false )
| ( ( ~ ( finite @ ( relation_dom @ SV29 ) )
| ( finite @ ( relation_rng @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[678]) ).
thf(756,plain,
! [SV30: $i,SV57: $i] :
( ( ( empty @ SV57 )
= $true )
| ( ( in @ SV30 @ SV57 )
= $true )
| ( ( element @ SV30 @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[679]) ).
thf(757,plain,
! [SV31: $i,SV67: $i,SV58: $i] :
( ( ( ~ ( element @ SV58 @ ( powerset @ SV67 ) ) )
= $true )
| ( ( ~ ( in @ SV31 @ SV58 ) )
= $true )
| ( ( element @ SV31 @ SV67 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[680]) ).
thf(758,plain,
! [SV32: $i,SV68: $i,SV59: $i] :
( ( ( ~ ( element @ SV59 @ ( powerset @ SV68 ) ) )
= $true )
| ( ( ~ ( in @ SV32 @ SV59 ) )
= $true )
| ( ( ~ ( empty @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[681]) ).
thf(759,plain,
! [SV60: $i,SV34: $i] :
( ( ( in @ SV34 @ SV60 )
= $false )
| ( ( empty @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[682]) ).
thf(760,plain,
! [SV61: $i,SV35: $i] :
( ( ( empty @ SV35 )
= $false )
| ( ( SV35 = SV61 )
= $true )
| ( ( ~ ( empty @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[683]) ).
thf(761,plain,
( ( ~ ( empty @ sK16_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[684]) ).
thf(762,plain,
( ( ~ ( relation @ sK16_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[684]) ).
thf(763,plain,
! [SV70: $i] :
( ( ( ~ ( ordinal @ SV70 ) )
= $true )
| ( ( epsilon_connected @ SV70 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[685]) ).
thf(764,plain,
! [SV71: $i] :
( ( ( ~ ( ordinal @ SV71 ) )
= $true )
| ( ( epsilon_transitive @ SV71 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[686]) ).
thf(765,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_connected @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[687]) ).
thf(766,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[687]) ).
thf(767,plain,
! [SV72: $i] :
( ( ( ~ ( empty @ SV72 ) )
= $true )
| ( ( ordinal @ SV72 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[688]) ).
thf(768,plain,
! [SV73: $i] :
( ( ( ~ ( empty @ SV73 ) )
= $true )
| ( ( empty @ ( relation_rng @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[689]) ).
thf(769,plain,
! [SV74: $i] :
( ( ( ~ ( empty @ SV74 ) )
= $true )
| ( ( relation @ ( relation_rng @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[690]) ).
thf(770,plain,
( ( ~ ( relation @ sK2_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[691]) ).
thf(771,plain,
( ( ~ ( relation_non_empty @ sK2_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[691]) ).
thf(772,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK7_A )
| ~ ( epsilon_transitive @ sK7_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[692]) ).
thf(773,plain,
( ( ~ ( epsilon_connected @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[692]) ).
thf(774,plain,
( ( ~ ~ ( ~ ~ ( ~ ( element @ sK18_A @ positive_rationals )
| ~ ~ ( empty @ sK18_A ) )
| ~ ( epsilon_transitive @ sK18_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[693]) ).
thf(775,plain,
( ( ~ ( epsilon_connected @ sK18_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[693]) ).
thf(776,plain,
( ( ~ ~ ( ~ ( epsilon_connected @ sK22_A )
| ~ ( epsilon_transitive @ sK22_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[694]) ).
thf(777,plain,
( ( ~ ( ordinal @ sK22_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[694]) ).
thf(778,plain,
( ( ~ ( function @ sK8_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[696]) ).
thf(779,plain,
( ( ~ ( relation @ sK8_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[696]) ).
thf(780,plain,
( ( ~ ( function @ sK25_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[697]) ).
thf(781,plain,
( ( ~ ( relation @ sK25_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[697]) ).
thf(782,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) )
| ~ ( epsilon_transitive @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[698]) ).
thf(783,plain,
( ( ~ ( epsilon_connected @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[698]) ).
thf(784,plain,
( ( ~ ! [SX0: $i,SX1: $i] : ( function @ ( first_projection_as_func_of @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[699]) ).
thf(785,plain,
( ( ~ ! [SX0: $i,SX1: $i] : ( quasi_total @ ( first_projection_as_func_of @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX0 @ SX1 ) @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[699]) ).
thf(786,plain,
! [SV86: $i,SV75: $i] :
( ( relation_of2_as_subset @ ( first_projection_as_func_of @ SV75 @ SV86 ) @ ( cartesian_product2 @ SV75 @ SV86 ) @ SV75 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(787,plain,
! [SV87: $i,SV36: $i] :
( ( ! [SY170: $i] :
( ~ ( relation_of2 @ SY170 @ SV36 @ SV87 )
| ( relation_of2_as_subset @ SY170 @ SV36 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(788,plain,
! [SV88: $i,SV36: $i] :
( ( ! [SY171: $i] :
( ~ ( relation_of2_as_subset @ SY171 @ SV36 @ SV88 )
| ( relation_of2 @ SY171 @ SV36 @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(789,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ sK10_A @ positive_rationals )
| ~ ( empty @ sK10_A ) )
| ~ ( epsilon_transitive @ sK10_A ) )
| ~ ( epsilon_connected @ sK10_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[703]) ).
thf(790,plain,
( ( ~ ( ordinal @ sK10_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[703]) ).
thf(791,plain,
! [SV89: $i,SV76: $i] :
( ( function @ ( first_projection @ SV76 @ SV89 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(792,plain,
! [SV90: $i,SV77: $i] :
( ( relation @ ( first_projection @ SV77 @ SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(793,plain,
! [SV37: $i] :
( ( ( ~ ( ~ ( element @ ( sK5_B @ SV37 ) @ ( powerset @ SV37 ) )
| ~ ~ ( empty @ ( sK5_B @ SV37 ) ) ) )
= $true )
| ( ( empty @ SV37 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[706]) ).
thf(794,plain,
! [SV37: $i] :
( ( ( finite @ ( sK5_B @ SV37 ) )
= $true )
| ( ( empty @ SV37 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[707]) ).
thf(795,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[708]) ).
thf(796,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[708]) ).
thf(797,plain,
! [SV78: $i] :
( ( ( ~ ( empty @ SV78 )
| ~ ( relation @ SV78 )
| ~ ( function @ SV78 ) )
= $true )
| ( ( one_to_one @ SV78 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[709]) ).
thf(798,plain,
( ( ~ ( epsilon_connected @ sK23_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[710]) ).
thf(799,plain,
( ( ~ ( epsilon_transitive @ sK23_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[710]) ).
thf(800,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[712]) ).
thf(801,plain,
( ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( ordinal @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[712]) ).
thf(802,plain,
! [SV79: $i] :
( ( ( ~ ( element @ SV79 @ positive_rationals ) )
= $true )
| ( ( ~ ( ordinal @ SV79 )
| ( natural @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[713]) ).
thf(803,plain,
! [SV38: $i] :
( ( ( ~ ~ ( ~ ! [SY152: $i] :
( ~ ( element @ SY152 @ SV38 )
| ( epsilon_connected @ SY152 ) )
| ~ ! [SY153: $i] :
( ~ ( element @ SY153 @ SV38 )
| ( epsilon_transitive @ SY153 ) ) ) )
= $false )
| ( ( ordinal @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[714]) ).
thf(804,plain,
! [SV38: $i] :
( ( ( ~ ! [SY154: $i] :
( ~ ( element @ SY154 @ SV38 )
| ( ordinal @ SY154 ) ) )
= $false )
| ( ( ordinal @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[714]) ).
thf(805,plain,
( ( ~ ( function @ sK3_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[715]) ).
thf(806,plain,
( ( ~ ( relation @ sK3_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[715]) ).
thf(807,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK15_A )
| ~ ( relation @ sK15_A ) )
| ~ ( one_to_one @ sK15_A ) )
| ~ ( empty @ sK15_A ) )
| ~ ( epsilon_transitive @ sK15_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[716]) ).
thf(808,plain,
( ( ~ ( epsilon_connected @ sK15_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[716]) ).
thf(809,plain,
! [SV80: $i] :
( ( ( ~ ( empty @ SV80 ) )
= $true )
| ( ( empty @ ( relation_dom @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[719]) ).
thf(810,plain,
! [SV81: $i] :
( ( ( ~ ( empty @ SV81 ) )
= $true )
| ( ( relation @ ( relation_dom @ SV81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[720]) ).
thf(811,plain,
( ( ~ ~ ( ~ ( function @ sK14_A )
| ~ ( relation @ sK14_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[721]) ).
thf(812,plain,
( ( ~ ( transfinite_sequence @ sK14_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[721]) ).
thf(813,plain,
! [SV40: $i] :
( ( ( element @ ( sK20_B @ SV40 ) @ ( powerset @ SV40 ) )
= $true )
| ( ( empty @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[723]) ).
thf(814,plain,
! [SV40: $i] :
( ( ( ~ ( empty @ ( sK20_B @ SV40 ) ) )
= $true )
| ( ( empty @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[724]) ).
thf(815,plain,
! [SV91: $i,SV82: $i] :
( ( ~ ( element @ SV82 @ ( powerset @ SV91 ) )
| ( subset @ SV82 @ SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(816,plain,
! [SV92: $i,SV83: $i] :
( ( ~ ( subset @ SV83 @ SV92 )
| ( element @ SV83 @ ( powerset @ SV92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(817,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[727]) ).
thf(818,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( ordinal @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[727]) ).
thf(819,plain,
! [SV84: $i] :
( ( ( ~ ( empty @ SV84 )
| ~ ( ordinal @ SV84 ) )
= $true )
| ( ( natural @ SV84 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[728]) ).
thf(820,plain,
! [SV41: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV41 ) @ ( powerset @ SV41 ) )
| ~ ( empty @ ( sK17_B @ SV41 ) ) )
| ~ ( relation @ ( sK17_B @ SV41 ) ) )
| ~ ( function @ ( sK17_B @ SV41 ) ) )
| ~ ( one_to_one @ ( sK17_B @ SV41 ) ) )
| ~ ( epsilon_transitive @ ( sK17_B @ SV41 ) ) )
| ~ ( epsilon_connected @ ( sK17_B @ SV41 ) ) )
| ~ ( ordinal @ ( sK17_B @ SV41 ) ) )
| ~ ( natural @ ( sK17_B @ SV41 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[729]) ).
thf(821,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[731]) ).
thf(822,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[731]) ).
thf(823,plain,
! [SV42: $i] :
( ( ( ~ ( ~ ( element @ ( sK9_B @ SV42 ) @ ( powerset @ SV42 ) )
| ~ ~ ( empty @ ( sK9_B @ SV42 ) ) ) )
= $true )
| ( ( empty @ SV42 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[732]) ).
thf(824,plain,
! [SV42: $i] :
( ( ( finite @ ( sK9_B @ SV42 ) )
= $true )
| ( ( empty @ SV42 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[733]) ).
thf(825,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK27_A )
| ~ ( epsilon_transitive @ sK27_A ) )
| ~ ( epsilon_connected @ sK27_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[734]) ).
thf(826,plain,
( ( ~ ( ordinal @ sK27_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[734]) ).
thf(827,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( transfinite_sequence @ SX0 )
| ( epsilon_connected @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[735]) ).
thf(828,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( transfinite_sequence @ SX0 )
| ( epsilon_transitive @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[735]) ).
thf(829,plain,
! [SV85: $i] :
( ( ( ~ ( function @ SV85 )
| ~ ( relation @ SV85 )
| ~ ( transfinite_sequence @ SV85 ) )
= $true )
| ( ( ordinal @ ( relation_dom @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[736]) ).
thf(830,plain,
( ( ~ ( relation @ sK4_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[737]) ).
thf(831,plain,
( ( ~ ( relation_empty_yielding @ sK4_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[737]) ).
thf(832,plain,
! [SV6: $i,SV69: $i] :
( ( ( element @ SV69 @ ( powerset @ SV6 ) )
= $false )
| ( ( finite @ SV69 )
= $true )
| ( ( finite @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[740]) ).
thf(833,plain,
! [SV45: $i,SV8: $i,SV63: $i] :
( ( ( ~ ( function @ SV63 ) )
= $true )
| ( ( ~ ( quasi_total @ SV63 @ SV8 @ SV45 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV63 @ SV8 @ SV45 ) )
= $true )
| ( ( ! [SY163: $i] : ( element @ ( function_image @ SV8 @ SV45 @ SV63 @ SY163 ) @ ( powerset @ SV45 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[742]) ).
thf(834,plain,
! [SV49: $i,SV13: $i] :
( ( ( function @ SV13 )
= $false )
| ( ( ~ ( relation @ SV13 ) )
= $true )
| ( ( ~ ( finite @ SV49 ) )
= $true )
| ( ( finite @ ( relation_image @ SV13 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[744]) ).
thf(835,plain,
! [SV14: $i,SV50: $i] :
( ( ( finite @ SV50 )
= $false )
| ( ( finite @ SV14 )
= $false )
| ( ( finite @ ( cartesian_product2 @ SV14 @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[745]) ).
thf(836,plain,
! [SV18: $i] :
( ( ( relation_non_empty @ SV18 )
= $false )
| ( ( relation @ SV18 )
= $false )
| ( ( ~ ( function @ SV18 ) )
= $true )
| ( ( with_non_empty_elements @ ( relation_rng @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[748]) ).
thf(837,plain,
! [SV52: $i,SV20: $i,SV65: $i] :
( ( ( ~ ( function @ SV65 ) )
= $true )
| ( ( ~ ( quasi_total @ SV65 @ SV20 @ SV52 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV65 @ SV20 @ SV52 ) )
= $true )
| ( ( ! [SY164: $i] :
( ( function_image @ SV20 @ SV52 @ SV65 @ SY164 )
= ( relation_image @ SV65 @ SY164 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[750]) ).
thf(838,plain,
! [SV66: $i,SV24: $i] :
( ( ( subset @ SV24 @ SV66 )
= $false )
| ( ( finite @ SV66 )
= $false )
| ( ( finite @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[752]) ).
thf(839,plain,
! [SV25: $i,SV54: $i] :
( ( ( relation @ SV54 )
= $false )
| ( ( function @ SV54 )
= $false )
| ( ( ~ ( finite @ SV25 )
| ( finite @ ( relation_image @ SV54 @ SV25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[753]) ).
thf(840,plain,
! [SV26: $i,SV55: $i] :
( ( ( finite @ SV55 )
= $false )
| ( ( finite @ SV26 )
= $false )
| ( ( finite @ ( cartesian_product2 @ SV26 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[754]) ).
thf(841,plain,
! [SV29: $i] :
( ( ( ~ ( finite @ ( relation_dom @ SV29 ) ) )
= $true )
| ( ( finite @ ( relation_rng @ SV29 ) )
= $true )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[755]) ).
thf(842,plain,
! [SV31: $i,SV67: $i,SV58: $i] :
( ( ( element @ SV58 @ ( powerset @ SV67 ) )
= $false )
| ( ( ~ ( in @ SV31 @ SV58 ) )
= $true )
| ( ( element @ SV31 @ SV67 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[757]) ).
thf(843,plain,
! [SV32: $i,SV68: $i,SV59: $i] :
( ( ( element @ SV59 @ ( powerset @ SV68 ) )
= $false )
| ( ( ~ ( in @ SV32 @ SV59 ) )
= $true )
| ( ( ~ ( empty @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[758]) ).
thf(844,plain,
! [SV35: $i,SV61: $i] :
( ( ( empty @ SV61 )
= $false )
| ( ( SV35 = SV61 )
= $true )
| ( ( empty @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[760]) ).
thf(845,plain,
( ( empty @ sK16_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[761]) ).
thf(846,plain,
( ( relation @ sK16_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[762]) ).
thf(847,plain,
! [SV70: $i] :
( ( ( ordinal @ SV70 )
= $false )
| ( ( epsilon_connected @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[763]) ).
thf(848,plain,
! [SV71: $i] :
( ( ( ordinal @ SV71 )
= $false )
| ( ( epsilon_transitive @ SV71 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[764]) ).
thf(849,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_connected @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[765]) ).
thf(850,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[766]) ).
thf(851,plain,
! [SV72: $i] :
( ( ( empty @ SV72 )
= $false )
| ( ( ordinal @ SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[767]) ).
thf(852,plain,
! [SV73: $i] :
( ( ( empty @ SV73 )
= $false )
| ( ( empty @ ( relation_rng @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[768]) ).
thf(853,plain,
! [SV74: $i] :
( ( ( empty @ SV74 )
= $false )
| ( ( relation @ ( relation_rng @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[769]) ).
thf(854,plain,
( ( relation @ sK2_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[770]) ).
thf(855,plain,
( ( relation_non_empty @ sK2_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[771]) ).
thf(856,plain,
( ( ~ ( ~ ~ ( empty @ sK7_A )
| ~ ( epsilon_transitive @ sK7_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[772]) ).
thf(857,plain,
( ( epsilon_connected @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[773]) ).
thf(858,plain,
( ( ~ ( ~ ~ ( ~ ( element @ sK18_A @ positive_rationals )
| ~ ~ ( empty @ sK18_A ) )
| ~ ( epsilon_transitive @ sK18_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[774]) ).
thf(859,plain,
( ( epsilon_connected @ sK18_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[775]) ).
thf(860,plain,
( ( ~ ( ~ ( epsilon_connected @ sK22_A )
| ~ ( epsilon_transitive @ sK22_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[776]) ).
thf(861,plain,
( ( ordinal @ sK22_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[777]) ).
thf(862,plain,
( ( function @ sK8_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[778]) ).
thf(863,plain,
( ( relation @ sK8_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[779]) ).
thf(864,plain,
( ( function @ sK25_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[780]) ).
thf(865,plain,
( ( relation @ sK25_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[781]) ).
thf(866,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) )
| ~ ( epsilon_transitive @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[782]) ).
thf(867,plain,
( ( epsilon_connected @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[783]) ).
thf(868,plain,
( ( ! [SX0: $i,SX1: $i] : ( function @ ( first_projection_as_func_of @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[784]) ).
thf(869,plain,
( ( ! [SX0: $i,SX1: $i] : ( quasi_total @ ( first_projection_as_func_of @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX0 @ SX1 ) @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[785]) ).
thf(870,plain,
! [SV87: $i,SV36: $i,SV93: $i] :
( ( ~ ( relation_of2 @ SV93 @ SV36 @ SV87 )
| ( relation_of2_as_subset @ SV93 @ SV36 @ SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(871,plain,
! [SV88: $i,SV36: $i,SV94: $i] :
( ( ~ ( relation_of2_as_subset @ SV94 @ SV36 @ SV88 )
| ( relation_of2 @ SV94 @ SV36 @ SV88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(872,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ sK10_A @ positive_rationals )
| ~ ( empty @ sK10_A ) )
| ~ ( epsilon_transitive @ sK10_A ) )
| ~ ( epsilon_connected @ sK10_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[789]) ).
thf(873,plain,
( ( ordinal @ sK10_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[790]) ).
thf(874,plain,
! [SV37: $i] :
( ( ( ~ ( element @ ( sK5_B @ SV37 ) @ ( powerset @ SV37 ) )
| ~ ~ ( empty @ ( sK5_B @ SV37 ) ) )
= $false )
| ( ( empty @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[793]) ).
thf(875,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[795]) ).
thf(876,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[796]) ).
thf(877,plain,
! [SV78: $i] :
( ( ( ~ ( empty @ SV78 )
| ~ ( relation @ SV78 ) )
= $true )
| ( ( ~ ( function @ SV78 ) )
= $true )
| ( ( one_to_one @ SV78 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[797]) ).
thf(878,plain,
( ( epsilon_connected @ sK23_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[798]) ).
thf(879,plain,
( ( epsilon_transitive @ sK23_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[799]) ).
thf(880,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[800]) ).
thf(881,plain,
( ( ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( ordinal @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[801]) ).
thf(882,plain,
! [SV79: $i] :
( ( ( element @ SV79 @ positive_rationals )
= $false )
| ( ( ~ ( ordinal @ SV79 )
| ( natural @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[802]) ).
thf(883,plain,
! [SV38: $i] :
( ( ( ~ ( ~ ! [SY152: $i] :
( ~ ( element @ SY152 @ SV38 )
| ( epsilon_connected @ SY152 ) )
| ~ ! [SY153: $i] :
( ~ ( element @ SY153 @ SV38 )
| ( epsilon_transitive @ SY153 ) ) ) )
= $true )
| ( ( ordinal @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[803]) ).
thf(884,plain,
! [SV38: $i] :
( ( ( ! [SY154: $i] :
( ~ ( element @ SY154 @ SV38 )
| ( ordinal @ SY154 ) ) )
= $true )
| ( ( ordinal @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[804]) ).
thf(885,plain,
( ( function @ sK3_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[805]) ).
thf(886,plain,
( ( relation @ sK3_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[806]) ).
thf(887,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK15_A )
| ~ ( relation @ sK15_A ) )
| ~ ( one_to_one @ sK15_A ) )
| ~ ( empty @ sK15_A ) )
| ~ ( epsilon_transitive @ sK15_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[807]) ).
thf(888,plain,
( ( epsilon_connected @ sK15_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[808]) ).
thf(889,plain,
! [SV80: $i] :
( ( ( empty @ SV80 )
= $false )
| ( ( empty @ ( relation_dom @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[809]) ).
thf(890,plain,
! [SV81: $i] :
( ( ( empty @ SV81 )
= $false )
| ( ( relation @ ( relation_dom @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[810]) ).
thf(891,plain,
( ( ~ ( ~ ( function @ sK14_A )
| ~ ( relation @ sK14_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[811]) ).
thf(892,plain,
( ( transfinite_sequence @ sK14_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[812]) ).
thf(893,plain,
! [SV40: $i] :
( ( ( empty @ ( sK20_B @ SV40 ) )
= $false )
| ( ( empty @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[814]) ).
thf(894,plain,
! [SV91: $i,SV82: $i] :
( ( ( ~ ( element @ SV82 @ ( powerset @ SV91 ) ) )
= $true )
| ( ( subset @ SV82 @ SV91 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[815]) ).
thf(895,plain,
! [SV92: $i,SV83: $i] :
( ( ( ~ ( subset @ SV83 @ SV92 ) )
= $true )
| ( ( element @ SV83 @ ( powerset @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[816]) ).
thf(896,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[817]) ).
thf(897,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( ordinal @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[818]) ).
thf(898,plain,
! [SV84: $i] :
( ( ( ~ ( empty @ SV84 ) )
= $true )
| ( ( ~ ( ordinal @ SV84 ) )
= $true )
| ( ( natural @ SV84 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[819]) ).
thf(899,plain,
! [SV41: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV41 ) @ ( powerset @ SV41 ) )
| ~ ( empty @ ( sK17_B @ SV41 ) ) )
| ~ ( relation @ ( sK17_B @ SV41 ) ) )
| ~ ( function @ ( sK17_B @ SV41 ) ) )
| ~ ( one_to_one @ ( sK17_B @ SV41 ) ) )
| ~ ( epsilon_transitive @ ( sK17_B @ SV41 ) ) )
| ~ ( epsilon_connected @ ( sK17_B @ SV41 ) ) )
| ~ ( ordinal @ ( sK17_B @ SV41 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[820]) ).
thf(900,plain,
! [SV41: $i] :
( ( ~ ( natural @ ( sK17_B @ SV41 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[820]) ).
thf(901,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[821]) ).
thf(902,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[822]) ).
thf(903,plain,
! [SV42: $i] :
( ( ( ~ ( element @ ( sK9_B @ SV42 ) @ ( powerset @ SV42 ) )
| ~ ~ ( empty @ ( sK9_B @ SV42 ) ) )
= $false )
| ( ( empty @ SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[823]) ).
thf(904,plain,
( ( ~ ( ~ ~ ( ~ ~ ( empty @ sK27_A )
| ~ ( epsilon_transitive @ sK27_A ) )
| ~ ( epsilon_connected @ sK27_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[825]) ).
thf(905,plain,
( ( ordinal @ sK27_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[826]) ).
thf(906,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( transfinite_sequence @ SX0 )
| ( epsilon_connected @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[827]) ).
thf(907,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( transfinite_sequence @ SX0 )
| ( epsilon_transitive @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[828]) ).
thf(908,plain,
! [SV85: $i] :
( ( ( ~ ( function @ SV85 )
| ~ ( relation @ SV85 ) )
= $true )
| ( ( ~ ( transfinite_sequence @ SV85 ) )
= $true )
| ( ( ordinal @ ( relation_dom @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[829]) ).
thf(909,plain,
( ( relation @ sK4_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[830]) ).
thf(910,plain,
( ( relation_empty_yielding @ sK4_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[831]) ).
thf(911,plain,
! [SV45: $i,SV8: $i,SV63: $i] :
( ( ( function @ SV63 )
= $false )
| ( ( ~ ( quasi_total @ SV63 @ SV8 @ SV45 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV63 @ SV8 @ SV45 ) )
= $true )
| ( ( ! [SY163: $i] : ( element @ ( function_image @ SV8 @ SV45 @ SV63 @ SY163 ) @ ( powerset @ SV45 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[833]) ).
thf(912,plain,
! [SV49: $i,SV13: $i] :
( ( ( relation @ SV13 )
= $false )
| ( ( function @ SV13 )
= $false )
| ( ( ~ ( finite @ SV49 ) )
= $true )
| ( ( finite @ ( relation_image @ SV13 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[834]) ).
thf(913,plain,
! [SV18: $i] :
( ( ( function @ SV18 )
= $false )
| ( ( relation @ SV18 )
= $false )
| ( ( relation_non_empty @ SV18 )
= $false )
| ( ( with_non_empty_elements @ ( relation_rng @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[836]) ).
thf(914,plain,
! [SV52: $i,SV20: $i,SV65: $i] :
( ( ( function @ SV65 )
= $false )
| ( ( ~ ( quasi_total @ SV65 @ SV20 @ SV52 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV65 @ SV20 @ SV52 ) )
= $true )
| ( ( ! [SY164: $i] :
( ( function_image @ SV20 @ SV52 @ SV65 @ SY164 )
= ( relation_image @ SV65 @ SY164 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[837]) ).
thf(915,plain,
! [SV54: $i,SV25: $i] :
( ( ( ~ ( finite @ SV25 ) )
= $true )
| ( ( finite @ ( relation_image @ SV54 @ SV25 ) )
= $true )
| ( ( function @ SV54 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[839]) ).
thf(916,plain,
! [SV29: $i] :
( ( ( finite @ ( relation_dom @ SV29 ) )
= $false )
| ( ( finite @ ( relation_rng @ SV29 ) )
= $true )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[841]) ).
thf(917,plain,
! [SV67: $i,SV58: $i,SV31: $i] :
( ( ( in @ SV31 @ SV58 )
= $false )
| ( ( element @ SV58 @ ( powerset @ SV67 ) )
= $false )
| ( ( element @ SV31 @ SV67 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[842]) ).
thf(918,plain,
! [SV68: $i,SV59: $i,SV32: $i] :
( ( ( in @ SV32 @ SV59 )
= $false )
| ( ( element @ SV59 @ ( powerset @ SV68 ) )
= $false )
| ( ( ~ ( empty @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[843]) ).
thf(919,plain,
! [SV95: $i] :
( ( ~ ( empty @ SV95 )
| ( epsilon_connected @ SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(920,plain,
! [SV96: $i] :
( ( ~ ( empty @ SV96 )
| ( epsilon_transitive @ SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(921,plain,
( ( ~ ~ ( empty @ sK7_A )
| ~ ( epsilon_transitive @ sK7_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[856]) ).
thf(922,plain,
( ( ~ ~ ( ~ ( element @ sK18_A @ positive_rationals )
| ~ ~ ( empty @ sK18_A ) )
| ~ ( epsilon_transitive @ sK18_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[858]) ).
thf(923,plain,
( ( ~ ( epsilon_connected @ sK22_A )
| ~ ( epsilon_transitive @ sK22_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[860]) ).
thf(924,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) )
| ~ ( epsilon_transitive @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[866]) ).
thf(925,plain,
! [SV97: $i] :
( ( ! [SY172: $i] : ( function @ ( first_projection_as_func_of @ SV97 @ SY172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(926,plain,
! [SV98: $i] :
( ( ! [SY173: $i] : ( quasi_total @ ( first_projection_as_func_of @ SV98 @ SY173 ) @ ( cartesian_product2 @ SV98 @ SY173 ) @ SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(927,plain,
! [SV87: $i,SV36: $i,SV93: $i] :
( ( ( ~ ( relation_of2 @ SV93 @ SV36 @ SV87 ) )
= $true )
| ( ( relation_of2_as_subset @ SV93 @ SV36 @ SV87 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[870]) ).
thf(928,plain,
! [SV88: $i,SV36: $i,SV94: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV94 @ SV36 @ SV88 ) )
= $true )
| ( ( relation_of2 @ SV94 @ SV36 @ SV88 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[871]) ).
thf(929,plain,
( ( ~ ~ ( ~ ~ ( ~ ( element @ sK10_A @ positive_rationals )
| ~ ( empty @ sK10_A ) )
| ~ ( epsilon_transitive @ sK10_A ) )
| ~ ( epsilon_connected @ sK10_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[872]) ).
thf(930,plain,
! [SV37: $i] :
( ( ( ~ ( element @ ( sK5_B @ SV37 ) @ ( powerset @ SV37 ) ) )
= $false )
| ( ( empty @ SV37 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[874]) ).
thf(931,plain,
! [SV37: $i] :
( ( ( ~ ~ ( empty @ ( sK5_B @ SV37 ) ) )
= $false )
| ( ( empty @ SV37 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[874]) ).
thf(932,plain,
! [SV99: $i] :
( ( ~ ( empty @ SV99 )
| ~ ( relation @ SV99 )
| ~ ( function @ SV99 )
| ( function @ SV99 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(933,plain,
! [SV100: $i] :
( ( ~ ( empty @ SV100 )
| ~ ( relation @ SV100 )
| ~ ( function @ SV100 )
| ( relation @ SV100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[876]) ).
thf(934,plain,
! [SV78: $i] :
( ( ( ~ ( empty @ SV78 ) )
= $true )
| ( ( ~ ( relation @ SV78 ) )
= $true )
| ( ( ~ ( function @ SV78 ) )
= $true )
| ( ( one_to_one @ SV78 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[877]) ).
thf(935,plain,
( ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[880]) ).
thf(936,plain,
! [SV101: $i] :
( ( ~ ( element @ SV101 @ positive_rationals )
| ~ ( ordinal @ SV101 )
| ( ordinal @ SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[881]) ).
thf(937,plain,
! [SV79: $i] :
( ( ( ~ ( ordinal @ SV79 ) )
= $true )
| ( ( natural @ SV79 )
= $true )
| ( ( element @ SV79 @ positive_rationals )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[882]) ).
thf(938,plain,
! [SV38: $i] :
( ( ( ~ ! [SY152: $i] :
( ~ ( element @ SY152 @ SV38 )
| ( epsilon_connected @ SY152 ) )
| ~ ! [SY153: $i] :
( ~ ( element @ SY153 @ SV38 )
| ( epsilon_transitive @ SY153 ) ) )
= $false )
| ( ( ordinal @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[883]) ).
thf(939,plain,
! [SV38: $i,SV102: $i] :
( ( ( ~ ( element @ SV102 @ SV38 )
| ( ordinal @ SV102 ) )
= $true )
| ( ( ordinal @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[884]) ).
thf(940,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK15_A )
| ~ ( relation @ sK15_A ) )
| ~ ( one_to_one @ sK15_A ) )
| ~ ( empty @ sK15_A ) )
| ~ ( epsilon_transitive @ sK15_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[887]) ).
thf(941,plain,
( ( ~ ( function @ sK14_A )
| ~ ( relation @ sK14_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[891]) ).
thf(942,plain,
! [SV91: $i,SV82: $i] :
( ( ( element @ SV82 @ ( powerset @ SV91 ) )
= $false )
| ( ( subset @ SV82 @ SV91 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[894]) ).
thf(943,plain,
! [SV92: $i,SV83: $i] :
( ( ( subset @ SV83 @ SV92 )
= $false )
| ( ( element @ SV83 @ ( powerset @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[895]) ).
thf(944,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[896]) ).
thf(945,plain,
! [SV103: $i] :
( ( ~ ( empty @ SV103 )
| ~ ( ordinal @ SV103 )
| ( ordinal @ SV103 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(946,plain,
! [SV84: $i] :
( ( ( empty @ SV84 )
= $false )
| ( ( ~ ( ordinal @ SV84 ) )
= $true )
| ( ( natural @ SV84 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[898]) ).
thf(947,plain,
! [SV41: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV41 ) @ ( powerset @ SV41 ) )
| ~ ( empty @ ( sK17_B @ SV41 ) ) )
| ~ ( relation @ ( sK17_B @ SV41 ) ) )
| ~ ( function @ ( sK17_B @ SV41 ) ) )
| ~ ( one_to_one @ ( sK17_B @ SV41 ) ) )
| ~ ( epsilon_transitive @ ( sK17_B @ SV41 ) ) )
| ~ ( epsilon_connected @ ( sK17_B @ SV41 ) ) )
| ~ ( ordinal @ ( sK17_B @ SV41 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[899]) ).
thf(948,plain,
! [SV41: $i] :
( ( natural @ ( sK17_B @ SV41 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[900]) ).
thf(949,plain,
! [SV42: $i] :
( ( ( ~ ( element @ ( sK9_B @ SV42 ) @ ( powerset @ SV42 ) ) )
= $false )
| ( ( empty @ SV42 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[903]) ).
thf(950,plain,
! [SV42: $i] :
( ( ( ~ ~ ( empty @ ( sK9_B @ SV42 ) ) )
= $false )
| ( ( empty @ SV42 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[903]) ).
thf(951,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK27_A )
| ~ ( epsilon_transitive @ sK27_A ) )
| ~ ( epsilon_connected @ sK27_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[904]) ).
thf(952,plain,
! [SV104: $i] :
( ( ~ ( function @ SV104 )
| ~ ( relation @ SV104 )
| ~ ( transfinite_sequence @ SV104 )
| ( epsilon_connected @ ( relation_dom @ SV104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[906]) ).
thf(953,plain,
! [SV105: $i] :
( ( ~ ( function @ SV105 )
| ~ ( relation @ SV105 )
| ~ ( transfinite_sequence @ SV105 )
| ( epsilon_transitive @ ( relation_dom @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(954,plain,
! [SV85: $i] :
( ( ( ~ ( function @ SV85 ) )
= $true )
| ( ( ~ ( relation @ SV85 ) )
= $true )
| ( ( ~ ( transfinite_sequence @ SV85 ) )
= $true )
| ( ( ordinal @ ( relation_dom @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[908]) ).
thf(955,plain,
! [SV45: $i,SV8: $i,SV63: $i] :
( ( ( quasi_total @ SV63 @ SV8 @ SV45 )
= $false )
| ( ( function @ SV63 )
= $false )
| ( ( ~ ( relation_of2 @ SV63 @ SV8 @ SV45 ) )
= $true )
| ( ( ! [SY163: $i] : ( element @ ( function_image @ SV8 @ SV45 @ SV63 @ SY163 ) @ ( powerset @ SV45 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[911]) ).
thf(956,plain,
! [SV13: $i,SV49: $i] :
( ( ( finite @ SV49 )
= $false )
| ( ( function @ SV13 )
= $false )
| ( ( relation @ SV13 )
= $false )
| ( ( finite @ ( relation_image @ SV13 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[912]) ).
thf(957,plain,
! [SV52: $i,SV20: $i,SV65: $i] :
( ( ( quasi_total @ SV65 @ SV20 @ SV52 )
= $false )
| ( ( function @ SV65 )
= $false )
| ( ( ~ ( relation_of2 @ SV65 @ SV20 @ SV52 ) )
= $true )
| ( ( ! [SY164: $i] :
( ( function_image @ SV20 @ SV52 @ SV65 @ SY164 )
= ( relation_image @ SV65 @ SY164 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[914]) ).
thf(958,plain,
! [SV54: $i,SV25: $i] :
( ( ( finite @ SV25 )
= $false )
| ( ( finite @ ( relation_image @ SV54 @ SV25 ) )
= $true )
| ( ( function @ SV54 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[915]) ).
thf(959,plain,
! [SV32: $i,SV59: $i,SV68: $i] :
( ( ( empty @ SV68 )
= $false )
| ( ( element @ SV59 @ ( powerset @ SV68 ) )
= $false )
| ( ( in @ SV32 @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[918]) ).
thf(960,plain,
! [SV95: $i] :
( ( ( ~ ( empty @ SV95 ) )
= $true )
| ( ( epsilon_connected @ SV95 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[919]) ).
thf(961,plain,
! [SV96: $i] :
( ( ( ~ ( empty @ SV96 ) )
= $true )
| ( ( epsilon_transitive @ SV96 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[920]) ).
thf(962,plain,
( ( ~ ~ ( empty @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[921]) ).
thf(963,plain,
( ( ~ ( epsilon_transitive @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[921]) ).
thf(964,plain,
( ( ~ ~ ( ~ ( element @ sK18_A @ positive_rationals )
| ~ ~ ( empty @ sK18_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[922]) ).
thf(965,plain,
( ( ~ ( epsilon_transitive @ sK18_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[922]) ).
thf(966,plain,
( ( ~ ( epsilon_connected @ sK22_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[923]) ).
thf(967,plain,
( ( ~ ( epsilon_transitive @ sK22_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[923]) ).
thf(968,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[924]) ).
thf(969,plain,
( ( ~ ( epsilon_transitive @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[924]) ).
thf(970,plain,
! [SV106: $i,SV97: $i] :
( ( function @ ( first_projection_as_func_of @ SV97 @ SV106 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(971,plain,
! [SV107: $i,SV98: $i] :
( ( quasi_total @ ( first_projection_as_func_of @ SV98 @ SV107 ) @ ( cartesian_product2 @ SV98 @ SV107 ) @ SV98 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[926]) ).
thf(972,plain,
! [SV87: $i,SV36: $i,SV93: $i] :
( ( ( relation_of2 @ SV93 @ SV36 @ SV87 )
= $false )
| ( ( relation_of2_as_subset @ SV93 @ SV36 @ SV87 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[927]) ).
thf(973,plain,
! [SV88: $i,SV36: $i,SV94: $i] :
( ( ( relation_of2_as_subset @ SV94 @ SV36 @ SV88 )
= $false )
| ( ( relation_of2 @ SV94 @ SV36 @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[928]) ).
thf(974,plain,
( ( ~ ~ ( ~ ~ ( ~ ( element @ sK10_A @ positive_rationals )
| ~ ( empty @ sK10_A ) )
| ~ ( epsilon_transitive @ sK10_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[929]) ).
thf(975,plain,
( ( ~ ( epsilon_connected @ sK10_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[929]) ).
thf(976,plain,
! [SV37: $i] :
( ( ( element @ ( sK5_B @ SV37 ) @ ( powerset @ SV37 ) )
= $true )
| ( ( empty @ SV37 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[930]) ).
thf(977,plain,
! [SV37: $i] :
( ( ( ~ ( empty @ ( sK5_B @ SV37 ) ) )
= $true )
| ( ( empty @ SV37 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[931]) ).
thf(978,plain,
! [SV99: $i] :
( ( ( ~ ( empty @ SV99 )
| ~ ( relation @ SV99 )
| ~ ( function @ SV99 ) )
= $true )
| ( ( function @ SV99 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[932]) ).
thf(979,plain,
! [SV100: $i] :
( ( ( ~ ( empty @ SV100 )
| ~ ( relation @ SV100 )
| ~ ( function @ SV100 ) )
= $true )
| ( ( relation @ SV100 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[933]) ).
thf(980,plain,
! [SV78: $i] :
( ( ( empty @ SV78 )
= $false )
| ( ( ~ ( relation @ SV78 ) )
= $true )
| ( ( ~ ( function @ SV78 ) )
= $true )
| ( ( one_to_one @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[934]) ).
thf(981,plain,
( ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[935]) ).
thf(982,plain,
( ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[935]) ).
thf(983,plain,
! [SV101: $i] :
( ( ( ~ ( element @ SV101 @ positive_rationals ) )
= $true )
| ( ( ~ ( ordinal @ SV101 )
| ( ordinal @ SV101 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[936]) ).
thf(984,plain,
! [SV79: $i] :
( ( ( ordinal @ SV79 )
= $false )
| ( ( natural @ SV79 )
= $true )
| ( ( element @ SV79 @ positive_rationals )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[937]) ).
thf(985,plain,
! [SV38: $i] :
( ( ( ~ ! [SY152: $i] :
( ~ ( element @ SY152 @ SV38 )
| ( epsilon_connected @ SY152 ) ) )
= $false )
| ( ( ordinal @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[938]) ).
thf(986,plain,
! [SV38: $i] :
( ( ( ~ ! [SY153: $i] :
( ~ ( element @ SY153 @ SV38 )
| ( epsilon_transitive @ SY153 ) ) )
= $false )
| ( ( ordinal @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[938]) ).
thf(987,plain,
! [SV38: $i,SV102: $i] :
( ( ( ~ ( element @ SV102 @ SV38 ) )
= $true )
| ( ( ordinal @ SV102 )
= $true )
| ( ( ordinal @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[939]) ).
thf(988,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK15_A )
| ~ ( relation @ sK15_A ) )
| ~ ( one_to_one @ sK15_A ) )
| ~ ( empty @ sK15_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[940]) ).
thf(989,plain,
( ( ~ ( epsilon_transitive @ sK15_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[940]) ).
thf(990,plain,
( ( ~ ( function @ sK14_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[941]) ).
thf(991,plain,
( ( ~ ( relation @ sK14_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[941]) ).
thf(992,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[944]) ).
thf(993,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[944]) ).
thf(994,plain,
! [SV103: $i] :
( ( ( ~ ( empty @ SV103 )
| ~ ( ordinal @ SV103 ) )
= $true )
| ( ( ordinal @ SV103 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[945]) ).
thf(995,plain,
! [SV84: $i] :
( ( ( ordinal @ SV84 )
= $false )
| ( ( empty @ SV84 )
= $false )
| ( ( natural @ SV84 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[946]) ).
thf(996,plain,
! [SV41: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV41 ) @ ( powerset @ SV41 ) )
| ~ ( empty @ ( sK17_B @ SV41 ) ) )
| ~ ( relation @ ( sK17_B @ SV41 ) ) )
| ~ ( function @ ( sK17_B @ SV41 ) ) )
| ~ ( one_to_one @ ( sK17_B @ SV41 ) ) )
| ~ ( epsilon_transitive @ ( sK17_B @ SV41 ) ) )
| ~ ( epsilon_connected @ ( sK17_B @ SV41 ) ) )
| ~ ( ordinal @ ( sK17_B @ SV41 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[947]) ).
thf(997,plain,
! [SV42: $i] :
( ( ( element @ ( sK9_B @ SV42 ) @ ( powerset @ SV42 ) )
= $true )
| ( ( empty @ SV42 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[949]) ).
thf(998,plain,
! [SV42: $i] :
( ( ( ~ ( empty @ ( sK9_B @ SV42 ) ) )
= $true )
| ( ( empty @ SV42 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[950]) ).
thf(999,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK27_A )
| ~ ( epsilon_transitive @ sK27_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[951]) ).
thf(1000,plain,
( ( ~ ( epsilon_connected @ sK27_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[951]) ).
thf(1001,plain,
! [SV104: $i] :
( ( ( ~ ( function @ SV104 )
| ~ ( relation @ SV104 )
| ~ ( transfinite_sequence @ SV104 ) )
= $true )
| ( ( epsilon_connected @ ( relation_dom @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[952]) ).
thf(1002,plain,
! [SV105: $i] :
( ( ( ~ ( function @ SV105 )
| ~ ( relation @ SV105 )
| ~ ( transfinite_sequence @ SV105 ) )
= $true )
| ( ( epsilon_transitive @ ( relation_dom @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[953]) ).
thf(1003,plain,
! [SV85: $i] :
( ( ( function @ SV85 )
= $false )
| ( ( ~ ( relation @ SV85 ) )
= $true )
| ( ( ~ ( transfinite_sequence @ SV85 ) )
= $true )
| ( ( ordinal @ ( relation_dom @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[954]) ).
thf(1004,plain,
! [SV45: $i,SV8: $i,SV63: $i] :
( ( ( relation_of2 @ SV63 @ SV8 @ SV45 )
= $false )
| ( ( function @ SV63 )
= $false )
| ( ( quasi_total @ SV63 @ SV8 @ SV45 )
= $false )
| ( ( ! [SY163: $i] : ( element @ ( function_image @ SV8 @ SV45 @ SV63 @ SY163 ) @ ( powerset @ SV45 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[955]) ).
thf(1005,plain,
! [SV52: $i,SV20: $i,SV65: $i] :
( ( ( relation_of2 @ SV65 @ SV20 @ SV52 )
= $false )
| ( ( function @ SV65 )
= $false )
| ( ( quasi_total @ SV65 @ SV20 @ SV52 )
= $false )
| ( ( ! [SY164: $i] :
( ( function_image @ SV20 @ SV52 @ SV65 @ SY164 )
= ( relation_image @ SV65 @ SY164 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[957]) ).
thf(1006,plain,
! [SV95: $i] :
( ( ( empty @ SV95 )
= $false )
| ( ( epsilon_connected @ SV95 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[960]) ).
thf(1007,plain,
! [SV96: $i] :
( ( ( empty @ SV96 )
= $false )
| ( ( epsilon_transitive @ SV96 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[961]) ).
thf(1008,plain,
( ( ~ ( empty @ sK7_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[962]) ).
thf(1009,plain,
( ( epsilon_transitive @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[963]) ).
thf(1010,plain,
( ( ~ ( ~ ( element @ sK18_A @ positive_rationals )
| ~ ~ ( empty @ sK18_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[964]) ).
thf(1011,plain,
( ( epsilon_transitive @ sK18_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[965]) ).
thf(1012,plain,
( ( epsilon_connected @ sK22_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[966]) ).
thf(1013,plain,
( ( epsilon_transitive @ sK22_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[967]) ).
thf(1014,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[968]) ).
thf(1015,plain,
( ( epsilon_transitive @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[969]) ).
thf(1016,plain,
( ( ~ ( ~ ~ ( ~ ( element @ sK10_A @ positive_rationals )
| ~ ( empty @ sK10_A ) )
| ~ ( epsilon_transitive @ sK10_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[974]) ).
thf(1017,plain,
( ( epsilon_connected @ sK10_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[975]) ).
thf(1018,plain,
! [SV37: $i] :
( ( ( empty @ ( sK5_B @ SV37 ) )
= $false )
| ( ( empty @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[977]) ).
thf(1019,plain,
! [SV99: $i] :
( ( ( ~ ( empty @ SV99 )
| ~ ( relation @ SV99 ) )
= $true )
| ( ( ~ ( function @ SV99 ) )
= $true )
| ( ( function @ SV99 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[978]) ).
thf(1020,plain,
! [SV100: $i] :
( ( ( ~ ( empty @ SV100 )
| ~ ( relation @ SV100 ) )
= $true )
| ( ( ~ ( function @ SV100 ) )
= $true )
| ( ( relation @ SV100 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[979]) ).
thf(1021,plain,
! [SV78: $i] :
( ( ( relation @ SV78 )
= $false )
| ( ( empty @ SV78 )
= $false )
| ( ( ~ ( function @ SV78 ) )
= $true )
| ( ( one_to_one @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[980]) ).
thf(1022,plain,
( ( ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[981]) ).
thf(1023,plain,
( ( ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[982]) ).
thf(1024,plain,
! [SV101: $i] :
( ( ( element @ SV101 @ positive_rationals )
= $false )
| ( ( ~ ( ordinal @ SV101 )
| ( ordinal @ SV101 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[983]) ).
thf(1025,plain,
! [SV38: $i] :
( ( ( ! [SY152: $i] :
( ~ ( element @ SY152 @ SV38 )
| ( epsilon_connected @ SY152 ) ) )
= $true )
| ( ( ordinal @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[985]) ).
thf(1026,plain,
! [SV38: $i] :
( ( ( ! [SY153: $i] :
( ~ ( element @ SY153 @ SV38 )
| ( epsilon_transitive @ SY153 ) ) )
= $true )
| ( ( ordinal @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[986]) ).
thf(1027,plain,
! [SV38: $i,SV102: $i] :
( ( ( element @ SV102 @ SV38 )
= $false )
| ( ( ordinal @ SV102 )
= $true )
| ( ( ordinal @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[987]) ).
thf(1028,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK15_A )
| ~ ( relation @ sK15_A ) )
| ~ ( one_to_one @ sK15_A ) )
| ~ ( empty @ sK15_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[988]) ).
thf(1029,plain,
( ( epsilon_transitive @ sK15_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[989]) ).
thf(1030,plain,
( ( function @ sK14_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[990]) ).
thf(1031,plain,
( ( relation @ sK14_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[991]) ).
thf(1032,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[992]) ).
thf(1033,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[993]) ).
thf(1034,plain,
! [SV103: $i] :
( ( ( ~ ( empty @ SV103 ) )
= $true )
| ( ( ~ ( ordinal @ SV103 ) )
= $true )
| ( ( ordinal @ SV103 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[994]) ).
thf(1035,plain,
! [SV41: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV41 ) @ ( powerset @ SV41 ) )
| ~ ( empty @ ( sK17_B @ SV41 ) ) )
| ~ ( relation @ ( sK17_B @ SV41 ) ) )
| ~ ( function @ ( sK17_B @ SV41 ) ) )
| ~ ( one_to_one @ ( sK17_B @ SV41 ) ) )
| ~ ( epsilon_transitive @ ( sK17_B @ SV41 ) ) )
| ~ ( epsilon_connected @ ( sK17_B @ SV41 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[996]) ).
thf(1036,plain,
! [SV41: $i] :
( ( ~ ( ordinal @ ( sK17_B @ SV41 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[996]) ).
thf(1037,plain,
! [SV42: $i] :
( ( ( empty @ ( sK9_B @ SV42 ) )
= $false )
| ( ( empty @ SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[998]) ).
thf(1038,plain,
( ( ~ ( ~ ~ ( empty @ sK27_A )
| ~ ( epsilon_transitive @ sK27_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[999]) ).
thf(1039,plain,
( ( epsilon_connected @ sK27_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1000]) ).
thf(1040,plain,
! [SV104: $i] :
( ( ( ~ ( function @ SV104 )
| ~ ( relation @ SV104 ) )
= $true )
| ( ( ~ ( transfinite_sequence @ SV104 ) )
= $true )
| ( ( epsilon_connected @ ( relation_dom @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1001]) ).
thf(1041,plain,
! [SV105: $i] :
( ( ( ~ ( function @ SV105 )
| ~ ( relation @ SV105 ) )
= $true )
| ( ( ~ ( transfinite_sequence @ SV105 ) )
= $true )
| ( ( epsilon_transitive @ ( relation_dom @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1002]) ).
thf(1042,plain,
! [SV85: $i] :
( ( ( relation @ SV85 )
= $false )
| ( ( function @ SV85 )
= $false )
| ( ( ~ ( transfinite_sequence @ SV85 ) )
= $true )
| ( ( ordinal @ ( relation_dom @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1003]) ).
thf(1043,plain,
! [SV108: $i,SV63: $i,SV45: $i,SV8: $i] :
( ( ( element @ ( function_image @ SV8 @ SV45 @ SV63 @ SV108 ) @ ( powerset @ SV45 ) )
= $true )
| ( ( quasi_total @ SV63 @ SV8 @ SV45 )
= $false )
| ( ( function @ SV63 )
= $false )
| ( ( relation_of2 @ SV63 @ SV8 @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1044,plain,
! [SV109: $i,SV65: $i,SV52: $i,SV20: $i] :
( ( ( ( function_image @ SV20 @ SV52 @ SV65 @ SV109 )
= ( relation_image @ SV65 @ SV109 ) )
= $true )
| ( ( quasi_total @ SV65 @ SV20 @ SV52 )
= $false )
| ( ( function @ SV65 )
= $false )
| ( ( relation_of2 @ SV65 @ SV20 @ SV52 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1045,plain,
( ( empty @ sK7_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1008]) ).
thf(1046,plain,
( ( ~ ( element @ sK18_A @ positive_rationals )
| ~ ~ ( empty @ sK18_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1010]) ).
thf(1047,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1014]) ).
thf(1048,plain,
( ( ~ ~ ( ~ ( element @ sK10_A @ positive_rationals )
| ~ ( empty @ sK10_A ) )
| ~ ( epsilon_transitive @ sK10_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1016]) ).
thf(1049,plain,
! [SV99: $i] :
( ( ( ~ ( empty @ SV99 ) )
= $true )
| ( ( ~ ( relation @ SV99 ) )
= $true )
| ( ( ~ ( function @ SV99 ) )
= $true )
| ( ( function @ SV99 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1019]) ).
thf(1050,plain,
! [SV100: $i] :
( ( ( ~ ( empty @ SV100 ) )
= $true )
| ( ( ~ ( relation @ SV100 ) )
= $true )
| ( ( ~ ( function @ SV100 ) )
= $true )
| ( ( relation @ SV100 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1020]) ).
thf(1051,plain,
! [SV78: $i] :
( ( ( function @ SV78 )
= $false )
| ( ( empty @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false )
| ( ( one_to_one @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1021]) ).
thf(1052,plain,
! [SV110: $i] :
( ( ~ ( element @ SV110 @ positive_rationals )
| ~ ( ordinal @ SV110 )
| ( epsilon_connected @ SV110 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1053,plain,
! [SV111: $i] :
( ( ~ ( element @ SV111 @ positive_rationals )
| ~ ( ordinal @ SV111 )
| ( epsilon_transitive @ SV111 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1023]) ).
thf(1054,plain,
! [SV101: $i] :
( ( ( ~ ( ordinal @ SV101 ) )
= $true )
| ( ( ordinal @ SV101 )
= $true )
| ( ( element @ SV101 @ positive_rationals )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1024]) ).
thf(1055,plain,
! [SV38: $i,SV112: $i] :
( ( ( ~ ( element @ SV112 @ SV38 )
| ( epsilon_connected @ SV112 ) )
= $true )
| ( ( ordinal @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1056,plain,
! [SV38: $i,SV113: $i] :
( ( ( ~ ( element @ SV113 @ SV38 )
| ( epsilon_transitive @ SV113 ) )
= $true )
| ( ( ordinal @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1057,plain,
( ( ~ ~ ( ~ ~ ( ~ ( function @ sK15_A )
| ~ ( relation @ sK15_A ) )
| ~ ( one_to_one @ sK15_A ) )
| ~ ( empty @ sK15_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1028]) ).
thf(1058,plain,
! [SV114: $i] :
( ( ~ ( empty @ SV114 )
| ~ ( ordinal @ SV114 )
| ( epsilon_connected @ SV114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1032]) ).
thf(1059,plain,
! [SV115: $i] :
( ( ~ ( empty @ SV115 )
| ~ ( ordinal @ SV115 )
| ( epsilon_transitive @ SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1060,plain,
! [SV103: $i] :
( ( ( empty @ SV103 )
= $false )
| ( ( ~ ( ordinal @ SV103 ) )
= $true )
| ( ( ordinal @ SV103 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1034]) ).
thf(1061,plain,
! [SV41: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV41 ) @ ( powerset @ SV41 ) )
| ~ ( empty @ ( sK17_B @ SV41 ) ) )
| ~ ( relation @ ( sK17_B @ SV41 ) ) )
| ~ ( function @ ( sK17_B @ SV41 ) ) )
| ~ ( one_to_one @ ( sK17_B @ SV41 ) ) )
| ~ ( epsilon_transitive @ ( sK17_B @ SV41 ) ) )
| ~ ( epsilon_connected @ ( sK17_B @ SV41 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1035]) ).
thf(1062,plain,
! [SV41: $i] :
( ( ordinal @ ( sK17_B @ SV41 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1036]) ).
thf(1063,plain,
( ( ~ ~ ( empty @ sK27_A )
| ~ ( epsilon_transitive @ sK27_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1038]) ).
thf(1064,plain,
! [SV104: $i] :
( ( ( ~ ( function @ SV104 ) )
= $true )
| ( ( ~ ( relation @ SV104 ) )
= $true )
| ( ( ~ ( transfinite_sequence @ SV104 ) )
= $true )
| ( ( epsilon_connected @ ( relation_dom @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1040]) ).
thf(1065,plain,
! [SV105: $i] :
( ( ( ~ ( function @ SV105 ) )
= $true )
| ( ( ~ ( relation @ SV105 ) )
= $true )
| ( ( ~ ( transfinite_sequence @ SV105 ) )
= $true )
| ( ( epsilon_transitive @ ( relation_dom @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1041]) ).
thf(1066,plain,
! [SV85: $i] :
( ( ( transfinite_sequence @ SV85 )
= $false )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false )
| ( ( ordinal @ ( relation_dom @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1042]) ).
thf(1067,plain,
( ( ~ ( element @ sK18_A @ positive_rationals ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1046]) ).
thf(1068,plain,
( ( ~ ~ ( empty @ sK18_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1046]) ).
thf(1069,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1047]) ).
thf(1070,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1047]) ).
thf(1071,plain,
( ( ~ ~ ( ~ ( element @ sK10_A @ positive_rationals )
| ~ ( empty @ sK10_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1048]) ).
thf(1072,plain,
( ( ~ ( epsilon_transitive @ sK10_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1048]) ).
thf(1073,plain,
! [SV99: $i] :
( ( ( empty @ SV99 )
= $false )
| ( ( ~ ( relation @ SV99 ) )
= $true )
| ( ( ~ ( function @ SV99 ) )
= $true )
| ( ( function @ SV99 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1049]) ).
thf(1074,plain,
! [SV100: $i] :
( ( ( empty @ SV100 )
= $false )
| ( ( ~ ( relation @ SV100 ) )
= $true )
| ( ( ~ ( function @ SV100 ) )
= $true )
| ( ( relation @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1050]) ).
thf(1075,plain,
! [SV110: $i] :
( ( ( ~ ( element @ SV110 @ positive_rationals ) )
= $true )
| ( ( ~ ( ordinal @ SV110 )
| ( epsilon_connected @ SV110 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1052]) ).
thf(1076,plain,
! [SV111: $i] :
( ( ( ~ ( element @ SV111 @ positive_rationals ) )
= $true )
| ( ( ~ ( ordinal @ SV111 )
| ( epsilon_transitive @ SV111 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1053]) ).
thf(1077,plain,
! [SV101: $i] :
( ( ( ordinal @ SV101 )
= $false )
| ( ( ordinal @ SV101 )
= $true )
| ( ( element @ SV101 @ positive_rationals )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1054]) ).
thf(1078,plain,
! [SV38: $i,SV112: $i] :
( ( ( ~ ( element @ SV112 @ SV38 ) )
= $true )
| ( ( epsilon_connected @ SV112 )
= $true )
| ( ( ordinal @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1055]) ).
thf(1079,plain,
! [SV38: $i,SV113: $i] :
( ( ( ~ ( element @ SV113 @ SV38 ) )
= $true )
| ( ( epsilon_transitive @ SV113 )
= $true )
| ( ( ordinal @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1056]) ).
thf(1080,plain,
( ( ~ ~ ( ~ ~ ( ~ ( function @ sK15_A )
| ~ ( relation @ sK15_A ) )
| ~ ( one_to_one @ sK15_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1057]) ).
thf(1081,plain,
( ( ~ ( empty @ sK15_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1057]) ).
thf(1082,plain,
! [SV114: $i] :
( ( ( ~ ( empty @ SV114 )
| ~ ( ordinal @ SV114 ) )
= $true )
| ( ( epsilon_connected @ SV114 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1058]) ).
thf(1083,plain,
! [SV115: $i] :
( ( ( ~ ( empty @ SV115 )
| ~ ( ordinal @ SV115 ) )
= $true )
| ( ( epsilon_transitive @ SV115 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1059]) ).
thf(1084,plain,
! [SV103: $i] :
( ( ( ordinal @ SV103 )
= $false )
| ( ( empty @ SV103 )
= $false )
| ( ( ordinal @ SV103 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1060]) ).
thf(1085,plain,
! [SV41: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV41 ) @ ( powerset @ SV41 ) )
| ~ ( empty @ ( sK17_B @ SV41 ) ) )
| ~ ( relation @ ( sK17_B @ SV41 ) ) )
| ~ ( function @ ( sK17_B @ SV41 ) ) )
| ~ ( one_to_one @ ( sK17_B @ SV41 ) ) )
| ~ ( epsilon_transitive @ ( sK17_B @ SV41 ) ) )
| ~ ( epsilon_connected @ ( sK17_B @ SV41 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1061]) ).
thf(1086,plain,
( ( ~ ~ ( empty @ sK27_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1063]) ).
thf(1087,plain,
( ( ~ ( epsilon_transitive @ sK27_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1063]) ).
thf(1088,plain,
! [SV104: $i] :
( ( ( function @ SV104 )
= $false )
| ( ( ~ ( relation @ SV104 ) )
= $true )
| ( ( ~ ( transfinite_sequence @ SV104 ) )
= $true )
| ( ( epsilon_connected @ ( relation_dom @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1064]) ).
thf(1089,plain,
! [SV105: $i] :
( ( ( function @ SV105 )
= $false )
| ( ( ~ ( relation @ SV105 ) )
= $true )
| ( ( ~ ( transfinite_sequence @ SV105 ) )
= $true )
| ( ( epsilon_transitive @ ( relation_dom @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1065]) ).
thf(1090,plain,
( ( element @ sK18_A @ positive_rationals )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1067]) ).
thf(1091,plain,
( ( ~ ( empty @ sK18_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1068]) ).
thf(1092,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1069]) ).
thf(1093,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1070]) ).
thf(1094,plain,
( ( ~ ( ~ ( element @ sK10_A @ positive_rationals )
| ~ ( empty @ sK10_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1071]) ).
thf(1095,plain,
( ( epsilon_transitive @ sK10_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1072]) ).
thf(1096,plain,
! [SV99: $i] :
( ( ( relation @ SV99 )
= $false )
| ( ( empty @ SV99 )
= $false )
| ( ( ~ ( function @ SV99 ) )
= $true )
| ( ( function @ SV99 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1073]) ).
thf(1097,plain,
! [SV100: $i] :
( ( ( relation @ SV100 )
= $false )
| ( ( empty @ SV100 )
= $false )
| ( ( ~ ( function @ SV100 ) )
= $true )
| ( ( relation @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1074]) ).
thf(1098,plain,
! [SV110: $i] :
( ( ( element @ SV110 @ positive_rationals )
= $false )
| ( ( ~ ( ordinal @ SV110 )
| ( epsilon_connected @ SV110 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1075]) ).
thf(1099,plain,
! [SV111: $i] :
( ( ( element @ SV111 @ positive_rationals )
= $false )
| ( ( ~ ( ordinal @ SV111 )
| ( epsilon_transitive @ SV111 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1076]) ).
thf(1100,plain,
! [SV38: $i,SV112: $i] :
( ( ( element @ SV112 @ SV38 )
= $false )
| ( ( epsilon_connected @ SV112 )
= $true )
| ( ( ordinal @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1078]) ).
thf(1101,plain,
! [SV38: $i,SV113: $i] :
( ( ( element @ SV113 @ SV38 )
= $false )
| ( ( epsilon_transitive @ SV113 )
= $true )
| ( ( ordinal @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1079]) ).
thf(1102,plain,
( ( ~ ( ~ ~ ( ~ ( function @ sK15_A )
| ~ ( relation @ sK15_A ) )
| ~ ( one_to_one @ sK15_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1080]) ).
thf(1103,plain,
( ( empty @ sK15_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1081]) ).
thf(1104,plain,
! [SV114: $i] :
( ( ( ~ ( empty @ SV114 ) )
= $true )
| ( ( ~ ( ordinal @ SV114 ) )
= $true )
| ( ( epsilon_connected @ SV114 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1082]) ).
thf(1105,plain,
! [SV115: $i] :
( ( ( ~ ( empty @ SV115 ) )
= $true )
| ( ( ~ ( ordinal @ SV115 ) )
= $true )
| ( ( epsilon_transitive @ SV115 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1083]) ).
thf(1106,plain,
! [SV41: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV41 ) @ ( powerset @ SV41 ) )
| ~ ( empty @ ( sK17_B @ SV41 ) ) )
| ~ ( relation @ ( sK17_B @ SV41 ) ) )
| ~ ( function @ ( sK17_B @ SV41 ) ) )
| ~ ( one_to_one @ ( sK17_B @ SV41 ) ) )
| ~ ( epsilon_transitive @ ( sK17_B @ SV41 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1085]) ).
thf(1107,plain,
! [SV41: $i] :
( ( ~ ( epsilon_connected @ ( sK17_B @ SV41 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1085]) ).
thf(1108,plain,
( ( ~ ( empty @ sK27_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1086]) ).
thf(1109,plain,
( ( epsilon_transitive @ sK27_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1087]) ).
thf(1110,plain,
! [SV104: $i] :
( ( ( relation @ SV104 )
= $false )
| ( ( function @ SV104 )
= $false )
| ( ( ~ ( transfinite_sequence @ SV104 ) )
= $true )
| ( ( epsilon_connected @ ( relation_dom @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1088]) ).
thf(1111,plain,
! [SV105: $i] :
( ( ( relation @ SV105 )
= $false )
| ( ( function @ SV105 )
= $false )
| ( ( ~ ( transfinite_sequence @ SV105 ) )
= $true )
| ( ( epsilon_transitive @ ( relation_dom @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1089]) ).
thf(1112,plain,
( ( empty @ sK18_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1091]) ).
thf(1113,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1092]) ).
thf(1114,plain,
( ( ~ ( element @ sK10_A @ positive_rationals )
| ~ ( empty @ sK10_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1094]) ).
thf(1115,plain,
! [SV99: $i] :
( ( ( function @ SV99 )
= $false )
| ( ( empty @ SV99 )
= $false )
| ( ( relation @ SV99 )
= $false )
| ( ( function @ SV99 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1096]) ).
thf(1116,plain,
! [SV100: $i] :
( ( ( function @ SV100 )
= $false )
| ( ( empty @ SV100 )
= $false )
| ( ( relation @ SV100 )
= $false )
| ( ( relation @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1097]) ).
thf(1117,plain,
! [SV110: $i] :
( ( ( ~ ( ordinal @ SV110 ) )
= $true )
| ( ( epsilon_connected @ SV110 )
= $true )
| ( ( element @ SV110 @ positive_rationals )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1098]) ).
thf(1118,plain,
! [SV111: $i] :
( ( ( ~ ( ordinal @ SV111 ) )
= $true )
| ( ( epsilon_transitive @ SV111 )
= $true )
| ( ( element @ SV111 @ positive_rationals )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1099]) ).
thf(1119,plain,
( ( ~ ~ ( ~ ( function @ sK15_A )
| ~ ( relation @ sK15_A ) )
| ~ ( one_to_one @ sK15_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1102]) ).
thf(1120,plain,
! [SV114: $i] :
( ( ( empty @ SV114 )
= $false )
| ( ( ~ ( ordinal @ SV114 ) )
= $true )
| ( ( epsilon_connected @ SV114 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1104]) ).
thf(1121,plain,
! [SV115: $i] :
( ( ( empty @ SV115 )
= $false )
| ( ( ~ ( ordinal @ SV115 ) )
= $true )
| ( ( epsilon_transitive @ SV115 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1105]) ).
thf(1122,plain,
! [SV41: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV41 ) @ ( powerset @ SV41 ) )
| ~ ( empty @ ( sK17_B @ SV41 ) ) )
| ~ ( relation @ ( sK17_B @ SV41 ) ) )
| ~ ( function @ ( sK17_B @ SV41 ) ) )
| ~ ( one_to_one @ ( sK17_B @ SV41 ) ) )
| ~ ( epsilon_transitive @ ( sK17_B @ SV41 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1106]) ).
thf(1123,plain,
! [SV41: $i] :
( ( epsilon_connected @ ( sK17_B @ SV41 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1107]) ).
thf(1124,plain,
( ( empty @ sK27_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1108]) ).
thf(1125,plain,
! [SV104: $i] :
( ( ( transfinite_sequence @ SV104 )
= $false )
| ( ( function @ SV104 )
= $false )
| ( ( relation @ SV104 )
= $false )
| ( ( epsilon_connected @ ( relation_dom @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1110]) ).
thf(1126,plain,
! [SV105: $i] :
( ( ( transfinite_sequence @ SV105 )
= $false )
| ( ( function @ SV105 )
= $false )
| ( ( relation @ SV105 )
= $false )
| ( ( epsilon_transitive @ ( relation_dom @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1111]) ).
thf(1127,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1113]) ).
thf(1128,plain,
( ( ~ ( one_to_one @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1113]) ).
thf(1129,plain,
( ( ~ ( element @ sK10_A @ positive_rationals ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1114]) ).
thf(1130,plain,
( ( ~ ( empty @ sK10_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1114]) ).
thf(1131,plain,
! [SV110: $i] :
( ( ( ordinal @ SV110 )
= $false )
| ( ( epsilon_connected @ SV110 )
= $true )
| ( ( element @ SV110 @ positive_rationals )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1117]) ).
thf(1132,plain,
! [SV111: $i] :
( ( ( ordinal @ SV111 )
= $false )
| ( ( epsilon_transitive @ SV111 )
= $true )
| ( ( element @ SV111 @ positive_rationals )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1118]) ).
thf(1133,plain,
( ( ~ ~ ( ~ ( function @ sK15_A )
| ~ ( relation @ sK15_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1119]) ).
thf(1134,plain,
( ( ~ ( one_to_one @ sK15_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1119]) ).
thf(1135,plain,
! [SV114: $i] :
( ( ( ordinal @ SV114 )
= $false )
| ( ( empty @ SV114 )
= $false )
| ( ( epsilon_connected @ SV114 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1120]) ).
thf(1136,plain,
! [SV115: $i] :
( ( ( ordinal @ SV115 )
= $false )
| ( ( empty @ SV115 )
= $false )
| ( ( epsilon_transitive @ SV115 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1121]) ).
thf(1137,plain,
! [SV41: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV41 ) @ ( powerset @ SV41 ) )
| ~ ( empty @ ( sK17_B @ SV41 ) ) )
| ~ ( relation @ ( sK17_B @ SV41 ) ) )
| ~ ( function @ ( sK17_B @ SV41 ) ) )
| ~ ( one_to_one @ ( sK17_B @ SV41 ) ) )
| ~ ( epsilon_transitive @ ( sK17_B @ SV41 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1122]) ).
thf(1138,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1127]) ).
thf(1139,plain,
( ( one_to_one @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1128]) ).
thf(1140,plain,
( ( element @ sK10_A @ positive_rationals )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1129]) ).
thf(1141,plain,
( ( empty @ sK10_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1130]) ).
thf(1142,plain,
( ( ~ ( ~ ( function @ sK15_A )
| ~ ( relation @ sK15_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1133]) ).
thf(1143,plain,
( ( one_to_one @ sK15_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1134]) ).
thf(1144,plain,
! [SV41: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV41 ) @ ( powerset @ SV41 ) )
| ~ ( empty @ ( sK17_B @ SV41 ) ) )
| ~ ( relation @ ( sK17_B @ SV41 ) ) )
| ~ ( function @ ( sK17_B @ SV41 ) ) )
| ~ ( one_to_one @ ( sK17_B @ SV41 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1137]) ).
thf(1145,plain,
! [SV41: $i] :
( ( ~ ( epsilon_transitive @ ( sK17_B @ SV41 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1137]) ).
thf(1146,plain,
( ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1138]) ).
thf(1147,plain,
( ( ~ ( function @ sK15_A )
| ~ ( relation @ sK15_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1142]) ).
thf(1148,plain,
! [SV41: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV41 ) @ ( powerset @ SV41 ) )
| ~ ( empty @ ( sK17_B @ SV41 ) ) )
| ~ ( relation @ ( sK17_B @ SV41 ) ) )
| ~ ( function @ ( sK17_B @ SV41 ) ) )
| ~ ( one_to_one @ ( sK17_B @ SV41 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1144]) ).
thf(1149,plain,
! [SV41: $i] :
( ( epsilon_transitive @ ( sK17_B @ SV41 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1145]) ).
thf(1150,plain,
( ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1146]) ).
thf(1151,plain,
( ( ~ ( function @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1146]) ).
thf(1152,plain,
( ( ~ ( function @ sK15_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1147]) ).
thf(1153,plain,
( ( ~ ( relation @ sK15_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1147]) ).
thf(1154,plain,
! [SV41: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV41 ) @ ( powerset @ SV41 ) )
| ~ ( empty @ ( sK17_B @ SV41 ) ) )
| ~ ( relation @ ( sK17_B @ SV41 ) ) )
| ~ ( function @ ( sK17_B @ SV41 ) ) )
| ~ ( one_to_one @ ( sK17_B @ SV41 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1148]) ).
thf(1155,plain,
( ( ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1150]) ).
thf(1156,plain,
( ( function @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1151]) ).
thf(1157,plain,
( ( function @ sK15_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1152]) ).
thf(1158,plain,
( ( relation @ sK15_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1153]) ).
thf(1159,plain,
! [SV41: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV41 ) @ ( powerset @ SV41 ) )
| ~ ( empty @ ( sK17_B @ SV41 ) ) )
| ~ ( relation @ ( sK17_B @ SV41 ) ) )
| ~ ( function @ ( sK17_B @ SV41 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1154]) ).
thf(1160,plain,
! [SV41: $i] :
( ( ~ ( one_to_one @ ( sK17_B @ SV41 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1154]) ).
thf(1161,plain,
( ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1155]) ).
thf(1162,plain,
! [SV41: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV41 ) @ ( powerset @ SV41 ) )
| ~ ( empty @ ( sK17_B @ SV41 ) ) )
| ~ ( relation @ ( sK17_B @ SV41 ) ) )
| ~ ( function @ ( sK17_B @ SV41 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1159]) ).
thf(1163,plain,
! [SV41: $i] :
( ( one_to_one @ ( sK17_B @ SV41 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1160]) ).
thf(1164,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1161]) ).
thf(1165,plain,
( ( ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1161]) ).
thf(1166,plain,
! [SV41: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV41 ) @ ( powerset @ SV41 ) )
| ~ ( empty @ ( sK17_B @ SV41 ) ) )
| ~ ( relation @ ( sK17_B @ SV41 ) ) )
| ~ ( function @ ( sK17_B @ SV41 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1162]) ).
thf(1167,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1164]) ).
thf(1168,plain,
( ( relation_empty_yielding @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1165]) ).
thf(1169,plain,
! [SV41: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV41 ) @ ( powerset @ SV41 ) )
| ~ ( empty @ ( sK17_B @ SV41 ) ) )
| ~ ( relation @ ( sK17_B @ SV41 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1166]) ).
thf(1170,plain,
! [SV41: $i] :
( ( ~ ( function @ ( sK17_B @ SV41 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1166]) ).
thf(1171,plain,
! [SV41: $i] :
( ( ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV41 ) @ ( powerset @ SV41 ) )
| ~ ( empty @ ( sK17_B @ SV41 ) ) )
| ~ ( relation @ ( sK17_B @ SV41 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1169]) ).
thf(1172,plain,
! [SV41: $i] :
( ( function @ ( sK17_B @ SV41 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1170]) ).
thf(1173,plain,
! [SV41: $i] :
( ( ~ ~ ( ~ ( element @ ( sK17_B @ SV41 ) @ ( powerset @ SV41 ) )
| ~ ( empty @ ( sK17_B @ SV41 ) ) )
| ~ ( relation @ ( sK17_B @ SV41 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1171]) ).
thf(1174,plain,
! [SV41: $i] :
( ( ~ ~ ( ~ ( element @ ( sK17_B @ SV41 ) @ ( powerset @ SV41 ) )
| ~ ( empty @ ( sK17_B @ SV41 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1173]) ).
thf(1175,plain,
! [SV41: $i] :
( ( ~ ( relation @ ( sK17_B @ SV41 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1173]) ).
thf(1176,plain,
! [SV41: $i] :
( ( ~ ( ~ ( element @ ( sK17_B @ SV41 ) @ ( powerset @ SV41 ) )
| ~ ( empty @ ( sK17_B @ SV41 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1174]) ).
thf(1177,plain,
! [SV41: $i] :
( ( relation @ ( sK17_B @ SV41 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1175]) ).
thf(1178,plain,
! [SV41: $i] :
( ( ~ ( element @ ( sK17_B @ SV41 ) @ ( powerset @ SV41 ) )
| ~ ( empty @ ( sK17_B @ SV41 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1176]) ).
thf(1179,plain,
! [SV41: $i] :
( ( ~ ( element @ ( sK17_B @ SV41 ) @ ( powerset @ SV41 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1178]) ).
thf(1180,plain,
! [SV41: $i] :
( ( ~ ( empty @ ( sK17_B @ SV41 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1178]) ).
thf(1181,plain,
! [SV41: $i] :
( ( element @ ( sK17_B @ SV41 ) @ ( powerset @ SV41 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1179]) ).
thf(1182,plain,
! [SV41: $i] :
( ( empty @ ( sK17_B @ SV41 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1180]) ).
thf(1183,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[268,1182,1181,1177,1172,1168,1167,1163,1158,1157,1156,1149,1143,1141,1140,1139,1136,1135,1132,1131,1126,1125,1124,1123,1116,1115,1112,1109,1103,1101,1100,1095,1093,1090,1084,1077,1066,1062,1051,1045,1044,1043,1039,1037,1031,1030,1029,1027,1018,1017,1015,1013,1012,1011,1009,1007,1006,997,995,984,976,973,972,971,970,959,958,956,948,943,942,917,916,913,910,909,905,902,901,893,892,890,889,888,886,885,879,878,873,867,865,864,863,862,861,859,857,855,854,853,852,851,848,847,846,845,844,840,838,835,832,824,813,794,792,791,786,759,756,751,749,747,746,743,741,739,738,730,722,718,717,711,695,677,659,655,652,643,641,635,633,632,631,629,628,624,622,615,609,607,605,602,601,599,597,595,593,592,587,586,583,579,574,556,555,554,464,458,455,454,390,387,386,377,324,323,287]) ).
thf(1184,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[243]) ).
thf(1185,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ( ! [B: $i] :
( ~ ( element @ B @ A )
| ( epsilon_connected @ B ) )
& ! [B: $i] :
( ~ ( element @ B @ A )
| ( epsilon_transitive @ B ) )
& ! [B: $i] :
( ~ ( element @ B @ A )
| ( ordinal @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[242]) ).
thf(1186,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[241]) ).
thf(1187,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[240]) ).
thf(1188,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_transitive @ A ) ) )
= $true ),
inference(copy,[status(thm)],[239]) ).
thf(1189,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[238]) ).
thf(1190,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
| ( relation @ C ) ) )
= $true ),
inference(copy,[status(thm)],[237]) ).
thf(1191,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ~ ( ordinal @ A )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ~ ( ordinal @ A )
| ( epsilon_transitive @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ~ ( ordinal @ A )
| ( ordinal @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ~ ( ordinal @ A )
| ( natural @ A ) ) )
= $true ),
inference(copy,[status(thm)],[236]) ).
thf(1192,plain,
( ( ! [A: $i] :
( ~ ( finite @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[235]) ).
thf(1193,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( function @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( one_to_one @ A ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(1194,plain,
( ( ! [A: $i] :
( ~ ( epsilon_connected @ A )
| ~ ( epsilon_transitive @ A )
| ( ordinal @ A ) ) )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(1195,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( epsilon_transitive @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( ordinal @ A ) ) )
= $true ),
inference(copy,[status(thm)],[232]) ).
thf(1196,plain,
( ( ! [A: $i] :
( ~ ( element @ A @ positive_rationals )
| ~ ( ordinal @ A )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( element @ A @ positive_rationals )
| ~ ( ordinal @ A )
| ( epsilon_transitive @ A ) )
& ! [A: $i] :
( ~ ( element @ A @ positive_rationals )
| ~ ( ordinal @ A )
| ( ordinal @ A ) )
& ! [A: $i] :
( ~ ( element @ A @ positive_rationals )
| ~ ( ordinal @ A )
| ( natural @ A ) ) )
= $true ),
inference(copy,[status(thm)],[231]) ).
thf(1197,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( quasi_total @ C @ A @ B )
| ~ ( relation_of2 @ C @ A @ B )
| ! [D: $i] : ( element @ ( function_image @ A @ B @ C @ D ) @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[230]) ).
thf(1198,plain,
( ( ! [A: $i,B: $i] : ( function @ ( first_projection @ A @ B ) )
& ! [A: $i,B: $i] : ( relation @ ( first_projection @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[229]) ).
thf(1199,plain,
( ( ! [A: $i,B: $i] : ( function @ ( first_projection_as_func_of @ A @ B ) )
& ! [A: $i,B: $i] : ( quasi_total @ ( first_projection_as_func_of @ A @ B ) @ ( cartesian_product2 @ A @ B ) @ A )
& ! [A: $i,B: $i] : ( relation_of2_as_subset @ ( first_projection_as_func_of @ A @ B ) @ ( cartesian_product2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[228]) ).
thf(1200,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[227]) ).
thf(1201,plain,
( ( ! [A: $i,B: $i] : ( relation_of2 @ ( sK30_C @ B @ A ) @ A @ B ) )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(1202,plain,
( ( ! [A: $i] : ( element @ ( sK29_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[225]) ).
thf(1203,plain,
( ( ! [A: $i,B: $i] : ( relation_of2_as_subset @ ( sK28_C @ B @ A ) @ A @ B ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(1204,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(1205,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( finite @ B )
| ( finite @ ( relation_image @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(1206,plain,
( ( ! [A: $i,B: $i] :
( ~ ( finite @ A )
| ~ ( finite @ B )
| ( finite @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(1207,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(1208,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(1209,plain,
( ( ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set )
& ( function @ empty_set )
& ( one_to_one @ empty_set )
& ( empty @ empty_set )
& ( epsilon_transitive @ empty_set )
& ( epsilon_connected @ empty_set )
& ( ordinal @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(1210,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(1211,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(1212,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( transfinite_sequence @ A )
| ( epsilon_connected @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( transfinite_sequence @ A )
| ( epsilon_transitive @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( transfinite_sequence @ A )
| ( ordinal @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[220]) ).
thf(1213,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[219]) ).
thf(1214,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ~ ( relation_non_empty @ A )
| ~ ( function @ A )
| ( with_non_empty_elements @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[218]) ).
thf(1215,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(1216,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(1217,plain,
( ( ~ ( empty @ positive_rationals ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(1218,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_rng @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[215]) ).
thf(1219,plain,
( ( ~ ( empty @ sK27_A )
& ( epsilon_transitive @ sK27_A )
& ( epsilon_connected @ sK27_A )
& ( ordinal @ sK27_A )
& ( natural @ sK27_A ) )
= $true ),
inference(copy,[status(thm)],[214]) ).
thf(1220,plain,
( ( ~ ( empty @ sK26_A )
& ( finite @ sK26_A ) )
= $true ),
inference(copy,[status(thm)],[213]) ).
thf(1221,plain,
( ( ( function @ sK25_A )
& ( relation @ sK25_A )
& ( function_yielding @ sK25_A ) )
= $true ),
inference(copy,[status(thm)],[212]) ).
thf(1222,plain,
( ( ( function @ sK24_A )
& ( relation @ sK24_A ) )
= $true ),
inference(copy,[status(thm)],[211]) ).
thf(1223,plain,
( ( ( epsilon_connected @ sK23_A )
& ( epsilon_transitive @ sK23_A )
& ( ordinal @ sK23_A ) )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(1224,plain,
( ( ( epsilon_connected @ sK22_A )
& ( epsilon_transitive @ sK22_A )
& ( ordinal @ sK22_A )
& ( being_limit_ordinal @ sK22_A ) )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(1225,plain,
( ( ( empty @ sK21_A )
& ( relation @ sK21_A ) )
= $true ),
inference(copy,[status(thm)],[208]) ).
thf(1226,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK20_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK20_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[207]) ).
thf(1227,plain,
( ( empty @ sK19_A )
= $true ),
inference(copy,[status(thm)],[206]) ).
thf(1228,plain,
( ( ( element @ sK18_A @ positive_rationals )
& ~ ( empty @ sK18_A )
& ( epsilon_transitive @ sK18_A )
& ( epsilon_connected @ sK18_A )
& ( ordinal @ sK18_A ) )
= $true ),
inference(copy,[status(thm)],[205]) ).
thf(1229,plain,
( ( ! [A: $i] :
( ( element @ ( sK17_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK17_B @ A ) )
& ( relation @ ( sK17_B @ A ) )
& ( function @ ( sK17_B @ A ) )
& ( one_to_one @ ( sK17_B @ A ) )
& ( epsilon_transitive @ ( sK17_B @ A ) )
& ( epsilon_connected @ ( sK17_B @ A ) )
& ( ordinal @ ( sK17_B @ A ) )
& ( natural @ ( sK17_B @ A ) )
& ( finite @ ( sK17_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[204]) ).
thf(1230,plain,
( ( ( empty @ sK16_A )
& ( relation @ sK16_A )
& ( function @ sK16_A ) )
= $true ),
inference(copy,[status(thm)],[203]) ).
thf(1231,plain,
( ( ( function @ sK15_A )
& ( relation @ sK15_A )
& ( one_to_one @ sK15_A )
& ( empty @ sK15_A )
& ( epsilon_transitive @ sK15_A )
& ( epsilon_connected @ sK15_A )
& ( ordinal @ sK15_A ) )
= $true ),
inference(copy,[status(thm)],[202]) ).
thf(1232,plain,
( ( ( function @ sK14_A )
& ( relation @ sK14_A )
& ( transfinite_sequence @ sK14_A )
& ( ordinal_yielding @ sK14_A ) )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(1233,plain,
( ( ~ ( empty @ sK13_A )
& ( relation @ sK13_A ) )
= $true ),
inference(copy,[status(thm)],[200]) ).
thf(1234,plain,
( ( ! [A: $i] :
( ( element @ ( sK12_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK12_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[199]) ).
thf(1235,plain,
( ( ~ ( empty @ sK11_A ) )
= $true ),
inference(copy,[status(thm)],[198]) ).
thf(1236,plain,
( ( ( element @ sK10_A @ positive_rationals )
& ( empty @ sK10_A )
& ( epsilon_transitive @ sK10_A )
& ( epsilon_connected @ sK10_A )
& ( ordinal @ sK10_A )
& ( natural @ sK10_A ) )
= $true ),
inference(copy,[status(thm)],[197]) ).
thf(1237,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK9_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK9_B @ A ) )
& ( finite @ ( sK9_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[196]) ).
thf(1238,plain,
( ( ( function @ sK8_A )
& ( relation @ sK8_A )
& ( one_to_one @ sK8_A ) )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(1239,plain,
( ( ~ ( empty @ sK7_A )
& ( epsilon_transitive @ sK7_A )
& ( epsilon_connected @ sK7_A )
& ( ordinal @ sK7_A ) )
= $true ),
inference(copy,[status(thm)],[194]) ).
thf(1240,plain,
( ( ( relation @ sK6_A )
& ( relation_empty_yielding @ sK6_A ) )
= $true ),
inference(copy,[status(thm)],[193]) ).
thf(1241,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK5_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK5_B @ A ) )
& ( finite @ ( sK5_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[192]) ).
thf(1242,plain,
( ( ( relation @ sK4_A )
& ( relation_empty_yielding @ sK4_A )
& ( function @ sK4_A ) )
= $true ),
inference(copy,[status(thm)],[191]) ).
thf(1243,plain,
( ( ( function @ sK3_A )
& ( relation @ sK3_A )
& ( transfinite_sequence @ sK3_A ) )
= $true ),
inference(copy,[status(thm)],[190]) ).
thf(1244,plain,
( ( ( relation @ sK2_A )
& ( relation_non_empty @ sK2_A )
& ( function @ sK2_A ) )
= $true ),
inference(copy,[status(thm)],[189]) ).
thf(1245,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( quasi_total @ C @ A @ B )
| ~ ( relation_of2 @ C @ A @ B )
| ! [D: $i] :
( ( function_image @ A @ B @ C @ D )
= ( relation_image @ C @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[188]) ).
thf(1246,plain,
( ( ! [A: $i,B: $i] :
( ( first_projection_as_func_of @ A @ B )
= ( first_projection @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(1247,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( relation_of2_as_subset @ C @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( relation_of2 @ C @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[187]) ).
thf(1248,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[186]) ).
thf(1249,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ( function_image @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) @ ( relation_dom @ A ) @ ( first_projection_as_func_of @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) @ A )
= ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[185]) ).
thf(1250,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ~ ( finite @ B )
| ~ ( subset @ A @ B ) )
| ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[184]) ).
thf(1251,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ~ ( finite @ A )
| ( finite @ ( relation_image @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[183]) ).
thf(1252,plain,
( ( ! [A: $i,B: $i] :
( ~ ( finite @ A )
| ~ ( finite @ B )
| ( finite @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[182]) ).
thf(1253,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[181]) ).
thf(1254,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[180]) ).
thf(1255,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( finite @ ( relation_dom @ A ) )
| ( finite @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[179]) ).
thf(1256,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[178]) ).
thf(1257,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[177]) ).
thf(1258,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[176]) ).
thf(1259,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[175]) ).
thf(1260,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[174]) ).
thf(1261,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[173]) ).
thf(1262,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[172]) ).
thf(1263,plain,
( ( function @ sK1_A )
= $true ),
inference(copy,[status(thm)],[164]) ).
thf(1264,plain,
( ( relation @ sK1_A )
= $true ),
inference(copy,[status(thm)],[163]) ).
thf(1265,plain,
( ( ( finite @ sK1_A )
& ~ ( finite @ ( relation_dom @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[171]) ).
thf(1266,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1210]) ).
thf(1267,plain,
( ( ~ ( ~ ~ ( ~ ( function @ sK25_A )
| ~ ( relation @ sK25_A ) )
| ~ ( function_yielding @ sK25_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1221]) ).
thf(1268,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1204]) ).
thf(1269,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1193]) ).
thf(1270,plain,
( ( ~ ( ~ ~ ( ~ ( function @ sK3_A )
| ~ ( relation @ sK3_A ) )
| ~ ( transfinite_sequence @ sK3_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1243]) ).
thf(1271,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK27_A )
| ~ ( epsilon_transitive @ sK27_A ) )
| ~ ( epsilon_connected @ sK27_A ) )
| ~ ( ordinal @ sK27_A ) )
| ~ ( natural @ sK27_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1219]) ).
thf(1272,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ sK18_A @ positive_rationals )
| ~ ~ ( empty @ sK18_A ) )
| ~ ( epsilon_transitive @ sK18_A ) )
| ~ ( epsilon_connected @ sK18_A ) )
| ~ ( ordinal @ sK18_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1228]) ).
thf(1273,plain,
( ( ! [SX0: $i] :
~ ( ~ ( element @ ( sK12_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ( empty @ ( sK12_B @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1234]) ).
thf(1274,plain,
( ( ~ ( ~ ( relation @ sK6_A )
| ~ ( relation_empty_yielding @ sK6_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1240]) ).
thf(1275,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( ordinal @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( natural @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1196]) ).
thf(1276,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK14_A )
| ~ ( relation @ sK14_A ) )
| ~ ( transfinite_sequence @ sK14_A ) )
| ~ ( ordinal_yielding @ sK14_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1232]) ).
thf(1277,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( ordinal @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1195]) ).
thf(1278,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ sK10_A @ positive_rationals )
| ~ ( empty @ sK10_A ) )
| ~ ( epsilon_transitive @ sK10_A ) )
| ~ ( epsilon_connected @ sK10_A ) )
| ~ ( ordinal @ sK10_A ) )
| ~ ( natural @ sK10_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1236]) ).
thf(1279,plain,
( ( ~ ( ~ ( finite @ sK1_A )
| ~ ~ ( finite @ ( relation_dom @ sK1_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1265]) ).
thf(1280,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1257]) ).
thf(1281,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ sK4_A )
| ~ ( relation_empty_yielding @ sK4_A ) )
| ~ ( function @ sK4_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1242]) ).
thf(1282,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( epsilon_connected @ sK22_A )
| ~ ( epsilon_transitive @ sK22_A ) )
| ~ ( ordinal @ sK22_A ) )
| ~ ( being_limit_ordinal @ sK22_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1224]) ).
thf(1283,plain,
( ( ! [SX0: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ( empty @ ( sK17_B @ SX0 ) ) )
| ~ ( relation @ ( sK17_B @ SX0 ) ) )
| ~ ( function @ ( sK17_B @ SX0 ) ) )
| ~ ( one_to_one @ ( sK17_B @ SX0 ) ) )
| ~ ( epsilon_transitive @ ( sK17_B @ SX0 ) ) )
| ~ ( epsilon_connected @ ( sK17_B @ SX0 ) ) )
| ~ ( ordinal @ ( sK17_B @ SX0 ) ) )
| ~ ( natural @ ( sK17_B @ SX0 ) ) )
| ~ ( finite @ ( sK17_B @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1229]) ).
thf(1284,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) )
| ~ ( epsilon_transitive @ empty_set ) )
| ~ ( epsilon_connected @ empty_set ) )
| ~ ( ordinal @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1209]) ).
thf(1285,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] : ( function @ ( first_projection @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] : ( relation @ ( first_projection @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1198]) ).
thf(1286,plain,
( ( ~ ( ~ ~ ( ~ ( function @ sK8_A )
| ~ ( relation @ sK8_A ) )
| ~ ( one_to_one @ sK8_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1238]) ).
thf(1287,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK15_A )
| ~ ( relation @ sK15_A ) )
| ~ ( one_to_one @ sK15_A ) )
| ~ ( empty @ sK15_A ) )
| ~ ( epsilon_transitive @ sK15_A ) )
| ~ ( epsilon_connected @ sK15_A ) )
| ~ ( ordinal @ sK15_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1231]) ).
thf(1288,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1188]) ).
thf(1289,plain,
( ( ~ ( ~ ~ ( empty @ sK26_A )
| ~ ( finite @ sK26_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1220]) ).
thf(1290,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1216]) ).
thf(1291,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( transfinite_sequence @ SX0 )
| ( epsilon_connected @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( transfinite_sequence @ SX0 )
| ( epsilon_transitive @ ( relation_dom @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( transfinite_sequence @ SX0 )
| ( ordinal @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1212]) ).
thf(1292,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( ordinal @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( natural @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1191]) ).
thf(1293,plain,
( ( ~ ( ~ ~ ( ~ ( epsilon_connected @ sK23_A )
| ~ ( epsilon_transitive @ sK23_A ) )
| ~ ( ordinal @ sK23_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1223]) ).
thf(1294,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2 @ SX2 @ SX0 @ SX1 )
| ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( relation_of2 @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1247]) ).
thf(1295,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ~ ( ~ ( element @ ( sK9_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK9_B @ SX0 ) ) )
| ~ ( finite @ ( sK9_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1237]) ).
thf(1296,plain,
( ( ~ ( ~ ( function @ sK24_A )
| ~ ( relation @ sK24_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1222]) ).
thf(1297,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ sK2_A )
| ~ ( relation_non_empty @ sK2_A ) )
| ~ ( function @ sK2_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1244]) ).
thf(1298,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK7_A )
| ~ ( epsilon_transitive @ sK7_A ) )
| ~ ( epsilon_connected @ sK7_A ) )
| ~ ( ordinal @ sK7_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1239]) ).
thf(1299,plain,
( ( ~ ( ~ ( empty @ sK21_A )
| ~ ( relation @ sK21_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1225]) ).
thf(1300,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ~ ~ ( ~ ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( epsilon_connected @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( epsilon_transitive @ SX1 ) ) )
| ~ ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( ordinal @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1185]) ).
thf(1301,plain,
( ( ~ ( ~ ~ ( empty @ sK13_A )
| ~ ( relation @ sK13_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1233]) ).
thf(1302,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1218]) ).
thf(1303,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] : ( function @ ( first_projection_as_func_of @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] : ( quasi_total @ ( first_projection_as_func_of @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX0 @ SX1 ) @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] : ( relation_of2_as_subset @ ( first_projection_as_func_of @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX0 @ SX1 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1199]) ).
thf(1304,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ( element @ ( sK20_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK20_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1226]) ).
thf(1305,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ sK16_A )
| ~ ( relation @ sK16_A ) )
| ~ ( function @ sK16_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1230]) ).
thf(1306,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ~ ( ~ ( element @ ( sK5_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK5_B @ SX0 ) ) )
| ~ ( finite @ ( sK5_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1241]) ).
thf(1307,plain,
! [SV116: $i] :
( ( ! [SY174: $i] :
( ~ ( in @ SV116 @ SY174 )
| ~ ( in @ SY174 @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1184]) ).
thf(1308,plain,
! [SV117: $i] :
( ( ~ ( empty @ SV117 )
| ( finite @ SV117 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1186]) ).
thf(1309,plain,
! [SV118: $i] :
( ( ~ ( empty @ SV118 )
| ( function @ SV118 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1187]) ).
thf(1310,plain,
! [SV119: $i] :
( ( ~ ( empty @ SV119 )
| ( relation @ SV119 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1189]) ).
thf(1311,plain,
! [SV120: $i] :
( ( ! [SY175: $i,SY176: $i] :
( ~ ( element @ SY176 @ ( powerset @ ( cartesian_product2 @ SV120 @ SY175 ) ) )
| ( relation @ SY176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1190]) ).
thf(1312,plain,
! [SV121: $i] :
( ( ~ ( finite @ SV121 )
| ! [SY177: $i] :
( ~ ( element @ SY177 @ ( powerset @ SV121 ) )
| ( finite @ SY177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1192]) ).
thf(1313,plain,
! [SV122: $i] :
( ( ~ ( epsilon_connected @ SV122 )
| ~ ( epsilon_transitive @ SV122 )
| ( ordinal @ SV122 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1314,plain,
! [SV123: $i] :
( ( ! [SY178: $i,SY179: $i] :
( ~ ( function @ SY179 )
| ~ ( quasi_total @ SY179 @ SV123 @ SY178 )
| ~ ( relation_of2 @ SY179 @ SV123 @ SY178 )
| ! [SY180: $i] : ( element @ ( function_image @ SV123 @ SY178 @ SY179 @ SY180 ) @ ( powerset @ SY178 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1197]) ).
thf(1315,plain,
! [SV124: $i] :
( ( ! [SY181: $i,SY182: $i] :
( ~ ( relation_of2_as_subset @ SY182 @ SV124 @ SY181 )
| ( element @ SY182 @ ( powerset @ ( cartesian_product2 @ SV124 @ SY181 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1200]) ).
thf(1316,plain,
! [SV125: $i] :
( ( ! [SY183: $i] : ( relation_of2 @ ( sK30_C @ SY183 @ SV125 ) @ SV125 @ SY183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1201]) ).
thf(1317,plain,
! [SV126: $i] :
( ( element @ ( sK29_B @ SV126 ) @ SV126 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1202]) ).
thf(1318,plain,
! [SV127: $i] :
( ( ! [SY184: $i] : ( relation_of2_as_subset @ ( sK28_C @ SY184 @ SV127 ) @ SV127 @ SY184 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1203]) ).
thf(1319,plain,
! [SV128: $i] :
( ( ! [SY185: $i] :
( ~ ( function @ SV128 )
| ~ ( relation @ SV128 )
| ~ ( finite @ SY185 )
| ( finite @ ( relation_image @ SV128 @ SY185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1205]) ).
thf(1320,plain,
! [SV129: $i] :
( ( ! [SY186: $i] :
( ~ ( finite @ SV129 )
| ~ ( finite @ SY186 )
| ( finite @ ( cartesian_product2 @ SV129 @ SY186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1206]) ).
thf(1321,plain,
! [SV130: $i] :
( ( ~ ( empty @ ( powerset @ SV130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1207]) ).
thf(1322,plain,
! [SV131: $i] :
( ( ! [SY187: $i] :
( ( empty @ SV131 )
| ( empty @ SY187 )
| ~ ( empty @ ( cartesian_product2 @ SV131 @ SY187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1211]) ).
thf(1323,plain,
! [SV132: $i] :
( ( ( empty @ SV132 )
| ~ ( relation @ SV132 )
| ~ ( empty @ ( relation_dom @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1213]) ).
thf(1324,plain,
! [SV133: $i] :
( ( ~ ( relation @ SV133 )
| ~ ( relation_non_empty @ SV133 )
| ~ ( function @ SV133 )
| ( with_non_empty_elements @ ( relation_rng @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1214]) ).
thf(1325,plain,
! [SV134: $i] :
( ( ( empty @ SV134 )
| ~ ( relation @ SV134 )
| ~ ( empty @ ( relation_rng @ SV134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1215]) ).
thf(1326,plain,
( ( empty @ positive_rationals )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1217]) ).
thf(1327,plain,
( ( empty @ sK11_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1235]) ).
thf(1328,plain,
! [SV135: $i] :
( ( ! [SY188: $i,SY189: $i] :
( ~ ( function @ SY189 )
| ~ ( quasi_total @ SY189 @ SV135 @ SY188 )
| ~ ( relation_of2 @ SY189 @ SV135 @ SY188 )
| ! [SY190: $i] :
( ( function_image @ SV135 @ SY188 @ SY189 @ SY190 )
= ( relation_image @ SY189 @ SY190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1245]) ).
thf(1329,plain,
! [SV136: $i] :
( ( ! [SY191: $i] :
( ( first_projection_as_func_of @ SV136 @ SY191 )
= ( first_projection @ SV136 @ SY191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1246]) ).
thf(1330,plain,
! [SV137: $i] :
( ( subset @ SV137 @ SV137 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1248]) ).
thf(1331,plain,
! [SV138: $i] :
( ( ~ ( function @ SV138 )
| ~ ( relation @ SV138 )
| ( ( function_image @ ( cartesian_product2 @ ( relation_dom @ SV138 ) @ ( relation_rng @ SV138 ) ) @ ( relation_dom @ SV138 ) @ ( first_projection_as_func_of @ ( relation_dom @ SV138 ) @ ( relation_rng @ SV138 ) ) @ SV138 )
= ( relation_dom @ SV138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1249]) ).
thf(1332,plain,
! [SV139: $i] :
( ( ! [SY192: $i] :
( ~ ( finite @ SY192 )
| ~ ( subset @ SV139 @ SY192 ) )
| ( finite @ SV139 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1250]) ).
thf(1333,plain,
! [SV140: $i] :
( ( ! [SY193: $i] :
( ~ ( function @ SY193 )
| ~ ( relation @ SY193 )
| ~ ( finite @ SV140 )
| ( finite @ ( relation_image @ SY193 @ SV140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1251]) ).
thf(1334,plain,
! [SV141: $i] :
( ( ! [SY194: $i] :
( ~ ( finite @ SV141 )
| ~ ( finite @ SY194 )
| ( finite @ ( cartesian_product2 @ SV141 @ SY194 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1335,plain,
! [SV142: $i] :
( ( ! [SY195: $i] :
( ~ ( in @ SV142 @ SY195 )
| ( element @ SV142 @ SY195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1253]) ).
thf(1336,plain,
! [SV143: $i] :
( ( ~ ( relation @ SV143 )
| ( subset @ SV143 @ ( cartesian_product2 @ ( relation_dom @ SV143 ) @ ( relation_rng @ SV143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1254]) ).
thf(1337,plain,
! [SV144: $i] :
( ( ~ ( function @ SV144 )
| ~ ( relation @ SV144 )
| ~ ( finite @ ( relation_dom @ SV144 ) )
| ( finite @ ( relation_rng @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1255]) ).
thf(1338,plain,
! [SV145: $i] :
( ( ! [SY196: $i] :
( ~ ( element @ SV145 @ SY196 )
| ( empty @ SY196 )
| ( in @ SV145 @ SY196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1256]) ).
thf(1339,plain,
! [SV146: $i] :
( ( ! [SY197: $i,SY198: $i] :
( ~ ( element @ SY197 @ ( powerset @ SY198 ) )
| ~ ( in @ SV146 @ SY197 )
| ( element @ SV146 @ SY198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1258]) ).
thf(1340,plain,
! [SV147: $i] :
( ( ! [SY199: $i,SY200: $i] :
( ~ ( element @ SY199 @ ( powerset @ SY200 ) )
| ~ ( in @ SV147 @ SY199 )
| ~ ( empty @ SY200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1259]) ).
thf(1341,plain,
! [SV148: $i] :
( ( ~ ( empty @ SV148 )
| ( SV148 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1260]) ).
thf(1342,plain,
! [SV149: $i] :
( ( ! [SY201: $i] :
( ~ ( empty @ SY201 )
| ~ ( in @ SV149 @ SY201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(1343,plain,
! [SV150: $i] :
( ( ! [SY202: $i] :
( ( SV150 = SY202 )
| ~ ( empty @ SV150 )
| ~ ( empty @ SY202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1262]) ).
thf(1344,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1266]) ).
thf(1345,plain,
( ( ~ ~ ( ~ ( function @ sK25_A )
| ~ ( relation @ sK25_A ) )
| ~ ( function_yielding @ sK25_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1267]) ).
thf(1346,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1268]) ).
thf(1347,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1269]) ).
thf(1348,plain,
( ( ~ ~ ( ~ ( function @ sK3_A )
| ~ ( relation @ sK3_A ) )
| ~ ( transfinite_sequence @ sK3_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1270]) ).
thf(1349,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK27_A )
| ~ ( epsilon_transitive @ sK27_A ) )
| ~ ( epsilon_connected @ sK27_A ) )
| ~ ( ordinal @ sK27_A ) )
| ~ ( natural @ sK27_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1271]) ).
thf(1350,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ sK18_A @ positive_rationals )
| ~ ~ ( empty @ sK18_A ) )
| ~ ( epsilon_transitive @ sK18_A ) )
| ~ ( epsilon_connected @ sK18_A ) )
| ~ ( ordinal @ sK18_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1272]) ).
thf(1351,plain,
! [SV151: $i] :
( ( ~ ( ~ ( element @ ( sK12_B @ SV151 ) @ ( powerset @ SV151 ) )
| ~ ( empty @ ( sK12_B @ SV151 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1273]) ).
thf(1352,plain,
( ( ~ ( relation @ sK6_A )
| ~ ( relation_empty_yielding @ sK6_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1274]) ).
thf(1353,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( ordinal @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( natural @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1275]) ).
thf(1354,plain,
( ( ~ ~ ( ~ ~ ( ~ ( function @ sK14_A )
| ~ ( relation @ sK14_A ) )
| ~ ( transfinite_sequence @ sK14_A ) )
| ~ ( ordinal_yielding @ sK14_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1276]) ).
thf(1355,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( ordinal @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1277]) ).
thf(1356,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ sK10_A @ positive_rationals )
| ~ ( empty @ sK10_A ) )
| ~ ( epsilon_transitive @ sK10_A ) )
| ~ ( epsilon_connected @ sK10_A ) )
| ~ ( ordinal @ sK10_A ) )
| ~ ( natural @ sK10_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1278]) ).
thf(1357,plain,
( ( ~ ( finite @ sK1_A )
| ~ ~ ( finite @ ( relation_dom @ sK1_A ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1279]) ).
thf(1358,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1280]) ).
thf(1359,plain,
( ( ~ ~ ( ~ ( relation @ sK4_A )
| ~ ( relation_empty_yielding @ sK4_A ) )
| ~ ( function @ sK4_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1281]) ).
thf(1360,plain,
( ( ~ ~ ( ~ ~ ( ~ ( epsilon_connected @ sK22_A )
| ~ ( epsilon_transitive @ sK22_A ) )
| ~ ( ordinal @ sK22_A ) )
| ~ ( being_limit_ordinal @ sK22_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1282]) ).
thf(1361,plain,
! [SV152: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV152 ) @ ( powerset @ SV152 ) )
| ~ ( empty @ ( sK17_B @ SV152 ) ) )
| ~ ( relation @ ( sK17_B @ SV152 ) ) )
| ~ ( function @ ( sK17_B @ SV152 ) ) )
| ~ ( one_to_one @ ( sK17_B @ SV152 ) ) )
| ~ ( epsilon_transitive @ ( sK17_B @ SV152 ) ) )
| ~ ( epsilon_connected @ ( sK17_B @ SV152 ) ) )
| ~ ( ordinal @ ( sK17_B @ SV152 ) ) )
| ~ ( natural @ ( sK17_B @ SV152 ) ) )
| ~ ( finite @ ( sK17_B @ SV152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1283]) ).
thf(1362,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) )
| ~ ( epsilon_transitive @ empty_set ) )
| ~ ( epsilon_connected @ empty_set ) )
| ~ ( ordinal @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1284]) ).
thf(1363,plain,
( ( ~ ! [SX0: $i,SX1: $i] : ( function @ ( first_projection @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] : ( relation @ ( first_projection @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1285]) ).
thf(1364,plain,
( ( ~ ~ ( ~ ( function @ sK8_A )
| ~ ( relation @ sK8_A ) )
| ~ ( one_to_one @ sK8_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1286]) ).
thf(1365,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK15_A )
| ~ ( relation @ sK15_A ) )
| ~ ( one_to_one @ sK15_A ) )
| ~ ( empty @ sK15_A ) )
| ~ ( epsilon_transitive @ sK15_A ) )
| ~ ( epsilon_connected @ sK15_A ) )
| ~ ( ordinal @ sK15_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1287]) ).
thf(1366,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1288]) ).
thf(1367,plain,
( ( ~ ~ ( empty @ sK26_A )
| ~ ( finite @ sK26_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1289]) ).
thf(1368,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1290]) ).
thf(1369,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( transfinite_sequence @ SX0 )
| ( epsilon_connected @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( transfinite_sequence @ SX0 )
| ( epsilon_transitive @ ( relation_dom @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( transfinite_sequence @ SX0 )
| ( ordinal @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1291]) ).
thf(1370,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( ordinal @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( natural @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1292]) ).
thf(1371,plain,
( ( ~ ~ ( ~ ( epsilon_connected @ sK23_A )
| ~ ( epsilon_transitive @ sK23_A ) )
| ~ ( ordinal @ sK23_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1293]) ).
thf(1372,plain,
! [SV153: $i] :
( ( ~ ( ~ ! [SY203: $i,SY204: $i] :
( ~ ( relation_of2 @ SY204 @ SV153 @ SY203 )
| ( relation_of2_as_subset @ SY204 @ SV153 @ SY203 ) )
| ~ ! [SY205: $i,SY206: $i] :
( ~ ( relation_of2_as_subset @ SY206 @ SV153 @ SY205 )
| ( relation_of2 @ SY206 @ SV153 @ SY205 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1294]) ).
thf(1373,plain,
! [SV154: $i] :
( ( ( empty @ SV154 )
| ~ ( ~ ~ ( ~ ( element @ ( sK9_B @ SV154 ) @ ( powerset @ SV154 ) )
| ~ ~ ( empty @ ( sK9_B @ SV154 ) ) )
| ~ ( finite @ ( sK9_B @ SV154 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1295]) ).
thf(1374,plain,
( ( ~ ( function @ sK24_A )
| ~ ( relation @ sK24_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1296]) ).
thf(1375,plain,
( ( ~ ~ ( ~ ( relation @ sK2_A )
| ~ ( relation_non_empty @ sK2_A ) )
| ~ ( function @ sK2_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1297]) ).
thf(1376,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK7_A )
| ~ ( epsilon_transitive @ sK7_A ) )
| ~ ( epsilon_connected @ sK7_A ) )
| ~ ( ordinal @ sK7_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1298]) ).
thf(1377,plain,
( ( ~ ( empty @ sK21_A )
| ~ ( relation @ sK21_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1299]) ).
thf(1378,plain,
! [SV155: $i] :
( ( ~ ( ordinal @ SV155 )
| ~ ( ~ ~ ( ~ ! [SY207: $i] :
( ~ ( element @ SY207 @ SV155 )
| ( epsilon_connected @ SY207 ) )
| ~ ! [SY208: $i] :
( ~ ( element @ SY208 @ SV155 )
| ( epsilon_transitive @ SY208 ) ) )
| ~ ! [SY209: $i] :
( ~ ( element @ SY209 @ SV155 )
| ( ordinal @ SY209 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1300]) ).
thf(1379,plain,
( ( ~ ~ ( empty @ sK13_A )
| ~ ( relation @ sK13_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1301]) ).
thf(1380,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1302]) ).
thf(1381,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] : ( function @ ( first_projection_as_func_of @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] : ( quasi_total @ ( first_projection_as_func_of @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX0 @ SX1 ) @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] : ( relation_of2_as_subset @ ( first_projection_as_func_of @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX0 @ SX1 ) @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1303]) ).
thf(1382,plain,
! [SV156: $i] :
( ( ( empty @ SV156 )
| ~ ( ~ ( element @ ( sK20_B @ SV156 ) @ ( powerset @ SV156 ) )
| ~ ~ ( empty @ ( sK20_B @ SV156 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1304]) ).
thf(1383,plain,
( ( ~ ~ ( ~ ( empty @ sK16_A )
| ~ ( relation @ sK16_A ) )
| ~ ( function @ sK16_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1305]) ).
thf(1384,plain,
! [SV157: $i] :
( ( ( empty @ SV157 )
| ~ ( ~ ~ ( ~ ( element @ ( sK5_B @ SV157 ) @ ( powerset @ SV157 ) )
| ~ ~ ( empty @ ( sK5_B @ SV157 ) ) )
| ~ ( finite @ ( sK5_B @ SV157 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1306]) ).
thf(1385,plain,
! [SV158: $i,SV116: $i] :
( ( ~ ( in @ SV116 @ SV158 )
| ~ ( in @ SV158 @ SV116 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1307]) ).
thf(1386,plain,
! [SV117: $i] :
( ( ( ~ ( empty @ SV117 ) )
= $true )
| ( ( finite @ SV117 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1308]) ).
thf(1387,plain,
! [SV118: $i] :
( ( ( ~ ( empty @ SV118 ) )
= $true )
| ( ( function @ SV118 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1309]) ).
thf(1388,plain,
! [SV119: $i] :
( ( ( ~ ( empty @ SV119 ) )
= $true )
| ( ( relation @ SV119 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1310]) ).
thf(1389,plain,
! [SV159: $i,SV120: $i] :
( ( ! [SY210: $i] :
( ~ ( element @ SY210 @ ( powerset @ ( cartesian_product2 @ SV120 @ SV159 ) ) )
| ( relation @ SY210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1311]) ).
thf(1390,plain,
! [SV121: $i] :
( ( ( ~ ( finite @ SV121 ) )
= $true )
| ( ( ! [SY177: $i] :
( ~ ( element @ SY177 @ ( powerset @ SV121 ) )
| ( finite @ SY177 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1312]) ).
thf(1391,plain,
! [SV122: $i] :
( ( ( ~ ( epsilon_connected @ SV122 )
| ~ ( epsilon_transitive @ SV122 ) )
= $true )
| ( ( ordinal @ SV122 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1313]) ).
thf(1392,plain,
! [SV160: $i,SV123: $i] :
( ( ! [SY211: $i] :
( ~ ( function @ SY211 )
| ~ ( quasi_total @ SY211 @ SV123 @ SV160 )
| ~ ( relation_of2 @ SY211 @ SV123 @ SV160 )
| ! [SY212: $i] : ( element @ ( function_image @ SV123 @ SV160 @ SY211 @ SY212 ) @ ( powerset @ SV160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1314]) ).
thf(1393,plain,
! [SV161: $i,SV124: $i] :
( ( ! [SY213: $i] :
( ~ ( relation_of2_as_subset @ SY213 @ SV124 @ SV161 )
| ( element @ SY213 @ ( powerset @ ( cartesian_product2 @ SV124 @ SV161 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1315]) ).
thf(1394,plain,
! [SV125: $i,SV162: $i] :
( ( relation_of2 @ ( sK30_C @ SV162 @ SV125 ) @ SV125 @ SV162 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1316]) ).
thf(1395,plain,
! [SV127: $i,SV163: $i] :
( ( relation_of2_as_subset @ ( sK28_C @ SV163 @ SV127 ) @ SV127 @ SV163 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1318]) ).
thf(1396,plain,
! [SV164: $i,SV128: $i] :
( ( ~ ( function @ SV128 )
| ~ ( relation @ SV128 )
| ~ ( finite @ SV164 )
| ( finite @ ( relation_image @ SV128 @ SV164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1319]) ).
thf(1397,plain,
! [SV165: $i,SV129: $i] :
( ( ~ ( finite @ SV129 )
| ~ ( finite @ SV165 )
| ( finite @ ( cartesian_product2 @ SV129 @ SV165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1320]) ).
thf(1398,plain,
! [SV130: $i] :
( ( empty @ ( powerset @ SV130 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1321]) ).
thf(1399,plain,
! [SV166: $i,SV131: $i] :
( ( ( empty @ SV131 )
| ( empty @ SV166 )
| ~ ( empty @ ( cartesian_product2 @ SV131 @ SV166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1322]) ).
thf(1400,plain,
! [SV132: $i] :
( ( ( ( empty @ SV132 )
| ~ ( relation @ SV132 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV132 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1323]) ).
thf(1401,plain,
! [SV133: $i] :
( ( ( ~ ( relation @ SV133 )
| ~ ( relation_non_empty @ SV133 )
| ~ ( function @ SV133 ) )
= $true )
| ( ( with_non_empty_elements @ ( relation_rng @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1324]) ).
thf(1402,plain,
! [SV134: $i] :
( ( ( ( empty @ SV134 )
| ~ ( relation @ SV134 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV134 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1325]) ).
thf(1403,plain,
! [SV167: $i,SV135: $i] :
( ( ! [SY214: $i] :
( ~ ( function @ SY214 )
| ~ ( quasi_total @ SY214 @ SV135 @ SV167 )
| ~ ( relation_of2 @ SY214 @ SV135 @ SV167 )
| ! [SY215: $i] :
( ( function_image @ SV135 @ SV167 @ SY214 @ SY215 )
= ( relation_image @ SY214 @ SY215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1328]) ).
thf(1404,plain,
! [SV168: $i,SV136: $i] :
( ( ( first_projection_as_func_of @ SV136 @ SV168 )
= ( first_projection @ SV136 @ SV168 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1329]) ).
thf(1405,plain,
! [SV138: $i] :
( ( ( ~ ( function @ SV138 )
| ~ ( relation @ SV138 ) )
= $true )
| ( ( ( function_image @ ( cartesian_product2 @ ( relation_dom @ SV138 ) @ ( relation_rng @ SV138 ) ) @ ( relation_dom @ SV138 ) @ ( first_projection_as_func_of @ ( relation_dom @ SV138 ) @ ( relation_rng @ SV138 ) ) @ SV138 )
= ( relation_dom @ SV138 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1331]) ).
thf(1406,plain,
! [SV139: $i] :
( ( ( ! [SY192: $i] :
( ~ ( finite @ SY192 )
| ~ ( subset @ SV139 @ SY192 ) ) )
= $true )
| ( ( finite @ SV139 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1332]) ).
thf(1407,plain,
! [SV140: $i,SV169: $i] :
( ( ~ ( function @ SV169 )
| ~ ( relation @ SV169 )
| ~ ( finite @ SV140 )
| ( finite @ ( relation_image @ SV169 @ SV140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1333]) ).
thf(1408,plain,
! [SV170: $i,SV141: $i] :
( ( ~ ( finite @ SV141 )
| ~ ( finite @ SV170 )
| ( finite @ ( cartesian_product2 @ SV141 @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1334]) ).
thf(1409,plain,
! [SV171: $i,SV142: $i] :
( ( ~ ( in @ SV142 @ SV171 )
| ( element @ SV142 @ SV171 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1335]) ).
thf(1410,plain,
! [SV143: $i] :
( ( ( ~ ( relation @ SV143 ) )
= $true )
| ( ( subset @ SV143 @ ( cartesian_product2 @ ( relation_dom @ SV143 ) @ ( relation_rng @ SV143 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1336]) ).
thf(1411,plain,
! [SV144: $i] :
( ( ( ~ ( function @ SV144 )
| ~ ( relation @ SV144 ) )
= $true )
| ( ( ~ ( finite @ ( relation_dom @ SV144 ) )
| ( finite @ ( relation_rng @ SV144 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1337]) ).
thf(1412,plain,
! [SV172: $i,SV145: $i] :
( ( ~ ( element @ SV145 @ SV172 )
| ( empty @ SV172 )
| ( in @ SV145 @ SV172 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1338]) ).
thf(1413,plain,
! [SV146: $i,SV173: $i] :
( ( ! [SY216: $i] :
( ~ ( element @ SV173 @ ( powerset @ SY216 ) )
| ~ ( in @ SV146 @ SV173 )
| ( element @ SV146 @ SY216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1339]) ).
thf(1414,plain,
! [SV147: $i,SV174: $i] :
( ( ! [SY217: $i] :
( ~ ( element @ SV174 @ ( powerset @ SY217 ) )
| ~ ( in @ SV147 @ SV174 )
| ~ ( empty @ SY217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1340]) ).
thf(1415,plain,
! [SV148: $i] :
( ( ( ~ ( empty @ SV148 ) )
= $true )
| ( ( SV148 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1341]) ).
thf(1416,plain,
! [SV149: $i,SV175: $i] :
( ( ~ ( empty @ SV175 )
| ~ ( in @ SV149 @ SV175 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1342]) ).
thf(1417,plain,
! [SV176: $i,SV150: $i] :
( ( ( SV150 = SV176 )
| ~ ( empty @ SV150 )
| ~ ( empty @ SV176 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1343]) ).
thf(1418,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1344]) ).
thf(1419,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1344]) ).
thf(1420,plain,
( ( ~ ~ ( ~ ( function @ sK25_A )
| ~ ( relation @ sK25_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1345]) ).
thf(1421,plain,
( ( ~ ( function_yielding @ sK25_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1345]) ).
thf(1422,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1346]) ).
thf(1423,plain,
( ( ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1346]) ).
thf(1424,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1347]) ).
thf(1425,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1347]) ).
thf(1426,plain,
( ( ~ ~ ( ~ ( function @ sK3_A )
| ~ ( relation @ sK3_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1348]) ).
thf(1427,plain,
( ( ~ ( transfinite_sequence @ sK3_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1348]) ).
thf(1428,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK27_A )
| ~ ( epsilon_transitive @ sK27_A ) )
| ~ ( epsilon_connected @ sK27_A ) )
| ~ ( ordinal @ sK27_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1349]) ).
thf(1429,plain,
( ( ~ ( natural @ sK27_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1349]) ).
thf(1430,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ sK18_A @ positive_rationals )
| ~ ~ ( empty @ sK18_A ) )
| ~ ( epsilon_transitive @ sK18_A ) )
| ~ ( epsilon_connected @ sK18_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1350]) ).
thf(1431,plain,
( ( ~ ( ordinal @ sK18_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1350]) ).
thf(1432,plain,
! [SV151: $i] :
( ( ~ ( element @ ( sK12_B @ SV151 ) @ ( powerset @ SV151 ) )
| ~ ( empty @ ( sK12_B @ SV151 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1351]) ).
thf(1433,plain,
( ( ~ ( relation @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1352]) ).
thf(1434,plain,
( ( ~ ( relation_empty_yielding @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1352]) ).
thf(1435,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( ordinal @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1353]) ).
thf(1436,plain,
( ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( natural @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1353]) ).
thf(1437,plain,
( ( ~ ~ ( ~ ~ ( ~ ( function @ sK14_A )
| ~ ( relation @ sK14_A ) )
| ~ ( transfinite_sequence @ sK14_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1354]) ).
thf(1438,plain,
( ( ~ ( ordinal_yielding @ sK14_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1354]) ).
thf(1439,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_transitive @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1355]) ).
thf(1440,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( ordinal @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1355]) ).
thf(1441,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ sK10_A @ positive_rationals )
| ~ ( empty @ sK10_A ) )
| ~ ( epsilon_transitive @ sK10_A ) )
| ~ ( epsilon_connected @ sK10_A ) )
| ~ ( ordinal @ sK10_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1356]) ).
thf(1442,plain,
( ( ~ ( natural @ sK10_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1356]) ).
thf(1443,plain,
( ( ~ ( finite @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1357]) ).
thf(1444,plain,
( ( ~ ~ ( finite @ ( relation_dom @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1357]) ).
thf(1445,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1358]) ).
thf(1446,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1358]) ).
thf(1447,plain,
( ( ~ ~ ( ~ ( relation @ sK4_A )
| ~ ( relation_empty_yielding @ sK4_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1359]) ).
thf(1448,plain,
( ( ~ ( function @ sK4_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1359]) ).
thf(1449,plain,
( ( ~ ~ ( ~ ~ ( ~ ( epsilon_connected @ sK22_A )
| ~ ( epsilon_transitive @ sK22_A ) )
| ~ ( ordinal @ sK22_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1360]) ).
thf(1450,plain,
( ( ~ ( being_limit_ordinal @ sK22_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1360]) ).
thf(1451,plain,
! [SV152: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV152 ) @ ( powerset @ SV152 ) )
| ~ ( empty @ ( sK17_B @ SV152 ) ) )
| ~ ( relation @ ( sK17_B @ SV152 ) ) )
| ~ ( function @ ( sK17_B @ SV152 ) ) )
| ~ ( one_to_one @ ( sK17_B @ SV152 ) ) )
| ~ ( epsilon_transitive @ ( sK17_B @ SV152 ) ) )
| ~ ( epsilon_connected @ ( sK17_B @ SV152 ) ) )
| ~ ( ordinal @ ( sK17_B @ SV152 ) ) )
| ~ ( natural @ ( sK17_B @ SV152 ) ) )
| ~ ( finite @ ( sK17_B @ SV152 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1361]) ).
thf(1452,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) )
| ~ ( epsilon_transitive @ empty_set ) )
| ~ ( epsilon_connected @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1362]) ).
thf(1453,plain,
( ( ~ ( ordinal @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1362]) ).
thf(1454,plain,
( ( ~ ! [SX0: $i,SX1: $i] : ( function @ ( first_projection @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1363]) ).
thf(1455,plain,
( ( ~ ! [SX0: $i,SX1: $i] : ( relation @ ( first_projection @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1363]) ).
thf(1456,plain,
( ( ~ ~ ( ~ ( function @ sK8_A )
| ~ ( relation @ sK8_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1364]) ).
thf(1457,plain,
( ( ~ ( one_to_one @ sK8_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1364]) ).
thf(1458,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK15_A )
| ~ ( relation @ sK15_A ) )
| ~ ( one_to_one @ sK15_A ) )
| ~ ( empty @ sK15_A ) )
| ~ ( epsilon_transitive @ sK15_A ) )
| ~ ( epsilon_connected @ sK15_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1365]) ).
thf(1459,plain,
( ( ~ ( ordinal @ sK15_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1365]) ).
thf(1460,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1366]) ).
thf(1461,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1366]) ).
thf(1462,plain,
( ( ~ ~ ( empty @ sK26_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1367]) ).
thf(1463,plain,
( ( ~ ( finite @ sK26_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1367]) ).
thf(1464,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1368]) ).
thf(1465,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1368]) ).
thf(1466,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( transfinite_sequence @ SX0 )
| ( epsilon_connected @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( transfinite_sequence @ SX0 )
| ( epsilon_transitive @ ( relation_dom @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1369]) ).
thf(1467,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( transfinite_sequence @ SX0 )
| ( ordinal @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1369]) ).
thf(1468,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( ordinal @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1370]) ).
thf(1469,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( natural @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1370]) ).
thf(1470,plain,
( ( ~ ~ ( ~ ( epsilon_connected @ sK23_A )
| ~ ( epsilon_transitive @ sK23_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1371]) ).
thf(1471,plain,
( ( ~ ( ordinal @ sK23_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1371]) ).
thf(1472,plain,
! [SV153: $i] :
( ( ~ ! [SY203: $i,SY204: $i] :
( ~ ( relation_of2 @ SY204 @ SV153 @ SY203 )
| ( relation_of2_as_subset @ SY204 @ SV153 @ SY203 ) )
| ~ ! [SY205: $i,SY206: $i] :
( ~ ( relation_of2_as_subset @ SY206 @ SV153 @ SY205 )
| ( relation_of2 @ SY206 @ SV153 @ SY205 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1372]) ).
thf(1473,plain,
! [SV154: $i] :
( ( ( empty @ SV154 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( element @ ( sK9_B @ SV154 ) @ ( powerset @ SV154 ) )
| ~ ~ ( empty @ ( sK9_B @ SV154 ) ) )
| ~ ( finite @ ( sK9_B @ SV154 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1373]) ).
thf(1474,plain,
( ( ~ ( function @ sK24_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1374]) ).
thf(1475,plain,
( ( ~ ( relation @ sK24_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1374]) ).
thf(1476,plain,
( ( ~ ~ ( ~ ( relation @ sK2_A )
| ~ ( relation_non_empty @ sK2_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1375]) ).
thf(1477,plain,
( ( ~ ( function @ sK2_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1375]) ).
thf(1478,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK7_A )
| ~ ( epsilon_transitive @ sK7_A ) )
| ~ ( epsilon_connected @ sK7_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1376]) ).
thf(1479,plain,
( ( ~ ( ordinal @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1376]) ).
thf(1480,plain,
( ( ~ ( empty @ sK21_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1377]) ).
thf(1481,plain,
( ( ~ ( relation @ sK21_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1377]) ).
thf(1482,plain,
! [SV155: $i] :
( ( ( ~ ( ordinal @ SV155 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY207: $i] :
( ~ ( element @ SY207 @ SV155 )
| ( epsilon_connected @ SY207 ) )
| ~ ! [SY208: $i] :
( ~ ( element @ SY208 @ SV155 )
| ( epsilon_transitive @ SY208 ) ) )
| ~ ! [SY209: $i] :
( ~ ( element @ SY209 @ SV155 )
| ( ordinal @ SY209 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1378]) ).
thf(1483,plain,
( ( ~ ~ ( empty @ sK13_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1379]) ).
thf(1484,plain,
( ( ~ ( relation @ sK13_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1379]) ).
thf(1485,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1380]) ).
thf(1486,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1380]) ).
thf(1487,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] : ( function @ ( first_projection_as_func_of @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] : ( quasi_total @ ( first_projection_as_func_of @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX0 @ SX1 ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1381]) ).
thf(1488,plain,
( ( ~ ! [SX0: $i,SX1: $i] : ( relation_of2_as_subset @ ( first_projection_as_func_of @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX0 @ SX1 ) @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1381]) ).
thf(1489,plain,
! [SV156: $i] :
( ( ( empty @ SV156 )
= $true )
| ( ( ~ ( ~ ( element @ ( sK20_B @ SV156 ) @ ( powerset @ SV156 ) )
| ~ ~ ( empty @ ( sK20_B @ SV156 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1382]) ).
thf(1490,plain,
( ( ~ ~ ( ~ ( empty @ sK16_A )
| ~ ( relation @ sK16_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1383]) ).
thf(1491,plain,
( ( ~ ( function @ sK16_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1383]) ).
thf(1492,plain,
! [SV157: $i] :
( ( ( empty @ SV157 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( element @ ( sK5_B @ SV157 ) @ ( powerset @ SV157 ) )
| ~ ~ ( empty @ ( sK5_B @ SV157 ) ) )
| ~ ( finite @ ( sK5_B @ SV157 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1384]) ).
thf(1493,plain,
! [SV158: $i,SV116: $i] :
( ( ( ~ ( in @ SV116 @ SV158 ) )
= $true )
| ( ( ~ ( in @ SV158 @ SV116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1385]) ).
thf(1494,plain,
! [SV117: $i] :
( ( ( empty @ SV117 )
= $false )
| ( ( finite @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1386]) ).
thf(1495,plain,
! [SV118: $i] :
( ( ( empty @ SV118 )
= $false )
| ( ( function @ SV118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1387]) ).
thf(1496,plain,
! [SV119: $i] :
( ( ( empty @ SV119 )
= $false )
| ( ( relation @ SV119 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1388]) ).
thf(1497,plain,
! [SV159: $i,SV120: $i,SV177: $i] :
( ( ~ ( element @ SV177 @ ( powerset @ ( cartesian_product2 @ SV120 @ SV159 ) ) )
| ( relation @ SV177 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1389]) ).
thf(1498,plain,
! [SV121: $i] :
( ( ( finite @ SV121 )
= $false )
| ( ( ! [SY177: $i] :
( ~ ( element @ SY177 @ ( powerset @ SV121 ) )
| ( finite @ SY177 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1390]) ).
thf(1499,plain,
! [SV122: $i] :
( ( ( ~ ( epsilon_connected @ SV122 ) )
= $true )
| ( ( ~ ( epsilon_transitive @ SV122 ) )
= $true )
| ( ( ordinal @ SV122 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1391]) ).
thf(1500,plain,
! [SV160: $i,SV123: $i,SV178: $i] :
( ( ~ ( function @ SV178 )
| ~ ( quasi_total @ SV178 @ SV123 @ SV160 )
| ~ ( relation_of2 @ SV178 @ SV123 @ SV160 )
| ! [SY218: $i] : ( element @ ( function_image @ SV123 @ SV160 @ SV178 @ SY218 ) @ ( powerset @ SV160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1392]) ).
thf(1501,plain,
! [SV161: $i,SV124: $i,SV179: $i] :
( ( ~ ( relation_of2_as_subset @ SV179 @ SV124 @ SV161 )
| ( element @ SV179 @ ( powerset @ ( cartesian_product2 @ SV124 @ SV161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1393]) ).
thf(1502,plain,
! [SV164: $i,SV128: $i] :
( ( ( ~ ( function @ SV128 )
| ~ ( relation @ SV128 )
| ~ ( finite @ SV164 ) )
= $true )
| ( ( finite @ ( relation_image @ SV128 @ SV164 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1396]) ).
thf(1503,plain,
! [SV165: $i,SV129: $i] :
( ( ( ~ ( finite @ SV129 )
| ~ ( finite @ SV165 ) )
= $true )
| ( ( finite @ ( cartesian_product2 @ SV129 @ SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1397]) ).
thf(1504,plain,
! [SV166: $i,SV131: $i] :
( ( ( ( empty @ SV131 )
| ( empty @ SV166 ) )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV131 @ SV166 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1399]) ).
thf(1505,plain,
! [SV132: $i] :
( ( ( empty @ SV132 )
= $true )
| ( ( ~ ( relation @ SV132 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV132 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1400]) ).
thf(1506,plain,
! [SV133: $i] :
( ( ( ~ ( relation @ SV133 )
| ~ ( relation_non_empty @ SV133 ) )
= $true )
| ( ( ~ ( function @ SV133 ) )
= $true )
| ( ( with_non_empty_elements @ ( relation_rng @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1401]) ).
thf(1507,plain,
! [SV134: $i] :
( ( ( empty @ SV134 )
= $true )
| ( ( ~ ( relation @ SV134 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV134 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1402]) ).
thf(1508,plain,
! [SV167: $i,SV135: $i,SV180: $i] :
( ( ~ ( function @ SV180 )
| ~ ( quasi_total @ SV180 @ SV135 @ SV167 )
| ~ ( relation_of2 @ SV180 @ SV135 @ SV167 )
| ! [SY219: $i] :
( ( function_image @ SV135 @ SV167 @ SV180 @ SY219 )
= ( relation_image @ SV180 @ SY219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1403]) ).
thf(1509,plain,
! [SV138: $i] :
( ( ( ~ ( function @ SV138 ) )
= $true )
| ( ( ~ ( relation @ SV138 ) )
= $true )
| ( ( ( function_image @ ( cartesian_product2 @ ( relation_dom @ SV138 ) @ ( relation_rng @ SV138 ) ) @ ( relation_dom @ SV138 ) @ ( first_projection_as_func_of @ ( relation_dom @ SV138 ) @ ( relation_rng @ SV138 ) ) @ SV138 )
= ( relation_dom @ SV138 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1405]) ).
thf(1510,plain,
! [SV139: $i,SV181: $i] :
( ( ( ~ ( finite @ SV181 )
| ~ ( subset @ SV139 @ SV181 ) )
= $true )
| ( ( finite @ SV139 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1406]) ).
thf(1511,plain,
! [SV140: $i,SV169: $i] :
( ( ( ~ ( function @ SV169 )
| ~ ( relation @ SV169 ) )
= $true )
| ( ( ~ ( finite @ SV140 )
| ( finite @ ( relation_image @ SV169 @ SV140 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1407]) ).
thf(1512,plain,
! [SV170: $i,SV141: $i] :
( ( ( ~ ( finite @ SV141 )
| ~ ( finite @ SV170 ) )
= $true )
| ( ( finite @ ( cartesian_product2 @ SV141 @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1408]) ).
thf(1513,plain,
! [SV171: $i,SV142: $i] :
( ( ( ~ ( in @ SV142 @ SV171 ) )
= $true )
| ( ( element @ SV142 @ SV171 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1409]) ).
thf(1514,plain,
! [SV143: $i] :
( ( ( relation @ SV143 )
= $false )
| ( ( subset @ SV143 @ ( cartesian_product2 @ ( relation_dom @ SV143 ) @ ( relation_rng @ SV143 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1410]) ).
thf(1515,plain,
! [SV144: $i] :
( ( ( ~ ( function @ SV144 ) )
= $true )
| ( ( ~ ( relation @ SV144 ) )
= $true )
| ( ( ~ ( finite @ ( relation_dom @ SV144 ) )
| ( finite @ ( relation_rng @ SV144 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1411]) ).
thf(1516,plain,
! [SV172: $i,SV145: $i] :
( ( ( ~ ( element @ SV145 @ SV172 ) )
= $true )
| ( ( ( empty @ SV172 )
| ( in @ SV145 @ SV172 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1412]) ).
thf(1517,plain,
! [SV146: $i,SV182: $i,SV173: $i] :
( ( ~ ( element @ SV173 @ ( powerset @ SV182 ) )
| ~ ( in @ SV146 @ SV173 )
| ( element @ SV146 @ SV182 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1413]) ).
thf(1518,plain,
! [SV147: $i,SV183: $i,SV174: $i] :
( ( ~ ( element @ SV174 @ ( powerset @ SV183 ) )
| ~ ( in @ SV147 @ SV174 )
| ~ ( empty @ SV183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1414]) ).
thf(1519,plain,
! [SV148: $i] :
( ( ( empty @ SV148 )
= $false )
| ( ( SV148 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1415]) ).
thf(1520,plain,
! [SV149: $i,SV175: $i] :
( ( ( ~ ( empty @ SV175 ) )
= $true )
| ( ( ~ ( in @ SV149 @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1416]) ).
thf(1521,plain,
! [SV176: $i,SV150: $i] :
( ( ( ( SV150 = SV176 )
| ~ ( empty @ SV150 ) )
= $true )
| ( ( ~ ( empty @ SV176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1417]) ).
thf(1522,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1418]) ).
thf(1523,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1419]) ).
thf(1524,plain,
( ( ~ ( ~ ( function @ sK25_A )
| ~ ( relation @ sK25_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1420]) ).
thf(1525,plain,
( ( function_yielding @ sK25_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1421]) ).
thf(1526,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1422]) ).
thf(1527,plain,
( ( relation_empty_yielding @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1423]) ).
thf(1528,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1424]) ).
thf(1529,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1425]) ).
thf(1530,plain,
( ( ~ ( ~ ( function @ sK3_A )
| ~ ( relation @ sK3_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1426]) ).
thf(1531,plain,
( ( transfinite_sequence @ sK3_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1427]) ).
thf(1532,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK27_A )
| ~ ( epsilon_transitive @ sK27_A ) )
| ~ ( epsilon_connected @ sK27_A ) )
| ~ ( ordinal @ sK27_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1428]) ).
thf(1533,plain,
( ( natural @ sK27_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1429]) ).
thf(1534,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ sK18_A @ positive_rationals )
| ~ ~ ( empty @ sK18_A ) )
| ~ ( epsilon_transitive @ sK18_A ) )
| ~ ( epsilon_connected @ sK18_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1430]) ).
thf(1535,plain,
( ( ordinal @ sK18_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1431]) ).
thf(1536,plain,
! [SV151: $i] :
( ( ~ ( element @ ( sK12_B @ SV151 ) @ ( powerset @ SV151 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1432]) ).
thf(1537,plain,
! [SV151: $i] :
( ( ~ ( empty @ ( sK12_B @ SV151 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1432]) ).
thf(1538,plain,
( ( relation @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1433]) ).
thf(1539,plain,
( ( relation_empty_yielding @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1434]) ).
thf(1540,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( ordinal @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1435]) ).
thf(1541,plain,
( ( ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( natural @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1436]) ).
thf(1542,plain,
( ( ~ ( ~ ~ ( ~ ( function @ sK14_A )
| ~ ( relation @ sK14_A ) )
| ~ ( transfinite_sequence @ sK14_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1437]) ).
thf(1543,plain,
( ( ordinal_yielding @ sK14_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1438]) ).
thf(1544,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_transitive @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1439]) ).
thf(1545,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( ordinal @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1440]) ).
thf(1546,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ sK10_A @ positive_rationals )
| ~ ( empty @ sK10_A ) )
| ~ ( epsilon_transitive @ sK10_A ) )
| ~ ( epsilon_connected @ sK10_A ) )
| ~ ( ordinal @ sK10_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1441]) ).
thf(1547,plain,
( ( natural @ sK10_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1442]) ).
thf(1548,plain,
( ( finite @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1443]) ).
thf(1549,plain,
( ( ~ ( finite @ ( relation_dom @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1444]) ).
thf(1550,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1445]) ).
thf(1551,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1446]) ).
thf(1552,plain,
( ( ~ ( ~ ( relation @ sK4_A )
| ~ ( relation_empty_yielding @ sK4_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1447]) ).
thf(1553,plain,
( ( function @ sK4_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1448]) ).
thf(1554,plain,
( ( ~ ( ~ ~ ( ~ ( epsilon_connected @ sK22_A )
| ~ ( epsilon_transitive @ sK22_A ) )
| ~ ( ordinal @ sK22_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1449]) ).
thf(1555,plain,
( ( being_limit_ordinal @ sK22_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1450]) ).
thf(1556,plain,
! [SV152: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV152 ) @ ( powerset @ SV152 ) )
| ~ ( empty @ ( sK17_B @ SV152 ) ) )
| ~ ( relation @ ( sK17_B @ SV152 ) ) )
| ~ ( function @ ( sK17_B @ SV152 ) ) )
| ~ ( one_to_one @ ( sK17_B @ SV152 ) ) )
| ~ ( epsilon_transitive @ ( sK17_B @ SV152 ) ) )
| ~ ( epsilon_connected @ ( sK17_B @ SV152 ) ) )
| ~ ( ordinal @ ( sK17_B @ SV152 ) ) )
| ~ ( natural @ ( sK17_B @ SV152 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1451]) ).
thf(1557,plain,
! [SV152: $i] :
( ( ~ ( finite @ ( sK17_B @ SV152 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1451]) ).
thf(1558,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) )
| ~ ( epsilon_transitive @ empty_set ) )
| ~ ( epsilon_connected @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1452]) ).
thf(1559,plain,
( ( ordinal @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1453]) ).
thf(1560,plain,
( ( ! [SX0: $i,SX1: $i] : ( function @ ( first_projection @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1454]) ).
thf(1561,plain,
( ( ! [SX0: $i,SX1: $i] : ( relation @ ( first_projection @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1455]) ).
thf(1562,plain,
( ( ~ ( ~ ( function @ sK8_A )
| ~ ( relation @ sK8_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1456]) ).
thf(1563,plain,
( ( one_to_one @ sK8_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1457]) ).
thf(1564,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK15_A )
| ~ ( relation @ sK15_A ) )
| ~ ( one_to_one @ sK15_A ) )
| ~ ( empty @ sK15_A ) )
| ~ ( epsilon_transitive @ sK15_A ) )
| ~ ( epsilon_connected @ sK15_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1458]) ).
thf(1565,plain,
( ( ordinal @ sK15_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1459]) ).
thf(1566,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1460]) ).
thf(1567,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1461]) ).
thf(1568,plain,
( ( ~ ( empty @ sK26_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1462]) ).
thf(1569,plain,
( ( finite @ sK26_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1463]) ).
thf(1570,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1464]) ).
thf(1571,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1465]) ).
thf(1572,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( transfinite_sequence @ SX0 )
| ( epsilon_connected @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( transfinite_sequence @ SX0 )
| ( epsilon_transitive @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1466]) ).
thf(1573,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( transfinite_sequence @ SX0 )
| ( ordinal @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1467]) ).
thf(1574,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( ordinal @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1468]) ).
thf(1575,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( natural @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1469]) ).
thf(1576,plain,
( ( ~ ( ~ ( epsilon_connected @ sK23_A )
| ~ ( epsilon_transitive @ sK23_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1470]) ).
thf(1577,plain,
( ( ordinal @ sK23_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1471]) ).
thf(1578,plain,
! [SV153: $i] :
( ( ~ ! [SY203: $i,SY204: $i] :
( ~ ( relation_of2 @ SY204 @ SV153 @ SY203 )
| ( relation_of2_as_subset @ SY204 @ SV153 @ SY203 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1472]) ).
thf(1579,plain,
! [SV153: $i] :
( ( ~ ! [SY205: $i,SY206: $i] :
( ~ ( relation_of2_as_subset @ SY206 @ SV153 @ SY205 )
| ( relation_of2 @ SY206 @ SV153 @ SY205 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1472]) ).
thf(1580,plain,
! [SV154: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK9_B @ SV154 ) @ ( powerset @ SV154 ) )
| ~ ~ ( empty @ ( sK9_B @ SV154 ) ) )
| ~ ( finite @ ( sK9_B @ SV154 ) ) )
= $false )
| ( ( empty @ SV154 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1473]) ).
thf(1581,plain,
( ( function @ sK24_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1474]) ).
thf(1582,plain,
( ( relation @ sK24_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1475]) ).
thf(1583,plain,
( ( ~ ( ~ ( relation @ sK2_A )
| ~ ( relation_non_empty @ sK2_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1476]) ).
thf(1584,plain,
( ( function @ sK2_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1477]) ).
thf(1585,plain,
( ( ~ ( ~ ~ ( ~ ~ ( empty @ sK7_A )
| ~ ( epsilon_transitive @ sK7_A ) )
| ~ ( epsilon_connected @ sK7_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1478]) ).
thf(1586,plain,
( ( ordinal @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1479]) ).
thf(1587,plain,
( ( empty @ sK21_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1480]) ).
thf(1588,plain,
( ( relation @ sK21_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1481]) ).
thf(1589,plain,
! [SV155: $i] :
( ( ( ordinal @ SV155 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY207: $i] :
( ~ ( element @ SY207 @ SV155 )
| ( epsilon_connected @ SY207 ) )
| ~ ! [SY208: $i] :
( ~ ( element @ SY208 @ SV155 )
| ( epsilon_transitive @ SY208 ) ) )
| ~ ! [SY209: $i] :
( ~ ( element @ SY209 @ SV155 )
| ( ordinal @ SY209 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1482]) ).
thf(1590,plain,
( ( ~ ( empty @ sK13_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1483]) ).
thf(1591,plain,
( ( relation @ sK13_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1484]) ).
thf(1592,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1485]) ).
thf(1593,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1486]) ).
thf(1594,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] : ( function @ ( first_projection_as_func_of @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] : ( quasi_total @ ( first_projection_as_func_of @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX0 @ SX1 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1487]) ).
thf(1595,plain,
( ( ! [SX0: $i,SX1: $i] : ( relation_of2_as_subset @ ( first_projection_as_func_of @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX0 @ SX1 ) @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1488]) ).
thf(1596,plain,
! [SV156: $i] :
( ( ( ~ ( element @ ( sK20_B @ SV156 ) @ ( powerset @ SV156 ) )
| ~ ~ ( empty @ ( sK20_B @ SV156 ) ) )
= $false )
| ( ( empty @ SV156 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1489]) ).
thf(1597,plain,
( ( ~ ( ~ ( empty @ sK16_A )
| ~ ( relation @ sK16_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1490]) ).
thf(1598,plain,
( ( function @ sK16_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1491]) ).
thf(1599,plain,
! [SV157: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK5_B @ SV157 ) @ ( powerset @ SV157 ) )
| ~ ~ ( empty @ ( sK5_B @ SV157 ) ) )
| ~ ( finite @ ( sK5_B @ SV157 ) ) )
= $false )
| ( ( empty @ SV157 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1492]) ).
thf(1600,plain,
! [SV158: $i,SV116: $i] :
( ( ( in @ SV116 @ SV158 )
= $false )
| ( ( ~ ( in @ SV158 @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1493]) ).
thf(1601,plain,
! [SV159: $i,SV120: $i,SV177: $i] :
( ( ( ~ ( element @ SV177 @ ( powerset @ ( cartesian_product2 @ SV120 @ SV159 ) ) ) )
= $true )
| ( ( relation @ SV177 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1497]) ).
thf(1602,plain,
! [SV121: $i,SV184: $i] :
( ( ( ~ ( element @ SV184 @ ( powerset @ SV121 ) )
| ( finite @ SV184 ) )
= $true )
| ( ( finite @ SV121 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1498]) ).
thf(1603,plain,
! [SV122: $i] :
( ( ( epsilon_connected @ SV122 )
= $false )
| ( ( ~ ( epsilon_transitive @ SV122 ) )
= $true )
| ( ( ordinal @ SV122 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1499]) ).
thf(1604,plain,
! [SV160: $i,SV123: $i,SV178: $i] :
( ( ( ~ ( function @ SV178 )
| ~ ( quasi_total @ SV178 @ SV123 @ SV160 )
| ~ ( relation_of2 @ SV178 @ SV123 @ SV160 ) )
= $true )
| ( ( ! [SY218: $i] : ( element @ ( function_image @ SV123 @ SV160 @ SV178 @ SY218 ) @ ( powerset @ SV160 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1500]) ).
thf(1605,plain,
! [SV161: $i,SV124: $i,SV179: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV179 @ SV124 @ SV161 ) )
= $true )
| ( ( element @ SV179 @ ( powerset @ ( cartesian_product2 @ SV124 @ SV161 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1501]) ).
thf(1606,plain,
! [SV164: $i,SV128: $i] :
( ( ( ~ ( function @ SV128 )
| ~ ( relation @ SV128 ) )
= $true )
| ( ( ~ ( finite @ SV164 ) )
= $true )
| ( ( finite @ ( relation_image @ SV128 @ SV164 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1502]) ).
thf(1607,plain,
! [SV165: $i,SV129: $i] :
( ( ( ~ ( finite @ SV129 ) )
= $true )
| ( ( ~ ( finite @ SV165 ) )
= $true )
| ( ( finite @ ( cartesian_product2 @ SV129 @ SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1503]) ).
thf(1608,plain,
! [SV166: $i,SV131: $i] :
( ( ( empty @ SV131 )
= $true )
| ( ( empty @ SV166 )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV131 @ SV166 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1504]) ).
thf(1609,plain,
! [SV132: $i] :
( ( ( relation @ SV132 )
= $false )
| ( ( empty @ SV132 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV132 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1505]) ).
thf(1610,plain,
! [SV133: $i] :
( ( ( ~ ( relation @ SV133 ) )
= $true )
| ( ( ~ ( relation_non_empty @ SV133 ) )
= $true )
| ( ( ~ ( function @ SV133 ) )
= $true )
| ( ( with_non_empty_elements @ ( relation_rng @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1506]) ).
thf(1611,plain,
! [SV134: $i] :
( ( ( relation @ SV134 )
= $false )
| ( ( empty @ SV134 )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV134 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1507]) ).
thf(1612,plain,
! [SV167: $i,SV135: $i,SV180: $i] :
( ( ( ~ ( function @ SV180 )
| ~ ( quasi_total @ SV180 @ SV135 @ SV167 )
| ~ ( relation_of2 @ SV180 @ SV135 @ SV167 ) )
= $true )
| ( ( ! [SY219: $i] :
( ( function_image @ SV135 @ SV167 @ SV180 @ SY219 )
= ( relation_image @ SV180 @ SY219 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1508]) ).
thf(1613,plain,
! [SV138: $i] :
( ( ( function @ SV138 )
= $false )
| ( ( ~ ( relation @ SV138 ) )
= $true )
| ( ( ( function_image @ ( cartesian_product2 @ ( relation_dom @ SV138 ) @ ( relation_rng @ SV138 ) ) @ ( relation_dom @ SV138 ) @ ( first_projection_as_func_of @ ( relation_dom @ SV138 ) @ ( relation_rng @ SV138 ) ) @ SV138 )
= ( relation_dom @ SV138 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1509]) ).
thf(1614,plain,
! [SV139: $i,SV181: $i] :
( ( ( ~ ( finite @ SV181 ) )
= $true )
| ( ( ~ ( subset @ SV139 @ SV181 ) )
= $true )
| ( ( finite @ SV139 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1510]) ).
thf(1615,plain,
! [SV140: $i,SV169: $i] :
( ( ( ~ ( function @ SV169 ) )
= $true )
| ( ( ~ ( relation @ SV169 ) )
= $true )
| ( ( ~ ( finite @ SV140 )
| ( finite @ ( relation_image @ SV169 @ SV140 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1511]) ).
thf(1616,plain,
! [SV170: $i,SV141: $i] :
( ( ( ~ ( finite @ SV141 ) )
= $true )
| ( ( ~ ( finite @ SV170 ) )
= $true )
| ( ( finite @ ( cartesian_product2 @ SV141 @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1512]) ).
thf(1617,plain,
! [SV171: $i,SV142: $i] :
( ( ( in @ SV142 @ SV171 )
= $false )
| ( ( element @ SV142 @ SV171 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1513]) ).
thf(1618,plain,
! [SV144: $i] :
( ( ( function @ SV144 )
= $false )
| ( ( ~ ( relation @ SV144 ) )
= $true )
| ( ( ~ ( finite @ ( relation_dom @ SV144 ) )
| ( finite @ ( relation_rng @ SV144 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1515]) ).
thf(1619,plain,
! [SV172: $i,SV145: $i] :
( ( ( element @ SV145 @ SV172 )
= $false )
| ( ( ( empty @ SV172 )
| ( in @ SV145 @ SV172 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1516]) ).
thf(1620,plain,
! [SV146: $i,SV182: $i,SV173: $i] :
( ( ( ~ ( element @ SV173 @ ( powerset @ SV182 ) )
| ~ ( in @ SV146 @ SV173 ) )
= $true )
| ( ( element @ SV146 @ SV182 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1517]) ).
thf(1621,plain,
! [SV147: $i,SV183: $i,SV174: $i] :
( ( ( ~ ( element @ SV174 @ ( powerset @ SV183 ) )
| ~ ( in @ SV147 @ SV174 ) )
= $true )
| ( ( ~ ( empty @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1518]) ).
thf(1622,plain,
! [SV149: $i,SV175: $i] :
( ( ( empty @ SV175 )
= $false )
| ( ( ~ ( in @ SV149 @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1520]) ).
thf(1623,plain,
! [SV176: $i,SV150: $i] :
( ( ( SV150 = SV176 )
= $true )
| ( ( ~ ( empty @ SV150 ) )
= $true )
| ( ( ~ ( empty @ SV176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1521]) ).
thf(1624,plain,
( ( ~ ( function @ sK25_A )
| ~ ( relation @ sK25_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1524]) ).
thf(1625,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1526]) ).
thf(1626,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1528]) ).
thf(1627,plain,
! [SV185: $i] :
( ( ~ ( empty @ SV185 )
| ~ ( relation @ SV185 )
| ~ ( function @ SV185 )
| ( one_to_one @ SV185 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1529]) ).
thf(1628,plain,
( ( ~ ( function @ sK3_A )
| ~ ( relation @ sK3_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1530]) ).
thf(1629,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK27_A )
| ~ ( epsilon_transitive @ sK27_A ) )
| ~ ( epsilon_connected @ sK27_A ) )
| ~ ( ordinal @ sK27_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1532]) ).
thf(1630,plain,
( ( ~ ~ ( ~ ~ ( ~ ( element @ sK18_A @ positive_rationals )
| ~ ~ ( empty @ sK18_A ) )
| ~ ( epsilon_transitive @ sK18_A ) )
| ~ ( epsilon_connected @ sK18_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1534]) ).
thf(1631,plain,
! [SV151: $i] :
( ( element @ ( sK12_B @ SV151 ) @ ( powerset @ SV151 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1536]) ).
thf(1632,plain,
! [SV151: $i] :
( ( empty @ ( sK12_B @ SV151 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1537]) ).
thf(1633,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( ordinal @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1540]) ).
thf(1634,plain,
! [SV186: $i] :
( ( ~ ( element @ SV186 @ positive_rationals )
| ~ ( ordinal @ SV186 )
| ( natural @ SV186 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1541]) ).
thf(1635,plain,
( ( ~ ~ ( ~ ( function @ sK14_A )
| ~ ( relation @ sK14_A ) )
| ~ ( transfinite_sequence @ sK14_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1542]) ).
thf(1636,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1544]) ).
thf(1637,plain,
! [SV187: $i] :
( ( ~ ( empty @ SV187 )
| ( ordinal @ SV187 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1545]) ).
thf(1638,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ sK10_A @ positive_rationals )
| ~ ( empty @ sK10_A ) )
| ~ ( epsilon_transitive @ sK10_A ) )
| ~ ( epsilon_connected @ sK10_A ) )
| ~ ( ordinal @ sK10_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1546]) ).
thf(1639,plain,
( ( finite @ ( relation_dom @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1549]) ).
thf(1640,plain,
! [SV188: $i] :
( ( ! [SY220: $i] :
( ~ ( element @ SV188 @ ( powerset @ SY220 ) )
| ( subset @ SV188 @ SY220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1550]) ).
thf(1641,plain,
! [SV189: $i] :
( ( ! [SY221: $i] :
( ~ ( subset @ SV189 @ SY221 )
| ( element @ SV189 @ ( powerset @ SY221 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1551]) ).
thf(1642,plain,
( ( ~ ( relation @ sK4_A )
| ~ ( relation_empty_yielding @ sK4_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1552]) ).
thf(1643,plain,
( ( ~ ~ ( ~ ( epsilon_connected @ sK22_A )
| ~ ( epsilon_transitive @ sK22_A ) )
| ~ ( ordinal @ sK22_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1554]) ).
thf(1644,plain,
! [SV152: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV152 ) @ ( powerset @ SV152 ) )
| ~ ( empty @ ( sK17_B @ SV152 ) ) )
| ~ ( relation @ ( sK17_B @ SV152 ) ) )
| ~ ( function @ ( sK17_B @ SV152 ) ) )
| ~ ( one_to_one @ ( sK17_B @ SV152 ) ) )
| ~ ( epsilon_transitive @ ( sK17_B @ SV152 ) ) )
| ~ ( epsilon_connected @ ( sK17_B @ SV152 ) ) )
| ~ ( ordinal @ ( sK17_B @ SV152 ) ) )
| ~ ( natural @ ( sK17_B @ SV152 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1556]) ).
thf(1645,plain,
! [SV152: $i] :
( ( finite @ ( sK17_B @ SV152 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1557]) ).
thf(1646,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) )
| ~ ( epsilon_transitive @ empty_set ) )
| ~ ( epsilon_connected @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1558]) ).
thf(1647,plain,
! [SV190: $i] :
( ( ! [SY222: $i] : ( function @ ( first_projection @ SV190 @ SY222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1560]) ).
thf(1648,plain,
! [SV191: $i] :
( ( ! [SY223: $i] : ( relation @ ( first_projection @ SV191 @ SY223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1561]) ).
thf(1649,plain,
( ( ~ ( function @ sK8_A )
| ~ ( relation @ sK8_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1562]) ).
thf(1650,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK15_A )
| ~ ( relation @ sK15_A ) )
| ~ ( one_to_one @ sK15_A ) )
| ~ ( empty @ sK15_A ) )
| ~ ( epsilon_transitive @ sK15_A ) )
| ~ ( epsilon_connected @ sK15_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1564]) ).
thf(1651,plain,
! [SV192: $i] :
( ( ~ ( ordinal @ SV192 )
| ( epsilon_connected @ SV192 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1566]) ).
thf(1652,plain,
! [SV193: $i] :
( ( ~ ( ordinal @ SV193 )
| ( epsilon_transitive @ SV193 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1567]) ).
thf(1653,plain,
( ( empty @ sK26_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1568]) ).
thf(1654,plain,
! [SV194: $i] :
( ( ~ ( empty @ SV194 )
| ( empty @ ( relation_dom @ SV194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1570]) ).
thf(1655,plain,
! [SV195: $i] :
( ( ~ ( empty @ SV195 )
| ( relation @ ( relation_dom @ SV195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1571]) ).
thf(1656,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( transfinite_sequence @ SX0 )
| ( epsilon_connected @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( transfinite_sequence @ SX0 )
| ( epsilon_transitive @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1572]) ).
thf(1657,plain,
! [SV196: $i] :
( ( ~ ( function @ SV196 )
| ~ ( relation @ SV196 )
| ~ ( transfinite_sequence @ SV196 )
| ( ordinal @ ( relation_dom @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1573]) ).
thf(1658,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( ordinal @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1574]) ).
thf(1659,plain,
! [SV197: $i] :
( ( ~ ( empty @ SV197 )
| ~ ( ordinal @ SV197 )
| ( natural @ SV197 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1575]) ).
thf(1660,plain,
( ( ~ ( epsilon_connected @ sK23_A )
| ~ ( epsilon_transitive @ sK23_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1576]) ).
thf(1661,plain,
! [SV153: $i] :
( ( ! [SY203: $i,SY204: $i] :
( ~ ( relation_of2 @ SY204 @ SV153 @ SY203 )
| ( relation_of2_as_subset @ SY204 @ SV153 @ SY203 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1578]) ).
thf(1662,plain,
! [SV153: $i] :
( ( ! [SY205: $i,SY206: $i] :
( ~ ( relation_of2_as_subset @ SY206 @ SV153 @ SY205 )
| ( relation_of2 @ SY206 @ SV153 @ SY205 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1579]) ).
thf(1663,plain,
! [SV154: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK9_B @ SV154 ) @ ( powerset @ SV154 ) )
| ~ ~ ( empty @ ( sK9_B @ SV154 ) ) ) )
= $false )
| ( ( empty @ SV154 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1580]) ).
thf(1664,plain,
! [SV154: $i] :
( ( ( ~ ( finite @ ( sK9_B @ SV154 ) ) )
= $false )
| ( ( empty @ SV154 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1580]) ).
thf(1665,plain,
( ( ~ ( relation @ sK2_A )
| ~ ( relation_non_empty @ sK2_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1583]) ).
thf(1666,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK7_A )
| ~ ( epsilon_transitive @ sK7_A ) )
| ~ ( epsilon_connected @ sK7_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1585]) ).
thf(1667,plain,
! [SV155: $i] :
( ( ( ~ ~ ( ~ ! [SY207: $i] :
( ~ ( element @ SY207 @ SV155 )
| ( epsilon_connected @ SY207 ) )
| ~ ! [SY208: $i] :
( ~ ( element @ SY208 @ SV155 )
| ( epsilon_transitive @ SY208 ) ) )
| ~ ! [SY209: $i] :
( ~ ( element @ SY209 @ SV155 )
| ( ordinal @ SY209 ) ) )
= $false )
| ( ( ordinal @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1589]) ).
thf(1668,plain,
( ( empty @ sK13_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1590]) ).
thf(1669,plain,
! [SV198: $i] :
( ( ~ ( empty @ SV198 )
| ( empty @ ( relation_rng @ SV198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1592]) ).
thf(1670,plain,
! [SV199: $i] :
( ( ~ ( empty @ SV199 )
| ( relation @ ( relation_rng @ SV199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1593]) ).
thf(1671,plain,
( ( ~ ! [SX0: $i,SX1: $i] : ( function @ ( first_projection_as_func_of @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] : ( quasi_total @ ( first_projection_as_func_of @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX0 @ SX1 ) @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1594]) ).
thf(1672,plain,
! [SV200: $i] :
( ( ! [SY224: $i] : ( relation_of2_as_subset @ ( first_projection_as_func_of @ SV200 @ SY224 ) @ ( cartesian_product2 @ SV200 @ SY224 ) @ SV200 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1595]) ).
thf(1673,plain,
! [SV156: $i] :
( ( ( ~ ( element @ ( sK20_B @ SV156 ) @ ( powerset @ SV156 ) ) )
= $false )
| ( ( empty @ SV156 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1596]) ).
thf(1674,plain,
! [SV156: $i] :
( ( ( ~ ~ ( empty @ ( sK20_B @ SV156 ) ) )
= $false )
| ( ( empty @ SV156 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1596]) ).
thf(1675,plain,
( ( ~ ( empty @ sK16_A )
| ~ ( relation @ sK16_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1597]) ).
thf(1676,plain,
! [SV157: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK5_B @ SV157 ) @ ( powerset @ SV157 ) )
| ~ ~ ( empty @ ( sK5_B @ SV157 ) ) ) )
= $false )
| ( ( empty @ SV157 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1599]) ).
thf(1677,plain,
! [SV157: $i] :
( ( ( ~ ( finite @ ( sK5_B @ SV157 ) ) )
= $false )
| ( ( empty @ SV157 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1599]) ).
thf(1678,plain,
! [SV116: $i,SV158: $i] :
( ( ( in @ SV158 @ SV116 )
= $false )
| ( ( in @ SV116 @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1600]) ).
thf(1679,plain,
! [SV159: $i,SV120: $i,SV177: $i] :
( ( ( element @ SV177 @ ( powerset @ ( cartesian_product2 @ SV120 @ SV159 ) ) )
= $false )
| ( ( relation @ SV177 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1601]) ).
thf(1680,plain,
! [SV121: $i,SV184: $i] :
( ( ( ~ ( element @ SV184 @ ( powerset @ SV121 ) ) )
= $true )
| ( ( finite @ SV184 )
= $true )
| ( ( finite @ SV121 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1602]) ).
thf(1681,plain,
! [SV122: $i] :
( ( ( epsilon_transitive @ SV122 )
= $false )
| ( ( epsilon_connected @ SV122 )
= $false )
| ( ( ordinal @ SV122 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1603]) ).
thf(1682,plain,
! [SV160: $i,SV123: $i,SV178: $i] :
( ( ( ~ ( function @ SV178 )
| ~ ( quasi_total @ SV178 @ SV123 @ SV160 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV178 @ SV123 @ SV160 ) )
= $true )
| ( ( ! [SY218: $i] : ( element @ ( function_image @ SV123 @ SV160 @ SV178 @ SY218 ) @ ( powerset @ SV160 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1604]) ).
thf(1683,plain,
! [SV161: $i,SV124: $i,SV179: $i] :
( ( ( relation_of2_as_subset @ SV179 @ SV124 @ SV161 )
= $false )
| ( ( element @ SV179 @ ( powerset @ ( cartesian_product2 @ SV124 @ SV161 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1605]) ).
thf(1684,plain,
! [SV164: $i,SV128: $i] :
( ( ( ~ ( function @ SV128 ) )
= $true )
| ( ( ~ ( relation @ SV128 ) )
= $true )
| ( ( ~ ( finite @ SV164 ) )
= $true )
| ( ( finite @ ( relation_image @ SV128 @ SV164 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1606]) ).
thf(1685,plain,
! [SV165: $i,SV129: $i] :
( ( ( finite @ SV129 )
= $false )
| ( ( ~ ( finite @ SV165 ) )
= $true )
| ( ( finite @ ( cartesian_product2 @ SV129 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1607]) ).
thf(1686,plain,
! [SV166: $i,SV131: $i] :
( ( ( empty @ ( cartesian_product2 @ SV131 @ SV166 ) )
= $false )
| ( ( empty @ SV166 )
= $true )
| ( ( empty @ SV131 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1608]) ).
thf(1687,plain,
! [SV132: $i] :
( ( ( empty @ ( relation_dom @ SV132 ) )
= $false )
| ( ( empty @ SV132 )
= $true )
| ( ( relation @ SV132 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1609]) ).
thf(1688,plain,
! [SV133: $i] :
( ( ( relation @ SV133 )
= $false )
| ( ( ~ ( relation_non_empty @ SV133 ) )
= $true )
| ( ( ~ ( function @ SV133 ) )
= $true )
| ( ( with_non_empty_elements @ ( relation_rng @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1610]) ).
thf(1689,plain,
! [SV134: $i] :
( ( ( empty @ ( relation_rng @ SV134 ) )
= $false )
| ( ( empty @ SV134 )
= $true )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1611]) ).
thf(1690,plain,
! [SV167: $i,SV135: $i,SV180: $i] :
( ( ( ~ ( function @ SV180 )
| ~ ( quasi_total @ SV180 @ SV135 @ SV167 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV180 @ SV135 @ SV167 ) )
= $true )
| ( ( ! [SY219: $i] :
( ( function_image @ SV135 @ SV167 @ SV180 @ SY219 )
= ( relation_image @ SV180 @ SY219 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1612]) ).
thf(1691,plain,
! [SV138: $i] :
( ( ( relation @ SV138 )
= $false )
| ( ( function @ SV138 )
= $false )
| ( ( ( function_image @ ( cartesian_product2 @ ( relation_dom @ SV138 ) @ ( relation_rng @ SV138 ) ) @ ( relation_dom @ SV138 ) @ ( first_projection_as_func_of @ ( relation_dom @ SV138 ) @ ( relation_rng @ SV138 ) ) @ SV138 )
= ( relation_dom @ SV138 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1613]) ).
thf(1692,plain,
! [SV139: $i,SV181: $i] :
( ( ( finite @ SV181 )
= $false )
| ( ( ~ ( subset @ SV139 @ SV181 ) )
= $true )
| ( ( finite @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1614]) ).
thf(1693,plain,
! [SV140: $i,SV169: $i] :
( ( ( function @ SV169 )
= $false )
| ( ( ~ ( relation @ SV169 ) )
= $true )
| ( ( ~ ( finite @ SV140 )
| ( finite @ ( relation_image @ SV169 @ SV140 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1615]) ).
thf(1694,plain,
! [SV170: $i,SV141: $i] :
( ( ( finite @ SV141 )
= $false )
| ( ( ~ ( finite @ SV170 ) )
= $true )
| ( ( finite @ ( cartesian_product2 @ SV141 @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1616]) ).
thf(1695,plain,
! [SV144: $i] :
( ( ( relation @ SV144 )
= $false )
| ( ( function @ SV144 )
= $false )
| ( ( ~ ( finite @ ( relation_dom @ SV144 ) )
| ( finite @ ( relation_rng @ SV144 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1618]) ).
thf(1696,plain,
! [SV145: $i,SV172: $i] :
( ( ( empty @ SV172 )
= $true )
| ( ( in @ SV145 @ SV172 )
= $true )
| ( ( element @ SV145 @ SV172 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1619]) ).
thf(1697,plain,
! [SV146: $i,SV182: $i,SV173: $i] :
( ( ( ~ ( element @ SV173 @ ( powerset @ SV182 ) ) )
= $true )
| ( ( ~ ( in @ SV146 @ SV173 ) )
= $true )
| ( ( element @ SV146 @ SV182 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1620]) ).
thf(1698,plain,
! [SV147: $i,SV183: $i,SV174: $i] :
( ( ( ~ ( element @ SV174 @ ( powerset @ SV183 ) ) )
= $true )
| ( ( ~ ( in @ SV147 @ SV174 ) )
= $true )
| ( ( ~ ( empty @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1621]) ).
thf(1699,plain,
! [SV175: $i,SV149: $i] :
( ( ( in @ SV149 @ SV175 )
= $false )
| ( ( empty @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1622]) ).
thf(1700,plain,
! [SV176: $i,SV150: $i] :
( ( ( empty @ SV150 )
= $false )
| ( ( SV150 = SV176 )
= $true )
| ( ( ~ ( empty @ SV176 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1623]) ).
thf(1701,plain,
( ( ~ ( function @ sK25_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1624]) ).
thf(1702,plain,
( ( ~ ( relation @ sK25_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1624]) ).
thf(1703,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1625]) ).
thf(1704,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1625]) ).
thf(1705,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1626]) ).
thf(1706,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1626]) ).
thf(1707,plain,
! [SV185: $i] :
( ( ( ~ ( empty @ SV185 )
| ~ ( relation @ SV185 )
| ~ ( function @ SV185 ) )
= $true )
| ( ( one_to_one @ SV185 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1627]) ).
thf(1708,plain,
( ( ~ ( function @ sK3_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1628]) ).
thf(1709,plain,
( ( ~ ( relation @ sK3_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1628]) ).
thf(1710,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK27_A )
| ~ ( epsilon_transitive @ sK27_A ) )
| ~ ( epsilon_connected @ sK27_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1629]) ).
thf(1711,plain,
( ( ~ ( ordinal @ sK27_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1629]) ).
thf(1712,plain,
( ( ~ ~ ( ~ ~ ( ~ ( element @ sK18_A @ positive_rationals )
| ~ ~ ( empty @ sK18_A ) )
| ~ ( epsilon_transitive @ sK18_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1630]) ).
thf(1713,plain,
( ( ~ ( epsilon_connected @ sK18_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1630]) ).
thf(1714,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1633]) ).
thf(1715,plain,
( ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( ordinal @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1633]) ).
thf(1716,plain,
! [SV186: $i] :
( ( ( ~ ( element @ SV186 @ positive_rationals ) )
= $true )
| ( ( ~ ( ordinal @ SV186 )
| ( natural @ SV186 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1634]) ).
thf(1717,plain,
( ( ~ ~ ( ~ ( function @ sK14_A )
| ~ ( relation @ sK14_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1635]) ).
thf(1718,plain,
( ( ~ ( transfinite_sequence @ sK14_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1635]) ).
thf(1719,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_connected @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1636]) ).
thf(1720,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1636]) ).
thf(1721,plain,
! [SV187: $i] :
( ( ( ~ ( empty @ SV187 ) )
= $true )
| ( ( ordinal @ SV187 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1637]) ).
thf(1722,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ sK10_A @ positive_rationals )
| ~ ( empty @ sK10_A ) )
| ~ ( epsilon_transitive @ sK10_A ) )
| ~ ( epsilon_connected @ sK10_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1638]) ).
thf(1723,plain,
( ( ~ ( ordinal @ sK10_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1638]) ).
thf(1724,plain,
! [SV201: $i,SV188: $i] :
( ( ~ ( element @ SV188 @ ( powerset @ SV201 ) )
| ( subset @ SV188 @ SV201 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(1725,plain,
! [SV202: $i,SV189: $i] :
( ( ~ ( subset @ SV189 @ SV202 )
| ( element @ SV189 @ ( powerset @ SV202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1641]) ).
thf(1726,plain,
( ( ~ ( relation @ sK4_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1642]) ).
thf(1727,plain,
( ( ~ ( relation_empty_yielding @ sK4_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1642]) ).
thf(1728,plain,
( ( ~ ~ ( ~ ( epsilon_connected @ sK22_A )
| ~ ( epsilon_transitive @ sK22_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1643]) ).
thf(1729,plain,
( ( ~ ( ordinal @ sK22_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1643]) ).
thf(1730,plain,
! [SV152: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV152 ) @ ( powerset @ SV152 ) )
| ~ ( empty @ ( sK17_B @ SV152 ) ) )
| ~ ( relation @ ( sK17_B @ SV152 ) ) )
| ~ ( function @ ( sK17_B @ SV152 ) ) )
| ~ ( one_to_one @ ( sK17_B @ SV152 ) ) )
| ~ ( epsilon_transitive @ ( sK17_B @ SV152 ) ) )
| ~ ( epsilon_connected @ ( sK17_B @ SV152 ) ) )
| ~ ( ordinal @ ( sK17_B @ SV152 ) ) )
| ~ ( natural @ ( sK17_B @ SV152 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1644]) ).
thf(1731,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) )
| ~ ( epsilon_transitive @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1646]) ).
thf(1732,plain,
( ( ~ ( epsilon_connected @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1646]) ).
thf(1733,plain,
! [SV203: $i,SV190: $i] :
( ( function @ ( first_projection @ SV190 @ SV203 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1647]) ).
thf(1734,plain,
! [SV204: $i,SV191: $i] :
( ( relation @ ( first_projection @ SV191 @ SV204 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1648]) ).
thf(1735,plain,
( ( ~ ( function @ sK8_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1649]) ).
thf(1736,plain,
( ( ~ ( relation @ sK8_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1649]) ).
thf(1737,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK15_A )
| ~ ( relation @ sK15_A ) )
| ~ ( one_to_one @ sK15_A ) )
| ~ ( empty @ sK15_A ) )
| ~ ( epsilon_transitive @ sK15_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1650]) ).
thf(1738,plain,
( ( ~ ( epsilon_connected @ sK15_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1650]) ).
thf(1739,plain,
! [SV192: $i] :
( ( ( ~ ( ordinal @ SV192 ) )
= $true )
| ( ( epsilon_connected @ SV192 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1651]) ).
thf(1740,plain,
! [SV193: $i] :
( ( ( ~ ( ordinal @ SV193 ) )
= $true )
| ( ( epsilon_transitive @ SV193 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1652]) ).
thf(1741,plain,
! [SV194: $i] :
( ( ( ~ ( empty @ SV194 ) )
= $true )
| ( ( empty @ ( relation_dom @ SV194 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1654]) ).
thf(1742,plain,
! [SV195: $i] :
( ( ( ~ ( empty @ SV195 ) )
= $true )
| ( ( relation @ ( relation_dom @ SV195 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1655]) ).
thf(1743,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( transfinite_sequence @ SX0 )
| ( epsilon_connected @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1656]) ).
thf(1744,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( transfinite_sequence @ SX0 )
| ( epsilon_transitive @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1656]) ).
thf(1745,plain,
! [SV196: $i] :
( ( ( ~ ( function @ SV196 )
| ~ ( relation @ SV196 )
| ~ ( transfinite_sequence @ SV196 ) )
= $true )
| ( ( ordinal @ ( relation_dom @ SV196 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1657]) ).
thf(1746,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1658]) ).
thf(1747,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( ordinal @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1658]) ).
thf(1748,plain,
! [SV197: $i] :
( ( ( ~ ( empty @ SV197 )
| ~ ( ordinal @ SV197 ) )
= $true )
| ( ( natural @ SV197 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1659]) ).
thf(1749,plain,
( ( ~ ( epsilon_connected @ sK23_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1660]) ).
thf(1750,plain,
( ( ~ ( epsilon_transitive @ sK23_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1660]) ).
thf(1751,plain,
! [SV205: $i,SV153: $i] :
( ( ! [SY225: $i] :
( ~ ( relation_of2 @ SY225 @ SV153 @ SV205 )
| ( relation_of2_as_subset @ SY225 @ SV153 @ SV205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1661]) ).
thf(1752,plain,
! [SV206: $i,SV153: $i] :
( ( ! [SY226: $i] :
( ~ ( relation_of2_as_subset @ SY226 @ SV153 @ SV206 )
| ( relation_of2 @ SY226 @ SV153 @ SV206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1662]) ).
thf(1753,plain,
! [SV154: $i] :
( ( ( ~ ( ~ ( element @ ( sK9_B @ SV154 ) @ ( powerset @ SV154 ) )
| ~ ~ ( empty @ ( sK9_B @ SV154 ) ) ) )
= $true )
| ( ( empty @ SV154 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1663]) ).
thf(1754,plain,
! [SV154: $i] :
( ( ( finite @ ( sK9_B @ SV154 ) )
= $true )
| ( ( empty @ SV154 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1664]) ).
thf(1755,plain,
( ( ~ ( relation @ sK2_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1665]) ).
thf(1756,plain,
( ( ~ ( relation_non_empty @ sK2_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1665]) ).
thf(1757,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK7_A )
| ~ ( epsilon_transitive @ sK7_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1666]) ).
thf(1758,plain,
( ( ~ ( epsilon_connected @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1666]) ).
thf(1759,plain,
! [SV155: $i] :
( ( ( ~ ~ ( ~ ! [SY207: $i] :
( ~ ( element @ SY207 @ SV155 )
| ( epsilon_connected @ SY207 ) )
| ~ ! [SY208: $i] :
( ~ ( element @ SY208 @ SV155 )
| ( epsilon_transitive @ SY208 ) ) ) )
= $false )
| ( ( ordinal @ SV155 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1667]) ).
thf(1760,plain,
! [SV155: $i] :
( ( ( ~ ! [SY209: $i] :
( ~ ( element @ SY209 @ SV155 )
| ( ordinal @ SY209 ) ) )
= $false )
| ( ( ordinal @ SV155 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1667]) ).
thf(1761,plain,
! [SV198: $i] :
( ( ( ~ ( empty @ SV198 ) )
= $true )
| ( ( empty @ ( relation_rng @ SV198 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1669]) ).
thf(1762,plain,
! [SV199: $i] :
( ( ( ~ ( empty @ SV199 ) )
= $true )
| ( ( relation @ ( relation_rng @ SV199 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1670]) ).
thf(1763,plain,
( ( ~ ! [SX0: $i,SX1: $i] : ( function @ ( first_projection_as_func_of @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1671]) ).
thf(1764,plain,
( ( ~ ! [SX0: $i,SX1: $i] : ( quasi_total @ ( first_projection_as_func_of @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX0 @ SX1 ) @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1671]) ).
thf(1765,plain,
! [SV207: $i,SV200: $i] :
( ( relation_of2_as_subset @ ( first_projection_as_func_of @ SV200 @ SV207 ) @ ( cartesian_product2 @ SV200 @ SV207 ) @ SV200 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1672]) ).
thf(1766,plain,
! [SV156: $i] :
( ( ( element @ ( sK20_B @ SV156 ) @ ( powerset @ SV156 ) )
= $true )
| ( ( empty @ SV156 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1673]) ).
thf(1767,plain,
! [SV156: $i] :
( ( ( ~ ( empty @ ( sK20_B @ SV156 ) ) )
= $true )
| ( ( empty @ SV156 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1674]) ).
thf(1768,plain,
( ( ~ ( empty @ sK16_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1675]) ).
thf(1769,plain,
( ( ~ ( relation @ sK16_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1675]) ).
thf(1770,plain,
! [SV157: $i] :
( ( ( ~ ( ~ ( element @ ( sK5_B @ SV157 ) @ ( powerset @ SV157 ) )
| ~ ~ ( empty @ ( sK5_B @ SV157 ) ) ) )
= $true )
| ( ( empty @ SV157 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1676]) ).
thf(1771,plain,
! [SV157: $i] :
( ( ( finite @ ( sK5_B @ SV157 ) )
= $true )
| ( ( empty @ SV157 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1677]) ).
thf(1772,plain,
! [SV121: $i,SV184: $i] :
( ( ( element @ SV184 @ ( powerset @ SV121 ) )
= $false )
| ( ( finite @ SV184 )
= $true )
| ( ( finite @ SV121 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1680]) ).
thf(1773,plain,
! [SV160: $i,SV123: $i,SV178: $i] :
( ( ( ~ ( function @ SV178 ) )
= $true )
| ( ( ~ ( quasi_total @ SV178 @ SV123 @ SV160 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV178 @ SV123 @ SV160 ) )
= $true )
| ( ( ! [SY218: $i] : ( element @ ( function_image @ SV123 @ SV160 @ SV178 @ SY218 ) @ ( powerset @ SV160 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1682]) ).
thf(1774,plain,
! [SV164: $i,SV128: $i] :
( ( ( function @ SV128 )
= $false )
| ( ( ~ ( relation @ SV128 ) )
= $true )
| ( ( ~ ( finite @ SV164 ) )
= $true )
| ( ( finite @ ( relation_image @ SV128 @ SV164 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1684]) ).
thf(1775,plain,
! [SV129: $i,SV165: $i] :
( ( ( finite @ SV165 )
= $false )
| ( ( finite @ SV129 )
= $false )
| ( ( finite @ ( cartesian_product2 @ SV129 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1685]) ).
thf(1776,plain,
! [SV133: $i] :
( ( ( relation_non_empty @ SV133 )
= $false )
| ( ( relation @ SV133 )
= $false )
| ( ( ~ ( function @ SV133 ) )
= $true )
| ( ( with_non_empty_elements @ ( relation_rng @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1688]) ).
thf(1777,plain,
! [SV167: $i,SV135: $i,SV180: $i] :
( ( ( ~ ( function @ SV180 ) )
= $true )
| ( ( ~ ( quasi_total @ SV180 @ SV135 @ SV167 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV180 @ SV135 @ SV167 ) )
= $true )
| ( ( ! [SY219: $i] :
( ( function_image @ SV135 @ SV167 @ SV180 @ SY219 )
= ( relation_image @ SV180 @ SY219 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1690]) ).
thf(1778,plain,
! [SV181: $i,SV139: $i] :
( ( ( subset @ SV139 @ SV181 )
= $false )
| ( ( finite @ SV181 )
= $false )
| ( ( finite @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1692]) ).
thf(1779,plain,
! [SV140: $i,SV169: $i] :
( ( ( relation @ SV169 )
= $false )
| ( ( function @ SV169 )
= $false )
| ( ( ~ ( finite @ SV140 )
| ( finite @ ( relation_image @ SV169 @ SV140 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1693]) ).
thf(1780,plain,
! [SV141: $i,SV170: $i] :
( ( ( finite @ SV170 )
= $false )
| ( ( finite @ SV141 )
= $false )
| ( ( finite @ ( cartesian_product2 @ SV141 @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1694]) ).
thf(1781,plain,
! [SV144: $i] :
( ( ( ~ ( finite @ ( relation_dom @ SV144 ) ) )
= $true )
| ( ( finite @ ( relation_rng @ SV144 ) )
= $true )
| ( ( function @ SV144 )
= $false )
| ( ( relation @ SV144 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1695]) ).
thf(1782,plain,
! [SV146: $i,SV182: $i,SV173: $i] :
( ( ( element @ SV173 @ ( powerset @ SV182 ) )
= $false )
| ( ( ~ ( in @ SV146 @ SV173 ) )
= $true )
| ( ( element @ SV146 @ SV182 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1697]) ).
thf(1783,plain,
! [SV147: $i,SV183: $i,SV174: $i] :
( ( ( element @ SV174 @ ( powerset @ SV183 ) )
= $false )
| ( ( ~ ( in @ SV147 @ SV174 ) )
= $true )
| ( ( ~ ( empty @ SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1698]) ).
thf(1784,plain,
! [SV150: $i,SV176: $i] :
( ( ( empty @ SV176 )
= $false )
| ( ( SV150 = SV176 )
= $true )
| ( ( empty @ SV150 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1700]) ).
thf(1785,plain,
( ( function @ sK25_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1701]) ).
thf(1786,plain,
( ( relation @ sK25_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1702]) ).
thf(1787,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1703]) ).
thf(1788,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1704]) ).
thf(1789,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1705]) ).
thf(1790,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1706]) ).
thf(1791,plain,
! [SV185: $i] :
( ( ( ~ ( empty @ SV185 )
| ~ ( relation @ SV185 ) )
= $true )
| ( ( ~ ( function @ SV185 ) )
= $true )
| ( ( one_to_one @ SV185 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1707]) ).
thf(1792,plain,
( ( function @ sK3_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1708]) ).
thf(1793,plain,
( ( relation @ sK3_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1709]) ).
thf(1794,plain,
( ( ~ ( ~ ~ ( ~ ~ ( empty @ sK27_A )
| ~ ( epsilon_transitive @ sK27_A ) )
| ~ ( epsilon_connected @ sK27_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1710]) ).
thf(1795,plain,
( ( ordinal @ sK27_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1711]) ).
thf(1796,plain,
( ( ~ ( ~ ~ ( ~ ( element @ sK18_A @ positive_rationals )
| ~ ~ ( empty @ sK18_A ) )
| ~ ( epsilon_transitive @ sK18_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1712]) ).
thf(1797,plain,
( ( epsilon_connected @ sK18_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1713]) ).
thf(1798,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1714]) ).
thf(1799,plain,
( ( ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( ordinal @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1715]) ).
thf(1800,plain,
! [SV186: $i] :
( ( ( element @ SV186 @ positive_rationals )
= $false )
| ( ( ~ ( ordinal @ SV186 )
| ( natural @ SV186 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1716]) ).
thf(1801,plain,
( ( ~ ( ~ ( function @ sK14_A )
| ~ ( relation @ sK14_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1717]) ).
thf(1802,plain,
( ( transfinite_sequence @ sK14_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1718]) ).
thf(1803,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_connected @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1719]) ).
thf(1804,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1720]) ).
thf(1805,plain,
! [SV187: $i] :
( ( ( empty @ SV187 )
= $false )
| ( ( ordinal @ SV187 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1721]) ).
thf(1806,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ sK10_A @ positive_rationals )
| ~ ( empty @ sK10_A ) )
| ~ ( epsilon_transitive @ sK10_A ) )
| ~ ( epsilon_connected @ sK10_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1722]) ).
thf(1807,plain,
( ( ordinal @ sK10_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1723]) ).
thf(1808,plain,
! [SV201: $i,SV188: $i] :
( ( ( ~ ( element @ SV188 @ ( powerset @ SV201 ) ) )
= $true )
| ( ( subset @ SV188 @ SV201 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1724]) ).
thf(1809,plain,
! [SV202: $i,SV189: $i] :
( ( ( ~ ( subset @ SV189 @ SV202 ) )
= $true )
| ( ( element @ SV189 @ ( powerset @ SV202 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1725]) ).
thf(1810,plain,
( ( relation @ sK4_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1726]) ).
thf(1811,plain,
( ( relation_empty_yielding @ sK4_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1727]) ).
thf(1812,plain,
( ( ~ ( ~ ( epsilon_connected @ sK22_A )
| ~ ( epsilon_transitive @ sK22_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1728]) ).
thf(1813,plain,
( ( ordinal @ sK22_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1729]) ).
thf(1814,plain,
! [SV152: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV152 ) @ ( powerset @ SV152 ) )
| ~ ( empty @ ( sK17_B @ SV152 ) ) )
| ~ ( relation @ ( sK17_B @ SV152 ) ) )
| ~ ( function @ ( sK17_B @ SV152 ) ) )
| ~ ( one_to_one @ ( sK17_B @ SV152 ) ) )
| ~ ( epsilon_transitive @ ( sK17_B @ SV152 ) ) )
| ~ ( epsilon_connected @ ( sK17_B @ SV152 ) ) )
| ~ ( ordinal @ ( sK17_B @ SV152 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1730]) ).
thf(1815,plain,
! [SV152: $i] :
( ( ~ ( natural @ ( sK17_B @ SV152 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1730]) ).
thf(1816,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) )
| ~ ( epsilon_transitive @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1731]) ).
thf(1817,plain,
( ( epsilon_connected @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1732]) ).
thf(1818,plain,
( ( function @ sK8_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1735]) ).
thf(1819,plain,
( ( relation @ sK8_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1736]) ).
thf(1820,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK15_A )
| ~ ( relation @ sK15_A ) )
| ~ ( one_to_one @ sK15_A ) )
| ~ ( empty @ sK15_A ) )
| ~ ( epsilon_transitive @ sK15_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1737]) ).
thf(1821,plain,
( ( epsilon_connected @ sK15_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1738]) ).
thf(1822,plain,
! [SV192: $i] :
( ( ( ordinal @ SV192 )
= $false )
| ( ( epsilon_connected @ SV192 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1739]) ).
thf(1823,plain,
! [SV193: $i] :
( ( ( ordinal @ SV193 )
= $false )
| ( ( epsilon_transitive @ SV193 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1740]) ).
thf(1824,plain,
! [SV194: $i] :
( ( ( empty @ SV194 )
= $false )
| ( ( empty @ ( relation_dom @ SV194 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1741]) ).
thf(1825,plain,
! [SV195: $i] :
( ( ( empty @ SV195 )
= $false )
| ( ( relation @ ( relation_dom @ SV195 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1742]) ).
thf(1826,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( transfinite_sequence @ SX0 )
| ( epsilon_connected @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1743]) ).
thf(1827,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( transfinite_sequence @ SX0 )
| ( epsilon_transitive @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1744]) ).
thf(1828,plain,
! [SV196: $i] :
( ( ( ~ ( function @ SV196 )
| ~ ( relation @ SV196 ) )
= $true )
| ( ( ~ ( transfinite_sequence @ SV196 ) )
= $true )
| ( ( ordinal @ ( relation_dom @ SV196 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1745]) ).
thf(1829,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1746]) ).
thf(1830,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( ordinal @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1747]) ).
thf(1831,plain,
! [SV197: $i] :
( ( ( ~ ( empty @ SV197 ) )
= $true )
| ( ( ~ ( ordinal @ SV197 ) )
= $true )
| ( ( natural @ SV197 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1748]) ).
thf(1832,plain,
( ( epsilon_connected @ sK23_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1749]) ).
thf(1833,plain,
( ( epsilon_transitive @ sK23_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1750]) ).
thf(1834,plain,
! [SV205: $i,SV153: $i,SV208: $i] :
( ( ~ ( relation_of2 @ SV208 @ SV153 @ SV205 )
| ( relation_of2_as_subset @ SV208 @ SV153 @ SV205 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1751]) ).
thf(1835,plain,
! [SV206: $i,SV153: $i,SV209: $i] :
( ( ~ ( relation_of2_as_subset @ SV209 @ SV153 @ SV206 )
| ( relation_of2 @ SV209 @ SV153 @ SV206 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1752]) ).
thf(1836,plain,
! [SV154: $i] :
( ( ( ~ ( element @ ( sK9_B @ SV154 ) @ ( powerset @ SV154 ) )
| ~ ~ ( empty @ ( sK9_B @ SV154 ) ) )
= $false )
| ( ( empty @ SV154 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1753]) ).
thf(1837,plain,
( ( relation @ sK2_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1755]) ).
thf(1838,plain,
( ( relation_non_empty @ sK2_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1756]) ).
thf(1839,plain,
( ( ~ ( ~ ~ ( empty @ sK7_A )
| ~ ( epsilon_transitive @ sK7_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1757]) ).
thf(1840,plain,
( ( epsilon_connected @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1758]) ).
thf(1841,plain,
! [SV155: $i] :
( ( ( ~ ( ~ ! [SY207: $i] :
( ~ ( element @ SY207 @ SV155 )
| ( epsilon_connected @ SY207 ) )
| ~ ! [SY208: $i] :
( ~ ( element @ SY208 @ SV155 )
| ( epsilon_transitive @ SY208 ) ) ) )
= $true )
| ( ( ordinal @ SV155 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1759]) ).
thf(1842,plain,
! [SV155: $i] :
( ( ( ! [SY209: $i] :
( ~ ( element @ SY209 @ SV155 )
| ( ordinal @ SY209 ) ) )
= $true )
| ( ( ordinal @ SV155 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1760]) ).
thf(1843,plain,
! [SV198: $i] :
( ( ( empty @ SV198 )
= $false )
| ( ( empty @ ( relation_rng @ SV198 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1761]) ).
thf(1844,plain,
! [SV199: $i] :
( ( ( empty @ SV199 )
= $false )
| ( ( relation @ ( relation_rng @ SV199 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1762]) ).
thf(1845,plain,
( ( ! [SX0: $i,SX1: $i] : ( function @ ( first_projection_as_func_of @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1763]) ).
thf(1846,plain,
( ( ! [SX0: $i,SX1: $i] : ( quasi_total @ ( first_projection_as_func_of @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX0 @ SX1 ) @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1764]) ).
thf(1847,plain,
! [SV156: $i] :
( ( ( empty @ ( sK20_B @ SV156 ) )
= $false )
| ( ( empty @ SV156 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1767]) ).
thf(1848,plain,
( ( empty @ sK16_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1768]) ).
thf(1849,plain,
( ( relation @ sK16_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1769]) ).
thf(1850,plain,
! [SV157: $i] :
( ( ( ~ ( element @ ( sK5_B @ SV157 ) @ ( powerset @ SV157 ) )
| ~ ~ ( empty @ ( sK5_B @ SV157 ) ) )
= $false )
| ( ( empty @ SV157 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1770]) ).
thf(1851,plain,
! [SV160: $i,SV123: $i,SV178: $i] :
( ( ( function @ SV178 )
= $false )
| ( ( ~ ( quasi_total @ SV178 @ SV123 @ SV160 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV178 @ SV123 @ SV160 ) )
= $true )
| ( ( ! [SY218: $i] : ( element @ ( function_image @ SV123 @ SV160 @ SV178 @ SY218 ) @ ( powerset @ SV160 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1773]) ).
thf(1852,plain,
! [SV164: $i,SV128: $i] :
( ( ( relation @ SV128 )
= $false )
| ( ( function @ SV128 )
= $false )
| ( ( ~ ( finite @ SV164 ) )
= $true )
| ( ( finite @ ( relation_image @ SV128 @ SV164 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1774]) ).
thf(1853,plain,
! [SV133: $i] :
( ( ( function @ SV133 )
= $false )
| ( ( relation @ SV133 )
= $false )
| ( ( relation_non_empty @ SV133 )
= $false )
| ( ( with_non_empty_elements @ ( relation_rng @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1776]) ).
thf(1854,plain,
! [SV167: $i,SV135: $i,SV180: $i] :
( ( ( function @ SV180 )
= $false )
| ( ( ~ ( quasi_total @ SV180 @ SV135 @ SV167 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV180 @ SV135 @ SV167 ) )
= $true )
| ( ( ! [SY219: $i] :
( ( function_image @ SV135 @ SV167 @ SV180 @ SY219 )
= ( relation_image @ SV180 @ SY219 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1777]) ).
thf(1855,plain,
! [SV169: $i,SV140: $i] :
( ( ( ~ ( finite @ SV140 ) )
= $true )
| ( ( finite @ ( relation_image @ SV169 @ SV140 ) )
= $true )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1779]) ).
thf(1856,plain,
! [SV144: $i] :
( ( ( finite @ ( relation_dom @ SV144 ) )
= $false )
| ( ( finite @ ( relation_rng @ SV144 ) )
= $true )
| ( ( function @ SV144 )
= $false )
| ( ( relation @ SV144 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1781]) ).
thf(1857,plain,
! [SV182: $i,SV173: $i,SV146: $i] :
( ( ( in @ SV146 @ SV173 )
= $false )
| ( ( element @ SV173 @ ( powerset @ SV182 ) )
= $false )
| ( ( element @ SV146 @ SV182 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1782]) ).
thf(1858,plain,
! [SV183: $i,SV174: $i,SV147: $i] :
( ( ( in @ SV147 @ SV174 )
= $false )
| ( ( element @ SV174 @ ( powerset @ SV183 ) )
= $false )
| ( ( ~ ( empty @ SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1783]) ).
thf(1859,plain,
! [SV210: $i] :
( ( ~ ( empty @ SV210 )
| ~ ( relation @ SV210 )
| ~ ( function @ SV210 )
| ( function @ SV210 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1789]) ).
thf(1860,plain,
! [SV211: $i] :
( ( ~ ( empty @ SV211 )
| ~ ( relation @ SV211 )
| ~ ( function @ SV211 )
| ( relation @ SV211 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1790]) ).
thf(1861,plain,
! [SV185: $i] :
( ( ( ~ ( empty @ SV185 ) )
= $true )
| ( ( ~ ( relation @ SV185 ) )
= $true )
| ( ( ~ ( function @ SV185 ) )
= $true )
| ( ( one_to_one @ SV185 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1791]) ).
thf(1862,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK27_A )
| ~ ( epsilon_transitive @ sK27_A ) )
| ~ ( epsilon_connected @ sK27_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1794]) ).
thf(1863,plain,
( ( ~ ~ ( ~ ( element @ sK18_A @ positive_rationals )
| ~ ~ ( empty @ sK18_A ) )
| ~ ( epsilon_transitive @ sK18_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1796]) ).
thf(1864,plain,
( ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1798]) ).
thf(1865,plain,
! [SV212: $i] :
( ( ~ ( element @ SV212 @ positive_rationals )
| ~ ( ordinal @ SV212 )
| ( ordinal @ SV212 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1799]) ).
thf(1866,plain,
! [SV186: $i] :
( ( ( ~ ( ordinal @ SV186 ) )
= $true )
| ( ( natural @ SV186 )
= $true )
| ( ( element @ SV186 @ positive_rationals )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1800]) ).
thf(1867,plain,
( ( ~ ( function @ sK14_A )
| ~ ( relation @ sK14_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1801]) ).
thf(1868,plain,
! [SV213: $i] :
( ( ~ ( empty @ SV213 )
| ( epsilon_connected @ SV213 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1803]) ).
thf(1869,plain,
! [SV214: $i] :
( ( ~ ( empty @ SV214 )
| ( epsilon_transitive @ SV214 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1804]) ).
thf(1870,plain,
( ( ~ ~ ( ~ ~ ( ~ ( element @ sK10_A @ positive_rationals )
| ~ ( empty @ sK10_A ) )
| ~ ( epsilon_transitive @ sK10_A ) )
| ~ ( epsilon_connected @ sK10_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1806]) ).
thf(1871,plain,
! [SV201: $i,SV188: $i] :
( ( ( element @ SV188 @ ( powerset @ SV201 ) )
= $false )
| ( ( subset @ SV188 @ SV201 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1808]) ).
thf(1872,plain,
! [SV202: $i,SV189: $i] :
( ( ( subset @ SV189 @ SV202 )
= $false )
| ( ( element @ SV189 @ ( powerset @ SV202 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1809]) ).
thf(1873,plain,
( ( ~ ( epsilon_connected @ sK22_A )
| ~ ( epsilon_transitive @ sK22_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1812]) ).
thf(1874,plain,
! [SV152: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV152 ) @ ( powerset @ SV152 ) )
| ~ ( empty @ ( sK17_B @ SV152 ) ) )
| ~ ( relation @ ( sK17_B @ SV152 ) ) )
| ~ ( function @ ( sK17_B @ SV152 ) ) )
| ~ ( one_to_one @ ( sK17_B @ SV152 ) ) )
| ~ ( epsilon_transitive @ ( sK17_B @ SV152 ) ) )
| ~ ( epsilon_connected @ ( sK17_B @ SV152 ) ) )
| ~ ( ordinal @ ( sK17_B @ SV152 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1814]) ).
thf(1875,plain,
! [SV152: $i] :
( ( natural @ ( sK17_B @ SV152 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1815]) ).
thf(1876,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) )
| ~ ( epsilon_transitive @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1816]) ).
thf(1877,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK15_A )
| ~ ( relation @ sK15_A ) )
| ~ ( one_to_one @ sK15_A ) )
| ~ ( empty @ sK15_A ) )
| ~ ( epsilon_transitive @ sK15_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1820]) ).
thf(1878,plain,
! [SV215: $i] :
( ( ~ ( function @ SV215 )
| ~ ( relation @ SV215 )
| ~ ( transfinite_sequence @ SV215 )
| ( epsilon_connected @ ( relation_dom @ SV215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1826]) ).
thf(1879,plain,
! [SV216: $i] :
( ( ~ ( function @ SV216 )
| ~ ( relation @ SV216 )
| ~ ( transfinite_sequence @ SV216 )
| ( epsilon_transitive @ ( relation_dom @ SV216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1827]) ).
thf(1880,plain,
! [SV196: $i] :
( ( ( ~ ( function @ SV196 ) )
= $true )
| ( ( ~ ( relation @ SV196 ) )
= $true )
| ( ( ~ ( transfinite_sequence @ SV196 ) )
= $true )
| ( ( ordinal @ ( relation_dom @ SV196 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1828]) ).
thf(1881,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1829]) ).
thf(1882,plain,
! [SV217: $i] :
( ( ~ ( empty @ SV217 )
| ~ ( ordinal @ SV217 )
| ( ordinal @ SV217 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1830]) ).
thf(1883,plain,
! [SV197: $i] :
( ( ( empty @ SV197 )
= $false )
| ( ( ~ ( ordinal @ SV197 ) )
= $true )
| ( ( natural @ SV197 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1831]) ).
thf(1884,plain,
! [SV205: $i,SV153: $i,SV208: $i] :
( ( ( ~ ( relation_of2 @ SV208 @ SV153 @ SV205 ) )
= $true )
| ( ( relation_of2_as_subset @ SV208 @ SV153 @ SV205 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1834]) ).
thf(1885,plain,
! [SV206: $i,SV153: $i,SV209: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV209 @ SV153 @ SV206 ) )
= $true )
| ( ( relation_of2 @ SV209 @ SV153 @ SV206 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1835]) ).
thf(1886,plain,
! [SV154: $i] :
( ( ( ~ ( element @ ( sK9_B @ SV154 ) @ ( powerset @ SV154 ) ) )
= $false )
| ( ( empty @ SV154 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1836]) ).
thf(1887,plain,
! [SV154: $i] :
( ( ( ~ ~ ( empty @ ( sK9_B @ SV154 ) ) )
= $false )
| ( ( empty @ SV154 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1836]) ).
thf(1888,plain,
( ( ~ ~ ( empty @ sK7_A )
| ~ ( epsilon_transitive @ sK7_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1839]) ).
thf(1889,plain,
! [SV155: $i] :
( ( ( ~ ! [SY207: $i] :
( ~ ( element @ SY207 @ SV155 )
| ( epsilon_connected @ SY207 ) )
| ~ ! [SY208: $i] :
( ~ ( element @ SY208 @ SV155 )
| ( epsilon_transitive @ SY208 ) ) )
= $false )
| ( ( ordinal @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1841]) ).
thf(1890,plain,
! [SV155: $i,SV218: $i] :
( ( ( ~ ( element @ SV218 @ SV155 )
| ( ordinal @ SV218 ) )
= $true )
| ( ( ordinal @ SV155 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1842]) ).
thf(1891,plain,
! [SV219: $i] :
( ( ! [SY227: $i] : ( function @ ( first_projection_as_func_of @ SV219 @ SY227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1845]) ).
thf(1892,plain,
! [SV220: $i] :
( ( ! [SY228: $i] : ( quasi_total @ ( first_projection_as_func_of @ SV220 @ SY228 ) @ ( cartesian_product2 @ SV220 @ SY228 ) @ SV220 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1846]) ).
thf(1893,plain,
! [SV157: $i] :
( ( ( ~ ( element @ ( sK5_B @ SV157 ) @ ( powerset @ SV157 ) ) )
= $false )
| ( ( empty @ SV157 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1850]) ).
thf(1894,plain,
! [SV157: $i] :
( ( ( ~ ~ ( empty @ ( sK5_B @ SV157 ) ) )
= $false )
| ( ( empty @ SV157 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1850]) ).
thf(1895,plain,
! [SV160: $i,SV123: $i,SV178: $i] :
( ( ( quasi_total @ SV178 @ SV123 @ SV160 )
= $false )
| ( ( function @ SV178 )
= $false )
| ( ( ~ ( relation_of2 @ SV178 @ SV123 @ SV160 ) )
= $true )
| ( ( ! [SY218: $i] : ( element @ ( function_image @ SV123 @ SV160 @ SV178 @ SY218 ) @ ( powerset @ SV160 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1851]) ).
thf(1896,plain,
! [SV128: $i,SV164: $i] :
( ( ( finite @ SV164 )
= $false )
| ( ( function @ SV128 )
= $false )
| ( ( relation @ SV128 )
= $false )
| ( ( finite @ ( relation_image @ SV128 @ SV164 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1852]) ).
thf(1897,plain,
! [SV167: $i,SV135: $i,SV180: $i] :
( ( ( quasi_total @ SV180 @ SV135 @ SV167 )
= $false )
| ( ( function @ SV180 )
= $false )
| ( ( ~ ( relation_of2 @ SV180 @ SV135 @ SV167 ) )
= $true )
| ( ( ! [SY219: $i] :
( ( function_image @ SV135 @ SV167 @ SV180 @ SY219 )
= ( relation_image @ SV180 @ SY219 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1854]) ).
thf(1898,plain,
! [SV169: $i,SV140: $i] :
( ( ( finite @ SV140 )
= $false )
| ( ( finite @ ( relation_image @ SV169 @ SV140 ) )
= $true )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1855]) ).
thf(1899,plain,
! [SV147: $i,SV174: $i,SV183: $i] :
( ( ( empty @ SV183 )
= $false )
| ( ( element @ SV174 @ ( powerset @ SV183 ) )
= $false )
| ( ( in @ SV147 @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1858]) ).
thf(1900,plain,
! [SV210: $i] :
( ( ( ~ ( empty @ SV210 )
| ~ ( relation @ SV210 )
| ~ ( function @ SV210 ) )
= $true )
| ( ( function @ SV210 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1859]) ).
thf(1901,plain,
! [SV211: $i] :
( ( ( ~ ( empty @ SV211 )
| ~ ( relation @ SV211 )
| ~ ( function @ SV211 ) )
= $true )
| ( ( relation @ SV211 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1860]) ).
thf(1902,plain,
! [SV185: $i] :
( ( ( empty @ SV185 )
= $false )
| ( ( ~ ( relation @ SV185 ) )
= $true )
| ( ( ~ ( function @ SV185 ) )
= $true )
| ( ( one_to_one @ SV185 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1861]) ).
thf(1903,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK27_A )
| ~ ( epsilon_transitive @ sK27_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1862]) ).
thf(1904,plain,
( ( ~ ( epsilon_connected @ sK27_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1862]) ).
thf(1905,plain,
( ( ~ ~ ( ~ ( element @ sK18_A @ positive_rationals )
| ~ ~ ( empty @ sK18_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1863]) ).
thf(1906,plain,
( ( ~ ( epsilon_transitive @ sK18_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1863]) ).
thf(1907,plain,
( ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1864]) ).
thf(1908,plain,
( ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1864]) ).
thf(1909,plain,
! [SV212: $i] :
( ( ( ~ ( element @ SV212 @ positive_rationals ) )
= $true )
| ( ( ~ ( ordinal @ SV212 )
| ( ordinal @ SV212 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1865]) ).
thf(1910,plain,
! [SV186: $i] :
( ( ( ordinal @ SV186 )
= $false )
| ( ( natural @ SV186 )
= $true )
| ( ( element @ SV186 @ positive_rationals )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1866]) ).
thf(1911,plain,
( ( ~ ( function @ sK14_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1867]) ).
thf(1912,plain,
( ( ~ ( relation @ sK14_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1867]) ).
thf(1913,plain,
! [SV213: $i] :
( ( ( ~ ( empty @ SV213 ) )
= $true )
| ( ( epsilon_connected @ SV213 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1868]) ).
thf(1914,plain,
! [SV214: $i] :
( ( ( ~ ( empty @ SV214 ) )
= $true )
| ( ( epsilon_transitive @ SV214 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1869]) ).
thf(1915,plain,
( ( ~ ~ ( ~ ~ ( ~ ( element @ sK10_A @ positive_rationals )
| ~ ( empty @ sK10_A ) )
| ~ ( epsilon_transitive @ sK10_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1870]) ).
thf(1916,plain,
( ( ~ ( epsilon_connected @ sK10_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1870]) ).
thf(1917,plain,
( ( ~ ( epsilon_connected @ sK22_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1873]) ).
thf(1918,plain,
( ( ~ ( epsilon_transitive @ sK22_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1873]) ).
thf(1919,plain,
! [SV152: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV152 ) @ ( powerset @ SV152 ) )
| ~ ( empty @ ( sK17_B @ SV152 ) ) )
| ~ ( relation @ ( sK17_B @ SV152 ) ) )
| ~ ( function @ ( sK17_B @ SV152 ) ) )
| ~ ( one_to_one @ ( sK17_B @ SV152 ) ) )
| ~ ( epsilon_transitive @ ( sK17_B @ SV152 ) ) )
| ~ ( epsilon_connected @ ( sK17_B @ SV152 ) ) )
| ~ ( ordinal @ ( sK17_B @ SV152 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1874]) ).
thf(1920,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1876]) ).
thf(1921,plain,
( ( ~ ( epsilon_transitive @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1876]) ).
thf(1922,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK15_A )
| ~ ( relation @ sK15_A ) )
| ~ ( one_to_one @ sK15_A ) )
| ~ ( empty @ sK15_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1877]) ).
thf(1923,plain,
( ( ~ ( epsilon_transitive @ sK15_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1877]) ).
thf(1924,plain,
! [SV215: $i] :
( ( ( ~ ( function @ SV215 )
| ~ ( relation @ SV215 )
| ~ ( transfinite_sequence @ SV215 ) )
= $true )
| ( ( epsilon_connected @ ( relation_dom @ SV215 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1878]) ).
thf(1925,plain,
! [SV216: $i] :
( ( ( ~ ( function @ SV216 )
| ~ ( relation @ SV216 )
| ~ ( transfinite_sequence @ SV216 ) )
= $true )
| ( ( epsilon_transitive @ ( relation_dom @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1879]) ).
thf(1926,plain,
! [SV196: $i] :
( ( ( function @ SV196 )
= $false )
| ( ( ~ ( relation @ SV196 ) )
= $true )
| ( ( ~ ( transfinite_sequence @ SV196 ) )
= $true )
| ( ( ordinal @ ( relation_dom @ SV196 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1880]) ).
thf(1927,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1881]) ).
thf(1928,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1881]) ).
thf(1929,plain,
! [SV217: $i] :
( ( ( ~ ( empty @ SV217 )
| ~ ( ordinal @ SV217 ) )
= $true )
| ( ( ordinal @ SV217 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1882]) ).
thf(1930,plain,
! [SV197: $i] :
( ( ( ordinal @ SV197 )
= $false )
| ( ( empty @ SV197 )
= $false )
| ( ( natural @ SV197 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1883]) ).
thf(1931,plain,
! [SV205: $i,SV153: $i,SV208: $i] :
( ( ( relation_of2 @ SV208 @ SV153 @ SV205 )
= $false )
| ( ( relation_of2_as_subset @ SV208 @ SV153 @ SV205 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1884]) ).
thf(1932,plain,
! [SV206: $i,SV153: $i,SV209: $i] :
( ( ( relation_of2_as_subset @ SV209 @ SV153 @ SV206 )
= $false )
| ( ( relation_of2 @ SV209 @ SV153 @ SV206 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1885]) ).
thf(1933,plain,
! [SV154: $i] :
( ( ( element @ ( sK9_B @ SV154 ) @ ( powerset @ SV154 ) )
= $true )
| ( ( empty @ SV154 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1886]) ).
thf(1934,plain,
! [SV154: $i] :
( ( ( ~ ( empty @ ( sK9_B @ SV154 ) ) )
= $true )
| ( ( empty @ SV154 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1887]) ).
thf(1935,plain,
( ( ~ ~ ( empty @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1888]) ).
thf(1936,plain,
( ( ~ ( epsilon_transitive @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1888]) ).
thf(1937,plain,
! [SV155: $i] :
( ( ( ~ ! [SY207: $i] :
( ~ ( element @ SY207 @ SV155 )
| ( epsilon_connected @ SY207 ) ) )
= $false )
| ( ( ordinal @ SV155 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1889]) ).
thf(1938,plain,
! [SV155: $i] :
( ( ( ~ ! [SY208: $i] :
( ~ ( element @ SY208 @ SV155 )
| ( epsilon_transitive @ SY208 ) ) )
= $false )
| ( ( ordinal @ SV155 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1889]) ).
thf(1939,plain,
! [SV155: $i,SV218: $i] :
( ( ( ~ ( element @ SV218 @ SV155 ) )
= $true )
| ( ( ordinal @ SV218 )
= $true )
| ( ( ordinal @ SV155 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1890]) ).
thf(1940,plain,
! [SV221: $i,SV219: $i] :
( ( function @ ( first_projection_as_func_of @ SV219 @ SV221 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1891]) ).
thf(1941,plain,
! [SV222: $i,SV220: $i] :
( ( quasi_total @ ( first_projection_as_func_of @ SV220 @ SV222 ) @ ( cartesian_product2 @ SV220 @ SV222 ) @ SV220 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1892]) ).
thf(1942,plain,
! [SV157: $i] :
( ( ( element @ ( sK5_B @ SV157 ) @ ( powerset @ SV157 ) )
= $true )
| ( ( empty @ SV157 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1893]) ).
thf(1943,plain,
! [SV157: $i] :
( ( ( ~ ( empty @ ( sK5_B @ SV157 ) ) )
= $true )
| ( ( empty @ SV157 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1894]) ).
thf(1944,plain,
! [SV160: $i,SV123: $i,SV178: $i] :
( ( ( relation_of2 @ SV178 @ SV123 @ SV160 )
= $false )
| ( ( function @ SV178 )
= $false )
| ( ( quasi_total @ SV178 @ SV123 @ SV160 )
= $false )
| ( ( ! [SY218: $i] : ( element @ ( function_image @ SV123 @ SV160 @ SV178 @ SY218 ) @ ( powerset @ SV160 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1895]) ).
thf(1945,plain,
! [SV167: $i,SV135: $i,SV180: $i] :
( ( ( relation_of2 @ SV180 @ SV135 @ SV167 )
= $false )
| ( ( function @ SV180 )
= $false )
| ( ( quasi_total @ SV180 @ SV135 @ SV167 )
= $false )
| ( ( ! [SY219: $i] :
( ( function_image @ SV135 @ SV167 @ SV180 @ SY219 )
= ( relation_image @ SV180 @ SY219 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1897]) ).
thf(1946,plain,
! [SV210: $i] :
( ( ( ~ ( empty @ SV210 )
| ~ ( relation @ SV210 ) )
= $true )
| ( ( ~ ( function @ SV210 ) )
= $true )
| ( ( function @ SV210 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1900]) ).
thf(1947,plain,
! [SV211: $i] :
( ( ( ~ ( empty @ SV211 )
| ~ ( relation @ SV211 ) )
= $true )
| ( ( ~ ( function @ SV211 ) )
= $true )
| ( ( relation @ SV211 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1901]) ).
thf(1948,plain,
! [SV185: $i] :
( ( ( relation @ SV185 )
= $false )
| ( ( empty @ SV185 )
= $false )
| ( ( ~ ( function @ SV185 ) )
= $true )
| ( ( one_to_one @ SV185 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1902]) ).
thf(1949,plain,
( ( ~ ( ~ ~ ( empty @ sK27_A )
| ~ ( epsilon_transitive @ sK27_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1903]) ).
thf(1950,plain,
( ( epsilon_connected @ sK27_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1904]) ).
thf(1951,plain,
( ( ~ ( ~ ( element @ sK18_A @ positive_rationals )
| ~ ~ ( empty @ sK18_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1905]) ).
thf(1952,plain,
( ( epsilon_transitive @ sK18_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1906]) ).
thf(1953,plain,
( ( ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1907]) ).
thf(1954,plain,
( ( ! [SX0: $i] :
( ~ ( element @ SX0 @ positive_rationals )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1908]) ).
thf(1955,plain,
! [SV212: $i] :
( ( ( element @ SV212 @ positive_rationals )
= $false )
| ( ( ~ ( ordinal @ SV212 )
| ( ordinal @ SV212 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1909]) ).
thf(1956,plain,
( ( function @ sK14_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1911]) ).
thf(1957,plain,
( ( relation @ sK14_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1912]) ).
thf(1958,plain,
! [SV213: $i] :
( ( ( empty @ SV213 )
= $false )
| ( ( epsilon_connected @ SV213 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1913]) ).
thf(1959,plain,
! [SV214: $i] :
( ( ( empty @ SV214 )
= $false )
| ( ( epsilon_transitive @ SV214 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1914]) ).
thf(1960,plain,
( ( ~ ( ~ ~ ( ~ ( element @ sK10_A @ positive_rationals )
| ~ ( empty @ sK10_A ) )
| ~ ( epsilon_transitive @ sK10_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1915]) ).
thf(1961,plain,
( ( epsilon_connected @ sK10_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1916]) ).
thf(1962,plain,
( ( epsilon_connected @ sK22_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1917]) ).
thf(1963,plain,
( ( epsilon_transitive @ sK22_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1918]) ).
thf(1964,plain,
! [SV152: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV152 ) @ ( powerset @ SV152 ) )
| ~ ( empty @ ( sK17_B @ SV152 ) ) )
| ~ ( relation @ ( sK17_B @ SV152 ) ) )
| ~ ( function @ ( sK17_B @ SV152 ) ) )
| ~ ( one_to_one @ ( sK17_B @ SV152 ) ) )
| ~ ( epsilon_transitive @ ( sK17_B @ SV152 ) ) )
| ~ ( epsilon_connected @ ( sK17_B @ SV152 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1919]) ).
thf(1965,plain,
! [SV152: $i] :
( ( ~ ( ordinal @ ( sK17_B @ SV152 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1919]) ).
thf(1966,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1920]) ).
thf(1967,plain,
( ( epsilon_transitive @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1921]) ).
thf(1968,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK15_A )
| ~ ( relation @ sK15_A ) )
| ~ ( one_to_one @ sK15_A ) )
| ~ ( empty @ sK15_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1922]) ).
thf(1969,plain,
( ( epsilon_transitive @ sK15_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1923]) ).
thf(1970,plain,
! [SV215: $i] :
( ( ( ~ ( function @ SV215 )
| ~ ( relation @ SV215 ) )
= $true )
| ( ( ~ ( transfinite_sequence @ SV215 ) )
= $true )
| ( ( epsilon_connected @ ( relation_dom @ SV215 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1924]) ).
thf(1971,plain,
! [SV216: $i] :
( ( ( ~ ( function @ SV216 )
| ~ ( relation @ SV216 ) )
= $true )
| ( ( ~ ( transfinite_sequence @ SV216 ) )
= $true )
| ( ( epsilon_transitive @ ( relation_dom @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1925]) ).
thf(1972,plain,
! [SV196: $i] :
( ( ( relation @ SV196 )
= $false )
| ( ( function @ SV196 )
= $false )
| ( ( ~ ( transfinite_sequence @ SV196 ) )
= $true )
| ( ( ordinal @ ( relation_dom @ SV196 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1926]) ).
thf(1973,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1927]) ).
thf(1974,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1928]) ).
thf(1975,plain,
! [SV217: $i] :
( ( ( ~ ( empty @ SV217 ) )
= $true )
| ( ( ~ ( ordinal @ SV217 ) )
= $true )
| ( ( ordinal @ SV217 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1929]) ).
thf(1976,plain,
! [SV154: $i] :
( ( ( empty @ ( sK9_B @ SV154 ) )
= $false )
| ( ( empty @ SV154 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1934]) ).
thf(1977,plain,
( ( ~ ( empty @ sK7_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1935]) ).
thf(1978,plain,
( ( epsilon_transitive @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1936]) ).
thf(1979,plain,
! [SV155: $i] :
( ( ( ! [SY207: $i] :
( ~ ( element @ SY207 @ SV155 )
| ( epsilon_connected @ SY207 ) ) )
= $true )
| ( ( ordinal @ SV155 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1937]) ).
thf(1980,plain,
! [SV155: $i] :
( ( ( ! [SY208: $i] :
( ~ ( element @ SY208 @ SV155 )
| ( epsilon_transitive @ SY208 ) ) )
= $true )
| ( ( ordinal @ SV155 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1938]) ).
thf(1981,plain,
! [SV155: $i,SV218: $i] :
( ( ( element @ SV218 @ SV155 )
= $false )
| ( ( ordinal @ SV218 )
= $true )
| ( ( ordinal @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1939]) ).
thf(1982,plain,
! [SV157: $i] :
( ( ( empty @ ( sK5_B @ SV157 ) )
= $false )
| ( ( empty @ SV157 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1943]) ).
thf(1983,plain,
! [SV223: $i,SV178: $i,SV160: $i,SV123: $i] :
( ( ( element @ ( function_image @ SV123 @ SV160 @ SV178 @ SV223 ) @ ( powerset @ SV160 ) )
= $true )
| ( ( quasi_total @ SV178 @ SV123 @ SV160 )
= $false )
| ( ( function @ SV178 )
= $false )
| ( ( relation_of2 @ SV178 @ SV123 @ SV160 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1944]) ).
thf(1984,plain,
! [SV224: $i,SV180: $i,SV167: $i,SV135: $i] :
( ( ( ( function_image @ SV135 @ SV167 @ SV180 @ SV224 )
= ( relation_image @ SV180 @ SV224 ) )
= $true )
| ( ( quasi_total @ SV180 @ SV135 @ SV167 )
= $false )
| ( ( function @ SV180 )
= $false )
| ( ( relation_of2 @ SV180 @ SV135 @ SV167 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1945]) ).
thf(1985,plain,
! [SV210: $i] :
( ( ( ~ ( empty @ SV210 ) )
= $true )
| ( ( ~ ( relation @ SV210 ) )
= $true )
| ( ( ~ ( function @ SV210 ) )
= $true )
| ( ( function @ SV210 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1946]) ).
thf(1986,plain,
! [SV211: $i] :
( ( ( ~ ( empty @ SV211 ) )
= $true )
| ( ( ~ ( relation @ SV211 ) )
= $true )
| ( ( ~ ( function @ SV211 ) )
= $true )
| ( ( relation @ SV211 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1947]) ).
thf(1987,plain,
! [SV185: $i] :
( ( ( function @ SV185 )
= $false )
| ( ( empty @ SV185 )
= $false )
| ( ( relation @ SV185 )
= $false )
| ( ( one_to_one @ SV185 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1948]) ).
thf(1988,plain,
( ( ~ ~ ( empty @ sK27_A )
| ~ ( epsilon_transitive @ sK27_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1949]) ).
thf(1989,plain,
( ( ~ ( element @ sK18_A @ positive_rationals )
| ~ ~ ( empty @ sK18_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1951]) ).
thf(1990,plain,
! [SV225: $i] :
( ( ~ ( element @ SV225 @ positive_rationals )
| ~ ( ordinal @ SV225 )
| ( epsilon_connected @ SV225 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1953]) ).
thf(1991,plain,
! [SV226: $i] :
( ( ~ ( element @ SV226 @ positive_rationals )
| ~ ( ordinal @ SV226 )
| ( epsilon_transitive @ SV226 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1954]) ).
thf(1992,plain,
! [SV212: $i] :
( ( ( ~ ( ordinal @ SV212 ) )
= $true )
| ( ( ordinal @ SV212 )
= $true )
| ( ( element @ SV212 @ positive_rationals )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1955]) ).
thf(1993,plain,
( ( ~ ~ ( ~ ( element @ sK10_A @ positive_rationals )
| ~ ( empty @ sK10_A ) )
| ~ ( epsilon_transitive @ sK10_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1960]) ).
thf(1994,plain,
! [SV152: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV152 ) @ ( powerset @ SV152 ) )
| ~ ( empty @ ( sK17_B @ SV152 ) ) )
| ~ ( relation @ ( sK17_B @ SV152 ) ) )
| ~ ( function @ ( sK17_B @ SV152 ) ) )
| ~ ( one_to_one @ ( sK17_B @ SV152 ) ) )
| ~ ( epsilon_transitive @ ( sK17_B @ SV152 ) ) )
| ~ ( epsilon_connected @ ( sK17_B @ SV152 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1964]) ).
thf(1995,plain,
! [SV152: $i] :
( ( ordinal @ ( sK17_B @ SV152 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1965]) ).
thf(1996,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1966]) ).
thf(1997,plain,
( ( ~ ~ ( ~ ~ ( ~ ( function @ sK15_A )
| ~ ( relation @ sK15_A ) )
| ~ ( one_to_one @ sK15_A ) )
| ~ ( empty @ sK15_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1968]) ).
thf(1998,plain,
! [SV215: $i] :
( ( ( ~ ( function @ SV215 ) )
= $true )
| ( ( ~ ( relation @ SV215 ) )
= $true )
| ( ( ~ ( transfinite_sequence @ SV215 ) )
= $true )
| ( ( epsilon_connected @ ( relation_dom @ SV215 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1970]) ).
thf(1999,plain,
! [SV216: $i] :
( ( ( ~ ( function @ SV216 ) )
= $true )
| ( ( ~ ( relation @ SV216 ) )
= $true )
| ( ( ~ ( transfinite_sequence @ SV216 ) )
= $true )
| ( ( epsilon_transitive @ ( relation_dom @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1971]) ).
thf(2000,plain,
! [SV196: $i] :
( ( ( transfinite_sequence @ SV196 )
= $false )
| ( ( function @ SV196 )
= $false )
| ( ( relation @ SV196 )
= $false )
| ( ( ordinal @ ( relation_dom @ SV196 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1972]) ).
thf(2001,plain,
! [SV227: $i] :
( ( ~ ( empty @ SV227 )
| ~ ( ordinal @ SV227 )
| ( epsilon_connected @ SV227 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1973]) ).
thf(2002,plain,
! [SV228: $i] :
( ( ~ ( empty @ SV228 )
| ~ ( ordinal @ SV228 )
| ( epsilon_transitive @ SV228 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1974]) ).
thf(2003,plain,
! [SV217: $i] :
( ( ( empty @ SV217 )
= $false )
| ( ( ~ ( ordinal @ SV217 ) )
= $true )
| ( ( ordinal @ SV217 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1975]) ).
thf(2004,plain,
( ( empty @ sK7_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1977]) ).
thf(2005,plain,
! [SV155: $i,SV229: $i] :
( ( ( ~ ( element @ SV229 @ SV155 )
| ( epsilon_connected @ SV229 ) )
= $true )
| ( ( ordinal @ SV155 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1979]) ).
thf(2006,plain,
! [SV155: $i,SV230: $i] :
( ( ( ~ ( element @ SV230 @ SV155 )
| ( epsilon_transitive @ SV230 ) )
= $true )
| ( ( ordinal @ SV155 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1980]) ).
thf(2007,plain,
! [SV210: $i] :
( ( ( empty @ SV210 )
= $false )
| ( ( ~ ( relation @ SV210 ) )
= $true )
| ( ( ~ ( function @ SV210 ) )
= $true )
| ( ( function @ SV210 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1985]) ).
thf(2008,plain,
! [SV211: $i] :
( ( ( empty @ SV211 )
= $false )
| ( ( ~ ( relation @ SV211 ) )
= $true )
| ( ( ~ ( function @ SV211 ) )
= $true )
| ( ( relation @ SV211 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1986]) ).
thf(2009,plain,
( ( ~ ~ ( empty @ sK27_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1988]) ).
thf(2010,plain,
( ( ~ ( epsilon_transitive @ sK27_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1988]) ).
thf(2011,plain,
( ( ~ ( element @ sK18_A @ positive_rationals ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1989]) ).
thf(2012,plain,
( ( ~ ~ ( empty @ sK18_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1989]) ).
thf(2013,plain,
! [SV225: $i] :
( ( ( ~ ( element @ SV225 @ positive_rationals ) )
= $true )
| ( ( ~ ( ordinal @ SV225 )
| ( epsilon_connected @ SV225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1990]) ).
thf(2014,plain,
! [SV226: $i] :
( ( ( ~ ( element @ SV226 @ positive_rationals ) )
= $true )
| ( ( ~ ( ordinal @ SV226 )
| ( epsilon_transitive @ SV226 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1991]) ).
thf(2015,plain,
! [SV212: $i] :
( ( ( ordinal @ SV212 )
= $false )
| ( ( ordinal @ SV212 )
= $true )
| ( ( element @ SV212 @ positive_rationals )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1992]) ).
thf(2016,plain,
( ( ~ ~ ( ~ ( element @ sK10_A @ positive_rationals )
| ~ ( empty @ sK10_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1993]) ).
thf(2017,plain,
( ( ~ ( epsilon_transitive @ sK10_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1993]) ).
thf(2018,plain,
! [SV152: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV152 ) @ ( powerset @ SV152 ) )
| ~ ( empty @ ( sK17_B @ SV152 ) ) )
| ~ ( relation @ ( sK17_B @ SV152 ) ) )
| ~ ( function @ ( sK17_B @ SV152 ) ) )
| ~ ( one_to_one @ ( sK17_B @ SV152 ) ) )
| ~ ( epsilon_transitive @ ( sK17_B @ SV152 ) ) )
| ~ ( epsilon_connected @ ( sK17_B @ SV152 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1994]) ).
thf(2019,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1996]) ).
thf(2020,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1996]) ).
thf(2021,plain,
( ( ~ ~ ( ~ ~ ( ~ ( function @ sK15_A )
| ~ ( relation @ sK15_A ) )
| ~ ( one_to_one @ sK15_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1997]) ).
thf(2022,plain,
( ( ~ ( empty @ sK15_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1997]) ).
thf(2023,plain,
! [SV215: $i] :
( ( ( function @ SV215 )
= $false )
| ( ( ~ ( relation @ SV215 ) )
= $true )
| ( ( ~ ( transfinite_sequence @ SV215 ) )
= $true )
| ( ( epsilon_connected @ ( relation_dom @ SV215 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1998]) ).
thf(2024,plain,
! [SV216: $i] :
( ( ( function @ SV216 )
= $false )
| ( ( ~ ( relation @ SV216 ) )
= $true )
| ( ( ~ ( transfinite_sequence @ SV216 ) )
= $true )
| ( ( epsilon_transitive @ ( relation_dom @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1999]) ).
thf(2025,plain,
! [SV227: $i] :
( ( ( ~ ( empty @ SV227 )
| ~ ( ordinal @ SV227 ) )
= $true )
| ( ( epsilon_connected @ SV227 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2001]) ).
thf(2026,plain,
! [SV228: $i] :
( ( ( ~ ( empty @ SV228 )
| ~ ( ordinal @ SV228 ) )
= $true )
| ( ( epsilon_transitive @ SV228 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2002]) ).
thf(2027,plain,
! [SV217: $i] :
( ( ( ordinal @ SV217 )
= $false )
| ( ( empty @ SV217 )
= $false )
| ( ( ordinal @ SV217 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2003]) ).
thf(2028,plain,
! [SV155: $i,SV229: $i] :
( ( ( ~ ( element @ SV229 @ SV155 ) )
= $true )
| ( ( epsilon_connected @ SV229 )
= $true )
| ( ( ordinal @ SV155 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2005]) ).
thf(2029,plain,
! [SV155: $i,SV230: $i] :
( ( ( ~ ( element @ SV230 @ SV155 ) )
= $true )
| ( ( epsilon_transitive @ SV230 )
= $true )
| ( ( ordinal @ SV155 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2006]) ).
thf(2030,plain,
! [SV210: $i] :
( ( ( relation @ SV210 )
= $false )
| ( ( empty @ SV210 )
= $false )
| ( ( ~ ( function @ SV210 ) )
= $true )
| ( ( function @ SV210 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2007]) ).
thf(2031,plain,
! [SV211: $i] :
( ( ( relation @ SV211 )
= $false )
| ( ( empty @ SV211 )
= $false )
| ( ( ~ ( function @ SV211 ) )
= $true )
| ( ( relation @ SV211 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2008]) ).
thf(2032,plain,
( ( ~ ( empty @ sK27_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2009]) ).
thf(2033,plain,
( ( epsilon_transitive @ sK27_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2010]) ).
thf(2034,plain,
( ( element @ sK18_A @ positive_rationals )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2011]) ).
thf(2035,plain,
( ( ~ ( empty @ sK18_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2012]) ).
thf(2036,plain,
! [SV225: $i] :
( ( ( element @ SV225 @ positive_rationals )
= $false )
| ( ( ~ ( ordinal @ SV225 )
| ( epsilon_connected @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2013]) ).
thf(2037,plain,
! [SV226: $i] :
( ( ( element @ SV226 @ positive_rationals )
= $false )
| ( ( ~ ( ordinal @ SV226 )
| ( epsilon_transitive @ SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2014]) ).
thf(2038,plain,
( ( ~ ( ~ ( element @ sK10_A @ positive_rationals )
| ~ ( empty @ sK10_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2016]) ).
thf(2039,plain,
( ( epsilon_transitive @ sK10_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2017]) ).
thf(2040,plain,
! [SV152: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV152 ) @ ( powerset @ SV152 ) )
| ~ ( empty @ ( sK17_B @ SV152 ) ) )
| ~ ( relation @ ( sK17_B @ SV152 ) ) )
| ~ ( function @ ( sK17_B @ SV152 ) ) )
| ~ ( one_to_one @ ( sK17_B @ SV152 ) ) )
| ~ ( epsilon_transitive @ ( sK17_B @ SV152 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2018]) ).
thf(2041,plain,
! [SV152: $i] :
( ( ~ ( epsilon_connected @ ( sK17_B @ SV152 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2018]) ).
thf(2042,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2019]) ).
thf(2043,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2020]) ).
thf(2044,plain,
( ( ~ ( ~ ~ ( ~ ( function @ sK15_A )
| ~ ( relation @ sK15_A ) )
| ~ ( one_to_one @ sK15_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2021]) ).
thf(2045,plain,
( ( empty @ sK15_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2022]) ).
thf(2046,plain,
! [SV215: $i] :
( ( ( relation @ SV215 )
= $false )
| ( ( function @ SV215 )
= $false )
| ( ( ~ ( transfinite_sequence @ SV215 ) )
= $true )
| ( ( epsilon_connected @ ( relation_dom @ SV215 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2023]) ).
thf(2047,plain,
! [SV216: $i] :
( ( ( relation @ SV216 )
= $false )
| ( ( function @ SV216 )
= $false )
| ( ( ~ ( transfinite_sequence @ SV216 ) )
= $true )
| ( ( epsilon_transitive @ ( relation_dom @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2024]) ).
thf(2048,plain,
! [SV227: $i] :
( ( ( ~ ( empty @ SV227 ) )
= $true )
| ( ( ~ ( ordinal @ SV227 ) )
= $true )
| ( ( epsilon_connected @ SV227 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2025]) ).
thf(2049,plain,
! [SV228: $i] :
( ( ( ~ ( empty @ SV228 ) )
= $true )
| ( ( ~ ( ordinal @ SV228 ) )
= $true )
| ( ( epsilon_transitive @ SV228 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2026]) ).
thf(2050,plain,
! [SV155: $i,SV229: $i] :
( ( ( element @ SV229 @ SV155 )
= $false )
| ( ( epsilon_connected @ SV229 )
= $true )
| ( ( ordinal @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2028]) ).
thf(2051,plain,
! [SV155: $i,SV230: $i] :
( ( ( element @ SV230 @ SV155 )
= $false )
| ( ( epsilon_transitive @ SV230 )
= $true )
| ( ( ordinal @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2029]) ).
thf(2052,plain,
! [SV210: $i] :
( ( ( function @ SV210 )
= $false )
| ( ( empty @ SV210 )
= $false )
| ( ( relation @ SV210 )
= $false )
| ( ( function @ SV210 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2030]) ).
thf(2053,plain,
! [SV211: $i] :
( ( ( function @ SV211 )
= $false )
| ( ( empty @ SV211 )
= $false )
| ( ( relation @ SV211 )
= $false )
| ( ( relation @ SV211 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2031]) ).
thf(2054,plain,
( ( empty @ sK27_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2032]) ).
thf(2055,plain,
( ( empty @ sK18_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2035]) ).
thf(2056,plain,
! [SV225: $i] :
( ( ( ~ ( ordinal @ SV225 ) )
= $true )
| ( ( epsilon_connected @ SV225 )
= $true )
| ( ( element @ SV225 @ positive_rationals )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2036]) ).
thf(2057,plain,
! [SV226: $i] :
( ( ( ~ ( ordinal @ SV226 ) )
= $true )
| ( ( epsilon_transitive @ SV226 )
= $true )
| ( ( element @ SV226 @ positive_rationals )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2037]) ).
thf(2058,plain,
( ( ~ ( element @ sK10_A @ positive_rationals )
| ~ ( empty @ sK10_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2038]) ).
thf(2059,plain,
! [SV152: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV152 ) @ ( powerset @ SV152 ) )
| ~ ( empty @ ( sK17_B @ SV152 ) ) )
| ~ ( relation @ ( sK17_B @ SV152 ) ) )
| ~ ( function @ ( sK17_B @ SV152 ) ) )
| ~ ( one_to_one @ ( sK17_B @ SV152 ) ) )
| ~ ( epsilon_transitive @ ( sK17_B @ SV152 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2040]) ).
thf(2060,plain,
! [SV152: $i] :
( ( epsilon_connected @ ( sK17_B @ SV152 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2041]) ).
thf(2061,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2042]) ).
thf(2062,plain,
( ( ~ ~ ( ~ ( function @ sK15_A )
| ~ ( relation @ sK15_A ) )
| ~ ( one_to_one @ sK15_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2044]) ).
thf(2063,plain,
! [SV215: $i] :
( ( ( transfinite_sequence @ SV215 )
= $false )
| ( ( function @ SV215 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( epsilon_connected @ ( relation_dom @ SV215 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2046]) ).
thf(2064,plain,
! [SV216: $i] :
( ( ( transfinite_sequence @ SV216 )
= $false )
| ( ( function @ SV216 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( epsilon_transitive @ ( relation_dom @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2047]) ).
thf(2065,plain,
! [SV227: $i] :
( ( ( empty @ SV227 )
= $false )
| ( ( ~ ( ordinal @ SV227 ) )
= $true )
| ( ( epsilon_connected @ SV227 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2048]) ).
thf(2066,plain,
! [SV228: $i] :
( ( ( empty @ SV228 )
= $false )
| ( ( ~ ( ordinal @ SV228 ) )
= $true )
| ( ( epsilon_transitive @ SV228 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2049]) ).
thf(2067,plain,
! [SV225: $i] :
( ( ( ordinal @ SV225 )
= $false )
| ( ( epsilon_connected @ SV225 )
= $true )
| ( ( element @ SV225 @ positive_rationals )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2056]) ).
thf(2068,plain,
! [SV226: $i] :
( ( ( ordinal @ SV226 )
= $false )
| ( ( epsilon_transitive @ SV226 )
= $true )
| ( ( element @ SV226 @ positive_rationals )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2057]) ).
thf(2069,plain,
( ( ~ ( element @ sK10_A @ positive_rationals ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2058]) ).
thf(2070,plain,
( ( ~ ( empty @ sK10_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2058]) ).
thf(2071,plain,
! [SV152: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV152 ) @ ( powerset @ SV152 ) )
| ~ ( empty @ ( sK17_B @ SV152 ) ) )
| ~ ( relation @ ( sK17_B @ SV152 ) ) )
| ~ ( function @ ( sK17_B @ SV152 ) ) )
| ~ ( one_to_one @ ( sK17_B @ SV152 ) ) )
| ~ ( epsilon_transitive @ ( sK17_B @ SV152 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2059]) ).
thf(2072,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2061]) ).
thf(2073,plain,
( ( ~ ( one_to_one @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2061]) ).
thf(2074,plain,
( ( ~ ~ ( ~ ( function @ sK15_A )
| ~ ( relation @ sK15_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2062]) ).
thf(2075,plain,
( ( ~ ( one_to_one @ sK15_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2062]) ).
thf(2076,plain,
! [SV227: $i] :
( ( ( ordinal @ SV227 )
= $false )
| ( ( empty @ SV227 )
= $false )
| ( ( epsilon_connected @ SV227 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2065]) ).
thf(2077,plain,
! [SV228: $i] :
( ( ( ordinal @ SV228 )
= $false )
| ( ( empty @ SV228 )
= $false )
| ( ( epsilon_transitive @ SV228 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2066]) ).
thf(2078,plain,
( ( element @ sK10_A @ positive_rationals )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2069]) ).
thf(2079,plain,
( ( empty @ sK10_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2070]) ).
thf(2080,plain,
! [SV152: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV152 ) @ ( powerset @ SV152 ) )
| ~ ( empty @ ( sK17_B @ SV152 ) ) )
| ~ ( relation @ ( sK17_B @ SV152 ) ) )
| ~ ( function @ ( sK17_B @ SV152 ) ) )
| ~ ( one_to_one @ ( sK17_B @ SV152 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2071]) ).
thf(2081,plain,
! [SV152: $i] :
( ( ~ ( epsilon_transitive @ ( sK17_B @ SV152 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2071]) ).
thf(2082,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2072]) ).
thf(2083,plain,
( ( one_to_one @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2073]) ).
thf(2084,plain,
( ( ~ ( ~ ( function @ sK15_A )
| ~ ( relation @ sK15_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2074]) ).
thf(2085,plain,
( ( one_to_one @ sK15_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2075]) ).
thf(2086,plain,
! [SV152: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV152 ) @ ( powerset @ SV152 ) )
| ~ ( empty @ ( sK17_B @ SV152 ) ) )
| ~ ( relation @ ( sK17_B @ SV152 ) ) )
| ~ ( function @ ( sK17_B @ SV152 ) ) )
| ~ ( one_to_one @ ( sK17_B @ SV152 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2080]) ).
thf(2087,plain,
! [SV152: $i] :
( ( epsilon_transitive @ ( sK17_B @ SV152 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2081]) ).
thf(2088,plain,
( ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2082]) ).
thf(2089,plain,
( ( ~ ( function @ sK15_A )
| ~ ( relation @ sK15_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2084]) ).
thf(2090,plain,
! [SV152: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV152 ) @ ( powerset @ SV152 ) )
| ~ ( empty @ ( sK17_B @ SV152 ) ) )
| ~ ( relation @ ( sK17_B @ SV152 ) ) )
| ~ ( function @ ( sK17_B @ SV152 ) ) )
| ~ ( one_to_one @ ( sK17_B @ SV152 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2086]) ).
thf(2091,plain,
( ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2088]) ).
thf(2092,plain,
( ( ~ ( function @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2088]) ).
thf(2093,plain,
( ( ~ ( function @ sK15_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2089]) ).
thf(2094,plain,
( ( ~ ( relation @ sK15_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2089]) ).
thf(2095,plain,
! [SV152: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV152 ) @ ( powerset @ SV152 ) )
| ~ ( empty @ ( sK17_B @ SV152 ) ) )
| ~ ( relation @ ( sK17_B @ SV152 ) ) )
| ~ ( function @ ( sK17_B @ SV152 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2090]) ).
thf(2096,plain,
! [SV152: $i] :
( ( ~ ( one_to_one @ ( sK17_B @ SV152 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2090]) ).
thf(2097,plain,
( ( ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2091]) ).
thf(2098,plain,
( ( function @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2092]) ).
thf(2099,plain,
( ( function @ sK15_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2093]) ).
thf(2100,plain,
( ( relation @ sK15_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2094]) ).
thf(2101,plain,
! [SV152: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV152 ) @ ( powerset @ SV152 ) )
| ~ ( empty @ ( sK17_B @ SV152 ) ) )
| ~ ( relation @ ( sK17_B @ SV152 ) ) )
| ~ ( function @ ( sK17_B @ SV152 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2095]) ).
thf(2102,plain,
! [SV152: $i] :
( ( one_to_one @ ( sK17_B @ SV152 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2096]) ).
thf(2103,plain,
( ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2097]) ).
thf(2104,plain,
! [SV152: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV152 ) @ ( powerset @ SV152 ) )
| ~ ( empty @ ( sK17_B @ SV152 ) ) )
| ~ ( relation @ ( sK17_B @ SV152 ) ) )
| ~ ( function @ ( sK17_B @ SV152 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2101]) ).
thf(2105,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2103]) ).
thf(2106,plain,
( ( ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2103]) ).
thf(2107,plain,
! [SV152: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV152 ) @ ( powerset @ SV152 ) )
| ~ ( empty @ ( sK17_B @ SV152 ) ) )
| ~ ( relation @ ( sK17_B @ SV152 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2104]) ).
thf(2108,plain,
! [SV152: $i] :
( ( ~ ( function @ ( sK17_B @ SV152 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2104]) ).
thf(2109,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2105]) ).
thf(2110,plain,
( ( relation_empty_yielding @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2106]) ).
thf(2111,plain,
! [SV152: $i] :
( ( ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV152 ) @ ( powerset @ SV152 ) )
| ~ ( empty @ ( sK17_B @ SV152 ) ) )
| ~ ( relation @ ( sK17_B @ SV152 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2107]) ).
thf(2112,plain,
! [SV152: $i] :
( ( function @ ( sK17_B @ SV152 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2108]) ).
thf(2113,plain,
! [SV152: $i] :
( ( ~ ~ ( ~ ( element @ ( sK17_B @ SV152 ) @ ( powerset @ SV152 ) )
| ~ ( empty @ ( sK17_B @ SV152 ) ) )
| ~ ( relation @ ( sK17_B @ SV152 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2111]) ).
thf(2114,plain,
! [SV152: $i] :
( ( ~ ~ ( ~ ( element @ ( sK17_B @ SV152 ) @ ( powerset @ SV152 ) )
| ~ ( empty @ ( sK17_B @ SV152 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2113]) ).
thf(2115,plain,
! [SV152: $i] :
( ( ~ ( relation @ ( sK17_B @ SV152 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2113]) ).
thf(2116,plain,
! [SV152: $i] :
( ( ~ ( ~ ( element @ ( sK17_B @ SV152 ) @ ( powerset @ SV152 ) )
| ~ ( empty @ ( sK17_B @ SV152 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2114]) ).
thf(2117,plain,
! [SV152: $i] :
( ( relation @ ( sK17_B @ SV152 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2115]) ).
thf(2118,plain,
! [SV152: $i] :
( ( ~ ( element @ ( sK17_B @ SV152 ) @ ( powerset @ SV152 ) )
| ~ ( empty @ ( sK17_B @ SV152 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2116]) ).
thf(2119,plain,
! [SV152: $i] :
( ( ~ ( element @ ( sK17_B @ SV152 ) @ ( powerset @ SV152 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2118]) ).
thf(2120,plain,
! [SV152: $i] :
( ( ~ ( empty @ ( sK17_B @ SV152 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2118]) ).
thf(2121,plain,
! [SV152: $i] :
( ( element @ ( sK17_B @ SV152 ) @ ( powerset @ SV152 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2119]) ).
thf(2122,plain,
! [SV152: $i] :
( ( empty @ ( sK17_B @ SV152 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2120]) ).
thf(2123,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[1208,2122,2121,2117,2112,2110,2109,2102,2100,2099,2098,2087,2085,2083,2079,2078,2077,2076,2068,2067,2064,2063,2060,2055,2054,2053,2052,2051,2050,2045,2043,2039,2034,2033,2027,2015,2004,2000,1995,1987,1984,1983,1982,1981,1978,1976,1969,1967,1963,1962,1961,1959,1958,1957,1956,1952,1950,1942,1941,1940,1933,1932,1931,1930,1910,1899,1898,1896,1875,1872,1871,1857,1856,1853,1849,1848,1847,1844,1843,1840,1838,1837,1833,1832,1825,1824,1823,1822,1821,1819,1818,1817,1813,1811,1810,1807,1805,1802,1797,1795,1793,1792,1788,1787,1786,1785,1784,1780,1778,1775,1772,1771,1766,1765,1754,1734,1733,1699,1696,1691,1689,1687,1686,1683,1681,1679,1678,1668,1653,1645,1639,1632,1631,1617,1598,1591,1588,1587,1586,1584,1582,1581,1577,1569,1565,1563,1559,1555,1553,1548,1547,1543,1539,1538,1535,1533,1531,1527,1525,1523,1522,1519,1514,1496,1495,1494,1404,1398,1395,1394,1330,1327,1326,1317,1264,1263,1227]) ).
thf(2124,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[2123,1183]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU098+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 18 23:37:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.37 .
% 0.12/0.37
% 0.12/0.37 No.of.Axioms: 79
% 0.12/0.37
% 0.12/0.37 Length.of.Defs: 0
% 0.12/0.37
% 0.12/0.37 Contains.Choice.Funs: false
% 0.18/0.40 .
% 0.18/0.42 (rf:0,axioms:79,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:81,loop_count:0,foatp_calls:0,translation:fof_full)............................................................................
% 1.88/2.06
% 1.88/2.06 ********************************
% 1.88/2.06 * All subproblems solved! *
% 1.88/2.06 ********************************
% 1.88/2.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:81,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2123,loop_count:0,foatp_calls:1,translation:fof_full)
% 3.04/3.24
% 3.04/3.24 %**** Beginning of derivation protocol ****
% 3.04/3.24 % SZS output start CNFRefutation
% See solution above
% 3.04/3.24
% 3.04/3.24 %**** End of derivation protocol ****
% 3.04/3.24 %**** no. of clauses in derivation: 2124 ****
% 3.04/3.24 %**** clause counter: 2123 ****
% 3.04/3.24
% 3.04/3.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:81,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2123,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------