TSTP Solution File: SEU187+2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU187+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n016.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 12:07:50 EDT 2022
% Result : Theorem 2.33s 2.57s
% Output : CNFRefutation 6.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 190
% Syntax : Number of formulae : 3365 (1626 unt; 70 typ; 0 def)
% Number of atoms : 23516 (8545 equ; 0 cnn)
% Maximal formula atoms : 11 ( 7 avg)
% Number of connectives : 48735 (8826 ~;8295 |; 400 &;30976 @)
% ( 84 <=>; 154 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 120 ( 120 >; 0 *; 0 +; 0 <<)
% Number of symbols : 73 ( 70 usr; 7 con; 0-3 aty)
% Number of variables : 9381 ( 0 ^9355 !; 26 ?;9381 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_are_equipotent,type,
are_equipotent: $i > $i > $o ).
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_cast_to_subset,type,
cast_to_subset: $i > $i ).
thf(tp_complements_of_subsets,type,
complements_of_subsets: $i > $i > $i ).
thf(tp_disjoint,type,
disjoint: $i > $i > $o ).
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_in,type,
in: $i > $i > $o ).
thf(tp_meet_of_subsets,type,
meet_of_subsets: $i > $i > $i ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_proper_subset,type,
proper_subset: $i > $i > $o ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_composition,type,
relation_composition: $i > $i > $i ).
thf(tp_relation_dom,type,
relation_dom: $i > $i ).
thf(tp_relation_field,type,
relation_field: $i > $i ).
thf(tp_relation_inverse,type,
relation_inverse: $i > $i ).
thf(tp_relation_rng,type,
relation_rng: $i > $i ).
thf(tp_sK10_C,type,
sK10_C: $i > $i > $i ).
thf(tp_sK11_SY272,type,
sK11_SY272: $i > $i > $i ).
thf(tp_sK12_D,type,
sK12_D: $i > $i > $i > $i ).
thf(tp_sK13_C,type,
sK13_C: $i > $i > $i ).
thf(tp_sK14_SY274,type,
sK14_SY274: $i > $i > $i ).
thf(tp_sK15_D,type,
sK15_D: $i > $i > $i > $i ).
thf(tp_sK16_D,type,
sK16_D: $i > $i > $i > $i ).
thf(tp_sK17_C,type,
sK17_C: $i > $i > $i ).
thf(tp_sK18_SY276,type,
sK18_SY276: $i > $i > $i ).
thf(tp_sK19_D,type,
sK19_D: $i > $i > $i > $i ).
thf(tp_sK1_B,type,
sK1_B: $i > $i ).
thf(tp_sK20_C,type,
sK20_C: $i > $i > $i ).
thf(tp_sK21_SY278,type,
sK21_SY278: $i > $i > $i ).
thf(tp_sK22_D,type,
sK22_D: $i > $i > $i > $i ).
thf(tp_sK23_C,type,
sK23_C: $i > $i > $i ).
thf(tp_sK24_D,type,
sK24_D: $i > $i > $i > $i ).
thf(tp_sK25_D,type,
sK25_D: $i > $i > $i > $i ).
thf(tp_sK26_C,type,
sK26_C: $i > $i > $i ).
thf(tp_sK27_C,type,
sK27_C: $i > $i > $i ).
thf(tp_sK28_C,type,
sK28_C: $i > $i > $i ).
thf(tp_sK29_SY279,type,
sK29_SY279: $i > $i > $i ).
thf(tp_sK2_SY267,type,
sK2_SY267: $i > $i > $i ).
thf(tp_sK30_B,type,
sK30_B: $i > $i ).
thf(tp_sK31_B,type,
sK31_B: $i > $i ).
thf(tp_sK32_SY282,type,
sK32_SY282: $i > $i ).
thf(tp_sK33_C,type,
sK33_C: $i > $i > $i ).
thf(tp_sK34_C,type,
sK34_C: $i > $i > $i ).
thf(tp_sK35_B,type,
sK35_B: $i > $i ).
thf(tp_sK36_C,type,
sK36_C: $i > $i > $i ).
thf(tp_sK37_B,type,
sK37_B: $i > $i ).
thf(tp_sK38_D,type,
sK38_D: $i > $i > $i > $i ).
thf(tp_sK39_C,type,
sK39_C: $i > $i > $i ).
thf(tp_sK3_C,type,
sK3_C: $i > $i > $i ).
thf(tp_sK40_SY287,type,
sK40_SY287: $i > $i > $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_B,type,
sK8_B: $i > $i ).
thf(tp_sK9_A,type,
sK9_A: $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_set_intersection2,type,
set_intersection2: $i > $i > $i ).
thf(tp_set_meet,type,
set_meet: $i > $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subset_complement,type,
subset_complement: $i > $i > $i ).
thf(tp_subset_difference,type,
subset_difference: $i > $i > $i > $i ).
thf(tp_union,type,
union: $i > $i ).
thf(tp_union_of_subsets,type,
union_of_subsets: $i > $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(1,axiom,
! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
( ( subset @ E @ C )
=> ( in @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_tarski) ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(4,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(7,axiom,
! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(9,axiom,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(12,axiom,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(14,axiom,
! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(16,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(20,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(21,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(22,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(23,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(24,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(25,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(28,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(32,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(33,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(35,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(37,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(39,axiom,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_relat_1) ).
thf(41,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(42,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(43,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(53,axiom,
! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relat_1) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
thf(71,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
thf(72,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( B
= ( relation_inverse @ A ) )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ B )
<=> ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_relat_1) ).
thf(73,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_1) ).
thf(76,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
thf(80,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_dom @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(82,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
thf(86,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
=> ( ( element @ B @ A )
<=> ( in @ B @ A ) ) )
& ( ( empty @ A )
=> ( ( element @ B @ A )
<=> ( empty @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
thf(87,axiom,
! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(88,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(89,axiom,
! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
thf(90,axiom,
! [A: $i,B: $i] :
( ( ( A != empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ! [D: $i] :
( ( in @ D @ A )
=> ( in @ C @ D ) ) ) ) )
& ( ( A = empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ( B = empty_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_setfam_1) ).
thf(91,axiom,
! [A: $i] :
( ( relation @ A )
<=> ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_1) ).
thf(92,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(93,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(94,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(96,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(98,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(99,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_zfmisc_1) ).
thf(100,axiom,
! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(101,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(104,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_difference @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).
thf(105,axiom,
! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(106,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(107,axiom,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
thf(108,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
= A )
<=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_zfmisc_1) ).
thf(109,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(110,axiom,
! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_xboole_1) ).
thf(111,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_relat_1) ).
thf(114,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(115,axiom,
! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).
thf(118,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_rng @ B ) )
=> ( ( relation_rng @ ( relation_composition @ B @ A ) )
= ( relation_rng @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_relat_1) ).
thf(119,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_zfmisc_1) ).
thf(121,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ ( relation_rng @ A ) @ ( relation_dom @ B ) )
=> ( ( relation_dom @ ( relation_composition @ A @ B ) )
= ( relation_dom @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_relat_1) ).
thf(122,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_xboole_1) ).
thf(123,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_relat_1) ).
thf(124,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_relat_1) ).
thf(126,axiom,
! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_xboole_1) ).
thf(127,axiom,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(128,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( in @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
& ( disjoint @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(129,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(130,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).
thf(131,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ C )
& ( in @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).
thf(132,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(133,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(134,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( relation_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( relation_inverse @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_relat_1) ).
thf(135,axiom,
! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(139,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(140,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(141,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(142,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) )
& ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relat_1) ).
thf(143,axiom,
! [A: $i] :
( ( relation @ A )
=> ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_relat_1) ).
thf(144,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_dom @ C ) )
& ( in @ B @ ( relation_rng @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).
thf(145,axiom,
( ( powerset @ empty_set )
= ( singleton @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(146,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(147,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(148,axiom,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(149,axiom,
! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( powerset @ C ) @ B ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t136_zfmisc_1) ).
thf(150,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(151,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(155,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l71_subset_1) ).
thf(157,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l50_zfmisc_1) ).
thf(158,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).
thf(159,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_zfmisc_1) ).
thf(160,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_subset_1) ).
thf(161,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_xboole_1) ).
thf(162,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(163,axiom,
! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l28_zfmisc_1) ).
thf(164,axiom,
! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l25_zfmisc_1) ).
thf(165,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l23_zfmisc_1) ).
thf(166,axiom,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
thf(167,conjecture,
( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).
thf(168,negated_conjecture,
( ( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) )
= $false ),
inference(negate_conjecture,[status(cth)],[167]) ).
thf(169,plain,
( ( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) )
= $false ),
inference(unfold_def,[status(thm)],[168]) ).
thf(170,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
( ( subset @ E @ C )
=> ( in @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(171,plain,
( ( ! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(172,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(173,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(174,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(175,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(176,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(177,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(178,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(179,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(180,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(181,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(182,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(183,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(184,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(185,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(186,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(187,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(188,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(189,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(190,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(191,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(192,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(193,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(194,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(195,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(196,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(197,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(198,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(199,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(200,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(201,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( B
= ( relation_inverse @ A ) )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ B )
<=> ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(202,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(203,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(204,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(205,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(206,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_dom @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(207,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(208,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(209,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(210,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(211,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
=> ( ( element @ B @ A )
<=> ( in @ B @ A ) ) )
& ( ( empty @ A )
=> ( ( element @ B @ A )
<=> ( empty @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(212,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(213,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(214,plain,
( ( ! [A: $i] :
( ( relation @ A )
<=> ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(215,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(216,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(217,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(218,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(219,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(220,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(221,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(222,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(223,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(224,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(225,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_difference @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(226,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(227,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(228,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(229,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
= A )
<=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(230,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(231,plain,
( ( ! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(232,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(233,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(234,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(235,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_rng @ B ) )
=> ( ( relation_rng @ ( relation_composition @ B @ A ) )
= ( relation_rng @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(236,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(237,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ ( relation_rng @ A ) @ ( relation_dom @ B ) )
=> ( ( relation_dom @ ( relation_composition @ A @ B ) )
= ( relation_dom @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(238,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(239,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(240,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(241,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(242,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( in @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
& ( disjoint @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(243,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(244,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ C )
& ( in @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(245,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(246,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(247,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(248,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(249,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(250,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(251,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_dom @ C ) )
& ( in @ B @ ( relation_rng @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(252,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(253,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(254,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(255,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( powerset @ C ) @ B ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(256,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(257,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(258,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(259,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(260,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(261,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(262,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(263,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(264,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(265,plain,
( ( ! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(266,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(267,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(268,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(269,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(270,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(271,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(272,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(273,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(274,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(275,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(276,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(277,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(278,plain,
( ( ! [A: $i,B: $i] :
( ( ( A != empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ! [D: $i] :
( ( in @ D @ A )
=> ( in @ C @ D ) ) ) ) )
& ( ( A = empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ( B = empty_set ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(279,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(280,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(281,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(282,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( relation_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( relation_inverse @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(283,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(284,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) )
& ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(285,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(286,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(287,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(288,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(289,plain,
( ( ( relation_dom @ empty_set )
= empty_set )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[169]) ).
thf(290,plain,
( ( ( relation_rng @ empty_set )
= empty_set )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[169]) ).
thf(291,plain,
( ( ( ( relation_dom @ empty_set )
!= empty_set ) )
= $true ),
inference(polarity_switch,[status(thm)],[289]) ).
thf(292,plain,
( ( ( ( relation_rng @ empty_set )
!= empty_set ) )
= $true ),
inference(polarity_switch,[status(thm)],[290]) ).
thf(293,plain,
( ( ! [A: $i] :
( ! [SY265: $i] :
( ~ ( subset @ SY265 @ ( sK1_B @ A ) )
| ( are_equipotent @ SY265 @ ( sK1_B @ A ) )
| ( in @ SY265 @ ( sK1_B @ A ) ) )
& ! [SY266: $i] :
( ( ! [SY271: $i] :
( ~ ( subset @ SY271 @ SY266 )
| ( in @ SY271 @ ( sK2_SY267 @ SY266 @ A ) ) )
& ( in @ ( sK2_SY267 @ SY266 @ A ) @ ( sK1_B @ A ) ) )
| ~ ( in @ SY266 @ ( sK1_B @ A ) ) )
& ! [SY269: $i,SY270: $i] :
( ~ ( in @ SY269 @ ( sK1_B @ A ) )
| ~ ( subset @ SY270 @ SY269 )
| ( in @ SY270 @ ( sK1_B @ A ) ) )
& ( in @ A @ ( sK1_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[170]) ).
thf(294,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[171]) ).
thf(295,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[172]) ).
thf(296,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[173]) ).
thf(297,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[174]) ).
thf(298,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)],[175]) ).
thf(299,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK3_C @ B @ A ) @ A )
| ~ ( in @ ( sK3_C @ B @ A ) @ B ) )
& ( ( in @ ( sK3_C @ B @ A ) @ A )
| ( in @ ( sK3_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[176]) ).
thf(300,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[177]) ).
thf(301,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[178]) ).
thf(302,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[179]) ).
thf(303,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[180]) ).
thf(304,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[181]) ).
thf(305,plain,
( ( ! [A: $i] :
( ( element @ ( sK5_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK5_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[182]) ).
thf(306,plain,
( ( ~ ( empty @ sK6_A )
& ( relation @ sK6_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[183]) ).
thf(307,plain,
( ( empty @ sK7_A )
= $true ),
inference(extcnf_combined,[status(esa)],[184]) ).
thf(308,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK8_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK8_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[185]) ).
thf(309,plain,
( ( ( empty @ sK9_A )
& ( relation @ sK9_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[186]) ).
thf(310,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[187]) ).
thf(311,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[188]) ).
thf(312,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[189]) ).
thf(313,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[190]) ).
thf(314,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[191]) ).
thf(315,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[193]) ).
thf(316,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[195]) ).
thf(317,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[198]) ).
thf(318,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[199]) ).
thf(319,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ( proper_subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( A != B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[200]) ).
thf(320,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK10_C @ B @ A ) @ ( sK11_SY272 @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK11_SY272 @ B @ A ) @ ( sK10_C @ B @ A ) ) @ A ) )
& ( ( in @ ( ordered_pair @ ( sK10_C @ B @ A ) @ ( sK11_SY272 @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK11_SY272 @ B @ A ) @ ( sK10_C @ B @ A ) ) @ A ) ) )
| ( B
= ( relation_inverse @ A ) ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ( B
!= ( relation_inverse @ A ) )
| ( ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ B )
| ( in @ ( ordered_pair @ D @ C ) @ A ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ D @ C ) @ A )
| ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[201]) ).
thf(321,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[202]) ).
thf(322,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY273: $i] :
~ ( in @ ( ordered_pair @ SY273 @ ( sK13_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK13_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK14_SY274 @ B @ A ) @ ( sK13_C @ B @ A ) ) @ A )
| ( in @ ( sK13_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_rng @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_rng @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ D @ C ) @ A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ ( sK12_D @ C @ B @ A ) @ C ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[203]) ).
thf(323,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK15_D @ C @ B @ A ) @ A )
| ( in @ ( sK15_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK15_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK15_D @ C @ B @ A ) @ A )
| ( in @ ( sK15_D @ C @ B @ A ) @ C ) )
& ( ~ ( in @ ( sK15_D @ C @ B @ A ) @ B )
| ( in @ ( sK15_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_difference @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_difference @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ~ ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[204]) ).
thf(324,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY275: $i] :
( ~ ( in @ ( sK17_C @ B @ A ) @ SY275 )
| ~ ( in @ SY275 @ A ) )
| ~ ( in @ ( sK17_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK17_C @ B @ A ) @ ( sK18_SY276 @ B @ A ) )
& ( in @ ( sK18_SY276 @ B @ A ) @ A ) )
| ( in @ ( sK17_C @ B @ A ) @ B ) ) )
| ( B
= ( union @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( union @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
( ~ ( in @ C @ D )
| ~ ( in @ D @ A ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( ( in @ C @ ( sK16_D @ C @ B @ A ) )
& ( in @ ( sK16_D @ C @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[205]) ).
thf(325,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY277: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ B @ A ) @ SY277 ) @ A )
| ~ ( in @ ( sK20_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK20_C @ B @ A ) @ ( sK21_SY278 @ B @ A ) ) @ A )
| ( in @ ( sK20_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_dom @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_dom @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ C @ ( sK19_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[206]) ).
thf(326,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK22_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK22_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK22_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK22_D @ C @ B @ A ) @ A )
| ( in @ ( sK22_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK22_D @ C @ B @ A ) @ B )
| ( in @ ( sK22_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_intersection2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_intersection2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ~ ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[207]) ).
thf(327,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK23_C @ B @ A ) @ A )
& ~ ( in @ ( sK23_C @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[208]) ).
thf(328,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK24_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK24_D @ C @ B @ A ) @ A ) )
& ( ~ ( in @ ( sK24_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK24_D @ C @ B @ A ) @ B ) )
& ( ( in @ ( sK24_D @ C @ B @ A ) @ C )
| ( in @ ( sK24_D @ C @ B @ A ) @ A )
| ( in @ ( sK24_D @ C @ B @ A ) @ B ) ) )
| ( C
= ( set_union2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_union2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A )
| ( in @ D @ B ) )
& ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[209]) ).
thf(329,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK25_D @ C @ B @ A ) @ C )
| ( ( sK25_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK25_D @ C @ B @ A ) @ C )
| ( ( sK25_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK25_D @ C @ B @ A ) @ C )
| ( ( sK25_D @ C @ B @ A )
= A )
| ( ( sK25_D @ C @ B @ A )
= B ) ) )
| ( C
= ( unordered_pair @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( unordered_pair @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( D = A )
| ( D = B ) )
& ! [D: $i] :
( ( D != A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ( D != B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[210]) ).
thf(330,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
( ~ ( element @ B @ A )
| ( in @ B @ A ) ) )
& ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
( ~ ( in @ B @ A )
| ( element @ B @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ! [B: $i] :
( ~ ( element @ B @ A )
| ( empty @ B ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ! [B: $i] :
( ~ ( empty @ B )
| ( element @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[211]) ).
thf(331,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK26_C @ B @ A ) @ B )
| ~ ( subset @ ( sK26_C @ B @ A ) @ A ) )
& ( ( in @ ( sK26_C @ B @ A ) @ B )
| ( subset @ ( sK26_C @ B @ A ) @ A ) ) )
| ( B
= ( powerset @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( powerset @ A ) )
| ( ! [C: $i] :
( ~ ( in @ C @ B )
| ( subset @ C @ A ) )
& ! [C: $i] :
( ~ ( subset @ C @ A )
| ( in @ C @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[212]) ).
thf(332,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK27_C @ B @ A )
!= A )
| ~ ( in @ ( sK27_C @ B @ A ) @ B ) )
& ( ( ( sK27_C @ B @ A )
= A )
| ( in @ ( sK27_C @ B @ A ) @ B ) ) )
| ( B
= ( singleton @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( singleton @ A ) )
| ( ! [C: $i] :
( ( C != A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( C = A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[213]) ).
thf(333,plain,
( ( ! [A: $i] :
( ( ! [SY280: $i,SY281: $i] :
( ( sK30_B @ A )
!= ( ordered_pair @ SY280 @ SY281 ) )
& ( in @ ( sK30_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK28_C @ B @ A ) @ ( sK29_SY279 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[214]) ).
thf(334,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[215]) ).
thf(335,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[218]) ).
thf(336,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[219]) ).
thf(337,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( B = C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[220]) ).
thf(338,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[222]) ).
thf(339,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[223]) ).
thf(340,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ B )
| ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[224]) ).
thf(341,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= A )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_difference @ A @ B )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[225]) ).
thf(342,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[227]) ).
thf(343,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
!= A )
| ~ ( in @ B @ A ) )
& ! [A: $i,B: $i] :
( ( in @ B @ A )
| ( ( set_difference @ A @ ( singleton @ B ) )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[229]) ).
thf(344,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[230]) ).
thf(345,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[231]) ).
thf(346,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( in @ ( ordered_pair @ ( sK31_B @ A ) @ ( sK32_SY282 @ A ) ) @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[232]) ).
thf(347,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sK33_C @ B @ A ) @ ( set_intersection2 @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[233]) ).
thf(348,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ ( relation_dom @ A ) @ ( relation_rng @ B ) )
| ( ( relation_rng @ ( relation_composition @ B @ A ) )
= ( relation_rng @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[235]) ).
thf(349,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[236]) ).
thf(350,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ ( relation_rng @ A ) @ ( relation_dom @ B ) )
| ( ( relation_dom @ ( relation_composition @ A @ B ) )
= ( relation_dom @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[237]) ).
thf(351,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[238]) ).
thf(352,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[239]) ).
thf(353,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[240]) ).
thf(354,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK34_C @ B @ A ) @ A )
& ( in @ ( sK34_C @ B @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ C @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[242]) ).
thf(355,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ C )
| ( subset @ ( unordered_pair @ A @ B ) @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ A @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[244]) ).
thf(356,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[245]) ).
thf(357,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[247]) ).
thf(358,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[248]) ).
thf(359,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[249]) ).
thf(360,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[250]) ).
thf(361,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ A @ ( relation_dom @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ B @ ( relation_rng @ C ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[251]) ).
thf(362,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[252]) ).
thf(363,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ A @ C )
| ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[253]) ).
thf(364,plain,
( ( ! [A: $i] :
( ! [SY283: $i] :
( ~ ( subset @ SY283 @ ( sK35_B @ A ) )
| ( are_equipotent @ SY283 @ ( sK35_B @ A ) )
| ( in @ SY283 @ ( sK35_B @ A ) ) )
& ! [SY284: $i] :
( ~ ( in @ SY284 @ ( sK35_B @ A ) )
| ( in @ ( powerset @ SY284 ) @ ( sK35_B @ A ) ) )
& ! [SY285: $i,SY286: $i] :
( ~ ( in @ SY285 @ ( sK35_B @ A ) )
| ~ ( subset @ SY286 @ SY285 )
| ( in @ SY286 @ ( sK35_B @ A ) ) )
& ( in @ A @ ( sK35_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[255]) ).
thf(365,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[256]) ).
thf(366,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ D )
| ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[257]) ).
thf(367,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) ) )
& ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[258]) ).
thf(368,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK36_C @ B @ A ) @ A )
& ~ ( in @ ( sK36_C @ B @ A ) @ B ) )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[259]) ).
thf(369,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[260]) ).
thf(370,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[261]) ).
thf(371,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ C @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[262]) ).
thf(372,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[263]) ).
thf(373,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
| ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[264]) ).
thf(374,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ ( singleton @ A ) @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[265]) ).
thf(375,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[266]) ).
thf(376,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[267]) ).
thf(377,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[272]) ).
thf(378,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[273]) ).
thf(379,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_intersection2 @ A @ B )
!= empty_set )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[276]) ).
thf(380,plain,
( ( ! [A: $i] :
( ( in @ ( sK37_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[277]) ).
thf(381,plain,
( ( ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( ( ( ( in @ ( sK40_SY287 @ B @ A ) @ A )
& ~ ( in @ ( sK39_C @ B @ A ) @ ( sK40_SY287 @ B @ A ) ) )
| ~ ( in @ ( sK39_C @ B @ A ) @ B ) )
& ( ! [SY288: $i] :
( ~ ( in @ SY288 @ A )
| ( in @ ( sK39_C @ B @ A ) @ SY288 ) )
| ( in @ ( sK39_C @ B @ A ) @ B ) ) )
| ( B
= ( set_meet @ A ) ) ) )
& ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( B
!= ( set_meet @ A ) )
| ( ! [C: $i] :
( ( ( in @ ( sK38_D @ C @ B @ A ) @ A )
& ~ ( in @ C @ ( sK38_D @ C @ B @ A ) ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ C @ D ) ) ) ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
( ( B
!= ( set_meet @ A ) )
| ( B = empty_set ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
( ( B != empty_set )
| ( B
= ( set_meet @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[278]) ).
thf(382,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[279]) ).
thf(383,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[280]) ).
thf(384,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[281]) ).
thf(385,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_rng @ A )
= ( relation_dom @ ( relation_inverse @ A ) ) ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_dom @ A )
= ( relation_rng @ ( relation_inverse @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[282]) ).
thf(386,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[284]) ).
thf(387,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[286]) ).
thf(388,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[287]) ).
thf(389,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(extcnf_combined,[status(esa)],[288]) ).
thf(390,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[389]) ).
thf(391,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[388]) ).
thf(392,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[387]) ).
thf(393,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[285]) ).
thf(394,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[386]) ).
thf(395,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[283]) ).
thf(396,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_rng @ A )
= ( relation_dom @ ( relation_inverse @ A ) ) ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_dom @ A )
= ( relation_rng @ ( relation_inverse @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[385]) ).
thf(397,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[384]) ).
thf(398,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[383]) ).
thf(399,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[382]) ).
thf(400,plain,
( ( ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( ( ( ( in @ ( sK40_SY287 @ B @ A ) @ A )
& ~ ( in @ ( sK39_C @ B @ A ) @ ( sK40_SY287 @ B @ A ) ) )
| ~ ( in @ ( sK39_C @ B @ A ) @ B ) )
& ( ! [SY288: $i] :
( ~ ( in @ SY288 @ A )
| ( in @ ( sK39_C @ B @ A ) @ SY288 ) )
| ( in @ ( sK39_C @ B @ A ) @ B ) ) )
| ( B
= ( set_meet @ A ) ) ) )
& ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( B
!= ( set_meet @ A ) )
| ( ! [C: $i] :
( ( ( in @ ( sK38_D @ C @ B @ A ) @ A )
& ~ ( in @ C @ ( sK38_D @ C @ B @ A ) ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ C @ D ) ) ) ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
( ( B
!= ( set_meet @ A ) )
| ( B = empty_set ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
( ( B != empty_set )
| ( B
= ( set_meet @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[381]) ).
thf(401,plain,
( ( ! [A: $i] :
( ( in @ ( sK37_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[380]) ).
thf(402,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_intersection2 @ A @ B )
!= empty_set )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[379]) ).
thf(403,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[275]) ).
thf(404,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[274]) ).
thf(405,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[378]) ).
thf(406,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(407,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[271]) ).
thf(408,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[270]) ).
thf(409,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[269]) ).
thf(410,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[268]) ).
thf(411,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[376]) ).
thf(412,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[375]) ).
thf(413,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ ( singleton @ A ) @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[374]) ).
thf(414,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
| ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(415,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(416,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(417,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(418,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(419,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK36_C @ B @ A ) @ A )
& ~ ( in @ ( sK36_C @ B @ A ) @ B ) )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(420,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) ) )
& ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(421,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ D )
| ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(422,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[365]) ).
thf(423,plain,
( ( ! [A: $i] :
( ! [SY283: $i] :
( ~ ( subset @ SY283 @ ( sK35_B @ A ) )
| ( are_equipotent @ SY283 @ ( sK35_B @ A ) )
| ( in @ SY283 @ ( sK35_B @ A ) ) )
& ! [SY284: $i] :
( ~ ( in @ SY284 @ ( sK35_B @ A ) )
| ( in @ ( powerset @ SY284 ) @ ( sK35_B @ A ) ) )
& ! [SY285: $i,SY286: $i] :
( ~ ( in @ SY285 @ ( sK35_B @ A ) )
| ~ ( subset @ SY286 @ SY285 )
| ( in @ SY286 @ ( sK35_B @ A ) ) )
& ( in @ A @ ( sK35_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(424,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[254]) ).
thf(425,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ A @ C )
| ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(426,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[362]) ).
thf(427,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ A @ ( relation_dom @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ B @ ( relation_rng @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[361]) ).
thf(428,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(429,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(430,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[358]) ).
thf(431,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[357]) ).
thf(432,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[246]) ).
thf(433,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[356]) ).
thf(434,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ C )
| ( subset @ ( unordered_pair @ A @ B ) @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ A @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[355]) ).
thf(435,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[243]) ).
thf(436,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK34_C @ B @ A ) @ A )
& ( in @ ( sK34_C @ B @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ C @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[354]) ).
thf(437,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[241]) ).
thf(438,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[353]) ).
thf(439,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[352]) ).
thf(440,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[351]) ).
thf(441,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ ( relation_rng @ A ) @ ( relation_dom @ B ) )
| ( ( relation_dom @ ( relation_composition @ A @ B ) )
= ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[350]) ).
thf(442,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[349]) ).
thf(443,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ ( relation_dom @ A ) @ ( relation_rng @ B ) )
| ( ( relation_rng @ ( relation_composition @ B @ A ) )
= ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[348]) ).
thf(444,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(445,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sK33_C @ B @ A ) @ ( set_intersection2 @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[347]) ).
thf(446,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( in @ ( ordered_pair @ ( sK31_B @ A ) @ ( sK32_SY282 @ A ) ) @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[346]) ).
thf(447,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[345]) ).
thf(448,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[344]) ).
thf(449,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
!= A )
| ~ ( in @ B @ A ) )
& ! [A: $i,B: $i] :
( ( in @ B @ A )
| ( ( set_difference @ A @ ( singleton @ B ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[343]) ).
thf(450,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[228]) ).
thf(451,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[342]) ).
thf(452,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(453,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= A )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_difference @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[341]) ).
thf(454,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ B )
| ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[340]) ).
thf(455,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[339]) ).
thf(456,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[338]) ).
thf(457,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(458,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[337]) ).
thf(459,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[336]) ).
thf(460,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[335]) ).
thf(461,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(462,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(463,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[334]) ).
thf(464,plain,
( ( ! [A: $i] :
( ( ! [SY280: $i,SY281: $i] :
( ( sK30_B @ A )
!= ( ordered_pair @ SY280 @ SY281 ) )
& ( in @ ( sK30_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK28_C @ B @ A ) @ ( sK29_SY279 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[333]) ).
thf(465,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK27_C @ B @ A )
!= A )
| ~ ( in @ ( sK27_C @ B @ A ) @ B ) )
& ( ( ( sK27_C @ B @ A )
= A )
| ( in @ ( sK27_C @ B @ A ) @ B ) ) )
| ( B
= ( singleton @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( singleton @ A ) )
| ( ! [C: $i] :
( ( C != A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( C = A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[332]) ).
thf(466,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK26_C @ B @ A ) @ B )
| ~ ( subset @ ( sK26_C @ B @ A ) @ A ) )
& ( ( in @ ( sK26_C @ B @ A ) @ B )
| ( subset @ ( sK26_C @ B @ A ) @ A ) ) )
| ( B
= ( powerset @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( powerset @ A ) )
| ( ! [C: $i] :
( ~ ( in @ C @ B )
| ( subset @ C @ A ) )
& ! [C: $i] :
( ~ ( subset @ C @ A )
| ( in @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[331]) ).
thf(467,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
( ~ ( element @ B @ A )
| ( in @ B @ A ) ) )
& ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
( ~ ( in @ B @ A )
| ( element @ B @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ! [B: $i] :
( ~ ( element @ B @ A )
| ( empty @ B ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ! [B: $i] :
( ~ ( empty @ B )
| ( element @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[330]) ).
thf(468,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK25_D @ C @ B @ A ) @ C )
| ( ( sK25_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK25_D @ C @ B @ A ) @ C )
| ( ( sK25_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK25_D @ C @ B @ A ) @ C )
| ( ( sK25_D @ C @ B @ A )
= A )
| ( ( sK25_D @ C @ B @ A )
= B ) ) )
| ( C
= ( unordered_pair @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( unordered_pair @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( D = A )
| ( D = B ) )
& ! [D: $i] :
( ( D != A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ( D != B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[329]) ).
thf(469,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK24_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK24_D @ C @ B @ A ) @ A ) )
& ( ~ ( in @ ( sK24_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK24_D @ C @ B @ A ) @ B ) )
& ( ( in @ ( sK24_D @ C @ B @ A ) @ C )
| ( in @ ( sK24_D @ C @ B @ A ) @ A )
| ( in @ ( sK24_D @ C @ B @ A ) @ B ) ) )
| ( C
= ( set_union2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_union2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A )
| ( in @ D @ B ) )
& ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[328]) ).
thf(470,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK23_C @ B @ A ) @ A )
& ~ ( in @ ( sK23_C @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[327]) ).
thf(471,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK22_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK22_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK22_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK22_D @ C @ B @ A ) @ A )
| ( in @ ( sK22_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK22_D @ C @ B @ A ) @ B )
| ( in @ ( sK22_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_intersection2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_intersection2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ~ ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[326]) ).
thf(472,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY277: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ B @ A ) @ SY277 ) @ A )
| ~ ( in @ ( sK20_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK20_C @ B @ A ) @ ( sK21_SY278 @ B @ A ) ) @ A )
| ( in @ ( sK20_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_dom @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_dom @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ C @ ( sK19_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[325]) ).
thf(473,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY275: $i] :
( ~ ( in @ ( sK17_C @ B @ A ) @ SY275 )
| ~ ( in @ SY275 @ A ) )
| ~ ( in @ ( sK17_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK17_C @ B @ A ) @ ( sK18_SY276 @ B @ A ) )
& ( in @ ( sK18_SY276 @ B @ A ) @ A ) )
| ( in @ ( sK17_C @ B @ A ) @ B ) ) )
| ( B
= ( union @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( union @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
( ~ ( in @ C @ D )
| ~ ( in @ D @ A ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( ( in @ C @ ( sK16_D @ C @ B @ A ) )
& ( in @ ( sK16_D @ C @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[324]) ).
thf(474,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK15_D @ C @ B @ A ) @ A )
| ( in @ ( sK15_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK15_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK15_D @ C @ B @ A ) @ A )
| ( in @ ( sK15_D @ C @ B @ A ) @ C ) )
& ( ~ ( in @ ( sK15_D @ C @ B @ A ) @ B )
| ( in @ ( sK15_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_difference @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_difference @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ~ ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[323]) ).
thf(475,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY273: $i] :
~ ( in @ ( ordered_pair @ SY273 @ ( sK13_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK13_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK14_SY274 @ B @ A ) @ ( sK13_C @ B @ A ) ) @ A )
| ( in @ ( sK13_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_rng @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_rng @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ D @ C ) @ A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ ( sK12_D @ C @ B @ A ) @ C ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[322]) ).
thf(476,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[321]) ).
thf(477,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK10_C @ B @ A ) @ ( sK11_SY272 @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK11_SY272 @ B @ A ) @ ( sK10_C @ B @ A ) ) @ A ) )
& ( ( in @ ( ordered_pair @ ( sK10_C @ B @ A ) @ ( sK11_SY272 @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK11_SY272 @ B @ A ) @ ( sK10_C @ B @ A ) ) @ A ) ) )
| ( B
= ( relation_inverse @ A ) ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ( B
!= ( relation_inverse @ A ) )
| ( ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ B )
| ( in @ ( ordered_pair @ D @ C ) @ A ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ D @ C ) @ A )
| ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[320]) ).
thf(478,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ( proper_subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( A != B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[319]) ).
thf(479,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[318]) ).
thf(480,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[317]) ).
thf(481,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[197]) ).
thf(482,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[196]) ).
thf(483,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[316]) ).
thf(484,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[194]) ).
thf(485,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[315]) ).
thf(486,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[192]) ).
thf(487,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[314]) ).
thf(488,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[313]) ).
thf(489,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[312]) ).
thf(490,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[311]) ).
thf(491,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[310]) ).
thf(492,plain,
( ( ( empty @ sK9_A )
& ( relation @ sK9_A ) )
= $true ),
inference(copy,[status(thm)],[309]) ).
thf(493,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK8_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK8_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[308]) ).
thf(494,plain,
( ( empty @ sK7_A )
= $true ),
inference(copy,[status(thm)],[307]) ).
thf(495,plain,
( ( ~ ( empty @ sK6_A )
& ( relation @ sK6_A ) )
= $true ),
inference(copy,[status(thm)],[306]) ).
thf(496,plain,
( ( ! [A: $i] :
( ( element @ ( sK5_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK5_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[305]) ).
thf(497,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(copy,[status(thm)],[304]) ).
thf(498,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[303]) ).
thf(499,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[302]) ).
thf(500,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[301]) ).
thf(501,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[300]) ).
thf(502,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK3_C @ B @ A ) @ A )
| ~ ( in @ ( sK3_C @ B @ A ) @ B ) )
& ( ( in @ ( sK3_C @ B @ A ) @ A )
| ( in @ ( sK3_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[299]) ).
thf(503,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)],[298]) ).
thf(504,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[297]) ).
thf(505,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[296]) ).
thf(506,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[295]) ).
thf(507,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[294]) ).
thf(508,plain,
( ( ! [A: $i] :
( ! [SY265: $i] :
( ~ ( subset @ SY265 @ ( sK1_B @ A ) )
| ( are_equipotent @ SY265 @ ( sK1_B @ A ) )
| ( in @ SY265 @ ( sK1_B @ A ) ) )
& ! [SY266: $i] :
( ( ! [SY271: $i] :
( ~ ( subset @ SY271 @ SY266 )
| ( in @ SY271 @ ( sK2_SY267 @ SY266 @ A ) ) )
& ( in @ ( sK2_SY267 @ SY266 @ A ) @ ( sK1_B @ A ) ) )
| ~ ( in @ SY266 @ ( sK1_B @ A ) ) )
& ! [SY269: $i,SY270: $i] :
( ~ ( in @ SY269 @ ( sK1_B @ A ) )
| ~ ( subset @ SY270 @ SY269 )
| ( in @ SY270 @ ( sK1_B @ A ) ) )
& ( in @ A @ ( sK1_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[293]) ).
thf(509,plain,
( ( ( ( relation_dom @ empty_set )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[291]) ).
thf(510,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK24_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK24_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ~ ( in @ ( sK24_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK24_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ( ( in @ ( sK24_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( in @ ( sK24_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK24_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX2
= ( set_union2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_union2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[469]) ).
thf(511,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK25_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK25_D @ SX2 @ SX1 @ SX0 )
!= SX0 ) )
| ~ ( ~ ( in @ ( sK25_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK25_D @ SX2 @ SX1 @ SX0 )
!= SX1 ) ) )
| ~ ( ( in @ ( sK25_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK25_D @ SX2 @ SX1 @ SX0 )
= SX0 )
| ( ( sK25_D @ SX2 @ SX1 @ SX0 )
= SX1 ) ) )
| ( SX2
= ( unordered_pair @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( unordered_pair @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ( SX3 != SX0 )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SX1 )
| ( in @ SX3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[468]) ).
thf(512,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK22_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK22_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK22_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK22_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK22_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ( in @ ( sK22_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK22_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) )
| ( SX2
= ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[471]) ).
thf(513,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SX1 @ SX0 ) @ SX2 ) @ SX0 )
| ~ ( in @ ( sK20_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_C @ SX1 @ SX0 ) @ ( sK21_SY278 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK20_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( relation_dom @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ( SX1
!= ( relation_dom @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ ( ordered_pair @ SX2 @ ( sK19_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[472]) ).
thf(514,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[467]) ).
thf(515,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( in @ ( sK37_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[401]) ).
thf(516,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK26_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK26_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK26_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK26_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[466]) ).
thf(517,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK33_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[445]) ).
thf(518,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ ( sK18_SY276 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK18_SY276 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK16_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK16_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[473]) ).
thf(519,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[396]) ).
thf(520,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ( element @ ( sK8_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK8_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[493]) ).
thf(521,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK34_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK34_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[436]) ).
thf(522,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[397]) ).
thf(523,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( relation_dom @ SX0 ) @ ( relation_dom @ SX1 ) ) )
| ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( relation_rng @ SX0 ) @ ( relation_rng @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[394]) ).
thf(524,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX1 @ ( sK35_B @ SX0 ) )
| ( are_equipotent @ SX1 @ ( sK35_B @ SX0 ) )
| ( in @ SX1 @ ( sK35_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK35_B @ SX0 ) )
| ( in @ ( powerset @ SX1 ) @ ( sK35_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( sK35_B @ SX0 ) )
| ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK35_B @ SX0 ) ) )
| ~ ( in @ SX0 @ ( sK35_B @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[423]) ).
thf(525,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)],[503]) ).
thf(526,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[463]) ).
thf(527,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[402]) ).
thf(528,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK36_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK36_C @ SX1 @ SX0 ) @ SX1 ) )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[419]) ).
thf(529,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK15_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK15_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK15_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( in @ ( sK15_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK15_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) )
| ( SX2
= ( set_difference @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_difference @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ~ ( in @ SX3 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[474]) ).
thf(530,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ SX2 @ ( sK13_C @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY274 @ SX1 @ SX0 ) @ ( sK13_C @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( relation_rng @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ( SX1
!= ( relation_rng @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ ( ordered_pair @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[475]) ).
thf(531,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[502]) ).
thf(532,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK40_SY287 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK39_C @ SX1 @ SX0 ) @ ( sK40_SY287 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK38_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK38_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[400]) ).
thf(533,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[478]) ).
thf(534,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SX1 @ SX0 ) @ ( sK11_SY272 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY272 @ SX1 @ SX0 ) @ ( sK10_C @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK10_C @ SX1 @ SX0 ) @ ( sK11_SY272 @ SX1 @ SX0 ) ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK11_SY272 @ SX1 @ SX0 ) @ ( sK10_C @ SX1 @ SX0 ) ) @ SX0 ) ) )
| ( SX1
= ( relation_inverse @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ( SX1
!= ( relation_inverse @ SX0 ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[477]) ).
thf(535,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX1 @ ( sK1_B @ SX0 ) )
| ( are_equipotent @ SX1 @ ( sK1_B @ SX0 ) )
| ( in @ SX1 @ ( sK1_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK2_SY267 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK2_SY267 @ SX1 @ SX0 ) @ ( sK1_B @ SX0 ) ) )
| ~ ( in @ SX1 @ ( sK1_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( sK1_B @ SX0 ) )
| ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK1_B @ SX0 ) ) )
| ~ ( in @ SX0 @ ( sK1_B @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[508]) ).
thf(536,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[453]) ).
thf(537,plain,
( ( ! [SX0: $i] :
~ ( ~ ( element @ ( sK5_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ( empty @ ( sK5_B @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[496]) ).
thf(538,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK30_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK30_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK28_C @ SX1 @ SX0 ) @ ( sK29_SY279 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[464]) ).
thf(539,plain,
( ( ~ ( ~ ~ ( empty @ sK6_A )
| ~ ( relation @ sK6_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[495]) ).
thf(540,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] : ( subset @ ( cartesian_product2 @ SX0 @ SX2 ) @ ( cartesian_product2 @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] : ( subset @ ( cartesian_product2 @ SX2 @ SX0 ) @ ( cartesian_product2 @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[420]) ).
thf(541,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[415]) ).
thf(542,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[470]) ).
thf(543,plain,
( ( ~ ( ~ ( empty @ sK9_A )
| ~ ( relation @ sK9_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[492]) ).
thf(544,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[398]) ).
thf(545,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[404]) ).
thf(546,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX2 )
| ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX0 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[434]) ).
thf(547,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[391]) ).
thf(548,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[392]) ).
thf(549,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[433]) ).
thf(550,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[449]) ).
thf(551,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK27_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK27_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK27_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK27_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[465]) ).
thf(552,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX0 @ ( relation_dom @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX1 @ ( relation_rng @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[427]) ).
thf(553,plain,
! [SV1: $i] :
( ( ( ( singleton @ SV1 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(554,plain,
! [SV2: $i] :
( ( subset @ empty_set @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(555,plain,
! [SV3: $i] :
( ( ~ ( subset @ SV3 @ empty_set )
| ( SV3 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(556,plain,
! [SV4: $i] :
( ( ( empty @ SV4 )
| ~ ( relation @ SV4 )
| ~ ( empty @ ( relation_dom @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(557,plain,
! [SV5: $i] :
( ( ( empty @ SV5 )
| ~ ( relation @ SV5 )
| ~ ( empty @ ( relation_rng @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(558,plain,
! [SV6: $i] :
( ( ( set_union2 @ SV6 @ empty_set )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(559,plain,
! [SV7: $i] :
( ( ( set_intersection2 @ SV7 @ empty_set )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(560,plain,
! [SV8: $i] :
( ( ( set_difference @ SV8 @ empty_set )
= SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(561,plain,
! [SV9: $i] :
( ( ( set_difference @ empty_set @ SV9 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(562,plain,
! [SV10: $i] :
( ( ~ ( empty @ SV10 )
| ( SV10 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(563,plain,
! [SV11: $i] :
( ( ! [SY289: $i] :
( ~ ( in @ SV11 @ SY289 )
| ( ( set_union2 @ ( singleton @ SV11 ) @ SY289 )
= SY289 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(564,plain,
! [SV12: $i] :
( ( ! [SY290: $i] :
( ~ ( disjoint @ ( singleton @ SV12 ) @ SY290 )
| ~ ( in @ SV12 @ SY290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(565,plain,
! [SV13: $i] :
( ( ! [SY291: $i] :
( ( in @ SV13 @ SY291 )
| ( disjoint @ ( singleton @ SV13 ) @ SY291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(566,plain,
! [SV14: $i] :
( ( ! [SY292: $i] :
( ~ ( element @ SY292 @ ( powerset @ SV14 ) )
| ! [SY293: $i] :
( ~ ( in @ SY293 @ SY292 )
| ( in @ SY293 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(567,plain,
! [SV15: $i] :
( ( ! [SY294: $i] :
( ~ ( subset @ SV15 @ SY294 )
| ! [SY295: $i] :
( ( in @ SY295 @ SV15 )
| ( subset @ SV15 @ ( set_difference @ SY294 @ ( singleton @ SY295 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(568,plain,
! [SV16: $i] :
( ( ! [SY296: $i] :
( ~ ( in @ SV16 @ SY296 )
| ( subset @ SV16 @ ( union @ SY296 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(569,plain,
! [SV17: $i] :
( ( ! [SY297: $i,SY298: $i,SY299: $i] :
( ~ ( subset @ SV17 @ SY297 )
| ~ ( subset @ SY298 @ SY299 )
| ( subset @ ( cartesian_product2 @ SV17 @ SY298 ) @ ( cartesian_product2 @ SY297 @ SY299 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(570,plain,
! [SV18: $i] :
( ( ! [SY300: $i] :
( ~ ( subset @ SV18 @ SY300 )
| ( ( set_union2 @ SV18 @ SY300 )
= SY300 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(571,plain,
! [SV19: $i] :
( ( ! [SY301: $i] : ( subset @ ( set_intersection2 @ SV19 @ SY301 ) @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(572,plain,
! [SV20: $i] :
( ( ! [SY302: $i,SY303: $i] :
( ~ ( subset @ SV20 @ SY302 )
| ~ ( subset @ SV20 @ SY303 )
| ( subset @ SV20 @ ( set_intersection2 @ SY302 @ SY303 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(573,plain,
! [SV21: $i] :
( ( ! [SY304: $i,SY305: $i] :
( ~ ( subset @ SV21 @ SY304 )
| ~ ( subset @ SY304 @ SY305 )
| ( subset @ SV21 @ SY305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(574,plain,
! [SV22: $i] :
( ( ~ ( relation @ SV22 )
| ( subset @ SV22 @ ( cartesian_product2 @ ( relation_dom @ SV22 ) @ ( relation_rng @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(575,plain,
! [SV23: $i] :
( ( ! [SY306: $i] :
( ~ ( subset @ SV23 @ SY306 )
| ! [SY307: $i] : ( subset @ ( set_intersection2 @ SV23 @ SY307 ) @ ( set_intersection2 @ SY306 @ SY307 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(576,plain,
! [SV24: $i] :
( ( ! [SY308: $i] :
( ~ ( subset @ SV24 @ SY308 )
| ( ( set_intersection2 @ SV24 @ SY308 )
= SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(577,plain,
! [SV25: $i] :
( ( ! [SY309: $i] :
( ~ ( subset @ SV25 @ SY309 )
| ! [SY310: $i] : ( subset @ ( set_difference @ SV25 @ SY310 ) @ ( set_difference @ SY309 @ SY310 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(578,plain,
! [SV26: $i] :
( ( ! [SY311: $i] : ( subset @ ( set_difference @ SV26 @ SY311 ) @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(579,plain,
! [SV27: $i] :
( ( ! [SY312: $i] :
( ( set_union2 @ SV27 @ ( set_difference @ SY312 @ SV27 ) )
= ( set_union2 @ SV27 @ SY312 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(580,plain,
! [SV28: $i] :
( ( ! [SY313: $i] :
( ( set_difference @ ( set_union2 @ SV28 @ SY313 ) @ SY313 )
= ( set_difference @ SV28 @ SY313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(581,plain,
! [SV29: $i] :
( ( ~ ( relation @ SV29 )
| ! [SY314: $i] :
( ~ ( relation @ SY314 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV29 @ SY314 ) ) @ ( relation_dom @ SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(582,plain,
! [SV30: $i] :
( ( ~ ( relation @ SV30 )
| ! [SY315: $i] :
( ~ ( relation @ SY315 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV30 @ SY315 ) ) @ ( relation_rng @ SY315 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(583,plain,
! [SV31: $i] :
( ( ! [SY316: $i] :
( ~ ( subset @ SV31 @ SY316 )
| ( SY316
= ( set_union2 @ SV31 @ ( set_difference @ SY316 @ SV31 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(584,plain,
! [SV32: $i] :
( ( ~ ( relation @ SV32 )
| ! [SY317: $i] :
( ~ ( relation @ SY317 )
| ~ ( subset @ ( relation_rng @ SV32 ) @ ( relation_dom @ SY317 ) )
| ( ( relation_dom @ ( relation_composition @ SV32 @ SY317 ) )
= ( relation_dom @ SV32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(585,plain,
! [SV33: $i] :
( ( ! [SY318: $i] :
( ~ ( in @ SV33 @ SY318 )
| ( ( set_union2 @ ( singleton @ SV33 ) @ SY318 )
= SY318 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(586,plain,
! [SV34: $i] :
( ( ~ ( relation @ SV34 )
| ! [SY319: $i] :
( ~ ( relation @ SY319 )
| ~ ( subset @ ( relation_dom @ SV34 ) @ ( relation_rng @ SY319 ) )
| ( ( relation_rng @ ( relation_composition @ SY319 @ SV34 ) )
= ( relation_rng @ SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(587,plain,
! [SV35: $i] :
( ( ! [SY320: $i] :
( ( set_difference @ SV35 @ ( set_difference @ SV35 @ SY320 ) )
= ( set_intersection2 @ SV35 @ SY320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(588,plain,
! [SV36: $i] :
( ( ~ ( relation @ SV36 )
| ( in @ ( ordered_pair @ ( sK31_B @ SV36 ) @ ( sK32_SY282 @ SV36 ) ) @ SV36 )
| ( SV36 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(589,plain,
! [SV37: $i] :
( ( ! [SY321: $i] :
( ~ ( proper_subset @ SY321 @ SV37 )
| ~ ( subset @ SV37 @ SY321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(590,plain,
! [SV38: $i] :
( ( ! [SY322: $i,SY323: $i] :
( ~ ( disjoint @ SY322 @ SY323 )
| ~ ( subset @ SV38 @ SY322 )
| ( disjoint @ SV38 @ SY323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(591,plain,
! [SV39: $i] :
( ( ( unordered_pair @ SV39 @ SV39 )
= ( singleton @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(592,plain,
! [SV40: $i] :
( ( ! [SY324: $i] :
( ~ ( subset @ ( singleton @ SV40 ) @ ( singleton @ SY324 ) )
| ( SV40 = SY324 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(593,plain,
! [SV41: $i] :
( ( ! [SY325: $i] : ( subset @ SV41 @ ( set_union2 @ SV41 @ SY325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(594,plain,
! [SV42: $i] :
( ( ! [SY326: $i,SY327: $i] :
( ~ ( subset @ SV42 @ SY326 )
| ~ ( subset @ SY327 @ SY326 )
| ( subset @ ( set_union2 @ SV42 @ SY327 ) @ SY326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(595,plain,
! [SV43: $i] :
( ( ! [SY328: $i] :
( ! [SY329: $i] :
( ( singleton @ SV43 )
!= ( unordered_pair @ SY328 @ SY329 ) )
| ( SV43 = SY328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(596,plain,
! [SV44: $i] :
( ( ! [SY330: $i] :
( ~ ( in @ SV44 @ SY330 )
| ( subset @ SV44 @ ( union @ SY330 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(597,plain,
! [SV45: $i] :
( ( ( union @ ( powerset @ SV45 ) )
= SV45 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(598,plain,
! [SV46: $i] :
( ( ! [SY331: $i,SY332: $i] :
( ( ( singleton @ SV46 )
!= ( unordered_pair @ SY331 @ SY332 ) )
| ( SY331 = SY332 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(599,plain,
! [SV47: $i] :
( ( ! [SY333: $i] :
( ~ ( in @ SV47 @ SY333 )
| ~ ( in @ SY333 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(600,plain,
! [SV48: $i] :
( ( ~ ( empty @ SV48 )
| ( relation @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(601,plain,
! [SV49: $i] :
( ( ! [SY334: $i] :
( ( set_union2 @ SV49 @ SY334 )
= ( set_union2 @ SY334 @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(602,plain,
! [SV50: $i] :
( ( ! [SY335: $i] :
( ( set_intersection2 @ SV50 @ SY335 )
= ( set_intersection2 @ SY335 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(603,plain,
! [SV51: $i] :
( ( ~ ( relation @ SV51 )
| ( ( relation_field @ SV51 )
= ( set_union2 @ ( relation_dom @ SV51 ) @ ( relation_rng @ SV51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(604,plain,
! [SV52: $i] :
( ( ~ ( relation @ SV52 )
| ( relation @ ( relation_inverse @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(605,plain,
! [SV53: $i] :
( ( ! [SY336: $i] :
( ~ ( relation @ SV53 )
| ~ ( relation @ SY336 )
| ( relation @ ( relation_composition @ SV53 @ SY336 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(606,plain,
! [SV54: $i] :
( ( ~ ( empty @ ( powerset @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(607,plain,
! [SV55: $i] :
( ( ! [SY337: $i] :
~ ( empty @ ( ordered_pair @ SV55 @ SY337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(608,plain,
! [SV56: $i] :
( ( ! [SY338: $i] :
( ~ ( relation @ SV56 )
| ~ ( relation @ SY338 )
| ( relation @ ( set_union2 @ SV56 @ SY338 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(609,plain,
! [SV57: $i] :
( ( ~ ( empty @ ( singleton @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(610,plain,
! [SV58: $i] :
( ( ( empty @ SV58 )
| ! [SY339: $i] :
~ ( empty @ ( set_union2 @ SV58 @ SY339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(611,plain,
! [SV59: $i] :
( ( ! [SY340: $i] :
~ ( empty @ ( unordered_pair @ SV59 @ SY340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(612,plain,
! [SV60: $i] :
( ( ( empty @ SV60 )
| ! [SY341: $i] :
~ ( empty @ ( set_union2 @ SY341 @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(613,plain,
! [SV61: $i] :
( ( ! [SY342: $i] :
( ( empty @ SV61 )
| ( empty @ SY342 )
| ~ ( empty @ ( cartesian_product2 @ SV61 @ SY342 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(614,plain,
! [SV62: $i] :
( ( ( set_union2 @ SV62 @ SV62 )
= SV62 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(615,plain,
! [SV63: $i] :
( ( ( set_intersection2 @ SV63 @ SV63 )
= SV63 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(616,plain,
! [SV64: $i] :
( ( ~ ( relation @ SV64 )
| ( ( relation_inverse @ ( relation_inverse @ SV64 ) )
= SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(617,plain,
( ( empty @ sK4_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(618,plain,
! [SV65: $i] :
( ( subset @ SV65 @ SV65 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(619,plain,
! [SV66: $i] :
( ( ! [SY343: $i] :
( ~ ( disjoint @ SV66 @ SY343 )
| ( disjoint @ SY343 @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(620,plain,
! [SV67: $i] :
( ( ! [SY344: $i] :
( ~ ( in @ SV67 @ SY344 )
| ( element @ SV67 @ SY344 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(621,plain,
! [SV68: $i] :
( ( ! [SY345: $i] :
( ~ ( element @ SV68 @ SY345 )
| ( empty @ SY345 )
| ( in @ SV68 @ SY345 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(622,plain,
! [SV69: $i] :
( ( ! [SY346: $i,SY347: $i] :
( ~ ( element @ SY346 @ ( powerset @ SY347 ) )
| ~ ( in @ SV69 @ SY346 )
| ( element @ SV69 @ SY347 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(623,plain,
! [SV70: $i] :
( ( ! [SY348: $i,SY349: $i] :
( ~ ( element @ SY348 @ ( powerset @ SY349 ) )
| ~ ( in @ SV70 @ SY348 )
| ~ ( empty @ SY349 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(624,plain,
! [SV71: $i] :
( ( ! [SY350: $i] :
( ~ ( empty @ SY350 )
| ~ ( in @ SV71 @ SY350 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(625,plain,
! [SV72: $i] :
( ( ! [SY351: $i] :
( ( SV72 = SY351 )
| ~ ( empty @ SV72 )
| ~ ( empty @ SY351 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(626,plain,
( ( ( relation_dom @ empty_set )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[509]) ).
thf(627,plain,
! [SV73: $i] :
( ( ~ ( ~ ! [SY352: $i,SY353: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK24_D @ SY353 @ SY352 @ SV73 ) @ SY353 )
| ~ ( in @ ( sK24_D @ SY353 @ SY352 @ SV73 ) @ SV73 ) )
| ~ ( ~ ( in @ ( sK24_D @ SY353 @ SY352 @ SV73 ) @ SY353 )
| ~ ( in @ ( sK24_D @ SY353 @ SY352 @ SV73 ) @ SY352 ) ) )
| ~ ( ( in @ ( sK24_D @ SY353 @ SY352 @ SV73 ) @ SY353 )
| ( in @ ( sK24_D @ SY353 @ SY352 @ SV73 ) @ SV73 )
| ( in @ ( sK24_D @ SY353 @ SY352 @ SV73 ) @ SY352 ) ) )
| ( SY353
= ( set_union2 @ SV73 @ SY352 ) ) )
| ~ ! [SY354: $i,SY355: $i] :
( ( SY355
!= ( set_union2 @ SV73 @ SY354 ) )
| ~ ( ~ ! [SY356: $i] :
( ~ ( in @ SY356 @ SY355 )
| ( in @ SY356 @ SV73 )
| ( in @ SY356 @ SY354 ) )
| ~ ~ ( ~ ! [SY357: $i] :
( ~ ( in @ SY357 @ SV73 )
| ( in @ SY357 @ SY355 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY354 )
| ( in @ SX3 @ SY355 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(628,plain,
! [SV74: $i] :
( ( ~ ( ~ ! [SY359: $i,SY360: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK25_D @ SY360 @ SY359 @ SV74 ) @ SY360 )
| ( ( sK25_D @ SY360 @ SY359 @ SV74 )
!= SV74 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY360 @ SY359 @ SV74 ) @ SY360 )
| ( ( sK25_D @ SY360 @ SY359 @ SV74 )
!= SY359 ) ) )
| ~ ( ( in @ ( sK25_D @ SY360 @ SY359 @ SV74 ) @ SY360 )
| ( ( sK25_D @ SY360 @ SY359 @ SV74 )
= SV74 )
| ( ( sK25_D @ SY360 @ SY359 @ SV74 )
= SY359 ) ) )
| ( SY360
= ( unordered_pair @ SV74 @ SY359 ) ) )
| ~ ! [SY361: $i,SY362: $i] :
( ( SY362
!= ( unordered_pair @ SV74 @ SY361 ) )
| ~ ( ~ ! [SY363: $i] :
( ~ ( in @ SY363 @ SY362 )
| ( SY363 = SV74 )
| ( SY363 = SY361 ) )
| ~ ~ ( ~ ! [SY364: $i] :
( ( SY364 != SV74 )
| ( in @ SY364 @ SY362 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY361 )
| ( in @ SX3 @ SY362 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(629,plain,
! [SV75: $i] :
( ( ~ ( ~ ! [SY366: $i,SY367: $i] :
( ~ ( ~ ( ~ ( in @ ( sK22_D @ SY367 @ SY366 @ SV75 ) @ SV75 )
| ~ ( in @ ( sK22_D @ SY367 @ SY366 @ SV75 ) @ SY366 )
| ~ ( in @ ( sK22_D @ SY367 @ SY366 @ SV75 ) @ SY367 ) )
| ~ ~ ( ~ ( ( in @ ( sK22_D @ SY367 @ SY366 @ SV75 ) @ SV75 )
| ( in @ ( sK22_D @ SY367 @ SY366 @ SV75 ) @ SY367 ) )
| ~ ( ( in @ ( sK22_D @ SY367 @ SY366 @ SV75 ) @ SY366 )
| ( in @ ( sK22_D @ SY367 @ SY366 @ SV75 ) @ SY367 ) ) ) )
| ( SY367
= ( set_intersection2 @ SV75 @ SY366 ) ) )
| ~ ! [SY368: $i,SY369: $i] :
( ( SY369
!= ( set_intersection2 @ SV75 @ SY368 ) )
| ~ ( ~ ! [SY370: $i] :
( ~ ( in @ SY370 @ SV75 )
| ~ ( in @ SY370 @ SY368 )
| ( in @ SY370 @ SY369 ) )
| ~ ~ ( ~ ! [SY371: $i] :
( ~ ( in @ SY371 @ SY369 )
| ( in @ SY371 @ SV75 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY369 )
| ( in @ SX3 @ SY368 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(630,plain,
! [SV76: $i] :
( ( ~ ( relation @ SV76 )
| ~ ( ~ ! [SY373: $i] :
( ~ ( ~ ( ! [SY374: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SY373 @ SV76 ) @ SY374 ) @ SV76 )
| ~ ( in @ ( sK20_C @ SY373 @ SV76 ) @ SY373 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_C @ SY373 @ SV76 ) @ ( sK21_SY278 @ SY373 @ SV76 ) ) @ SV76 )
| ( in @ ( sK20_C @ SY373 @ SV76 ) @ SY373 ) ) )
| ( SY373
= ( relation_dom @ SV76 ) ) )
| ~ ! [SY375: $i] :
( ( SY375
!= ( relation_dom @ SV76 ) )
| ~ ( ~ ! [SY376: $i] :
( ! [SY377: $i] :
~ ( in @ ( ordered_pair @ SY376 @ SY377 ) @ SV76 )
| ( in @ SY376 @ SY375 ) )
| ~ ! [SY378: $i] :
( ~ ( in @ SY378 @ SY375 )
| ( in @ ( ordered_pair @ SY378 @ ( sK19_D @ SY378 @ SY375 @ SV76 ) ) @ SV76 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(631,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[514]) ).
thf(632,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK37_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[515]) ).
thf(633,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK26_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK26_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK26_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK26_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[516]) ).
thf(634,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK33_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(635,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ ( sK18_SY276 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK18_SY276 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK16_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK16_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(636,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[519]) ).
thf(637,plain,
! [SV77: $i] :
( ( ( empty @ SV77 )
| ~ ( ~ ( element @ ( sK8_B @ SV77 ) @ ( powerset @ SV77 ) )
| ~ ~ ( empty @ ( sK8_B @ SV77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(638,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK34_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK34_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[521]) ).
thf(639,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[522]) ).
thf(640,plain,
! [SV78: $i] :
( ( ~ ( relation @ SV78 )
| ~ ( ~ ! [SY379: $i] :
( ~ ( relation @ SY379 )
| ~ ( subset @ SV78 @ SY379 )
| ( subset @ ( relation_dom @ SV78 ) @ ( relation_dom @ SY379 ) ) )
| ~ ! [SY380: $i] :
( ~ ( relation @ SY380 )
| ~ ( subset @ SV78 @ SY380 )
| ( subset @ ( relation_rng @ SV78 ) @ ( relation_rng @ SY380 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(641,plain,
! [SV79: $i] :
( ( ~ ( ~ ! [SY381: $i] :
( ~ ( subset @ SY381 @ ( sK35_B @ SV79 ) )
| ( are_equipotent @ SY381 @ ( sK35_B @ SV79 ) )
| ( in @ SY381 @ ( sK35_B @ SV79 ) ) )
| ~ ~ ( ~ ! [SY382: $i] :
( ~ ( in @ SY382 @ ( sK35_B @ SV79 ) )
| ( in @ ( powerset @ SY382 ) @ ( sK35_B @ SV79 ) ) )
| ~ ~ ( ~ ! [SY383: $i,SY384: $i] :
( ~ ( in @ SY383 @ ( sK35_B @ SV79 ) )
| ~ ( subset @ SY384 @ SY383 )
| ( in @ SY384 @ ( sK35_B @ SV79 ) ) )
| ~ ( in @ SV79 @ ( sK35_B @ SV79 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(642,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)],[525]) ).
thf(643,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(644,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[527]) ).
thf(645,plain,
! [SV80: $i] :
( ( ! [SY385: $i] :
( ~ ( ~ ( in @ ( sK36_C @ SY385 @ SV80 ) @ SV80 )
| ~ ~ ( in @ ( sK36_C @ SY385 @ SV80 ) @ SY385 ) )
| ( element @ SV80 @ ( powerset @ SY385 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(646,plain,
! [SV81: $i] :
( ( ~ ( ~ ! [SY386: $i,SY387: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SY387 @ SY386 @ SV81 ) @ SV81 )
| ( in @ ( sK15_D @ SY387 @ SY386 @ SV81 ) @ SY386 )
| ~ ( in @ ( sK15_D @ SY387 @ SY386 @ SV81 ) @ SY387 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SY387 @ SY386 @ SV81 ) @ SV81 )
| ( in @ ( sK15_D @ SY387 @ SY386 @ SV81 ) @ SY387 ) )
| ~ ( ~ ( in @ ( sK15_D @ SY387 @ SY386 @ SV81 ) @ SY386 )
| ( in @ ( sK15_D @ SY387 @ SY386 @ SV81 ) @ SY387 ) ) ) )
| ( SY387
= ( set_difference @ SV81 @ SY386 ) ) )
| ~ ! [SY388: $i,SY389: $i] :
( ( SY389
!= ( set_difference @ SV81 @ SY388 ) )
| ~ ( ~ ! [SY390: $i] :
( ~ ( in @ SY390 @ SV81 )
| ( in @ SY390 @ SY388 )
| ( in @ SY390 @ SY389 ) )
| ~ ~ ( ~ ! [SY391: $i] :
( ~ ( in @ SY391 @ SY389 )
| ( in @ SY391 @ SV81 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY389 )
| ~ ( in @ SX3 @ SY388 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(647,plain,
! [SV82: $i] :
( ( ~ ( relation @ SV82 )
| ~ ( ~ ! [SY393: $i] :
( ~ ( ~ ( ! [SY394: $i] :
~ ( in @ ( ordered_pair @ SY394 @ ( sK13_C @ SY393 @ SV82 ) ) @ SV82 )
| ~ ( in @ ( sK13_C @ SY393 @ SV82 ) @ SY393 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY274 @ SY393 @ SV82 ) @ ( sK13_C @ SY393 @ SV82 ) ) @ SV82 )
| ( in @ ( sK13_C @ SY393 @ SV82 ) @ SY393 ) ) )
| ( SY393
= ( relation_rng @ SV82 ) ) )
| ~ ! [SY395: $i] :
( ( SY395
!= ( relation_rng @ SV82 ) )
| ~ ( ~ ! [SY396: $i] :
( ! [SY397: $i] :
~ ( in @ ( ordered_pair @ SY397 @ SY396 ) @ SV82 )
| ( in @ SY396 @ SY395 ) )
| ~ ! [SY398: $i] :
( ~ ( in @ SY398 @ SY395 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY398 @ SY395 @ SV82 ) @ SY398 ) @ SV82 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(648,plain,
! [SV83: $i] :
( ( ! [SY399: $i] :
( ~ ( ~ ( ~ ( in @ ( sK3_C @ SY399 @ SV83 ) @ SV83 )
| ~ ( in @ ( sK3_C @ SY399 @ SV83 ) @ SY399 ) )
| ~ ( ( in @ ( sK3_C @ SY399 @ SV83 ) @ SV83 )
| ( in @ ( sK3_C @ SY399 @ SV83 ) @ SY399 ) ) )
| ( SV83 = SY399 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(649,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK40_SY287 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK39_C @ SX1 @ SX0 ) @ ( sK40_SY287 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK38_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK38_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[532]) ).
thf(650,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[533]) ).
thf(651,plain,
! [SV84: $i] :
( ( ~ ( relation @ SV84 )
| ~ ( ~ ! [SY400: $i] :
( ~ ( relation @ SY400 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SY400 @ SV84 ) @ ( sK11_SY272 @ SY400 @ SV84 ) ) @ SY400 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY272 @ SY400 @ SV84 ) @ ( sK10_C @ SY400 @ SV84 ) ) @ SV84 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK10_C @ SY400 @ SV84 ) @ ( sK11_SY272 @ SY400 @ SV84 ) ) @ SY400 )
| ( in @ ( ordered_pair @ ( sK11_SY272 @ SY400 @ SV84 ) @ ( sK10_C @ SY400 @ SV84 ) ) @ SV84 ) ) )
| ( SY400
= ( relation_inverse @ SV84 ) ) )
| ~ ! [SY401: $i] :
( ~ ( relation @ SY401 )
| ( SY401
!= ( relation_inverse @ SV84 ) )
| ~ ( ~ ! [SY402: $i,SY403: $i] :
( ~ ( in @ ( ordered_pair @ SY402 @ SY403 ) @ SY401 )
| ( in @ ( ordered_pair @ SY403 @ SY402 ) @ SV84 ) )
| ~ ! [SY404: $i,SY405: $i] :
( ~ ( in @ ( ordered_pair @ SY405 @ SY404 ) @ SV84 )
| ( in @ ( ordered_pair @ SY404 @ SY405 ) @ SY401 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(652,plain,
! [SV85: $i] :
( ( ~ ( ~ ! [SY406: $i] :
( ~ ( subset @ SY406 @ ( sK1_B @ SV85 ) )
| ( are_equipotent @ SY406 @ ( sK1_B @ SV85 ) )
| ( in @ SY406 @ ( sK1_B @ SV85 ) ) )
| ~ ~ ( ~ ! [SY407: $i] :
( ~ ( ~ ! [SY408: $i] :
( ~ ( subset @ SY408 @ SY407 )
| ( in @ SY408 @ ( sK2_SY267 @ SY407 @ SV85 ) ) )
| ~ ( in @ ( sK2_SY267 @ SY407 @ SV85 ) @ ( sK1_B @ SV85 ) ) )
| ~ ( in @ SY407 @ ( sK1_B @ SV85 ) ) )
| ~ ~ ( ~ ! [SY409: $i,SY410: $i] :
( ~ ( in @ SY409 @ ( sK1_B @ SV85 ) )
| ~ ( subset @ SY410 @ SY409 )
| ( in @ SY410 @ ( sK1_B @ SV85 ) ) )
| ~ ( in @ SV85 @ ( sK1_B @ SV85 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(653,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[536]) ).
thf(654,plain,
! [SV86: $i] :
( ( ~ ( ~ ( element @ ( sK5_B @ SV86 ) @ ( powerset @ SV86 ) )
| ~ ( empty @ ( sK5_B @ SV86 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(655,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK30_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK30_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK28_C @ SX1 @ SX0 ) @ ( sK29_SY279 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[538]) ).
thf(656,plain,
( ( ~ ~ ( empty @ sK6_A )
| ~ ( relation @ sK6_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[539]) ).
thf(657,plain,
! [SV87: $i] :
( ( ~ ( ~ ! [SY411: $i] :
( ~ ( subset @ SV87 @ SY411 )
| ! [SY412: $i] : ( subset @ ( cartesian_product2 @ SV87 @ SY412 ) @ ( cartesian_product2 @ SY411 @ SY412 ) ) )
| ~ ! [SY413: $i] :
( ~ ( subset @ SV87 @ SY413 )
| ! [SY414: $i] : ( subset @ ( cartesian_product2 @ SY414 @ SV87 ) @ ( cartesian_product2 @ SY414 @ SY413 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(658,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[541]) ).
thf(659,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(660,plain,
( ( ~ ( empty @ sK9_A )
| ~ ( relation @ sK9_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[543]) ).
thf(661,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[544]) ).
thf(662,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[545]) ).
thf(663,plain,
! [SV88: $i] :
( ( ~ ( ~ ! [SY415: $i,SY416: $i] :
( ~ ( in @ SV88 @ SY416 )
| ~ ( in @ SY415 @ SY416 )
| ( subset @ ( unordered_pair @ SV88 @ SY415 ) @ SY416 ) )
| ~ ~ ( ~ ! [SY417: $i,SY418: $i] :
( ~ ( subset @ ( unordered_pair @ SV88 @ SY417 ) @ SY418 )
| ( in @ SV88 @ SY418 ) )
| ~ ! [SY419: $i,SY420: $i] :
( ~ ( subset @ ( unordered_pair @ SV88 @ SY419 ) @ SY420 )
| ( in @ SY419 @ SY420 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(664,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[547]) ).
thf(665,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[548]) ).
thf(666,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[549]) ).
thf(667,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[550]) ).
thf(668,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK27_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK27_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK27_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK27_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[551]) ).
thf(669,plain,
! [SV89: $i] :
( ( ~ ( ~ ! [SY421: $i,SY422: $i] :
( ~ ( relation @ SY422 )
| ~ ( in @ ( ordered_pair @ SV89 @ SY421 ) @ SY422 )
| ( in @ SV89 @ ( relation_dom @ SY422 ) ) )
| ~ ! [SY423: $i,SY424: $i] :
( ~ ( relation @ SY424 )
| ~ ( in @ ( ordered_pair @ SV89 @ SY423 ) @ SY424 )
| ( in @ SY423 @ ( relation_rng @ SY424 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(670,plain,
! [SV1: $i] :
( ( ( singleton @ SV1 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(671,plain,
! [SV3: $i] :
( ( ( ~ ( subset @ SV3 @ empty_set ) )
= $true )
| ( ( SV3 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[555]) ).
thf(672,plain,
! [SV4: $i] :
( ( ( ( empty @ SV4 )
| ~ ( relation @ SV4 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[556]) ).
thf(673,plain,
! [SV5: $i] :
( ( ( ( empty @ SV5 )
| ~ ( relation @ SV5 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[557]) ).
thf(674,plain,
! [SV10: $i] :
( ( ( ~ ( empty @ SV10 ) )
= $true )
| ( ( SV10 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[562]) ).
thf(675,plain,
! [SV90: $i,SV11: $i] :
( ( ~ ( in @ SV11 @ SV90 )
| ( ( set_union2 @ ( singleton @ SV11 ) @ SV90 )
= SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(676,plain,
! [SV91: $i,SV12: $i] :
( ( ~ ( disjoint @ ( singleton @ SV12 ) @ SV91 )
| ~ ( in @ SV12 @ SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(677,plain,
! [SV92: $i,SV13: $i] :
( ( ( in @ SV13 @ SV92 )
| ( disjoint @ ( singleton @ SV13 ) @ SV92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(678,plain,
! [SV14: $i,SV93: $i] :
( ( ~ ( element @ SV93 @ ( powerset @ SV14 ) )
| ! [SY425: $i] :
( ~ ( in @ SY425 @ SV93 )
| ( in @ SY425 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(679,plain,
! [SV94: $i,SV15: $i] :
( ( ~ ( subset @ SV15 @ SV94 )
| ! [SY426: $i] :
( ( in @ SY426 @ SV15 )
| ( subset @ SV15 @ ( set_difference @ SV94 @ ( singleton @ SY426 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(680,plain,
! [SV95: $i,SV16: $i] :
( ( ~ ( in @ SV16 @ SV95 )
| ( subset @ SV16 @ ( union @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(681,plain,
! [SV96: $i,SV17: $i] :
( ( ! [SY427: $i,SY428: $i] :
( ~ ( subset @ SV17 @ SV96 )
| ~ ( subset @ SY427 @ SY428 )
| ( subset @ ( cartesian_product2 @ SV17 @ SY427 ) @ ( cartesian_product2 @ SV96 @ SY428 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(682,plain,
! [SV97: $i,SV18: $i] :
( ( ~ ( subset @ SV18 @ SV97 )
| ( ( set_union2 @ SV18 @ SV97 )
= SV97 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(683,plain,
! [SV98: $i,SV19: $i] :
( ( subset @ ( set_intersection2 @ SV19 @ SV98 ) @ SV19 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(684,plain,
! [SV99: $i,SV20: $i] :
( ( ! [SY429: $i] :
( ~ ( subset @ SV20 @ SV99 )
| ~ ( subset @ SV20 @ SY429 )
| ( subset @ SV20 @ ( set_intersection2 @ SV99 @ SY429 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(685,plain,
! [SV100: $i,SV21: $i] :
( ( ! [SY430: $i] :
( ~ ( subset @ SV21 @ SV100 )
| ~ ( subset @ SV100 @ SY430 )
| ( subset @ SV21 @ SY430 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(686,plain,
! [SV22: $i] :
( ( ( ~ ( relation @ SV22 ) )
= $true )
| ( ( subset @ SV22 @ ( cartesian_product2 @ ( relation_dom @ SV22 ) @ ( relation_rng @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[574]) ).
thf(687,plain,
! [SV101: $i,SV23: $i] :
( ( ~ ( subset @ SV23 @ SV101 )
| ! [SY431: $i] : ( subset @ ( set_intersection2 @ SV23 @ SY431 ) @ ( set_intersection2 @ SV101 @ SY431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(688,plain,
! [SV102: $i,SV24: $i] :
( ( ~ ( subset @ SV24 @ SV102 )
| ( ( set_intersection2 @ SV24 @ SV102 )
= SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(689,plain,
! [SV103: $i,SV25: $i] :
( ( ~ ( subset @ SV25 @ SV103 )
| ! [SY432: $i] : ( subset @ ( set_difference @ SV25 @ SY432 ) @ ( set_difference @ SV103 @ SY432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(690,plain,
! [SV104: $i,SV26: $i] :
( ( subset @ ( set_difference @ SV26 @ SV104 ) @ SV26 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(691,plain,
! [SV105: $i,SV27: $i] :
( ( ( set_union2 @ SV27 @ ( set_difference @ SV105 @ SV27 ) )
= ( set_union2 @ SV27 @ SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[579]) ).
thf(692,plain,
! [SV106: $i,SV28: $i] :
( ( ( set_difference @ ( set_union2 @ SV28 @ SV106 ) @ SV106 )
= ( set_difference @ SV28 @ SV106 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(693,plain,
! [SV29: $i] :
( ( ( ~ ( relation @ SV29 ) )
= $true )
| ( ( ! [SY314: $i] :
( ~ ( relation @ SY314 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV29 @ SY314 ) ) @ ( relation_dom @ SV29 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[581]) ).
thf(694,plain,
! [SV30: $i] :
( ( ( ~ ( relation @ SV30 ) )
= $true )
| ( ( ! [SY315: $i] :
( ~ ( relation @ SY315 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV30 @ SY315 ) ) @ ( relation_rng @ SY315 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[582]) ).
thf(695,plain,
! [SV107: $i,SV31: $i] :
( ( ~ ( subset @ SV31 @ SV107 )
| ( SV107
= ( set_union2 @ SV31 @ ( set_difference @ SV107 @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(696,plain,
! [SV32: $i] :
( ( ( ~ ( relation @ SV32 ) )
= $true )
| ( ( ! [SY317: $i] :
( ~ ( relation @ SY317 )
| ~ ( subset @ ( relation_rng @ SV32 ) @ ( relation_dom @ SY317 ) )
| ( ( relation_dom @ ( relation_composition @ SV32 @ SY317 ) )
= ( relation_dom @ SV32 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[584]) ).
thf(697,plain,
! [SV108: $i,SV33: $i] :
( ( ~ ( in @ SV33 @ SV108 )
| ( ( set_union2 @ ( singleton @ SV33 ) @ SV108 )
= SV108 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(698,plain,
! [SV34: $i] :
( ( ( ~ ( relation @ SV34 ) )
= $true )
| ( ( ! [SY319: $i] :
( ~ ( relation @ SY319 )
| ~ ( subset @ ( relation_dom @ SV34 ) @ ( relation_rng @ SY319 ) )
| ( ( relation_rng @ ( relation_composition @ SY319 @ SV34 ) )
= ( relation_rng @ SV34 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[586]) ).
thf(699,plain,
! [SV109: $i,SV35: $i] :
( ( ( set_difference @ SV35 @ ( set_difference @ SV35 @ SV109 ) )
= ( set_intersection2 @ SV35 @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(700,plain,
! [SV36: $i] :
( ( ( ~ ( relation @ SV36 ) )
= $true )
| ( ( ( in @ ( ordered_pair @ ( sK31_B @ SV36 ) @ ( sK32_SY282 @ SV36 ) ) @ SV36 )
| ( SV36 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[588]) ).
thf(701,plain,
! [SV37: $i,SV110: $i] :
( ( ~ ( proper_subset @ SV110 @ SV37 )
| ~ ( subset @ SV37 @ SV110 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(702,plain,
! [SV38: $i,SV111: $i] :
( ( ! [SY433: $i] :
( ~ ( disjoint @ SV111 @ SY433 )
| ~ ( subset @ SV38 @ SV111 )
| ( disjoint @ SV38 @ SY433 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(703,plain,
! [SV112: $i,SV40: $i] :
( ( ~ ( subset @ ( singleton @ SV40 ) @ ( singleton @ SV112 ) )
| ( SV40 = SV112 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(704,plain,
! [SV113: $i,SV41: $i] :
( ( subset @ SV41 @ ( set_union2 @ SV41 @ SV113 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(705,plain,
! [SV114: $i,SV42: $i] :
( ( ! [SY434: $i] :
( ~ ( subset @ SV42 @ SV114 )
| ~ ( subset @ SY434 @ SV114 )
| ( subset @ ( set_union2 @ SV42 @ SY434 ) @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(706,plain,
! [SV115: $i,SV43: $i] :
( ( ! [SY435: $i] :
( ( singleton @ SV43 )
!= ( unordered_pair @ SV115 @ SY435 ) )
| ( SV43 = SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(707,plain,
! [SV116: $i,SV44: $i] :
( ( ~ ( in @ SV44 @ SV116 )
| ( subset @ SV44 @ ( union @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(708,plain,
! [SV117: $i,SV46: $i] :
( ( ! [SY436: $i] :
( ( ( singleton @ SV46 )
!= ( unordered_pair @ SV117 @ SY436 ) )
| ( SV117 = SY436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(709,plain,
! [SV118: $i,SV47: $i] :
( ( ~ ( in @ SV47 @ SV118 )
| ~ ( in @ SV118 @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(710,plain,
! [SV48: $i] :
( ( ( ~ ( empty @ SV48 ) )
= $true )
| ( ( relation @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[600]) ).
thf(711,plain,
! [SV119: $i,SV49: $i] :
( ( ( set_union2 @ SV49 @ SV119 )
= ( set_union2 @ SV119 @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(712,plain,
! [SV120: $i,SV50: $i] :
( ( ( set_intersection2 @ SV50 @ SV120 )
= ( set_intersection2 @ SV120 @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(713,plain,
! [SV51: $i] :
( ( ( ~ ( relation @ SV51 ) )
= $true )
| ( ( ( relation_field @ SV51 )
= ( set_union2 @ ( relation_dom @ SV51 ) @ ( relation_rng @ SV51 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[603]) ).
thf(714,plain,
! [SV52: $i] :
( ( ( ~ ( relation @ SV52 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[604]) ).
thf(715,plain,
! [SV121: $i,SV53: $i] :
( ( ~ ( relation @ SV53 )
| ~ ( relation @ SV121 )
| ( relation @ ( relation_composition @ SV53 @ SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[605]) ).
thf(716,plain,
! [SV54: $i] :
( ( empty @ ( powerset @ SV54 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[606]) ).
thf(717,plain,
! [SV122: $i,SV55: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV55 @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(718,plain,
! [SV123: $i,SV56: $i] :
( ( ~ ( relation @ SV56 )
| ~ ( relation @ SV123 )
| ( relation @ ( set_union2 @ SV56 @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(719,plain,
! [SV57: $i] :
( ( empty @ ( singleton @ SV57 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[609]) ).
thf(720,plain,
! [SV58: $i] :
( ( ( empty @ SV58 )
= $true )
| ( ( ! [SY339: $i] :
~ ( empty @ ( set_union2 @ SV58 @ SY339 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[610]) ).
thf(721,plain,
! [SV124: $i,SV59: $i] :
( ( ~ ( empty @ ( unordered_pair @ SV59 @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(722,plain,
! [SV60: $i] :
( ( ( empty @ SV60 )
= $true )
| ( ( ! [SY341: $i] :
~ ( empty @ ( set_union2 @ SY341 @ SV60 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[612]) ).
thf(723,plain,
! [SV125: $i,SV61: $i] :
( ( ( empty @ SV61 )
| ( empty @ SV125 )
| ~ ( empty @ ( cartesian_product2 @ SV61 @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(724,plain,
! [SV64: $i] :
( ( ( ~ ( relation @ SV64 ) )
= $true )
| ( ( ( relation_inverse @ ( relation_inverse @ SV64 ) )
= SV64 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[616]) ).
thf(725,plain,
! [SV126: $i,SV66: $i] :
( ( ~ ( disjoint @ SV66 @ SV126 )
| ( disjoint @ SV126 @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(726,plain,
! [SV127: $i,SV67: $i] :
( ( ~ ( in @ SV67 @ SV127 )
| ( element @ SV67 @ SV127 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(727,plain,
! [SV128: $i,SV68: $i] :
( ( ~ ( element @ SV68 @ SV128 )
| ( empty @ SV128 )
| ( in @ SV68 @ SV128 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(728,plain,
! [SV69: $i,SV129: $i] :
( ( ! [SY437: $i] :
( ~ ( element @ SV129 @ ( powerset @ SY437 ) )
| ~ ( in @ SV69 @ SV129 )
| ( element @ SV69 @ SY437 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(729,plain,
! [SV70: $i,SV130: $i] :
( ( ! [SY438: $i] :
( ~ ( element @ SV130 @ ( powerset @ SY438 ) )
| ~ ( in @ SV70 @ SV130 )
| ~ ( empty @ SY438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(730,plain,
! [SV71: $i,SV131: $i] :
( ( ~ ( empty @ SV131 )
| ~ ( in @ SV71 @ SV131 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(731,plain,
! [SV132: $i,SV72: $i] :
( ( ( SV72 = SV132 )
| ~ ( empty @ SV72 )
| ~ ( empty @ SV132 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(732,plain,
! [SV73: $i] :
( ( ~ ! [SY352: $i,SY353: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK24_D @ SY353 @ SY352 @ SV73 ) @ SY353 )
| ~ ( in @ ( sK24_D @ SY353 @ SY352 @ SV73 ) @ SV73 ) )
| ~ ( ~ ( in @ ( sK24_D @ SY353 @ SY352 @ SV73 ) @ SY353 )
| ~ ( in @ ( sK24_D @ SY353 @ SY352 @ SV73 ) @ SY352 ) ) )
| ~ ( ( in @ ( sK24_D @ SY353 @ SY352 @ SV73 ) @ SY353 )
| ( in @ ( sK24_D @ SY353 @ SY352 @ SV73 ) @ SV73 )
| ( in @ ( sK24_D @ SY353 @ SY352 @ SV73 ) @ SY352 ) ) )
| ( SY353
= ( set_union2 @ SV73 @ SY352 ) ) )
| ~ ! [SY354: $i,SY355: $i] :
( ( SY355
!= ( set_union2 @ SV73 @ SY354 ) )
| ~ ( ~ ! [SY356: $i] :
( ~ ( in @ SY356 @ SY355 )
| ( in @ SY356 @ SV73 )
| ( in @ SY356 @ SY354 ) )
| ~ ~ ( ~ ! [SY357: $i] :
( ~ ( in @ SY357 @ SV73 )
| ( in @ SY357 @ SY355 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY354 )
| ( in @ SX3 @ SY355 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[627]) ).
thf(733,plain,
! [SV74: $i] :
( ( ~ ! [SY359: $i,SY360: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK25_D @ SY360 @ SY359 @ SV74 ) @ SY360 )
| ( ( sK25_D @ SY360 @ SY359 @ SV74 )
!= SV74 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY360 @ SY359 @ SV74 ) @ SY360 )
| ( ( sK25_D @ SY360 @ SY359 @ SV74 )
!= SY359 ) ) )
| ~ ( ( in @ ( sK25_D @ SY360 @ SY359 @ SV74 ) @ SY360 )
| ( ( sK25_D @ SY360 @ SY359 @ SV74 )
= SV74 )
| ( ( sK25_D @ SY360 @ SY359 @ SV74 )
= SY359 ) ) )
| ( SY360
= ( unordered_pair @ SV74 @ SY359 ) ) )
| ~ ! [SY361: $i,SY362: $i] :
( ( SY362
!= ( unordered_pair @ SV74 @ SY361 ) )
| ~ ( ~ ! [SY363: $i] :
( ~ ( in @ SY363 @ SY362 )
| ( SY363 = SV74 )
| ( SY363 = SY361 ) )
| ~ ~ ( ~ ! [SY364: $i] :
( ( SY364 != SV74 )
| ( in @ SY364 @ SY362 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY361 )
| ( in @ SX3 @ SY362 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[628]) ).
thf(734,plain,
! [SV75: $i] :
( ( ~ ! [SY366: $i,SY367: $i] :
( ~ ( ~ ( ~ ( in @ ( sK22_D @ SY367 @ SY366 @ SV75 ) @ SV75 )
| ~ ( in @ ( sK22_D @ SY367 @ SY366 @ SV75 ) @ SY366 )
| ~ ( in @ ( sK22_D @ SY367 @ SY366 @ SV75 ) @ SY367 ) )
| ~ ~ ( ~ ( ( in @ ( sK22_D @ SY367 @ SY366 @ SV75 ) @ SV75 )
| ( in @ ( sK22_D @ SY367 @ SY366 @ SV75 ) @ SY367 ) )
| ~ ( ( in @ ( sK22_D @ SY367 @ SY366 @ SV75 ) @ SY366 )
| ( in @ ( sK22_D @ SY367 @ SY366 @ SV75 ) @ SY367 ) ) ) )
| ( SY367
= ( set_intersection2 @ SV75 @ SY366 ) ) )
| ~ ! [SY368: $i,SY369: $i] :
( ( SY369
!= ( set_intersection2 @ SV75 @ SY368 ) )
| ~ ( ~ ! [SY370: $i] :
( ~ ( in @ SY370 @ SV75 )
| ~ ( in @ SY370 @ SY368 )
| ( in @ SY370 @ SY369 ) )
| ~ ~ ( ~ ! [SY371: $i] :
( ~ ( in @ SY371 @ SY369 )
| ( in @ SY371 @ SV75 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY369 )
| ( in @ SX3 @ SY368 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[629]) ).
thf(735,plain,
! [SV76: $i] :
( ( ( ~ ( relation @ SV76 ) )
= $true )
| ( ( ~ ( ~ ! [SY373: $i] :
( ~ ( ~ ( ! [SY374: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SY373 @ SV76 ) @ SY374 ) @ SV76 )
| ~ ( in @ ( sK20_C @ SY373 @ SV76 ) @ SY373 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_C @ SY373 @ SV76 ) @ ( sK21_SY278 @ SY373 @ SV76 ) ) @ SV76 )
| ( in @ ( sK20_C @ SY373 @ SV76 ) @ SY373 ) ) )
| ( SY373
= ( relation_dom @ SV76 ) ) )
| ~ ! [SY375: $i] :
( ( SY375
!= ( relation_dom @ SV76 ) )
| ~ ( ~ ! [SY376: $i] :
( ! [SY377: $i] :
~ ( in @ ( ordered_pair @ SY376 @ SY377 ) @ SV76 )
| ( in @ SY376 @ SY375 ) )
| ~ ! [SY378: $i] :
( ~ ( in @ SY378 @ SY375 )
| ( in @ ( ordered_pair @ SY378 @ ( sK19_D @ SY378 @ SY375 @ SV76 ) ) @ SV76 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[630]) ).
thf(736,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[631]) ).
thf(737,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[631]) ).
thf(738,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK37_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[632]) ).
thf(739,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[632]) ).
thf(740,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK26_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK26_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK26_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK26_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[633]) ).
thf(741,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[633]) ).
thf(742,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK33_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[634]) ).
thf(743,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[634]) ).
thf(744,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ ( sK18_SY276 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK18_SY276 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[635]) ).
thf(745,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK16_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK16_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[635]) ).
thf(746,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[636]) ).
thf(747,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[636]) ).
thf(748,plain,
! [SV77: $i] :
( ( ( empty @ SV77 )
= $true )
| ( ( ~ ( ~ ( element @ ( sK8_B @ SV77 ) @ ( powerset @ SV77 ) )
| ~ ~ ( empty @ ( sK8_B @ SV77 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[637]) ).
thf(749,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK34_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK34_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[638]) ).
thf(750,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[638]) ).
thf(751,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[639]) ).
thf(752,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[639]) ).
thf(753,plain,
! [SV78: $i] :
( ( ( ~ ( relation @ SV78 ) )
= $true )
| ( ( ~ ( ~ ! [SY379: $i] :
( ~ ( relation @ SY379 )
| ~ ( subset @ SV78 @ SY379 )
| ( subset @ ( relation_dom @ SV78 ) @ ( relation_dom @ SY379 ) ) )
| ~ ! [SY380: $i] :
( ~ ( relation @ SY380 )
| ~ ( subset @ SV78 @ SY380 )
| ( subset @ ( relation_rng @ SV78 ) @ ( relation_rng @ SY380 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[640]) ).
thf(754,plain,
! [SV79: $i] :
( ( ~ ! [SY381: $i] :
( ~ ( subset @ SY381 @ ( sK35_B @ SV79 ) )
| ( are_equipotent @ SY381 @ ( sK35_B @ SV79 ) )
| ( in @ SY381 @ ( sK35_B @ SV79 ) ) )
| ~ ~ ( ~ ! [SY382: $i] :
( ~ ( in @ SY382 @ ( sK35_B @ SV79 ) )
| ( in @ ( powerset @ SY382 ) @ ( sK35_B @ SV79 ) ) )
| ~ ~ ( ~ ! [SY383: $i,SY384: $i] :
( ~ ( in @ SY383 @ ( sK35_B @ SV79 ) )
| ~ ( subset @ SY384 @ SY383 )
| ( in @ SY384 @ ( sK35_B @ SV79 ) ) )
| ~ ( in @ SV79 @ ( sK35_B @ SV79 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[641]) ).
thf(755,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[642]) ).
thf(756,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[642]) ).
thf(757,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[643]) ).
thf(758,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[643]) ).
thf(759,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[644]) ).
thf(760,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[644]) ).
thf(761,plain,
! [SV80: $i,SV133: $i] :
( ( ~ ( ~ ( in @ ( sK36_C @ SV133 @ SV80 ) @ SV80 )
| ~ ~ ( in @ ( sK36_C @ SV133 @ SV80 ) @ SV133 ) )
| ( element @ SV80 @ ( powerset @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(762,plain,
! [SV81: $i] :
( ( ~ ! [SY386: $i,SY387: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SY387 @ SY386 @ SV81 ) @ SV81 )
| ( in @ ( sK15_D @ SY387 @ SY386 @ SV81 ) @ SY386 )
| ~ ( in @ ( sK15_D @ SY387 @ SY386 @ SV81 ) @ SY387 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SY387 @ SY386 @ SV81 ) @ SV81 )
| ( in @ ( sK15_D @ SY387 @ SY386 @ SV81 ) @ SY387 ) )
| ~ ( ~ ( in @ ( sK15_D @ SY387 @ SY386 @ SV81 ) @ SY386 )
| ( in @ ( sK15_D @ SY387 @ SY386 @ SV81 ) @ SY387 ) ) ) )
| ( SY387
= ( set_difference @ SV81 @ SY386 ) ) )
| ~ ! [SY388: $i,SY389: $i] :
( ( SY389
!= ( set_difference @ SV81 @ SY388 ) )
| ~ ( ~ ! [SY390: $i] :
( ~ ( in @ SY390 @ SV81 )
| ( in @ SY390 @ SY388 )
| ( in @ SY390 @ SY389 ) )
| ~ ~ ( ~ ! [SY391: $i] :
( ~ ( in @ SY391 @ SY389 )
| ( in @ SY391 @ SV81 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY389 )
| ~ ( in @ SX3 @ SY388 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[646]) ).
thf(763,plain,
! [SV82: $i] :
( ( ( ~ ( relation @ SV82 ) )
= $true )
| ( ( ~ ( ~ ! [SY393: $i] :
( ~ ( ~ ( ! [SY394: $i] :
~ ( in @ ( ordered_pair @ SY394 @ ( sK13_C @ SY393 @ SV82 ) ) @ SV82 )
| ~ ( in @ ( sK13_C @ SY393 @ SV82 ) @ SY393 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY274 @ SY393 @ SV82 ) @ ( sK13_C @ SY393 @ SV82 ) ) @ SV82 )
| ( in @ ( sK13_C @ SY393 @ SV82 ) @ SY393 ) ) )
| ( SY393
= ( relation_rng @ SV82 ) ) )
| ~ ! [SY395: $i] :
( ( SY395
!= ( relation_rng @ SV82 ) )
| ~ ( ~ ! [SY396: $i] :
( ! [SY397: $i] :
~ ( in @ ( ordered_pair @ SY397 @ SY396 ) @ SV82 )
| ( in @ SY396 @ SY395 ) )
| ~ ! [SY398: $i] :
( ~ ( in @ SY398 @ SY395 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY398 @ SY395 @ SV82 ) @ SY398 ) @ SV82 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[647]) ).
thf(764,plain,
! [SV83: $i,SV134: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK3_C @ SV134 @ SV83 ) @ SV83 )
| ~ ( in @ ( sK3_C @ SV134 @ SV83 ) @ SV134 ) )
| ~ ( ( in @ ( sK3_C @ SV134 @ SV83 ) @ SV83 )
| ( in @ ( sK3_C @ SV134 @ SV83 ) @ SV134 ) ) )
| ( SV83 = SV134 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(765,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK40_SY287 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK39_C @ SX1 @ SX0 ) @ ( sK40_SY287 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK38_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK38_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[649]) ).
thf(766,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[649]) ).
thf(767,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[650]) ).
thf(768,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[650]) ).
thf(769,plain,
! [SV84: $i] :
( ( ( ~ ( relation @ SV84 ) )
= $true )
| ( ( ~ ( ~ ! [SY400: $i] :
( ~ ( relation @ SY400 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SY400 @ SV84 ) @ ( sK11_SY272 @ SY400 @ SV84 ) ) @ SY400 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY272 @ SY400 @ SV84 ) @ ( sK10_C @ SY400 @ SV84 ) ) @ SV84 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK10_C @ SY400 @ SV84 ) @ ( sK11_SY272 @ SY400 @ SV84 ) ) @ SY400 )
| ( in @ ( ordered_pair @ ( sK11_SY272 @ SY400 @ SV84 ) @ ( sK10_C @ SY400 @ SV84 ) ) @ SV84 ) ) )
| ( SY400
= ( relation_inverse @ SV84 ) ) )
| ~ ! [SY401: $i] :
( ~ ( relation @ SY401 )
| ( SY401
!= ( relation_inverse @ SV84 ) )
| ~ ( ~ ! [SY402: $i,SY403: $i] :
( ~ ( in @ ( ordered_pair @ SY402 @ SY403 ) @ SY401 )
| ( in @ ( ordered_pair @ SY403 @ SY402 ) @ SV84 ) )
| ~ ! [SY404: $i,SY405: $i] :
( ~ ( in @ ( ordered_pair @ SY405 @ SY404 ) @ SV84 )
| ( in @ ( ordered_pair @ SY404 @ SY405 ) @ SY401 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[651]) ).
thf(770,plain,
! [SV85: $i] :
( ( ~ ! [SY406: $i] :
( ~ ( subset @ SY406 @ ( sK1_B @ SV85 ) )
| ( are_equipotent @ SY406 @ ( sK1_B @ SV85 ) )
| ( in @ SY406 @ ( sK1_B @ SV85 ) ) )
| ~ ~ ( ~ ! [SY407: $i] :
( ~ ( ~ ! [SY408: $i] :
( ~ ( subset @ SY408 @ SY407 )
| ( in @ SY408 @ ( sK2_SY267 @ SY407 @ SV85 ) ) )
| ~ ( in @ ( sK2_SY267 @ SY407 @ SV85 ) @ ( sK1_B @ SV85 ) ) )
| ~ ( in @ SY407 @ ( sK1_B @ SV85 ) ) )
| ~ ~ ( ~ ! [SY409: $i,SY410: $i] :
( ~ ( in @ SY409 @ ( sK1_B @ SV85 ) )
| ~ ( subset @ SY410 @ SY409 )
| ( in @ SY410 @ ( sK1_B @ SV85 ) ) )
| ~ ( in @ SV85 @ ( sK1_B @ SV85 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[652]) ).
thf(771,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[653]) ).
thf(772,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[653]) ).
thf(773,plain,
! [SV86: $i] :
( ( ~ ( element @ ( sK5_B @ SV86 ) @ ( powerset @ SV86 ) )
| ~ ( empty @ ( sK5_B @ SV86 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[654]) ).
thf(774,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK30_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK30_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[655]) ).
thf(775,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK28_C @ SX1 @ SX0 ) @ ( sK29_SY279 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[655]) ).
thf(776,plain,
( ( ~ ~ ( empty @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[656]) ).
thf(777,plain,
( ( ~ ( relation @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[656]) ).
thf(778,plain,
! [SV87: $i] :
( ( ~ ! [SY411: $i] :
( ~ ( subset @ SV87 @ SY411 )
| ! [SY412: $i] : ( subset @ ( cartesian_product2 @ SV87 @ SY412 ) @ ( cartesian_product2 @ SY411 @ SY412 ) ) )
| ~ ! [SY413: $i] :
( ~ ( subset @ SV87 @ SY413 )
| ! [SY414: $i] : ( subset @ ( cartesian_product2 @ SY414 @ SV87 ) @ ( cartesian_product2 @ SY414 @ SY413 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[657]) ).
thf(779,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[658]) ).
thf(780,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[658]) ).
thf(781,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[659]) ).
thf(782,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[659]) ).
thf(783,plain,
( ( ~ ( empty @ sK9_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[660]) ).
thf(784,plain,
( ( ~ ( relation @ sK9_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[660]) ).
thf(785,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[661]) ).
thf(786,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[661]) ).
thf(787,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[662]) ).
thf(788,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[662]) ).
thf(789,plain,
! [SV88: $i] :
( ( ~ ! [SY415: $i,SY416: $i] :
( ~ ( in @ SV88 @ SY416 )
| ~ ( in @ SY415 @ SY416 )
| ( subset @ ( unordered_pair @ SV88 @ SY415 ) @ SY416 ) )
| ~ ~ ( ~ ! [SY417: $i,SY418: $i] :
( ~ ( subset @ ( unordered_pair @ SV88 @ SY417 ) @ SY418 )
| ( in @ SV88 @ SY418 ) )
| ~ ! [SY419: $i,SY420: $i] :
( ~ ( subset @ ( unordered_pair @ SV88 @ SY419 ) @ SY420 )
| ( in @ SY419 @ SY420 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[663]) ).
thf(790,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[664]) ).
thf(791,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[664]) ).
thf(792,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[665]) ).
thf(793,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[665]) ).
thf(794,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[666]) ).
thf(795,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[666]) ).
thf(796,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[667]) ).
thf(797,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[667]) ).
thf(798,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK27_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK27_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK27_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK27_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[668]) ).
thf(799,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[668]) ).
thf(800,plain,
! [SV89: $i] :
( ( ~ ! [SY421: $i,SY422: $i] :
( ~ ( relation @ SY422 )
| ~ ( in @ ( ordered_pair @ SV89 @ SY421 ) @ SY422 )
| ( in @ SV89 @ ( relation_dom @ SY422 ) ) )
| ~ ! [SY423: $i,SY424: $i] :
( ~ ( relation @ SY424 )
| ~ ( in @ ( ordered_pair @ SV89 @ SY423 ) @ SY424 )
| ( in @ SY423 @ ( relation_rng @ SY424 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[669]) ).
thf(801,plain,
! [SV3: $i] :
( ( ( subset @ SV3 @ empty_set )
= $false )
| ( ( SV3 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[671]) ).
thf(802,plain,
! [SV4: $i] :
( ( ( empty @ SV4 )
= $true )
| ( ( ~ ( relation @ SV4 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[672]) ).
thf(803,plain,
! [SV5: $i] :
( ( ( empty @ SV5 )
= $true )
| ( ( ~ ( relation @ SV5 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[673]) ).
thf(804,plain,
! [SV10: $i] :
( ( ( empty @ SV10 )
= $false )
| ( ( SV10 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[674]) ).
thf(805,plain,
! [SV90: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ SV90 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV11 ) @ SV90 )
= SV90 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[675]) ).
thf(806,plain,
! [SV91: $i,SV12: $i] :
( ( ( ~ ( disjoint @ ( singleton @ SV12 ) @ SV91 ) )
= $true )
| ( ( ~ ( in @ SV12 @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[676]) ).
thf(807,plain,
! [SV92: $i,SV13: $i] :
( ( ( in @ SV13 @ SV92 )
= $true )
| ( ( disjoint @ ( singleton @ SV13 ) @ SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[677]) ).
thf(808,plain,
! [SV14: $i,SV93: $i] :
( ( ( ~ ( element @ SV93 @ ( powerset @ SV14 ) ) )
= $true )
| ( ( ! [SY425: $i] :
( ~ ( in @ SY425 @ SV93 )
| ( in @ SY425 @ SV14 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[678]) ).
thf(809,plain,
! [SV94: $i,SV15: $i] :
( ( ( ~ ( subset @ SV15 @ SV94 ) )
= $true )
| ( ( ! [SY426: $i] :
( ( in @ SY426 @ SV15 )
| ( subset @ SV15 @ ( set_difference @ SV94 @ ( singleton @ SY426 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[679]) ).
thf(810,plain,
! [SV95: $i,SV16: $i] :
( ( ( ~ ( in @ SV16 @ SV95 ) )
= $true )
| ( ( subset @ SV16 @ ( union @ SV95 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[680]) ).
thf(811,plain,
! [SV135: $i,SV96: $i,SV17: $i] :
( ( ! [SY439: $i] :
( ~ ( subset @ SV17 @ SV96 )
| ~ ( subset @ SV135 @ SY439 )
| ( subset @ ( cartesian_product2 @ SV17 @ SV135 ) @ ( cartesian_product2 @ SV96 @ SY439 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(812,plain,
! [SV97: $i,SV18: $i] :
( ( ( ~ ( subset @ SV18 @ SV97 ) )
= $true )
| ( ( ( set_union2 @ SV18 @ SV97 )
= SV97 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[682]) ).
thf(813,plain,
! [SV136: $i,SV99: $i,SV20: $i] :
( ( ~ ( subset @ SV20 @ SV99 )
| ~ ( subset @ SV20 @ SV136 )
| ( subset @ SV20 @ ( set_intersection2 @ SV99 @ SV136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(814,plain,
! [SV137: $i,SV100: $i,SV21: $i] :
( ( ~ ( subset @ SV21 @ SV100 )
| ~ ( subset @ SV100 @ SV137 )
| ( subset @ SV21 @ SV137 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(815,plain,
! [SV22: $i] :
( ( ( relation @ SV22 )
= $false )
| ( ( subset @ SV22 @ ( cartesian_product2 @ ( relation_dom @ SV22 ) @ ( relation_rng @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[686]) ).
thf(816,plain,
! [SV101: $i,SV23: $i] :
( ( ( ~ ( subset @ SV23 @ SV101 ) )
= $true )
| ( ( ! [SY431: $i] : ( subset @ ( set_intersection2 @ SV23 @ SY431 ) @ ( set_intersection2 @ SV101 @ SY431 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[687]) ).
thf(817,plain,
! [SV102: $i,SV24: $i] :
( ( ( ~ ( subset @ SV24 @ SV102 ) )
= $true )
| ( ( ( set_intersection2 @ SV24 @ SV102 )
= SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[688]) ).
thf(818,plain,
! [SV103: $i,SV25: $i] :
( ( ( ~ ( subset @ SV25 @ SV103 ) )
= $true )
| ( ( ! [SY432: $i] : ( subset @ ( set_difference @ SV25 @ SY432 ) @ ( set_difference @ SV103 @ SY432 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[689]) ).
thf(819,plain,
! [SV29: $i] :
( ( ( relation @ SV29 )
= $false )
| ( ( ! [SY314: $i] :
( ~ ( relation @ SY314 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV29 @ SY314 ) ) @ ( relation_dom @ SV29 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[693]) ).
thf(820,plain,
! [SV30: $i] :
( ( ( relation @ SV30 )
= $false )
| ( ( ! [SY315: $i] :
( ~ ( relation @ SY315 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV30 @ SY315 ) ) @ ( relation_rng @ SY315 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[694]) ).
thf(821,plain,
! [SV107: $i,SV31: $i] :
( ( ( ~ ( subset @ SV31 @ SV107 ) )
= $true )
| ( ( SV107
= ( set_union2 @ SV31 @ ( set_difference @ SV107 @ SV31 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[695]) ).
thf(822,plain,
! [SV32: $i] :
( ( ( relation @ SV32 )
= $false )
| ( ( ! [SY317: $i] :
( ~ ( relation @ SY317 )
| ~ ( subset @ ( relation_rng @ SV32 ) @ ( relation_dom @ SY317 ) )
| ( ( relation_dom @ ( relation_composition @ SV32 @ SY317 ) )
= ( relation_dom @ SV32 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[696]) ).
thf(823,plain,
! [SV108: $i,SV33: $i] :
( ( ( ~ ( in @ SV33 @ SV108 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV33 ) @ SV108 )
= SV108 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[697]) ).
thf(824,plain,
! [SV34: $i] :
( ( ( relation @ SV34 )
= $false )
| ( ( ! [SY319: $i] :
( ~ ( relation @ SY319 )
| ~ ( subset @ ( relation_dom @ SV34 ) @ ( relation_rng @ SY319 ) )
| ( ( relation_rng @ ( relation_composition @ SY319 @ SV34 ) )
= ( relation_rng @ SV34 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[698]) ).
thf(825,plain,
! [SV36: $i] :
( ( ( relation @ SV36 )
= $false )
| ( ( ( in @ ( ordered_pair @ ( sK31_B @ SV36 ) @ ( sK32_SY282 @ SV36 ) ) @ SV36 )
| ( SV36 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[700]) ).
thf(826,plain,
! [SV37: $i,SV110: $i] :
( ( ( ~ ( proper_subset @ SV110 @ SV37 ) )
= $true )
| ( ( ~ ( subset @ SV37 @ SV110 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[701]) ).
thf(827,plain,
! [SV38: $i,SV138: $i,SV111: $i] :
( ( ~ ( disjoint @ SV111 @ SV138 )
| ~ ( subset @ SV38 @ SV111 )
| ( disjoint @ SV38 @ SV138 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(828,plain,
! [SV112: $i,SV40: $i] :
( ( ( ~ ( subset @ ( singleton @ SV40 ) @ ( singleton @ SV112 ) ) )
= $true )
| ( ( SV40 = SV112 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[703]) ).
thf(829,plain,
! [SV139: $i,SV114: $i,SV42: $i] :
( ( ~ ( subset @ SV42 @ SV114 )
| ~ ( subset @ SV139 @ SV114 )
| ( subset @ ( set_union2 @ SV42 @ SV139 ) @ SV114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(830,plain,
! [SV115: $i,SV43: $i] :
( ( ( ! [SY435: $i] :
( ( singleton @ SV43 )
!= ( unordered_pair @ SV115 @ SY435 ) ) )
= $true )
| ( ( SV43 = SV115 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[706]) ).
thf(831,plain,
! [SV116: $i,SV44: $i] :
( ( ( ~ ( in @ SV44 @ SV116 ) )
= $true )
| ( ( subset @ SV44 @ ( union @ SV116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[707]) ).
thf(832,plain,
! [SV140: $i,SV117: $i,SV46: $i] :
( ( ( ( singleton @ SV46 )
!= ( unordered_pair @ SV117 @ SV140 ) )
| ( SV117 = SV140 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(833,plain,
! [SV118: $i,SV47: $i] :
( ( ( ~ ( in @ SV47 @ SV118 ) )
= $true )
| ( ( ~ ( in @ SV118 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[709]) ).
thf(834,plain,
! [SV48: $i] :
( ( ( empty @ SV48 )
= $false )
| ( ( relation @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[710]) ).
thf(835,plain,
! [SV51: $i] :
( ( ( relation @ SV51 )
= $false )
| ( ( ( relation_field @ SV51 )
= ( set_union2 @ ( relation_dom @ SV51 ) @ ( relation_rng @ SV51 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[713]) ).
thf(836,plain,
! [SV52: $i] :
( ( ( relation @ SV52 )
= $false )
| ( ( relation @ ( relation_inverse @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[714]) ).
thf(837,plain,
! [SV121: $i,SV53: $i] :
( ( ( ~ ( relation @ SV53 )
| ~ ( relation @ SV121 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV53 @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[715]) ).
thf(838,plain,
! [SV122: $i,SV55: $i] :
( ( empty @ ( ordered_pair @ SV55 @ SV122 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[717]) ).
thf(839,plain,
! [SV123: $i,SV56: $i] :
( ( ( ~ ( relation @ SV56 )
| ~ ( relation @ SV123 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV56 @ SV123 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[718]) ).
thf(840,plain,
! [SV141: $i,SV58: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV58 @ SV141 ) ) )
= $true )
| ( ( empty @ SV58 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(841,plain,
! [SV124: $i,SV59: $i] :
( ( empty @ ( unordered_pair @ SV59 @ SV124 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[721]) ).
thf(842,plain,
! [SV60: $i,SV142: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV142 @ SV60 ) ) )
= $true )
| ( ( empty @ SV60 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(843,plain,
! [SV125: $i,SV61: $i] :
( ( ( ( empty @ SV61 )
| ( empty @ SV125 ) )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV61 @ SV125 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[723]) ).
thf(844,plain,
! [SV64: $i] :
( ( ( relation @ SV64 )
= $false )
| ( ( ( relation_inverse @ ( relation_inverse @ SV64 ) )
= SV64 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[724]) ).
thf(845,plain,
! [SV126: $i,SV66: $i] :
( ( ( ~ ( disjoint @ SV66 @ SV126 ) )
= $true )
| ( ( disjoint @ SV126 @ SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[725]) ).
thf(846,plain,
! [SV127: $i,SV67: $i] :
( ( ( ~ ( in @ SV67 @ SV127 ) )
= $true )
| ( ( element @ SV67 @ SV127 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[726]) ).
thf(847,plain,
! [SV128: $i,SV68: $i] :
( ( ( ~ ( element @ SV68 @ SV128 ) )
= $true )
| ( ( ( empty @ SV128 )
| ( in @ SV68 @ SV128 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[727]) ).
thf(848,plain,
! [SV69: $i,SV143: $i,SV129: $i] :
( ( ~ ( element @ SV129 @ ( powerset @ SV143 ) )
| ~ ( in @ SV69 @ SV129 )
| ( element @ SV69 @ SV143 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(849,plain,
! [SV70: $i,SV144: $i,SV130: $i] :
( ( ~ ( element @ SV130 @ ( powerset @ SV144 ) )
| ~ ( in @ SV70 @ SV130 )
| ~ ( empty @ SV144 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(850,plain,
! [SV71: $i,SV131: $i] :
( ( ( ~ ( empty @ SV131 ) )
= $true )
| ( ( ~ ( in @ SV71 @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[730]) ).
thf(851,plain,
! [SV132: $i,SV72: $i] :
( ( ( ( SV72 = SV132 )
| ~ ( empty @ SV72 ) )
= $true )
| ( ( ~ ( empty @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[731]) ).
thf(852,plain,
! [SV73: $i] :
( ( ~ ! [SY352: $i,SY353: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK24_D @ SY353 @ SY352 @ SV73 ) @ SY353 )
| ~ ( in @ ( sK24_D @ SY353 @ SY352 @ SV73 ) @ SV73 ) )
| ~ ( ~ ( in @ ( sK24_D @ SY353 @ SY352 @ SV73 ) @ SY353 )
| ~ ( in @ ( sK24_D @ SY353 @ SY352 @ SV73 ) @ SY352 ) ) )
| ~ ( ( in @ ( sK24_D @ SY353 @ SY352 @ SV73 ) @ SY353 )
| ( in @ ( sK24_D @ SY353 @ SY352 @ SV73 ) @ SV73 )
| ( in @ ( sK24_D @ SY353 @ SY352 @ SV73 ) @ SY352 ) ) )
| ( SY353
= ( set_union2 @ SV73 @ SY352 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[732]) ).
thf(853,plain,
! [SV73: $i] :
( ( ~ ! [SY354: $i,SY355: $i] :
( ( SY355
!= ( set_union2 @ SV73 @ SY354 ) )
| ~ ( ~ ! [SY356: $i] :
( ~ ( in @ SY356 @ SY355 )
| ( in @ SY356 @ SV73 )
| ( in @ SY356 @ SY354 ) )
| ~ ~ ( ~ ! [SY357: $i] :
( ~ ( in @ SY357 @ SV73 )
| ( in @ SY357 @ SY355 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY354 )
| ( in @ SX3 @ SY355 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[732]) ).
thf(854,plain,
! [SV74: $i] :
( ( ~ ! [SY359: $i,SY360: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK25_D @ SY360 @ SY359 @ SV74 ) @ SY360 )
| ( ( sK25_D @ SY360 @ SY359 @ SV74 )
!= SV74 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY360 @ SY359 @ SV74 ) @ SY360 )
| ( ( sK25_D @ SY360 @ SY359 @ SV74 )
!= SY359 ) ) )
| ~ ( ( in @ ( sK25_D @ SY360 @ SY359 @ SV74 ) @ SY360 )
| ( ( sK25_D @ SY360 @ SY359 @ SV74 )
= SV74 )
| ( ( sK25_D @ SY360 @ SY359 @ SV74 )
= SY359 ) ) )
| ( SY360
= ( unordered_pair @ SV74 @ SY359 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[733]) ).
thf(855,plain,
! [SV74: $i] :
( ( ~ ! [SY361: $i,SY362: $i] :
( ( SY362
!= ( unordered_pair @ SV74 @ SY361 ) )
| ~ ( ~ ! [SY363: $i] :
( ~ ( in @ SY363 @ SY362 )
| ( SY363 = SV74 )
| ( SY363 = SY361 ) )
| ~ ~ ( ~ ! [SY364: $i] :
( ( SY364 != SV74 )
| ( in @ SY364 @ SY362 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY361 )
| ( in @ SX3 @ SY362 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[733]) ).
thf(856,plain,
! [SV75: $i] :
( ( ~ ! [SY366: $i,SY367: $i] :
( ~ ( ~ ( ~ ( in @ ( sK22_D @ SY367 @ SY366 @ SV75 ) @ SV75 )
| ~ ( in @ ( sK22_D @ SY367 @ SY366 @ SV75 ) @ SY366 )
| ~ ( in @ ( sK22_D @ SY367 @ SY366 @ SV75 ) @ SY367 ) )
| ~ ~ ( ~ ( ( in @ ( sK22_D @ SY367 @ SY366 @ SV75 ) @ SV75 )
| ( in @ ( sK22_D @ SY367 @ SY366 @ SV75 ) @ SY367 ) )
| ~ ( ( in @ ( sK22_D @ SY367 @ SY366 @ SV75 ) @ SY366 )
| ( in @ ( sK22_D @ SY367 @ SY366 @ SV75 ) @ SY367 ) ) ) )
| ( SY367
= ( set_intersection2 @ SV75 @ SY366 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[734]) ).
thf(857,plain,
! [SV75: $i] :
( ( ~ ! [SY368: $i,SY369: $i] :
( ( SY369
!= ( set_intersection2 @ SV75 @ SY368 ) )
| ~ ( ~ ! [SY370: $i] :
( ~ ( in @ SY370 @ SV75 )
| ~ ( in @ SY370 @ SY368 )
| ( in @ SY370 @ SY369 ) )
| ~ ~ ( ~ ! [SY371: $i] :
( ~ ( in @ SY371 @ SY369 )
| ( in @ SY371 @ SV75 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY369 )
| ( in @ SX3 @ SY368 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[734]) ).
thf(858,plain,
! [SV76: $i] :
( ( ( relation @ SV76 )
= $false )
| ( ( ~ ( ~ ! [SY373: $i] :
( ~ ( ~ ( ! [SY374: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SY373 @ SV76 ) @ SY374 ) @ SV76 )
| ~ ( in @ ( sK20_C @ SY373 @ SV76 ) @ SY373 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_C @ SY373 @ SV76 ) @ ( sK21_SY278 @ SY373 @ SV76 ) ) @ SV76 )
| ( in @ ( sK20_C @ SY373 @ SV76 ) @ SY373 ) ) )
| ( SY373
= ( relation_dom @ SV76 ) ) )
| ~ ! [SY375: $i] :
( ( SY375
!= ( relation_dom @ SV76 ) )
| ~ ( ~ ! [SY376: $i] :
( ! [SY377: $i] :
~ ( in @ ( ordered_pair @ SY376 @ SY377 ) @ SV76 )
| ( in @ SY376 @ SY375 ) )
| ~ ! [SY378: $i] :
( ~ ( in @ SY378 @ SY375 )
| ( in @ ( ordered_pair @ SY378 @ ( sK19_D @ SY378 @ SY375 @ SV76 ) ) @ SV76 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[735]) ).
thf(859,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[736]) ).
thf(860,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[737]) ).
thf(861,plain,
( ( ! [SX0: $i] :
( ( in @ ( sK37_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[738]) ).
thf(862,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[739]) ).
thf(863,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK26_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK26_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK26_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK26_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[740]) ).
thf(864,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[741]) ).
thf(865,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK33_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[742]) ).
thf(866,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[743]) ).
thf(867,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ ( sK18_SY276 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK18_SY276 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[744]) ).
thf(868,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK16_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK16_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[745]) ).
thf(869,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[746]) ).
thf(870,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[747]) ).
thf(871,plain,
! [SV77: $i] :
( ( ( ~ ( element @ ( sK8_B @ SV77 ) @ ( powerset @ SV77 ) )
| ~ ~ ( empty @ ( sK8_B @ SV77 ) ) )
= $false )
| ( ( empty @ SV77 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[748]) ).
thf(872,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK34_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK34_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[749]) ).
thf(873,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[750]) ).
thf(874,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[751]) ).
thf(875,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[752]) ).
thf(876,plain,
! [SV78: $i] :
( ( ( relation @ SV78 )
= $false )
| ( ( ~ ( ~ ! [SY379: $i] :
( ~ ( relation @ SY379 )
| ~ ( subset @ SV78 @ SY379 )
| ( subset @ ( relation_dom @ SV78 ) @ ( relation_dom @ SY379 ) ) )
| ~ ! [SY380: $i] :
( ~ ( relation @ SY380 )
| ~ ( subset @ SV78 @ SY380 )
| ( subset @ ( relation_rng @ SV78 ) @ ( relation_rng @ SY380 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[753]) ).
thf(877,plain,
! [SV79: $i] :
( ( ~ ! [SY381: $i] :
( ~ ( subset @ SY381 @ ( sK35_B @ SV79 ) )
| ( are_equipotent @ SY381 @ ( sK35_B @ SV79 ) )
| ( in @ SY381 @ ( sK35_B @ SV79 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[754]) ).
thf(878,plain,
! [SV79: $i] :
( ( ~ ~ ( ~ ! [SY382: $i] :
( ~ ( in @ SY382 @ ( sK35_B @ SV79 ) )
| ( in @ ( powerset @ SY382 ) @ ( sK35_B @ SV79 ) ) )
| ~ ~ ( ~ ! [SY383: $i,SY384: $i] :
( ~ ( in @ SY383 @ ( sK35_B @ SV79 ) )
| ~ ( subset @ SY384 @ SY383 )
| ( in @ SY384 @ ( sK35_B @ SV79 ) ) )
| ~ ( in @ SV79 @ ( sK35_B @ SV79 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[754]) ).
thf(879,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[755]) ).
thf(880,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[756]) ).
thf(881,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[757]) ).
thf(882,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[758]) ).
thf(883,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[759]) ).
thf(884,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[760]) ).
thf(885,plain,
! [SV80: $i,SV133: $i] :
( ( ( ~ ( ~ ( in @ ( sK36_C @ SV133 @ SV80 ) @ SV80 )
| ~ ~ ( in @ ( sK36_C @ SV133 @ SV80 ) @ SV133 ) ) )
= $true )
| ( ( element @ SV80 @ ( powerset @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[761]) ).
thf(886,plain,
! [SV81: $i] :
( ( ~ ! [SY386: $i,SY387: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SY387 @ SY386 @ SV81 ) @ SV81 )
| ( in @ ( sK15_D @ SY387 @ SY386 @ SV81 ) @ SY386 )
| ~ ( in @ ( sK15_D @ SY387 @ SY386 @ SV81 ) @ SY387 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SY387 @ SY386 @ SV81 ) @ SV81 )
| ( in @ ( sK15_D @ SY387 @ SY386 @ SV81 ) @ SY387 ) )
| ~ ( ~ ( in @ ( sK15_D @ SY387 @ SY386 @ SV81 ) @ SY386 )
| ( in @ ( sK15_D @ SY387 @ SY386 @ SV81 ) @ SY387 ) ) ) )
| ( SY387
= ( set_difference @ SV81 @ SY386 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[762]) ).
thf(887,plain,
! [SV81: $i] :
( ( ~ ! [SY388: $i,SY389: $i] :
( ( SY389
!= ( set_difference @ SV81 @ SY388 ) )
| ~ ( ~ ! [SY390: $i] :
( ~ ( in @ SY390 @ SV81 )
| ( in @ SY390 @ SY388 )
| ( in @ SY390 @ SY389 ) )
| ~ ~ ( ~ ! [SY391: $i] :
( ~ ( in @ SY391 @ SY389 )
| ( in @ SY391 @ SV81 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY389 )
| ~ ( in @ SX3 @ SY388 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[762]) ).
thf(888,plain,
! [SV82: $i] :
( ( ( relation @ SV82 )
= $false )
| ( ( ~ ( ~ ! [SY393: $i] :
( ~ ( ~ ( ! [SY394: $i] :
~ ( in @ ( ordered_pair @ SY394 @ ( sK13_C @ SY393 @ SV82 ) ) @ SV82 )
| ~ ( in @ ( sK13_C @ SY393 @ SV82 ) @ SY393 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY274 @ SY393 @ SV82 ) @ ( sK13_C @ SY393 @ SV82 ) ) @ SV82 )
| ( in @ ( sK13_C @ SY393 @ SV82 ) @ SY393 ) ) )
| ( SY393
= ( relation_rng @ SV82 ) ) )
| ~ ! [SY395: $i] :
( ( SY395
!= ( relation_rng @ SV82 ) )
| ~ ( ~ ! [SY396: $i] :
( ! [SY397: $i] :
~ ( in @ ( ordered_pair @ SY397 @ SY396 ) @ SV82 )
| ( in @ SY396 @ SY395 ) )
| ~ ! [SY398: $i] :
( ~ ( in @ SY398 @ SY395 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY398 @ SY395 @ SV82 ) @ SY398 ) @ SV82 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[763]) ).
thf(889,plain,
! [SV83: $i,SV134: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK3_C @ SV134 @ SV83 ) @ SV83 )
| ~ ( in @ ( sK3_C @ SV134 @ SV83 ) @ SV134 ) )
| ~ ( ( in @ ( sK3_C @ SV134 @ SV83 ) @ SV83 )
| ( in @ ( sK3_C @ SV134 @ SV83 ) @ SV134 ) ) ) )
= $true )
| ( ( SV83 = SV134 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[764]) ).
thf(890,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK40_SY287 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK39_C @ SX1 @ SX0 ) @ ( sK40_SY287 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK38_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK38_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[765]) ).
thf(891,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[766]) ).
thf(892,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[767]) ).
thf(893,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[768]) ).
thf(894,plain,
! [SV84: $i] :
( ( ( relation @ SV84 )
= $false )
| ( ( ~ ( ~ ! [SY400: $i] :
( ~ ( relation @ SY400 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SY400 @ SV84 ) @ ( sK11_SY272 @ SY400 @ SV84 ) ) @ SY400 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY272 @ SY400 @ SV84 ) @ ( sK10_C @ SY400 @ SV84 ) ) @ SV84 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK10_C @ SY400 @ SV84 ) @ ( sK11_SY272 @ SY400 @ SV84 ) ) @ SY400 )
| ( in @ ( ordered_pair @ ( sK11_SY272 @ SY400 @ SV84 ) @ ( sK10_C @ SY400 @ SV84 ) ) @ SV84 ) ) )
| ( SY400
= ( relation_inverse @ SV84 ) ) )
| ~ ! [SY401: $i] :
( ~ ( relation @ SY401 )
| ( SY401
!= ( relation_inverse @ SV84 ) )
| ~ ( ~ ! [SY402: $i,SY403: $i] :
( ~ ( in @ ( ordered_pair @ SY402 @ SY403 ) @ SY401 )
| ( in @ ( ordered_pair @ SY403 @ SY402 ) @ SV84 ) )
| ~ ! [SY404: $i,SY405: $i] :
( ~ ( in @ ( ordered_pair @ SY405 @ SY404 ) @ SV84 )
| ( in @ ( ordered_pair @ SY404 @ SY405 ) @ SY401 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[769]) ).
thf(895,plain,
! [SV85: $i] :
( ( ~ ! [SY406: $i] :
( ~ ( subset @ SY406 @ ( sK1_B @ SV85 ) )
| ( are_equipotent @ SY406 @ ( sK1_B @ SV85 ) )
| ( in @ SY406 @ ( sK1_B @ SV85 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[770]) ).
thf(896,plain,
! [SV85: $i] :
( ( ~ ~ ( ~ ! [SY407: $i] :
( ~ ( ~ ! [SY408: $i] :
( ~ ( subset @ SY408 @ SY407 )
| ( in @ SY408 @ ( sK2_SY267 @ SY407 @ SV85 ) ) )
| ~ ( in @ ( sK2_SY267 @ SY407 @ SV85 ) @ ( sK1_B @ SV85 ) ) )
| ~ ( in @ SY407 @ ( sK1_B @ SV85 ) ) )
| ~ ~ ( ~ ! [SY409: $i,SY410: $i] :
( ~ ( in @ SY409 @ ( sK1_B @ SV85 ) )
| ~ ( subset @ SY410 @ SY409 )
| ( in @ SY410 @ ( sK1_B @ SV85 ) ) )
| ~ ( in @ SV85 @ ( sK1_B @ SV85 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[770]) ).
thf(897,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[771]) ).
thf(898,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[772]) ).
thf(899,plain,
! [SV86: $i] :
( ( ~ ( element @ ( sK5_B @ SV86 ) @ ( powerset @ SV86 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[773]) ).
thf(900,plain,
! [SV86: $i] :
( ( ~ ( empty @ ( sK5_B @ SV86 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[773]) ).
thf(901,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK30_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK30_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[774]) ).
thf(902,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK28_C @ SX1 @ SX0 ) @ ( sK29_SY279 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[775]) ).
thf(903,plain,
( ( ~ ( empty @ sK6_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[776]) ).
thf(904,plain,
( ( relation @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[777]) ).
thf(905,plain,
! [SV87: $i] :
( ( ~ ! [SY411: $i] :
( ~ ( subset @ SV87 @ SY411 )
| ! [SY412: $i] : ( subset @ ( cartesian_product2 @ SV87 @ SY412 ) @ ( cartesian_product2 @ SY411 @ SY412 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[778]) ).
thf(906,plain,
! [SV87: $i] :
( ( ~ ! [SY413: $i] :
( ~ ( subset @ SV87 @ SY413 )
| ! [SY414: $i] : ( subset @ ( cartesian_product2 @ SY414 @ SV87 ) @ ( cartesian_product2 @ SY414 @ SY413 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[778]) ).
thf(907,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[779]) ).
thf(908,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[780]) ).
thf(909,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[781]) ).
thf(910,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[782]) ).
thf(911,plain,
( ( empty @ sK9_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[783]) ).
thf(912,plain,
( ( relation @ sK9_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[784]) ).
thf(913,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[785]) ).
thf(914,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[786]) ).
thf(915,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[787]) ).
thf(916,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[788]) ).
thf(917,plain,
! [SV88: $i] :
( ( ~ ! [SY415: $i,SY416: $i] :
( ~ ( in @ SV88 @ SY416 )
| ~ ( in @ SY415 @ SY416 )
| ( subset @ ( unordered_pair @ SV88 @ SY415 ) @ SY416 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[789]) ).
thf(918,plain,
! [SV88: $i] :
( ( ~ ~ ( ~ ! [SY417: $i,SY418: $i] :
( ~ ( subset @ ( unordered_pair @ SV88 @ SY417 ) @ SY418 )
| ( in @ SV88 @ SY418 ) )
| ~ ! [SY419: $i,SY420: $i] :
( ~ ( subset @ ( unordered_pair @ SV88 @ SY419 ) @ SY420 )
| ( in @ SY419 @ SY420 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[789]) ).
thf(919,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[790]) ).
thf(920,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[791]) ).
thf(921,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[792]) ).
thf(922,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[793]) ).
thf(923,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[794]) ).
thf(924,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[795]) ).
thf(925,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[796]) ).
thf(926,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[797]) ).
thf(927,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK27_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK27_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK27_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK27_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[798]) ).
thf(928,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[799]) ).
thf(929,plain,
! [SV89: $i] :
( ( ~ ! [SY421: $i,SY422: $i] :
( ~ ( relation @ SY422 )
| ~ ( in @ ( ordered_pair @ SV89 @ SY421 ) @ SY422 )
| ( in @ SV89 @ ( relation_dom @ SY422 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[800]) ).
thf(930,plain,
! [SV89: $i] :
( ( ~ ! [SY423: $i,SY424: $i] :
( ~ ( relation @ SY424 )
| ~ ( in @ ( ordered_pair @ SV89 @ SY423 ) @ SY424 )
| ( in @ SY423 @ ( relation_rng @ SY424 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[800]) ).
thf(931,plain,
! [SV4: $i] :
( ( ( relation @ SV4 )
= $false )
| ( ( empty @ SV4 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[802]) ).
thf(932,plain,
! [SV5: $i] :
( ( ( relation @ SV5 )
= $false )
| ( ( empty @ SV5 )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[803]) ).
thf(933,plain,
! [SV90: $i,SV11: $i] :
( ( ( in @ SV11 @ SV90 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV11 ) @ SV90 )
= SV90 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[805]) ).
thf(934,plain,
! [SV91: $i,SV12: $i] :
( ( ( disjoint @ ( singleton @ SV12 ) @ SV91 )
= $false )
| ( ( ~ ( in @ SV12 @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[806]) ).
thf(935,plain,
! [SV14: $i,SV93: $i] :
( ( ( element @ SV93 @ ( powerset @ SV14 ) )
= $false )
| ( ( ! [SY425: $i] :
( ~ ( in @ SY425 @ SV93 )
| ( in @ SY425 @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[808]) ).
thf(936,plain,
! [SV94: $i,SV15: $i] :
( ( ( subset @ SV15 @ SV94 )
= $false )
| ( ( ! [SY426: $i] :
( ( in @ SY426 @ SV15 )
| ( subset @ SV15 @ ( set_difference @ SV94 @ ( singleton @ SY426 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[809]) ).
thf(937,plain,
! [SV95: $i,SV16: $i] :
( ( ( in @ SV16 @ SV95 )
= $false )
| ( ( subset @ SV16 @ ( union @ SV95 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[810]) ).
thf(938,plain,
! [SV145: $i,SV135: $i,SV96: $i,SV17: $i] :
( ( ~ ( subset @ SV17 @ SV96 )
| ~ ( subset @ SV135 @ SV145 )
| ( subset @ ( cartesian_product2 @ SV17 @ SV135 ) @ ( cartesian_product2 @ SV96 @ SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(939,plain,
! [SV97: $i,SV18: $i] :
( ( ( subset @ SV18 @ SV97 )
= $false )
| ( ( ( set_union2 @ SV18 @ SV97 )
= SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[812]) ).
thf(940,plain,
! [SV136: $i,SV99: $i,SV20: $i] :
( ( ( ~ ( subset @ SV20 @ SV99 )
| ~ ( subset @ SV20 @ SV136 ) )
= $true )
| ( ( subset @ SV20 @ ( set_intersection2 @ SV99 @ SV136 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[813]) ).
thf(941,plain,
! [SV137: $i,SV100: $i,SV21: $i] :
( ( ( ~ ( subset @ SV21 @ SV100 )
| ~ ( subset @ SV100 @ SV137 ) )
= $true )
| ( ( subset @ SV21 @ SV137 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[814]) ).
thf(942,plain,
! [SV101: $i,SV23: $i] :
( ( ( subset @ SV23 @ SV101 )
= $false )
| ( ( ! [SY431: $i] : ( subset @ ( set_intersection2 @ SV23 @ SY431 ) @ ( set_intersection2 @ SV101 @ SY431 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[816]) ).
thf(943,plain,
! [SV102: $i,SV24: $i] :
( ( ( subset @ SV24 @ SV102 )
= $false )
| ( ( ( set_intersection2 @ SV24 @ SV102 )
= SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[817]) ).
thf(944,plain,
! [SV103: $i,SV25: $i] :
( ( ( subset @ SV25 @ SV103 )
= $false )
| ( ( ! [SY432: $i] : ( subset @ ( set_difference @ SV25 @ SY432 ) @ ( set_difference @ SV103 @ SY432 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[818]) ).
thf(945,plain,
! [SV29: $i,SV146: $i] :
( ( ( ~ ( relation @ SV146 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV29 @ SV146 ) ) @ ( relation_dom @ SV29 ) ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(946,plain,
! [SV30: $i,SV147: $i] :
( ( ( ~ ( relation @ SV147 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV30 @ SV147 ) ) @ ( relation_rng @ SV147 ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(947,plain,
! [SV107: $i,SV31: $i] :
( ( ( subset @ SV31 @ SV107 )
= $false )
| ( ( SV107
= ( set_union2 @ SV31 @ ( set_difference @ SV107 @ SV31 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[821]) ).
thf(948,plain,
! [SV32: $i,SV148: $i] :
( ( ( ~ ( relation @ SV148 )
| ~ ( subset @ ( relation_rng @ SV32 ) @ ( relation_dom @ SV148 ) )
| ( ( relation_dom @ ( relation_composition @ SV32 @ SV148 ) )
= ( relation_dom @ SV32 ) ) )
= $true )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(949,plain,
! [SV108: $i,SV33: $i] :
( ( ( in @ SV33 @ SV108 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV33 ) @ SV108 )
= SV108 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[823]) ).
thf(950,plain,
! [SV34: $i,SV149: $i] :
( ( ( ~ ( relation @ SV149 )
| ~ ( subset @ ( relation_dom @ SV34 ) @ ( relation_rng @ SV149 ) )
| ( ( relation_rng @ ( relation_composition @ SV149 @ SV34 ) )
= ( relation_rng @ SV34 ) ) )
= $true )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(951,plain,
! [SV36: $i] :
( ( ( in @ ( ordered_pair @ ( sK31_B @ SV36 ) @ ( sK32_SY282 @ SV36 ) ) @ SV36 )
= $true )
| ( ( SV36 = empty_set )
= $true )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[825]) ).
thf(952,plain,
! [SV37: $i,SV110: $i] :
( ( ( proper_subset @ SV110 @ SV37 )
= $false )
| ( ( ~ ( subset @ SV37 @ SV110 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[826]) ).
thf(953,plain,
! [SV38: $i,SV138: $i,SV111: $i] :
( ( ( ~ ( disjoint @ SV111 @ SV138 )
| ~ ( subset @ SV38 @ SV111 ) )
= $true )
| ( ( disjoint @ SV38 @ SV138 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[827]) ).
thf(954,plain,
! [SV112: $i,SV40: $i] :
( ( ( subset @ ( singleton @ SV40 ) @ ( singleton @ SV112 ) )
= $false )
| ( ( SV40 = SV112 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[828]) ).
thf(955,plain,
! [SV139: $i,SV114: $i,SV42: $i] :
( ( ( ~ ( subset @ SV42 @ SV114 )
| ~ ( subset @ SV139 @ SV114 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV42 @ SV139 ) @ SV114 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[829]) ).
thf(956,plain,
! [SV150: $i,SV115: $i,SV43: $i] :
( ( ( ( ( singleton @ SV43 )
!= ( unordered_pair @ SV115 @ SV150 ) ) )
= $true )
| ( ( SV43 = SV115 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(957,plain,
! [SV116: $i,SV44: $i] :
( ( ( in @ SV44 @ SV116 )
= $false )
| ( ( subset @ SV44 @ ( union @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[831]) ).
thf(958,plain,
! [SV140: $i,SV117: $i,SV46: $i] :
( ( ( ( ( singleton @ SV46 )
!= ( unordered_pair @ SV117 @ SV140 ) ) )
= $true )
| ( ( SV117 = SV140 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[832]) ).
thf(959,plain,
! [SV118: $i,SV47: $i] :
( ( ( in @ SV47 @ SV118 )
= $false )
| ( ( ~ ( in @ SV118 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[833]) ).
thf(960,plain,
! [SV121: $i,SV53: $i] :
( ( ( ~ ( relation @ SV53 ) )
= $true )
| ( ( ~ ( relation @ SV121 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV53 @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[837]) ).
thf(961,plain,
! [SV123: $i,SV56: $i] :
( ( ( ~ ( relation @ SV56 ) )
= $true )
| ( ( ~ ( relation @ SV123 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV56 @ SV123 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[839]) ).
thf(962,plain,
! [SV141: $i,SV58: $i] :
( ( ( empty @ ( set_union2 @ SV58 @ SV141 ) )
= $false )
| ( ( empty @ SV58 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[840]) ).
thf(963,plain,
! [SV60: $i,SV142: $i] :
( ( ( empty @ ( set_union2 @ SV142 @ SV60 ) )
= $false )
| ( ( empty @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[842]) ).
thf(964,plain,
! [SV125: $i,SV61: $i] :
( ( ( empty @ SV61 )
= $true )
| ( ( empty @ SV125 )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV61 @ SV125 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[843]) ).
thf(965,plain,
! [SV126: $i,SV66: $i] :
( ( ( disjoint @ SV66 @ SV126 )
= $false )
| ( ( disjoint @ SV126 @ SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[845]) ).
thf(966,plain,
! [SV127: $i,SV67: $i] :
( ( ( in @ SV67 @ SV127 )
= $false )
| ( ( element @ SV67 @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[846]) ).
thf(967,plain,
! [SV128: $i,SV68: $i] :
( ( ( element @ SV68 @ SV128 )
= $false )
| ( ( ( empty @ SV128 )
| ( in @ SV68 @ SV128 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[847]) ).
thf(968,plain,
! [SV69: $i,SV143: $i,SV129: $i] :
( ( ( ~ ( element @ SV129 @ ( powerset @ SV143 ) )
| ~ ( in @ SV69 @ SV129 ) )
= $true )
| ( ( element @ SV69 @ SV143 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[848]) ).
thf(969,plain,
! [SV70: $i,SV144: $i,SV130: $i] :
( ( ( ~ ( element @ SV130 @ ( powerset @ SV144 ) )
| ~ ( in @ SV70 @ SV130 ) )
= $true )
| ( ( ~ ( empty @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[849]) ).
thf(970,plain,
! [SV71: $i,SV131: $i] :
( ( ( empty @ SV131 )
= $false )
| ( ( ~ ( in @ SV71 @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[850]) ).
thf(971,plain,
! [SV132: $i,SV72: $i] :
( ( ( SV72 = SV132 )
= $true )
| ( ( ~ ( empty @ SV72 ) )
= $true )
| ( ( ~ ( empty @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[851]) ).
thf(972,plain,
! [SV73: $i] :
( ( ! [SY352: $i,SY353: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK24_D @ SY353 @ SY352 @ SV73 ) @ SY353 )
| ~ ( in @ ( sK24_D @ SY353 @ SY352 @ SV73 ) @ SV73 ) )
| ~ ( ~ ( in @ ( sK24_D @ SY353 @ SY352 @ SV73 ) @ SY353 )
| ~ ( in @ ( sK24_D @ SY353 @ SY352 @ SV73 ) @ SY352 ) ) )
| ~ ( ( in @ ( sK24_D @ SY353 @ SY352 @ SV73 ) @ SY353 )
| ( in @ ( sK24_D @ SY353 @ SY352 @ SV73 ) @ SV73 )
| ( in @ ( sK24_D @ SY353 @ SY352 @ SV73 ) @ SY352 ) ) )
| ( SY353
= ( set_union2 @ SV73 @ SY352 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[852]) ).
thf(973,plain,
! [SV73: $i] :
( ( ! [SY354: $i,SY355: $i] :
( ( SY355
!= ( set_union2 @ SV73 @ SY354 ) )
| ~ ( ~ ! [SY356: $i] :
( ~ ( in @ SY356 @ SY355 )
| ( in @ SY356 @ SV73 )
| ( in @ SY356 @ SY354 ) )
| ~ ~ ( ~ ! [SY357: $i] :
( ~ ( in @ SY357 @ SV73 )
| ( in @ SY357 @ SY355 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY354 )
| ( in @ SX3 @ SY355 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[853]) ).
thf(974,plain,
! [SV74: $i] :
( ( ! [SY359: $i,SY360: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK25_D @ SY360 @ SY359 @ SV74 ) @ SY360 )
| ( ( sK25_D @ SY360 @ SY359 @ SV74 )
!= SV74 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY360 @ SY359 @ SV74 ) @ SY360 )
| ( ( sK25_D @ SY360 @ SY359 @ SV74 )
!= SY359 ) ) )
| ~ ( ( in @ ( sK25_D @ SY360 @ SY359 @ SV74 ) @ SY360 )
| ( ( sK25_D @ SY360 @ SY359 @ SV74 )
= SV74 )
| ( ( sK25_D @ SY360 @ SY359 @ SV74 )
= SY359 ) ) )
| ( SY360
= ( unordered_pair @ SV74 @ SY359 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[854]) ).
thf(975,plain,
! [SV74: $i] :
( ( ! [SY361: $i,SY362: $i] :
( ( SY362
!= ( unordered_pair @ SV74 @ SY361 ) )
| ~ ( ~ ! [SY363: $i] :
( ~ ( in @ SY363 @ SY362 )
| ( SY363 = SV74 )
| ( SY363 = SY361 ) )
| ~ ~ ( ~ ! [SY364: $i] :
( ( SY364 != SV74 )
| ( in @ SY364 @ SY362 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY361 )
| ( in @ SX3 @ SY362 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[855]) ).
thf(976,plain,
! [SV75: $i] :
( ( ! [SY366: $i,SY367: $i] :
( ~ ( ~ ( ~ ( in @ ( sK22_D @ SY367 @ SY366 @ SV75 ) @ SV75 )
| ~ ( in @ ( sK22_D @ SY367 @ SY366 @ SV75 ) @ SY366 )
| ~ ( in @ ( sK22_D @ SY367 @ SY366 @ SV75 ) @ SY367 ) )
| ~ ~ ( ~ ( ( in @ ( sK22_D @ SY367 @ SY366 @ SV75 ) @ SV75 )
| ( in @ ( sK22_D @ SY367 @ SY366 @ SV75 ) @ SY367 ) )
| ~ ( ( in @ ( sK22_D @ SY367 @ SY366 @ SV75 ) @ SY366 )
| ( in @ ( sK22_D @ SY367 @ SY366 @ SV75 ) @ SY367 ) ) ) )
| ( SY367
= ( set_intersection2 @ SV75 @ SY366 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[856]) ).
thf(977,plain,
! [SV75: $i] :
( ( ! [SY368: $i,SY369: $i] :
( ( SY369
!= ( set_intersection2 @ SV75 @ SY368 ) )
| ~ ( ~ ! [SY370: $i] :
( ~ ( in @ SY370 @ SV75 )
| ~ ( in @ SY370 @ SY368 )
| ( in @ SY370 @ SY369 ) )
| ~ ~ ( ~ ! [SY371: $i] :
( ~ ( in @ SY371 @ SY369 )
| ( in @ SY371 @ SV75 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY369 )
| ( in @ SX3 @ SY368 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[857]) ).
thf(978,plain,
! [SV76: $i] :
( ( ( ~ ! [SY373: $i] :
( ~ ( ~ ( ! [SY374: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SY373 @ SV76 ) @ SY374 ) @ SV76 )
| ~ ( in @ ( sK20_C @ SY373 @ SV76 ) @ SY373 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_C @ SY373 @ SV76 ) @ ( sK21_SY278 @ SY373 @ SV76 ) ) @ SV76 )
| ( in @ ( sK20_C @ SY373 @ SV76 ) @ SY373 ) ) )
| ( SY373
= ( relation_dom @ SV76 ) ) )
| ~ ! [SY375: $i] :
( ( SY375
!= ( relation_dom @ SV76 ) )
| ~ ( ~ ! [SY376: $i] :
( ! [SY377: $i] :
~ ( in @ ( ordered_pair @ SY376 @ SY377 ) @ SV76 )
| ( in @ SY376 @ SY375 ) )
| ~ ! [SY378: $i] :
( ~ ( in @ SY378 @ SY375 )
| ( in @ ( ordered_pair @ SY378 @ ( sK19_D @ SY378 @ SY375 @ SV76 ) ) @ SV76 ) ) ) ) )
= $false )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[858]) ).
thf(979,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[859]) ).
thf(980,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[860]) ).
thf(981,plain,
! [SV151: $i] :
( ( ( in @ ( sK37_B @ SV151 ) @ SV151 )
| ( SV151 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(982,plain,
! [SV152: $i] :
( ( ( SV152 != empty_set )
| ! [SY440: $i] :
~ ( in @ SY440 @ SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(983,plain,
! [SV153: $i] :
( ( ! [SY441: $i] :
( ~ ( ~ ( ~ ( in @ ( sK26_C @ SY441 @ SV153 ) @ SY441 )
| ~ ( subset @ ( sK26_C @ SY441 @ SV153 ) @ SV153 ) )
| ~ ( ( in @ ( sK26_C @ SY441 @ SV153 ) @ SY441 )
| ( subset @ ( sK26_C @ SY441 @ SV153 ) @ SV153 ) ) )
| ( SY441
= ( powerset @ SV153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[863]) ).
thf(984,plain,
! [SV154: $i] :
( ( ! [SY442: $i] :
( ( SY442
!= ( powerset @ SV154 ) )
| ~ ( ~ ! [SY443: $i] :
( ~ ( in @ SY443 @ SY442 )
| ( subset @ SY443 @ SV154 ) )
| ~ ! [SY444: $i] :
( ~ ( subset @ SY444 @ SV154 )
| ( in @ SY444 @ SY442 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(985,plain,
! [SV155: $i] :
( ( ! [SY445: $i] :
( ( disjoint @ SV155 @ SY445 )
| ( in @ ( sK33_C @ SY445 @ SV155 ) @ ( set_intersection2 @ SV155 @ SY445 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(986,plain,
! [SV156: $i] :
( ( ! [SY446: $i] :
( ! [SY447: $i] :
~ ( in @ SY447 @ ( set_intersection2 @ SV156 @ SY446 ) )
| ~ ( disjoint @ SV156 @ SY446 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(987,plain,
! [SV157: $i] :
( ( ! [SY448: $i] :
( ~ ( ~ ( ! [SY449: $i] :
( ~ ( in @ ( sK17_C @ SY448 @ SV157 ) @ SY449 )
| ~ ( in @ SY449 @ SV157 ) )
| ~ ( in @ ( sK17_C @ SY448 @ SV157 ) @ SY448 ) )
| ~ ( ~ ( ~ ( in @ ( sK17_C @ SY448 @ SV157 ) @ ( sK18_SY276 @ SY448 @ SV157 ) )
| ~ ( in @ ( sK18_SY276 @ SY448 @ SV157 ) @ SV157 ) )
| ( in @ ( sK17_C @ SY448 @ SV157 ) @ SY448 ) ) )
| ( SY448
= ( union @ SV157 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(988,plain,
! [SV158: $i] :
( ( ! [SY450: $i] :
( ( SY450
!= ( union @ SV158 ) )
| ~ ( ~ ! [SY451: $i] :
( ! [SY452: $i] :
( ~ ( in @ SY451 @ SY452 )
| ~ ( in @ SY452 @ SV158 ) )
| ( in @ SY451 @ SY450 ) )
| ~ ! [SY453: $i] :
( ~ ( in @ SY453 @ SY450 )
| ~ ( ~ ( in @ SY453 @ ( sK16_D @ SY453 @ SY450 @ SV158 ) )
| ~ ( in @ ( sK16_D @ SY453 @ SY450 @ SV158 ) @ SV158 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(989,plain,
! [SV159: $i] :
( ( ~ ( relation @ SV159 )
| ( ( relation_rng @ SV159 )
= ( relation_dom @ ( relation_inverse @ SV159 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(990,plain,
! [SV160: $i] :
( ( ~ ( relation @ SV160 )
| ( ( relation_dom @ SV160 )
= ( relation_rng @ ( relation_inverse @ SV160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[870]) ).
thf(991,plain,
! [SV77: $i] :
( ( ( ~ ( element @ ( sK8_B @ SV77 ) @ ( powerset @ SV77 ) ) )
= $false )
| ( ( empty @ SV77 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[871]) ).
thf(992,plain,
! [SV77: $i] :
( ( ( ~ ~ ( empty @ ( sK8_B @ SV77 ) ) )
= $false )
| ( ( empty @ SV77 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[871]) ).
thf(993,plain,
! [SV161: $i] :
( ( ! [SY454: $i] :
( ( disjoint @ SV161 @ SY454 )
| ~ ( ~ ( in @ ( sK34_C @ SY454 @ SV161 ) @ SV161 )
| ~ ( in @ ( sK34_C @ SY454 @ SV161 ) @ SY454 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[872]) ).
thf(994,plain,
! [SV162: $i] :
( ( ! [SY455: $i] :
( ! [SY456: $i] :
( ~ ( in @ SY456 @ SV162 )
| ~ ( in @ SY456 @ SY455 ) )
| ~ ( disjoint @ SV162 @ SY455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[873]) ).
thf(995,plain,
! [SV163: $i] :
( ( ! [SY457: $i] :
( ( ( set_difference @ SV163 @ SY457 )
!= empty_set )
| ( subset @ SV163 @ SY457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(996,plain,
! [SV164: $i] :
( ( ! [SY458: $i] :
( ~ ( subset @ SV164 @ SY458 )
| ( ( set_difference @ SV164 @ SY458 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(997,plain,
! [SV78: $i] :
( ( ( ~ ! [SY379: $i] :
( ~ ( relation @ SY379 )
| ~ ( subset @ SV78 @ SY379 )
| ( subset @ ( relation_dom @ SV78 ) @ ( relation_dom @ SY379 ) ) )
| ~ ! [SY380: $i] :
( ~ ( relation @ SY380 )
| ~ ( subset @ SV78 @ SY380 )
| ( subset @ ( relation_rng @ SV78 ) @ ( relation_rng @ SY380 ) ) ) )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[876]) ).
thf(998,plain,
! [SV79: $i] :
( ( ! [SY381: $i] :
( ~ ( subset @ SY381 @ ( sK35_B @ SV79 ) )
| ( are_equipotent @ SY381 @ ( sK35_B @ SV79 ) )
| ( in @ SY381 @ ( sK35_B @ SV79 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[877]) ).
thf(999,plain,
! [SV79: $i] :
( ( ~ ( ~ ! [SY382: $i] :
( ~ ( in @ SY382 @ ( sK35_B @ SV79 ) )
| ( in @ ( powerset @ SY382 ) @ ( sK35_B @ SV79 ) ) )
| ~ ~ ( ~ ! [SY383: $i,SY384: $i] :
( ~ ( in @ SY383 @ ( sK35_B @ SV79 ) )
| ~ ( subset @ SY384 @ SY383 )
| ( in @ SY384 @ ( sK35_B @ SV79 ) ) )
| ~ ( in @ SV79 @ ( sK35_B @ SV79 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[878]) ).
thf(1000,plain,
! [SV165: $i] :
( ( ! [SY459: $i] :
( ~ ( element @ SV165 @ ( powerset @ SY459 ) )
| ( subset @ SV165 @ SY459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[879]) ).
thf(1001,plain,
! [SV166: $i] :
( ( ! [SY460: $i] :
( ~ ( subset @ SV166 @ SY460 )
| ( element @ SV166 @ ( powerset @ SY460 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(1002,plain,
! [SV167: $i] :
( ( ! [SY461: $i] :
( ~ ( subset @ SV167 @ SY461 )
| ~ ( subset @ SY461 @ SV167 )
| ( SV167 = SY461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[881]) ).
thf(1003,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[882]) ).
thf(1004,plain,
! [SV168: $i] :
( ( ! [SY462: $i] :
( ( ( set_intersection2 @ SV168 @ SY462 )
!= empty_set )
| ( disjoint @ SV168 @ SY462 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(1005,plain,
! [SV169: $i] :
( ( ! [SY463: $i] :
( ~ ( disjoint @ SV169 @ SY463 )
| ( ( set_intersection2 @ SV169 @ SY463 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[884]) ).
thf(1006,plain,
! [SV80: $i,SV133: $i] :
( ( ( ~ ( in @ ( sK36_C @ SV133 @ SV80 ) @ SV80 )
| ~ ~ ( in @ ( sK36_C @ SV133 @ SV80 ) @ SV133 ) )
= $false )
| ( ( element @ SV80 @ ( powerset @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[885]) ).
thf(1007,plain,
! [SV81: $i] :
( ( ! [SY386: $i,SY387: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SY387 @ SY386 @ SV81 ) @ SV81 )
| ( in @ ( sK15_D @ SY387 @ SY386 @ SV81 ) @ SY386 )
| ~ ( in @ ( sK15_D @ SY387 @ SY386 @ SV81 ) @ SY387 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SY387 @ SY386 @ SV81 ) @ SV81 )
| ( in @ ( sK15_D @ SY387 @ SY386 @ SV81 ) @ SY387 ) )
| ~ ( ~ ( in @ ( sK15_D @ SY387 @ SY386 @ SV81 ) @ SY386 )
| ( in @ ( sK15_D @ SY387 @ SY386 @ SV81 ) @ SY387 ) ) ) )
| ( SY387
= ( set_difference @ SV81 @ SY386 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[886]) ).
thf(1008,plain,
! [SV81: $i] :
( ( ! [SY388: $i,SY389: $i] :
( ( SY389
!= ( set_difference @ SV81 @ SY388 ) )
| ~ ( ~ ! [SY390: $i] :
( ~ ( in @ SY390 @ SV81 )
| ( in @ SY390 @ SY388 )
| ( in @ SY390 @ SY389 ) )
| ~ ~ ( ~ ! [SY391: $i] :
( ~ ( in @ SY391 @ SY389 )
| ( in @ SY391 @ SV81 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY389 )
| ~ ( in @ SX3 @ SY388 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[887]) ).
thf(1009,plain,
! [SV82: $i] :
( ( ( ~ ! [SY393: $i] :
( ~ ( ~ ( ! [SY394: $i] :
~ ( in @ ( ordered_pair @ SY394 @ ( sK13_C @ SY393 @ SV82 ) ) @ SV82 )
| ~ ( in @ ( sK13_C @ SY393 @ SV82 ) @ SY393 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY274 @ SY393 @ SV82 ) @ ( sK13_C @ SY393 @ SV82 ) ) @ SV82 )
| ( in @ ( sK13_C @ SY393 @ SV82 ) @ SY393 ) ) )
| ( SY393
= ( relation_rng @ SV82 ) ) )
| ~ ! [SY395: $i] :
( ( SY395
!= ( relation_rng @ SV82 ) )
| ~ ( ~ ! [SY396: $i] :
( ! [SY397: $i] :
~ ( in @ ( ordered_pair @ SY397 @ SY396 ) @ SV82 )
| ( in @ SY396 @ SY395 ) )
| ~ ! [SY398: $i] :
( ~ ( in @ SY398 @ SY395 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY398 @ SY395 @ SV82 ) @ SY398 ) @ SV82 ) ) ) ) )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[888]) ).
thf(1010,plain,
! [SV83: $i,SV134: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_C @ SV134 @ SV83 ) @ SV83 )
| ~ ( in @ ( sK3_C @ SV134 @ SV83 ) @ SV134 ) )
| ~ ( ( in @ ( sK3_C @ SV134 @ SV83 ) @ SV83 )
| ( in @ ( sK3_C @ SV134 @ SV83 ) @ SV134 ) ) )
= $false )
| ( ( SV83 = SV134 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[889]) ).
thf(1011,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK40_SY287 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK39_C @ SX1 @ SX0 ) @ ( sK40_SY287 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK38_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK38_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[890]) ).
thf(1012,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[891]) ).
thf(1013,plain,
! [SV170: $i] :
( ( ! [SY464: $i] :
( ( SV170 = SY464 )
| ~ ( subset @ SV170 @ SY464 )
| ( proper_subset @ SV170 @ SY464 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[892]) ).
thf(1014,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[893]) ).
thf(1015,plain,
! [SV84: $i] :
( ( ( ~ ! [SY400: $i] :
( ~ ( relation @ SY400 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SY400 @ SV84 ) @ ( sK11_SY272 @ SY400 @ SV84 ) ) @ SY400 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY272 @ SY400 @ SV84 ) @ ( sK10_C @ SY400 @ SV84 ) ) @ SV84 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK10_C @ SY400 @ SV84 ) @ ( sK11_SY272 @ SY400 @ SV84 ) ) @ SY400 )
| ( in @ ( ordered_pair @ ( sK11_SY272 @ SY400 @ SV84 ) @ ( sK10_C @ SY400 @ SV84 ) ) @ SV84 ) ) )
| ( SY400
= ( relation_inverse @ SV84 ) ) )
| ~ ! [SY401: $i] :
( ~ ( relation @ SY401 )
| ( SY401
!= ( relation_inverse @ SV84 ) )
| ~ ( ~ ! [SY402: $i,SY403: $i] :
( ~ ( in @ ( ordered_pair @ SY402 @ SY403 ) @ SY401 )
| ( in @ ( ordered_pair @ SY403 @ SY402 ) @ SV84 ) )
| ~ ! [SY404: $i,SY405: $i] :
( ~ ( in @ ( ordered_pair @ SY405 @ SY404 ) @ SV84 )
| ( in @ ( ordered_pair @ SY404 @ SY405 ) @ SY401 ) ) ) ) )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[894]) ).
thf(1016,plain,
! [SV85: $i] :
( ( ! [SY406: $i] :
( ~ ( subset @ SY406 @ ( sK1_B @ SV85 ) )
| ( are_equipotent @ SY406 @ ( sK1_B @ SV85 ) )
| ( in @ SY406 @ ( sK1_B @ SV85 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[895]) ).
thf(1017,plain,
! [SV85: $i] :
( ( ~ ( ~ ! [SY407: $i] :
( ~ ( ~ ! [SY408: $i] :
( ~ ( subset @ SY408 @ SY407 )
| ( in @ SY408 @ ( sK2_SY267 @ SY407 @ SV85 ) ) )
| ~ ( in @ ( sK2_SY267 @ SY407 @ SV85 ) @ ( sK1_B @ SV85 ) ) )
| ~ ( in @ SY407 @ ( sK1_B @ SV85 ) ) )
| ~ ~ ( ~ ! [SY409: $i,SY410: $i] :
( ~ ( in @ SY409 @ ( sK1_B @ SV85 ) )
| ~ ( subset @ SY410 @ SY409 )
| ( in @ SY410 @ ( sK1_B @ SV85 ) ) )
| ~ ( in @ SV85 @ ( sK1_B @ SV85 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[896]) ).
thf(1018,plain,
! [SV171: $i] :
( ( ! [SY465: $i] :
( ( ( set_difference @ SV171 @ SY465 )
!= SV171 )
| ( disjoint @ SV171 @ SY465 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(1019,plain,
! [SV172: $i] :
( ( ! [SY466: $i] :
( ~ ( disjoint @ SV172 @ SY466 )
| ( ( set_difference @ SV172 @ SY466 )
= SV172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[898]) ).
thf(1020,plain,
! [SV86: $i] :
( ( element @ ( sK5_B @ SV86 ) @ ( powerset @ SV86 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[899]) ).
thf(1021,plain,
! [SV86: $i] :
( ( empty @ ( sK5_B @ SV86 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[900]) ).
thf(1022,plain,
! [SV173: $i] :
( ( ~ ( ~ ! [SY467: $i,SY468: $i] :
( ( sK30_B @ SV173 )
!= ( ordered_pair @ SY467 @ SY468 ) )
| ~ ( in @ ( sK30_B @ SV173 ) @ SV173 ) )
| ( relation @ SV173 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(1023,plain,
! [SV174: $i] :
( ( ~ ( relation @ SV174 )
| ! [SY469: $i] :
( ( SY469
= ( ordered_pair @ ( sK28_C @ SY469 @ SV174 ) @ ( sK29_SY279 @ SY469 @ SV174 ) ) )
| ~ ( in @ SY469 @ SV174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[902]) ).
thf(1024,plain,
( ( empty @ sK6_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[903]) ).
thf(1025,plain,
! [SV87: $i] :
( ( ! [SY411: $i] :
( ~ ( subset @ SV87 @ SY411 )
| ! [SY412: $i] : ( subset @ ( cartesian_product2 @ SV87 @ SY412 ) @ ( cartesian_product2 @ SY411 @ SY412 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[905]) ).
thf(1026,plain,
! [SV87: $i] :
( ( ! [SY413: $i] :
( ~ ( subset @ SV87 @ SY413 )
| ! [SY414: $i] : ( subset @ ( cartesian_product2 @ SY414 @ SV87 ) @ ( cartesian_product2 @ SY414 @ SY413 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[906]) ).
thf(1027,plain,
! [SV175: $i] :
( ( ! [SY470: $i] :
( ~ ( in @ SV175 @ SY470 )
| ( subset @ ( singleton @ SV175 ) @ SY470 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(1028,plain,
! [SV176: $i] :
( ( ! [SY471: $i] :
( ~ ( subset @ ( singleton @ SV176 ) @ SY471 )
| ( in @ SV176 @ SY471 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[908]) ).
thf(1029,plain,
! [SV177: $i] :
( ( ! [SY472: $i] :
( ~ ( ~ ( in @ ( sK23_C @ SY472 @ SV177 ) @ SV177 )
| ~ ~ ( in @ ( sK23_C @ SY472 @ SV177 ) @ SY472 ) )
| ( subset @ SV177 @ SY472 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[909]) ).
thf(1030,plain,
! [SV178: $i] :
( ( ! [SY473: $i] :
( ~ ( subset @ SV178 @ SY473 )
| ! [SY474: $i] :
( ~ ( in @ SY474 @ SV178 )
| ( in @ SY474 @ SY473 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(1031,plain,
! [SV179: $i] :
( ( ! [SY475: $i] :
( ~ ( subset @ SV179 @ ( singleton @ SY475 ) )
| ( SV179 = empty_set )
| ( SV179
= ( singleton @ SY475 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[913]) ).
thf(1032,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[914]) ).
thf(1033,plain,
! [SV88: $i] :
( ( ! [SY415: $i,SY416: $i] :
( ~ ( in @ SV88 @ SY416 )
| ~ ( in @ SY415 @ SY416 )
| ( subset @ ( unordered_pair @ SV88 @ SY415 ) @ SY416 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[917]) ).
thf(1034,plain,
! [SV88: $i] :
( ( ~ ( ~ ! [SY417: $i,SY418: $i] :
( ~ ( subset @ ( unordered_pair @ SV88 @ SY417 ) @ SY418 )
| ( in @ SV88 @ SY418 ) )
| ~ ! [SY419: $i,SY420: $i] :
( ~ ( subset @ ( unordered_pair @ SV88 @ SY419 ) @ SY420 )
| ( in @ SY419 @ SY420 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[918]) ).
thf(1035,plain,
! [SV180: $i] :
( ( ! [SY476: $i] :
( ( ( set_difference @ SV180 @ SY476 )
!= empty_set )
| ( subset @ SV180 @ SY476 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(1036,plain,
! [SV181: $i] :
( ( ! [SY477: $i] :
( ~ ( subset @ SV181 @ SY477 )
| ( ( set_difference @ SV181 @ SY477 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(1037,plain,
! [SV182: $i] :
( ( ! [SY478: $i] :
( ~ ( subset @ SV182 @ ( singleton @ SY478 ) )
| ( SV182 = empty_set )
| ( SV182
= ( singleton @ SY478 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(1038,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[922]) ).
thf(1039,plain,
! [SV183: $i] :
( ( ! [SY479: $i] :
( ~ ( in @ SV183 @ SY479 )
| ( subset @ ( singleton @ SV183 ) @ SY479 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[923]) ).
thf(1040,plain,
! [SV184: $i] :
( ( ! [SY480: $i] :
( ~ ( subset @ ( singleton @ SV184 ) @ SY480 )
| ( in @ SV184 @ SY480 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(1041,plain,
! [SV185: $i] :
( ( ! [SY481: $i] :
( ( ( set_difference @ SV185 @ ( singleton @ SY481 ) )
!= SV185 )
| ~ ( in @ SY481 @ SV185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(1042,plain,
! [SV186: $i] :
( ( ! [SY482: $i] :
( ( in @ SY482 @ SV186 )
| ( ( set_difference @ SV186 @ ( singleton @ SY482 ) )
= SV186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[926]) ).
thf(1043,plain,
! [SV187: $i] :
( ( ! [SY483: $i] :
( ~ ( ~ ( ( ( sK27_C @ SY483 @ SV187 )
!= SV187 )
| ~ ( in @ ( sK27_C @ SY483 @ SV187 ) @ SY483 ) )
| ~ ( ( ( sK27_C @ SY483 @ SV187 )
= SV187 )
| ( in @ ( sK27_C @ SY483 @ SV187 ) @ SY483 ) ) )
| ( SY483
= ( singleton @ SV187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(1044,plain,
! [SV188: $i] :
( ( ! [SY484: $i] :
( ( SY484
!= ( singleton @ SV188 ) )
| ~ ( ~ ! [SY485: $i] :
( ( SY485 != SV188 )
| ( in @ SY485 @ SY484 ) )
| ~ ! [SY486: $i] :
( ~ ( in @ SY486 @ SY484 )
| ( SY486 = SV188 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[928]) ).
thf(1045,plain,
! [SV89: $i] :
( ( ! [SY421: $i,SY422: $i] :
( ~ ( relation @ SY422 )
| ~ ( in @ ( ordered_pair @ SV89 @ SY421 ) @ SY422 )
| ( in @ SV89 @ ( relation_dom @ SY422 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[929]) ).
thf(1046,plain,
! [SV89: $i] :
( ( ! [SY423: $i,SY424: $i] :
( ~ ( relation @ SY424 )
| ~ ( in @ ( ordered_pair @ SV89 @ SY423 ) @ SY424 )
| ( in @ SY423 @ ( relation_rng @ SY424 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[930]) ).
thf(1047,plain,
! [SV4: $i] :
( ( ( empty @ ( relation_dom @ SV4 ) )
= $false )
| ( ( empty @ SV4 )
= $true )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[931]) ).
thf(1048,plain,
! [SV5: $i] :
( ( ( empty @ ( relation_rng @ SV5 ) )
= $false )
| ( ( empty @ SV5 )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[932]) ).
thf(1049,plain,
! [SV91: $i,SV12: $i] :
( ( ( in @ SV12 @ SV91 )
= $false )
| ( ( disjoint @ ( singleton @ SV12 ) @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[934]) ).
thf(1050,plain,
! [SV14: $i,SV93: $i,SV189: $i] :
( ( ( ~ ( in @ SV189 @ SV93 )
| ( in @ SV189 @ SV14 ) )
= $true )
| ( ( element @ SV93 @ ( powerset @ SV14 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[935]) ).
thf(1051,plain,
! [SV94: $i,SV15: $i,SV190: $i] :
( ( ( ( in @ SV190 @ SV15 )
| ( subset @ SV15 @ ( set_difference @ SV94 @ ( singleton @ SV190 ) ) ) )
= $true )
| ( ( subset @ SV15 @ SV94 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1052,plain,
! [SV145: $i,SV135: $i,SV96: $i,SV17: $i] :
( ( ( ~ ( subset @ SV17 @ SV96 )
| ~ ( subset @ SV135 @ SV145 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV17 @ SV135 ) @ ( cartesian_product2 @ SV96 @ SV145 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[938]) ).
thf(1053,plain,
! [SV136: $i,SV99: $i,SV20: $i] :
( ( ( ~ ( subset @ SV20 @ SV99 ) )
= $true )
| ( ( ~ ( subset @ SV20 @ SV136 ) )
= $true )
| ( ( subset @ SV20 @ ( set_intersection2 @ SV99 @ SV136 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[940]) ).
thf(1054,plain,
! [SV137: $i,SV100: $i,SV21: $i] :
( ( ( ~ ( subset @ SV21 @ SV100 ) )
= $true )
| ( ( ~ ( subset @ SV100 @ SV137 ) )
= $true )
| ( ( subset @ SV21 @ SV137 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[941]) ).
thf(1055,plain,
! [SV101: $i,SV191: $i,SV23: $i] :
( ( ( subset @ ( set_intersection2 @ SV23 @ SV191 ) @ ( set_intersection2 @ SV101 @ SV191 ) )
= $true )
| ( ( subset @ SV23 @ SV101 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[942]) ).
thf(1056,plain,
! [SV103: $i,SV192: $i,SV25: $i] :
( ( ( subset @ ( set_difference @ SV25 @ SV192 ) @ ( set_difference @ SV103 @ SV192 ) )
= $true )
| ( ( subset @ SV25 @ SV103 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[944]) ).
thf(1057,plain,
! [SV29: $i,SV146: $i] :
( ( ( ~ ( relation @ SV146 ) )
= $true )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV29 @ SV146 ) ) @ ( relation_dom @ SV29 ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[945]) ).
thf(1058,plain,
! [SV30: $i,SV147: $i] :
( ( ( ~ ( relation @ SV147 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV30 @ SV147 ) ) @ ( relation_rng @ SV147 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[946]) ).
thf(1059,plain,
! [SV32: $i,SV148: $i] :
( ( ( ~ ( relation @ SV148 ) )
= $true )
| ( ( ~ ( subset @ ( relation_rng @ SV32 ) @ ( relation_dom @ SV148 ) )
| ( ( relation_dom @ ( relation_composition @ SV32 @ SV148 ) )
= ( relation_dom @ SV32 ) ) )
= $true )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[948]) ).
thf(1060,plain,
! [SV34: $i,SV149: $i] :
( ( ( ~ ( relation @ SV149 ) )
= $true )
| ( ( ~ ( subset @ ( relation_dom @ SV34 ) @ ( relation_rng @ SV149 ) )
| ( ( relation_rng @ ( relation_composition @ SV149 @ SV34 ) )
= ( relation_rng @ SV34 ) ) )
= $true )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[950]) ).
thf(1061,plain,
! [SV110: $i,SV37: $i] :
( ( ( subset @ SV37 @ SV110 )
= $false )
| ( ( proper_subset @ SV110 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[952]) ).
thf(1062,plain,
! [SV38: $i,SV138: $i,SV111: $i] :
( ( ( ~ ( disjoint @ SV111 @ SV138 ) )
= $true )
| ( ( ~ ( subset @ SV38 @ SV111 ) )
= $true )
| ( ( disjoint @ SV38 @ SV138 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[953]) ).
thf(1063,plain,
! [SV139: $i,SV114: $i,SV42: $i] :
( ( ( ~ ( subset @ SV42 @ SV114 ) )
= $true )
| ( ( ~ ( subset @ SV139 @ SV114 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV42 @ SV139 ) @ SV114 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[955]) ).
thf(1064,plain,
! [SV150: $i,SV115: $i,SV43: $i] :
( ( ( ( singleton @ SV43 )
= ( unordered_pair @ SV115 @ SV150 ) )
= $false )
| ( ( SV43 = SV115 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[956]) ).
thf(1065,plain,
! [SV140: $i,SV117: $i,SV46: $i] :
( ( ( ( singleton @ SV46 )
= ( unordered_pair @ SV117 @ SV140 ) )
= $false )
| ( ( SV117 = SV140 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[958]) ).
thf(1066,plain,
! [SV47: $i,SV118: $i] :
( ( ( in @ SV118 @ SV47 )
= $false )
| ( ( in @ SV47 @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[959]) ).
thf(1067,plain,
! [SV121: $i,SV53: $i] :
( ( ( relation @ SV53 )
= $false )
| ( ( ~ ( relation @ SV121 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV53 @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[960]) ).
thf(1068,plain,
! [SV123: $i,SV56: $i] :
( ( ( relation @ SV56 )
= $false )
| ( ( ~ ( relation @ SV123 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV56 @ SV123 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[961]) ).
thf(1069,plain,
! [SV125: $i,SV61: $i] :
( ( ( empty @ ( cartesian_product2 @ SV61 @ SV125 ) )
= $false )
| ( ( empty @ SV125 )
= $true )
| ( ( empty @ SV61 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[964]) ).
thf(1070,plain,
! [SV68: $i,SV128: $i] :
( ( ( empty @ SV128 )
= $true )
| ( ( in @ SV68 @ SV128 )
= $true )
| ( ( element @ SV68 @ SV128 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[967]) ).
thf(1071,plain,
! [SV69: $i,SV143: $i,SV129: $i] :
( ( ( ~ ( element @ SV129 @ ( powerset @ SV143 ) ) )
= $true )
| ( ( ~ ( in @ SV69 @ SV129 ) )
= $true )
| ( ( element @ SV69 @ SV143 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[968]) ).
thf(1072,plain,
! [SV70: $i,SV144: $i,SV130: $i] :
( ( ( ~ ( element @ SV130 @ ( powerset @ SV144 ) ) )
= $true )
| ( ( ~ ( in @ SV70 @ SV130 ) )
= $true )
| ( ( ~ ( empty @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[969]) ).
thf(1073,plain,
! [SV131: $i,SV71: $i] :
( ( ( in @ SV71 @ SV131 )
= $false )
| ( ( empty @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[970]) ).
thf(1074,plain,
! [SV132: $i,SV72: $i] :
( ( ( empty @ SV72 )
= $false )
| ( ( SV72 = SV132 )
= $true )
| ( ( ~ ( empty @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[971]) ).
thf(1075,plain,
! [SV73: $i,SV193: $i] :
( ( ! [SY487: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK24_D @ SY487 @ SV193 @ SV73 ) @ SY487 )
| ~ ( in @ ( sK24_D @ SY487 @ SV193 @ SV73 ) @ SV73 ) )
| ~ ( ~ ( in @ ( sK24_D @ SY487 @ SV193 @ SV73 ) @ SY487 )
| ~ ( in @ ( sK24_D @ SY487 @ SV193 @ SV73 ) @ SV193 ) ) )
| ~ ( ( in @ ( sK24_D @ SY487 @ SV193 @ SV73 ) @ SY487 )
| ( in @ ( sK24_D @ SY487 @ SV193 @ SV73 ) @ SV73 )
| ( in @ ( sK24_D @ SY487 @ SV193 @ SV73 ) @ SV193 ) ) )
| ( SY487
= ( set_union2 @ SV73 @ SV193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1076,plain,
! [SV194: $i,SV73: $i] :
( ( ! [SY488: $i] :
( ( SY488
!= ( set_union2 @ SV73 @ SV194 ) )
| ~ ( ~ ! [SY489: $i] :
( ~ ( in @ SY489 @ SY488 )
| ( in @ SY489 @ SV73 )
| ( in @ SY489 @ SV194 ) )
| ~ ~ ( ~ ! [SY357: $i] :
( ~ ( in @ SY357 @ SV73 )
| ( in @ SY357 @ SY488 ) )
| ~ ! [SY491: $i] :
( ~ ( in @ SY491 @ SV194 )
| ( in @ SY491 @ SY488 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1077,plain,
! [SV74: $i,SV195: $i] :
( ( ! [SY492: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK25_D @ SY492 @ SV195 @ SV74 ) @ SY492 )
| ( ( sK25_D @ SY492 @ SV195 @ SV74 )
!= SV74 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY492 @ SV195 @ SV74 ) @ SY492 )
| ( ( sK25_D @ SY492 @ SV195 @ SV74 )
!= SV195 ) ) )
| ~ ( ( in @ ( sK25_D @ SY492 @ SV195 @ SV74 ) @ SY492 )
| ( ( sK25_D @ SY492 @ SV195 @ SV74 )
= SV74 )
| ( ( sK25_D @ SY492 @ SV195 @ SV74 )
= SV195 ) ) )
| ( SY492
= ( unordered_pair @ SV74 @ SV195 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1078,plain,
! [SV196: $i,SV74: $i] :
( ( ! [SY493: $i] :
( ( SY493
!= ( unordered_pair @ SV74 @ SV196 ) )
| ~ ( ~ ! [SY494: $i] :
( ~ ( in @ SY494 @ SY493 )
| ( SY494 = SV74 )
| ( SY494 = SV196 ) )
| ~ ~ ( ~ ! [SY364: $i] :
( ( SY364 != SV74 )
| ( in @ SY364 @ SY493 ) )
| ~ ! [SY496: $i] :
( ( SY496 != SV196 )
| ( in @ SY496 @ SY493 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1079,plain,
! [SV75: $i,SV197: $i] :
( ( ! [SY497: $i] :
( ~ ( ~ ( ~ ( in @ ( sK22_D @ SY497 @ SV197 @ SV75 ) @ SV75 )
| ~ ( in @ ( sK22_D @ SY497 @ SV197 @ SV75 ) @ SV197 )
| ~ ( in @ ( sK22_D @ SY497 @ SV197 @ SV75 ) @ SY497 ) )
| ~ ~ ( ~ ( ( in @ ( sK22_D @ SY497 @ SV197 @ SV75 ) @ SV75 )
| ( in @ ( sK22_D @ SY497 @ SV197 @ SV75 ) @ SY497 ) )
| ~ ( ( in @ ( sK22_D @ SY497 @ SV197 @ SV75 ) @ SV197 )
| ( in @ ( sK22_D @ SY497 @ SV197 @ SV75 ) @ SY497 ) ) ) )
| ( SY497
= ( set_intersection2 @ SV75 @ SV197 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1080,plain,
! [SV198: $i,SV75: $i] :
( ( ! [SY498: $i] :
( ( SY498
!= ( set_intersection2 @ SV75 @ SV198 ) )
| ~ ( ~ ! [SY499: $i] :
( ~ ( in @ SY499 @ SV75 )
| ~ ( in @ SY499 @ SV198 )
| ( in @ SY499 @ SY498 ) )
| ~ ~ ( ~ ! [SY371: $i] :
( ~ ( in @ SY371 @ SY498 )
| ( in @ SY371 @ SV75 ) )
| ~ ! [SY501: $i] :
( ~ ( in @ SY501 @ SY498 )
| ( in @ SY501 @ SV198 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[977]) ).
thf(1081,plain,
! [SV76: $i] :
( ( ( ~ ! [SY373: $i] :
( ~ ( ~ ( ! [SY374: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SY373 @ SV76 ) @ SY374 ) @ SV76 )
| ~ ( in @ ( sK20_C @ SY373 @ SV76 ) @ SY373 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_C @ SY373 @ SV76 ) @ ( sK21_SY278 @ SY373 @ SV76 ) ) @ SV76 )
| ( in @ ( sK20_C @ SY373 @ SV76 ) @ SY373 ) ) )
| ( SY373
= ( relation_dom @ SV76 ) ) ) )
= $false )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[978]) ).
thf(1082,plain,
! [SV76: $i] :
( ( ( ~ ! [SY375: $i] :
( ( SY375
!= ( relation_dom @ SV76 ) )
| ~ ( ~ ! [SY376: $i] :
( ! [SY377: $i] :
~ ( in @ ( ordered_pair @ SY376 @ SY377 ) @ SV76 )
| ( in @ SY376 @ SY375 ) )
| ~ ! [SY378: $i] :
( ~ ( in @ SY378 @ SY375 )
| ( in @ ( ordered_pair @ SY378 @ ( sK19_D @ SY378 @ SY375 @ SV76 ) ) @ SV76 ) ) ) ) )
= $false )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[978]) ).
thf(1083,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[979]) ).
thf(1084,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[979]) ).
thf(1085,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[980]) ).
thf(1086,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[980]) ).
thf(1087,plain,
! [SV151: $i] :
( ( ( in @ ( sK37_B @ SV151 ) @ SV151 )
= $true )
| ( ( SV151 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[981]) ).
thf(1088,plain,
! [SV152: $i] :
( ( ( ( SV152 != empty_set ) )
= $true )
| ( ( ! [SY440: $i] :
~ ( in @ SY440 @ SV152 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[982]) ).
thf(1089,plain,
! [SV153: $i,SV199: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK26_C @ SV199 @ SV153 ) @ SV199 )
| ~ ( subset @ ( sK26_C @ SV199 @ SV153 ) @ SV153 ) )
| ~ ( ( in @ ( sK26_C @ SV199 @ SV153 ) @ SV199 )
| ( subset @ ( sK26_C @ SV199 @ SV153 ) @ SV153 ) ) )
| ( SV199
= ( powerset @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1090,plain,
! [SV154: $i,SV200: $i] :
( ( ( SV200
!= ( powerset @ SV154 ) )
| ~ ( ~ ! [SY502: $i] :
( ~ ( in @ SY502 @ SV200 )
| ( subset @ SY502 @ SV154 ) )
| ~ ! [SY503: $i] :
( ~ ( subset @ SY503 @ SV154 )
| ( in @ SY503 @ SV200 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(1091,plain,
! [SV201: $i,SV155: $i] :
( ( ( disjoint @ SV155 @ SV201 )
| ( in @ ( sK33_C @ SV201 @ SV155 ) @ ( set_intersection2 @ SV155 @ SV201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1092,plain,
! [SV202: $i,SV156: $i] :
( ( ! [SY504: $i] :
~ ( in @ SY504 @ ( set_intersection2 @ SV156 @ SV202 ) )
| ~ ( disjoint @ SV156 @ SV202 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1093,plain,
! [SV157: $i,SV203: $i] :
( ( ~ ( ~ ( ! [SY505: $i] :
( ~ ( in @ ( sK17_C @ SV203 @ SV157 ) @ SY505 )
| ~ ( in @ SY505 @ SV157 ) )
| ~ ( in @ ( sK17_C @ SV203 @ SV157 ) @ SV203 ) )
| ~ ( ~ ( ~ ( in @ ( sK17_C @ SV203 @ SV157 ) @ ( sK18_SY276 @ SV203 @ SV157 ) )
| ~ ( in @ ( sK18_SY276 @ SV203 @ SV157 ) @ SV157 ) )
| ( in @ ( sK17_C @ SV203 @ SV157 ) @ SV203 ) ) )
| ( SV203
= ( union @ SV157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(1094,plain,
! [SV158: $i,SV204: $i] :
( ( ( SV204
!= ( union @ SV158 ) )
| ~ ( ~ ! [SY506: $i] :
( ! [SY452: $i] :
( ~ ( in @ SY506 @ SY452 )
| ~ ( in @ SY452 @ SV158 ) )
| ( in @ SY506 @ SV204 ) )
| ~ ! [SY508: $i] :
( ~ ( in @ SY508 @ SV204 )
| ~ ( ~ ( in @ SY508 @ ( sK16_D @ SY508 @ SV204 @ SV158 ) )
| ~ ( in @ ( sK16_D @ SY508 @ SV204 @ SV158 ) @ SV158 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1095,plain,
! [SV159: $i] :
( ( ( ~ ( relation @ SV159 ) )
= $true )
| ( ( ( relation_rng @ SV159 )
= ( relation_dom @ ( relation_inverse @ SV159 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[989]) ).
thf(1096,plain,
! [SV160: $i] :
( ( ( ~ ( relation @ SV160 ) )
= $true )
| ( ( ( relation_dom @ SV160 )
= ( relation_rng @ ( relation_inverse @ SV160 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[990]) ).
thf(1097,plain,
! [SV77: $i] :
( ( ( element @ ( sK8_B @ SV77 ) @ ( powerset @ SV77 ) )
= $true )
| ( ( empty @ SV77 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[991]) ).
thf(1098,plain,
! [SV77: $i] :
( ( ( ~ ( empty @ ( sK8_B @ SV77 ) ) )
= $true )
| ( ( empty @ SV77 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[992]) ).
thf(1099,plain,
! [SV205: $i,SV161: $i] :
( ( ( disjoint @ SV161 @ SV205 )
| ~ ( ~ ( in @ ( sK34_C @ SV205 @ SV161 ) @ SV161 )
| ~ ( in @ ( sK34_C @ SV205 @ SV161 ) @ SV205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1100,plain,
! [SV206: $i,SV162: $i] :
( ( ! [SY509: $i] :
( ~ ( in @ SY509 @ SV162 )
| ~ ( in @ SY509 @ SV206 ) )
| ~ ( disjoint @ SV162 @ SV206 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1101,plain,
! [SV207: $i,SV163: $i] :
( ( ( ( set_difference @ SV163 @ SV207 )
!= empty_set )
| ( subset @ SV163 @ SV207 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1102,plain,
! [SV208: $i,SV164: $i] :
( ( ~ ( subset @ SV164 @ SV208 )
| ( ( set_difference @ SV164 @ SV208 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1103,plain,
! [SV78: $i] :
( ( ( ~ ! [SY379: $i] :
( ~ ( relation @ SY379 )
| ~ ( subset @ SV78 @ SY379 )
| ( subset @ ( relation_dom @ SV78 ) @ ( relation_dom @ SY379 ) ) ) )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[997]) ).
thf(1104,plain,
! [SV78: $i] :
( ( ( ~ ! [SY380: $i] :
( ~ ( relation @ SY380 )
| ~ ( subset @ SV78 @ SY380 )
| ( subset @ ( relation_rng @ SV78 ) @ ( relation_rng @ SY380 ) ) ) )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[997]) ).
thf(1105,plain,
! [SV79: $i,SV209: $i] :
( ( ~ ( subset @ SV209 @ ( sK35_B @ SV79 ) )
| ( are_equipotent @ SV209 @ ( sK35_B @ SV79 ) )
| ( in @ SV209 @ ( sK35_B @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1106,plain,
! [SV79: $i] :
( ( ~ ! [SY382: $i] :
( ~ ( in @ SY382 @ ( sK35_B @ SV79 ) )
| ( in @ ( powerset @ SY382 ) @ ( sK35_B @ SV79 ) ) )
| ~ ~ ( ~ ! [SY383: $i,SY384: $i] :
( ~ ( in @ SY383 @ ( sK35_B @ SV79 ) )
| ~ ( subset @ SY384 @ SY383 )
| ( in @ SY384 @ ( sK35_B @ SV79 ) ) )
| ~ ( in @ SV79 @ ( sK35_B @ SV79 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[999]) ).
thf(1107,plain,
! [SV210: $i,SV165: $i] :
( ( ~ ( element @ SV165 @ ( powerset @ SV210 ) )
| ( subset @ SV165 @ SV210 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1000]) ).
thf(1108,plain,
! [SV211: $i,SV166: $i] :
( ( ~ ( subset @ SV166 @ SV211 )
| ( element @ SV166 @ ( powerset @ SV211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1001]) ).
thf(1109,plain,
! [SV212: $i,SV167: $i] :
( ( ~ ( subset @ SV167 @ SV212 )
| ~ ( subset @ SV212 @ SV167 )
| ( SV167 = SV212 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1110,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1003]) ).
thf(1111,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1003]) ).
thf(1112,plain,
! [SV213: $i,SV168: $i] :
( ( ( ( set_intersection2 @ SV168 @ SV213 )
!= empty_set )
| ( disjoint @ SV168 @ SV213 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1113,plain,
! [SV214: $i,SV169: $i] :
( ( ~ ( disjoint @ SV169 @ SV214 )
| ( ( set_intersection2 @ SV169 @ SV214 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1114,plain,
! [SV80: $i,SV133: $i] :
( ( ( ~ ( in @ ( sK36_C @ SV133 @ SV80 ) @ SV80 ) )
= $false )
| ( ( element @ SV80 @ ( powerset @ SV133 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1006]) ).
thf(1115,plain,
! [SV80: $i,SV133: $i] :
( ( ( ~ ~ ( in @ ( sK36_C @ SV133 @ SV80 ) @ SV133 ) )
= $false )
| ( ( element @ SV80 @ ( powerset @ SV133 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1006]) ).
thf(1116,plain,
! [SV81: $i,SV215: $i] :
( ( ! [SY510: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SY510 @ SV215 @ SV81 ) @ SV81 )
| ( in @ ( sK15_D @ SY510 @ SV215 @ SV81 ) @ SV215 )
| ~ ( in @ ( sK15_D @ SY510 @ SV215 @ SV81 ) @ SY510 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SY510 @ SV215 @ SV81 ) @ SV81 )
| ( in @ ( sK15_D @ SY510 @ SV215 @ SV81 ) @ SY510 ) )
| ~ ( ~ ( in @ ( sK15_D @ SY510 @ SV215 @ SV81 ) @ SV215 )
| ( in @ ( sK15_D @ SY510 @ SV215 @ SV81 ) @ SY510 ) ) ) )
| ( SY510
= ( set_difference @ SV81 @ SV215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1007]) ).
thf(1117,plain,
! [SV216: $i,SV81: $i] :
( ( ! [SY511: $i] :
( ( SY511
!= ( set_difference @ SV81 @ SV216 ) )
| ~ ( ~ ! [SY512: $i] :
( ~ ( in @ SY512 @ SV81 )
| ( in @ SY512 @ SV216 )
| ( in @ SY512 @ SY511 ) )
| ~ ~ ( ~ ! [SY391: $i] :
( ~ ( in @ SY391 @ SY511 )
| ( in @ SY391 @ SV81 ) )
| ~ ! [SY514: $i] :
( ~ ( in @ SY514 @ SY511 )
| ~ ( in @ SY514 @ SV216 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1118,plain,
! [SV82: $i] :
( ( ( ~ ! [SY393: $i] :
( ~ ( ~ ( ! [SY394: $i] :
~ ( in @ ( ordered_pair @ SY394 @ ( sK13_C @ SY393 @ SV82 ) ) @ SV82 )
| ~ ( in @ ( sK13_C @ SY393 @ SV82 ) @ SY393 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY274 @ SY393 @ SV82 ) @ ( sK13_C @ SY393 @ SV82 ) ) @ SV82 )
| ( in @ ( sK13_C @ SY393 @ SV82 ) @ SY393 ) ) )
| ( SY393
= ( relation_rng @ SV82 ) ) ) )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1009]) ).
thf(1119,plain,
! [SV82: $i] :
( ( ( ~ ! [SY395: $i] :
( ( SY395
!= ( relation_rng @ SV82 ) )
| ~ ( ~ ! [SY396: $i] :
( ! [SY397: $i] :
~ ( in @ ( ordered_pair @ SY397 @ SY396 ) @ SV82 )
| ( in @ SY396 @ SY395 ) )
| ~ ! [SY398: $i] :
( ~ ( in @ SY398 @ SY395 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY398 @ SY395 @ SV82 ) @ SY398 ) @ SV82 ) ) ) ) )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1009]) ).
thf(1120,plain,
! [SV83: $i,SV134: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_C @ SV134 @ SV83 ) @ SV83 )
| ~ ( in @ ( sK3_C @ SV134 @ SV83 ) @ SV134 ) ) )
= $false )
| ( ( SV83 = SV134 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1010]) ).
thf(1121,plain,
! [SV83: $i,SV134: $i] :
( ( ( ~ ( ( in @ ( sK3_C @ SV134 @ SV83 ) @ SV83 )
| ( in @ ( sK3_C @ SV134 @ SV83 ) @ SV134 ) ) )
= $false )
| ( ( SV83 = SV134 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1010]) ).
thf(1122,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK40_SY287 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK39_C @ SX1 @ SX0 ) @ ( sK40_SY287 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1011]) ).
thf(1123,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK38_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK38_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1011]) ).
thf(1124,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1012]) ).
thf(1125,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1012]) ).
thf(1126,plain,
! [SV217: $i,SV170: $i] :
( ( ( SV170 = SV217 )
| ~ ( subset @ SV170 @ SV217 )
| ( proper_subset @ SV170 @ SV217 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1013]) ).
thf(1127,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1014]) ).
thf(1128,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1014]) ).
thf(1129,plain,
! [SV84: $i] :
( ( ( ~ ! [SY400: $i] :
( ~ ( relation @ SY400 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SY400 @ SV84 ) @ ( sK11_SY272 @ SY400 @ SV84 ) ) @ SY400 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY272 @ SY400 @ SV84 ) @ ( sK10_C @ SY400 @ SV84 ) ) @ SV84 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK10_C @ SY400 @ SV84 ) @ ( sK11_SY272 @ SY400 @ SV84 ) ) @ SY400 )
| ( in @ ( ordered_pair @ ( sK11_SY272 @ SY400 @ SV84 ) @ ( sK10_C @ SY400 @ SV84 ) ) @ SV84 ) ) )
| ( SY400
= ( relation_inverse @ SV84 ) ) ) )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1015]) ).
thf(1130,plain,
! [SV84: $i] :
( ( ( ~ ! [SY401: $i] :
( ~ ( relation @ SY401 )
| ( SY401
!= ( relation_inverse @ SV84 ) )
| ~ ( ~ ! [SY402: $i,SY403: $i] :
( ~ ( in @ ( ordered_pair @ SY402 @ SY403 ) @ SY401 )
| ( in @ ( ordered_pair @ SY403 @ SY402 ) @ SV84 ) )
| ~ ! [SY404: $i,SY405: $i] :
( ~ ( in @ ( ordered_pair @ SY405 @ SY404 ) @ SV84 )
| ( in @ ( ordered_pair @ SY404 @ SY405 ) @ SY401 ) ) ) ) )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1015]) ).
thf(1131,plain,
! [SV85: $i,SV218: $i] :
( ( ~ ( subset @ SV218 @ ( sK1_B @ SV85 ) )
| ( are_equipotent @ SV218 @ ( sK1_B @ SV85 ) )
| ( in @ SV218 @ ( sK1_B @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1132,plain,
! [SV85: $i] :
( ( ~ ! [SY407: $i] :
( ~ ( ~ ! [SY408: $i] :
( ~ ( subset @ SY408 @ SY407 )
| ( in @ SY408 @ ( sK2_SY267 @ SY407 @ SV85 ) ) )
| ~ ( in @ ( sK2_SY267 @ SY407 @ SV85 ) @ ( sK1_B @ SV85 ) ) )
| ~ ( in @ SY407 @ ( sK1_B @ SV85 ) ) )
| ~ ~ ( ~ ! [SY409: $i,SY410: $i] :
( ~ ( in @ SY409 @ ( sK1_B @ SV85 ) )
| ~ ( subset @ SY410 @ SY409 )
| ( in @ SY410 @ ( sK1_B @ SV85 ) ) )
| ~ ( in @ SV85 @ ( sK1_B @ SV85 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1017]) ).
thf(1133,plain,
! [SV219: $i,SV171: $i] :
( ( ( ( set_difference @ SV171 @ SV219 )
!= SV171 )
| ( disjoint @ SV171 @ SV219 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1134,plain,
! [SV220: $i,SV172: $i] :
( ( ~ ( disjoint @ SV172 @ SV220 )
| ( ( set_difference @ SV172 @ SV220 )
= SV172 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1019]) ).
thf(1135,plain,
! [SV173: $i] :
( ( ( ~ ( ~ ! [SY467: $i,SY468: $i] :
( ( sK30_B @ SV173 )
!= ( ordered_pair @ SY467 @ SY468 ) )
| ~ ( in @ ( sK30_B @ SV173 ) @ SV173 ) ) )
= $true )
| ( ( relation @ SV173 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1022]) ).
thf(1136,plain,
! [SV174: $i] :
( ( ( ~ ( relation @ SV174 ) )
= $true )
| ( ( ! [SY469: $i] :
( ( SY469
= ( ordered_pair @ ( sK28_C @ SY469 @ SV174 ) @ ( sK29_SY279 @ SY469 @ SV174 ) ) )
| ~ ( in @ SY469 @ SV174 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1023]) ).
thf(1137,plain,
! [SV221: $i,SV87: $i] :
( ( ~ ( subset @ SV87 @ SV221 )
| ! [SY515: $i] : ( subset @ ( cartesian_product2 @ SV87 @ SY515 ) @ ( cartesian_product2 @ SV221 @ SY515 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1138,plain,
! [SV222: $i,SV87: $i] :
( ( ~ ( subset @ SV87 @ SV222 )
| ! [SY516: $i] : ( subset @ ( cartesian_product2 @ SY516 @ SV87 ) @ ( cartesian_product2 @ SY516 @ SV222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1139,plain,
! [SV223: $i,SV175: $i] :
( ( ~ ( in @ SV175 @ SV223 )
| ( subset @ ( singleton @ SV175 ) @ SV223 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1027]) ).
thf(1140,plain,
! [SV224: $i,SV176: $i] :
( ( ~ ( subset @ ( singleton @ SV176 ) @ SV224 )
| ( in @ SV176 @ SV224 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1141,plain,
! [SV177: $i,SV225: $i] :
( ( ~ ( ~ ( in @ ( sK23_C @ SV225 @ SV177 ) @ SV177 )
| ~ ~ ( in @ ( sK23_C @ SV225 @ SV177 ) @ SV225 ) )
| ( subset @ SV177 @ SV225 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1029]) ).
thf(1142,plain,
! [SV226: $i,SV178: $i] :
( ( ~ ( subset @ SV178 @ SV226 )
| ! [SY517: $i] :
( ~ ( in @ SY517 @ SV178 )
| ( in @ SY517 @ SV226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1030]) ).
thf(1143,plain,
! [SV227: $i,SV179: $i] :
( ( ~ ( subset @ SV179 @ ( singleton @ SV227 ) )
| ( SV179 = empty_set )
| ( SV179
= ( singleton @ SV227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1144,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1032]) ).
thf(1145,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1032]) ).
thf(1146,plain,
! [SV228: $i,SV88: $i] :
( ( ! [SY518: $i] :
( ~ ( in @ SV88 @ SY518 )
| ~ ( in @ SV228 @ SY518 )
| ( subset @ ( unordered_pair @ SV88 @ SV228 ) @ SY518 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1147,plain,
! [SV88: $i] :
( ( ~ ! [SY417: $i,SY418: $i] :
( ~ ( subset @ ( unordered_pair @ SV88 @ SY417 ) @ SY418 )
| ( in @ SV88 @ SY418 ) )
| ~ ! [SY419: $i,SY420: $i] :
( ~ ( subset @ ( unordered_pair @ SV88 @ SY419 ) @ SY420 )
| ( in @ SY419 @ SY420 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1034]) ).
thf(1148,plain,
! [SV229: $i,SV180: $i] :
( ( ( ( set_difference @ SV180 @ SV229 )
!= empty_set )
| ( subset @ SV180 @ SV229 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1149,plain,
! [SV230: $i,SV181: $i] :
( ( ~ ( subset @ SV181 @ SV230 )
| ( ( set_difference @ SV181 @ SV230 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1036]) ).
thf(1150,plain,
! [SV231: $i,SV182: $i] :
( ( ~ ( subset @ SV182 @ ( singleton @ SV231 ) )
| ( SV182 = empty_set )
| ( SV182
= ( singleton @ SV231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1037]) ).
thf(1151,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1038]) ).
thf(1152,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1038]) ).
thf(1153,plain,
! [SV232: $i,SV183: $i] :
( ( ~ ( in @ SV183 @ SV232 )
| ( subset @ ( singleton @ SV183 ) @ SV232 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1154,plain,
! [SV233: $i,SV184: $i] :
( ( ~ ( subset @ ( singleton @ SV184 ) @ SV233 )
| ( in @ SV184 @ SV233 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1040]) ).
thf(1155,plain,
! [SV234: $i,SV185: $i] :
( ( ( ( set_difference @ SV185 @ ( singleton @ SV234 ) )
!= SV185 )
| ~ ( in @ SV234 @ SV185 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1156,plain,
! [SV186: $i,SV235: $i] :
( ( ( in @ SV235 @ SV186 )
| ( ( set_difference @ SV186 @ ( singleton @ SV235 ) )
= SV186 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1042]) ).
thf(1157,plain,
! [SV187: $i,SV236: $i] :
( ( ~ ( ~ ( ( ( sK27_C @ SV236 @ SV187 )
!= SV187 )
| ~ ( in @ ( sK27_C @ SV236 @ SV187 ) @ SV236 ) )
| ~ ( ( ( sK27_C @ SV236 @ SV187 )
= SV187 )
| ( in @ ( sK27_C @ SV236 @ SV187 ) @ SV236 ) ) )
| ( SV236
= ( singleton @ SV187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1158,plain,
! [SV188: $i,SV237: $i] :
( ( ( SV237
!= ( singleton @ SV188 ) )
| ~ ( ~ ! [SY519: $i] :
( ( SY519 != SV188 )
| ( in @ SY519 @ SV237 ) )
| ~ ! [SY520: $i] :
( ~ ( in @ SY520 @ SV237 )
| ( SY520 = SV188 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1159,plain,
! [SV238: $i,SV89: $i] :
( ( ! [SY521: $i] :
( ~ ( relation @ SY521 )
| ~ ( in @ ( ordered_pair @ SV89 @ SV238 ) @ SY521 )
| ( in @ SV89 @ ( relation_dom @ SY521 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1160,plain,
! [SV239: $i,SV89: $i] :
( ( ! [SY522: $i] :
( ~ ( relation @ SY522 )
| ~ ( in @ ( ordered_pair @ SV89 @ SV239 ) @ SY522 )
| ( in @ SV239 @ ( relation_rng @ SY522 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1161,plain,
! [SV14: $i,SV93: $i,SV189: $i] :
( ( ( ~ ( in @ SV189 @ SV93 ) )
= $true )
| ( ( in @ SV189 @ SV14 )
= $true )
| ( ( element @ SV93 @ ( powerset @ SV14 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1050]) ).
thf(1162,plain,
! [SV94: $i,SV15: $i,SV190: $i] :
( ( ( in @ SV190 @ SV15 )
= $true )
| ( ( subset @ SV15 @ ( set_difference @ SV94 @ ( singleton @ SV190 ) ) )
= $true )
| ( ( subset @ SV15 @ SV94 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1051]) ).
thf(1163,plain,
! [SV145: $i,SV135: $i,SV96: $i,SV17: $i] :
( ( ( ~ ( subset @ SV17 @ SV96 ) )
= $true )
| ( ( ~ ( subset @ SV135 @ SV145 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV17 @ SV135 ) @ ( cartesian_product2 @ SV96 @ SV145 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1052]) ).
thf(1164,plain,
! [SV136: $i,SV99: $i,SV20: $i] :
( ( ( subset @ SV20 @ SV99 )
= $false )
| ( ( ~ ( subset @ SV20 @ SV136 ) )
= $true )
| ( ( subset @ SV20 @ ( set_intersection2 @ SV99 @ SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1053]) ).
thf(1165,plain,
! [SV137: $i,SV100: $i,SV21: $i] :
( ( ( subset @ SV21 @ SV100 )
= $false )
| ( ( ~ ( subset @ SV100 @ SV137 ) )
= $true )
| ( ( subset @ SV21 @ SV137 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1054]) ).
thf(1166,plain,
! [SV29: $i,SV146: $i] :
( ( ( relation @ SV146 )
= $false )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV29 @ SV146 ) ) @ ( relation_dom @ SV29 ) )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1057]) ).
thf(1167,plain,
! [SV30: $i,SV147: $i] :
( ( ( relation @ SV147 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV30 @ SV147 ) ) @ ( relation_rng @ SV147 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1058]) ).
thf(1168,plain,
! [SV32: $i,SV148: $i] :
( ( ( relation @ SV148 )
= $false )
| ( ( ~ ( subset @ ( relation_rng @ SV32 ) @ ( relation_dom @ SV148 ) )
| ( ( relation_dom @ ( relation_composition @ SV32 @ SV148 ) )
= ( relation_dom @ SV32 ) ) )
= $true )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1059]) ).
thf(1169,plain,
! [SV34: $i,SV149: $i] :
( ( ( relation @ SV149 )
= $false )
| ( ( ~ ( subset @ ( relation_dom @ SV34 ) @ ( relation_rng @ SV149 ) )
| ( ( relation_rng @ ( relation_composition @ SV149 @ SV34 ) )
= ( relation_rng @ SV34 ) ) )
= $true )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1060]) ).
thf(1170,plain,
! [SV38: $i,SV138: $i,SV111: $i] :
( ( ( disjoint @ SV111 @ SV138 )
= $false )
| ( ( ~ ( subset @ SV38 @ SV111 ) )
= $true )
| ( ( disjoint @ SV38 @ SV138 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1062]) ).
thf(1171,plain,
! [SV139: $i,SV114: $i,SV42: $i] :
( ( ( subset @ SV42 @ SV114 )
= $false )
| ( ( ~ ( subset @ SV139 @ SV114 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV42 @ SV139 ) @ SV114 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1063]) ).
thf(1172,plain,
! [SV53: $i,SV121: $i] :
( ( ( relation @ SV121 )
= $false )
| ( ( relation @ SV53 )
= $false )
| ( ( relation @ ( relation_composition @ SV53 @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1067]) ).
thf(1173,plain,
! [SV56: $i,SV123: $i] :
( ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV56 )
= $false )
| ( ( relation @ ( set_union2 @ SV56 @ SV123 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1068]) ).
thf(1174,plain,
! [SV69: $i,SV143: $i,SV129: $i] :
( ( ( element @ SV129 @ ( powerset @ SV143 ) )
= $false )
| ( ( ~ ( in @ SV69 @ SV129 ) )
= $true )
| ( ( element @ SV69 @ SV143 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1071]) ).
thf(1175,plain,
! [SV70: $i,SV144: $i,SV130: $i] :
( ( ( element @ SV130 @ ( powerset @ SV144 ) )
= $false )
| ( ( ~ ( in @ SV70 @ SV130 ) )
= $true )
| ( ( ~ ( empty @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1072]) ).
thf(1176,plain,
! [SV72: $i,SV132: $i] :
( ( ( empty @ SV132 )
= $false )
| ( ( SV72 = SV132 )
= $true )
| ( ( empty @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1074]) ).
thf(1177,plain,
! [SV73: $i,SV193: $i,SV240: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV240 )
| ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV73 ) )
| ~ ( ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV240 )
| ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV193 ) ) )
| ~ ( ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV240 )
| ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV73 )
| ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV193 ) ) )
| ( SV240
= ( set_union2 @ SV73 @ SV193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1178,plain,
! [SV194: $i,SV73: $i,SV241: $i] :
( ( ( SV241
!= ( set_union2 @ SV73 @ SV194 ) )
| ~ ( ~ ! [SY523: $i] :
( ~ ( in @ SY523 @ SV241 )
| ( in @ SY523 @ SV73 )
| ( in @ SY523 @ SV194 ) )
| ~ ~ ( ~ ! [SY524: $i] :
( ~ ( in @ SY524 @ SV73 )
| ( in @ SY524 @ SV241 ) )
| ~ ! [SY525: $i] :
( ~ ( in @ SY525 @ SV194 )
| ( in @ SY525 @ SV241 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1076]) ).
thf(1179,plain,
! [SV74: $i,SV195: $i,SV242: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK25_D @ SV242 @ SV195 @ SV74 ) @ SV242 )
| ( ( sK25_D @ SV242 @ SV195 @ SV74 )
!= SV74 ) )
| ~ ( ~ ( in @ ( sK25_D @ SV242 @ SV195 @ SV74 ) @ SV242 )
| ( ( sK25_D @ SV242 @ SV195 @ SV74 )
!= SV195 ) ) )
| ~ ( ( in @ ( sK25_D @ SV242 @ SV195 @ SV74 ) @ SV242 )
| ( ( sK25_D @ SV242 @ SV195 @ SV74 )
= SV74 )
| ( ( sK25_D @ SV242 @ SV195 @ SV74 )
= SV195 ) ) )
| ( SV242
= ( unordered_pair @ SV74 @ SV195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1077]) ).
thf(1180,plain,
! [SV196: $i,SV74: $i,SV243: $i] :
( ( ( SV243
!= ( unordered_pair @ SV74 @ SV196 ) )
| ~ ( ~ ! [SY526: $i] :
( ~ ( in @ SY526 @ SV243 )
| ( SY526 = SV74 )
| ( SY526 = SV196 ) )
| ~ ~ ( ~ ! [SY527: $i] :
( ( SY527 != SV74 )
| ( in @ SY527 @ SV243 ) )
| ~ ! [SY528: $i] :
( ( SY528 != SV196 )
| ( in @ SY528 @ SV243 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1078]) ).
thf(1181,plain,
! [SV75: $i,SV197: $i,SV244: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV75 )
| ~ ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV197 )
| ~ ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV244 ) )
| ~ ~ ( ~ ( ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV75 )
| ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV244 ) )
| ~ ( ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV197 )
| ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV244 ) ) ) )
| ( SV244
= ( set_intersection2 @ SV75 @ SV197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1079]) ).
thf(1182,plain,
! [SV198: $i,SV75: $i,SV245: $i] :
( ( ( SV245
!= ( set_intersection2 @ SV75 @ SV198 ) )
| ~ ( ~ ! [SY529: $i] :
( ~ ( in @ SY529 @ SV75 )
| ~ ( in @ SY529 @ SV198 )
| ( in @ SY529 @ SV245 ) )
| ~ ~ ( ~ ! [SY530: $i] :
( ~ ( in @ SY530 @ SV245 )
| ( in @ SY530 @ SV75 ) )
| ~ ! [SY531: $i] :
( ~ ( in @ SY531 @ SV245 )
| ( in @ SY531 @ SV198 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1183,plain,
! [SV76: $i] :
( ( ( ! [SY373: $i] :
( ~ ( ~ ( ! [SY374: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SY373 @ SV76 ) @ SY374 ) @ SV76 )
| ~ ( in @ ( sK20_C @ SY373 @ SV76 ) @ SY373 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_C @ SY373 @ SV76 ) @ ( sK21_SY278 @ SY373 @ SV76 ) ) @ SV76 )
| ( in @ ( sK20_C @ SY373 @ SV76 ) @ SY373 ) ) )
| ( SY373
= ( relation_dom @ SV76 ) ) ) )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1081]) ).
thf(1184,plain,
! [SV76: $i] :
( ( ( ! [SY375: $i] :
( ( SY375
!= ( relation_dom @ SV76 ) )
| ~ ( ~ ! [SY376: $i] :
( ! [SY377: $i] :
~ ( in @ ( ordered_pair @ SY376 @ SY377 ) @ SV76 )
| ( in @ SY376 @ SY375 ) )
| ~ ! [SY378: $i] :
( ~ ( in @ SY378 @ SY375 )
| ( in @ ( ordered_pair @ SY378 @ ( sK19_D @ SY378 @ SY375 @ SV76 ) ) @ SV76 ) ) ) ) )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1082]) ).
thf(1185,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1083]) ).
thf(1186,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1084]) ).
thf(1187,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1085]) ).
thf(1188,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1086]) ).
thf(1189,plain,
! [SV152: $i] :
( ( ( SV152 = empty_set )
= $false )
| ( ( ! [SY440: $i] :
~ ( in @ SY440 @ SV152 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1088]) ).
thf(1190,plain,
! [SV153: $i,SV199: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK26_C @ SV199 @ SV153 ) @ SV199 )
| ~ ( subset @ ( sK26_C @ SV199 @ SV153 ) @ SV153 ) )
| ~ ( ( in @ ( sK26_C @ SV199 @ SV153 ) @ SV199 )
| ( subset @ ( sK26_C @ SV199 @ SV153 ) @ SV153 ) ) ) )
= $true )
| ( ( SV199
= ( powerset @ SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1089]) ).
thf(1191,plain,
! [SV154: $i,SV200: $i] :
( ( ( ( SV200
!= ( powerset @ SV154 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY502: $i] :
( ~ ( in @ SY502 @ SV200 )
| ( subset @ SY502 @ SV154 ) )
| ~ ! [SY503: $i] :
( ~ ( subset @ SY503 @ SV154 )
| ( in @ SY503 @ SV200 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1090]) ).
thf(1192,plain,
! [SV201: $i,SV155: $i] :
( ( ( disjoint @ SV155 @ SV201 )
= $true )
| ( ( in @ ( sK33_C @ SV201 @ SV155 ) @ ( set_intersection2 @ SV155 @ SV201 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1091]) ).
thf(1193,plain,
! [SV202: $i,SV156: $i] :
( ( ( ! [SY504: $i] :
~ ( in @ SY504 @ ( set_intersection2 @ SV156 @ SV202 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV156 @ SV202 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1092]) ).
thf(1194,plain,
! [SV157: $i,SV203: $i] :
( ( ( ~ ( ~ ( ! [SY505: $i] :
( ~ ( in @ ( sK17_C @ SV203 @ SV157 ) @ SY505 )
| ~ ( in @ SY505 @ SV157 ) )
| ~ ( in @ ( sK17_C @ SV203 @ SV157 ) @ SV203 ) )
| ~ ( ~ ( ~ ( in @ ( sK17_C @ SV203 @ SV157 ) @ ( sK18_SY276 @ SV203 @ SV157 ) )
| ~ ( in @ ( sK18_SY276 @ SV203 @ SV157 ) @ SV157 ) )
| ( in @ ( sK17_C @ SV203 @ SV157 ) @ SV203 ) ) ) )
= $true )
| ( ( SV203
= ( union @ SV157 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1093]) ).
thf(1195,plain,
! [SV158: $i,SV204: $i] :
( ( ( ( SV204
!= ( union @ SV158 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY506: $i] :
( ! [SY452: $i] :
( ~ ( in @ SY506 @ SY452 )
| ~ ( in @ SY452 @ SV158 ) )
| ( in @ SY506 @ SV204 ) )
| ~ ! [SY508: $i] :
( ~ ( in @ SY508 @ SV204 )
| ~ ( ~ ( in @ SY508 @ ( sK16_D @ SY508 @ SV204 @ SV158 ) )
| ~ ( in @ ( sK16_D @ SY508 @ SV204 @ SV158 ) @ SV158 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1094]) ).
thf(1196,plain,
! [SV159: $i] :
( ( ( relation @ SV159 )
= $false )
| ( ( ( relation_rng @ SV159 )
= ( relation_dom @ ( relation_inverse @ SV159 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1095]) ).
thf(1197,plain,
! [SV160: $i] :
( ( ( relation @ SV160 )
= $false )
| ( ( ( relation_dom @ SV160 )
= ( relation_rng @ ( relation_inverse @ SV160 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1096]) ).
thf(1198,plain,
! [SV77: $i] :
( ( ( empty @ ( sK8_B @ SV77 ) )
= $false )
| ( ( empty @ SV77 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1098]) ).
thf(1199,plain,
! [SV205: $i,SV161: $i] :
( ( ( disjoint @ SV161 @ SV205 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK34_C @ SV205 @ SV161 ) @ SV161 )
| ~ ( in @ ( sK34_C @ SV205 @ SV161 ) @ SV205 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1099]) ).
thf(1200,plain,
! [SV206: $i,SV162: $i] :
( ( ( ! [SY509: $i] :
( ~ ( in @ SY509 @ SV162 )
| ~ ( in @ SY509 @ SV206 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV162 @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1100]) ).
thf(1201,plain,
! [SV207: $i,SV163: $i] :
( ( ( ( ( set_difference @ SV163 @ SV207 )
!= empty_set ) )
= $true )
| ( ( subset @ SV163 @ SV207 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1101]) ).
thf(1202,plain,
! [SV208: $i,SV164: $i] :
( ( ( ~ ( subset @ SV164 @ SV208 ) )
= $true )
| ( ( ( set_difference @ SV164 @ SV208 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1102]) ).
thf(1203,plain,
! [SV78: $i] :
( ( ( ! [SY379: $i] :
( ~ ( relation @ SY379 )
| ~ ( subset @ SV78 @ SY379 )
| ( subset @ ( relation_dom @ SV78 ) @ ( relation_dom @ SY379 ) ) ) )
= $true )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1103]) ).
thf(1204,plain,
! [SV78: $i] :
( ( ( ! [SY380: $i] :
( ~ ( relation @ SY380 )
| ~ ( subset @ SV78 @ SY380 )
| ( subset @ ( relation_rng @ SV78 ) @ ( relation_rng @ SY380 ) ) ) )
= $true )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1104]) ).
thf(1205,plain,
! [SV79: $i,SV209: $i] :
( ( ( ~ ( subset @ SV209 @ ( sK35_B @ SV79 ) )
| ( are_equipotent @ SV209 @ ( sK35_B @ SV79 ) ) )
= $true )
| ( ( in @ SV209 @ ( sK35_B @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1105]) ).
thf(1206,plain,
! [SV79: $i] :
( ( ~ ! [SY382: $i] :
( ~ ( in @ SY382 @ ( sK35_B @ SV79 ) )
| ( in @ ( powerset @ SY382 ) @ ( sK35_B @ SV79 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1106]) ).
thf(1207,plain,
! [SV79: $i] :
( ( ~ ~ ( ~ ! [SY383: $i,SY384: $i] :
( ~ ( in @ SY383 @ ( sK35_B @ SV79 ) )
| ~ ( subset @ SY384 @ SY383 )
| ( in @ SY384 @ ( sK35_B @ SV79 ) ) )
| ~ ( in @ SV79 @ ( sK35_B @ SV79 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1106]) ).
thf(1208,plain,
! [SV210: $i,SV165: $i] :
( ( ( ~ ( element @ SV165 @ ( powerset @ SV210 ) ) )
= $true )
| ( ( subset @ SV165 @ SV210 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1107]) ).
thf(1209,plain,
! [SV211: $i,SV166: $i] :
( ( ( ~ ( subset @ SV166 @ SV211 ) )
= $true )
| ( ( element @ SV166 @ ( powerset @ SV211 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1108]) ).
thf(1210,plain,
! [SV212: $i,SV167: $i] :
( ( ( ~ ( subset @ SV167 @ SV212 )
| ~ ( subset @ SV212 @ SV167 ) )
= $true )
| ( ( SV167 = SV212 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1109]) ).
thf(1211,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1110]) ).
thf(1212,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1111]) ).
thf(1213,plain,
! [SV213: $i,SV168: $i] :
( ( ( ( ( set_intersection2 @ SV168 @ SV213 )
!= empty_set ) )
= $true )
| ( ( disjoint @ SV168 @ SV213 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1112]) ).
thf(1214,plain,
! [SV214: $i,SV169: $i] :
( ( ( ~ ( disjoint @ SV169 @ SV214 ) )
= $true )
| ( ( ( set_intersection2 @ SV169 @ SV214 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1113]) ).
thf(1215,plain,
! [SV80: $i,SV133: $i] :
( ( ( in @ ( sK36_C @ SV133 @ SV80 ) @ SV80 )
= $true )
| ( ( element @ SV80 @ ( powerset @ SV133 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1114]) ).
thf(1216,plain,
! [SV80: $i,SV133: $i] :
( ( ( ~ ( in @ ( sK36_C @ SV133 @ SV80 ) @ SV133 ) )
= $true )
| ( ( element @ SV80 @ ( powerset @ SV133 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1115]) ).
thf(1217,plain,
! [SV81: $i,SV215: $i,SV246: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV81 )
| ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV215 )
| ~ ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV246 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV81 )
| ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV246 ) )
| ~ ( ~ ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV215 )
| ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV246 ) ) ) )
| ( SV246
= ( set_difference @ SV81 @ SV215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1218,plain,
! [SV216: $i,SV81: $i,SV247: $i] :
( ( ( SV247
!= ( set_difference @ SV81 @ SV216 ) )
| ~ ( ~ ! [SY532: $i] :
( ~ ( in @ SY532 @ SV81 )
| ( in @ SY532 @ SV216 )
| ( in @ SY532 @ SV247 ) )
| ~ ~ ( ~ ! [SY533: $i] :
( ~ ( in @ SY533 @ SV247 )
| ( in @ SY533 @ SV81 ) )
| ~ ! [SY534: $i] :
( ~ ( in @ SY534 @ SV247 )
| ~ ( in @ SY534 @ SV216 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1219,plain,
! [SV82: $i] :
( ( ( ! [SY393: $i] :
( ~ ( ~ ( ! [SY394: $i] :
~ ( in @ ( ordered_pair @ SY394 @ ( sK13_C @ SY393 @ SV82 ) ) @ SV82 )
| ~ ( in @ ( sK13_C @ SY393 @ SV82 ) @ SY393 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY274 @ SY393 @ SV82 ) @ ( sK13_C @ SY393 @ SV82 ) ) @ SV82 )
| ( in @ ( sK13_C @ SY393 @ SV82 ) @ SY393 ) ) )
| ( SY393
= ( relation_rng @ SV82 ) ) ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1118]) ).
thf(1220,plain,
! [SV82: $i] :
( ( ( ! [SY395: $i] :
( ( SY395
!= ( relation_rng @ SV82 ) )
| ~ ( ~ ! [SY396: $i] :
( ! [SY397: $i] :
~ ( in @ ( ordered_pair @ SY397 @ SY396 ) @ SV82 )
| ( in @ SY396 @ SY395 ) )
| ~ ! [SY398: $i] :
( ~ ( in @ SY398 @ SY395 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY398 @ SY395 @ SV82 ) @ SY398 ) @ SV82 ) ) ) ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1119]) ).
thf(1221,plain,
! [SV83: $i,SV134: $i] :
( ( ( ~ ( in @ ( sK3_C @ SV134 @ SV83 ) @ SV83 )
| ~ ( in @ ( sK3_C @ SV134 @ SV83 ) @ SV134 ) )
= $true )
| ( ( SV83 = SV134 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1120]) ).
thf(1222,plain,
! [SV83: $i,SV134: $i] :
( ( ( ( in @ ( sK3_C @ SV134 @ SV83 ) @ SV83 )
| ( in @ ( sK3_C @ SV134 @ SV83 ) @ SV134 ) )
= $true )
| ( ( SV83 = SV134 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1121]) ).
thf(1223,plain,
( ( ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK40_SY287 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK39_C @ SX1 @ SX0 ) @ ( sK40_SY287 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1122]) ).
thf(1224,plain,
( ( ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK38_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK38_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1123]) ).
thf(1225,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1124]) ).
thf(1226,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1125]) ).
thf(1227,plain,
! [SV217: $i,SV170: $i] :
( ( ( ( SV170 = SV217 )
| ~ ( subset @ SV170 @ SV217 ) )
= $true )
| ( ( proper_subset @ SV170 @ SV217 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1126]) ).
thf(1228,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1127]) ).
thf(1229,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1128]) ).
thf(1230,plain,
! [SV84: $i] :
( ( ( ! [SY400: $i] :
( ~ ( relation @ SY400 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SY400 @ SV84 ) @ ( sK11_SY272 @ SY400 @ SV84 ) ) @ SY400 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY272 @ SY400 @ SV84 ) @ ( sK10_C @ SY400 @ SV84 ) ) @ SV84 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK10_C @ SY400 @ SV84 ) @ ( sK11_SY272 @ SY400 @ SV84 ) ) @ SY400 )
| ( in @ ( ordered_pair @ ( sK11_SY272 @ SY400 @ SV84 ) @ ( sK10_C @ SY400 @ SV84 ) ) @ SV84 ) ) )
| ( SY400
= ( relation_inverse @ SV84 ) ) ) )
= $true )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1129]) ).
thf(1231,plain,
! [SV84: $i] :
( ( ( ! [SY401: $i] :
( ~ ( relation @ SY401 )
| ( SY401
!= ( relation_inverse @ SV84 ) )
| ~ ( ~ ! [SY402: $i,SY403: $i] :
( ~ ( in @ ( ordered_pair @ SY402 @ SY403 ) @ SY401 )
| ( in @ ( ordered_pair @ SY403 @ SY402 ) @ SV84 ) )
| ~ ! [SY404: $i,SY405: $i] :
( ~ ( in @ ( ordered_pair @ SY405 @ SY404 ) @ SV84 )
| ( in @ ( ordered_pair @ SY404 @ SY405 ) @ SY401 ) ) ) ) )
= $true )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1130]) ).
thf(1232,plain,
! [SV85: $i,SV218: $i] :
( ( ( ~ ( subset @ SV218 @ ( sK1_B @ SV85 ) )
| ( are_equipotent @ SV218 @ ( sK1_B @ SV85 ) ) )
= $true )
| ( ( in @ SV218 @ ( sK1_B @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1131]) ).
thf(1233,plain,
! [SV85: $i] :
( ( ~ ! [SY407: $i] :
( ~ ( ~ ! [SY408: $i] :
( ~ ( subset @ SY408 @ SY407 )
| ( in @ SY408 @ ( sK2_SY267 @ SY407 @ SV85 ) ) )
| ~ ( in @ ( sK2_SY267 @ SY407 @ SV85 ) @ ( sK1_B @ SV85 ) ) )
| ~ ( in @ SY407 @ ( sK1_B @ SV85 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1132]) ).
thf(1234,plain,
! [SV85: $i] :
( ( ~ ~ ( ~ ! [SY409: $i,SY410: $i] :
( ~ ( in @ SY409 @ ( sK1_B @ SV85 ) )
| ~ ( subset @ SY410 @ SY409 )
| ( in @ SY410 @ ( sK1_B @ SV85 ) ) )
| ~ ( in @ SV85 @ ( sK1_B @ SV85 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1132]) ).
thf(1235,plain,
! [SV219: $i,SV171: $i] :
( ( ( ( ( set_difference @ SV171 @ SV219 )
!= SV171 ) )
= $true )
| ( ( disjoint @ SV171 @ SV219 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1133]) ).
thf(1236,plain,
! [SV220: $i,SV172: $i] :
( ( ( ~ ( disjoint @ SV172 @ SV220 ) )
= $true )
| ( ( ( set_difference @ SV172 @ SV220 )
= SV172 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1134]) ).
thf(1237,plain,
! [SV173: $i] :
( ( ( ~ ! [SY467: $i,SY468: $i] :
( ( sK30_B @ SV173 )
!= ( ordered_pair @ SY467 @ SY468 ) )
| ~ ( in @ ( sK30_B @ SV173 ) @ SV173 ) )
= $false )
| ( ( relation @ SV173 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1135]) ).
thf(1238,plain,
! [SV174: $i] :
( ( ( relation @ SV174 )
= $false )
| ( ( ! [SY469: $i] :
( ( SY469
= ( ordered_pair @ ( sK28_C @ SY469 @ SV174 ) @ ( sK29_SY279 @ SY469 @ SV174 ) ) )
| ~ ( in @ SY469 @ SV174 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1136]) ).
thf(1239,plain,
! [SV221: $i,SV87: $i] :
( ( ( ~ ( subset @ SV87 @ SV221 ) )
= $true )
| ( ( ! [SY515: $i] : ( subset @ ( cartesian_product2 @ SV87 @ SY515 ) @ ( cartesian_product2 @ SV221 @ SY515 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1137]) ).
thf(1240,plain,
! [SV222: $i,SV87: $i] :
( ( ( ~ ( subset @ SV87 @ SV222 ) )
= $true )
| ( ( ! [SY516: $i] : ( subset @ ( cartesian_product2 @ SY516 @ SV87 ) @ ( cartesian_product2 @ SY516 @ SV222 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1138]) ).
thf(1241,plain,
! [SV223: $i,SV175: $i] :
( ( ( ~ ( in @ SV175 @ SV223 ) )
= $true )
| ( ( subset @ ( singleton @ SV175 ) @ SV223 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1139]) ).
thf(1242,plain,
! [SV224: $i,SV176: $i] :
( ( ( ~ ( subset @ ( singleton @ SV176 ) @ SV224 ) )
= $true )
| ( ( in @ SV176 @ SV224 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1140]) ).
thf(1243,plain,
! [SV177: $i,SV225: $i] :
( ( ( ~ ( ~ ( in @ ( sK23_C @ SV225 @ SV177 ) @ SV177 )
| ~ ~ ( in @ ( sK23_C @ SV225 @ SV177 ) @ SV225 ) ) )
= $true )
| ( ( subset @ SV177 @ SV225 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1141]) ).
thf(1244,plain,
! [SV226: $i,SV178: $i] :
( ( ( ~ ( subset @ SV178 @ SV226 ) )
= $true )
| ( ( ! [SY517: $i] :
( ~ ( in @ SY517 @ SV178 )
| ( in @ SY517 @ SV226 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1142]) ).
thf(1245,plain,
! [SV227: $i,SV179: $i] :
( ( ( ~ ( subset @ SV179 @ ( singleton @ SV227 ) ) )
= $true )
| ( ( ( SV179 = empty_set )
| ( SV179
= ( singleton @ SV227 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1143]) ).
thf(1246,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1144]) ).
thf(1247,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1145]) ).
thf(1248,plain,
! [SV228: $i,SV248: $i,SV88: $i] :
( ( ~ ( in @ SV88 @ SV248 )
| ~ ( in @ SV228 @ SV248 )
| ( subset @ ( unordered_pair @ SV88 @ SV228 ) @ SV248 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1249,plain,
! [SV88: $i] :
( ( ~ ! [SY417: $i,SY418: $i] :
( ~ ( subset @ ( unordered_pair @ SV88 @ SY417 ) @ SY418 )
| ( in @ SV88 @ SY418 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1147]) ).
thf(1250,plain,
! [SV88: $i] :
( ( ~ ! [SY419: $i,SY420: $i] :
( ~ ( subset @ ( unordered_pair @ SV88 @ SY419 ) @ SY420 )
| ( in @ SY419 @ SY420 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1147]) ).
thf(1251,plain,
! [SV229: $i,SV180: $i] :
( ( ( ( ( set_difference @ SV180 @ SV229 )
!= empty_set ) )
= $true )
| ( ( subset @ SV180 @ SV229 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1148]) ).
thf(1252,plain,
! [SV230: $i,SV181: $i] :
( ( ( ~ ( subset @ SV181 @ SV230 ) )
= $true )
| ( ( ( set_difference @ SV181 @ SV230 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1149]) ).
thf(1253,plain,
! [SV231: $i,SV182: $i] :
( ( ( ~ ( subset @ SV182 @ ( singleton @ SV231 ) ) )
= $true )
| ( ( ( SV182 = empty_set )
| ( SV182
= ( singleton @ SV231 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1150]) ).
thf(1254,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1151]) ).
thf(1255,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1152]) ).
thf(1256,plain,
! [SV232: $i,SV183: $i] :
( ( ( ~ ( in @ SV183 @ SV232 ) )
= $true )
| ( ( subset @ ( singleton @ SV183 ) @ SV232 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1153]) ).
thf(1257,plain,
! [SV233: $i,SV184: $i] :
( ( ( ~ ( subset @ ( singleton @ SV184 ) @ SV233 ) )
= $true )
| ( ( in @ SV184 @ SV233 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1154]) ).
thf(1258,plain,
! [SV234: $i,SV185: $i] :
( ( ( ( ( set_difference @ SV185 @ ( singleton @ SV234 ) )
!= SV185 ) )
= $true )
| ( ( ~ ( in @ SV234 @ SV185 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1155]) ).
thf(1259,plain,
! [SV186: $i,SV235: $i] :
( ( ( in @ SV235 @ SV186 )
= $true )
| ( ( ( set_difference @ SV186 @ ( singleton @ SV235 ) )
= SV186 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1156]) ).
thf(1260,plain,
! [SV187: $i,SV236: $i] :
( ( ( ~ ( ~ ( ( ( sK27_C @ SV236 @ SV187 )
!= SV187 )
| ~ ( in @ ( sK27_C @ SV236 @ SV187 ) @ SV236 ) )
| ~ ( ( ( sK27_C @ SV236 @ SV187 )
= SV187 )
| ( in @ ( sK27_C @ SV236 @ SV187 ) @ SV236 ) ) ) )
= $true )
| ( ( SV236
= ( singleton @ SV187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1157]) ).
thf(1261,plain,
! [SV188: $i,SV237: $i] :
( ( ( ( SV237
!= ( singleton @ SV188 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY519: $i] :
( ( SY519 != SV188 )
| ( in @ SY519 @ SV237 ) )
| ~ ! [SY520: $i] :
( ~ ( in @ SY520 @ SV237 )
| ( SY520 = SV188 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1158]) ).
thf(1262,plain,
! [SV238: $i,SV89: $i,SV249: $i] :
( ( ~ ( relation @ SV249 )
| ~ ( in @ ( ordered_pair @ SV89 @ SV238 ) @ SV249 )
| ( in @ SV89 @ ( relation_dom @ SV249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1159]) ).
thf(1263,plain,
! [SV239: $i,SV89: $i,SV250: $i] :
( ( ~ ( relation @ SV250 )
| ~ ( in @ ( ordered_pair @ SV89 @ SV239 ) @ SV250 )
| ( in @ SV239 @ ( relation_rng @ SV250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1160]) ).
thf(1264,plain,
! [SV14: $i,SV93: $i,SV189: $i] :
( ( ( in @ SV189 @ SV93 )
= $false )
| ( ( in @ SV189 @ SV14 )
= $true )
| ( ( element @ SV93 @ ( powerset @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1161]) ).
thf(1265,plain,
! [SV145: $i,SV135: $i,SV96: $i,SV17: $i] :
( ( ( subset @ SV17 @ SV96 )
= $false )
| ( ( ~ ( subset @ SV135 @ SV145 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV17 @ SV135 ) @ ( cartesian_product2 @ SV96 @ SV145 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1163]) ).
thf(1266,plain,
! [SV99: $i,SV136: $i,SV20: $i] :
( ( ( subset @ SV20 @ SV136 )
= $false )
| ( ( subset @ SV20 @ SV99 )
= $false )
| ( ( subset @ SV20 @ ( set_intersection2 @ SV99 @ SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1164]) ).
thf(1267,plain,
! [SV21: $i,SV137: $i,SV100: $i] :
( ( ( subset @ SV100 @ SV137 )
= $false )
| ( ( subset @ SV21 @ SV100 )
= $false )
| ( ( subset @ SV21 @ SV137 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1165]) ).
thf(1268,plain,
! [SV148: $i,SV32: $i] :
( ( ( ~ ( subset @ ( relation_rng @ SV32 ) @ ( relation_dom @ SV148 ) ) )
= $true )
| ( ( ( relation_dom @ ( relation_composition @ SV32 @ SV148 ) )
= ( relation_dom @ SV32 ) )
= $true )
| ( ( relation @ SV148 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1168]) ).
thf(1269,plain,
! [SV149: $i,SV34: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV34 ) @ ( relation_rng @ SV149 ) ) )
= $true )
| ( ( ( relation_rng @ ( relation_composition @ SV149 @ SV34 ) )
= ( relation_rng @ SV34 ) )
= $true )
| ( ( relation @ SV149 )
= $false )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1169]) ).
thf(1270,plain,
! [SV138: $i,SV111: $i,SV38: $i] :
( ( ( subset @ SV38 @ SV111 )
= $false )
| ( ( disjoint @ SV111 @ SV138 )
= $false )
| ( ( disjoint @ SV38 @ SV138 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1170]) ).
thf(1271,plain,
! [SV42: $i,SV114: $i,SV139: $i] :
( ( ( subset @ SV139 @ SV114 )
= $false )
| ( ( subset @ SV42 @ SV114 )
= $false )
| ( ( subset @ ( set_union2 @ SV42 @ SV139 ) @ SV114 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1171]) ).
thf(1272,plain,
! [SV143: $i,SV129: $i,SV69: $i] :
( ( ( in @ SV69 @ SV129 )
= $false )
| ( ( element @ SV129 @ ( powerset @ SV143 ) )
= $false )
| ( ( element @ SV69 @ SV143 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1174]) ).
thf(1273,plain,
! [SV144: $i,SV130: $i,SV70: $i] :
( ( ( in @ SV70 @ SV130 )
= $false )
| ( ( element @ SV130 @ ( powerset @ SV144 ) )
= $false )
| ( ( ~ ( empty @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1175]) ).
thf(1274,plain,
! [SV73: $i,SV193: $i,SV240: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV240 )
| ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV73 ) )
| ~ ( ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV240 )
| ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV193 ) ) )
| ~ ( ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV240 )
| ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV73 )
| ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV193 ) ) ) )
= $true )
| ( ( SV240
= ( set_union2 @ SV73 @ SV193 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1177]) ).
thf(1275,plain,
! [SV194: $i,SV73: $i,SV241: $i] :
( ( ( ( SV241
!= ( set_union2 @ SV73 @ SV194 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY523: $i] :
( ~ ( in @ SY523 @ SV241 )
| ( in @ SY523 @ SV73 )
| ( in @ SY523 @ SV194 ) )
| ~ ~ ( ~ ! [SY524: $i] :
( ~ ( in @ SY524 @ SV73 )
| ( in @ SY524 @ SV241 ) )
| ~ ! [SY525: $i] :
( ~ ( in @ SY525 @ SV194 )
| ( in @ SY525 @ SV241 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1178]) ).
thf(1276,plain,
! [SV74: $i,SV195: $i,SV242: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK25_D @ SV242 @ SV195 @ SV74 ) @ SV242 )
| ( ( sK25_D @ SV242 @ SV195 @ SV74 )
!= SV74 ) )
| ~ ( ~ ( in @ ( sK25_D @ SV242 @ SV195 @ SV74 ) @ SV242 )
| ( ( sK25_D @ SV242 @ SV195 @ SV74 )
!= SV195 ) ) )
| ~ ( ( in @ ( sK25_D @ SV242 @ SV195 @ SV74 ) @ SV242 )
| ( ( sK25_D @ SV242 @ SV195 @ SV74 )
= SV74 )
| ( ( sK25_D @ SV242 @ SV195 @ SV74 )
= SV195 ) ) ) )
= $true )
| ( ( SV242
= ( unordered_pair @ SV74 @ SV195 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1179]) ).
thf(1277,plain,
! [SV196: $i,SV74: $i,SV243: $i] :
( ( ( ( SV243
!= ( unordered_pair @ SV74 @ SV196 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY526: $i] :
( ~ ( in @ SY526 @ SV243 )
| ( SY526 = SV74 )
| ( SY526 = SV196 ) )
| ~ ~ ( ~ ! [SY527: $i] :
( ( SY527 != SV74 )
| ( in @ SY527 @ SV243 ) )
| ~ ! [SY528: $i] :
( ( SY528 != SV196 )
| ( in @ SY528 @ SV243 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1180]) ).
thf(1278,plain,
! [SV75: $i,SV197: $i,SV244: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV75 )
| ~ ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV197 )
| ~ ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV244 ) )
| ~ ~ ( ~ ( ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV75 )
| ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV244 ) )
| ~ ( ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV197 )
| ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV244 ) ) ) ) )
= $true )
| ( ( SV244
= ( set_intersection2 @ SV75 @ SV197 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1181]) ).
thf(1279,plain,
! [SV198: $i,SV75: $i,SV245: $i] :
( ( ( ( SV245
!= ( set_intersection2 @ SV75 @ SV198 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY529: $i] :
( ~ ( in @ SY529 @ SV75 )
| ~ ( in @ SY529 @ SV198 )
| ( in @ SY529 @ SV245 ) )
| ~ ~ ( ~ ! [SY530: $i] :
( ~ ( in @ SY530 @ SV245 )
| ( in @ SY530 @ SV75 ) )
| ~ ! [SY531: $i] :
( ~ ( in @ SY531 @ SV245 )
| ( in @ SY531 @ SV198 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1182]) ).
thf(1280,plain,
! [SV76: $i,SV251: $i] :
( ( ( ~ ( ~ ( ! [SY535: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SV251 @ SV76 ) @ SY535 ) @ SV76 )
| ~ ( in @ ( sK20_C @ SV251 @ SV76 ) @ SV251 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_C @ SV251 @ SV76 ) @ ( sK21_SY278 @ SV251 @ SV76 ) ) @ SV76 )
| ( in @ ( sK20_C @ SV251 @ SV76 ) @ SV251 ) ) )
| ( SV251
= ( relation_dom @ SV76 ) ) )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1183]) ).
thf(1281,plain,
! [SV76: $i,SV252: $i] :
( ( ( ( SV252
!= ( relation_dom @ SV76 ) )
| ~ ( ~ ! [SY536: $i] :
( ! [SY377: $i] :
~ ( in @ ( ordered_pair @ SY536 @ SY377 ) @ SV76 )
| ( in @ SY536 @ SV252 ) )
| ~ ! [SY538: $i] :
( ~ ( in @ SY538 @ SV252 )
| ( in @ ( ordered_pair @ SY538 @ ( sK19_D @ SY538 @ SV252 @ SV76 ) ) @ SV76 ) ) ) )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1184]) ).
thf(1282,plain,
! [SV253: $i] :
( ( ( empty @ SV253 )
| ! [SY539: $i] :
( ~ ( element @ SY539 @ SV253 )
| ( in @ SY539 @ SV253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1185]) ).
thf(1283,plain,
! [SV254: $i] :
( ( ( empty @ SV254 )
| ! [SY540: $i] :
( ~ ( in @ SY540 @ SV254 )
| ( element @ SY540 @ SV254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1186]) ).
thf(1284,plain,
! [SV255: $i] :
( ( ~ ( empty @ SV255 )
| ! [SY541: $i] :
( ~ ( element @ SY541 @ SV255 )
| ( empty @ SY541 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1187]) ).
thf(1285,plain,
! [SV256: $i] :
( ( ~ ( empty @ SV256 )
| ! [SY542: $i] :
( ~ ( empty @ SY542 )
| ( element @ SY542 @ SV256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1188]) ).
thf(1286,plain,
! [SV152: $i,SV257: $i] :
( ( ( ~ ( in @ SV257 @ SV152 ) )
= $true )
| ( ( SV152 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1189]) ).
thf(1287,plain,
! [SV153: $i,SV199: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_C @ SV199 @ SV153 ) @ SV199 )
| ~ ( subset @ ( sK26_C @ SV199 @ SV153 ) @ SV153 ) )
| ~ ( ( in @ ( sK26_C @ SV199 @ SV153 ) @ SV199 )
| ( subset @ ( sK26_C @ SV199 @ SV153 ) @ SV153 ) ) )
= $false )
| ( ( SV199
= ( powerset @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1190]) ).
thf(1288,plain,
! [SV154: $i,SV200: $i] :
( ( ( SV200
= ( powerset @ SV154 ) )
= $false )
| ( ( ~ ( ~ ! [SY502: $i] :
( ~ ( in @ SY502 @ SV200 )
| ( subset @ SY502 @ SV154 ) )
| ~ ! [SY503: $i] :
( ~ ( subset @ SY503 @ SV154 )
| ( in @ SY503 @ SV200 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1191]) ).
thf(1289,plain,
! [SV202: $i,SV156: $i,SV258: $i] :
( ( ( ~ ( in @ SV258 @ ( set_intersection2 @ SV156 @ SV202 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV156 @ SV202 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1193]) ).
thf(1290,plain,
! [SV157: $i,SV203: $i] :
( ( ( ~ ( ! [SY505: $i] :
( ~ ( in @ ( sK17_C @ SV203 @ SV157 ) @ SY505 )
| ~ ( in @ SY505 @ SV157 ) )
| ~ ( in @ ( sK17_C @ SV203 @ SV157 ) @ SV203 ) )
| ~ ( ~ ( ~ ( in @ ( sK17_C @ SV203 @ SV157 ) @ ( sK18_SY276 @ SV203 @ SV157 ) )
| ~ ( in @ ( sK18_SY276 @ SV203 @ SV157 ) @ SV157 ) )
| ( in @ ( sK17_C @ SV203 @ SV157 ) @ SV203 ) ) )
= $false )
| ( ( SV203
= ( union @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1194]) ).
thf(1291,plain,
! [SV158: $i,SV204: $i] :
( ( ( SV204
= ( union @ SV158 ) )
= $false )
| ( ( ~ ( ~ ! [SY506: $i] :
( ! [SY452: $i] :
( ~ ( in @ SY506 @ SY452 )
| ~ ( in @ SY452 @ SV158 ) )
| ( in @ SY506 @ SV204 ) )
| ~ ! [SY508: $i] :
( ~ ( in @ SY508 @ SV204 )
| ~ ( ~ ( in @ SY508 @ ( sK16_D @ SY508 @ SV204 @ SV158 ) )
| ~ ( in @ ( sK16_D @ SY508 @ SV204 @ SV158 ) @ SV158 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1195]) ).
thf(1292,plain,
! [SV161: $i,SV205: $i] :
( ( ( ~ ( in @ ( sK34_C @ SV205 @ SV161 ) @ SV161 )
| ~ ( in @ ( sK34_C @ SV205 @ SV161 ) @ SV205 ) )
= $false )
| ( ( disjoint @ SV161 @ SV205 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1199]) ).
thf(1293,plain,
! [SV206: $i,SV162: $i,SV259: $i] :
( ( ( ~ ( in @ SV259 @ SV162 )
| ~ ( in @ SV259 @ SV206 ) )
= $true )
| ( ( ~ ( disjoint @ SV162 @ SV206 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1200]) ).
thf(1294,plain,
! [SV207: $i,SV163: $i] :
( ( ( ( set_difference @ SV163 @ SV207 )
= empty_set )
= $false )
| ( ( subset @ SV163 @ SV207 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1201]) ).
thf(1295,plain,
! [SV208: $i,SV164: $i] :
( ( ( subset @ SV164 @ SV208 )
= $false )
| ( ( ( set_difference @ SV164 @ SV208 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1202]) ).
thf(1296,plain,
! [SV78: $i,SV260: $i] :
( ( ( ~ ( relation @ SV260 )
| ~ ( subset @ SV78 @ SV260 )
| ( subset @ ( relation_dom @ SV78 ) @ ( relation_dom @ SV260 ) ) )
= $true )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1203]) ).
thf(1297,plain,
! [SV78: $i,SV261: $i] :
( ( ( ~ ( relation @ SV261 )
| ~ ( subset @ SV78 @ SV261 )
| ( subset @ ( relation_rng @ SV78 ) @ ( relation_rng @ SV261 ) ) )
= $true )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1204]) ).
thf(1298,plain,
! [SV79: $i,SV209: $i] :
( ( ( ~ ( subset @ SV209 @ ( sK35_B @ SV79 ) ) )
= $true )
| ( ( are_equipotent @ SV209 @ ( sK35_B @ SV79 ) )
= $true )
| ( ( in @ SV209 @ ( sK35_B @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1205]) ).
thf(1299,plain,
! [SV79: $i] :
( ( ! [SY382: $i] :
( ~ ( in @ SY382 @ ( sK35_B @ SV79 ) )
| ( in @ ( powerset @ SY382 ) @ ( sK35_B @ SV79 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1206]) ).
thf(1300,plain,
! [SV79: $i] :
( ( ~ ( ~ ! [SY383: $i,SY384: $i] :
( ~ ( in @ SY383 @ ( sK35_B @ SV79 ) )
| ~ ( subset @ SY384 @ SY383 )
| ( in @ SY384 @ ( sK35_B @ SV79 ) ) )
| ~ ( in @ SV79 @ ( sK35_B @ SV79 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1207]) ).
thf(1301,plain,
! [SV210: $i,SV165: $i] :
( ( ( element @ SV165 @ ( powerset @ SV210 ) )
= $false )
| ( ( subset @ SV165 @ SV210 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1208]) ).
thf(1302,plain,
! [SV211: $i,SV166: $i] :
( ( ( subset @ SV166 @ SV211 )
= $false )
| ( ( element @ SV166 @ ( powerset @ SV211 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1209]) ).
thf(1303,plain,
! [SV212: $i,SV167: $i] :
( ( ( ~ ( subset @ SV167 @ SV212 ) )
= $true )
| ( ( ~ ( subset @ SV212 @ SV167 ) )
= $true )
| ( ( SV167 = SV212 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1210]) ).
thf(1304,plain,
! [SV262: $i] :
( ( ! [SY543: $i] :
( ( SV262 != SY543 )
| ( subset @ SV262 @ SY543 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1211]) ).
thf(1305,plain,
! [SV263: $i] :
( ( ! [SY544: $i] :
( ( SV263 != SY544 )
| ( subset @ SY544 @ SV263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1212]) ).
thf(1306,plain,
! [SV213: $i,SV168: $i] :
( ( ( ( set_intersection2 @ SV168 @ SV213 )
= empty_set )
= $false )
| ( ( disjoint @ SV168 @ SV213 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1213]) ).
thf(1307,plain,
! [SV214: $i,SV169: $i] :
( ( ( disjoint @ SV169 @ SV214 )
= $false )
| ( ( ( set_intersection2 @ SV169 @ SV214 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1214]) ).
thf(1308,plain,
! [SV80: $i,SV133: $i] :
( ( ( in @ ( sK36_C @ SV133 @ SV80 ) @ SV133 )
= $false )
| ( ( element @ SV80 @ ( powerset @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1216]) ).
thf(1309,plain,
! [SV81: $i,SV215: $i,SV246: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV81 )
| ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV215 )
| ~ ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV246 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV81 )
| ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV246 ) )
| ~ ( ~ ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV215 )
| ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV246 ) ) ) ) )
= $true )
| ( ( SV246
= ( set_difference @ SV81 @ SV215 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1217]) ).
thf(1310,plain,
! [SV216: $i,SV81: $i,SV247: $i] :
( ( ( ( SV247
!= ( set_difference @ SV81 @ SV216 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY532: $i] :
( ~ ( in @ SY532 @ SV81 )
| ( in @ SY532 @ SV216 )
| ( in @ SY532 @ SV247 ) )
| ~ ~ ( ~ ! [SY533: $i] :
( ~ ( in @ SY533 @ SV247 )
| ( in @ SY533 @ SV81 ) )
| ~ ! [SY534: $i] :
( ~ ( in @ SY534 @ SV247 )
| ~ ( in @ SY534 @ SV216 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1218]) ).
thf(1311,plain,
! [SV82: $i,SV264: $i] :
( ( ( ~ ( ~ ( ! [SY545: $i] :
~ ( in @ ( ordered_pair @ SY545 @ ( sK13_C @ SV264 @ SV82 ) ) @ SV82 )
| ~ ( in @ ( sK13_C @ SV264 @ SV82 ) @ SV264 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY274 @ SV264 @ SV82 ) @ ( sK13_C @ SV264 @ SV82 ) ) @ SV82 )
| ( in @ ( sK13_C @ SV264 @ SV82 ) @ SV264 ) ) )
| ( SV264
= ( relation_rng @ SV82 ) ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1219]) ).
thf(1312,plain,
! [SV82: $i,SV265: $i] :
( ( ( ( SV265
!= ( relation_rng @ SV82 ) )
| ~ ( ~ ! [SY546: $i] :
( ! [SY397: $i] :
~ ( in @ ( ordered_pair @ SY397 @ SY546 ) @ SV82 )
| ( in @ SY546 @ SV265 ) )
| ~ ! [SY548: $i] :
( ~ ( in @ SY548 @ SV265 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY548 @ SV265 @ SV82 ) @ SY548 ) @ SV82 ) ) ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1220]) ).
thf(1313,plain,
! [SV83: $i,SV134: $i] :
( ( ( ~ ( in @ ( sK3_C @ SV134 @ SV83 ) @ SV83 ) )
= $true )
| ( ( ~ ( in @ ( sK3_C @ SV134 @ SV83 ) @ SV134 ) )
= $true )
| ( ( SV83 = SV134 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1221]) ).
thf(1314,plain,
! [SV83: $i,SV134: $i] :
( ( ( in @ ( sK3_C @ SV134 @ SV83 ) @ SV83 )
= $true )
| ( ( in @ ( sK3_C @ SV134 @ SV83 ) @ SV134 )
= $true )
| ( ( SV83 = SV134 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1222]) ).
thf(1315,plain,
! [SV266: $i] :
( ( ( SV266 = empty_set )
| ! [SY549: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK40_SY287 @ SY549 @ SV266 ) @ SV266 )
| ~ ~ ( in @ ( sK39_C @ SY549 @ SV266 ) @ ( sK40_SY287 @ SY549 @ SV266 ) ) )
| ~ ( in @ ( sK39_C @ SY549 @ SV266 ) @ SY549 ) )
| ~ ( ! [SY550: $i] :
( ~ ( in @ SY550 @ SV266 )
| ( in @ ( sK39_C @ SY549 @ SV266 ) @ SY550 ) )
| ( in @ ( sK39_C @ SY549 @ SV266 ) @ SY549 ) ) )
| ( SY549
= ( set_meet @ SV266 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1223]) ).
thf(1316,plain,
! [SV267: $i] :
( ( ( SV267 = empty_set )
| ! [SY551: $i] :
( ( SY551
!= ( set_meet @ SV267 ) )
| ~ ( ~ ! [SY552: $i] :
( ~ ( ~ ( in @ ( sK38_D @ SY552 @ SY551 @ SV267 ) @ SV267 )
| ~ ~ ( in @ SY552 @ ( sK38_D @ SY552 @ SY551 @ SV267 ) ) )
| ( in @ SY552 @ SY551 ) )
| ~ ! [SY553: $i] :
( ~ ( in @ SY553 @ SY551 )
| ! [SY554: $i] :
( ~ ( in @ SY554 @ SV267 )
| ( in @ SY553 @ SY554 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1224]) ).
thf(1317,plain,
! [SV268: $i] :
( ( ( SV268 != empty_set )
| ! [SY555: $i] :
( ( SY555
!= ( set_meet @ SV268 ) )
| ( SY555 = empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1318,plain,
! [SV269: $i] :
( ( ( SV269 != empty_set )
| ! [SY556: $i] :
( ( SY556 != empty_set )
| ( SY556
= ( set_meet @ SV269 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1226]) ).
thf(1319,plain,
! [SV217: $i,SV170: $i] :
( ( ( SV170 = SV217 )
= $true )
| ( ( ~ ( subset @ SV170 @ SV217 ) )
= $true )
| ( ( proper_subset @ SV170 @ SV217 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1227]) ).
thf(1320,plain,
! [SV270: $i] :
( ( ! [SY557: $i] :
( ~ ( proper_subset @ SV270 @ SY557 )
| ( SV270 != SY557 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1228]) ).
thf(1321,plain,
! [SV271: $i] :
( ( ! [SY558: $i] :
( ~ ( proper_subset @ SV271 @ SY558 )
| ( subset @ SV271 @ SY558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1229]) ).
thf(1322,plain,
! [SV84: $i,SV272: $i] :
( ( ( ~ ( relation @ SV272 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SV272 @ SV84 ) @ ( sK11_SY272 @ SV272 @ SV84 ) ) @ SV272 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY272 @ SV272 @ SV84 ) @ ( sK10_C @ SV272 @ SV84 ) ) @ SV84 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK10_C @ SV272 @ SV84 ) @ ( sK11_SY272 @ SV272 @ SV84 ) ) @ SV272 )
| ( in @ ( ordered_pair @ ( sK11_SY272 @ SV272 @ SV84 ) @ ( sK10_C @ SV272 @ SV84 ) ) @ SV84 ) ) )
| ( SV272
= ( relation_inverse @ SV84 ) ) )
= $true )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1230]) ).
thf(1323,plain,
! [SV84: $i,SV273: $i] :
( ( ( ~ ( relation @ SV273 )
| ( SV273
!= ( relation_inverse @ SV84 ) )
| ~ ( ~ ! [SY559: $i,SY560: $i] :
( ~ ( in @ ( ordered_pair @ SY559 @ SY560 ) @ SV273 )
| ( in @ ( ordered_pair @ SY560 @ SY559 ) @ SV84 ) )
| ~ ! [SY561: $i,SY562: $i] :
( ~ ( in @ ( ordered_pair @ SY562 @ SY561 ) @ SV84 )
| ( in @ ( ordered_pair @ SY561 @ SY562 ) @ SV273 ) ) ) )
= $true )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1231]) ).
thf(1324,plain,
! [SV85: $i,SV218: $i] :
( ( ( ~ ( subset @ SV218 @ ( sK1_B @ SV85 ) ) )
= $true )
| ( ( are_equipotent @ SV218 @ ( sK1_B @ SV85 ) )
= $true )
| ( ( in @ SV218 @ ( sK1_B @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1232]) ).
thf(1325,plain,
! [SV85: $i] :
( ( ! [SY407: $i] :
( ~ ( ~ ! [SY408: $i] :
( ~ ( subset @ SY408 @ SY407 )
| ( in @ SY408 @ ( sK2_SY267 @ SY407 @ SV85 ) ) )
| ~ ( in @ ( sK2_SY267 @ SY407 @ SV85 ) @ ( sK1_B @ SV85 ) ) )
| ~ ( in @ SY407 @ ( sK1_B @ SV85 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1233]) ).
thf(1326,plain,
! [SV85: $i] :
( ( ~ ( ~ ! [SY409: $i,SY410: $i] :
( ~ ( in @ SY409 @ ( sK1_B @ SV85 ) )
| ~ ( subset @ SY410 @ SY409 )
| ( in @ SY410 @ ( sK1_B @ SV85 ) ) )
| ~ ( in @ SV85 @ ( sK1_B @ SV85 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1234]) ).
thf(1327,plain,
! [SV219: $i,SV171: $i] :
( ( ( ( set_difference @ SV171 @ SV219 )
= SV171 )
= $false )
| ( ( disjoint @ SV171 @ SV219 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1235]) ).
thf(1328,plain,
! [SV220: $i,SV172: $i] :
( ( ( disjoint @ SV172 @ SV220 )
= $false )
| ( ( ( set_difference @ SV172 @ SV220 )
= SV172 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1236]) ).
thf(1329,plain,
! [SV173: $i] :
( ( ( ~ ! [SY467: $i,SY468: $i] :
( ( sK30_B @ SV173 )
!= ( ordered_pair @ SY467 @ SY468 ) ) )
= $false )
| ( ( relation @ SV173 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1237]) ).
thf(1330,plain,
! [SV173: $i] :
( ( ( ~ ( in @ ( sK30_B @ SV173 ) @ SV173 ) )
= $false )
| ( ( relation @ SV173 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1237]) ).
thf(1331,plain,
! [SV174: $i,SV274: $i] :
( ( ( ( SV274
= ( ordered_pair @ ( sK28_C @ SV274 @ SV174 ) @ ( sK29_SY279 @ SV274 @ SV174 ) ) )
| ~ ( in @ SV274 @ SV174 ) )
= $true )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1238]) ).
thf(1332,plain,
! [SV221: $i,SV87: $i] :
( ( ( subset @ SV87 @ SV221 )
= $false )
| ( ( ! [SY515: $i] : ( subset @ ( cartesian_product2 @ SV87 @ SY515 ) @ ( cartesian_product2 @ SV221 @ SY515 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1239]) ).
thf(1333,plain,
! [SV222: $i,SV87: $i] :
( ( ( subset @ SV87 @ SV222 )
= $false )
| ( ( ! [SY516: $i] : ( subset @ ( cartesian_product2 @ SY516 @ SV87 ) @ ( cartesian_product2 @ SY516 @ SV222 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1240]) ).
thf(1334,plain,
! [SV223: $i,SV175: $i] :
( ( ( in @ SV175 @ SV223 )
= $false )
| ( ( subset @ ( singleton @ SV175 ) @ SV223 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1241]) ).
thf(1335,plain,
! [SV224: $i,SV176: $i] :
( ( ( subset @ ( singleton @ SV176 ) @ SV224 )
= $false )
| ( ( in @ SV176 @ SV224 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1242]) ).
thf(1336,plain,
! [SV177: $i,SV225: $i] :
( ( ( ~ ( in @ ( sK23_C @ SV225 @ SV177 ) @ SV177 )
| ~ ~ ( in @ ( sK23_C @ SV225 @ SV177 ) @ SV225 ) )
= $false )
| ( ( subset @ SV177 @ SV225 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1243]) ).
thf(1337,plain,
! [SV226: $i,SV178: $i] :
( ( ( subset @ SV178 @ SV226 )
= $false )
| ( ( ! [SY517: $i] :
( ~ ( in @ SY517 @ SV178 )
| ( in @ SY517 @ SV226 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1244]) ).
thf(1338,plain,
! [SV227: $i,SV179: $i] :
( ( ( subset @ SV179 @ ( singleton @ SV227 ) )
= $false )
| ( ( ( SV179 = empty_set )
| ( SV179
= ( singleton @ SV227 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1245]) ).
thf(1339,plain,
! [SV275: $i] :
( ( ( SV275 != empty_set )
| ! [SY563: $i] : ( subset @ SV275 @ ( singleton @ SY563 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1246]) ).
thf(1340,plain,
! [SV276: $i] :
( ( ! [SY564: $i] :
( ( SV276
!= ( singleton @ SY564 ) )
| ( subset @ SV276 @ ( singleton @ SY564 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1247]) ).
thf(1341,plain,
! [SV228: $i,SV248: $i,SV88: $i] :
( ( ( ~ ( in @ SV88 @ SV248 )
| ~ ( in @ SV228 @ SV248 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV88 @ SV228 ) @ SV248 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1248]) ).
thf(1342,plain,
! [SV88: $i] :
( ( ! [SY417: $i,SY418: $i] :
( ~ ( subset @ ( unordered_pair @ SV88 @ SY417 ) @ SY418 )
| ( in @ SV88 @ SY418 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1249]) ).
thf(1343,plain,
! [SV88: $i] :
( ( ! [SY419: $i,SY420: $i] :
( ~ ( subset @ ( unordered_pair @ SV88 @ SY419 ) @ SY420 )
| ( in @ SY419 @ SY420 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1250]) ).
thf(1344,plain,
! [SV229: $i,SV180: $i] :
( ( ( ( set_difference @ SV180 @ SV229 )
= empty_set )
= $false )
| ( ( subset @ SV180 @ SV229 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1251]) ).
thf(1345,plain,
! [SV230: $i,SV181: $i] :
( ( ( subset @ SV181 @ SV230 )
= $false )
| ( ( ( set_difference @ SV181 @ SV230 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1252]) ).
thf(1346,plain,
! [SV231: $i,SV182: $i] :
( ( ( subset @ SV182 @ ( singleton @ SV231 ) )
= $false )
| ( ( ( SV182 = empty_set )
| ( SV182
= ( singleton @ SV231 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1253]) ).
thf(1347,plain,
! [SV277: $i] :
( ( ( SV277 != empty_set )
| ! [SY565: $i] : ( subset @ SV277 @ ( singleton @ SY565 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1254]) ).
thf(1348,plain,
! [SV278: $i] :
( ( ! [SY566: $i] :
( ( SV278
!= ( singleton @ SY566 ) )
| ( subset @ SV278 @ ( singleton @ SY566 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1255]) ).
thf(1349,plain,
! [SV232: $i,SV183: $i] :
( ( ( in @ SV183 @ SV232 )
= $false )
| ( ( subset @ ( singleton @ SV183 ) @ SV232 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1256]) ).
thf(1350,plain,
! [SV233: $i,SV184: $i] :
( ( ( subset @ ( singleton @ SV184 ) @ SV233 )
= $false )
| ( ( in @ SV184 @ SV233 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1257]) ).
thf(1351,plain,
! [SV234: $i,SV185: $i] :
( ( ( ( set_difference @ SV185 @ ( singleton @ SV234 ) )
= SV185 )
= $false )
| ( ( ~ ( in @ SV234 @ SV185 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1258]) ).
thf(1352,plain,
! [SV187: $i,SV236: $i] :
( ( ( ~ ( ( ( sK27_C @ SV236 @ SV187 )
!= SV187 )
| ~ ( in @ ( sK27_C @ SV236 @ SV187 ) @ SV236 ) )
| ~ ( ( ( sK27_C @ SV236 @ SV187 )
= SV187 )
| ( in @ ( sK27_C @ SV236 @ SV187 ) @ SV236 ) ) )
= $false )
| ( ( SV236
= ( singleton @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1260]) ).
thf(1353,plain,
! [SV188: $i,SV237: $i] :
( ( ( SV237
= ( singleton @ SV188 ) )
= $false )
| ( ( ~ ( ~ ! [SY519: $i] :
( ( SY519 != SV188 )
| ( in @ SY519 @ SV237 ) )
| ~ ! [SY520: $i] :
( ~ ( in @ SY520 @ SV237 )
| ( SY520 = SV188 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1261]) ).
thf(1354,plain,
! [SV238: $i,SV89: $i,SV249: $i] :
( ( ( ~ ( relation @ SV249 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV89 @ SV238 ) @ SV249 )
| ( in @ SV89 @ ( relation_dom @ SV249 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1262]) ).
thf(1355,plain,
! [SV239: $i,SV89: $i,SV250: $i] :
( ( ( ~ ( relation @ SV250 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV89 @ SV239 ) @ SV250 )
| ( in @ SV239 @ ( relation_rng @ SV250 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1263]) ).
thf(1356,plain,
! [SV96: $i,SV17: $i,SV145: $i,SV135: $i] :
( ( ( subset @ SV135 @ SV145 )
= $false )
| ( ( subset @ SV17 @ SV96 )
= $false )
| ( ( subset @ ( cartesian_product2 @ SV17 @ SV135 ) @ ( cartesian_product2 @ SV96 @ SV145 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1265]) ).
thf(1357,plain,
! [SV148: $i,SV32: $i] :
( ( ( subset @ ( relation_rng @ SV32 ) @ ( relation_dom @ SV148 ) )
= $false )
| ( ( ( relation_dom @ ( relation_composition @ SV32 @ SV148 ) )
= ( relation_dom @ SV32 ) )
= $true )
| ( ( relation @ SV148 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1268]) ).
thf(1358,plain,
! [SV149: $i,SV34: $i] :
( ( ( subset @ ( relation_dom @ SV34 ) @ ( relation_rng @ SV149 ) )
= $false )
| ( ( ( relation_rng @ ( relation_composition @ SV149 @ SV34 ) )
= ( relation_rng @ SV34 ) )
= $true )
| ( ( relation @ SV149 )
= $false )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1269]) ).
thf(1359,plain,
! [SV70: $i,SV130: $i,SV144: $i] :
( ( ( empty @ SV144 )
= $false )
| ( ( element @ SV130 @ ( powerset @ SV144 ) )
= $false )
| ( ( in @ SV70 @ SV130 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1273]) ).
thf(1360,plain,
! [SV73: $i,SV193: $i,SV240: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV240 )
| ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV73 ) )
| ~ ( ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV240 )
| ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV193 ) ) )
| ~ ( ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV240 )
| ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV73 )
| ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV193 ) ) )
= $false )
| ( ( SV240
= ( set_union2 @ SV73 @ SV193 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1274]) ).
thf(1361,plain,
! [SV194: $i,SV73: $i,SV241: $i] :
( ( ( SV241
= ( set_union2 @ SV73 @ SV194 ) )
= $false )
| ( ( ~ ( ~ ! [SY523: $i] :
( ~ ( in @ SY523 @ SV241 )
| ( in @ SY523 @ SV73 )
| ( in @ SY523 @ SV194 ) )
| ~ ~ ( ~ ! [SY524: $i] :
( ~ ( in @ SY524 @ SV73 )
| ( in @ SY524 @ SV241 ) )
| ~ ! [SY525: $i] :
( ~ ( in @ SY525 @ SV194 )
| ( in @ SY525 @ SV241 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1275]) ).
thf(1362,plain,
! [SV74: $i,SV195: $i,SV242: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK25_D @ SV242 @ SV195 @ SV74 ) @ SV242 )
| ( ( sK25_D @ SV242 @ SV195 @ SV74 )
!= SV74 ) )
| ~ ( ~ ( in @ ( sK25_D @ SV242 @ SV195 @ SV74 ) @ SV242 )
| ( ( sK25_D @ SV242 @ SV195 @ SV74 )
!= SV195 ) ) )
| ~ ( ( in @ ( sK25_D @ SV242 @ SV195 @ SV74 ) @ SV242 )
| ( ( sK25_D @ SV242 @ SV195 @ SV74 )
= SV74 )
| ( ( sK25_D @ SV242 @ SV195 @ SV74 )
= SV195 ) ) )
= $false )
| ( ( SV242
= ( unordered_pair @ SV74 @ SV195 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1276]) ).
thf(1363,plain,
! [SV196: $i,SV74: $i,SV243: $i] :
( ( ( SV243
= ( unordered_pair @ SV74 @ SV196 ) )
= $false )
| ( ( ~ ( ~ ! [SY526: $i] :
( ~ ( in @ SY526 @ SV243 )
| ( SY526 = SV74 )
| ( SY526 = SV196 ) )
| ~ ~ ( ~ ! [SY527: $i] :
( ( SY527 != SV74 )
| ( in @ SY527 @ SV243 ) )
| ~ ! [SY528: $i] :
( ( SY528 != SV196 )
| ( in @ SY528 @ SV243 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1277]) ).
thf(1364,plain,
! [SV75: $i,SV197: $i,SV244: $i] :
( ( ( ~ ( ~ ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV75 )
| ~ ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV197 )
| ~ ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV244 ) )
| ~ ~ ( ~ ( ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV75 )
| ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV244 ) )
| ~ ( ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV197 )
| ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV244 ) ) ) )
= $false )
| ( ( SV244
= ( set_intersection2 @ SV75 @ SV197 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1278]) ).
thf(1365,plain,
! [SV198: $i,SV75: $i,SV245: $i] :
( ( ( SV245
= ( set_intersection2 @ SV75 @ SV198 ) )
= $false )
| ( ( ~ ( ~ ! [SY529: $i] :
( ~ ( in @ SY529 @ SV75 )
| ~ ( in @ SY529 @ SV198 )
| ( in @ SY529 @ SV245 ) )
| ~ ~ ( ~ ! [SY530: $i] :
( ~ ( in @ SY530 @ SV245 )
| ( in @ SY530 @ SV75 ) )
| ~ ! [SY531: $i] :
( ~ ( in @ SY531 @ SV245 )
| ( in @ SY531 @ SV198 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1279]) ).
thf(1366,plain,
! [SV76: $i,SV251: $i] :
( ( ( ~ ( ~ ( ! [SY535: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SV251 @ SV76 ) @ SY535 ) @ SV76 )
| ~ ( in @ ( sK20_C @ SV251 @ SV76 ) @ SV251 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_C @ SV251 @ SV76 ) @ ( sK21_SY278 @ SV251 @ SV76 ) ) @ SV76 )
| ( in @ ( sK20_C @ SV251 @ SV76 ) @ SV251 ) ) ) )
= $true )
| ( ( SV251
= ( relation_dom @ SV76 ) )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1280]) ).
thf(1367,plain,
! [SV76: $i,SV252: $i] :
( ( ( ( SV252
!= ( relation_dom @ SV76 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY536: $i] :
( ! [SY377: $i] :
~ ( in @ ( ordered_pair @ SY536 @ SY377 ) @ SV76 )
| ( in @ SY536 @ SV252 ) )
| ~ ! [SY538: $i] :
( ~ ( in @ SY538 @ SV252 )
| ( in @ ( ordered_pair @ SY538 @ ( sK19_D @ SY538 @ SV252 @ SV76 ) ) @ SV76 ) ) ) )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1281]) ).
thf(1368,plain,
! [SV253: $i] :
( ( ( empty @ SV253 )
= $true )
| ( ( ! [SY539: $i] :
( ~ ( element @ SY539 @ SV253 )
| ( in @ SY539 @ SV253 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1282]) ).
thf(1369,plain,
! [SV254: $i] :
( ( ( empty @ SV254 )
= $true )
| ( ( ! [SY540: $i] :
( ~ ( in @ SY540 @ SV254 )
| ( element @ SY540 @ SV254 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1283]) ).
thf(1370,plain,
! [SV255: $i] :
( ( ( ~ ( empty @ SV255 ) )
= $true )
| ( ( ! [SY541: $i] :
( ~ ( element @ SY541 @ SV255 )
| ( empty @ SY541 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1284]) ).
thf(1371,plain,
! [SV256: $i] :
( ( ( ~ ( empty @ SV256 ) )
= $true )
| ( ( ! [SY542: $i] :
( ~ ( empty @ SY542 )
| ( element @ SY542 @ SV256 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1285]) ).
thf(1372,plain,
! [SV152: $i,SV257: $i] :
( ( ( in @ SV257 @ SV152 )
= $false )
| ( ( SV152 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1286]) ).
thf(1373,plain,
! [SV153: $i,SV199: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_C @ SV199 @ SV153 ) @ SV199 )
| ~ ( subset @ ( sK26_C @ SV199 @ SV153 ) @ SV153 ) ) )
= $false )
| ( ( SV199
= ( powerset @ SV153 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1287]) ).
thf(1374,plain,
! [SV153: $i,SV199: $i] :
( ( ( ~ ( ( in @ ( sK26_C @ SV199 @ SV153 ) @ SV199 )
| ( subset @ ( sK26_C @ SV199 @ SV153 ) @ SV153 ) ) )
= $false )
| ( ( SV199
= ( powerset @ SV153 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1287]) ).
thf(1375,plain,
! [SV154: $i,SV200: $i] :
( ( ( ~ ! [SY502: $i] :
( ~ ( in @ SY502 @ SV200 )
| ( subset @ SY502 @ SV154 ) )
| ~ ! [SY503: $i] :
( ~ ( subset @ SY503 @ SV154 )
| ( in @ SY503 @ SV200 ) ) )
= $false )
| ( ( SV200
= ( powerset @ SV154 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1288]) ).
thf(1376,plain,
! [SV202: $i,SV156: $i,SV258: $i] :
( ( ( in @ SV258 @ ( set_intersection2 @ SV156 @ SV202 ) )
= $false )
| ( ( ~ ( disjoint @ SV156 @ SV202 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1289]) ).
thf(1377,plain,
! [SV157: $i,SV203: $i] :
( ( ( ~ ( ! [SY505: $i] :
( ~ ( in @ ( sK17_C @ SV203 @ SV157 ) @ SY505 )
| ~ ( in @ SY505 @ SV157 ) )
| ~ ( in @ ( sK17_C @ SV203 @ SV157 ) @ SV203 ) ) )
= $false )
| ( ( SV203
= ( union @ SV157 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1290]) ).
thf(1378,plain,
! [SV157: $i,SV203: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK17_C @ SV203 @ SV157 ) @ ( sK18_SY276 @ SV203 @ SV157 ) )
| ~ ( in @ ( sK18_SY276 @ SV203 @ SV157 ) @ SV157 ) )
| ( in @ ( sK17_C @ SV203 @ SV157 ) @ SV203 ) ) )
= $false )
| ( ( SV203
= ( union @ SV157 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1290]) ).
thf(1379,plain,
! [SV204: $i,SV158: $i] :
( ( ( ~ ! [SY506: $i] :
( ! [SY452: $i] :
( ~ ( in @ SY506 @ SY452 )
| ~ ( in @ SY452 @ SV158 ) )
| ( in @ SY506 @ SV204 ) )
| ~ ! [SY508: $i] :
( ~ ( in @ SY508 @ SV204 )
| ~ ( ~ ( in @ SY508 @ ( sK16_D @ SY508 @ SV204 @ SV158 ) )
| ~ ( in @ ( sK16_D @ SY508 @ SV204 @ SV158 ) @ SV158 ) ) ) )
= $false )
| ( ( SV204
= ( union @ SV158 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1291]) ).
thf(1380,plain,
! [SV161: $i,SV205: $i] :
( ( ( ~ ( in @ ( sK34_C @ SV205 @ SV161 ) @ SV161 ) )
= $false )
| ( ( disjoint @ SV161 @ SV205 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1292]) ).
thf(1381,plain,
! [SV161: $i,SV205: $i] :
( ( ( ~ ( in @ ( sK34_C @ SV205 @ SV161 ) @ SV205 ) )
= $false )
| ( ( disjoint @ SV161 @ SV205 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1292]) ).
thf(1382,plain,
! [SV206: $i,SV162: $i,SV259: $i] :
( ( ( ~ ( in @ SV259 @ SV162 ) )
= $true )
| ( ( ~ ( in @ SV259 @ SV206 ) )
= $true )
| ( ( ~ ( disjoint @ SV162 @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1293]) ).
thf(1383,plain,
! [SV78: $i,SV260: $i] :
( ( ( ~ ( relation @ SV260 ) )
= $true )
| ( ( ~ ( subset @ SV78 @ SV260 )
| ( subset @ ( relation_dom @ SV78 ) @ ( relation_dom @ SV260 ) ) )
= $true )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1296]) ).
thf(1384,plain,
! [SV78: $i,SV261: $i] :
( ( ( ~ ( relation @ SV261 ) )
= $true )
| ( ( ~ ( subset @ SV78 @ SV261 )
| ( subset @ ( relation_rng @ SV78 ) @ ( relation_rng @ SV261 ) ) )
= $true )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1297]) ).
thf(1385,plain,
! [SV79: $i,SV209: $i] :
( ( ( subset @ SV209 @ ( sK35_B @ SV79 ) )
= $false )
| ( ( are_equipotent @ SV209 @ ( sK35_B @ SV79 ) )
= $true )
| ( ( in @ SV209 @ ( sK35_B @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1298]) ).
thf(1386,plain,
! [SV79: $i,SV279: $i] :
( ( ~ ( in @ SV279 @ ( sK35_B @ SV79 ) )
| ( in @ ( powerset @ SV279 ) @ ( sK35_B @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1299]) ).
thf(1387,plain,
! [SV79: $i] :
( ( ~ ! [SY383: $i,SY384: $i] :
( ~ ( in @ SY383 @ ( sK35_B @ SV79 ) )
| ~ ( subset @ SY384 @ SY383 )
| ( in @ SY384 @ ( sK35_B @ SV79 ) ) )
| ~ ( in @ SV79 @ ( sK35_B @ SV79 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1300]) ).
thf(1388,plain,
! [SV212: $i,SV167: $i] :
( ( ( subset @ SV167 @ SV212 )
= $false )
| ( ( ~ ( subset @ SV212 @ SV167 ) )
= $true )
| ( ( SV167 = SV212 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1303]) ).
thf(1389,plain,
! [SV280: $i,SV262: $i] :
( ( ( SV262 != SV280 )
| ( subset @ SV262 @ SV280 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1304]) ).
thf(1390,plain,
! [SV281: $i,SV263: $i] :
( ( ( SV263 != SV281 )
| ( subset @ SV281 @ SV263 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1305]) ).
thf(1391,plain,
! [SV81: $i,SV215: $i,SV246: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV81 )
| ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV215 )
| ~ ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV246 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV81 )
| ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV246 ) )
| ~ ( ~ ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV215 )
| ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV246 ) ) ) )
= $false )
| ( ( SV246
= ( set_difference @ SV81 @ SV215 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1309]) ).
thf(1392,plain,
! [SV216: $i,SV81: $i,SV247: $i] :
( ( ( SV247
= ( set_difference @ SV81 @ SV216 ) )
= $false )
| ( ( ~ ( ~ ! [SY532: $i] :
( ~ ( in @ SY532 @ SV81 )
| ( in @ SY532 @ SV216 )
| ( in @ SY532 @ SV247 ) )
| ~ ~ ( ~ ! [SY533: $i] :
( ~ ( in @ SY533 @ SV247 )
| ( in @ SY533 @ SV81 ) )
| ~ ! [SY534: $i] :
( ~ ( in @ SY534 @ SV247 )
| ~ ( in @ SY534 @ SV216 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1310]) ).
thf(1393,plain,
! [SV82: $i,SV264: $i] :
( ( ( ~ ( ~ ( ! [SY545: $i] :
~ ( in @ ( ordered_pair @ SY545 @ ( sK13_C @ SV264 @ SV82 ) ) @ SV82 )
| ~ ( in @ ( sK13_C @ SV264 @ SV82 ) @ SV264 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY274 @ SV264 @ SV82 ) @ ( sK13_C @ SV264 @ SV82 ) ) @ SV82 )
| ( in @ ( sK13_C @ SV264 @ SV82 ) @ SV264 ) ) ) )
= $true )
| ( ( SV264
= ( relation_rng @ SV82 ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1311]) ).
thf(1394,plain,
! [SV82: $i,SV265: $i] :
( ( ( ( SV265
!= ( relation_rng @ SV82 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY546: $i] :
( ! [SY397: $i] :
~ ( in @ ( ordered_pair @ SY397 @ SY546 ) @ SV82 )
| ( in @ SY546 @ SV265 ) )
| ~ ! [SY548: $i] :
( ~ ( in @ SY548 @ SV265 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY548 @ SV265 @ SV82 ) @ SY548 ) @ SV82 ) ) ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1312]) ).
thf(1395,plain,
! [SV83: $i,SV134: $i] :
( ( ( in @ ( sK3_C @ SV134 @ SV83 ) @ SV83 )
= $false )
| ( ( ~ ( in @ ( sK3_C @ SV134 @ SV83 ) @ SV134 ) )
= $true )
| ( ( SV83 = SV134 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1313]) ).
thf(1396,plain,
! [SV266: $i] :
( ( ( SV266 = empty_set )
= $true )
| ( ( ! [SY549: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK40_SY287 @ SY549 @ SV266 ) @ SV266 )
| ~ ~ ( in @ ( sK39_C @ SY549 @ SV266 ) @ ( sK40_SY287 @ SY549 @ SV266 ) ) )
| ~ ( in @ ( sK39_C @ SY549 @ SV266 ) @ SY549 ) )
| ~ ( ! [SY550: $i] :
( ~ ( in @ SY550 @ SV266 )
| ( in @ ( sK39_C @ SY549 @ SV266 ) @ SY550 ) )
| ( in @ ( sK39_C @ SY549 @ SV266 ) @ SY549 ) ) )
| ( SY549
= ( set_meet @ SV266 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1315]) ).
thf(1397,plain,
! [SV267: $i] :
( ( ( SV267 = empty_set )
= $true )
| ( ( ! [SY551: $i] :
( ( SY551
!= ( set_meet @ SV267 ) )
| ~ ( ~ ! [SY552: $i] :
( ~ ( ~ ( in @ ( sK38_D @ SY552 @ SY551 @ SV267 ) @ SV267 )
| ~ ~ ( in @ SY552 @ ( sK38_D @ SY552 @ SY551 @ SV267 ) ) )
| ( in @ SY552 @ SY551 ) )
| ~ ! [SY553: $i] :
( ~ ( in @ SY553 @ SY551 )
| ! [SY554: $i] :
( ~ ( in @ SY554 @ SV267 )
| ( in @ SY553 @ SY554 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1316]) ).
thf(1398,plain,
! [SV268: $i] :
( ( ( ( SV268 != empty_set ) )
= $true )
| ( ( ! [SY555: $i] :
( ( SY555
!= ( set_meet @ SV268 ) )
| ( SY555 = empty_set ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1317]) ).
thf(1399,plain,
! [SV269: $i] :
( ( ( ( SV269 != empty_set ) )
= $true )
| ( ( ! [SY556: $i] :
( ( SY556 != empty_set )
| ( SY556
= ( set_meet @ SV269 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1318]) ).
thf(1400,plain,
! [SV217: $i,SV170: $i] :
( ( ( subset @ SV170 @ SV217 )
= $false )
| ( ( SV170 = SV217 )
= $true )
| ( ( proper_subset @ SV170 @ SV217 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1319]) ).
thf(1401,plain,
! [SV282: $i,SV270: $i] :
( ( ~ ( proper_subset @ SV270 @ SV282 )
| ( SV270 != SV282 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1320]) ).
thf(1402,plain,
! [SV283: $i,SV271: $i] :
( ( ~ ( proper_subset @ SV271 @ SV283 )
| ( subset @ SV271 @ SV283 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1321]) ).
thf(1403,plain,
! [SV84: $i,SV272: $i] :
( ( ( ~ ( relation @ SV272 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SV272 @ SV84 ) @ ( sK11_SY272 @ SV272 @ SV84 ) ) @ SV272 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY272 @ SV272 @ SV84 ) @ ( sK10_C @ SV272 @ SV84 ) ) @ SV84 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK10_C @ SV272 @ SV84 ) @ ( sK11_SY272 @ SV272 @ SV84 ) ) @ SV272 )
| ( in @ ( ordered_pair @ ( sK11_SY272 @ SV272 @ SV84 ) @ ( sK10_C @ SV272 @ SV84 ) ) @ SV84 ) ) )
| ( SV272
= ( relation_inverse @ SV84 ) ) )
= $true )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1322]) ).
thf(1404,plain,
! [SV84: $i,SV273: $i] :
( ( ( ~ ( relation @ SV273 ) )
= $true )
| ( ( ( SV273
!= ( relation_inverse @ SV84 ) )
| ~ ( ~ ! [SY559: $i,SY560: $i] :
( ~ ( in @ ( ordered_pair @ SY559 @ SY560 ) @ SV273 )
| ( in @ ( ordered_pair @ SY560 @ SY559 ) @ SV84 ) )
| ~ ! [SY561: $i,SY562: $i] :
( ~ ( in @ ( ordered_pair @ SY562 @ SY561 ) @ SV84 )
| ( in @ ( ordered_pair @ SY561 @ SY562 ) @ SV273 ) ) ) )
= $true )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1323]) ).
thf(1405,plain,
! [SV85: $i,SV218: $i] :
( ( ( subset @ SV218 @ ( sK1_B @ SV85 ) )
= $false )
| ( ( are_equipotent @ SV218 @ ( sK1_B @ SV85 ) )
= $true )
| ( ( in @ SV218 @ ( sK1_B @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1324]) ).
thf(1406,plain,
! [SV85: $i,SV284: $i] :
( ( ~ ( ~ ! [SY567: $i] :
( ~ ( subset @ SY567 @ SV284 )
| ( in @ SY567 @ ( sK2_SY267 @ SV284 @ SV85 ) ) )
| ~ ( in @ ( sK2_SY267 @ SV284 @ SV85 ) @ ( sK1_B @ SV85 ) ) )
| ~ ( in @ SV284 @ ( sK1_B @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1325]) ).
thf(1407,plain,
! [SV85: $i] :
( ( ~ ! [SY409: $i,SY410: $i] :
( ~ ( in @ SY409 @ ( sK1_B @ SV85 ) )
| ~ ( subset @ SY410 @ SY409 )
| ( in @ SY410 @ ( sK1_B @ SV85 ) ) )
| ~ ( in @ SV85 @ ( sK1_B @ SV85 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1326]) ).
thf(1408,plain,
! [SV173: $i] :
( ( ( ! [SY467: $i,SY468: $i] :
( ( sK30_B @ SV173 )
!= ( ordered_pair @ SY467 @ SY468 ) ) )
= $true )
| ( ( relation @ SV173 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1329]) ).
thf(1409,plain,
! [SV173: $i] :
( ( ( in @ ( sK30_B @ SV173 ) @ SV173 )
= $true )
| ( ( relation @ SV173 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1330]) ).
thf(1410,plain,
! [SV174: $i,SV274: $i] :
( ( ( SV274
= ( ordered_pair @ ( sK28_C @ SV274 @ SV174 ) @ ( sK29_SY279 @ SV274 @ SV174 ) ) )
= $true )
| ( ( ~ ( in @ SV274 @ SV174 ) )
= $true )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1331]) ).
thf(1411,plain,
! [SV221: $i,SV285: $i,SV87: $i] :
( ( ( subset @ ( cartesian_product2 @ SV87 @ SV285 ) @ ( cartesian_product2 @ SV221 @ SV285 ) )
= $true )
| ( ( subset @ SV87 @ SV221 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1332]) ).
thf(1412,plain,
! [SV222: $i,SV87: $i,SV286: $i] :
( ( ( subset @ ( cartesian_product2 @ SV286 @ SV87 ) @ ( cartesian_product2 @ SV286 @ SV222 ) )
= $true )
| ( ( subset @ SV87 @ SV222 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1333]) ).
thf(1413,plain,
! [SV177: $i,SV225: $i] :
( ( ( ~ ( in @ ( sK23_C @ SV225 @ SV177 ) @ SV177 ) )
= $false )
| ( ( subset @ SV177 @ SV225 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1336]) ).
thf(1414,plain,
! [SV177: $i,SV225: $i] :
( ( ( ~ ~ ( in @ ( sK23_C @ SV225 @ SV177 ) @ SV225 ) )
= $false )
| ( ( subset @ SV177 @ SV225 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1336]) ).
thf(1415,plain,
! [SV226: $i,SV178: $i,SV287: $i] :
( ( ( ~ ( in @ SV287 @ SV178 )
| ( in @ SV287 @ SV226 ) )
= $true )
| ( ( subset @ SV178 @ SV226 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1337]) ).
thf(1416,plain,
! [SV227: $i,SV179: $i] :
( ( ( SV179 = empty_set )
= $true )
| ( ( SV179
= ( singleton @ SV227 ) )
= $true )
| ( ( subset @ SV179 @ ( singleton @ SV227 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1338]) ).
thf(1417,plain,
! [SV275: $i] :
( ( ( ( SV275 != empty_set ) )
= $true )
| ( ( ! [SY563: $i] : ( subset @ SV275 @ ( singleton @ SY563 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1339]) ).
thf(1418,plain,
! [SV288: $i,SV276: $i] :
( ( ( SV276
!= ( singleton @ SV288 ) )
| ( subset @ SV276 @ ( singleton @ SV288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1340]) ).
thf(1419,plain,
! [SV228: $i,SV248: $i,SV88: $i] :
( ( ( ~ ( in @ SV88 @ SV248 ) )
= $true )
| ( ( ~ ( in @ SV228 @ SV248 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV88 @ SV228 ) @ SV248 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1341]) ).
thf(1420,plain,
! [SV289: $i,SV88: $i] :
( ( ! [SY568: $i] :
( ~ ( subset @ ( unordered_pair @ SV88 @ SV289 ) @ SY568 )
| ( in @ SV88 @ SY568 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1342]) ).
thf(1421,plain,
! [SV290: $i,SV88: $i] :
( ( ! [SY569: $i] :
( ~ ( subset @ ( unordered_pair @ SV88 @ SV290 ) @ SY569 )
| ( in @ SV290 @ SY569 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1343]) ).
thf(1422,plain,
! [SV231: $i,SV182: $i] :
( ( ( SV182 = empty_set )
= $true )
| ( ( SV182
= ( singleton @ SV231 ) )
= $true )
| ( ( subset @ SV182 @ ( singleton @ SV231 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1346]) ).
thf(1423,plain,
! [SV277: $i] :
( ( ( ( SV277 != empty_set ) )
= $true )
| ( ( ! [SY565: $i] : ( subset @ SV277 @ ( singleton @ SY565 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1347]) ).
thf(1424,plain,
! [SV291: $i,SV278: $i] :
( ( ( SV278
!= ( singleton @ SV291 ) )
| ( subset @ SV278 @ ( singleton @ SV291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1348]) ).
thf(1425,plain,
! [SV185: $i,SV234: $i] :
( ( ( in @ SV234 @ SV185 )
= $false )
| ( ( ( set_difference @ SV185 @ ( singleton @ SV234 ) )
= SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1351]) ).
thf(1426,plain,
! [SV187: $i,SV236: $i] :
( ( ( ~ ( ( ( sK27_C @ SV236 @ SV187 )
!= SV187 )
| ~ ( in @ ( sK27_C @ SV236 @ SV187 ) @ SV236 ) ) )
= $false )
| ( ( SV236
= ( singleton @ SV187 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1352]) ).
thf(1427,plain,
! [SV187: $i,SV236: $i] :
( ( ( ~ ( ( ( sK27_C @ SV236 @ SV187 )
= SV187 )
| ( in @ ( sK27_C @ SV236 @ SV187 ) @ SV236 ) ) )
= $false )
| ( ( SV236
= ( singleton @ SV187 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1352]) ).
thf(1428,plain,
! [SV237: $i,SV188: $i] :
( ( ( ~ ! [SY519: $i] :
( ( SY519 != SV188 )
| ( in @ SY519 @ SV237 ) )
| ~ ! [SY520: $i] :
( ~ ( in @ SY520 @ SV237 )
| ( SY520 = SV188 ) ) )
= $false )
| ( ( SV237
= ( singleton @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1353]) ).
thf(1429,plain,
! [SV238: $i,SV89: $i,SV249: $i] :
( ( ( relation @ SV249 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV89 @ SV238 ) @ SV249 )
| ( in @ SV89 @ ( relation_dom @ SV249 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1354]) ).
thf(1430,plain,
! [SV239: $i,SV89: $i,SV250: $i] :
( ( ( relation @ SV250 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV89 @ SV239 ) @ SV250 )
| ( in @ SV239 @ ( relation_rng @ SV250 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1355]) ).
thf(1431,plain,
! [SV73: $i,SV193: $i,SV240: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV240 )
| ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV73 ) )
| ~ ( ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV240 )
| ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV193 ) ) ) )
= $false )
| ( ( SV240
= ( set_union2 @ SV73 @ SV193 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1360]) ).
thf(1432,plain,
! [SV73: $i,SV193: $i,SV240: $i] :
( ( ( ~ ( ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV240 )
| ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV73 )
| ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV193 ) ) )
= $false )
| ( ( SV240
= ( set_union2 @ SV73 @ SV193 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1360]) ).
thf(1433,plain,
! [SV194: $i,SV73: $i,SV241: $i] :
( ( ( ~ ! [SY523: $i] :
( ~ ( in @ SY523 @ SV241 )
| ( in @ SY523 @ SV73 )
| ( in @ SY523 @ SV194 ) )
| ~ ~ ( ~ ! [SY524: $i] :
( ~ ( in @ SY524 @ SV73 )
| ( in @ SY524 @ SV241 ) )
| ~ ! [SY525: $i] :
( ~ ( in @ SY525 @ SV194 )
| ( in @ SY525 @ SV241 ) ) ) )
= $false )
| ( ( SV241
= ( set_union2 @ SV73 @ SV194 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1361]) ).
thf(1434,plain,
! [SV74: $i,SV195: $i,SV242: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK25_D @ SV242 @ SV195 @ SV74 ) @ SV242 )
| ( ( sK25_D @ SV242 @ SV195 @ SV74 )
!= SV74 ) )
| ~ ( ~ ( in @ ( sK25_D @ SV242 @ SV195 @ SV74 ) @ SV242 )
| ( ( sK25_D @ SV242 @ SV195 @ SV74 )
!= SV195 ) ) ) )
= $false )
| ( ( SV242
= ( unordered_pair @ SV74 @ SV195 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1362]) ).
thf(1435,plain,
! [SV74: $i,SV195: $i,SV242: $i] :
( ( ( ~ ( ( in @ ( sK25_D @ SV242 @ SV195 @ SV74 ) @ SV242 )
| ( ( sK25_D @ SV242 @ SV195 @ SV74 )
= SV74 )
| ( ( sK25_D @ SV242 @ SV195 @ SV74 )
= SV195 ) ) )
= $false )
| ( ( SV242
= ( unordered_pair @ SV74 @ SV195 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1362]) ).
thf(1436,plain,
! [SV196: $i,SV74: $i,SV243: $i] :
( ( ( ~ ! [SY526: $i] :
( ~ ( in @ SY526 @ SV243 )
| ( SY526 = SV74 )
| ( SY526 = SV196 ) )
| ~ ~ ( ~ ! [SY527: $i] :
( ( SY527 != SV74 )
| ( in @ SY527 @ SV243 ) )
| ~ ! [SY528: $i] :
( ( SY528 != SV196 )
| ( in @ SY528 @ SV243 ) ) ) )
= $false )
| ( ( SV243
= ( unordered_pair @ SV74 @ SV196 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1363]) ).
thf(1437,plain,
! [SV75: $i,SV197: $i,SV244: $i] :
( ( ( ~ ( ~ ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV75 )
| ~ ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV197 )
| ~ ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV244 ) ) )
= $false )
| ( ( SV244
= ( set_intersection2 @ SV75 @ SV197 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1364]) ).
thf(1438,plain,
! [SV75: $i,SV197: $i,SV244: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV75 )
| ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV244 ) )
| ~ ( ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV197 )
| ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV244 ) ) ) )
= $false )
| ( ( SV244
= ( set_intersection2 @ SV75 @ SV197 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1364]) ).
thf(1439,plain,
! [SV245: $i,SV198: $i,SV75: $i] :
( ( ( ~ ! [SY529: $i] :
( ~ ( in @ SY529 @ SV75 )
| ~ ( in @ SY529 @ SV198 )
| ( in @ SY529 @ SV245 ) )
| ~ ~ ( ~ ! [SY530: $i] :
( ~ ( in @ SY530 @ SV245 )
| ( in @ SY530 @ SV75 ) )
| ~ ! [SY531: $i] :
( ~ ( in @ SY531 @ SV245 )
| ( in @ SY531 @ SV198 ) ) ) )
= $false )
| ( ( SV245
= ( set_intersection2 @ SV75 @ SV198 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1365]) ).
thf(1440,plain,
! [SV76: $i,SV251: $i] :
( ( ( ~ ( ! [SY535: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SV251 @ SV76 ) @ SY535 ) @ SV76 )
| ~ ( in @ ( sK20_C @ SV251 @ SV76 ) @ SV251 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_C @ SV251 @ SV76 ) @ ( sK21_SY278 @ SV251 @ SV76 ) ) @ SV76 )
| ( in @ ( sK20_C @ SV251 @ SV76 ) @ SV251 ) ) )
= $false )
| ( ( SV251
= ( relation_dom @ SV76 ) )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1366]) ).
thf(1441,plain,
! [SV76: $i,SV252: $i] :
( ( ( SV252
= ( relation_dom @ SV76 ) )
= $false )
| ( ( ~ ( ~ ! [SY536: $i] :
( ! [SY377: $i] :
~ ( in @ ( ordered_pair @ SY536 @ SY377 ) @ SV76 )
| ( in @ SY536 @ SV252 ) )
| ~ ! [SY538: $i] :
( ~ ( in @ SY538 @ SV252 )
| ( in @ ( ordered_pair @ SY538 @ ( sK19_D @ SY538 @ SV252 @ SV76 ) ) @ SV76 ) ) ) )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1367]) ).
thf(1442,plain,
! [SV253: $i,SV292: $i] :
( ( ( ~ ( element @ SV292 @ SV253 )
| ( in @ SV292 @ SV253 ) )
= $true )
| ( ( empty @ SV253 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1368]) ).
thf(1443,plain,
! [SV254: $i,SV293: $i] :
( ( ( ~ ( in @ SV293 @ SV254 )
| ( element @ SV293 @ SV254 ) )
= $true )
| ( ( empty @ SV254 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1369]) ).
thf(1444,plain,
! [SV255: $i] :
( ( ( empty @ SV255 )
= $false )
| ( ( ! [SY541: $i] :
( ~ ( element @ SY541 @ SV255 )
| ( empty @ SY541 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1370]) ).
thf(1445,plain,
! [SV256: $i] :
( ( ( empty @ SV256 )
= $false )
| ( ( ! [SY542: $i] :
( ~ ( empty @ SY542 )
| ( element @ SY542 @ SV256 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1371]) ).
thf(1446,plain,
! [SV153: $i,SV199: $i] :
( ( ( ~ ( in @ ( sK26_C @ SV199 @ SV153 ) @ SV199 )
| ~ ( subset @ ( sK26_C @ SV199 @ SV153 ) @ SV153 ) )
= $true )
| ( ( SV199
= ( powerset @ SV153 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1373]) ).
thf(1447,plain,
! [SV153: $i,SV199: $i] :
( ( ( ( in @ ( sK26_C @ SV199 @ SV153 ) @ SV199 )
| ( subset @ ( sK26_C @ SV199 @ SV153 ) @ SV153 ) )
= $true )
| ( ( SV199
= ( powerset @ SV153 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1374]) ).
thf(1448,plain,
! [SV154: $i,SV200: $i] :
( ( ( ~ ! [SY502: $i] :
( ~ ( in @ SY502 @ SV200 )
| ( subset @ SY502 @ SV154 ) ) )
= $false )
| ( ( SV200
= ( powerset @ SV154 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1375]) ).
thf(1449,plain,
! [SV200: $i,SV154: $i] :
( ( ( ~ ! [SY503: $i] :
( ~ ( subset @ SY503 @ SV154 )
| ( in @ SY503 @ SV200 ) ) )
= $false )
| ( ( SV200
= ( powerset @ SV154 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1375]) ).
thf(1450,plain,
! [SV258: $i,SV202: $i,SV156: $i] :
( ( ( disjoint @ SV156 @ SV202 )
= $false )
| ( ( in @ SV258 @ ( set_intersection2 @ SV156 @ SV202 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1376]) ).
thf(1451,plain,
! [SV157: $i,SV203: $i] :
( ( ( ! [SY505: $i] :
( ~ ( in @ ( sK17_C @ SV203 @ SV157 ) @ SY505 )
| ~ ( in @ SY505 @ SV157 ) )
| ~ ( in @ ( sK17_C @ SV203 @ SV157 ) @ SV203 ) )
= $true )
| ( ( SV203
= ( union @ SV157 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1377]) ).
thf(1452,plain,
! [SV157: $i,SV203: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_C @ SV203 @ SV157 ) @ ( sK18_SY276 @ SV203 @ SV157 ) )
| ~ ( in @ ( sK18_SY276 @ SV203 @ SV157 ) @ SV157 ) )
| ( in @ ( sK17_C @ SV203 @ SV157 ) @ SV203 ) )
= $true )
| ( ( SV203
= ( union @ SV157 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1378]) ).
thf(1453,plain,
! [SV204: $i,SV158: $i] :
( ( ( ~ ! [SY506: $i] :
( ! [SY452: $i] :
( ~ ( in @ SY506 @ SY452 )
| ~ ( in @ SY452 @ SV158 ) )
| ( in @ SY506 @ SV204 ) ) )
= $false )
| ( ( SV204
= ( union @ SV158 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1379]) ).
thf(1454,plain,
! [SV158: $i,SV204: $i] :
( ( ( ~ ! [SY508: $i] :
( ~ ( in @ SY508 @ SV204 )
| ~ ( ~ ( in @ SY508 @ ( sK16_D @ SY508 @ SV204 @ SV158 ) )
| ~ ( in @ ( sK16_D @ SY508 @ SV204 @ SV158 ) @ SV158 ) ) ) )
= $false )
| ( ( SV204
= ( union @ SV158 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1379]) ).
thf(1455,plain,
! [SV161: $i,SV205: $i] :
( ( ( in @ ( sK34_C @ SV205 @ SV161 ) @ SV161 )
= $true )
| ( ( disjoint @ SV161 @ SV205 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1380]) ).
thf(1456,plain,
! [SV161: $i,SV205: $i] :
( ( ( in @ ( sK34_C @ SV205 @ SV161 ) @ SV205 )
= $true )
| ( ( disjoint @ SV161 @ SV205 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1381]) ).
thf(1457,plain,
! [SV206: $i,SV162: $i,SV259: $i] :
( ( ( in @ SV259 @ SV162 )
= $false )
| ( ( ~ ( in @ SV259 @ SV206 ) )
= $true )
| ( ( ~ ( disjoint @ SV162 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1382]) ).
thf(1458,plain,
! [SV78: $i,SV260: $i] :
( ( ( relation @ SV260 )
= $false )
| ( ( ~ ( subset @ SV78 @ SV260 )
| ( subset @ ( relation_dom @ SV78 ) @ ( relation_dom @ SV260 ) ) )
= $true )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1383]) ).
thf(1459,plain,
! [SV78: $i,SV261: $i] :
( ( ( relation @ SV261 )
= $false )
| ( ( ~ ( subset @ SV78 @ SV261 )
| ( subset @ ( relation_rng @ SV78 ) @ ( relation_rng @ SV261 ) ) )
= $true )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1384]) ).
thf(1460,plain,
! [SV79: $i,SV279: $i] :
( ( ( ~ ( in @ SV279 @ ( sK35_B @ SV79 ) ) )
= $true )
| ( ( in @ ( powerset @ SV279 ) @ ( sK35_B @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1386]) ).
thf(1461,plain,
! [SV79: $i] :
( ( ~ ! [SY383: $i,SY384: $i] :
( ~ ( in @ SY383 @ ( sK35_B @ SV79 ) )
| ~ ( subset @ SY384 @ SY383 )
| ( in @ SY384 @ ( sK35_B @ SV79 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1387]) ).
thf(1462,plain,
! [SV79: $i] :
( ( ~ ( in @ SV79 @ ( sK35_B @ SV79 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1387]) ).
thf(1463,plain,
! [SV167: $i,SV212: $i] :
( ( ( subset @ SV212 @ SV167 )
= $false )
| ( ( subset @ SV167 @ SV212 )
= $false )
| ( ( SV167 = SV212 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1388]) ).
thf(1464,plain,
! [SV280: $i,SV262: $i] :
( ( ( ( SV262 != SV280 ) )
= $true )
| ( ( subset @ SV262 @ SV280 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1389]) ).
thf(1465,plain,
! [SV281: $i,SV263: $i] :
( ( ( ( SV263 != SV281 ) )
= $true )
| ( ( subset @ SV281 @ SV263 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1390]) ).
thf(1466,plain,
! [SV81: $i,SV215: $i,SV246: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV81 )
| ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV215 )
| ~ ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV246 ) ) )
= $false )
| ( ( SV246
= ( set_difference @ SV81 @ SV215 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1391]) ).
thf(1467,plain,
! [SV81: $i,SV215: $i,SV246: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV81 )
| ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV246 ) )
| ~ ( ~ ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV215 )
| ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV246 ) ) ) )
= $false )
| ( ( SV246
= ( set_difference @ SV81 @ SV215 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1391]) ).
thf(1468,plain,
! [SV247: $i,SV216: $i,SV81: $i] :
( ( ( ~ ! [SY532: $i] :
( ~ ( in @ SY532 @ SV81 )
| ( in @ SY532 @ SV216 )
| ( in @ SY532 @ SV247 ) )
| ~ ~ ( ~ ! [SY533: $i] :
( ~ ( in @ SY533 @ SV247 )
| ( in @ SY533 @ SV81 ) )
| ~ ! [SY534: $i] :
( ~ ( in @ SY534 @ SV247 )
| ~ ( in @ SY534 @ SV216 ) ) ) )
= $false )
| ( ( SV247
= ( set_difference @ SV81 @ SV216 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1392]) ).
thf(1469,plain,
! [SV82: $i,SV264: $i] :
( ( ( ~ ( ! [SY545: $i] :
~ ( in @ ( ordered_pair @ SY545 @ ( sK13_C @ SV264 @ SV82 ) ) @ SV82 )
| ~ ( in @ ( sK13_C @ SV264 @ SV82 ) @ SV264 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY274 @ SV264 @ SV82 ) @ ( sK13_C @ SV264 @ SV82 ) ) @ SV82 )
| ( in @ ( sK13_C @ SV264 @ SV82 ) @ SV264 ) ) )
= $false )
| ( ( SV264
= ( relation_rng @ SV82 ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1393]) ).
thf(1470,plain,
! [SV82: $i,SV265: $i] :
( ( ( SV265
= ( relation_rng @ SV82 ) )
= $false )
| ( ( ~ ( ~ ! [SY546: $i] :
( ! [SY397: $i] :
~ ( in @ ( ordered_pair @ SY397 @ SY546 ) @ SV82 )
| ( in @ SY546 @ SV265 ) )
| ~ ! [SY548: $i] :
( ~ ( in @ SY548 @ SV265 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY548 @ SV265 @ SV82 ) @ SY548 ) @ SV82 ) ) ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1394]) ).
thf(1471,plain,
! [SV83: $i,SV134: $i] :
( ( ( in @ ( sK3_C @ SV134 @ SV83 ) @ SV134 )
= $false )
| ( ( in @ ( sK3_C @ SV134 @ SV83 ) @ SV83 )
= $false )
| ( ( SV83 = SV134 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1395]) ).
thf(1472,plain,
! [SV266: $i,SV294: $i] :
( ( ( ~ ( ~ ( ~ ( ~ ( in @ ( sK40_SY287 @ SV294 @ SV266 ) @ SV266 )
| ~ ~ ( in @ ( sK39_C @ SV294 @ SV266 ) @ ( sK40_SY287 @ SV294 @ SV266 ) ) )
| ~ ( in @ ( sK39_C @ SV294 @ SV266 ) @ SV294 ) )
| ~ ( ! [SY570: $i] :
( ~ ( in @ SY570 @ SV266 )
| ( in @ ( sK39_C @ SV294 @ SV266 ) @ SY570 ) )
| ( in @ ( sK39_C @ SV294 @ SV266 ) @ SV294 ) ) )
| ( SV294
= ( set_meet @ SV266 ) ) )
= $true )
| ( ( SV266 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1396]) ).
thf(1473,plain,
! [SV267: $i,SV295: $i] :
( ( ( ( SV295
!= ( set_meet @ SV267 ) )
| ~ ( ~ ! [SY571: $i] :
( ~ ( ~ ( in @ ( sK38_D @ SY571 @ SV295 @ SV267 ) @ SV267 )
| ~ ~ ( in @ SY571 @ ( sK38_D @ SY571 @ SV295 @ SV267 ) ) )
| ( in @ SY571 @ SV295 ) )
| ~ ! [SY572: $i] :
( ~ ( in @ SY572 @ SV295 )
| ! [SY554: $i] :
( ~ ( in @ SY554 @ SV267 )
| ( in @ SY572 @ SY554 ) ) ) ) )
= $true )
| ( ( SV267 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1397]) ).
thf(1474,plain,
! [SV268: $i] :
( ( ( SV268 = empty_set )
= $false )
| ( ( ! [SY555: $i] :
( ( SY555
!= ( set_meet @ SV268 ) )
| ( SY555 = empty_set ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1398]) ).
thf(1475,plain,
! [SV269: $i] :
( ( ( SV269 = empty_set )
= $false )
| ( ( ! [SY556: $i] :
( ( SY556 != empty_set )
| ( SY556
= ( set_meet @ SV269 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1399]) ).
thf(1476,plain,
! [SV282: $i,SV270: $i] :
( ( ( ~ ( proper_subset @ SV270 @ SV282 ) )
= $true )
| ( ( ( SV270 != SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1401]) ).
thf(1477,plain,
! [SV283: $i,SV271: $i] :
( ( ( ~ ( proper_subset @ SV271 @ SV283 ) )
= $true )
| ( ( subset @ SV271 @ SV283 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1402]) ).
thf(1478,plain,
! [SV84: $i,SV272: $i] :
( ( ( relation @ SV272 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SV272 @ SV84 ) @ ( sK11_SY272 @ SV272 @ SV84 ) ) @ SV272 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY272 @ SV272 @ SV84 ) @ ( sK10_C @ SV272 @ SV84 ) ) @ SV84 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK10_C @ SV272 @ SV84 ) @ ( sK11_SY272 @ SV272 @ SV84 ) ) @ SV272 )
| ( in @ ( ordered_pair @ ( sK11_SY272 @ SV272 @ SV84 ) @ ( sK10_C @ SV272 @ SV84 ) ) @ SV84 ) ) )
| ( SV272
= ( relation_inverse @ SV84 ) ) )
= $true )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1403]) ).
thf(1479,plain,
! [SV84: $i,SV273: $i] :
( ( ( relation @ SV273 )
= $false )
| ( ( ( SV273
!= ( relation_inverse @ SV84 ) )
| ~ ( ~ ! [SY559: $i,SY560: $i] :
( ~ ( in @ ( ordered_pair @ SY559 @ SY560 ) @ SV273 )
| ( in @ ( ordered_pair @ SY560 @ SY559 ) @ SV84 ) )
| ~ ! [SY561: $i,SY562: $i] :
( ~ ( in @ ( ordered_pair @ SY562 @ SY561 ) @ SV84 )
| ( in @ ( ordered_pair @ SY561 @ SY562 ) @ SV273 ) ) ) )
= $true )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1404]) ).
thf(1480,plain,
! [SV85: $i,SV284: $i] :
( ( ( ~ ( ~ ! [SY567: $i] :
( ~ ( subset @ SY567 @ SV284 )
| ( in @ SY567 @ ( sK2_SY267 @ SV284 @ SV85 ) ) )
| ~ ( in @ ( sK2_SY267 @ SV284 @ SV85 ) @ ( sK1_B @ SV85 ) ) ) )
= $true )
| ( ( ~ ( in @ SV284 @ ( sK1_B @ SV85 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1406]) ).
thf(1481,plain,
! [SV85: $i] :
( ( ~ ! [SY409: $i,SY410: $i] :
( ~ ( in @ SY409 @ ( sK1_B @ SV85 ) )
| ~ ( subset @ SY410 @ SY409 )
| ( in @ SY410 @ ( sK1_B @ SV85 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1407]) ).
thf(1482,plain,
! [SV85: $i] :
( ( ~ ( in @ SV85 @ ( sK1_B @ SV85 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1407]) ).
thf(1483,plain,
! [SV296: $i,SV173: $i] :
( ( ( ! [SY574: $i] :
( ( sK30_B @ SV173 )
!= ( ordered_pair @ SV296 @ SY574 ) ) )
= $true )
| ( ( relation @ SV173 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1408]) ).
thf(1484,plain,
! [SV174: $i,SV274: $i] :
( ( ( in @ SV274 @ SV174 )
= $false )
| ( ( SV274
= ( ordered_pair @ ( sK28_C @ SV274 @ SV174 ) @ ( sK29_SY279 @ SV274 @ SV174 ) ) )
= $true )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1410]) ).
thf(1485,plain,
! [SV177: $i,SV225: $i] :
( ( ( in @ ( sK23_C @ SV225 @ SV177 ) @ SV177 )
= $true )
| ( ( subset @ SV177 @ SV225 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1413]) ).
thf(1486,plain,
! [SV177: $i,SV225: $i] :
( ( ( ~ ( in @ ( sK23_C @ SV225 @ SV177 ) @ SV225 ) )
= $true )
| ( ( subset @ SV177 @ SV225 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1414]) ).
thf(1487,plain,
! [SV226: $i,SV178: $i,SV287: $i] :
( ( ( ~ ( in @ SV287 @ SV178 ) )
= $true )
| ( ( in @ SV287 @ SV226 )
= $true )
| ( ( subset @ SV178 @ SV226 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1415]) ).
thf(1488,plain,
! [SV275: $i] :
( ( ( SV275 = empty_set )
= $false )
| ( ( ! [SY563: $i] : ( subset @ SV275 @ ( singleton @ SY563 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1417]) ).
thf(1489,plain,
! [SV288: $i,SV276: $i] :
( ( ( ( SV276
!= ( singleton @ SV288 ) ) )
= $true )
| ( ( subset @ SV276 @ ( singleton @ SV288 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1418]) ).
thf(1490,plain,
! [SV228: $i,SV248: $i,SV88: $i] :
( ( ( in @ SV88 @ SV248 )
= $false )
| ( ( ~ ( in @ SV228 @ SV248 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV88 @ SV228 ) @ SV248 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1419]) ).
thf(1491,plain,
! [SV297: $i,SV289: $i,SV88: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV88 @ SV289 ) @ SV297 )
| ( in @ SV88 @ SV297 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1420]) ).
thf(1492,plain,
! [SV298: $i,SV290: $i,SV88: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV88 @ SV290 ) @ SV298 )
| ( in @ SV290 @ SV298 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1421]) ).
thf(1493,plain,
! [SV277: $i] :
( ( ( SV277 = empty_set )
= $false )
| ( ( ! [SY565: $i] : ( subset @ SV277 @ ( singleton @ SY565 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1423]) ).
thf(1494,plain,
! [SV291: $i,SV278: $i] :
( ( ( ( SV278
!= ( singleton @ SV291 ) ) )
= $true )
| ( ( subset @ SV278 @ ( singleton @ SV291 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1424]) ).
thf(1495,plain,
! [SV187: $i,SV236: $i] :
( ( ( ( ( sK27_C @ SV236 @ SV187 )
!= SV187 )
| ~ ( in @ ( sK27_C @ SV236 @ SV187 ) @ SV236 ) )
= $true )
| ( ( SV236
= ( singleton @ SV187 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1426]) ).
thf(1496,plain,
! [SV187: $i,SV236: $i] :
( ( ( ( ( sK27_C @ SV236 @ SV187 )
= SV187 )
| ( in @ ( sK27_C @ SV236 @ SV187 ) @ SV236 ) )
= $true )
| ( ( SV236
= ( singleton @ SV187 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1427]) ).
thf(1497,plain,
! [SV237: $i,SV188: $i] :
( ( ( ~ ! [SY519: $i] :
( ( SY519 != SV188 )
| ( in @ SY519 @ SV237 ) ) )
= $false )
| ( ( SV237
= ( singleton @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1428]) ).
thf(1498,plain,
! [SV188: $i,SV237: $i] :
( ( ( ~ ! [SY520: $i] :
( ~ ( in @ SY520 @ SV237 )
| ( SY520 = SV188 ) ) )
= $false )
| ( ( SV237
= ( singleton @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1428]) ).
thf(1499,plain,
! [SV249: $i,SV238: $i,SV89: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV89 @ SV238 ) @ SV249 ) )
= $true )
| ( ( in @ SV89 @ ( relation_dom @ SV249 ) )
= $true )
| ( ( relation @ SV249 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1429]) ).
thf(1500,plain,
! [SV250: $i,SV239: $i,SV89: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV89 @ SV239 ) @ SV250 ) )
= $true )
| ( ( in @ SV239 @ ( relation_rng @ SV250 ) )
= $true )
| ( ( relation @ SV250 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1430]) ).
thf(1501,plain,
! [SV73: $i,SV193: $i,SV240: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV240 )
| ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV73 ) )
| ~ ( ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV240 )
| ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV193 ) ) ) )
= $true )
| ( ( SV240
= ( set_union2 @ SV73 @ SV193 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1431]) ).
thf(1502,plain,
! [SV73: $i,SV193: $i,SV240: $i] :
( ( ( ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV240 )
| ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV73 )
| ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV193 ) )
= $true )
| ( ( SV240
= ( set_union2 @ SV73 @ SV193 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1432]) ).
thf(1503,plain,
! [SV194: $i,SV73: $i,SV241: $i] :
( ( ( ~ ! [SY523: $i] :
( ~ ( in @ SY523 @ SV241 )
| ( in @ SY523 @ SV73 )
| ( in @ SY523 @ SV194 ) ) )
= $false )
| ( ( SV241
= ( set_union2 @ SV73 @ SV194 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1433]) ).
thf(1504,plain,
! [SV194: $i,SV241: $i,SV73: $i] :
( ( ( ~ ~ ( ~ ! [SY524: $i] :
( ~ ( in @ SY524 @ SV73 )
| ( in @ SY524 @ SV241 ) )
| ~ ! [SY525: $i] :
( ~ ( in @ SY525 @ SV194 )
| ( in @ SY525 @ SV241 ) ) ) )
= $false )
| ( ( SV241
= ( set_union2 @ SV73 @ SV194 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1433]) ).
thf(1505,plain,
! [SV74: $i,SV195: $i,SV242: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK25_D @ SV242 @ SV195 @ SV74 ) @ SV242 )
| ( ( sK25_D @ SV242 @ SV195 @ SV74 )
!= SV74 ) )
| ~ ( ~ ( in @ ( sK25_D @ SV242 @ SV195 @ SV74 ) @ SV242 )
| ( ( sK25_D @ SV242 @ SV195 @ SV74 )
!= SV195 ) ) ) )
= $true )
| ( ( SV242
= ( unordered_pair @ SV74 @ SV195 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1434]) ).
thf(1506,plain,
! [SV74: $i,SV195: $i,SV242: $i] :
( ( ( ( in @ ( sK25_D @ SV242 @ SV195 @ SV74 ) @ SV242 )
| ( ( sK25_D @ SV242 @ SV195 @ SV74 )
= SV74 )
| ( ( sK25_D @ SV242 @ SV195 @ SV74 )
= SV195 ) )
= $true )
| ( ( SV242
= ( unordered_pair @ SV74 @ SV195 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1435]) ).
thf(1507,plain,
! [SV196: $i,SV74: $i,SV243: $i] :
( ( ( ~ ! [SY526: $i] :
( ~ ( in @ SY526 @ SV243 )
| ( SY526 = SV74 )
| ( SY526 = SV196 ) ) )
= $false )
| ( ( SV243
= ( unordered_pair @ SV74 @ SV196 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1436]) ).
thf(1508,plain,
! [SV196: $i,SV243: $i,SV74: $i] :
( ( ( ~ ~ ( ~ ! [SY527: $i] :
( ( SY527 != SV74 )
| ( in @ SY527 @ SV243 ) )
| ~ ! [SY528: $i] :
( ( SY528 != SV196 )
| ( in @ SY528 @ SV243 ) ) ) )
= $false )
| ( ( SV243
= ( unordered_pair @ SV74 @ SV196 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1436]) ).
thf(1509,plain,
! [SV75: $i,SV197: $i,SV244: $i] :
( ( ( ~ ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV75 )
| ~ ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV197 )
| ~ ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV244 ) )
= $true )
| ( ( SV244
= ( set_intersection2 @ SV75 @ SV197 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1437]) ).
thf(1510,plain,
! [SV75: $i,SV197: $i,SV244: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV75 )
| ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV244 ) )
| ~ ( ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV197 )
| ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV244 ) ) ) )
= $true )
| ( ( SV244
= ( set_intersection2 @ SV75 @ SV197 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1438]) ).
thf(1511,plain,
! [SV245: $i,SV198: $i,SV75: $i] :
( ( ( ~ ! [SY529: $i] :
( ~ ( in @ SY529 @ SV75 )
| ~ ( in @ SY529 @ SV198 )
| ( in @ SY529 @ SV245 ) ) )
= $false )
| ( ( SV245
= ( set_intersection2 @ SV75 @ SV198 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1439]) ).
thf(1512,plain,
! [SV198: $i,SV75: $i,SV245: $i] :
( ( ( ~ ~ ( ~ ! [SY530: $i] :
( ~ ( in @ SY530 @ SV245 )
| ( in @ SY530 @ SV75 ) )
| ~ ! [SY531: $i] :
( ~ ( in @ SY531 @ SV245 )
| ( in @ SY531 @ SV198 ) ) ) )
= $false )
| ( ( SV245
= ( set_intersection2 @ SV75 @ SV198 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1439]) ).
thf(1513,plain,
! [SV76: $i,SV251: $i] :
( ( ( ~ ( ! [SY535: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SV251 @ SV76 ) @ SY535 ) @ SV76 )
| ~ ( in @ ( sK20_C @ SV251 @ SV76 ) @ SV251 ) ) )
= $false )
| ( ( SV251
= ( relation_dom @ SV76 ) )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1440]) ).
thf(1514,plain,
! [SV76: $i,SV251: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK20_C @ SV251 @ SV76 ) @ ( sK21_SY278 @ SV251 @ SV76 ) ) @ SV76 )
| ( in @ ( sK20_C @ SV251 @ SV76 ) @ SV251 ) ) )
= $false )
| ( ( SV251
= ( relation_dom @ SV76 ) )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1440]) ).
thf(1515,plain,
! [SV252: $i,SV76: $i] :
( ( ( ~ ! [SY536: $i] :
( ! [SY377: $i] :
~ ( in @ ( ordered_pair @ SY536 @ SY377 ) @ SV76 )
| ( in @ SY536 @ SV252 ) )
| ~ ! [SY538: $i] :
( ~ ( in @ SY538 @ SV252 )
| ( in @ ( ordered_pair @ SY538 @ ( sK19_D @ SY538 @ SV252 @ SV76 ) ) @ SV76 ) ) )
= $false )
| ( ( SV252
= ( relation_dom @ SV76 ) )
= $false )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1441]) ).
thf(1516,plain,
! [SV253: $i,SV292: $i] :
( ( ( ~ ( element @ SV292 @ SV253 ) )
= $true )
| ( ( in @ SV292 @ SV253 )
= $true )
| ( ( empty @ SV253 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1442]) ).
thf(1517,plain,
! [SV254: $i,SV293: $i] :
( ( ( ~ ( in @ SV293 @ SV254 ) )
= $true )
| ( ( element @ SV293 @ SV254 )
= $true )
| ( ( empty @ SV254 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1443]) ).
thf(1518,plain,
! [SV255: $i,SV299: $i] :
( ( ( ~ ( element @ SV299 @ SV255 )
| ( empty @ SV299 ) )
= $true )
| ( ( empty @ SV255 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1444]) ).
thf(1519,plain,
! [SV256: $i,SV300: $i] :
( ( ( ~ ( empty @ SV300 )
| ( element @ SV300 @ SV256 ) )
= $true )
| ( ( empty @ SV256 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1445]) ).
thf(1520,plain,
! [SV153: $i,SV199: $i] :
( ( ( ~ ( in @ ( sK26_C @ SV199 @ SV153 ) @ SV199 ) )
= $true )
| ( ( ~ ( subset @ ( sK26_C @ SV199 @ SV153 ) @ SV153 ) )
= $true )
| ( ( SV199
= ( powerset @ SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1446]) ).
thf(1521,plain,
! [SV153: $i,SV199: $i] :
( ( ( in @ ( sK26_C @ SV199 @ SV153 ) @ SV199 )
= $true )
| ( ( subset @ ( sK26_C @ SV199 @ SV153 ) @ SV153 )
= $true )
| ( ( SV199
= ( powerset @ SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1447]) ).
thf(1522,plain,
! [SV154: $i,SV200: $i] :
( ( ( ! [SY502: $i] :
( ~ ( in @ SY502 @ SV200 )
| ( subset @ SY502 @ SV154 ) ) )
= $true )
| ( ( SV200
= ( powerset @ SV154 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1448]) ).
thf(1523,plain,
! [SV200: $i,SV154: $i] :
( ( ( ! [SY503: $i] :
( ~ ( subset @ SY503 @ SV154 )
| ( in @ SY503 @ SV200 ) ) )
= $true )
| ( ( SV200
= ( powerset @ SV154 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1449]) ).
thf(1524,plain,
! [SV157: $i,SV203: $i] :
( ( ( ! [SY505: $i] :
( ~ ( in @ ( sK17_C @ SV203 @ SV157 ) @ SY505 )
| ~ ( in @ SY505 @ SV157 ) ) )
= $true )
| ( ( ~ ( in @ ( sK17_C @ SV203 @ SV157 ) @ SV203 ) )
= $true )
| ( ( SV203
= ( union @ SV157 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1451]) ).
thf(1525,plain,
! [SV157: $i,SV203: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_C @ SV203 @ SV157 ) @ ( sK18_SY276 @ SV203 @ SV157 ) )
| ~ ( in @ ( sK18_SY276 @ SV203 @ SV157 ) @ SV157 ) ) )
= $true )
| ( ( in @ ( sK17_C @ SV203 @ SV157 ) @ SV203 )
= $true )
| ( ( SV203
= ( union @ SV157 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1452]) ).
thf(1526,plain,
! [SV204: $i,SV158: $i] :
( ( ( ! [SY506: $i] :
( ! [SY452: $i] :
( ~ ( in @ SY506 @ SY452 )
| ~ ( in @ SY452 @ SV158 ) )
| ( in @ SY506 @ SV204 ) ) )
= $true )
| ( ( SV204
= ( union @ SV158 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1453]) ).
thf(1527,plain,
! [SV158: $i,SV204: $i] :
( ( ( ! [SY508: $i] :
( ~ ( in @ SY508 @ SV204 )
| ~ ( ~ ( in @ SY508 @ ( sK16_D @ SY508 @ SV204 @ SV158 ) )
| ~ ( in @ ( sK16_D @ SY508 @ SV204 @ SV158 ) @ SV158 ) ) ) )
= $true )
| ( ( SV204
= ( union @ SV158 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1454]) ).
thf(1528,plain,
! [SV162: $i,SV206: $i,SV259: $i] :
( ( ( in @ SV259 @ SV206 )
= $false )
| ( ( in @ SV259 @ SV162 )
= $false )
| ( ( ~ ( disjoint @ SV162 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1457]) ).
thf(1529,plain,
! [SV260: $i,SV78: $i] :
( ( ( ~ ( subset @ SV78 @ SV260 ) )
= $true )
| ( ( subset @ ( relation_dom @ SV78 ) @ ( relation_dom @ SV260 ) )
= $true )
| ( ( relation @ SV260 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1458]) ).
thf(1530,plain,
! [SV261: $i,SV78: $i] :
( ( ( ~ ( subset @ SV78 @ SV261 ) )
= $true )
| ( ( subset @ ( relation_rng @ SV78 ) @ ( relation_rng @ SV261 ) )
= $true )
| ( ( relation @ SV261 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1459]) ).
thf(1531,plain,
! [SV79: $i,SV279: $i] :
( ( ( in @ SV279 @ ( sK35_B @ SV79 ) )
= $false )
| ( ( in @ ( powerset @ SV279 ) @ ( sK35_B @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1460]) ).
thf(1532,plain,
! [SV79: $i] :
( ( ! [SY383: $i,SY384: $i] :
( ~ ( in @ SY383 @ ( sK35_B @ SV79 ) )
| ~ ( subset @ SY384 @ SY383 )
| ( in @ SY384 @ ( sK35_B @ SV79 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1461]) ).
thf(1533,plain,
! [SV79: $i] :
( ( in @ SV79 @ ( sK35_B @ SV79 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1462]) ).
thf(1534,plain,
! [SV280: $i,SV262: $i] :
( ( ( SV262 = SV280 )
= $false )
| ( ( subset @ SV262 @ SV280 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1464]) ).
thf(1535,plain,
! [SV281: $i,SV263: $i] :
( ( ( SV263 = SV281 )
= $false )
| ( ( subset @ SV281 @ SV263 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1465]) ).
thf(1536,plain,
! [SV81: $i,SV215: $i,SV246: $i] :
( ( ( ~ ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV81 )
| ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV215 )
| ~ ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV246 ) )
= $true )
| ( ( SV246
= ( set_difference @ SV81 @ SV215 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1466]) ).
thf(1537,plain,
! [SV81: $i,SV215: $i,SV246: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV81 )
| ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV246 ) )
| ~ ( ~ ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV215 )
| ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV246 ) ) ) )
= $true )
| ( ( SV246
= ( set_difference @ SV81 @ SV215 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1467]) ).
thf(1538,plain,
! [SV247: $i,SV216: $i,SV81: $i] :
( ( ( ~ ! [SY532: $i] :
( ~ ( in @ SY532 @ SV81 )
| ( in @ SY532 @ SV216 )
| ( in @ SY532 @ SV247 ) ) )
= $false )
| ( ( SV247
= ( set_difference @ SV81 @ SV216 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1468]) ).
thf(1539,plain,
! [SV216: $i,SV81: $i,SV247: $i] :
( ( ( ~ ~ ( ~ ! [SY533: $i] :
( ~ ( in @ SY533 @ SV247 )
| ( in @ SY533 @ SV81 ) )
| ~ ! [SY534: $i] :
( ~ ( in @ SY534 @ SV247 )
| ~ ( in @ SY534 @ SV216 ) ) ) )
= $false )
| ( ( SV247
= ( set_difference @ SV81 @ SV216 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1468]) ).
thf(1540,plain,
! [SV82: $i,SV264: $i] :
( ( ( ~ ( ! [SY545: $i] :
~ ( in @ ( ordered_pair @ SY545 @ ( sK13_C @ SV264 @ SV82 ) ) @ SV82 )
| ~ ( in @ ( sK13_C @ SV264 @ SV82 ) @ SV264 ) ) )
= $false )
| ( ( SV264
= ( relation_rng @ SV82 ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1469]) ).
thf(1541,plain,
! [SV82: $i,SV264: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK14_SY274 @ SV264 @ SV82 ) @ ( sK13_C @ SV264 @ SV82 ) ) @ SV82 )
| ( in @ ( sK13_C @ SV264 @ SV82 ) @ SV264 ) ) )
= $false )
| ( ( SV264
= ( relation_rng @ SV82 ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1469]) ).
thf(1542,plain,
! [SV265: $i,SV82: $i] :
( ( ( ~ ! [SY546: $i] :
( ! [SY397: $i] :
~ ( in @ ( ordered_pair @ SY397 @ SY546 ) @ SV82 )
| ( in @ SY546 @ SV265 ) )
| ~ ! [SY548: $i] :
( ~ ( in @ SY548 @ SV265 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY548 @ SV265 @ SV82 ) @ SY548 ) @ SV82 ) ) )
= $false )
| ( ( SV265
= ( relation_rng @ SV82 ) )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1470]) ).
thf(1543,plain,
! [SV266: $i,SV294: $i] :
( ( ( ~ ( ~ ( ~ ( ~ ( in @ ( sK40_SY287 @ SV294 @ SV266 ) @ SV266 )
| ~ ~ ( in @ ( sK39_C @ SV294 @ SV266 ) @ ( sK40_SY287 @ SV294 @ SV266 ) ) )
| ~ ( in @ ( sK39_C @ SV294 @ SV266 ) @ SV294 ) )
| ~ ( ! [SY570: $i] :
( ~ ( in @ SY570 @ SV266 )
| ( in @ ( sK39_C @ SV294 @ SV266 ) @ SY570 ) )
| ( in @ ( sK39_C @ SV294 @ SV266 ) @ SV294 ) ) ) )
= $true )
| ( ( SV294
= ( set_meet @ SV266 ) )
= $true )
| ( ( SV266 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1472]) ).
thf(1544,plain,
! [SV267: $i,SV295: $i] :
( ( ( ( SV295
!= ( set_meet @ SV267 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY571: $i] :
( ~ ( ~ ( in @ ( sK38_D @ SY571 @ SV295 @ SV267 ) @ SV267 )
| ~ ~ ( in @ SY571 @ ( sK38_D @ SY571 @ SV295 @ SV267 ) ) )
| ( in @ SY571 @ SV295 ) )
| ~ ! [SY572: $i] :
( ~ ( in @ SY572 @ SV295 )
| ! [SY554: $i] :
( ~ ( in @ SY554 @ SV267 )
| ( in @ SY572 @ SY554 ) ) ) ) )
= $true )
| ( ( SV267 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1473]) ).
thf(1545,plain,
! [SV268: $i,SV301: $i] :
( ( ( ( SV301
!= ( set_meet @ SV268 ) )
| ( SV301 = empty_set ) )
= $true )
| ( ( SV268 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1474]) ).
thf(1546,plain,
! [SV269: $i,SV302: $i] :
( ( ( ( SV302 != empty_set )
| ( SV302
= ( set_meet @ SV269 ) ) )
= $true )
| ( ( SV269 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1475]) ).
thf(1547,plain,
! [SV282: $i,SV270: $i] :
( ( ( proper_subset @ SV270 @ SV282 )
= $false )
| ( ( ( SV270 != SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1476]) ).
thf(1548,plain,
! [SV283: $i,SV271: $i] :
( ( ( proper_subset @ SV271 @ SV283 )
= $false )
| ( ( subset @ SV271 @ SV283 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1477]) ).
thf(1549,plain,
! [SV84: $i,SV272: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SV272 @ SV84 ) @ ( sK11_SY272 @ SV272 @ SV84 ) ) @ SV272 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY272 @ SV272 @ SV84 ) @ ( sK10_C @ SV272 @ SV84 ) ) @ SV84 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK10_C @ SV272 @ SV84 ) @ ( sK11_SY272 @ SV272 @ SV84 ) ) @ SV272 )
| ( in @ ( ordered_pair @ ( sK11_SY272 @ SV272 @ SV84 ) @ ( sK10_C @ SV272 @ SV84 ) ) @ SV84 ) ) ) )
= $true )
| ( ( SV272
= ( relation_inverse @ SV84 ) )
= $true )
| ( ( relation @ SV272 )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1478]) ).
thf(1550,plain,
! [SV84: $i,SV273: $i] :
( ( ( ( SV273
!= ( relation_inverse @ SV84 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY559: $i,SY560: $i] :
( ~ ( in @ ( ordered_pair @ SY559 @ SY560 ) @ SV273 )
| ( in @ ( ordered_pair @ SY560 @ SY559 ) @ SV84 ) )
| ~ ! [SY561: $i,SY562: $i] :
( ~ ( in @ ( ordered_pair @ SY562 @ SY561 ) @ SV84 )
| ( in @ ( ordered_pair @ SY561 @ SY562 ) @ SV273 ) ) ) )
= $true )
| ( ( relation @ SV273 )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1479]) ).
thf(1551,plain,
! [SV85: $i,SV284: $i] :
( ( ( ~ ! [SY567: $i] :
( ~ ( subset @ SY567 @ SV284 )
| ( in @ SY567 @ ( sK2_SY267 @ SV284 @ SV85 ) ) )
| ~ ( in @ ( sK2_SY267 @ SV284 @ SV85 ) @ ( sK1_B @ SV85 ) ) )
= $false )
| ( ( ~ ( in @ SV284 @ ( sK1_B @ SV85 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1480]) ).
thf(1552,plain,
! [SV85: $i] :
( ( ! [SY409: $i,SY410: $i] :
( ~ ( in @ SY409 @ ( sK1_B @ SV85 ) )
| ~ ( subset @ SY410 @ SY409 )
| ( in @ SY410 @ ( sK1_B @ SV85 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1481]) ).
thf(1553,plain,
! [SV85: $i] :
( ( in @ SV85 @ ( sK1_B @ SV85 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1482]) ).
thf(1554,plain,
! [SV303: $i,SV296: $i,SV173: $i] :
( ( ( ( ( sK30_B @ SV173 )
!= ( ordered_pair @ SV296 @ SV303 ) ) )
= $true )
| ( ( relation @ SV173 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1483]) ).
thf(1555,plain,
! [SV177: $i,SV225: $i] :
( ( ( in @ ( sK23_C @ SV225 @ SV177 ) @ SV225 )
= $false )
| ( ( subset @ SV177 @ SV225 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1486]) ).
thf(1556,plain,
! [SV226: $i,SV178: $i,SV287: $i] :
( ( ( in @ SV287 @ SV178 )
= $false )
| ( ( in @ SV287 @ SV226 )
= $true )
| ( ( subset @ SV178 @ SV226 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1487]) ).
thf(1557,plain,
! [SV304: $i,SV275: $i] :
( ( ( subset @ SV275 @ ( singleton @ SV304 ) )
= $true )
| ( ( SV275 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1488]) ).
thf(1558,plain,
! [SV288: $i,SV276: $i] :
( ( ( SV276
= ( singleton @ SV288 ) )
= $false )
| ( ( subset @ SV276 @ ( singleton @ SV288 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1489]) ).
thf(1559,plain,
! [SV88: $i,SV248: $i,SV228: $i] :
( ( ( in @ SV228 @ SV248 )
= $false )
| ( ( in @ SV88 @ SV248 )
= $false )
| ( ( subset @ ( unordered_pair @ SV88 @ SV228 ) @ SV248 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1490]) ).
thf(1560,plain,
! [SV297: $i,SV289: $i,SV88: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV88 @ SV289 ) @ SV297 ) )
= $true )
| ( ( in @ SV88 @ SV297 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1491]) ).
thf(1561,plain,
! [SV298: $i,SV290: $i,SV88: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV88 @ SV290 ) @ SV298 ) )
= $true )
| ( ( in @ SV290 @ SV298 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1492]) ).
thf(1562,plain,
! [SV305: $i,SV277: $i] :
( ( ( subset @ SV277 @ ( singleton @ SV305 ) )
= $true )
| ( ( SV277 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1493]) ).
thf(1563,plain,
! [SV291: $i,SV278: $i] :
( ( ( SV278
= ( singleton @ SV291 ) )
= $false )
| ( ( subset @ SV278 @ ( singleton @ SV291 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1494]) ).
thf(1564,plain,
! [SV187: $i,SV236: $i] :
( ( ( ( ( sK27_C @ SV236 @ SV187 )
!= SV187 ) )
= $true )
| ( ( ~ ( in @ ( sK27_C @ SV236 @ SV187 ) @ SV236 ) )
= $true )
| ( ( SV236
= ( singleton @ SV187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1495]) ).
thf(1565,plain,
! [SV187: $i,SV236: $i] :
( ( ( ( sK27_C @ SV236 @ SV187 )
= SV187 )
= $true )
| ( ( in @ ( sK27_C @ SV236 @ SV187 ) @ SV236 )
= $true )
| ( ( SV236
= ( singleton @ SV187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1496]) ).
thf(1566,plain,
! [SV237: $i,SV188: $i] :
( ( ( ! [SY519: $i] :
( ( SY519 != SV188 )
| ( in @ SY519 @ SV237 ) ) )
= $true )
| ( ( SV237
= ( singleton @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1497]) ).
thf(1567,plain,
! [SV188: $i,SV237: $i] :
( ( ( ! [SY520: $i] :
( ~ ( in @ SY520 @ SV237 )
| ( SY520 = SV188 ) ) )
= $true )
| ( ( SV237
= ( singleton @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1498]) ).
thf(1568,plain,
! [SV249: $i,SV238: $i,SV89: $i] :
( ( ( in @ ( ordered_pair @ SV89 @ SV238 ) @ SV249 )
= $false )
| ( ( in @ SV89 @ ( relation_dom @ SV249 ) )
= $true )
| ( ( relation @ SV249 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1499]) ).
thf(1569,plain,
! [SV250: $i,SV239: $i,SV89: $i] :
( ( ( in @ ( ordered_pair @ SV89 @ SV239 ) @ SV250 )
= $false )
| ( ( in @ SV239 @ ( relation_rng @ SV250 ) )
= $true )
| ( ( relation @ SV250 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1500]) ).
thf(1570,plain,
! [SV73: $i,SV193: $i,SV240: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV240 )
| ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV73 ) )
| ~ ( ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV240 )
| ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV193 ) ) )
= $false )
| ( ( SV240
= ( set_union2 @ SV73 @ SV193 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1501]) ).
thf(1571,plain,
! [SV73: $i,SV193: $i,SV240: $i] :
( ( ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV240 )
= $true )
| ( ( ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV73 )
| ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV193 ) )
= $true )
| ( ( SV240
= ( set_union2 @ SV73 @ SV193 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1502]) ).
thf(1572,plain,
! [SV194: $i,SV73: $i,SV241: $i] :
( ( ( ! [SY523: $i] :
( ~ ( in @ SY523 @ SV241 )
| ( in @ SY523 @ SV73 )
| ( in @ SY523 @ SV194 ) ) )
= $true )
| ( ( SV241
= ( set_union2 @ SV73 @ SV194 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1503]) ).
thf(1573,plain,
! [SV194: $i,SV241: $i,SV73: $i] :
( ( ( ~ ( ~ ! [SY524: $i] :
( ~ ( in @ SY524 @ SV73 )
| ( in @ SY524 @ SV241 ) )
| ~ ! [SY525: $i] :
( ~ ( in @ SY525 @ SV194 )
| ( in @ SY525 @ SV241 ) ) ) )
= $true )
| ( ( SV241
= ( set_union2 @ SV73 @ SV194 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1504]) ).
thf(1574,plain,
! [SV74: $i,SV195: $i,SV242: $i] :
( ( ( ~ ( ~ ( in @ ( sK25_D @ SV242 @ SV195 @ SV74 ) @ SV242 )
| ( ( sK25_D @ SV242 @ SV195 @ SV74 )
!= SV74 ) )
| ~ ( ~ ( in @ ( sK25_D @ SV242 @ SV195 @ SV74 ) @ SV242 )
| ( ( sK25_D @ SV242 @ SV195 @ SV74 )
!= SV195 ) ) )
= $false )
| ( ( SV242
= ( unordered_pair @ SV74 @ SV195 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1505]) ).
thf(1575,plain,
! [SV74: $i,SV195: $i,SV242: $i] :
( ( ( in @ ( sK25_D @ SV242 @ SV195 @ SV74 ) @ SV242 )
= $true )
| ( ( ( ( sK25_D @ SV242 @ SV195 @ SV74 )
= SV74 )
| ( ( sK25_D @ SV242 @ SV195 @ SV74 )
= SV195 ) )
= $true )
| ( ( SV242
= ( unordered_pair @ SV74 @ SV195 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1506]) ).
thf(1576,plain,
! [SV196: $i,SV74: $i,SV243: $i] :
( ( ( ! [SY526: $i] :
( ~ ( in @ SY526 @ SV243 )
| ( SY526 = SV74 )
| ( SY526 = SV196 ) ) )
= $true )
| ( ( SV243
= ( unordered_pair @ SV74 @ SV196 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1507]) ).
thf(1577,plain,
! [SV196: $i,SV243: $i,SV74: $i] :
( ( ( ~ ( ~ ! [SY527: $i] :
( ( SY527 != SV74 )
| ( in @ SY527 @ SV243 ) )
| ~ ! [SY528: $i] :
( ( SY528 != SV196 )
| ( in @ SY528 @ SV243 ) ) ) )
= $true )
| ( ( SV243
= ( unordered_pair @ SV74 @ SV196 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1508]) ).
thf(1578,plain,
! [SV75: $i,SV197: $i,SV244: $i] :
( ( ( ~ ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV75 )
| ~ ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV197 ) )
= $true )
| ( ( ~ ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV244 ) )
= $true )
| ( ( SV244
= ( set_intersection2 @ SV75 @ SV197 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1509]) ).
thf(1579,plain,
! [SV75: $i,SV197: $i,SV244: $i] :
( ( ( ~ ( ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV75 )
| ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV244 ) )
| ~ ( ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV197 )
| ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV244 ) ) )
= $false )
| ( ( SV244
= ( set_intersection2 @ SV75 @ SV197 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1510]) ).
thf(1580,plain,
! [SV245: $i,SV198: $i,SV75: $i] :
( ( ( ! [SY529: $i] :
( ~ ( in @ SY529 @ SV75 )
| ~ ( in @ SY529 @ SV198 )
| ( in @ SY529 @ SV245 ) ) )
= $true )
| ( ( SV245
= ( set_intersection2 @ SV75 @ SV198 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1511]) ).
thf(1581,plain,
! [SV198: $i,SV75: $i,SV245: $i] :
( ( ( ~ ( ~ ! [SY530: $i] :
( ~ ( in @ SY530 @ SV245 )
| ( in @ SY530 @ SV75 ) )
| ~ ! [SY531: $i] :
( ~ ( in @ SY531 @ SV245 )
| ( in @ SY531 @ SV198 ) ) ) )
= $true )
| ( ( SV245
= ( set_intersection2 @ SV75 @ SV198 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1512]) ).
thf(1582,plain,
! [SV76: $i,SV251: $i] :
( ( ( ! [SY535: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SV251 @ SV76 ) @ SY535 ) @ SV76 )
| ~ ( in @ ( sK20_C @ SV251 @ SV76 ) @ SV251 ) )
= $true )
| ( ( SV251
= ( relation_dom @ SV76 ) )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1513]) ).
thf(1583,plain,
! [SV76: $i,SV251: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK20_C @ SV251 @ SV76 ) @ ( sK21_SY278 @ SV251 @ SV76 ) ) @ SV76 )
| ( in @ ( sK20_C @ SV251 @ SV76 ) @ SV251 ) )
= $true )
| ( ( SV251
= ( relation_dom @ SV76 ) )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1514]) ).
thf(1584,plain,
! [SV252: $i,SV76: $i] :
( ( ( ~ ! [SY536: $i] :
( ! [SY377: $i] :
~ ( in @ ( ordered_pair @ SY536 @ SY377 ) @ SV76 )
| ( in @ SY536 @ SV252 ) ) )
= $false )
| ( ( SV252
= ( relation_dom @ SV76 ) )
= $false )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1515]) ).
thf(1585,plain,
! [SV76: $i,SV252: $i] :
( ( ( ~ ! [SY538: $i] :
( ~ ( in @ SY538 @ SV252 )
| ( in @ ( ordered_pair @ SY538 @ ( sK19_D @ SY538 @ SV252 @ SV76 ) ) @ SV76 ) ) )
= $false )
| ( ( SV252
= ( relation_dom @ SV76 ) )
= $false )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1515]) ).
thf(1586,plain,
! [SV253: $i,SV292: $i] :
( ( ( element @ SV292 @ SV253 )
= $false )
| ( ( in @ SV292 @ SV253 )
= $true )
| ( ( empty @ SV253 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1516]) ).
thf(1587,plain,
! [SV254: $i,SV293: $i] :
( ( ( in @ SV293 @ SV254 )
= $false )
| ( ( element @ SV293 @ SV254 )
= $true )
| ( ( empty @ SV254 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1517]) ).
thf(1588,plain,
! [SV255: $i,SV299: $i] :
( ( ( ~ ( element @ SV299 @ SV255 ) )
= $true )
| ( ( empty @ SV299 )
= $true )
| ( ( empty @ SV255 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1518]) ).
thf(1589,plain,
! [SV256: $i,SV300: $i] :
( ( ( ~ ( empty @ SV300 ) )
= $true )
| ( ( element @ SV300 @ SV256 )
= $true )
| ( ( empty @ SV256 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1519]) ).
thf(1590,plain,
! [SV153: $i,SV199: $i] :
( ( ( in @ ( sK26_C @ SV199 @ SV153 ) @ SV199 )
= $false )
| ( ( ~ ( subset @ ( sK26_C @ SV199 @ SV153 ) @ SV153 ) )
= $true )
| ( ( SV199
= ( powerset @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1520]) ).
thf(1591,plain,
! [SV154: $i,SV200: $i,SV306: $i] :
( ( ( ~ ( in @ SV306 @ SV200 )
| ( subset @ SV306 @ SV154 ) )
= $true )
| ( ( SV200
= ( powerset @ SV154 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1522]) ).
thf(1592,plain,
! [SV200: $i,SV154: $i,SV307: $i] :
( ( ( ~ ( subset @ SV307 @ SV154 )
| ( in @ SV307 @ SV200 ) )
= $true )
| ( ( SV200
= ( powerset @ SV154 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1523]) ).
thf(1593,plain,
! [SV308: $i,SV157: $i,SV203: $i] :
( ( ( ~ ( in @ ( sK17_C @ SV203 @ SV157 ) @ SV308 )
| ~ ( in @ SV308 @ SV157 ) )
= $true )
| ( ( ~ ( in @ ( sK17_C @ SV203 @ SV157 ) @ SV203 ) )
= $true )
| ( ( SV203
= ( union @ SV157 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1524]) ).
thf(1594,plain,
! [SV157: $i,SV203: $i] :
( ( ( ~ ( in @ ( sK17_C @ SV203 @ SV157 ) @ ( sK18_SY276 @ SV203 @ SV157 ) )
| ~ ( in @ ( sK18_SY276 @ SV203 @ SV157 ) @ SV157 ) )
= $false )
| ( ( in @ ( sK17_C @ SV203 @ SV157 ) @ SV203 )
= $true )
| ( ( SV203
= ( union @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1525]) ).
thf(1595,plain,
! [SV204: $i,SV158: $i,SV309: $i] :
( ( ( ! [SY575: $i] :
( ~ ( in @ SV309 @ SY575 )
| ~ ( in @ SY575 @ SV158 ) )
| ( in @ SV309 @ SV204 ) )
= $true )
| ( ( SV204
= ( union @ SV158 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1526]) ).
thf(1596,plain,
! [SV158: $i,SV204: $i,SV310: $i] :
( ( ( ~ ( in @ SV310 @ SV204 )
| ~ ( ~ ( in @ SV310 @ ( sK16_D @ SV310 @ SV204 @ SV158 ) )
| ~ ( in @ ( sK16_D @ SV310 @ SV204 @ SV158 ) @ SV158 ) ) )
= $true )
| ( ( SV204
= ( union @ SV158 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1527]) ).
thf(1597,plain,
! [SV259: $i,SV206: $i,SV162: $i] :
( ( ( disjoint @ SV162 @ SV206 )
= $false )
| ( ( in @ SV259 @ SV162 )
= $false )
| ( ( in @ SV259 @ SV206 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1528]) ).
thf(1598,plain,
! [SV260: $i,SV78: $i] :
( ( ( subset @ SV78 @ SV260 )
= $false )
| ( ( subset @ ( relation_dom @ SV78 ) @ ( relation_dom @ SV260 ) )
= $true )
| ( ( relation @ SV260 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1529]) ).
thf(1599,plain,
! [SV261: $i,SV78: $i] :
( ( ( subset @ SV78 @ SV261 )
= $false )
| ( ( subset @ ( relation_rng @ SV78 ) @ ( relation_rng @ SV261 ) )
= $true )
| ( ( relation @ SV261 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1530]) ).
thf(1600,plain,
! [SV79: $i,SV311: $i] :
( ( ! [SY576: $i] :
( ~ ( in @ SV311 @ ( sK35_B @ SV79 ) )
| ~ ( subset @ SY576 @ SV311 )
| ( in @ SY576 @ ( sK35_B @ SV79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1532]) ).
thf(1601,plain,
! [SV81: $i,SV215: $i,SV246: $i] :
( ( ( ~ ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV81 )
| ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV215 ) )
= $true )
| ( ( ~ ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV246 ) )
= $true )
| ( ( SV246
= ( set_difference @ SV81 @ SV215 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1536]) ).
thf(1602,plain,
! [SV81: $i,SV215: $i,SV246: $i] :
( ( ( ~ ( ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV81 )
| ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV246 ) )
| ~ ( ~ ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV215 )
| ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV246 ) ) )
= $false )
| ( ( SV246
= ( set_difference @ SV81 @ SV215 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1537]) ).
thf(1603,plain,
! [SV247: $i,SV216: $i,SV81: $i] :
( ( ( ! [SY532: $i] :
( ~ ( in @ SY532 @ SV81 )
| ( in @ SY532 @ SV216 )
| ( in @ SY532 @ SV247 ) ) )
= $true )
| ( ( SV247
= ( set_difference @ SV81 @ SV216 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1538]) ).
thf(1604,plain,
! [SV216: $i,SV81: $i,SV247: $i] :
( ( ( ~ ( ~ ! [SY533: $i] :
( ~ ( in @ SY533 @ SV247 )
| ( in @ SY533 @ SV81 ) )
| ~ ! [SY534: $i] :
( ~ ( in @ SY534 @ SV247 )
| ~ ( in @ SY534 @ SV216 ) ) ) )
= $true )
| ( ( SV247
= ( set_difference @ SV81 @ SV216 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1539]) ).
thf(1605,plain,
! [SV82: $i,SV264: $i] :
( ( ( ! [SY545: $i] :
~ ( in @ ( ordered_pair @ SY545 @ ( sK13_C @ SV264 @ SV82 ) ) @ SV82 )
| ~ ( in @ ( sK13_C @ SV264 @ SV82 ) @ SV264 ) )
= $true )
| ( ( SV264
= ( relation_rng @ SV82 ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1540]) ).
thf(1606,plain,
! [SV82: $i,SV264: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK14_SY274 @ SV264 @ SV82 ) @ ( sK13_C @ SV264 @ SV82 ) ) @ SV82 )
| ( in @ ( sK13_C @ SV264 @ SV82 ) @ SV264 ) )
= $true )
| ( ( SV264
= ( relation_rng @ SV82 ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1541]) ).
thf(1607,plain,
! [SV265: $i,SV82: $i] :
( ( ( ~ ! [SY546: $i] :
( ! [SY397: $i] :
~ ( in @ ( ordered_pair @ SY397 @ SY546 ) @ SV82 )
| ( in @ SY546 @ SV265 ) ) )
= $false )
| ( ( SV265
= ( relation_rng @ SV82 ) )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1542]) ).
thf(1608,plain,
! [SV82: $i,SV265: $i] :
( ( ( ~ ! [SY548: $i] :
( ~ ( in @ SY548 @ SV265 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY548 @ SV265 @ SV82 ) @ SY548 ) @ SV82 ) ) )
= $false )
| ( ( SV265
= ( relation_rng @ SV82 ) )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1542]) ).
thf(1609,plain,
! [SV266: $i,SV294: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK40_SY287 @ SV294 @ SV266 ) @ SV266 )
| ~ ~ ( in @ ( sK39_C @ SV294 @ SV266 ) @ ( sK40_SY287 @ SV294 @ SV266 ) ) )
| ~ ( in @ ( sK39_C @ SV294 @ SV266 ) @ SV294 ) )
| ~ ( ! [SY570: $i] :
( ~ ( in @ SY570 @ SV266 )
| ( in @ ( sK39_C @ SV294 @ SV266 ) @ SY570 ) )
| ( in @ ( sK39_C @ SV294 @ SV266 ) @ SV294 ) ) )
= $false )
| ( ( SV294
= ( set_meet @ SV266 ) )
= $true )
| ( ( SV266 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1543]) ).
thf(1610,plain,
! [SV267: $i,SV295: $i] :
( ( ( SV295
= ( set_meet @ SV267 ) )
= $false )
| ( ( ~ ( ~ ! [SY571: $i] :
( ~ ( ~ ( in @ ( sK38_D @ SY571 @ SV295 @ SV267 ) @ SV267 )
| ~ ~ ( in @ SY571 @ ( sK38_D @ SY571 @ SV295 @ SV267 ) ) )
| ( in @ SY571 @ SV295 ) )
| ~ ! [SY572: $i] :
( ~ ( in @ SY572 @ SV295 )
| ! [SY554: $i] :
( ~ ( in @ SY554 @ SV267 )
| ( in @ SY572 @ SY554 ) ) ) ) )
= $true )
| ( ( SV267 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1544]) ).
thf(1611,plain,
! [SV268: $i,SV301: $i] :
( ( ( ( SV301
!= ( set_meet @ SV268 ) ) )
= $true )
| ( ( SV301 = empty_set )
= $true )
| ( ( SV268 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1545]) ).
thf(1612,plain,
! [SV269: $i,SV302: $i] :
( ( ( ( SV302 != empty_set ) )
= $true )
| ( ( SV302
= ( set_meet @ SV269 ) )
= $true )
| ( ( SV269 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1546]) ).
thf(1613,plain,
! [SV282: $i,SV270: $i] :
( ( ( SV270 = SV282 )
= $false )
| ( ( proper_subset @ SV270 @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1547]) ).
thf(1614,plain,
! [SV84: $i,SV272: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SV272 @ SV84 ) @ ( sK11_SY272 @ SV272 @ SV84 ) ) @ SV272 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY272 @ SV272 @ SV84 ) @ ( sK10_C @ SV272 @ SV84 ) ) @ SV84 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK10_C @ SV272 @ SV84 ) @ ( sK11_SY272 @ SV272 @ SV84 ) ) @ SV272 )
| ( in @ ( ordered_pair @ ( sK11_SY272 @ SV272 @ SV84 ) @ ( sK10_C @ SV272 @ SV84 ) ) @ SV84 ) ) )
= $false )
| ( ( SV272
= ( relation_inverse @ SV84 ) )
= $true )
| ( ( relation @ SV272 )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1549]) ).
thf(1615,plain,
! [SV84: $i,SV273: $i] :
( ( ( SV273
= ( relation_inverse @ SV84 ) )
= $false )
| ( ( ~ ( ~ ! [SY559: $i,SY560: $i] :
( ~ ( in @ ( ordered_pair @ SY559 @ SY560 ) @ SV273 )
| ( in @ ( ordered_pair @ SY560 @ SY559 ) @ SV84 ) )
| ~ ! [SY561: $i,SY562: $i] :
( ~ ( in @ ( ordered_pair @ SY562 @ SY561 ) @ SV84 )
| ( in @ ( ordered_pair @ SY561 @ SY562 ) @ SV273 ) ) ) )
= $true )
| ( ( relation @ SV273 )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1550]) ).
thf(1616,plain,
! [SV85: $i,SV284: $i] :
( ( ( ~ ! [SY567: $i] :
( ~ ( subset @ SY567 @ SV284 )
| ( in @ SY567 @ ( sK2_SY267 @ SV284 @ SV85 ) ) ) )
= $false )
| ( ( ~ ( in @ SV284 @ ( sK1_B @ SV85 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1551]) ).
thf(1617,plain,
! [SV85: $i,SV284: $i] :
( ( ( ~ ( in @ ( sK2_SY267 @ SV284 @ SV85 ) @ ( sK1_B @ SV85 ) ) )
= $false )
| ( ( ~ ( in @ SV284 @ ( sK1_B @ SV85 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1551]) ).
thf(1618,plain,
! [SV85: $i,SV312: $i] :
( ( ! [SY577: $i] :
( ~ ( in @ SV312 @ ( sK1_B @ SV85 ) )
| ~ ( subset @ SY577 @ SV312 )
| ( in @ SY577 @ ( sK1_B @ SV85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1552]) ).
thf(1619,plain,
! [SV303: $i,SV296: $i,SV173: $i] :
( ( ( ( sK30_B @ SV173 )
= ( ordered_pair @ SV296 @ SV303 ) )
= $false )
| ( ( relation @ SV173 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1554]) ).
thf(1620,plain,
! [SV297: $i,SV289: $i,SV88: $i] :
( ( ( subset @ ( unordered_pair @ SV88 @ SV289 ) @ SV297 )
= $false )
| ( ( in @ SV88 @ SV297 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1560]) ).
thf(1621,plain,
! [SV298: $i,SV290: $i,SV88: $i] :
( ( ( subset @ ( unordered_pair @ SV88 @ SV290 ) @ SV298 )
= $false )
| ( ( in @ SV290 @ SV298 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1561]) ).
thf(1622,plain,
! [SV187: $i,SV236: $i] :
( ( ( ( sK27_C @ SV236 @ SV187 )
= SV187 )
= $false )
| ( ( ~ ( in @ ( sK27_C @ SV236 @ SV187 ) @ SV236 ) )
= $true )
| ( ( SV236
= ( singleton @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1564]) ).
thf(1623,plain,
! [SV237: $i,SV188: $i,SV313: $i] :
( ( ( ( SV313 != SV188 )
| ( in @ SV313 @ SV237 ) )
= $true )
| ( ( SV237
= ( singleton @ SV188 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1566]) ).
thf(1624,plain,
! [SV188: $i,SV237: $i,SV314: $i] :
( ( ( ~ ( in @ SV314 @ SV237 )
| ( SV314 = SV188 ) )
= $true )
| ( ( SV237
= ( singleton @ SV188 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1567]) ).
thf(1625,plain,
! [SV73: $i,SV193: $i,SV240: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV240 )
| ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV73 ) ) )
= $false )
| ( ( SV240
= ( set_union2 @ SV73 @ SV193 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1570]) ).
thf(1626,plain,
! [SV73: $i,SV193: $i,SV240: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV240 )
| ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV193 ) ) )
= $false )
| ( ( SV240
= ( set_union2 @ SV73 @ SV193 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1570]) ).
thf(1627,plain,
! [SV73: $i,SV193: $i,SV240: $i] :
( ( ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV73 )
= $true )
| ( ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV193 )
= $true )
| ( ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV240 )
= $true )
| ( ( SV240
= ( set_union2 @ SV73 @ SV193 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1571]) ).
thf(1628,plain,
! [SV194: $i,SV73: $i,SV241: $i,SV315: $i] :
( ( ( ~ ( in @ SV315 @ SV241 )
| ( in @ SV315 @ SV73 )
| ( in @ SV315 @ SV194 ) )
= $true )
| ( ( SV241
= ( set_union2 @ SV73 @ SV194 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1572]) ).
thf(1629,plain,
! [SV194: $i,SV241: $i,SV73: $i] :
( ( ( ~ ! [SY524: $i] :
( ~ ( in @ SY524 @ SV73 )
| ( in @ SY524 @ SV241 ) )
| ~ ! [SY525: $i] :
( ~ ( in @ SY525 @ SV194 )
| ( in @ SY525 @ SV241 ) ) )
= $false )
| ( ( SV241
= ( set_union2 @ SV73 @ SV194 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1573]) ).
thf(1630,plain,
! [SV74: $i,SV195: $i,SV242: $i] :
( ( ( ~ ( ~ ( in @ ( sK25_D @ SV242 @ SV195 @ SV74 ) @ SV242 )
| ( ( sK25_D @ SV242 @ SV195 @ SV74 )
!= SV74 ) ) )
= $false )
| ( ( SV242
= ( unordered_pair @ SV74 @ SV195 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1574]) ).
thf(1631,plain,
! [SV74: $i,SV195: $i,SV242: $i] :
( ( ( ~ ( ~ ( in @ ( sK25_D @ SV242 @ SV195 @ SV74 ) @ SV242 )
| ( ( sK25_D @ SV242 @ SV195 @ SV74 )
!= SV195 ) ) )
= $false )
| ( ( SV242
= ( unordered_pair @ SV74 @ SV195 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1574]) ).
thf(1632,plain,
! [SV74: $i,SV195: $i,SV242: $i] :
( ( ( ( sK25_D @ SV242 @ SV195 @ SV74 )
= SV74 )
= $true )
| ( ( ( sK25_D @ SV242 @ SV195 @ SV74 )
= SV195 )
= $true )
| ( ( in @ ( sK25_D @ SV242 @ SV195 @ SV74 ) @ SV242 )
= $true )
| ( ( SV242
= ( unordered_pair @ SV74 @ SV195 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1575]) ).
thf(1633,plain,
! [SV196: $i,SV74: $i,SV243: $i,SV316: $i] :
( ( ( ~ ( in @ SV316 @ SV243 )
| ( SV316 = SV74 )
| ( SV316 = SV196 ) )
= $true )
| ( ( SV243
= ( unordered_pair @ SV74 @ SV196 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1576]) ).
thf(1634,plain,
! [SV196: $i,SV243: $i,SV74: $i] :
( ( ( ~ ! [SY527: $i] :
( ( SY527 != SV74 )
| ( in @ SY527 @ SV243 ) )
| ~ ! [SY528: $i] :
( ( SY528 != SV196 )
| ( in @ SY528 @ SV243 ) ) )
= $false )
| ( ( SV243
= ( unordered_pair @ SV74 @ SV196 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1577]) ).
thf(1635,plain,
! [SV75: $i,SV197: $i,SV244: $i] :
( ( ( ~ ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV75 ) )
= $true )
| ( ( ~ ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV197 ) )
= $true )
| ( ( ~ ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV244 ) )
= $true )
| ( ( SV244
= ( set_intersection2 @ SV75 @ SV197 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1578]) ).
thf(1636,plain,
! [SV75: $i,SV197: $i,SV244: $i] :
( ( ( ~ ( ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV75 )
| ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV244 ) ) )
= $false )
| ( ( SV244
= ( set_intersection2 @ SV75 @ SV197 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1579]) ).
thf(1637,plain,
! [SV75: $i,SV197: $i,SV244: $i] :
( ( ( ~ ( ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV197 )
| ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV244 ) ) )
= $false )
| ( ( SV244
= ( set_intersection2 @ SV75 @ SV197 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1579]) ).
thf(1638,plain,
! [SV245: $i,SV198: $i,SV75: $i,SV317: $i] :
( ( ( ~ ( in @ SV317 @ SV75 )
| ~ ( in @ SV317 @ SV198 )
| ( in @ SV317 @ SV245 ) )
= $true )
| ( ( SV245
= ( set_intersection2 @ SV75 @ SV198 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1580]) ).
thf(1639,plain,
! [SV198: $i,SV75: $i,SV245: $i] :
( ( ( ~ ! [SY530: $i] :
( ~ ( in @ SY530 @ SV245 )
| ( in @ SY530 @ SV75 ) )
| ~ ! [SY531: $i] :
( ~ ( in @ SY531 @ SV245 )
| ( in @ SY531 @ SV198 ) ) )
= $false )
| ( ( SV245
= ( set_intersection2 @ SV75 @ SV198 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1581]) ).
thf(1640,plain,
! [SV76: $i,SV251: $i] :
( ( ( ! [SY535: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SV251 @ SV76 ) @ SY535 ) @ SV76 ) )
= $true )
| ( ( ~ ( in @ ( sK20_C @ SV251 @ SV76 ) @ SV251 ) )
= $true )
| ( ( SV251
= ( relation_dom @ SV76 ) )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1582]) ).
thf(1641,plain,
! [SV76: $i,SV251: $i] :
( ( ( in @ ( ordered_pair @ ( sK20_C @ SV251 @ SV76 ) @ ( sK21_SY278 @ SV251 @ SV76 ) ) @ SV76 )
= $true )
| ( ( in @ ( sK20_C @ SV251 @ SV76 ) @ SV251 )
= $true )
| ( ( SV251
= ( relation_dom @ SV76 ) )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1583]) ).
thf(1642,plain,
! [SV252: $i,SV76: $i] :
( ( ( ! [SY536: $i] :
( ! [SY377: $i] :
~ ( in @ ( ordered_pair @ SY536 @ SY377 ) @ SV76 )
| ( in @ SY536 @ SV252 ) ) )
= $true )
| ( ( SV252
= ( relation_dom @ SV76 ) )
= $false )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1584]) ).
thf(1643,plain,
! [SV76: $i,SV252: $i] :
( ( ( ! [SY538: $i] :
( ~ ( in @ SY538 @ SV252 )
| ( in @ ( ordered_pair @ SY538 @ ( sK19_D @ SY538 @ SV252 @ SV76 ) ) @ SV76 ) ) )
= $true )
| ( ( SV252
= ( relation_dom @ SV76 ) )
= $false )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1585]) ).
thf(1644,plain,
! [SV255: $i,SV299: $i] :
( ( ( element @ SV299 @ SV255 )
= $false )
| ( ( empty @ SV299 )
= $true )
| ( ( empty @ SV255 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1588]) ).
thf(1645,plain,
! [SV256: $i,SV300: $i] :
( ( ( empty @ SV300 )
= $false )
| ( ( element @ SV300 @ SV256 )
= $true )
| ( ( empty @ SV256 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1589]) ).
thf(1646,plain,
! [SV153: $i,SV199: $i] :
( ( ( subset @ ( sK26_C @ SV199 @ SV153 ) @ SV153 )
= $false )
| ( ( in @ ( sK26_C @ SV199 @ SV153 ) @ SV199 )
= $false )
| ( ( SV199
= ( powerset @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1590]) ).
thf(1647,plain,
! [SV154: $i,SV200: $i,SV306: $i] :
( ( ( ~ ( in @ SV306 @ SV200 ) )
= $true )
| ( ( subset @ SV306 @ SV154 )
= $true )
| ( ( SV200
= ( powerset @ SV154 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1591]) ).
thf(1648,plain,
! [SV200: $i,SV154: $i,SV307: $i] :
( ( ( ~ ( subset @ SV307 @ SV154 ) )
= $true )
| ( ( in @ SV307 @ SV200 )
= $true )
| ( ( SV200
= ( powerset @ SV154 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1592]) ).
thf(1649,plain,
! [SV308: $i,SV157: $i,SV203: $i] :
( ( ( ~ ( in @ ( sK17_C @ SV203 @ SV157 ) @ SV308 ) )
= $true )
| ( ( ~ ( in @ SV308 @ SV157 ) )
= $true )
| ( ( ~ ( in @ ( sK17_C @ SV203 @ SV157 ) @ SV203 ) )
= $true )
| ( ( SV203
= ( union @ SV157 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1593]) ).
thf(1650,plain,
! [SV157: $i,SV203: $i] :
( ( ( ~ ( in @ ( sK17_C @ SV203 @ SV157 ) @ ( sK18_SY276 @ SV203 @ SV157 ) ) )
= $false )
| ( ( in @ ( sK17_C @ SV203 @ SV157 ) @ SV203 )
= $true )
| ( ( SV203
= ( union @ SV157 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1594]) ).
thf(1651,plain,
! [SV157: $i,SV203: $i] :
( ( ( ~ ( in @ ( sK18_SY276 @ SV203 @ SV157 ) @ SV157 ) )
= $false )
| ( ( in @ ( sK17_C @ SV203 @ SV157 ) @ SV203 )
= $true )
| ( ( SV203
= ( union @ SV157 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1594]) ).
thf(1652,plain,
! [SV204: $i,SV158: $i,SV309: $i] :
( ( ( ! [SY575: $i] :
( ~ ( in @ SV309 @ SY575 )
| ~ ( in @ SY575 @ SV158 ) ) )
= $true )
| ( ( in @ SV309 @ SV204 )
= $true )
| ( ( SV204
= ( union @ SV158 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1595]) ).
thf(1653,plain,
! [SV158: $i,SV204: $i,SV310: $i] :
( ( ( ~ ( in @ SV310 @ SV204 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV310 @ ( sK16_D @ SV310 @ SV204 @ SV158 ) )
| ~ ( in @ ( sK16_D @ SV310 @ SV204 @ SV158 ) @ SV158 ) ) )
= $true )
| ( ( SV204
= ( union @ SV158 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1596]) ).
thf(1654,plain,
! [SV318: $i,SV79: $i,SV311: $i] :
( ( ~ ( in @ SV311 @ ( sK35_B @ SV79 ) )
| ~ ( subset @ SV318 @ SV311 )
| ( in @ SV318 @ ( sK35_B @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1600]) ).
thf(1655,plain,
! [SV81: $i,SV215: $i,SV246: $i] :
( ( ( ~ ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV81 ) )
= $true )
| ( ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV215 )
= $true )
| ( ( ~ ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV246 ) )
= $true )
| ( ( SV246
= ( set_difference @ SV81 @ SV215 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1601]) ).
thf(1656,plain,
! [SV81: $i,SV215: $i,SV246: $i] :
( ( ( ~ ( ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV81 )
| ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV246 ) ) )
= $false )
| ( ( SV246
= ( set_difference @ SV81 @ SV215 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1602]) ).
thf(1657,plain,
! [SV81: $i,SV215: $i,SV246: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV215 )
| ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV246 ) ) )
= $false )
| ( ( SV246
= ( set_difference @ SV81 @ SV215 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1602]) ).
thf(1658,plain,
! [SV247: $i,SV216: $i,SV81: $i,SV319: $i] :
( ( ( ~ ( in @ SV319 @ SV81 )
| ( in @ SV319 @ SV216 )
| ( in @ SV319 @ SV247 ) )
= $true )
| ( ( SV247
= ( set_difference @ SV81 @ SV216 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1603]) ).
thf(1659,plain,
! [SV216: $i,SV81: $i,SV247: $i] :
( ( ( ~ ! [SY533: $i] :
( ~ ( in @ SY533 @ SV247 )
| ( in @ SY533 @ SV81 ) )
| ~ ! [SY534: $i] :
( ~ ( in @ SY534 @ SV247 )
| ~ ( in @ SY534 @ SV216 ) ) )
= $false )
| ( ( SV247
= ( set_difference @ SV81 @ SV216 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1604]) ).
thf(1660,plain,
! [SV82: $i,SV264: $i] :
( ( ( ! [SY545: $i] :
~ ( in @ ( ordered_pair @ SY545 @ ( sK13_C @ SV264 @ SV82 ) ) @ SV82 ) )
= $true )
| ( ( ~ ( in @ ( sK13_C @ SV264 @ SV82 ) @ SV264 ) )
= $true )
| ( ( SV264
= ( relation_rng @ SV82 ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1605]) ).
thf(1661,plain,
! [SV82: $i,SV264: $i] :
( ( ( in @ ( ordered_pair @ ( sK14_SY274 @ SV264 @ SV82 ) @ ( sK13_C @ SV264 @ SV82 ) ) @ SV82 )
= $true )
| ( ( in @ ( sK13_C @ SV264 @ SV82 ) @ SV264 )
= $true )
| ( ( SV264
= ( relation_rng @ SV82 ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1606]) ).
thf(1662,plain,
! [SV265: $i,SV82: $i] :
( ( ( ! [SY546: $i] :
( ! [SY397: $i] :
~ ( in @ ( ordered_pair @ SY397 @ SY546 ) @ SV82 )
| ( in @ SY546 @ SV265 ) ) )
= $true )
| ( ( SV265
= ( relation_rng @ SV82 ) )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1607]) ).
thf(1663,plain,
! [SV82: $i,SV265: $i] :
( ( ( ! [SY548: $i] :
( ~ ( in @ SY548 @ SV265 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY548 @ SV265 @ SV82 ) @ SY548 ) @ SV82 ) ) )
= $true )
| ( ( SV265
= ( relation_rng @ SV82 ) )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1608]) ).
thf(1664,plain,
! [SV266: $i,SV294: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK40_SY287 @ SV294 @ SV266 ) @ SV266 )
| ~ ~ ( in @ ( sK39_C @ SV294 @ SV266 ) @ ( sK40_SY287 @ SV294 @ SV266 ) ) )
| ~ ( in @ ( sK39_C @ SV294 @ SV266 ) @ SV294 ) ) )
= $false )
| ( ( SV294
= ( set_meet @ SV266 ) )
= $true )
| ( ( SV266 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1609]) ).
thf(1665,plain,
! [SV294: $i,SV266: $i] :
( ( ( ~ ( ! [SY570: $i] :
( ~ ( in @ SY570 @ SV266 )
| ( in @ ( sK39_C @ SV294 @ SV266 ) @ SY570 ) )
| ( in @ ( sK39_C @ SV294 @ SV266 ) @ SV294 ) ) )
= $false )
| ( ( SV294
= ( set_meet @ SV266 ) )
= $true )
| ( ( SV266 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1609]) ).
thf(1666,plain,
! [SV267: $i,SV295: $i] :
( ( ( ~ ! [SY571: $i] :
( ~ ( ~ ( in @ ( sK38_D @ SY571 @ SV295 @ SV267 ) @ SV267 )
| ~ ~ ( in @ SY571 @ ( sK38_D @ SY571 @ SV295 @ SV267 ) ) )
| ( in @ SY571 @ SV295 ) )
| ~ ! [SY572: $i] :
( ~ ( in @ SY572 @ SV295 )
| ! [SY554: $i] :
( ~ ( in @ SY554 @ SV267 )
| ( in @ SY572 @ SY554 ) ) ) )
= $false )
| ( ( SV295
= ( set_meet @ SV267 ) )
= $false )
| ( ( SV267 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1610]) ).
thf(1667,plain,
! [SV268: $i,SV301: $i] :
( ( ( SV301
= ( set_meet @ SV268 ) )
= $false )
| ( ( SV301 = empty_set )
= $true )
| ( ( SV268 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1611]) ).
thf(1668,plain,
! [SV269: $i,SV302: $i] :
( ( ( SV302 = empty_set )
= $false )
| ( ( SV302
= ( set_meet @ SV269 ) )
= $true )
| ( ( SV269 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1612]) ).
thf(1669,plain,
! [SV84: $i,SV272: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SV272 @ SV84 ) @ ( sK11_SY272 @ SV272 @ SV84 ) ) @ SV272 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY272 @ SV272 @ SV84 ) @ ( sK10_C @ SV272 @ SV84 ) ) @ SV84 ) ) )
= $false )
| ( ( SV272
= ( relation_inverse @ SV84 ) )
= $true )
| ( ( relation @ SV272 )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1614]) ).
thf(1670,plain,
! [SV84: $i,SV272: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK10_C @ SV272 @ SV84 ) @ ( sK11_SY272 @ SV272 @ SV84 ) ) @ SV272 )
| ( in @ ( ordered_pair @ ( sK11_SY272 @ SV272 @ SV84 ) @ ( sK10_C @ SV272 @ SV84 ) ) @ SV84 ) ) )
= $false )
| ( ( SV272
= ( relation_inverse @ SV84 ) )
= $true )
| ( ( relation @ SV272 )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1614]) ).
thf(1671,plain,
! [SV84: $i,SV273: $i] :
( ( ( ~ ! [SY559: $i,SY560: $i] :
( ~ ( in @ ( ordered_pair @ SY559 @ SY560 ) @ SV273 )
| ( in @ ( ordered_pair @ SY560 @ SY559 ) @ SV84 ) )
| ~ ! [SY561: $i,SY562: $i] :
( ~ ( in @ ( ordered_pair @ SY562 @ SY561 ) @ SV84 )
| ( in @ ( ordered_pair @ SY561 @ SY562 ) @ SV273 ) ) )
= $false )
| ( ( SV273
= ( relation_inverse @ SV84 ) )
= $false )
| ( ( relation @ SV273 )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1615]) ).
thf(1672,plain,
! [SV85: $i,SV284: $i] :
( ( ( ! [SY567: $i] :
( ~ ( subset @ SY567 @ SV284 )
| ( in @ SY567 @ ( sK2_SY267 @ SV284 @ SV85 ) ) ) )
= $true )
| ( ( ~ ( in @ SV284 @ ( sK1_B @ SV85 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1616]) ).
thf(1673,plain,
! [SV85: $i,SV284: $i] :
( ( ( in @ ( sK2_SY267 @ SV284 @ SV85 ) @ ( sK1_B @ SV85 ) )
= $true )
| ( ( ~ ( in @ SV284 @ ( sK1_B @ SV85 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1617]) ).
thf(1674,plain,
! [SV320: $i,SV85: $i,SV312: $i] :
( ( ~ ( in @ SV312 @ ( sK1_B @ SV85 ) )
| ~ ( subset @ SV320 @ SV312 )
| ( in @ SV320 @ ( sK1_B @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1618]) ).
thf(1675,plain,
! [SV187: $i,SV236: $i] :
( ( ( in @ ( sK27_C @ SV236 @ SV187 ) @ SV236 )
= $false )
| ( ( ( sK27_C @ SV236 @ SV187 )
= SV187 )
= $false )
| ( ( SV236
= ( singleton @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1622]) ).
thf(1676,plain,
! [SV237: $i,SV188: $i,SV313: $i] :
( ( ( ( SV313 != SV188 ) )
= $true )
| ( ( in @ SV313 @ SV237 )
= $true )
| ( ( SV237
= ( singleton @ SV188 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1623]) ).
thf(1677,plain,
! [SV188: $i,SV237: $i,SV314: $i] :
( ( ( ~ ( in @ SV314 @ SV237 ) )
= $true )
| ( ( SV314 = SV188 )
= $true )
| ( ( SV237
= ( singleton @ SV188 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1624]) ).
thf(1678,plain,
! [SV73: $i,SV193: $i,SV240: $i] :
( ( ( ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV240 )
| ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV73 ) )
= $true )
| ( ( SV240
= ( set_union2 @ SV73 @ SV193 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1625]) ).
thf(1679,plain,
! [SV73: $i,SV193: $i,SV240: $i] :
( ( ( ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV240 )
| ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV193 ) )
= $true )
| ( ( SV240
= ( set_union2 @ SV73 @ SV193 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1626]) ).
thf(1680,plain,
! [SV194: $i,SV73: $i,SV241: $i,SV315: $i] :
( ( ( ~ ( in @ SV315 @ SV241 ) )
= $true )
| ( ( ( in @ SV315 @ SV73 )
| ( in @ SV315 @ SV194 ) )
= $true )
| ( ( SV241
= ( set_union2 @ SV73 @ SV194 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1628]) ).
thf(1681,plain,
! [SV194: $i,SV241: $i,SV73: $i] :
( ( ( ~ ! [SY524: $i] :
( ~ ( in @ SY524 @ SV73 )
| ( in @ SY524 @ SV241 ) ) )
= $false )
| ( ( SV241
= ( set_union2 @ SV73 @ SV194 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1629]) ).
thf(1682,plain,
! [SV73: $i,SV241: $i,SV194: $i] :
( ( ( ~ ! [SY525: $i] :
( ~ ( in @ SY525 @ SV194 )
| ( in @ SY525 @ SV241 ) ) )
= $false )
| ( ( SV241
= ( set_union2 @ SV73 @ SV194 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1629]) ).
thf(1683,plain,
! [SV74: $i,SV195: $i,SV242: $i] :
( ( ( ~ ( in @ ( sK25_D @ SV242 @ SV195 @ SV74 ) @ SV242 )
| ( ( sK25_D @ SV242 @ SV195 @ SV74 )
!= SV74 ) )
= $true )
| ( ( SV242
= ( unordered_pair @ SV74 @ SV195 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1630]) ).
thf(1684,plain,
! [SV74: $i,SV195: $i,SV242: $i] :
( ( ( ~ ( in @ ( sK25_D @ SV242 @ SV195 @ SV74 ) @ SV242 )
| ( ( sK25_D @ SV242 @ SV195 @ SV74 )
!= SV195 ) )
= $true )
| ( ( SV242
= ( unordered_pair @ SV74 @ SV195 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1631]) ).
thf(1685,plain,
! [SV196: $i,SV74: $i,SV243: $i,SV316: $i] :
( ( ( ~ ( in @ SV316 @ SV243 ) )
= $true )
| ( ( ( SV316 = SV74 )
| ( SV316 = SV196 ) )
= $true )
| ( ( SV243
= ( unordered_pair @ SV74 @ SV196 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1633]) ).
thf(1686,plain,
! [SV196: $i,SV243: $i,SV74: $i] :
( ( ( ~ ! [SY527: $i] :
( ( SY527 != SV74 )
| ( in @ SY527 @ SV243 ) ) )
= $false )
| ( ( SV243
= ( unordered_pair @ SV74 @ SV196 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1634]) ).
thf(1687,plain,
! [SV74: $i,SV243: $i,SV196: $i] :
( ( ( ~ ! [SY528: $i] :
( ( SY528 != SV196 )
| ( in @ SY528 @ SV243 ) ) )
= $false )
| ( ( SV243
= ( unordered_pair @ SV74 @ SV196 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1634]) ).
thf(1688,plain,
! [SV75: $i,SV197: $i,SV244: $i] :
( ( ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV75 )
= $false )
| ( ( ~ ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV197 ) )
= $true )
| ( ( ~ ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV244 ) )
= $true )
| ( ( SV244
= ( set_intersection2 @ SV75 @ SV197 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1635]) ).
thf(1689,plain,
! [SV75: $i,SV197: $i,SV244: $i] :
( ( ( ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV75 )
| ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV244 ) )
= $true )
| ( ( SV244
= ( set_intersection2 @ SV75 @ SV197 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1636]) ).
thf(1690,plain,
! [SV75: $i,SV197: $i,SV244: $i] :
( ( ( ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV197 )
| ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV244 ) )
= $true )
| ( ( SV244
= ( set_intersection2 @ SV75 @ SV197 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1637]) ).
thf(1691,plain,
! [SV245: $i,SV198: $i,SV75: $i,SV317: $i] :
( ( ( ~ ( in @ SV317 @ SV75 )
| ~ ( in @ SV317 @ SV198 ) )
= $true )
| ( ( in @ SV317 @ SV245 )
= $true )
| ( ( SV245
= ( set_intersection2 @ SV75 @ SV198 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1638]) ).
thf(1692,plain,
! [SV198: $i,SV75: $i,SV245: $i] :
( ( ( ~ ! [SY530: $i] :
( ~ ( in @ SY530 @ SV245 )
| ( in @ SY530 @ SV75 ) ) )
= $false )
| ( ( SV245
= ( set_intersection2 @ SV75 @ SV198 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1639]) ).
thf(1693,plain,
! [SV75: $i,SV198: $i,SV245: $i] :
( ( ( ~ ! [SY531: $i] :
( ~ ( in @ SY531 @ SV245 )
| ( in @ SY531 @ SV198 ) ) )
= $false )
| ( ( SV245
= ( set_intersection2 @ SV75 @ SV198 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1639]) ).
thf(1694,plain,
! [SV321: $i,SV76: $i,SV251: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK20_C @ SV251 @ SV76 ) @ SV321 ) @ SV76 ) )
= $true )
| ( ( ~ ( in @ ( sK20_C @ SV251 @ SV76 ) @ SV251 ) )
= $true )
| ( ( SV251
= ( relation_dom @ SV76 ) )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(1695,plain,
! [SV252: $i,SV76: $i,SV322: $i] :
( ( ( ! [SY578: $i] :
~ ( in @ ( ordered_pair @ SV322 @ SY578 ) @ SV76 )
| ( in @ SV322 @ SV252 ) )
= $true )
| ( ( SV252
= ( relation_dom @ SV76 ) )
= $false )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1642]) ).
thf(1696,plain,
! [SV76: $i,SV252: $i,SV323: $i] :
( ( ( ~ ( in @ SV323 @ SV252 )
| ( in @ ( ordered_pair @ SV323 @ ( sK19_D @ SV323 @ SV252 @ SV76 ) ) @ SV76 ) )
= $true )
| ( ( SV252
= ( relation_dom @ SV76 ) )
= $false )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1643]) ).
thf(1697,plain,
! [SV154: $i,SV200: $i,SV306: $i] :
( ( ( in @ SV306 @ SV200 )
= $false )
| ( ( subset @ SV306 @ SV154 )
= $true )
| ( ( SV200
= ( powerset @ SV154 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1647]) ).
thf(1698,plain,
! [SV200: $i,SV154: $i,SV307: $i] :
( ( ( subset @ SV307 @ SV154 )
= $false )
| ( ( in @ SV307 @ SV200 )
= $true )
| ( ( SV200
= ( powerset @ SV154 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1648]) ).
thf(1699,plain,
! [SV308: $i,SV157: $i,SV203: $i] :
( ( ( in @ ( sK17_C @ SV203 @ SV157 ) @ SV308 )
= $false )
| ( ( ~ ( in @ SV308 @ SV157 ) )
= $true )
| ( ( ~ ( in @ ( sK17_C @ SV203 @ SV157 ) @ SV203 ) )
= $true )
| ( ( SV203
= ( union @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1649]) ).
thf(1700,plain,
! [SV157: $i,SV203: $i] :
( ( ( in @ ( sK17_C @ SV203 @ SV157 ) @ ( sK18_SY276 @ SV203 @ SV157 ) )
= $true )
| ( ( in @ ( sK17_C @ SV203 @ SV157 ) @ SV203 )
= $true )
| ( ( SV203
= ( union @ SV157 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1650]) ).
thf(1701,plain,
! [SV157: $i,SV203: $i] :
( ( ( in @ ( sK18_SY276 @ SV203 @ SV157 ) @ SV157 )
= $true )
| ( ( in @ ( sK17_C @ SV203 @ SV157 ) @ SV203 )
= $true )
| ( ( SV203
= ( union @ SV157 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1651]) ).
thf(1702,plain,
! [SV204: $i,SV158: $i,SV324: $i,SV309: $i] :
( ( ( ~ ( in @ SV309 @ SV324 )
| ~ ( in @ SV324 @ SV158 ) )
= $true )
| ( ( in @ SV309 @ SV204 )
= $true )
| ( ( SV204
= ( union @ SV158 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1652]) ).
thf(1703,plain,
! [SV158: $i,SV204: $i,SV310: $i] :
( ( ( in @ SV310 @ SV204 )
= $false )
| ( ( ~ ( ~ ( in @ SV310 @ ( sK16_D @ SV310 @ SV204 @ SV158 ) )
| ~ ( in @ ( sK16_D @ SV310 @ SV204 @ SV158 ) @ SV158 ) ) )
= $true )
| ( ( SV204
= ( union @ SV158 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1653]) ).
thf(1704,plain,
! [SV318: $i,SV79: $i,SV311: $i] :
( ( ( ~ ( in @ SV311 @ ( sK35_B @ SV79 ) )
| ~ ( subset @ SV318 @ SV311 ) )
= $true )
| ( ( in @ SV318 @ ( sK35_B @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1654]) ).
thf(1705,plain,
! [SV81: $i,SV215: $i,SV246: $i] :
( ( ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV81 )
= $false )
| ( ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV215 )
= $true )
| ( ( ~ ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV246 ) )
= $true )
| ( ( SV246
= ( set_difference @ SV81 @ SV215 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1655]) ).
thf(1706,plain,
! [SV81: $i,SV215: $i,SV246: $i] :
( ( ( ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV81 )
| ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV246 ) )
= $true )
| ( ( SV246
= ( set_difference @ SV81 @ SV215 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1656]) ).
thf(1707,plain,
! [SV81: $i,SV215: $i,SV246: $i] :
( ( ( ~ ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV215 )
| ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV246 ) )
= $true )
| ( ( SV246
= ( set_difference @ SV81 @ SV215 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1657]) ).
thf(1708,plain,
! [SV247: $i,SV216: $i,SV81: $i,SV319: $i] :
( ( ( ~ ( in @ SV319 @ SV81 )
| ( in @ SV319 @ SV216 ) )
= $true )
| ( ( in @ SV319 @ SV247 )
= $true )
| ( ( SV247
= ( set_difference @ SV81 @ SV216 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1658]) ).
thf(1709,plain,
! [SV216: $i,SV81: $i,SV247: $i] :
( ( ( ~ ! [SY533: $i] :
( ~ ( in @ SY533 @ SV247 )
| ( in @ SY533 @ SV81 ) ) )
= $false )
| ( ( SV247
= ( set_difference @ SV81 @ SV216 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1659]) ).
thf(1710,plain,
! [SV81: $i,SV216: $i,SV247: $i] :
( ( ( ~ ! [SY534: $i] :
( ~ ( in @ SY534 @ SV247 )
| ~ ( in @ SY534 @ SV216 ) ) )
= $false )
| ( ( SV247
= ( set_difference @ SV81 @ SV216 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1659]) ).
thf(1711,plain,
! [SV82: $i,SV264: $i,SV325: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV325 @ ( sK13_C @ SV264 @ SV82 ) ) @ SV82 ) )
= $true )
| ( ( ~ ( in @ ( sK13_C @ SV264 @ SV82 ) @ SV264 ) )
= $true )
| ( ( SV264
= ( relation_rng @ SV82 ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1660]) ).
thf(1712,plain,
! [SV265: $i,SV82: $i,SV326: $i] :
( ( ( ! [SY579: $i] :
~ ( in @ ( ordered_pair @ SY579 @ SV326 ) @ SV82 )
| ( in @ SV326 @ SV265 ) )
= $true )
| ( ( SV265
= ( relation_rng @ SV82 ) )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1662]) ).
thf(1713,plain,
! [SV82: $i,SV265: $i,SV327: $i] :
( ( ( ~ ( in @ SV327 @ SV265 )
| ( in @ ( ordered_pair @ ( sK12_D @ SV327 @ SV265 @ SV82 ) @ SV327 ) @ SV82 ) )
= $true )
| ( ( SV265
= ( relation_rng @ SV82 ) )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1663]) ).
thf(1714,plain,
! [SV266: $i,SV294: $i] :
( ( ( ~ ( ~ ( in @ ( sK40_SY287 @ SV294 @ SV266 ) @ SV266 )
| ~ ~ ( in @ ( sK39_C @ SV294 @ SV266 ) @ ( sK40_SY287 @ SV294 @ SV266 ) ) )
| ~ ( in @ ( sK39_C @ SV294 @ SV266 ) @ SV294 ) )
= $true )
| ( ( SV294
= ( set_meet @ SV266 ) )
= $true )
| ( ( SV266 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1664]) ).
thf(1715,plain,
! [SV294: $i,SV266: $i] :
( ( ( ! [SY570: $i] :
( ~ ( in @ SY570 @ SV266 )
| ( in @ ( sK39_C @ SV294 @ SV266 ) @ SY570 ) )
| ( in @ ( sK39_C @ SV294 @ SV266 ) @ SV294 ) )
= $true )
| ( ( SV294
= ( set_meet @ SV266 ) )
= $true )
| ( ( SV266 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1665]) ).
thf(1716,plain,
! [SV267: $i,SV295: $i] :
( ( ( ~ ! [SY571: $i] :
( ~ ( ~ ( in @ ( sK38_D @ SY571 @ SV295 @ SV267 ) @ SV267 )
| ~ ~ ( in @ SY571 @ ( sK38_D @ SY571 @ SV295 @ SV267 ) ) )
| ( in @ SY571 @ SV295 ) ) )
= $false )
| ( ( SV295
= ( set_meet @ SV267 ) )
= $false )
| ( ( SV267 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1666]) ).
thf(1717,plain,
! [SV267: $i,SV295: $i] :
( ( ( ~ ! [SY572: $i] :
( ~ ( in @ SY572 @ SV295 )
| ! [SY554: $i] :
( ~ ( in @ SY554 @ SV267 )
| ( in @ SY572 @ SY554 ) ) ) )
= $false )
| ( ( SV295
= ( set_meet @ SV267 ) )
= $false )
| ( ( SV267 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1666]) ).
thf(1718,plain,
! [SV84: $i,SV272: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SV272 @ SV84 ) @ ( sK11_SY272 @ SV272 @ SV84 ) ) @ SV272 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY272 @ SV272 @ SV84 ) @ ( sK10_C @ SV272 @ SV84 ) ) @ SV84 ) )
= $true )
| ( ( SV272
= ( relation_inverse @ SV84 ) )
= $true )
| ( ( relation @ SV272 )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1669]) ).
thf(1719,plain,
! [SV84: $i,SV272: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK10_C @ SV272 @ SV84 ) @ ( sK11_SY272 @ SV272 @ SV84 ) ) @ SV272 )
| ( in @ ( ordered_pair @ ( sK11_SY272 @ SV272 @ SV84 ) @ ( sK10_C @ SV272 @ SV84 ) ) @ SV84 ) )
= $true )
| ( ( SV272
= ( relation_inverse @ SV84 ) )
= $true )
| ( ( relation @ SV272 )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1670]) ).
thf(1720,plain,
! [SV84: $i,SV273: $i] :
( ( ( ~ ! [SY559: $i,SY560: $i] :
( ~ ( in @ ( ordered_pair @ SY559 @ SY560 ) @ SV273 )
| ( in @ ( ordered_pair @ SY560 @ SY559 ) @ SV84 ) ) )
= $false )
| ( ( SV273
= ( relation_inverse @ SV84 ) )
= $false )
| ( ( relation @ SV273 )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1671]) ).
thf(1721,plain,
! [SV273: $i,SV84: $i] :
( ( ( ~ ! [SY561: $i,SY562: $i] :
( ~ ( in @ ( ordered_pair @ SY562 @ SY561 ) @ SV84 )
| ( in @ ( ordered_pair @ SY561 @ SY562 ) @ SV273 ) ) )
= $false )
| ( ( SV273
= ( relation_inverse @ SV84 ) )
= $false )
| ( ( relation @ SV273 )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1671]) ).
thf(1722,plain,
! [SV85: $i,SV284: $i,SV328: $i] :
( ( ( ~ ( subset @ SV328 @ SV284 )
| ( in @ SV328 @ ( sK2_SY267 @ SV284 @ SV85 ) ) )
= $true )
| ( ( ~ ( in @ SV284 @ ( sK1_B @ SV85 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1672]) ).
thf(1723,plain,
! [SV85: $i,SV284: $i] :
( ( ( in @ SV284 @ ( sK1_B @ SV85 ) )
= $false )
| ( ( in @ ( sK2_SY267 @ SV284 @ SV85 ) @ ( sK1_B @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1673]) ).
thf(1724,plain,
! [SV320: $i,SV85: $i,SV312: $i] :
( ( ( ~ ( in @ SV312 @ ( sK1_B @ SV85 ) )
| ~ ( subset @ SV320 @ SV312 ) )
= $true )
| ( ( in @ SV320 @ ( sK1_B @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1674]) ).
thf(1725,plain,
! [SV237: $i,SV188: $i,SV313: $i] :
( ( ( SV313 = SV188 )
= $false )
| ( ( in @ SV313 @ SV237 )
= $true )
| ( ( SV237
= ( singleton @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1676]) ).
thf(1726,plain,
! [SV188: $i,SV237: $i,SV314: $i] :
( ( ( in @ SV314 @ SV237 )
= $false )
| ( ( SV314 = SV188 )
= $true )
| ( ( SV237
= ( singleton @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1677]) ).
thf(1727,plain,
! [SV73: $i,SV193: $i,SV240: $i] :
( ( ( ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV240 ) )
= $true )
| ( ( ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV73 ) )
= $true )
| ( ( SV240
= ( set_union2 @ SV73 @ SV193 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1678]) ).
thf(1728,plain,
! [SV73: $i,SV193: $i,SV240: $i] :
( ( ( ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV240 ) )
= $true )
| ( ( ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV193 ) )
= $true )
| ( ( SV240
= ( set_union2 @ SV73 @ SV193 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1679]) ).
thf(1729,plain,
! [SV194: $i,SV73: $i,SV241: $i,SV315: $i] :
( ( ( in @ SV315 @ SV241 )
= $false )
| ( ( ( in @ SV315 @ SV73 )
| ( in @ SV315 @ SV194 ) )
= $true )
| ( ( SV241
= ( set_union2 @ SV73 @ SV194 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1680]) ).
thf(1730,plain,
! [SV194: $i,SV241: $i,SV73: $i] :
( ( ( ! [SY524: $i] :
( ~ ( in @ SY524 @ SV73 )
| ( in @ SY524 @ SV241 ) ) )
= $true )
| ( ( SV241
= ( set_union2 @ SV73 @ SV194 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1681]) ).
thf(1731,plain,
! [SV73: $i,SV241: $i,SV194: $i] :
( ( ( ! [SY525: $i] :
( ~ ( in @ SY525 @ SV194 )
| ( in @ SY525 @ SV241 ) ) )
= $true )
| ( ( SV241
= ( set_union2 @ SV73 @ SV194 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1682]) ).
thf(1732,plain,
! [SV74: $i,SV195: $i,SV242: $i] :
( ( ( ~ ( in @ ( sK25_D @ SV242 @ SV195 @ SV74 ) @ SV242 ) )
= $true )
| ( ( ( ( sK25_D @ SV242 @ SV195 @ SV74 )
!= SV74 ) )
= $true )
| ( ( SV242
= ( unordered_pair @ SV74 @ SV195 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1683]) ).
thf(1733,plain,
! [SV74: $i,SV195: $i,SV242: $i] :
( ( ( ~ ( in @ ( sK25_D @ SV242 @ SV195 @ SV74 ) @ SV242 ) )
= $true )
| ( ( ( ( sK25_D @ SV242 @ SV195 @ SV74 )
!= SV195 ) )
= $true )
| ( ( SV242
= ( unordered_pair @ SV74 @ SV195 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1684]) ).
thf(1734,plain,
! [SV196: $i,SV74: $i,SV243: $i,SV316: $i] :
( ( ( in @ SV316 @ SV243 )
= $false )
| ( ( ( SV316 = SV74 )
| ( SV316 = SV196 ) )
= $true )
| ( ( SV243
= ( unordered_pair @ SV74 @ SV196 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1685]) ).
thf(1735,plain,
! [SV196: $i,SV243: $i,SV74: $i] :
( ( ( ! [SY527: $i] :
( ( SY527 != SV74 )
| ( in @ SY527 @ SV243 ) ) )
= $true )
| ( ( SV243
= ( unordered_pair @ SV74 @ SV196 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1686]) ).
thf(1736,plain,
! [SV74: $i,SV243: $i,SV196: $i] :
( ( ( ! [SY528: $i] :
( ( SY528 != SV196 )
| ( in @ SY528 @ SV243 ) ) )
= $true )
| ( ( SV243
= ( unordered_pair @ SV74 @ SV196 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1687]) ).
thf(1737,plain,
! [SV75: $i,SV197: $i,SV244: $i] :
( ( ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV197 )
= $false )
| ( ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV75 )
= $false )
| ( ( ~ ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV244 ) )
= $true )
| ( ( SV244
= ( set_intersection2 @ SV75 @ SV197 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1688]) ).
thf(1738,plain,
! [SV75: $i,SV197: $i,SV244: $i] :
( ( ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV75 )
= $true )
| ( ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV244 )
= $true )
| ( ( SV244
= ( set_intersection2 @ SV75 @ SV197 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1689]) ).
thf(1739,plain,
! [SV75: $i,SV197: $i,SV244: $i] :
( ( ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV197 )
= $true )
| ( ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV244 )
= $true )
| ( ( SV244
= ( set_intersection2 @ SV75 @ SV197 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1690]) ).
thf(1740,plain,
! [SV245: $i,SV198: $i,SV75: $i,SV317: $i] :
( ( ( ~ ( in @ SV317 @ SV75 ) )
= $true )
| ( ( ~ ( in @ SV317 @ SV198 ) )
= $true )
| ( ( in @ SV317 @ SV245 )
= $true )
| ( ( SV245
= ( set_intersection2 @ SV75 @ SV198 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1691]) ).
thf(1741,plain,
! [SV198: $i,SV75: $i,SV245: $i] :
( ( ( ! [SY530: $i] :
( ~ ( in @ SY530 @ SV245 )
| ( in @ SY530 @ SV75 ) ) )
= $true )
| ( ( SV245
= ( set_intersection2 @ SV75 @ SV198 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1692]) ).
thf(1742,plain,
! [SV75: $i,SV198: $i,SV245: $i] :
( ( ( ! [SY531: $i] :
( ~ ( in @ SY531 @ SV245 )
| ( in @ SY531 @ SV198 ) ) )
= $true )
| ( ( SV245
= ( set_intersection2 @ SV75 @ SV198 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1693]) ).
thf(1743,plain,
! [SV321: $i,SV76: $i,SV251: $i] :
( ( ( in @ ( ordered_pair @ ( sK20_C @ SV251 @ SV76 ) @ SV321 ) @ SV76 )
= $false )
| ( ( ~ ( in @ ( sK20_C @ SV251 @ SV76 ) @ SV251 ) )
= $true )
| ( ( SV251
= ( relation_dom @ SV76 ) )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1694]) ).
thf(1744,plain,
! [SV252: $i,SV76: $i,SV322: $i] :
( ( ( ! [SY578: $i] :
~ ( in @ ( ordered_pair @ SV322 @ SY578 ) @ SV76 ) )
= $true )
| ( ( in @ SV322 @ SV252 )
= $true )
| ( ( SV252
= ( relation_dom @ SV76 ) )
= $false )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1695]) ).
thf(1745,plain,
! [SV76: $i,SV252: $i,SV323: $i] :
( ( ( ~ ( in @ SV323 @ SV252 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV323 @ ( sK19_D @ SV323 @ SV252 @ SV76 ) ) @ SV76 )
= $true )
| ( ( SV252
= ( relation_dom @ SV76 ) )
= $false )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1696]) ).
thf(1746,plain,
! [SV203: $i,SV157: $i,SV308: $i] :
( ( ( in @ SV308 @ SV157 )
= $false )
| ( ( in @ ( sK17_C @ SV203 @ SV157 ) @ SV308 )
= $false )
| ( ( ~ ( in @ ( sK17_C @ SV203 @ SV157 ) @ SV203 ) )
= $true )
| ( ( SV203
= ( union @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1699]) ).
thf(1747,plain,
! [SV204: $i,SV158: $i,SV324: $i,SV309: $i] :
( ( ( ~ ( in @ SV309 @ SV324 ) )
= $true )
| ( ( ~ ( in @ SV324 @ SV158 ) )
= $true )
| ( ( in @ SV309 @ SV204 )
= $true )
| ( ( SV204
= ( union @ SV158 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1702]) ).
thf(1748,plain,
! [SV158: $i,SV204: $i,SV310: $i] :
( ( ( ~ ( in @ SV310 @ ( sK16_D @ SV310 @ SV204 @ SV158 ) )
| ~ ( in @ ( sK16_D @ SV310 @ SV204 @ SV158 ) @ SV158 ) )
= $false )
| ( ( in @ SV310 @ SV204 )
= $false )
| ( ( SV204
= ( union @ SV158 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1703]) ).
thf(1749,plain,
! [SV318: $i,SV79: $i,SV311: $i] :
( ( ( ~ ( in @ SV311 @ ( sK35_B @ SV79 ) ) )
= $true )
| ( ( ~ ( subset @ SV318 @ SV311 ) )
= $true )
| ( ( in @ SV318 @ ( sK35_B @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1704]) ).
thf(1750,plain,
! [SV81: $i,SV215: $i,SV246: $i] :
( ( ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV246 )
= $false )
| ( ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV215 )
= $true )
| ( ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV81 )
= $false )
| ( ( SV246
= ( set_difference @ SV81 @ SV215 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1705]) ).
thf(1751,plain,
! [SV81: $i,SV215: $i,SV246: $i] :
( ( ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV81 )
= $true )
| ( ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV246 )
= $true )
| ( ( SV246
= ( set_difference @ SV81 @ SV215 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1706]) ).
thf(1752,plain,
! [SV81: $i,SV215: $i,SV246: $i] :
( ( ( ~ ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV215 ) )
= $true )
| ( ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV246 )
= $true )
| ( ( SV246
= ( set_difference @ SV81 @ SV215 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1707]) ).
thf(1753,plain,
! [SV247: $i,SV216: $i,SV81: $i,SV319: $i] :
( ( ( ~ ( in @ SV319 @ SV81 ) )
= $true )
| ( ( in @ SV319 @ SV216 )
= $true )
| ( ( in @ SV319 @ SV247 )
= $true )
| ( ( SV247
= ( set_difference @ SV81 @ SV216 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1708]) ).
thf(1754,plain,
! [SV216: $i,SV81: $i,SV247: $i] :
( ( ( ! [SY533: $i] :
( ~ ( in @ SY533 @ SV247 )
| ( in @ SY533 @ SV81 ) ) )
= $true )
| ( ( SV247
= ( set_difference @ SV81 @ SV216 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1709]) ).
thf(1755,plain,
! [SV81: $i,SV216: $i,SV247: $i] :
( ( ( ! [SY534: $i] :
( ~ ( in @ SY534 @ SV247 )
| ~ ( in @ SY534 @ SV216 ) ) )
= $true )
| ( ( SV247
= ( set_difference @ SV81 @ SV216 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1710]) ).
thf(1756,plain,
! [SV82: $i,SV264: $i,SV325: $i] :
( ( ( in @ ( ordered_pair @ SV325 @ ( sK13_C @ SV264 @ SV82 ) ) @ SV82 )
= $false )
| ( ( ~ ( in @ ( sK13_C @ SV264 @ SV82 ) @ SV264 ) )
= $true )
| ( ( SV264
= ( relation_rng @ SV82 ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1711]) ).
thf(1757,plain,
! [SV265: $i,SV82: $i,SV326: $i] :
( ( ( ! [SY579: $i] :
~ ( in @ ( ordered_pair @ SY579 @ SV326 ) @ SV82 ) )
= $true )
| ( ( in @ SV326 @ SV265 )
= $true )
| ( ( SV265
= ( relation_rng @ SV82 ) )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1712]) ).
thf(1758,plain,
! [SV82: $i,SV265: $i,SV327: $i] :
( ( ( ~ ( in @ SV327 @ SV265 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK12_D @ SV327 @ SV265 @ SV82 ) @ SV327 ) @ SV82 )
= $true )
| ( ( SV265
= ( relation_rng @ SV82 ) )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1713]) ).
thf(1759,plain,
! [SV266: $i,SV294: $i] :
( ( ( ~ ( ~ ( in @ ( sK40_SY287 @ SV294 @ SV266 ) @ SV266 )
| ~ ~ ( in @ ( sK39_C @ SV294 @ SV266 ) @ ( sK40_SY287 @ SV294 @ SV266 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK39_C @ SV294 @ SV266 ) @ SV294 ) )
= $true )
| ( ( SV294
= ( set_meet @ SV266 ) )
= $true )
| ( ( SV266 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1714]) ).
thf(1760,plain,
! [SV294: $i,SV266: $i] :
( ( ( ! [SY570: $i] :
( ~ ( in @ SY570 @ SV266 )
| ( in @ ( sK39_C @ SV294 @ SV266 ) @ SY570 ) ) )
= $true )
| ( ( in @ ( sK39_C @ SV294 @ SV266 ) @ SV294 )
= $true )
| ( ( SV294
= ( set_meet @ SV266 ) )
= $true )
| ( ( SV266 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1715]) ).
thf(1761,plain,
! [SV267: $i,SV295: $i] :
( ( ( ! [SY571: $i] :
( ~ ( ~ ( in @ ( sK38_D @ SY571 @ SV295 @ SV267 ) @ SV267 )
| ~ ~ ( in @ SY571 @ ( sK38_D @ SY571 @ SV295 @ SV267 ) ) )
| ( in @ SY571 @ SV295 ) ) )
= $true )
| ( ( SV295
= ( set_meet @ SV267 ) )
= $false )
| ( ( SV267 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1716]) ).
thf(1762,plain,
! [SV267: $i,SV295: $i] :
( ( ( ! [SY572: $i] :
( ~ ( in @ SY572 @ SV295 )
| ! [SY554: $i] :
( ~ ( in @ SY554 @ SV267 )
| ( in @ SY572 @ SY554 ) ) ) )
= $true )
| ( ( SV295
= ( set_meet @ SV267 ) )
= $false )
| ( ( SV267 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1717]) ).
thf(1763,plain,
! [SV84: $i,SV272: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SV272 @ SV84 ) @ ( sK11_SY272 @ SV272 @ SV84 ) ) @ SV272 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK11_SY272 @ SV272 @ SV84 ) @ ( sK10_C @ SV272 @ SV84 ) ) @ SV84 ) )
= $true )
| ( ( SV272
= ( relation_inverse @ SV84 ) )
= $true )
| ( ( relation @ SV272 )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1718]) ).
thf(1764,plain,
! [SV84: $i,SV272: $i] :
( ( ( in @ ( ordered_pair @ ( sK10_C @ SV272 @ SV84 ) @ ( sK11_SY272 @ SV272 @ SV84 ) ) @ SV272 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK11_SY272 @ SV272 @ SV84 ) @ ( sK10_C @ SV272 @ SV84 ) ) @ SV84 )
= $true )
| ( ( SV272
= ( relation_inverse @ SV84 ) )
= $true )
| ( ( relation @ SV272 )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1719]) ).
thf(1765,plain,
! [SV84: $i,SV273: $i] :
( ( ( ! [SY559: $i,SY560: $i] :
( ~ ( in @ ( ordered_pair @ SY559 @ SY560 ) @ SV273 )
| ( in @ ( ordered_pair @ SY560 @ SY559 ) @ SV84 ) ) )
= $true )
| ( ( SV273
= ( relation_inverse @ SV84 ) )
= $false )
| ( ( relation @ SV273 )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1720]) ).
thf(1766,plain,
! [SV273: $i,SV84: $i] :
( ( ( ! [SY561: $i,SY562: $i] :
( ~ ( in @ ( ordered_pair @ SY562 @ SY561 ) @ SV84 )
| ( in @ ( ordered_pair @ SY561 @ SY562 ) @ SV273 ) ) )
= $true )
| ( ( SV273
= ( relation_inverse @ SV84 ) )
= $false )
| ( ( relation @ SV273 )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1721]) ).
thf(1767,plain,
! [SV85: $i,SV284: $i,SV328: $i] :
( ( ( ~ ( subset @ SV328 @ SV284 ) )
= $true )
| ( ( in @ SV328 @ ( sK2_SY267 @ SV284 @ SV85 ) )
= $true )
| ( ( ~ ( in @ SV284 @ ( sK1_B @ SV85 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1722]) ).
thf(1768,plain,
! [SV320: $i,SV85: $i,SV312: $i] :
( ( ( ~ ( in @ SV312 @ ( sK1_B @ SV85 ) ) )
= $true )
| ( ( ~ ( subset @ SV320 @ SV312 ) )
= $true )
| ( ( in @ SV320 @ ( sK1_B @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1724]) ).
thf(1769,plain,
! [SV73: $i,SV193: $i,SV240: $i] :
( ( ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV240 )
= $false )
| ( ( ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV73 ) )
= $true )
| ( ( SV240
= ( set_union2 @ SV73 @ SV193 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1727]) ).
thf(1770,plain,
! [SV73: $i,SV193: $i,SV240: $i] :
( ( ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV240 )
= $false )
| ( ( ~ ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV193 ) )
= $true )
| ( ( SV240
= ( set_union2 @ SV73 @ SV193 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1728]) ).
thf(1771,plain,
! [SV241: $i,SV194: $i,SV73: $i,SV315: $i] :
( ( ( in @ SV315 @ SV73 )
= $true )
| ( ( in @ SV315 @ SV194 )
= $true )
| ( ( in @ SV315 @ SV241 )
= $false )
| ( ( SV241
= ( set_union2 @ SV73 @ SV194 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1729]) ).
thf(1772,plain,
! [SV194: $i,SV241: $i,SV73: $i,SV329: $i] :
( ( ( ~ ( in @ SV329 @ SV73 )
| ( in @ SV329 @ SV241 ) )
= $true )
| ( ( SV241
= ( set_union2 @ SV73 @ SV194 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1730]) ).
thf(1773,plain,
! [SV73: $i,SV241: $i,SV194: $i,SV330: $i] :
( ( ( ~ ( in @ SV330 @ SV194 )
| ( in @ SV330 @ SV241 ) )
= $true )
| ( ( SV241
= ( set_union2 @ SV73 @ SV194 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1731]) ).
thf(1774,plain,
! [SV74: $i,SV195: $i,SV242: $i] :
( ( ( in @ ( sK25_D @ SV242 @ SV195 @ SV74 ) @ SV242 )
= $false )
| ( ( ( ( sK25_D @ SV242 @ SV195 @ SV74 )
!= SV74 ) )
= $true )
| ( ( SV242
= ( unordered_pair @ SV74 @ SV195 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1732]) ).
thf(1775,plain,
! [SV74: $i,SV195: $i,SV242: $i] :
( ( ( in @ ( sK25_D @ SV242 @ SV195 @ SV74 ) @ SV242 )
= $false )
| ( ( ( ( sK25_D @ SV242 @ SV195 @ SV74 )
!= SV195 ) )
= $true )
| ( ( SV242
= ( unordered_pair @ SV74 @ SV195 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1733]) ).
thf(1776,plain,
! [SV243: $i,SV196: $i,SV74: $i,SV316: $i] :
( ( ( SV316 = SV74 )
= $true )
| ( ( SV316 = SV196 )
= $true )
| ( ( in @ SV316 @ SV243 )
= $false )
| ( ( SV243
= ( unordered_pair @ SV74 @ SV196 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1734]) ).
thf(1777,plain,
! [SV196: $i,SV243: $i,SV74: $i,SV331: $i] :
( ( ( ( SV331 != SV74 )
| ( in @ SV331 @ SV243 ) )
= $true )
| ( ( SV243
= ( unordered_pair @ SV74 @ SV196 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1735]) ).
thf(1778,plain,
! [SV74: $i,SV243: $i,SV196: $i,SV332: $i] :
( ( ( ( SV332 != SV196 )
| ( in @ SV332 @ SV243 ) )
= $true )
| ( ( SV243
= ( unordered_pair @ SV74 @ SV196 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1736]) ).
thf(1779,plain,
! [SV75: $i,SV197: $i,SV244: $i] :
( ( ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV244 )
= $false )
| ( ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV75 )
= $false )
| ( ( in @ ( sK22_D @ SV244 @ SV197 @ SV75 ) @ SV197 )
= $false )
| ( ( SV244
= ( set_intersection2 @ SV75 @ SV197 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1737]) ).
thf(1780,plain,
! [SV245: $i,SV198: $i,SV75: $i,SV317: $i] :
( ( ( in @ SV317 @ SV75 )
= $false )
| ( ( ~ ( in @ SV317 @ SV198 ) )
= $true )
| ( ( in @ SV317 @ SV245 )
= $true )
| ( ( SV245
= ( set_intersection2 @ SV75 @ SV198 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1740]) ).
thf(1781,plain,
! [SV198: $i,SV75: $i,SV245: $i,SV333: $i] :
( ( ( ~ ( in @ SV333 @ SV245 )
| ( in @ SV333 @ SV75 ) )
= $true )
| ( ( SV245
= ( set_intersection2 @ SV75 @ SV198 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1741]) ).
thf(1782,plain,
! [SV75: $i,SV198: $i,SV245: $i,SV334: $i] :
( ( ( ~ ( in @ SV334 @ SV245 )
| ( in @ SV334 @ SV198 ) )
= $true )
| ( ( SV245
= ( set_intersection2 @ SV75 @ SV198 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1742]) ).
thf(1783,plain,
! [SV321: $i,SV76: $i,SV251: $i] :
( ( ( in @ ( sK20_C @ SV251 @ SV76 ) @ SV251 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK20_C @ SV251 @ SV76 ) @ SV321 ) @ SV76 )
= $false )
| ( ( SV251
= ( relation_dom @ SV76 ) )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1743]) ).
thf(1784,plain,
! [SV252: $i,SV76: $i,SV335: $i,SV322: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV322 @ SV335 ) @ SV76 ) )
= $true )
| ( ( in @ SV322 @ SV252 )
= $true )
| ( ( SV252
= ( relation_dom @ SV76 ) )
= $false )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1744]) ).
thf(1785,plain,
! [SV76: $i,SV252: $i,SV323: $i] :
( ( ( in @ SV323 @ SV252 )
= $false )
| ( ( in @ ( ordered_pair @ SV323 @ ( sK19_D @ SV323 @ SV252 @ SV76 ) ) @ SV76 )
= $true )
| ( ( SV252
= ( relation_dom @ SV76 ) )
= $false )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1745]) ).
thf(1786,plain,
! [SV308: $i,SV157: $i,SV203: $i] :
( ( ( in @ ( sK17_C @ SV203 @ SV157 ) @ SV203 )
= $false )
| ( ( in @ ( sK17_C @ SV203 @ SV157 ) @ SV308 )
= $false )
| ( ( in @ SV308 @ SV157 )
= $false )
| ( ( SV203
= ( union @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1746]) ).
thf(1787,plain,
! [SV204: $i,SV158: $i,SV324: $i,SV309: $i] :
( ( ( in @ SV309 @ SV324 )
= $false )
| ( ( ~ ( in @ SV324 @ SV158 ) )
= $true )
| ( ( in @ SV309 @ SV204 )
= $true )
| ( ( SV204
= ( union @ SV158 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1747]) ).
thf(1788,plain,
! [SV158: $i,SV204: $i,SV310: $i] :
( ( ( ~ ( in @ SV310 @ ( sK16_D @ SV310 @ SV204 @ SV158 ) ) )
= $false )
| ( ( in @ SV310 @ SV204 )
= $false )
| ( ( SV204
= ( union @ SV158 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1748]) ).
thf(1789,plain,
! [SV158: $i,SV204: $i,SV310: $i] :
( ( ( ~ ( in @ ( sK16_D @ SV310 @ SV204 @ SV158 ) @ SV158 ) )
= $false )
| ( ( in @ SV310 @ SV204 )
= $false )
| ( ( SV204
= ( union @ SV158 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1748]) ).
thf(1790,plain,
! [SV318: $i,SV79: $i,SV311: $i] :
( ( ( in @ SV311 @ ( sK35_B @ SV79 ) )
= $false )
| ( ( ~ ( subset @ SV318 @ SV311 ) )
= $true )
| ( ( in @ SV318 @ ( sK35_B @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1749]) ).
thf(1791,plain,
! [SV81: $i,SV215: $i,SV246: $i] :
( ( ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV215 )
= $false )
| ( ( in @ ( sK15_D @ SV246 @ SV215 @ SV81 ) @ SV246 )
= $true )
| ( ( SV246
= ( set_difference @ SV81 @ SV215 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1752]) ).
thf(1792,plain,
! [SV247: $i,SV216: $i,SV81: $i,SV319: $i] :
( ( ( in @ SV319 @ SV81 )
= $false )
| ( ( in @ SV319 @ SV216 )
= $true )
| ( ( in @ SV319 @ SV247 )
= $true )
| ( ( SV247
= ( set_difference @ SV81 @ SV216 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1753]) ).
thf(1793,plain,
! [SV216: $i,SV81: $i,SV247: $i,SV336: $i] :
( ( ( ~ ( in @ SV336 @ SV247 )
| ( in @ SV336 @ SV81 ) )
= $true )
| ( ( SV247
= ( set_difference @ SV81 @ SV216 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1754]) ).
thf(1794,plain,
! [SV81: $i,SV216: $i,SV247: $i,SV337: $i] :
( ( ( ~ ( in @ SV337 @ SV247 )
| ~ ( in @ SV337 @ SV216 ) )
= $true )
| ( ( SV247
= ( set_difference @ SV81 @ SV216 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1755]) ).
thf(1795,plain,
! [SV325: $i,SV82: $i,SV264: $i] :
( ( ( in @ ( sK13_C @ SV264 @ SV82 ) @ SV264 )
= $false )
| ( ( in @ ( ordered_pair @ SV325 @ ( sK13_C @ SV264 @ SV82 ) ) @ SV82 )
= $false )
| ( ( SV264
= ( relation_rng @ SV82 ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1756]) ).
thf(1796,plain,
! [SV265: $i,SV82: $i,SV326: $i,SV338: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV338 @ SV326 ) @ SV82 ) )
= $true )
| ( ( in @ SV326 @ SV265 )
= $true )
| ( ( SV265
= ( relation_rng @ SV82 ) )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1757]) ).
thf(1797,plain,
! [SV82: $i,SV265: $i,SV327: $i] :
( ( ( in @ SV327 @ SV265 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK12_D @ SV327 @ SV265 @ SV82 ) @ SV327 ) @ SV82 )
= $true )
| ( ( SV265
= ( relation_rng @ SV82 ) )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1758]) ).
thf(1798,plain,
! [SV266: $i,SV294: $i] :
( ( ( ~ ( in @ ( sK40_SY287 @ SV294 @ SV266 ) @ SV266 )
| ~ ~ ( in @ ( sK39_C @ SV294 @ SV266 ) @ ( sK40_SY287 @ SV294 @ SV266 ) ) )
= $false )
| ( ( ~ ( in @ ( sK39_C @ SV294 @ SV266 ) @ SV294 ) )
= $true )
| ( ( SV294
= ( set_meet @ SV266 ) )
= $true )
| ( ( SV266 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1759]) ).
thf(1799,plain,
! [SV294: $i,SV266: $i,SV339: $i] :
( ( ( ~ ( in @ SV339 @ SV266 )
| ( in @ ( sK39_C @ SV294 @ SV266 ) @ SV339 ) )
= $true )
| ( ( in @ ( sK39_C @ SV294 @ SV266 ) @ SV294 )
= $true )
| ( ( SV294
= ( set_meet @ SV266 ) )
= $true )
| ( ( SV266 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1760]) ).
thf(1800,plain,
! [SV267: $i,SV295: $i,SV340: $i] :
( ( ( ~ ( ~ ( in @ ( sK38_D @ SV340 @ SV295 @ SV267 ) @ SV267 )
| ~ ~ ( in @ SV340 @ ( sK38_D @ SV340 @ SV295 @ SV267 ) ) )
| ( in @ SV340 @ SV295 ) )
= $true )
| ( ( SV295
= ( set_meet @ SV267 ) )
= $false )
| ( ( SV267 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1761]) ).
thf(1801,plain,
! [SV267: $i,SV295: $i,SV341: $i] :
( ( ( ~ ( in @ SV341 @ SV295 )
| ! [SY580: $i] :
( ~ ( in @ SY580 @ SV267 )
| ( in @ SV341 @ SY580 ) ) )
= $true )
| ( ( SV295
= ( set_meet @ SV267 ) )
= $false )
| ( ( SV267 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1762]) ).
thf(1802,plain,
! [SV84: $i,SV272: $i] :
( ( ( in @ ( ordered_pair @ ( sK10_C @ SV272 @ SV84 ) @ ( sK11_SY272 @ SV272 @ SV84 ) ) @ SV272 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK11_SY272 @ SV272 @ SV84 ) @ ( sK10_C @ SV272 @ SV84 ) ) @ SV84 ) )
= $true )
| ( ( SV272
= ( relation_inverse @ SV84 ) )
= $true )
| ( ( relation @ SV272 )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1763]) ).
thf(1803,plain,
! [SV84: $i,SV273: $i,SV342: $i] :
( ( ( ! [SY581: $i] :
( ~ ( in @ ( ordered_pair @ SV342 @ SY581 ) @ SV273 )
| ( in @ ( ordered_pair @ SY581 @ SV342 ) @ SV84 ) ) )
= $true )
| ( ( SV273
= ( relation_inverse @ SV84 ) )
= $false )
| ( ( relation @ SV273 )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1765]) ).
thf(1804,plain,
! [SV273: $i,SV84: $i,SV343: $i] :
( ( ( ! [SY582: $i] :
( ~ ( in @ ( ordered_pair @ SY582 @ SV343 ) @ SV84 )
| ( in @ ( ordered_pair @ SV343 @ SY582 ) @ SV273 ) ) )
= $true )
| ( ( SV273
= ( relation_inverse @ SV84 ) )
= $false )
| ( ( relation @ SV273 )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1766]) ).
thf(1805,plain,
! [SV85: $i,SV284: $i,SV328: $i] :
( ( ( subset @ SV328 @ SV284 )
= $false )
| ( ( in @ SV328 @ ( sK2_SY267 @ SV284 @ SV85 ) )
= $true )
| ( ( ~ ( in @ SV284 @ ( sK1_B @ SV85 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1767]) ).
thf(1806,plain,
! [SV320: $i,SV85: $i,SV312: $i] :
( ( ( in @ SV312 @ ( sK1_B @ SV85 ) )
= $false )
| ( ( ~ ( subset @ SV320 @ SV312 ) )
= $true )
| ( ( in @ SV320 @ ( sK1_B @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1768]) ).
thf(1807,plain,
! [SV73: $i,SV193: $i,SV240: $i] :
( ( ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV73 )
= $false )
| ( ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV240 )
= $false )
| ( ( SV240
= ( set_union2 @ SV73 @ SV193 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1769]) ).
thf(1808,plain,
! [SV73: $i,SV193: $i,SV240: $i] :
( ( ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV193 )
= $false )
| ( ( in @ ( sK24_D @ SV240 @ SV193 @ SV73 ) @ SV240 )
= $false )
| ( ( SV240
= ( set_union2 @ SV73 @ SV193 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1770]) ).
thf(1809,plain,
! [SV194: $i,SV241: $i,SV73: $i,SV329: $i] :
( ( ( ~ ( in @ SV329 @ SV73 ) )
= $true )
| ( ( in @ SV329 @ SV241 )
= $true )
| ( ( SV241
= ( set_union2 @ SV73 @ SV194 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1772]) ).
thf(1810,plain,
! [SV73: $i,SV241: $i,SV194: $i,SV330: $i] :
( ( ( ~ ( in @ SV330 @ SV194 ) )
= $true )
| ( ( in @ SV330 @ SV241 )
= $true )
| ( ( SV241
= ( set_union2 @ SV73 @ SV194 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1773]) ).
thf(1811,plain,
! [SV74: $i,SV195: $i,SV242: $i] :
( ( ( ( sK25_D @ SV242 @ SV195 @ SV74 )
= SV74 )
= $false )
| ( ( in @ ( sK25_D @ SV242 @ SV195 @ SV74 ) @ SV242 )
= $false )
| ( ( SV242
= ( unordered_pair @ SV74 @ SV195 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1774]) ).
thf(1812,plain,
! [SV74: $i,SV195: $i,SV242: $i] :
( ( ( ( sK25_D @ SV242 @ SV195 @ SV74 )
= SV195 )
= $false )
| ( ( in @ ( sK25_D @ SV242 @ SV195 @ SV74 ) @ SV242 )
= $false )
| ( ( SV242
= ( unordered_pair @ SV74 @ SV195 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1775]) ).
thf(1813,plain,
! [SV196: $i,SV243: $i,SV74: $i,SV331: $i] :
( ( ( ( SV331 != SV74 ) )
= $true )
| ( ( in @ SV331 @ SV243 )
= $true )
| ( ( SV243
= ( unordered_pair @ SV74 @ SV196 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1777]) ).
thf(1814,plain,
! [SV74: $i,SV243: $i,SV196: $i,SV332: $i] :
( ( ( ( SV332 != SV196 ) )
= $true )
| ( ( in @ SV332 @ SV243 )
= $true )
| ( ( SV243
= ( unordered_pair @ SV74 @ SV196 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1778]) ).
thf(1815,plain,
! [SV245: $i,SV75: $i,SV198: $i,SV317: $i] :
( ( ( in @ SV317 @ SV198 )
= $false )
| ( ( in @ SV317 @ SV75 )
= $false )
| ( ( in @ SV317 @ SV245 )
= $true )
| ( ( SV245
= ( set_intersection2 @ SV75 @ SV198 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1780]) ).
thf(1816,plain,
! [SV198: $i,SV75: $i,SV245: $i,SV333: $i] :
( ( ( ~ ( in @ SV333 @ SV245 ) )
= $true )
| ( ( in @ SV333 @ SV75 )
= $true )
| ( ( SV245
= ( set_intersection2 @ SV75 @ SV198 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1781]) ).
thf(1817,plain,
! [SV75: $i,SV198: $i,SV245: $i,SV334: $i] :
( ( ( ~ ( in @ SV334 @ SV245 ) )
= $true )
| ( ( in @ SV334 @ SV198 )
= $true )
| ( ( SV245
= ( set_intersection2 @ SV75 @ SV198 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1782]) ).
thf(1818,plain,
! [SV252: $i,SV76: $i,SV335: $i,SV322: $i] :
( ( ( in @ ( ordered_pair @ SV322 @ SV335 ) @ SV76 )
= $false )
| ( ( in @ SV322 @ SV252 )
= $true )
| ( ( SV252
= ( relation_dom @ SV76 ) )
= $false )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1784]) ).
thf(1819,plain,
! [SV204: $i,SV309: $i,SV158: $i,SV324: $i] :
( ( ( in @ SV324 @ SV158 )
= $false )
| ( ( in @ SV309 @ SV324 )
= $false )
| ( ( in @ SV309 @ SV204 )
= $true )
| ( ( SV204
= ( union @ SV158 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1787]) ).
thf(1820,plain,
! [SV158: $i,SV204: $i,SV310: $i] :
( ( ( in @ SV310 @ ( sK16_D @ SV310 @ SV204 @ SV158 ) )
= $true )
| ( ( in @ SV310 @ SV204 )
= $false )
| ( ( SV204
= ( union @ SV158 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1788]) ).
thf(1821,plain,
! [SV158: $i,SV204: $i,SV310: $i] :
( ( ( in @ ( sK16_D @ SV310 @ SV204 @ SV158 ) @ SV158 )
= $true )
| ( ( in @ SV310 @ SV204 )
= $false )
| ( ( SV204
= ( union @ SV158 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1789]) ).
thf(1822,plain,
! [SV79: $i,SV311: $i,SV318: $i] :
( ( ( subset @ SV318 @ SV311 )
= $false )
| ( ( in @ SV311 @ ( sK35_B @ SV79 ) )
= $false )
| ( ( in @ SV318 @ ( sK35_B @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1790]) ).
thf(1823,plain,
! [SV216: $i,SV81: $i,SV247: $i,SV336: $i] :
( ( ( ~ ( in @ SV336 @ SV247 ) )
= $true )
| ( ( in @ SV336 @ SV81 )
= $true )
| ( ( SV247
= ( set_difference @ SV81 @ SV216 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1793]) ).
thf(1824,plain,
! [SV81: $i,SV216: $i,SV247: $i,SV337: $i] :
( ( ( ~ ( in @ SV337 @ SV247 ) )
= $true )
| ( ( ~ ( in @ SV337 @ SV216 ) )
= $true )
| ( ( SV247
= ( set_difference @ SV81 @ SV216 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1794]) ).
thf(1825,plain,
! [SV265: $i,SV82: $i,SV326: $i,SV338: $i] :
( ( ( in @ ( ordered_pair @ SV338 @ SV326 ) @ SV82 )
= $false )
| ( ( in @ SV326 @ SV265 )
= $true )
| ( ( SV265
= ( relation_rng @ SV82 ) )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1796]) ).
thf(1826,plain,
! [SV266: $i,SV294: $i] :
( ( ( ~ ( in @ ( sK40_SY287 @ SV294 @ SV266 ) @ SV266 ) )
= $false )
| ( ( ~ ( in @ ( sK39_C @ SV294 @ SV266 ) @ SV294 ) )
= $true )
| ( ( SV294
= ( set_meet @ SV266 ) )
= $true )
| ( ( SV266 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1798]) ).
thf(1827,plain,
! [SV266: $i,SV294: $i] :
( ( ( ~ ~ ( in @ ( sK39_C @ SV294 @ SV266 ) @ ( sK40_SY287 @ SV294 @ SV266 ) ) )
= $false )
| ( ( ~ ( in @ ( sK39_C @ SV294 @ SV266 ) @ SV294 ) )
= $true )
| ( ( SV294
= ( set_meet @ SV266 ) )
= $true )
| ( ( SV266 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1798]) ).
thf(1828,plain,
! [SV294: $i,SV266: $i,SV339: $i] :
( ( ( ~ ( in @ SV339 @ SV266 ) )
= $true )
| ( ( in @ ( sK39_C @ SV294 @ SV266 ) @ SV339 )
= $true )
| ( ( in @ ( sK39_C @ SV294 @ SV266 ) @ SV294 )
= $true )
| ( ( SV294
= ( set_meet @ SV266 ) )
= $true )
| ( ( SV266 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1799]) ).
thf(1829,plain,
! [SV267: $i,SV295: $i,SV340: $i] :
( ( ( ~ ( ~ ( in @ ( sK38_D @ SV340 @ SV295 @ SV267 ) @ SV267 )
| ~ ~ ( in @ SV340 @ ( sK38_D @ SV340 @ SV295 @ SV267 ) ) ) )
= $true )
| ( ( in @ SV340 @ SV295 )
= $true )
| ( ( SV295
= ( set_meet @ SV267 ) )
= $false )
| ( ( SV267 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1800]) ).
thf(1830,plain,
! [SV267: $i,SV295: $i,SV341: $i] :
( ( ( ~ ( in @ SV341 @ SV295 ) )
= $true )
| ( ( ! [SY580: $i] :
( ~ ( in @ SY580 @ SV267 )
| ( in @ SV341 @ SY580 ) ) )
= $true )
| ( ( SV295
= ( set_meet @ SV267 ) )
= $false )
| ( ( SV267 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1801]) ).
thf(1831,plain,
! [SV84: $i,SV272: $i] :
( ( ( in @ ( ordered_pair @ ( sK11_SY272 @ SV272 @ SV84 ) @ ( sK10_C @ SV272 @ SV84 ) ) @ SV84 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK10_C @ SV272 @ SV84 ) @ ( sK11_SY272 @ SV272 @ SV84 ) ) @ SV272 )
= $false )
| ( ( SV272
= ( relation_inverse @ SV84 ) )
= $true )
| ( ( relation @ SV272 )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1802]) ).
thf(1832,plain,
! [SV84: $i,SV273: $i,SV344: $i,SV342: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV342 @ SV344 ) @ SV273 )
| ( in @ ( ordered_pair @ SV344 @ SV342 ) @ SV84 ) )
= $true )
| ( ( SV273
= ( relation_inverse @ SV84 ) )
= $false )
| ( ( relation @ SV273 )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1803]) ).
thf(1833,plain,
! [SV273: $i,SV84: $i,SV343: $i,SV345: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV345 @ SV343 ) @ SV84 )
| ( in @ ( ordered_pair @ SV343 @ SV345 ) @ SV273 ) )
= $true )
| ( ( SV273
= ( relation_inverse @ SV84 ) )
= $false )
| ( ( relation @ SV273 )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1804]) ).
thf(1834,plain,
! [SV328: $i,SV85: $i,SV284: $i] :
( ( ( in @ SV284 @ ( sK1_B @ SV85 ) )
= $false )
| ( ( in @ SV328 @ ( sK2_SY267 @ SV284 @ SV85 ) )
= $true )
| ( ( subset @ SV328 @ SV284 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1805]) ).
thf(1835,plain,
! [SV85: $i,SV312: $i,SV320: $i] :
( ( ( subset @ SV320 @ SV312 )
= $false )
| ( ( in @ SV312 @ ( sK1_B @ SV85 ) )
= $false )
| ( ( in @ SV320 @ ( sK1_B @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1806]) ).
thf(1836,plain,
! [SV194: $i,SV241: $i,SV73: $i,SV329: $i] :
( ( ( in @ SV329 @ SV73 )
= $false )
| ( ( in @ SV329 @ SV241 )
= $true )
| ( ( SV241
= ( set_union2 @ SV73 @ SV194 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1809]) ).
thf(1837,plain,
! [SV73: $i,SV241: $i,SV194: $i,SV330: $i] :
( ( ( in @ SV330 @ SV194 )
= $false )
| ( ( in @ SV330 @ SV241 )
= $true )
| ( ( SV241
= ( set_union2 @ SV73 @ SV194 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1810]) ).
thf(1838,plain,
! [SV196: $i,SV243: $i,SV74: $i,SV331: $i] :
( ( ( SV331 = SV74 )
= $false )
| ( ( in @ SV331 @ SV243 )
= $true )
| ( ( SV243
= ( unordered_pair @ SV74 @ SV196 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1813]) ).
thf(1839,plain,
! [SV74: $i,SV243: $i,SV196: $i,SV332: $i] :
( ( ( SV332 = SV196 )
= $false )
| ( ( in @ SV332 @ SV243 )
= $true )
| ( ( SV243
= ( unordered_pair @ SV74 @ SV196 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1814]) ).
thf(1840,plain,
! [SV198: $i,SV75: $i,SV245: $i,SV333: $i] :
( ( ( in @ SV333 @ SV245 )
= $false )
| ( ( in @ SV333 @ SV75 )
= $true )
| ( ( SV245
= ( set_intersection2 @ SV75 @ SV198 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1816]) ).
thf(1841,plain,
! [SV75: $i,SV198: $i,SV245: $i,SV334: $i] :
( ( ( in @ SV334 @ SV245 )
= $false )
| ( ( in @ SV334 @ SV198 )
= $true )
| ( ( SV245
= ( set_intersection2 @ SV75 @ SV198 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1817]) ).
thf(1842,plain,
! [SV216: $i,SV81: $i,SV247: $i,SV336: $i] :
( ( ( in @ SV336 @ SV247 )
= $false )
| ( ( in @ SV336 @ SV81 )
= $true )
| ( ( SV247
= ( set_difference @ SV81 @ SV216 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1823]) ).
thf(1843,plain,
! [SV81: $i,SV216: $i,SV247: $i,SV337: $i] :
( ( ( in @ SV337 @ SV247 )
= $false )
| ( ( ~ ( in @ SV337 @ SV216 ) )
= $true )
| ( ( SV247
= ( set_difference @ SV81 @ SV216 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1824]) ).
thf(1844,plain,
! [SV266: $i,SV294: $i] :
( ( ( in @ ( sK40_SY287 @ SV294 @ SV266 ) @ SV266 )
= $true )
| ( ( ~ ( in @ ( sK39_C @ SV294 @ SV266 ) @ SV294 ) )
= $true )
| ( ( SV294
= ( set_meet @ SV266 ) )
= $true )
| ( ( SV266 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1826]) ).
thf(1845,plain,
! [SV266: $i,SV294: $i] :
( ( ( ~ ( in @ ( sK39_C @ SV294 @ SV266 ) @ ( sK40_SY287 @ SV294 @ SV266 ) ) )
= $true )
| ( ( ~ ( in @ ( sK39_C @ SV294 @ SV266 ) @ SV294 ) )
= $true )
| ( ( SV294
= ( set_meet @ SV266 ) )
= $true )
| ( ( SV266 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1827]) ).
thf(1846,plain,
! [SV294: $i,SV266: $i,SV339: $i] :
( ( ( in @ SV339 @ SV266 )
= $false )
| ( ( in @ ( sK39_C @ SV294 @ SV266 ) @ SV339 )
= $true )
| ( ( in @ ( sK39_C @ SV294 @ SV266 ) @ SV294 )
= $true )
| ( ( SV294
= ( set_meet @ SV266 ) )
= $true )
| ( ( SV266 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1828]) ).
thf(1847,plain,
! [SV267: $i,SV295: $i,SV340: $i] :
( ( ( ~ ( in @ ( sK38_D @ SV340 @ SV295 @ SV267 ) @ SV267 )
| ~ ~ ( in @ SV340 @ ( sK38_D @ SV340 @ SV295 @ SV267 ) ) )
= $false )
| ( ( in @ SV340 @ SV295 )
= $true )
| ( ( SV295
= ( set_meet @ SV267 ) )
= $false )
| ( ( SV267 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1829]) ).
thf(1848,plain,
! [SV267: $i,SV295: $i,SV341: $i] :
( ( ( in @ SV341 @ SV295 )
= $false )
| ( ( ! [SY580: $i] :
( ~ ( in @ SY580 @ SV267 )
| ( in @ SV341 @ SY580 ) ) )
= $true )
| ( ( SV295
= ( set_meet @ SV267 ) )
= $false )
| ( ( SV267 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1830]) ).
thf(1849,plain,
! [SV84: $i,SV273: $i,SV344: $i,SV342: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV342 @ SV344 ) @ SV273 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV344 @ SV342 ) @ SV84 )
= $true )
| ( ( SV273
= ( relation_inverse @ SV84 ) )
= $false )
| ( ( relation @ SV273 )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1832]) ).
thf(1850,plain,
! [SV273: $i,SV84: $i,SV343: $i,SV345: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV345 @ SV343 ) @ SV84 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV343 @ SV345 ) @ SV273 )
= $true )
| ( ( SV273
= ( relation_inverse @ SV84 ) )
= $false )
| ( ( relation @ SV273 )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1833]) ).
thf(1851,plain,
! [SV81: $i,SV247: $i,SV216: $i,SV337: $i] :
( ( ( in @ SV337 @ SV216 )
= $false )
| ( ( in @ SV337 @ SV247 )
= $false )
| ( ( SV247
= ( set_difference @ SV81 @ SV216 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1843]) ).
thf(1852,plain,
! [SV266: $i,SV294: $i] :
( ( ( in @ ( sK39_C @ SV294 @ SV266 ) @ SV294 )
= $false )
| ( ( in @ ( sK40_SY287 @ SV294 @ SV266 ) @ SV266 )
= $true )
| ( ( SV294
= ( set_meet @ SV266 ) )
= $true )
| ( ( SV266 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1844]) ).
thf(1853,plain,
! [SV266: $i,SV294: $i] :
( ( ( in @ ( sK39_C @ SV294 @ SV266 ) @ ( sK40_SY287 @ SV294 @ SV266 ) )
= $false )
| ( ( ~ ( in @ ( sK39_C @ SV294 @ SV266 ) @ SV294 ) )
= $true )
| ( ( SV294
= ( set_meet @ SV266 ) )
= $true )
| ( ( SV266 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1845]) ).
thf(1854,plain,
! [SV267: $i,SV295: $i,SV340: $i] :
( ( ( ~ ( in @ ( sK38_D @ SV340 @ SV295 @ SV267 ) @ SV267 ) )
= $false )
| ( ( in @ SV340 @ SV295 )
= $true )
| ( ( SV295
= ( set_meet @ SV267 ) )
= $false )
| ( ( SV267 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1847]) ).
thf(1855,plain,
! [SV267: $i,SV295: $i,SV340: $i] :
( ( ( ~ ~ ( in @ SV340 @ ( sK38_D @ SV340 @ SV295 @ SV267 ) ) )
= $false )
| ( ( in @ SV340 @ SV295 )
= $true )
| ( ( SV295
= ( set_meet @ SV267 ) )
= $false )
| ( ( SV267 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1847]) ).
thf(1856,plain,
! [SV295: $i,SV341: $i,SV267: $i,SV346: $i] :
( ( ( ~ ( in @ SV346 @ SV267 )
| ( in @ SV341 @ SV346 ) )
= $true )
| ( ( in @ SV341 @ SV295 )
= $false )
| ( ( SV295
= ( set_meet @ SV267 ) )
= $false )
| ( ( SV267 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1848]) ).
thf(1857,plain,
! [SV84: $i,SV273: $i,SV344: $i,SV342: $i] :
( ( ( in @ ( ordered_pair @ SV342 @ SV344 ) @ SV273 )
= $false )
| ( ( in @ ( ordered_pair @ SV344 @ SV342 ) @ SV84 )
= $true )
| ( ( SV273
= ( relation_inverse @ SV84 ) )
= $false )
| ( ( relation @ SV273 )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1849]) ).
thf(1858,plain,
! [SV273: $i,SV84: $i,SV343: $i,SV345: $i] :
( ( ( in @ ( ordered_pair @ SV345 @ SV343 ) @ SV84 )
= $false )
| ( ( in @ ( ordered_pair @ SV343 @ SV345 ) @ SV273 )
= $true )
| ( ( SV273
= ( relation_inverse @ SV84 ) )
= $false )
| ( ( relation @ SV273 )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1850]) ).
thf(1859,plain,
! [SV266: $i,SV294: $i] :
( ( ( in @ ( sK39_C @ SV294 @ SV266 ) @ SV294 )
= $false )
| ( ( in @ ( sK39_C @ SV294 @ SV266 ) @ ( sK40_SY287 @ SV294 @ SV266 ) )
= $false )
| ( ( SV294
= ( set_meet @ SV266 ) )
= $true )
| ( ( SV266 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1853]) ).
thf(1860,plain,
! [SV267: $i,SV295: $i,SV340: $i] :
( ( ( in @ ( sK38_D @ SV340 @ SV295 @ SV267 ) @ SV267 )
= $true )
| ( ( in @ SV340 @ SV295 )
= $true )
| ( ( SV295
= ( set_meet @ SV267 ) )
= $false )
| ( ( SV267 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1854]) ).
thf(1861,plain,
! [SV267: $i,SV295: $i,SV340: $i] :
( ( ( ~ ( in @ SV340 @ ( sK38_D @ SV340 @ SV295 @ SV267 ) ) )
= $true )
| ( ( in @ SV340 @ SV295 )
= $true )
| ( ( SV295
= ( set_meet @ SV267 ) )
= $false )
| ( ( SV267 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1855]) ).
thf(1862,plain,
! [SV295: $i,SV341: $i,SV267: $i,SV346: $i] :
( ( ( ~ ( in @ SV346 @ SV267 ) )
= $true )
| ( ( in @ SV341 @ SV346 )
= $true )
| ( ( in @ SV341 @ SV295 )
= $false )
| ( ( SV295
= ( set_meet @ SV267 ) )
= $false )
| ( ( SV267 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1856]) ).
thf(1863,plain,
! [SV267: $i,SV295: $i,SV340: $i] :
( ( ( in @ SV340 @ ( sK38_D @ SV340 @ SV295 @ SV267 ) )
= $false )
| ( ( in @ SV340 @ SV295 )
= $true )
| ( ( SV295
= ( set_meet @ SV267 ) )
= $false )
| ( ( SV267 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1861]) ).
thf(1864,plain,
! [SV295: $i,SV341: $i,SV267: $i,SV346: $i] :
( ( ( in @ SV346 @ SV267 )
= $false )
| ( ( in @ SV341 @ SV346 )
= $true )
| ( ( in @ SV341 @ SV295 )
= $false )
| ( ( SV295
= ( set_meet @ SV267 ) )
= $false )
| ( ( SV267 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1862]) ).
thf(1865,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[393,1864,1863,1860,1859,1858,1857,1852,1851,1846,1842,1841,1840,1839,1838,1837,1836,1835,1834,1831,1825,1822,1821,1820,1819,1818,1815,1812,1811,1808,1807,1797,1795,1792,1791,1786,1785,1783,1779,1776,1771,1764,1751,1750,1739,1738,1726,1725,1723,1701,1700,1698,1697,1675,1668,1667,1661,1646,1645,1644,1641,1632,1627,1621,1620,1619,1613,1599,1598,1597,1587,1586,1569,1568,1565,1563,1562,1559,1558,1557,1556,1555,1553,1548,1535,1534,1533,1531,1521,1485,1484,1471,1463,1456,1455,1450,1425,1422,1416,1412,1411,1409,1405,1400,1385,1372,1359,1358,1357,1356,1350,1349,1345,1344,1335,1334,1328,1327,1314,1308,1307,1306,1302,1301,1295,1294,1272,1271,1270,1267,1266,1264,1259,1215,1198,1197,1196,1192,1176,1173,1172,1167,1166,1162,1097,1087,1073,1070,1069,1066,1065,1064,1061,1056,1055,1049,1048,1047,1024,1021,1020,966,965,963,962,957,954,951,949,947,943,939,937,933,916,915,912,911,904,844,841,838,836,835,834,815,807,804,801,719,716,712,711,704,699,692,691,690,683,670,626,618,617,615,614,597,591,561,560,559,558,554,494,403]) ).
thf(1866,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[389]) ).
thf(1867,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[388]) ).
thf(1868,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[387]) ).
thf(1869,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[285]) ).
thf(1870,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[386]) ).
thf(1871,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[283]) ).
thf(1872,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_rng @ A )
= ( relation_dom @ ( relation_inverse @ A ) ) ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_dom @ A )
= ( relation_rng @ ( relation_inverse @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[385]) ).
thf(1873,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[384]) ).
thf(1874,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[383]) ).
thf(1875,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[382]) ).
thf(1876,plain,
( ( ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( ( ( ( in @ ( sK40_SY287 @ B @ A ) @ A )
& ~ ( in @ ( sK39_C @ B @ A ) @ ( sK40_SY287 @ B @ A ) ) )
| ~ ( in @ ( sK39_C @ B @ A ) @ B ) )
& ( ! [SY288: $i] :
( ~ ( in @ SY288 @ A )
| ( in @ ( sK39_C @ B @ A ) @ SY288 ) )
| ( in @ ( sK39_C @ B @ A ) @ B ) ) )
| ( B
= ( set_meet @ A ) ) ) )
& ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( B
!= ( set_meet @ A ) )
| ( ! [C: $i] :
( ( ( in @ ( sK38_D @ C @ B @ A ) @ A )
& ~ ( in @ C @ ( sK38_D @ C @ B @ A ) ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ C @ D ) ) ) ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
( ( B
!= ( set_meet @ A ) )
| ( B = empty_set ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
( ( B != empty_set )
| ( B
= ( set_meet @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[381]) ).
thf(1877,plain,
( ( ! [A: $i] :
( ( in @ ( sK37_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[380]) ).
thf(1878,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_intersection2 @ A @ B )
!= empty_set )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[379]) ).
thf(1879,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[275]) ).
thf(1880,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[274]) ).
thf(1881,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[378]) ).
thf(1882,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(1883,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[271]) ).
thf(1884,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[270]) ).
thf(1885,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[269]) ).
thf(1886,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[268]) ).
thf(1887,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[376]) ).
thf(1888,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[375]) ).
thf(1889,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ ( singleton @ A ) @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[374]) ).
thf(1890,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
| ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(1891,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(1892,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(1893,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(1894,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(1895,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK36_C @ B @ A ) @ A )
& ~ ( in @ ( sK36_C @ B @ A ) @ B ) )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(1896,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) ) )
& ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(1897,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ D )
| ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(1898,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[365]) ).
thf(1899,plain,
( ( ! [A: $i] :
( ! [SY283: $i] :
( ~ ( subset @ SY283 @ ( sK35_B @ A ) )
| ( are_equipotent @ SY283 @ ( sK35_B @ A ) )
| ( in @ SY283 @ ( sK35_B @ A ) ) )
& ! [SY284: $i] :
( ~ ( in @ SY284 @ ( sK35_B @ A ) )
| ( in @ ( powerset @ SY284 ) @ ( sK35_B @ A ) ) )
& ! [SY285: $i,SY286: $i] :
( ~ ( in @ SY285 @ ( sK35_B @ A ) )
| ~ ( subset @ SY286 @ SY285 )
| ( in @ SY286 @ ( sK35_B @ A ) ) )
& ( in @ A @ ( sK35_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(1900,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[254]) ).
thf(1901,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ A @ C )
| ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(1902,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[362]) ).
thf(1903,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ A @ ( relation_dom @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ B @ ( relation_rng @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[361]) ).
thf(1904,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(1905,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(1906,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[358]) ).
thf(1907,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[357]) ).
thf(1908,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[246]) ).
thf(1909,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[356]) ).
thf(1910,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ C )
| ( subset @ ( unordered_pair @ A @ B ) @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ A @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[355]) ).
thf(1911,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[243]) ).
thf(1912,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK34_C @ B @ A ) @ A )
& ( in @ ( sK34_C @ B @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ C @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[354]) ).
thf(1913,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[241]) ).
thf(1914,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[353]) ).
thf(1915,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[352]) ).
thf(1916,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[351]) ).
thf(1917,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ ( relation_rng @ A ) @ ( relation_dom @ B ) )
| ( ( relation_dom @ ( relation_composition @ A @ B ) )
= ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[350]) ).
thf(1918,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[349]) ).
thf(1919,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ ( relation_dom @ A ) @ ( relation_rng @ B ) )
| ( ( relation_rng @ ( relation_composition @ B @ A ) )
= ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[348]) ).
thf(1920,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(1921,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sK33_C @ B @ A ) @ ( set_intersection2 @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[347]) ).
thf(1922,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( in @ ( ordered_pair @ ( sK31_B @ A ) @ ( sK32_SY282 @ A ) ) @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[346]) ).
thf(1923,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[345]) ).
thf(1924,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[344]) ).
thf(1925,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
!= A )
| ~ ( in @ B @ A ) )
& ! [A: $i,B: $i] :
( ( in @ B @ A )
| ( ( set_difference @ A @ ( singleton @ B ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[343]) ).
thf(1926,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[228]) ).
thf(1927,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[342]) ).
thf(1928,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(1929,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= A )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_difference @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[341]) ).
thf(1930,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ B )
| ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[340]) ).
thf(1931,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[339]) ).
thf(1932,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[338]) ).
thf(1933,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(1934,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[337]) ).
thf(1935,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[336]) ).
thf(1936,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[335]) ).
thf(1937,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(1938,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(1939,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[334]) ).
thf(1940,plain,
( ( ! [A: $i] :
( ( ! [SY280: $i,SY281: $i] :
( ( sK30_B @ A )
!= ( ordered_pair @ SY280 @ SY281 ) )
& ( in @ ( sK30_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK28_C @ B @ A ) @ ( sK29_SY279 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[333]) ).
thf(1941,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK27_C @ B @ A )
!= A )
| ~ ( in @ ( sK27_C @ B @ A ) @ B ) )
& ( ( ( sK27_C @ B @ A )
= A )
| ( in @ ( sK27_C @ B @ A ) @ B ) ) )
| ( B
= ( singleton @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( singleton @ A ) )
| ( ! [C: $i] :
( ( C != A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( C = A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[332]) ).
thf(1942,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK26_C @ B @ A ) @ B )
| ~ ( subset @ ( sK26_C @ B @ A ) @ A ) )
& ( ( in @ ( sK26_C @ B @ A ) @ B )
| ( subset @ ( sK26_C @ B @ A ) @ A ) ) )
| ( B
= ( powerset @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( powerset @ A ) )
| ( ! [C: $i] :
( ~ ( in @ C @ B )
| ( subset @ C @ A ) )
& ! [C: $i] :
( ~ ( subset @ C @ A )
| ( in @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[331]) ).
thf(1943,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
( ~ ( element @ B @ A )
| ( in @ B @ A ) ) )
& ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
( ~ ( in @ B @ A )
| ( element @ B @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ! [B: $i] :
( ~ ( element @ B @ A )
| ( empty @ B ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ! [B: $i] :
( ~ ( empty @ B )
| ( element @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[330]) ).
thf(1944,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK25_D @ C @ B @ A ) @ C )
| ( ( sK25_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK25_D @ C @ B @ A ) @ C )
| ( ( sK25_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK25_D @ C @ B @ A ) @ C )
| ( ( sK25_D @ C @ B @ A )
= A )
| ( ( sK25_D @ C @ B @ A )
= B ) ) )
| ( C
= ( unordered_pair @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( unordered_pair @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( D = A )
| ( D = B ) )
& ! [D: $i] :
( ( D != A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ( D != B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[329]) ).
thf(1945,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK24_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK24_D @ C @ B @ A ) @ A ) )
& ( ~ ( in @ ( sK24_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK24_D @ C @ B @ A ) @ B ) )
& ( ( in @ ( sK24_D @ C @ B @ A ) @ C )
| ( in @ ( sK24_D @ C @ B @ A ) @ A )
| ( in @ ( sK24_D @ C @ B @ A ) @ B ) ) )
| ( C
= ( set_union2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_union2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A )
| ( in @ D @ B ) )
& ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[328]) ).
thf(1946,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK23_C @ B @ A ) @ A )
& ~ ( in @ ( sK23_C @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[327]) ).
thf(1947,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK22_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK22_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK22_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK22_D @ C @ B @ A ) @ A )
| ( in @ ( sK22_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK22_D @ C @ B @ A ) @ B )
| ( in @ ( sK22_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_intersection2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_intersection2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ~ ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[326]) ).
thf(1948,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY277: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ B @ A ) @ SY277 ) @ A )
| ~ ( in @ ( sK20_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK20_C @ B @ A ) @ ( sK21_SY278 @ B @ A ) ) @ A )
| ( in @ ( sK20_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_dom @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_dom @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ C @ ( sK19_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[325]) ).
thf(1949,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY275: $i] :
( ~ ( in @ ( sK17_C @ B @ A ) @ SY275 )
| ~ ( in @ SY275 @ A ) )
| ~ ( in @ ( sK17_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK17_C @ B @ A ) @ ( sK18_SY276 @ B @ A ) )
& ( in @ ( sK18_SY276 @ B @ A ) @ A ) )
| ( in @ ( sK17_C @ B @ A ) @ B ) ) )
| ( B
= ( union @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( union @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
( ~ ( in @ C @ D )
| ~ ( in @ D @ A ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( ( in @ C @ ( sK16_D @ C @ B @ A ) )
& ( in @ ( sK16_D @ C @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[324]) ).
thf(1950,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK15_D @ C @ B @ A ) @ A )
| ( in @ ( sK15_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK15_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK15_D @ C @ B @ A ) @ A )
| ( in @ ( sK15_D @ C @ B @ A ) @ C ) )
& ( ~ ( in @ ( sK15_D @ C @ B @ A ) @ B )
| ( in @ ( sK15_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_difference @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_difference @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ~ ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[323]) ).
thf(1951,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY273: $i] :
~ ( in @ ( ordered_pair @ SY273 @ ( sK13_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK13_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK14_SY274 @ B @ A ) @ ( sK13_C @ B @ A ) ) @ A )
| ( in @ ( sK13_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_rng @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_rng @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ D @ C ) @ A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ ( sK12_D @ C @ B @ A ) @ C ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[322]) ).
thf(1952,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[321]) ).
thf(1953,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK10_C @ B @ A ) @ ( sK11_SY272 @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK11_SY272 @ B @ A ) @ ( sK10_C @ B @ A ) ) @ A ) )
& ( ( in @ ( ordered_pair @ ( sK10_C @ B @ A ) @ ( sK11_SY272 @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK11_SY272 @ B @ A ) @ ( sK10_C @ B @ A ) ) @ A ) ) )
| ( B
= ( relation_inverse @ A ) ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ( B
!= ( relation_inverse @ A ) )
| ( ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ B )
| ( in @ ( ordered_pair @ D @ C ) @ A ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ D @ C ) @ A )
| ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[320]) ).
thf(1954,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ( proper_subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( A != B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[319]) ).
thf(1955,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[318]) ).
thf(1956,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[317]) ).
thf(1957,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[197]) ).
thf(1958,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[196]) ).
thf(1959,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[316]) ).
thf(1960,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[194]) ).
thf(1961,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[315]) ).
thf(1962,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[192]) ).
thf(1963,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[314]) ).
thf(1964,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[313]) ).
thf(1965,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[312]) ).
thf(1966,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[311]) ).
thf(1967,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[310]) ).
thf(1968,plain,
( ( ( empty @ sK9_A )
& ( relation @ sK9_A ) )
= $true ),
inference(copy,[status(thm)],[309]) ).
thf(1969,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK8_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK8_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[308]) ).
thf(1970,plain,
( ( empty @ sK7_A )
= $true ),
inference(copy,[status(thm)],[307]) ).
thf(1971,plain,
( ( ~ ( empty @ sK6_A )
& ( relation @ sK6_A ) )
= $true ),
inference(copy,[status(thm)],[306]) ).
thf(1972,plain,
( ( ! [A: $i] :
( ( element @ ( sK5_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK5_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[305]) ).
thf(1973,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(copy,[status(thm)],[304]) ).
thf(1974,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[303]) ).
thf(1975,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[302]) ).
thf(1976,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[301]) ).
thf(1977,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[300]) ).
thf(1978,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK3_C @ B @ A ) @ A )
| ~ ( in @ ( sK3_C @ B @ A ) @ B ) )
& ( ( in @ ( sK3_C @ B @ A ) @ A )
| ( in @ ( sK3_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[299]) ).
thf(1979,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)],[298]) ).
thf(1980,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[297]) ).
thf(1981,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[296]) ).
thf(1982,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[295]) ).
thf(1983,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[294]) ).
thf(1984,plain,
( ( ! [A: $i] :
( ! [SY265: $i] :
( ~ ( subset @ SY265 @ ( sK1_B @ A ) )
| ( are_equipotent @ SY265 @ ( sK1_B @ A ) )
| ( in @ SY265 @ ( sK1_B @ A ) ) )
& ! [SY266: $i] :
( ( ! [SY271: $i] :
( ~ ( subset @ SY271 @ SY266 )
| ( in @ SY271 @ ( sK2_SY267 @ SY266 @ A ) ) )
& ( in @ ( sK2_SY267 @ SY266 @ A ) @ ( sK1_B @ A ) ) )
| ~ ( in @ SY266 @ ( sK1_B @ A ) ) )
& ! [SY269: $i,SY270: $i] :
( ~ ( in @ SY269 @ ( sK1_B @ A ) )
| ~ ( subset @ SY270 @ SY269 )
| ( in @ SY270 @ ( sK1_B @ A ) ) )
& ( in @ A @ ( sK1_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[293]) ).
thf(1985,plain,
( ( ( ( relation_rng @ empty_set )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[292]) ).
thf(1986,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX2 )
| ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX0 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1910]) ).
thf(1987,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SX1 @ SX0 ) @ ( sK11_SY272 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY272 @ SX1 @ SX0 ) @ ( sK10_C @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK10_C @ SX1 @ SX0 ) @ ( sK11_SY272 @ SX1 @ SX0 ) ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK11_SY272 @ SX1 @ SX0 ) @ ( sK10_C @ SX1 @ SX0 ) ) @ SX0 ) ) )
| ( SX1
= ( relation_inverse @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ( SX1
!= ( relation_inverse @ SX0 ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1953]) ).
thf(1988,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK33_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1921]) ).
thf(1989,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1978]) ).
thf(1990,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX0 @ ( relation_dom @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX1 @ ( relation_rng @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1903]) ).
thf(1991,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1868]) ).
thf(1992,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1929]) ).
thf(1993,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK24_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK24_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ~ ( in @ ( sK24_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK24_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ( ( in @ ( sK24_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( in @ ( sK24_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK24_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX2
= ( set_union2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_union2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1945]) ).
thf(1994,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1874]) ).
thf(1995,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1954]) ).
thf(1996,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK34_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK34_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1912]) ).
thf(1997,plain,
( ( ~ ( ~ ( empty @ sK9_A )
| ~ ( relation @ sK9_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1968]) ).
thf(1998,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX1 @ ( sK35_B @ SX0 ) )
| ( are_equipotent @ SX1 @ ( sK35_B @ SX0 ) )
| ( in @ SX1 @ ( sK35_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK35_B @ SX0 ) )
| ( in @ ( powerset @ SX1 ) @ ( sK35_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( sK35_B @ SX0 ) )
| ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK35_B @ SX0 ) ) )
| ~ ( in @ SX0 @ ( sK35_B @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1899]) ).
thf(1999,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( relation_dom @ SX0 ) @ ( relation_dom @ SX1 ) ) )
| ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( relation_rng @ SX0 ) @ ( relation_rng @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1870]) ).
thf(2000,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1909]) ).
thf(2001,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( in @ ( sK37_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1877]) ).
thf(2002,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX1 @ ( sK1_B @ SX0 ) )
| ( are_equipotent @ SX1 @ ( sK1_B @ SX0 ) )
| ( in @ SX1 @ ( sK1_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK2_SY267 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK2_SY267 @ SX1 @ SX0 ) @ ( sK1_B @ SX0 ) ) )
| ~ ( in @ SX1 @ ( sK1_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( sK1_B @ SX0 ) )
| ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK1_B @ SX0 ) ) )
| ~ ( in @ SX0 @ ( sK1_B @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1984]) ).
thf(2003,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1880]) ).
thf(2004,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK26_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK26_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK26_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK26_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1942]) ).
thf(2005,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1943]) ).
thf(2006,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1925]) ).
thf(2007,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK30_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK30_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK28_C @ SX1 @ SX0 ) @ ( sK29_SY279 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1940]) ).
thf(2008,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1878]) ).
thf(2009,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1939]) ).
thf(2010,plain,
( ( ~ ( ~ ~ ( empty @ sK6_A )
| ~ ( relation @ sK6_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1971]) ).
thf(2011,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)],[1979]) ).
thf(2012,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SX1 @ SX0 ) @ SX2 ) @ SX0 )
| ~ ( in @ ( sK20_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_C @ SX1 @ SX0 ) @ ( sK21_SY278 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK20_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( relation_dom @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ( SX1
!= ( relation_dom @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ ( ordered_pair @ SX2 @ ( sK19_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1948]) ).
thf(2013,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK15_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK15_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK15_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( in @ ( sK15_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK15_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) )
| ( SX2
= ( set_difference @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_difference @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ~ ( in @ SX3 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1950]) ).
thf(2014,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1872]) ).
thf(2015,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1891]) ).
thf(2016,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK22_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK22_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK22_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK22_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK22_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ( in @ ( sK22_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK22_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) )
| ( SX2
= ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1947]) ).
thf(2017,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ SX2 @ ( sK13_C @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY274 @ SX1 @ SX0 ) @ ( sK13_C @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( relation_rng @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ( SX1
!= ( relation_rng @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ ( ordered_pair @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1951]) ).
thf(2018,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ ( sK18_SY276 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK18_SY276 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK16_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK16_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1949]) ).
thf(2019,plain,
( ( ! [SX0: $i] :
~ ( ~ ( element @ ( sK5_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ( empty @ ( sK5_B @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1972]) ).
thf(2020,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK36_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK36_C @ SX1 @ SX0 ) @ SX1 ) )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1895]) ).
thf(2021,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1873]) ).
thf(2022,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1946]) ).
thf(2023,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1867]) ).
thf(2024,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK25_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK25_D @ SX2 @ SX1 @ SX0 )
!= SX0 ) )
| ~ ( ~ ( in @ ( sK25_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK25_D @ SX2 @ SX1 @ SX0 )
!= SX1 ) ) )
| ~ ( ( in @ ( sK25_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK25_D @ SX2 @ SX1 @ SX0 )
= SX0 )
| ( ( sK25_D @ SX2 @ SX1 @ SX0 )
= SX1 ) ) )
| ( SX2
= ( unordered_pair @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( unordered_pair @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ( SX3 != SX0 )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SX1 )
| ( in @ SX3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1944]) ).
thf(2025,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK40_SY287 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK39_C @ SX1 @ SX0 ) @ ( sK40_SY287 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK38_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK38_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1876]) ).
thf(2026,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK27_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK27_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK27_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK27_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1941]) ).
thf(2027,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] : ( subset @ ( cartesian_product2 @ SX0 @ SX2 ) @ ( cartesian_product2 @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] : ( subset @ ( cartesian_product2 @ SX2 @ SX0 ) @ ( cartesian_product2 @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1896]) ).
thf(2028,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ( element @ ( sK8_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK8_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1969]) ).
thf(2029,plain,
! [SV347: $i] :
( ( ( ( singleton @ SV347 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1866]) ).
thf(2030,plain,
! [SV348: $i] :
( ( subset @ empty_set @ SV348 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1871]) ).
thf(2031,plain,
! [SV349: $i] :
( ( ~ ( subset @ SV349 @ empty_set )
| ( SV349 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1875]) ).
thf(2032,plain,
! [SV350: $i] :
( ( ( empty @ SV350 )
| ~ ( relation @ SV350 )
| ~ ( empty @ ( relation_dom @ SV350 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1881]) ).
thf(2033,plain,
! [SV351: $i] :
( ( ( empty @ SV351 )
| ~ ( relation @ SV351 )
| ~ ( empty @ ( relation_rng @ SV351 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1882]) ).
thf(2034,plain,
! [SV352: $i] :
( ( ( set_union2 @ SV352 @ empty_set )
= SV352 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1883]) ).
thf(2035,plain,
! [SV353: $i] :
( ( ( set_intersection2 @ SV353 @ empty_set )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1884]) ).
thf(2036,plain,
! [SV354: $i] :
( ( ( set_difference @ SV354 @ empty_set )
= SV354 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1885]) ).
thf(2037,plain,
! [SV355: $i] :
( ( ( set_difference @ empty_set @ SV355 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1886]) ).
thf(2038,plain,
! [SV356: $i] :
( ( ~ ( empty @ SV356 )
| ( SV356 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1887]) ).
thf(2039,plain,
! [SV357: $i] :
( ( ! [SY583: $i] :
( ~ ( in @ SV357 @ SY583 )
| ( ( set_union2 @ ( singleton @ SV357 ) @ SY583 )
= SY583 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1888]) ).
thf(2040,plain,
! [SV358: $i] :
( ( ! [SY584: $i] :
( ~ ( disjoint @ ( singleton @ SV358 ) @ SY584 )
| ~ ( in @ SV358 @ SY584 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1889]) ).
thf(2041,plain,
! [SV359: $i] :
( ( ! [SY585: $i] :
( ( in @ SV359 @ SY585 )
| ( disjoint @ ( singleton @ SV359 ) @ SY585 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1890]) ).
thf(2042,plain,
! [SV360: $i] :
( ( ! [SY586: $i] :
( ~ ( element @ SY586 @ ( powerset @ SV360 ) )
| ! [SY587: $i] :
( ~ ( in @ SY587 @ SY586 )
| ( in @ SY587 @ SV360 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1892]) ).
thf(2043,plain,
! [SV361: $i] :
( ( ! [SY588: $i] :
( ~ ( subset @ SV361 @ SY588 )
| ! [SY589: $i] :
( ( in @ SY589 @ SV361 )
| ( subset @ SV361 @ ( set_difference @ SY588 @ ( singleton @ SY589 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1893]) ).
thf(2044,plain,
! [SV362: $i] :
( ( ! [SY590: $i] :
( ~ ( in @ SV362 @ SY590 )
| ( subset @ SV362 @ ( union @ SY590 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1894]) ).
thf(2045,plain,
! [SV363: $i] :
( ( ! [SY591: $i,SY592: $i,SY593: $i] :
( ~ ( subset @ SV363 @ SY591 )
| ~ ( subset @ SY592 @ SY593 )
| ( subset @ ( cartesian_product2 @ SV363 @ SY592 ) @ ( cartesian_product2 @ SY591 @ SY593 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1897]) ).
thf(2046,plain,
! [SV364: $i] :
( ( ! [SY594: $i] :
( ~ ( subset @ SV364 @ SY594 )
| ( ( set_union2 @ SV364 @ SY594 )
= SY594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1898]) ).
thf(2047,plain,
! [SV365: $i] :
( ( ! [SY595: $i] : ( subset @ ( set_intersection2 @ SV365 @ SY595 ) @ SV365 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1900]) ).
thf(2048,plain,
! [SV366: $i] :
( ( ! [SY596: $i,SY597: $i] :
( ~ ( subset @ SV366 @ SY596 )
| ~ ( subset @ SV366 @ SY597 )
| ( subset @ SV366 @ ( set_intersection2 @ SY596 @ SY597 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1901]) ).
thf(2049,plain,
! [SV367: $i] :
( ( ! [SY598: $i,SY599: $i] :
( ~ ( subset @ SV367 @ SY598 )
| ~ ( subset @ SY598 @ SY599 )
| ( subset @ SV367 @ SY599 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1902]) ).
thf(2050,plain,
! [SV368: $i] :
( ( ~ ( relation @ SV368 )
| ( subset @ SV368 @ ( cartesian_product2 @ ( relation_dom @ SV368 ) @ ( relation_rng @ SV368 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1904]) ).
thf(2051,plain,
! [SV369: $i] :
( ( ! [SY600: $i] :
( ~ ( subset @ SV369 @ SY600 )
| ! [SY601: $i] : ( subset @ ( set_intersection2 @ SV369 @ SY601 ) @ ( set_intersection2 @ SY600 @ SY601 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1905]) ).
thf(2052,plain,
! [SV370: $i] :
( ( ! [SY602: $i] :
( ~ ( subset @ SV370 @ SY602 )
| ( ( set_intersection2 @ SV370 @ SY602 )
= SV370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1906]) ).
thf(2053,plain,
! [SV371: $i] :
( ( ! [SY603: $i] :
( ~ ( subset @ SV371 @ SY603 )
| ! [SY604: $i] : ( subset @ ( set_difference @ SV371 @ SY604 ) @ ( set_difference @ SY603 @ SY604 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1907]) ).
thf(2054,plain,
! [SV372: $i] :
( ( ! [SY605: $i] : ( subset @ ( set_difference @ SV372 @ SY605 ) @ SV372 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1908]) ).
thf(2055,plain,
! [SV373: $i] :
( ( ! [SY606: $i] :
( ( set_union2 @ SV373 @ ( set_difference @ SY606 @ SV373 ) )
= ( set_union2 @ SV373 @ SY606 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1911]) ).
thf(2056,plain,
! [SV374: $i] :
( ( ! [SY607: $i] :
( ( set_difference @ ( set_union2 @ SV374 @ SY607 ) @ SY607 )
= ( set_difference @ SV374 @ SY607 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1913]) ).
thf(2057,plain,
! [SV375: $i] :
( ( ~ ( relation @ SV375 )
| ! [SY608: $i] :
( ~ ( relation @ SY608 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV375 @ SY608 ) ) @ ( relation_dom @ SV375 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1914]) ).
thf(2058,plain,
! [SV376: $i] :
( ( ~ ( relation @ SV376 )
| ! [SY609: $i] :
( ~ ( relation @ SY609 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV376 @ SY609 ) ) @ ( relation_rng @ SY609 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1915]) ).
thf(2059,plain,
! [SV377: $i] :
( ( ! [SY610: $i] :
( ~ ( subset @ SV377 @ SY610 )
| ( SY610
= ( set_union2 @ SV377 @ ( set_difference @ SY610 @ SV377 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1916]) ).
thf(2060,plain,
! [SV378: $i] :
( ( ~ ( relation @ SV378 )
| ! [SY611: $i] :
( ~ ( relation @ SY611 )
| ~ ( subset @ ( relation_rng @ SV378 ) @ ( relation_dom @ SY611 ) )
| ( ( relation_dom @ ( relation_composition @ SV378 @ SY611 ) )
= ( relation_dom @ SV378 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1917]) ).
thf(2061,plain,
! [SV379: $i] :
( ( ! [SY612: $i] :
( ~ ( in @ SV379 @ SY612 )
| ( ( set_union2 @ ( singleton @ SV379 ) @ SY612 )
= SY612 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1918]) ).
thf(2062,plain,
! [SV380: $i] :
( ( ~ ( relation @ SV380 )
| ! [SY613: $i] :
( ~ ( relation @ SY613 )
| ~ ( subset @ ( relation_dom @ SV380 ) @ ( relation_rng @ SY613 ) )
| ( ( relation_rng @ ( relation_composition @ SY613 @ SV380 ) )
= ( relation_rng @ SV380 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1919]) ).
thf(2063,plain,
! [SV381: $i] :
( ( ! [SY614: $i] :
( ( set_difference @ SV381 @ ( set_difference @ SV381 @ SY614 ) )
= ( set_intersection2 @ SV381 @ SY614 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1920]) ).
thf(2064,plain,
! [SV382: $i] :
( ( ~ ( relation @ SV382 )
| ( in @ ( ordered_pair @ ( sK31_B @ SV382 ) @ ( sK32_SY282 @ SV382 ) ) @ SV382 )
| ( SV382 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1922]) ).
thf(2065,plain,
! [SV383: $i] :
( ( ! [SY615: $i] :
( ~ ( proper_subset @ SY615 @ SV383 )
| ~ ( subset @ SV383 @ SY615 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1923]) ).
thf(2066,plain,
! [SV384: $i] :
( ( ! [SY616: $i,SY617: $i] :
( ~ ( disjoint @ SY616 @ SY617 )
| ~ ( subset @ SV384 @ SY616 )
| ( disjoint @ SV384 @ SY617 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1924]) ).
thf(2067,plain,
! [SV385: $i] :
( ( ( unordered_pair @ SV385 @ SV385 )
= ( singleton @ SV385 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1926]) ).
thf(2068,plain,
! [SV386: $i] :
( ( ! [SY618: $i] :
( ~ ( subset @ ( singleton @ SV386 ) @ ( singleton @ SY618 ) )
| ( SV386 = SY618 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1927]) ).
thf(2069,plain,
! [SV387: $i] :
( ( ! [SY619: $i] : ( subset @ SV387 @ ( set_union2 @ SV387 @ SY619 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1928]) ).
thf(2070,plain,
! [SV388: $i] :
( ( ! [SY620: $i,SY621: $i] :
( ~ ( subset @ SV388 @ SY620 )
| ~ ( subset @ SY621 @ SY620 )
| ( subset @ ( set_union2 @ SV388 @ SY621 ) @ SY620 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1930]) ).
thf(2071,plain,
! [SV389: $i] :
( ( ! [SY622: $i] :
( ! [SY623: $i] :
( ( singleton @ SV389 )
!= ( unordered_pair @ SY622 @ SY623 ) )
| ( SV389 = SY622 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1931]) ).
thf(2072,plain,
! [SV390: $i] :
( ( ! [SY624: $i] :
( ~ ( in @ SV390 @ SY624 )
| ( subset @ SV390 @ ( union @ SY624 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1932]) ).
thf(2073,plain,
! [SV391: $i] :
( ( ( union @ ( powerset @ SV391 ) )
= SV391 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1933]) ).
thf(2074,plain,
! [SV392: $i] :
( ( ! [SY625: $i,SY626: $i] :
( ( ( singleton @ SV392 )
!= ( unordered_pair @ SY625 @ SY626 ) )
| ( SY625 = SY626 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1934]) ).
thf(2075,plain,
! [SV393: $i] :
( ( ! [SY627: $i] :
( ~ ( in @ SV393 @ SY627 )
| ~ ( in @ SY627 @ SV393 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1935]) ).
thf(2076,plain,
! [SV394: $i] :
( ( ~ ( empty @ SV394 )
| ( relation @ SV394 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1936]) ).
thf(2077,plain,
! [SV395: $i] :
( ( ! [SY628: $i] :
( ( set_union2 @ SV395 @ SY628 )
= ( set_union2 @ SY628 @ SV395 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1937]) ).
thf(2078,plain,
! [SV396: $i] :
( ( ! [SY629: $i] :
( ( set_intersection2 @ SV396 @ SY629 )
= ( set_intersection2 @ SY629 @ SV396 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1938]) ).
thf(2079,plain,
! [SV397: $i] :
( ( ~ ( relation @ SV397 )
| ( ( relation_field @ SV397 )
= ( set_union2 @ ( relation_dom @ SV397 ) @ ( relation_rng @ SV397 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1952]) ).
thf(2080,plain,
! [SV398: $i] :
( ( ~ ( relation @ SV398 )
| ( relation @ ( relation_inverse @ SV398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1955]) ).
thf(2081,plain,
! [SV399: $i] :
( ( ! [SY630: $i] :
( ~ ( relation @ SV399 )
| ~ ( relation @ SY630 )
| ( relation @ ( relation_composition @ SV399 @ SY630 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1956]) ).
thf(2082,plain,
! [SV400: $i] :
( ( ~ ( empty @ ( powerset @ SV400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1957]) ).
thf(2083,plain,
! [SV401: $i] :
( ( ! [SY631: $i] :
~ ( empty @ ( ordered_pair @ SV401 @ SY631 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1958]) ).
thf(2084,plain,
! [SV402: $i] :
( ( ! [SY632: $i] :
( ~ ( relation @ SV402 )
| ~ ( relation @ SY632 )
| ( relation @ ( set_union2 @ SV402 @ SY632 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1959]) ).
thf(2085,plain,
! [SV403: $i] :
( ( ~ ( empty @ ( singleton @ SV403 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1960]) ).
thf(2086,plain,
! [SV404: $i] :
( ( ( empty @ SV404 )
| ! [SY633: $i] :
~ ( empty @ ( set_union2 @ SV404 @ SY633 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1961]) ).
thf(2087,plain,
! [SV405: $i] :
( ( ! [SY634: $i] :
~ ( empty @ ( unordered_pair @ SV405 @ SY634 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1962]) ).
thf(2088,plain,
! [SV406: $i] :
( ( ( empty @ SV406 )
| ! [SY635: $i] :
~ ( empty @ ( set_union2 @ SY635 @ SV406 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1963]) ).
thf(2089,plain,
! [SV407: $i] :
( ( ! [SY636: $i] :
( ( empty @ SV407 )
| ( empty @ SY636 )
| ~ ( empty @ ( cartesian_product2 @ SV407 @ SY636 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1964]) ).
thf(2090,plain,
! [SV408: $i] :
( ( ( set_union2 @ SV408 @ SV408 )
= SV408 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1965]) ).
thf(2091,plain,
! [SV409: $i] :
( ( ( set_intersection2 @ SV409 @ SV409 )
= SV409 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1966]) ).
thf(2092,plain,
! [SV410: $i] :
( ( ~ ( relation @ SV410 )
| ( ( relation_inverse @ ( relation_inverse @ SV410 ) )
= SV410 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1967]) ).
thf(2093,plain,
( ( empty @ sK4_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1973]) ).
thf(2094,plain,
! [SV411: $i] :
( ( subset @ SV411 @ SV411 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1974]) ).
thf(2095,plain,
! [SV412: $i] :
( ( ! [SY637: $i] :
( ~ ( disjoint @ SV412 @ SY637 )
| ( disjoint @ SY637 @ SV412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1975]) ).
thf(2096,plain,
! [SV413: $i] :
( ( ! [SY638: $i] :
( ~ ( in @ SV413 @ SY638 )
| ( element @ SV413 @ SY638 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1976]) ).
thf(2097,plain,
! [SV414: $i] :
( ( ! [SY639: $i] :
( ~ ( element @ SV414 @ SY639 )
| ( empty @ SY639 )
| ( in @ SV414 @ SY639 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1977]) ).
thf(2098,plain,
! [SV415: $i] :
( ( ! [SY640: $i,SY641: $i] :
( ~ ( element @ SY640 @ ( powerset @ SY641 ) )
| ~ ( in @ SV415 @ SY640 )
| ( element @ SV415 @ SY641 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1980]) ).
thf(2099,plain,
! [SV416: $i] :
( ( ! [SY642: $i,SY643: $i] :
( ~ ( element @ SY642 @ ( powerset @ SY643 ) )
| ~ ( in @ SV416 @ SY642 )
| ~ ( empty @ SY643 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1981]) ).
thf(2100,plain,
! [SV417: $i] :
( ( ! [SY644: $i] :
( ~ ( empty @ SY644 )
| ~ ( in @ SV417 @ SY644 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1982]) ).
thf(2101,plain,
! [SV418: $i] :
( ( ! [SY645: $i] :
( ( SV418 = SY645 )
| ~ ( empty @ SV418 )
| ~ ( empty @ SY645 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1983]) ).
thf(2102,plain,
( ( ( relation_rng @ empty_set )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1985]) ).
thf(2103,plain,
! [SV419: $i] :
( ( ~ ( ~ ! [SY646: $i,SY647: $i] :
( ~ ( in @ SV419 @ SY647 )
| ~ ( in @ SY646 @ SY647 )
| ( subset @ ( unordered_pair @ SV419 @ SY646 ) @ SY647 ) )
| ~ ~ ( ~ ! [SY648: $i,SY649: $i] :
( ~ ( subset @ ( unordered_pair @ SV419 @ SY648 ) @ SY649 )
| ( in @ SV419 @ SY649 ) )
| ~ ! [SY650: $i,SY651: $i] :
( ~ ( subset @ ( unordered_pair @ SV419 @ SY650 ) @ SY651 )
| ( in @ SY650 @ SY651 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1986]) ).
thf(2104,plain,
! [SV420: $i] :
( ( ~ ( relation @ SV420 )
| ~ ( ~ ! [SY652: $i] :
( ~ ( relation @ SY652 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SY652 @ SV420 ) @ ( sK11_SY272 @ SY652 @ SV420 ) ) @ SY652 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY272 @ SY652 @ SV420 ) @ ( sK10_C @ SY652 @ SV420 ) ) @ SV420 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK10_C @ SY652 @ SV420 ) @ ( sK11_SY272 @ SY652 @ SV420 ) ) @ SY652 )
| ( in @ ( ordered_pair @ ( sK11_SY272 @ SY652 @ SV420 ) @ ( sK10_C @ SY652 @ SV420 ) ) @ SV420 ) ) )
| ( SY652
= ( relation_inverse @ SV420 ) ) )
| ~ ! [SY653: $i] :
( ~ ( relation @ SY653 )
| ( SY653
!= ( relation_inverse @ SV420 ) )
| ~ ( ~ ! [SY654: $i,SY655: $i] :
( ~ ( in @ ( ordered_pair @ SY654 @ SY655 ) @ SY653 )
| ( in @ ( ordered_pair @ SY655 @ SY654 ) @ SV420 ) )
| ~ ! [SY656: $i,SY657: $i] :
( ~ ( in @ ( ordered_pair @ SY657 @ SY656 ) @ SV420 )
| ( in @ ( ordered_pair @ SY656 @ SY657 ) @ SY653 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1987]) ).
thf(2105,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK33_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1988]) ).
thf(2106,plain,
! [SV421: $i] :
( ( ! [SY658: $i] :
( ~ ( ~ ( ~ ( in @ ( sK3_C @ SY658 @ SV421 ) @ SV421 )
| ~ ( in @ ( sK3_C @ SY658 @ SV421 ) @ SY658 ) )
| ~ ( ( in @ ( sK3_C @ SY658 @ SV421 ) @ SV421 )
| ( in @ ( sK3_C @ SY658 @ SV421 ) @ SY658 ) ) )
| ( SV421 = SY658 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1989]) ).
thf(2107,plain,
! [SV422: $i] :
( ( ~ ( ~ ! [SY659: $i,SY660: $i] :
( ~ ( relation @ SY660 )
| ~ ( in @ ( ordered_pair @ SV422 @ SY659 ) @ SY660 )
| ( in @ SV422 @ ( relation_dom @ SY660 ) ) )
| ~ ! [SY661: $i,SY662: $i] :
( ~ ( relation @ SY662 )
| ~ ( in @ ( ordered_pair @ SV422 @ SY661 ) @ SY662 )
| ( in @ SY661 @ ( relation_rng @ SY662 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1990]) ).
thf(2108,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1991]) ).
thf(2109,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1992]) ).
thf(2110,plain,
! [SV423: $i] :
( ( ~ ( ~ ! [SY663: $i,SY664: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK24_D @ SY664 @ SY663 @ SV423 ) @ SY664 )
| ~ ( in @ ( sK24_D @ SY664 @ SY663 @ SV423 ) @ SV423 ) )
| ~ ( ~ ( in @ ( sK24_D @ SY664 @ SY663 @ SV423 ) @ SY664 )
| ~ ( in @ ( sK24_D @ SY664 @ SY663 @ SV423 ) @ SY663 ) ) )
| ~ ( ( in @ ( sK24_D @ SY664 @ SY663 @ SV423 ) @ SY664 )
| ( in @ ( sK24_D @ SY664 @ SY663 @ SV423 ) @ SV423 )
| ( in @ ( sK24_D @ SY664 @ SY663 @ SV423 ) @ SY663 ) ) )
| ( SY664
= ( set_union2 @ SV423 @ SY663 ) ) )
| ~ ! [SY665: $i,SY666: $i] :
( ( SY666
!= ( set_union2 @ SV423 @ SY665 ) )
| ~ ( ~ ! [SY667: $i] :
( ~ ( in @ SY667 @ SY666 )
| ( in @ SY667 @ SV423 )
| ( in @ SY667 @ SY665 ) )
| ~ ~ ( ~ ! [SY668: $i] :
( ~ ( in @ SY668 @ SV423 )
| ( in @ SY668 @ SY666 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY665 )
| ( in @ SX3 @ SY666 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1993]) ).
thf(2111,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1994]) ).
thf(2112,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1995]) ).
thf(2113,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK34_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK34_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1996]) ).
thf(2114,plain,
( ( ~ ( empty @ sK9_A )
| ~ ( relation @ sK9_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1997]) ).
thf(2115,plain,
! [SV424: $i] :
( ( ~ ( ~ ! [SY670: $i] :
( ~ ( subset @ SY670 @ ( sK35_B @ SV424 ) )
| ( are_equipotent @ SY670 @ ( sK35_B @ SV424 ) )
| ( in @ SY670 @ ( sK35_B @ SV424 ) ) )
| ~ ~ ( ~ ! [SY671: $i] :
( ~ ( in @ SY671 @ ( sK35_B @ SV424 ) )
| ( in @ ( powerset @ SY671 ) @ ( sK35_B @ SV424 ) ) )
| ~ ~ ( ~ ! [SY672: $i,SY673: $i] :
( ~ ( in @ SY672 @ ( sK35_B @ SV424 ) )
| ~ ( subset @ SY673 @ SY672 )
| ( in @ SY673 @ ( sK35_B @ SV424 ) ) )
| ~ ( in @ SV424 @ ( sK35_B @ SV424 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1998]) ).
thf(2116,plain,
! [SV425: $i] :
( ( ~ ( relation @ SV425 )
| ~ ( ~ ! [SY674: $i] :
( ~ ( relation @ SY674 )
| ~ ( subset @ SV425 @ SY674 )
| ( subset @ ( relation_dom @ SV425 ) @ ( relation_dom @ SY674 ) ) )
| ~ ! [SY675: $i] :
( ~ ( relation @ SY675 )
| ~ ( subset @ SV425 @ SY675 )
| ( subset @ ( relation_rng @ SV425 ) @ ( relation_rng @ SY675 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1999]) ).
thf(2117,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2000]) ).
thf(2118,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK37_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2001]) ).
thf(2119,plain,
! [SV426: $i] :
( ( ~ ( ~ ! [SY676: $i] :
( ~ ( subset @ SY676 @ ( sK1_B @ SV426 ) )
| ( are_equipotent @ SY676 @ ( sK1_B @ SV426 ) )
| ( in @ SY676 @ ( sK1_B @ SV426 ) ) )
| ~ ~ ( ~ ! [SY677: $i] :
( ~ ( ~ ! [SY678: $i] :
( ~ ( subset @ SY678 @ SY677 )
| ( in @ SY678 @ ( sK2_SY267 @ SY677 @ SV426 ) ) )
| ~ ( in @ ( sK2_SY267 @ SY677 @ SV426 ) @ ( sK1_B @ SV426 ) ) )
| ~ ( in @ SY677 @ ( sK1_B @ SV426 ) ) )
| ~ ~ ( ~ ! [SY679: $i,SY680: $i] :
( ~ ( in @ SY679 @ ( sK1_B @ SV426 ) )
| ~ ( subset @ SY680 @ SY679 )
| ( in @ SY680 @ ( sK1_B @ SV426 ) ) )
| ~ ( in @ SV426 @ ( sK1_B @ SV426 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2002]) ).
thf(2120,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2003]) ).
thf(2121,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK26_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK26_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK26_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK26_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2004]) ).
thf(2122,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2005]) ).
thf(2123,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2006]) ).
thf(2124,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK30_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK30_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK28_C @ SX1 @ SX0 ) @ ( sK29_SY279 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2007]) ).
thf(2125,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2008]) ).
thf(2126,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2009]) ).
thf(2127,plain,
( ( ~ ~ ( empty @ sK6_A )
| ~ ( relation @ sK6_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2010]) ).
thf(2128,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)],[2011]) ).
thf(2129,plain,
! [SV427: $i] :
( ( ~ ( relation @ SV427 )
| ~ ( ~ ! [SY681: $i] :
( ~ ( ~ ( ! [SY682: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SY681 @ SV427 ) @ SY682 ) @ SV427 )
| ~ ( in @ ( sK20_C @ SY681 @ SV427 ) @ SY681 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_C @ SY681 @ SV427 ) @ ( sK21_SY278 @ SY681 @ SV427 ) ) @ SV427 )
| ( in @ ( sK20_C @ SY681 @ SV427 ) @ SY681 ) ) )
| ( SY681
= ( relation_dom @ SV427 ) ) )
| ~ ! [SY683: $i] :
( ( SY683
!= ( relation_dom @ SV427 ) )
| ~ ( ~ ! [SY684: $i] :
( ! [SY685: $i] :
~ ( in @ ( ordered_pair @ SY684 @ SY685 ) @ SV427 )
| ( in @ SY684 @ SY683 ) )
| ~ ! [SY686: $i] :
( ~ ( in @ SY686 @ SY683 )
| ( in @ ( ordered_pair @ SY686 @ ( sK19_D @ SY686 @ SY683 @ SV427 ) ) @ SV427 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2012]) ).
thf(2130,plain,
! [SV428: $i] :
( ( ~ ( ~ ! [SY687: $i,SY688: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SY688 @ SY687 @ SV428 ) @ SV428 )
| ( in @ ( sK15_D @ SY688 @ SY687 @ SV428 ) @ SY687 )
| ~ ( in @ ( sK15_D @ SY688 @ SY687 @ SV428 ) @ SY688 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SY688 @ SY687 @ SV428 ) @ SV428 )
| ( in @ ( sK15_D @ SY688 @ SY687 @ SV428 ) @ SY688 ) )
| ~ ( ~ ( in @ ( sK15_D @ SY688 @ SY687 @ SV428 ) @ SY687 )
| ( in @ ( sK15_D @ SY688 @ SY687 @ SV428 ) @ SY688 ) ) ) )
| ( SY688
= ( set_difference @ SV428 @ SY687 ) ) )
| ~ ! [SY689: $i,SY690: $i] :
( ( SY690
!= ( set_difference @ SV428 @ SY689 ) )
| ~ ( ~ ! [SY691: $i] :
( ~ ( in @ SY691 @ SV428 )
| ( in @ SY691 @ SY689 )
| ( in @ SY691 @ SY690 ) )
| ~ ~ ( ~ ! [SY692: $i] :
( ~ ( in @ SY692 @ SY690 )
| ( in @ SY692 @ SV428 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY690 )
| ~ ( in @ SX3 @ SY689 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2013]) ).
thf(2131,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2014]) ).
thf(2132,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2015]) ).
thf(2133,plain,
! [SV429: $i] :
( ( ~ ( ~ ! [SY694: $i,SY695: $i] :
( ~ ( ~ ( ~ ( in @ ( sK22_D @ SY695 @ SY694 @ SV429 ) @ SV429 )
| ~ ( in @ ( sK22_D @ SY695 @ SY694 @ SV429 ) @ SY694 )
| ~ ( in @ ( sK22_D @ SY695 @ SY694 @ SV429 ) @ SY695 ) )
| ~ ~ ( ~ ( ( in @ ( sK22_D @ SY695 @ SY694 @ SV429 ) @ SV429 )
| ( in @ ( sK22_D @ SY695 @ SY694 @ SV429 ) @ SY695 ) )
| ~ ( ( in @ ( sK22_D @ SY695 @ SY694 @ SV429 ) @ SY694 )
| ( in @ ( sK22_D @ SY695 @ SY694 @ SV429 ) @ SY695 ) ) ) )
| ( SY695
= ( set_intersection2 @ SV429 @ SY694 ) ) )
| ~ ! [SY696: $i,SY697: $i] :
( ( SY697
!= ( set_intersection2 @ SV429 @ SY696 ) )
| ~ ( ~ ! [SY698: $i] :
( ~ ( in @ SY698 @ SV429 )
| ~ ( in @ SY698 @ SY696 )
| ( in @ SY698 @ SY697 ) )
| ~ ~ ( ~ ! [SY699: $i] :
( ~ ( in @ SY699 @ SY697 )
| ( in @ SY699 @ SV429 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY697 )
| ( in @ SX3 @ SY696 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2016]) ).
thf(2134,plain,
! [SV430: $i] :
( ( ~ ( relation @ SV430 )
| ~ ( ~ ! [SY701: $i] :
( ~ ( ~ ( ! [SY702: $i] :
~ ( in @ ( ordered_pair @ SY702 @ ( sK13_C @ SY701 @ SV430 ) ) @ SV430 )
| ~ ( in @ ( sK13_C @ SY701 @ SV430 ) @ SY701 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY274 @ SY701 @ SV430 ) @ ( sK13_C @ SY701 @ SV430 ) ) @ SV430 )
| ( in @ ( sK13_C @ SY701 @ SV430 ) @ SY701 ) ) )
| ( SY701
= ( relation_rng @ SV430 ) ) )
| ~ ! [SY703: $i] :
( ( SY703
!= ( relation_rng @ SV430 ) )
| ~ ( ~ ! [SY704: $i] :
( ! [SY705: $i] :
~ ( in @ ( ordered_pair @ SY705 @ SY704 ) @ SV430 )
| ( in @ SY704 @ SY703 ) )
| ~ ! [SY706: $i] :
( ~ ( in @ SY706 @ SY703 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY706 @ SY703 @ SV430 ) @ SY706 ) @ SV430 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2017]) ).
thf(2135,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ ( sK18_SY276 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK18_SY276 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK16_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK16_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2018]) ).
thf(2136,plain,
! [SV431: $i] :
( ( ~ ( ~ ( element @ ( sK5_B @ SV431 ) @ ( powerset @ SV431 ) )
| ~ ( empty @ ( sK5_B @ SV431 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2019]) ).
thf(2137,plain,
! [SV432: $i] :
( ( ! [SY707: $i] :
( ~ ( ~ ( in @ ( sK36_C @ SY707 @ SV432 ) @ SV432 )
| ~ ~ ( in @ ( sK36_C @ SY707 @ SV432 ) @ SY707 ) )
| ( element @ SV432 @ ( powerset @ SY707 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2020]) ).
thf(2138,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2021]) ).
thf(2139,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2022]) ).
thf(2140,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2023]) ).
thf(2141,plain,
! [SV433: $i] :
( ( ~ ( ~ ! [SY708: $i,SY709: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK25_D @ SY709 @ SY708 @ SV433 ) @ SY709 )
| ( ( sK25_D @ SY709 @ SY708 @ SV433 )
!= SV433 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY709 @ SY708 @ SV433 ) @ SY709 )
| ( ( sK25_D @ SY709 @ SY708 @ SV433 )
!= SY708 ) ) )
| ~ ( ( in @ ( sK25_D @ SY709 @ SY708 @ SV433 ) @ SY709 )
| ( ( sK25_D @ SY709 @ SY708 @ SV433 )
= SV433 )
| ( ( sK25_D @ SY709 @ SY708 @ SV433 )
= SY708 ) ) )
| ( SY709
= ( unordered_pair @ SV433 @ SY708 ) ) )
| ~ ! [SY710: $i,SY711: $i] :
( ( SY711
!= ( unordered_pair @ SV433 @ SY710 ) )
| ~ ( ~ ! [SY712: $i] :
( ~ ( in @ SY712 @ SY711 )
| ( SY712 = SV433 )
| ( SY712 = SY710 ) )
| ~ ~ ( ~ ! [SY713: $i] :
( ( SY713 != SV433 )
| ( in @ SY713 @ SY711 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY710 )
| ( in @ SX3 @ SY711 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2024]) ).
thf(2142,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK40_SY287 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK39_C @ SX1 @ SX0 ) @ ( sK40_SY287 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK38_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK38_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2025]) ).
thf(2143,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK27_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK27_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK27_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK27_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2026]) ).
thf(2144,plain,
! [SV434: $i] :
( ( ~ ( ~ ! [SY715: $i] :
( ~ ( subset @ SV434 @ SY715 )
| ! [SY716: $i] : ( subset @ ( cartesian_product2 @ SV434 @ SY716 ) @ ( cartesian_product2 @ SY715 @ SY716 ) ) )
| ~ ! [SY717: $i] :
( ~ ( subset @ SV434 @ SY717 )
| ! [SY718: $i] : ( subset @ ( cartesian_product2 @ SY718 @ SV434 ) @ ( cartesian_product2 @ SY718 @ SY717 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2027]) ).
thf(2145,plain,
! [SV435: $i] :
( ( ( empty @ SV435 )
| ~ ( ~ ( element @ ( sK8_B @ SV435 ) @ ( powerset @ SV435 ) )
| ~ ~ ( empty @ ( sK8_B @ SV435 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2028]) ).
thf(2146,plain,
! [SV347: $i] :
( ( ( singleton @ SV347 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2029]) ).
thf(2147,plain,
! [SV349: $i] :
( ( ( ~ ( subset @ SV349 @ empty_set ) )
= $true )
| ( ( SV349 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2031]) ).
thf(2148,plain,
! [SV350: $i] :
( ( ( ( empty @ SV350 )
| ~ ( relation @ SV350 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV350 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2032]) ).
thf(2149,plain,
! [SV351: $i] :
( ( ( ( empty @ SV351 )
| ~ ( relation @ SV351 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV351 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2033]) ).
thf(2150,plain,
! [SV356: $i] :
( ( ( ~ ( empty @ SV356 ) )
= $true )
| ( ( SV356 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2038]) ).
thf(2151,plain,
! [SV436: $i,SV357: $i] :
( ( ~ ( in @ SV357 @ SV436 )
| ( ( set_union2 @ ( singleton @ SV357 ) @ SV436 )
= SV436 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2039]) ).
thf(2152,plain,
! [SV437: $i,SV358: $i] :
( ( ~ ( disjoint @ ( singleton @ SV358 ) @ SV437 )
| ~ ( in @ SV358 @ SV437 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2040]) ).
thf(2153,plain,
! [SV438: $i,SV359: $i] :
( ( ( in @ SV359 @ SV438 )
| ( disjoint @ ( singleton @ SV359 ) @ SV438 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2041]) ).
thf(2154,plain,
! [SV360: $i,SV439: $i] :
( ( ~ ( element @ SV439 @ ( powerset @ SV360 ) )
| ! [SY719: $i] :
( ~ ( in @ SY719 @ SV439 )
| ( in @ SY719 @ SV360 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2042]) ).
thf(2155,plain,
! [SV440: $i,SV361: $i] :
( ( ~ ( subset @ SV361 @ SV440 )
| ! [SY720: $i] :
( ( in @ SY720 @ SV361 )
| ( subset @ SV361 @ ( set_difference @ SV440 @ ( singleton @ SY720 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2043]) ).
thf(2156,plain,
! [SV441: $i,SV362: $i] :
( ( ~ ( in @ SV362 @ SV441 )
| ( subset @ SV362 @ ( union @ SV441 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2044]) ).
thf(2157,plain,
! [SV442: $i,SV363: $i] :
( ( ! [SY721: $i,SY722: $i] :
( ~ ( subset @ SV363 @ SV442 )
| ~ ( subset @ SY721 @ SY722 )
| ( subset @ ( cartesian_product2 @ SV363 @ SY721 ) @ ( cartesian_product2 @ SV442 @ SY722 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2045]) ).
thf(2158,plain,
! [SV443: $i,SV364: $i] :
( ( ~ ( subset @ SV364 @ SV443 )
| ( ( set_union2 @ SV364 @ SV443 )
= SV443 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2046]) ).
thf(2159,plain,
! [SV444: $i,SV365: $i] :
( ( subset @ ( set_intersection2 @ SV365 @ SV444 ) @ SV365 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2047]) ).
thf(2160,plain,
! [SV445: $i,SV366: $i] :
( ( ! [SY723: $i] :
( ~ ( subset @ SV366 @ SV445 )
| ~ ( subset @ SV366 @ SY723 )
| ( subset @ SV366 @ ( set_intersection2 @ SV445 @ SY723 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2048]) ).
thf(2161,plain,
! [SV446: $i,SV367: $i] :
( ( ! [SY724: $i] :
( ~ ( subset @ SV367 @ SV446 )
| ~ ( subset @ SV446 @ SY724 )
| ( subset @ SV367 @ SY724 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2049]) ).
thf(2162,plain,
! [SV368: $i] :
( ( ( ~ ( relation @ SV368 ) )
= $true )
| ( ( subset @ SV368 @ ( cartesian_product2 @ ( relation_dom @ SV368 ) @ ( relation_rng @ SV368 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2050]) ).
thf(2163,plain,
! [SV447: $i,SV369: $i] :
( ( ~ ( subset @ SV369 @ SV447 )
| ! [SY725: $i] : ( subset @ ( set_intersection2 @ SV369 @ SY725 ) @ ( set_intersection2 @ SV447 @ SY725 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2051]) ).
thf(2164,plain,
! [SV448: $i,SV370: $i] :
( ( ~ ( subset @ SV370 @ SV448 )
| ( ( set_intersection2 @ SV370 @ SV448 )
= SV370 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2052]) ).
thf(2165,plain,
! [SV449: $i,SV371: $i] :
( ( ~ ( subset @ SV371 @ SV449 )
| ! [SY726: $i] : ( subset @ ( set_difference @ SV371 @ SY726 ) @ ( set_difference @ SV449 @ SY726 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2053]) ).
thf(2166,plain,
! [SV450: $i,SV372: $i] :
( ( subset @ ( set_difference @ SV372 @ SV450 ) @ SV372 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2054]) ).
thf(2167,plain,
! [SV451: $i,SV373: $i] :
( ( ( set_union2 @ SV373 @ ( set_difference @ SV451 @ SV373 ) )
= ( set_union2 @ SV373 @ SV451 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2055]) ).
thf(2168,plain,
! [SV452: $i,SV374: $i] :
( ( ( set_difference @ ( set_union2 @ SV374 @ SV452 ) @ SV452 )
= ( set_difference @ SV374 @ SV452 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2056]) ).
thf(2169,plain,
! [SV375: $i] :
( ( ( ~ ( relation @ SV375 ) )
= $true )
| ( ( ! [SY608: $i] :
( ~ ( relation @ SY608 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV375 @ SY608 ) ) @ ( relation_dom @ SV375 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2057]) ).
thf(2170,plain,
! [SV376: $i] :
( ( ( ~ ( relation @ SV376 ) )
= $true )
| ( ( ! [SY609: $i] :
( ~ ( relation @ SY609 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV376 @ SY609 ) ) @ ( relation_rng @ SY609 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2058]) ).
thf(2171,plain,
! [SV453: $i,SV377: $i] :
( ( ~ ( subset @ SV377 @ SV453 )
| ( SV453
= ( set_union2 @ SV377 @ ( set_difference @ SV453 @ SV377 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2059]) ).
thf(2172,plain,
! [SV378: $i] :
( ( ( ~ ( relation @ SV378 ) )
= $true )
| ( ( ! [SY611: $i] :
( ~ ( relation @ SY611 )
| ~ ( subset @ ( relation_rng @ SV378 ) @ ( relation_dom @ SY611 ) )
| ( ( relation_dom @ ( relation_composition @ SV378 @ SY611 ) )
= ( relation_dom @ SV378 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2060]) ).
thf(2173,plain,
! [SV454: $i,SV379: $i] :
( ( ~ ( in @ SV379 @ SV454 )
| ( ( set_union2 @ ( singleton @ SV379 ) @ SV454 )
= SV454 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2061]) ).
thf(2174,plain,
! [SV380: $i] :
( ( ( ~ ( relation @ SV380 ) )
= $true )
| ( ( ! [SY613: $i] :
( ~ ( relation @ SY613 )
| ~ ( subset @ ( relation_dom @ SV380 ) @ ( relation_rng @ SY613 ) )
| ( ( relation_rng @ ( relation_composition @ SY613 @ SV380 ) )
= ( relation_rng @ SV380 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2062]) ).
thf(2175,plain,
! [SV455: $i,SV381: $i] :
( ( ( set_difference @ SV381 @ ( set_difference @ SV381 @ SV455 ) )
= ( set_intersection2 @ SV381 @ SV455 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2063]) ).
thf(2176,plain,
! [SV382: $i] :
( ( ( ~ ( relation @ SV382 ) )
= $true )
| ( ( ( in @ ( ordered_pair @ ( sK31_B @ SV382 ) @ ( sK32_SY282 @ SV382 ) ) @ SV382 )
| ( SV382 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2064]) ).
thf(2177,plain,
! [SV383: $i,SV456: $i] :
( ( ~ ( proper_subset @ SV456 @ SV383 )
| ~ ( subset @ SV383 @ SV456 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2065]) ).
thf(2178,plain,
! [SV384: $i,SV457: $i] :
( ( ! [SY727: $i] :
( ~ ( disjoint @ SV457 @ SY727 )
| ~ ( subset @ SV384 @ SV457 )
| ( disjoint @ SV384 @ SY727 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2066]) ).
thf(2179,plain,
! [SV458: $i,SV386: $i] :
( ( ~ ( subset @ ( singleton @ SV386 ) @ ( singleton @ SV458 ) )
| ( SV386 = SV458 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2068]) ).
thf(2180,plain,
! [SV459: $i,SV387: $i] :
( ( subset @ SV387 @ ( set_union2 @ SV387 @ SV459 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2069]) ).
thf(2181,plain,
! [SV460: $i,SV388: $i] :
( ( ! [SY728: $i] :
( ~ ( subset @ SV388 @ SV460 )
| ~ ( subset @ SY728 @ SV460 )
| ( subset @ ( set_union2 @ SV388 @ SY728 ) @ SV460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2070]) ).
thf(2182,plain,
! [SV461: $i,SV389: $i] :
( ( ! [SY729: $i] :
( ( singleton @ SV389 )
!= ( unordered_pair @ SV461 @ SY729 ) )
| ( SV389 = SV461 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2071]) ).
thf(2183,plain,
! [SV462: $i,SV390: $i] :
( ( ~ ( in @ SV390 @ SV462 )
| ( subset @ SV390 @ ( union @ SV462 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2072]) ).
thf(2184,plain,
! [SV463: $i,SV392: $i] :
( ( ! [SY730: $i] :
( ( ( singleton @ SV392 )
!= ( unordered_pair @ SV463 @ SY730 ) )
| ( SV463 = SY730 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2074]) ).
thf(2185,plain,
! [SV464: $i,SV393: $i] :
( ( ~ ( in @ SV393 @ SV464 )
| ~ ( in @ SV464 @ SV393 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2075]) ).
thf(2186,plain,
! [SV394: $i] :
( ( ( ~ ( empty @ SV394 ) )
= $true )
| ( ( relation @ SV394 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2076]) ).
thf(2187,plain,
! [SV465: $i,SV395: $i] :
( ( ( set_union2 @ SV395 @ SV465 )
= ( set_union2 @ SV465 @ SV395 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2077]) ).
thf(2188,plain,
! [SV466: $i,SV396: $i] :
( ( ( set_intersection2 @ SV396 @ SV466 )
= ( set_intersection2 @ SV466 @ SV396 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2078]) ).
thf(2189,plain,
! [SV397: $i] :
( ( ( ~ ( relation @ SV397 ) )
= $true )
| ( ( ( relation_field @ SV397 )
= ( set_union2 @ ( relation_dom @ SV397 ) @ ( relation_rng @ SV397 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2079]) ).
thf(2190,plain,
! [SV398: $i] :
( ( ( ~ ( relation @ SV398 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV398 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2080]) ).
thf(2191,plain,
! [SV467: $i,SV399: $i] :
( ( ~ ( relation @ SV399 )
| ~ ( relation @ SV467 )
| ( relation @ ( relation_composition @ SV399 @ SV467 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2081]) ).
thf(2192,plain,
! [SV400: $i] :
( ( empty @ ( powerset @ SV400 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2082]) ).
thf(2193,plain,
! [SV468: $i,SV401: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV401 @ SV468 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2083]) ).
thf(2194,plain,
! [SV469: $i,SV402: $i] :
( ( ~ ( relation @ SV402 )
| ~ ( relation @ SV469 )
| ( relation @ ( set_union2 @ SV402 @ SV469 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2084]) ).
thf(2195,plain,
! [SV403: $i] :
( ( empty @ ( singleton @ SV403 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2085]) ).
thf(2196,plain,
! [SV404: $i] :
( ( ( empty @ SV404 )
= $true )
| ( ( ! [SY633: $i] :
~ ( empty @ ( set_union2 @ SV404 @ SY633 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2086]) ).
thf(2197,plain,
! [SV470: $i,SV405: $i] :
( ( ~ ( empty @ ( unordered_pair @ SV405 @ SV470 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2087]) ).
thf(2198,plain,
! [SV406: $i] :
( ( ( empty @ SV406 )
= $true )
| ( ( ! [SY635: $i] :
~ ( empty @ ( set_union2 @ SY635 @ SV406 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2088]) ).
thf(2199,plain,
! [SV471: $i,SV407: $i] :
( ( ( empty @ SV407 )
| ( empty @ SV471 )
| ~ ( empty @ ( cartesian_product2 @ SV407 @ SV471 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2089]) ).
thf(2200,plain,
! [SV410: $i] :
( ( ( ~ ( relation @ SV410 ) )
= $true )
| ( ( ( relation_inverse @ ( relation_inverse @ SV410 ) )
= SV410 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2092]) ).
thf(2201,plain,
! [SV472: $i,SV412: $i] :
( ( ~ ( disjoint @ SV412 @ SV472 )
| ( disjoint @ SV472 @ SV412 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2095]) ).
thf(2202,plain,
! [SV473: $i,SV413: $i] :
( ( ~ ( in @ SV413 @ SV473 )
| ( element @ SV413 @ SV473 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2096]) ).
thf(2203,plain,
! [SV474: $i,SV414: $i] :
( ( ~ ( element @ SV414 @ SV474 )
| ( empty @ SV474 )
| ( in @ SV414 @ SV474 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2097]) ).
thf(2204,plain,
! [SV415: $i,SV475: $i] :
( ( ! [SY731: $i] :
( ~ ( element @ SV475 @ ( powerset @ SY731 ) )
| ~ ( in @ SV415 @ SV475 )
| ( element @ SV415 @ SY731 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2098]) ).
thf(2205,plain,
! [SV416: $i,SV476: $i] :
( ( ! [SY732: $i] :
( ~ ( element @ SV476 @ ( powerset @ SY732 ) )
| ~ ( in @ SV416 @ SV476 )
| ~ ( empty @ SY732 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2099]) ).
thf(2206,plain,
! [SV417: $i,SV477: $i] :
( ( ~ ( empty @ SV477 )
| ~ ( in @ SV417 @ SV477 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2100]) ).
thf(2207,plain,
! [SV478: $i,SV418: $i] :
( ( ( SV418 = SV478 )
| ~ ( empty @ SV418 )
| ~ ( empty @ SV478 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2101]) ).
thf(2208,plain,
! [SV419: $i] :
( ( ~ ! [SY646: $i,SY647: $i] :
( ~ ( in @ SV419 @ SY647 )
| ~ ( in @ SY646 @ SY647 )
| ( subset @ ( unordered_pair @ SV419 @ SY646 ) @ SY647 ) )
| ~ ~ ( ~ ! [SY648: $i,SY649: $i] :
( ~ ( subset @ ( unordered_pair @ SV419 @ SY648 ) @ SY649 )
| ( in @ SV419 @ SY649 ) )
| ~ ! [SY650: $i,SY651: $i] :
( ~ ( subset @ ( unordered_pair @ SV419 @ SY650 ) @ SY651 )
| ( in @ SY650 @ SY651 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2103]) ).
thf(2209,plain,
! [SV420: $i] :
( ( ( ~ ( relation @ SV420 ) )
= $true )
| ( ( ~ ( ~ ! [SY652: $i] :
( ~ ( relation @ SY652 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SY652 @ SV420 ) @ ( sK11_SY272 @ SY652 @ SV420 ) ) @ SY652 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY272 @ SY652 @ SV420 ) @ ( sK10_C @ SY652 @ SV420 ) ) @ SV420 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK10_C @ SY652 @ SV420 ) @ ( sK11_SY272 @ SY652 @ SV420 ) ) @ SY652 )
| ( in @ ( ordered_pair @ ( sK11_SY272 @ SY652 @ SV420 ) @ ( sK10_C @ SY652 @ SV420 ) ) @ SV420 ) ) )
| ( SY652
= ( relation_inverse @ SV420 ) ) )
| ~ ! [SY653: $i] :
( ~ ( relation @ SY653 )
| ( SY653
!= ( relation_inverse @ SV420 ) )
| ~ ( ~ ! [SY654: $i,SY655: $i] :
( ~ ( in @ ( ordered_pair @ SY654 @ SY655 ) @ SY653 )
| ( in @ ( ordered_pair @ SY655 @ SY654 ) @ SV420 ) )
| ~ ! [SY656: $i,SY657: $i] :
( ~ ( in @ ( ordered_pair @ SY657 @ SY656 ) @ SV420 )
| ( in @ ( ordered_pair @ SY656 @ SY657 ) @ SY653 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2104]) ).
thf(2210,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK33_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2105]) ).
thf(2211,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2105]) ).
thf(2212,plain,
! [SV421: $i,SV479: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK3_C @ SV479 @ SV421 ) @ SV421 )
| ~ ( in @ ( sK3_C @ SV479 @ SV421 ) @ SV479 ) )
| ~ ( ( in @ ( sK3_C @ SV479 @ SV421 ) @ SV421 )
| ( in @ ( sK3_C @ SV479 @ SV421 ) @ SV479 ) ) )
| ( SV421 = SV479 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2106]) ).
thf(2213,plain,
! [SV422: $i] :
( ( ~ ! [SY659: $i,SY660: $i] :
( ~ ( relation @ SY660 )
| ~ ( in @ ( ordered_pair @ SV422 @ SY659 ) @ SY660 )
| ( in @ SV422 @ ( relation_dom @ SY660 ) ) )
| ~ ! [SY661: $i,SY662: $i] :
( ~ ( relation @ SY662 )
| ~ ( in @ ( ordered_pair @ SV422 @ SY661 ) @ SY662 )
| ( in @ SY661 @ ( relation_rng @ SY662 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2107]) ).
thf(2214,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2108]) ).
thf(2215,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2108]) ).
thf(2216,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2109]) ).
thf(2217,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2109]) ).
thf(2218,plain,
! [SV423: $i] :
( ( ~ ! [SY663: $i,SY664: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK24_D @ SY664 @ SY663 @ SV423 ) @ SY664 )
| ~ ( in @ ( sK24_D @ SY664 @ SY663 @ SV423 ) @ SV423 ) )
| ~ ( ~ ( in @ ( sK24_D @ SY664 @ SY663 @ SV423 ) @ SY664 )
| ~ ( in @ ( sK24_D @ SY664 @ SY663 @ SV423 ) @ SY663 ) ) )
| ~ ( ( in @ ( sK24_D @ SY664 @ SY663 @ SV423 ) @ SY664 )
| ( in @ ( sK24_D @ SY664 @ SY663 @ SV423 ) @ SV423 )
| ( in @ ( sK24_D @ SY664 @ SY663 @ SV423 ) @ SY663 ) ) )
| ( SY664
= ( set_union2 @ SV423 @ SY663 ) ) )
| ~ ! [SY665: $i,SY666: $i] :
( ( SY666
!= ( set_union2 @ SV423 @ SY665 ) )
| ~ ( ~ ! [SY667: $i] :
( ~ ( in @ SY667 @ SY666 )
| ( in @ SY667 @ SV423 )
| ( in @ SY667 @ SY665 ) )
| ~ ~ ( ~ ! [SY668: $i] :
( ~ ( in @ SY668 @ SV423 )
| ( in @ SY668 @ SY666 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY665 )
| ( in @ SX3 @ SY666 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2110]) ).
thf(2219,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2111]) ).
thf(2220,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2111]) ).
thf(2221,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2112]) ).
thf(2222,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2112]) ).
thf(2223,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK34_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK34_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2113]) ).
thf(2224,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2113]) ).
thf(2225,plain,
( ( ~ ( empty @ sK9_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2114]) ).
thf(2226,plain,
( ( ~ ( relation @ sK9_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2114]) ).
thf(2227,plain,
! [SV424: $i] :
( ( ~ ! [SY670: $i] :
( ~ ( subset @ SY670 @ ( sK35_B @ SV424 ) )
| ( are_equipotent @ SY670 @ ( sK35_B @ SV424 ) )
| ( in @ SY670 @ ( sK35_B @ SV424 ) ) )
| ~ ~ ( ~ ! [SY671: $i] :
( ~ ( in @ SY671 @ ( sK35_B @ SV424 ) )
| ( in @ ( powerset @ SY671 ) @ ( sK35_B @ SV424 ) ) )
| ~ ~ ( ~ ! [SY672: $i,SY673: $i] :
( ~ ( in @ SY672 @ ( sK35_B @ SV424 ) )
| ~ ( subset @ SY673 @ SY672 )
| ( in @ SY673 @ ( sK35_B @ SV424 ) ) )
| ~ ( in @ SV424 @ ( sK35_B @ SV424 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2115]) ).
thf(2228,plain,
! [SV425: $i] :
( ( ( ~ ( relation @ SV425 ) )
= $true )
| ( ( ~ ( ~ ! [SY674: $i] :
( ~ ( relation @ SY674 )
| ~ ( subset @ SV425 @ SY674 )
| ( subset @ ( relation_dom @ SV425 ) @ ( relation_dom @ SY674 ) ) )
| ~ ! [SY675: $i] :
( ~ ( relation @ SY675 )
| ~ ( subset @ SV425 @ SY675 )
| ( subset @ ( relation_rng @ SV425 ) @ ( relation_rng @ SY675 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2116]) ).
thf(2229,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2117]) ).
thf(2230,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2117]) ).
thf(2231,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK37_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2118]) ).
thf(2232,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2118]) ).
thf(2233,plain,
! [SV426: $i] :
( ( ~ ! [SY676: $i] :
( ~ ( subset @ SY676 @ ( sK1_B @ SV426 ) )
| ( are_equipotent @ SY676 @ ( sK1_B @ SV426 ) )
| ( in @ SY676 @ ( sK1_B @ SV426 ) ) )
| ~ ~ ( ~ ! [SY677: $i] :
( ~ ( ~ ! [SY678: $i] :
( ~ ( subset @ SY678 @ SY677 )
| ( in @ SY678 @ ( sK2_SY267 @ SY677 @ SV426 ) ) )
| ~ ( in @ ( sK2_SY267 @ SY677 @ SV426 ) @ ( sK1_B @ SV426 ) ) )
| ~ ( in @ SY677 @ ( sK1_B @ SV426 ) ) )
| ~ ~ ( ~ ! [SY679: $i,SY680: $i] :
( ~ ( in @ SY679 @ ( sK1_B @ SV426 ) )
| ~ ( subset @ SY680 @ SY679 )
| ( in @ SY680 @ ( sK1_B @ SV426 ) ) )
| ~ ( in @ SV426 @ ( sK1_B @ SV426 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2119]) ).
thf(2234,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2120]) ).
thf(2235,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2120]) ).
thf(2236,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK26_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK26_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK26_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK26_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2121]) ).
thf(2237,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2121]) ).
thf(2238,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2122]) ).
thf(2239,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2122]) ).
thf(2240,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2123]) ).
thf(2241,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2123]) ).
thf(2242,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK30_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK30_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2124]) ).
thf(2243,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK28_C @ SX1 @ SX0 ) @ ( sK29_SY279 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2124]) ).
thf(2244,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2125]) ).
thf(2245,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2125]) ).
thf(2246,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2126]) ).
thf(2247,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2126]) ).
thf(2248,plain,
( ( ~ ~ ( empty @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2127]) ).
thf(2249,plain,
( ( ~ ( relation @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2127]) ).
thf(2250,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2128]) ).
thf(2251,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2128]) ).
thf(2252,plain,
! [SV427: $i] :
( ( ( ~ ( relation @ SV427 ) )
= $true )
| ( ( ~ ( ~ ! [SY681: $i] :
( ~ ( ~ ( ! [SY682: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SY681 @ SV427 ) @ SY682 ) @ SV427 )
| ~ ( in @ ( sK20_C @ SY681 @ SV427 ) @ SY681 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_C @ SY681 @ SV427 ) @ ( sK21_SY278 @ SY681 @ SV427 ) ) @ SV427 )
| ( in @ ( sK20_C @ SY681 @ SV427 ) @ SY681 ) ) )
| ( SY681
= ( relation_dom @ SV427 ) ) )
| ~ ! [SY683: $i] :
( ( SY683
!= ( relation_dom @ SV427 ) )
| ~ ( ~ ! [SY684: $i] :
( ! [SY685: $i] :
~ ( in @ ( ordered_pair @ SY684 @ SY685 ) @ SV427 )
| ( in @ SY684 @ SY683 ) )
| ~ ! [SY686: $i] :
( ~ ( in @ SY686 @ SY683 )
| ( in @ ( ordered_pair @ SY686 @ ( sK19_D @ SY686 @ SY683 @ SV427 ) ) @ SV427 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2129]) ).
thf(2253,plain,
! [SV428: $i] :
( ( ~ ! [SY687: $i,SY688: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SY688 @ SY687 @ SV428 ) @ SV428 )
| ( in @ ( sK15_D @ SY688 @ SY687 @ SV428 ) @ SY687 )
| ~ ( in @ ( sK15_D @ SY688 @ SY687 @ SV428 ) @ SY688 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SY688 @ SY687 @ SV428 ) @ SV428 )
| ( in @ ( sK15_D @ SY688 @ SY687 @ SV428 ) @ SY688 ) )
| ~ ( ~ ( in @ ( sK15_D @ SY688 @ SY687 @ SV428 ) @ SY687 )
| ( in @ ( sK15_D @ SY688 @ SY687 @ SV428 ) @ SY688 ) ) ) )
| ( SY688
= ( set_difference @ SV428 @ SY687 ) ) )
| ~ ! [SY689: $i,SY690: $i] :
( ( SY690
!= ( set_difference @ SV428 @ SY689 ) )
| ~ ( ~ ! [SY691: $i] :
( ~ ( in @ SY691 @ SV428 )
| ( in @ SY691 @ SY689 )
| ( in @ SY691 @ SY690 ) )
| ~ ~ ( ~ ! [SY692: $i] :
( ~ ( in @ SY692 @ SY690 )
| ( in @ SY692 @ SV428 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY690 )
| ~ ( in @ SX3 @ SY689 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2130]) ).
thf(2254,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2131]) ).
thf(2255,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2131]) ).
thf(2256,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2132]) ).
thf(2257,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2132]) ).
thf(2258,plain,
! [SV429: $i] :
( ( ~ ! [SY694: $i,SY695: $i] :
( ~ ( ~ ( ~ ( in @ ( sK22_D @ SY695 @ SY694 @ SV429 ) @ SV429 )
| ~ ( in @ ( sK22_D @ SY695 @ SY694 @ SV429 ) @ SY694 )
| ~ ( in @ ( sK22_D @ SY695 @ SY694 @ SV429 ) @ SY695 ) )
| ~ ~ ( ~ ( ( in @ ( sK22_D @ SY695 @ SY694 @ SV429 ) @ SV429 )
| ( in @ ( sK22_D @ SY695 @ SY694 @ SV429 ) @ SY695 ) )
| ~ ( ( in @ ( sK22_D @ SY695 @ SY694 @ SV429 ) @ SY694 )
| ( in @ ( sK22_D @ SY695 @ SY694 @ SV429 ) @ SY695 ) ) ) )
| ( SY695
= ( set_intersection2 @ SV429 @ SY694 ) ) )
| ~ ! [SY696: $i,SY697: $i] :
( ( SY697
!= ( set_intersection2 @ SV429 @ SY696 ) )
| ~ ( ~ ! [SY698: $i] :
( ~ ( in @ SY698 @ SV429 )
| ~ ( in @ SY698 @ SY696 )
| ( in @ SY698 @ SY697 ) )
| ~ ~ ( ~ ! [SY699: $i] :
( ~ ( in @ SY699 @ SY697 )
| ( in @ SY699 @ SV429 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY697 )
| ( in @ SX3 @ SY696 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2133]) ).
thf(2259,plain,
! [SV430: $i] :
( ( ( ~ ( relation @ SV430 ) )
= $true )
| ( ( ~ ( ~ ! [SY701: $i] :
( ~ ( ~ ( ! [SY702: $i] :
~ ( in @ ( ordered_pair @ SY702 @ ( sK13_C @ SY701 @ SV430 ) ) @ SV430 )
| ~ ( in @ ( sK13_C @ SY701 @ SV430 ) @ SY701 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY274 @ SY701 @ SV430 ) @ ( sK13_C @ SY701 @ SV430 ) ) @ SV430 )
| ( in @ ( sK13_C @ SY701 @ SV430 ) @ SY701 ) ) )
| ( SY701
= ( relation_rng @ SV430 ) ) )
| ~ ! [SY703: $i] :
( ( SY703
!= ( relation_rng @ SV430 ) )
| ~ ( ~ ! [SY704: $i] :
( ! [SY705: $i] :
~ ( in @ ( ordered_pair @ SY705 @ SY704 ) @ SV430 )
| ( in @ SY704 @ SY703 ) )
| ~ ! [SY706: $i] :
( ~ ( in @ SY706 @ SY703 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY706 @ SY703 @ SV430 ) @ SY706 ) @ SV430 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2134]) ).
thf(2260,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ ( sK18_SY276 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK18_SY276 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2135]) ).
thf(2261,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK16_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK16_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2135]) ).
thf(2262,plain,
! [SV431: $i] :
( ( ~ ( element @ ( sK5_B @ SV431 ) @ ( powerset @ SV431 ) )
| ~ ( empty @ ( sK5_B @ SV431 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2136]) ).
thf(2263,plain,
! [SV432: $i,SV480: $i] :
( ( ~ ( ~ ( in @ ( sK36_C @ SV480 @ SV432 ) @ SV432 )
| ~ ~ ( in @ ( sK36_C @ SV480 @ SV432 ) @ SV480 ) )
| ( element @ SV432 @ ( powerset @ SV480 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2137]) ).
thf(2264,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2138]) ).
thf(2265,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2138]) ).
thf(2266,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2139]) ).
thf(2267,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2139]) ).
thf(2268,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2140]) ).
thf(2269,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2140]) ).
thf(2270,plain,
! [SV433: $i] :
( ( ~ ! [SY708: $i,SY709: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK25_D @ SY709 @ SY708 @ SV433 ) @ SY709 )
| ( ( sK25_D @ SY709 @ SY708 @ SV433 )
!= SV433 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY709 @ SY708 @ SV433 ) @ SY709 )
| ( ( sK25_D @ SY709 @ SY708 @ SV433 )
!= SY708 ) ) )
| ~ ( ( in @ ( sK25_D @ SY709 @ SY708 @ SV433 ) @ SY709 )
| ( ( sK25_D @ SY709 @ SY708 @ SV433 )
= SV433 )
| ( ( sK25_D @ SY709 @ SY708 @ SV433 )
= SY708 ) ) )
| ( SY709
= ( unordered_pair @ SV433 @ SY708 ) ) )
| ~ ! [SY710: $i,SY711: $i] :
( ( SY711
!= ( unordered_pair @ SV433 @ SY710 ) )
| ~ ( ~ ! [SY712: $i] :
( ~ ( in @ SY712 @ SY711 )
| ( SY712 = SV433 )
| ( SY712 = SY710 ) )
| ~ ~ ( ~ ! [SY713: $i] :
( ( SY713 != SV433 )
| ( in @ SY713 @ SY711 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY710 )
| ( in @ SX3 @ SY711 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2141]) ).
thf(2271,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK40_SY287 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK39_C @ SX1 @ SX0 ) @ ( sK40_SY287 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK38_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK38_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2142]) ).
thf(2272,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2142]) ).
thf(2273,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK27_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK27_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK27_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK27_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2143]) ).
thf(2274,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2143]) ).
thf(2275,plain,
! [SV434: $i] :
( ( ~ ! [SY715: $i] :
( ~ ( subset @ SV434 @ SY715 )
| ! [SY716: $i] : ( subset @ ( cartesian_product2 @ SV434 @ SY716 ) @ ( cartesian_product2 @ SY715 @ SY716 ) ) )
| ~ ! [SY717: $i] :
( ~ ( subset @ SV434 @ SY717 )
| ! [SY718: $i] : ( subset @ ( cartesian_product2 @ SY718 @ SV434 ) @ ( cartesian_product2 @ SY718 @ SY717 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2144]) ).
thf(2276,plain,
! [SV435: $i] :
( ( ( empty @ SV435 )
= $true )
| ( ( ~ ( ~ ( element @ ( sK8_B @ SV435 ) @ ( powerset @ SV435 ) )
| ~ ~ ( empty @ ( sK8_B @ SV435 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2145]) ).
thf(2277,plain,
! [SV349: $i] :
( ( ( subset @ SV349 @ empty_set )
= $false )
| ( ( SV349 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2147]) ).
thf(2278,plain,
! [SV350: $i] :
( ( ( empty @ SV350 )
= $true )
| ( ( ~ ( relation @ SV350 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV350 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2148]) ).
thf(2279,plain,
! [SV351: $i] :
( ( ( empty @ SV351 )
= $true )
| ( ( ~ ( relation @ SV351 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV351 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2149]) ).
thf(2280,plain,
! [SV356: $i] :
( ( ( empty @ SV356 )
= $false )
| ( ( SV356 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2150]) ).
thf(2281,plain,
! [SV436: $i,SV357: $i] :
( ( ( ~ ( in @ SV357 @ SV436 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV357 ) @ SV436 )
= SV436 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2151]) ).
thf(2282,plain,
! [SV437: $i,SV358: $i] :
( ( ( ~ ( disjoint @ ( singleton @ SV358 ) @ SV437 ) )
= $true )
| ( ( ~ ( in @ SV358 @ SV437 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2152]) ).
thf(2283,plain,
! [SV438: $i,SV359: $i] :
( ( ( in @ SV359 @ SV438 )
= $true )
| ( ( disjoint @ ( singleton @ SV359 ) @ SV438 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2153]) ).
thf(2284,plain,
! [SV360: $i,SV439: $i] :
( ( ( ~ ( element @ SV439 @ ( powerset @ SV360 ) ) )
= $true )
| ( ( ! [SY719: $i] :
( ~ ( in @ SY719 @ SV439 )
| ( in @ SY719 @ SV360 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2154]) ).
thf(2285,plain,
! [SV440: $i,SV361: $i] :
( ( ( ~ ( subset @ SV361 @ SV440 ) )
= $true )
| ( ( ! [SY720: $i] :
( ( in @ SY720 @ SV361 )
| ( subset @ SV361 @ ( set_difference @ SV440 @ ( singleton @ SY720 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2155]) ).
thf(2286,plain,
! [SV441: $i,SV362: $i] :
( ( ( ~ ( in @ SV362 @ SV441 ) )
= $true )
| ( ( subset @ SV362 @ ( union @ SV441 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2156]) ).
thf(2287,plain,
! [SV481: $i,SV442: $i,SV363: $i] :
( ( ! [SY733: $i] :
( ~ ( subset @ SV363 @ SV442 )
| ~ ( subset @ SV481 @ SY733 )
| ( subset @ ( cartesian_product2 @ SV363 @ SV481 ) @ ( cartesian_product2 @ SV442 @ SY733 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2157]) ).
thf(2288,plain,
! [SV443: $i,SV364: $i] :
( ( ( ~ ( subset @ SV364 @ SV443 ) )
= $true )
| ( ( ( set_union2 @ SV364 @ SV443 )
= SV443 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2158]) ).
thf(2289,plain,
! [SV482: $i,SV445: $i,SV366: $i] :
( ( ~ ( subset @ SV366 @ SV445 )
| ~ ( subset @ SV366 @ SV482 )
| ( subset @ SV366 @ ( set_intersection2 @ SV445 @ SV482 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2160]) ).
thf(2290,plain,
! [SV483: $i,SV446: $i,SV367: $i] :
( ( ~ ( subset @ SV367 @ SV446 )
| ~ ( subset @ SV446 @ SV483 )
| ( subset @ SV367 @ SV483 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2161]) ).
thf(2291,plain,
! [SV368: $i] :
( ( ( relation @ SV368 )
= $false )
| ( ( subset @ SV368 @ ( cartesian_product2 @ ( relation_dom @ SV368 ) @ ( relation_rng @ SV368 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2162]) ).
thf(2292,plain,
! [SV447: $i,SV369: $i] :
( ( ( ~ ( subset @ SV369 @ SV447 ) )
= $true )
| ( ( ! [SY725: $i] : ( subset @ ( set_intersection2 @ SV369 @ SY725 ) @ ( set_intersection2 @ SV447 @ SY725 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2163]) ).
thf(2293,plain,
! [SV448: $i,SV370: $i] :
( ( ( ~ ( subset @ SV370 @ SV448 ) )
= $true )
| ( ( ( set_intersection2 @ SV370 @ SV448 )
= SV370 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2164]) ).
thf(2294,plain,
! [SV449: $i,SV371: $i] :
( ( ( ~ ( subset @ SV371 @ SV449 ) )
= $true )
| ( ( ! [SY726: $i] : ( subset @ ( set_difference @ SV371 @ SY726 ) @ ( set_difference @ SV449 @ SY726 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2165]) ).
thf(2295,plain,
! [SV375: $i] :
( ( ( relation @ SV375 )
= $false )
| ( ( ! [SY608: $i] :
( ~ ( relation @ SY608 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV375 @ SY608 ) ) @ ( relation_dom @ SV375 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2169]) ).
thf(2296,plain,
! [SV376: $i] :
( ( ( relation @ SV376 )
= $false )
| ( ( ! [SY609: $i] :
( ~ ( relation @ SY609 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV376 @ SY609 ) ) @ ( relation_rng @ SY609 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2170]) ).
thf(2297,plain,
! [SV453: $i,SV377: $i] :
( ( ( ~ ( subset @ SV377 @ SV453 ) )
= $true )
| ( ( SV453
= ( set_union2 @ SV377 @ ( set_difference @ SV453 @ SV377 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2171]) ).
thf(2298,plain,
! [SV378: $i] :
( ( ( relation @ SV378 )
= $false )
| ( ( ! [SY611: $i] :
( ~ ( relation @ SY611 )
| ~ ( subset @ ( relation_rng @ SV378 ) @ ( relation_dom @ SY611 ) )
| ( ( relation_dom @ ( relation_composition @ SV378 @ SY611 ) )
= ( relation_dom @ SV378 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2172]) ).
thf(2299,plain,
! [SV454: $i,SV379: $i] :
( ( ( ~ ( in @ SV379 @ SV454 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV379 ) @ SV454 )
= SV454 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2173]) ).
thf(2300,plain,
! [SV380: $i] :
( ( ( relation @ SV380 )
= $false )
| ( ( ! [SY613: $i] :
( ~ ( relation @ SY613 )
| ~ ( subset @ ( relation_dom @ SV380 ) @ ( relation_rng @ SY613 ) )
| ( ( relation_rng @ ( relation_composition @ SY613 @ SV380 ) )
= ( relation_rng @ SV380 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2174]) ).
thf(2301,plain,
! [SV382: $i] :
( ( ( relation @ SV382 )
= $false )
| ( ( ( in @ ( ordered_pair @ ( sK31_B @ SV382 ) @ ( sK32_SY282 @ SV382 ) ) @ SV382 )
| ( SV382 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2176]) ).
thf(2302,plain,
! [SV383: $i,SV456: $i] :
( ( ( ~ ( proper_subset @ SV456 @ SV383 ) )
= $true )
| ( ( ~ ( subset @ SV383 @ SV456 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2177]) ).
thf(2303,plain,
! [SV384: $i,SV484: $i,SV457: $i] :
( ( ~ ( disjoint @ SV457 @ SV484 )
| ~ ( subset @ SV384 @ SV457 )
| ( disjoint @ SV384 @ SV484 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2178]) ).
thf(2304,plain,
! [SV458: $i,SV386: $i] :
( ( ( ~ ( subset @ ( singleton @ SV386 ) @ ( singleton @ SV458 ) ) )
= $true )
| ( ( SV386 = SV458 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2179]) ).
thf(2305,plain,
! [SV485: $i,SV460: $i,SV388: $i] :
( ( ~ ( subset @ SV388 @ SV460 )
| ~ ( subset @ SV485 @ SV460 )
| ( subset @ ( set_union2 @ SV388 @ SV485 ) @ SV460 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2181]) ).
thf(2306,plain,
! [SV461: $i,SV389: $i] :
( ( ( ! [SY729: $i] :
( ( singleton @ SV389 )
!= ( unordered_pair @ SV461 @ SY729 ) ) )
= $true )
| ( ( SV389 = SV461 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2182]) ).
thf(2307,plain,
! [SV462: $i,SV390: $i] :
( ( ( ~ ( in @ SV390 @ SV462 ) )
= $true )
| ( ( subset @ SV390 @ ( union @ SV462 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2183]) ).
thf(2308,plain,
! [SV486: $i,SV463: $i,SV392: $i] :
( ( ( ( singleton @ SV392 )
!= ( unordered_pair @ SV463 @ SV486 ) )
| ( SV463 = SV486 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2184]) ).
thf(2309,plain,
! [SV464: $i,SV393: $i] :
( ( ( ~ ( in @ SV393 @ SV464 ) )
= $true )
| ( ( ~ ( in @ SV464 @ SV393 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2185]) ).
thf(2310,plain,
! [SV394: $i] :
( ( ( empty @ SV394 )
= $false )
| ( ( relation @ SV394 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2186]) ).
thf(2311,plain,
! [SV397: $i] :
( ( ( relation @ SV397 )
= $false )
| ( ( ( relation_field @ SV397 )
= ( set_union2 @ ( relation_dom @ SV397 ) @ ( relation_rng @ SV397 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2189]) ).
thf(2312,plain,
! [SV398: $i] :
( ( ( relation @ SV398 )
= $false )
| ( ( relation @ ( relation_inverse @ SV398 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2190]) ).
thf(2313,plain,
! [SV467: $i,SV399: $i] :
( ( ( ~ ( relation @ SV399 )
| ~ ( relation @ SV467 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV399 @ SV467 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2191]) ).
thf(2314,plain,
! [SV468: $i,SV401: $i] :
( ( empty @ ( ordered_pair @ SV401 @ SV468 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2193]) ).
thf(2315,plain,
! [SV469: $i,SV402: $i] :
( ( ( ~ ( relation @ SV402 )
| ~ ( relation @ SV469 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV402 @ SV469 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2194]) ).
thf(2316,plain,
! [SV487: $i,SV404: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV404 @ SV487 ) ) )
= $true )
| ( ( empty @ SV404 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2196]) ).
thf(2317,plain,
! [SV470: $i,SV405: $i] :
( ( empty @ ( unordered_pair @ SV405 @ SV470 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2197]) ).
thf(2318,plain,
! [SV406: $i,SV488: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV488 @ SV406 ) ) )
= $true )
| ( ( empty @ SV406 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2198]) ).
thf(2319,plain,
! [SV471: $i,SV407: $i] :
( ( ( ( empty @ SV407 )
| ( empty @ SV471 ) )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV407 @ SV471 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2199]) ).
thf(2320,plain,
! [SV410: $i] :
( ( ( relation @ SV410 )
= $false )
| ( ( ( relation_inverse @ ( relation_inverse @ SV410 ) )
= SV410 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2200]) ).
thf(2321,plain,
! [SV472: $i,SV412: $i] :
( ( ( ~ ( disjoint @ SV412 @ SV472 ) )
= $true )
| ( ( disjoint @ SV472 @ SV412 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2201]) ).
thf(2322,plain,
! [SV473: $i,SV413: $i] :
( ( ( ~ ( in @ SV413 @ SV473 ) )
= $true )
| ( ( element @ SV413 @ SV473 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2202]) ).
thf(2323,plain,
! [SV474: $i,SV414: $i] :
( ( ( ~ ( element @ SV414 @ SV474 ) )
= $true )
| ( ( ( empty @ SV474 )
| ( in @ SV414 @ SV474 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2203]) ).
thf(2324,plain,
! [SV415: $i,SV489: $i,SV475: $i] :
( ( ~ ( element @ SV475 @ ( powerset @ SV489 ) )
| ~ ( in @ SV415 @ SV475 )
| ( element @ SV415 @ SV489 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2204]) ).
thf(2325,plain,
! [SV416: $i,SV490: $i,SV476: $i] :
( ( ~ ( element @ SV476 @ ( powerset @ SV490 ) )
| ~ ( in @ SV416 @ SV476 )
| ~ ( empty @ SV490 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2205]) ).
thf(2326,plain,
! [SV417: $i,SV477: $i] :
( ( ( ~ ( empty @ SV477 ) )
= $true )
| ( ( ~ ( in @ SV417 @ SV477 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2206]) ).
thf(2327,plain,
! [SV478: $i,SV418: $i] :
( ( ( ( SV418 = SV478 )
| ~ ( empty @ SV418 ) )
= $true )
| ( ( ~ ( empty @ SV478 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2207]) ).
thf(2328,plain,
! [SV419: $i] :
( ( ~ ! [SY646: $i,SY647: $i] :
( ~ ( in @ SV419 @ SY647 )
| ~ ( in @ SY646 @ SY647 )
| ( subset @ ( unordered_pair @ SV419 @ SY646 ) @ SY647 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2208]) ).
thf(2329,plain,
! [SV419: $i] :
( ( ~ ~ ( ~ ! [SY648: $i,SY649: $i] :
( ~ ( subset @ ( unordered_pair @ SV419 @ SY648 ) @ SY649 )
| ( in @ SV419 @ SY649 ) )
| ~ ! [SY650: $i,SY651: $i] :
( ~ ( subset @ ( unordered_pair @ SV419 @ SY650 ) @ SY651 )
| ( in @ SY650 @ SY651 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2208]) ).
thf(2330,plain,
! [SV420: $i] :
( ( ( relation @ SV420 )
= $false )
| ( ( ~ ( ~ ! [SY652: $i] :
( ~ ( relation @ SY652 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SY652 @ SV420 ) @ ( sK11_SY272 @ SY652 @ SV420 ) ) @ SY652 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY272 @ SY652 @ SV420 ) @ ( sK10_C @ SY652 @ SV420 ) ) @ SV420 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK10_C @ SY652 @ SV420 ) @ ( sK11_SY272 @ SY652 @ SV420 ) ) @ SY652 )
| ( in @ ( ordered_pair @ ( sK11_SY272 @ SY652 @ SV420 ) @ ( sK10_C @ SY652 @ SV420 ) ) @ SV420 ) ) )
| ( SY652
= ( relation_inverse @ SV420 ) ) )
| ~ ! [SY653: $i] :
( ~ ( relation @ SY653 )
| ( SY653
!= ( relation_inverse @ SV420 ) )
| ~ ( ~ ! [SY654: $i,SY655: $i] :
( ~ ( in @ ( ordered_pair @ SY654 @ SY655 ) @ SY653 )
| ( in @ ( ordered_pair @ SY655 @ SY654 ) @ SV420 ) )
| ~ ! [SY656: $i,SY657: $i] :
( ~ ( in @ ( ordered_pair @ SY657 @ SY656 ) @ SV420 )
| ( in @ ( ordered_pair @ SY656 @ SY657 ) @ SY653 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2209]) ).
thf(2331,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK33_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2210]) ).
thf(2332,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2211]) ).
thf(2333,plain,
! [SV421: $i,SV479: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK3_C @ SV479 @ SV421 ) @ SV421 )
| ~ ( in @ ( sK3_C @ SV479 @ SV421 ) @ SV479 ) )
| ~ ( ( in @ ( sK3_C @ SV479 @ SV421 ) @ SV421 )
| ( in @ ( sK3_C @ SV479 @ SV421 ) @ SV479 ) ) ) )
= $true )
| ( ( SV421 = SV479 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2212]) ).
thf(2334,plain,
! [SV422: $i] :
( ( ~ ! [SY659: $i,SY660: $i] :
( ~ ( relation @ SY660 )
| ~ ( in @ ( ordered_pair @ SV422 @ SY659 ) @ SY660 )
| ( in @ SV422 @ ( relation_dom @ SY660 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2213]) ).
thf(2335,plain,
! [SV422: $i] :
( ( ~ ! [SY661: $i,SY662: $i] :
( ~ ( relation @ SY662 )
| ~ ( in @ ( ordered_pair @ SV422 @ SY661 ) @ SY662 )
| ( in @ SY661 @ ( relation_rng @ SY662 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2213]) ).
thf(2336,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2214]) ).
thf(2337,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2215]) ).
thf(2338,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2216]) ).
thf(2339,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2217]) ).
thf(2340,plain,
! [SV423: $i] :
( ( ~ ! [SY663: $i,SY664: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK24_D @ SY664 @ SY663 @ SV423 ) @ SY664 )
| ~ ( in @ ( sK24_D @ SY664 @ SY663 @ SV423 ) @ SV423 ) )
| ~ ( ~ ( in @ ( sK24_D @ SY664 @ SY663 @ SV423 ) @ SY664 )
| ~ ( in @ ( sK24_D @ SY664 @ SY663 @ SV423 ) @ SY663 ) ) )
| ~ ( ( in @ ( sK24_D @ SY664 @ SY663 @ SV423 ) @ SY664 )
| ( in @ ( sK24_D @ SY664 @ SY663 @ SV423 ) @ SV423 )
| ( in @ ( sK24_D @ SY664 @ SY663 @ SV423 ) @ SY663 ) ) )
| ( SY664
= ( set_union2 @ SV423 @ SY663 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2218]) ).
thf(2341,plain,
! [SV423: $i] :
( ( ~ ! [SY665: $i,SY666: $i] :
( ( SY666
!= ( set_union2 @ SV423 @ SY665 ) )
| ~ ( ~ ! [SY667: $i] :
( ~ ( in @ SY667 @ SY666 )
| ( in @ SY667 @ SV423 )
| ( in @ SY667 @ SY665 ) )
| ~ ~ ( ~ ! [SY668: $i] :
( ~ ( in @ SY668 @ SV423 )
| ( in @ SY668 @ SY666 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY665 )
| ( in @ SX3 @ SY666 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2218]) ).
thf(2342,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2219]) ).
thf(2343,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2220]) ).
thf(2344,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2221]) ).
thf(2345,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2222]) ).
thf(2346,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK34_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK34_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2223]) ).
thf(2347,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2224]) ).
thf(2348,plain,
( ( empty @ sK9_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2225]) ).
thf(2349,plain,
( ( relation @ sK9_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2226]) ).
thf(2350,plain,
! [SV424: $i] :
( ( ~ ! [SY670: $i] :
( ~ ( subset @ SY670 @ ( sK35_B @ SV424 ) )
| ( are_equipotent @ SY670 @ ( sK35_B @ SV424 ) )
| ( in @ SY670 @ ( sK35_B @ SV424 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2227]) ).
thf(2351,plain,
! [SV424: $i] :
( ( ~ ~ ( ~ ! [SY671: $i] :
( ~ ( in @ SY671 @ ( sK35_B @ SV424 ) )
| ( in @ ( powerset @ SY671 ) @ ( sK35_B @ SV424 ) ) )
| ~ ~ ( ~ ! [SY672: $i,SY673: $i] :
( ~ ( in @ SY672 @ ( sK35_B @ SV424 ) )
| ~ ( subset @ SY673 @ SY672 )
| ( in @ SY673 @ ( sK35_B @ SV424 ) ) )
| ~ ( in @ SV424 @ ( sK35_B @ SV424 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2227]) ).
thf(2352,plain,
! [SV425: $i] :
( ( ( relation @ SV425 )
= $false )
| ( ( ~ ( ~ ! [SY674: $i] :
( ~ ( relation @ SY674 )
| ~ ( subset @ SV425 @ SY674 )
| ( subset @ ( relation_dom @ SV425 ) @ ( relation_dom @ SY674 ) ) )
| ~ ! [SY675: $i] :
( ~ ( relation @ SY675 )
| ~ ( subset @ SV425 @ SY675 )
| ( subset @ ( relation_rng @ SV425 ) @ ( relation_rng @ SY675 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2228]) ).
thf(2353,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2229]) ).
thf(2354,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2230]) ).
thf(2355,plain,
( ( ! [SX0: $i] :
( ( in @ ( sK37_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2231]) ).
thf(2356,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2232]) ).
thf(2357,plain,
! [SV426: $i] :
( ( ~ ! [SY676: $i] :
( ~ ( subset @ SY676 @ ( sK1_B @ SV426 ) )
| ( are_equipotent @ SY676 @ ( sK1_B @ SV426 ) )
| ( in @ SY676 @ ( sK1_B @ SV426 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2233]) ).
thf(2358,plain,
! [SV426: $i] :
( ( ~ ~ ( ~ ! [SY677: $i] :
( ~ ( ~ ! [SY678: $i] :
( ~ ( subset @ SY678 @ SY677 )
| ( in @ SY678 @ ( sK2_SY267 @ SY677 @ SV426 ) ) )
| ~ ( in @ ( sK2_SY267 @ SY677 @ SV426 ) @ ( sK1_B @ SV426 ) ) )
| ~ ( in @ SY677 @ ( sK1_B @ SV426 ) ) )
| ~ ~ ( ~ ! [SY679: $i,SY680: $i] :
( ~ ( in @ SY679 @ ( sK1_B @ SV426 ) )
| ~ ( subset @ SY680 @ SY679 )
| ( in @ SY680 @ ( sK1_B @ SV426 ) ) )
| ~ ( in @ SV426 @ ( sK1_B @ SV426 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2233]) ).
thf(2359,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2234]) ).
thf(2360,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2235]) ).
thf(2361,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK26_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK26_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK26_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK26_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2236]) ).
thf(2362,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2237]) ).
thf(2363,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2238]) ).
thf(2364,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2239]) ).
thf(2365,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2240]) ).
thf(2366,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2241]) ).
thf(2367,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK30_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK30_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2242]) ).
thf(2368,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK28_C @ SX1 @ SX0 ) @ ( sK29_SY279 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2243]) ).
thf(2369,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2244]) ).
thf(2370,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2245]) ).
thf(2371,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2246]) ).
thf(2372,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2247]) ).
thf(2373,plain,
( ( ~ ( empty @ sK6_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2248]) ).
thf(2374,plain,
( ( relation @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2249]) ).
thf(2375,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2250]) ).
thf(2376,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2251]) ).
thf(2377,plain,
! [SV427: $i] :
( ( ( relation @ SV427 )
= $false )
| ( ( ~ ( ~ ! [SY681: $i] :
( ~ ( ~ ( ! [SY682: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SY681 @ SV427 ) @ SY682 ) @ SV427 )
| ~ ( in @ ( sK20_C @ SY681 @ SV427 ) @ SY681 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_C @ SY681 @ SV427 ) @ ( sK21_SY278 @ SY681 @ SV427 ) ) @ SV427 )
| ( in @ ( sK20_C @ SY681 @ SV427 ) @ SY681 ) ) )
| ( SY681
= ( relation_dom @ SV427 ) ) )
| ~ ! [SY683: $i] :
( ( SY683
!= ( relation_dom @ SV427 ) )
| ~ ( ~ ! [SY684: $i] :
( ! [SY685: $i] :
~ ( in @ ( ordered_pair @ SY684 @ SY685 ) @ SV427 )
| ( in @ SY684 @ SY683 ) )
| ~ ! [SY686: $i] :
( ~ ( in @ SY686 @ SY683 )
| ( in @ ( ordered_pair @ SY686 @ ( sK19_D @ SY686 @ SY683 @ SV427 ) ) @ SV427 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2252]) ).
thf(2378,plain,
! [SV428: $i] :
( ( ~ ! [SY687: $i,SY688: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SY688 @ SY687 @ SV428 ) @ SV428 )
| ( in @ ( sK15_D @ SY688 @ SY687 @ SV428 ) @ SY687 )
| ~ ( in @ ( sK15_D @ SY688 @ SY687 @ SV428 ) @ SY688 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SY688 @ SY687 @ SV428 ) @ SV428 )
| ( in @ ( sK15_D @ SY688 @ SY687 @ SV428 ) @ SY688 ) )
| ~ ( ~ ( in @ ( sK15_D @ SY688 @ SY687 @ SV428 ) @ SY687 )
| ( in @ ( sK15_D @ SY688 @ SY687 @ SV428 ) @ SY688 ) ) ) )
| ( SY688
= ( set_difference @ SV428 @ SY687 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2253]) ).
thf(2379,plain,
! [SV428: $i] :
( ( ~ ! [SY689: $i,SY690: $i] :
( ( SY690
!= ( set_difference @ SV428 @ SY689 ) )
| ~ ( ~ ! [SY691: $i] :
( ~ ( in @ SY691 @ SV428 )
| ( in @ SY691 @ SY689 )
| ( in @ SY691 @ SY690 ) )
| ~ ~ ( ~ ! [SY692: $i] :
( ~ ( in @ SY692 @ SY690 )
| ( in @ SY692 @ SV428 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY690 )
| ~ ( in @ SX3 @ SY689 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2253]) ).
thf(2380,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2254]) ).
thf(2381,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2255]) ).
thf(2382,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2256]) ).
thf(2383,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2257]) ).
thf(2384,plain,
! [SV429: $i] :
( ( ~ ! [SY694: $i,SY695: $i] :
( ~ ( ~ ( ~ ( in @ ( sK22_D @ SY695 @ SY694 @ SV429 ) @ SV429 )
| ~ ( in @ ( sK22_D @ SY695 @ SY694 @ SV429 ) @ SY694 )
| ~ ( in @ ( sK22_D @ SY695 @ SY694 @ SV429 ) @ SY695 ) )
| ~ ~ ( ~ ( ( in @ ( sK22_D @ SY695 @ SY694 @ SV429 ) @ SV429 )
| ( in @ ( sK22_D @ SY695 @ SY694 @ SV429 ) @ SY695 ) )
| ~ ( ( in @ ( sK22_D @ SY695 @ SY694 @ SV429 ) @ SY694 )
| ( in @ ( sK22_D @ SY695 @ SY694 @ SV429 ) @ SY695 ) ) ) )
| ( SY695
= ( set_intersection2 @ SV429 @ SY694 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2258]) ).
thf(2385,plain,
! [SV429: $i] :
( ( ~ ! [SY696: $i,SY697: $i] :
( ( SY697
!= ( set_intersection2 @ SV429 @ SY696 ) )
| ~ ( ~ ! [SY698: $i] :
( ~ ( in @ SY698 @ SV429 )
| ~ ( in @ SY698 @ SY696 )
| ( in @ SY698 @ SY697 ) )
| ~ ~ ( ~ ! [SY699: $i] :
( ~ ( in @ SY699 @ SY697 )
| ( in @ SY699 @ SV429 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY697 )
| ( in @ SX3 @ SY696 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2258]) ).
thf(2386,plain,
! [SV430: $i] :
( ( ( relation @ SV430 )
= $false )
| ( ( ~ ( ~ ! [SY701: $i] :
( ~ ( ~ ( ! [SY702: $i] :
~ ( in @ ( ordered_pair @ SY702 @ ( sK13_C @ SY701 @ SV430 ) ) @ SV430 )
| ~ ( in @ ( sK13_C @ SY701 @ SV430 ) @ SY701 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY274 @ SY701 @ SV430 ) @ ( sK13_C @ SY701 @ SV430 ) ) @ SV430 )
| ( in @ ( sK13_C @ SY701 @ SV430 ) @ SY701 ) ) )
| ( SY701
= ( relation_rng @ SV430 ) ) )
| ~ ! [SY703: $i] :
( ( SY703
!= ( relation_rng @ SV430 ) )
| ~ ( ~ ! [SY704: $i] :
( ! [SY705: $i] :
~ ( in @ ( ordered_pair @ SY705 @ SY704 ) @ SV430 )
| ( in @ SY704 @ SY703 ) )
| ~ ! [SY706: $i] :
( ~ ( in @ SY706 @ SY703 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY706 @ SY703 @ SV430 ) @ SY706 ) @ SV430 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2259]) ).
thf(2387,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ ( sK18_SY276 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK18_SY276 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2260]) ).
thf(2388,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK16_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK16_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2261]) ).
thf(2389,plain,
! [SV431: $i] :
( ( ~ ( element @ ( sK5_B @ SV431 ) @ ( powerset @ SV431 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2262]) ).
thf(2390,plain,
! [SV431: $i] :
( ( ~ ( empty @ ( sK5_B @ SV431 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2262]) ).
thf(2391,plain,
! [SV432: $i,SV480: $i] :
( ( ( ~ ( ~ ( in @ ( sK36_C @ SV480 @ SV432 ) @ SV432 )
| ~ ~ ( in @ ( sK36_C @ SV480 @ SV432 ) @ SV480 ) ) )
= $true )
| ( ( element @ SV432 @ ( powerset @ SV480 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2263]) ).
thf(2392,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2264]) ).
thf(2393,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2265]) ).
thf(2394,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2266]) ).
thf(2395,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2267]) ).
thf(2396,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2268]) ).
thf(2397,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2269]) ).
thf(2398,plain,
! [SV433: $i] :
( ( ~ ! [SY708: $i,SY709: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK25_D @ SY709 @ SY708 @ SV433 ) @ SY709 )
| ( ( sK25_D @ SY709 @ SY708 @ SV433 )
!= SV433 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY709 @ SY708 @ SV433 ) @ SY709 )
| ( ( sK25_D @ SY709 @ SY708 @ SV433 )
!= SY708 ) ) )
| ~ ( ( in @ ( sK25_D @ SY709 @ SY708 @ SV433 ) @ SY709 )
| ( ( sK25_D @ SY709 @ SY708 @ SV433 )
= SV433 )
| ( ( sK25_D @ SY709 @ SY708 @ SV433 )
= SY708 ) ) )
| ( SY709
= ( unordered_pair @ SV433 @ SY708 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2270]) ).
thf(2399,plain,
! [SV433: $i] :
( ( ~ ! [SY710: $i,SY711: $i] :
( ( SY711
!= ( unordered_pair @ SV433 @ SY710 ) )
| ~ ( ~ ! [SY712: $i] :
( ~ ( in @ SY712 @ SY711 )
| ( SY712 = SV433 )
| ( SY712 = SY710 ) )
| ~ ~ ( ~ ! [SY713: $i] :
( ( SY713 != SV433 )
| ( in @ SY713 @ SY711 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY710 )
| ( in @ SX3 @ SY711 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2270]) ).
thf(2400,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK40_SY287 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK39_C @ SX1 @ SX0 ) @ ( sK40_SY287 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK38_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK38_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2271]) ).
thf(2401,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2272]) ).
thf(2402,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK27_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK27_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK27_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK27_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2273]) ).
thf(2403,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2274]) ).
thf(2404,plain,
! [SV434: $i] :
( ( ~ ! [SY715: $i] :
( ~ ( subset @ SV434 @ SY715 )
| ! [SY716: $i] : ( subset @ ( cartesian_product2 @ SV434 @ SY716 ) @ ( cartesian_product2 @ SY715 @ SY716 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2275]) ).
thf(2405,plain,
! [SV434: $i] :
( ( ~ ! [SY717: $i] :
( ~ ( subset @ SV434 @ SY717 )
| ! [SY718: $i] : ( subset @ ( cartesian_product2 @ SY718 @ SV434 ) @ ( cartesian_product2 @ SY718 @ SY717 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2275]) ).
thf(2406,plain,
! [SV435: $i] :
( ( ( ~ ( element @ ( sK8_B @ SV435 ) @ ( powerset @ SV435 ) )
| ~ ~ ( empty @ ( sK8_B @ SV435 ) ) )
= $false )
| ( ( empty @ SV435 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2276]) ).
thf(2407,plain,
! [SV350: $i] :
( ( ( relation @ SV350 )
= $false )
| ( ( empty @ SV350 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV350 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2278]) ).
thf(2408,plain,
! [SV351: $i] :
( ( ( relation @ SV351 )
= $false )
| ( ( empty @ SV351 )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV351 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2279]) ).
thf(2409,plain,
! [SV436: $i,SV357: $i] :
( ( ( in @ SV357 @ SV436 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV357 ) @ SV436 )
= SV436 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2281]) ).
thf(2410,plain,
! [SV437: $i,SV358: $i] :
( ( ( disjoint @ ( singleton @ SV358 ) @ SV437 )
= $false )
| ( ( ~ ( in @ SV358 @ SV437 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2282]) ).
thf(2411,plain,
! [SV360: $i,SV439: $i] :
( ( ( element @ SV439 @ ( powerset @ SV360 ) )
= $false )
| ( ( ! [SY719: $i] :
( ~ ( in @ SY719 @ SV439 )
| ( in @ SY719 @ SV360 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2284]) ).
thf(2412,plain,
! [SV440: $i,SV361: $i] :
( ( ( subset @ SV361 @ SV440 )
= $false )
| ( ( ! [SY720: $i] :
( ( in @ SY720 @ SV361 )
| ( subset @ SV361 @ ( set_difference @ SV440 @ ( singleton @ SY720 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2285]) ).
thf(2413,plain,
! [SV441: $i,SV362: $i] :
( ( ( in @ SV362 @ SV441 )
= $false )
| ( ( subset @ SV362 @ ( union @ SV441 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2286]) ).
thf(2414,plain,
! [SV491: $i,SV481: $i,SV442: $i,SV363: $i] :
( ( ~ ( subset @ SV363 @ SV442 )
| ~ ( subset @ SV481 @ SV491 )
| ( subset @ ( cartesian_product2 @ SV363 @ SV481 ) @ ( cartesian_product2 @ SV442 @ SV491 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2287]) ).
thf(2415,plain,
! [SV443: $i,SV364: $i] :
( ( ( subset @ SV364 @ SV443 )
= $false )
| ( ( ( set_union2 @ SV364 @ SV443 )
= SV443 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2288]) ).
thf(2416,plain,
! [SV482: $i,SV445: $i,SV366: $i] :
( ( ( ~ ( subset @ SV366 @ SV445 )
| ~ ( subset @ SV366 @ SV482 ) )
= $true )
| ( ( subset @ SV366 @ ( set_intersection2 @ SV445 @ SV482 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2289]) ).
thf(2417,plain,
! [SV483: $i,SV446: $i,SV367: $i] :
( ( ( ~ ( subset @ SV367 @ SV446 )
| ~ ( subset @ SV446 @ SV483 ) )
= $true )
| ( ( subset @ SV367 @ SV483 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2290]) ).
thf(2418,plain,
! [SV447: $i,SV369: $i] :
( ( ( subset @ SV369 @ SV447 )
= $false )
| ( ( ! [SY725: $i] : ( subset @ ( set_intersection2 @ SV369 @ SY725 ) @ ( set_intersection2 @ SV447 @ SY725 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2292]) ).
thf(2419,plain,
! [SV448: $i,SV370: $i] :
( ( ( subset @ SV370 @ SV448 )
= $false )
| ( ( ( set_intersection2 @ SV370 @ SV448 )
= SV370 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2293]) ).
thf(2420,plain,
! [SV449: $i,SV371: $i] :
( ( ( subset @ SV371 @ SV449 )
= $false )
| ( ( ! [SY726: $i] : ( subset @ ( set_difference @ SV371 @ SY726 ) @ ( set_difference @ SV449 @ SY726 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2294]) ).
thf(2421,plain,
! [SV375: $i,SV492: $i] :
( ( ( ~ ( relation @ SV492 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV375 @ SV492 ) ) @ ( relation_dom @ SV375 ) ) )
= $true )
| ( ( relation @ SV375 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2295]) ).
thf(2422,plain,
! [SV376: $i,SV493: $i] :
( ( ( ~ ( relation @ SV493 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV376 @ SV493 ) ) @ ( relation_rng @ SV493 ) ) )
= $true )
| ( ( relation @ SV376 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2296]) ).
thf(2423,plain,
! [SV453: $i,SV377: $i] :
( ( ( subset @ SV377 @ SV453 )
= $false )
| ( ( SV453
= ( set_union2 @ SV377 @ ( set_difference @ SV453 @ SV377 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2297]) ).
thf(2424,plain,
! [SV378: $i,SV494: $i] :
( ( ( ~ ( relation @ SV494 )
| ~ ( subset @ ( relation_rng @ SV378 ) @ ( relation_dom @ SV494 ) )
| ( ( relation_dom @ ( relation_composition @ SV378 @ SV494 ) )
= ( relation_dom @ SV378 ) ) )
= $true )
| ( ( relation @ SV378 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2298]) ).
thf(2425,plain,
! [SV454: $i,SV379: $i] :
( ( ( in @ SV379 @ SV454 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV379 ) @ SV454 )
= SV454 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2299]) ).
thf(2426,plain,
! [SV380: $i,SV495: $i] :
( ( ( ~ ( relation @ SV495 )
| ~ ( subset @ ( relation_dom @ SV380 ) @ ( relation_rng @ SV495 ) )
| ( ( relation_rng @ ( relation_composition @ SV495 @ SV380 ) )
= ( relation_rng @ SV380 ) ) )
= $true )
| ( ( relation @ SV380 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2300]) ).
thf(2427,plain,
! [SV382: $i] :
( ( ( in @ ( ordered_pair @ ( sK31_B @ SV382 ) @ ( sK32_SY282 @ SV382 ) ) @ SV382 )
= $true )
| ( ( SV382 = empty_set )
= $true )
| ( ( relation @ SV382 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2301]) ).
thf(2428,plain,
! [SV383: $i,SV456: $i] :
( ( ( proper_subset @ SV456 @ SV383 )
= $false )
| ( ( ~ ( subset @ SV383 @ SV456 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2302]) ).
thf(2429,plain,
! [SV384: $i,SV484: $i,SV457: $i] :
( ( ( ~ ( disjoint @ SV457 @ SV484 )
| ~ ( subset @ SV384 @ SV457 ) )
= $true )
| ( ( disjoint @ SV384 @ SV484 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2303]) ).
thf(2430,plain,
! [SV458: $i,SV386: $i] :
( ( ( subset @ ( singleton @ SV386 ) @ ( singleton @ SV458 ) )
= $false )
| ( ( SV386 = SV458 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2304]) ).
thf(2431,plain,
! [SV485: $i,SV460: $i,SV388: $i] :
( ( ( ~ ( subset @ SV388 @ SV460 )
| ~ ( subset @ SV485 @ SV460 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV388 @ SV485 ) @ SV460 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2305]) ).
thf(2432,plain,
! [SV496: $i,SV461: $i,SV389: $i] :
( ( ( ( ( singleton @ SV389 )
!= ( unordered_pair @ SV461 @ SV496 ) ) )
= $true )
| ( ( SV389 = SV461 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2306]) ).
thf(2433,plain,
! [SV462: $i,SV390: $i] :
( ( ( in @ SV390 @ SV462 )
= $false )
| ( ( subset @ SV390 @ ( union @ SV462 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2307]) ).
thf(2434,plain,
! [SV486: $i,SV463: $i,SV392: $i] :
( ( ( ( ( singleton @ SV392 )
!= ( unordered_pair @ SV463 @ SV486 ) ) )
= $true )
| ( ( SV463 = SV486 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2308]) ).
thf(2435,plain,
! [SV464: $i,SV393: $i] :
( ( ( in @ SV393 @ SV464 )
= $false )
| ( ( ~ ( in @ SV464 @ SV393 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2309]) ).
thf(2436,plain,
! [SV467: $i,SV399: $i] :
( ( ( ~ ( relation @ SV399 ) )
= $true )
| ( ( ~ ( relation @ SV467 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV399 @ SV467 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2313]) ).
thf(2437,plain,
! [SV469: $i,SV402: $i] :
( ( ( ~ ( relation @ SV402 ) )
= $true )
| ( ( ~ ( relation @ SV469 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV402 @ SV469 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2315]) ).
thf(2438,plain,
! [SV487: $i,SV404: $i] :
( ( ( empty @ ( set_union2 @ SV404 @ SV487 ) )
= $false )
| ( ( empty @ SV404 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2316]) ).
thf(2439,plain,
! [SV406: $i,SV488: $i] :
( ( ( empty @ ( set_union2 @ SV488 @ SV406 ) )
= $false )
| ( ( empty @ SV406 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2318]) ).
thf(2440,plain,
! [SV471: $i,SV407: $i] :
( ( ( empty @ SV407 )
= $true )
| ( ( empty @ SV471 )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV407 @ SV471 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2319]) ).
thf(2441,plain,
! [SV472: $i,SV412: $i] :
( ( ( disjoint @ SV412 @ SV472 )
= $false )
| ( ( disjoint @ SV472 @ SV412 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2321]) ).
thf(2442,plain,
! [SV473: $i,SV413: $i] :
( ( ( in @ SV413 @ SV473 )
= $false )
| ( ( element @ SV413 @ SV473 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2322]) ).
thf(2443,plain,
! [SV474: $i,SV414: $i] :
( ( ( element @ SV414 @ SV474 )
= $false )
| ( ( ( empty @ SV474 )
| ( in @ SV414 @ SV474 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2323]) ).
thf(2444,plain,
! [SV415: $i,SV489: $i,SV475: $i] :
( ( ( ~ ( element @ SV475 @ ( powerset @ SV489 ) )
| ~ ( in @ SV415 @ SV475 ) )
= $true )
| ( ( element @ SV415 @ SV489 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2324]) ).
thf(2445,plain,
! [SV416: $i,SV490: $i,SV476: $i] :
( ( ( ~ ( element @ SV476 @ ( powerset @ SV490 ) )
| ~ ( in @ SV416 @ SV476 ) )
= $true )
| ( ( ~ ( empty @ SV490 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2325]) ).
thf(2446,plain,
! [SV417: $i,SV477: $i] :
( ( ( empty @ SV477 )
= $false )
| ( ( ~ ( in @ SV417 @ SV477 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2326]) ).
thf(2447,plain,
! [SV478: $i,SV418: $i] :
( ( ( SV418 = SV478 )
= $true )
| ( ( ~ ( empty @ SV418 ) )
= $true )
| ( ( ~ ( empty @ SV478 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2327]) ).
thf(2448,plain,
! [SV419: $i] :
( ( ! [SY646: $i,SY647: $i] :
( ~ ( in @ SV419 @ SY647 )
| ~ ( in @ SY646 @ SY647 )
| ( subset @ ( unordered_pair @ SV419 @ SY646 ) @ SY647 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2328]) ).
thf(2449,plain,
! [SV419: $i] :
( ( ~ ( ~ ! [SY648: $i,SY649: $i] :
( ~ ( subset @ ( unordered_pair @ SV419 @ SY648 ) @ SY649 )
| ( in @ SV419 @ SY649 ) )
| ~ ! [SY650: $i,SY651: $i] :
( ~ ( subset @ ( unordered_pair @ SV419 @ SY650 ) @ SY651 )
| ( in @ SY650 @ SY651 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2329]) ).
thf(2450,plain,
! [SV420: $i] :
( ( ( ~ ! [SY652: $i] :
( ~ ( relation @ SY652 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SY652 @ SV420 ) @ ( sK11_SY272 @ SY652 @ SV420 ) ) @ SY652 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY272 @ SY652 @ SV420 ) @ ( sK10_C @ SY652 @ SV420 ) ) @ SV420 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK10_C @ SY652 @ SV420 ) @ ( sK11_SY272 @ SY652 @ SV420 ) ) @ SY652 )
| ( in @ ( ordered_pair @ ( sK11_SY272 @ SY652 @ SV420 ) @ ( sK10_C @ SY652 @ SV420 ) ) @ SV420 ) ) )
| ( SY652
= ( relation_inverse @ SV420 ) ) )
| ~ ! [SY653: $i] :
( ~ ( relation @ SY653 )
| ( SY653
!= ( relation_inverse @ SV420 ) )
| ~ ( ~ ! [SY654: $i,SY655: $i] :
( ~ ( in @ ( ordered_pair @ SY654 @ SY655 ) @ SY653 )
| ( in @ ( ordered_pair @ SY655 @ SY654 ) @ SV420 ) )
| ~ ! [SY656: $i,SY657: $i] :
( ~ ( in @ ( ordered_pair @ SY657 @ SY656 ) @ SV420 )
| ( in @ ( ordered_pair @ SY656 @ SY657 ) @ SY653 ) ) ) ) )
= $false )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2330]) ).
thf(2451,plain,
! [SV497: $i] :
( ( ! [SY734: $i] :
( ( disjoint @ SV497 @ SY734 )
| ( in @ ( sK33_C @ SY734 @ SV497 ) @ ( set_intersection2 @ SV497 @ SY734 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2331]) ).
thf(2452,plain,
! [SV498: $i] :
( ( ! [SY735: $i] :
( ! [SY736: $i] :
~ ( in @ SY736 @ ( set_intersection2 @ SV498 @ SY735 ) )
| ~ ( disjoint @ SV498 @ SY735 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2332]) ).
thf(2453,plain,
! [SV421: $i,SV479: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_C @ SV479 @ SV421 ) @ SV421 )
| ~ ( in @ ( sK3_C @ SV479 @ SV421 ) @ SV479 ) )
| ~ ( ( in @ ( sK3_C @ SV479 @ SV421 ) @ SV421 )
| ( in @ ( sK3_C @ SV479 @ SV421 ) @ SV479 ) ) )
= $false )
| ( ( SV421 = SV479 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2333]) ).
thf(2454,plain,
! [SV422: $i] :
( ( ! [SY659: $i,SY660: $i] :
( ~ ( relation @ SY660 )
| ~ ( in @ ( ordered_pair @ SV422 @ SY659 ) @ SY660 )
| ( in @ SV422 @ ( relation_dom @ SY660 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2334]) ).
thf(2455,plain,
! [SV422: $i] :
( ( ! [SY661: $i,SY662: $i] :
( ~ ( relation @ SY662 )
| ~ ( in @ ( ordered_pair @ SV422 @ SY661 ) @ SY662 )
| ( in @ SY661 @ ( relation_rng @ SY662 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2335]) ).
thf(2456,plain,
! [SV499: $i] :
( ( ! [SY737: $i] :
( ~ ( subset @ SV499 @ ( singleton @ SY737 ) )
| ( SV499 = empty_set )
| ( SV499
= ( singleton @ SY737 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2336]) ).
thf(2457,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2337]) ).
thf(2458,plain,
! [SV500: $i] :
( ( ! [SY738: $i] :
( ( ( set_difference @ SV500 @ SY738 )
!= SV500 )
| ( disjoint @ SV500 @ SY738 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2338]) ).
thf(2459,plain,
! [SV501: $i] :
( ( ! [SY739: $i] :
( ~ ( disjoint @ SV501 @ SY739 )
| ( ( set_difference @ SV501 @ SY739 )
= SV501 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2339]) ).
thf(2460,plain,
! [SV423: $i] :
( ( ! [SY663: $i,SY664: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK24_D @ SY664 @ SY663 @ SV423 ) @ SY664 )
| ~ ( in @ ( sK24_D @ SY664 @ SY663 @ SV423 ) @ SV423 ) )
| ~ ( ~ ( in @ ( sK24_D @ SY664 @ SY663 @ SV423 ) @ SY664 )
| ~ ( in @ ( sK24_D @ SY664 @ SY663 @ SV423 ) @ SY663 ) ) )
| ~ ( ( in @ ( sK24_D @ SY664 @ SY663 @ SV423 ) @ SY664 )
| ( in @ ( sK24_D @ SY664 @ SY663 @ SV423 ) @ SV423 )
| ( in @ ( sK24_D @ SY664 @ SY663 @ SV423 ) @ SY663 ) ) )
| ( SY664
= ( set_union2 @ SV423 @ SY663 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2340]) ).
thf(2461,plain,
! [SV423: $i] :
( ( ! [SY665: $i,SY666: $i] :
( ( SY666
!= ( set_union2 @ SV423 @ SY665 ) )
| ~ ( ~ ! [SY667: $i] :
( ~ ( in @ SY667 @ SY666 )
| ( in @ SY667 @ SV423 )
| ( in @ SY667 @ SY665 ) )
| ~ ~ ( ~ ! [SY668: $i] :
( ~ ( in @ SY668 @ SV423 )
| ( in @ SY668 @ SY666 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY665 )
| ( in @ SX3 @ SY666 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2341]) ).
thf(2462,plain,
! [SV502: $i] :
( ( ! [SY740: $i] :
( ~ ( subset @ SV502 @ ( singleton @ SY740 ) )
| ( SV502 = empty_set )
| ( SV502
= ( singleton @ SY740 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2342]) ).
thf(2463,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2343]) ).
thf(2464,plain,
! [SV503: $i] :
( ( ! [SY741: $i] :
( ( SV503 = SY741 )
| ~ ( subset @ SV503 @ SY741 )
| ( proper_subset @ SV503 @ SY741 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2344]) ).
thf(2465,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2345]) ).
thf(2466,plain,
! [SV504: $i] :
( ( ! [SY742: $i] :
( ( disjoint @ SV504 @ SY742 )
| ~ ( ~ ( in @ ( sK34_C @ SY742 @ SV504 ) @ SV504 )
| ~ ( in @ ( sK34_C @ SY742 @ SV504 ) @ SY742 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2346]) ).
thf(2467,plain,
! [SV505: $i] :
( ( ! [SY743: $i] :
( ! [SY744: $i] :
( ~ ( in @ SY744 @ SV505 )
| ~ ( in @ SY744 @ SY743 ) )
| ~ ( disjoint @ SV505 @ SY743 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2347]) ).
thf(2468,plain,
! [SV424: $i] :
( ( ! [SY670: $i] :
( ~ ( subset @ SY670 @ ( sK35_B @ SV424 ) )
| ( are_equipotent @ SY670 @ ( sK35_B @ SV424 ) )
| ( in @ SY670 @ ( sK35_B @ SV424 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2350]) ).
thf(2469,plain,
! [SV424: $i] :
( ( ~ ( ~ ! [SY671: $i] :
( ~ ( in @ SY671 @ ( sK35_B @ SV424 ) )
| ( in @ ( powerset @ SY671 ) @ ( sK35_B @ SV424 ) ) )
| ~ ~ ( ~ ! [SY672: $i,SY673: $i] :
( ~ ( in @ SY672 @ ( sK35_B @ SV424 ) )
| ~ ( subset @ SY673 @ SY672 )
| ( in @ SY673 @ ( sK35_B @ SV424 ) ) )
| ~ ( in @ SV424 @ ( sK35_B @ SV424 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2351]) ).
thf(2470,plain,
! [SV425: $i] :
( ( ( ~ ! [SY674: $i] :
( ~ ( relation @ SY674 )
| ~ ( subset @ SV425 @ SY674 )
| ( subset @ ( relation_dom @ SV425 ) @ ( relation_dom @ SY674 ) ) )
| ~ ! [SY675: $i] :
( ~ ( relation @ SY675 )
| ~ ( subset @ SV425 @ SY675 )
| ( subset @ ( relation_rng @ SV425 ) @ ( relation_rng @ SY675 ) ) ) )
= $false )
| ( ( relation @ SV425 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2352]) ).
thf(2471,plain,
! [SV506: $i] :
( ( ! [SY745: $i] :
( ~ ( in @ SV506 @ SY745 )
| ( subset @ ( singleton @ SV506 ) @ SY745 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2353]) ).
thf(2472,plain,
! [SV507: $i] :
( ( ! [SY746: $i] :
( ~ ( subset @ ( singleton @ SV507 ) @ SY746 )
| ( in @ SV507 @ SY746 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2354]) ).
thf(2473,plain,
! [SV508: $i] :
( ( ( in @ ( sK37_B @ SV508 ) @ SV508 )
| ( SV508 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2355]) ).
thf(2474,plain,
! [SV509: $i] :
( ( ( SV509 != empty_set )
| ! [SY747: $i] :
~ ( in @ SY747 @ SV509 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2356]) ).
thf(2475,plain,
! [SV426: $i] :
( ( ! [SY676: $i] :
( ~ ( subset @ SY676 @ ( sK1_B @ SV426 ) )
| ( are_equipotent @ SY676 @ ( sK1_B @ SV426 ) )
| ( in @ SY676 @ ( sK1_B @ SV426 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2357]) ).
thf(2476,plain,
! [SV426: $i] :
( ( ~ ( ~ ! [SY677: $i] :
( ~ ( ~ ! [SY678: $i] :
( ~ ( subset @ SY678 @ SY677 )
| ( in @ SY678 @ ( sK2_SY267 @ SY677 @ SV426 ) ) )
| ~ ( in @ ( sK2_SY267 @ SY677 @ SV426 ) @ ( sK1_B @ SV426 ) ) )
| ~ ( in @ SY677 @ ( sK1_B @ SV426 ) ) )
| ~ ~ ( ~ ! [SY679: $i,SY680: $i] :
( ~ ( in @ SY679 @ ( sK1_B @ SV426 ) )
| ~ ( subset @ SY680 @ SY679 )
| ( in @ SY680 @ ( sK1_B @ SV426 ) ) )
| ~ ( in @ SV426 @ ( sK1_B @ SV426 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2358]) ).
thf(2477,plain,
! [SV510: $i] :
( ( ! [SY748: $i] :
( ~ ( ~ ( ~ ( in @ ( sK26_C @ SY748 @ SV510 ) @ SY748 )
| ~ ( subset @ ( sK26_C @ SY748 @ SV510 ) @ SV510 ) )
| ~ ( ( in @ ( sK26_C @ SY748 @ SV510 ) @ SY748 )
| ( subset @ ( sK26_C @ SY748 @ SV510 ) @ SV510 ) ) )
| ( SY748
= ( powerset @ SV510 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2361]) ).
thf(2478,plain,
! [SV511: $i] :
( ( ! [SY749: $i] :
( ( SY749
!= ( powerset @ SV511 ) )
| ~ ( ~ ! [SY750: $i] :
( ~ ( in @ SY750 @ SY749 )
| ( subset @ SY750 @ SV511 ) )
| ~ ! [SY751: $i] :
( ~ ( subset @ SY751 @ SV511 )
| ( in @ SY751 @ SY749 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2362]) ).
thf(2479,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2363]) ).
thf(2480,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2364]) ).
thf(2481,plain,
! [SV512: $i] :
( ( ! [SY752: $i] :
( ( ( set_difference @ SV512 @ ( singleton @ SY752 ) )
!= SV512 )
| ~ ( in @ SY752 @ SV512 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2365]) ).
thf(2482,plain,
! [SV513: $i] :
( ( ! [SY753: $i] :
( ( in @ SY753 @ SV513 )
| ( ( set_difference @ SV513 @ ( singleton @ SY753 ) )
= SV513 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2366]) ).
thf(2483,plain,
! [SV514: $i] :
( ( ~ ( ~ ! [SY754: $i,SY755: $i] :
( ( sK30_B @ SV514 )
!= ( ordered_pair @ SY754 @ SY755 ) )
| ~ ( in @ ( sK30_B @ SV514 ) @ SV514 ) )
| ( relation @ SV514 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2367]) ).
thf(2484,plain,
! [SV515: $i] :
( ( ~ ( relation @ SV515 )
| ! [SY756: $i] :
( ( SY756
= ( ordered_pair @ ( sK28_C @ SY756 @ SV515 ) @ ( sK29_SY279 @ SY756 @ SV515 ) ) )
| ~ ( in @ SY756 @ SV515 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2368]) ).
thf(2485,plain,
! [SV516: $i] :
( ( ! [SY757: $i] :
( ( ( set_intersection2 @ SV516 @ SY757 )
!= empty_set )
| ( disjoint @ SV516 @ SY757 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2369]) ).
thf(2486,plain,
! [SV517: $i] :
( ( ! [SY758: $i] :
( ~ ( disjoint @ SV517 @ SY758 )
| ( ( set_intersection2 @ SV517 @ SY758 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2370]) ).
thf(2487,plain,
! [SV518: $i] :
( ( ! [SY759: $i] :
( ~ ( subset @ SV518 @ SY759 )
| ~ ( subset @ SY759 @ SV518 )
| ( SV518 = SY759 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2371]) ).
thf(2488,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2372]) ).
thf(2489,plain,
( ( empty @ sK6_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2373]) ).
thf(2490,plain,
! [SV519: $i] :
( ( ! [SY760: $i] :
( ~ ( element @ SV519 @ ( powerset @ SY760 ) )
| ( subset @ SV519 @ SY760 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2375]) ).
thf(2491,plain,
! [SV520: $i] :
( ( ! [SY761: $i] :
( ~ ( subset @ SV520 @ SY761 )
| ( element @ SV520 @ ( powerset @ SY761 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2376]) ).
thf(2492,plain,
! [SV427: $i] :
( ( ( ~ ! [SY681: $i] :
( ~ ( ~ ( ! [SY682: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SY681 @ SV427 ) @ SY682 ) @ SV427 )
| ~ ( in @ ( sK20_C @ SY681 @ SV427 ) @ SY681 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_C @ SY681 @ SV427 ) @ ( sK21_SY278 @ SY681 @ SV427 ) ) @ SV427 )
| ( in @ ( sK20_C @ SY681 @ SV427 ) @ SY681 ) ) )
| ( SY681
= ( relation_dom @ SV427 ) ) )
| ~ ! [SY683: $i] :
( ( SY683
!= ( relation_dom @ SV427 ) )
| ~ ( ~ ! [SY684: $i] :
( ! [SY685: $i] :
~ ( in @ ( ordered_pair @ SY684 @ SY685 ) @ SV427 )
| ( in @ SY684 @ SY683 ) )
| ~ ! [SY686: $i] :
( ~ ( in @ SY686 @ SY683 )
| ( in @ ( ordered_pair @ SY686 @ ( sK19_D @ SY686 @ SY683 @ SV427 ) ) @ SV427 ) ) ) ) )
= $false )
| ( ( relation @ SV427 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2377]) ).
thf(2493,plain,
! [SV428: $i] :
( ( ! [SY687: $i,SY688: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SY688 @ SY687 @ SV428 ) @ SV428 )
| ( in @ ( sK15_D @ SY688 @ SY687 @ SV428 ) @ SY687 )
| ~ ( in @ ( sK15_D @ SY688 @ SY687 @ SV428 ) @ SY688 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SY688 @ SY687 @ SV428 ) @ SV428 )
| ( in @ ( sK15_D @ SY688 @ SY687 @ SV428 ) @ SY688 ) )
| ~ ( ~ ( in @ ( sK15_D @ SY688 @ SY687 @ SV428 ) @ SY687 )
| ( in @ ( sK15_D @ SY688 @ SY687 @ SV428 ) @ SY688 ) ) ) )
| ( SY688
= ( set_difference @ SV428 @ SY687 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2378]) ).
thf(2494,plain,
! [SV428: $i] :
( ( ! [SY689: $i,SY690: $i] :
( ( SY690
!= ( set_difference @ SV428 @ SY689 ) )
| ~ ( ~ ! [SY691: $i] :
( ~ ( in @ SY691 @ SV428 )
| ( in @ SY691 @ SY689 )
| ( in @ SY691 @ SY690 ) )
| ~ ~ ( ~ ! [SY692: $i] :
( ~ ( in @ SY692 @ SY690 )
| ( in @ SY692 @ SV428 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY690 )
| ~ ( in @ SX3 @ SY689 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2379]) ).
thf(2495,plain,
! [SV521: $i] :
( ( ~ ( relation @ SV521 )
| ( ( relation_rng @ SV521 )
= ( relation_dom @ ( relation_inverse @ SV521 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2380]) ).
thf(2496,plain,
! [SV522: $i] :
( ( ~ ( relation @ SV522 )
| ( ( relation_dom @ SV522 )
= ( relation_rng @ ( relation_inverse @ SV522 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2381]) ).
thf(2497,plain,
! [SV523: $i] :
( ( ! [SY762: $i] :
( ~ ( in @ SV523 @ SY762 )
| ( subset @ ( singleton @ SV523 ) @ SY762 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2382]) ).
thf(2498,plain,
! [SV524: $i] :
( ( ! [SY763: $i] :
( ~ ( subset @ ( singleton @ SV524 ) @ SY763 )
| ( in @ SV524 @ SY763 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2383]) ).
thf(2499,plain,
! [SV429: $i] :
( ( ! [SY694: $i,SY695: $i] :
( ~ ( ~ ( ~ ( in @ ( sK22_D @ SY695 @ SY694 @ SV429 ) @ SV429 )
| ~ ( in @ ( sK22_D @ SY695 @ SY694 @ SV429 ) @ SY694 )
| ~ ( in @ ( sK22_D @ SY695 @ SY694 @ SV429 ) @ SY695 ) )
| ~ ~ ( ~ ( ( in @ ( sK22_D @ SY695 @ SY694 @ SV429 ) @ SV429 )
| ( in @ ( sK22_D @ SY695 @ SY694 @ SV429 ) @ SY695 ) )
| ~ ( ( in @ ( sK22_D @ SY695 @ SY694 @ SV429 ) @ SY694 )
| ( in @ ( sK22_D @ SY695 @ SY694 @ SV429 ) @ SY695 ) ) ) )
| ( SY695
= ( set_intersection2 @ SV429 @ SY694 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2384]) ).
thf(2500,plain,
! [SV429: $i] :
( ( ! [SY696: $i,SY697: $i] :
( ( SY697
!= ( set_intersection2 @ SV429 @ SY696 ) )
| ~ ( ~ ! [SY698: $i] :
( ~ ( in @ SY698 @ SV429 )
| ~ ( in @ SY698 @ SY696 )
| ( in @ SY698 @ SY697 ) )
| ~ ~ ( ~ ! [SY699: $i] :
( ~ ( in @ SY699 @ SY697 )
| ( in @ SY699 @ SV429 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY697 )
| ( in @ SX3 @ SY696 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2385]) ).
thf(2501,plain,
! [SV430: $i] :
( ( ( ~ ! [SY701: $i] :
( ~ ( ~ ( ! [SY702: $i] :
~ ( in @ ( ordered_pair @ SY702 @ ( sK13_C @ SY701 @ SV430 ) ) @ SV430 )
| ~ ( in @ ( sK13_C @ SY701 @ SV430 ) @ SY701 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY274 @ SY701 @ SV430 ) @ ( sK13_C @ SY701 @ SV430 ) ) @ SV430 )
| ( in @ ( sK13_C @ SY701 @ SV430 ) @ SY701 ) ) )
| ( SY701
= ( relation_rng @ SV430 ) ) )
| ~ ! [SY703: $i] :
( ( SY703
!= ( relation_rng @ SV430 ) )
| ~ ( ~ ! [SY704: $i] :
( ! [SY705: $i] :
~ ( in @ ( ordered_pair @ SY705 @ SY704 ) @ SV430 )
| ( in @ SY704 @ SY703 ) )
| ~ ! [SY706: $i] :
( ~ ( in @ SY706 @ SY703 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY706 @ SY703 @ SV430 ) @ SY706 ) @ SV430 ) ) ) ) )
= $false )
| ( ( relation @ SV430 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2386]) ).
thf(2502,plain,
! [SV525: $i] :
( ( ! [SY764: $i] :
( ~ ( ~ ( ! [SY765: $i] :
( ~ ( in @ ( sK17_C @ SY764 @ SV525 ) @ SY765 )
| ~ ( in @ SY765 @ SV525 ) )
| ~ ( in @ ( sK17_C @ SY764 @ SV525 ) @ SY764 ) )
| ~ ( ~ ( ~ ( in @ ( sK17_C @ SY764 @ SV525 ) @ ( sK18_SY276 @ SY764 @ SV525 ) )
| ~ ( in @ ( sK18_SY276 @ SY764 @ SV525 ) @ SV525 ) )
| ( in @ ( sK17_C @ SY764 @ SV525 ) @ SY764 ) ) )
| ( SY764
= ( union @ SV525 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2387]) ).
thf(2503,plain,
! [SV526: $i] :
( ( ! [SY766: $i] :
( ( SY766
!= ( union @ SV526 ) )
| ~ ( ~ ! [SY767: $i] :
( ! [SY768: $i] :
( ~ ( in @ SY767 @ SY768 )
| ~ ( in @ SY768 @ SV526 ) )
| ( in @ SY767 @ SY766 ) )
| ~ ! [SY769: $i] :
( ~ ( in @ SY769 @ SY766 )
| ~ ( ~ ( in @ SY769 @ ( sK16_D @ SY769 @ SY766 @ SV526 ) )
| ~ ( in @ ( sK16_D @ SY769 @ SY766 @ SV526 ) @ SV526 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2388]) ).
thf(2504,plain,
! [SV431: $i] :
( ( element @ ( sK5_B @ SV431 ) @ ( powerset @ SV431 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2389]) ).
thf(2505,plain,
! [SV431: $i] :
( ( empty @ ( sK5_B @ SV431 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2390]) ).
thf(2506,plain,
! [SV432: $i,SV480: $i] :
( ( ( ~ ( in @ ( sK36_C @ SV480 @ SV432 ) @ SV432 )
| ~ ~ ( in @ ( sK36_C @ SV480 @ SV432 ) @ SV480 ) )
= $false )
| ( ( element @ SV432 @ ( powerset @ SV480 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2391]) ).
thf(2507,plain,
! [SV527: $i] :
( ( ! [SY770: $i] :
( ( ( set_difference @ SV527 @ SY770 )
!= empty_set )
| ( subset @ SV527 @ SY770 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2392]) ).
thf(2508,plain,
! [SV528: $i] :
( ( ! [SY771: $i] :
( ~ ( subset @ SV528 @ SY771 )
| ( ( set_difference @ SV528 @ SY771 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2393]) ).
thf(2509,plain,
! [SV529: $i] :
( ( ! [SY772: $i] :
( ~ ( ~ ( in @ ( sK23_C @ SY772 @ SV529 ) @ SV529 )
| ~ ~ ( in @ ( sK23_C @ SY772 @ SV529 ) @ SY772 ) )
| ( subset @ SV529 @ SY772 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2394]) ).
thf(2510,plain,
! [SV530: $i] :
( ( ! [SY773: $i] :
( ~ ( subset @ SV530 @ SY773 )
| ! [SY774: $i] :
( ~ ( in @ SY774 @ SV530 )
| ( in @ SY774 @ SY773 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2395]) ).
thf(2511,plain,
! [SV531: $i] :
( ( ! [SY775: $i] :
( ( ( set_difference @ SV531 @ SY775 )
!= empty_set )
| ( subset @ SV531 @ SY775 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2396]) ).
thf(2512,plain,
! [SV532: $i] :
( ( ! [SY776: $i] :
( ~ ( subset @ SV532 @ SY776 )
| ( ( set_difference @ SV532 @ SY776 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2397]) ).
thf(2513,plain,
! [SV433: $i] :
( ( ! [SY708: $i,SY709: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK25_D @ SY709 @ SY708 @ SV433 ) @ SY709 )
| ( ( sK25_D @ SY709 @ SY708 @ SV433 )
!= SV433 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY709 @ SY708 @ SV433 ) @ SY709 )
| ( ( sK25_D @ SY709 @ SY708 @ SV433 )
!= SY708 ) ) )
| ~ ( ( in @ ( sK25_D @ SY709 @ SY708 @ SV433 ) @ SY709 )
| ( ( sK25_D @ SY709 @ SY708 @ SV433 )
= SV433 )
| ( ( sK25_D @ SY709 @ SY708 @ SV433 )
= SY708 ) ) )
| ( SY709
= ( unordered_pair @ SV433 @ SY708 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2398]) ).
thf(2514,plain,
! [SV433: $i] :
( ( ! [SY710: $i,SY711: $i] :
( ( SY711
!= ( unordered_pair @ SV433 @ SY710 ) )
| ~ ( ~ ! [SY712: $i] :
( ~ ( in @ SY712 @ SY711 )
| ( SY712 = SV433 )
| ( SY712 = SY710 ) )
| ~ ~ ( ~ ! [SY713: $i] :
( ( SY713 != SV433 )
| ( in @ SY713 @ SY711 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY710 )
| ( in @ SX3 @ SY711 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2399]) ).
thf(2515,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK40_SY287 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK39_C @ SX1 @ SX0 ) @ ( sK40_SY287 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK38_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK38_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2400]) ).
thf(2516,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2401]) ).
thf(2517,plain,
! [SV533: $i] :
( ( ! [SY777: $i] :
( ~ ( ~ ( ( ( sK27_C @ SY777 @ SV533 )
!= SV533 )
| ~ ( in @ ( sK27_C @ SY777 @ SV533 ) @ SY777 ) )
| ~ ( ( ( sK27_C @ SY777 @ SV533 )
= SV533 )
| ( in @ ( sK27_C @ SY777 @ SV533 ) @ SY777 ) ) )
| ( SY777
= ( singleton @ SV533 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2402]) ).
thf(2518,plain,
! [SV534: $i] :
( ( ! [SY778: $i] :
( ( SY778
!= ( singleton @ SV534 ) )
| ~ ( ~ ! [SY779: $i] :
( ( SY779 != SV534 )
| ( in @ SY779 @ SY778 ) )
| ~ ! [SY780: $i] :
( ~ ( in @ SY780 @ SY778 )
| ( SY780 = SV534 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2403]) ).
thf(2519,plain,
! [SV434: $i] :
( ( ! [SY715: $i] :
( ~ ( subset @ SV434 @ SY715 )
| ! [SY716: $i] : ( subset @ ( cartesian_product2 @ SV434 @ SY716 ) @ ( cartesian_product2 @ SY715 @ SY716 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2404]) ).
thf(2520,plain,
! [SV434: $i] :
( ( ! [SY717: $i] :
( ~ ( subset @ SV434 @ SY717 )
| ! [SY718: $i] : ( subset @ ( cartesian_product2 @ SY718 @ SV434 ) @ ( cartesian_product2 @ SY718 @ SY717 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2405]) ).
thf(2521,plain,
! [SV435: $i] :
( ( ( ~ ( element @ ( sK8_B @ SV435 ) @ ( powerset @ SV435 ) ) )
= $false )
| ( ( empty @ SV435 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2406]) ).
thf(2522,plain,
! [SV435: $i] :
( ( ( ~ ~ ( empty @ ( sK8_B @ SV435 ) ) )
= $false )
| ( ( empty @ SV435 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2406]) ).
thf(2523,plain,
! [SV350: $i] :
( ( ( empty @ ( relation_dom @ SV350 ) )
= $false )
| ( ( empty @ SV350 )
= $true )
| ( ( relation @ SV350 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2407]) ).
thf(2524,plain,
! [SV351: $i] :
( ( ( empty @ ( relation_rng @ SV351 ) )
= $false )
| ( ( empty @ SV351 )
= $true )
| ( ( relation @ SV351 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2408]) ).
thf(2525,plain,
! [SV437: $i,SV358: $i] :
( ( ( in @ SV358 @ SV437 )
= $false )
| ( ( disjoint @ ( singleton @ SV358 ) @ SV437 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2410]) ).
thf(2526,plain,
! [SV360: $i,SV439: $i,SV535: $i] :
( ( ( ~ ( in @ SV535 @ SV439 )
| ( in @ SV535 @ SV360 ) )
= $true )
| ( ( element @ SV439 @ ( powerset @ SV360 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2411]) ).
thf(2527,plain,
! [SV440: $i,SV361: $i,SV536: $i] :
( ( ( ( in @ SV536 @ SV361 )
| ( subset @ SV361 @ ( set_difference @ SV440 @ ( singleton @ SV536 ) ) ) )
= $true )
| ( ( subset @ SV361 @ SV440 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2412]) ).
thf(2528,plain,
! [SV491: $i,SV481: $i,SV442: $i,SV363: $i] :
( ( ( ~ ( subset @ SV363 @ SV442 )
| ~ ( subset @ SV481 @ SV491 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV363 @ SV481 ) @ ( cartesian_product2 @ SV442 @ SV491 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2414]) ).
thf(2529,plain,
! [SV482: $i,SV445: $i,SV366: $i] :
( ( ( ~ ( subset @ SV366 @ SV445 ) )
= $true )
| ( ( ~ ( subset @ SV366 @ SV482 ) )
= $true )
| ( ( subset @ SV366 @ ( set_intersection2 @ SV445 @ SV482 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2416]) ).
thf(2530,plain,
! [SV483: $i,SV446: $i,SV367: $i] :
( ( ( ~ ( subset @ SV367 @ SV446 ) )
= $true )
| ( ( ~ ( subset @ SV446 @ SV483 ) )
= $true )
| ( ( subset @ SV367 @ SV483 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2417]) ).
thf(2531,plain,
! [SV447: $i,SV537: $i,SV369: $i] :
( ( ( subset @ ( set_intersection2 @ SV369 @ SV537 ) @ ( set_intersection2 @ SV447 @ SV537 ) )
= $true )
| ( ( subset @ SV369 @ SV447 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2418]) ).
thf(2532,plain,
! [SV449: $i,SV538: $i,SV371: $i] :
( ( ( subset @ ( set_difference @ SV371 @ SV538 ) @ ( set_difference @ SV449 @ SV538 ) )
= $true )
| ( ( subset @ SV371 @ SV449 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2420]) ).
thf(2533,plain,
! [SV375: $i,SV492: $i] :
( ( ( ~ ( relation @ SV492 ) )
= $true )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV375 @ SV492 ) ) @ ( relation_dom @ SV375 ) )
= $true )
| ( ( relation @ SV375 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2421]) ).
thf(2534,plain,
! [SV376: $i,SV493: $i] :
( ( ( ~ ( relation @ SV493 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV376 @ SV493 ) ) @ ( relation_rng @ SV493 ) )
= $true )
| ( ( relation @ SV376 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2422]) ).
thf(2535,plain,
! [SV378: $i,SV494: $i] :
( ( ( ~ ( relation @ SV494 ) )
= $true )
| ( ( ~ ( subset @ ( relation_rng @ SV378 ) @ ( relation_dom @ SV494 ) )
| ( ( relation_dom @ ( relation_composition @ SV378 @ SV494 ) )
= ( relation_dom @ SV378 ) ) )
= $true )
| ( ( relation @ SV378 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2424]) ).
thf(2536,plain,
! [SV380: $i,SV495: $i] :
( ( ( ~ ( relation @ SV495 ) )
= $true )
| ( ( ~ ( subset @ ( relation_dom @ SV380 ) @ ( relation_rng @ SV495 ) )
| ( ( relation_rng @ ( relation_composition @ SV495 @ SV380 ) )
= ( relation_rng @ SV380 ) ) )
= $true )
| ( ( relation @ SV380 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2426]) ).
thf(2537,plain,
! [SV456: $i,SV383: $i] :
( ( ( subset @ SV383 @ SV456 )
= $false )
| ( ( proper_subset @ SV456 @ SV383 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2428]) ).
thf(2538,plain,
! [SV384: $i,SV484: $i,SV457: $i] :
( ( ( ~ ( disjoint @ SV457 @ SV484 ) )
= $true )
| ( ( ~ ( subset @ SV384 @ SV457 ) )
= $true )
| ( ( disjoint @ SV384 @ SV484 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2429]) ).
thf(2539,plain,
! [SV485: $i,SV460: $i,SV388: $i] :
( ( ( ~ ( subset @ SV388 @ SV460 ) )
= $true )
| ( ( ~ ( subset @ SV485 @ SV460 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV388 @ SV485 ) @ SV460 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2431]) ).
thf(2540,plain,
! [SV496: $i,SV461: $i,SV389: $i] :
( ( ( ( singleton @ SV389 )
= ( unordered_pair @ SV461 @ SV496 ) )
= $false )
| ( ( SV389 = SV461 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2432]) ).
thf(2541,plain,
! [SV486: $i,SV463: $i,SV392: $i] :
( ( ( ( singleton @ SV392 )
= ( unordered_pair @ SV463 @ SV486 ) )
= $false )
| ( ( SV463 = SV486 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2434]) ).
thf(2542,plain,
! [SV393: $i,SV464: $i] :
( ( ( in @ SV464 @ SV393 )
= $false )
| ( ( in @ SV393 @ SV464 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2435]) ).
thf(2543,plain,
! [SV467: $i,SV399: $i] :
( ( ( relation @ SV399 )
= $false )
| ( ( ~ ( relation @ SV467 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV399 @ SV467 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2436]) ).
thf(2544,plain,
! [SV469: $i,SV402: $i] :
( ( ( relation @ SV402 )
= $false )
| ( ( ~ ( relation @ SV469 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV402 @ SV469 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2437]) ).
thf(2545,plain,
! [SV471: $i,SV407: $i] :
( ( ( empty @ ( cartesian_product2 @ SV407 @ SV471 ) )
= $false )
| ( ( empty @ SV471 )
= $true )
| ( ( empty @ SV407 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2440]) ).
thf(2546,plain,
! [SV414: $i,SV474: $i] :
( ( ( empty @ SV474 )
= $true )
| ( ( in @ SV414 @ SV474 )
= $true )
| ( ( element @ SV414 @ SV474 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2443]) ).
thf(2547,plain,
! [SV415: $i,SV489: $i,SV475: $i] :
( ( ( ~ ( element @ SV475 @ ( powerset @ SV489 ) ) )
= $true )
| ( ( ~ ( in @ SV415 @ SV475 ) )
= $true )
| ( ( element @ SV415 @ SV489 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2444]) ).
thf(2548,plain,
! [SV416: $i,SV490: $i,SV476: $i] :
( ( ( ~ ( element @ SV476 @ ( powerset @ SV490 ) ) )
= $true )
| ( ( ~ ( in @ SV416 @ SV476 ) )
= $true )
| ( ( ~ ( empty @ SV490 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2445]) ).
thf(2549,plain,
! [SV477: $i,SV417: $i] :
( ( ( in @ SV417 @ SV477 )
= $false )
| ( ( empty @ SV477 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2446]) ).
thf(2550,plain,
! [SV478: $i,SV418: $i] :
( ( ( empty @ SV418 )
= $false )
| ( ( SV418 = SV478 )
= $true )
| ( ( ~ ( empty @ SV478 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2447]) ).
thf(2551,plain,
! [SV539: $i,SV419: $i] :
( ( ! [SY781: $i] :
( ~ ( in @ SV419 @ SY781 )
| ~ ( in @ SV539 @ SY781 )
| ( subset @ ( unordered_pair @ SV419 @ SV539 ) @ SY781 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2448]) ).
thf(2552,plain,
! [SV419: $i] :
( ( ~ ! [SY648: $i,SY649: $i] :
( ~ ( subset @ ( unordered_pair @ SV419 @ SY648 ) @ SY649 )
| ( in @ SV419 @ SY649 ) )
| ~ ! [SY650: $i,SY651: $i] :
( ~ ( subset @ ( unordered_pair @ SV419 @ SY650 ) @ SY651 )
| ( in @ SY650 @ SY651 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2449]) ).
thf(2553,plain,
! [SV420: $i] :
( ( ( ~ ! [SY652: $i] :
( ~ ( relation @ SY652 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SY652 @ SV420 ) @ ( sK11_SY272 @ SY652 @ SV420 ) ) @ SY652 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY272 @ SY652 @ SV420 ) @ ( sK10_C @ SY652 @ SV420 ) ) @ SV420 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK10_C @ SY652 @ SV420 ) @ ( sK11_SY272 @ SY652 @ SV420 ) ) @ SY652 )
| ( in @ ( ordered_pair @ ( sK11_SY272 @ SY652 @ SV420 ) @ ( sK10_C @ SY652 @ SV420 ) ) @ SV420 ) ) )
| ( SY652
= ( relation_inverse @ SV420 ) ) ) )
= $false )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2450]) ).
thf(2554,plain,
! [SV420: $i] :
( ( ( ~ ! [SY653: $i] :
( ~ ( relation @ SY653 )
| ( SY653
!= ( relation_inverse @ SV420 ) )
| ~ ( ~ ! [SY654: $i,SY655: $i] :
( ~ ( in @ ( ordered_pair @ SY654 @ SY655 ) @ SY653 )
| ( in @ ( ordered_pair @ SY655 @ SY654 ) @ SV420 ) )
| ~ ! [SY656: $i,SY657: $i] :
( ~ ( in @ ( ordered_pair @ SY657 @ SY656 ) @ SV420 )
| ( in @ ( ordered_pair @ SY656 @ SY657 ) @ SY653 ) ) ) ) )
= $false )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2450]) ).
thf(2555,plain,
! [SV540: $i,SV497: $i] :
( ( ( disjoint @ SV497 @ SV540 )
| ( in @ ( sK33_C @ SV540 @ SV497 ) @ ( set_intersection2 @ SV497 @ SV540 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2451]) ).
thf(2556,plain,
! [SV541: $i,SV498: $i] :
( ( ! [SY782: $i] :
~ ( in @ SY782 @ ( set_intersection2 @ SV498 @ SV541 ) )
| ~ ( disjoint @ SV498 @ SV541 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2452]) ).
thf(2557,plain,
! [SV421: $i,SV479: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_C @ SV479 @ SV421 ) @ SV421 )
| ~ ( in @ ( sK3_C @ SV479 @ SV421 ) @ SV479 ) ) )
= $false )
| ( ( SV421 = SV479 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2453]) ).
thf(2558,plain,
! [SV421: $i,SV479: $i] :
( ( ( ~ ( ( in @ ( sK3_C @ SV479 @ SV421 ) @ SV421 )
| ( in @ ( sK3_C @ SV479 @ SV421 ) @ SV479 ) ) )
= $false )
| ( ( SV421 = SV479 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2453]) ).
thf(2559,plain,
! [SV542: $i,SV422: $i] :
( ( ! [SY783: $i] :
( ~ ( relation @ SY783 )
| ~ ( in @ ( ordered_pair @ SV422 @ SV542 ) @ SY783 )
| ( in @ SV422 @ ( relation_dom @ SY783 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2454]) ).
thf(2560,plain,
! [SV543: $i,SV422: $i] :
( ( ! [SY784: $i] :
( ~ ( relation @ SY784 )
| ~ ( in @ ( ordered_pair @ SV422 @ SV543 ) @ SY784 )
| ( in @ SV543 @ ( relation_rng @ SY784 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2455]) ).
thf(2561,plain,
! [SV544: $i,SV499: $i] :
( ( ~ ( subset @ SV499 @ ( singleton @ SV544 ) )
| ( SV499 = empty_set )
| ( SV499
= ( singleton @ SV544 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2456]) ).
thf(2562,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2457]) ).
thf(2563,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2457]) ).
thf(2564,plain,
! [SV545: $i,SV500: $i] :
( ( ( ( set_difference @ SV500 @ SV545 )
!= SV500 )
| ( disjoint @ SV500 @ SV545 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2458]) ).
thf(2565,plain,
! [SV546: $i,SV501: $i] :
( ( ~ ( disjoint @ SV501 @ SV546 )
| ( ( set_difference @ SV501 @ SV546 )
= SV501 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2459]) ).
thf(2566,plain,
! [SV423: $i,SV547: $i] :
( ( ! [SY785: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK24_D @ SY785 @ SV547 @ SV423 ) @ SY785 )
| ~ ( in @ ( sK24_D @ SY785 @ SV547 @ SV423 ) @ SV423 ) )
| ~ ( ~ ( in @ ( sK24_D @ SY785 @ SV547 @ SV423 ) @ SY785 )
| ~ ( in @ ( sK24_D @ SY785 @ SV547 @ SV423 ) @ SV547 ) ) )
| ~ ( ( in @ ( sK24_D @ SY785 @ SV547 @ SV423 ) @ SY785 )
| ( in @ ( sK24_D @ SY785 @ SV547 @ SV423 ) @ SV423 )
| ( in @ ( sK24_D @ SY785 @ SV547 @ SV423 ) @ SV547 ) ) )
| ( SY785
= ( set_union2 @ SV423 @ SV547 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2460]) ).
thf(2567,plain,
! [SV548: $i,SV423: $i] :
( ( ! [SY786: $i] :
( ( SY786
!= ( set_union2 @ SV423 @ SV548 ) )
| ~ ( ~ ! [SY787: $i] :
( ~ ( in @ SY787 @ SY786 )
| ( in @ SY787 @ SV423 )
| ( in @ SY787 @ SV548 ) )
| ~ ~ ( ~ ! [SY668: $i] :
( ~ ( in @ SY668 @ SV423 )
| ( in @ SY668 @ SY786 ) )
| ~ ! [SY789: $i] :
( ~ ( in @ SY789 @ SV548 )
| ( in @ SY789 @ SY786 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2461]) ).
thf(2568,plain,
! [SV549: $i,SV502: $i] :
( ( ~ ( subset @ SV502 @ ( singleton @ SV549 ) )
| ( SV502 = empty_set )
| ( SV502
= ( singleton @ SV549 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2462]) ).
thf(2569,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2463]) ).
thf(2570,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2463]) ).
thf(2571,plain,
! [SV550: $i,SV503: $i] :
( ( ( SV503 = SV550 )
| ~ ( subset @ SV503 @ SV550 )
| ( proper_subset @ SV503 @ SV550 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2464]) ).
thf(2572,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2465]) ).
thf(2573,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2465]) ).
thf(2574,plain,
! [SV551: $i,SV504: $i] :
( ( ( disjoint @ SV504 @ SV551 )
| ~ ( ~ ( in @ ( sK34_C @ SV551 @ SV504 ) @ SV504 )
| ~ ( in @ ( sK34_C @ SV551 @ SV504 ) @ SV551 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2466]) ).
thf(2575,plain,
! [SV552: $i,SV505: $i] :
( ( ! [SY790: $i] :
( ~ ( in @ SY790 @ SV505 )
| ~ ( in @ SY790 @ SV552 ) )
| ~ ( disjoint @ SV505 @ SV552 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2467]) ).
thf(2576,plain,
! [SV424: $i,SV553: $i] :
( ( ~ ( subset @ SV553 @ ( sK35_B @ SV424 ) )
| ( are_equipotent @ SV553 @ ( sK35_B @ SV424 ) )
| ( in @ SV553 @ ( sK35_B @ SV424 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2468]) ).
thf(2577,plain,
! [SV424: $i] :
( ( ~ ! [SY671: $i] :
( ~ ( in @ SY671 @ ( sK35_B @ SV424 ) )
| ( in @ ( powerset @ SY671 ) @ ( sK35_B @ SV424 ) ) )
| ~ ~ ( ~ ! [SY672: $i,SY673: $i] :
( ~ ( in @ SY672 @ ( sK35_B @ SV424 ) )
| ~ ( subset @ SY673 @ SY672 )
| ( in @ SY673 @ ( sK35_B @ SV424 ) ) )
| ~ ( in @ SV424 @ ( sK35_B @ SV424 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2469]) ).
thf(2578,plain,
! [SV425: $i] :
( ( ( ~ ! [SY674: $i] :
( ~ ( relation @ SY674 )
| ~ ( subset @ SV425 @ SY674 )
| ( subset @ ( relation_dom @ SV425 ) @ ( relation_dom @ SY674 ) ) ) )
= $false )
| ( ( relation @ SV425 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2470]) ).
thf(2579,plain,
! [SV425: $i] :
( ( ( ~ ! [SY675: $i] :
( ~ ( relation @ SY675 )
| ~ ( subset @ SV425 @ SY675 )
| ( subset @ ( relation_rng @ SV425 ) @ ( relation_rng @ SY675 ) ) ) )
= $false )
| ( ( relation @ SV425 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2470]) ).
thf(2580,plain,
! [SV554: $i,SV506: $i] :
( ( ~ ( in @ SV506 @ SV554 )
| ( subset @ ( singleton @ SV506 ) @ SV554 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2471]) ).
thf(2581,plain,
! [SV555: $i,SV507: $i] :
( ( ~ ( subset @ ( singleton @ SV507 ) @ SV555 )
| ( in @ SV507 @ SV555 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2472]) ).
thf(2582,plain,
! [SV508: $i] :
( ( ( in @ ( sK37_B @ SV508 ) @ SV508 )
= $true )
| ( ( SV508 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2473]) ).
thf(2583,plain,
! [SV509: $i] :
( ( ( ( SV509 != empty_set ) )
= $true )
| ( ( ! [SY747: $i] :
~ ( in @ SY747 @ SV509 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2474]) ).
thf(2584,plain,
! [SV426: $i,SV556: $i] :
( ( ~ ( subset @ SV556 @ ( sK1_B @ SV426 ) )
| ( are_equipotent @ SV556 @ ( sK1_B @ SV426 ) )
| ( in @ SV556 @ ( sK1_B @ SV426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2475]) ).
thf(2585,plain,
! [SV426: $i] :
( ( ~ ! [SY677: $i] :
( ~ ( ~ ! [SY678: $i] :
( ~ ( subset @ SY678 @ SY677 )
| ( in @ SY678 @ ( sK2_SY267 @ SY677 @ SV426 ) ) )
| ~ ( in @ ( sK2_SY267 @ SY677 @ SV426 ) @ ( sK1_B @ SV426 ) ) )
| ~ ( in @ SY677 @ ( sK1_B @ SV426 ) ) )
| ~ ~ ( ~ ! [SY679: $i,SY680: $i] :
( ~ ( in @ SY679 @ ( sK1_B @ SV426 ) )
| ~ ( subset @ SY680 @ SY679 )
| ( in @ SY680 @ ( sK1_B @ SV426 ) ) )
| ~ ( in @ SV426 @ ( sK1_B @ SV426 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2476]) ).
thf(2586,plain,
! [SV510: $i,SV557: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK26_C @ SV557 @ SV510 ) @ SV557 )
| ~ ( subset @ ( sK26_C @ SV557 @ SV510 ) @ SV510 ) )
| ~ ( ( in @ ( sK26_C @ SV557 @ SV510 ) @ SV557 )
| ( subset @ ( sK26_C @ SV557 @ SV510 ) @ SV510 ) ) )
| ( SV557
= ( powerset @ SV510 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2477]) ).
thf(2587,plain,
! [SV511: $i,SV558: $i] :
( ( ( SV558
!= ( powerset @ SV511 ) )
| ~ ( ~ ! [SY791: $i] :
( ~ ( in @ SY791 @ SV558 )
| ( subset @ SY791 @ SV511 ) )
| ~ ! [SY792: $i] :
( ~ ( subset @ SY792 @ SV511 )
| ( in @ SY792 @ SV558 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2478]) ).
thf(2588,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2479]) ).
thf(2589,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2479]) ).
thf(2590,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2480]) ).
thf(2591,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2480]) ).
thf(2592,plain,
! [SV559: $i,SV512: $i] :
( ( ( ( set_difference @ SV512 @ ( singleton @ SV559 ) )
!= SV512 )
| ~ ( in @ SV559 @ SV512 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2481]) ).
thf(2593,plain,
! [SV513: $i,SV560: $i] :
( ( ( in @ SV560 @ SV513 )
| ( ( set_difference @ SV513 @ ( singleton @ SV560 ) )
= SV513 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2482]) ).
thf(2594,plain,
! [SV514: $i] :
( ( ( ~ ( ~ ! [SY754: $i,SY755: $i] :
( ( sK30_B @ SV514 )
!= ( ordered_pair @ SY754 @ SY755 ) )
| ~ ( in @ ( sK30_B @ SV514 ) @ SV514 ) ) )
= $true )
| ( ( relation @ SV514 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2483]) ).
thf(2595,plain,
! [SV515: $i] :
( ( ( ~ ( relation @ SV515 ) )
= $true )
| ( ( ! [SY756: $i] :
( ( SY756
= ( ordered_pair @ ( sK28_C @ SY756 @ SV515 ) @ ( sK29_SY279 @ SY756 @ SV515 ) ) )
| ~ ( in @ SY756 @ SV515 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2484]) ).
thf(2596,plain,
! [SV561: $i,SV516: $i] :
( ( ( ( set_intersection2 @ SV516 @ SV561 )
!= empty_set )
| ( disjoint @ SV516 @ SV561 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2485]) ).
thf(2597,plain,
! [SV562: $i,SV517: $i] :
( ( ~ ( disjoint @ SV517 @ SV562 )
| ( ( set_intersection2 @ SV517 @ SV562 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2486]) ).
thf(2598,plain,
! [SV563: $i,SV518: $i] :
( ( ~ ( subset @ SV518 @ SV563 )
| ~ ( subset @ SV563 @ SV518 )
| ( SV518 = SV563 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2487]) ).
thf(2599,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2488]) ).
thf(2600,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2488]) ).
thf(2601,plain,
! [SV564: $i,SV519: $i] :
( ( ~ ( element @ SV519 @ ( powerset @ SV564 ) )
| ( subset @ SV519 @ SV564 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2490]) ).
thf(2602,plain,
! [SV565: $i,SV520: $i] :
( ( ~ ( subset @ SV520 @ SV565 )
| ( element @ SV520 @ ( powerset @ SV565 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2491]) ).
thf(2603,plain,
! [SV427: $i] :
( ( ( ~ ! [SY681: $i] :
( ~ ( ~ ( ! [SY682: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SY681 @ SV427 ) @ SY682 ) @ SV427 )
| ~ ( in @ ( sK20_C @ SY681 @ SV427 ) @ SY681 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_C @ SY681 @ SV427 ) @ ( sK21_SY278 @ SY681 @ SV427 ) ) @ SV427 )
| ( in @ ( sK20_C @ SY681 @ SV427 ) @ SY681 ) ) )
| ( SY681
= ( relation_dom @ SV427 ) ) ) )
= $false )
| ( ( relation @ SV427 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2492]) ).
thf(2604,plain,
! [SV427: $i] :
( ( ( ~ ! [SY683: $i] :
( ( SY683
!= ( relation_dom @ SV427 ) )
| ~ ( ~ ! [SY684: $i] :
( ! [SY685: $i] :
~ ( in @ ( ordered_pair @ SY684 @ SY685 ) @ SV427 )
| ( in @ SY684 @ SY683 ) )
| ~ ! [SY686: $i] :
( ~ ( in @ SY686 @ SY683 )
| ( in @ ( ordered_pair @ SY686 @ ( sK19_D @ SY686 @ SY683 @ SV427 ) ) @ SV427 ) ) ) ) )
= $false )
| ( ( relation @ SV427 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2492]) ).
thf(2605,plain,
! [SV428: $i,SV566: $i] :
( ( ! [SY793: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SY793 @ SV566 @ SV428 ) @ SV428 )
| ( in @ ( sK15_D @ SY793 @ SV566 @ SV428 ) @ SV566 )
| ~ ( in @ ( sK15_D @ SY793 @ SV566 @ SV428 ) @ SY793 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SY793 @ SV566 @ SV428 ) @ SV428 )
| ( in @ ( sK15_D @ SY793 @ SV566 @ SV428 ) @ SY793 ) )
| ~ ( ~ ( in @ ( sK15_D @ SY793 @ SV566 @ SV428 ) @ SV566 )
| ( in @ ( sK15_D @ SY793 @ SV566 @ SV428 ) @ SY793 ) ) ) )
| ( SY793
= ( set_difference @ SV428 @ SV566 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2493]) ).
thf(2606,plain,
! [SV567: $i,SV428: $i] :
( ( ! [SY794: $i] :
( ( SY794
!= ( set_difference @ SV428 @ SV567 ) )
| ~ ( ~ ! [SY795: $i] :
( ~ ( in @ SY795 @ SV428 )
| ( in @ SY795 @ SV567 )
| ( in @ SY795 @ SY794 ) )
| ~ ~ ( ~ ! [SY692: $i] :
( ~ ( in @ SY692 @ SY794 )
| ( in @ SY692 @ SV428 ) )
| ~ ! [SY797: $i] :
( ~ ( in @ SY797 @ SY794 )
| ~ ( in @ SY797 @ SV567 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2494]) ).
thf(2607,plain,
! [SV521: $i] :
( ( ( ~ ( relation @ SV521 ) )
= $true )
| ( ( ( relation_rng @ SV521 )
= ( relation_dom @ ( relation_inverse @ SV521 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2495]) ).
thf(2608,plain,
! [SV522: $i] :
( ( ( ~ ( relation @ SV522 ) )
= $true )
| ( ( ( relation_dom @ SV522 )
= ( relation_rng @ ( relation_inverse @ SV522 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2496]) ).
thf(2609,plain,
! [SV568: $i,SV523: $i] :
( ( ~ ( in @ SV523 @ SV568 )
| ( subset @ ( singleton @ SV523 ) @ SV568 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2497]) ).
thf(2610,plain,
! [SV569: $i,SV524: $i] :
( ( ~ ( subset @ ( singleton @ SV524 ) @ SV569 )
| ( in @ SV524 @ SV569 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2498]) ).
thf(2611,plain,
! [SV429: $i,SV570: $i] :
( ( ! [SY798: $i] :
( ~ ( ~ ( ~ ( in @ ( sK22_D @ SY798 @ SV570 @ SV429 ) @ SV429 )
| ~ ( in @ ( sK22_D @ SY798 @ SV570 @ SV429 ) @ SV570 )
| ~ ( in @ ( sK22_D @ SY798 @ SV570 @ SV429 ) @ SY798 ) )
| ~ ~ ( ~ ( ( in @ ( sK22_D @ SY798 @ SV570 @ SV429 ) @ SV429 )
| ( in @ ( sK22_D @ SY798 @ SV570 @ SV429 ) @ SY798 ) )
| ~ ( ( in @ ( sK22_D @ SY798 @ SV570 @ SV429 ) @ SV570 )
| ( in @ ( sK22_D @ SY798 @ SV570 @ SV429 ) @ SY798 ) ) ) )
| ( SY798
= ( set_intersection2 @ SV429 @ SV570 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2499]) ).
thf(2612,plain,
! [SV571: $i,SV429: $i] :
( ( ! [SY799: $i] :
( ( SY799
!= ( set_intersection2 @ SV429 @ SV571 ) )
| ~ ( ~ ! [SY800: $i] :
( ~ ( in @ SY800 @ SV429 )
| ~ ( in @ SY800 @ SV571 )
| ( in @ SY800 @ SY799 ) )
| ~ ~ ( ~ ! [SY699: $i] :
( ~ ( in @ SY699 @ SY799 )
| ( in @ SY699 @ SV429 ) )
| ~ ! [SY802: $i] :
( ~ ( in @ SY802 @ SY799 )
| ( in @ SY802 @ SV571 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2500]) ).
thf(2613,plain,
! [SV430: $i] :
( ( ( ~ ! [SY701: $i] :
( ~ ( ~ ( ! [SY702: $i] :
~ ( in @ ( ordered_pair @ SY702 @ ( sK13_C @ SY701 @ SV430 ) ) @ SV430 )
| ~ ( in @ ( sK13_C @ SY701 @ SV430 ) @ SY701 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY274 @ SY701 @ SV430 ) @ ( sK13_C @ SY701 @ SV430 ) ) @ SV430 )
| ( in @ ( sK13_C @ SY701 @ SV430 ) @ SY701 ) ) )
| ( SY701
= ( relation_rng @ SV430 ) ) ) )
= $false )
| ( ( relation @ SV430 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2501]) ).
thf(2614,plain,
! [SV430: $i] :
( ( ( ~ ! [SY703: $i] :
( ( SY703
!= ( relation_rng @ SV430 ) )
| ~ ( ~ ! [SY704: $i] :
( ! [SY705: $i] :
~ ( in @ ( ordered_pair @ SY705 @ SY704 ) @ SV430 )
| ( in @ SY704 @ SY703 ) )
| ~ ! [SY706: $i] :
( ~ ( in @ SY706 @ SY703 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY706 @ SY703 @ SV430 ) @ SY706 ) @ SV430 ) ) ) ) )
= $false )
| ( ( relation @ SV430 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2501]) ).
thf(2615,plain,
! [SV525: $i,SV572: $i] :
( ( ~ ( ~ ( ! [SY803: $i] :
( ~ ( in @ ( sK17_C @ SV572 @ SV525 ) @ SY803 )
| ~ ( in @ SY803 @ SV525 ) )
| ~ ( in @ ( sK17_C @ SV572 @ SV525 ) @ SV572 ) )
| ~ ( ~ ( ~ ( in @ ( sK17_C @ SV572 @ SV525 ) @ ( sK18_SY276 @ SV572 @ SV525 ) )
| ~ ( in @ ( sK18_SY276 @ SV572 @ SV525 ) @ SV525 ) )
| ( in @ ( sK17_C @ SV572 @ SV525 ) @ SV572 ) ) )
| ( SV572
= ( union @ SV525 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2502]) ).
thf(2616,plain,
! [SV526: $i,SV573: $i] :
( ( ( SV573
!= ( union @ SV526 ) )
| ~ ( ~ ! [SY804: $i] :
( ! [SY768: $i] :
( ~ ( in @ SY804 @ SY768 )
| ~ ( in @ SY768 @ SV526 ) )
| ( in @ SY804 @ SV573 ) )
| ~ ! [SY806: $i] :
( ~ ( in @ SY806 @ SV573 )
| ~ ( ~ ( in @ SY806 @ ( sK16_D @ SY806 @ SV573 @ SV526 ) )
| ~ ( in @ ( sK16_D @ SY806 @ SV573 @ SV526 ) @ SV526 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2503]) ).
thf(2617,plain,
! [SV432: $i,SV480: $i] :
( ( ( ~ ( in @ ( sK36_C @ SV480 @ SV432 ) @ SV432 ) )
= $false )
| ( ( element @ SV432 @ ( powerset @ SV480 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2506]) ).
thf(2618,plain,
! [SV432: $i,SV480: $i] :
( ( ( ~ ~ ( in @ ( sK36_C @ SV480 @ SV432 ) @ SV480 ) )
= $false )
| ( ( element @ SV432 @ ( powerset @ SV480 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2506]) ).
thf(2619,plain,
! [SV574: $i,SV527: $i] :
( ( ( ( set_difference @ SV527 @ SV574 )
!= empty_set )
| ( subset @ SV527 @ SV574 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2507]) ).
thf(2620,plain,
! [SV575: $i,SV528: $i] :
( ( ~ ( subset @ SV528 @ SV575 )
| ( ( set_difference @ SV528 @ SV575 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2508]) ).
thf(2621,plain,
! [SV529: $i,SV576: $i] :
( ( ~ ( ~ ( in @ ( sK23_C @ SV576 @ SV529 ) @ SV529 )
| ~ ~ ( in @ ( sK23_C @ SV576 @ SV529 ) @ SV576 ) )
| ( subset @ SV529 @ SV576 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2509]) ).
thf(2622,plain,
! [SV577: $i,SV530: $i] :
( ( ~ ( subset @ SV530 @ SV577 )
| ! [SY807: $i] :
( ~ ( in @ SY807 @ SV530 )
| ( in @ SY807 @ SV577 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2510]) ).
thf(2623,plain,
! [SV578: $i,SV531: $i] :
( ( ( ( set_difference @ SV531 @ SV578 )
!= empty_set )
| ( subset @ SV531 @ SV578 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2511]) ).
thf(2624,plain,
! [SV579: $i,SV532: $i] :
( ( ~ ( subset @ SV532 @ SV579 )
| ( ( set_difference @ SV532 @ SV579 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2512]) ).
thf(2625,plain,
! [SV433: $i,SV580: $i] :
( ( ! [SY808: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK25_D @ SY808 @ SV580 @ SV433 ) @ SY808 )
| ( ( sK25_D @ SY808 @ SV580 @ SV433 )
!= SV433 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY808 @ SV580 @ SV433 ) @ SY808 )
| ( ( sK25_D @ SY808 @ SV580 @ SV433 )
!= SV580 ) ) )
| ~ ( ( in @ ( sK25_D @ SY808 @ SV580 @ SV433 ) @ SY808 )
| ( ( sK25_D @ SY808 @ SV580 @ SV433 )
= SV433 )
| ( ( sK25_D @ SY808 @ SV580 @ SV433 )
= SV580 ) ) )
| ( SY808
= ( unordered_pair @ SV433 @ SV580 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2513]) ).
thf(2626,plain,
! [SV581: $i,SV433: $i] :
( ( ! [SY809: $i] :
( ( SY809
!= ( unordered_pair @ SV433 @ SV581 ) )
| ~ ( ~ ! [SY810: $i] :
( ~ ( in @ SY810 @ SY809 )
| ( SY810 = SV433 )
| ( SY810 = SV581 ) )
| ~ ~ ( ~ ! [SY713: $i] :
( ( SY713 != SV433 )
| ( in @ SY713 @ SY809 ) )
| ~ ! [SY812: $i] :
( ( SY812 != SV581 )
| ( in @ SY812 @ SY809 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2514]) ).
thf(2627,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK40_SY287 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK39_C @ SX1 @ SX0 ) @ ( sK40_SY287 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2515]) ).
thf(2628,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK38_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK38_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2515]) ).
thf(2629,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2516]) ).
thf(2630,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2516]) ).
thf(2631,plain,
! [SV533: $i,SV582: $i] :
( ( ~ ( ~ ( ( ( sK27_C @ SV582 @ SV533 )
!= SV533 )
| ~ ( in @ ( sK27_C @ SV582 @ SV533 ) @ SV582 ) )
| ~ ( ( ( sK27_C @ SV582 @ SV533 )
= SV533 )
| ( in @ ( sK27_C @ SV582 @ SV533 ) @ SV582 ) ) )
| ( SV582
= ( singleton @ SV533 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2517]) ).
thf(2632,plain,
! [SV534: $i,SV583: $i] :
( ( ( SV583
!= ( singleton @ SV534 ) )
| ~ ( ~ ! [SY813: $i] :
( ( SY813 != SV534 )
| ( in @ SY813 @ SV583 ) )
| ~ ! [SY814: $i] :
( ~ ( in @ SY814 @ SV583 )
| ( SY814 = SV534 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2518]) ).
thf(2633,plain,
! [SV584: $i,SV434: $i] :
( ( ~ ( subset @ SV434 @ SV584 )
| ! [SY815: $i] : ( subset @ ( cartesian_product2 @ SV434 @ SY815 ) @ ( cartesian_product2 @ SV584 @ SY815 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2519]) ).
thf(2634,plain,
! [SV585: $i,SV434: $i] :
( ( ~ ( subset @ SV434 @ SV585 )
| ! [SY816: $i] : ( subset @ ( cartesian_product2 @ SY816 @ SV434 ) @ ( cartesian_product2 @ SY816 @ SV585 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2520]) ).
thf(2635,plain,
! [SV435: $i] :
( ( ( element @ ( sK8_B @ SV435 ) @ ( powerset @ SV435 ) )
= $true )
| ( ( empty @ SV435 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2521]) ).
thf(2636,plain,
! [SV435: $i] :
( ( ( ~ ( empty @ ( sK8_B @ SV435 ) ) )
= $true )
| ( ( empty @ SV435 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2522]) ).
thf(2637,plain,
! [SV360: $i,SV439: $i,SV535: $i] :
( ( ( ~ ( in @ SV535 @ SV439 ) )
= $true )
| ( ( in @ SV535 @ SV360 )
= $true )
| ( ( element @ SV439 @ ( powerset @ SV360 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2526]) ).
thf(2638,plain,
! [SV440: $i,SV361: $i,SV536: $i] :
( ( ( in @ SV536 @ SV361 )
= $true )
| ( ( subset @ SV361 @ ( set_difference @ SV440 @ ( singleton @ SV536 ) ) )
= $true )
| ( ( subset @ SV361 @ SV440 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2527]) ).
thf(2639,plain,
! [SV491: $i,SV481: $i,SV442: $i,SV363: $i] :
( ( ( ~ ( subset @ SV363 @ SV442 ) )
= $true )
| ( ( ~ ( subset @ SV481 @ SV491 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV363 @ SV481 ) @ ( cartesian_product2 @ SV442 @ SV491 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2528]) ).
thf(2640,plain,
! [SV482: $i,SV445: $i,SV366: $i] :
( ( ( subset @ SV366 @ SV445 )
= $false )
| ( ( ~ ( subset @ SV366 @ SV482 ) )
= $true )
| ( ( subset @ SV366 @ ( set_intersection2 @ SV445 @ SV482 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2529]) ).
thf(2641,plain,
! [SV483: $i,SV446: $i,SV367: $i] :
( ( ( subset @ SV367 @ SV446 )
= $false )
| ( ( ~ ( subset @ SV446 @ SV483 ) )
= $true )
| ( ( subset @ SV367 @ SV483 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2530]) ).
thf(2642,plain,
! [SV375: $i,SV492: $i] :
( ( ( relation @ SV492 )
= $false )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV375 @ SV492 ) ) @ ( relation_dom @ SV375 ) )
= $true )
| ( ( relation @ SV375 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2533]) ).
thf(2643,plain,
! [SV376: $i,SV493: $i] :
( ( ( relation @ SV493 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV376 @ SV493 ) ) @ ( relation_rng @ SV493 ) )
= $true )
| ( ( relation @ SV376 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2534]) ).
thf(2644,plain,
! [SV378: $i,SV494: $i] :
( ( ( relation @ SV494 )
= $false )
| ( ( ~ ( subset @ ( relation_rng @ SV378 ) @ ( relation_dom @ SV494 ) )
| ( ( relation_dom @ ( relation_composition @ SV378 @ SV494 ) )
= ( relation_dom @ SV378 ) ) )
= $true )
| ( ( relation @ SV378 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2535]) ).
thf(2645,plain,
! [SV380: $i,SV495: $i] :
( ( ( relation @ SV495 )
= $false )
| ( ( ~ ( subset @ ( relation_dom @ SV380 ) @ ( relation_rng @ SV495 ) )
| ( ( relation_rng @ ( relation_composition @ SV495 @ SV380 ) )
= ( relation_rng @ SV380 ) ) )
= $true )
| ( ( relation @ SV380 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2536]) ).
thf(2646,plain,
! [SV384: $i,SV484: $i,SV457: $i] :
( ( ( disjoint @ SV457 @ SV484 )
= $false )
| ( ( ~ ( subset @ SV384 @ SV457 ) )
= $true )
| ( ( disjoint @ SV384 @ SV484 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2538]) ).
thf(2647,plain,
! [SV485: $i,SV460: $i,SV388: $i] :
( ( ( subset @ SV388 @ SV460 )
= $false )
| ( ( ~ ( subset @ SV485 @ SV460 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV388 @ SV485 ) @ SV460 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2539]) ).
thf(2648,plain,
! [SV399: $i,SV467: $i] :
( ( ( relation @ SV467 )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ ( relation_composition @ SV399 @ SV467 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2543]) ).
thf(2649,plain,
! [SV402: $i,SV469: $i] :
( ( ( relation @ SV469 )
= $false )
| ( ( relation @ SV402 )
= $false )
| ( ( relation @ ( set_union2 @ SV402 @ SV469 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2544]) ).
thf(2650,plain,
! [SV415: $i,SV489: $i,SV475: $i] :
( ( ( element @ SV475 @ ( powerset @ SV489 ) )
= $false )
| ( ( ~ ( in @ SV415 @ SV475 ) )
= $true )
| ( ( element @ SV415 @ SV489 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2547]) ).
thf(2651,plain,
! [SV416: $i,SV490: $i,SV476: $i] :
( ( ( element @ SV476 @ ( powerset @ SV490 ) )
= $false )
| ( ( ~ ( in @ SV416 @ SV476 ) )
= $true )
| ( ( ~ ( empty @ SV490 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2548]) ).
thf(2652,plain,
! [SV418: $i,SV478: $i] :
( ( ( empty @ SV478 )
= $false )
| ( ( SV418 = SV478 )
= $true )
| ( ( empty @ SV418 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2550]) ).
thf(2653,plain,
! [SV539: $i,SV586: $i,SV419: $i] :
( ( ~ ( in @ SV419 @ SV586 )
| ~ ( in @ SV539 @ SV586 )
| ( subset @ ( unordered_pair @ SV419 @ SV539 ) @ SV586 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2551]) ).
thf(2654,plain,
! [SV419: $i] :
( ( ~ ! [SY648: $i,SY649: $i] :
( ~ ( subset @ ( unordered_pair @ SV419 @ SY648 ) @ SY649 )
| ( in @ SV419 @ SY649 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2552]) ).
thf(2655,plain,
! [SV419: $i] :
( ( ~ ! [SY650: $i,SY651: $i] :
( ~ ( subset @ ( unordered_pair @ SV419 @ SY650 ) @ SY651 )
| ( in @ SY650 @ SY651 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2552]) ).
thf(2656,plain,
! [SV420: $i] :
( ( ( ! [SY652: $i] :
( ~ ( relation @ SY652 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SY652 @ SV420 ) @ ( sK11_SY272 @ SY652 @ SV420 ) ) @ SY652 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY272 @ SY652 @ SV420 ) @ ( sK10_C @ SY652 @ SV420 ) ) @ SV420 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK10_C @ SY652 @ SV420 ) @ ( sK11_SY272 @ SY652 @ SV420 ) ) @ SY652 )
| ( in @ ( ordered_pair @ ( sK11_SY272 @ SY652 @ SV420 ) @ ( sK10_C @ SY652 @ SV420 ) ) @ SV420 ) ) )
| ( SY652
= ( relation_inverse @ SV420 ) ) ) )
= $true )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2553]) ).
thf(2657,plain,
! [SV420: $i] :
( ( ( ! [SY653: $i] :
( ~ ( relation @ SY653 )
| ( SY653
!= ( relation_inverse @ SV420 ) )
| ~ ( ~ ! [SY654: $i,SY655: $i] :
( ~ ( in @ ( ordered_pair @ SY654 @ SY655 ) @ SY653 )
| ( in @ ( ordered_pair @ SY655 @ SY654 ) @ SV420 ) )
| ~ ! [SY656: $i,SY657: $i] :
( ~ ( in @ ( ordered_pair @ SY657 @ SY656 ) @ SV420 )
| ( in @ ( ordered_pair @ SY656 @ SY657 ) @ SY653 ) ) ) ) )
= $true )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2554]) ).
thf(2658,plain,
! [SV540: $i,SV497: $i] :
( ( ( disjoint @ SV497 @ SV540 )
= $true )
| ( ( in @ ( sK33_C @ SV540 @ SV497 ) @ ( set_intersection2 @ SV497 @ SV540 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2555]) ).
thf(2659,plain,
! [SV541: $i,SV498: $i] :
( ( ( ! [SY782: $i] :
~ ( in @ SY782 @ ( set_intersection2 @ SV498 @ SV541 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV498 @ SV541 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2556]) ).
thf(2660,plain,
! [SV421: $i,SV479: $i] :
( ( ( ~ ( in @ ( sK3_C @ SV479 @ SV421 ) @ SV421 )
| ~ ( in @ ( sK3_C @ SV479 @ SV421 ) @ SV479 ) )
= $true )
| ( ( SV421 = SV479 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2557]) ).
thf(2661,plain,
! [SV421: $i,SV479: $i] :
( ( ( ( in @ ( sK3_C @ SV479 @ SV421 ) @ SV421 )
| ( in @ ( sK3_C @ SV479 @ SV421 ) @ SV479 ) )
= $true )
| ( ( SV421 = SV479 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2558]) ).
thf(2662,plain,
! [SV542: $i,SV422: $i,SV587: $i] :
( ( ~ ( relation @ SV587 )
| ~ ( in @ ( ordered_pair @ SV422 @ SV542 ) @ SV587 )
| ( in @ SV422 @ ( relation_dom @ SV587 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2559]) ).
thf(2663,plain,
! [SV543: $i,SV422: $i,SV588: $i] :
( ( ~ ( relation @ SV588 )
| ~ ( in @ ( ordered_pair @ SV422 @ SV543 ) @ SV588 )
| ( in @ SV543 @ ( relation_rng @ SV588 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2560]) ).
thf(2664,plain,
! [SV544: $i,SV499: $i] :
( ( ( ~ ( subset @ SV499 @ ( singleton @ SV544 ) ) )
= $true )
| ( ( ( SV499 = empty_set )
| ( SV499
= ( singleton @ SV544 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2561]) ).
thf(2665,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2562]) ).
thf(2666,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2563]) ).
thf(2667,plain,
! [SV545: $i,SV500: $i] :
( ( ( ( ( set_difference @ SV500 @ SV545 )
!= SV500 ) )
= $true )
| ( ( disjoint @ SV500 @ SV545 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2564]) ).
thf(2668,plain,
! [SV546: $i,SV501: $i] :
( ( ( ~ ( disjoint @ SV501 @ SV546 ) )
= $true )
| ( ( ( set_difference @ SV501 @ SV546 )
= SV501 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2565]) ).
thf(2669,plain,
! [SV423: $i,SV547: $i,SV589: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV589 )
| ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV423 ) )
| ~ ( ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV589 )
| ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV547 ) ) )
| ~ ( ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV589 )
| ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV423 )
| ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV547 ) ) )
| ( SV589
= ( set_union2 @ SV423 @ SV547 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2566]) ).
thf(2670,plain,
! [SV548: $i,SV423: $i,SV590: $i] :
( ( ( SV590
!= ( set_union2 @ SV423 @ SV548 ) )
| ~ ( ~ ! [SY817: $i] :
( ~ ( in @ SY817 @ SV590 )
| ( in @ SY817 @ SV423 )
| ( in @ SY817 @ SV548 ) )
| ~ ~ ( ~ ! [SY818: $i] :
( ~ ( in @ SY818 @ SV423 )
| ( in @ SY818 @ SV590 ) )
| ~ ! [SY819: $i] :
( ~ ( in @ SY819 @ SV548 )
| ( in @ SY819 @ SV590 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2567]) ).
thf(2671,plain,
! [SV549: $i,SV502: $i] :
( ( ( ~ ( subset @ SV502 @ ( singleton @ SV549 ) ) )
= $true )
| ( ( ( SV502 = empty_set )
| ( SV502
= ( singleton @ SV549 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2568]) ).
thf(2672,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2569]) ).
thf(2673,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2570]) ).
thf(2674,plain,
! [SV550: $i,SV503: $i] :
( ( ( ( SV503 = SV550 )
| ~ ( subset @ SV503 @ SV550 ) )
= $true )
| ( ( proper_subset @ SV503 @ SV550 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2571]) ).
thf(2675,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2572]) ).
thf(2676,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2573]) ).
thf(2677,plain,
! [SV551: $i,SV504: $i] :
( ( ( disjoint @ SV504 @ SV551 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK34_C @ SV551 @ SV504 ) @ SV504 )
| ~ ( in @ ( sK34_C @ SV551 @ SV504 ) @ SV551 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2574]) ).
thf(2678,plain,
! [SV552: $i,SV505: $i] :
( ( ( ! [SY790: $i] :
( ~ ( in @ SY790 @ SV505 )
| ~ ( in @ SY790 @ SV552 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV505 @ SV552 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2575]) ).
thf(2679,plain,
! [SV424: $i,SV553: $i] :
( ( ( ~ ( subset @ SV553 @ ( sK35_B @ SV424 ) )
| ( are_equipotent @ SV553 @ ( sK35_B @ SV424 ) ) )
= $true )
| ( ( in @ SV553 @ ( sK35_B @ SV424 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2576]) ).
thf(2680,plain,
! [SV424: $i] :
( ( ~ ! [SY671: $i] :
( ~ ( in @ SY671 @ ( sK35_B @ SV424 ) )
| ( in @ ( powerset @ SY671 ) @ ( sK35_B @ SV424 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2577]) ).
thf(2681,plain,
! [SV424: $i] :
( ( ~ ~ ( ~ ! [SY672: $i,SY673: $i] :
( ~ ( in @ SY672 @ ( sK35_B @ SV424 ) )
| ~ ( subset @ SY673 @ SY672 )
| ( in @ SY673 @ ( sK35_B @ SV424 ) ) )
| ~ ( in @ SV424 @ ( sK35_B @ SV424 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2577]) ).
thf(2682,plain,
! [SV425: $i] :
( ( ( ! [SY674: $i] :
( ~ ( relation @ SY674 )
| ~ ( subset @ SV425 @ SY674 )
| ( subset @ ( relation_dom @ SV425 ) @ ( relation_dom @ SY674 ) ) ) )
= $true )
| ( ( relation @ SV425 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2578]) ).
thf(2683,plain,
! [SV425: $i] :
( ( ( ! [SY675: $i] :
( ~ ( relation @ SY675 )
| ~ ( subset @ SV425 @ SY675 )
| ( subset @ ( relation_rng @ SV425 ) @ ( relation_rng @ SY675 ) ) ) )
= $true )
| ( ( relation @ SV425 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2579]) ).
thf(2684,plain,
! [SV554: $i,SV506: $i] :
( ( ( ~ ( in @ SV506 @ SV554 ) )
= $true )
| ( ( subset @ ( singleton @ SV506 ) @ SV554 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2580]) ).
thf(2685,plain,
! [SV555: $i,SV507: $i] :
( ( ( ~ ( subset @ ( singleton @ SV507 ) @ SV555 ) )
= $true )
| ( ( in @ SV507 @ SV555 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2581]) ).
thf(2686,plain,
! [SV509: $i] :
( ( ( SV509 = empty_set )
= $false )
| ( ( ! [SY747: $i] :
~ ( in @ SY747 @ SV509 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2583]) ).
thf(2687,plain,
! [SV426: $i,SV556: $i] :
( ( ( ~ ( subset @ SV556 @ ( sK1_B @ SV426 ) )
| ( are_equipotent @ SV556 @ ( sK1_B @ SV426 ) ) )
= $true )
| ( ( in @ SV556 @ ( sK1_B @ SV426 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2584]) ).
thf(2688,plain,
! [SV426: $i] :
( ( ~ ! [SY677: $i] :
( ~ ( ~ ! [SY678: $i] :
( ~ ( subset @ SY678 @ SY677 )
| ( in @ SY678 @ ( sK2_SY267 @ SY677 @ SV426 ) ) )
| ~ ( in @ ( sK2_SY267 @ SY677 @ SV426 ) @ ( sK1_B @ SV426 ) ) )
| ~ ( in @ SY677 @ ( sK1_B @ SV426 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2585]) ).
thf(2689,plain,
! [SV426: $i] :
( ( ~ ~ ( ~ ! [SY679: $i,SY680: $i] :
( ~ ( in @ SY679 @ ( sK1_B @ SV426 ) )
| ~ ( subset @ SY680 @ SY679 )
| ( in @ SY680 @ ( sK1_B @ SV426 ) ) )
| ~ ( in @ SV426 @ ( sK1_B @ SV426 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2585]) ).
thf(2690,plain,
! [SV510: $i,SV557: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK26_C @ SV557 @ SV510 ) @ SV557 )
| ~ ( subset @ ( sK26_C @ SV557 @ SV510 ) @ SV510 ) )
| ~ ( ( in @ ( sK26_C @ SV557 @ SV510 ) @ SV557 )
| ( subset @ ( sK26_C @ SV557 @ SV510 ) @ SV510 ) ) ) )
= $true )
| ( ( SV557
= ( powerset @ SV510 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2586]) ).
thf(2691,plain,
! [SV511: $i,SV558: $i] :
( ( ( ( SV558
!= ( powerset @ SV511 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY791: $i] :
( ~ ( in @ SY791 @ SV558 )
| ( subset @ SY791 @ SV511 ) )
| ~ ! [SY792: $i] :
( ~ ( subset @ SY792 @ SV511 )
| ( in @ SY792 @ SV558 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2587]) ).
thf(2692,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2588]) ).
thf(2693,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2589]) ).
thf(2694,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2590]) ).
thf(2695,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2591]) ).
thf(2696,plain,
! [SV559: $i,SV512: $i] :
( ( ( ( ( set_difference @ SV512 @ ( singleton @ SV559 ) )
!= SV512 ) )
= $true )
| ( ( ~ ( in @ SV559 @ SV512 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2592]) ).
thf(2697,plain,
! [SV513: $i,SV560: $i] :
( ( ( in @ SV560 @ SV513 )
= $true )
| ( ( ( set_difference @ SV513 @ ( singleton @ SV560 ) )
= SV513 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2593]) ).
thf(2698,plain,
! [SV514: $i] :
( ( ( ~ ! [SY754: $i,SY755: $i] :
( ( sK30_B @ SV514 )
!= ( ordered_pair @ SY754 @ SY755 ) )
| ~ ( in @ ( sK30_B @ SV514 ) @ SV514 ) )
= $false )
| ( ( relation @ SV514 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2594]) ).
thf(2699,plain,
! [SV515: $i] :
( ( ( relation @ SV515 )
= $false )
| ( ( ! [SY756: $i] :
( ( SY756
= ( ordered_pair @ ( sK28_C @ SY756 @ SV515 ) @ ( sK29_SY279 @ SY756 @ SV515 ) ) )
| ~ ( in @ SY756 @ SV515 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2595]) ).
thf(2700,plain,
! [SV561: $i,SV516: $i] :
( ( ( ( ( set_intersection2 @ SV516 @ SV561 )
!= empty_set ) )
= $true )
| ( ( disjoint @ SV516 @ SV561 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2596]) ).
thf(2701,plain,
! [SV562: $i,SV517: $i] :
( ( ( ~ ( disjoint @ SV517 @ SV562 ) )
= $true )
| ( ( ( set_intersection2 @ SV517 @ SV562 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2597]) ).
thf(2702,plain,
! [SV563: $i,SV518: $i] :
( ( ( ~ ( subset @ SV518 @ SV563 )
| ~ ( subset @ SV563 @ SV518 ) )
= $true )
| ( ( SV518 = SV563 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2598]) ).
thf(2703,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2599]) ).
thf(2704,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2600]) ).
thf(2705,plain,
! [SV564: $i,SV519: $i] :
( ( ( ~ ( element @ SV519 @ ( powerset @ SV564 ) ) )
= $true )
| ( ( subset @ SV519 @ SV564 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2601]) ).
thf(2706,plain,
! [SV565: $i,SV520: $i] :
( ( ( ~ ( subset @ SV520 @ SV565 ) )
= $true )
| ( ( element @ SV520 @ ( powerset @ SV565 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2602]) ).
thf(2707,plain,
! [SV427: $i] :
( ( ( ! [SY681: $i] :
( ~ ( ~ ( ! [SY682: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SY681 @ SV427 ) @ SY682 ) @ SV427 )
| ~ ( in @ ( sK20_C @ SY681 @ SV427 ) @ SY681 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_C @ SY681 @ SV427 ) @ ( sK21_SY278 @ SY681 @ SV427 ) ) @ SV427 )
| ( in @ ( sK20_C @ SY681 @ SV427 ) @ SY681 ) ) )
| ( SY681
= ( relation_dom @ SV427 ) ) ) )
= $true )
| ( ( relation @ SV427 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2603]) ).
thf(2708,plain,
! [SV427: $i] :
( ( ( ! [SY683: $i] :
( ( SY683
!= ( relation_dom @ SV427 ) )
| ~ ( ~ ! [SY684: $i] :
( ! [SY685: $i] :
~ ( in @ ( ordered_pair @ SY684 @ SY685 ) @ SV427 )
| ( in @ SY684 @ SY683 ) )
| ~ ! [SY686: $i] :
( ~ ( in @ SY686 @ SY683 )
| ( in @ ( ordered_pair @ SY686 @ ( sK19_D @ SY686 @ SY683 @ SV427 ) ) @ SV427 ) ) ) ) )
= $true )
| ( ( relation @ SV427 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2604]) ).
thf(2709,plain,
! [SV428: $i,SV566: $i,SV591: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV428 )
| ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV566 )
| ~ ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV591 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV428 )
| ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV591 ) )
| ~ ( ~ ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV566 )
| ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV591 ) ) ) )
| ( SV591
= ( set_difference @ SV428 @ SV566 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2605]) ).
thf(2710,plain,
! [SV567: $i,SV428: $i,SV592: $i] :
( ( ( SV592
!= ( set_difference @ SV428 @ SV567 ) )
| ~ ( ~ ! [SY820: $i] :
( ~ ( in @ SY820 @ SV428 )
| ( in @ SY820 @ SV567 )
| ( in @ SY820 @ SV592 ) )
| ~ ~ ( ~ ! [SY821: $i] :
( ~ ( in @ SY821 @ SV592 )
| ( in @ SY821 @ SV428 ) )
| ~ ! [SY822: $i] :
( ~ ( in @ SY822 @ SV592 )
| ~ ( in @ SY822 @ SV567 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2606]) ).
thf(2711,plain,
! [SV521: $i] :
( ( ( relation @ SV521 )
= $false )
| ( ( ( relation_rng @ SV521 )
= ( relation_dom @ ( relation_inverse @ SV521 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2607]) ).
thf(2712,plain,
! [SV522: $i] :
( ( ( relation @ SV522 )
= $false )
| ( ( ( relation_dom @ SV522 )
= ( relation_rng @ ( relation_inverse @ SV522 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2608]) ).
thf(2713,plain,
! [SV568: $i,SV523: $i] :
( ( ( ~ ( in @ SV523 @ SV568 ) )
= $true )
| ( ( subset @ ( singleton @ SV523 ) @ SV568 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2609]) ).
thf(2714,plain,
! [SV569: $i,SV524: $i] :
( ( ( ~ ( subset @ ( singleton @ SV524 ) @ SV569 ) )
= $true )
| ( ( in @ SV524 @ SV569 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2610]) ).
thf(2715,plain,
! [SV429: $i,SV570: $i,SV593: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV429 )
| ~ ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV570 )
| ~ ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV593 ) )
| ~ ~ ( ~ ( ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV429 )
| ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV593 ) )
| ~ ( ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV570 )
| ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV593 ) ) ) )
| ( SV593
= ( set_intersection2 @ SV429 @ SV570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2611]) ).
thf(2716,plain,
! [SV571: $i,SV429: $i,SV594: $i] :
( ( ( SV594
!= ( set_intersection2 @ SV429 @ SV571 ) )
| ~ ( ~ ! [SY823: $i] :
( ~ ( in @ SY823 @ SV429 )
| ~ ( in @ SY823 @ SV571 )
| ( in @ SY823 @ SV594 ) )
| ~ ~ ( ~ ! [SY824: $i] :
( ~ ( in @ SY824 @ SV594 )
| ( in @ SY824 @ SV429 ) )
| ~ ! [SY825: $i] :
( ~ ( in @ SY825 @ SV594 )
| ( in @ SY825 @ SV571 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2612]) ).
thf(2717,plain,
! [SV430: $i] :
( ( ( ! [SY701: $i] :
( ~ ( ~ ( ! [SY702: $i] :
~ ( in @ ( ordered_pair @ SY702 @ ( sK13_C @ SY701 @ SV430 ) ) @ SV430 )
| ~ ( in @ ( sK13_C @ SY701 @ SV430 ) @ SY701 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY274 @ SY701 @ SV430 ) @ ( sK13_C @ SY701 @ SV430 ) ) @ SV430 )
| ( in @ ( sK13_C @ SY701 @ SV430 ) @ SY701 ) ) )
| ( SY701
= ( relation_rng @ SV430 ) ) ) )
= $true )
| ( ( relation @ SV430 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2613]) ).
thf(2718,plain,
! [SV430: $i] :
( ( ( ! [SY703: $i] :
( ( SY703
!= ( relation_rng @ SV430 ) )
| ~ ( ~ ! [SY704: $i] :
( ! [SY705: $i] :
~ ( in @ ( ordered_pair @ SY705 @ SY704 ) @ SV430 )
| ( in @ SY704 @ SY703 ) )
| ~ ! [SY706: $i] :
( ~ ( in @ SY706 @ SY703 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY706 @ SY703 @ SV430 ) @ SY706 ) @ SV430 ) ) ) ) )
= $true )
| ( ( relation @ SV430 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2614]) ).
thf(2719,plain,
! [SV525: $i,SV572: $i] :
( ( ( ~ ( ~ ( ! [SY803: $i] :
( ~ ( in @ ( sK17_C @ SV572 @ SV525 ) @ SY803 )
| ~ ( in @ SY803 @ SV525 ) )
| ~ ( in @ ( sK17_C @ SV572 @ SV525 ) @ SV572 ) )
| ~ ( ~ ( ~ ( in @ ( sK17_C @ SV572 @ SV525 ) @ ( sK18_SY276 @ SV572 @ SV525 ) )
| ~ ( in @ ( sK18_SY276 @ SV572 @ SV525 ) @ SV525 ) )
| ( in @ ( sK17_C @ SV572 @ SV525 ) @ SV572 ) ) ) )
= $true )
| ( ( SV572
= ( union @ SV525 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2615]) ).
thf(2720,plain,
! [SV526: $i,SV573: $i] :
( ( ( ( SV573
!= ( union @ SV526 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY804: $i] :
( ! [SY768: $i] :
( ~ ( in @ SY804 @ SY768 )
| ~ ( in @ SY768 @ SV526 ) )
| ( in @ SY804 @ SV573 ) )
| ~ ! [SY806: $i] :
( ~ ( in @ SY806 @ SV573 )
| ~ ( ~ ( in @ SY806 @ ( sK16_D @ SY806 @ SV573 @ SV526 ) )
| ~ ( in @ ( sK16_D @ SY806 @ SV573 @ SV526 ) @ SV526 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2616]) ).
thf(2721,plain,
! [SV432: $i,SV480: $i] :
( ( ( in @ ( sK36_C @ SV480 @ SV432 ) @ SV432 )
= $true )
| ( ( element @ SV432 @ ( powerset @ SV480 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2617]) ).
thf(2722,plain,
! [SV432: $i,SV480: $i] :
( ( ( ~ ( in @ ( sK36_C @ SV480 @ SV432 ) @ SV480 ) )
= $true )
| ( ( element @ SV432 @ ( powerset @ SV480 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2618]) ).
thf(2723,plain,
! [SV574: $i,SV527: $i] :
( ( ( ( ( set_difference @ SV527 @ SV574 )
!= empty_set ) )
= $true )
| ( ( subset @ SV527 @ SV574 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2619]) ).
thf(2724,plain,
! [SV575: $i,SV528: $i] :
( ( ( ~ ( subset @ SV528 @ SV575 ) )
= $true )
| ( ( ( set_difference @ SV528 @ SV575 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2620]) ).
thf(2725,plain,
! [SV529: $i,SV576: $i] :
( ( ( ~ ( ~ ( in @ ( sK23_C @ SV576 @ SV529 ) @ SV529 )
| ~ ~ ( in @ ( sK23_C @ SV576 @ SV529 ) @ SV576 ) ) )
= $true )
| ( ( subset @ SV529 @ SV576 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2621]) ).
thf(2726,plain,
! [SV577: $i,SV530: $i] :
( ( ( ~ ( subset @ SV530 @ SV577 ) )
= $true )
| ( ( ! [SY807: $i] :
( ~ ( in @ SY807 @ SV530 )
| ( in @ SY807 @ SV577 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2622]) ).
thf(2727,plain,
! [SV578: $i,SV531: $i] :
( ( ( ( ( set_difference @ SV531 @ SV578 )
!= empty_set ) )
= $true )
| ( ( subset @ SV531 @ SV578 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2623]) ).
thf(2728,plain,
! [SV579: $i,SV532: $i] :
( ( ( ~ ( subset @ SV532 @ SV579 ) )
= $true )
| ( ( ( set_difference @ SV532 @ SV579 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2624]) ).
thf(2729,plain,
! [SV433: $i,SV580: $i,SV595: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK25_D @ SV595 @ SV580 @ SV433 ) @ SV595 )
| ( ( sK25_D @ SV595 @ SV580 @ SV433 )
!= SV433 ) )
| ~ ( ~ ( in @ ( sK25_D @ SV595 @ SV580 @ SV433 ) @ SV595 )
| ( ( sK25_D @ SV595 @ SV580 @ SV433 )
!= SV580 ) ) )
| ~ ( ( in @ ( sK25_D @ SV595 @ SV580 @ SV433 ) @ SV595 )
| ( ( sK25_D @ SV595 @ SV580 @ SV433 )
= SV433 )
| ( ( sK25_D @ SV595 @ SV580 @ SV433 )
= SV580 ) ) )
| ( SV595
= ( unordered_pair @ SV433 @ SV580 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2625]) ).
thf(2730,plain,
! [SV581: $i,SV433: $i,SV596: $i] :
( ( ( SV596
!= ( unordered_pair @ SV433 @ SV581 ) )
| ~ ( ~ ! [SY826: $i] :
( ~ ( in @ SY826 @ SV596 )
| ( SY826 = SV433 )
| ( SY826 = SV581 ) )
| ~ ~ ( ~ ! [SY827: $i] :
( ( SY827 != SV433 )
| ( in @ SY827 @ SV596 ) )
| ~ ! [SY828: $i] :
( ( SY828 != SV581 )
| ( in @ SY828 @ SV596 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2626]) ).
thf(2731,plain,
( ( ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK40_SY287 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK39_C @ SX1 @ SX0 ) @ ( sK40_SY287 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2627]) ).
thf(2732,plain,
( ( ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK38_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK38_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2628]) ).
thf(2733,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2629]) ).
thf(2734,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2630]) ).
thf(2735,plain,
! [SV533: $i,SV582: $i] :
( ( ( ~ ( ~ ( ( ( sK27_C @ SV582 @ SV533 )
!= SV533 )
| ~ ( in @ ( sK27_C @ SV582 @ SV533 ) @ SV582 ) )
| ~ ( ( ( sK27_C @ SV582 @ SV533 )
= SV533 )
| ( in @ ( sK27_C @ SV582 @ SV533 ) @ SV582 ) ) ) )
= $true )
| ( ( SV582
= ( singleton @ SV533 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2631]) ).
thf(2736,plain,
! [SV534: $i,SV583: $i] :
( ( ( ( SV583
!= ( singleton @ SV534 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY813: $i] :
( ( SY813 != SV534 )
| ( in @ SY813 @ SV583 ) )
| ~ ! [SY814: $i] :
( ~ ( in @ SY814 @ SV583 )
| ( SY814 = SV534 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2632]) ).
thf(2737,plain,
! [SV584: $i,SV434: $i] :
( ( ( ~ ( subset @ SV434 @ SV584 ) )
= $true )
| ( ( ! [SY815: $i] : ( subset @ ( cartesian_product2 @ SV434 @ SY815 ) @ ( cartesian_product2 @ SV584 @ SY815 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2633]) ).
thf(2738,plain,
! [SV585: $i,SV434: $i] :
( ( ( ~ ( subset @ SV434 @ SV585 ) )
= $true )
| ( ( ! [SY816: $i] : ( subset @ ( cartesian_product2 @ SY816 @ SV434 ) @ ( cartesian_product2 @ SY816 @ SV585 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2634]) ).
thf(2739,plain,
! [SV435: $i] :
( ( ( empty @ ( sK8_B @ SV435 ) )
= $false )
| ( ( empty @ SV435 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2636]) ).
thf(2740,plain,
! [SV360: $i,SV439: $i,SV535: $i] :
( ( ( in @ SV535 @ SV439 )
= $false )
| ( ( in @ SV535 @ SV360 )
= $true )
| ( ( element @ SV439 @ ( powerset @ SV360 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2637]) ).
thf(2741,plain,
! [SV491: $i,SV481: $i,SV442: $i,SV363: $i] :
( ( ( subset @ SV363 @ SV442 )
= $false )
| ( ( ~ ( subset @ SV481 @ SV491 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV363 @ SV481 ) @ ( cartesian_product2 @ SV442 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2639]) ).
thf(2742,plain,
! [SV445: $i,SV482: $i,SV366: $i] :
( ( ( subset @ SV366 @ SV482 )
= $false )
| ( ( subset @ SV366 @ SV445 )
= $false )
| ( ( subset @ SV366 @ ( set_intersection2 @ SV445 @ SV482 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2640]) ).
thf(2743,plain,
! [SV367: $i,SV483: $i,SV446: $i] :
( ( ( subset @ SV446 @ SV483 )
= $false )
| ( ( subset @ SV367 @ SV446 )
= $false )
| ( ( subset @ SV367 @ SV483 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2641]) ).
thf(2744,plain,
! [SV494: $i,SV378: $i] :
( ( ( ~ ( subset @ ( relation_rng @ SV378 ) @ ( relation_dom @ SV494 ) ) )
= $true )
| ( ( ( relation_dom @ ( relation_composition @ SV378 @ SV494 ) )
= ( relation_dom @ SV378 ) )
= $true )
| ( ( relation @ SV494 )
= $false )
| ( ( relation @ SV378 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2644]) ).
thf(2745,plain,
! [SV495: $i,SV380: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV380 ) @ ( relation_rng @ SV495 ) ) )
= $true )
| ( ( ( relation_rng @ ( relation_composition @ SV495 @ SV380 ) )
= ( relation_rng @ SV380 ) )
= $true )
| ( ( relation @ SV495 )
= $false )
| ( ( relation @ SV380 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2645]) ).
thf(2746,plain,
! [SV484: $i,SV457: $i,SV384: $i] :
( ( ( subset @ SV384 @ SV457 )
= $false )
| ( ( disjoint @ SV457 @ SV484 )
= $false )
| ( ( disjoint @ SV384 @ SV484 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2646]) ).
thf(2747,plain,
! [SV388: $i,SV460: $i,SV485: $i] :
( ( ( subset @ SV485 @ SV460 )
= $false )
| ( ( subset @ SV388 @ SV460 )
= $false )
| ( ( subset @ ( set_union2 @ SV388 @ SV485 ) @ SV460 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2647]) ).
thf(2748,plain,
! [SV489: $i,SV475: $i,SV415: $i] :
( ( ( in @ SV415 @ SV475 )
= $false )
| ( ( element @ SV475 @ ( powerset @ SV489 ) )
= $false )
| ( ( element @ SV415 @ SV489 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2650]) ).
thf(2749,plain,
! [SV490: $i,SV476: $i,SV416: $i] :
( ( ( in @ SV416 @ SV476 )
= $false )
| ( ( element @ SV476 @ ( powerset @ SV490 ) )
= $false )
| ( ( ~ ( empty @ SV490 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2651]) ).
thf(2750,plain,
! [SV539: $i,SV586: $i,SV419: $i] :
( ( ( ~ ( in @ SV419 @ SV586 )
| ~ ( in @ SV539 @ SV586 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV419 @ SV539 ) @ SV586 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2653]) ).
thf(2751,plain,
! [SV419: $i] :
( ( ! [SY648: $i,SY649: $i] :
( ~ ( subset @ ( unordered_pair @ SV419 @ SY648 ) @ SY649 )
| ( in @ SV419 @ SY649 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2654]) ).
thf(2752,plain,
! [SV419: $i] :
( ( ! [SY650: $i,SY651: $i] :
( ~ ( subset @ ( unordered_pair @ SV419 @ SY650 ) @ SY651 )
| ( in @ SY650 @ SY651 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2655]) ).
thf(2753,plain,
! [SV420: $i,SV597: $i] :
( ( ( ~ ( relation @ SV597 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SV597 @ SV420 ) @ ( sK11_SY272 @ SV597 @ SV420 ) ) @ SV597 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY272 @ SV597 @ SV420 ) @ ( sK10_C @ SV597 @ SV420 ) ) @ SV420 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK10_C @ SV597 @ SV420 ) @ ( sK11_SY272 @ SV597 @ SV420 ) ) @ SV597 )
| ( in @ ( ordered_pair @ ( sK11_SY272 @ SV597 @ SV420 ) @ ( sK10_C @ SV597 @ SV420 ) ) @ SV420 ) ) )
| ( SV597
= ( relation_inverse @ SV420 ) ) )
= $true )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2656]) ).
thf(2754,plain,
! [SV420: $i,SV598: $i] :
( ( ( ~ ( relation @ SV598 )
| ( SV598
!= ( relation_inverse @ SV420 ) )
| ~ ( ~ ! [SY829: $i,SY830: $i] :
( ~ ( in @ ( ordered_pair @ SY829 @ SY830 ) @ SV598 )
| ( in @ ( ordered_pair @ SY830 @ SY829 ) @ SV420 ) )
| ~ ! [SY831: $i,SY832: $i] :
( ~ ( in @ ( ordered_pair @ SY832 @ SY831 ) @ SV420 )
| ( in @ ( ordered_pair @ SY831 @ SY832 ) @ SV598 ) ) ) )
= $true )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2657]) ).
thf(2755,plain,
! [SV541: $i,SV498: $i,SV599: $i] :
( ( ( ~ ( in @ SV599 @ ( set_intersection2 @ SV498 @ SV541 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV498 @ SV541 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2659]) ).
thf(2756,plain,
! [SV421: $i,SV479: $i] :
( ( ( ~ ( in @ ( sK3_C @ SV479 @ SV421 ) @ SV421 ) )
= $true )
| ( ( ~ ( in @ ( sK3_C @ SV479 @ SV421 ) @ SV479 ) )
= $true )
| ( ( SV421 = SV479 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2660]) ).
thf(2757,plain,
! [SV421: $i,SV479: $i] :
( ( ( in @ ( sK3_C @ SV479 @ SV421 ) @ SV421 )
= $true )
| ( ( in @ ( sK3_C @ SV479 @ SV421 ) @ SV479 )
= $true )
| ( ( SV421 = SV479 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2661]) ).
thf(2758,plain,
! [SV542: $i,SV422: $i,SV587: $i] :
( ( ( ~ ( relation @ SV587 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV422 @ SV542 ) @ SV587 )
| ( in @ SV422 @ ( relation_dom @ SV587 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2662]) ).
thf(2759,plain,
! [SV543: $i,SV422: $i,SV588: $i] :
( ( ( ~ ( relation @ SV588 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV422 @ SV543 ) @ SV588 )
| ( in @ SV543 @ ( relation_rng @ SV588 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2663]) ).
thf(2760,plain,
! [SV544: $i,SV499: $i] :
( ( ( subset @ SV499 @ ( singleton @ SV544 ) )
= $false )
| ( ( ( SV499 = empty_set )
| ( SV499
= ( singleton @ SV544 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2664]) ).
thf(2761,plain,
! [SV600: $i] :
( ( ( SV600 != empty_set )
| ! [SY833: $i] : ( subset @ SV600 @ ( singleton @ SY833 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2665]) ).
thf(2762,plain,
! [SV601: $i] :
( ( ! [SY834: $i] :
( ( SV601
!= ( singleton @ SY834 ) )
| ( subset @ SV601 @ ( singleton @ SY834 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2666]) ).
thf(2763,plain,
! [SV545: $i,SV500: $i] :
( ( ( ( set_difference @ SV500 @ SV545 )
= SV500 )
= $false )
| ( ( disjoint @ SV500 @ SV545 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2667]) ).
thf(2764,plain,
! [SV546: $i,SV501: $i] :
( ( ( disjoint @ SV501 @ SV546 )
= $false )
| ( ( ( set_difference @ SV501 @ SV546 )
= SV501 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2668]) ).
thf(2765,plain,
! [SV423: $i,SV547: $i,SV589: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV589 )
| ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV423 ) )
| ~ ( ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV589 )
| ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV547 ) ) )
| ~ ( ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV589 )
| ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV423 )
| ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV547 ) ) ) )
= $true )
| ( ( SV589
= ( set_union2 @ SV423 @ SV547 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2669]) ).
thf(2766,plain,
! [SV548: $i,SV423: $i,SV590: $i] :
( ( ( ( SV590
!= ( set_union2 @ SV423 @ SV548 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY817: $i] :
( ~ ( in @ SY817 @ SV590 )
| ( in @ SY817 @ SV423 )
| ( in @ SY817 @ SV548 ) )
| ~ ~ ( ~ ! [SY818: $i] :
( ~ ( in @ SY818 @ SV423 )
| ( in @ SY818 @ SV590 ) )
| ~ ! [SY819: $i] :
( ~ ( in @ SY819 @ SV548 )
| ( in @ SY819 @ SV590 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2670]) ).
thf(2767,plain,
! [SV549: $i,SV502: $i] :
( ( ( subset @ SV502 @ ( singleton @ SV549 ) )
= $false )
| ( ( ( SV502 = empty_set )
| ( SV502
= ( singleton @ SV549 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2671]) ).
thf(2768,plain,
! [SV602: $i] :
( ( ( SV602 != empty_set )
| ! [SY835: $i] : ( subset @ SV602 @ ( singleton @ SY835 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2672]) ).
thf(2769,plain,
! [SV603: $i] :
( ( ! [SY836: $i] :
( ( SV603
!= ( singleton @ SY836 ) )
| ( subset @ SV603 @ ( singleton @ SY836 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2673]) ).
thf(2770,plain,
! [SV550: $i,SV503: $i] :
( ( ( SV503 = SV550 )
= $true )
| ( ( ~ ( subset @ SV503 @ SV550 ) )
= $true )
| ( ( proper_subset @ SV503 @ SV550 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2674]) ).
thf(2771,plain,
! [SV604: $i] :
( ( ! [SY837: $i] :
( ~ ( proper_subset @ SV604 @ SY837 )
| ( SV604 != SY837 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2675]) ).
thf(2772,plain,
! [SV605: $i] :
( ( ! [SY838: $i] :
( ~ ( proper_subset @ SV605 @ SY838 )
| ( subset @ SV605 @ SY838 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2676]) ).
thf(2773,plain,
! [SV504: $i,SV551: $i] :
( ( ( ~ ( in @ ( sK34_C @ SV551 @ SV504 ) @ SV504 )
| ~ ( in @ ( sK34_C @ SV551 @ SV504 ) @ SV551 ) )
= $false )
| ( ( disjoint @ SV504 @ SV551 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2677]) ).
thf(2774,plain,
! [SV552: $i,SV505: $i,SV606: $i] :
( ( ( ~ ( in @ SV606 @ SV505 )
| ~ ( in @ SV606 @ SV552 ) )
= $true )
| ( ( ~ ( disjoint @ SV505 @ SV552 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2678]) ).
thf(2775,plain,
! [SV424: $i,SV553: $i] :
( ( ( ~ ( subset @ SV553 @ ( sK35_B @ SV424 ) ) )
= $true )
| ( ( are_equipotent @ SV553 @ ( sK35_B @ SV424 ) )
= $true )
| ( ( in @ SV553 @ ( sK35_B @ SV424 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2679]) ).
thf(2776,plain,
! [SV424: $i] :
( ( ! [SY671: $i] :
( ~ ( in @ SY671 @ ( sK35_B @ SV424 ) )
| ( in @ ( powerset @ SY671 ) @ ( sK35_B @ SV424 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2680]) ).
thf(2777,plain,
! [SV424: $i] :
( ( ~ ( ~ ! [SY672: $i,SY673: $i] :
( ~ ( in @ SY672 @ ( sK35_B @ SV424 ) )
| ~ ( subset @ SY673 @ SY672 )
| ( in @ SY673 @ ( sK35_B @ SV424 ) ) )
| ~ ( in @ SV424 @ ( sK35_B @ SV424 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2681]) ).
thf(2778,plain,
! [SV425: $i,SV607: $i] :
( ( ( ~ ( relation @ SV607 )
| ~ ( subset @ SV425 @ SV607 )
| ( subset @ ( relation_dom @ SV425 ) @ ( relation_dom @ SV607 ) ) )
= $true )
| ( ( relation @ SV425 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2682]) ).
thf(2779,plain,
! [SV425: $i,SV608: $i] :
( ( ( ~ ( relation @ SV608 )
| ~ ( subset @ SV425 @ SV608 )
| ( subset @ ( relation_rng @ SV425 ) @ ( relation_rng @ SV608 ) ) )
= $true )
| ( ( relation @ SV425 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2683]) ).
thf(2780,plain,
! [SV554: $i,SV506: $i] :
( ( ( in @ SV506 @ SV554 )
= $false )
| ( ( subset @ ( singleton @ SV506 ) @ SV554 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2684]) ).
thf(2781,plain,
! [SV555: $i,SV507: $i] :
( ( ( subset @ ( singleton @ SV507 ) @ SV555 )
= $false )
| ( ( in @ SV507 @ SV555 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2685]) ).
thf(2782,plain,
! [SV509: $i,SV609: $i] :
( ( ( ~ ( in @ SV609 @ SV509 ) )
= $true )
| ( ( SV509 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2686]) ).
thf(2783,plain,
! [SV426: $i,SV556: $i] :
( ( ( ~ ( subset @ SV556 @ ( sK1_B @ SV426 ) ) )
= $true )
| ( ( are_equipotent @ SV556 @ ( sK1_B @ SV426 ) )
= $true )
| ( ( in @ SV556 @ ( sK1_B @ SV426 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2687]) ).
thf(2784,plain,
! [SV426: $i] :
( ( ! [SY677: $i] :
( ~ ( ~ ! [SY678: $i] :
( ~ ( subset @ SY678 @ SY677 )
| ( in @ SY678 @ ( sK2_SY267 @ SY677 @ SV426 ) ) )
| ~ ( in @ ( sK2_SY267 @ SY677 @ SV426 ) @ ( sK1_B @ SV426 ) ) )
| ~ ( in @ SY677 @ ( sK1_B @ SV426 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2688]) ).
thf(2785,plain,
! [SV426: $i] :
( ( ~ ( ~ ! [SY679: $i,SY680: $i] :
( ~ ( in @ SY679 @ ( sK1_B @ SV426 ) )
| ~ ( subset @ SY680 @ SY679 )
| ( in @ SY680 @ ( sK1_B @ SV426 ) ) )
| ~ ( in @ SV426 @ ( sK1_B @ SV426 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2689]) ).
thf(2786,plain,
! [SV510: $i,SV557: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_C @ SV557 @ SV510 ) @ SV557 )
| ~ ( subset @ ( sK26_C @ SV557 @ SV510 ) @ SV510 ) )
| ~ ( ( in @ ( sK26_C @ SV557 @ SV510 ) @ SV557 )
| ( subset @ ( sK26_C @ SV557 @ SV510 ) @ SV510 ) ) )
= $false )
| ( ( SV557
= ( powerset @ SV510 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2690]) ).
thf(2787,plain,
! [SV511: $i,SV558: $i] :
( ( ( SV558
= ( powerset @ SV511 ) )
= $false )
| ( ( ~ ( ~ ! [SY791: $i] :
( ~ ( in @ SY791 @ SV558 )
| ( subset @ SY791 @ SV511 ) )
| ~ ! [SY792: $i] :
( ~ ( subset @ SY792 @ SV511 )
| ( in @ SY792 @ SV558 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2691]) ).
thf(2788,plain,
! [SV610: $i] :
( ( ( empty @ SV610 )
| ! [SY839: $i] :
( ~ ( element @ SY839 @ SV610 )
| ( in @ SY839 @ SV610 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2692]) ).
thf(2789,plain,
! [SV611: $i] :
( ( ( empty @ SV611 )
| ! [SY840: $i] :
( ~ ( in @ SY840 @ SV611 )
| ( element @ SY840 @ SV611 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2693]) ).
thf(2790,plain,
! [SV612: $i] :
( ( ~ ( empty @ SV612 )
| ! [SY841: $i] :
( ~ ( element @ SY841 @ SV612 )
| ( empty @ SY841 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2694]) ).
thf(2791,plain,
! [SV613: $i] :
( ( ~ ( empty @ SV613 )
| ! [SY842: $i] :
( ~ ( empty @ SY842 )
| ( element @ SY842 @ SV613 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2695]) ).
thf(2792,plain,
! [SV559: $i,SV512: $i] :
( ( ( ( set_difference @ SV512 @ ( singleton @ SV559 ) )
= SV512 )
= $false )
| ( ( ~ ( in @ SV559 @ SV512 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2696]) ).
thf(2793,plain,
! [SV514: $i] :
( ( ( ~ ! [SY754: $i,SY755: $i] :
( ( sK30_B @ SV514 )
!= ( ordered_pair @ SY754 @ SY755 ) ) )
= $false )
| ( ( relation @ SV514 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2698]) ).
thf(2794,plain,
! [SV514: $i] :
( ( ( ~ ( in @ ( sK30_B @ SV514 ) @ SV514 ) )
= $false )
| ( ( relation @ SV514 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2698]) ).
thf(2795,plain,
! [SV515: $i,SV614: $i] :
( ( ( ( SV614
= ( ordered_pair @ ( sK28_C @ SV614 @ SV515 ) @ ( sK29_SY279 @ SV614 @ SV515 ) ) )
| ~ ( in @ SV614 @ SV515 ) )
= $true )
| ( ( relation @ SV515 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2699]) ).
thf(2796,plain,
! [SV561: $i,SV516: $i] :
( ( ( ( set_intersection2 @ SV516 @ SV561 )
= empty_set )
= $false )
| ( ( disjoint @ SV516 @ SV561 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2700]) ).
thf(2797,plain,
! [SV562: $i,SV517: $i] :
( ( ( disjoint @ SV517 @ SV562 )
= $false )
| ( ( ( set_intersection2 @ SV517 @ SV562 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2701]) ).
thf(2798,plain,
! [SV563: $i,SV518: $i] :
( ( ( ~ ( subset @ SV518 @ SV563 ) )
= $true )
| ( ( ~ ( subset @ SV563 @ SV518 ) )
= $true )
| ( ( SV518 = SV563 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2702]) ).
thf(2799,plain,
! [SV615: $i] :
( ( ! [SY843: $i] :
( ( SV615 != SY843 )
| ( subset @ SV615 @ SY843 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2703]) ).
thf(2800,plain,
! [SV616: $i] :
( ( ! [SY844: $i] :
( ( SV616 != SY844 )
| ( subset @ SY844 @ SV616 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2704]) ).
thf(2801,plain,
! [SV564: $i,SV519: $i] :
( ( ( element @ SV519 @ ( powerset @ SV564 ) )
= $false )
| ( ( subset @ SV519 @ SV564 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2705]) ).
thf(2802,plain,
! [SV565: $i,SV520: $i] :
( ( ( subset @ SV520 @ SV565 )
= $false )
| ( ( element @ SV520 @ ( powerset @ SV565 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2706]) ).
thf(2803,plain,
! [SV427: $i,SV617: $i] :
( ( ( ~ ( ~ ( ! [SY845: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SV617 @ SV427 ) @ SY845 ) @ SV427 )
| ~ ( in @ ( sK20_C @ SV617 @ SV427 ) @ SV617 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_C @ SV617 @ SV427 ) @ ( sK21_SY278 @ SV617 @ SV427 ) ) @ SV427 )
| ( in @ ( sK20_C @ SV617 @ SV427 ) @ SV617 ) ) )
| ( SV617
= ( relation_dom @ SV427 ) ) )
= $true )
| ( ( relation @ SV427 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2707]) ).
thf(2804,plain,
! [SV427: $i,SV618: $i] :
( ( ( ( SV618
!= ( relation_dom @ SV427 ) )
| ~ ( ~ ! [SY846: $i] :
( ! [SY685: $i] :
~ ( in @ ( ordered_pair @ SY846 @ SY685 ) @ SV427 )
| ( in @ SY846 @ SV618 ) )
| ~ ! [SY848: $i] :
( ~ ( in @ SY848 @ SV618 )
| ( in @ ( ordered_pair @ SY848 @ ( sK19_D @ SY848 @ SV618 @ SV427 ) ) @ SV427 ) ) ) )
= $true )
| ( ( relation @ SV427 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2708]) ).
thf(2805,plain,
! [SV428: $i,SV566: $i,SV591: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV428 )
| ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV566 )
| ~ ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV591 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV428 )
| ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV591 ) )
| ~ ( ~ ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV566 )
| ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV591 ) ) ) ) )
= $true )
| ( ( SV591
= ( set_difference @ SV428 @ SV566 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2709]) ).
thf(2806,plain,
! [SV567: $i,SV428: $i,SV592: $i] :
( ( ( ( SV592
!= ( set_difference @ SV428 @ SV567 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY820: $i] :
( ~ ( in @ SY820 @ SV428 )
| ( in @ SY820 @ SV567 )
| ( in @ SY820 @ SV592 ) )
| ~ ~ ( ~ ! [SY821: $i] :
( ~ ( in @ SY821 @ SV592 )
| ( in @ SY821 @ SV428 ) )
| ~ ! [SY822: $i] :
( ~ ( in @ SY822 @ SV592 )
| ~ ( in @ SY822 @ SV567 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2710]) ).
thf(2807,plain,
! [SV568: $i,SV523: $i] :
( ( ( in @ SV523 @ SV568 )
= $false )
| ( ( subset @ ( singleton @ SV523 ) @ SV568 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2713]) ).
thf(2808,plain,
! [SV569: $i,SV524: $i] :
( ( ( subset @ ( singleton @ SV524 ) @ SV569 )
= $false )
| ( ( in @ SV524 @ SV569 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2714]) ).
thf(2809,plain,
! [SV429: $i,SV570: $i,SV593: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV429 )
| ~ ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV570 )
| ~ ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV593 ) )
| ~ ~ ( ~ ( ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV429 )
| ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV593 ) )
| ~ ( ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV570 )
| ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV593 ) ) ) ) )
= $true )
| ( ( SV593
= ( set_intersection2 @ SV429 @ SV570 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2715]) ).
thf(2810,plain,
! [SV571: $i,SV429: $i,SV594: $i] :
( ( ( ( SV594
!= ( set_intersection2 @ SV429 @ SV571 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY823: $i] :
( ~ ( in @ SY823 @ SV429 )
| ~ ( in @ SY823 @ SV571 )
| ( in @ SY823 @ SV594 ) )
| ~ ~ ( ~ ! [SY824: $i] :
( ~ ( in @ SY824 @ SV594 )
| ( in @ SY824 @ SV429 ) )
| ~ ! [SY825: $i] :
( ~ ( in @ SY825 @ SV594 )
| ( in @ SY825 @ SV571 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2716]) ).
thf(2811,plain,
! [SV430: $i,SV619: $i] :
( ( ( ~ ( ~ ( ! [SY849: $i] :
~ ( in @ ( ordered_pair @ SY849 @ ( sK13_C @ SV619 @ SV430 ) ) @ SV430 )
| ~ ( in @ ( sK13_C @ SV619 @ SV430 ) @ SV619 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY274 @ SV619 @ SV430 ) @ ( sK13_C @ SV619 @ SV430 ) ) @ SV430 )
| ( in @ ( sK13_C @ SV619 @ SV430 ) @ SV619 ) ) )
| ( SV619
= ( relation_rng @ SV430 ) ) )
= $true )
| ( ( relation @ SV430 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2717]) ).
thf(2812,plain,
! [SV430: $i,SV620: $i] :
( ( ( ( SV620
!= ( relation_rng @ SV430 ) )
| ~ ( ~ ! [SY850: $i] :
( ! [SY705: $i] :
~ ( in @ ( ordered_pair @ SY705 @ SY850 ) @ SV430 )
| ( in @ SY850 @ SV620 ) )
| ~ ! [SY852: $i] :
( ~ ( in @ SY852 @ SV620 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY852 @ SV620 @ SV430 ) @ SY852 ) @ SV430 ) ) ) )
= $true )
| ( ( relation @ SV430 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2718]) ).
thf(2813,plain,
! [SV525: $i,SV572: $i] :
( ( ( ~ ( ! [SY803: $i] :
( ~ ( in @ ( sK17_C @ SV572 @ SV525 ) @ SY803 )
| ~ ( in @ SY803 @ SV525 ) )
| ~ ( in @ ( sK17_C @ SV572 @ SV525 ) @ SV572 ) )
| ~ ( ~ ( ~ ( in @ ( sK17_C @ SV572 @ SV525 ) @ ( sK18_SY276 @ SV572 @ SV525 ) )
| ~ ( in @ ( sK18_SY276 @ SV572 @ SV525 ) @ SV525 ) )
| ( in @ ( sK17_C @ SV572 @ SV525 ) @ SV572 ) ) )
= $false )
| ( ( SV572
= ( union @ SV525 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2719]) ).
thf(2814,plain,
! [SV526: $i,SV573: $i] :
( ( ( SV573
= ( union @ SV526 ) )
= $false )
| ( ( ~ ( ~ ! [SY804: $i] :
( ! [SY768: $i] :
( ~ ( in @ SY804 @ SY768 )
| ~ ( in @ SY768 @ SV526 ) )
| ( in @ SY804 @ SV573 ) )
| ~ ! [SY806: $i] :
( ~ ( in @ SY806 @ SV573 )
| ~ ( ~ ( in @ SY806 @ ( sK16_D @ SY806 @ SV573 @ SV526 ) )
| ~ ( in @ ( sK16_D @ SY806 @ SV573 @ SV526 ) @ SV526 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2720]) ).
thf(2815,plain,
! [SV432: $i,SV480: $i] :
( ( ( in @ ( sK36_C @ SV480 @ SV432 ) @ SV480 )
= $false )
| ( ( element @ SV432 @ ( powerset @ SV480 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2722]) ).
thf(2816,plain,
! [SV574: $i,SV527: $i] :
( ( ( ( set_difference @ SV527 @ SV574 )
= empty_set )
= $false )
| ( ( subset @ SV527 @ SV574 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2723]) ).
thf(2817,plain,
! [SV575: $i,SV528: $i] :
( ( ( subset @ SV528 @ SV575 )
= $false )
| ( ( ( set_difference @ SV528 @ SV575 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2724]) ).
thf(2818,plain,
! [SV529: $i,SV576: $i] :
( ( ( ~ ( in @ ( sK23_C @ SV576 @ SV529 ) @ SV529 )
| ~ ~ ( in @ ( sK23_C @ SV576 @ SV529 ) @ SV576 ) )
= $false )
| ( ( subset @ SV529 @ SV576 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2725]) ).
thf(2819,plain,
! [SV577: $i,SV530: $i] :
( ( ( subset @ SV530 @ SV577 )
= $false )
| ( ( ! [SY807: $i] :
( ~ ( in @ SY807 @ SV530 )
| ( in @ SY807 @ SV577 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2726]) ).
thf(2820,plain,
! [SV578: $i,SV531: $i] :
( ( ( ( set_difference @ SV531 @ SV578 )
= empty_set )
= $false )
| ( ( subset @ SV531 @ SV578 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2727]) ).
thf(2821,plain,
! [SV579: $i,SV532: $i] :
( ( ( subset @ SV532 @ SV579 )
= $false )
| ( ( ( set_difference @ SV532 @ SV579 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2728]) ).
thf(2822,plain,
! [SV433: $i,SV580: $i,SV595: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK25_D @ SV595 @ SV580 @ SV433 ) @ SV595 )
| ( ( sK25_D @ SV595 @ SV580 @ SV433 )
!= SV433 ) )
| ~ ( ~ ( in @ ( sK25_D @ SV595 @ SV580 @ SV433 ) @ SV595 )
| ( ( sK25_D @ SV595 @ SV580 @ SV433 )
!= SV580 ) ) )
| ~ ( ( in @ ( sK25_D @ SV595 @ SV580 @ SV433 ) @ SV595 )
| ( ( sK25_D @ SV595 @ SV580 @ SV433 )
= SV433 )
| ( ( sK25_D @ SV595 @ SV580 @ SV433 )
= SV580 ) ) ) )
= $true )
| ( ( SV595
= ( unordered_pair @ SV433 @ SV580 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2729]) ).
thf(2823,plain,
! [SV581: $i,SV433: $i,SV596: $i] :
( ( ( ( SV596
!= ( unordered_pair @ SV433 @ SV581 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY826: $i] :
( ~ ( in @ SY826 @ SV596 )
| ( SY826 = SV433 )
| ( SY826 = SV581 ) )
| ~ ~ ( ~ ! [SY827: $i] :
( ( SY827 != SV433 )
| ( in @ SY827 @ SV596 ) )
| ~ ! [SY828: $i] :
( ( SY828 != SV581 )
| ( in @ SY828 @ SV596 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2730]) ).
thf(2824,plain,
! [SV621: $i] :
( ( ( SV621 = empty_set )
| ! [SY853: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK40_SY287 @ SY853 @ SV621 ) @ SV621 )
| ~ ~ ( in @ ( sK39_C @ SY853 @ SV621 ) @ ( sK40_SY287 @ SY853 @ SV621 ) ) )
| ~ ( in @ ( sK39_C @ SY853 @ SV621 ) @ SY853 ) )
| ~ ( ! [SY854: $i] :
( ~ ( in @ SY854 @ SV621 )
| ( in @ ( sK39_C @ SY853 @ SV621 ) @ SY854 ) )
| ( in @ ( sK39_C @ SY853 @ SV621 ) @ SY853 ) ) )
| ( SY853
= ( set_meet @ SV621 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2731]) ).
thf(2825,plain,
! [SV622: $i] :
( ( ( SV622 = empty_set )
| ! [SY855: $i] :
( ( SY855
!= ( set_meet @ SV622 ) )
| ~ ( ~ ! [SY856: $i] :
( ~ ( ~ ( in @ ( sK38_D @ SY856 @ SY855 @ SV622 ) @ SV622 )
| ~ ~ ( in @ SY856 @ ( sK38_D @ SY856 @ SY855 @ SV622 ) ) )
| ( in @ SY856 @ SY855 ) )
| ~ ! [SY857: $i] :
( ~ ( in @ SY857 @ SY855 )
| ! [SY858: $i] :
( ~ ( in @ SY858 @ SV622 )
| ( in @ SY857 @ SY858 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2732]) ).
thf(2826,plain,
! [SV623: $i] :
( ( ( SV623 != empty_set )
| ! [SY859: $i] :
( ( SY859
!= ( set_meet @ SV623 ) )
| ( SY859 = empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2733]) ).
thf(2827,plain,
! [SV624: $i] :
( ( ( SV624 != empty_set )
| ! [SY860: $i] :
( ( SY860 != empty_set )
| ( SY860
= ( set_meet @ SV624 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2734]) ).
thf(2828,plain,
! [SV533: $i,SV582: $i] :
( ( ( ~ ( ( ( sK27_C @ SV582 @ SV533 )
!= SV533 )
| ~ ( in @ ( sK27_C @ SV582 @ SV533 ) @ SV582 ) )
| ~ ( ( ( sK27_C @ SV582 @ SV533 )
= SV533 )
| ( in @ ( sK27_C @ SV582 @ SV533 ) @ SV582 ) ) )
= $false )
| ( ( SV582
= ( singleton @ SV533 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2735]) ).
thf(2829,plain,
! [SV534: $i,SV583: $i] :
( ( ( SV583
= ( singleton @ SV534 ) )
= $false )
| ( ( ~ ( ~ ! [SY813: $i] :
( ( SY813 != SV534 )
| ( in @ SY813 @ SV583 ) )
| ~ ! [SY814: $i] :
( ~ ( in @ SY814 @ SV583 )
| ( SY814 = SV534 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2736]) ).
thf(2830,plain,
! [SV584: $i,SV434: $i] :
( ( ( subset @ SV434 @ SV584 )
= $false )
| ( ( ! [SY815: $i] : ( subset @ ( cartesian_product2 @ SV434 @ SY815 ) @ ( cartesian_product2 @ SV584 @ SY815 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2737]) ).
thf(2831,plain,
! [SV585: $i,SV434: $i] :
( ( ( subset @ SV434 @ SV585 )
= $false )
| ( ( ! [SY816: $i] : ( subset @ ( cartesian_product2 @ SY816 @ SV434 ) @ ( cartesian_product2 @ SY816 @ SV585 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2738]) ).
thf(2832,plain,
! [SV442: $i,SV363: $i,SV491: $i,SV481: $i] :
( ( ( subset @ SV481 @ SV491 )
= $false )
| ( ( subset @ SV363 @ SV442 )
= $false )
| ( ( subset @ ( cartesian_product2 @ SV363 @ SV481 ) @ ( cartesian_product2 @ SV442 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2741]) ).
thf(2833,plain,
! [SV494: $i,SV378: $i] :
( ( ( subset @ ( relation_rng @ SV378 ) @ ( relation_dom @ SV494 ) )
= $false )
| ( ( ( relation_dom @ ( relation_composition @ SV378 @ SV494 ) )
= ( relation_dom @ SV378 ) )
= $true )
| ( ( relation @ SV494 )
= $false )
| ( ( relation @ SV378 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2744]) ).
thf(2834,plain,
! [SV495: $i,SV380: $i] :
( ( ( subset @ ( relation_dom @ SV380 ) @ ( relation_rng @ SV495 ) )
= $false )
| ( ( ( relation_rng @ ( relation_composition @ SV495 @ SV380 ) )
= ( relation_rng @ SV380 ) )
= $true )
| ( ( relation @ SV495 )
= $false )
| ( ( relation @ SV380 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2745]) ).
thf(2835,plain,
! [SV416: $i,SV476: $i,SV490: $i] :
( ( ( empty @ SV490 )
= $false )
| ( ( element @ SV476 @ ( powerset @ SV490 ) )
= $false )
| ( ( in @ SV416 @ SV476 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2749]) ).
thf(2836,plain,
! [SV539: $i,SV586: $i,SV419: $i] :
( ( ( ~ ( in @ SV419 @ SV586 ) )
= $true )
| ( ( ~ ( in @ SV539 @ SV586 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV419 @ SV539 ) @ SV586 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2750]) ).
thf(2837,plain,
! [SV625: $i,SV419: $i] :
( ( ! [SY861: $i] :
( ~ ( subset @ ( unordered_pair @ SV419 @ SV625 ) @ SY861 )
| ( in @ SV419 @ SY861 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2751]) ).
thf(2838,plain,
! [SV626: $i,SV419: $i] :
( ( ! [SY862: $i] :
( ~ ( subset @ ( unordered_pair @ SV419 @ SV626 ) @ SY862 )
| ( in @ SV626 @ SY862 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2752]) ).
thf(2839,plain,
! [SV420: $i,SV597: $i] :
( ( ( ~ ( relation @ SV597 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SV597 @ SV420 ) @ ( sK11_SY272 @ SV597 @ SV420 ) ) @ SV597 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY272 @ SV597 @ SV420 ) @ ( sK10_C @ SV597 @ SV420 ) ) @ SV420 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK10_C @ SV597 @ SV420 ) @ ( sK11_SY272 @ SV597 @ SV420 ) ) @ SV597 )
| ( in @ ( ordered_pair @ ( sK11_SY272 @ SV597 @ SV420 ) @ ( sK10_C @ SV597 @ SV420 ) ) @ SV420 ) ) )
| ( SV597
= ( relation_inverse @ SV420 ) ) )
= $true )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2753]) ).
thf(2840,plain,
! [SV420: $i,SV598: $i] :
( ( ( ~ ( relation @ SV598 ) )
= $true )
| ( ( ( SV598
!= ( relation_inverse @ SV420 ) )
| ~ ( ~ ! [SY829: $i,SY830: $i] :
( ~ ( in @ ( ordered_pair @ SY829 @ SY830 ) @ SV598 )
| ( in @ ( ordered_pair @ SY830 @ SY829 ) @ SV420 ) )
| ~ ! [SY831: $i,SY832: $i] :
( ~ ( in @ ( ordered_pair @ SY832 @ SY831 ) @ SV420 )
| ( in @ ( ordered_pair @ SY831 @ SY832 ) @ SV598 ) ) ) )
= $true )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2754]) ).
thf(2841,plain,
! [SV541: $i,SV498: $i,SV599: $i] :
( ( ( in @ SV599 @ ( set_intersection2 @ SV498 @ SV541 ) )
= $false )
| ( ( ~ ( disjoint @ SV498 @ SV541 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2755]) ).
thf(2842,plain,
! [SV421: $i,SV479: $i] :
( ( ( in @ ( sK3_C @ SV479 @ SV421 ) @ SV421 )
= $false )
| ( ( ~ ( in @ ( sK3_C @ SV479 @ SV421 ) @ SV479 ) )
= $true )
| ( ( SV421 = SV479 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2756]) ).
thf(2843,plain,
! [SV542: $i,SV422: $i,SV587: $i] :
( ( ( relation @ SV587 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV422 @ SV542 ) @ SV587 )
| ( in @ SV422 @ ( relation_dom @ SV587 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2758]) ).
thf(2844,plain,
! [SV543: $i,SV422: $i,SV588: $i] :
( ( ( relation @ SV588 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV422 @ SV543 ) @ SV588 )
| ( in @ SV543 @ ( relation_rng @ SV588 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2759]) ).
thf(2845,plain,
! [SV544: $i,SV499: $i] :
( ( ( SV499 = empty_set )
= $true )
| ( ( SV499
= ( singleton @ SV544 ) )
= $true )
| ( ( subset @ SV499 @ ( singleton @ SV544 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2760]) ).
thf(2846,plain,
! [SV600: $i] :
( ( ( ( SV600 != empty_set ) )
= $true )
| ( ( ! [SY833: $i] : ( subset @ SV600 @ ( singleton @ SY833 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2761]) ).
thf(2847,plain,
! [SV627: $i,SV601: $i] :
( ( ( SV601
!= ( singleton @ SV627 ) )
| ( subset @ SV601 @ ( singleton @ SV627 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2762]) ).
thf(2848,plain,
! [SV423: $i,SV547: $i,SV589: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV589 )
| ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV423 ) )
| ~ ( ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV589 )
| ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV547 ) ) )
| ~ ( ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV589 )
| ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV423 )
| ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV547 ) ) )
= $false )
| ( ( SV589
= ( set_union2 @ SV423 @ SV547 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2765]) ).
thf(2849,plain,
! [SV548: $i,SV423: $i,SV590: $i] :
( ( ( SV590
= ( set_union2 @ SV423 @ SV548 ) )
= $false )
| ( ( ~ ( ~ ! [SY817: $i] :
( ~ ( in @ SY817 @ SV590 )
| ( in @ SY817 @ SV423 )
| ( in @ SY817 @ SV548 ) )
| ~ ~ ( ~ ! [SY818: $i] :
( ~ ( in @ SY818 @ SV423 )
| ( in @ SY818 @ SV590 ) )
| ~ ! [SY819: $i] :
( ~ ( in @ SY819 @ SV548 )
| ( in @ SY819 @ SV590 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2766]) ).
thf(2850,plain,
! [SV549: $i,SV502: $i] :
( ( ( SV502 = empty_set )
= $true )
| ( ( SV502
= ( singleton @ SV549 ) )
= $true )
| ( ( subset @ SV502 @ ( singleton @ SV549 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2767]) ).
thf(2851,plain,
! [SV602: $i] :
( ( ( ( SV602 != empty_set ) )
= $true )
| ( ( ! [SY835: $i] : ( subset @ SV602 @ ( singleton @ SY835 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2768]) ).
thf(2852,plain,
! [SV628: $i,SV603: $i] :
( ( ( SV603
!= ( singleton @ SV628 ) )
| ( subset @ SV603 @ ( singleton @ SV628 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2769]) ).
thf(2853,plain,
! [SV550: $i,SV503: $i] :
( ( ( subset @ SV503 @ SV550 )
= $false )
| ( ( SV503 = SV550 )
= $true )
| ( ( proper_subset @ SV503 @ SV550 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2770]) ).
thf(2854,plain,
! [SV629: $i,SV604: $i] :
( ( ~ ( proper_subset @ SV604 @ SV629 )
| ( SV604 != SV629 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2771]) ).
thf(2855,plain,
! [SV630: $i,SV605: $i] :
( ( ~ ( proper_subset @ SV605 @ SV630 )
| ( subset @ SV605 @ SV630 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2772]) ).
thf(2856,plain,
! [SV504: $i,SV551: $i] :
( ( ( ~ ( in @ ( sK34_C @ SV551 @ SV504 ) @ SV504 ) )
= $false )
| ( ( disjoint @ SV504 @ SV551 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2773]) ).
thf(2857,plain,
! [SV504: $i,SV551: $i] :
( ( ( ~ ( in @ ( sK34_C @ SV551 @ SV504 ) @ SV551 ) )
= $false )
| ( ( disjoint @ SV504 @ SV551 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2773]) ).
thf(2858,plain,
! [SV552: $i,SV505: $i,SV606: $i] :
( ( ( ~ ( in @ SV606 @ SV505 ) )
= $true )
| ( ( ~ ( in @ SV606 @ SV552 ) )
= $true )
| ( ( ~ ( disjoint @ SV505 @ SV552 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2774]) ).
thf(2859,plain,
! [SV424: $i,SV553: $i] :
( ( ( subset @ SV553 @ ( sK35_B @ SV424 ) )
= $false )
| ( ( are_equipotent @ SV553 @ ( sK35_B @ SV424 ) )
= $true )
| ( ( in @ SV553 @ ( sK35_B @ SV424 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2775]) ).
thf(2860,plain,
! [SV424: $i,SV631: $i] :
( ( ~ ( in @ SV631 @ ( sK35_B @ SV424 ) )
| ( in @ ( powerset @ SV631 ) @ ( sK35_B @ SV424 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2776]) ).
thf(2861,plain,
! [SV424: $i] :
( ( ~ ! [SY672: $i,SY673: $i] :
( ~ ( in @ SY672 @ ( sK35_B @ SV424 ) )
| ~ ( subset @ SY673 @ SY672 )
| ( in @ SY673 @ ( sK35_B @ SV424 ) ) )
| ~ ( in @ SV424 @ ( sK35_B @ SV424 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2777]) ).
thf(2862,plain,
! [SV425: $i,SV607: $i] :
( ( ( ~ ( relation @ SV607 ) )
= $true )
| ( ( ~ ( subset @ SV425 @ SV607 )
| ( subset @ ( relation_dom @ SV425 ) @ ( relation_dom @ SV607 ) ) )
= $true )
| ( ( relation @ SV425 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2778]) ).
thf(2863,plain,
! [SV425: $i,SV608: $i] :
( ( ( ~ ( relation @ SV608 ) )
= $true )
| ( ( ~ ( subset @ SV425 @ SV608 )
| ( subset @ ( relation_rng @ SV425 ) @ ( relation_rng @ SV608 ) ) )
= $true )
| ( ( relation @ SV425 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2779]) ).
thf(2864,plain,
! [SV509: $i,SV609: $i] :
( ( ( in @ SV609 @ SV509 )
= $false )
| ( ( SV509 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2782]) ).
thf(2865,plain,
! [SV426: $i,SV556: $i] :
( ( ( subset @ SV556 @ ( sK1_B @ SV426 ) )
= $false )
| ( ( are_equipotent @ SV556 @ ( sK1_B @ SV426 ) )
= $true )
| ( ( in @ SV556 @ ( sK1_B @ SV426 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2783]) ).
thf(2866,plain,
! [SV426: $i,SV632: $i] :
( ( ~ ( ~ ! [SY863: $i] :
( ~ ( subset @ SY863 @ SV632 )
| ( in @ SY863 @ ( sK2_SY267 @ SV632 @ SV426 ) ) )
| ~ ( in @ ( sK2_SY267 @ SV632 @ SV426 ) @ ( sK1_B @ SV426 ) ) )
| ~ ( in @ SV632 @ ( sK1_B @ SV426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2784]) ).
thf(2867,plain,
! [SV426: $i] :
( ( ~ ! [SY679: $i,SY680: $i] :
( ~ ( in @ SY679 @ ( sK1_B @ SV426 ) )
| ~ ( subset @ SY680 @ SY679 )
| ( in @ SY680 @ ( sK1_B @ SV426 ) ) )
| ~ ( in @ SV426 @ ( sK1_B @ SV426 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2785]) ).
thf(2868,plain,
! [SV510: $i,SV557: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_C @ SV557 @ SV510 ) @ SV557 )
| ~ ( subset @ ( sK26_C @ SV557 @ SV510 ) @ SV510 ) ) )
= $false )
| ( ( SV557
= ( powerset @ SV510 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2786]) ).
thf(2869,plain,
! [SV510: $i,SV557: $i] :
( ( ( ~ ( ( in @ ( sK26_C @ SV557 @ SV510 ) @ SV557 )
| ( subset @ ( sK26_C @ SV557 @ SV510 ) @ SV510 ) ) )
= $false )
| ( ( SV557
= ( powerset @ SV510 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2786]) ).
thf(2870,plain,
! [SV511: $i,SV558: $i] :
( ( ( ~ ! [SY791: $i] :
( ~ ( in @ SY791 @ SV558 )
| ( subset @ SY791 @ SV511 ) )
| ~ ! [SY792: $i] :
( ~ ( subset @ SY792 @ SV511 )
| ( in @ SY792 @ SV558 ) ) )
= $false )
| ( ( SV558
= ( powerset @ SV511 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2787]) ).
thf(2871,plain,
! [SV610: $i] :
( ( ( empty @ SV610 )
= $true )
| ( ( ! [SY839: $i] :
( ~ ( element @ SY839 @ SV610 )
| ( in @ SY839 @ SV610 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2788]) ).
thf(2872,plain,
! [SV611: $i] :
( ( ( empty @ SV611 )
= $true )
| ( ( ! [SY840: $i] :
( ~ ( in @ SY840 @ SV611 )
| ( element @ SY840 @ SV611 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2789]) ).
thf(2873,plain,
! [SV612: $i] :
( ( ( ~ ( empty @ SV612 ) )
= $true )
| ( ( ! [SY841: $i] :
( ~ ( element @ SY841 @ SV612 )
| ( empty @ SY841 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2790]) ).
thf(2874,plain,
! [SV613: $i] :
( ( ( ~ ( empty @ SV613 ) )
= $true )
| ( ( ! [SY842: $i] :
( ~ ( empty @ SY842 )
| ( element @ SY842 @ SV613 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2791]) ).
thf(2875,plain,
! [SV512: $i,SV559: $i] :
( ( ( in @ SV559 @ SV512 )
= $false )
| ( ( ( set_difference @ SV512 @ ( singleton @ SV559 ) )
= SV512 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2792]) ).
thf(2876,plain,
! [SV514: $i] :
( ( ( ! [SY754: $i,SY755: $i] :
( ( sK30_B @ SV514 )
!= ( ordered_pair @ SY754 @ SY755 ) ) )
= $true )
| ( ( relation @ SV514 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2793]) ).
thf(2877,plain,
! [SV514: $i] :
( ( ( in @ ( sK30_B @ SV514 ) @ SV514 )
= $true )
| ( ( relation @ SV514 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2794]) ).
thf(2878,plain,
! [SV515: $i,SV614: $i] :
( ( ( SV614
= ( ordered_pair @ ( sK28_C @ SV614 @ SV515 ) @ ( sK29_SY279 @ SV614 @ SV515 ) ) )
= $true )
| ( ( ~ ( in @ SV614 @ SV515 ) )
= $true )
| ( ( relation @ SV515 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2795]) ).
thf(2879,plain,
! [SV563: $i,SV518: $i] :
( ( ( subset @ SV518 @ SV563 )
= $false )
| ( ( ~ ( subset @ SV563 @ SV518 ) )
= $true )
| ( ( SV518 = SV563 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2798]) ).
thf(2880,plain,
! [SV633: $i,SV615: $i] :
( ( ( SV615 != SV633 )
| ( subset @ SV615 @ SV633 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2799]) ).
thf(2881,plain,
! [SV634: $i,SV616: $i] :
( ( ( SV616 != SV634 )
| ( subset @ SV634 @ SV616 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2800]) ).
thf(2882,plain,
! [SV427: $i,SV617: $i] :
( ( ( ~ ( ~ ( ! [SY845: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SV617 @ SV427 ) @ SY845 ) @ SV427 )
| ~ ( in @ ( sK20_C @ SV617 @ SV427 ) @ SV617 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_C @ SV617 @ SV427 ) @ ( sK21_SY278 @ SV617 @ SV427 ) ) @ SV427 )
| ( in @ ( sK20_C @ SV617 @ SV427 ) @ SV617 ) ) ) )
= $true )
| ( ( SV617
= ( relation_dom @ SV427 ) )
= $true )
| ( ( relation @ SV427 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2803]) ).
thf(2883,plain,
! [SV427: $i,SV618: $i] :
( ( ( ( SV618
!= ( relation_dom @ SV427 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY846: $i] :
( ! [SY685: $i] :
~ ( in @ ( ordered_pair @ SY846 @ SY685 ) @ SV427 )
| ( in @ SY846 @ SV618 ) )
| ~ ! [SY848: $i] :
( ~ ( in @ SY848 @ SV618 )
| ( in @ ( ordered_pair @ SY848 @ ( sK19_D @ SY848 @ SV618 @ SV427 ) ) @ SV427 ) ) ) )
= $true )
| ( ( relation @ SV427 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2804]) ).
thf(2884,plain,
! [SV428: $i,SV566: $i,SV591: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV428 )
| ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV566 )
| ~ ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV591 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV428 )
| ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV591 ) )
| ~ ( ~ ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV566 )
| ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV591 ) ) ) )
= $false )
| ( ( SV591
= ( set_difference @ SV428 @ SV566 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2805]) ).
thf(2885,plain,
! [SV567: $i,SV428: $i,SV592: $i] :
( ( ( SV592
= ( set_difference @ SV428 @ SV567 ) )
= $false )
| ( ( ~ ( ~ ! [SY820: $i] :
( ~ ( in @ SY820 @ SV428 )
| ( in @ SY820 @ SV567 )
| ( in @ SY820 @ SV592 ) )
| ~ ~ ( ~ ! [SY821: $i] :
( ~ ( in @ SY821 @ SV592 )
| ( in @ SY821 @ SV428 ) )
| ~ ! [SY822: $i] :
( ~ ( in @ SY822 @ SV592 )
| ~ ( in @ SY822 @ SV567 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2806]) ).
thf(2886,plain,
! [SV429: $i,SV570: $i,SV593: $i] :
( ( ( ~ ( ~ ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV429 )
| ~ ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV570 )
| ~ ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV593 ) )
| ~ ~ ( ~ ( ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV429 )
| ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV593 ) )
| ~ ( ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV570 )
| ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV593 ) ) ) )
= $false )
| ( ( SV593
= ( set_intersection2 @ SV429 @ SV570 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2809]) ).
thf(2887,plain,
! [SV571: $i,SV429: $i,SV594: $i] :
( ( ( SV594
= ( set_intersection2 @ SV429 @ SV571 ) )
= $false )
| ( ( ~ ( ~ ! [SY823: $i] :
( ~ ( in @ SY823 @ SV429 )
| ~ ( in @ SY823 @ SV571 )
| ( in @ SY823 @ SV594 ) )
| ~ ~ ( ~ ! [SY824: $i] :
( ~ ( in @ SY824 @ SV594 )
| ( in @ SY824 @ SV429 ) )
| ~ ! [SY825: $i] :
( ~ ( in @ SY825 @ SV594 )
| ( in @ SY825 @ SV571 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2810]) ).
thf(2888,plain,
! [SV430: $i,SV619: $i] :
( ( ( ~ ( ~ ( ! [SY849: $i] :
~ ( in @ ( ordered_pair @ SY849 @ ( sK13_C @ SV619 @ SV430 ) ) @ SV430 )
| ~ ( in @ ( sK13_C @ SV619 @ SV430 ) @ SV619 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY274 @ SV619 @ SV430 ) @ ( sK13_C @ SV619 @ SV430 ) ) @ SV430 )
| ( in @ ( sK13_C @ SV619 @ SV430 ) @ SV619 ) ) ) )
= $true )
| ( ( SV619
= ( relation_rng @ SV430 ) )
= $true )
| ( ( relation @ SV430 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2811]) ).
thf(2889,plain,
! [SV430: $i,SV620: $i] :
( ( ( ( SV620
!= ( relation_rng @ SV430 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY850: $i] :
( ! [SY705: $i] :
~ ( in @ ( ordered_pair @ SY705 @ SY850 ) @ SV430 )
| ( in @ SY850 @ SV620 ) )
| ~ ! [SY852: $i] :
( ~ ( in @ SY852 @ SV620 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY852 @ SV620 @ SV430 ) @ SY852 ) @ SV430 ) ) ) )
= $true )
| ( ( relation @ SV430 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2812]) ).
thf(2890,plain,
! [SV525: $i,SV572: $i] :
( ( ( ~ ( ! [SY803: $i] :
( ~ ( in @ ( sK17_C @ SV572 @ SV525 ) @ SY803 )
| ~ ( in @ SY803 @ SV525 ) )
| ~ ( in @ ( sK17_C @ SV572 @ SV525 ) @ SV572 ) ) )
= $false )
| ( ( SV572
= ( union @ SV525 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2813]) ).
thf(2891,plain,
! [SV525: $i,SV572: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK17_C @ SV572 @ SV525 ) @ ( sK18_SY276 @ SV572 @ SV525 ) )
| ~ ( in @ ( sK18_SY276 @ SV572 @ SV525 ) @ SV525 ) )
| ( in @ ( sK17_C @ SV572 @ SV525 ) @ SV572 ) ) )
= $false )
| ( ( SV572
= ( union @ SV525 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2813]) ).
thf(2892,plain,
! [SV573: $i,SV526: $i] :
( ( ( ~ ! [SY804: $i] :
( ! [SY768: $i] :
( ~ ( in @ SY804 @ SY768 )
| ~ ( in @ SY768 @ SV526 ) )
| ( in @ SY804 @ SV573 ) )
| ~ ! [SY806: $i] :
( ~ ( in @ SY806 @ SV573 )
| ~ ( ~ ( in @ SY806 @ ( sK16_D @ SY806 @ SV573 @ SV526 ) )
| ~ ( in @ ( sK16_D @ SY806 @ SV573 @ SV526 ) @ SV526 ) ) ) )
= $false )
| ( ( SV573
= ( union @ SV526 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2814]) ).
thf(2893,plain,
! [SV529: $i,SV576: $i] :
( ( ( ~ ( in @ ( sK23_C @ SV576 @ SV529 ) @ SV529 ) )
= $false )
| ( ( subset @ SV529 @ SV576 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2818]) ).
thf(2894,plain,
! [SV529: $i,SV576: $i] :
( ( ( ~ ~ ( in @ ( sK23_C @ SV576 @ SV529 ) @ SV576 ) )
= $false )
| ( ( subset @ SV529 @ SV576 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2818]) ).
thf(2895,plain,
! [SV577: $i,SV530: $i,SV635: $i] :
( ( ( ~ ( in @ SV635 @ SV530 )
| ( in @ SV635 @ SV577 ) )
= $true )
| ( ( subset @ SV530 @ SV577 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2819]) ).
thf(2896,plain,
! [SV433: $i,SV580: $i,SV595: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK25_D @ SV595 @ SV580 @ SV433 ) @ SV595 )
| ( ( sK25_D @ SV595 @ SV580 @ SV433 )
!= SV433 ) )
| ~ ( ~ ( in @ ( sK25_D @ SV595 @ SV580 @ SV433 ) @ SV595 )
| ( ( sK25_D @ SV595 @ SV580 @ SV433 )
!= SV580 ) ) )
| ~ ( ( in @ ( sK25_D @ SV595 @ SV580 @ SV433 ) @ SV595 )
| ( ( sK25_D @ SV595 @ SV580 @ SV433 )
= SV433 )
| ( ( sK25_D @ SV595 @ SV580 @ SV433 )
= SV580 ) ) )
= $false )
| ( ( SV595
= ( unordered_pair @ SV433 @ SV580 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2822]) ).
thf(2897,plain,
! [SV581: $i,SV433: $i,SV596: $i] :
( ( ( SV596
= ( unordered_pair @ SV433 @ SV581 ) )
= $false )
| ( ( ~ ( ~ ! [SY826: $i] :
( ~ ( in @ SY826 @ SV596 )
| ( SY826 = SV433 )
| ( SY826 = SV581 ) )
| ~ ~ ( ~ ! [SY827: $i] :
( ( SY827 != SV433 )
| ( in @ SY827 @ SV596 ) )
| ~ ! [SY828: $i] :
( ( SY828 != SV581 )
| ( in @ SY828 @ SV596 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2823]) ).
thf(2898,plain,
! [SV621: $i] :
( ( ( SV621 = empty_set )
= $true )
| ( ( ! [SY853: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK40_SY287 @ SY853 @ SV621 ) @ SV621 )
| ~ ~ ( in @ ( sK39_C @ SY853 @ SV621 ) @ ( sK40_SY287 @ SY853 @ SV621 ) ) )
| ~ ( in @ ( sK39_C @ SY853 @ SV621 ) @ SY853 ) )
| ~ ( ! [SY854: $i] :
( ~ ( in @ SY854 @ SV621 )
| ( in @ ( sK39_C @ SY853 @ SV621 ) @ SY854 ) )
| ( in @ ( sK39_C @ SY853 @ SV621 ) @ SY853 ) ) )
| ( SY853
= ( set_meet @ SV621 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2824]) ).
thf(2899,plain,
! [SV622: $i] :
( ( ( SV622 = empty_set )
= $true )
| ( ( ! [SY855: $i] :
( ( SY855
!= ( set_meet @ SV622 ) )
| ~ ( ~ ! [SY856: $i] :
( ~ ( ~ ( in @ ( sK38_D @ SY856 @ SY855 @ SV622 ) @ SV622 )
| ~ ~ ( in @ SY856 @ ( sK38_D @ SY856 @ SY855 @ SV622 ) ) )
| ( in @ SY856 @ SY855 ) )
| ~ ! [SY857: $i] :
( ~ ( in @ SY857 @ SY855 )
| ! [SY858: $i] :
( ~ ( in @ SY858 @ SV622 )
| ( in @ SY857 @ SY858 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2825]) ).
thf(2900,plain,
! [SV623: $i] :
( ( ( ( SV623 != empty_set ) )
= $true )
| ( ( ! [SY859: $i] :
( ( SY859
!= ( set_meet @ SV623 ) )
| ( SY859 = empty_set ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2826]) ).
thf(2901,plain,
! [SV624: $i] :
( ( ( ( SV624 != empty_set ) )
= $true )
| ( ( ! [SY860: $i] :
( ( SY860 != empty_set )
| ( SY860
= ( set_meet @ SV624 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2827]) ).
thf(2902,plain,
! [SV533: $i,SV582: $i] :
( ( ( ~ ( ( ( sK27_C @ SV582 @ SV533 )
!= SV533 )
| ~ ( in @ ( sK27_C @ SV582 @ SV533 ) @ SV582 ) ) )
= $false )
| ( ( SV582
= ( singleton @ SV533 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2828]) ).
thf(2903,plain,
! [SV533: $i,SV582: $i] :
( ( ( ~ ( ( ( sK27_C @ SV582 @ SV533 )
= SV533 )
| ( in @ ( sK27_C @ SV582 @ SV533 ) @ SV582 ) ) )
= $false )
| ( ( SV582
= ( singleton @ SV533 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2828]) ).
thf(2904,plain,
! [SV583: $i,SV534: $i] :
( ( ( ~ ! [SY813: $i] :
( ( SY813 != SV534 )
| ( in @ SY813 @ SV583 ) )
| ~ ! [SY814: $i] :
( ~ ( in @ SY814 @ SV583 )
| ( SY814 = SV534 ) ) )
= $false )
| ( ( SV583
= ( singleton @ SV534 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2829]) ).
thf(2905,plain,
! [SV584: $i,SV636: $i,SV434: $i] :
( ( ( subset @ ( cartesian_product2 @ SV434 @ SV636 ) @ ( cartesian_product2 @ SV584 @ SV636 ) )
= $true )
| ( ( subset @ SV434 @ SV584 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2830]) ).
thf(2906,plain,
! [SV585: $i,SV434: $i,SV637: $i] :
( ( ( subset @ ( cartesian_product2 @ SV637 @ SV434 ) @ ( cartesian_product2 @ SV637 @ SV585 ) )
= $true )
| ( ( subset @ SV434 @ SV585 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2831]) ).
thf(2907,plain,
! [SV539: $i,SV586: $i,SV419: $i] :
( ( ( in @ SV419 @ SV586 )
= $false )
| ( ( ~ ( in @ SV539 @ SV586 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV419 @ SV539 ) @ SV586 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2836]) ).
thf(2908,plain,
! [SV638: $i,SV625: $i,SV419: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV419 @ SV625 ) @ SV638 )
| ( in @ SV419 @ SV638 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2837]) ).
thf(2909,plain,
! [SV639: $i,SV626: $i,SV419: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV419 @ SV626 ) @ SV639 )
| ( in @ SV626 @ SV639 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2838]) ).
thf(2910,plain,
! [SV420: $i,SV597: $i] :
( ( ( relation @ SV597 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SV597 @ SV420 ) @ ( sK11_SY272 @ SV597 @ SV420 ) ) @ SV597 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY272 @ SV597 @ SV420 ) @ ( sK10_C @ SV597 @ SV420 ) ) @ SV420 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK10_C @ SV597 @ SV420 ) @ ( sK11_SY272 @ SV597 @ SV420 ) ) @ SV597 )
| ( in @ ( ordered_pair @ ( sK11_SY272 @ SV597 @ SV420 ) @ ( sK10_C @ SV597 @ SV420 ) ) @ SV420 ) ) )
| ( SV597
= ( relation_inverse @ SV420 ) ) )
= $true )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2839]) ).
thf(2911,plain,
! [SV420: $i,SV598: $i] :
( ( ( relation @ SV598 )
= $false )
| ( ( ( SV598
!= ( relation_inverse @ SV420 ) )
| ~ ( ~ ! [SY829: $i,SY830: $i] :
( ~ ( in @ ( ordered_pair @ SY829 @ SY830 ) @ SV598 )
| ( in @ ( ordered_pair @ SY830 @ SY829 ) @ SV420 ) )
| ~ ! [SY831: $i,SY832: $i] :
( ~ ( in @ ( ordered_pair @ SY832 @ SY831 ) @ SV420 )
| ( in @ ( ordered_pair @ SY831 @ SY832 ) @ SV598 ) ) ) )
= $true )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2840]) ).
thf(2912,plain,
! [SV599: $i,SV541: $i,SV498: $i] :
( ( ( disjoint @ SV498 @ SV541 )
= $false )
| ( ( in @ SV599 @ ( set_intersection2 @ SV498 @ SV541 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2841]) ).
thf(2913,plain,
! [SV421: $i,SV479: $i] :
( ( ( in @ ( sK3_C @ SV479 @ SV421 ) @ SV479 )
= $false )
| ( ( in @ ( sK3_C @ SV479 @ SV421 ) @ SV421 )
= $false )
| ( ( SV421 = SV479 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2842]) ).
thf(2914,plain,
! [SV587: $i,SV542: $i,SV422: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV422 @ SV542 ) @ SV587 ) )
= $true )
| ( ( in @ SV422 @ ( relation_dom @ SV587 ) )
= $true )
| ( ( relation @ SV587 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2843]) ).
thf(2915,plain,
! [SV588: $i,SV543: $i,SV422: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV422 @ SV543 ) @ SV588 ) )
= $true )
| ( ( in @ SV543 @ ( relation_rng @ SV588 ) )
= $true )
| ( ( relation @ SV588 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2844]) ).
thf(2916,plain,
! [SV600: $i] :
( ( ( SV600 = empty_set )
= $false )
| ( ( ! [SY833: $i] : ( subset @ SV600 @ ( singleton @ SY833 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2846]) ).
thf(2917,plain,
! [SV627: $i,SV601: $i] :
( ( ( ( SV601
!= ( singleton @ SV627 ) ) )
= $true )
| ( ( subset @ SV601 @ ( singleton @ SV627 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2847]) ).
thf(2918,plain,
! [SV423: $i,SV547: $i,SV589: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV589 )
| ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV423 ) )
| ~ ( ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV589 )
| ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV547 ) ) ) )
= $false )
| ( ( SV589
= ( set_union2 @ SV423 @ SV547 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2848]) ).
thf(2919,plain,
! [SV423: $i,SV547: $i,SV589: $i] :
( ( ( ~ ( ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV589 )
| ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV423 )
| ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV547 ) ) )
= $false )
| ( ( SV589
= ( set_union2 @ SV423 @ SV547 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2848]) ).
thf(2920,plain,
! [SV548: $i,SV423: $i,SV590: $i] :
( ( ( ~ ! [SY817: $i] :
( ~ ( in @ SY817 @ SV590 )
| ( in @ SY817 @ SV423 )
| ( in @ SY817 @ SV548 ) )
| ~ ~ ( ~ ! [SY818: $i] :
( ~ ( in @ SY818 @ SV423 )
| ( in @ SY818 @ SV590 ) )
| ~ ! [SY819: $i] :
( ~ ( in @ SY819 @ SV548 )
| ( in @ SY819 @ SV590 ) ) ) )
= $false )
| ( ( SV590
= ( set_union2 @ SV423 @ SV548 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2849]) ).
thf(2921,plain,
! [SV602: $i] :
( ( ( SV602 = empty_set )
= $false )
| ( ( ! [SY835: $i] : ( subset @ SV602 @ ( singleton @ SY835 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2851]) ).
thf(2922,plain,
! [SV628: $i,SV603: $i] :
( ( ( ( SV603
!= ( singleton @ SV628 ) ) )
= $true )
| ( ( subset @ SV603 @ ( singleton @ SV628 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2852]) ).
thf(2923,plain,
! [SV629: $i,SV604: $i] :
( ( ( ~ ( proper_subset @ SV604 @ SV629 ) )
= $true )
| ( ( ( SV604 != SV629 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2854]) ).
thf(2924,plain,
! [SV630: $i,SV605: $i] :
( ( ( ~ ( proper_subset @ SV605 @ SV630 ) )
= $true )
| ( ( subset @ SV605 @ SV630 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2855]) ).
thf(2925,plain,
! [SV504: $i,SV551: $i] :
( ( ( in @ ( sK34_C @ SV551 @ SV504 ) @ SV504 )
= $true )
| ( ( disjoint @ SV504 @ SV551 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2856]) ).
thf(2926,plain,
! [SV504: $i,SV551: $i] :
( ( ( in @ ( sK34_C @ SV551 @ SV504 ) @ SV551 )
= $true )
| ( ( disjoint @ SV504 @ SV551 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2857]) ).
thf(2927,plain,
! [SV552: $i,SV505: $i,SV606: $i] :
( ( ( in @ SV606 @ SV505 )
= $false )
| ( ( ~ ( in @ SV606 @ SV552 ) )
= $true )
| ( ( ~ ( disjoint @ SV505 @ SV552 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2858]) ).
thf(2928,plain,
! [SV424: $i,SV631: $i] :
( ( ( ~ ( in @ SV631 @ ( sK35_B @ SV424 ) ) )
= $true )
| ( ( in @ ( powerset @ SV631 ) @ ( sK35_B @ SV424 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2860]) ).
thf(2929,plain,
! [SV424: $i] :
( ( ~ ! [SY672: $i,SY673: $i] :
( ~ ( in @ SY672 @ ( sK35_B @ SV424 ) )
| ~ ( subset @ SY673 @ SY672 )
| ( in @ SY673 @ ( sK35_B @ SV424 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2861]) ).
thf(2930,plain,
! [SV424: $i] :
( ( ~ ( in @ SV424 @ ( sK35_B @ SV424 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2861]) ).
thf(2931,plain,
! [SV425: $i,SV607: $i] :
( ( ( relation @ SV607 )
= $false )
| ( ( ~ ( subset @ SV425 @ SV607 )
| ( subset @ ( relation_dom @ SV425 ) @ ( relation_dom @ SV607 ) ) )
= $true )
| ( ( relation @ SV425 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2862]) ).
thf(2932,plain,
! [SV425: $i,SV608: $i] :
( ( ( relation @ SV608 )
= $false )
| ( ( ~ ( subset @ SV425 @ SV608 )
| ( subset @ ( relation_rng @ SV425 ) @ ( relation_rng @ SV608 ) ) )
= $true )
| ( ( relation @ SV425 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2863]) ).
thf(2933,plain,
! [SV426: $i,SV632: $i] :
( ( ( ~ ( ~ ! [SY863: $i] :
( ~ ( subset @ SY863 @ SV632 )
| ( in @ SY863 @ ( sK2_SY267 @ SV632 @ SV426 ) ) )
| ~ ( in @ ( sK2_SY267 @ SV632 @ SV426 ) @ ( sK1_B @ SV426 ) ) ) )
= $true )
| ( ( ~ ( in @ SV632 @ ( sK1_B @ SV426 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2866]) ).
thf(2934,plain,
! [SV426: $i] :
( ( ~ ! [SY679: $i,SY680: $i] :
( ~ ( in @ SY679 @ ( sK1_B @ SV426 ) )
| ~ ( subset @ SY680 @ SY679 )
| ( in @ SY680 @ ( sK1_B @ SV426 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2867]) ).
thf(2935,plain,
! [SV426: $i] :
( ( ~ ( in @ SV426 @ ( sK1_B @ SV426 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2867]) ).
thf(2936,plain,
! [SV510: $i,SV557: $i] :
( ( ( ~ ( in @ ( sK26_C @ SV557 @ SV510 ) @ SV557 )
| ~ ( subset @ ( sK26_C @ SV557 @ SV510 ) @ SV510 ) )
= $true )
| ( ( SV557
= ( powerset @ SV510 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2868]) ).
thf(2937,plain,
! [SV510: $i,SV557: $i] :
( ( ( ( in @ ( sK26_C @ SV557 @ SV510 ) @ SV557 )
| ( subset @ ( sK26_C @ SV557 @ SV510 ) @ SV510 ) )
= $true )
| ( ( SV557
= ( powerset @ SV510 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2869]) ).
thf(2938,plain,
! [SV511: $i,SV558: $i] :
( ( ( ~ ! [SY791: $i] :
( ~ ( in @ SY791 @ SV558 )
| ( subset @ SY791 @ SV511 ) ) )
= $false )
| ( ( SV558
= ( powerset @ SV511 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2870]) ).
thf(2939,plain,
! [SV558: $i,SV511: $i] :
( ( ( ~ ! [SY792: $i] :
( ~ ( subset @ SY792 @ SV511 )
| ( in @ SY792 @ SV558 ) ) )
= $false )
| ( ( SV558
= ( powerset @ SV511 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2870]) ).
thf(2940,plain,
! [SV610: $i,SV640: $i] :
( ( ( ~ ( element @ SV640 @ SV610 )
| ( in @ SV640 @ SV610 ) )
= $true )
| ( ( empty @ SV610 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2871]) ).
thf(2941,plain,
! [SV611: $i,SV641: $i] :
( ( ( ~ ( in @ SV641 @ SV611 )
| ( element @ SV641 @ SV611 ) )
= $true )
| ( ( empty @ SV611 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2872]) ).
thf(2942,plain,
! [SV612: $i] :
( ( ( empty @ SV612 )
= $false )
| ( ( ! [SY841: $i] :
( ~ ( element @ SY841 @ SV612 )
| ( empty @ SY841 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2873]) ).
thf(2943,plain,
! [SV613: $i] :
( ( ( empty @ SV613 )
= $false )
| ( ( ! [SY842: $i] :
( ~ ( empty @ SY842 )
| ( element @ SY842 @ SV613 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2874]) ).
thf(2944,plain,
! [SV642: $i,SV514: $i] :
( ( ( ! [SY864: $i] :
( ( sK30_B @ SV514 )
!= ( ordered_pair @ SV642 @ SY864 ) ) )
= $true )
| ( ( relation @ SV514 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2876]) ).
thf(2945,plain,
! [SV515: $i,SV614: $i] :
( ( ( in @ SV614 @ SV515 )
= $false )
| ( ( SV614
= ( ordered_pair @ ( sK28_C @ SV614 @ SV515 ) @ ( sK29_SY279 @ SV614 @ SV515 ) ) )
= $true )
| ( ( relation @ SV515 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2878]) ).
thf(2946,plain,
! [SV518: $i,SV563: $i] :
( ( ( subset @ SV563 @ SV518 )
= $false )
| ( ( subset @ SV518 @ SV563 )
= $false )
| ( ( SV518 = SV563 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2879]) ).
thf(2947,plain,
! [SV633: $i,SV615: $i] :
( ( ( ( SV615 != SV633 ) )
= $true )
| ( ( subset @ SV615 @ SV633 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2880]) ).
thf(2948,plain,
! [SV634: $i,SV616: $i] :
( ( ( ( SV616 != SV634 ) )
= $true )
| ( ( subset @ SV634 @ SV616 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2881]) ).
thf(2949,plain,
! [SV427: $i,SV617: $i] :
( ( ( ~ ( ! [SY845: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SV617 @ SV427 ) @ SY845 ) @ SV427 )
| ~ ( in @ ( sK20_C @ SV617 @ SV427 ) @ SV617 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_C @ SV617 @ SV427 ) @ ( sK21_SY278 @ SV617 @ SV427 ) ) @ SV427 )
| ( in @ ( sK20_C @ SV617 @ SV427 ) @ SV617 ) ) )
= $false )
| ( ( SV617
= ( relation_dom @ SV427 ) )
= $true )
| ( ( relation @ SV427 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2882]) ).
thf(2950,plain,
! [SV427: $i,SV618: $i] :
( ( ( SV618
= ( relation_dom @ SV427 ) )
= $false )
| ( ( ~ ( ~ ! [SY846: $i] :
( ! [SY685: $i] :
~ ( in @ ( ordered_pair @ SY846 @ SY685 ) @ SV427 )
| ( in @ SY846 @ SV618 ) )
| ~ ! [SY848: $i] :
( ~ ( in @ SY848 @ SV618 )
| ( in @ ( ordered_pair @ SY848 @ ( sK19_D @ SY848 @ SV618 @ SV427 ) ) @ SV427 ) ) ) )
= $true )
| ( ( relation @ SV427 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2883]) ).
thf(2951,plain,
! [SV428: $i,SV566: $i,SV591: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV428 )
| ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV566 )
| ~ ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV591 ) ) )
= $false )
| ( ( SV591
= ( set_difference @ SV428 @ SV566 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2884]) ).
thf(2952,plain,
! [SV428: $i,SV566: $i,SV591: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV428 )
| ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV591 ) )
| ~ ( ~ ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV566 )
| ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV591 ) ) ) )
= $false )
| ( ( SV591
= ( set_difference @ SV428 @ SV566 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2884]) ).
thf(2953,plain,
! [SV592: $i,SV567: $i,SV428: $i] :
( ( ( ~ ! [SY820: $i] :
( ~ ( in @ SY820 @ SV428 )
| ( in @ SY820 @ SV567 )
| ( in @ SY820 @ SV592 ) )
| ~ ~ ( ~ ! [SY821: $i] :
( ~ ( in @ SY821 @ SV592 )
| ( in @ SY821 @ SV428 ) )
| ~ ! [SY822: $i] :
( ~ ( in @ SY822 @ SV592 )
| ~ ( in @ SY822 @ SV567 ) ) ) )
= $false )
| ( ( SV592
= ( set_difference @ SV428 @ SV567 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2885]) ).
thf(2954,plain,
! [SV429: $i,SV570: $i,SV593: $i] :
( ( ( ~ ( ~ ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV429 )
| ~ ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV570 )
| ~ ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV593 ) ) )
= $false )
| ( ( SV593
= ( set_intersection2 @ SV429 @ SV570 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2886]) ).
thf(2955,plain,
! [SV429: $i,SV570: $i,SV593: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV429 )
| ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV593 ) )
| ~ ( ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV570 )
| ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV593 ) ) ) )
= $false )
| ( ( SV593
= ( set_intersection2 @ SV429 @ SV570 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2886]) ).
thf(2956,plain,
! [SV594: $i,SV571: $i,SV429: $i] :
( ( ( ~ ! [SY823: $i] :
( ~ ( in @ SY823 @ SV429 )
| ~ ( in @ SY823 @ SV571 )
| ( in @ SY823 @ SV594 ) )
| ~ ~ ( ~ ! [SY824: $i] :
( ~ ( in @ SY824 @ SV594 )
| ( in @ SY824 @ SV429 ) )
| ~ ! [SY825: $i] :
( ~ ( in @ SY825 @ SV594 )
| ( in @ SY825 @ SV571 ) ) ) )
= $false )
| ( ( SV594
= ( set_intersection2 @ SV429 @ SV571 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2887]) ).
thf(2957,plain,
! [SV430: $i,SV619: $i] :
( ( ( ~ ( ! [SY849: $i] :
~ ( in @ ( ordered_pair @ SY849 @ ( sK13_C @ SV619 @ SV430 ) ) @ SV430 )
| ~ ( in @ ( sK13_C @ SV619 @ SV430 ) @ SV619 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_SY274 @ SV619 @ SV430 ) @ ( sK13_C @ SV619 @ SV430 ) ) @ SV430 )
| ( in @ ( sK13_C @ SV619 @ SV430 ) @ SV619 ) ) )
= $false )
| ( ( SV619
= ( relation_rng @ SV430 ) )
= $true )
| ( ( relation @ SV430 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2888]) ).
thf(2958,plain,
! [SV430: $i,SV620: $i] :
( ( ( SV620
= ( relation_rng @ SV430 ) )
= $false )
| ( ( ~ ( ~ ! [SY850: $i] :
( ! [SY705: $i] :
~ ( in @ ( ordered_pair @ SY705 @ SY850 ) @ SV430 )
| ( in @ SY850 @ SV620 ) )
| ~ ! [SY852: $i] :
( ~ ( in @ SY852 @ SV620 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY852 @ SV620 @ SV430 ) @ SY852 ) @ SV430 ) ) ) )
= $true )
| ( ( relation @ SV430 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2889]) ).
thf(2959,plain,
! [SV525: $i,SV572: $i] :
( ( ( ! [SY803: $i] :
( ~ ( in @ ( sK17_C @ SV572 @ SV525 ) @ SY803 )
| ~ ( in @ SY803 @ SV525 ) )
| ~ ( in @ ( sK17_C @ SV572 @ SV525 ) @ SV572 ) )
= $true )
| ( ( SV572
= ( union @ SV525 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2890]) ).
thf(2960,plain,
! [SV525: $i,SV572: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_C @ SV572 @ SV525 ) @ ( sK18_SY276 @ SV572 @ SV525 ) )
| ~ ( in @ ( sK18_SY276 @ SV572 @ SV525 ) @ SV525 ) )
| ( in @ ( sK17_C @ SV572 @ SV525 ) @ SV572 ) )
= $true )
| ( ( SV572
= ( union @ SV525 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2891]) ).
thf(2961,plain,
! [SV573: $i,SV526: $i] :
( ( ( ~ ! [SY804: $i] :
( ! [SY768: $i] :
( ~ ( in @ SY804 @ SY768 )
| ~ ( in @ SY768 @ SV526 ) )
| ( in @ SY804 @ SV573 ) ) )
= $false )
| ( ( SV573
= ( union @ SV526 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2892]) ).
thf(2962,plain,
! [SV526: $i,SV573: $i] :
( ( ( ~ ! [SY806: $i] :
( ~ ( in @ SY806 @ SV573 )
| ~ ( ~ ( in @ SY806 @ ( sK16_D @ SY806 @ SV573 @ SV526 ) )
| ~ ( in @ ( sK16_D @ SY806 @ SV573 @ SV526 ) @ SV526 ) ) ) )
= $false )
| ( ( SV573
= ( union @ SV526 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2892]) ).
thf(2963,plain,
! [SV529: $i,SV576: $i] :
( ( ( in @ ( sK23_C @ SV576 @ SV529 ) @ SV529 )
= $true )
| ( ( subset @ SV529 @ SV576 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2893]) ).
thf(2964,plain,
! [SV529: $i,SV576: $i] :
( ( ( ~ ( in @ ( sK23_C @ SV576 @ SV529 ) @ SV576 ) )
= $true )
| ( ( subset @ SV529 @ SV576 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2894]) ).
thf(2965,plain,
! [SV577: $i,SV530: $i,SV635: $i] :
( ( ( ~ ( in @ SV635 @ SV530 ) )
= $true )
| ( ( in @ SV635 @ SV577 )
= $true )
| ( ( subset @ SV530 @ SV577 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2895]) ).
thf(2966,plain,
! [SV433: $i,SV580: $i,SV595: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK25_D @ SV595 @ SV580 @ SV433 ) @ SV595 )
| ( ( sK25_D @ SV595 @ SV580 @ SV433 )
!= SV433 ) )
| ~ ( ~ ( in @ ( sK25_D @ SV595 @ SV580 @ SV433 ) @ SV595 )
| ( ( sK25_D @ SV595 @ SV580 @ SV433 )
!= SV580 ) ) ) )
= $false )
| ( ( SV595
= ( unordered_pair @ SV433 @ SV580 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2896]) ).
thf(2967,plain,
! [SV433: $i,SV580: $i,SV595: $i] :
( ( ( ~ ( ( in @ ( sK25_D @ SV595 @ SV580 @ SV433 ) @ SV595 )
| ( ( sK25_D @ SV595 @ SV580 @ SV433 )
= SV433 )
| ( ( sK25_D @ SV595 @ SV580 @ SV433 )
= SV580 ) ) )
= $false )
| ( ( SV595
= ( unordered_pair @ SV433 @ SV580 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2896]) ).
thf(2968,plain,
! [SV581: $i,SV433: $i,SV596: $i] :
( ( ( ~ ! [SY826: $i] :
( ~ ( in @ SY826 @ SV596 )
| ( SY826 = SV433 )
| ( SY826 = SV581 ) )
| ~ ~ ( ~ ! [SY827: $i] :
( ( SY827 != SV433 )
| ( in @ SY827 @ SV596 ) )
| ~ ! [SY828: $i] :
( ( SY828 != SV581 )
| ( in @ SY828 @ SV596 ) ) ) )
= $false )
| ( ( SV596
= ( unordered_pair @ SV433 @ SV581 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2897]) ).
thf(2969,plain,
! [SV621: $i,SV643: $i] :
( ( ( ~ ( ~ ( ~ ( ~ ( in @ ( sK40_SY287 @ SV643 @ SV621 ) @ SV621 )
| ~ ~ ( in @ ( sK39_C @ SV643 @ SV621 ) @ ( sK40_SY287 @ SV643 @ SV621 ) ) )
| ~ ( in @ ( sK39_C @ SV643 @ SV621 ) @ SV643 ) )
| ~ ( ! [SY865: $i] :
( ~ ( in @ SY865 @ SV621 )
| ( in @ ( sK39_C @ SV643 @ SV621 ) @ SY865 ) )
| ( in @ ( sK39_C @ SV643 @ SV621 ) @ SV643 ) ) )
| ( SV643
= ( set_meet @ SV621 ) ) )
= $true )
| ( ( SV621 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2898]) ).
thf(2970,plain,
! [SV622: $i,SV644: $i] :
( ( ( ( SV644
!= ( set_meet @ SV622 ) )
| ~ ( ~ ! [SY866: $i] :
( ~ ( ~ ( in @ ( sK38_D @ SY866 @ SV644 @ SV622 ) @ SV622 )
| ~ ~ ( in @ SY866 @ ( sK38_D @ SY866 @ SV644 @ SV622 ) ) )
| ( in @ SY866 @ SV644 ) )
| ~ ! [SY867: $i] :
( ~ ( in @ SY867 @ SV644 )
| ! [SY858: $i] :
( ~ ( in @ SY858 @ SV622 )
| ( in @ SY867 @ SY858 ) ) ) ) )
= $true )
| ( ( SV622 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2899]) ).
thf(2971,plain,
! [SV623: $i] :
( ( ( SV623 = empty_set )
= $false )
| ( ( ! [SY859: $i] :
( ( SY859
!= ( set_meet @ SV623 ) )
| ( SY859 = empty_set ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2900]) ).
thf(2972,plain,
! [SV624: $i] :
( ( ( SV624 = empty_set )
= $false )
| ( ( ! [SY860: $i] :
( ( SY860 != empty_set )
| ( SY860
= ( set_meet @ SV624 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2901]) ).
thf(2973,plain,
! [SV533: $i,SV582: $i] :
( ( ( ( ( sK27_C @ SV582 @ SV533 )
!= SV533 )
| ~ ( in @ ( sK27_C @ SV582 @ SV533 ) @ SV582 ) )
= $true )
| ( ( SV582
= ( singleton @ SV533 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2902]) ).
thf(2974,plain,
! [SV533: $i,SV582: $i] :
( ( ( ( ( sK27_C @ SV582 @ SV533 )
= SV533 )
| ( in @ ( sK27_C @ SV582 @ SV533 ) @ SV582 ) )
= $true )
| ( ( SV582
= ( singleton @ SV533 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2903]) ).
thf(2975,plain,
! [SV583: $i,SV534: $i] :
( ( ( ~ ! [SY813: $i] :
( ( SY813 != SV534 )
| ( in @ SY813 @ SV583 ) ) )
= $false )
| ( ( SV583
= ( singleton @ SV534 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2904]) ).
thf(2976,plain,
! [SV534: $i,SV583: $i] :
( ( ( ~ ! [SY814: $i] :
( ~ ( in @ SY814 @ SV583 )
| ( SY814 = SV534 ) ) )
= $false )
| ( ( SV583
= ( singleton @ SV534 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2904]) ).
thf(2977,plain,
! [SV419: $i,SV586: $i,SV539: $i] :
( ( ( in @ SV539 @ SV586 )
= $false )
| ( ( in @ SV419 @ SV586 )
= $false )
| ( ( subset @ ( unordered_pair @ SV419 @ SV539 ) @ SV586 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2907]) ).
thf(2978,plain,
! [SV638: $i,SV625: $i,SV419: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV419 @ SV625 ) @ SV638 ) )
= $true )
| ( ( in @ SV419 @ SV638 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2908]) ).
thf(2979,plain,
! [SV639: $i,SV626: $i,SV419: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV419 @ SV626 ) @ SV639 ) )
= $true )
| ( ( in @ SV626 @ SV639 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2909]) ).
thf(2980,plain,
! [SV420: $i,SV597: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SV597 @ SV420 ) @ ( sK11_SY272 @ SV597 @ SV420 ) ) @ SV597 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY272 @ SV597 @ SV420 ) @ ( sK10_C @ SV597 @ SV420 ) ) @ SV420 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK10_C @ SV597 @ SV420 ) @ ( sK11_SY272 @ SV597 @ SV420 ) ) @ SV597 )
| ( in @ ( ordered_pair @ ( sK11_SY272 @ SV597 @ SV420 ) @ ( sK10_C @ SV597 @ SV420 ) ) @ SV420 ) ) ) )
= $true )
| ( ( SV597
= ( relation_inverse @ SV420 ) )
= $true )
| ( ( relation @ SV597 )
= $false )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2910]) ).
thf(2981,plain,
! [SV420: $i,SV598: $i] :
( ( ( ( SV598
!= ( relation_inverse @ SV420 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY829: $i,SY830: $i] :
( ~ ( in @ ( ordered_pair @ SY829 @ SY830 ) @ SV598 )
| ( in @ ( ordered_pair @ SY830 @ SY829 ) @ SV420 ) )
| ~ ! [SY831: $i,SY832: $i] :
( ~ ( in @ ( ordered_pair @ SY832 @ SY831 ) @ SV420 )
| ( in @ ( ordered_pair @ SY831 @ SY832 ) @ SV598 ) ) ) )
= $true )
| ( ( relation @ SV598 )
= $false )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2911]) ).
thf(2982,plain,
! [SV587: $i,SV542: $i,SV422: $i] :
( ( ( in @ ( ordered_pair @ SV422 @ SV542 ) @ SV587 )
= $false )
| ( ( in @ SV422 @ ( relation_dom @ SV587 ) )
= $true )
| ( ( relation @ SV587 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2914]) ).
thf(2983,plain,
! [SV588: $i,SV543: $i,SV422: $i] :
( ( ( in @ ( ordered_pair @ SV422 @ SV543 ) @ SV588 )
= $false )
| ( ( in @ SV543 @ ( relation_rng @ SV588 ) )
= $true )
| ( ( relation @ SV588 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2915]) ).
thf(2984,plain,
! [SV645: $i,SV600: $i] :
( ( ( subset @ SV600 @ ( singleton @ SV645 ) )
= $true )
| ( ( SV600 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2916]) ).
thf(2985,plain,
! [SV627: $i,SV601: $i] :
( ( ( SV601
= ( singleton @ SV627 ) )
= $false )
| ( ( subset @ SV601 @ ( singleton @ SV627 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2917]) ).
thf(2986,plain,
! [SV423: $i,SV547: $i,SV589: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV589 )
| ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV423 ) )
| ~ ( ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV589 )
| ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV547 ) ) ) )
= $true )
| ( ( SV589
= ( set_union2 @ SV423 @ SV547 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2918]) ).
thf(2987,plain,
! [SV423: $i,SV547: $i,SV589: $i] :
( ( ( ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV589 )
| ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV423 )
| ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV547 ) )
= $true )
| ( ( SV589
= ( set_union2 @ SV423 @ SV547 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2919]) ).
thf(2988,plain,
! [SV548: $i,SV423: $i,SV590: $i] :
( ( ( ~ ! [SY817: $i] :
( ~ ( in @ SY817 @ SV590 )
| ( in @ SY817 @ SV423 )
| ( in @ SY817 @ SV548 ) ) )
= $false )
| ( ( SV590
= ( set_union2 @ SV423 @ SV548 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2920]) ).
thf(2989,plain,
! [SV548: $i,SV590: $i,SV423: $i] :
( ( ( ~ ~ ( ~ ! [SY818: $i] :
( ~ ( in @ SY818 @ SV423 )
| ( in @ SY818 @ SV590 ) )
| ~ ! [SY819: $i] :
( ~ ( in @ SY819 @ SV548 )
| ( in @ SY819 @ SV590 ) ) ) )
= $false )
| ( ( SV590
= ( set_union2 @ SV423 @ SV548 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2920]) ).
thf(2990,plain,
! [SV646: $i,SV602: $i] :
( ( ( subset @ SV602 @ ( singleton @ SV646 ) )
= $true )
| ( ( SV602 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2921]) ).
thf(2991,plain,
! [SV628: $i,SV603: $i] :
( ( ( SV603
= ( singleton @ SV628 ) )
= $false )
| ( ( subset @ SV603 @ ( singleton @ SV628 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2922]) ).
thf(2992,plain,
! [SV629: $i,SV604: $i] :
( ( ( proper_subset @ SV604 @ SV629 )
= $false )
| ( ( ( SV604 != SV629 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2923]) ).
thf(2993,plain,
! [SV630: $i,SV605: $i] :
( ( ( proper_subset @ SV605 @ SV630 )
= $false )
| ( ( subset @ SV605 @ SV630 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2924]) ).
thf(2994,plain,
! [SV505: $i,SV552: $i,SV606: $i] :
( ( ( in @ SV606 @ SV552 )
= $false )
| ( ( in @ SV606 @ SV505 )
= $false )
| ( ( ~ ( disjoint @ SV505 @ SV552 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2927]) ).
thf(2995,plain,
! [SV424: $i,SV631: $i] :
( ( ( in @ SV631 @ ( sK35_B @ SV424 ) )
= $false )
| ( ( in @ ( powerset @ SV631 ) @ ( sK35_B @ SV424 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2928]) ).
thf(2996,plain,
! [SV424: $i] :
( ( ! [SY672: $i,SY673: $i] :
( ~ ( in @ SY672 @ ( sK35_B @ SV424 ) )
| ~ ( subset @ SY673 @ SY672 )
| ( in @ SY673 @ ( sK35_B @ SV424 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2929]) ).
thf(2997,plain,
! [SV424: $i] :
( ( in @ SV424 @ ( sK35_B @ SV424 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2930]) ).
thf(2998,plain,
! [SV607: $i,SV425: $i] :
( ( ( ~ ( subset @ SV425 @ SV607 ) )
= $true )
| ( ( subset @ ( relation_dom @ SV425 ) @ ( relation_dom @ SV607 ) )
= $true )
| ( ( relation @ SV607 )
= $false )
| ( ( relation @ SV425 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2931]) ).
thf(2999,plain,
! [SV608: $i,SV425: $i] :
( ( ( ~ ( subset @ SV425 @ SV608 ) )
= $true )
| ( ( subset @ ( relation_rng @ SV425 ) @ ( relation_rng @ SV608 ) )
= $true )
| ( ( relation @ SV608 )
= $false )
| ( ( relation @ SV425 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2932]) ).
thf(3000,plain,
! [SV426: $i,SV632: $i] :
( ( ( ~ ! [SY863: $i] :
( ~ ( subset @ SY863 @ SV632 )
| ( in @ SY863 @ ( sK2_SY267 @ SV632 @ SV426 ) ) )
| ~ ( in @ ( sK2_SY267 @ SV632 @ SV426 ) @ ( sK1_B @ SV426 ) ) )
= $false )
| ( ( ~ ( in @ SV632 @ ( sK1_B @ SV426 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2933]) ).
thf(3001,plain,
! [SV426: $i] :
( ( ! [SY679: $i,SY680: $i] :
( ~ ( in @ SY679 @ ( sK1_B @ SV426 ) )
| ~ ( subset @ SY680 @ SY679 )
| ( in @ SY680 @ ( sK1_B @ SV426 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2934]) ).
thf(3002,plain,
! [SV426: $i] :
( ( in @ SV426 @ ( sK1_B @ SV426 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2935]) ).
thf(3003,plain,
! [SV510: $i,SV557: $i] :
( ( ( ~ ( in @ ( sK26_C @ SV557 @ SV510 ) @ SV557 ) )
= $true )
| ( ( ~ ( subset @ ( sK26_C @ SV557 @ SV510 ) @ SV510 ) )
= $true )
| ( ( SV557
= ( powerset @ SV510 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2936]) ).
thf(3004,plain,
! [SV510: $i,SV557: $i] :
( ( ( in @ ( sK26_C @ SV557 @ SV510 ) @ SV557 )
= $true )
| ( ( subset @ ( sK26_C @ SV557 @ SV510 ) @ SV510 )
= $true )
| ( ( SV557
= ( powerset @ SV510 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2937]) ).
thf(3005,plain,
! [SV511: $i,SV558: $i] :
( ( ( ! [SY791: $i] :
( ~ ( in @ SY791 @ SV558 )
| ( subset @ SY791 @ SV511 ) ) )
= $true )
| ( ( SV558
= ( powerset @ SV511 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2938]) ).
thf(3006,plain,
! [SV558: $i,SV511: $i] :
( ( ( ! [SY792: $i] :
( ~ ( subset @ SY792 @ SV511 )
| ( in @ SY792 @ SV558 ) ) )
= $true )
| ( ( SV558
= ( powerset @ SV511 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2939]) ).
thf(3007,plain,
! [SV610: $i,SV640: $i] :
( ( ( ~ ( element @ SV640 @ SV610 ) )
= $true )
| ( ( in @ SV640 @ SV610 )
= $true )
| ( ( empty @ SV610 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2940]) ).
thf(3008,plain,
! [SV611: $i,SV641: $i] :
( ( ( ~ ( in @ SV641 @ SV611 ) )
= $true )
| ( ( element @ SV641 @ SV611 )
= $true )
| ( ( empty @ SV611 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2941]) ).
thf(3009,plain,
! [SV612: $i,SV647: $i] :
( ( ( ~ ( element @ SV647 @ SV612 )
| ( empty @ SV647 ) )
= $true )
| ( ( empty @ SV612 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2942]) ).
thf(3010,plain,
! [SV613: $i,SV648: $i] :
( ( ( ~ ( empty @ SV648 )
| ( element @ SV648 @ SV613 ) )
= $true )
| ( ( empty @ SV613 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2943]) ).
thf(3011,plain,
! [SV649: $i,SV642: $i,SV514: $i] :
( ( ( ( ( sK30_B @ SV514 )
!= ( ordered_pair @ SV642 @ SV649 ) ) )
= $true )
| ( ( relation @ SV514 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2944]) ).
thf(3012,plain,
! [SV633: $i,SV615: $i] :
( ( ( SV615 = SV633 )
= $false )
| ( ( subset @ SV615 @ SV633 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2947]) ).
thf(3013,plain,
! [SV634: $i,SV616: $i] :
( ( ( SV616 = SV634 )
= $false )
| ( ( subset @ SV634 @ SV616 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2948]) ).
thf(3014,plain,
! [SV427: $i,SV617: $i] :
( ( ( ~ ( ! [SY845: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SV617 @ SV427 ) @ SY845 ) @ SV427 )
| ~ ( in @ ( sK20_C @ SV617 @ SV427 ) @ SV617 ) ) )
= $false )
| ( ( SV617
= ( relation_dom @ SV427 ) )
= $true )
| ( ( relation @ SV427 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2949]) ).
thf(3015,plain,
! [SV427: $i,SV617: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK20_C @ SV617 @ SV427 ) @ ( sK21_SY278 @ SV617 @ SV427 ) ) @ SV427 )
| ( in @ ( sK20_C @ SV617 @ SV427 ) @ SV617 ) ) )
= $false )
| ( ( SV617
= ( relation_dom @ SV427 ) )
= $true )
| ( ( relation @ SV427 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2949]) ).
thf(3016,plain,
! [SV618: $i,SV427: $i] :
( ( ( ~ ! [SY846: $i] :
( ! [SY685: $i] :
~ ( in @ ( ordered_pair @ SY846 @ SY685 ) @ SV427 )
| ( in @ SY846 @ SV618 ) )
| ~ ! [SY848: $i] :
( ~ ( in @ SY848 @ SV618 )
| ( in @ ( ordered_pair @ SY848 @ ( sK19_D @ SY848 @ SV618 @ SV427 ) ) @ SV427 ) ) )
= $false )
| ( ( SV618
= ( relation_dom @ SV427 ) )
= $false )
| ( ( relation @ SV427 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2950]) ).
thf(3017,plain,
! [SV428: $i,SV566: $i,SV591: $i] :
( ( ( ~ ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV428 )
| ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV566 )
| ~ ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV591 ) )
= $true )
| ( ( SV591
= ( set_difference @ SV428 @ SV566 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2951]) ).
thf(3018,plain,
! [SV428: $i,SV566: $i,SV591: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV428 )
| ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV591 ) )
| ~ ( ~ ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV566 )
| ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV591 ) ) ) )
= $true )
| ( ( SV591
= ( set_difference @ SV428 @ SV566 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2952]) ).
thf(3019,plain,
! [SV592: $i,SV567: $i,SV428: $i] :
( ( ( ~ ! [SY820: $i] :
( ~ ( in @ SY820 @ SV428 )
| ( in @ SY820 @ SV567 )
| ( in @ SY820 @ SV592 ) ) )
= $false )
| ( ( SV592
= ( set_difference @ SV428 @ SV567 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2953]) ).
thf(3020,plain,
! [SV567: $i,SV428: $i,SV592: $i] :
( ( ( ~ ~ ( ~ ! [SY821: $i] :
( ~ ( in @ SY821 @ SV592 )
| ( in @ SY821 @ SV428 ) )
| ~ ! [SY822: $i] :
( ~ ( in @ SY822 @ SV592 )
| ~ ( in @ SY822 @ SV567 ) ) ) )
= $false )
| ( ( SV592
= ( set_difference @ SV428 @ SV567 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2953]) ).
thf(3021,plain,
! [SV429: $i,SV570: $i,SV593: $i] :
( ( ( ~ ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV429 )
| ~ ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV570 )
| ~ ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV593 ) )
= $true )
| ( ( SV593
= ( set_intersection2 @ SV429 @ SV570 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2954]) ).
thf(3022,plain,
! [SV429: $i,SV570: $i,SV593: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV429 )
| ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV593 ) )
| ~ ( ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV570 )
| ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV593 ) ) ) )
= $true )
| ( ( SV593
= ( set_intersection2 @ SV429 @ SV570 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2955]) ).
thf(3023,plain,
! [SV594: $i,SV571: $i,SV429: $i] :
( ( ( ~ ! [SY823: $i] :
( ~ ( in @ SY823 @ SV429 )
| ~ ( in @ SY823 @ SV571 )
| ( in @ SY823 @ SV594 ) ) )
= $false )
| ( ( SV594
= ( set_intersection2 @ SV429 @ SV571 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2956]) ).
thf(3024,plain,
! [SV571: $i,SV429: $i,SV594: $i] :
( ( ( ~ ~ ( ~ ! [SY824: $i] :
( ~ ( in @ SY824 @ SV594 )
| ( in @ SY824 @ SV429 ) )
| ~ ! [SY825: $i] :
( ~ ( in @ SY825 @ SV594 )
| ( in @ SY825 @ SV571 ) ) ) )
= $false )
| ( ( SV594
= ( set_intersection2 @ SV429 @ SV571 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2956]) ).
thf(3025,plain,
! [SV430: $i,SV619: $i] :
( ( ( ~ ( ! [SY849: $i] :
~ ( in @ ( ordered_pair @ SY849 @ ( sK13_C @ SV619 @ SV430 ) ) @ SV430 )
| ~ ( in @ ( sK13_C @ SV619 @ SV430 ) @ SV619 ) ) )
= $false )
| ( ( SV619
= ( relation_rng @ SV430 ) )
= $true )
| ( ( relation @ SV430 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2957]) ).
thf(3026,plain,
! [SV430: $i,SV619: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK14_SY274 @ SV619 @ SV430 ) @ ( sK13_C @ SV619 @ SV430 ) ) @ SV430 )
| ( in @ ( sK13_C @ SV619 @ SV430 ) @ SV619 ) ) )
= $false )
| ( ( SV619
= ( relation_rng @ SV430 ) )
= $true )
| ( ( relation @ SV430 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2957]) ).
thf(3027,plain,
! [SV620: $i,SV430: $i] :
( ( ( ~ ! [SY850: $i] :
( ! [SY705: $i] :
~ ( in @ ( ordered_pair @ SY705 @ SY850 ) @ SV430 )
| ( in @ SY850 @ SV620 ) )
| ~ ! [SY852: $i] :
( ~ ( in @ SY852 @ SV620 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY852 @ SV620 @ SV430 ) @ SY852 ) @ SV430 ) ) )
= $false )
| ( ( SV620
= ( relation_rng @ SV430 ) )
= $false )
| ( ( relation @ SV430 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2958]) ).
thf(3028,plain,
! [SV525: $i,SV572: $i] :
( ( ( ! [SY803: $i] :
( ~ ( in @ ( sK17_C @ SV572 @ SV525 ) @ SY803 )
| ~ ( in @ SY803 @ SV525 ) ) )
= $true )
| ( ( ~ ( in @ ( sK17_C @ SV572 @ SV525 ) @ SV572 ) )
= $true )
| ( ( SV572
= ( union @ SV525 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2959]) ).
thf(3029,plain,
! [SV525: $i,SV572: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_C @ SV572 @ SV525 ) @ ( sK18_SY276 @ SV572 @ SV525 ) )
| ~ ( in @ ( sK18_SY276 @ SV572 @ SV525 ) @ SV525 ) ) )
= $true )
| ( ( in @ ( sK17_C @ SV572 @ SV525 ) @ SV572 )
= $true )
| ( ( SV572
= ( union @ SV525 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2960]) ).
thf(3030,plain,
! [SV573: $i,SV526: $i] :
( ( ( ! [SY804: $i] :
( ! [SY768: $i] :
( ~ ( in @ SY804 @ SY768 )
| ~ ( in @ SY768 @ SV526 ) )
| ( in @ SY804 @ SV573 ) ) )
= $true )
| ( ( SV573
= ( union @ SV526 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2961]) ).
thf(3031,plain,
! [SV526: $i,SV573: $i] :
( ( ( ! [SY806: $i] :
( ~ ( in @ SY806 @ SV573 )
| ~ ( ~ ( in @ SY806 @ ( sK16_D @ SY806 @ SV573 @ SV526 ) )
| ~ ( in @ ( sK16_D @ SY806 @ SV573 @ SV526 ) @ SV526 ) ) ) )
= $true )
| ( ( SV573
= ( union @ SV526 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2962]) ).
thf(3032,plain,
! [SV529: $i,SV576: $i] :
( ( ( in @ ( sK23_C @ SV576 @ SV529 ) @ SV576 )
= $false )
| ( ( subset @ SV529 @ SV576 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2964]) ).
thf(3033,plain,
! [SV577: $i,SV530: $i,SV635: $i] :
( ( ( in @ SV635 @ SV530 )
= $false )
| ( ( in @ SV635 @ SV577 )
= $true )
| ( ( subset @ SV530 @ SV577 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2965]) ).
thf(3034,plain,
! [SV433: $i,SV580: $i,SV595: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK25_D @ SV595 @ SV580 @ SV433 ) @ SV595 )
| ( ( sK25_D @ SV595 @ SV580 @ SV433 )
!= SV433 ) )
| ~ ( ~ ( in @ ( sK25_D @ SV595 @ SV580 @ SV433 ) @ SV595 )
| ( ( sK25_D @ SV595 @ SV580 @ SV433 )
!= SV580 ) ) ) )
= $true )
| ( ( SV595
= ( unordered_pair @ SV433 @ SV580 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2966]) ).
thf(3035,plain,
! [SV433: $i,SV580: $i,SV595: $i] :
( ( ( ( in @ ( sK25_D @ SV595 @ SV580 @ SV433 ) @ SV595 )
| ( ( sK25_D @ SV595 @ SV580 @ SV433 )
= SV433 )
| ( ( sK25_D @ SV595 @ SV580 @ SV433 )
= SV580 ) )
= $true )
| ( ( SV595
= ( unordered_pair @ SV433 @ SV580 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2967]) ).
thf(3036,plain,
! [SV581: $i,SV433: $i,SV596: $i] :
( ( ( ~ ! [SY826: $i] :
( ~ ( in @ SY826 @ SV596 )
| ( SY826 = SV433 )
| ( SY826 = SV581 ) ) )
= $false )
| ( ( SV596
= ( unordered_pair @ SV433 @ SV581 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2968]) ).
thf(3037,plain,
! [SV581: $i,SV596: $i,SV433: $i] :
( ( ( ~ ~ ( ~ ! [SY827: $i] :
( ( SY827 != SV433 )
| ( in @ SY827 @ SV596 ) )
| ~ ! [SY828: $i] :
( ( SY828 != SV581 )
| ( in @ SY828 @ SV596 ) ) ) )
= $false )
| ( ( SV596
= ( unordered_pair @ SV433 @ SV581 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2968]) ).
thf(3038,plain,
! [SV621: $i,SV643: $i] :
( ( ( ~ ( ~ ( ~ ( ~ ( in @ ( sK40_SY287 @ SV643 @ SV621 ) @ SV621 )
| ~ ~ ( in @ ( sK39_C @ SV643 @ SV621 ) @ ( sK40_SY287 @ SV643 @ SV621 ) ) )
| ~ ( in @ ( sK39_C @ SV643 @ SV621 ) @ SV643 ) )
| ~ ( ! [SY865: $i] :
( ~ ( in @ SY865 @ SV621 )
| ( in @ ( sK39_C @ SV643 @ SV621 ) @ SY865 ) )
| ( in @ ( sK39_C @ SV643 @ SV621 ) @ SV643 ) ) ) )
= $true )
| ( ( SV643
= ( set_meet @ SV621 ) )
= $true )
| ( ( SV621 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2969]) ).
thf(3039,plain,
! [SV622: $i,SV644: $i] :
( ( ( ( SV644
!= ( set_meet @ SV622 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY866: $i] :
( ~ ( ~ ( in @ ( sK38_D @ SY866 @ SV644 @ SV622 ) @ SV622 )
| ~ ~ ( in @ SY866 @ ( sK38_D @ SY866 @ SV644 @ SV622 ) ) )
| ( in @ SY866 @ SV644 ) )
| ~ ! [SY867: $i] :
( ~ ( in @ SY867 @ SV644 )
| ! [SY858: $i] :
( ~ ( in @ SY858 @ SV622 )
| ( in @ SY867 @ SY858 ) ) ) ) )
= $true )
| ( ( SV622 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2970]) ).
thf(3040,plain,
! [SV623: $i,SV650: $i] :
( ( ( ( SV650
!= ( set_meet @ SV623 ) )
| ( SV650 = empty_set ) )
= $true )
| ( ( SV623 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2971]) ).
thf(3041,plain,
! [SV624: $i,SV651: $i] :
( ( ( ( SV651 != empty_set )
| ( SV651
= ( set_meet @ SV624 ) ) )
= $true )
| ( ( SV624 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2972]) ).
thf(3042,plain,
! [SV533: $i,SV582: $i] :
( ( ( ( ( sK27_C @ SV582 @ SV533 )
!= SV533 ) )
= $true )
| ( ( ~ ( in @ ( sK27_C @ SV582 @ SV533 ) @ SV582 ) )
= $true )
| ( ( SV582
= ( singleton @ SV533 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2973]) ).
thf(3043,plain,
! [SV533: $i,SV582: $i] :
( ( ( ( sK27_C @ SV582 @ SV533 )
= SV533 )
= $true )
| ( ( in @ ( sK27_C @ SV582 @ SV533 ) @ SV582 )
= $true )
| ( ( SV582
= ( singleton @ SV533 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2974]) ).
thf(3044,plain,
! [SV583: $i,SV534: $i] :
( ( ( ! [SY813: $i] :
( ( SY813 != SV534 )
| ( in @ SY813 @ SV583 ) ) )
= $true )
| ( ( SV583
= ( singleton @ SV534 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2975]) ).
thf(3045,plain,
! [SV534: $i,SV583: $i] :
( ( ( ! [SY814: $i] :
( ~ ( in @ SY814 @ SV583 )
| ( SY814 = SV534 ) ) )
= $true )
| ( ( SV583
= ( singleton @ SV534 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2976]) ).
thf(3046,plain,
! [SV638: $i,SV625: $i,SV419: $i] :
( ( ( subset @ ( unordered_pair @ SV419 @ SV625 ) @ SV638 )
= $false )
| ( ( in @ SV419 @ SV638 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2978]) ).
thf(3047,plain,
! [SV639: $i,SV626: $i,SV419: $i] :
( ( ( subset @ ( unordered_pair @ SV419 @ SV626 ) @ SV639 )
= $false )
| ( ( in @ SV626 @ SV639 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2979]) ).
thf(3048,plain,
! [SV420: $i,SV597: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SV597 @ SV420 ) @ ( sK11_SY272 @ SV597 @ SV420 ) ) @ SV597 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY272 @ SV597 @ SV420 ) @ ( sK10_C @ SV597 @ SV420 ) ) @ SV420 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK10_C @ SV597 @ SV420 ) @ ( sK11_SY272 @ SV597 @ SV420 ) ) @ SV597 )
| ( in @ ( ordered_pair @ ( sK11_SY272 @ SV597 @ SV420 ) @ ( sK10_C @ SV597 @ SV420 ) ) @ SV420 ) ) )
= $false )
| ( ( SV597
= ( relation_inverse @ SV420 ) )
= $true )
| ( ( relation @ SV597 )
= $false )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2980]) ).
thf(3049,plain,
! [SV420: $i,SV598: $i] :
( ( ( SV598
= ( relation_inverse @ SV420 ) )
= $false )
| ( ( ~ ( ~ ! [SY829: $i,SY830: $i] :
( ~ ( in @ ( ordered_pair @ SY829 @ SY830 ) @ SV598 )
| ( in @ ( ordered_pair @ SY830 @ SY829 ) @ SV420 ) )
| ~ ! [SY831: $i,SY832: $i] :
( ~ ( in @ ( ordered_pair @ SY832 @ SY831 ) @ SV420 )
| ( in @ ( ordered_pair @ SY831 @ SY832 ) @ SV598 ) ) ) )
= $true )
| ( ( relation @ SV598 )
= $false )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2981]) ).
thf(3050,plain,
! [SV423: $i,SV547: $i,SV589: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV589 )
| ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV423 ) )
| ~ ( ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV589 )
| ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV547 ) ) )
= $false )
| ( ( SV589
= ( set_union2 @ SV423 @ SV547 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2986]) ).
thf(3051,plain,
! [SV423: $i,SV547: $i,SV589: $i] :
( ( ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV589 )
= $true )
| ( ( ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV423 )
| ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV547 ) )
= $true )
| ( ( SV589
= ( set_union2 @ SV423 @ SV547 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2987]) ).
thf(3052,plain,
! [SV548: $i,SV423: $i,SV590: $i] :
( ( ( ! [SY817: $i] :
( ~ ( in @ SY817 @ SV590 )
| ( in @ SY817 @ SV423 )
| ( in @ SY817 @ SV548 ) ) )
= $true )
| ( ( SV590
= ( set_union2 @ SV423 @ SV548 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2988]) ).
thf(3053,plain,
! [SV548: $i,SV590: $i,SV423: $i] :
( ( ( ~ ( ~ ! [SY818: $i] :
( ~ ( in @ SY818 @ SV423 )
| ( in @ SY818 @ SV590 ) )
| ~ ! [SY819: $i] :
( ~ ( in @ SY819 @ SV548 )
| ( in @ SY819 @ SV590 ) ) ) )
= $true )
| ( ( SV590
= ( set_union2 @ SV423 @ SV548 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2989]) ).
thf(3054,plain,
! [SV629: $i,SV604: $i] :
( ( ( SV604 = SV629 )
= $false )
| ( ( proper_subset @ SV604 @ SV629 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2992]) ).
thf(3055,plain,
! [SV606: $i,SV552: $i,SV505: $i] :
( ( ( disjoint @ SV505 @ SV552 )
= $false )
| ( ( in @ SV606 @ SV505 )
= $false )
| ( ( in @ SV606 @ SV552 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2994]) ).
thf(3056,plain,
! [SV424: $i,SV652: $i] :
( ( ! [SY869: $i] :
( ~ ( in @ SV652 @ ( sK35_B @ SV424 ) )
| ~ ( subset @ SY869 @ SV652 )
| ( in @ SY869 @ ( sK35_B @ SV424 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2996]) ).
thf(3057,plain,
! [SV607: $i,SV425: $i] :
( ( ( subset @ SV425 @ SV607 )
= $false )
| ( ( subset @ ( relation_dom @ SV425 ) @ ( relation_dom @ SV607 ) )
= $true )
| ( ( relation @ SV607 )
= $false )
| ( ( relation @ SV425 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2998]) ).
thf(3058,plain,
! [SV608: $i,SV425: $i] :
( ( ( subset @ SV425 @ SV608 )
= $false )
| ( ( subset @ ( relation_rng @ SV425 ) @ ( relation_rng @ SV608 ) )
= $true )
| ( ( relation @ SV608 )
= $false )
| ( ( relation @ SV425 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2999]) ).
thf(3059,plain,
! [SV426: $i,SV632: $i] :
( ( ( ~ ! [SY863: $i] :
( ~ ( subset @ SY863 @ SV632 )
| ( in @ SY863 @ ( sK2_SY267 @ SV632 @ SV426 ) ) ) )
= $false )
| ( ( ~ ( in @ SV632 @ ( sK1_B @ SV426 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3000]) ).
thf(3060,plain,
! [SV426: $i,SV632: $i] :
( ( ( ~ ( in @ ( sK2_SY267 @ SV632 @ SV426 ) @ ( sK1_B @ SV426 ) ) )
= $false )
| ( ( ~ ( in @ SV632 @ ( sK1_B @ SV426 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3000]) ).
thf(3061,plain,
! [SV426: $i,SV653: $i] :
( ( ! [SY870: $i] :
( ~ ( in @ SV653 @ ( sK1_B @ SV426 ) )
| ~ ( subset @ SY870 @ SV653 )
| ( in @ SY870 @ ( sK1_B @ SV426 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3001]) ).
thf(3062,plain,
! [SV510: $i,SV557: $i] :
( ( ( in @ ( sK26_C @ SV557 @ SV510 ) @ SV557 )
= $false )
| ( ( ~ ( subset @ ( sK26_C @ SV557 @ SV510 ) @ SV510 ) )
= $true )
| ( ( SV557
= ( powerset @ SV510 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3003]) ).
thf(3063,plain,
! [SV511: $i,SV558: $i,SV654: $i] :
( ( ( ~ ( in @ SV654 @ SV558 )
| ( subset @ SV654 @ SV511 ) )
= $true )
| ( ( SV558
= ( powerset @ SV511 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3005]) ).
thf(3064,plain,
! [SV558: $i,SV511: $i,SV655: $i] :
( ( ( ~ ( subset @ SV655 @ SV511 )
| ( in @ SV655 @ SV558 ) )
= $true )
| ( ( SV558
= ( powerset @ SV511 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3006]) ).
thf(3065,plain,
! [SV610: $i,SV640: $i] :
( ( ( element @ SV640 @ SV610 )
= $false )
| ( ( in @ SV640 @ SV610 )
= $true )
| ( ( empty @ SV610 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3007]) ).
thf(3066,plain,
! [SV611: $i,SV641: $i] :
( ( ( in @ SV641 @ SV611 )
= $false )
| ( ( element @ SV641 @ SV611 )
= $true )
| ( ( empty @ SV611 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3008]) ).
thf(3067,plain,
! [SV612: $i,SV647: $i] :
( ( ( ~ ( element @ SV647 @ SV612 ) )
= $true )
| ( ( empty @ SV647 )
= $true )
| ( ( empty @ SV612 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3009]) ).
thf(3068,plain,
! [SV613: $i,SV648: $i] :
( ( ( ~ ( empty @ SV648 ) )
= $true )
| ( ( element @ SV648 @ SV613 )
= $true )
| ( ( empty @ SV613 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3010]) ).
thf(3069,plain,
! [SV649: $i,SV642: $i,SV514: $i] :
( ( ( ( sK30_B @ SV514 )
= ( ordered_pair @ SV642 @ SV649 ) )
= $false )
| ( ( relation @ SV514 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3011]) ).
thf(3070,plain,
! [SV427: $i,SV617: $i] :
( ( ( ! [SY845: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SV617 @ SV427 ) @ SY845 ) @ SV427 )
| ~ ( in @ ( sK20_C @ SV617 @ SV427 ) @ SV617 ) )
= $true )
| ( ( SV617
= ( relation_dom @ SV427 ) )
= $true )
| ( ( relation @ SV427 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3014]) ).
thf(3071,plain,
! [SV427: $i,SV617: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK20_C @ SV617 @ SV427 ) @ ( sK21_SY278 @ SV617 @ SV427 ) ) @ SV427 )
| ( in @ ( sK20_C @ SV617 @ SV427 ) @ SV617 ) )
= $true )
| ( ( SV617
= ( relation_dom @ SV427 ) )
= $true )
| ( ( relation @ SV427 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3015]) ).
thf(3072,plain,
! [SV618: $i,SV427: $i] :
( ( ( ~ ! [SY846: $i] :
( ! [SY685: $i] :
~ ( in @ ( ordered_pair @ SY846 @ SY685 ) @ SV427 )
| ( in @ SY846 @ SV618 ) ) )
= $false )
| ( ( SV618
= ( relation_dom @ SV427 ) )
= $false )
| ( ( relation @ SV427 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3016]) ).
thf(3073,plain,
! [SV427: $i,SV618: $i] :
( ( ( ~ ! [SY848: $i] :
( ~ ( in @ SY848 @ SV618 )
| ( in @ ( ordered_pair @ SY848 @ ( sK19_D @ SY848 @ SV618 @ SV427 ) ) @ SV427 ) ) )
= $false )
| ( ( SV618
= ( relation_dom @ SV427 ) )
= $false )
| ( ( relation @ SV427 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3016]) ).
thf(3074,plain,
! [SV428: $i,SV566: $i,SV591: $i] :
( ( ( ~ ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV428 )
| ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV566 ) )
= $true )
| ( ( ~ ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV591 ) )
= $true )
| ( ( SV591
= ( set_difference @ SV428 @ SV566 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3017]) ).
thf(3075,plain,
! [SV428: $i,SV566: $i,SV591: $i] :
( ( ( ~ ( ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV428 )
| ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV591 ) )
| ~ ( ~ ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV566 )
| ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV591 ) ) )
= $false )
| ( ( SV591
= ( set_difference @ SV428 @ SV566 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3018]) ).
thf(3076,plain,
! [SV592: $i,SV567: $i,SV428: $i] :
( ( ( ! [SY820: $i] :
( ~ ( in @ SY820 @ SV428 )
| ( in @ SY820 @ SV567 )
| ( in @ SY820 @ SV592 ) ) )
= $true )
| ( ( SV592
= ( set_difference @ SV428 @ SV567 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3019]) ).
thf(3077,plain,
! [SV567: $i,SV428: $i,SV592: $i] :
( ( ( ~ ( ~ ! [SY821: $i] :
( ~ ( in @ SY821 @ SV592 )
| ( in @ SY821 @ SV428 ) )
| ~ ! [SY822: $i] :
( ~ ( in @ SY822 @ SV592 )
| ~ ( in @ SY822 @ SV567 ) ) ) )
= $true )
| ( ( SV592
= ( set_difference @ SV428 @ SV567 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3020]) ).
thf(3078,plain,
! [SV429: $i,SV570: $i,SV593: $i] :
( ( ( ~ ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV429 )
| ~ ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV570 ) )
= $true )
| ( ( ~ ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV593 ) )
= $true )
| ( ( SV593
= ( set_intersection2 @ SV429 @ SV570 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3021]) ).
thf(3079,plain,
! [SV429: $i,SV570: $i,SV593: $i] :
( ( ( ~ ( ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV429 )
| ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV593 ) )
| ~ ( ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV570 )
| ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV593 ) ) )
= $false )
| ( ( SV593
= ( set_intersection2 @ SV429 @ SV570 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3022]) ).
thf(3080,plain,
! [SV594: $i,SV571: $i,SV429: $i] :
( ( ( ! [SY823: $i] :
( ~ ( in @ SY823 @ SV429 )
| ~ ( in @ SY823 @ SV571 )
| ( in @ SY823 @ SV594 ) ) )
= $true )
| ( ( SV594
= ( set_intersection2 @ SV429 @ SV571 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3023]) ).
thf(3081,plain,
! [SV571: $i,SV429: $i,SV594: $i] :
( ( ( ~ ( ~ ! [SY824: $i] :
( ~ ( in @ SY824 @ SV594 )
| ( in @ SY824 @ SV429 ) )
| ~ ! [SY825: $i] :
( ~ ( in @ SY825 @ SV594 )
| ( in @ SY825 @ SV571 ) ) ) )
= $true )
| ( ( SV594
= ( set_intersection2 @ SV429 @ SV571 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3024]) ).
thf(3082,plain,
! [SV430: $i,SV619: $i] :
( ( ( ! [SY849: $i] :
~ ( in @ ( ordered_pair @ SY849 @ ( sK13_C @ SV619 @ SV430 ) ) @ SV430 )
| ~ ( in @ ( sK13_C @ SV619 @ SV430 ) @ SV619 ) )
= $true )
| ( ( SV619
= ( relation_rng @ SV430 ) )
= $true )
| ( ( relation @ SV430 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3025]) ).
thf(3083,plain,
! [SV430: $i,SV619: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK14_SY274 @ SV619 @ SV430 ) @ ( sK13_C @ SV619 @ SV430 ) ) @ SV430 )
| ( in @ ( sK13_C @ SV619 @ SV430 ) @ SV619 ) )
= $true )
| ( ( SV619
= ( relation_rng @ SV430 ) )
= $true )
| ( ( relation @ SV430 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3026]) ).
thf(3084,plain,
! [SV620: $i,SV430: $i] :
( ( ( ~ ! [SY850: $i] :
( ! [SY705: $i] :
~ ( in @ ( ordered_pair @ SY705 @ SY850 ) @ SV430 )
| ( in @ SY850 @ SV620 ) ) )
= $false )
| ( ( SV620
= ( relation_rng @ SV430 ) )
= $false )
| ( ( relation @ SV430 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3027]) ).
thf(3085,plain,
! [SV430: $i,SV620: $i] :
( ( ( ~ ! [SY852: $i] :
( ~ ( in @ SY852 @ SV620 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY852 @ SV620 @ SV430 ) @ SY852 ) @ SV430 ) ) )
= $false )
| ( ( SV620
= ( relation_rng @ SV430 ) )
= $false )
| ( ( relation @ SV430 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3027]) ).
thf(3086,plain,
! [SV656: $i,SV525: $i,SV572: $i] :
( ( ( ~ ( in @ ( sK17_C @ SV572 @ SV525 ) @ SV656 )
| ~ ( in @ SV656 @ SV525 ) )
= $true )
| ( ( ~ ( in @ ( sK17_C @ SV572 @ SV525 ) @ SV572 ) )
= $true )
| ( ( SV572
= ( union @ SV525 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3028]) ).
thf(3087,plain,
! [SV525: $i,SV572: $i] :
( ( ( ~ ( in @ ( sK17_C @ SV572 @ SV525 ) @ ( sK18_SY276 @ SV572 @ SV525 ) )
| ~ ( in @ ( sK18_SY276 @ SV572 @ SV525 ) @ SV525 ) )
= $false )
| ( ( in @ ( sK17_C @ SV572 @ SV525 ) @ SV572 )
= $true )
| ( ( SV572
= ( union @ SV525 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3029]) ).
thf(3088,plain,
! [SV573: $i,SV526: $i,SV657: $i] :
( ( ( ! [SY871: $i] :
( ~ ( in @ SV657 @ SY871 )
| ~ ( in @ SY871 @ SV526 ) )
| ( in @ SV657 @ SV573 ) )
= $true )
| ( ( SV573
= ( union @ SV526 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3030]) ).
thf(3089,plain,
! [SV526: $i,SV573: $i,SV658: $i] :
( ( ( ~ ( in @ SV658 @ SV573 )
| ~ ( ~ ( in @ SV658 @ ( sK16_D @ SV658 @ SV573 @ SV526 ) )
| ~ ( in @ ( sK16_D @ SV658 @ SV573 @ SV526 ) @ SV526 ) ) )
= $true )
| ( ( SV573
= ( union @ SV526 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3031]) ).
thf(3090,plain,
! [SV433: $i,SV580: $i,SV595: $i] :
( ( ( ~ ( ~ ( in @ ( sK25_D @ SV595 @ SV580 @ SV433 ) @ SV595 )
| ( ( sK25_D @ SV595 @ SV580 @ SV433 )
!= SV433 ) )
| ~ ( ~ ( in @ ( sK25_D @ SV595 @ SV580 @ SV433 ) @ SV595 )
| ( ( sK25_D @ SV595 @ SV580 @ SV433 )
!= SV580 ) ) )
= $false )
| ( ( SV595
= ( unordered_pair @ SV433 @ SV580 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3034]) ).
thf(3091,plain,
! [SV433: $i,SV580: $i,SV595: $i] :
( ( ( in @ ( sK25_D @ SV595 @ SV580 @ SV433 ) @ SV595 )
= $true )
| ( ( ( ( sK25_D @ SV595 @ SV580 @ SV433 )
= SV433 )
| ( ( sK25_D @ SV595 @ SV580 @ SV433 )
= SV580 ) )
= $true )
| ( ( SV595
= ( unordered_pair @ SV433 @ SV580 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3035]) ).
thf(3092,plain,
! [SV581: $i,SV433: $i,SV596: $i] :
( ( ( ! [SY826: $i] :
( ~ ( in @ SY826 @ SV596 )
| ( SY826 = SV433 )
| ( SY826 = SV581 ) ) )
= $true )
| ( ( SV596
= ( unordered_pair @ SV433 @ SV581 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3036]) ).
thf(3093,plain,
! [SV581: $i,SV596: $i,SV433: $i] :
( ( ( ~ ( ~ ! [SY827: $i] :
( ( SY827 != SV433 )
| ( in @ SY827 @ SV596 ) )
| ~ ! [SY828: $i] :
( ( SY828 != SV581 )
| ( in @ SY828 @ SV596 ) ) ) )
= $true )
| ( ( SV596
= ( unordered_pair @ SV433 @ SV581 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3037]) ).
thf(3094,plain,
! [SV621: $i,SV643: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK40_SY287 @ SV643 @ SV621 ) @ SV621 )
| ~ ~ ( in @ ( sK39_C @ SV643 @ SV621 ) @ ( sK40_SY287 @ SV643 @ SV621 ) ) )
| ~ ( in @ ( sK39_C @ SV643 @ SV621 ) @ SV643 ) )
| ~ ( ! [SY865: $i] :
( ~ ( in @ SY865 @ SV621 )
| ( in @ ( sK39_C @ SV643 @ SV621 ) @ SY865 ) )
| ( in @ ( sK39_C @ SV643 @ SV621 ) @ SV643 ) ) )
= $false )
| ( ( SV643
= ( set_meet @ SV621 ) )
= $true )
| ( ( SV621 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3038]) ).
thf(3095,plain,
! [SV622: $i,SV644: $i] :
( ( ( SV644
= ( set_meet @ SV622 ) )
= $false )
| ( ( ~ ( ~ ! [SY866: $i] :
( ~ ( ~ ( in @ ( sK38_D @ SY866 @ SV644 @ SV622 ) @ SV622 )
| ~ ~ ( in @ SY866 @ ( sK38_D @ SY866 @ SV644 @ SV622 ) ) )
| ( in @ SY866 @ SV644 ) )
| ~ ! [SY867: $i] :
( ~ ( in @ SY867 @ SV644 )
| ! [SY858: $i] :
( ~ ( in @ SY858 @ SV622 )
| ( in @ SY867 @ SY858 ) ) ) ) )
= $true )
| ( ( SV622 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3039]) ).
thf(3096,plain,
! [SV623: $i,SV650: $i] :
( ( ( ( SV650
!= ( set_meet @ SV623 ) ) )
= $true )
| ( ( SV650 = empty_set )
= $true )
| ( ( SV623 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3040]) ).
thf(3097,plain,
! [SV624: $i,SV651: $i] :
( ( ( ( SV651 != empty_set ) )
= $true )
| ( ( SV651
= ( set_meet @ SV624 ) )
= $true )
| ( ( SV624 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3041]) ).
thf(3098,plain,
! [SV533: $i,SV582: $i] :
( ( ( ( sK27_C @ SV582 @ SV533 )
= SV533 )
= $false )
| ( ( ~ ( in @ ( sK27_C @ SV582 @ SV533 ) @ SV582 ) )
= $true )
| ( ( SV582
= ( singleton @ SV533 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3042]) ).
thf(3099,plain,
! [SV583: $i,SV534: $i,SV659: $i] :
( ( ( ( SV659 != SV534 )
| ( in @ SV659 @ SV583 ) )
= $true )
| ( ( SV583
= ( singleton @ SV534 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3044]) ).
thf(3100,plain,
! [SV534: $i,SV583: $i,SV660: $i] :
( ( ( ~ ( in @ SV660 @ SV583 )
| ( SV660 = SV534 ) )
= $true )
| ( ( SV583
= ( singleton @ SV534 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3045]) ).
thf(3101,plain,
! [SV420: $i,SV597: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SV597 @ SV420 ) @ ( sK11_SY272 @ SV597 @ SV420 ) ) @ SV597 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY272 @ SV597 @ SV420 ) @ ( sK10_C @ SV597 @ SV420 ) ) @ SV420 ) ) )
= $false )
| ( ( SV597
= ( relation_inverse @ SV420 ) )
= $true )
| ( ( relation @ SV597 )
= $false )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3048]) ).
thf(3102,plain,
! [SV420: $i,SV597: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK10_C @ SV597 @ SV420 ) @ ( sK11_SY272 @ SV597 @ SV420 ) ) @ SV597 )
| ( in @ ( ordered_pair @ ( sK11_SY272 @ SV597 @ SV420 ) @ ( sK10_C @ SV597 @ SV420 ) ) @ SV420 ) ) )
= $false )
| ( ( SV597
= ( relation_inverse @ SV420 ) )
= $true )
| ( ( relation @ SV597 )
= $false )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3048]) ).
thf(3103,plain,
! [SV420: $i,SV598: $i] :
( ( ( ~ ! [SY829: $i,SY830: $i] :
( ~ ( in @ ( ordered_pair @ SY829 @ SY830 ) @ SV598 )
| ( in @ ( ordered_pair @ SY830 @ SY829 ) @ SV420 ) )
| ~ ! [SY831: $i,SY832: $i] :
( ~ ( in @ ( ordered_pair @ SY832 @ SY831 ) @ SV420 )
| ( in @ ( ordered_pair @ SY831 @ SY832 ) @ SV598 ) ) )
= $false )
| ( ( SV598
= ( relation_inverse @ SV420 ) )
= $false )
| ( ( relation @ SV598 )
= $false )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3049]) ).
thf(3104,plain,
! [SV423: $i,SV547: $i,SV589: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV589 )
| ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV423 ) ) )
= $false )
| ( ( SV589
= ( set_union2 @ SV423 @ SV547 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3050]) ).
thf(3105,plain,
! [SV423: $i,SV547: $i,SV589: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV589 )
| ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV547 ) ) )
= $false )
| ( ( SV589
= ( set_union2 @ SV423 @ SV547 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3050]) ).
thf(3106,plain,
! [SV423: $i,SV547: $i,SV589: $i] :
( ( ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV423 )
= $true )
| ( ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV547 )
= $true )
| ( ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV589 )
= $true )
| ( ( SV589
= ( set_union2 @ SV423 @ SV547 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3051]) ).
thf(3107,plain,
! [SV548: $i,SV423: $i,SV590: $i,SV661: $i] :
( ( ( ~ ( in @ SV661 @ SV590 )
| ( in @ SV661 @ SV423 )
| ( in @ SV661 @ SV548 ) )
= $true )
| ( ( SV590
= ( set_union2 @ SV423 @ SV548 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3052]) ).
thf(3108,plain,
! [SV548: $i,SV590: $i,SV423: $i] :
( ( ( ~ ! [SY818: $i] :
( ~ ( in @ SY818 @ SV423 )
| ( in @ SY818 @ SV590 ) )
| ~ ! [SY819: $i] :
( ~ ( in @ SY819 @ SV548 )
| ( in @ SY819 @ SV590 ) ) )
= $false )
| ( ( SV590
= ( set_union2 @ SV423 @ SV548 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3053]) ).
thf(3109,plain,
! [SV662: $i,SV424: $i,SV652: $i] :
( ( ~ ( in @ SV652 @ ( sK35_B @ SV424 ) )
| ~ ( subset @ SV662 @ SV652 )
| ( in @ SV662 @ ( sK35_B @ SV424 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3056]) ).
thf(3110,plain,
! [SV426: $i,SV632: $i] :
( ( ( ! [SY863: $i] :
( ~ ( subset @ SY863 @ SV632 )
| ( in @ SY863 @ ( sK2_SY267 @ SV632 @ SV426 ) ) ) )
= $true )
| ( ( ~ ( in @ SV632 @ ( sK1_B @ SV426 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3059]) ).
thf(3111,plain,
! [SV426: $i,SV632: $i] :
( ( ( in @ ( sK2_SY267 @ SV632 @ SV426 ) @ ( sK1_B @ SV426 ) )
= $true )
| ( ( ~ ( in @ SV632 @ ( sK1_B @ SV426 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3060]) ).
thf(3112,plain,
! [SV663: $i,SV426: $i,SV653: $i] :
( ( ~ ( in @ SV653 @ ( sK1_B @ SV426 ) )
| ~ ( subset @ SV663 @ SV653 )
| ( in @ SV663 @ ( sK1_B @ SV426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3061]) ).
thf(3113,plain,
! [SV510: $i,SV557: $i] :
( ( ( subset @ ( sK26_C @ SV557 @ SV510 ) @ SV510 )
= $false )
| ( ( in @ ( sK26_C @ SV557 @ SV510 ) @ SV557 )
= $false )
| ( ( SV557
= ( powerset @ SV510 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3062]) ).
thf(3114,plain,
! [SV511: $i,SV558: $i,SV654: $i] :
( ( ( ~ ( in @ SV654 @ SV558 ) )
= $true )
| ( ( subset @ SV654 @ SV511 )
= $true )
| ( ( SV558
= ( powerset @ SV511 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3063]) ).
thf(3115,plain,
! [SV558: $i,SV511: $i,SV655: $i] :
( ( ( ~ ( subset @ SV655 @ SV511 ) )
= $true )
| ( ( in @ SV655 @ SV558 )
= $true )
| ( ( SV558
= ( powerset @ SV511 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3064]) ).
thf(3116,plain,
! [SV612: $i,SV647: $i] :
( ( ( element @ SV647 @ SV612 )
= $false )
| ( ( empty @ SV647 )
= $true )
| ( ( empty @ SV612 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3067]) ).
thf(3117,plain,
! [SV613: $i,SV648: $i] :
( ( ( empty @ SV648 )
= $false )
| ( ( element @ SV648 @ SV613 )
= $true )
| ( ( empty @ SV613 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3068]) ).
thf(3118,plain,
! [SV427: $i,SV617: $i] :
( ( ( ! [SY845: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SV617 @ SV427 ) @ SY845 ) @ SV427 ) )
= $true )
| ( ( ~ ( in @ ( sK20_C @ SV617 @ SV427 ) @ SV617 ) )
= $true )
| ( ( SV617
= ( relation_dom @ SV427 ) )
= $true )
| ( ( relation @ SV427 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3070]) ).
thf(3119,plain,
! [SV427: $i,SV617: $i] :
( ( ( in @ ( ordered_pair @ ( sK20_C @ SV617 @ SV427 ) @ ( sK21_SY278 @ SV617 @ SV427 ) ) @ SV427 )
= $true )
| ( ( in @ ( sK20_C @ SV617 @ SV427 ) @ SV617 )
= $true )
| ( ( SV617
= ( relation_dom @ SV427 ) )
= $true )
| ( ( relation @ SV427 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3071]) ).
thf(3120,plain,
! [SV618: $i,SV427: $i] :
( ( ( ! [SY846: $i] :
( ! [SY685: $i] :
~ ( in @ ( ordered_pair @ SY846 @ SY685 ) @ SV427 )
| ( in @ SY846 @ SV618 ) ) )
= $true )
| ( ( SV618
= ( relation_dom @ SV427 ) )
= $false )
| ( ( relation @ SV427 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3072]) ).
thf(3121,plain,
! [SV427: $i,SV618: $i] :
( ( ( ! [SY848: $i] :
( ~ ( in @ SY848 @ SV618 )
| ( in @ ( ordered_pair @ SY848 @ ( sK19_D @ SY848 @ SV618 @ SV427 ) ) @ SV427 ) ) )
= $true )
| ( ( SV618
= ( relation_dom @ SV427 ) )
= $false )
| ( ( relation @ SV427 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3073]) ).
thf(3122,plain,
! [SV428: $i,SV566: $i,SV591: $i] :
( ( ( ~ ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV428 ) )
= $true )
| ( ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV566 )
= $true )
| ( ( ~ ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV591 ) )
= $true )
| ( ( SV591
= ( set_difference @ SV428 @ SV566 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3074]) ).
thf(3123,plain,
! [SV428: $i,SV566: $i,SV591: $i] :
( ( ( ~ ( ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV428 )
| ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV591 ) ) )
= $false )
| ( ( SV591
= ( set_difference @ SV428 @ SV566 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3075]) ).
thf(3124,plain,
! [SV428: $i,SV566: $i,SV591: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV566 )
| ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV591 ) ) )
= $false )
| ( ( SV591
= ( set_difference @ SV428 @ SV566 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3075]) ).
thf(3125,plain,
! [SV592: $i,SV567: $i,SV428: $i,SV664: $i] :
( ( ( ~ ( in @ SV664 @ SV428 )
| ( in @ SV664 @ SV567 )
| ( in @ SV664 @ SV592 ) )
= $true )
| ( ( SV592
= ( set_difference @ SV428 @ SV567 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3076]) ).
thf(3126,plain,
! [SV567: $i,SV428: $i,SV592: $i] :
( ( ( ~ ! [SY821: $i] :
( ~ ( in @ SY821 @ SV592 )
| ( in @ SY821 @ SV428 ) )
| ~ ! [SY822: $i] :
( ~ ( in @ SY822 @ SV592 )
| ~ ( in @ SY822 @ SV567 ) ) )
= $false )
| ( ( SV592
= ( set_difference @ SV428 @ SV567 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3077]) ).
thf(3127,plain,
! [SV429: $i,SV570: $i,SV593: $i] :
( ( ( ~ ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV429 ) )
= $true )
| ( ( ~ ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV570 ) )
= $true )
| ( ( ~ ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV593 ) )
= $true )
| ( ( SV593
= ( set_intersection2 @ SV429 @ SV570 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3078]) ).
thf(3128,plain,
! [SV429: $i,SV570: $i,SV593: $i] :
( ( ( ~ ( ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV429 )
| ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV593 ) ) )
= $false )
| ( ( SV593
= ( set_intersection2 @ SV429 @ SV570 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3079]) ).
thf(3129,plain,
! [SV429: $i,SV570: $i,SV593: $i] :
( ( ( ~ ( ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV570 )
| ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV593 ) ) )
= $false )
| ( ( SV593
= ( set_intersection2 @ SV429 @ SV570 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3079]) ).
thf(3130,plain,
! [SV594: $i,SV571: $i,SV429: $i,SV665: $i] :
( ( ( ~ ( in @ SV665 @ SV429 )
| ~ ( in @ SV665 @ SV571 )
| ( in @ SV665 @ SV594 ) )
= $true )
| ( ( SV594
= ( set_intersection2 @ SV429 @ SV571 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3080]) ).
thf(3131,plain,
! [SV571: $i,SV429: $i,SV594: $i] :
( ( ( ~ ! [SY824: $i] :
( ~ ( in @ SY824 @ SV594 )
| ( in @ SY824 @ SV429 ) )
| ~ ! [SY825: $i] :
( ~ ( in @ SY825 @ SV594 )
| ( in @ SY825 @ SV571 ) ) )
= $false )
| ( ( SV594
= ( set_intersection2 @ SV429 @ SV571 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3081]) ).
thf(3132,plain,
! [SV430: $i,SV619: $i] :
( ( ( ! [SY849: $i] :
~ ( in @ ( ordered_pair @ SY849 @ ( sK13_C @ SV619 @ SV430 ) ) @ SV430 ) )
= $true )
| ( ( ~ ( in @ ( sK13_C @ SV619 @ SV430 ) @ SV619 ) )
= $true )
| ( ( SV619
= ( relation_rng @ SV430 ) )
= $true )
| ( ( relation @ SV430 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3082]) ).
thf(3133,plain,
! [SV430: $i,SV619: $i] :
( ( ( in @ ( ordered_pair @ ( sK14_SY274 @ SV619 @ SV430 ) @ ( sK13_C @ SV619 @ SV430 ) ) @ SV430 )
= $true )
| ( ( in @ ( sK13_C @ SV619 @ SV430 ) @ SV619 )
= $true )
| ( ( SV619
= ( relation_rng @ SV430 ) )
= $true )
| ( ( relation @ SV430 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3083]) ).
thf(3134,plain,
! [SV620: $i,SV430: $i] :
( ( ( ! [SY850: $i] :
( ! [SY705: $i] :
~ ( in @ ( ordered_pair @ SY705 @ SY850 ) @ SV430 )
| ( in @ SY850 @ SV620 ) ) )
= $true )
| ( ( SV620
= ( relation_rng @ SV430 ) )
= $false )
| ( ( relation @ SV430 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3084]) ).
thf(3135,plain,
! [SV430: $i,SV620: $i] :
( ( ( ! [SY852: $i] :
( ~ ( in @ SY852 @ SV620 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY852 @ SV620 @ SV430 ) @ SY852 ) @ SV430 ) ) )
= $true )
| ( ( SV620
= ( relation_rng @ SV430 ) )
= $false )
| ( ( relation @ SV430 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3085]) ).
thf(3136,plain,
! [SV656: $i,SV525: $i,SV572: $i] :
( ( ( ~ ( in @ ( sK17_C @ SV572 @ SV525 ) @ SV656 ) )
= $true )
| ( ( ~ ( in @ SV656 @ SV525 ) )
= $true )
| ( ( ~ ( in @ ( sK17_C @ SV572 @ SV525 ) @ SV572 ) )
= $true )
| ( ( SV572
= ( union @ SV525 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3086]) ).
thf(3137,plain,
! [SV525: $i,SV572: $i] :
( ( ( ~ ( in @ ( sK17_C @ SV572 @ SV525 ) @ ( sK18_SY276 @ SV572 @ SV525 ) ) )
= $false )
| ( ( in @ ( sK17_C @ SV572 @ SV525 ) @ SV572 )
= $true )
| ( ( SV572
= ( union @ SV525 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3087]) ).
thf(3138,plain,
! [SV525: $i,SV572: $i] :
( ( ( ~ ( in @ ( sK18_SY276 @ SV572 @ SV525 ) @ SV525 ) )
= $false )
| ( ( in @ ( sK17_C @ SV572 @ SV525 ) @ SV572 )
= $true )
| ( ( SV572
= ( union @ SV525 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3087]) ).
thf(3139,plain,
! [SV573: $i,SV526: $i,SV657: $i] :
( ( ( ! [SY871: $i] :
( ~ ( in @ SV657 @ SY871 )
| ~ ( in @ SY871 @ SV526 ) ) )
= $true )
| ( ( in @ SV657 @ SV573 )
= $true )
| ( ( SV573
= ( union @ SV526 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3088]) ).
thf(3140,plain,
! [SV526: $i,SV573: $i,SV658: $i] :
( ( ( ~ ( in @ SV658 @ SV573 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV658 @ ( sK16_D @ SV658 @ SV573 @ SV526 ) )
| ~ ( in @ ( sK16_D @ SV658 @ SV573 @ SV526 ) @ SV526 ) ) )
= $true )
| ( ( SV573
= ( union @ SV526 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3089]) ).
thf(3141,plain,
! [SV433: $i,SV580: $i,SV595: $i] :
( ( ( ~ ( ~ ( in @ ( sK25_D @ SV595 @ SV580 @ SV433 ) @ SV595 )
| ( ( sK25_D @ SV595 @ SV580 @ SV433 )
!= SV433 ) ) )
= $false )
| ( ( SV595
= ( unordered_pair @ SV433 @ SV580 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3090]) ).
thf(3142,plain,
! [SV433: $i,SV580: $i,SV595: $i] :
( ( ( ~ ( ~ ( in @ ( sK25_D @ SV595 @ SV580 @ SV433 ) @ SV595 )
| ( ( sK25_D @ SV595 @ SV580 @ SV433 )
!= SV580 ) ) )
= $false )
| ( ( SV595
= ( unordered_pair @ SV433 @ SV580 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3090]) ).
thf(3143,plain,
! [SV433: $i,SV580: $i,SV595: $i] :
( ( ( ( sK25_D @ SV595 @ SV580 @ SV433 )
= SV433 )
= $true )
| ( ( ( sK25_D @ SV595 @ SV580 @ SV433 )
= SV580 )
= $true )
| ( ( in @ ( sK25_D @ SV595 @ SV580 @ SV433 ) @ SV595 )
= $true )
| ( ( SV595
= ( unordered_pair @ SV433 @ SV580 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3091]) ).
thf(3144,plain,
! [SV581: $i,SV433: $i,SV596: $i,SV666: $i] :
( ( ( ~ ( in @ SV666 @ SV596 )
| ( SV666 = SV433 )
| ( SV666 = SV581 ) )
= $true )
| ( ( SV596
= ( unordered_pair @ SV433 @ SV581 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3092]) ).
thf(3145,plain,
! [SV581: $i,SV596: $i,SV433: $i] :
( ( ( ~ ! [SY827: $i] :
( ( SY827 != SV433 )
| ( in @ SY827 @ SV596 ) )
| ~ ! [SY828: $i] :
( ( SY828 != SV581 )
| ( in @ SY828 @ SV596 ) ) )
= $false )
| ( ( SV596
= ( unordered_pair @ SV433 @ SV581 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3093]) ).
thf(3146,plain,
! [SV621: $i,SV643: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK40_SY287 @ SV643 @ SV621 ) @ SV621 )
| ~ ~ ( in @ ( sK39_C @ SV643 @ SV621 ) @ ( sK40_SY287 @ SV643 @ SV621 ) ) )
| ~ ( in @ ( sK39_C @ SV643 @ SV621 ) @ SV643 ) ) )
= $false )
| ( ( SV643
= ( set_meet @ SV621 ) )
= $true )
| ( ( SV621 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3094]) ).
thf(3147,plain,
! [SV643: $i,SV621: $i] :
( ( ( ~ ( ! [SY865: $i] :
( ~ ( in @ SY865 @ SV621 )
| ( in @ ( sK39_C @ SV643 @ SV621 ) @ SY865 ) )
| ( in @ ( sK39_C @ SV643 @ SV621 ) @ SV643 ) ) )
= $false )
| ( ( SV643
= ( set_meet @ SV621 ) )
= $true )
| ( ( SV621 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3094]) ).
thf(3148,plain,
! [SV622: $i,SV644: $i] :
( ( ( ~ ! [SY866: $i] :
( ~ ( ~ ( in @ ( sK38_D @ SY866 @ SV644 @ SV622 ) @ SV622 )
| ~ ~ ( in @ SY866 @ ( sK38_D @ SY866 @ SV644 @ SV622 ) ) )
| ( in @ SY866 @ SV644 ) )
| ~ ! [SY867: $i] :
( ~ ( in @ SY867 @ SV644 )
| ! [SY858: $i] :
( ~ ( in @ SY858 @ SV622 )
| ( in @ SY867 @ SY858 ) ) ) )
= $false )
| ( ( SV644
= ( set_meet @ SV622 ) )
= $false )
| ( ( SV622 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3095]) ).
thf(3149,plain,
! [SV623: $i,SV650: $i] :
( ( ( SV650
= ( set_meet @ SV623 ) )
= $false )
| ( ( SV650 = empty_set )
= $true )
| ( ( SV623 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3096]) ).
thf(3150,plain,
! [SV624: $i,SV651: $i] :
( ( ( SV651 = empty_set )
= $false )
| ( ( SV651
= ( set_meet @ SV624 ) )
= $true )
| ( ( SV624 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3097]) ).
thf(3151,plain,
! [SV533: $i,SV582: $i] :
( ( ( in @ ( sK27_C @ SV582 @ SV533 ) @ SV582 )
= $false )
| ( ( ( sK27_C @ SV582 @ SV533 )
= SV533 )
= $false )
| ( ( SV582
= ( singleton @ SV533 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3098]) ).
thf(3152,plain,
! [SV583: $i,SV534: $i,SV659: $i] :
( ( ( ( SV659 != SV534 ) )
= $true )
| ( ( in @ SV659 @ SV583 )
= $true )
| ( ( SV583
= ( singleton @ SV534 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3099]) ).
thf(3153,plain,
! [SV534: $i,SV583: $i,SV660: $i] :
( ( ( ~ ( in @ SV660 @ SV583 ) )
= $true )
| ( ( SV660 = SV534 )
= $true )
| ( ( SV583
= ( singleton @ SV534 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3100]) ).
thf(3154,plain,
! [SV420: $i,SV597: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SV597 @ SV420 ) @ ( sK11_SY272 @ SV597 @ SV420 ) ) @ SV597 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY272 @ SV597 @ SV420 ) @ ( sK10_C @ SV597 @ SV420 ) ) @ SV420 ) )
= $true )
| ( ( SV597
= ( relation_inverse @ SV420 ) )
= $true )
| ( ( relation @ SV597 )
= $false )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3101]) ).
thf(3155,plain,
! [SV420: $i,SV597: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK10_C @ SV597 @ SV420 ) @ ( sK11_SY272 @ SV597 @ SV420 ) ) @ SV597 )
| ( in @ ( ordered_pair @ ( sK11_SY272 @ SV597 @ SV420 ) @ ( sK10_C @ SV597 @ SV420 ) ) @ SV420 ) )
= $true )
| ( ( SV597
= ( relation_inverse @ SV420 ) )
= $true )
| ( ( relation @ SV597 )
= $false )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3102]) ).
thf(3156,plain,
! [SV420: $i,SV598: $i] :
( ( ( ~ ! [SY829: $i,SY830: $i] :
( ~ ( in @ ( ordered_pair @ SY829 @ SY830 ) @ SV598 )
| ( in @ ( ordered_pair @ SY830 @ SY829 ) @ SV420 ) ) )
= $false )
| ( ( SV598
= ( relation_inverse @ SV420 ) )
= $false )
| ( ( relation @ SV598 )
= $false )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3103]) ).
thf(3157,plain,
! [SV598: $i,SV420: $i] :
( ( ( ~ ! [SY831: $i,SY832: $i] :
( ~ ( in @ ( ordered_pair @ SY832 @ SY831 ) @ SV420 )
| ( in @ ( ordered_pair @ SY831 @ SY832 ) @ SV598 ) ) )
= $false )
| ( ( SV598
= ( relation_inverse @ SV420 ) )
= $false )
| ( ( relation @ SV598 )
= $false )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3103]) ).
thf(3158,plain,
! [SV423: $i,SV547: $i,SV589: $i] :
( ( ( ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV589 )
| ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV423 ) )
= $true )
| ( ( SV589
= ( set_union2 @ SV423 @ SV547 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3104]) ).
thf(3159,plain,
! [SV423: $i,SV547: $i,SV589: $i] :
( ( ( ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV589 )
| ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV547 ) )
= $true )
| ( ( SV589
= ( set_union2 @ SV423 @ SV547 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3105]) ).
thf(3160,plain,
! [SV548: $i,SV423: $i,SV590: $i,SV661: $i] :
( ( ( ~ ( in @ SV661 @ SV590 ) )
= $true )
| ( ( ( in @ SV661 @ SV423 )
| ( in @ SV661 @ SV548 ) )
= $true )
| ( ( SV590
= ( set_union2 @ SV423 @ SV548 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3107]) ).
thf(3161,plain,
! [SV548: $i,SV590: $i,SV423: $i] :
( ( ( ~ ! [SY818: $i] :
( ~ ( in @ SY818 @ SV423 )
| ( in @ SY818 @ SV590 ) ) )
= $false )
| ( ( SV590
= ( set_union2 @ SV423 @ SV548 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3108]) ).
thf(3162,plain,
! [SV423: $i,SV590: $i,SV548: $i] :
( ( ( ~ ! [SY819: $i] :
( ~ ( in @ SY819 @ SV548 )
| ( in @ SY819 @ SV590 ) ) )
= $false )
| ( ( SV590
= ( set_union2 @ SV423 @ SV548 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3108]) ).
thf(3163,plain,
! [SV662: $i,SV424: $i,SV652: $i] :
( ( ( ~ ( in @ SV652 @ ( sK35_B @ SV424 ) )
| ~ ( subset @ SV662 @ SV652 ) )
= $true )
| ( ( in @ SV662 @ ( sK35_B @ SV424 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3109]) ).
thf(3164,plain,
! [SV426: $i,SV632: $i,SV667: $i] :
( ( ( ~ ( subset @ SV667 @ SV632 )
| ( in @ SV667 @ ( sK2_SY267 @ SV632 @ SV426 ) ) )
= $true )
| ( ( ~ ( in @ SV632 @ ( sK1_B @ SV426 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3110]) ).
thf(3165,plain,
! [SV426: $i,SV632: $i] :
( ( ( in @ SV632 @ ( sK1_B @ SV426 ) )
= $false )
| ( ( in @ ( sK2_SY267 @ SV632 @ SV426 ) @ ( sK1_B @ SV426 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3111]) ).
thf(3166,plain,
! [SV663: $i,SV426: $i,SV653: $i] :
( ( ( ~ ( in @ SV653 @ ( sK1_B @ SV426 ) )
| ~ ( subset @ SV663 @ SV653 ) )
= $true )
| ( ( in @ SV663 @ ( sK1_B @ SV426 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3112]) ).
thf(3167,plain,
! [SV511: $i,SV558: $i,SV654: $i] :
( ( ( in @ SV654 @ SV558 )
= $false )
| ( ( subset @ SV654 @ SV511 )
= $true )
| ( ( SV558
= ( powerset @ SV511 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3114]) ).
thf(3168,plain,
! [SV558: $i,SV511: $i,SV655: $i] :
( ( ( subset @ SV655 @ SV511 )
= $false )
| ( ( in @ SV655 @ SV558 )
= $true )
| ( ( SV558
= ( powerset @ SV511 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3115]) ).
thf(3169,plain,
! [SV668: $i,SV427: $i,SV617: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK20_C @ SV617 @ SV427 ) @ SV668 ) @ SV427 ) )
= $true )
| ( ( ~ ( in @ ( sK20_C @ SV617 @ SV427 ) @ SV617 ) )
= $true )
| ( ( SV617
= ( relation_dom @ SV427 ) )
= $true )
| ( ( relation @ SV427 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3118]) ).
thf(3170,plain,
! [SV618: $i,SV427: $i,SV669: $i] :
( ( ( ! [SY872: $i] :
~ ( in @ ( ordered_pair @ SV669 @ SY872 ) @ SV427 )
| ( in @ SV669 @ SV618 ) )
= $true )
| ( ( SV618
= ( relation_dom @ SV427 ) )
= $false )
| ( ( relation @ SV427 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3120]) ).
thf(3171,plain,
! [SV427: $i,SV618: $i,SV670: $i] :
( ( ( ~ ( in @ SV670 @ SV618 )
| ( in @ ( ordered_pair @ SV670 @ ( sK19_D @ SV670 @ SV618 @ SV427 ) ) @ SV427 ) )
= $true )
| ( ( SV618
= ( relation_dom @ SV427 ) )
= $false )
| ( ( relation @ SV427 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3121]) ).
thf(3172,plain,
! [SV428: $i,SV566: $i,SV591: $i] :
( ( ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV428 )
= $false )
| ( ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV566 )
= $true )
| ( ( ~ ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV591 ) )
= $true )
| ( ( SV591
= ( set_difference @ SV428 @ SV566 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3122]) ).
thf(3173,plain,
! [SV428: $i,SV566: $i,SV591: $i] :
( ( ( ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV428 )
| ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV591 ) )
= $true )
| ( ( SV591
= ( set_difference @ SV428 @ SV566 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3123]) ).
thf(3174,plain,
! [SV428: $i,SV566: $i,SV591: $i] :
( ( ( ~ ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV566 )
| ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV591 ) )
= $true )
| ( ( SV591
= ( set_difference @ SV428 @ SV566 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3124]) ).
thf(3175,plain,
! [SV592: $i,SV567: $i,SV428: $i,SV664: $i] :
( ( ( ~ ( in @ SV664 @ SV428 )
| ( in @ SV664 @ SV567 ) )
= $true )
| ( ( in @ SV664 @ SV592 )
= $true )
| ( ( SV592
= ( set_difference @ SV428 @ SV567 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3125]) ).
thf(3176,plain,
! [SV567: $i,SV428: $i,SV592: $i] :
( ( ( ~ ! [SY821: $i] :
( ~ ( in @ SY821 @ SV592 )
| ( in @ SY821 @ SV428 ) ) )
= $false )
| ( ( SV592
= ( set_difference @ SV428 @ SV567 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3126]) ).
thf(3177,plain,
! [SV428: $i,SV567: $i,SV592: $i] :
( ( ( ~ ! [SY822: $i] :
( ~ ( in @ SY822 @ SV592 )
| ~ ( in @ SY822 @ SV567 ) ) )
= $false )
| ( ( SV592
= ( set_difference @ SV428 @ SV567 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3126]) ).
thf(3178,plain,
! [SV429: $i,SV570: $i,SV593: $i] :
( ( ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV429 )
= $false )
| ( ( ~ ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV570 ) )
= $true )
| ( ( ~ ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV593 ) )
= $true )
| ( ( SV593
= ( set_intersection2 @ SV429 @ SV570 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3127]) ).
thf(3179,plain,
! [SV429: $i,SV570: $i,SV593: $i] :
( ( ( ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV429 )
| ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV593 ) )
= $true )
| ( ( SV593
= ( set_intersection2 @ SV429 @ SV570 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3128]) ).
thf(3180,plain,
! [SV429: $i,SV570: $i,SV593: $i] :
( ( ( ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV570 )
| ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV593 ) )
= $true )
| ( ( SV593
= ( set_intersection2 @ SV429 @ SV570 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3129]) ).
thf(3181,plain,
! [SV594: $i,SV571: $i,SV429: $i,SV665: $i] :
( ( ( ~ ( in @ SV665 @ SV429 )
| ~ ( in @ SV665 @ SV571 ) )
= $true )
| ( ( in @ SV665 @ SV594 )
= $true )
| ( ( SV594
= ( set_intersection2 @ SV429 @ SV571 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3130]) ).
thf(3182,plain,
! [SV571: $i,SV429: $i,SV594: $i] :
( ( ( ~ ! [SY824: $i] :
( ~ ( in @ SY824 @ SV594 )
| ( in @ SY824 @ SV429 ) ) )
= $false )
| ( ( SV594
= ( set_intersection2 @ SV429 @ SV571 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3131]) ).
thf(3183,plain,
! [SV429: $i,SV571: $i,SV594: $i] :
( ( ( ~ ! [SY825: $i] :
( ~ ( in @ SY825 @ SV594 )
| ( in @ SY825 @ SV571 ) ) )
= $false )
| ( ( SV594
= ( set_intersection2 @ SV429 @ SV571 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3131]) ).
thf(3184,plain,
! [SV430: $i,SV619: $i,SV671: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV671 @ ( sK13_C @ SV619 @ SV430 ) ) @ SV430 ) )
= $true )
| ( ( ~ ( in @ ( sK13_C @ SV619 @ SV430 ) @ SV619 ) )
= $true )
| ( ( SV619
= ( relation_rng @ SV430 ) )
= $true )
| ( ( relation @ SV430 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3132]) ).
thf(3185,plain,
! [SV620: $i,SV430: $i,SV672: $i] :
( ( ( ! [SY873: $i] :
~ ( in @ ( ordered_pair @ SY873 @ SV672 ) @ SV430 )
| ( in @ SV672 @ SV620 ) )
= $true )
| ( ( SV620
= ( relation_rng @ SV430 ) )
= $false )
| ( ( relation @ SV430 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3134]) ).
thf(3186,plain,
! [SV430: $i,SV620: $i,SV673: $i] :
( ( ( ~ ( in @ SV673 @ SV620 )
| ( in @ ( ordered_pair @ ( sK12_D @ SV673 @ SV620 @ SV430 ) @ SV673 ) @ SV430 ) )
= $true )
| ( ( SV620
= ( relation_rng @ SV430 ) )
= $false )
| ( ( relation @ SV430 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3135]) ).
thf(3187,plain,
! [SV656: $i,SV525: $i,SV572: $i] :
( ( ( in @ ( sK17_C @ SV572 @ SV525 ) @ SV656 )
= $false )
| ( ( ~ ( in @ SV656 @ SV525 ) )
= $true )
| ( ( ~ ( in @ ( sK17_C @ SV572 @ SV525 ) @ SV572 ) )
= $true )
| ( ( SV572
= ( union @ SV525 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3136]) ).
thf(3188,plain,
! [SV525: $i,SV572: $i] :
( ( ( in @ ( sK17_C @ SV572 @ SV525 ) @ ( sK18_SY276 @ SV572 @ SV525 ) )
= $true )
| ( ( in @ ( sK17_C @ SV572 @ SV525 ) @ SV572 )
= $true )
| ( ( SV572
= ( union @ SV525 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3137]) ).
thf(3189,plain,
! [SV525: $i,SV572: $i] :
( ( ( in @ ( sK18_SY276 @ SV572 @ SV525 ) @ SV525 )
= $true )
| ( ( in @ ( sK17_C @ SV572 @ SV525 ) @ SV572 )
= $true )
| ( ( SV572
= ( union @ SV525 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3138]) ).
thf(3190,plain,
! [SV573: $i,SV526: $i,SV674: $i,SV657: $i] :
( ( ( ~ ( in @ SV657 @ SV674 )
| ~ ( in @ SV674 @ SV526 ) )
= $true )
| ( ( in @ SV657 @ SV573 )
= $true )
| ( ( SV573
= ( union @ SV526 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3139]) ).
thf(3191,plain,
! [SV526: $i,SV573: $i,SV658: $i] :
( ( ( in @ SV658 @ SV573 )
= $false )
| ( ( ~ ( ~ ( in @ SV658 @ ( sK16_D @ SV658 @ SV573 @ SV526 ) )
| ~ ( in @ ( sK16_D @ SV658 @ SV573 @ SV526 ) @ SV526 ) ) )
= $true )
| ( ( SV573
= ( union @ SV526 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3140]) ).
thf(3192,plain,
! [SV433: $i,SV580: $i,SV595: $i] :
( ( ( ~ ( in @ ( sK25_D @ SV595 @ SV580 @ SV433 ) @ SV595 )
| ( ( sK25_D @ SV595 @ SV580 @ SV433 )
!= SV433 ) )
= $true )
| ( ( SV595
= ( unordered_pair @ SV433 @ SV580 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3141]) ).
thf(3193,plain,
! [SV433: $i,SV580: $i,SV595: $i] :
( ( ( ~ ( in @ ( sK25_D @ SV595 @ SV580 @ SV433 ) @ SV595 )
| ( ( sK25_D @ SV595 @ SV580 @ SV433 )
!= SV580 ) )
= $true )
| ( ( SV595
= ( unordered_pair @ SV433 @ SV580 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3142]) ).
thf(3194,plain,
! [SV581: $i,SV433: $i,SV596: $i,SV666: $i] :
( ( ( ~ ( in @ SV666 @ SV596 ) )
= $true )
| ( ( ( SV666 = SV433 )
| ( SV666 = SV581 ) )
= $true )
| ( ( SV596
= ( unordered_pair @ SV433 @ SV581 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3144]) ).
thf(3195,plain,
! [SV581: $i,SV596: $i,SV433: $i] :
( ( ( ~ ! [SY827: $i] :
( ( SY827 != SV433 )
| ( in @ SY827 @ SV596 ) ) )
= $false )
| ( ( SV596
= ( unordered_pair @ SV433 @ SV581 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3145]) ).
thf(3196,plain,
! [SV433: $i,SV596: $i,SV581: $i] :
( ( ( ~ ! [SY828: $i] :
( ( SY828 != SV581 )
| ( in @ SY828 @ SV596 ) ) )
= $false )
| ( ( SV596
= ( unordered_pair @ SV433 @ SV581 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3145]) ).
thf(3197,plain,
! [SV621: $i,SV643: $i] :
( ( ( ~ ( ~ ( in @ ( sK40_SY287 @ SV643 @ SV621 ) @ SV621 )
| ~ ~ ( in @ ( sK39_C @ SV643 @ SV621 ) @ ( sK40_SY287 @ SV643 @ SV621 ) ) )
| ~ ( in @ ( sK39_C @ SV643 @ SV621 ) @ SV643 ) )
= $true )
| ( ( SV643
= ( set_meet @ SV621 ) )
= $true )
| ( ( SV621 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3146]) ).
thf(3198,plain,
! [SV643: $i,SV621: $i] :
( ( ( ! [SY865: $i] :
( ~ ( in @ SY865 @ SV621 )
| ( in @ ( sK39_C @ SV643 @ SV621 ) @ SY865 ) )
| ( in @ ( sK39_C @ SV643 @ SV621 ) @ SV643 ) )
= $true )
| ( ( SV643
= ( set_meet @ SV621 ) )
= $true )
| ( ( SV621 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3147]) ).
thf(3199,plain,
! [SV622: $i,SV644: $i] :
( ( ( ~ ! [SY866: $i] :
( ~ ( ~ ( in @ ( sK38_D @ SY866 @ SV644 @ SV622 ) @ SV622 )
| ~ ~ ( in @ SY866 @ ( sK38_D @ SY866 @ SV644 @ SV622 ) ) )
| ( in @ SY866 @ SV644 ) ) )
= $false )
| ( ( SV644
= ( set_meet @ SV622 ) )
= $false )
| ( ( SV622 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3148]) ).
thf(3200,plain,
! [SV622: $i,SV644: $i] :
( ( ( ~ ! [SY867: $i] :
( ~ ( in @ SY867 @ SV644 )
| ! [SY858: $i] :
( ~ ( in @ SY858 @ SV622 )
| ( in @ SY867 @ SY858 ) ) ) )
= $false )
| ( ( SV644
= ( set_meet @ SV622 ) )
= $false )
| ( ( SV622 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3148]) ).
thf(3201,plain,
! [SV583: $i,SV534: $i,SV659: $i] :
( ( ( SV659 = SV534 )
= $false )
| ( ( in @ SV659 @ SV583 )
= $true )
| ( ( SV583
= ( singleton @ SV534 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3152]) ).
thf(3202,plain,
! [SV534: $i,SV583: $i,SV660: $i] :
( ( ( in @ SV660 @ SV583 )
= $false )
| ( ( SV660 = SV534 )
= $true )
| ( ( SV583
= ( singleton @ SV534 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3153]) ).
thf(3203,plain,
! [SV420: $i,SV597: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SV597 @ SV420 ) @ ( sK11_SY272 @ SV597 @ SV420 ) ) @ SV597 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK11_SY272 @ SV597 @ SV420 ) @ ( sK10_C @ SV597 @ SV420 ) ) @ SV420 ) )
= $true )
| ( ( SV597
= ( relation_inverse @ SV420 ) )
= $true )
| ( ( relation @ SV597 )
= $false )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3154]) ).
thf(3204,plain,
! [SV420: $i,SV597: $i] :
( ( ( in @ ( ordered_pair @ ( sK10_C @ SV597 @ SV420 ) @ ( sK11_SY272 @ SV597 @ SV420 ) ) @ SV597 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK11_SY272 @ SV597 @ SV420 ) @ ( sK10_C @ SV597 @ SV420 ) ) @ SV420 )
= $true )
| ( ( SV597
= ( relation_inverse @ SV420 ) )
= $true )
| ( ( relation @ SV597 )
= $false )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3155]) ).
thf(3205,plain,
! [SV420: $i,SV598: $i] :
( ( ( ! [SY829: $i,SY830: $i] :
( ~ ( in @ ( ordered_pair @ SY829 @ SY830 ) @ SV598 )
| ( in @ ( ordered_pair @ SY830 @ SY829 ) @ SV420 ) ) )
= $true )
| ( ( SV598
= ( relation_inverse @ SV420 ) )
= $false )
| ( ( relation @ SV598 )
= $false )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3156]) ).
thf(3206,plain,
! [SV598: $i,SV420: $i] :
( ( ( ! [SY831: $i,SY832: $i] :
( ~ ( in @ ( ordered_pair @ SY832 @ SY831 ) @ SV420 )
| ( in @ ( ordered_pair @ SY831 @ SY832 ) @ SV598 ) ) )
= $true )
| ( ( SV598
= ( relation_inverse @ SV420 ) )
= $false )
| ( ( relation @ SV598 )
= $false )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3157]) ).
thf(3207,plain,
! [SV423: $i,SV547: $i,SV589: $i] :
( ( ( ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV589 ) )
= $true )
| ( ( ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV423 ) )
= $true )
| ( ( SV589
= ( set_union2 @ SV423 @ SV547 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3158]) ).
thf(3208,plain,
! [SV423: $i,SV547: $i,SV589: $i] :
( ( ( ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV589 ) )
= $true )
| ( ( ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV547 ) )
= $true )
| ( ( SV589
= ( set_union2 @ SV423 @ SV547 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3159]) ).
thf(3209,plain,
! [SV548: $i,SV423: $i,SV590: $i,SV661: $i] :
( ( ( in @ SV661 @ SV590 )
= $false )
| ( ( ( in @ SV661 @ SV423 )
| ( in @ SV661 @ SV548 ) )
= $true )
| ( ( SV590
= ( set_union2 @ SV423 @ SV548 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3160]) ).
thf(3210,plain,
! [SV548: $i,SV590: $i,SV423: $i] :
( ( ( ! [SY818: $i] :
( ~ ( in @ SY818 @ SV423 )
| ( in @ SY818 @ SV590 ) ) )
= $true )
| ( ( SV590
= ( set_union2 @ SV423 @ SV548 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3161]) ).
thf(3211,plain,
! [SV423: $i,SV590: $i,SV548: $i] :
( ( ( ! [SY819: $i] :
( ~ ( in @ SY819 @ SV548 )
| ( in @ SY819 @ SV590 ) ) )
= $true )
| ( ( SV590
= ( set_union2 @ SV423 @ SV548 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3162]) ).
thf(3212,plain,
! [SV662: $i,SV424: $i,SV652: $i] :
( ( ( ~ ( in @ SV652 @ ( sK35_B @ SV424 ) ) )
= $true )
| ( ( ~ ( subset @ SV662 @ SV652 ) )
= $true )
| ( ( in @ SV662 @ ( sK35_B @ SV424 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3163]) ).
thf(3213,plain,
! [SV426: $i,SV632: $i,SV667: $i] :
( ( ( ~ ( subset @ SV667 @ SV632 ) )
= $true )
| ( ( in @ SV667 @ ( sK2_SY267 @ SV632 @ SV426 ) )
= $true )
| ( ( ~ ( in @ SV632 @ ( sK1_B @ SV426 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3164]) ).
thf(3214,plain,
! [SV663: $i,SV426: $i,SV653: $i] :
( ( ( ~ ( in @ SV653 @ ( sK1_B @ SV426 ) ) )
= $true )
| ( ( ~ ( subset @ SV663 @ SV653 ) )
= $true )
| ( ( in @ SV663 @ ( sK1_B @ SV426 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3166]) ).
thf(3215,plain,
! [SV668: $i,SV427: $i,SV617: $i] :
( ( ( in @ ( ordered_pair @ ( sK20_C @ SV617 @ SV427 ) @ SV668 ) @ SV427 )
= $false )
| ( ( ~ ( in @ ( sK20_C @ SV617 @ SV427 ) @ SV617 ) )
= $true )
| ( ( SV617
= ( relation_dom @ SV427 ) )
= $true )
| ( ( relation @ SV427 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3169]) ).
thf(3216,plain,
! [SV618: $i,SV427: $i,SV669: $i] :
( ( ( ! [SY872: $i] :
~ ( in @ ( ordered_pair @ SV669 @ SY872 ) @ SV427 ) )
= $true )
| ( ( in @ SV669 @ SV618 )
= $true )
| ( ( SV618
= ( relation_dom @ SV427 ) )
= $false )
| ( ( relation @ SV427 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3170]) ).
thf(3217,plain,
! [SV427: $i,SV618: $i,SV670: $i] :
( ( ( ~ ( in @ SV670 @ SV618 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV670 @ ( sK19_D @ SV670 @ SV618 @ SV427 ) ) @ SV427 )
= $true )
| ( ( SV618
= ( relation_dom @ SV427 ) )
= $false )
| ( ( relation @ SV427 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3171]) ).
thf(3218,plain,
! [SV428: $i,SV566: $i,SV591: $i] :
( ( ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV591 )
= $false )
| ( ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV566 )
= $true )
| ( ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV428 )
= $false )
| ( ( SV591
= ( set_difference @ SV428 @ SV566 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3172]) ).
thf(3219,plain,
! [SV428: $i,SV566: $i,SV591: $i] :
( ( ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV591 )
= $true )
| ( ( SV591
= ( set_difference @ SV428 @ SV566 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3173]) ).
thf(3220,plain,
! [SV428: $i,SV566: $i,SV591: $i] :
( ( ( ~ ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV566 ) )
= $true )
| ( ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV591 )
= $true )
| ( ( SV591
= ( set_difference @ SV428 @ SV566 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3174]) ).
thf(3221,plain,
! [SV592: $i,SV567: $i,SV428: $i,SV664: $i] :
( ( ( ~ ( in @ SV664 @ SV428 ) )
= $true )
| ( ( in @ SV664 @ SV567 )
= $true )
| ( ( in @ SV664 @ SV592 )
= $true )
| ( ( SV592
= ( set_difference @ SV428 @ SV567 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3175]) ).
thf(3222,plain,
! [SV567: $i,SV428: $i,SV592: $i] :
( ( ( ! [SY821: $i] :
( ~ ( in @ SY821 @ SV592 )
| ( in @ SY821 @ SV428 ) ) )
= $true )
| ( ( SV592
= ( set_difference @ SV428 @ SV567 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3176]) ).
thf(3223,plain,
! [SV428: $i,SV567: $i,SV592: $i] :
( ( ( ! [SY822: $i] :
( ~ ( in @ SY822 @ SV592 )
| ~ ( in @ SY822 @ SV567 ) ) )
= $true )
| ( ( SV592
= ( set_difference @ SV428 @ SV567 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3177]) ).
thf(3224,plain,
! [SV429: $i,SV570: $i,SV593: $i] :
( ( ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV570 )
= $false )
| ( ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV429 )
= $false )
| ( ( ~ ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV593 ) )
= $true )
| ( ( SV593
= ( set_intersection2 @ SV429 @ SV570 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3178]) ).
thf(3225,plain,
! [SV429: $i,SV570: $i,SV593: $i] :
( ( ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV429 )
= $true )
| ( ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV593 )
= $true )
| ( ( SV593
= ( set_intersection2 @ SV429 @ SV570 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3179]) ).
thf(3226,plain,
! [SV429: $i,SV570: $i,SV593: $i] :
( ( ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV570 )
= $true )
| ( ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV593 )
= $true )
| ( ( SV593
= ( set_intersection2 @ SV429 @ SV570 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3180]) ).
thf(3227,plain,
! [SV594: $i,SV571: $i,SV429: $i,SV665: $i] :
( ( ( ~ ( in @ SV665 @ SV429 ) )
= $true )
| ( ( ~ ( in @ SV665 @ SV571 ) )
= $true )
| ( ( in @ SV665 @ SV594 )
= $true )
| ( ( SV594
= ( set_intersection2 @ SV429 @ SV571 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3181]) ).
thf(3228,plain,
! [SV571: $i,SV429: $i,SV594: $i] :
( ( ( ! [SY824: $i] :
( ~ ( in @ SY824 @ SV594 )
| ( in @ SY824 @ SV429 ) ) )
= $true )
| ( ( SV594
= ( set_intersection2 @ SV429 @ SV571 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3182]) ).
thf(3229,plain,
! [SV429: $i,SV571: $i,SV594: $i] :
( ( ( ! [SY825: $i] :
( ~ ( in @ SY825 @ SV594 )
| ( in @ SY825 @ SV571 ) ) )
= $true )
| ( ( SV594
= ( set_intersection2 @ SV429 @ SV571 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3183]) ).
thf(3230,plain,
! [SV430: $i,SV619: $i,SV671: $i] :
( ( ( in @ ( ordered_pair @ SV671 @ ( sK13_C @ SV619 @ SV430 ) ) @ SV430 )
= $false )
| ( ( ~ ( in @ ( sK13_C @ SV619 @ SV430 ) @ SV619 ) )
= $true )
| ( ( SV619
= ( relation_rng @ SV430 ) )
= $true )
| ( ( relation @ SV430 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3184]) ).
thf(3231,plain,
! [SV620: $i,SV430: $i,SV672: $i] :
( ( ( ! [SY873: $i] :
~ ( in @ ( ordered_pair @ SY873 @ SV672 ) @ SV430 ) )
= $true )
| ( ( in @ SV672 @ SV620 )
= $true )
| ( ( SV620
= ( relation_rng @ SV430 ) )
= $false )
| ( ( relation @ SV430 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3185]) ).
thf(3232,plain,
! [SV430: $i,SV620: $i,SV673: $i] :
( ( ( ~ ( in @ SV673 @ SV620 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK12_D @ SV673 @ SV620 @ SV430 ) @ SV673 ) @ SV430 )
= $true )
| ( ( SV620
= ( relation_rng @ SV430 ) )
= $false )
| ( ( relation @ SV430 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3186]) ).
thf(3233,plain,
! [SV572: $i,SV525: $i,SV656: $i] :
( ( ( in @ SV656 @ SV525 )
= $false )
| ( ( in @ ( sK17_C @ SV572 @ SV525 ) @ SV656 )
= $false )
| ( ( ~ ( in @ ( sK17_C @ SV572 @ SV525 ) @ SV572 ) )
= $true )
| ( ( SV572
= ( union @ SV525 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3187]) ).
thf(3234,plain,
! [SV573: $i,SV526: $i,SV674: $i,SV657: $i] :
( ( ( ~ ( in @ SV657 @ SV674 ) )
= $true )
| ( ( ~ ( in @ SV674 @ SV526 ) )
= $true )
| ( ( in @ SV657 @ SV573 )
= $true )
| ( ( SV573
= ( union @ SV526 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3190]) ).
thf(3235,plain,
! [SV526: $i,SV573: $i,SV658: $i] :
( ( ( ~ ( in @ SV658 @ ( sK16_D @ SV658 @ SV573 @ SV526 ) )
| ~ ( in @ ( sK16_D @ SV658 @ SV573 @ SV526 ) @ SV526 ) )
= $false )
| ( ( in @ SV658 @ SV573 )
= $false )
| ( ( SV573
= ( union @ SV526 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3191]) ).
thf(3236,plain,
! [SV433: $i,SV580: $i,SV595: $i] :
( ( ( ~ ( in @ ( sK25_D @ SV595 @ SV580 @ SV433 ) @ SV595 ) )
= $true )
| ( ( ( ( sK25_D @ SV595 @ SV580 @ SV433 )
!= SV433 ) )
= $true )
| ( ( SV595
= ( unordered_pair @ SV433 @ SV580 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3192]) ).
thf(3237,plain,
! [SV433: $i,SV580: $i,SV595: $i] :
( ( ( ~ ( in @ ( sK25_D @ SV595 @ SV580 @ SV433 ) @ SV595 ) )
= $true )
| ( ( ( ( sK25_D @ SV595 @ SV580 @ SV433 )
!= SV580 ) )
= $true )
| ( ( SV595
= ( unordered_pair @ SV433 @ SV580 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3193]) ).
thf(3238,plain,
! [SV581: $i,SV433: $i,SV596: $i,SV666: $i] :
( ( ( in @ SV666 @ SV596 )
= $false )
| ( ( ( SV666 = SV433 )
| ( SV666 = SV581 ) )
= $true )
| ( ( SV596
= ( unordered_pair @ SV433 @ SV581 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3194]) ).
thf(3239,plain,
! [SV581: $i,SV596: $i,SV433: $i] :
( ( ( ! [SY827: $i] :
( ( SY827 != SV433 )
| ( in @ SY827 @ SV596 ) ) )
= $true )
| ( ( SV596
= ( unordered_pair @ SV433 @ SV581 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3195]) ).
thf(3240,plain,
! [SV433: $i,SV596: $i,SV581: $i] :
( ( ( ! [SY828: $i] :
( ( SY828 != SV581 )
| ( in @ SY828 @ SV596 ) ) )
= $true )
| ( ( SV596
= ( unordered_pair @ SV433 @ SV581 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3196]) ).
thf(3241,plain,
! [SV621: $i,SV643: $i] :
( ( ( ~ ( ~ ( in @ ( sK40_SY287 @ SV643 @ SV621 ) @ SV621 )
| ~ ~ ( in @ ( sK39_C @ SV643 @ SV621 ) @ ( sK40_SY287 @ SV643 @ SV621 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK39_C @ SV643 @ SV621 ) @ SV643 ) )
= $true )
| ( ( SV643
= ( set_meet @ SV621 ) )
= $true )
| ( ( SV621 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3197]) ).
thf(3242,plain,
! [SV643: $i,SV621: $i] :
( ( ( ! [SY865: $i] :
( ~ ( in @ SY865 @ SV621 )
| ( in @ ( sK39_C @ SV643 @ SV621 ) @ SY865 ) ) )
= $true )
| ( ( in @ ( sK39_C @ SV643 @ SV621 ) @ SV643 )
= $true )
| ( ( SV643
= ( set_meet @ SV621 ) )
= $true )
| ( ( SV621 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3198]) ).
thf(3243,plain,
! [SV622: $i,SV644: $i] :
( ( ( ! [SY866: $i] :
( ~ ( ~ ( in @ ( sK38_D @ SY866 @ SV644 @ SV622 ) @ SV622 )
| ~ ~ ( in @ SY866 @ ( sK38_D @ SY866 @ SV644 @ SV622 ) ) )
| ( in @ SY866 @ SV644 ) ) )
= $true )
| ( ( SV644
= ( set_meet @ SV622 ) )
= $false )
| ( ( SV622 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3199]) ).
thf(3244,plain,
! [SV622: $i,SV644: $i] :
( ( ( ! [SY867: $i] :
( ~ ( in @ SY867 @ SV644 )
| ! [SY858: $i] :
( ~ ( in @ SY858 @ SV622 )
| ( in @ SY867 @ SY858 ) ) ) )
= $true )
| ( ( SV644
= ( set_meet @ SV622 ) )
= $false )
| ( ( SV622 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3200]) ).
thf(3245,plain,
! [SV420: $i,SV597: $i] :
( ( ( in @ ( ordered_pair @ ( sK10_C @ SV597 @ SV420 ) @ ( sK11_SY272 @ SV597 @ SV420 ) ) @ SV597 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK11_SY272 @ SV597 @ SV420 ) @ ( sK10_C @ SV597 @ SV420 ) ) @ SV420 ) )
= $true )
| ( ( SV597
= ( relation_inverse @ SV420 ) )
= $true )
| ( ( relation @ SV597 )
= $false )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3203]) ).
thf(3246,plain,
! [SV420: $i,SV598: $i,SV675: $i] :
( ( ( ! [SY874: $i] :
( ~ ( in @ ( ordered_pair @ SV675 @ SY874 ) @ SV598 )
| ( in @ ( ordered_pair @ SY874 @ SV675 ) @ SV420 ) ) )
= $true )
| ( ( SV598
= ( relation_inverse @ SV420 ) )
= $false )
| ( ( relation @ SV598 )
= $false )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3205]) ).
thf(3247,plain,
! [SV598: $i,SV420: $i,SV676: $i] :
( ( ( ! [SY875: $i] :
( ~ ( in @ ( ordered_pair @ SY875 @ SV676 ) @ SV420 )
| ( in @ ( ordered_pair @ SV676 @ SY875 ) @ SV598 ) ) )
= $true )
| ( ( SV598
= ( relation_inverse @ SV420 ) )
= $false )
| ( ( relation @ SV598 )
= $false )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3206]) ).
thf(3248,plain,
! [SV423: $i,SV547: $i,SV589: $i] :
( ( ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV589 )
= $false )
| ( ( ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV423 ) )
= $true )
| ( ( SV589
= ( set_union2 @ SV423 @ SV547 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3207]) ).
thf(3249,plain,
! [SV423: $i,SV547: $i,SV589: $i] :
( ( ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV589 )
= $false )
| ( ( ~ ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV547 ) )
= $true )
| ( ( SV589
= ( set_union2 @ SV423 @ SV547 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3208]) ).
thf(3250,plain,
! [SV590: $i,SV548: $i,SV423: $i,SV661: $i] :
( ( ( in @ SV661 @ SV423 )
= $true )
| ( ( in @ SV661 @ SV548 )
= $true )
| ( ( in @ SV661 @ SV590 )
= $false )
| ( ( SV590
= ( set_union2 @ SV423 @ SV548 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3209]) ).
thf(3251,plain,
! [SV548: $i,SV590: $i,SV423: $i,SV677: $i] :
( ( ( ~ ( in @ SV677 @ SV423 )
| ( in @ SV677 @ SV590 ) )
= $true )
| ( ( SV590
= ( set_union2 @ SV423 @ SV548 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3210]) ).
thf(3252,plain,
! [SV423: $i,SV590: $i,SV548: $i,SV678: $i] :
( ( ( ~ ( in @ SV678 @ SV548 )
| ( in @ SV678 @ SV590 ) )
= $true )
| ( ( SV590
= ( set_union2 @ SV423 @ SV548 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3211]) ).
thf(3253,plain,
! [SV662: $i,SV424: $i,SV652: $i] :
( ( ( in @ SV652 @ ( sK35_B @ SV424 ) )
= $false )
| ( ( ~ ( subset @ SV662 @ SV652 ) )
= $true )
| ( ( in @ SV662 @ ( sK35_B @ SV424 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3212]) ).
thf(3254,plain,
! [SV426: $i,SV632: $i,SV667: $i] :
( ( ( subset @ SV667 @ SV632 )
= $false )
| ( ( in @ SV667 @ ( sK2_SY267 @ SV632 @ SV426 ) )
= $true )
| ( ( ~ ( in @ SV632 @ ( sK1_B @ SV426 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3213]) ).
thf(3255,plain,
! [SV663: $i,SV426: $i,SV653: $i] :
( ( ( in @ SV653 @ ( sK1_B @ SV426 ) )
= $false )
| ( ( ~ ( subset @ SV663 @ SV653 ) )
= $true )
| ( ( in @ SV663 @ ( sK1_B @ SV426 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3214]) ).
thf(3256,plain,
! [SV668: $i,SV427: $i,SV617: $i] :
( ( ( in @ ( sK20_C @ SV617 @ SV427 ) @ SV617 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK20_C @ SV617 @ SV427 ) @ SV668 ) @ SV427 )
= $false )
| ( ( SV617
= ( relation_dom @ SV427 ) )
= $true )
| ( ( relation @ SV427 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3215]) ).
thf(3257,plain,
! [SV618: $i,SV427: $i,SV679: $i,SV669: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV669 @ SV679 ) @ SV427 ) )
= $true )
| ( ( in @ SV669 @ SV618 )
= $true )
| ( ( SV618
= ( relation_dom @ SV427 ) )
= $false )
| ( ( relation @ SV427 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3216]) ).
thf(3258,plain,
! [SV427: $i,SV618: $i,SV670: $i] :
( ( ( in @ SV670 @ SV618 )
= $false )
| ( ( in @ ( ordered_pair @ SV670 @ ( sK19_D @ SV670 @ SV618 @ SV427 ) ) @ SV427 )
= $true )
| ( ( SV618
= ( relation_dom @ SV427 ) )
= $false )
| ( ( relation @ SV427 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3217]) ).
thf(3259,plain,
! [SV428: $i,SV566: $i,SV591: $i] :
( ( ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV566 )
= $false )
| ( ( in @ ( sK15_D @ SV591 @ SV566 @ SV428 ) @ SV591 )
= $true )
| ( ( SV591
= ( set_difference @ SV428 @ SV566 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3220]) ).
thf(3260,plain,
! [SV592: $i,SV567: $i,SV428: $i,SV664: $i] :
( ( ( in @ SV664 @ SV428 )
= $false )
| ( ( in @ SV664 @ SV567 )
= $true )
| ( ( in @ SV664 @ SV592 )
= $true )
| ( ( SV592
= ( set_difference @ SV428 @ SV567 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3221]) ).
thf(3261,plain,
! [SV567: $i,SV428: $i,SV592: $i,SV680: $i] :
( ( ( ~ ( in @ SV680 @ SV592 )
| ( in @ SV680 @ SV428 ) )
= $true )
| ( ( SV592
= ( set_difference @ SV428 @ SV567 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3222]) ).
thf(3262,plain,
! [SV428: $i,SV567: $i,SV592: $i,SV681: $i] :
( ( ( ~ ( in @ SV681 @ SV592 )
| ~ ( in @ SV681 @ SV567 ) )
= $true )
| ( ( SV592
= ( set_difference @ SV428 @ SV567 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3223]) ).
thf(3263,plain,
! [SV429: $i,SV570: $i,SV593: $i] :
( ( ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV593 )
= $false )
| ( ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV429 )
= $false )
| ( ( in @ ( sK22_D @ SV593 @ SV570 @ SV429 ) @ SV570 )
= $false )
| ( ( SV593
= ( set_intersection2 @ SV429 @ SV570 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3224]) ).
thf(3264,plain,
! [SV594: $i,SV571: $i,SV429: $i,SV665: $i] :
( ( ( in @ SV665 @ SV429 )
= $false )
| ( ( ~ ( in @ SV665 @ SV571 ) )
= $true )
| ( ( in @ SV665 @ SV594 )
= $true )
| ( ( SV594
= ( set_intersection2 @ SV429 @ SV571 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3227]) ).
thf(3265,plain,
! [SV571: $i,SV429: $i,SV594: $i,SV682: $i] :
( ( ( ~ ( in @ SV682 @ SV594 )
| ( in @ SV682 @ SV429 ) )
= $true )
| ( ( SV594
= ( set_intersection2 @ SV429 @ SV571 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3228]) ).
thf(3266,plain,
! [SV429: $i,SV571: $i,SV594: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV594 )
| ( in @ SV683 @ SV571 ) )
= $true )
| ( ( SV594
= ( set_intersection2 @ SV429 @ SV571 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3229]) ).
thf(3267,plain,
! [SV671: $i,SV430: $i,SV619: $i] :
( ( ( in @ ( sK13_C @ SV619 @ SV430 ) @ SV619 )
= $false )
| ( ( in @ ( ordered_pair @ SV671 @ ( sK13_C @ SV619 @ SV430 ) ) @ SV430 )
= $false )
| ( ( SV619
= ( relation_rng @ SV430 ) )
= $true )
| ( ( relation @ SV430 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3230]) ).
thf(3268,plain,
! [SV620: $i,SV430: $i,SV672: $i,SV684: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV684 @ SV672 ) @ SV430 ) )
= $true )
| ( ( in @ SV672 @ SV620 )
= $true )
| ( ( SV620
= ( relation_rng @ SV430 ) )
= $false )
| ( ( relation @ SV430 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3231]) ).
thf(3269,plain,
! [SV430: $i,SV620: $i,SV673: $i] :
( ( ( in @ SV673 @ SV620 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK12_D @ SV673 @ SV620 @ SV430 ) @ SV673 ) @ SV430 )
= $true )
| ( ( SV620
= ( relation_rng @ SV430 ) )
= $false )
| ( ( relation @ SV430 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3232]) ).
thf(3270,plain,
! [SV656: $i,SV525: $i,SV572: $i] :
( ( ( in @ ( sK17_C @ SV572 @ SV525 ) @ SV572 )
= $false )
| ( ( in @ ( sK17_C @ SV572 @ SV525 ) @ SV656 )
= $false )
| ( ( in @ SV656 @ SV525 )
= $false )
| ( ( SV572
= ( union @ SV525 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3233]) ).
thf(3271,plain,
! [SV573: $i,SV526: $i,SV674: $i,SV657: $i] :
( ( ( in @ SV657 @ SV674 )
= $false )
| ( ( ~ ( in @ SV674 @ SV526 ) )
= $true )
| ( ( in @ SV657 @ SV573 )
= $true )
| ( ( SV573
= ( union @ SV526 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3234]) ).
thf(3272,plain,
! [SV526: $i,SV573: $i,SV658: $i] :
( ( ( ~ ( in @ SV658 @ ( sK16_D @ SV658 @ SV573 @ SV526 ) ) )
= $false )
| ( ( in @ SV658 @ SV573 )
= $false )
| ( ( SV573
= ( union @ SV526 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3235]) ).
thf(3273,plain,
! [SV526: $i,SV573: $i,SV658: $i] :
( ( ( ~ ( in @ ( sK16_D @ SV658 @ SV573 @ SV526 ) @ SV526 ) )
= $false )
| ( ( in @ SV658 @ SV573 )
= $false )
| ( ( SV573
= ( union @ SV526 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3235]) ).
thf(3274,plain,
! [SV433: $i,SV580: $i,SV595: $i] :
( ( ( in @ ( sK25_D @ SV595 @ SV580 @ SV433 ) @ SV595 )
= $false )
| ( ( ( ( sK25_D @ SV595 @ SV580 @ SV433 )
!= SV433 ) )
= $true )
| ( ( SV595
= ( unordered_pair @ SV433 @ SV580 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3236]) ).
thf(3275,plain,
! [SV433: $i,SV580: $i,SV595: $i] :
( ( ( in @ ( sK25_D @ SV595 @ SV580 @ SV433 ) @ SV595 )
= $false )
| ( ( ( ( sK25_D @ SV595 @ SV580 @ SV433 )
!= SV580 ) )
= $true )
| ( ( SV595
= ( unordered_pair @ SV433 @ SV580 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3237]) ).
thf(3276,plain,
! [SV596: $i,SV581: $i,SV433: $i,SV666: $i] :
( ( ( SV666 = SV433 )
= $true )
| ( ( SV666 = SV581 )
= $true )
| ( ( in @ SV666 @ SV596 )
= $false )
| ( ( SV596
= ( unordered_pair @ SV433 @ SV581 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3238]) ).
thf(3277,plain,
! [SV581: $i,SV596: $i,SV433: $i,SV685: $i] :
( ( ( ( SV685 != SV433 )
| ( in @ SV685 @ SV596 ) )
= $true )
| ( ( SV596
= ( unordered_pair @ SV433 @ SV581 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3239]) ).
thf(3278,plain,
! [SV433: $i,SV596: $i,SV581: $i,SV686: $i] :
( ( ( ( SV686 != SV581 )
| ( in @ SV686 @ SV596 ) )
= $true )
| ( ( SV596
= ( unordered_pair @ SV433 @ SV581 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3240]) ).
thf(3279,plain,
! [SV621: $i,SV643: $i] :
( ( ( ~ ( in @ ( sK40_SY287 @ SV643 @ SV621 ) @ SV621 )
| ~ ~ ( in @ ( sK39_C @ SV643 @ SV621 ) @ ( sK40_SY287 @ SV643 @ SV621 ) ) )
= $false )
| ( ( ~ ( in @ ( sK39_C @ SV643 @ SV621 ) @ SV643 ) )
= $true )
| ( ( SV643
= ( set_meet @ SV621 ) )
= $true )
| ( ( SV621 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3241]) ).
thf(3280,plain,
! [SV643: $i,SV621: $i,SV687: $i] :
( ( ( ~ ( in @ SV687 @ SV621 )
| ( in @ ( sK39_C @ SV643 @ SV621 ) @ SV687 ) )
= $true )
| ( ( in @ ( sK39_C @ SV643 @ SV621 ) @ SV643 )
= $true )
| ( ( SV643
= ( set_meet @ SV621 ) )
= $true )
| ( ( SV621 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3242]) ).
thf(3281,plain,
! [SV622: $i,SV644: $i,SV688: $i] :
( ( ( ~ ( ~ ( in @ ( sK38_D @ SV688 @ SV644 @ SV622 ) @ SV622 )
| ~ ~ ( in @ SV688 @ ( sK38_D @ SV688 @ SV644 @ SV622 ) ) )
| ( in @ SV688 @ SV644 ) )
= $true )
| ( ( SV644
= ( set_meet @ SV622 ) )
= $false )
| ( ( SV622 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3243]) ).
thf(3282,plain,
! [SV622: $i,SV644: $i,SV689: $i] :
( ( ( ~ ( in @ SV689 @ SV644 )
| ! [SY876: $i] :
( ~ ( in @ SY876 @ SV622 )
| ( in @ SV689 @ SY876 ) ) )
= $true )
| ( ( SV644
= ( set_meet @ SV622 ) )
= $false )
| ( ( SV622 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3244]) ).
thf(3283,plain,
! [SV420: $i,SV597: $i] :
( ( ( in @ ( ordered_pair @ ( sK11_SY272 @ SV597 @ SV420 ) @ ( sK10_C @ SV597 @ SV420 ) ) @ SV420 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK10_C @ SV597 @ SV420 ) @ ( sK11_SY272 @ SV597 @ SV420 ) ) @ SV597 )
= $false )
| ( ( SV597
= ( relation_inverse @ SV420 ) )
= $true )
| ( ( relation @ SV597 )
= $false )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3245]) ).
thf(3284,plain,
! [SV420: $i,SV598: $i,SV690: $i,SV675: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV675 @ SV690 ) @ SV598 )
| ( in @ ( ordered_pair @ SV690 @ SV675 ) @ SV420 ) )
= $true )
| ( ( SV598
= ( relation_inverse @ SV420 ) )
= $false )
| ( ( relation @ SV598 )
= $false )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3246]) ).
thf(3285,plain,
! [SV598: $i,SV420: $i,SV676: $i,SV691: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV691 @ SV676 ) @ SV420 )
| ( in @ ( ordered_pair @ SV676 @ SV691 ) @ SV598 ) )
= $true )
| ( ( SV598
= ( relation_inverse @ SV420 ) )
= $false )
| ( ( relation @ SV598 )
= $false )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3247]) ).
thf(3286,plain,
! [SV423: $i,SV547: $i,SV589: $i] :
( ( ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV423 )
= $false )
| ( ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV589 )
= $false )
| ( ( SV589
= ( set_union2 @ SV423 @ SV547 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3248]) ).
thf(3287,plain,
! [SV423: $i,SV547: $i,SV589: $i] :
( ( ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV547 )
= $false )
| ( ( in @ ( sK24_D @ SV589 @ SV547 @ SV423 ) @ SV589 )
= $false )
| ( ( SV589
= ( set_union2 @ SV423 @ SV547 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3249]) ).
thf(3288,plain,
! [SV548: $i,SV590: $i,SV423: $i,SV677: $i] :
( ( ( ~ ( in @ SV677 @ SV423 ) )
= $true )
| ( ( in @ SV677 @ SV590 )
= $true )
| ( ( SV590
= ( set_union2 @ SV423 @ SV548 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3251]) ).
thf(3289,plain,
! [SV423: $i,SV590: $i,SV548: $i,SV678: $i] :
( ( ( ~ ( in @ SV678 @ SV548 ) )
= $true )
| ( ( in @ SV678 @ SV590 )
= $true )
| ( ( SV590
= ( set_union2 @ SV423 @ SV548 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3252]) ).
thf(3290,plain,
! [SV424: $i,SV652: $i,SV662: $i] :
( ( ( subset @ SV662 @ SV652 )
= $false )
| ( ( in @ SV652 @ ( sK35_B @ SV424 ) )
= $false )
| ( ( in @ SV662 @ ( sK35_B @ SV424 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3253]) ).
thf(3291,plain,
! [SV667: $i,SV426: $i,SV632: $i] :
( ( ( in @ SV632 @ ( sK1_B @ SV426 ) )
= $false )
| ( ( in @ SV667 @ ( sK2_SY267 @ SV632 @ SV426 ) )
= $true )
| ( ( subset @ SV667 @ SV632 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3254]) ).
thf(3292,plain,
! [SV426: $i,SV653: $i,SV663: $i] :
( ( ( subset @ SV663 @ SV653 )
= $false )
| ( ( in @ SV653 @ ( sK1_B @ SV426 ) )
= $false )
| ( ( in @ SV663 @ ( sK1_B @ SV426 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3255]) ).
thf(3293,plain,
! [SV618: $i,SV427: $i,SV679: $i,SV669: $i] :
( ( ( in @ ( ordered_pair @ SV669 @ SV679 ) @ SV427 )
= $false )
| ( ( in @ SV669 @ SV618 )
= $true )
| ( ( SV618
= ( relation_dom @ SV427 ) )
= $false )
| ( ( relation @ SV427 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3257]) ).
thf(3294,plain,
! [SV567: $i,SV428: $i,SV592: $i,SV680: $i] :
( ( ( ~ ( in @ SV680 @ SV592 ) )
= $true )
| ( ( in @ SV680 @ SV428 )
= $true )
| ( ( SV592
= ( set_difference @ SV428 @ SV567 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3261]) ).
thf(3295,plain,
! [SV428: $i,SV567: $i,SV592: $i,SV681: $i] :
( ( ( ~ ( in @ SV681 @ SV592 ) )
= $true )
| ( ( ~ ( in @ SV681 @ SV567 ) )
= $true )
| ( ( SV592
= ( set_difference @ SV428 @ SV567 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3262]) ).
thf(3296,plain,
! [SV594: $i,SV429: $i,SV571: $i,SV665: $i] :
( ( ( in @ SV665 @ SV571 )
= $false )
| ( ( in @ SV665 @ SV429 )
= $false )
| ( ( in @ SV665 @ SV594 )
= $true )
| ( ( SV594
= ( set_intersection2 @ SV429 @ SV571 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3264]) ).
thf(3297,plain,
! [SV571: $i,SV429: $i,SV594: $i,SV682: $i] :
( ( ( ~ ( in @ SV682 @ SV594 ) )
= $true )
| ( ( in @ SV682 @ SV429 )
= $true )
| ( ( SV594
= ( set_intersection2 @ SV429 @ SV571 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3265]) ).
thf(3298,plain,
! [SV429: $i,SV571: $i,SV594: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV594 ) )
= $true )
| ( ( in @ SV683 @ SV571 )
= $true )
| ( ( SV594
= ( set_intersection2 @ SV429 @ SV571 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3266]) ).
thf(3299,plain,
! [SV620: $i,SV430: $i,SV672: $i,SV684: $i] :
( ( ( in @ ( ordered_pair @ SV684 @ SV672 ) @ SV430 )
= $false )
| ( ( in @ SV672 @ SV620 )
= $true )
| ( ( SV620
= ( relation_rng @ SV430 ) )
= $false )
| ( ( relation @ SV430 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3268]) ).
thf(3300,plain,
! [SV573: $i,SV657: $i,SV526: $i,SV674: $i] :
( ( ( in @ SV674 @ SV526 )
= $false )
| ( ( in @ SV657 @ SV674 )
= $false )
| ( ( in @ SV657 @ SV573 )
= $true )
| ( ( SV573
= ( union @ SV526 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3271]) ).
thf(3301,plain,
! [SV526: $i,SV573: $i,SV658: $i] :
( ( ( in @ SV658 @ ( sK16_D @ SV658 @ SV573 @ SV526 ) )
= $true )
| ( ( in @ SV658 @ SV573 )
= $false )
| ( ( SV573
= ( union @ SV526 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3272]) ).
thf(3302,plain,
! [SV526: $i,SV573: $i,SV658: $i] :
( ( ( in @ ( sK16_D @ SV658 @ SV573 @ SV526 ) @ SV526 )
= $true )
| ( ( in @ SV658 @ SV573 )
= $false )
| ( ( SV573
= ( union @ SV526 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3273]) ).
thf(3303,plain,
! [SV433: $i,SV580: $i,SV595: $i] :
( ( ( ( sK25_D @ SV595 @ SV580 @ SV433 )
= SV433 )
= $false )
| ( ( in @ ( sK25_D @ SV595 @ SV580 @ SV433 ) @ SV595 )
= $false )
| ( ( SV595
= ( unordered_pair @ SV433 @ SV580 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3274]) ).
thf(3304,plain,
! [SV433: $i,SV580: $i,SV595: $i] :
( ( ( ( sK25_D @ SV595 @ SV580 @ SV433 )
= SV580 )
= $false )
| ( ( in @ ( sK25_D @ SV595 @ SV580 @ SV433 ) @ SV595 )
= $false )
| ( ( SV595
= ( unordered_pair @ SV433 @ SV580 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3275]) ).
thf(3305,plain,
! [SV581: $i,SV596: $i,SV433: $i,SV685: $i] :
( ( ( ( SV685 != SV433 ) )
= $true )
| ( ( in @ SV685 @ SV596 )
= $true )
| ( ( SV596
= ( unordered_pair @ SV433 @ SV581 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3277]) ).
thf(3306,plain,
! [SV433: $i,SV596: $i,SV581: $i,SV686: $i] :
( ( ( ( SV686 != SV581 ) )
= $true )
| ( ( in @ SV686 @ SV596 )
= $true )
| ( ( SV596
= ( unordered_pair @ SV433 @ SV581 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3278]) ).
thf(3307,plain,
! [SV621: $i,SV643: $i] :
( ( ( ~ ( in @ ( sK40_SY287 @ SV643 @ SV621 ) @ SV621 ) )
= $false )
| ( ( ~ ( in @ ( sK39_C @ SV643 @ SV621 ) @ SV643 ) )
= $true )
| ( ( SV643
= ( set_meet @ SV621 ) )
= $true )
| ( ( SV621 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3279]) ).
thf(3308,plain,
! [SV621: $i,SV643: $i] :
( ( ( ~ ~ ( in @ ( sK39_C @ SV643 @ SV621 ) @ ( sK40_SY287 @ SV643 @ SV621 ) ) )
= $false )
| ( ( ~ ( in @ ( sK39_C @ SV643 @ SV621 ) @ SV643 ) )
= $true )
| ( ( SV643
= ( set_meet @ SV621 ) )
= $true )
| ( ( SV621 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3279]) ).
thf(3309,plain,
! [SV643: $i,SV621: $i,SV687: $i] :
( ( ( ~ ( in @ SV687 @ SV621 ) )
= $true )
| ( ( in @ ( sK39_C @ SV643 @ SV621 ) @ SV687 )
= $true )
| ( ( in @ ( sK39_C @ SV643 @ SV621 ) @ SV643 )
= $true )
| ( ( SV643
= ( set_meet @ SV621 ) )
= $true )
| ( ( SV621 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3280]) ).
thf(3310,plain,
! [SV622: $i,SV644: $i,SV688: $i] :
( ( ( ~ ( ~ ( in @ ( sK38_D @ SV688 @ SV644 @ SV622 ) @ SV622 )
| ~ ~ ( in @ SV688 @ ( sK38_D @ SV688 @ SV644 @ SV622 ) ) ) )
= $true )
| ( ( in @ SV688 @ SV644 )
= $true )
| ( ( SV644
= ( set_meet @ SV622 ) )
= $false )
| ( ( SV622 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3281]) ).
thf(3311,plain,
! [SV622: $i,SV644: $i,SV689: $i] :
( ( ( ~ ( in @ SV689 @ SV644 ) )
= $true )
| ( ( ! [SY876: $i] :
( ~ ( in @ SY876 @ SV622 )
| ( in @ SV689 @ SY876 ) ) )
= $true )
| ( ( SV644
= ( set_meet @ SV622 ) )
= $false )
| ( ( SV622 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3282]) ).
thf(3312,plain,
! [SV420: $i,SV598: $i,SV690: $i,SV675: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV675 @ SV690 ) @ SV598 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV690 @ SV675 ) @ SV420 )
= $true )
| ( ( SV598
= ( relation_inverse @ SV420 ) )
= $false )
| ( ( relation @ SV598 )
= $false )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3284]) ).
thf(3313,plain,
! [SV598: $i,SV420: $i,SV676: $i,SV691: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV691 @ SV676 ) @ SV420 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV676 @ SV691 ) @ SV598 )
= $true )
| ( ( SV598
= ( relation_inverse @ SV420 ) )
= $false )
| ( ( relation @ SV598 )
= $false )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3285]) ).
thf(3314,plain,
! [SV548: $i,SV590: $i,SV423: $i,SV677: $i] :
( ( ( in @ SV677 @ SV423 )
= $false )
| ( ( in @ SV677 @ SV590 )
= $true )
| ( ( SV590
= ( set_union2 @ SV423 @ SV548 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3288]) ).
thf(3315,plain,
! [SV423: $i,SV590: $i,SV548: $i,SV678: $i] :
( ( ( in @ SV678 @ SV548 )
= $false )
| ( ( in @ SV678 @ SV590 )
= $true )
| ( ( SV590
= ( set_union2 @ SV423 @ SV548 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3289]) ).
thf(3316,plain,
! [SV567: $i,SV428: $i,SV592: $i,SV680: $i] :
( ( ( in @ SV680 @ SV592 )
= $false )
| ( ( in @ SV680 @ SV428 )
= $true )
| ( ( SV592
= ( set_difference @ SV428 @ SV567 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3294]) ).
thf(3317,plain,
! [SV428: $i,SV567: $i,SV592: $i,SV681: $i] :
( ( ( in @ SV681 @ SV592 )
= $false )
| ( ( ~ ( in @ SV681 @ SV567 ) )
= $true )
| ( ( SV592
= ( set_difference @ SV428 @ SV567 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3295]) ).
thf(3318,plain,
! [SV571: $i,SV429: $i,SV594: $i,SV682: $i] :
( ( ( in @ SV682 @ SV594 )
= $false )
| ( ( in @ SV682 @ SV429 )
= $true )
| ( ( SV594
= ( set_intersection2 @ SV429 @ SV571 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3297]) ).
thf(3319,plain,
! [SV429: $i,SV571: $i,SV594: $i,SV683: $i] :
( ( ( in @ SV683 @ SV594 )
= $false )
| ( ( in @ SV683 @ SV571 )
= $true )
| ( ( SV594
= ( set_intersection2 @ SV429 @ SV571 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3298]) ).
thf(3320,plain,
! [SV581: $i,SV596: $i,SV433: $i,SV685: $i] :
( ( ( SV685 = SV433 )
= $false )
| ( ( in @ SV685 @ SV596 )
= $true )
| ( ( SV596
= ( unordered_pair @ SV433 @ SV581 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3305]) ).
thf(3321,plain,
! [SV433: $i,SV596: $i,SV581: $i,SV686: $i] :
( ( ( SV686 = SV581 )
= $false )
| ( ( in @ SV686 @ SV596 )
= $true )
| ( ( SV596
= ( unordered_pair @ SV433 @ SV581 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3306]) ).
thf(3322,plain,
! [SV621: $i,SV643: $i] :
( ( ( in @ ( sK40_SY287 @ SV643 @ SV621 ) @ SV621 )
= $true )
| ( ( ~ ( in @ ( sK39_C @ SV643 @ SV621 ) @ SV643 ) )
= $true )
| ( ( SV643
= ( set_meet @ SV621 ) )
= $true )
| ( ( SV621 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3307]) ).
thf(3323,plain,
! [SV621: $i,SV643: $i] :
( ( ( ~ ( in @ ( sK39_C @ SV643 @ SV621 ) @ ( sK40_SY287 @ SV643 @ SV621 ) ) )
= $true )
| ( ( ~ ( in @ ( sK39_C @ SV643 @ SV621 ) @ SV643 ) )
= $true )
| ( ( SV643
= ( set_meet @ SV621 ) )
= $true )
| ( ( SV621 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3308]) ).
thf(3324,plain,
! [SV643: $i,SV621: $i,SV687: $i] :
( ( ( in @ SV687 @ SV621 )
= $false )
| ( ( in @ ( sK39_C @ SV643 @ SV621 ) @ SV687 )
= $true )
| ( ( in @ ( sK39_C @ SV643 @ SV621 ) @ SV643 )
= $true )
| ( ( SV643
= ( set_meet @ SV621 ) )
= $true )
| ( ( SV621 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3309]) ).
thf(3325,plain,
! [SV622: $i,SV644: $i,SV688: $i] :
( ( ( ~ ( in @ ( sK38_D @ SV688 @ SV644 @ SV622 ) @ SV622 )
| ~ ~ ( in @ SV688 @ ( sK38_D @ SV688 @ SV644 @ SV622 ) ) )
= $false )
| ( ( in @ SV688 @ SV644 )
= $true )
| ( ( SV644
= ( set_meet @ SV622 ) )
= $false )
| ( ( SV622 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3310]) ).
thf(3326,plain,
! [SV622: $i,SV644: $i,SV689: $i] :
( ( ( in @ SV689 @ SV644 )
= $false )
| ( ( ! [SY876: $i] :
( ~ ( in @ SY876 @ SV622 )
| ( in @ SV689 @ SY876 ) ) )
= $true )
| ( ( SV644
= ( set_meet @ SV622 ) )
= $false )
| ( ( SV622 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3311]) ).
thf(3327,plain,
! [SV420: $i,SV598: $i,SV690: $i,SV675: $i] :
( ( ( in @ ( ordered_pair @ SV675 @ SV690 ) @ SV598 )
= $false )
| ( ( in @ ( ordered_pair @ SV690 @ SV675 ) @ SV420 )
= $true )
| ( ( SV598
= ( relation_inverse @ SV420 ) )
= $false )
| ( ( relation @ SV598 )
= $false )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3312]) ).
thf(3328,plain,
! [SV598: $i,SV420: $i,SV676: $i,SV691: $i] :
( ( ( in @ ( ordered_pair @ SV691 @ SV676 ) @ SV420 )
= $false )
| ( ( in @ ( ordered_pair @ SV676 @ SV691 ) @ SV598 )
= $true )
| ( ( SV598
= ( relation_inverse @ SV420 ) )
= $false )
| ( ( relation @ SV598 )
= $false )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3313]) ).
thf(3329,plain,
! [SV428: $i,SV592: $i,SV567: $i,SV681: $i] :
( ( ( in @ SV681 @ SV567 )
= $false )
| ( ( in @ SV681 @ SV592 )
= $false )
| ( ( SV592
= ( set_difference @ SV428 @ SV567 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3317]) ).
thf(3330,plain,
! [SV621: $i,SV643: $i] :
( ( ( in @ ( sK39_C @ SV643 @ SV621 ) @ SV643 )
= $false )
| ( ( in @ ( sK40_SY287 @ SV643 @ SV621 ) @ SV621 )
= $true )
| ( ( SV643
= ( set_meet @ SV621 ) )
= $true )
| ( ( SV621 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3322]) ).
thf(3331,plain,
! [SV621: $i,SV643: $i] :
( ( ( in @ ( sK39_C @ SV643 @ SV621 ) @ ( sK40_SY287 @ SV643 @ SV621 ) )
= $false )
| ( ( ~ ( in @ ( sK39_C @ SV643 @ SV621 ) @ SV643 ) )
= $true )
| ( ( SV643
= ( set_meet @ SV621 ) )
= $true )
| ( ( SV621 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3323]) ).
thf(3332,plain,
! [SV622: $i,SV644: $i,SV688: $i] :
( ( ( ~ ( in @ ( sK38_D @ SV688 @ SV644 @ SV622 ) @ SV622 ) )
= $false )
| ( ( in @ SV688 @ SV644 )
= $true )
| ( ( SV644
= ( set_meet @ SV622 ) )
= $false )
| ( ( SV622 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3325]) ).
thf(3333,plain,
! [SV622: $i,SV644: $i,SV688: $i] :
( ( ( ~ ~ ( in @ SV688 @ ( sK38_D @ SV688 @ SV644 @ SV622 ) ) )
= $false )
| ( ( in @ SV688 @ SV644 )
= $true )
| ( ( SV644
= ( set_meet @ SV622 ) )
= $false )
| ( ( SV622 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3325]) ).
thf(3334,plain,
! [SV644: $i,SV689: $i,SV622: $i,SV692: $i] :
( ( ( ~ ( in @ SV692 @ SV622 )
| ( in @ SV689 @ SV692 ) )
= $true )
| ( ( in @ SV689 @ SV644 )
= $false )
| ( ( SV644
= ( set_meet @ SV622 ) )
= $false )
| ( ( SV622 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3326]) ).
thf(3335,plain,
! [SV621: $i,SV643: $i] :
( ( ( in @ ( sK39_C @ SV643 @ SV621 ) @ SV643 )
= $false )
| ( ( in @ ( sK39_C @ SV643 @ SV621 ) @ ( sK40_SY287 @ SV643 @ SV621 ) )
= $false )
| ( ( SV643
= ( set_meet @ SV621 ) )
= $true )
| ( ( SV621 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3331]) ).
thf(3336,plain,
! [SV622: $i,SV644: $i,SV688: $i] :
( ( ( in @ ( sK38_D @ SV688 @ SV644 @ SV622 ) @ SV622 )
= $true )
| ( ( in @ SV688 @ SV644 )
= $true )
| ( ( SV644
= ( set_meet @ SV622 ) )
= $false )
| ( ( SV622 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3332]) ).
thf(3337,plain,
! [SV622: $i,SV644: $i,SV688: $i] :
( ( ( ~ ( in @ SV688 @ ( sK38_D @ SV688 @ SV644 @ SV622 ) ) )
= $true )
| ( ( in @ SV688 @ SV644 )
= $true )
| ( ( SV644
= ( set_meet @ SV622 ) )
= $false )
| ( ( SV622 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3333]) ).
thf(3338,plain,
! [SV644: $i,SV689: $i,SV622: $i,SV692: $i] :
( ( ( ~ ( in @ SV692 @ SV622 ) )
= $true )
| ( ( in @ SV689 @ SV692 )
= $true )
| ( ( in @ SV689 @ SV644 )
= $false )
| ( ( SV644
= ( set_meet @ SV622 ) )
= $false )
| ( ( SV622 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3334]) ).
thf(3339,plain,
! [SV622: $i,SV644: $i,SV688: $i] :
( ( ( in @ SV688 @ ( sK38_D @ SV688 @ SV644 @ SV622 ) )
= $false )
| ( ( in @ SV688 @ SV644 )
= $true )
| ( ( SV644
= ( set_meet @ SV622 ) )
= $false )
| ( ( SV622 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3337]) ).
thf(3340,plain,
! [SV644: $i,SV689: $i,SV622: $i,SV692: $i] :
( ( ( in @ SV692 @ SV622 )
= $false )
| ( ( in @ SV689 @ SV692 )
= $true )
| ( ( in @ SV689 @ SV644 )
= $false )
| ( ( SV644
= ( set_meet @ SV622 ) )
= $false )
| ( ( SV622 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3338]) ).
thf(3341,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[1869,3340,3339,3336,3335,3330,3329,3328,3327,3324,3321,3320,3319,3318,3316,3315,3314,3304,3303,3302,3301,3300,3299,3296,3293,3292,3291,3290,3287,3286,3283,3276,3270,3269,3267,3263,3260,3259,3258,3256,3250,3226,3225,3219,3218,3204,3202,3201,3189,3188,3168,3167,3165,3151,3150,3149,3143,3133,3119,3117,3116,3113,3106,3069,3066,3065,3058,3057,3055,3054,3047,3046,3043,3033,3032,3013,3012,3004,3002,2997,2995,2993,2991,2990,2985,2984,2983,2982,2977,2963,2946,2945,2926,2925,2913,2912,2906,2905,2877,2875,2865,2864,2859,2853,2850,2845,2835,2834,2833,2832,2821,2820,2817,2816,2815,2808,2807,2802,2801,2797,2796,2781,2780,2764,2763,2757,2748,2747,2746,2743,2742,2740,2739,2721,2712,2711,2697,2658,2652,2649,2648,2643,2642,2638,2635,2582,2549,2546,2545,2542,2541,2540,2537,2532,2531,2525,2524,2523,2505,2504,2489,2442,2441,2439,2438,2433,2430,2427,2425,2423,2419,2415,2413,2409,2374,2360,2359,2349,2348,2320,2317,2314,2312,2311,2310,2291,2283,2280,2277,2195,2192,2188,2187,2180,2175,2168,2167,2166,2159,2146,2102,2094,2093,2091,2090,2073,2067,2037,2036,2035,2034,2030,1970,1879]) ).
thf(3342,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[3341,1865]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU187+2 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 19 02:22:38 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.41 ....
% 0.20/0.47
% 0.20/0.47 No.of.Axioms: 166
% 0.20/0.47
% 0.20/0.47 Length.of.Defs: 0
% 0.20/0.47
% 0.20/0.47 Contains.Choice.Funs: false
% 0.20/0.52 ..........
% 0.41/0.57 (rf:2,axioms:119,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:168,loop_count:0,foatp_calls:0,translation:fof_full)..................................................................................................................................................................................................................
% 2.33/2.57
% 2.33/2.57 ********************************
% 2.33/2.57 * All subproblems solved! *
% 2.33/2.57 ********************************
% 2.33/2.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:119,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:73,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:3341,loop_count:0,foatp_calls:1,translation:fof_full)
% 6.32/6.51
% 6.32/6.51 %**** Beginning of derivation protocol ****
% 6.32/6.51 % SZS output start CNFRefutation
% See solution above
% 6.32/6.52
% 6.32/6.52 %**** End of derivation protocol ****
% 6.32/6.52 %**** no. of clauses in derivation: 3295 ****
% 6.32/6.52 %**** clause counter: 3341 ****
% 6.32/6.52
% 6.32/6.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:119,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:73,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:3341,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------