%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU158+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:43:08 AM UTC 2026
% Result : Theorem 7.98s 1.50s
% Output : CNFRefutation 7.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 53
% Syntax : Number of formulae : 1598 ( 614 unt; 0 typ; 0 def)
% Number of atoms : 12607 (4890 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 25461 (6032 ~;4462 |; 68 &;14728 @)
% ( 89 <=>; 82 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 48 ( 45 usr; 5 con; 0-3 aty)
% Number of variables : 4503 ( 0 ^;4495 !; 8 ?;4503 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_disjoint,type,
disjoint: $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_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_sK10_SY222,type,
sK10_SY222: $i > $i > $i > $i ).
thf(tp_sK11_SY224,type,
sK11_SY224: $i > $i > $i > $i ).
thf(tp_sK12_SY226,type,
sK12_SY226: $i > $i > $i > $i ).
thf(tp_sK13_SY194,type,
sK13_SY194: $i > $i > $i ).
thf(tp_sK14_SY227,type,
sK14_SY227: $i > $i > $i > $i ).
thf(tp_sK15_SY230,type,
sK15_SY230: $i > $i > $i ).
thf(tp_sK16_SY230,type,
sK16_SY230: $i > $i > $i > $i ).
thf(tp_sK17_SY318,type,
sK17_SY318: $i > $i > $i ).
thf(tp_sK18_SY278,type,
sK18_SY278: $i > $i ).
thf(tp_sK19_SY309,type,
sK19_SY309: $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_SY314,type,
sK20_SY314: $i > $i > $i ).
thf(tp_sK21_SY330,type,
sK21_SY330: $i > $i > $i ).
thf(tp_sK22_SY332,type,
sK22_SY332: $i > $i > $i ).
thf(tp_sK23_SY343,type,
sK23_SY343: $i > $i > $i > $i ).
thf(tp_sK24_SY345,type,
sK24_SY345: $i > $i > $i > $i ).
thf(tp_sK25_SY347,type,
sK25_SY347: $i > $i > $i > $i ).
thf(tp_sK26_SY349,type,
sK26_SY349: $i > $i > $i > $i ).
thf(tp_sK27_SY321,type,
sK27_SY321: $i > $i > $i ).
thf(tp_sK28_SY350,type,
sK28_SY350: $i > $i > $i > $i ).
thf(tp_sK29_SY353,type,
sK29_SY353: $i > $i > $i ).
thf(tp_sK2_SY107,type,
sK2_SY107: $i ).
thf(tp_sK30_SY353,type,
sK30_SY353: $i > $i > $i > $i ).
thf(tp_sK3_SY205,type,
sK3_SY205: $i > $i > $i ).
thf(tp_sK4_SY137,type,
sK4_SY137: $i > $i ).
thf(tp_sK5_SY185,type,
sK5_SY185: $i > $i > $i ).
thf(tp_sK6_SY191,type,
sK6_SY191: $i > $i > $i ).
thf(tp_sK7_SY203,type,
sK7_SY203: $i > $i > $i ).
thf(tp_sK8_SY215,type,
sK8_SY215: $i > $i > $i ).
thf(tp_sK9_SY220,type,
sK9_SY220: $i > $i > $i > $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_set_intersection2,type,
set_intersection2: $i > $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_union,type,
union: $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(6,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(10,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(20,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(21,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(22,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(23,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_tarski) ).
thf(24,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(25,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(26,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(27,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(28,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(29,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(30,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(33,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(34,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(35,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(36,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(38,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(39,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(40,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(41,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(42,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(43,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(49,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(50,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(51,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(53,axiom,
! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(55,axiom,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
thf(56,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(57,axiom,
! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_xboole_1) ).
thf(62,axiom,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(63,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(66,axiom,
! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(68,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(69,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(70,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(71,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(73,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(74,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(75,axiom,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(79,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l50_zfmisc_1) ).
thf(80,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(81,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(83,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(84,axiom,
! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l28_zfmisc_1) ).
thf(85,axiom,
! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l25_zfmisc_1) ).
thf(86,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(87,axiom,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
thf(88,conjecture,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(89,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[88]) ).
thf(90,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $false ),
inference(unfold_def,[status(thm)],[89]) ).
thf(91,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(92,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(93,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(94,plain,
$true = $true,
inference(unfold_def,[status(thm)],[20]) ).
thf(95,plain,
$true = $true,
inference(unfold_def,[status(thm)],[21]) ).
thf(96,plain,
$true = $true,
inference(unfold_def,[status(thm)],[22]) ).
thf(97,plain,
$true = $true,
inference(unfold_def,[status(thm)],[23]) ).
thf(98,plain,
$true = $true,
inference(unfold_def,[status(thm)],[24]) ).
thf(99,plain,
$true = $true,
inference(unfold_def,[status(thm)],[25]) ).
thf(100,plain,
$true = $true,
inference(unfold_def,[status(thm)],[26]) ).
thf(101,plain,
$true = $true,
inference(unfold_def,[status(thm)],[27]) ).
thf(102,plain,
$true = $true,
inference(unfold_def,[status(thm)],[28]) ).
thf(103,plain,
$true = $true,
inference(unfold_def,[status(thm)],[29]) ).
thf(104,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(105,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)],[33]) ).
thf(106,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)],[34]) ).
thf(107,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)],[35]) ).
thf(108,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(109,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)],[38]) ).
thf(110,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)],[39]) ).
thf(111,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(112,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(113,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(114,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(115,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(116,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(117,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(118,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)],[51]) ).
thf(119,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(120,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(121,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(122,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(123,plain,
( ( ! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(124,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(125,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)],[63]) ).
thf(126,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(127,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)],[68]) ).
thf(128,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(129,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(130,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)],[71]) ).
thf(131,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(132,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)],[74]) ).
thf(133,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(134,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(135,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(136,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(137,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)],[81]) ).
thf(138,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(139,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(140,plain,
( ( ! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(141,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(142,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(143,plain,
( ( ! [SY107: $i] :
( ( subset @ ( singleton @ sK1_A ) @ SY107 )
<=> ( in @ sK1_A @ SY107 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[90]) ).
thf(144,plain,
( ( ( subset @ ( singleton @ sK1_A ) @ sK2_SY107 )
<=> ( in @ sK1_A @ sK2_SY107 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[143]) ).
thf(145,plain,
( ( ( subset @ ( singleton @ sK1_A ) @ sK2_SY107 )
=> ( in @ sK1_A @ sK2_SY107 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[144]) ).
thf(146,plain,
( ( ( in @ sK1_A @ sK2_SY107 )
=> ( subset @ ( singleton @ sK1_A ) @ sK2_SY107 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[144]) ).
thf(147,plain,
( ( ~ ( ( subset @ ( singleton @ sK1_A ) @ sK2_SY107 )
=> ( in @ sK1_A @ sK2_SY107 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[145]) ).
thf(148,plain,
( ( ~ ( ( in @ sK1_A @ sK2_SY107 )
=> ( subset @ ( singleton @ sK1_A ) @ sK2_SY107 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[146]) ).
thf(149,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[142]) ).
thf(150,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(151,plain,
( ( ! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[140]) ).
thf(152,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(153,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(154,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(155,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(156,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(157,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(158,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(159,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(160,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(161,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(162,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(163,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(164,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(165,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(166,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(copy,[status(thm)],[125]) ).
thf(167,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(168,plain,
( ( ! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(169,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(170,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(171,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(172,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(173,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(174,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(175,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(176,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(177,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(178,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(179,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(180,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(181,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(182,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(copy,[status(thm)],[109]) ).
thf(183,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(184,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(copy,[status(thm)],[107]) ).
thf(185,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(186,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(copy,[status(thm)],[105]) ).
thf(187,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(188,plain,
$true = $true,
inference(copy,[status(thm)],[103]) ).
thf(189,plain,
$true = $true,
inference(copy,[status(thm)],[102]) ).
thf(190,plain,
$true = $true,
inference(copy,[status(thm)],[101]) ).
thf(191,plain,
$true = $true,
inference(copy,[status(thm)],[100]) ).
thf(192,plain,
$true = $true,
inference(copy,[status(thm)],[99]) ).
thf(193,plain,
$true = $true,
inference(copy,[status(thm)],[98]) ).
thf(194,plain,
$true = $true,
inference(copy,[status(thm)],[97]) ).
thf(195,plain,
$true = $true,
inference(copy,[status(thm)],[96]) ).
thf(196,plain,
$true = $true,
inference(copy,[status(thm)],[95]) ).
thf(197,plain,
$true = $true,
inference(copy,[status(thm)],[94]) ).
thf(198,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(199,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(200,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(201,plain,
( ( ~ ( ( subset @ ( singleton @ sK1_A ) @ sK2_SY107 )
=> ( in @ sK1_A @ sK2_SY107 ) ) )
= $true ),
inference(copy,[status(thm)],[147]) ).
thf(202,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX0 != SX1 )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(203,plain,
( ( ! [SX0: $i] :
( ( singleton @ SX0 )
!= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(204,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX2 @ SX1 ) )
| ( subset @ ( set_union2 @ SX0 @ SX2 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(205,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX1
!= ( singleton @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) )
| ~ ( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) )
| ~ ( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(206,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( disjoint @ ( singleton @ SX0 ) @ SX1 )
| ~ ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(207,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( in @ SX2 @ SX0 )
| ( subset @ SX0 @ ( set_difference @ SX1 @ ( singleton @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(208,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ( ~ ( ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(209,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ SX0 @ ( union @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(210,plain,
( ( ! [SX0: $i] :
( ~ ( subset @ SX0 @ empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(211,plain,
( ( ~ ( ~ ( subset @ ( singleton @ sK1_A ) @ sK2_SY107 )
| ( in @ sK1_A @ sK2_SY107 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(212,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( set_difference @ SX0 @ SX2 ) @ ( set_difference @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(213,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX1
!= ( union @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(214,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(215,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SX0 @ SX1 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) ) )
| ~ ~ ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(216,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) )
| ~ ( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(217,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( singleton @ SX0 )
!= ( unordered_pair @ SX1 @ SX2 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(218,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) )
| ~ ( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(219,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( singleton @ SX0 )
!= ( unordered_pair @ SX1 @ SX2 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(220,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(221,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( set_intersection2 @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( set_intersection2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(222,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( disjoint @ SX1 @ SX2 ) )
| ( disjoint @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(223,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ ( singleton @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(224,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[183]) ).
thf(225,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_union2 @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(226,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( set_intersection2 @ SX0 @ SX2 ) @ ( set_intersection2 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(227,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( proper_subset @ SX0 @ SX1 )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) )
| ( proper_subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(228,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( ( set_union2 @ ( singleton @ SX0 ) @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(229,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(230,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( set_difference @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( set_difference @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(231,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(232,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( unordered_pair @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ( ~ ( ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ( ~ ( ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( unordered_pair @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(233,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX0 @ SX2 ) )
| ( subset @ SX0 @ ( set_intersection2 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(234,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX2 ) )
| ( subset @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(235,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( in @ SX0 @ SX1 )
| ( disjoint @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(236,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( proper_subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(237,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX1
!= ( powerset @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(238,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( set_union2 @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ( ~ ( ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ( ~ ( ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( set_union2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(239,plain,
! [SV1: $i] :
( ( ! [SY108: $i] : ( subset @ ( set_intersection2 @ SV1 @ SY108 ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(240,plain,
! [SV2: $i] :
( ( subset @ empty_set @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(241,plain,
! [SV3: $i] :
( ( ! [SY109: $i] : ( subset @ ( set_difference @ SV3 @ SY109 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(242,plain,
! [SV4: $i] :
( ( ( unordered_pair @ SV4 @ SV4 )
= ( singleton @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(243,plain,
! [SV5: $i] :
( ( ! [SY110: $i] : ( subset @ SV5 @ ( set_union2 @ SV5 @ SY110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(244,plain,
! [SV6: $i] :
( ( ! [SY111: $i] : ( subset @ SV6 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(245,plain,
! [SV7: $i] :
( ( ! [SY112: $i] :
~ ( ~ ( ( SV7 != SY112 )
| ~ ( ~ ( subset @ SV7 @ SY112 )
| ~ ( subset @ SY112 @ SV7 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV7 @ SY112 )
| ~ ( subset @ SY112 @ SV7 ) )
| ( SV7 = SY112 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(246,plain,
! [SV8: $i] :
( ( ( singleton @ SV8 )
!= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(247,plain,
! [SV9: $i] :
( ( ! [SY113: $i,SY114: $i] :
( ~ ~ ( ~ ( subset @ SV9 @ SY113 )
| ~ ( subset @ SY114 @ SY113 ) )
| ( subset @ ( set_union2 @ SV9 @ SY114 ) @ SY113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(248,plain,
! [SV10: $i] :
( ( ! [SY115: $i] :
~ ( ~ ( ( SY115
!= ( singleton @ SV10 ) )
| ! [SY116: $i] :
~ ( ~ ( ~ ( in @ SY116 @ SY115 )
| ( SY116 = SV10 ) )
| ~ ( ( SY116 != SV10 )
| ( in @ SY116 @ SY115 ) ) ) )
| ~ ( ~ ! [SY117: $i] :
~ ( ~ ( ~ ( in @ SY117 @ SY115 )
| ( SY117 = SV10 ) )
| ~ ( ( SY117 != SV10 )
| ( in @ SY117 @ SY115 ) ) )
| ( SY115
= ( singleton @ SV10 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(249,plain,
! [SV11: $i] :
( ( ! [SY118: $i] :
~ ~ ( ~ ( disjoint @ ( singleton @ SV11 ) @ SY118 )
| ~ ( in @ SV11 @ SY118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(250,plain,
! [SV12: $i] :
( ( ! [SY119: $i,SY120: $i] :
( ~ ( subset @ SV12 @ SY119 )
| ( in @ SY120 @ SV12 )
| ( subset @ SV12 @ ( set_difference @ SY119 @ ( singleton @ SY120 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(251,plain,
! [SV13: $i] :
( ( ! [SY121: $i] :
~ ( ~ ( ~ ( subset @ SV13 @ ( singleton @ SY121 ) )
| ( SV13 = empty_set )
| ( SV13
= ( singleton @ SY121 ) ) )
| ~ ( ~ ( ( SV13 = empty_set )
| ( SV13
= ( singleton @ SY121 ) ) )
| ( subset @ SV13 @ ( singleton @ SY121 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(252,plain,
! [SV14: $i] :
( ( ! [SY122: $i] :
( ~ ( in @ SV14 @ SY122 )
| ( subset @ SV14 @ ( union @ SY122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(253,plain,
! [SV15: $i] :
( ( ~ ( subset @ SV15 @ empty_set )
| ( SV15 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(254,plain,
( ( ~ ( subset @ ( singleton @ sK1_A ) @ sK2_SY107 )
| ( in @ sK1_A @ sK2_SY107 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(255,plain,
! [SV16: $i] :
( ( ! [SY123: $i,SY124: $i] :
( ~ ( subset @ SV16 @ SY123 )
| ( subset @ ( set_difference @ SV16 @ SY124 ) @ ( set_difference @ SY123 @ SY124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(256,plain,
! [SV17: $i] :
( ( ! [SY125: $i] :
~ ( ~ ( ( SY125
!= ( union @ SV17 ) )
| ! [SY126: $i] :
~ ( ~ ( ~ ( in @ SY126 @ SY125 )
| ~ ! [SY127: $i] :
~ ~ ( ~ ( in @ SY126 @ SY127 )
| ~ ( in @ SY127 @ SV17 ) ) )
| ~ ( ~ ~ ! [SY128: $i] :
~ ~ ( ~ ( in @ SY126 @ SY128 )
| ~ ( in @ SY128 @ SV17 ) )
| ( in @ SY126 @ SY125 ) ) ) )
| ~ ( ~ ! [SY129: $i] :
~ ( ~ ( ~ ( in @ SY129 @ SY125 )
| ~ ! [SY130: $i] :
~ ~ ( ~ ( in @ SY129 @ SY130 )
| ~ ( in @ SY130 @ SV17 ) ) )
| ~ ( ~ ~ ! [SY131: $i] :
~ ~ ( ~ ( in @ SY129 @ SY131 )
| ~ ( in @ SY131 @ SV17 ) )
| ( in @ SY129 @ SY125 ) ) )
| ( SY125
= ( union @ SV17 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(257,plain,
! [SV18: $i] :
( ( ! [SY132: $i] :
~ ~ ( ~ ( in @ SV18 @ SY132 )
| ~ ( empty @ SY132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(258,plain,
! [SV19: $i] :
( ( ! [SY133: $i] :
~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SV19 @ SY133 )
| ~ ! [SY134: $i] :
~ ~ ( ~ ( in @ SY134 @ SV19 )
| ~ ( in @ SY134 @ SY133 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY135: $i] :
~ ~ ( ~ ( in @ SY135 @ SV19 )
| ~ ( in @ SY135 @ SY133 ) )
| ~ ( disjoint @ SV19 @ SY133 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(259,plain,
! [SV20: $i] :
( ( ~ ( ~ ( ( SV20 != empty_set )
| ! [SY136: $i] :
~ ( in @ SY136 @ SV20 ) )
| ~ ( ~ ! [SY137: $i] :
~ ( in @ SY137 @ SV20 )
| ( SV20 = empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(260,plain,
! [SV21: $i] :
( ( ! [SY138: $i,SY139: $i] :
( ( ( singleton @ SV21 )
!= ( unordered_pair @ SY138 @ SY139 ) )
| ( SV21 = SY138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(261,plain,
! [SV22: $i] :
( ( ! [SY140: $i] :
~ ( ~ ( ~ ( subset @ ( singleton @ SV22 ) @ SY140 )
| ( in @ SV22 @ SY140 ) )
| ~ ( ~ ( in @ SV22 @ SY140 )
| ( subset @ ( singleton @ SV22 ) @ SY140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(262,plain,
! [SV23: $i] :
( ( ! [SY141: $i,SY142: $i] :
( ( ( singleton @ SV23 )
!= ( unordered_pair @ SY141 @ SY142 ) )
| ( SY141 = SY142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(263,plain,
! [SV24: $i] :
( ( ! [SY143: $i] :
( ~ ( subset @ SV24 @ SY143 )
| ( ( set_intersection2 @ SV24 @ SY143 )
= SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(264,plain,
! [SV25: $i] :
( ( ! [SY144: $i,SY145: $i] :
~ ( ~ ( ( SY145
!= ( set_intersection2 @ SV25 @ SY144 ) )
| ! [SY146: $i] :
~ ( ~ ( ~ ( in @ SY146 @ SY145 )
| ~ ( ~ ( in @ SY146 @ SV25 )
| ~ ( in @ SY146 @ SY144 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY146 @ SV25 )
| ~ ( in @ SY146 @ SY144 ) )
| ( in @ SY146 @ SY145 ) ) ) )
| ~ ( ~ ! [SY147: $i] :
~ ( ~ ( ~ ( in @ SY147 @ SY145 )
| ~ ( ~ ( in @ SY147 @ SV25 )
| ~ ( in @ SY147 @ SY144 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY147 @ SV25 )
| ~ ( in @ SY147 @ SY144 ) )
| ( in @ SY147 @ SY145 ) ) )
| ( SY145
= ( set_intersection2 @ SV25 @ SY144 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(265,plain,
! [SV26: $i] :
( ( ! [SY148: $i,SY149: $i] :
( ~ ~ ( ~ ( subset @ SV26 @ SY148 )
| ~ ( disjoint @ SY148 @ SY149 ) )
| ( disjoint @ SV26 @ SY149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(266,plain,
! [SV27: $i] :
( ( ! [SY150: $i] :
( ~ ( subset @ ( singleton @ SV27 ) @ ( singleton @ SY150 ) )
| ( SV27 = SY150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(267,plain,
! [SV28: $i] :
( ( ! [SY151: $i] :
~ ( ~ ( ~ ( subset @ SV28 @ SY151 )
| ! [SY152: $i] :
( ~ ( in @ SY152 @ SV28 )
| ( in @ SY152 @ SY151 ) ) )
| ~ ( ~ ! [SY153: $i] :
( ~ ( in @ SY153 @ SV28 )
| ( in @ SY153 @ SY151 ) )
| ( subset @ SV28 @ SY151 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(268,plain,
! [SV29: $i] :
( ( ! [SY154: $i] :
( ~ ( subset @ SV29 @ SY154 )
| ( ( set_union2 @ SV29 @ SY154 )
= SY154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(269,plain,
! [SV30: $i] :
( ( ! [SY155: $i,SY156: $i] :
( ~ ( subset @ SV30 @ SY155 )
| ( subset @ ( set_intersection2 @ SV30 @ SY156 ) @ ( set_intersection2 @ SY155 @ SY156 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(270,plain,
! [SV31: $i] :
( ( ! [SY157: $i] :
~ ( ~ ( ~ ( proper_subset @ SV31 @ SY157 )
| ~ ( ~ ( subset @ SV31 @ SY157 )
| ~ ( ( SV31 != SY157 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV31 @ SY157 )
| ~ ( ( SV31 != SY157 ) ) )
| ( proper_subset @ SV31 @ SY157 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(271,plain,
! [SV32: $i] :
( ( ! [SY158: $i] :
( ~ ( in @ SV32 @ SY158 )
| ( ( set_union2 @ ( singleton @ SV32 ) @ SY158 )
= SY158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(272,plain,
! [SV33: $i] :
( ( ! [SY159: $i] :
( ~ ! [SY160: $i] :
~ ( ~ ( ~ ( in @ SY160 @ SV33 )
| ( in @ SY160 @ SY159 ) )
| ~ ( ~ ( in @ SY160 @ SY159 )
| ( in @ SY160 @ SV33 ) ) )
| ( SV33 = SY159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(273,plain,
! [SV34: $i] :
( ( ! [SY161: $i,SY162: $i] :
~ ( ~ ( ( SY162
!= ( set_difference @ SV34 @ SY161 ) )
| ! [SY163: $i] :
~ ( ~ ( ~ ( in @ SY163 @ SY162 )
| ~ ( ~ ( in @ SY163 @ SV34 )
| ~ ~ ( in @ SY163 @ SY161 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY163 @ SV34 )
| ~ ~ ( in @ SY163 @ SY161 ) )
| ( in @ SY163 @ SY162 ) ) ) )
| ~ ( ~ ! [SY164: $i] :
~ ( ~ ( ~ ( in @ SY164 @ SY162 )
| ~ ( ~ ( in @ SY164 @ SV34 )
| ~ ~ ( in @ SY164 @ SY161 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY164 @ SV34 )
| ~ ~ ( in @ SY164 @ SY161 ) )
| ( in @ SY164 @ SY162 ) ) )
| ( SY162
= ( set_difference @ SV34 @ SY161 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(274,plain,
! [SV35: $i] :
( ( ! [SY165: $i] :
( ~ ( in @ SV35 @ SY165 )
| ~ ( in @ SY165 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(275,plain,
! [SV36: $i] :
( ( ! [SY166: $i,SY167: $i] :
~ ( ~ ( ( SY167
!= ( unordered_pair @ SV36 @ SY166 ) )
| ! [SY168: $i] :
~ ( ~ ( ~ ( in @ SY168 @ SY167 )
| ( SY168 = SV36 )
| ( SY168 = SY166 ) )
| ~ ( ~ ( ( SY168 = SV36 )
| ( SY168 = SY166 ) )
| ( in @ SY168 @ SY167 ) ) ) )
| ~ ( ~ ! [SY169: $i] :
~ ( ~ ( ~ ( in @ SY169 @ SY167 )
| ( SY169 = SV36 )
| ( SY169 = SY166 ) )
| ~ ( ~ ( ( SY169 = SV36 )
| ( SY169 = SY166 ) )
| ( in @ SY169 @ SY167 ) ) )
| ( SY167
= ( unordered_pair @ SV36 @ SY166 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(276,plain,
! [SV37: $i] :
( ( ! [SY170: $i,SY171: $i] :
( ~ ~ ( ~ ( subset @ SV37 @ SY170 )
| ~ ( subset @ SV37 @ SY171 ) )
| ( subset @ SV37 @ ( set_intersection2 @ SY170 @ SY171 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(277,plain,
! [SV38: $i] :
( ( ! [SY172: $i,SY173: $i] :
( ~ ~ ( ~ ( subset @ SV38 @ SY172 )
| ~ ( subset @ SY172 @ SY173 ) )
| ( subset @ SV38 @ SY173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(278,plain,
! [SV39: $i] :
( ( ! [SY174: $i] :
( ~ ~ ( in @ SV39 @ SY174 )
| ( disjoint @ ( singleton @ SV39 ) @ SY174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(279,plain,
! [SV40: $i] :
( ( ! [SY175: $i] :
~ ~ ( ~ ( subset @ SV40 @ SY175 )
| ~ ( proper_subset @ SY175 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(280,plain,
! [SV41: $i] :
( ( ! [SY176: $i] :
~ ( ~ ( ( SY176
!= ( powerset @ SV41 ) )
| ! [SY177: $i] :
~ ( ~ ( ~ ( in @ SY177 @ SY176 )
| ( subset @ SY177 @ SV41 ) )
| ~ ( ~ ( subset @ SY177 @ SV41 )
| ( in @ SY177 @ SY176 ) ) ) )
| ~ ( ~ ! [SY178: $i] :
~ ( ~ ( ~ ( in @ SY178 @ SY176 )
| ( subset @ SY178 @ SV41 ) )
| ~ ( ~ ( subset @ SY178 @ SV41 )
| ( in @ SY178 @ SY176 ) ) )
| ( SY176
= ( powerset @ SV41 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(281,plain,
! [SV42: $i] :
( ( ! [SY179: $i,SY180: $i] :
~ ( ~ ( ( SY180
!= ( set_union2 @ SV42 @ SY179 ) )
| ! [SY181: $i] :
~ ( ~ ( ~ ( in @ SY181 @ SY180 )
| ( in @ SY181 @ SV42 )
| ( in @ SY181 @ SY179 ) )
| ~ ( ~ ( ( in @ SY181 @ SV42 )
| ( in @ SY181 @ SY179 ) )
| ( in @ SY181 @ SY180 ) ) ) )
| ~ ( ~ ! [SY182: $i] :
~ ( ~ ( ~ ( in @ SY182 @ SY180 )
| ( in @ SY182 @ SV42 )
| ( in @ SY182 @ SY179 ) )
| ~ ( ~ ( ( in @ SY182 @ SV42 )
| ( in @ SY182 @ SY179 ) )
| ( in @ SY182 @ SY180 ) ) )
| ( SY180
= ( set_union2 @ SV42 @ SY179 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(282,plain,
! [SV43: $i,SV1: $i] :
( ( subset @ ( set_intersection2 @ SV1 @ SV43 ) @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(283,plain,
! [SV44: $i,SV3: $i] :
( ( subset @ ( set_difference @ SV3 @ SV44 ) @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(284,plain,
! [SV45: $i,SV5: $i] :
( ( subset @ SV5 @ ( set_union2 @ SV5 @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(285,plain,
! [SV6: $i] :
( ( subset @ SV6 @ SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(286,plain,
! [SV47: $i,SV7: $i] :
( ( ~ ( ~ ( ( SV7 != SV47 )
| ~ ( ~ ( subset @ SV7 @ SV47 )
| ~ ( subset @ SV47 @ SV7 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV7 @ SV47 )
| ~ ( subset @ SV47 @ SV7 ) )
| ( SV7 = SV47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(287,plain,
! [SV8: $i] :
( ( ( singleton @ SV8 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(288,plain,
! [SV48: $i,SV9: $i] :
( ( ! [SY183: $i] :
( ~ ~ ( ~ ( subset @ SV9 @ SV48 )
| ~ ( subset @ SY183 @ SV48 ) )
| ( subset @ ( set_union2 @ SV9 @ SY183 ) @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(289,plain,
! [SV10: $i,SV49: $i] :
( ( ~ ( ~ ( ( SV49
!= ( singleton @ SV10 ) )
| ! [SY184: $i] :
~ ( ~ ( ~ ( in @ SY184 @ SV49 )
| ( SY184 = SV10 ) )
| ~ ( ( SY184 != SV10 )
| ( in @ SY184 @ SV49 ) ) ) )
| ~ ( ~ ! [SY185: $i] :
~ ( ~ ( ~ ( in @ SY185 @ SV49 )
| ( SY185 = SV10 ) )
| ~ ( ( SY185 != SV10 )
| ( in @ SY185 @ SV49 ) ) )
| ( SV49
= ( singleton @ SV10 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(290,plain,
! [SV50: $i,SV11: $i] :
( ( ~ ~ ( ~ ( disjoint @ ( singleton @ SV11 ) @ SV50 )
| ~ ( in @ SV11 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(291,plain,
! [SV51: $i,SV12: $i] :
( ( ! [SY186: $i] :
( ~ ( subset @ SV12 @ SV51 )
| ( in @ SY186 @ SV12 )
| ( subset @ SV12 @ ( set_difference @ SV51 @ ( singleton @ SY186 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(292,plain,
! [SV52: $i,SV13: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV13 @ ( singleton @ SV52 ) )
| ( SV13 = empty_set )
| ( SV13
= ( singleton @ SV52 ) ) )
| ~ ( ~ ( ( SV13 = empty_set )
| ( SV13
= ( singleton @ SV52 ) ) )
| ( subset @ SV13 @ ( singleton @ SV52 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(293,plain,
! [SV53: $i,SV14: $i] :
( ( ~ ( in @ SV14 @ SV53 )
| ( subset @ SV14 @ ( union @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(294,plain,
! [SV15: $i] :
( ( ( ~ ( subset @ SV15 @ empty_set ) )
= $true )
| ( ( SV15 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(295,plain,
( ( ~ ( subset @ ( singleton @ sK1_A ) @ sK2_SY107 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[254]) ).
thf(296,plain,
( ( in @ sK1_A @ sK2_SY107 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[254]) ).
thf(297,plain,
! [SV54: $i,SV16: $i] :
( ( ! [SY187: $i] :
( ~ ( subset @ SV16 @ SV54 )
| ( subset @ ( set_difference @ SV16 @ SY187 ) @ ( set_difference @ SV54 @ SY187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(298,plain,
! [SV17: $i,SV55: $i] :
( ( ~ ( ~ ( ( SV55
!= ( union @ SV17 ) )
| ! [SY188: $i] :
~ ( ~ ( ~ ( in @ SY188 @ SV55 )
| ~ ! [SY127: $i] :
~ ~ ( ~ ( in @ SY188 @ SY127 )
| ~ ( in @ SY127 @ SV17 ) ) )
| ~ ( ~ ~ ! [SY128: $i] :
~ ~ ( ~ ( in @ SY188 @ SY128 )
| ~ ( in @ SY128 @ SV17 ) )
| ( in @ SY188 @ SV55 ) ) ) )
| ~ ( ~ ! [SY191: $i] :
~ ( ~ ( ~ ( in @ SY191 @ SV55 )
| ~ ! [SY130: $i] :
~ ~ ( ~ ( in @ SY191 @ SY130 )
| ~ ( in @ SY130 @ SV17 ) ) )
| ~ ( ~ ~ ! [SY131: $i] :
~ ~ ( ~ ( in @ SY191 @ SY131 )
| ~ ( in @ SY131 @ SV17 ) )
| ( in @ SY191 @ SV55 ) ) )
| ( SV55
= ( union @ SV17 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(299,plain,
! [SV56: $i,SV18: $i] :
( ( ~ ~ ( ~ ( in @ SV18 @ SV56 )
| ~ ( empty @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(300,plain,
! [SV57: $i,SV19: $i] :
( ( ~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SV19 @ SV57 )
| ~ ! [SY194: $i] :
~ ~ ( ~ ( in @ SY194 @ SV19 )
| ~ ( in @ SY194 @ SV57 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY195: $i] :
~ ~ ( ~ ( in @ SY195 @ SV19 )
| ~ ( in @ SY195 @ SV57 ) )
| ~ ( disjoint @ SV19 @ SV57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(301,plain,
! [SV20: $i] :
( ( ~ ( ( SV20 != empty_set )
| ! [SY136: $i] :
~ ( in @ SY136 @ SV20 ) )
| ~ ( ~ ! [SY137: $i] :
~ ( in @ SY137 @ SV20 )
| ( SV20 = empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(302,plain,
! [SV58: $i,SV21: $i] :
( ( ! [SY196: $i] :
( ( ( singleton @ SV21 )
!= ( unordered_pair @ SV58 @ SY196 ) )
| ( SV21 = SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(303,plain,
! [SV59: $i,SV22: $i] :
( ( ~ ( ~ ( ~ ( subset @ ( singleton @ SV22 ) @ SV59 )
| ( in @ SV22 @ SV59 ) )
| ~ ( ~ ( in @ SV22 @ SV59 )
| ( subset @ ( singleton @ SV22 ) @ SV59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(304,plain,
! [SV60: $i,SV23: $i] :
( ( ! [SY197: $i] :
( ( ( singleton @ SV23 )
!= ( unordered_pair @ SV60 @ SY197 ) )
| ( SV60 = SY197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(305,plain,
! [SV61: $i,SV24: $i] :
( ( ~ ( subset @ SV24 @ SV61 )
| ( ( set_intersection2 @ SV24 @ SV61 )
= SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(306,plain,
! [SV62: $i,SV25: $i] :
( ( ! [SY198: $i] :
~ ( ~ ( ( SY198
!= ( set_intersection2 @ SV25 @ SV62 ) )
| ! [SY199: $i] :
~ ( ~ ( ~ ( in @ SY199 @ SY198 )
| ~ ( ~ ( in @ SY199 @ SV25 )
| ~ ( in @ SY199 @ SV62 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY199 @ SV25 )
| ~ ( in @ SY199 @ SV62 ) )
| ( in @ SY199 @ SY198 ) ) ) )
| ~ ( ~ ! [SY200: $i] :
~ ( ~ ( ~ ( in @ SY200 @ SY198 )
| ~ ( ~ ( in @ SY200 @ SV25 )
| ~ ( in @ SY200 @ SV62 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY200 @ SV25 )
| ~ ( in @ SY200 @ SV62 ) )
| ( in @ SY200 @ SY198 ) ) )
| ( SY198
= ( set_intersection2 @ SV25 @ SV62 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(307,plain,
! [SV63: $i,SV26: $i] :
( ( ! [SY201: $i] :
( ~ ~ ( ~ ( subset @ SV26 @ SV63 )
| ~ ( disjoint @ SV63 @ SY201 ) )
| ( disjoint @ SV26 @ SY201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(308,plain,
! [SV64: $i,SV27: $i] :
( ( ~ ( subset @ ( singleton @ SV27 ) @ ( singleton @ SV64 ) )
| ( SV27 = SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(309,plain,
! [SV65: $i,SV28: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV28 @ SV65 )
| ! [SY202: $i] :
( ~ ( in @ SY202 @ SV28 )
| ( in @ SY202 @ SV65 ) ) )
| ~ ( ~ ! [SY203: $i] :
( ~ ( in @ SY203 @ SV28 )
| ( in @ SY203 @ SV65 ) )
| ( subset @ SV28 @ SV65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(310,plain,
! [SV66: $i,SV29: $i] :
( ( ~ ( subset @ SV29 @ SV66 )
| ( ( set_union2 @ SV29 @ SV66 )
= SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(311,plain,
! [SV67: $i,SV30: $i] :
( ( ! [SY204: $i] :
( ~ ( subset @ SV30 @ SV67 )
| ( subset @ ( set_intersection2 @ SV30 @ SY204 ) @ ( set_intersection2 @ SV67 @ SY204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(312,plain,
! [SV68: $i,SV31: $i] :
( ( ~ ( ~ ( ~ ( proper_subset @ SV31 @ SV68 )
| ~ ( ~ ( subset @ SV31 @ SV68 )
| ~ ( ( SV31 != SV68 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV31 @ SV68 )
| ~ ( ( SV31 != SV68 ) ) )
| ( proper_subset @ SV31 @ SV68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(313,plain,
! [SV69: $i,SV32: $i] :
( ( ~ ( in @ SV32 @ SV69 )
| ( ( set_union2 @ ( singleton @ SV32 ) @ SV69 )
= SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(314,plain,
! [SV70: $i,SV33: $i] :
( ( ~ ! [SY205: $i] :
~ ( ~ ( ~ ( in @ SY205 @ SV33 )
| ( in @ SY205 @ SV70 ) )
| ~ ( ~ ( in @ SY205 @ SV70 )
| ( in @ SY205 @ SV33 ) ) )
| ( SV33 = SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(315,plain,
! [SV71: $i,SV34: $i] :
( ( ! [SY206: $i] :
~ ( ~ ( ( SY206
!= ( set_difference @ SV34 @ SV71 ) )
| ! [SY207: $i] :
~ ( ~ ( ~ ( in @ SY207 @ SY206 )
| ~ ( ~ ( in @ SY207 @ SV34 )
| ~ ~ ( in @ SY207 @ SV71 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY207 @ SV34 )
| ~ ~ ( in @ SY207 @ SV71 ) )
| ( in @ SY207 @ SY206 ) ) ) )
| ~ ( ~ ! [SY208: $i] :
~ ( ~ ( ~ ( in @ SY208 @ SY206 )
| ~ ( ~ ( in @ SY208 @ SV34 )
| ~ ~ ( in @ SY208 @ SV71 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY208 @ SV34 )
| ~ ~ ( in @ SY208 @ SV71 ) )
| ( in @ SY208 @ SY206 ) ) )
| ( SY206
= ( set_difference @ SV34 @ SV71 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(316,plain,
! [SV72: $i,SV35: $i] :
( ( ~ ( in @ SV35 @ SV72 )
| ~ ( in @ SV72 @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(317,plain,
! [SV73: $i,SV36: $i] :
( ( ! [SY209: $i] :
~ ( ~ ( ( SY209
!= ( unordered_pair @ SV36 @ SV73 ) )
| ! [SY210: $i] :
~ ( ~ ( ~ ( in @ SY210 @ SY209 )
| ( SY210 = SV36 )
| ( SY210 = SV73 ) )
| ~ ( ~ ( ( SY210 = SV36 )
| ( SY210 = SV73 ) )
| ( in @ SY210 @ SY209 ) ) ) )
| ~ ( ~ ! [SY211: $i] :
~ ( ~ ( ~ ( in @ SY211 @ SY209 )
| ( SY211 = SV36 )
| ( SY211 = SV73 ) )
| ~ ( ~ ( ( SY211 = SV36 )
| ( SY211 = SV73 ) )
| ( in @ SY211 @ SY209 ) ) )
| ( SY209
= ( unordered_pair @ SV36 @ SV73 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(318,plain,
! [SV74: $i,SV37: $i] :
( ( ! [SY212: $i] :
( ~ ~ ( ~ ( subset @ SV37 @ SV74 )
| ~ ( subset @ SV37 @ SY212 ) )
| ( subset @ SV37 @ ( set_intersection2 @ SV74 @ SY212 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(319,plain,
! [SV75: $i,SV38: $i] :
( ( ! [SY213: $i] :
( ~ ~ ( ~ ( subset @ SV38 @ SV75 )
| ~ ( subset @ SV75 @ SY213 ) )
| ( subset @ SV38 @ SY213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(320,plain,
! [SV76: $i,SV39: $i] :
( ( ~ ~ ( in @ SV39 @ SV76 )
| ( disjoint @ ( singleton @ SV39 ) @ SV76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(321,plain,
! [SV77: $i,SV40: $i] :
( ( ~ ~ ( ~ ( subset @ SV40 @ SV77 )
| ~ ( proper_subset @ SV77 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(322,plain,
! [SV41: $i,SV78: $i] :
( ( ~ ( ~ ( ( SV78
!= ( powerset @ SV41 ) )
| ! [SY214: $i] :
~ ( ~ ( ~ ( in @ SY214 @ SV78 )
| ( subset @ SY214 @ SV41 ) )
| ~ ( ~ ( subset @ SY214 @ SV41 )
| ( in @ SY214 @ SV78 ) ) ) )
| ~ ( ~ ! [SY215: $i] :
~ ( ~ ( ~ ( in @ SY215 @ SV78 )
| ( subset @ SY215 @ SV41 ) )
| ~ ( ~ ( subset @ SY215 @ SV41 )
| ( in @ SY215 @ SV78 ) ) )
| ( SV78
= ( powerset @ SV41 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(323,plain,
! [SV79: $i,SV42: $i] :
( ( ! [SY216: $i] :
~ ( ~ ( ( SY216
!= ( set_union2 @ SV42 @ SV79 ) )
| ! [SY217: $i] :
~ ( ~ ( ~ ( in @ SY217 @ SY216 )
| ( in @ SY217 @ SV42 )
| ( in @ SY217 @ SV79 ) )
| ~ ( ~ ( ( in @ SY217 @ SV42 )
| ( in @ SY217 @ SV79 ) )
| ( in @ SY217 @ SY216 ) ) ) )
| ~ ( ~ ! [SY218: $i] :
~ ( ~ ( ~ ( in @ SY218 @ SY216 )
| ( in @ SY218 @ SV42 )
| ( in @ SY218 @ SV79 ) )
| ~ ( ~ ( ( in @ SY218 @ SV42 )
| ( in @ SY218 @ SV79 ) )
| ( in @ SY218 @ SY216 ) ) )
| ( SY216
= ( set_union2 @ SV42 @ SV79 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(324,plain,
! [SV47: $i,SV7: $i] :
( ( ~ ( ( SV7 != SV47 )
| ~ ( ~ ( subset @ SV7 @ SV47 )
| ~ ( subset @ SV47 @ SV7 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV7 @ SV47 )
| ~ ( subset @ SV47 @ SV7 ) )
| ( SV7 = SV47 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(325,plain,
! [SV80: $i,SV48: $i,SV9: $i] :
( ( ~ ~ ( ~ ( subset @ SV9 @ SV48 )
| ~ ( subset @ SV80 @ SV48 ) )
| ( subset @ ( set_union2 @ SV9 @ SV80 ) @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(326,plain,
! [SV10: $i,SV49: $i] :
( ( ~ ( ( SV49
!= ( singleton @ SV10 ) )
| ! [SY184: $i] :
~ ( ~ ( ~ ( in @ SY184 @ SV49 )
| ( SY184 = SV10 ) )
| ~ ( ( SY184 != SV10 )
| ( in @ SY184 @ SV49 ) ) ) )
| ~ ( ~ ! [SY185: $i] :
~ ( ~ ( ~ ( in @ SY185 @ SV49 )
| ( SY185 = SV10 ) )
| ~ ( ( SY185 != SV10 )
| ( in @ SY185 @ SV49 ) ) )
| ( SV49
= ( singleton @ SV10 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(327,plain,
! [SV50: $i,SV11: $i] :
( ( ~ ( ~ ( disjoint @ ( singleton @ SV11 ) @ SV50 )
| ~ ( in @ SV11 @ SV50 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(328,plain,
! [SV81: $i,SV51: $i,SV12: $i] :
( ( ~ ( subset @ SV12 @ SV51 )
| ( in @ SV81 @ SV12 )
| ( subset @ SV12 @ ( set_difference @ SV51 @ ( singleton @ SV81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(329,plain,
! [SV52: $i,SV13: $i] :
( ( ~ ( ~ ( subset @ SV13 @ ( singleton @ SV52 ) )
| ( SV13 = empty_set )
| ( SV13
= ( singleton @ SV52 ) ) )
| ~ ( ~ ( ( SV13 = empty_set )
| ( SV13
= ( singleton @ SV52 ) ) )
| ( subset @ SV13 @ ( singleton @ SV52 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(330,plain,
! [SV53: $i,SV14: $i] :
( ( ( ~ ( in @ SV14 @ SV53 ) )
= $true )
| ( ( subset @ SV14 @ ( union @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[293]) ).
thf(331,plain,
! [SV15: $i] :
( ( ( subset @ SV15 @ empty_set )
= $false )
| ( ( SV15 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(332,plain,
( ( subset @ ( singleton @ sK1_A ) @ sK2_SY107 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[295]) ).
thf(333,plain,
! [SV82: $i,SV54: $i,SV16: $i] :
( ( ~ ( subset @ SV16 @ SV54 )
| ( subset @ ( set_difference @ SV16 @ SV82 ) @ ( set_difference @ SV54 @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(334,plain,
! [SV17: $i,SV55: $i] :
( ( ~ ( ( SV55
!= ( union @ SV17 ) )
| ! [SY188: $i] :
~ ( ~ ( ~ ( in @ SY188 @ SV55 )
| ~ ! [SY127: $i] :
~ ~ ( ~ ( in @ SY188 @ SY127 )
| ~ ( in @ SY127 @ SV17 ) ) )
| ~ ( ~ ~ ! [SY128: $i] :
~ ~ ( ~ ( in @ SY188 @ SY128 )
| ~ ( in @ SY128 @ SV17 ) )
| ( in @ SY188 @ SV55 ) ) ) )
| ~ ( ~ ! [SY191: $i] :
~ ( ~ ( ~ ( in @ SY191 @ SV55 )
| ~ ! [SY130: $i] :
~ ~ ( ~ ( in @ SY191 @ SY130 )
| ~ ( in @ SY130 @ SV17 ) ) )
| ~ ( ~ ~ ! [SY131: $i] :
~ ~ ( ~ ( in @ SY191 @ SY131 )
| ~ ( in @ SY131 @ SV17 ) )
| ( in @ SY191 @ SV55 ) ) )
| ( SV55
= ( union @ SV17 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(335,plain,
! [SV56: $i,SV18: $i] :
( ( ~ ( ~ ( in @ SV18 @ SV56 )
| ~ ( empty @ SV56 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(336,plain,
! [SV57: $i,SV19: $i] :
( ( ~ ~ ~ ( ~ ~ ( disjoint @ SV19 @ SV57 )
| ~ ! [SY194: $i] :
~ ~ ( ~ ( in @ SY194 @ SV19 )
| ~ ( in @ SY194 @ SV57 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY195: $i] :
~ ~ ( ~ ( in @ SY195 @ SV19 )
| ~ ( in @ SY195 @ SV57 ) )
| ~ ( disjoint @ SV19 @ SV57 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(337,plain,
! [SV20: $i] :
( ( ~ ( ( SV20 != empty_set )
| ! [SY136: $i] :
~ ( in @ SY136 @ SV20 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[301]) ).
thf(338,plain,
! [SV20: $i] :
( ( ~ ( ~ ! [SY137: $i] :
~ ( in @ SY137 @ SV20 )
| ( SV20 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[301]) ).
thf(339,plain,
! [SV83: $i,SV58: $i,SV21: $i] :
( ( ( ( singleton @ SV21 )
!= ( unordered_pair @ SV58 @ SV83 ) )
| ( SV21 = SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(340,plain,
! [SV59: $i,SV22: $i] :
( ( ~ ( ~ ( subset @ ( singleton @ SV22 ) @ SV59 )
| ( in @ SV22 @ SV59 ) )
| ~ ( ~ ( in @ SV22 @ SV59 )
| ( subset @ ( singleton @ SV22 ) @ SV59 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(341,plain,
! [SV84: $i,SV60: $i,SV23: $i] :
( ( ( ( singleton @ SV23 )
!= ( unordered_pair @ SV60 @ SV84 ) )
| ( SV60 = SV84 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(342,plain,
! [SV61: $i,SV24: $i] :
( ( ( ~ ( subset @ SV24 @ SV61 ) )
= $true )
| ( ( ( set_intersection2 @ SV24 @ SV61 )
= SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[305]) ).
thf(343,plain,
! [SV62: $i,SV25: $i,SV85: $i] :
( ( ~ ( ~ ( ( SV85
!= ( set_intersection2 @ SV25 @ SV62 ) )
| ! [SY219: $i] :
~ ( ~ ( ~ ( in @ SY219 @ SV85 )
| ~ ( ~ ( in @ SY219 @ SV25 )
| ~ ( in @ SY219 @ SV62 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY219 @ SV25 )
| ~ ( in @ SY219 @ SV62 ) )
| ( in @ SY219 @ SV85 ) ) ) )
| ~ ( ~ ! [SY220: $i] :
~ ( ~ ( ~ ( in @ SY220 @ SV85 )
| ~ ( ~ ( in @ SY220 @ SV25 )
| ~ ( in @ SY220 @ SV62 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY220 @ SV25 )
| ~ ( in @ SY220 @ SV62 ) )
| ( in @ SY220 @ SV85 ) ) )
| ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(344,plain,
! [SV86: $i,SV63: $i,SV26: $i] :
( ( ~ ~ ( ~ ( subset @ SV26 @ SV63 )
| ~ ( disjoint @ SV63 @ SV86 ) )
| ( disjoint @ SV26 @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(345,plain,
! [SV64: $i,SV27: $i] :
( ( ( ~ ( subset @ ( singleton @ SV27 ) @ ( singleton @ SV64 ) ) )
= $true )
| ( ( SV27 = SV64 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[308]) ).
thf(346,plain,
! [SV65: $i,SV28: $i] :
( ( ~ ( ~ ( subset @ SV28 @ SV65 )
| ! [SY202: $i] :
( ~ ( in @ SY202 @ SV28 )
| ( in @ SY202 @ SV65 ) ) )
| ~ ( ~ ! [SY203: $i] :
( ~ ( in @ SY203 @ SV28 )
| ( in @ SY203 @ SV65 ) )
| ( subset @ SV28 @ SV65 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(347,plain,
! [SV66: $i,SV29: $i] :
( ( ( ~ ( subset @ SV29 @ SV66 ) )
= $true )
| ( ( ( set_union2 @ SV29 @ SV66 )
= SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[310]) ).
thf(348,plain,
! [SV87: $i,SV67: $i,SV30: $i] :
( ( ~ ( subset @ SV30 @ SV67 )
| ( subset @ ( set_intersection2 @ SV30 @ SV87 ) @ ( set_intersection2 @ SV67 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(349,plain,
! [SV68: $i,SV31: $i] :
( ( ~ ( ~ ( proper_subset @ SV31 @ SV68 )
| ~ ( ~ ( subset @ SV31 @ SV68 )
| ~ ( ( SV31 != SV68 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV31 @ SV68 )
| ~ ( ( SV31 != SV68 ) ) )
| ( proper_subset @ SV31 @ SV68 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(350,plain,
! [SV69: $i,SV32: $i] :
( ( ( ~ ( in @ SV32 @ SV69 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV32 ) @ SV69 )
= SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(351,plain,
! [SV70: $i,SV33: $i] :
( ( ( ~ ! [SY205: $i] :
~ ( ~ ( ~ ( in @ SY205 @ SV33 )
| ( in @ SY205 @ SV70 ) )
| ~ ( ~ ( in @ SY205 @ SV70 )
| ( in @ SY205 @ SV33 ) ) ) )
= $true )
| ( ( SV33 = SV70 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[314]) ).
thf(352,plain,
! [SV71: $i,SV34: $i,SV88: $i] :
( ( ~ ( ~ ( ( SV88
!= ( set_difference @ SV34 @ SV71 ) )
| ! [SY221: $i] :
~ ( ~ ( ~ ( in @ SY221 @ SV88 )
| ~ ( ~ ( in @ SY221 @ SV34 )
| ~ ~ ( in @ SY221 @ SV71 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY221 @ SV34 )
| ~ ~ ( in @ SY221 @ SV71 ) )
| ( in @ SY221 @ SV88 ) ) ) )
| ~ ( ~ ! [SY222: $i] :
~ ( ~ ( ~ ( in @ SY222 @ SV88 )
| ~ ( ~ ( in @ SY222 @ SV34 )
| ~ ~ ( in @ SY222 @ SV71 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY222 @ SV34 )
| ~ ~ ( in @ SY222 @ SV71 ) )
| ( in @ SY222 @ SV88 ) ) )
| ( SV88
= ( set_difference @ SV34 @ SV71 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(353,plain,
! [SV72: $i,SV35: $i] :
( ( ( ~ ( in @ SV35 @ SV72 ) )
= $true )
| ( ( ~ ( in @ SV72 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[316]) ).
thf(354,plain,
! [SV73: $i,SV36: $i,SV89: $i] :
( ( ~ ( ~ ( ( SV89
!= ( unordered_pair @ SV36 @ SV73 ) )
| ! [SY223: $i] :
~ ( ~ ( ~ ( in @ SY223 @ SV89 )
| ( SY223 = SV36 )
| ( SY223 = SV73 ) )
| ~ ( ~ ( ( SY223 = SV36 )
| ( SY223 = SV73 ) )
| ( in @ SY223 @ SV89 ) ) ) )
| ~ ( ~ ! [SY224: $i] :
~ ( ~ ( ~ ( in @ SY224 @ SV89 )
| ( SY224 = SV36 )
| ( SY224 = SV73 ) )
| ~ ( ~ ( ( SY224 = SV36 )
| ( SY224 = SV73 ) )
| ( in @ SY224 @ SV89 ) ) )
| ( SV89
= ( unordered_pair @ SV36 @ SV73 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(355,plain,
! [SV90: $i,SV74: $i,SV37: $i] :
( ( ~ ~ ( ~ ( subset @ SV37 @ SV74 )
| ~ ( subset @ SV37 @ SV90 ) )
| ( subset @ SV37 @ ( set_intersection2 @ SV74 @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(356,plain,
! [SV91: $i,SV75: $i,SV38: $i] :
( ( ~ ~ ( ~ ( subset @ SV38 @ SV75 )
| ~ ( subset @ SV75 @ SV91 ) )
| ( subset @ SV38 @ SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(357,plain,
! [SV76: $i,SV39: $i] :
( ( ( ~ ~ ( in @ SV39 @ SV76 ) )
= $true )
| ( ( disjoint @ ( singleton @ SV39 ) @ SV76 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(358,plain,
! [SV77: $i,SV40: $i] :
( ( ~ ( ~ ( subset @ SV40 @ SV77 )
| ~ ( proper_subset @ SV77 @ SV40 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(359,plain,
! [SV41: $i,SV78: $i] :
( ( ~ ( ( SV78
!= ( powerset @ SV41 ) )
| ! [SY214: $i] :
~ ( ~ ( ~ ( in @ SY214 @ SV78 )
| ( subset @ SY214 @ SV41 ) )
| ~ ( ~ ( subset @ SY214 @ SV41 )
| ( in @ SY214 @ SV78 ) ) ) )
| ~ ( ~ ! [SY215: $i] :
~ ( ~ ( ~ ( in @ SY215 @ SV78 )
| ( subset @ SY215 @ SV41 ) )
| ~ ( ~ ( subset @ SY215 @ SV41 )
| ( in @ SY215 @ SV78 ) ) )
| ( SV78
= ( powerset @ SV41 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(360,plain,
! [SV79: $i,SV42: $i,SV92: $i] :
( ( ~ ( ~ ( ( SV92
!= ( set_union2 @ SV42 @ SV79 ) )
| ! [SY225: $i] :
~ ( ~ ( ~ ( in @ SY225 @ SV92 )
| ( in @ SY225 @ SV42 )
| ( in @ SY225 @ SV79 ) )
| ~ ( ~ ( ( in @ SY225 @ SV42 )
| ( in @ SY225 @ SV79 ) )
| ( in @ SY225 @ SV92 ) ) ) )
| ~ ( ~ ! [SY226: $i] :
~ ( ~ ( ~ ( in @ SY226 @ SV92 )
| ( in @ SY226 @ SV42 )
| ( in @ SY226 @ SV79 ) )
| ~ ( ~ ( ( in @ SY226 @ SV42 )
| ( in @ SY226 @ SV79 ) )
| ( in @ SY226 @ SV92 ) ) )
| ( SV92
= ( set_union2 @ SV42 @ SV79 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(361,plain,
! [SV47: $i,SV7: $i] :
( ( ~ ( ( SV7 != SV47 )
| ~ ( ~ ( subset @ SV7 @ SV47 )
| ~ ( subset @ SV47 @ SV7 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[324]) ).
thf(362,plain,
! [SV47: $i,SV7: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV7 @ SV47 )
| ~ ( subset @ SV47 @ SV7 ) )
| ( SV7 = SV47 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[324]) ).
thf(363,plain,
! [SV80: $i,SV48: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV9 @ SV48 )
| ~ ( subset @ SV80 @ SV48 ) ) )
= $true )
| ( ( subset @ ( set_union2 @ SV9 @ SV80 ) @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(364,plain,
! [SV10: $i,SV49: $i] :
( ( ~ ( ( SV49
!= ( singleton @ SV10 ) )
| ! [SY184: $i] :
~ ( ~ ( ~ ( in @ SY184 @ SV49 )
| ( SY184 = SV10 ) )
| ~ ( ( SY184 != SV10 )
| ( in @ SY184 @ SV49 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[326]) ).
thf(365,plain,
! [SV10: $i,SV49: $i] :
( ( ~ ( ~ ! [SY185: $i] :
~ ( ~ ( ~ ( in @ SY185 @ SV49 )
| ( SY185 = SV10 ) )
| ~ ( ( SY185 != SV10 )
| ( in @ SY185 @ SV49 ) ) )
| ( SV49
= ( singleton @ SV10 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[326]) ).
thf(366,plain,
! [SV50: $i,SV11: $i] :
( ( ~ ( disjoint @ ( singleton @ SV11 ) @ SV50 )
| ~ ( in @ SV11 @ SV50 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[327]) ).
thf(367,plain,
! [SV81: $i,SV51: $i,SV12: $i] :
( ( ( ~ ( subset @ SV12 @ SV51 ) )
= $true )
| ( ( ( in @ SV81 @ SV12 )
| ( subset @ SV12 @ ( set_difference @ SV51 @ ( singleton @ SV81 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[328]) ).
thf(368,plain,
! [SV52: $i,SV13: $i] :
( ( ~ ( ~ ( subset @ SV13 @ ( singleton @ SV52 ) )
| ( SV13 = empty_set )
| ( SV13
= ( singleton @ SV52 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[329]) ).
thf(369,plain,
! [SV52: $i,SV13: $i] :
( ( ~ ( ~ ( ( SV13 = empty_set )
| ( SV13
= ( singleton @ SV52 ) ) )
| ( subset @ SV13 @ ( singleton @ SV52 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[329]) ).
thf(370,plain,
! [SV53: $i,SV14: $i] :
( ( ( in @ SV14 @ SV53 )
= $false )
| ( ( subset @ SV14 @ ( union @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(371,plain,
! [SV82: $i,SV54: $i,SV16: $i] :
( ( ( ~ ( subset @ SV16 @ SV54 ) )
= $true )
| ( ( subset @ ( set_difference @ SV16 @ SV82 ) @ ( set_difference @ SV54 @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(372,plain,
! [SV17: $i,SV55: $i] :
( ( ~ ( ( SV55
!= ( union @ SV17 ) )
| ! [SY188: $i] :
~ ( ~ ( ~ ( in @ SY188 @ SV55 )
| ~ ! [SY127: $i] :
~ ~ ( ~ ( in @ SY188 @ SY127 )
| ~ ( in @ SY127 @ SV17 ) ) )
| ~ ( ~ ~ ! [SY128: $i] :
~ ~ ( ~ ( in @ SY188 @ SY128 )
| ~ ( in @ SY128 @ SV17 ) )
| ( in @ SY188 @ SV55 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[334]) ).
thf(373,plain,
! [SV17: $i,SV55: $i] :
( ( ~ ( ~ ! [SY191: $i] :
~ ( ~ ( ~ ( in @ SY191 @ SV55 )
| ~ ! [SY130: $i] :
~ ~ ( ~ ( in @ SY191 @ SY130 )
| ~ ( in @ SY130 @ SV17 ) ) )
| ~ ( ~ ~ ! [SY131: $i] :
~ ~ ( ~ ( in @ SY191 @ SY131 )
| ~ ( in @ SY131 @ SV17 ) )
| ( in @ SY191 @ SV55 ) ) )
| ( SV55
= ( union @ SV17 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[334]) ).
thf(374,plain,
! [SV56: $i,SV18: $i] :
( ( ~ ( in @ SV18 @ SV56 )
| ~ ( empty @ SV56 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[335]) ).
thf(375,plain,
! [SV57: $i,SV19: $i] :
( ( ~ ~ ~ ( ~ ~ ( disjoint @ SV19 @ SV57 )
| ~ ! [SY194: $i] :
~ ~ ( ~ ( in @ SY194 @ SV19 )
| ~ ( in @ SY194 @ SV57 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[336]) ).
thf(376,plain,
! [SV57: $i,SV19: $i] :
( ( ~ ~ ~ ( ~ ~ ! [SY195: $i] :
~ ~ ( ~ ( in @ SY195 @ SV19 )
| ~ ( in @ SY195 @ SV57 ) )
| ~ ( disjoint @ SV19 @ SV57 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[336]) ).
thf(377,plain,
! [SV20: $i] :
( ( ( SV20 != empty_set )
| ! [SY136: $i] :
~ ( in @ SY136 @ SV20 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[337]) ).
thf(378,plain,
! [SV20: $i] :
( ( ~ ! [SY137: $i] :
~ ( in @ SY137 @ SV20 )
| ( SV20 = empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[338]) ).
thf(379,plain,
! [SV83: $i,SV58: $i,SV21: $i] :
( ( ( ( singleton @ SV21 )
!= ( unordered_pair @ SV58 @ SV83 ) )
= $true )
| ( ( SV21 = SV58 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[339]) ).
thf(380,plain,
! [SV59: $i,SV22: $i] :
( ( ~ ( ~ ( subset @ ( singleton @ SV22 ) @ SV59 )
| ( in @ SV22 @ SV59 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[340]) ).
thf(381,plain,
! [SV59: $i,SV22: $i] :
( ( ~ ( ~ ( in @ SV22 @ SV59 )
| ( subset @ ( singleton @ SV22 ) @ SV59 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[340]) ).
thf(382,plain,
! [SV84: $i,SV60: $i,SV23: $i] :
( ( ( ( singleton @ SV23 )
!= ( unordered_pair @ SV60 @ SV84 ) )
= $true )
| ( ( SV60 = SV84 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[341]) ).
thf(383,plain,
! [SV61: $i,SV24: $i] :
( ( ( subset @ SV24 @ SV61 )
= $false )
| ( ( ( set_intersection2 @ SV24 @ SV61 )
= SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(384,plain,
! [SV62: $i,SV25: $i,SV85: $i] :
( ( ~ ( ( SV85
!= ( set_intersection2 @ SV25 @ SV62 ) )
| ! [SY219: $i] :
~ ( ~ ( ~ ( in @ SY219 @ SV85 )
| ~ ( ~ ( in @ SY219 @ SV25 )
| ~ ( in @ SY219 @ SV62 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY219 @ SV25 )
| ~ ( in @ SY219 @ SV62 ) )
| ( in @ SY219 @ SV85 ) ) ) )
| ~ ( ~ ! [SY220: $i] :
~ ( ~ ( ~ ( in @ SY220 @ SV85 )
| ~ ( ~ ( in @ SY220 @ SV25 )
| ~ ( in @ SY220 @ SV62 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY220 @ SV25 )
| ~ ( in @ SY220 @ SV62 ) )
| ( in @ SY220 @ SV85 ) ) )
| ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(385,plain,
! [SV86: $i,SV63: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV26 @ SV63 )
| ~ ( disjoint @ SV63 @ SV86 ) ) )
= $true )
| ( ( disjoint @ SV26 @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[344]) ).
thf(386,plain,
! [SV64: $i,SV27: $i] :
( ( ( subset @ ( singleton @ SV27 ) @ ( singleton @ SV64 ) )
= $false )
| ( ( SV27 = SV64 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(387,plain,
! [SV65: $i,SV28: $i] :
( ( ~ ( ~ ( subset @ SV28 @ SV65 )
| ! [SY202: $i] :
( ~ ( in @ SY202 @ SV28 )
| ( in @ SY202 @ SV65 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[346]) ).
thf(388,plain,
! [SV65: $i,SV28: $i] :
( ( ~ ( ~ ! [SY203: $i] :
( ~ ( in @ SY203 @ SV28 )
| ( in @ SY203 @ SV65 ) )
| ( subset @ SV28 @ SV65 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[346]) ).
thf(389,plain,
! [SV66: $i,SV29: $i] :
( ( ( subset @ SV29 @ SV66 )
= $false )
| ( ( ( set_union2 @ SV29 @ SV66 )
= SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(390,plain,
! [SV87: $i,SV67: $i,SV30: $i] :
( ( ( ~ ( subset @ SV30 @ SV67 ) )
= $true )
| ( ( subset @ ( set_intersection2 @ SV30 @ SV87 ) @ ( set_intersection2 @ SV67 @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[348]) ).
thf(391,plain,
! [SV68: $i,SV31: $i] :
( ( ~ ( ~ ( proper_subset @ SV31 @ SV68 )
| ~ ( ~ ( subset @ SV31 @ SV68 )
| ~ ( ( SV31 != SV68 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[349]) ).
thf(392,plain,
! [SV68: $i,SV31: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV31 @ SV68 )
| ~ ( ( SV31 != SV68 ) ) )
| ( proper_subset @ SV31 @ SV68 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[349]) ).
thf(393,plain,
! [SV69: $i,SV32: $i] :
( ( ( in @ SV32 @ SV69 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV32 ) @ SV69 )
= SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(394,plain,
! [SV70: $i,SV33: $i] :
( ( ( ! [SY205: $i] :
~ ( ~ ( ~ ( in @ SY205 @ SV33 )
| ( in @ SY205 @ SV70 ) )
| ~ ( ~ ( in @ SY205 @ SV70 )
| ( in @ SY205 @ SV33 ) ) ) )
= $false )
| ( ( SV33 = SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(395,plain,
! [SV71: $i,SV34: $i,SV88: $i] :
( ( ~ ( ( SV88
!= ( set_difference @ SV34 @ SV71 ) )
| ! [SY221: $i] :
~ ( ~ ( ~ ( in @ SY221 @ SV88 )
| ~ ( ~ ( in @ SY221 @ SV34 )
| ~ ~ ( in @ SY221 @ SV71 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY221 @ SV34 )
| ~ ~ ( in @ SY221 @ SV71 ) )
| ( in @ SY221 @ SV88 ) ) ) )
| ~ ( ~ ! [SY222: $i] :
~ ( ~ ( ~ ( in @ SY222 @ SV88 )
| ~ ( ~ ( in @ SY222 @ SV34 )
| ~ ~ ( in @ SY222 @ SV71 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY222 @ SV34 )
| ~ ~ ( in @ SY222 @ SV71 ) )
| ( in @ SY222 @ SV88 ) ) )
| ( SV88
= ( set_difference @ SV34 @ SV71 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(396,plain,
! [SV72: $i,SV35: $i] :
( ( ( in @ SV35 @ SV72 )
= $false )
| ( ( ~ ( in @ SV72 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(397,plain,
! [SV73: $i,SV36: $i,SV89: $i] :
( ( ~ ( ( SV89
!= ( unordered_pair @ SV36 @ SV73 ) )
| ! [SY223: $i] :
~ ( ~ ( ~ ( in @ SY223 @ SV89 )
| ( SY223 = SV36 )
| ( SY223 = SV73 ) )
| ~ ( ~ ( ( SY223 = SV36 )
| ( SY223 = SV73 ) )
| ( in @ SY223 @ SV89 ) ) ) )
| ~ ( ~ ! [SY224: $i] :
~ ( ~ ( ~ ( in @ SY224 @ SV89 )
| ( SY224 = SV36 )
| ( SY224 = SV73 ) )
| ~ ( ~ ( ( SY224 = SV36 )
| ( SY224 = SV73 ) )
| ( in @ SY224 @ SV89 ) ) )
| ( SV89
= ( unordered_pair @ SV36 @ SV73 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[354]) ).
thf(398,plain,
! [SV90: $i,SV74: $i,SV37: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV37 @ SV74 )
| ~ ( subset @ SV37 @ SV90 ) ) )
= $true )
| ( ( subset @ SV37 @ ( set_intersection2 @ SV74 @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[355]) ).
thf(399,plain,
! [SV91: $i,SV75: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV38 @ SV75 )
| ~ ( subset @ SV75 @ SV91 ) ) )
= $true )
| ( ( subset @ SV38 @ SV91 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[356]) ).
thf(400,plain,
! [SV76: $i,SV39: $i] :
( ( ( ~ ( in @ SV39 @ SV76 ) )
= $false )
| ( ( disjoint @ ( singleton @ SV39 ) @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(401,plain,
! [SV77: $i,SV40: $i] :
( ( ~ ( subset @ SV40 @ SV77 )
| ~ ( proper_subset @ SV77 @ SV40 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[358]) ).
thf(402,plain,
! [SV41: $i,SV78: $i] :
( ( ~ ( ( SV78
!= ( powerset @ SV41 ) )
| ! [SY214: $i] :
~ ( ~ ( ~ ( in @ SY214 @ SV78 )
| ( subset @ SY214 @ SV41 ) )
| ~ ( ~ ( subset @ SY214 @ SV41 )
| ( in @ SY214 @ SV78 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[359]) ).
thf(403,plain,
! [SV41: $i,SV78: $i] :
( ( ~ ( ~ ! [SY215: $i] :
~ ( ~ ( ~ ( in @ SY215 @ SV78 )
| ( subset @ SY215 @ SV41 ) )
| ~ ( ~ ( subset @ SY215 @ SV41 )
| ( in @ SY215 @ SV78 ) ) )
| ( SV78
= ( powerset @ SV41 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[359]) ).
thf(404,plain,
! [SV79: $i,SV42: $i,SV92: $i] :
( ( ~ ( ( SV92
!= ( set_union2 @ SV42 @ SV79 ) )
| ! [SY225: $i] :
~ ( ~ ( ~ ( in @ SY225 @ SV92 )
| ( in @ SY225 @ SV42 )
| ( in @ SY225 @ SV79 ) )
| ~ ( ~ ( ( in @ SY225 @ SV42 )
| ( in @ SY225 @ SV79 ) )
| ( in @ SY225 @ SV92 ) ) ) )
| ~ ( ~ ! [SY226: $i] :
~ ( ~ ( ~ ( in @ SY226 @ SV92 )
| ( in @ SY226 @ SV42 )
| ( in @ SY226 @ SV79 ) )
| ~ ( ~ ( ( in @ SY226 @ SV42 )
| ( in @ SY226 @ SV79 ) )
| ( in @ SY226 @ SV92 ) ) )
| ( SV92
= ( set_union2 @ SV42 @ SV79 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(405,plain,
! [SV47: $i,SV7: $i] :
( ( ( SV7 != SV47 )
| ~ ( ~ ( subset @ SV7 @ SV47 )
| ~ ( subset @ SV47 @ SV7 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[361]) ).
thf(406,plain,
! [SV47: $i,SV7: $i] :
( ( ~ ~ ( ~ ( subset @ SV7 @ SV47 )
| ~ ( subset @ SV47 @ SV7 ) )
| ( SV7 = SV47 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[362]) ).
thf(407,plain,
! [SV80: $i,SV48: $i,SV9: $i] :
( ( ( ~ ( ~ ( subset @ SV9 @ SV48 )
| ~ ( subset @ SV80 @ SV48 ) ) )
= $false )
| ( ( subset @ ( set_union2 @ SV9 @ SV80 ) @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(408,plain,
! [SV10: $i,SV49: $i] :
( ( ( SV49
!= ( singleton @ SV10 ) )
| ! [SY184: $i] :
~ ( ~ ( ~ ( in @ SY184 @ SV49 )
| ( SY184 = SV10 ) )
| ~ ( ( SY184 != SV10 )
| ( in @ SY184 @ SV49 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[364]) ).
thf(409,plain,
! [SV10: $i,SV49: $i] :
( ( ~ ! [SY185: $i] :
~ ( ~ ( ~ ( in @ SY185 @ SV49 )
| ( SY185 = SV10 ) )
| ~ ( ( SY185 != SV10 )
| ( in @ SY185 @ SV49 ) ) )
| ( SV49
= ( singleton @ SV10 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[365]) ).
thf(410,plain,
! [SV50: $i,SV11: $i] :
( ( ( ~ ( disjoint @ ( singleton @ SV11 ) @ SV50 ) )
= $true )
| ( ( ~ ( in @ SV11 @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[366]) ).
thf(411,plain,
! [SV81: $i,SV51: $i,SV12: $i] :
( ( ( subset @ SV12 @ SV51 )
= $false )
| ( ( ( in @ SV81 @ SV12 )
| ( subset @ SV12 @ ( set_difference @ SV51 @ ( singleton @ SV81 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(412,plain,
! [SV52: $i,SV13: $i] :
( ( ~ ( subset @ SV13 @ ( singleton @ SV52 ) )
| ( SV13 = empty_set )
| ( SV13
= ( singleton @ SV52 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[368]) ).
thf(413,plain,
! [SV52: $i,SV13: $i] :
( ( ~ ( ( SV13 = empty_set )
| ( SV13
= ( singleton @ SV52 ) ) )
| ( subset @ SV13 @ ( singleton @ SV52 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[369]) ).
thf(414,plain,
! [SV82: $i,SV54: $i,SV16: $i] :
( ( ( subset @ SV16 @ SV54 )
= $false )
| ( ( subset @ ( set_difference @ SV16 @ SV82 ) @ ( set_difference @ SV54 @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[371]) ).
thf(415,plain,
! [SV17: $i,SV55: $i] :
( ( ( SV55
!= ( union @ SV17 ) )
| ! [SY188: $i] :
~ ( ~ ( ~ ( in @ SY188 @ SV55 )
| ~ ! [SY127: $i] :
~ ~ ( ~ ( in @ SY188 @ SY127 )
| ~ ( in @ SY127 @ SV17 ) ) )
| ~ ( ~ ~ ! [SY128: $i] :
~ ~ ( ~ ( in @ SY188 @ SY128 )
| ~ ( in @ SY128 @ SV17 ) )
| ( in @ SY188 @ SV55 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[372]) ).
thf(416,plain,
! [SV17: $i,SV55: $i] :
( ( ~ ! [SY191: $i] :
~ ( ~ ( ~ ( in @ SY191 @ SV55 )
| ~ ! [SY130: $i] :
~ ~ ( ~ ( in @ SY191 @ SY130 )
| ~ ( in @ SY130 @ SV17 ) ) )
| ~ ( ~ ~ ! [SY131: $i] :
~ ~ ( ~ ( in @ SY191 @ SY131 )
| ~ ( in @ SY131 @ SV17 ) )
| ( in @ SY191 @ SV55 ) ) )
| ( SV55
= ( union @ SV17 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[373]) ).
thf(417,plain,
! [SV56: $i,SV18: $i] :
( ( ( ~ ( in @ SV18 @ SV56 ) )
= $true )
| ( ( ~ ( empty @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[374]) ).
thf(418,plain,
! [SV57: $i,SV19: $i] :
( ( ~ ~ ( ~ ~ ( disjoint @ SV19 @ SV57 )
| ~ ! [SY194: $i] :
~ ~ ( ~ ( in @ SY194 @ SV19 )
| ~ ( in @ SY194 @ SV57 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[375]) ).
thf(419,plain,
! [SV57: $i,SV19: $i] :
( ( ~ ~ ( ~ ~ ! [SY195: $i] :
~ ~ ( ~ ( in @ SY195 @ SV19 )
| ~ ( in @ SY195 @ SV57 ) )
| ~ ( disjoint @ SV19 @ SV57 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[376]) ).
thf(420,plain,
! [SV20: $i] :
( ( ( SV20 != empty_set )
= $true )
| ( ( ! [SY136: $i] :
~ ( in @ SY136 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[377]) ).
thf(421,plain,
! [SV20: $i] :
( ( ( ~ ! [SY137: $i] :
~ ( in @ SY137 @ SV20 ) )
= $true )
| ( ( SV20 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[378]) ).
thf(422,plain,
! [SV83: $i,SV58: $i,SV21: $i] :
( ( ( ( singleton @ SV21 )
= ( unordered_pair @ SV58 @ SV83 ) )
= $false )
| ( ( SV21 = SV58 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(423,plain,
! [SV59: $i,SV22: $i] :
( ( ~ ( subset @ ( singleton @ SV22 ) @ SV59 )
| ( in @ SV22 @ SV59 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[380]) ).
thf(424,plain,
! [SV59: $i,SV22: $i] :
( ( ~ ( in @ SV22 @ SV59 )
| ( subset @ ( singleton @ SV22 ) @ SV59 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[381]) ).
thf(425,plain,
! [SV84: $i,SV60: $i,SV23: $i] :
( ( ( ( singleton @ SV23 )
= ( unordered_pair @ SV60 @ SV84 ) )
= $false )
| ( ( SV60 = SV84 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(426,plain,
! [SV62: $i,SV25: $i,SV85: $i] :
( ( ~ ( ( SV85
!= ( set_intersection2 @ SV25 @ SV62 ) )
| ! [SY219: $i] :
~ ( ~ ( ~ ( in @ SY219 @ SV85 )
| ~ ( ~ ( in @ SY219 @ SV25 )
| ~ ( in @ SY219 @ SV62 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY219 @ SV25 )
| ~ ( in @ SY219 @ SV62 ) )
| ( in @ SY219 @ SV85 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[384]) ).
thf(427,plain,
! [SV62: $i,SV25: $i,SV85: $i] :
( ( ~ ( ~ ! [SY220: $i] :
~ ( ~ ( ~ ( in @ SY220 @ SV85 )
| ~ ( ~ ( in @ SY220 @ SV25 )
| ~ ( in @ SY220 @ SV62 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY220 @ SV25 )
| ~ ( in @ SY220 @ SV62 ) )
| ( in @ SY220 @ SV85 ) ) )
| ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[384]) ).
thf(428,plain,
! [SV86: $i,SV63: $i,SV26: $i] :
( ( ( ~ ( ~ ( subset @ SV26 @ SV63 )
| ~ ( disjoint @ SV63 @ SV86 ) ) )
= $false )
| ( ( disjoint @ SV26 @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(429,plain,
! [SV65: $i,SV28: $i] :
( ( ~ ( subset @ SV28 @ SV65 )
| ! [SY202: $i] :
( ~ ( in @ SY202 @ SV28 )
| ( in @ SY202 @ SV65 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[387]) ).
thf(430,plain,
! [SV65: $i,SV28: $i] :
( ( ~ ! [SY203: $i] :
( ~ ( in @ SY203 @ SV28 )
| ( in @ SY203 @ SV65 ) )
| ( subset @ SV28 @ SV65 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[388]) ).
thf(431,plain,
! [SV87: $i,SV67: $i,SV30: $i] :
( ( ( subset @ SV30 @ SV67 )
= $false )
| ( ( subset @ ( set_intersection2 @ SV30 @ SV87 ) @ ( set_intersection2 @ SV67 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(432,plain,
! [SV68: $i,SV31: $i] :
( ( ~ ( proper_subset @ SV31 @ SV68 )
| ~ ( ~ ( subset @ SV31 @ SV68 )
| ~ ( ( SV31 != SV68 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[391]) ).
thf(433,plain,
! [SV68: $i,SV31: $i] :
( ( ~ ~ ( ~ ( subset @ SV31 @ SV68 )
| ~ ( ( SV31 != SV68 ) ) )
| ( proper_subset @ SV31 @ SV68 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[392]) ).
thf(434,plain,
! [SV33: $i,SV70: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV33 )
| ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV70 ) )
| ~ ( ~ ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV70 )
| ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV33 ) ) ) )
= $false )
| ( ( SV33 = SV70 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[394]) ).
thf(435,plain,
! [SV71: $i,SV34: $i,SV88: $i] :
( ( ~ ( ( SV88
!= ( set_difference @ SV34 @ SV71 ) )
| ! [SY221: $i] :
~ ( ~ ( ~ ( in @ SY221 @ SV88 )
| ~ ( ~ ( in @ SY221 @ SV34 )
| ~ ~ ( in @ SY221 @ SV71 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY221 @ SV34 )
| ~ ~ ( in @ SY221 @ SV71 ) )
| ( in @ SY221 @ SV88 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[395]) ).
thf(436,plain,
! [SV71: $i,SV34: $i,SV88: $i] :
( ( ~ ( ~ ! [SY222: $i] :
~ ( ~ ( ~ ( in @ SY222 @ SV88 )
| ~ ( ~ ( in @ SY222 @ SV34 )
| ~ ~ ( in @ SY222 @ SV71 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY222 @ SV34 )
| ~ ~ ( in @ SY222 @ SV71 ) )
| ( in @ SY222 @ SV88 ) ) )
| ( SV88
= ( set_difference @ SV34 @ SV71 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[395]) ).
thf(437,plain,
! [SV35: $i,SV72: $i] :
( ( ( in @ SV72 @ SV35 )
= $false )
| ( ( in @ SV35 @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(438,plain,
! [SV73: $i,SV36: $i,SV89: $i] :
( ( ~ ( ( SV89
!= ( unordered_pair @ SV36 @ SV73 ) )
| ! [SY223: $i] :
~ ( ~ ( ~ ( in @ SY223 @ SV89 )
| ( SY223 = SV36 )
| ( SY223 = SV73 ) )
| ~ ( ~ ( ( SY223 = SV36 )
| ( SY223 = SV73 ) )
| ( in @ SY223 @ SV89 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[397]) ).
thf(439,plain,
! [SV73: $i,SV36: $i,SV89: $i] :
( ( ~ ( ~ ! [SY224: $i] :
~ ( ~ ( ~ ( in @ SY224 @ SV89 )
| ( SY224 = SV36 )
| ( SY224 = SV73 ) )
| ~ ( ~ ( ( SY224 = SV36 )
| ( SY224 = SV73 ) )
| ( in @ SY224 @ SV89 ) ) )
| ( SV89
= ( unordered_pair @ SV36 @ SV73 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[397]) ).
thf(440,plain,
! [SV90: $i,SV74: $i,SV37: $i] :
( ( ( ~ ( ~ ( subset @ SV37 @ SV74 )
| ~ ( subset @ SV37 @ SV90 ) ) )
= $false )
| ( ( subset @ SV37 @ ( set_intersection2 @ SV74 @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(441,plain,
! [SV91: $i,SV75: $i,SV38: $i] :
( ( ( ~ ( ~ ( subset @ SV38 @ SV75 )
| ~ ( subset @ SV75 @ SV91 ) ) )
= $false )
| ( ( subset @ SV38 @ SV91 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(442,plain,
! [SV76: $i,SV39: $i] :
( ( ( in @ SV39 @ SV76 )
= $true )
| ( ( disjoint @ ( singleton @ SV39 ) @ SV76 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[400]) ).
thf(443,plain,
! [SV77: $i,SV40: $i] :
( ( ( ~ ( subset @ SV40 @ SV77 ) )
= $true )
| ( ( ~ ( proper_subset @ SV77 @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[401]) ).
thf(444,plain,
! [SV41: $i,SV78: $i] :
( ( ( SV78
!= ( powerset @ SV41 ) )
| ! [SY214: $i] :
~ ( ~ ( ~ ( in @ SY214 @ SV78 )
| ( subset @ SY214 @ SV41 ) )
| ~ ( ~ ( subset @ SY214 @ SV41 )
| ( in @ SY214 @ SV78 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[402]) ).
thf(445,plain,
! [SV41: $i,SV78: $i] :
( ( ~ ! [SY215: $i] :
~ ( ~ ( ~ ( in @ SY215 @ SV78 )
| ( subset @ SY215 @ SV41 ) )
| ~ ( ~ ( subset @ SY215 @ SV41 )
| ( in @ SY215 @ SV78 ) ) )
| ( SV78
= ( powerset @ SV41 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[403]) ).
thf(446,plain,
! [SV79: $i,SV42: $i,SV92: $i] :
( ( ~ ( ( SV92
!= ( set_union2 @ SV42 @ SV79 ) )
| ! [SY225: $i] :
~ ( ~ ( ~ ( in @ SY225 @ SV92 )
| ( in @ SY225 @ SV42 )
| ( in @ SY225 @ SV79 ) )
| ~ ( ~ ( ( in @ SY225 @ SV42 )
| ( in @ SY225 @ SV79 ) )
| ( in @ SY225 @ SV92 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[404]) ).
thf(447,plain,
! [SV79: $i,SV42: $i,SV92: $i] :
( ( ~ ( ~ ! [SY226: $i] :
~ ( ~ ( ~ ( in @ SY226 @ SV92 )
| ( in @ SY226 @ SV42 )
| ( in @ SY226 @ SV79 ) )
| ~ ( ~ ( ( in @ SY226 @ SV42 )
| ( in @ SY226 @ SV79 ) )
| ( in @ SY226 @ SV92 ) ) )
| ( SV92
= ( set_union2 @ SV42 @ SV79 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[404]) ).
thf(448,plain,
! [SV47: $i,SV7: $i] :
( ( ( SV7 != SV47 )
= $true )
| ( ( ~ ( ~ ( subset @ SV7 @ SV47 )
| ~ ( subset @ SV47 @ SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[405]) ).
thf(449,plain,
! [SV47: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV7 @ SV47 )
| ~ ( subset @ SV47 @ SV7 ) ) )
= $true )
| ( ( SV7 = SV47 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[406]) ).
thf(450,plain,
! [SV80: $i,SV48: $i,SV9: $i] :
( ( ( ~ ( subset @ SV9 @ SV48 )
| ~ ( subset @ SV80 @ SV48 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV9 @ SV80 ) @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[407]) ).
thf(451,plain,
! [SV10: $i,SV49: $i] :
( ( ( SV49
!= ( singleton @ SV10 ) )
= $true )
| ( ( ! [SY184: $i] :
~ ( ~ ( ~ ( in @ SY184 @ SV49 )
| ( SY184 = SV10 ) )
| ~ ( ( SY184 != SV10 )
| ( in @ SY184 @ SV49 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[408]) ).
thf(452,plain,
! [SV10: $i,SV49: $i] :
( ( ( ~ ! [SY185: $i] :
~ ( ~ ( ~ ( in @ SY185 @ SV49 )
| ( SY185 = SV10 ) )
| ~ ( ( SY185 != SV10 )
| ( in @ SY185 @ SV49 ) ) ) )
= $true )
| ( ( SV49
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[409]) ).
thf(453,plain,
! [SV50: $i,SV11: $i] :
( ( ( disjoint @ ( singleton @ SV11 ) @ SV50 )
= $false )
| ( ( ~ ( in @ SV11 @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[410]) ).
thf(454,plain,
! [SV51: $i,SV12: $i,SV81: $i] :
( ( ( in @ SV81 @ SV12 )
= $true )
| ( ( subset @ SV12 @ ( set_difference @ SV51 @ ( singleton @ SV81 ) ) )
= $true )
| ( ( subset @ SV12 @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[411]) ).
thf(455,plain,
! [SV52: $i,SV13: $i] :
( ( ( ~ ( subset @ SV13 @ ( singleton @ SV52 ) ) )
= $true )
| ( ( ( SV13 = empty_set )
| ( SV13
= ( singleton @ SV52 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[412]) ).
thf(456,plain,
! [SV52: $i,SV13: $i] :
( ( ( ~ ( ( SV13 = empty_set )
| ( SV13
= ( singleton @ SV52 ) ) ) )
= $true )
| ( ( subset @ SV13 @ ( singleton @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(457,plain,
! [SV17: $i,SV55: $i] :
( ( ( SV55
!= ( union @ SV17 ) )
= $true )
| ( ( ! [SY188: $i] :
~ ( ~ ( ~ ( in @ SY188 @ SV55 )
| ~ ! [SY127: $i] :
~ ~ ( ~ ( in @ SY188 @ SY127 )
| ~ ( in @ SY127 @ SV17 ) ) )
| ~ ( ~ ~ ! [SY128: $i] :
~ ~ ( ~ ( in @ SY188 @ SY128 )
| ~ ( in @ SY128 @ SV17 ) )
| ( in @ SY188 @ SV55 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(458,plain,
! [SV17: $i,SV55: $i] :
( ( ( ~ ! [SY191: $i] :
~ ( ~ ( ~ ( in @ SY191 @ SV55 )
| ~ ! [SY130: $i] :
~ ~ ( ~ ( in @ SY191 @ SY130 )
| ~ ( in @ SY130 @ SV17 ) ) )
| ~ ( ~ ~ ! [SY131: $i] :
~ ~ ( ~ ( in @ SY191 @ SY131 )
| ~ ( in @ SY131 @ SV17 ) )
| ( in @ SY191 @ SV55 ) ) ) )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[416]) ).
thf(459,plain,
! [SV56: $i,SV18: $i] :
( ( ( in @ SV18 @ SV56 )
= $false )
| ( ( ~ ( empty @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(460,plain,
! [SV57: $i,SV19: $i] :
( ( ~ ( ~ ~ ( disjoint @ SV19 @ SV57 )
| ~ ! [SY194: $i] :
~ ~ ( ~ ( in @ SY194 @ SV19 )
| ~ ( in @ SY194 @ SV57 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(461,plain,
! [SV57: $i,SV19: $i] :
( ( ~ ( ~ ~ ! [SY195: $i] :
~ ~ ( ~ ( in @ SY195 @ SV19 )
| ~ ( in @ SY195 @ SV57 ) )
| ~ ( disjoint @ SV19 @ SV57 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(462,plain,
! [SV20: $i] :
( ( ( SV20 = empty_set )
= $false )
| ( ( ! [SY136: $i] :
~ ( in @ SY136 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(463,plain,
! [SV20: $i] :
( ( ( ! [SY137: $i] :
~ ( in @ SY137 @ SV20 ) )
= $false )
| ( ( SV20 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(464,plain,
! [SV59: $i,SV22: $i] :
( ( ( ~ ( subset @ ( singleton @ SV22 ) @ SV59 ) )
= $true )
| ( ( in @ SV22 @ SV59 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[423]) ).
thf(465,plain,
! [SV59: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ SV59 ) )
= $true )
| ( ( subset @ ( singleton @ SV22 ) @ SV59 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[424]) ).
thf(466,plain,
! [SV62: $i,SV25: $i,SV85: $i] :
( ( ( SV85
!= ( set_intersection2 @ SV25 @ SV62 ) )
| ! [SY219: $i] :
~ ( ~ ( ~ ( in @ SY219 @ SV85 )
| ~ ( ~ ( in @ SY219 @ SV25 )
| ~ ( in @ SY219 @ SV62 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY219 @ SV25 )
| ~ ( in @ SY219 @ SV62 ) )
| ( in @ SY219 @ SV85 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[426]) ).
thf(467,plain,
! [SV62: $i,SV25: $i,SV85: $i] :
( ( ~ ! [SY220: $i] :
~ ( ~ ( ~ ( in @ SY220 @ SV85 )
| ~ ( ~ ( in @ SY220 @ SV25 )
| ~ ( in @ SY220 @ SV62 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY220 @ SV25 )
| ~ ( in @ SY220 @ SV62 ) )
| ( in @ SY220 @ SV85 ) ) )
| ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[427]) ).
thf(468,plain,
! [SV86: $i,SV63: $i,SV26: $i] :
( ( ( ~ ( subset @ SV26 @ SV63 )
| ~ ( disjoint @ SV63 @ SV86 ) )
= $true )
| ( ( disjoint @ SV26 @ SV86 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[428]) ).
thf(469,plain,
! [SV65: $i,SV28: $i] :
( ( ( ~ ( subset @ SV28 @ SV65 ) )
= $true )
| ( ( ! [SY202: $i] :
( ~ ( in @ SY202 @ SV28 )
| ( in @ SY202 @ SV65 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[429]) ).
thf(470,plain,
! [SV65: $i,SV28: $i] :
( ( ( ~ ! [SY203: $i] :
( ~ ( in @ SY203 @ SV28 )
| ( in @ SY203 @ SV65 ) ) )
= $true )
| ( ( subset @ SV28 @ SV65 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[430]) ).
thf(471,plain,
! [SV68: $i,SV31: $i] :
( ( ( ~ ( proper_subset @ SV31 @ SV68 ) )
= $true )
| ( ( ~ ( ~ ( subset @ SV31 @ SV68 )
| ~ ( ( SV31 != SV68 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[432]) ).
thf(472,plain,
! [SV68: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV31 @ SV68 )
| ~ ( ( SV31 != SV68 ) ) ) )
= $true )
| ( ( proper_subset @ SV31 @ SV68 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[433]) ).
thf(473,plain,
! [SV33: $i,SV70: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV33 )
| ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV70 ) )
| ~ ( ~ ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV70 )
| ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV33 ) ) )
= $true )
| ( ( SV33 = SV70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[434]) ).
thf(474,plain,
! [SV71: $i,SV34: $i,SV88: $i] :
( ( ( SV88
!= ( set_difference @ SV34 @ SV71 ) )
| ! [SY221: $i] :
~ ( ~ ( ~ ( in @ SY221 @ SV88 )
| ~ ( ~ ( in @ SY221 @ SV34 )
| ~ ~ ( in @ SY221 @ SV71 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY221 @ SV34 )
| ~ ~ ( in @ SY221 @ SV71 ) )
| ( in @ SY221 @ SV88 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[435]) ).
thf(475,plain,
! [SV71: $i,SV34: $i,SV88: $i] :
( ( ~ ! [SY222: $i] :
~ ( ~ ( ~ ( in @ SY222 @ SV88 )
| ~ ( ~ ( in @ SY222 @ SV34 )
| ~ ~ ( in @ SY222 @ SV71 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY222 @ SV34 )
| ~ ~ ( in @ SY222 @ SV71 ) )
| ( in @ SY222 @ SV88 ) ) )
| ( SV88
= ( set_difference @ SV34 @ SV71 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[436]) ).
thf(476,plain,
! [SV73: $i,SV36: $i,SV89: $i] :
( ( ( SV89
!= ( unordered_pair @ SV36 @ SV73 ) )
| ! [SY223: $i] :
~ ( ~ ( ~ ( in @ SY223 @ SV89 )
| ( SY223 = SV36 )
| ( SY223 = SV73 ) )
| ~ ( ~ ( ( SY223 = SV36 )
| ( SY223 = SV73 ) )
| ( in @ SY223 @ SV89 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[438]) ).
thf(477,plain,
! [SV73: $i,SV36: $i,SV89: $i] :
( ( ~ ! [SY224: $i] :
~ ( ~ ( ~ ( in @ SY224 @ SV89 )
| ( SY224 = SV36 )
| ( SY224 = SV73 ) )
| ~ ( ~ ( ( SY224 = SV36 )
| ( SY224 = SV73 ) )
| ( in @ SY224 @ SV89 ) ) )
| ( SV89
= ( unordered_pair @ SV36 @ SV73 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[439]) ).
thf(478,plain,
! [SV90: $i,SV74: $i,SV37: $i] :
( ( ( ~ ( subset @ SV37 @ SV74 )
| ~ ( subset @ SV37 @ SV90 ) )
= $true )
| ( ( subset @ SV37 @ ( set_intersection2 @ SV74 @ SV90 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[440]) ).
thf(479,plain,
! [SV91: $i,SV75: $i,SV38: $i] :
( ( ( ~ ( subset @ SV38 @ SV75 )
| ~ ( subset @ SV75 @ SV91 ) )
= $true )
| ( ( subset @ SV38 @ SV91 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[441]) ).
thf(480,plain,
! [SV77: $i,SV40: $i] :
( ( ( subset @ SV40 @ SV77 )
= $false )
| ( ( ~ ( proper_subset @ SV77 @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[443]) ).
thf(481,plain,
! [SV41: $i,SV78: $i] :
( ( ( SV78
!= ( powerset @ SV41 ) )
= $true )
| ( ( ! [SY214: $i] :
~ ( ~ ( ~ ( in @ SY214 @ SV78 )
| ( subset @ SY214 @ SV41 ) )
| ~ ( ~ ( subset @ SY214 @ SV41 )
| ( in @ SY214 @ SV78 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[444]) ).
thf(482,plain,
! [SV41: $i,SV78: $i] :
( ( ( ~ ! [SY215: $i] :
~ ( ~ ( ~ ( in @ SY215 @ SV78 )
| ( subset @ SY215 @ SV41 ) )
| ~ ( ~ ( subset @ SY215 @ SV41 )
| ( in @ SY215 @ SV78 ) ) ) )
= $true )
| ( ( SV78
= ( powerset @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[445]) ).
thf(483,plain,
! [SV79: $i,SV42: $i,SV92: $i] :
( ( ( SV92
!= ( set_union2 @ SV42 @ SV79 ) )
| ! [SY225: $i] :
~ ( ~ ( ~ ( in @ SY225 @ SV92 )
| ( in @ SY225 @ SV42 )
| ( in @ SY225 @ SV79 ) )
| ~ ( ~ ( ( in @ SY225 @ SV42 )
| ( in @ SY225 @ SV79 ) )
| ( in @ SY225 @ SV92 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[446]) ).
thf(484,plain,
! [SV79: $i,SV42: $i,SV92: $i] :
( ( ~ ! [SY226: $i] :
~ ( ~ ( ~ ( in @ SY226 @ SV92 )
| ( in @ SY226 @ SV42 )
| ( in @ SY226 @ SV79 ) )
| ~ ( ~ ( ( in @ SY226 @ SV42 )
| ( in @ SY226 @ SV79 ) )
| ( in @ SY226 @ SV92 ) ) )
| ( SV92
= ( set_union2 @ SV42 @ SV79 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[447]) ).
thf(485,plain,
! [SV47: $i,SV7: $i] :
( ( ( SV7 = SV47 )
= $false )
| ( ( ~ ( ~ ( subset @ SV7 @ SV47 )
| ~ ( subset @ SV47 @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(486,plain,
! [SV47: $i,SV7: $i] :
( ( ( ~ ( ~ ( subset @ SV7 @ SV47 )
| ~ ( subset @ SV47 @ SV7 ) ) )
= $false )
| ( ( SV7 = SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[449]) ).
thf(487,plain,
! [SV80: $i,SV48: $i,SV9: $i] :
( ( ( ~ ( subset @ SV9 @ SV48 ) )
= $true )
| ( ( ~ ( subset @ SV80 @ SV48 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV9 @ SV80 ) @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[450]) ).
thf(488,plain,
! [SV10: $i,SV49: $i] :
( ( ( SV49
= ( singleton @ SV10 ) )
= $false )
| ( ( ! [SY184: $i] :
~ ( ~ ( ~ ( in @ SY184 @ SV49 )
| ( SY184 = SV10 ) )
| ~ ( ( SY184 != SV10 )
| ( in @ SY184 @ SV49 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[451]) ).
thf(489,plain,
! [SV10: $i,SV49: $i] :
( ( ( ! [SY185: $i] :
~ ( ~ ( ~ ( in @ SY185 @ SV49 )
| ( SY185 = SV10 ) )
| ~ ( ( SY185 != SV10 )
| ( in @ SY185 @ SV49 ) ) ) )
= $false )
| ( ( SV49
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[452]) ).
thf(490,plain,
! [SV50: $i,SV11: $i] :
( ( ( in @ SV11 @ SV50 )
= $false )
| ( ( disjoint @ ( singleton @ SV11 ) @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[453]) ).
thf(491,plain,
! [SV52: $i,SV13: $i] :
( ( ( subset @ SV13 @ ( singleton @ SV52 ) )
= $false )
| ( ( ( SV13 = empty_set )
| ( SV13
= ( singleton @ SV52 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(492,plain,
! [SV52: $i,SV13: $i] :
( ( ( ( SV13 = empty_set )
| ( SV13
= ( singleton @ SV52 ) ) )
= $false )
| ( ( subset @ SV13 @ ( singleton @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(493,plain,
! [SV17: $i,SV55: $i] :
( ( ( SV55
= ( union @ SV17 ) )
= $false )
| ( ( ! [SY188: $i] :
~ ( ~ ( ~ ( in @ SY188 @ SV55 )
| ~ ! [SY127: $i] :
~ ~ ( ~ ( in @ SY188 @ SY127 )
| ~ ( in @ SY127 @ SV17 ) ) )
| ~ ( ~ ~ ! [SY128: $i] :
~ ~ ( ~ ( in @ SY188 @ SY128 )
| ~ ( in @ SY128 @ SV17 ) )
| ( in @ SY188 @ SV55 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[457]) ).
thf(494,plain,
! [SV17: $i,SV55: $i] :
( ( ( ! [SY191: $i] :
~ ( ~ ( ~ ( in @ SY191 @ SV55 )
| ~ ! [SY130: $i] :
~ ~ ( ~ ( in @ SY191 @ SY130 )
| ~ ( in @ SY130 @ SV17 ) ) )
| ~ ( ~ ~ ! [SY131: $i] :
~ ~ ( ~ ( in @ SY191 @ SY131 )
| ~ ( in @ SY131 @ SV17 ) )
| ( in @ SY191 @ SV55 ) ) ) )
= $false )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[458]) ).
thf(495,plain,
! [SV18: $i,SV56: $i] :
( ( ( empty @ SV56 )
= $false )
| ( ( in @ SV18 @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[459]) ).
thf(496,plain,
! [SV57: $i,SV19: $i] :
( ( ~ ~ ( disjoint @ SV19 @ SV57 )
| ~ ! [SY194: $i] :
~ ~ ( ~ ( in @ SY194 @ SV19 )
| ~ ( in @ SY194 @ SV57 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[460]) ).
thf(497,plain,
! [SV57: $i,SV19: $i] :
( ( ~ ~ ! [SY195: $i] :
~ ~ ( ~ ( in @ SY195 @ SV19 )
| ~ ( in @ SY195 @ SV57 ) )
| ~ ( disjoint @ SV19 @ SV57 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[461]) ).
thf(498,plain,
! [SV20: $i,SV93: $i] :
( ( ( ~ ( in @ SV93 @ SV20 ) )
= $true )
| ( ( SV20 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(499,plain,
! [SV20: $i] :
( ( ( ~ ( in @ ( sK4_SY137 @ SV20 ) @ SV20 ) )
= $false )
| ( ( SV20 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[463]) ).
thf(500,plain,
! [SV59: $i,SV22: $i] :
( ( ( subset @ ( singleton @ SV22 ) @ SV59 )
= $false )
| ( ( in @ SV22 @ SV59 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(501,plain,
! [SV59: $i,SV22: $i] :
( ( ( in @ SV22 @ SV59 )
= $false )
| ( ( subset @ ( singleton @ SV22 ) @ SV59 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(502,plain,
! [SV62: $i,SV25: $i,SV85: $i] :
( ( ( SV85
!= ( set_intersection2 @ SV25 @ SV62 ) )
= $true )
| ( ( ! [SY219: $i] :
~ ( ~ ( ~ ( in @ SY219 @ SV85 )
| ~ ( ~ ( in @ SY219 @ SV25 )
| ~ ( in @ SY219 @ SV62 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY219 @ SV25 )
| ~ ( in @ SY219 @ SV62 ) )
| ( in @ SY219 @ SV85 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[466]) ).
thf(503,plain,
! [SV62: $i,SV25: $i,SV85: $i] :
( ( ( ~ ! [SY220: $i] :
~ ( ~ ( ~ ( in @ SY220 @ SV85 )
| ~ ( ~ ( in @ SY220 @ SV25 )
| ~ ( in @ SY220 @ SV62 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY220 @ SV25 )
| ~ ( in @ SY220 @ SV62 ) )
| ( in @ SY220 @ SV85 ) ) ) )
= $true )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[467]) ).
thf(504,plain,
! [SV86: $i,SV63: $i,SV26: $i] :
( ( ( ~ ( subset @ SV26 @ SV63 ) )
= $true )
| ( ( ~ ( disjoint @ SV63 @ SV86 ) )
= $true )
| ( ( disjoint @ SV26 @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[468]) ).
thf(505,plain,
! [SV65: $i,SV28: $i] :
( ( ( subset @ SV28 @ SV65 )
= $false )
| ( ( ! [SY202: $i] :
( ~ ( in @ SY202 @ SV28 )
| ( in @ SY202 @ SV65 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(506,plain,
! [SV65: $i,SV28: $i] :
( ( ( ! [SY203: $i] :
( ~ ( in @ SY203 @ SV28 )
| ( in @ SY203 @ SV65 ) ) )
= $false )
| ( ( subset @ SV28 @ SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[470]) ).
thf(507,plain,
! [SV68: $i,SV31: $i] :
( ( ( proper_subset @ SV31 @ SV68 )
= $false )
| ( ( ~ ( ~ ( subset @ SV31 @ SV68 )
| ~ ( ( SV31 != SV68 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(508,plain,
! [SV68: $i,SV31: $i] :
( ( ( ~ ( ~ ( subset @ SV31 @ SV68 )
| ~ ( ( SV31 != SV68 ) ) ) )
= $false )
| ( ( proper_subset @ SV31 @ SV68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[472]) ).
thf(509,plain,
! [SV33: $i,SV70: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV33 )
| ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV70 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV70 )
| ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV33 ) ) )
= $true )
| ( ( SV33 = SV70 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[473]) ).
thf(510,plain,
! [SV71: $i,SV34: $i,SV88: $i] :
( ( ( SV88
!= ( set_difference @ SV34 @ SV71 ) )
= $true )
| ( ( ! [SY221: $i] :
~ ( ~ ( ~ ( in @ SY221 @ SV88 )
| ~ ( ~ ( in @ SY221 @ SV34 )
| ~ ~ ( in @ SY221 @ SV71 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY221 @ SV34 )
| ~ ~ ( in @ SY221 @ SV71 ) )
| ( in @ SY221 @ SV88 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[474]) ).
thf(511,plain,
! [SV71: $i,SV34: $i,SV88: $i] :
( ( ( ~ ! [SY222: $i] :
~ ( ~ ( ~ ( in @ SY222 @ SV88 )
| ~ ( ~ ( in @ SY222 @ SV34 )
| ~ ~ ( in @ SY222 @ SV71 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY222 @ SV34 )
| ~ ~ ( in @ SY222 @ SV71 ) )
| ( in @ SY222 @ SV88 ) ) ) )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[475]) ).
thf(512,plain,
! [SV73: $i,SV36: $i,SV89: $i] :
( ( ( SV89
!= ( unordered_pair @ SV36 @ SV73 ) )
= $true )
| ( ( ! [SY223: $i] :
~ ( ~ ( ~ ( in @ SY223 @ SV89 )
| ( SY223 = SV36 )
| ( SY223 = SV73 ) )
| ~ ( ~ ( ( SY223 = SV36 )
| ( SY223 = SV73 ) )
| ( in @ SY223 @ SV89 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[476]) ).
thf(513,plain,
! [SV73: $i,SV36: $i,SV89: $i] :
( ( ( ~ ! [SY224: $i] :
~ ( ~ ( ~ ( in @ SY224 @ SV89 )
| ( SY224 = SV36 )
| ( SY224 = SV73 ) )
| ~ ( ~ ( ( SY224 = SV36 )
| ( SY224 = SV73 ) )
| ( in @ SY224 @ SV89 ) ) ) )
= $true )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[477]) ).
thf(514,plain,
! [SV90: $i,SV74: $i,SV37: $i] :
( ( ( ~ ( subset @ SV37 @ SV74 ) )
= $true )
| ( ( ~ ( subset @ SV37 @ SV90 ) )
= $true )
| ( ( subset @ SV37 @ ( set_intersection2 @ SV74 @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[478]) ).
thf(515,plain,
! [SV91: $i,SV75: $i,SV38: $i] :
( ( ( ~ ( subset @ SV38 @ SV75 ) )
= $true )
| ( ( ~ ( subset @ SV75 @ SV91 ) )
= $true )
| ( ( subset @ SV38 @ SV91 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[479]) ).
thf(516,plain,
! [SV40: $i,SV77: $i] :
( ( ( proper_subset @ SV77 @ SV40 )
= $false )
| ( ( subset @ SV40 @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[480]) ).
thf(517,plain,
! [SV41: $i,SV78: $i] :
( ( ( SV78
= ( powerset @ SV41 ) )
= $false )
| ( ( ! [SY214: $i] :
~ ( ~ ( ~ ( in @ SY214 @ SV78 )
| ( subset @ SY214 @ SV41 ) )
| ~ ( ~ ( subset @ SY214 @ SV41 )
| ( in @ SY214 @ SV78 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[481]) ).
thf(518,plain,
! [SV41: $i,SV78: $i] :
( ( ( ! [SY215: $i] :
~ ( ~ ( ~ ( in @ SY215 @ SV78 )
| ( subset @ SY215 @ SV41 ) )
| ~ ( ~ ( subset @ SY215 @ SV41 )
| ( in @ SY215 @ SV78 ) ) ) )
= $false )
| ( ( SV78
= ( powerset @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[482]) ).
thf(519,plain,
! [SV79: $i,SV42: $i,SV92: $i] :
( ( ( SV92
!= ( set_union2 @ SV42 @ SV79 ) )
= $true )
| ( ( ! [SY225: $i] :
~ ( ~ ( ~ ( in @ SY225 @ SV92 )
| ( in @ SY225 @ SV42 )
| ( in @ SY225 @ SV79 ) )
| ~ ( ~ ( ( in @ SY225 @ SV42 )
| ( in @ SY225 @ SV79 ) )
| ( in @ SY225 @ SV92 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[483]) ).
thf(520,plain,
! [SV79: $i,SV42: $i,SV92: $i] :
( ( ( ~ ! [SY226: $i] :
~ ( ~ ( ~ ( in @ SY226 @ SV92 )
| ( in @ SY226 @ SV42 )
| ( in @ SY226 @ SV79 ) )
| ~ ( ~ ( ( in @ SY226 @ SV42 )
| ( in @ SY226 @ SV79 ) )
| ( in @ SY226 @ SV92 ) ) ) )
= $true )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[484]) ).
thf(521,plain,
! [SV47: $i,SV7: $i] :
( ( ( ~ ( subset @ SV7 @ SV47 )
| ~ ( subset @ SV47 @ SV7 ) )
= $false )
| ( ( SV7 = SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[485]) ).
thf(522,plain,
! [SV47: $i,SV7: $i] :
( ( ( ~ ( subset @ SV7 @ SV47 )
| ~ ( subset @ SV47 @ SV7 ) )
= $true )
| ( ( SV7 = SV47 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[486]) ).
thf(523,plain,
! [SV80: $i,SV48: $i,SV9: $i] :
( ( ( subset @ SV9 @ SV48 )
= $false )
| ( ( ~ ( subset @ SV80 @ SV48 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV9 @ SV80 ) @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[487]) ).
thf(524,plain,
! [SV10: $i,SV49: $i,SV94: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV94 @ SV49 )
| ( SV94 = SV10 ) )
| ~ ( ( SV94 != SV10 )
| ( in @ SV94 @ SV49 ) ) ) )
= $true )
| ( ( SV49
= ( singleton @ SV10 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(525,plain,
! [SV49: $i,SV10: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK5_SY185 @ SV10 @ SV49 ) @ SV49 )
| ( ( sK5_SY185 @ SV10 @ SV49 )
= SV10 ) )
| ~ ( ( ( sK5_SY185 @ SV10 @ SV49 )
!= SV10 )
| ( in @ ( sK5_SY185 @ SV10 @ SV49 ) @ SV49 ) ) ) )
= $false )
| ( ( SV49
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[489]) ).
thf(526,plain,
! [SV52: $i,SV13: $i] :
( ( ( SV13 = empty_set )
= $true )
| ( ( SV13
= ( singleton @ SV52 ) )
= $true )
| ( ( subset @ SV13 @ ( singleton @ SV52 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[491]) ).
thf(527,plain,
! [SV52: $i,SV13: $i] :
( ( ( SV13 = empty_set )
= $false )
| ( ( subset @ SV13 @ ( singleton @ SV52 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[492]) ).
thf(528,plain,
! [SV52: $i,SV13: $i] :
( ( ( SV13
= ( singleton @ SV52 ) )
= $false )
| ( ( subset @ SV13 @ ( singleton @ SV52 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[492]) ).
thf(529,plain,
! [SV17: $i,SV55: $i,SV95: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV95 @ SV55 )
| ~ ! [SY227: $i] :
~ ~ ( ~ ( in @ SV95 @ SY227 )
| ~ ( in @ SY227 @ SV17 ) ) )
| ~ ( ~ ~ ! [SY228: $i] :
~ ~ ( ~ ( in @ SV95 @ SY228 )
| ~ ( in @ SY228 @ SV17 ) )
| ( in @ SV95 @ SV55 ) ) ) )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(530,plain,
! [SV55: $i,SV17: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV55 )
| ~ ! [SY229: $i] :
~ ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SY229 )
| ~ ( in @ SY229 @ SV17 ) ) )
| ~ ( ~ ~ ! [SY230: $i] :
~ ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SY230 )
| ~ ( in @ SY230 @ SV17 ) )
| ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV55 ) ) ) )
= $false )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[494]) ).
thf(531,plain,
! [SV57: $i,SV19: $i] :
( ( ( ~ ~ ( disjoint @ SV19 @ SV57 ) )
= $true )
| ( ( ~ ! [SY194: $i] :
~ ~ ( ~ ( in @ SY194 @ SV19 )
| ~ ( in @ SY194 @ SV57 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[496]) ).
thf(532,plain,
! [SV57: $i,SV19: $i] :
( ( ( ~ ~ ! [SY195: $i] :
~ ~ ( ~ ( in @ SY195 @ SV19 )
| ~ ( in @ SY195 @ SV57 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV19 @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[497]) ).
thf(533,plain,
! [SV20: $i,SV93: $i] :
( ( ( in @ SV93 @ SV20 )
= $false )
| ( ( SV20 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(534,plain,
! [SV20: $i] :
( ( ( in @ ( sK4_SY137 @ SV20 ) @ SV20 )
= $true )
| ( ( SV20 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[499]) ).
thf(535,plain,
! [SV62: $i,SV25: $i,SV85: $i] :
( ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $false )
| ( ( ! [SY219: $i] :
~ ( ~ ( ~ ( in @ SY219 @ SV85 )
| ~ ( ~ ( in @ SY219 @ SV25 )
| ~ ( in @ SY219 @ SV62 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY219 @ SV25 )
| ~ ( in @ SY219 @ SV62 ) )
| ( in @ SY219 @ SV85 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(536,plain,
! [SV62: $i,SV25: $i,SV85: $i] :
( ( ( ! [SY220: $i] :
~ ( ~ ( ~ ( in @ SY220 @ SV85 )
| ~ ( ~ ( in @ SY220 @ SV25 )
| ~ ( in @ SY220 @ SV62 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY220 @ SV25 )
| ~ ( in @ SY220 @ SV62 ) )
| ( in @ SY220 @ SV85 ) ) ) )
= $false )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(537,plain,
! [SV86: $i,SV63: $i,SV26: $i] :
( ( ( subset @ SV26 @ SV63 )
= $false )
| ( ( ~ ( disjoint @ SV63 @ SV86 ) )
= $true )
| ( ( disjoint @ SV26 @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(538,plain,
! [SV65: $i,SV28: $i,SV96: $i] :
( ( ( ~ ( in @ SV96 @ SV28 )
| ( in @ SV96 @ SV65 ) )
= $true )
| ( ( subset @ SV28 @ SV65 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(539,plain,
! [SV28: $i,SV65: $i] :
( ( ( ~ ( in @ ( sK7_SY203 @ SV65 @ SV28 ) @ SV28 )
| ( in @ ( sK7_SY203 @ SV65 @ SV28 ) @ SV65 ) )
= $false )
| ( ( subset @ SV28 @ SV65 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[506]) ).
thf(540,plain,
! [SV68: $i,SV31: $i] :
( ( ( ~ ( subset @ SV31 @ SV68 )
| ~ ( ( SV31 != SV68 ) ) )
= $false )
| ( ( proper_subset @ SV31 @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[507]) ).
thf(541,plain,
! [SV68: $i,SV31: $i] :
( ( ( ~ ( subset @ SV31 @ SV68 )
| ~ ( ( SV31 != SV68 ) ) )
= $true )
| ( ( proper_subset @ SV31 @ SV68 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[508]) ).
thf(542,plain,
! [SV33: $i,SV70: $i] :
( ( ( ~ ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV33 )
| ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV70 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV70 )
| ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV33 ) ) )
= $true )
| ( ( SV33 = SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[509]) ).
thf(543,plain,
! [SV71: $i,SV34: $i,SV88: $i] :
( ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $false )
| ( ( ! [SY221: $i] :
~ ( ~ ( ~ ( in @ SY221 @ SV88 )
| ~ ( ~ ( in @ SY221 @ SV34 )
| ~ ~ ( in @ SY221 @ SV71 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY221 @ SV34 )
| ~ ~ ( in @ SY221 @ SV71 ) )
| ( in @ SY221 @ SV88 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(544,plain,
! [SV71: $i,SV34: $i,SV88: $i] :
( ( ( ! [SY222: $i] :
~ ( ~ ( ~ ( in @ SY222 @ SV88 )
| ~ ( ~ ( in @ SY222 @ SV34 )
| ~ ~ ( in @ SY222 @ SV71 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY222 @ SV34 )
| ~ ~ ( in @ SY222 @ SV71 ) )
| ( in @ SY222 @ SV88 ) ) ) )
= $false )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[511]) ).
thf(545,plain,
! [SV73: $i,SV36: $i,SV89: $i] :
( ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $false )
| ( ( ! [SY223: $i] :
~ ( ~ ( ~ ( in @ SY223 @ SV89 )
| ( SY223 = SV36 )
| ( SY223 = SV73 ) )
| ~ ( ~ ( ( SY223 = SV36 )
| ( SY223 = SV73 ) )
| ( in @ SY223 @ SV89 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[512]) ).
thf(546,plain,
! [SV73: $i,SV36: $i,SV89: $i] :
( ( ( ! [SY224: $i] :
~ ( ~ ( ~ ( in @ SY224 @ SV89 )
| ( SY224 = SV36 )
| ( SY224 = SV73 ) )
| ~ ( ~ ( ( SY224 = SV36 )
| ( SY224 = SV73 ) )
| ( in @ SY224 @ SV89 ) ) ) )
= $false )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[513]) ).
thf(547,plain,
! [SV90: $i,SV74: $i,SV37: $i] :
( ( ( subset @ SV37 @ SV74 )
= $false )
| ( ( ~ ( subset @ SV37 @ SV90 ) )
= $true )
| ( ( subset @ SV37 @ ( set_intersection2 @ SV74 @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[514]) ).
thf(548,plain,
! [SV91: $i,SV75: $i,SV38: $i] :
( ( ( subset @ SV38 @ SV75 )
= $false )
| ( ( ~ ( subset @ SV75 @ SV91 ) )
= $true )
| ( ( subset @ SV38 @ SV91 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[515]) ).
thf(549,plain,
! [SV41: $i,SV78: $i,SV97: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV97 @ SV78 )
| ( subset @ SV97 @ SV41 ) )
| ~ ( ~ ( subset @ SV97 @ SV41 )
| ( in @ SV97 @ SV78 ) ) ) )
= $true )
| ( ( SV78
= ( powerset @ SV41 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(550,plain,
! [SV78: $i,SV41: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV78 )
| ( subset @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV41 ) )
| ~ ( ~ ( subset @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV41 )
| ( in @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV78 ) ) ) )
= $false )
| ( ( SV78
= ( powerset @ SV41 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[518]) ).
thf(551,plain,
! [SV79: $i,SV42: $i,SV92: $i] :
( ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $false )
| ( ( ! [SY225: $i] :
~ ( ~ ( ~ ( in @ SY225 @ SV92 )
| ( in @ SY225 @ SV42 )
| ( in @ SY225 @ SV79 ) )
| ~ ( ~ ( ( in @ SY225 @ SV42 )
| ( in @ SY225 @ SV79 ) )
| ( in @ SY225 @ SV92 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[519]) ).
thf(552,plain,
! [SV79: $i,SV42: $i,SV92: $i] :
( ( ( ! [SY226: $i] :
~ ( ~ ( ~ ( in @ SY226 @ SV92 )
| ( in @ SY226 @ SV42 )
| ( in @ SY226 @ SV79 ) )
| ~ ( ~ ( ( in @ SY226 @ SV42 )
| ( in @ SY226 @ SV79 ) )
| ( in @ SY226 @ SV92 ) ) ) )
= $false )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[520]) ).
thf(553,plain,
! [SV47: $i,SV7: $i] :
( ( ( ~ ( subset @ SV7 @ SV47 ) )
= $false )
| ( ( SV7 = SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[521]) ).
thf(554,plain,
! [SV7: $i,SV47: $i] :
( ( ( ~ ( subset @ SV47 @ SV7 ) )
= $false )
| ( ( SV7 = SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[521]) ).
thf(555,plain,
! [SV47: $i,SV7: $i] :
( ( ( ~ ( subset @ SV7 @ SV47 ) )
= $true )
| ( ( ~ ( subset @ SV47 @ SV7 ) )
= $true )
| ( ( SV7 = SV47 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[522]) ).
thf(556,plain,
! [SV9: $i,SV48: $i,SV80: $i] :
( ( ( subset @ SV80 @ SV48 )
= $false )
| ( ( subset @ SV9 @ SV48 )
= $false )
| ( ( subset @ ( set_union2 @ SV9 @ SV80 ) @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[523]) ).
thf(557,plain,
! [SV10: $i,SV49: $i,SV94: $i] :
( ( ( ~ ( ~ ( in @ SV94 @ SV49 )
| ( SV94 = SV10 ) )
| ~ ( ( SV94 != SV10 )
| ( in @ SV94 @ SV49 ) ) )
= $false )
| ( ( SV49
= ( singleton @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(558,plain,
! [SV49: $i,SV10: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY185 @ SV10 @ SV49 ) @ SV49 )
| ( ( sK5_SY185 @ SV10 @ SV49 )
= SV10 ) )
| ~ ( ( ( sK5_SY185 @ SV10 @ SV49 )
!= SV10 )
| ( in @ ( sK5_SY185 @ SV10 @ SV49 ) @ SV49 ) ) )
= $true )
| ( ( SV49
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[525]) ).
thf(559,plain,
! [SV17: $i,SV55: $i,SV95: $i] :
( ( ( ~ ( ~ ( in @ SV95 @ SV55 )
| ~ ! [SY227: $i] :
~ ~ ( ~ ( in @ SV95 @ SY227 )
| ~ ( in @ SY227 @ SV17 ) ) )
| ~ ( ~ ~ ! [SY228: $i] :
~ ~ ( ~ ( in @ SV95 @ SY228 )
| ~ ( in @ SY228 @ SV17 ) )
| ( in @ SV95 @ SV55 ) ) )
= $false )
| ( ( SV55
= ( union @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[529]) ).
thf(560,plain,
! [SV55: $i,SV17: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV55 )
| ~ ! [SY229: $i] :
~ ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SY229 )
| ~ ( in @ SY229 @ SV17 ) ) )
| ~ ( ~ ~ ! [SY230: $i] :
~ ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SY230 )
| ~ ( in @ SY230 @ SV17 ) )
| ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV55 ) ) )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[530]) ).
thf(561,plain,
! [SV57: $i,SV19: $i] :
( ( ( ~ ( disjoint @ SV19 @ SV57 ) )
= $false )
| ( ( ~ ! [SY194: $i] :
~ ~ ( ~ ( in @ SY194 @ SV19 )
| ~ ( in @ SY194 @ SV57 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[531]) ).
thf(562,plain,
! [SV57: $i,SV19: $i] :
( ( ( ~ ! [SY195: $i] :
~ ~ ( ~ ( in @ SY195 @ SV19 )
| ~ ( in @ SY195 @ SV57 ) ) )
= $false )
| ( ( ~ ( disjoint @ SV19 @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[532]) ).
thf(563,plain,
! [SV62: $i,SV25: $i,SV85: $i,SV98: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV98 @ SV85 )
| ~ ( ~ ( in @ SV98 @ SV25 )
| ~ ( in @ SV98 @ SV62 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV98 @ SV25 )
| ~ ( in @ SV98 @ SV62 ) )
| ( in @ SV98 @ SV85 ) ) ) )
= $true )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(564,plain,
! [SV85: $i,SV25: $i,SV62: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV85 )
| ~ ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
| ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
| ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 ) )
| ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV85 ) ) ) )
= $false )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[536]) ).
thf(565,plain,
! [SV26: $i,SV86: $i,SV63: $i] :
( ( ( disjoint @ SV63 @ SV86 )
= $false )
| ( ( subset @ SV26 @ SV63 )
= $false )
| ( ( disjoint @ SV26 @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[537]) ).
thf(566,plain,
! [SV65: $i,SV28: $i,SV96: $i] :
( ( ( ~ ( in @ SV96 @ SV28 ) )
= $true )
| ( ( in @ SV96 @ SV65 )
= $true )
| ( ( subset @ SV28 @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[538]) ).
thf(567,plain,
! [SV28: $i,SV65: $i] :
( ( ( ~ ( in @ ( sK7_SY203 @ SV65 @ SV28 ) @ SV28 ) )
= $false )
| ( ( subset @ SV28 @ SV65 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[539]) ).
thf(568,plain,
! [SV28: $i,SV65: $i] :
( ( ( in @ ( sK7_SY203 @ SV65 @ SV28 ) @ SV65 )
= $false )
| ( ( subset @ SV28 @ SV65 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[539]) ).
thf(569,plain,
! [SV68: $i,SV31: $i] :
( ( ( ~ ( subset @ SV31 @ SV68 ) )
= $false )
| ( ( proper_subset @ SV31 @ SV68 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[540]) ).
thf(570,plain,
! [SV68: $i,SV31: $i] :
( ( ( ~ ( ( SV31 != SV68 ) ) )
= $false )
| ( ( proper_subset @ SV31 @ SV68 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[540]) ).
thf(571,plain,
! [SV68: $i,SV31: $i] :
( ( ( ~ ( subset @ SV31 @ SV68 ) )
= $true )
| ( ( ~ ( ( SV31 != SV68 ) ) )
= $true )
| ( ( proper_subset @ SV31 @ SV68 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[541]) ).
thf(572,plain,
! [SV33: $i,SV70: $i] :
( ( ( ~ ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV33 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV70 )
| ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV33 ) ) )
= $true )
| ( ( SV33 = SV70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[542]) ).
thf(573,plain,
! [SV33: $i,SV70: $i] :
( ( ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV70 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV70 )
| ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV33 ) ) )
= $true )
| ( ( SV33 = SV70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[542]) ).
thf(574,plain,
! [SV71: $i,SV34: $i,SV88: $i,SV99: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV99 @ SV88 )
| ~ ( ~ ( in @ SV99 @ SV34 )
| ~ ~ ( in @ SV99 @ SV71 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV99 @ SV34 )
| ~ ~ ( in @ SV99 @ SV71 ) )
| ( in @ SV99 @ SV88 ) ) ) )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(575,plain,
! [SV88: $i,SV34: $i,SV71: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV88 )
| ~ ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
| ~ ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
| ~ ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 ) )
| ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV88 ) ) ) )
= $false )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[544]) ).
thf(576,plain,
! [SV73: $i,SV36: $i,SV89: $i,SV100: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV100 @ SV89 )
| ( SV100 = SV36 )
| ( SV100 = SV73 ) )
| ~ ( ~ ( ( SV100 = SV36 )
| ( SV100 = SV73 ) )
| ( in @ SV100 @ SV89 ) ) ) )
= $true )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(577,plain,
! [SV89: $i,SV36: $i,SV73: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK11_SY224 @ SV73 @ SV36 @ SV89 ) @ SV89 )
| ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV36 )
| ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV73 ) )
| ~ ( ~ ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV36 )
| ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV73 ) )
| ( in @ ( sK11_SY224 @ SV73 @ SV36 @ SV89 ) @ SV89 ) ) ) )
= $false )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[546]) ).
thf(578,plain,
! [SV74: $i,SV90: $i,SV37: $i] :
( ( ( subset @ SV37 @ SV90 )
= $false )
| ( ( subset @ SV37 @ SV74 )
= $false )
| ( ( subset @ SV37 @ ( set_intersection2 @ SV74 @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[547]) ).
thf(579,plain,
! [SV38: $i,SV91: $i,SV75: $i] :
( ( ( subset @ SV75 @ SV91 )
= $false )
| ( ( subset @ SV38 @ SV75 )
= $false )
| ( ( subset @ SV38 @ SV91 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[548]) ).
thf(580,plain,
! [SV41: $i,SV78: $i,SV97: $i] :
( ( ( ~ ( ~ ( in @ SV97 @ SV78 )
| ( subset @ SV97 @ SV41 ) )
| ~ ( ~ ( subset @ SV97 @ SV41 )
| ( in @ SV97 @ SV78 ) ) )
= $false )
| ( ( SV78
= ( powerset @ SV41 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[549]) ).
thf(581,plain,
! [SV78: $i,SV41: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV78 )
| ( subset @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV41 ) )
| ~ ( ~ ( subset @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV41 )
| ( in @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV78 ) ) )
= $true )
| ( ( SV78
= ( powerset @ SV41 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[550]) ).
thf(582,plain,
! [SV79: $i,SV42: $i,SV92: $i,SV101: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV101 @ SV92 )
| ( in @ SV101 @ SV42 )
| ( in @ SV101 @ SV79 ) )
| ~ ( ~ ( ( in @ SV101 @ SV42 )
| ( in @ SV101 @ SV79 ) )
| ( in @ SV101 @ SV92 ) ) ) )
= $true )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(583,plain,
! [SV92: $i,SV42: $i,SV79: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV92 )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV42 )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV79 ) )
| ~ ( ~ ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV42 )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV79 ) )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV92 ) ) ) )
= $false )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[552]) ).
thf(584,plain,
! [SV47: $i,SV7: $i] :
( ( ( subset @ SV7 @ SV47 )
= $true )
| ( ( SV7 = SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[553]) ).
thf(585,plain,
! [SV7: $i,SV47: $i] :
( ( ( subset @ SV47 @ SV7 )
= $true )
| ( ( SV7 = SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[554]) ).
thf(586,plain,
! [SV47: $i,SV7: $i] :
( ( ( subset @ SV7 @ SV47 )
= $false )
| ( ( ~ ( subset @ SV47 @ SV7 ) )
= $true )
| ( ( SV7 = SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[555]) ).
thf(587,plain,
! [SV10: $i,SV49: $i,SV94: $i] :
( ( ( ~ ( ~ ( in @ SV94 @ SV49 )
| ( SV94 = SV10 ) ) )
= $false )
| ( ( SV49
= ( singleton @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[557]) ).
thf(588,plain,
! [SV49: $i,SV10: $i,SV94: $i] :
( ( ( ~ ( ( SV94 != SV10 )
| ( in @ SV94 @ SV49 ) ) )
= $false )
| ( ( SV49
= ( singleton @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[557]) ).
thf(589,plain,
! [SV49: $i,SV10: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY185 @ SV10 @ SV49 ) @ SV49 )
| ( ( sK5_SY185 @ SV10 @ SV49 )
= SV10 ) ) )
= $true )
| ( ( ~ ( ( ( sK5_SY185 @ SV10 @ SV49 )
!= SV10 )
| ( in @ ( sK5_SY185 @ SV10 @ SV49 ) @ SV49 ) ) )
= $true )
| ( ( SV49
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[558]) ).
thf(590,plain,
! [SV17: $i,SV55: $i,SV95: $i] :
( ( ( ~ ( ~ ( in @ SV95 @ SV55 )
| ~ ! [SY227: $i] :
~ ~ ( ~ ( in @ SV95 @ SY227 )
| ~ ( in @ SY227 @ SV17 ) ) ) )
= $false )
| ( ( SV55
= ( union @ SV17 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[559]) ).
thf(591,plain,
! [SV55: $i,SV17: $i,SV95: $i] :
( ( ( ~ ( ~ ~ ! [SY228: $i] :
~ ~ ( ~ ( in @ SV95 @ SY228 )
| ~ ( in @ SY228 @ SV17 ) )
| ( in @ SV95 @ SV55 ) ) )
= $false )
| ( ( SV55
= ( union @ SV17 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[559]) ).
thf(592,plain,
! [SV55: $i,SV17: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV55 )
| ~ ! [SY229: $i] :
~ ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SY229 )
| ~ ( in @ SY229 @ SV17 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY230: $i] :
~ ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SY230 )
| ~ ( in @ SY230 @ SV17 ) )
| ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV55 ) ) )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[560]) ).
thf(593,plain,
! [SV57: $i,SV19: $i] :
( ( ( disjoint @ SV19 @ SV57 )
= $true )
| ( ( ~ ! [SY194: $i] :
~ ~ ( ~ ( in @ SY194 @ SV19 )
| ~ ( in @ SY194 @ SV57 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[561]) ).
thf(594,plain,
! [SV57: $i,SV19: $i] :
( ( ( ! [SY195: $i] :
~ ~ ( ~ ( in @ SY195 @ SV19 )
| ~ ( in @ SY195 @ SV57 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV19 @ SV57 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[562]) ).
thf(595,plain,
! [SV62: $i,SV25: $i,SV85: $i,SV98: $i] :
( ( ( ~ ( ~ ( in @ SV98 @ SV85 )
| ~ ( ~ ( in @ SV98 @ SV25 )
| ~ ( in @ SV98 @ SV62 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV98 @ SV25 )
| ~ ( in @ SV98 @ SV62 ) )
| ( in @ SV98 @ SV85 ) ) )
= $false )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[563]) ).
thf(596,plain,
! [SV85: $i,SV25: $i,SV62: $i] :
( ( ( ~ ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV85 )
| ~ ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
| ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
| ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 ) )
| ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[564]) ).
thf(597,plain,
! [SV65: $i,SV28: $i,SV96: $i] :
( ( ( in @ SV96 @ SV28 )
= $false )
| ( ( in @ SV96 @ SV65 )
= $true )
| ( ( subset @ SV28 @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[566]) ).
thf(598,plain,
! [SV28: $i,SV65: $i] :
( ( ( in @ ( sK7_SY203 @ SV65 @ SV28 ) @ SV28 )
= $true )
| ( ( subset @ SV28 @ SV65 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[567]) ).
thf(599,plain,
! [SV68: $i,SV31: $i] :
( ( ( subset @ SV31 @ SV68 )
= $true )
| ( ( proper_subset @ SV31 @ SV68 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[569]) ).
thf(600,plain,
! [SV68: $i,SV31: $i] :
( ( ( SV31 != SV68 )
= $true )
| ( ( proper_subset @ SV31 @ SV68 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[570]) ).
thf(601,plain,
! [SV68: $i,SV31: $i] :
( ( ( subset @ SV31 @ SV68 )
= $false )
| ( ( ~ ( ( SV31 != SV68 ) ) )
= $true )
| ( ( proper_subset @ SV31 @ SV68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(602,plain,
! [SV33: $i,SV70: $i] :
( ( ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV33 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV70 )
| ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV33 ) ) )
= $true )
| ( ( SV33 = SV70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[572]) ).
thf(603,plain,
! [SV33: $i,SV70: $i] :
( ( ( ~ ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV70 )
| ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV33 ) )
= $false )
| ( ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV70 )
= $false )
| ( ( SV33 = SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[573]) ).
thf(604,plain,
! [SV71: $i,SV34: $i,SV88: $i,SV99: $i] :
( ( ( ~ ( ~ ( in @ SV99 @ SV88 )
| ~ ( ~ ( in @ SV99 @ SV34 )
| ~ ~ ( in @ SV99 @ SV71 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV99 @ SV34 )
| ~ ~ ( in @ SV99 @ SV71 ) )
| ( in @ SV99 @ SV88 ) ) )
= $false )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[574]) ).
thf(605,plain,
! [SV88: $i,SV34: $i,SV71: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV88 )
| ~ ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
| ~ ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
| ~ ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 ) )
| ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV88 ) ) )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[575]) ).
thf(606,plain,
! [SV73: $i,SV36: $i,SV89: $i,SV100: $i] :
( ( ( ~ ( ~ ( in @ SV100 @ SV89 )
| ( SV100 = SV36 )
| ( SV100 = SV73 ) )
| ~ ( ~ ( ( SV100 = SV36 )
| ( SV100 = SV73 ) )
| ( in @ SV100 @ SV89 ) ) )
= $false )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(607,plain,
! [SV89: $i,SV36: $i,SV73: $i] :
( ( ( ~ ( ~ ( in @ ( sK11_SY224 @ SV73 @ SV36 @ SV89 ) @ SV89 )
| ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV36 )
| ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV73 ) )
| ~ ( ~ ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV36 )
| ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV73 ) )
| ( in @ ( sK11_SY224 @ SV73 @ SV36 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[577]) ).
thf(608,plain,
! [SV41: $i,SV78: $i,SV97: $i] :
( ( ( ~ ( ~ ( in @ SV97 @ SV78 )
| ( subset @ SV97 @ SV41 ) ) )
= $false )
| ( ( SV78
= ( powerset @ SV41 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[580]) ).
thf(609,plain,
! [SV78: $i,SV41: $i,SV97: $i] :
( ( ( ~ ( ~ ( subset @ SV97 @ SV41 )
| ( in @ SV97 @ SV78 ) ) )
= $false )
| ( ( SV78
= ( powerset @ SV41 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[580]) ).
thf(610,plain,
! [SV78: $i,SV41: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV78 )
| ( subset @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV41 ) ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV41 )
| ( in @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV78 ) ) )
= $true )
| ( ( SV78
= ( powerset @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[581]) ).
thf(611,plain,
! [SV79: $i,SV42: $i,SV92: $i,SV101: $i] :
( ( ( ~ ( ~ ( in @ SV101 @ SV92 )
| ( in @ SV101 @ SV42 )
| ( in @ SV101 @ SV79 ) )
| ~ ( ~ ( ( in @ SV101 @ SV42 )
| ( in @ SV101 @ SV79 ) )
| ( in @ SV101 @ SV92 ) ) )
= $false )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[582]) ).
thf(612,plain,
! [SV92: $i,SV42: $i,SV79: $i] :
( ( ( ~ ( ~ ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV92 )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV42 )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV79 ) )
| ~ ( ~ ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV42 )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV79 ) )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV92 ) ) )
= $true )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[583]) ).
thf(613,plain,
! [SV7: $i,SV47: $i] :
( ( ( subset @ SV47 @ SV7 )
= $false )
| ( ( subset @ SV7 @ SV47 )
= $false )
| ( ( SV7 = SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(614,plain,
! [SV10: $i,SV49: $i,SV94: $i] :
( ( ( ~ ( in @ SV94 @ SV49 )
| ( SV94 = SV10 ) )
= $true )
| ( ( SV49
= ( singleton @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[587]) ).
thf(615,plain,
! [SV49: $i,SV10: $i,SV94: $i] :
( ( ( ( SV94 != SV10 )
| ( in @ SV94 @ SV49 ) )
= $true )
| ( ( SV49
= ( singleton @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[588]) ).
thf(616,plain,
! [SV49: $i,SV10: $i] :
( ( ( ~ ( in @ ( sK5_SY185 @ SV10 @ SV49 ) @ SV49 )
| ( ( sK5_SY185 @ SV10 @ SV49 )
= SV10 ) )
= $false )
| ( ( ~ ( ( ( sK5_SY185 @ SV10 @ SV49 )
!= SV10 )
| ( in @ ( sK5_SY185 @ SV10 @ SV49 ) @ SV49 ) ) )
= $true )
| ( ( SV49
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[589]) ).
thf(617,plain,
! [SV17: $i,SV55: $i,SV95: $i] :
( ( ( ~ ( in @ SV95 @ SV55 )
| ~ ! [SY227: $i] :
~ ~ ( ~ ( in @ SV95 @ SY227 )
| ~ ( in @ SY227 @ SV17 ) ) )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[590]) ).
thf(618,plain,
! [SV55: $i,SV17: $i,SV95: $i] :
( ( ( ~ ~ ! [SY228: $i] :
~ ~ ( ~ ( in @ SV95 @ SY228 )
| ~ ( in @ SY228 @ SV17 ) )
| ( in @ SV95 @ SV55 ) )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[591]) ).
thf(619,plain,
! [SV55: $i,SV17: $i] :
( ( ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV55 )
| ~ ! [SY229: $i] :
~ ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SY229 )
| ~ ( in @ SY229 @ SV17 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY230: $i] :
~ ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SY230 )
| ~ ( in @ SY230 @ SV17 ) )
| ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV55 ) ) )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[592]) ).
thf(620,plain,
! [SV57: $i,SV19: $i] :
( ( ( ! [SY194: $i] :
~ ~ ( ~ ( in @ SY194 @ SV19 )
| ~ ( in @ SY194 @ SV57 ) ) )
= $false )
| ( ( disjoint @ SV19 @ SV57 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[593]) ).
thf(621,plain,
! [SV57: $i,SV19: $i,SV102: $i] :
( ( ( ~ ~ ( ~ ( in @ SV102 @ SV19 )
| ~ ( in @ SV102 @ SV57 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV19 @ SV57 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(622,plain,
! [SV62: $i,SV25: $i,SV85: $i,SV98: $i] :
( ( ( ~ ( ~ ( in @ SV98 @ SV85 )
| ~ ( ~ ( in @ SV98 @ SV25 )
| ~ ( in @ SV98 @ SV62 ) ) ) )
= $false )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[595]) ).
thf(623,plain,
! [SV85: $i,SV62: $i,SV25: $i,SV98: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV98 @ SV25 )
| ~ ( in @ SV98 @ SV62 ) )
| ( in @ SV98 @ SV85 ) ) )
= $false )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[595]) ).
thf(624,plain,
! [SV85: $i,SV25: $i,SV62: $i] :
( ( ( ~ ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV85 )
| ~ ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
| ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
| ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 ) )
| ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[596]) ).
thf(625,plain,
! [SV68: $i,SV31: $i] :
( ( ( SV31 = SV68 )
= $false )
| ( ( proper_subset @ SV31 @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[600]) ).
thf(626,plain,
! [SV68: $i,SV31: $i] :
( ( ( SV31 != SV68 )
= $false )
| ( ( subset @ SV31 @ SV68 )
= $false )
| ( ( proper_subset @ SV31 @ SV68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[601]) ).
thf(627,plain,
! [SV33: $i,SV70: $i] :
( ( ( ~ ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV70 )
| ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV33 ) )
= $false )
| ( ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV33 )
= $true )
| ( ( SV33 = SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[602]) ).
thf(628,plain,
! [SV33: $i,SV70: $i] :
( ( ( ~ ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV70 ) )
= $false )
| ( ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV70 )
= $false )
| ( ( SV33 = SV70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[603]) ).
thf(629,plain,
! [SV33: $i,SV70: $i] :
( ( ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV33 )
= $false )
| ( ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV70 )
= $false )
| ( ( SV33 = SV70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[603]) ).
thf(630,plain,
! [SV71: $i,SV34: $i,SV88: $i,SV99: $i] :
( ( ( ~ ( ~ ( in @ SV99 @ SV88 )
| ~ ( ~ ( in @ SV99 @ SV34 )
| ~ ~ ( in @ SV99 @ SV71 ) ) ) )
= $false )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[604]) ).
thf(631,plain,
! [SV88: $i,SV71: $i,SV34: $i,SV99: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV99 @ SV34 )
| ~ ~ ( in @ SV99 @ SV71 ) )
| ( in @ SV99 @ SV88 ) ) )
= $false )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[604]) ).
thf(632,plain,
! [SV88: $i,SV34: $i,SV71: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV88 )
| ~ ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
| ~ ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
| ~ ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 ) )
| ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV88 ) ) )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[605]) ).
thf(633,plain,
! [SV73: $i,SV36: $i,SV89: $i,SV100: $i] :
( ( ( ~ ( ~ ( in @ SV100 @ SV89 )
| ( SV100 = SV36 )
| ( SV100 = SV73 ) ) )
= $false )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[606]) ).
thf(634,plain,
! [SV89: $i,SV73: $i,SV36: $i,SV100: $i] :
( ( ( ~ ( ~ ( ( SV100 = SV36 )
| ( SV100 = SV73 ) )
| ( in @ SV100 @ SV89 ) ) )
= $false )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[606]) ).
thf(635,plain,
! [SV89: $i,SV36: $i,SV73: $i] :
( ( ( ~ ( ~ ( in @ ( sK11_SY224 @ SV73 @ SV36 @ SV89 ) @ SV89 )
| ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV36 )
| ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV73 ) ) )
= $true )
| ( ( ~ ( ~ ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV36 )
| ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV73 ) )
| ( in @ ( sK11_SY224 @ SV73 @ SV36 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[607]) ).
thf(636,plain,
! [SV41: $i,SV78: $i,SV97: $i] :
( ( ( ~ ( in @ SV97 @ SV78 )
| ( subset @ SV97 @ SV41 ) )
= $true )
| ( ( SV78
= ( powerset @ SV41 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[608]) ).
thf(637,plain,
! [SV78: $i,SV41: $i,SV97: $i] :
( ( ( ~ ( subset @ SV97 @ SV41 )
| ( in @ SV97 @ SV78 ) )
= $true )
| ( ( SV78
= ( powerset @ SV41 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[609]) ).
thf(638,plain,
! [SV78: $i,SV41: $i] :
( ( ( ~ ( in @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV78 )
| ( subset @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV41 ) )
= $false )
| ( ( ~ ( ~ ( subset @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV41 )
| ( in @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV78 ) ) )
= $true )
| ( ( SV78
= ( powerset @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[610]) ).
thf(639,plain,
! [SV79: $i,SV42: $i,SV92: $i,SV101: $i] :
( ( ( ~ ( ~ ( in @ SV101 @ SV92 )
| ( in @ SV101 @ SV42 )
| ( in @ SV101 @ SV79 ) ) )
= $false )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[611]) ).
thf(640,plain,
! [SV92: $i,SV79: $i,SV42: $i,SV101: $i] :
( ( ( ~ ( ~ ( ( in @ SV101 @ SV42 )
| ( in @ SV101 @ SV79 ) )
| ( in @ SV101 @ SV92 ) ) )
= $false )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[611]) ).
thf(641,plain,
! [SV92: $i,SV42: $i,SV79: $i] :
( ( ( ~ ( ~ ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV92 )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV42 )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV79 ) ) )
= $true )
| ( ( ~ ( ~ ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV42 )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV79 ) )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV92 ) ) )
= $true )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[612]) ).
thf(642,plain,
! [SV10: $i,SV49: $i,SV94: $i] :
( ( ( ~ ( in @ SV94 @ SV49 ) )
= $true )
| ( ( SV94 = SV10 )
= $true )
| ( ( SV49
= ( singleton @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[614]) ).
thf(643,plain,
! [SV49: $i,SV10: $i,SV94: $i] :
( ( ( SV94 != SV10 )
= $true )
| ( ( in @ SV94 @ SV49 )
= $true )
| ( ( SV49
= ( singleton @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[615]) ).
thf(644,plain,
! [SV49: $i,SV10: $i] :
( ( ( ~ ( in @ ( sK5_SY185 @ SV10 @ SV49 ) @ SV49 ) )
= $false )
| ( ( ~ ( ( ( sK5_SY185 @ SV10 @ SV49 )
!= SV10 )
| ( in @ ( sK5_SY185 @ SV10 @ SV49 ) @ SV49 ) ) )
= $true )
| ( ( SV49
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[616]) ).
thf(645,plain,
! [SV49: $i,SV10: $i] :
( ( ( ( sK5_SY185 @ SV10 @ SV49 )
= SV10 )
= $false )
| ( ( ~ ( ( ( sK5_SY185 @ SV10 @ SV49 )
!= SV10 )
| ( in @ ( sK5_SY185 @ SV10 @ SV49 ) @ SV49 ) ) )
= $true )
| ( ( SV49
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[616]) ).
thf(646,plain,
! [SV17: $i,SV55: $i,SV95: $i] :
( ( ( ~ ( in @ SV95 @ SV55 ) )
= $true )
| ( ( ~ ! [SY227: $i] :
~ ~ ( ~ ( in @ SV95 @ SY227 )
| ~ ( in @ SY227 @ SV17 ) ) )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[617]) ).
thf(647,plain,
! [SV55: $i,SV17: $i,SV95: $i] :
( ( ( ~ ~ ! [SY228: $i] :
~ ~ ( ~ ( in @ SV95 @ SY228 )
| ~ ( in @ SY228 @ SV17 ) ) )
= $true )
| ( ( in @ SV95 @ SV55 )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[618]) ).
thf(648,plain,
! [SV55: $i,SV17: $i] :
( ( ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV55 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY230: $i] :
~ ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SY230 )
| ~ ( in @ SY230 @ SV17 ) )
| ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV55 ) ) )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[619]) ).
thf(649,plain,
! [SV55: $i,SV17: $i] :
( ( ( ~ ! [SY229: $i] :
~ ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SY229 )
| ~ ( in @ SY229 @ SV17 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY230: $i] :
~ ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SY230 )
| ~ ( in @ SY230 @ SV17 ) )
| ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV55 ) ) )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[619]) ).
thf(650,plain,
! [SV19: $i,SV57: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK13_SY194 @ SV57 @ SV19 ) @ SV19 )
| ~ ( in @ ( sK13_SY194 @ SV57 @ SV19 ) @ SV57 ) ) )
= $false )
| ( ( disjoint @ SV19 @ SV57 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[620]) ).
thf(651,plain,
! [SV57: $i,SV19: $i,SV102: $i] :
( ( ( ~ ( ~ ( in @ SV102 @ SV19 )
| ~ ( in @ SV102 @ SV57 ) ) )
= $false )
| ( ( ~ ( disjoint @ SV19 @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[621]) ).
thf(652,plain,
! [SV62: $i,SV25: $i,SV85: $i,SV98: $i] :
( ( ( ~ ( in @ SV98 @ SV85 )
| ~ ( ~ ( in @ SV98 @ SV25 )
| ~ ( in @ SV98 @ SV62 ) ) )
= $true )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[622]) ).
thf(653,plain,
! [SV85: $i,SV62: $i,SV25: $i,SV98: $i] :
( ( ( ~ ~ ( ~ ( in @ SV98 @ SV25 )
| ~ ( in @ SV98 @ SV62 ) )
| ( in @ SV98 @ SV85 ) )
= $true )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[623]) ).
thf(654,plain,
! [SV85: $i,SV25: $i,SV62: $i] :
( ( ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV85 )
| ~ ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
| ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
| ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 ) )
| ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[624]) ).
thf(655,plain,
! [SV68: $i,SV31: $i] :
( ( ( SV31 = SV68 )
= $true )
| ( ( subset @ SV31 @ SV68 )
= $false )
| ( ( proper_subset @ SV31 @ SV68 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[626]) ).
thf(656,plain,
! [SV33: $i,SV70: $i] :
( ( ( ~ ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV70 ) )
= $false )
| ( ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV33 )
= $true )
| ( ( SV33 = SV70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[627]) ).
thf(657,plain,
! [SV33: $i,SV70: $i] :
( ( ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV33 )
= $false )
| ( ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV33 )
= $true )
| ( ( SV33 = SV70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[627]) ).
thf(658,plain,
! [SV33: $i,SV70: $i] :
( ( ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV70 )
= $true )
| ( ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV70 )
= $false )
| ( ( SV33 = SV70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[628]) ).
thf(659,plain,
! [SV71: $i,SV34: $i,SV88: $i,SV99: $i] :
( ( ( ~ ( in @ SV99 @ SV88 )
| ~ ( ~ ( in @ SV99 @ SV34 )
| ~ ~ ( in @ SV99 @ SV71 ) ) )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[630]) ).
thf(660,plain,
! [SV88: $i,SV71: $i,SV34: $i,SV99: $i] :
( ( ( ~ ~ ( ~ ( in @ SV99 @ SV34 )
| ~ ~ ( in @ SV99 @ SV71 ) )
| ( in @ SV99 @ SV88 ) )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[631]) ).
thf(661,plain,
! [SV88: $i,SV34: $i,SV71: $i] :
( ( ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV88 )
| ~ ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
| ~ ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
| ~ ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 ) )
| ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV88 ) ) )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[632]) ).
thf(662,plain,
! [SV73: $i,SV36: $i,SV89: $i,SV100: $i] :
( ( ( ~ ( in @ SV100 @ SV89 )
| ( SV100 = SV36 )
| ( SV100 = SV73 ) )
= $true )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[633]) ).
thf(663,plain,
! [SV89: $i,SV73: $i,SV36: $i,SV100: $i] :
( ( ( ~ ( ( SV100 = SV36 )
| ( SV100 = SV73 ) )
| ( in @ SV100 @ SV89 ) )
= $true )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[634]) ).
thf(664,plain,
! [SV89: $i,SV36: $i,SV73: $i] :
( ( ( ~ ( in @ ( sK11_SY224 @ SV73 @ SV36 @ SV89 ) @ SV89 )
| ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV36 )
| ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV73 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV36 )
| ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV73 ) )
| ( in @ ( sK11_SY224 @ SV73 @ SV36 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[635]) ).
thf(665,plain,
! [SV41: $i,SV78: $i,SV97: $i] :
( ( ( ~ ( in @ SV97 @ SV78 ) )
= $true )
| ( ( subset @ SV97 @ SV41 )
= $true )
| ( ( SV78
= ( powerset @ SV41 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[636]) ).
thf(666,plain,
! [SV78: $i,SV41: $i,SV97: $i] :
( ( ( ~ ( subset @ SV97 @ SV41 ) )
= $true )
| ( ( in @ SV97 @ SV78 )
= $true )
| ( ( SV78
= ( powerset @ SV41 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[637]) ).
thf(667,plain,
! [SV78: $i,SV41: $i] :
( ( ( ~ ( in @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV78 ) )
= $false )
| ( ( ~ ( ~ ( subset @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV41 )
| ( in @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV78 ) ) )
= $true )
| ( ( SV78
= ( powerset @ SV41 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[638]) ).
thf(668,plain,
! [SV78: $i,SV41: $i] :
( ( ( subset @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV41 )
= $false )
| ( ( ~ ( ~ ( subset @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV41 )
| ( in @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV78 ) ) )
= $true )
| ( ( SV78
= ( powerset @ SV41 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[638]) ).
thf(669,plain,
! [SV79: $i,SV42: $i,SV92: $i,SV101: $i] :
( ( ( ~ ( in @ SV101 @ SV92 )
| ( in @ SV101 @ SV42 )
| ( in @ SV101 @ SV79 ) )
= $true )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[639]) ).
thf(670,plain,
! [SV92: $i,SV79: $i,SV42: $i,SV101: $i] :
( ( ( ~ ( ( in @ SV101 @ SV42 )
| ( in @ SV101 @ SV79 ) )
| ( in @ SV101 @ SV92 ) )
= $true )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[640]) ).
thf(671,plain,
! [SV92: $i,SV42: $i,SV79: $i] :
( ( ( ~ ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV92 )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV42 )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV79 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV42 )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV79 ) )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV92 ) ) )
= $true )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[641]) ).
thf(672,plain,
! [SV10: $i,SV49: $i,SV94: $i] :
( ( ( in @ SV94 @ SV49 )
= $false )
| ( ( SV94 = SV10 )
= $true )
| ( ( SV49
= ( singleton @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[642]) ).
thf(673,plain,
! [SV49: $i,SV10: $i,SV94: $i] :
( ( ( SV94 = SV10 )
= $false )
| ( ( in @ SV94 @ SV49 )
= $true )
| ( ( SV49
= ( singleton @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[643]) ).
thf(674,plain,
! [SV49: $i,SV10: $i] :
( ( ( in @ ( sK5_SY185 @ SV10 @ SV49 ) @ SV49 )
= $true )
| ( ( ~ ( ( ( sK5_SY185 @ SV10 @ SV49 )
!= SV10 )
| ( in @ ( sK5_SY185 @ SV10 @ SV49 ) @ SV49 ) ) )
= $true )
| ( ( SV49
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[644]) ).
thf(675,plain,
! [SV49: $i,SV10: $i] :
( ( ( ( ( sK5_SY185 @ SV10 @ SV49 )
!= SV10 )
| ( in @ ( sK5_SY185 @ SV10 @ SV49 ) @ SV49 ) )
= $false )
| ( ( ( sK5_SY185 @ SV10 @ SV49 )
= SV10 )
= $false )
| ( ( SV49
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[645]) ).
thf(676,plain,
! [SV17: $i,SV55: $i,SV95: $i] :
( ( ( in @ SV95 @ SV55 )
= $false )
| ( ( ~ ! [SY227: $i] :
~ ~ ( ~ ( in @ SV95 @ SY227 )
| ~ ( in @ SY227 @ SV17 ) ) )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[646]) ).
thf(677,plain,
! [SV55: $i,SV17: $i,SV95: $i] :
( ( ( ~ ! [SY228: $i] :
~ ~ ( ~ ( in @ SV95 @ SY228 )
| ~ ( in @ SY228 @ SV17 ) ) )
= $false )
| ( ( in @ SV95 @ SV55 )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[647]) ).
thf(678,plain,
! [SV55: $i,SV17: $i] :
( ( ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV55 )
= $true )
| ( ( ~ ( ~ ~ ! [SY230: $i] :
~ ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SY230 )
| ~ ( in @ SY230 @ SV17 ) )
| ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV55 ) ) )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[648]) ).
thf(679,plain,
! [SV55: $i,SV17: $i] :
( ( ( ! [SY229: $i] :
~ ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SY229 )
| ~ ( in @ SY229 @ SV17 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY230: $i] :
~ ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SY230 )
| ~ ( in @ SY230 @ SV17 ) )
| ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV55 ) ) )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[649]) ).
thf(680,plain,
! [SV19: $i,SV57: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_SY194 @ SV57 @ SV19 ) @ SV19 )
| ~ ( in @ ( sK13_SY194 @ SV57 @ SV19 ) @ SV57 ) ) )
= $true )
| ( ( disjoint @ SV19 @ SV57 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[650]) ).
thf(681,plain,
! [SV57: $i,SV19: $i,SV102: $i] :
( ( ( ~ ( in @ SV102 @ SV19 )
| ~ ( in @ SV102 @ SV57 ) )
= $true )
| ( ( ~ ( disjoint @ SV19 @ SV57 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[651]) ).
thf(682,plain,
! [SV62: $i,SV25: $i,SV85: $i,SV98: $i] :
( ( ( ~ ( in @ SV98 @ SV85 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV98 @ SV25 )
| ~ ( in @ SV98 @ SV62 ) ) )
= $true )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[652]) ).
thf(683,plain,
! [SV85: $i,SV62: $i,SV25: $i,SV98: $i] :
( ( ( ~ ~ ( ~ ( in @ SV98 @ SV25 )
| ~ ( in @ SV98 @ SV62 ) ) )
= $true )
| ( ( in @ SV98 @ SV85 )
= $true )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[653]) ).
thf(684,plain,
! [SV85: $i,SV25: $i,SV62: $i] :
( ( ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV85 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
| ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 ) )
| ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[654]) ).
thf(685,plain,
! [SV85: $i,SV25: $i,SV62: $i] :
( ( ( ~ ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
| ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
| ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 ) )
| ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[654]) ).
thf(686,plain,
! [SV33: $i,SV70: $i] :
( ( ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV70 )
= $true )
| ( ( in @ ( sK3_SY205 @ SV70 @ SV33 ) @ SV33 )
= $true )
| ( ( SV33 = SV70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[656]) ).
thf(687,plain,
! [SV71: $i,SV34: $i,SV88: $i,SV99: $i] :
( ( ( ~ ( in @ SV99 @ SV88 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV99 @ SV34 )
| ~ ~ ( in @ SV99 @ SV71 ) ) )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[659]) ).
thf(688,plain,
! [SV88: $i,SV71: $i,SV34: $i,SV99: $i] :
( ( ( ~ ~ ( ~ ( in @ SV99 @ SV34 )
| ~ ~ ( in @ SV99 @ SV71 ) ) )
= $true )
| ( ( in @ SV99 @ SV88 )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[660]) ).
thf(689,plain,
! [SV88: $i,SV34: $i,SV71: $i] :
( ( ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV88 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
| ~ ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 ) )
| ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV88 ) ) )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[661]) ).
thf(690,plain,
! [SV88: $i,SV34: $i,SV71: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
| ~ ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
| ~ ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 ) )
| ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV88 ) ) )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[661]) ).
thf(691,plain,
! [SV73: $i,SV36: $i,SV89: $i,SV100: $i] :
( ( ( ~ ( in @ SV100 @ SV89 ) )
= $true )
| ( ( ( SV100 = SV36 )
| ( SV100 = SV73 ) )
= $true )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[662]) ).
thf(692,plain,
! [SV89: $i,SV73: $i,SV36: $i,SV100: $i] :
( ( ( ~ ( ( SV100 = SV36 )
| ( SV100 = SV73 ) ) )
= $true )
| ( ( in @ SV100 @ SV89 )
= $true )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[663]) ).
thf(693,plain,
! [SV89: $i,SV36: $i,SV73: $i] :
( ( ( ~ ( in @ ( sK11_SY224 @ SV73 @ SV36 @ SV89 ) @ SV89 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV36 )
| ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV73 ) )
| ( in @ ( sK11_SY224 @ SV73 @ SV36 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[664]) ).
thf(694,plain,
! [SV89: $i,SV36: $i,SV73: $i] :
( ( ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV36 )
| ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV73 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV36 )
| ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV73 ) )
| ( in @ ( sK11_SY224 @ SV73 @ SV36 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[664]) ).
thf(695,plain,
! [SV41: $i,SV78: $i,SV97: $i] :
( ( ( in @ SV97 @ SV78 )
= $false )
| ( ( subset @ SV97 @ SV41 )
= $true )
| ( ( SV78
= ( powerset @ SV41 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[665]) ).
thf(696,plain,
! [SV78: $i,SV41: $i,SV97: $i] :
( ( ( subset @ SV97 @ SV41 )
= $false )
| ( ( in @ SV97 @ SV78 )
= $true )
| ( ( SV78
= ( powerset @ SV41 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[666]) ).
thf(697,plain,
! [SV78: $i,SV41: $i] :
( ( ( in @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV78 )
= $true )
| ( ( ~ ( ~ ( subset @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV41 )
| ( in @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV78 ) ) )
= $true )
| ( ( SV78
= ( powerset @ SV41 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[667]) ).
thf(698,plain,
! [SV78: $i,SV41: $i] :
( ( ( ~ ( subset @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV41 )
| ( in @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV78 ) )
= $false )
| ( ( subset @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV41 )
= $false )
| ( ( SV78
= ( powerset @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[668]) ).
thf(699,plain,
! [SV79: $i,SV42: $i,SV92: $i,SV101: $i] :
( ( ( ~ ( in @ SV101 @ SV92 ) )
= $true )
| ( ( ( in @ SV101 @ SV42 )
| ( in @ SV101 @ SV79 ) )
= $true )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[669]) ).
thf(700,plain,
! [SV92: $i,SV79: $i,SV42: $i,SV101: $i] :
( ( ( ~ ( ( in @ SV101 @ SV42 )
| ( in @ SV101 @ SV79 ) ) )
= $true )
| ( ( in @ SV101 @ SV92 )
= $true )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[670]) ).
thf(701,plain,
! [SV92: $i,SV42: $i,SV79: $i] :
( ( ( ~ ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV92 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV42 )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV79 ) )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV92 ) ) )
= $true )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[671]) ).
thf(702,plain,
! [SV92: $i,SV42: $i,SV79: $i] :
( ( ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV42 )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV79 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV42 )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV79 ) )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV92 ) ) )
= $true )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[671]) ).
thf(703,plain,
! [SV49: $i,SV10: $i] :
( ( ( ( ( sK5_SY185 @ SV10 @ SV49 )
!= SV10 )
| ( in @ ( sK5_SY185 @ SV10 @ SV49 ) @ SV49 ) )
= $false )
| ( ( in @ ( sK5_SY185 @ SV10 @ SV49 ) @ SV49 )
= $true )
| ( ( SV49
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[674]) ).
thf(704,plain,
! [SV49: $i,SV10: $i] :
( ( ( ( sK5_SY185 @ SV10 @ SV49 )
!= SV10 )
= $false )
| ( ( ( sK5_SY185 @ SV10 @ SV49 )
= SV10 )
= $false )
| ( ( SV49
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[675]) ).
thf(705,plain,
! [SV49: $i,SV10: $i] :
( ( ( in @ ( sK5_SY185 @ SV10 @ SV49 ) @ SV49 )
= $false )
| ( ( ( sK5_SY185 @ SV10 @ SV49 )
= SV10 )
= $false )
| ( ( SV49
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[675]) ).
thf(706,plain,
! [SV55: $i,SV17: $i,SV95: $i] :
( ( ( ! [SY227: $i] :
~ ~ ( ~ ( in @ SV95 @ SY227 )
| ~ ( in @ SY227 @ SV17 ) ) )
= $false )
| ( ( in @ SV95 @ SV55 )
= $false )
| ( ( SV55
= ( union @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[676]) ).
thf(707,plain,
! [SV55: $i,SV17: $i,SV95: $i] :
( ( ( ! [SY228: $i] :
~ ~ ( ~ ( in @ SV95 @ SY228 )
| ~ ( in @ SY228 @ SV17 ) ) )
= $true )
| ( ( in @ SV95 @ SV55 )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[677]) ).
thf(708,plain,
! [SV55: $i,SV17: $i] :
( ( ( ~ ~ ! [SY230: $i] :
~ ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SY230 )
| ~ ( in @ SY230 @ SV17 ) )
| ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV55 ) )
= $false )
| ( ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV55 )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[678]) ).
thf(709,plain,
! [SV103: $i,SV55: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV103 )
| ~ ( in @ SV103 @ SV17 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY230: $i] :
~ ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SY230 )
| ~ ( in @ SY230 @ SV17 ) )
| ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV55 ) ) )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(710,plain,
! [SV19: $i,SV57: $i] :
( ( ( ~ ( in @ ( sK13_SY194 @ SV57 @ SV19 ) @ SV19 )
| ~ ( in @ ( sK13_SY194 @ SV57 @ SV19 ) @ SV57 ) )
= $false )
| ( ( disjoint @ SV19 @ SV57 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[680]) ).
thf(711,plain,
! [SV57: $i,SV19: $i,SV102: $i] :
( ( ( ~ ( in @ SV102 @ SV19 ) )
= $true )
| ( ( ~ ( in @ SV102 @ SV57 ) )
= $true )
| ( ( ~ ( disjoint @ SV19 @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[681]) ).
thf(712,plain,
! [SV62: $i,SV25: $i,SV85: $i,SV98: $i] :
( ( ( in @ SV98 @ SV85 )
= $false )
| ( ( ~ ( ~ ( in @ SV98 @ SV25 )
| ~ ( in @ SV98 @ SV62 ) ) )
= $true )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[682]) ).
thf(713,plain,
! [SV85: $i,SV62: $i,SV25: $i,SV98: $i] :
( ( ( ~ ( ~ ( in @ SV98 @ SV25 )
| ~ ( in @ SV98 @ SV62 ) ) )
= $false )
| ( ( in @ SV98 @ SV85 )
= $true )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[683]) ).
thf(714,plain,
! [SV85: $i,SV25: $i,SV62: $i] :
( ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV85 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
| ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 ) )
| ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[684]) ).
thf(715,plain,
! [SV85: $i,SV25: $i,SV62: $i] :
( ( ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
| ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
| ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 ) )
| ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[685]) ).
thf(716,plain,
! [SV71: $i,SV34: $i,SV88: $i,SV99: $i] :
( ( ( in @ SV99 @ SV88 )
= $false )
| ( ( ~ ( ~ ( in @ SV99 @ SV34 )
| ~ ~ ( in @ SV99 @ SV71 ) ) )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[687]) ).
thf(717,plain,
! [SV88: $i,SV71: $i,SV34: $i,SV99: $i] :
( ( ( ~ ( ~ ( in @ SV99 @ SV34 )
| ~ ~ ( in @ SV99 @ SV71 ) ) )
= $false )
| ( ( in @ SV99 @ SV88 )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[688]) ).
thf(718,plain,
! [SV88: $i,SV34: $i,SV71: $i] :
( ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV88 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
| ~ ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 ) )
| ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV88 ) ) )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[689]) ).
thf(719,plain,
! [SV88: $i,SV34: $i,SV71: $i] :
( ( ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
| ~ ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
| ~ ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 ) )
| ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV88 ) ) )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[690]) ).
thf(720,plain,
! [SV73: $i,SV36: $i,SV89: $i,SV100: $i] :
( ( ( in @ SV100 @ SV89 )
= $false )
| ( ( ( SV100 = SV36 )
| ( SV100 = SV73 ) )
= $true )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[691]) ).
thf(721,plain,
! [SV89: $i,SV73: $i,SV36: $i,SV100: $i] :
( ( ( ( SV100 = SV36 )
| ( SV100 = SV73 ) )
= $false )
| ( ( in @ SV100 @ SV89 )
= $true )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[692]) ).
thf(722,plain,
! [SV89: $i,SV36: $i,SV73: $i] :
( ( ( in @ ( sK11_SY224 @ SV73 @ SV36 @ SV89 ) @ SV89 )
= $true )
| ( ( ~ ( ~ ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV36 )
| ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV73 ) )
| ( in @ ( sK11_SY224 @ SV73 @ SV36 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[693]) ).
thf(723,plain,
! [SV89: $i,SV36: $i,SV73: $i] :
( ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV36 )
= $false )
| ( ( ~ ( ~ ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV36 )
| ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV73 ) )
| ( in @ ( sK11_SY224 @ SV73 @ SV36 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[694]) ).
thf(724,plain,
! [SV89: $i,SV36: $i,SV73: $i] :
( ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV73 )
= $false )
| ( ( ~ ( ~ ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV36 )
| ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV73 ) )
| ( in @ ( sK11_SY224 @ SV73 @ SV36 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[694]) ).
thf(725,plain,
! [SV78: $i,SV41: $i] :
( ( ( ~ ( subset @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV41 )
| ( in @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV78 ) )
= $false )
| ( ( in @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV78 )
= $true )
| ( ( SV78
= ( powerset @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[697]) ).
thf(726,plain,
! [SV78: $i,SV41: $i] :
( ( ( ~ ( subset @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV41 ) )
= $false )
| ( ( subset @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV41 )
= $false )
| ( ( SV78
= ( powerset @ SV41 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[698]) ).
thf(727,plain,
! [SV78: $i,SV41: $i] :
( ( ( in @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV78 )
= $false )
| ( ( subset @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV41 )
= $false )
| ( ( SV78
= ( powerset @ SV41 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[698]) ).
thf(728,plain,
! [SV79: $i,SV42: $i,SV92: $i,SV101: $i] :
( ( ( in @ SV101 @ SV92 )
= $false )
| ( ( ( in @ SV101 @ SV42 )
| ( in @ SV101 @ SV79 ) )
= $true )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[699]) ).
thf(729,plain,
! [SV92: $i,SV79: $i,SV42: $i,SV101: $i] :
( ( ( ( in @ SV101 @ SV42 )
| ( in @ SV101 @ SV79 ) )
= $false )
| ( ( in @ SV101 @ SV92 )
= $true )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[700]) ).
thf(730,plain,
! [SV92: $i,SV42: $i,SV79: $i] :
( ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV92 )
= $true )
| ( ( ~ ( ~ ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV42 )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV79 ) )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV92 ) ) )
= $true )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[701]) ).
thf(731,plain,
! [SV92: $i,SV42: $i,SV79: $i] :
( ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV42 )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV42 )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV79 ) )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV92 ) ) )
= $true )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[702]) ).
thf(732,plain,
! [SV92: $i,SV42: $i,SV79: $i] :
( ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV79 )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV42 )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV79 ) )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV92 ) ) )
= $true )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[702]) ).
thf(733,plain,
! [SV49: $i,SV10: $i] :
( ( ( ( sK5_SY185 @ SV10 @ SV49 )
!= SV10 )
= $false )
| ( ( in @ ( sK5_SY185 @ SV10 @ SV49 ) @ SV49 )
= $true )
| ( ( SV49
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[703]) ).
thf(734,plain,
! [SV49: $i,SV10: $i] :
( ( ( in @ ( sK5_SY185 @ SV10 @ SV49 ) @ SV49 )
= $false )
| ( ( in @ ( sK5_SY185 @ SV10 @ SV49 ) @ SV49 )
= $true )
| ( ( SV49
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[703]) ).
thf(735,plain,
! [SV49: $i,SV10: $i] :
( ( ( ( sK5_SY185 @ SV10 @ SV49 )
= SV10 )
= $true )
| ( ( ( sK5_SY185 @ SV10 @ SV49 )
= SV10 )
= $false )
| ( ( SV49
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[704]) ).
thf(736,plain,
! [SV17: $i,SV55: $i,SV95: $i] :
( ( ( ~ ~ ( ~ ( in @ SV95 @ ( sK14_SY227 @ SV55 @ SV17 @ SV95 ) )
| ~ ( in @ ( sK14_SY227 @ SV55 @ SV17 @ SV95 ) @ SV17 ) ) )
= $false )
| ( ( in @ SV95 @ SV55 )
= $false )
| ( ( SV55
= ( union @ SV17 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[706]) ).
thf(737,plain,
! [SV55: $i,SV17: $i,SV104: $i,SV95: $i] :
( ( ( ~ ~ ( ~ ( in @ SV95 @ SV104 )
| ~ ( in @ SV104 @ SV17 ) ) )
= $true )
| ( ( in @ SV95 @ SV55 )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(738,plain,
! [SV55: $i,SV17: $i] :
( ( ( ~ ~ ! [SY230: $i] :
~ ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SY230 )
| ~ ( in @ SY230 @ SV17 ) ) )
= $false )
| ( ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV55 )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[708]) ).
thf(739,plain,
! [SV55: $i,SV17: $i] :
( ( ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV55 )
= $false )
| ( ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV55 )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[708]) ).
thf(740,plain,
! [SV103: $i,SV55: $i,SV17: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV103 )
| ~ ( in @ SV103 @ SV17 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY230: $i] :
~ ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SY230 )
| ~ ( in @ SY230 @ SV17 ) )
| ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV55 ) ) )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[709]) ).
thf(741,plain,
! [SV19: $i,SV57: $i] :
( ( ( ~ ( in @ ( sK13_SY194 @ SV57 @ SV19 ) @ SV19 ) )
= $false )
| ( ( disjoint @ SV19 @ SV57 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[710]) ).
thf(742,plain,
! [SV19: $i,SV57: $i] :
( ( ( ~ ( in @ ( sK13_SY194 @ SV57 @ SV19 ) @ SV57 ) )
= $false )
| ( ( disjoint @ SV19 @ SV57 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[710]) ).
thf(743,plain,
! [SV57: $i,SV19: $i,SV102: $i] :
( ( ( in @ SV102 @ SV19 )
= $false )
| ( ( ~ ( in @ SV102 @ SV57 ) )
= $true )
| ( ( ~ ( disjoint @ SV19 @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[711]) ).
thf(744,plain,
! [SV85: $i,SV62: $i,SV25: $i,SV98: $i] :
( ( ( ~ ( in @ SV98 @ SV25 )
| ~ ( in @ SV98 @ SV62 ) )
= $false )
| ( ( in @ SV98 @ SV85 )
= $false )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[712]) ).
thf(745,plain,
! [SV85: $i,SV62: $i,SV25: $i,SV98: $i] :
( ( ( ~ ( in @ SV98 @ SV25 )
| ~ ( in @ SV98 @ SV62 ) )
= $true )
| ( ( in @ SV98 @ SV85 )
= $true )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[713]) ).
thf(746,plain,
! [SV85: $i,SV25: $i,SV62: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
| ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 ) )
| ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV85 ) )
= $false )
| ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[714]) ).
thf(747,plain,
! [SV85: $i,SV25: $i,SV62: $i] :
( ( ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 ) )
= $true )
| ( ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
| ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 ) )
| ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[715]) ).
thf(748,plain,
! [SV88: $i,SV71: $i,SV34: $i,SV99: $i] :
( ( ( ~ ( in @ SV99 @ SV34 )
| ~ ~ ( in @ SV99 @ SV71 ) )
= $false )
| ( ( in @ SV99 @ SV88 )
= $false )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[716]) ).
thf(749,plain,
! [SV88: $i,SV71: $i,SV34: $i,SV99: $i] :
( ( ( ~ ( in @ SV99 @ SV34 )
| ~ ~ ( in @ SV99 @ SV71 ) )
= $true )
| ( ( in @ SV99 @ SV88 )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[717]) ).
thf(750,plain,
! [SV88: $i,SV34: $i,SV71: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
| ~ ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 ) )
| ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV88 ) )
= $false )
| ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV88 )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[718]) ).
thf(751,plain,
! [SV88: $i,SV34: $i,SV71: $i] :
( ( ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 ) )
= $true )
| ( ( ~ ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
| ~ ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 ) )
| ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV88 ) ) )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[719]) ).
thf(752,plain,
! [SV89: $i,SV73: $i,SV36: $i,SV100: $i] :
( ( ( SV100 = SV36 )
= $true )
| ( ( SV100 = SV73 )
= $true )
| ( ( in @ SV100 @ SV89 )
= $false )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[720]) ).
thf(753,plain,
! [SV73: $i,SV89: $i,SV36: $i,SV100: $i] :
( ( ( SV100 = SV36 )
= $false )
| ( ( in @ SV100 @ SV89 )
= $true )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[721]) ).
thf(754,plain,
! [SV36: $i,SV89: $i,SV73: $i,SV100: $i] :
( ( ( SV100 = SV73 )
= $false )
| ( ( in @ SV100 @ SV89 )
= $true )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[721]) ).
thf(755,plain,
! [SV89: $i,SV36: $i,SV73: $i] :
( ( ( ~ ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV36 )
| ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV73 ) )
| ( in @ ( sK11_SY224 @ SV73 @ SV36 @ SV89 ) @ SV89 ) )
= $false )
| ( ( in @ ( sK11_SY224 @ SV73 @ SV36 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[722]) ).
thf(756,plain,
! [SV89: $i,SV36: $i,SV73: $i] :
( ( ( ~ ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV36 )
| ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV73 ) )
| ( in @ ( sK11_SY224 @ SV73 @ SV36 @ SV89 ) @ SV89 ) )
= $false )
| ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV36 )
= $false )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[723]) ).
thf(757,plain,
! [SV89: $i,SV36: $i,SV73: $i] :
( ( ( ~ ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV36 )
| ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV73 ) )
| ( in @ ( sK11_SY224 @ SV73 @ SV36 @ SV89 ) @ SV89 ) )
= $false )
| ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV73 )
= $false )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[724]) ).
thf(758,plain,
! [SV78: $i,SV41: $i] :
( ( ( ~ ( subset @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV41 ) )
= $false )
| ( ( in @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV78 )
= $true )
| ( ( SV78
= ( powerset @ SV41 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[725]) ).
thf(759,plain,
! [SV78: $i,SV41: $i] :
( ( ( in @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV78 )
= $false )
| ( ( in @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV78 )
= $true )
| ( ( SV78
= ( powerset @ SV41 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[725]) ).
thf(760,plain,
! [SV78: $i,SV41: $i] :
( ( ( subset @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV41 )
= $true )
| ( ( subset @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV41 )
= $false )
| ( ( SV78
= ( powerset @ SV41 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[726]) ).
thf(761,plain,
! [SV92: $i,SV79: $i,SV42: $i,SV101: $i] :
( ( ( in @ SV101 @ SV42 )
= $true )
| ( ( in @ SV101 @ SV79 )
= $true )
| ( ( in @ SV101 @ SV92 )
= $false )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[728]) ).
thf(762,plain,
! [SV79: $i,SV92: $i,SV42: $i,SV101: $i] :
( ( ( in @ SV101 @ SV42 )
= $false )
| ( ( in @ SV101 @ SV92 )
= $true )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[729]) ).
thf(763,plain,
! [SV42: $i,SV92: $i,SV79: $i,SV101: $i] :
( ( ( in @ SV101 @ SV79 )
= $false )
| ( ( in @ SV101 @ SV92 )
= $true )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[729]) ).
thf(764,plain,
! [SV92: $i,SV42: $i,SV79: $i] :
( ( ( ~ ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV42 )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV79 ) )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV92 ) )
= $false )
| ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV92 )
= $true )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[730]) ).
thf(765,plain,
! [SV92: $i,SV42: $i,SV79: $i] :
( ( ( ~ ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV42 )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV79 ) )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV92 ) )
= $false )
| ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV42 )
= $false )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[731]) ).
thf(766,plain,
! [SV92: $i,SV42: $i,SV79: $i] :
( ( ( ~ ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV42 )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV79 ) )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV92 ) )
= $false )
| ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV79 )
= $false )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[732]) ).
thf(767,plain,
! [SV49: $i,SV10: $i] :
( ( ( ( sK5_SY185 @ SV10 @ SV49 )
= SV10 )
= $true )
| ( ( in @ ( sK5_SY185 @ SV10 @ SV49 ) @ SV49 )
= $true )
| ( ( SV49
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[733]) ).
thf(768,plain,
! [SV17: $i,SV55: $i,SV95: $i] :
( ( ( ~ ( ~ ( in @ SV95 @ ( sK14_SY227 @ SV55 @ SV17 @ SV95 ) )
| ~ ( in @ ( sK14_SY227 @ SV55 @ SV17 @ SV95 ) @ SV17 ) ) )
= $true )
| ( ( in @ SV95 @ SV55 )
= $false )
| ( ( SV55
= ( union @ SV17 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[736]) ).
thf(769,plain,
! [SV55: $i,SV17: $i,SV104: $i,SV95: $i] :
( ( ( ~ ( ~ ( in @ SV95 @ SV104 )
| ~ ( in @ SV104 @ SV17 ) ) )
= $false )
| ( ( in @ SV95 @ SV55 )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[737]) ).
thf(770,plain,
! [SV55: $i,SV17: $i] :
( ( ( ~ ! [SY230: $i] :
~ ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SY230 )
| ~ ( in @ SY230 @ SV17 ) ) )
= $true )
| ( ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV55 )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[738]) ).
thf(771,plain,
! [SV103: $i,SV55: $i,SV17: $i] :
( ( ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV103 )
| ~ ( in @ SV103 @ SV17 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY230: $i] :
~ ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SY230 )
| ~ ( in @ SY230 @ SV17 ) )
| ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV55 ) ) )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[740]) ).
thf(772,plain,
! [SV19: $i,SV57: $i] :
( ( ( in @ ( sK13_SY194 @ SV57 @ SV19 ) @ SV19 )
= $true )
| ( ( disjoint @ SV19 @ SV57 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[741]) ).
thf(773,plain,
! [SV19: $i,SV57: $i] :
( ( ( in @ ( sK13_SY194 @ SV57 @ SV19 ) @ SV57 )
= $true )
| ( ( disjoint @ SV19 @ SV57 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[742]) ).
thf(774,plain,
! [SV19: $i,SV57: $i,SV102: $i] :
( ( ( in @ SV102 @ SV57 )
= $false )
| ( ( in @ SV102 @ SV19 )
= $false )
| ( ( ~ ( disjoint @ SV19 @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[743]) ).
thf(775,plain,
! [SV62: $i,SV85: $i,SV25: $i,SV98: $i] :
( ( ( ~ ( in @ SV98 @ SV25 ) )
= $false )
| ( ( in @ SV98 @ SV85 )
= $false )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[744]) ).
thf(776,plain,
! [SV25: $i,SV85: $i,SV62: $i,SV98: $i] :
( ( ( ~ ( in @ SV98 @ SV62 ) )
= $false )
| ( ( in @ SV98 @ SV85 )
= $false )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[744]) ).
thf(777,plain,
! [SV85: $i,SV62: $i,SV25: $i,SV98: $i] :
( ( ( ~ ( in @ SV98 @ SV25 ) )
= $true )
| ( ( ~ ( in @ SV98 @ SV62 ) )
= $true )
| ( ( in @ SV98 @ SV85 )
= $true )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[745]) ).
thf(778,plain,
! [SV85: $i,SV25: $i,SV62: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
| ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 ) ) )
= $false )
| ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[746]) ).
thf(779,plain,
! [SV85: $i,SV25: $i,SV62: $i] :
( ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV85 )
= $false )
| ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[746]) ).
thf(780,plain,
! [SV85: $i,SV25: $i,SV62: $i] :
( ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
= $false )
| ( ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
| ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 ) )
| ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[747]) ).
thf(781,plain,
! [SV71: $i,SV88: $i,SV34: $i,SV99: $i] :
( ( ( ~ ( in @ SV99 @ SV34 ) )
= $false )
| ( ( in @ SV99 @ SV88 )
= $false )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[748]) ).
thf(782,plain,
! [SV34: $i,SV88: $i,SV71: $i,SV99: $i] :
( ( ( ~ ~ ( in @ SV99 @ SV71 ) )
= $false )
| ( ( in @ SV99 @ SV88 )
= $false )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[748]) ).
thf(783,plain,
! [SV88: $i,SV71: $i,SV34: $i,SV99: $i] :
( ( ( ~ ( in @ SV99 @ SV34 ) )
= $true )
| ( ( ~ ~ ( in @ SV99 @ SV71 ) )
= $true )
| ( ( in @ SV99 @ SV88 )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[749]) ).
thf(784,plain,
! [SV88: $i,SV34: $i,SV71: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
| ~ ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 ) ) )
= $false )
| ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV88 )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[750]) ).
thf(785,plain,
! [SV88: $i,SV34: $i,SV71: $i] :
( ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV88 )
= $false )
| ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV88 )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[750]) ).
thf(786,plain,
! [SV88: $i,SV34: $i,SV71: $i] :
( ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
= $false )
| ( ( ~ ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
| ~ ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 ) )
| ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV88 ) ) )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[751]) ).
thf(787,plain,
! [SV89: $i,SV36: $i,SV73: $i] :
( ( ( ~ ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV36 )
| ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV73 ) ) )
= $false )
| ( ( in @ ( sK11_SY224 @ SV73 @ SV36 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[755]) ).
thf(788,plain,
! [SV89: $i,SV36: $i,SV73: $i] :
( ( ( in @ ( sK11_SY224 @ SV73 @ SV36 @ SV89 ) @ SV89 )
= $false )
| ( ( in @ ( sK11_SY224 @ SV73 @ SV36 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[755]) ).
thf(789,plain,
! [SV89: $i,SV36: $i,SV73: $i] :
( ( ( ~ ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV36 )
| ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV73 ) ) )
= $false )
| ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV36 )
= $false )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[756]) ).
thf(790,plain,
! [SV89: $i,SV36: $i,SV73: $i] :
( ( ( in @ ( sK11_SY224 @ SV73 @ SV36 @ SV89 ) @ SV89 )
= $false )
| ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV36 )
= $false )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[756]) ).
thf(791,plain,
! [SV89: $i,SV36: $i,SV73: $i] :
( ( ( ~ ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV36 )
| ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV73 ) ) )
= $false )
| ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV73 )
= $false )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[757]) ).
thf(792,plain,
! [SV89: $i,SV36: $i,SV73: $i] :
( ( ( in @ ( sK11_SY224 @ SV73 @ SV36 @ SV89 ) @ SV89 )
= $false )
| ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV73 )
= $false )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[757]) ).
thf(793,plain,
! [SV78: $i,SV41: $i] :
( ( ( subset @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV41 )
= $true )
| ( ( in @ ( sK8_SY215 @ SV41 @ SV78 ) @ SV78 )
= $true )
| ( ( SV78
= ( powerset @ SV41 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[758]) ).
thf(794,plain,
! [SV92: $i,SV42: $i,SV79: $i] :
( ( ( ~ ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV42 )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV79 ) ) )
= $false )
| ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV92 )
= $true )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[764]) ).
thf(795,plain,
! [SV92: $i,SV42: $i,SV79: $i] :
( ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV92 )
= $false )
| ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV92 )
= $true )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[764]) ).
thf(796,plain,
! [SV92: $i,SV42: $i,SV79: $i] :
( ( ( ~ ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV42 )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV79 ) ) )
= $false )
| ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV42 )
= $false )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[765]) ).
thf(797,plain,
! [SV92: $i,SV42: $i,SV79: $i] :
( ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV92 )
= $false )
| ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV42 )
= $false )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[765]) ).
thf(798,plain,
! [SV92: $i,SV42: $i,SV79: $i] :
( ( ( ~ ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV42 )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV79 ) ) )
= $false )
| ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV79 )
= $false )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[766]) ).
thf(799,plain,
! [SV92: $i,SV42: $i,SV79: $i] :
( ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV92 )
= $false )
| ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV79 )
= $false )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[766]) ).
thf(800,plain,
! [SV17: $i,SV55: $i,SV95: $i] :
( ( ( ~ ( in @ SV95 @ ( sK14_SY227 @ SV55 @ SV17 @ SV95 ) )
| ~ ( in @ ( sK14_SY227 @ SV55 @ SV17 @ SV95 ) @ SV17 ) )
= $false )
| ( ( in @ SV95 @ SV55 )
= $false )
| ( ( SV55
= ( union @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[768]) ).
thf(801,plain,
! [SV55: $i,SV17: $i,SV104: $i,SV95: $i] :
( ( ( ~ ( in @ SV95 @ SV104 )
| ~ ( in @ SV104 @ SV17 ) )
= $true )
| ( ( in @ SV95 @ SV55 )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[769]) ).
thf(802,plain,
! [SV55: $i,SV17: $i] :
( ( ( ! [SY230: $i] :
~ ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SY230 )
| ~ ( in @ SY230 @ SV17 ) ) )
= $false )
| ( ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV55 )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[770]) ).
thf(803,plain,
! [SV103: $i,SV55: $i,SV17: $i] :
( ( ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV103 ) )
= $true )
| ( ( ~ ( in @ SV103 @ SV17 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY230: $i] :
~ ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SY230 )
| ~ ( in @ SY230 @ SV17 ) )
| ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV55 ) ) )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[771]) ).
thf(804,plain,
! [SV102: $i,SV57: $i,SV19: $i] :
( ( ( disjoint @ SV19 @ SV57 )
= $false )
| ( ( in @ SV102 @ SV19 )
= $false )
| ( ( in @ SV102 @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[774]) ).
thf(805,plain,
! [SV62: $i,SV85: $i,SV25: $i,SV98: $i] :
( ( ( in @ SV98 @ SV25 )
= $true )
| ( ( in @ SV98 @ SV85 )
= $false )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[775]) ).
thf(806,plain,
! [SV25: $i,SV85: $i,SV62: $i,SV98: $i] :
( ( ( in @ SV98 @ SV62 )
= $true )
| ( ( in @ SV98 @ SV85 )
= $false )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[776]) ).
thf(807,plain,
! [SV85: $i,SV62: $i,SV25: $i,SV98: $i] :
( ( ( in @ SV98 @ SV25 )
= $false )
| ( ( ~ ( in @ SV98 @ SV62 ) )
= $true )
| ( ( in @ SV98 @ SV85 )
= $true )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[777]) ).
thf(808,plain,
! [SV85: $i,SV25: $i,SV62: $i] :
( ( ( ~ ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
| ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 ) ) )
= $true )
| ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[778]) ).
thf(809,plain,
! [SV85: $i,SV25: $i,SV62: $i] :
( ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 )
= $false )
| ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
| ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 ) )
| ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[780]) ).
thf(810,plain,
! [SV71: $i,SV88: $i,SV34: $i,SV99: $i] :
( ( ( in @ SV99 @ SV34 )
= $true )
| ( ( in @ SV99 @ SV88 )
= $false )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[781]) ).
thf(811,plain,
! [SV34: $i,SV88: $i,SV71: $i,SV99: $i] :
( ( ( ~ ( in @ SV99 @ SV71 ) )
= $true )
| ( ( in @ SV99 @ SV88 )
= $false )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[782]) ).
thf(812,plain,
! [SV88: $i,SV71: $i,SV34: $i,SV99: $i] :
( ( ( in @ SV99 @ SV34 )
= $false )
| ( ( ~ ~ ( in @ SV99 @ SV71 ) )
= $true )
| ( ( in @ SV99 @ SV88 )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[783]) ).
thf(813,plain,
! [SV88: $i,SV34: $i,SV71: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
| ~ ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 ) ) )
= $true )
| ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV88 )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[784]) ).
thf(814,plain,
! [SV88: $i,SV34: $i,SV71: $i] :
( ( ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 ) )
= $false )
| ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
| ~ ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 ) )
| ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV88 ) ) )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[786]) ).
thf(815,plain,
! [SV89: $i,SV36: $i,SV73: $i] :
( ( ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV36 )
| ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV73 ) )
= $true )
| ( ( in @ ( sK11_SY224 @ SV73 @ SV36 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[787]) ).
thf(816,plain,
! [SV89: $i,SV36: $i,SV73: $i] :
( ( ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV36 )
| ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV73 ) )
= $true )
| ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV36 )
= $false )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[789]) ).
thf(817,plain,
! [SV89: $i,SV36: $i,SV73: $i] :
( ( ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV36 )
| ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV73 ) )
= $true )
| ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV73 )
= $false )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[791]) ).
thf(818,plain,
! [SV92: $i,SV42: $i,SV79: $i] :
( ( ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV42 )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV79 ) )
= $true )
| ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV92 )
= $true )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[794]) ).
thf(819,plain,
! [SV92: $i,SV42: $i,SV79: $i] :
( ( ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV42 )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV79 ) )
= $true )
| ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV42 )
= $false )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[796]) ).
thf(820,plain,
! [SV92: $i,SV42: $i,SV79: $i] :
( ( ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV42 )
| ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV79 ) )
= $true )
| ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV79 )
= $false )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[798]) ).
thf(821,plain,
! [SV17: $i,SV55: $i,SV95: $i] :
( ( ( ~ ( in @ SV95 @ ( sK14_SY227 @ SV55 @ SV17 @ SV95 ) ) )
= $false )
| ( ( in @ SV95 @ SV55 )
= $false )
| ( ( SV55
= ( union @ SV17 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[800]) ).
thf(822,plain,
! [SV95: $i,SV17: $i,SV55: $i] :
( ( ( ~ ( in @ ( sK14_SY227 @ SV55 @ SV17 @ SV95 ) @ SV17 ) )
= $false )
| ( ( in @ SV95 @ SV55 )
= $false )
| ( ( SV55
= ( union @ SV17 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[800]) ).
thf(823,plain,
! [SV55: $i,SV17: $i,SV104: $i,SV95: $i] :
( ( ( ~ ( in @ SV95 @ SV104 ) )
= $true )
| ( ( ~ ( in @ SV104 @ SV17 ) )
= $true )
| ( ( in @ SV95 @ SV55 )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[801]) ).
thf(824,plain,
! [SV55: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ ( sK15_SY230 @ SV55 @ SV17 ) )
| ~ ( in @ ( sK15_SY230 @ SV55 @ SV17 ) @ SV17 ) ) )
= $false )
| ( ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV55 )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[802]) ).
thf(825,plain,
! [SV103: $i,SV55: $i,SV17: $i] :
( ( ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV103 )
= $false )
| ( ( ~ ( in @ SV103 @ SV17 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY230: $i] :
~ ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SY230 )
| ~ ( in @ SY230 @ SV17 ) )
| ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV55 ) ) )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[803]) ).
thf(826,plain,
! [SV85: $i,SV25: $i,SV62: $i,SV98: $i] :
( ( ( in @ SV98 @ SV62 )
= $false )
| ( ( in @ SV98 @ SV25 )
= $false )
| ( ( in @ SV98 @ SV85 )
= $true )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[807]) ).
thf(827,plain,
! [SV85: $i,SV25: $i,SV62: $i] :
( ( ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
| ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 ) )
= $false )
| ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[808]) ).
thf(828,plain,
! [SV85: $i,SV25: $i,SV62: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
| ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 ) )
| ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV85 ) )
= $false )
| ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
= $false )
| ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 )
= $false )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[809]) ).
thf(829,plain,
! [SV34: $i,SV88: $i,SV71: $i,SV99: $i] :
( ( ( in @ SV99 @ SV71 )
= $false )
| ( ( in @ SV99 @ SV88 )
= $false )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[811]) ).
thf(830,plain,
! [SV88: $i,SV34: $i,SV71: $i,SV99: $i] :
( ( ( ~ ( in @ SV99 @ SV71 ) )
= $false )
| ( ( in @ SV99 @ SV34 )
= $false )
| ( ( in @ SV99 @ SV88 )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[812]) ).
thf(831,plain,
! [SV88: $i,SV34: $i,SV71: $i] :
( ( ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
| ~ ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 ) )
= $false )
| ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV88 )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[813]) ).
thf(832,plain,
! [SV88: $i,SV34: $i,SV71: $i] :
( ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 )
= $true )
| ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
| ~ ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 ) )
| ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV88 ) ) )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[814]) ).
thf(833,plain,
! [SV89: $i,SV36: $i,SV73: $i] :
( ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV36 )
= $true )
| ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV73 )
= $true )
| ( ( in @ ( sK11_SY224 @ SV73 @ SV36 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[815]) ).
thf(834,plain,
! [SV89: $i,SV36: $i,SV73: $i] :
( ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV36 )
= $true )
| ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV73 )
= $true )
| ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV36 )
= $false )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[816]) ).
thf(835,plain,
! [SV89: $i,SV36: $i,SV73: $i] :
( ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV36 )
= $true )
| ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV73 )
= $true )
| ( ( ( sK11_SY224 @ SV73 @ SV36 @ SV89 )
= SV73 )
= $false )
| ( ( SV89
= ( unordered_pair @ SV36 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[817]) ).
thf(836,plain,
! [SV92: $i,SV42: $i,SV79: $i] :
( ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV42 )
= $true )
| ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV79 )
= $true )
| ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV92 )
= $true )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[818]) ).
thf(837,plain,
! [SV92: $i,SV42: $i,SV79: $i] :
( ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV42 )
= $true )
| ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV79 )
= $true )
| ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV42 )
= $false )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[819]) ).
thf(838,plain,
! [SV92: $i,SV42: $i,SV79: $i] :
( ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV42 )
= $true )
| ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV79 )
= $true )
| ( ( in @ ( sK12_SY226 @ SV79 @ SV42 @ SV92 ) @ SV79 )
= $false )
| ( ( SV92
= ( set_union2 @ SV42 @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[820]) ).
thf(839,plain,
! [SV17: $i,SV55: $i,SV95: $i] :
( ( ( in @ SV95 @ ( sK14_SY227 @ SV55 @ SV17 @ SV95 ) )
= $true )
| ( ( in @ SV95 @ SV55 )
= $false )
| ( ( SV55
= ( union @ SV17 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[821]) ).
thf(840,plain,
! [SV95: $i,SV17: $i,SV55: $i] :
( ( ( in @ ( sK14_SY227 @ SV55 @ SV17 @ SV95 ) @ SV17 )
= $true )
| ( ( in @ SV95 @ SV55 )
= $false )
| ( ( SV55
= ( union @ SV17 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[822]) ).
thf(841,plain,
! [SV55: $i,SV17: $i,SV104: $i,SV95: $i] :
( ( ( in @ SV95 @ SV104 )
= $false )
| ( ( ~ ( in @ SV104 @ SV17 ) )
= $true )
| ( ( in @ SV95 @ SV55 )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[823]) ).
thf(842,plain,
! [SV55: $i,SV17: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ ( sK15_SY230 @ SV55 @ SV17 ) )
| ~ ( in @ ( sK15_SY230 @ SV55 @ SV17 ) @ SV17 ) ) )
= $true )
| ( ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV55 )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[824]) ).
thf(843,plain,
! [SV55: $i,SV17: $i,SV103: $i] :
( ( ( in @ SV103 @ SV17 )
= $false )
| ( ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV103 )
= $false )
| ( ( ~ ( ~ ~ ! [SY230: $i] :
~ ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SY230 )
| ~ ( in @ SY230 @ SV17 ) )
| ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV55 ) ) )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[825]) ).
thf(844,plain,
! [SV85: $i,SV25: $i,SV62: $i] :
( ( ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 ) )
= $false )
| ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[827]) ).
thf(845,plain,
! [SV85: $i,SV25: $i,SV62: $i] :
( ( ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 ) )
= $false )
| ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[827]) ).
thf(846,plain,
! [SV85: $i,SV25: $i,SV62: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
| ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 ) ) )
= $false )
| ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
= $false )
| ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 )
= $false )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[828]) ).
thf(847,plain,
! [SV85: $i,SV25: $i,SV62: $i] :
( ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV85 )
= $false )
| ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
= $false )
| ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 )
= $false )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[828]) ).
thf(848,plain,
! [SV88: $i,SV34: $i,SV71: $i,SV99: $i] :
( ( ( in @ SV99 @ SV71 )
= $true )
| ( ( in @ SV99 @ SV34 )
= $false )
| ( ( in @ SV99 @ SV88 )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[830]) ).
thf(849,plain,
! [SV88: $i,SV34: $i,SV71: $i] :
( ( ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 ) )
= $false )
| ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV88 )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[831]) ).
thf(850,plain,
! [SV88: $i,SV34: $i,SV71: $i] :
( ( ( ~ ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 ) )
= $false )
| ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV88 )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[831]) ).
thf(851,plain,
! [SV88: $i,SV34: $i,SV71: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
| ~ ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 ) )
| ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV88 ) )
= $false )
| ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
= $false )
| ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[832]) ).
thf(852,plain,
! [SV55: $i,SV95: $i,SV17: $i,SV104: $i] :
( ( ( in @ SV104 @ SV17 )
= $false )
| ( ( in @ SV95 @ SV104 )
= $false )
| ( ( in @ SV95 @ SV55 )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[841]) ).
thf(853,plain,
! [SV55: $i,SV17: $i] :
( ( ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ ( sK15_SY230 @ SV55 @ SV17 ) )
| ~ ( in @ ( sK15_SY230 @ SV55 @ SV17 ) @ SV17 ) )
= $false )
| ( ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV55 )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[842]) ).
thf(854,plain,
! [SV103: $i,SV55: $i,SV17: $i] :
( ( ( ~ ~ ! [SY230: $i] :
~ ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SY230 )
| ~ ( in @ SY230 @ SV17 ) )
| ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV55 ) )
= $false )
| ( ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV103 )
= $false )
| ( ( in @ SV103 @ SV17 )
= $false )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[843]) ).
thf(855,plain,
! [SV85: $i,SV25: $i,SV62: $i] :
( ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
= $true )
| ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[844]) ).
thf(856,plain,
! [SV85: $i,SV25: $i,SV62: $i] :
( ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 )
= $true )
| ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[845]) ).
thf(857,plain,
! [SV85: $i,SV25: $i,SV62: $i] :
( ( ( ~ ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
| ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 ) ) )
= $true )
| ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
= $false )
| ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 )
= $false )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[846]) ).
thf(858,plain,
! [SV88: $i,SV34: $i,SV71: $i] :
( ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
= $true )
| ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV88 )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[849]) ).
thf(859,plain,
! [SV88: $i,SV34: $i,SV71: $i] :
( ( ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 ) )
= $true )
| ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV88 )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[850]) ).
thf(860,plain,
! [SV88: $i,SV34: $i,SV71: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
| ~ ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 ) ) )
= $false )
| ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
= $false )
| ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[851]) ).
thf(861,plain,
! [SV88: $i,SV34: $i,SV71: $i] :
( ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV88 )
= $false )
| ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
= $false )
| ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[851]) ).
thf(862,plain,
! [SV55: $i,SV17: $i] :
( ( ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ ( sK15_SY230 @ SV55 @ SV17 ) ) )
= $false )
| ( ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV55 )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[853]) ).
thf(863,plain,
! [SV17: $i,SV55: $i] :
( ( ( ~ ( in @ ( sK15_SY230 @ SV55 @ SV17 ) @ SV17 ) )
= $false )
| ( ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV55 )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[853]) ).
thf(864,plain,
! [SV103: $i,SV55: $i,SV17: $i] :
( ( ( ~ ~ ! [SY230: $i] :
~ ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SY230 )
| ~ ( in @ SY230 @ SV17 ) ) )
= $false )
| ( ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV103 )
= $false )
| ( ( in @ SV103 @ SV17 )
= $false )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[854]) ).
thf(865,plain,
! [SV103: $i,SV55: $i,SV17: $i] :
( ( ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV55 )
= $false )
| ( ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV103 )
= $false )
| ( ( in @ SV103 @ SV17 )
= $false )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[854]) ).
thf(866,plain,
! [SV85: $i,SV25: $i,SV62: $i] :
( ( ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
| ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 ) )
= $false )
| ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
= $false )
| ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 )
= $false )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[857]) ).
thf(867,plain,
! [SV88: $i,SV34: $i,SV71: $i] :
( ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 )
= $false )
| ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV88 )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[859]) ).
thf(868,plain,
! [SV88: $i,SV34: $i,SV71: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
| ~ ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 ) ) )
= $true )
| ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
= $false )
| ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[860]) ).
thf(869,plain,
! [SV55: $i,SV17: $i] :
( ( ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ ( sK15_SY230 @ SV55 @ SV17 ) )
= $true )
| ( ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV55 )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[862]) ).
thf(870,plain,
! [SV17: $i,SV55: $i] :
( ( ( in @ ( sK15_SY230 @ SV55 @ SV17 ) @ SV17 )
= $true )
| ( ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV55 )
= $true )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[863]) ).
thf(871,plain,
! [SV103: $i,SV55: $i,SV17: $i] :
( ( ( ~ ! [SY230: $i] :
~ ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SY230 )
| ~ ( in @ SY230 @ SV17 ) ) )
= $true )
| ( ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV103 )
= $false )
| ( ( in @ SV103 @ SV17 )
= $false )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[864]) ).
thf(872,plain,
! [SV85: $i,SV25: $i,SV62: $i] :
( ( ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 ) )
= $false )
| ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
= $false )
| ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 )
= $false )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[866]) ).
thf(873,plain,
! [SV85: $i,SV25: $i,SV62: $i] :
( ( ( ~ ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 ) )
= $false )
| ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
= $false )
| ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 )
= $false )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[866]) ).
thf(874,plain,
! [SV88: $i,SV34: $i,SV71: $i] :
( ( ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
| ~ ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 ) )
= $false )
| ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
= $false )
| ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[868]) ).
thf(875,plain,
! [SV103: $i,SV55: $i,SV17: $i] :
( ( ( ! [SY230: $i] :
~ ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SY230 )
| ~ ( in @ SY230 @ SV17 ) ) )
= $false )
| ( ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV103 )
= $false )
| ( ( in @ SV103 @ SV17 )
= $false )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[871]) ).
thf(876,plain,
! [SV85: $i,SV25: $i,SV62: $i] :
( ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
= $true )
| ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
= $false )
| ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 )
= $false )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[872]) ).
thf(877,plain,
! [SV85: $i,SV25: $i,SV62: $i] :
( ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 )
= $true )
| ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV25 )
= $false )
| ( ( in @ ( sK9_SY220 @ SV62 @ SV25 @ SV85 ) @ SV62 )
= $false )
| ( ( SV85
= ( set_intersection2 @ SV25 @ SV62 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[873]) ).
thf(878,plain,
! [SV88: $i,SV34: $i,SV71: $i] :
( ( ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 ) )
= $false )
| ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
= $false )
| ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[874]) ).
thf(879,plain,
! [SV88: $i,SV34: $i,SV71: $i] :
( ( ( ~ ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 ) )
= $false )
| ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
= $false )
| ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[874]) ).
thf(880,plain,
! [SV103: $i,SV55: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ ( sK16_SY230 @ SV103 @ SV55 @ SV17 ) )
| ~ ( in @ ( sK16_SY230 @ SV103 @ SV55 @ SV17 ) @ SV17 ) ) )
= $false )
| ( ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV103 )
= $false )
| ( ( in @ SV103 @ SV17 )
= $false )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[875]) ).
thf(881,plain,
! [SV88: $i,SV34: $i,SV71: $i] :
( ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
= $true )
| ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
= $false )
| ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[878]) ).
thf(882,plain,
! [SV88: $i,SV34: $i,SV71: $i] :
( ( ( ~ ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 ) )
= $true )
| ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
= $false )
| ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[879]) ).
thf(883,plain,
! [SV103: $i,SV55: $i,SV17: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ ( sK16_SY230 @ SV103 @ SV55 @ SV17 ) )
| ~ ( in @ ( sK16_SY230 @ SV103 @ SV55 @ SV17 ) @ SV17 ) ) )
= $true )
| ( ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV103 )
= $false )
| ( ( in @ SV103 @ SV17 )
= $false )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[880]) ).
thf(884,plain,
! [SV88: $i,SV34: $i,SV71: $i] :
( ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 )
= $false )
| ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV34 )
= $false )
| ( ( in @ ( sK10_SY222 @ SV71 @ SV34 @ SV88 ) @ SV71 )
= $true )
| ( ( SV88
= ( set_difference @ SV34 @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[882]) ).
thf(885,plain,
! [SV103: $i,SV55: $i,SV17: $i] :
( ( ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ ( sK16_SY230 @ SV103 @ SV55 @ SV17 ) )
| ~ ( in @ ( sK16_SY230 @ SV103 @ SV55 @ SV17 ) @ SV17 ) )
= $false )
| ( ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV103 )
= $false )
| ( ( in @ SV103 @ SV17 )
= $false )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[883]) ).
thf(886,plain,
! [SV103: $i,SV55: $i,SV17: $i] :
( ( ( ~ ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ ( sK16_SY230 @ SV103 @ SV55 @ SV17 ) ) )
= $false )
| ( ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV103 )
= $false )
| ( ( in @ SV103 @ SV17 )
= $false )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[885]) ).
thf(887,plain,
! [SV17: $i,SV55: $i,SV103: $i] :
( ( ( ~ ( in @ ( sK16_SY230 @ SV103 @ SV55 @ SV17 ) @ SV17 ) )
= $false )
| ( ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV103 )
= $false )
| ( ( in @ SV103 @ SV17 )
= $false )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[885]) ).
thf(888,plain,
! [SV103: $i,SV55: $i,SV17: $i] :
( ( ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ ( sK16_SY230 @ SV103 @ SV55 @ SV17 ) )
= $true )
| ( ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV103 )
= $false )
| ( ( in @ SV103 @ SV17 )
= $false )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[886]) ).
thf(889,plain,
! [SV17: $i,SV55: $i,SV103: $i] :
( ( ( in @ ( sK16_SY230 @ SV103 @ SV55 @ SV17 ) @ SV17 )
= $true )
| ( ( in @ ( sK6_SY191 @ SV17 @ SV55 ) @ SV103 )
= $false )
| ( ( in @ SV103 @ SV17 )
= $false )
| ( ( SV55
= ( union @ SV17 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[887]) ).
thf(890,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[188,889,888,884,881,877,876,870,869,867,865,861,858,856,855,852,848,847,840,839,838,837,836,835,834,833,829,826,810,806,805,804,799,797,795,793,792,790,788,785,779,773,772,767,763,762,761,760,759,754,753,752,739,735,734,727,705,696,695,686,673,672,658,657,655,629,625,613,599,598,597,585,584,579,578,568,565,556,534,533,528,527,526,516,501,500,495,490,454,442,437,431,425,422,414,393,389,386,383,370,332,331,296,287,285,284,283,282,242,240,197,196,195,194,193,192,191,190,189]) ).
thf(891,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[142]) ).
thf(892,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(893,plain,
( ( ! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[140]) ).
thf(894,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(895,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(896,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(897,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(898,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(899,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(900,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(901,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(902,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(903,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(904,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(905,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(906,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(907,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(908,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(copy,[status(thm)],[125]) ).
thf(909,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(910,plain,
( ( ! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(911,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(912,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(913,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(914,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(915,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(916,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(917,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(918,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(919,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(920,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(921,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(922,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(923,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(924,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(copy,[status(thm)],[109]) ).
thf(925,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(926,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(copy,[status(thm)],[107]) ).
thf(927,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(928,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(copy,[status(thm)],[105]) ).
thf(929,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(930,plain,
$true = $true,
inference(copy,[status(thm)],[103]) ).
thf(931,plain,
$true = $true,
inference(copy,[status(thm)],[102]) ).
thf(932,plain,
$true = $true,
inference(copy,[status(thm)],[101]) ).
thf(933,plain,
$true = $true,
inference(copy,[status(thm)],[100]) ).
thf(934,plain,
$true = $true,
inference(copy,[status(thm)],[99]) ).
thf(935,plain,
$true = $true,
inference(copy,[status(thm)],[98]) ).
thf(936,plain,
$true = $true,
inference(copy,[status(thm)],[97]) ).
thf(937,plain,
$true = $true,
inference(copy,[status(thm)],[96]) ).
thf(938,plain,
$true = $true,
inference(copy,[status(thm)],[95]) ).
thf(939,plain,
$true = $true,
inference(copy,[status(thm)],[94]) ).
thf(940,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(941,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(942,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(943,plain,
( ( ~ ( ( in @ sK1_A @ sK2_SY107 )
=> ( subset @ ( singleton @ sK1_A ) @ sK2_SY107 ) ) )
= $true ),
inference(copy,[status(thm)],[148]) ).
thf(944,plain,
( ( ! [SX0: $i] :
( ( singleton @ SX0 )
!= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[891]) ).
thf(945,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX1
!= ( union @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[927]) ).
thf(946,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) )
| ~ ( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[895]) ).
thf(947,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX2 @ SX1 ) )
| ( subset @ ( set_union2 @ SX0 @ SX2 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[915]) ).
thf(948,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[904]) ).
thf(949,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[925]) ).
thf(950,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( proper_subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[910]) ).
thf(951,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( set_union2 @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ( ~ ( ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ( ~ ( ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( set_union2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[924]) ).
thf(952,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( proper_subset @ SX0 @ SX1 )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) )
| ( proper_subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[929]) ).
thf(953,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[942]) ).
thf(954,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ( ~ ( ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[897]) ).
thf(955,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[941]) ).
thf(956,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( singleton @ SX0 )
!= ( unordered_pair @ SX1 @ SX2 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[917]) ).
thf(957,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ SX0 @ ( union @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[898]) ).
thf(958,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( set_difference @ SX0 @ SX2 ) @ ( set_difference @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[906]) ).
thf(959,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[918]) ).
thf(960,plain,
( ( ! [SX0: $i] :
( ~ ( subset @ SX0 @ empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[909]) ).
thf(961,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX0 != SX1 )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[919]) ).
thf(962,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SX0 @ SX1 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) ) )
| ~ ~ ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[908]) ).
thf(963,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( set_intersection2 @ SX0 @ SX2 ) @ ( set_intersection2 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[903]) ).
thf(964,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( set_difference @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( set_difference @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[928]) ).
thf(965,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( in @ SX2 @ SX0 )
| ( subset @ SX0 @ ( set_difference @ SX1 @ ( singleton @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[896]) ).
thf(966,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) )
| ~ ( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[921]) ).
thf(967,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_union2 @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[899]) ).
thf(968,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX2 ) )
| ( subset @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[902]) ).
thf(969,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX1
!= ( powerset @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[922]) ).
thf(970,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( disjoint @ ( singleton @ SX0 ) @ SX1 )
| ~ ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[893]) ).
thf(971,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX1
!= ( singleton @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) )
| ~ ( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) )
| ~ ( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[920]) ).
thf(972,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( in @ SX0 @ SX1 )
| ( disjoint @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[894]) ).
thf(973,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( singleton @ SX0 )
!= ( unordered_pair @ SX1 @ SX2 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[916]) ).
thf(974,plain,
( ( ~ ( ~ ( in @ sK1_A @ sK2_SY107 )
| ( subset @ ( singleton @ sK1_A ) @ sK2_SY107 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[943]) ).
thf(975,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( ( set_union2 @ ( singleton @ SX0 ) @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[892]) ).
thf(976,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( set_intersection2 @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( set_intersection2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[926]) ).
thf(977,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( disjoint @ SX1 @ SX2 ) )
| ( disjoint @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[911]) ).
thf(978,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( unordered_pair @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ( ~ ( ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ( ~ ( ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( unordered_pair @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[923]) ).
thf(979,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX0 @ SX2 ) )
| ( subset @ SX0 @ ( set_intersection2 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[901]) ).
thf(980,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ ( singleton @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[913]) ).
thf(981,plain,
! [SV105: $i] :
( ( ! [SY231: $i] : ( subset @ ( set_intersection2 @ SV105 @ SY231 ) @ SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(982,plain,
! [SV106: $i] :
( ( subset @ empty_set @ SV106 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(983,plain,
! [SV107: $i] :
( ( ! [SY232: $i] : ( subset @ ( set_difference @ SV107 @ SY232 ) @ SV107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(984,plain,
! [SV108: $i] :
( ( ( unordered_pair @ SV108 @ SV108 )
= ( singleton @ SV108 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[912]) ).
thf(985,plain,
! [SV109: $i] :
( ( ! [SY233: $i] : ( subset @ SV109 @ ( set_union2 @ SV109 @ SY233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(986,plain,
! [SV110: $i] :
( ( ! [SY234: $i] : ( subset @ SV110 @ SV110 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[940]) ).
thf(987,plain,
! [SV111: $i] :
( ( ( singleton @ SV111 )
!= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[944]) ).
thf(988,plain,
! [SV112: $i] :
( ( ! [SY235: $i] :
~ ( ~ ( ( SY235
!= ( union @ SV112 ) )
| ! [SY236: $i] :
~ ( ~ ( ~ ( in @ SY236 @ SY235 )
| ~ ! [SY237: $i] :
~ ~ ( ~ ( in @ SY236 @ SY237 )
| ~ ( in @ SY237 @ SV112 ) ) )
| ~ ( ~ ~ ! [SY238: $i] :
~ ~ ( ~ ( in @ SY236 @ SY238 )
| ~ ( in @ SY238 @ SV112 ) )
| ( in @ SY236 @ SY235 ) ) ) )
| ~ ( ~ ! [SY239: $i] :
~ ( ~ ( ~ ( in @ SY239 @ SY235 )
| ~ ! [SY240: $i] :
~ ~ ( ~ ( in @ SY239 @ SY240 )
| ~ ( in @ SY240 @ SV112 ) ) )
| ~ ( ~ ~ ! [SY241: $i] :
~ ~ ( ~ ( in @ SY239 @ SY241 )
| ~ ( in @ SY241 @ SV112 ) )
| ( in @ SY239 @ SY235 ) ) )
| ( SY235
= ( union @ SV112 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(989,plain,
! [SV113: $i] :
( ( ! [SY242: $i] :
~ ( ~ ( ~ ( subset @ ( singleton @ SV113 ) @ SY242 )
| ( in @ SV113 @ SY242 ) )
| ~ ( ~ ( in @ SV113 @ SY242 )
| ( subset @ ( singleton @ SV113 ) @ SY242 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(990,plain,
! [SV114: $i] :
( ( ! [SY243: $i,SY244: $i] :
( ~ ~ ( ~ ( subset @ SV114 @ SY243 )
| ~ ( subset @ SY244 @ SY243 ) )
| ( subset @ ( set_union2 @ SV114 @ SY244 ) @ SY243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(991,plain,
! [SV115: $i] :
( ( ! [SY245: $i] :
( ~ ( subset @ SV115 @ SY245 )
| ( ( set_intersection2 @ SV115 @ SY245 )
= SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(992,plain,
! [SV116: $i] :
( ( ! [SY246: $i] :
~ ( ~ ( ~ ( subset @ SV116 @ SY246 )
| ! [SY247: $i] :
( ~ ( in @ SY247 @ SV116 )
| ( in @ SY247 @ SY246 ) ) )
| ~ ( ~ ! [SY248: $i] :
( ~ ( in @ SY248 @ SV116 )
| ( in @ SY248 @ SY246 ) )
| ( subset @ SV116 @ SY246 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[949]) ).
thf(993,plain,
! [SV117: $i] :
( ( ! [SY249: $i] :
~ ~ ( ~ ( subset @ SV117 @ SY249 )
| ~ ( proper_subset @ SY249 @ SV117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(994,plain,
! [SV118: $i] :
( ( ! [SY250: $i,SY251: $i] :
~ ( ~ ( ( SY251
!= ( set_union2 @ SV118 @ SY250 ) )
| ! [SY252: $i] :
~ ( ~ ( ~ ( in @ SY252 @ SY251 )
| ( in @ SY252 @ SV118 )
| ( in @ SY252 @ SY250 ) )
| ~ ( ~ ( ( in @ SY252 @ SV118 )
| ( in @ SY252 @ SY250 ) )
| ( in @ SY252 @ SY251 ) ) ) )
| ~ ( ~ ! [SY253: $i] :
~ ( ~ ( ~ ( in @ SY253 @ SY251 )
| ( in @ SY253 @ SV118 )
| ( in @ SY253 @ SY250 ) )
| ~ ( ~ ( ( in @ SY253 @ SV118 )
| ( in @ SY253 @ SY250 ) )
| ( in @ SY253 @ SY251 ) ) )
| ( SY251
= ( set_union2 @ SV118 @ SY250 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(995,plain,
! [SV119: $i] :
( ( ! [SY254: $i] :
~ ( ~ ( ~ ( proper_subset @ SV119 @ SY254 )
| ~ ( ~ ( subset @ SV119 @ SY254 )
| ~ ( ( SV119 != SY254 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV119 @ SY254 )
| ~ ( ( SV119 != SY254 ) ) )
| ( proper_subset @ SV119 @ SY254 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(996,plain,
! [SV120: $i] :
( ( ! [SY255: $i] :
~ ~ ( ~ ( in @ SV120 @ SY255 )
| ~ ( empty @ SY255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(997,plain,
! [SV121: $i] :
( ( ! [SY256: $i] :
~ ( ~ ( ~ ( subset @ SV121 @ ( singleton @ SY256 ) )
| ( SV121 = empty_set )
| ( SV121
= ( singleton @ SY256 ) ) )
| ~ ( ~ ( ( SV121 = empty_set )
| ( SV121
= ( singleton @ SY256 ) ) )
| ( subset @ SV121 @ ( singleton @ SY256 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(998,plain,
! [SV122: $i] :
( ( ! [SY257: $i] :
( ~ ! [SY258: $i] :
~ ( ~ ( ~ ( in @ SY258 @ SV122 )
| ( in @ SY258 @ SY257 ) )
| ~ ( ~ ( in @ SY258 @ SY257 )
| ( in @ SY258 @ SV122 ) ) )
| ( SV122 = SY257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(999,plain,
! [SV123: $i] :
( ( ! [SY259: $i,SY260: $i] :
( ( ( singleton @ SV123 )
!= ( unordered_pair @ SY259 @ SY260 ) )
| ( SY259 = SY260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[956]) ).
thf(1000,plain,
! [SV124: $i] :
( ( ! [SY261: $i] :
( ~ ( in @ SV124 @ SY261 )
| ( subset @ SV124 @ ( union @ SY261 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(1001,plain,
! [SV125: $i] :
( ( ! [SY262: $i,SY263: $i] :
( ~ ( subset @ SV125 @ SY262 )
| ( subset @ ( set_difference @ SV125 @ SY263 ) @ ( set_difference @ SY262 @ SY263 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1002,plain,
! [SV126: $i] :
( ( ! [SY264: $i] :
( ~ ( in @ SV126 @ SY264 )
| ~ ( in @ SY264 @ SV126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1003,plain,
! [SV127: $i] :
( ( ~ ( subset @ SV127 @ empty_set )
| ( SV127 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[960]) ).
thf(1004,plain,
! [SV128: $i] :
( ( ! [SY265: $i] :
~ ( ~ ( ( SV128 != SY265 )
| ~ ( ~ ( subset @ SV128 @ SY265 )
| ~ ( subset @ SY265 @ SV128 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV128 @ SY265 )
| ~ ( subset @ SY265 @ SV128 ) )
| ( SV128 = SY265 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1005,plain,
! [SV129: $i] :
( ( ! [SY266: $i] :
~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SV129 @ SY266 )
| ~ ! [SY267: $i] :
~ ~ ( ~ ( in @ SY267 @ SV129 )
| ~ ( in @ SY267 @ SY266 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY268: $i] :
~ ~ ( ~ ( in @ SY268 @ SV129 )
| ~ ( in @ SY268 @ SY266 ) )
| ~ ( disjoint @ SV129 @ SY266 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1006,plain,
! [SV130: $i] :
( ( ! [SY269: $i,SY270: $i] :
( ~ ( subset @ SV130 @ SY269 )
| ( subset @ ( set_intersection2 @ SV130 @ SY270 ) @ ( set_intersection2 @ SY269 @ SY270 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[963]) ).
thf(1007,plain,
! [SV131: $i] :
( ( ! [SY271: $i,SY272: $i] :
~ ( ~ ( ( SY272
!= ( set_difference @ SV131 @ SY271 ) )
| ! [SY273: $i] :
~ ( ~ ( ~ ( in @ SY273 @ SY272 )
| ~ ( ~ ( in @ SY273 @ SV131 )
| ~ ~ ( in @ SY273 @ SY271 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY273 @ SV131 )
| ~ ~ ( in @ SY273 @ SY271 ) )
| ( in @ SY273 @ SY272 ) ) ) )
| ~ ( ~ ! [SY274: $i] :
~ ( ~ ( ~ ( in @ SY274 @ SY272 )
| ~ ( ~ ( in @ SY274 @ SV131 )
| ~ ~ ( in @ SY274 @ SY271 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY274 @ SV131 )
| ~ ~ ( in @ SY274 @ SY271 ) )
| ( in @ SY274 @ SY272 ) ) )
| ( SY272
= ( set_difference @ SV131 @ SY271 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[964]) ).
thf(1008,plain,
! [SV132: $i] :
( ( ! [SY275: $i,SY276: $i] :
( ~ ( subset @ SV132 @ SY275 )
| ( in @ SY276 @ SV132 )
| ( subset @ SV132 @ ( set_difference @ SY275 @ ( singleton @ SY276 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[965]) ).
thf(1009,plain,
! [SV133: $i] :
( ( ~ ( ~ ( ( SV133 != empty_set )
| ! [SY277: $i] :
~ ( in @ SY277 @ SV133 ) )
| ~ ( ~ ! [SY278: $i] :
~ ( in @ SY278 @ SV133 )
| ( SV133 = empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(1010,plain,
! [SV134: $i] :
( ( ! [SY279: $i] :
( ~ ( subset @ SV134 @ SY279 )
| ( ( set_union2 @ SV134 @ SY279 )
= SY279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1011,plain,
! [SV135: $i] :
( ( ! [SY280: $i,SY281: $i] :
( ~ ~ ( ~ ( subset @ SV135 @ SY280 )
| ~ ( subset @ SY280 @ SY281 ) )
| ( subset @ SV135 @ SY281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1012,plain,
! [SV136: $i] :
( ( ! [SY282: $i] :
~ ( ~ ( ( SY282
!= ( powerset @ SV136 ) )
| ! [SY283: $i] :
~ ( ~ ( ~ ( in @ SY283 @ SY282 )
| ( subset @ SY283 @ SV136 ) )
| ~ ( ~ ( subset @ SY283 @ SV136 )
| ( in @ SY283 @ SY282 ) ) ) )
| ~ ( ~ ! [SY284: $i] :
~ ( ~ ( ~ ( in @ SY284 @ SY282 )
| ( subset @ SY284 @ SV136 ) )
| ~ ( ~ ( subset @ SY284 @ SV136 )
| ( in @ SY284 @ SY282 ) ) )
| ( SY282
= ( powerset @ SV136 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1013,plain,
! [SV137: $i] :
( ( ! [SY285: $i] :
~ ~ ( ~ ( disjoint @ ( singleton @ SV137 ) @ SY285 )
| ~ ( in @ SV137 @ SY285 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1014,plain,
! [SV138: $i] :
( ( ! [SY286: $i] :
~ ( ~ ( ( SY286
!= ( singleton @ SV138 ) )
| ! [SY287: $i] :
~ ( ~ ( ~ ( in @ SY287 @ SY286 )
| ( SY287 = SV138 ) )
| ~ ( ( SY287 != SV138 )
| ( in @ SY287 @ SY286 ) ) ) )
| ~ ( ~ ! [SY288: $i] :
~ ( ~ ( ~ ( in @ SY288 @ SY286 )
| ( SY288 = SV138 ) )
| ~ ( ( SY288 != SV138 )
| ( in @ SY288 @ SY286 ) ) )
| ( SY286
= ( singleton @ SV138 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1015,plain,
! [SV139: $i] :
( ( ! [SY289: $i] :
( ~ ~ ( in @ SV139 @ SY289 )
| ( disjoint @ ( singleton @ SV139 ) @ SY289 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1016,plain,
! [SV140: $i] :
( ( ! [SY290: $i,SY291: $i] :
( ( ( singleton @ SV140 )
!= ( unordered_pair @ SY290 @ SY291 ) )
| ( SV140 = SY290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1017,plain,
( ( ~ ( in @ sK1_A @ sK2_SY107 )
| ( subset @ ( singleton @ sK1_A ) @ sK2_SY107 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[974]) ).
thf(1018,plain,
! [SV141: $i] :
( ( ! [SY292: $i] :
( ~ ( in @ SV141 @ SY292 )
| ( ( set_union2 @ ( singleton @ SV141 ) @ SY292 )
= SY292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1019,plain,
! [SV142: $i] :
( ( ! [SY293: $i,SY294: $i] :
~ ( ~ ( ( SY294
!= ( set_intersection2 @ SV142 @ SY293 ) )
| ! [SY295: $i] :
~ ( ~ ( ~ ( in @ SY295 @ SY294 )
| ~ ( ~ ( in @ SY295 @ SV142 )
| ~ ( in @ SY295 @ SY293 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY295 @ SV142 )
| ~ ( in @ SY295 @ SY293 ) )
| ( in @ SY295 @ SY294 ) ) ) )
| ~ ( ~ ! [SY296: $i] :
~ ( ~ ( ~ ( in @ SY296 @ SY294 )
| ~ ( ~ ( in @ SY296 @ SV142 )
| ~ ( in @ SY296 @ SY293 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY296 @ SV142 )
| ~ ( in @ SY296 @ SY293 ) )
| ( in @ SY296 @ SY294 ) ) )
| ( SY294
= ( set_intersection2 @ SV142 @ SY293 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1020,plain,
! [SV143: $i] :
( ( ! [SY297: $i,SY298: $i] :
( ~ ~ ( ~ ( subset @ SV143 @ SY297 )
| ~ ( disjoint @ SY297 @ SY298 ) )
| ( disjoint @ SV143 @ SY298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[977]) ).
thf(1021,plain,
! [SV144: $i] :
( ( ! [SY299: $i,SY300: $i] :
~ ( ~ ( ( SY300
!= ( unordered_pair @ SV144 @ SY299 ) )
| ! [SY301: $i] :
~ ( ~ ( ~ ( in @ SY301 @ SY300 )
| ( SY301 = SV144 )
| ( SY301 = SY299 ) )
| ~ ( ~ ( ( SY301 = SV144 )
| ( SY301 = SY299 ) )
| ( in @ SY301 @ SY300 ) ) ) )
| ~ ( ~ ! [SY302: $i] :
~ ( ~ ( ~ ( in @ SY302 @ SY300 )
| ( SY302 = SV144 )
| ( SY302 = SY299 ) )
| ~ ( ~ ( ( SY302 = SV144 )
| ( SY302 = SY299 ) )
| ( in @ SY302 @ SY300 ) ) )
| ( SY300
= ( unordered_pair @ SV144 @ SY299 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(1022,plain,
! [SV145: $i] :
( ( ! [SY303: $i,SY304: $i] :
( ~ ~ ( ~ ( subset @ SV145 @ SY303 )
| ~ ( subset @ SV145 @ SY304 ) )
| ( subset @ SV145 @ ( set_intersection2 @ SY303 @ SY304 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(1023,plain,
! [SV146: $i] :
( ( ! [SY305: $i] :
( ~ ( subset @ ( singleton @ SV146 ) @ ( singleton @ SY305 ) )
| ( SV146 = SY305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[980]) ).
thf(1024,plain,
! [SV147: $i,SV105: $i] :
( ( subset @ ( set_intersection2 @ SV105 @ SV147 ) @ SV105 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[981]) ).
thf(1025,plain,
! [SV148: $i,SV107: $i] :
( ( subset @ ( set_difference @ SV107 @ SV148 ) @ SV107 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1026,plain,
! [SV149: $i,SV109: $i] :
( ( subset @ SV109 @ ( set_union2 @ SV109 @ SV149 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1027,plain,
! [SV110: $i] :
( ( subset @ SV110 @ SV110 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1028,plain,
! [SV111: $i] :
( ( ( singleton @ SV111 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[987]) ).
thf(1029,plain,
! [SV112: $i,SV151: $i] :
( ( ~ ( ~ ( ( SV151
!= ( union @ SV112 ) )
| ! [SY306: $i] :
~ ( ~ ( ~ ( in @ SY306 @ SV151 )
| ~ ! [SY237: $i] :
~ ~ ( ~ ( in @ SY306 @ SY237 )
| ~ ( in @ SY237 @ SV112 ) ) )
| ~ ( ~ ~ ! [SY238: $i] :
~ ~ ( ~ ( in @ SY306 @ SY238 )
| ~ ( in @ SY238 @ SV112 ) )
| ( in @ SY306 @ SV151 ) ) ) )
| ~ ( ~ ! [SY309: $i] :
~ ( ~ ( ~ ( in @ SY309 @ SV151 )
| ~ ! [SY240: $i] :
~ ~ ( ~ ( in @ SY309 @ SY240 )
| ~ ( in @ SY240 @ SV112 ) ) )
| ~ ( ~ ~ ! [SY241: $i] :
~ ~ ( ~ ( in @ SY309 @ SY241 )
| ~ ( in @ SY241 @ SV112 ) )
| ( in @ SY309 @ SV151 ) ) )
| ( SV151
= ( union @ SV112 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1030,plain,
! [SV152: $i,SV113: $i] :
( ( ~ ( ~ ( ~ ( subset @ ( singleton @ SV113 ) @ SV152 )
| ( in @ SV113 @ SV152 ) )
| ~ ( ~ ( in @ SV113 @ SV152 )
| ( subset @ ( singleton @ SV113 ) @ SV152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[989]) ).
thf(1031,plain,
! [SV153: $i,SV114: $i] :
( ( ! [SY312: $i] :
( ~ ~ ( ~ ( subset @ SV114 @ SV153 )
| ~ ( subset @ SY312 @ SV153 ) )
| ( subset @ ( set_union2 @ SV114 @ SY312 ) @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[990]) ).
thf(1032,plain,
! [SV154: $i,SV115: $i] :
( ( ~ ( subset @ SV115 @ SV154 )
| ( ( set_intersection2 @ SV115 @ SV154 )
= SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(1033,plain,
! [SV155: $i,SV116: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV116 @ SV155 )
| ! [SY313: $i] :
( ~ ( in @ SY313 @ SV116 )
| ( in @ SY313 @ SV155 ) ) )
| ~ ( ~ ! [SY314: $i] :
( ~ ( in @ SY314 @ SV116 )
| ( in @ SY314 @ SV155 ) )
| ( subset @ SV116 @ SV155 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[992]) ).
thf(1034,plain,
! [SV156: $i,SV117: $i] :
( ( ~ ~ ( ~ ( subset @ SV117 @ SV156 )
| ~ ( proper_subset @ SV156 @ SV117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1035,plain,
! [SV157: $i,SV118: $i] :
( ( ! [SY315: $i] :
~ ( ~ ( ( SY315
!= ( set_union2 @ SV118 @ SV157 ) )
| ! [SY316: $i] :
~ ( ~ ( ~ ( in @ SY316 @ SY315 )
| ( in @ SY316 @ SV118 )
| ( in @ SY316 @ SV157 ) )
| ~ ( ~ ( ( in @ SY316 @ SV118 )
| ( in @ SY316 @ SV157 ) )
| ( in @ SY316 @ SY315 ) ) ) )
| ~ ( ~ ! [SY317: $i] :
~ ( ~ ( ~ ( in @ SY317 @ SY315 )
| ( in @ SY317 @ SV118 )
| ( in @ SY317 @ SV157 ) )
| ~ ( ~ ( ( in @ SY317 @ SV118 )
| ( in @ SY317 @ SV157 ) )
| ( in @ SY317 @ SY315 ) ) )
| ( SY315
= ( set_union2 @ SV118 @ SV157 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1036,plain,
! [SV158: $i,SV119: $i] :
( ( ~ ( ~ ( ~ ( proper_subset @ SV119 @ SV158 )
| ~ ( ~ ( subset @ SV119 @ SV158 )
| ~ ( ( SV119 != SV158 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV119 @ SV158 )
| ~ ( ( SV119 != SV158 ) ) )
| ( proper_subset @ SV119 @ SV158 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1037,plain,
! [SV159: $i,SV120: $i] :
( ( ~ ~ ( ~ ( in @ SV120 @ SV159 )
| ~ ( empty @ SV159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1038,plain,
! [SV160: $i,SV121: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV121 @ ( singleton @ SV160 ) )
| ( SV121 = empty_set )
| ( SV121
= ( singleton @ SV160 ) ) )
| ~ ( ~ ( ( SV121 = empty_set )
| ( SV121
= ( singleton @ SV160 ) ) )
| ( subset @ SV121 @ ( singleton @ SV160 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[997]) ).
thf(1039,plain,
! [SV161: $i,SV122: $i] :
( ( ~ ! [SY318: $i] :
~ ( ~ ( ~ ( in @ SY318 @ SV122 )
| ( in @ SY318 @ SV161 ) )
| ~ ( ~ ( in @ SY318 @ SV161 )
| ( in @ SY318 @ SV122 ) ) )
| ( SV122 = SV161 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1040,plain,
! [SV162: $i,SV123: $i] :
( ( ! [SY319: $i] :
( ( ( singleton @ SV123 )
!= ( unordered_pair @ SV162 @ SY319 ) )
| ( SV162 = SY319 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[999]) ).
thf(1041,plain,
! [SV163: $i,SV124: $i] :
( ( ~ ( in @ SV124 @ SV163 )
| ( subset @ SV124 @ ( union @ SV163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1000]) ).
thf(1042,plain,
! [SV164: $i,SV125: $i] :
( ( ! [SY320: $i] :
( ~ ( subset @ SV125 @ SV164 )
| ( subset @ ( set_difference @ SV125 @ SY320 ) @ ( set_difference @ SV164 @ SY320 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1001]) ).
thf(1043,plain,
! [SV165: $i,SV126: $i] :
( ( ~ ( in @ SV126 @ SV165 )
| ~ ( in @ SV165 @ SV126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1044,plain,
! [SV127: $i] :
( ( ( ~ ( subset @ SV127 @ empty_set ) )
= $true )
| ( ( SV127 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1003]) ).
thf(1045,plain,
! [SV166: $i,SV128: $i] :
( ( ~ ( ~ ( ( SV128 != SV166 )
| ~ ( ~ ( subset @ SV128 @ SV166 )
| ~ ( subset @ SV166 @ SV128 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV128 @ SV166 )
| ~ ( subset @ SV166 @ SV128 ) )
| ( SV128 = SV166 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1046,plain,
! [SV167: $i,SV129: $i] :
( ( ~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SV129 @ SV167 )
| ~ ! [SY321: $i] :
~ ~ ( ~ ( in @ SY321 @ SV129 )
| ~ ( in @ SY321 @ SV167 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY322: $i] :
~ ~ ( ~ ( in @ SY322 @ SV129 )
| ~ ( in @ SY322 @ SV167 ) )
| ~ ( disjoint @ SV129 @ SV167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1047,plain,
! [SV168: $i,SV130: $i] :
( ( ! [SY323: $i] :
( ~ ( subset @ SV130 @ SV168 )
| ( subset @ ( set_intersection2 @ SV130 @ SY323 ) @ ( set_intersection2 @ SV168 @ SY323 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1048,plain,
! [SV169: $i,SV131: $i] :
( ( ! [SY324: $i] :
~ ( ~ ( ( SY324
!= ( set_difference @ SV131 @ SV169 ) )
| ! [SY325: $i] :
~ ( ~ ( ~ ( in @ SY325 @ SY324 )
| ~ ( ~ ( in @ SY325 @ SV131 )
| ~ ~ ( in @ SY325 @ SV169 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY325 @ SV131 )
| ~ ~ ( in @ SY325 @ SV169 ) )
| ( in @ SY325 @ SY324 ) ) ) )
| ~ ( ~ ! [SY326: $i] :
~ ( ~ ( ~ ( in @ SY326 @ SY324 )
| ~ ( ~ ( in @ SY326 @ SV131 )
| ~ ~ ( in @ SY326 @ SV169 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY326 @ SV131 )
| ~ ~ ( in @ SY326 @ SV169 ) )
| ( in @ SY326 @ SY324 ) ) )
| ( SY324
= ( set_difference @ SV131 @ SV169 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1007]) ).
thf(1049,plain,
! [SV170: $i,SV132: $i] :
( ( ! [SY327: $i] :
( ~ ( subset @ SV132 @ SV170 )
| ( in @ SY327 @ SV132 )
| ( subset @ SV132 @ ( set_difference @ SV170 @ ( singleton @ SY327 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1050,plain,
! [SV133: $i] :
( ( ~ ( ( SV133 != empty_set )
| ! [SY277: $i] :
~ ( in @ SY277 @ SV133 ) )
| ~ ( ~ ! [SY278: $i] :
~ ( in @ SY278 @ SV133 )
| ( SV133 = empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1009]) ).
thf(1051,plain,
! [SV171: $i,SV134: $i] :
( ( ~ ( subset @ SV134 @ SV171 )
| ( ( set_union2 @ SV134 @ SV171 )
= SV171 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1052,plain,
! [SV172: $i,SV135: $i] :
( ( ! [SY328: $i] :
( ~ ~ ( ~ ( subset @ SV135 @ SV172 )
| ~ ( subset @ SV172 @ SY328 ) )
| ( subset @ SV135 @ SY328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1053,plain,
! [SV136: $i,SV173: $i] :
( ( ~ ( ~ ( ( SV173
!= ( powerset @ SV136 ) )
| ! [SY329: $i] :
~ ( ~ ( ~ ( in @ SY329 @ SV173 )
| ( subset @ SY329 @ SV136 ) )
| ~ ( ~ ( subset @ SY329 @ SV136 )
| ( in @ SY329 @ SV173 ) ) ) )
| ~ ( ~ ! [SY330: $i] :
~ ( ~ ( ~ ( in @ SY330 @ SV173 )
| ( subset @ SY330 @ SV136 ) )
| ~ ( ~ ( subset @ SY330 @ SV136 )
| ( in @ SY330 @ SV173 ) ) )
| ( SV173
= ( powerset @ SV136 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1054,plain,
! [SV174: $i,SV137: $i] :
( ( ~ ~ ( ~ ( disjoint @ ( singleton @ SV137 ) @ SV174 )
| ~ ( in @ SV137 @ SV174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1013]) ).
thf(1055,plain,
! [SV138: $i,SV175: $i] :
( ( ~ ( ~ ( ( SV175
!= ( singleton @ SV138 ) )
| ! [SY331: $i] :
~ ( ~ ( ~ ( in @ SY331 @ SV175 )
| ( SY331 = SV138 ) )
| ~ ( ( SY331 != SV138 )
| ( in @ SY331 @ SV175 ) ) ) )
| ~ ( ~ ! [SY332: $i] :
~ ( ~ ( ~ ( in @ SY332 @ SV175 )
| ( SY332 = SV138 ) )
| ~ ( ( SY332 != SV138 )
| ( in @ SY332 @ SV175 ) ) )
| ( SV175
= ( singleton @ SV138 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1014]) ).
thf(1056,plain,
! [SV176: $i,SV139: $i] :
( ( ~ ~ ( in @ SV139 @ SV176 )
| ( disjoint @ ( singleton @ SV139 ) @ SV176 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1015]) ).
thf(1057,plain,
! [SV177: $i,SV140: $i] :
( ( ! [SY333: $i] :
( ( ( singleton @ SV140 )
!= ( unordered_pair @ SV177 @ SY333 ) )
| ( SV140 = SV177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1058,plain,
( ( ~ ( in @ sK1_A @ sK2_SY107 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1017]) ).
thf(1059,plain,
( ( subset @ ( singleton @ sK1_A ) @ sK2_SY107 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1017]) ).
thf(1060,plain,
! [SV178: $i,SV141: $i] :
( ( ~ ( in @ SV141 @ SV178 )
| ( ( set_union2 @ ( singleton @ SV141 ) @ SV178 )
= SV178 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1061,plain,
! [SV179: $i,SV142: $i] :
( ( ! [SY334: $i] :
~ ( ~ ( ( SY334
!= ( set_intersection2 @ SV142 @ SV179 ) )
| ! [SY335: $i] :
~ ( ~ ( ~ ( in @ SY335 @ SY334 )
| ~ ( ~ ( in @ SY335 @ SV142 )
| ~ ( in @ SY335 @ SV179 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY335 @ SV142 )
| ~ ( in @ SY335 @ SV179 ) )
| ( in @ SY335 @ SY334 ) ) ) )
| ~ ( ~ ! [SY336: $i] :
~ ( ~ ( ~ ( in @ SY336 @ SY334 )
| ~ ( ~ ( in @ SY336 @ SV142 )
| ~ ( in @ SY336 @ SV179 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY336 @ SV142 )
| ~ ( in @ SY336 @ SV179 ) )
| ( in @ SY336 @ SY334 ) ) )
| ( SY334
= ( set_intersection2 @ SV142 @ SV179 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1019]) ).
thf(1062,plain,
! [SV180: $i,SV143: $i] :
( ( ! [SY337: $i] :
( ~ ~ ( ~ ( subset @ SV143 @ SV180 )
| ~ ( disjoint @ SV180 @ SY337 ) )
| ( disjoint @ SV143 @ SY337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1063,plain,
! [SV181: $i,SV144: $i] :
( ( ! [SY338: $i] :
~ ( ~ ( ( SY338
!= ( unordered_pair @ SV144 @ SV181 ) )
| ! [SY339: $i] :
~ ( ~ ( ~ ( in @ SY339 @ SY338 )
| ( SY339 = SV144 )
| ( SY339 = SV181 ) )
| ~ ( ~ ( ( SY339 = SV144 )
| ( SY339 = SV181 ) )
| ( in @ SY339 @ SY338 ) ) ) )
| ~ ( ~ ! [SY340: $i] :
~ ( ~ ( ~ ( in @ SY340 @ SY338 )
| ( SY340 = SV144 )
| ( SY340 = SV181 ) )
| ~ ( ~ ( ( SY340 = SV144 )
| ( SY340 = SV181 ) )
| ( in @ SY340 @ SY338 ) ) )
| ( SY338
= ( unordered_pair @ SV144 @ SV181 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1064,plain,
! [SV182: $i,SV145: $i] :
( ( ! [SY341: $i] :
( ~ ~ ( ~ ( subset @ SV145 @ SV182 )
| ~ ( subset @ SV145 @ SY341 ) )
| ( subset @ SV145 @ ( set_intersection2 @ SV182 @ SY341 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1065,plain,
! [SV183: $i,SV146: $i] :
( ( ~ ( subset @ ( singleton @ SV146 ) @ ( singleton @ SV183 ) )
| ( SV146 = SV183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1023]) ).
thf(1066,plain,
! [SV112: $i,SV151: $i] :
( ( ~ ( ( SV151
!= ( union @ SV112 ) )
| ! [SY306: $i] :
~ ( ~ ( ~ ( in @ SY306 @ SV151 )
| ~ ! [SY237: $i] :
~ ~ ( ~ ( in @ SY306 @ SY237 )
| ~ ( in @ SY237 @ SV112 ) ) )
| ~ ( ~ ~ ! [SY238: $i] :
~ ~ ( ~ ( in @ SY306 @ SY238 )
| ~ ( in @ SY238 @ SV112 ) )
| ( in @ SY306 @ SV151 ) ) ) )
| ~ ( ~ ! [SY309: $i] :
~ ( ~ ( ~ ( in @ SY309 @ SV151 )
| ~ ! [SY240: $i] :
~ ~ ( ~ ( in @ SY309 @ SY240 )
| ~ ( in @ SY240 @ SV112 ) ) )
| ~ ( ~ ~ ! [SY241: $i] :
~ ~ ( ~ ( in @ SY309 @ SY241 )
| ~ ( in @ SY241 @ SV112 ) )
| ( in @ SY309 @ SV151 ) ) )
| ( SV151
= ( union @ SV112 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1029]) ).
thf(1067,plain,
! [SV152: $i,SV113: $i] :
( ( ~ ( ~ ( subset @ ( singleton @ SV113 ) @ SV152 )
| ( in @ SV113 @ SV152 ) )
| ~ ( ~ ( in @ SV113 @ SV152 )
| ( subset @ ( singleton @ SV113 ) @ SV152 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1030]) ).
thf(1068,plain,
! [SV184: $i,SV153: $i,SV114: $i] :
( ( ~ ~ ( ~ ( subset @ SV114 @ SV153 )
| ~ ( subset @ SV184 @ SV153 ) )
| ( subset @ ( set_union2 @ SV114 @ SV184 ) @ SV153 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1069,plain,
! [SV154: $i,SV115: $i] :
( ( ( ~ ( subset @ SV115 @ SV154 ) )
= $true )
| ( ( ( set_intersection2 @ SV115 @ SV154 )
= SV115 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1032]) ).
thf(1070,plain,
! [SV155: $i,SV116: $i] :
( ( ~ ( ~ ( subset @ SV116 @ SV155 )
| ! [SY313: $i] :
( ~ ( in @ SY313 @ SV116 )
| ( in @ SY313 @ SV155 ) ) )
| ~ ( ~ ! [SY314: $i] :
( ~ ( in @ SY314 @ SV116 )
| ( in @ SY314 @ SV155 ) )
| ( subset @ SV116 @ SV155 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1033]) ).
thf(1071,plain,
! [SV156: $i,SV117: $i] :
( ( ~ ( ~ ( subset @ SV117 @ SV156 )
| ~ ( proper_subset @ SV156 @ SV117 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1034]) ).
thf(1072,plain,
! [SV157: $i,SV118: $i,SV185: $i] :
( ( ~ ( ~ ( ( SV185
!= ( set_union2 @ SV118 @ SV157 ) )
| ! [SY342: $i] :
~ ( ~ ( ~ ( in @ SY342 @ SV185 )
| ( in @ SY342 @ SV118 )
| ( in @ SY342 @ SV157 ) )
| ~ ( ~ ( ( in @ SY342 @ SV118 )
| ( in @ SY342 @ SV157 ) )
| ( in @ SY342 @ SV185 ) ) ) )
| ~ ( ~ ! [SY343: $i] :
~ ( ~ ( ~ ( in @ SY343 @ SV185 )
| ( in @ SY343 @ SV118 )
| ( in @ SY343 @ SV157 ) )
| ~ ( ~ ( ( in @ SY343 @ SV118 )
| ( in @ SY343 @ SV157 ) )
| ( in @ SY343 @ SV185 ) ) )
| ( SV185
= ( set_union2 @ SV118 @ SV157 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1073,plain,
! [SV158: $i,SV119: $i] :
( ( ~ ( ~ ( proper_subset @ SV119 @ SV158 )
| ~ ( ~ ( subset @ SV119 @ SV158 )
| ~ ( ( SV119 != SV158 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV119 @ SV158 )
| ~ ( ( SV119 != SV158 ) ) )
| ( proper_subset @ SV119 @ SV158 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1036]) ).
thf(1074,plain,
! [SV159: $i,SV120: $i] :
( ( ~ ( ~ ( in @ SV120 @ SV159 )
| ~ ( empty @ SV159 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1037]) ).
thf(1075,plain,
! [SV160: $i,SV121: $i] :
( ( ~ ( ~ ( subset @ SV121 @ ( singleton @ SV160 ) )
| ( SV121 = empty_set )
| ( SV121
= ( singleton @ SV160 ) ) )
| ~ ( ~ ( ( SV121 = empty_set )
| ( SV121
= ( singleton @ SV160 ) ) )
| ( subset @ SV121 @ ( singleton @ SV160 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1038]) ).
thf(1076,plain,
! [SV161: $i,SV122: $i] :
( ( ( ~ ! [SY318: $i] :
~ ( ~ ( ~ ( in @ SY318 @ SV122 )
| ( in @ SY318 @ SV161 ) )
| ~ ( ~ ( in @ SY318 @ SV161 )
| ( in @ SY318 @ SV122 ) ) ) )
= $true )
| ( ( SV122 = SV161 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1039]) ).
thf(1077,plain,
! [SV186: $i,SV162: $i,SV123: $i] :
( ( ( ( singleton @ SV123 )
!= ( unordered_pair @ SV162 @ SV186 ) )
| ( SV162 = SV186 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1040]) ).
thf(1078,plain,
! [SV163: $i,SV124: $i] :
( ( ( ~ ( in @ SV124 @ SV163 ) )
= $true )
| ( ( subset @ SV124 @ ( union @ SV163 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1041]) ).
thf(1079,plain,
! [SV187: $i,SV164: $i,SV125: $i] :
( ( ~ ( subset @ SV125 @ SV164 )
| ( subset @ ( set_difference @ SV125 @ SV187 ) @ ( set_difference @ SV164 @ SV187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1042]) ).
thf(1080,plain,
! [SV165: $i,SV126: $i] :
( ( ( ~ ( in @ SV126 @ SV165 ) )
= $true )
| ( ( ~ ( in @ SV165 @ SV126 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1043]) ).
thf(1081,plain,
! [SV127: $i] :
( ( ( subset @ SV127 @ empty_set )
= $false )
| ( ( SV127 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1044]) ).
thf(1082,plain,
! [SV166: $i,SV128: $i] :
( ( ~ ( ( SV128 != SV166 )
| ~ ( ~ ( subset @ SV128 @ SV166 )
| ~ ( subset @ SV166 @ SV128 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV128 @ SV166 )
| ~ ( subset @ SV166 @ SV128 ) )
| ( SV128 = SV166 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1045]) ).
thf(1083,plain,
! [SV167: $i,SV129: $i] :
( ( ~ ~ ~ ( ~ ~ ( disjoint @ SV129 @ SV167 )
| ~ ! [SY321: $i] :
~ ~ ( ~ ( in @ SY321 @ SV129 )
| ~ ( in @ SY321 @ SV167 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY322: $i] :
~ ~ ( ~ ( in @ SY322 @ SV129 )
| ~ ( in @ SY322 @ SV167 ) )
| ~ ( disjoint @ SV129 @ SV167 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1046]) ).
thf(1084,plain,
! [SV188: $i,SV168: $i,SV130: $i] :
( ( ~ ( subset @ SV130 @ SV168 )
| ( subset @ ( set_intersection2 @ SV130 @ SV188 ) @ ( set_intersection2 @ SV168 @ SV188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1047]) ).
thf(1085,plain,
! [SV169: $i,SV131: $i,SV189: $i] :
( ( ~ ( ~ ( ( SV189
!= ( set_difference @ SV131 @ SV169 ) )
| ! [SY344: $i] :
~ ( ~ ( ~ ( in @ SY344 @ SV189 )
| ~ ( ~ ( in @ SY344 @ SV131 )
| ~ ~ ( in @ SY344 @ SV169 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY344 @ SV131 )
| ~ ~ ( in @ SY344 @ SV169 ) )
| ( in @ SY344 @ SV189 ) ) ) )
| ~ ( ~ ! [SY345: $i] :
~ ( ~ ( ~ ( in @ SY345 @ SV189 )
| ~ ( ~ ( in @ SY345 @ SV131 )
| ~ ~ ( in @ SY345 @ SV169 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY345 @ SV131 )
| ~ ~ ( in @ SY345 @ SV169 ) )
| ( in @ SY345 @ SV189 ) ) )
| ( SV189
= ( set_difference @ SV131 @ SV169 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1048]) ).
thf(1086,plain,
! [SV190: $i,SV170: $i,SV132: $i] :
( ( ~ ( subset @ SV132 @ SV170 )
| ( in @ SV190 @ SV132 )
| ( subset @ SV132 @ ( set_difference @ SV170 @ ( singleton @ SV190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1087,plain,
! [SV133: $i] :
( ( ~ ( ( SV133 != empty_set )
| ! [SY277: $i] :
~ ( in @ SY277 @ SV133 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1050]) ).
thf(1088,plain,
! [SV133: $i] :
( ( ~ ( ~ ! [SY278: $i] :
~ ( in @ SY278 @ SV133 )
| ( SV133 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1050]) ).
thf(1089,plain,
! [SV171: $i,SV134: $i] :
( ( ( ~ ( subset @ SV134 @ SV171 ) )
= $true )
| ( ( ( set_union2 @ SV134 @ SV171 )
= SV171 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1051]) ).
thf(1090,plain,
! [SV191: $i,SV172: $i,SV135: $i] :
( ( ~ ~ ( ~ ( subset @ SV135 @ SV172 )
| ~ ( subset @ SV172 @ SV191 ) )
| ( subset @ SV135 @ SV191 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1052]) ).
thf(1091,plain,
! [SV136: $i,SV173: $i] :
( ( ~ ( ( SV173
!= ( powerset @ SV136 ) )
| ! [SY329: $i] :
~ ( ~ ( ~ ( in @ SY329 @ SV173 )
| ( subset @ SY329 @ SV136 ) )
| ~ ( ~ ( subset @ SY329 @ SV136 )
| ( in @ SY329 @ SV173 ) ) ) )
| ~ ( ~ ! [SY330: $i] :
~ ( ~ ( ~ ( in @ SY330 @ SV173 )
| ( subset @ SY330 @ SV136 ) )
| ~ ( ~ ( subset @ SY330 @ SV136 )
| ( in @ SY330 @ SV173 ) ) )
| ( SV173
= ( powerset @ SV136 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1053]) ).
thf(1092,plain,
! [SV174: $i,SV137: $i] :
( ( ~ ( ~ ( disjoint @ ( singleton @ SV137 ) @ SV174 )
| ~ ( in @ SV137 @ SV174 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1054]) ).
thf(1093,plain,
! [SV138: $i,SV175: $i] :
( ( ~ ( ( SV175
!= ( singleton @ SV138 ) )
| ! [SY331: $i] :
~ ( ~ ( ~ ( in @ SY331 @ SV175 )
| ( SY331 = SV138 ) )
| ~ ( ( SY331 != SV138 )
| ( in @ SY331 @ SV175 ) ) ) )
| ~ ( ~ ! [SY332: $i] :
~ ( ~ ( ~ ( in @ SY332 @ SV175 )
| ( SY332 = SV138 ) )
| ~ ( ( SY332 != SV138 )
| ( in @ SY332 @ SV175 ) ) )
| ( SV175
= ( singleton @ SV138 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1055]) ).
thf(1094,plain,
! [SV176: $i,SV139: $i] :
( ( ( ~ ~ ( in @ SV139 @ SV176 ) )
= $true )
| ( ( disjoint @ ( singleton @ SV139 ) @ SV176 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1056]) ).
thf(1095,plain,
! [SV192: $i,SV177: $i,SV140: $i] :
( ( ( ( singleton @ SV140 )
!= ( unordered_pair @ SV177 @ SV192 ) )
| ( SV140 = SV177 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1057]) ).
thf(1096,plain,
( ( in @ sK1_A @ sK2_SY107 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1058]) ).
thf(1097,plain,
! [SV178: $i,SV141: $i] :
( ( ( ~ ( in @ SV141 @ SV178 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV141 ) @ SV178 )
= SV178 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1060]) ).
thf(1098,plain,
! [SV179: $i,SV142: $i,SV193: $i] :
( ( ~ ( ~ ( ( SV193
!= ( set_intersection2 @ SV142 @ SV179 ) )
| ! [SY346: $i] :
~ ( ~ ( ~ ( in @ SY346 @ SV193 )
| ~ ( ~ ( in @ SY346 @ SV142 )
| ~ ( in @ SY346 @ SV179 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY346 @ SV142 )
| ~ ( in @ SY346 @ SV179 ) )
| ( in @ SY346 @ SV193 ) ) ) )
| ~ ( ~ ! [SY347: $i] :
~ ( ~ ( ~ ( in @ SY347 @ SV193 )
| ~ ( ~ ( in @ SY347 @ SV142 )
| ~ ( in @ SY347 @ SV179 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY347 @ SV142 )
| ~ ( in @ SY347 @ SV179 ) )
| ( in @ SY347 @ SV193 ) ) )
| ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1061]) ).
thf(1099,plain,
! [SV194: $i,SV180: $i,SV143: $i] :
( ( ~ ~ ( ~ ( subset @ SV143 @ SV180 )
| ~ ( disjoint @ SV180 @ SV194 ) )
| ( disjoint @ SV143 @ SV194 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1062]) ).
thf(1100,plain,
! [SV181: $i,SV144: $i,SV195: $i] :
( ( ~ ( ~ ( ( SV195
!= ( unordered_pair @ SV144 @ SV181 ) )
| ! [SY348: $i] :
~ ( ~ ( ~ ( in @ SY348 @ SV195 )
| ( SY348 = SV144 )
| ( SY348 = SV181 ) )
| ~ ( ~ ( ( SY348 = SV144 )
| ( SY348 = SV181 ) )
| ( in @ SY348 @ SV195 ) ) ) )
| ~ ( ~ ! [SY349: $i] :
~ ( ~ ( ~ ( in @ SY349 @ SV195 )
| ( SY349 = SV144 )
| ( SY349 = SV181 ) )
| ~ ( ~ ( ( SY349 = SV144 )
| ( SY349 = SV181 ) )
| ( in @ SY349 @ SV195 ) ) )
| ( SV195
= ( unordered_pair @ SV144 @ SV181 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1101,plain,
! [SV196: $i,SV182: $i,SV145: $i] :
( ( ~ ~ ( ~ ( subset @ SV145 @ SV182 )
| ~ ( subset @ SV145 @ SV196 ) )
| ( subset @ SV145 @ ( set_intersection2 @ SV182 @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1102,plain,
! [SV183: $i,SV146: $i] :
( ( ( ~ ( subset @ ( singleton @ SV146 ) @ ( singleton @ SV183 ) ) )
= $true )
| ( ( SV146 = SV183 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1065]) ).
thf(1103,plain,
! [SV112: $i,SV151: $i] :
( ( ~ ( ( SV151
!= ( union @ SV112 ) )
| ! [SY306: $i] :
~ ( ~ ( ~ ( in @ SY306 @ SV151 )
| ~ ! [SY237: $i] :
~ ~ ( ~ ( in @ SY306 @ SY237 )
| ~ ( in @ SY237 @ SV112 ) ) )
| ~ ( ~ ~ ! [SY238: $i] :
~ ~ ( ~ ( in @ SY306 @ SY238 )
| ~ ( in @ SY238 @ SV112 ) )
| ( in @ SY306 @ SV151 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1066]) ).
thf(1104,plain,
! [SV112: $i,SV151: $i] :
( ( ~ ( ~ ! [SY309: $i] :
~ ( ~ ( ~ ( in @ SY309 @ SV151 )
| ~ ! [SY240: $i] :
~ ~ ( ~ ( in @ SY309 @ SY240 )
| ~ ( in @ SY240 @ SV112 ) ) )
| ~ ( ~ ~ ! [SY241: $i] :
~ ~ ( ~ ( in @ SY309 @ SY241 )
| ~ ( in @ SY241 @ SV112 ) )
| ( in @ SY309 @ SV151 ) ) )
| ( SV151
= ( union @ SV112 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1066]) ).
thf(1105,plain,
! [SV152: $i,SV113: $i] :
( ( ~ ( ~ ( subset @ ( singleton @ SV113 ) @ SV152 )
| ( in @ SV113 @ SV152 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1067]) ).
thf(1106,plain,
! [SV152: $i,SV113: $i] :
( ( ~ ( ~ ( in @ SV113 @ SV152 )
| ( subset @ ( singleton @ SV113 ) @ SV152 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1067]) ).
thf(1107,plain,
! [SV184: $i,SV153: $i,SV114: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV114 @ SV153 )
| ~ ( subset @ SV184 @ SV153 ) ) )
= $true )
| ( ( subset @ ( set_union2 @ SV114 @ SV184 ) @ SV153 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1068]) ).
thf(1108,plain,
! [SV154: $i,SV115: $i] :
( ( ( subset @ SV115 @ SV154 )
= $false )
| ( ( ( set_intersection2 @ SV115 @ SV154 )
= SV115 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1069]) ).
thf(1109,plain,
! [SV155: $i,SV116: $i] :
( ( ~ ( ~ ( subset @ SV116 @ SV155 )
| ! [SY313: $i] :
( ~ ( in @ SY313 @ SV116 )
| ( in @ SY313 @ SV155 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1070]) ).
thf(1110,plain,
! [SV155: $i,SV116: $i] :
( ( ~ ( ~ ! [SY314: $i] :
( ~ ( in @ SY314 @ SV116 )
| ( in @ SY314 @ SV155 ) )
| ( subset @ SV116 @ SV155 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1070]) ).
thf(1111,plain,
! [SV156: $i,SV117: $i] :
( ( ~ ( subset @ SV117 @ SV156 )
| ~ ( proper_subset @ SV156 @ SV117 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1071]) ).
thf(1112,plain,
! [SV157: $i,SV118: $i,SV185: $i] :
( ( ~ ( ( SV185
!= ( set_union2 @ SV118 @ SV157 ) )
| ! [SY342: $i] :
~ ( ~ ( ~ ( in @ SY342 @ SV185 )
| ( in @ SY342 @ SV118 )
| ( in @ SY342 @ SV157 ) )
| ~ ( ~ ( ( in @ SY342 @ SV118 )
| ( in @ SY342 @ SV157 ) )
| ( in @ SY342 @ SV185 ) ) ) )
| ~ ( ~ ! [SY343: $i] :
~ ( ~ ( ~ ( in @ SY343 @ SV185 )
| ( in @ SY343 @ SV118 )
| ( in @ SY343 @ SV157 ) )
| ~ ( ~ ( ( in @ SY343 @ SV118 )
| ( in @ SY343 @ SV157 ) )
| ( in @ SY343 @ SV185 ) ) )
| ( SV185
= ( set_union2 @ SV118 @ SV157 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1072]) ).
thf(1113,plain,
! [SV158: $i,SV119: $i] :
( ( ~ ( ~ ( proper_subset @ SV119 @ SV158 )
| ~ ( ~ ( subset @ SV119 @ SV158 )
| ~ ( ( SV119 != SV158 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1073]) ).
thf(1114,plain,
! [SV158: $i,SV119: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV119 @ SV158 )
| ~ ( ( SV119 != SV158 ) ) )
| ( proper_subset @ SV119 @ SV158 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1073]) ).
thf(1115,plain,
! [SV159: $i,SV120: $i] :
( ( ~ ( in @ SV120 @ SV159 )
| ~ ( empty @ SV159 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1074]) ).
thf(1116,plain,
! [SV160: $i,SV121: $i] :
( ( ~ ( ~ ( subset @ SV121 @ ( singleton @ SV160 ) )
| ( SV121 = empty_set )
| ( SV121
= ( singleton @ SV160 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1075]) ).
thf(1117,plain,
! [SV160: $i,SV121: $i] :
( ( ~ ( ~ ( ( SV121 = empty_set )
| ( SV121
= ( singleton @ SV160 ) ) )
| ( subset @ SV121 @ ( singleton @ SV160 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1075]) ).
thf(1118,plain,
! [SV161: $i,SV122: $i] :
( ( ( ! [SY318: $i] :
~ ( ~ ( ~ ( in @ SY318 @ SV122 )
| ( in @ SY318 @ SV161 ) )
| ~ ( ~ ( in @ SY318 @ SV161 )
| ( in @ SY318 @ SV122 ) ) ) )
= $false )
| ( ( SV122 = SV161 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1076]) ).
thf(1119,plain,
! [SV186: $i,SV162: $i,SV123: $i] :
( ( ( ( singleton @ SV123 )
!= ( unordered_pair @ SV162 @ SV186 ) )
= $true )
| ( ( SV162 = SV186 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1077]) ).
thf(1120,plain,
! [SV163: $i,SV124: $i] :
( ( ( in @ SV124 @ SV163 )
= $false )
| ( ( subset @ SV124 @ ( union @ SV163 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1078]) ).
thf(1121,plain,
! [SV187: $i,SV164: $i,SV125: $i] :
( ( ( ~ ( subset @ SV125 @ SV164 ) )
= $true )
| ( ( subset @ ( set_difference @ SV125 @ SV187 ) @ ( set_difference @ SV164 @ SV187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1079]) ).
thf(1122,plain,
! [SV165: $i,SV126: $i] :
( ( ( in @ SV126 @ SV165 )
= $false )
| ( ( ~ ( in @ SV165 @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1080]) ).
thf(1123,plain,
! [SV166: $i,SV128: $i] :
( ( ~ ( ( SV128 != SV166 )
| ~ ( ~ ( subset @ SV128 @ SV166 )
| ~ ( subset @ SV166 @ SV128 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1082]) ).
thf(1124,plain,
! [SV166: $i,SV128: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV128 @ SV166 )
| ~ ( subset @ SV166 @ SV128 ) )
| ( SV128 = SV166 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1082]) ).
thf(1125,plain,
! [SV167: $i,SV129: $i] :
( ( ~ ~ ~ ( ~ ~ ( disjoint @ SV129 @ SV167 )
| ~ ! [SY321: $i] :
~ ~ ( ~ ( in @ SY321 @ SV129 )
| ~ ( in @ SY321 @ SV167 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1083]) ).
thf(1126,plain,
! [SV167: $i,SV129: $i] :
( ( ~ ~ ~ ( ~ ~ ! [SY322: $i] :
~ ~ ( ~ ( in @ SY322 @ SV129 )
| ~ ( in @ SY322 @ SV167 ) )
| ~ ( disjoint @ SV129 @ SV167 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1083]) ).
thf(1127,plain,
! [SV188: $i,SV168: $i,SV130: $i] :
( ( ( ~ ( subset @ SV130 @ SV168 ) )
= $true )
| ( ( subset @ ( set_intersection2 @ SV130 @ SV188 ) @ ( set_intersection2 @ SV168 @ SV188 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1084]) ).
thf(1128,plain,
! [SV169: $i,SV131: $i,SV189: $i] :
( ( ~ ( ( SV189
!= ( set_difference @ SV131 @ SV169 ) )
| ! [SY344: $i] :
~ ( ~ ( ~ ( in @ SY344 @ SV189 )
| ~ ( ~ ( in @ SY344 @ SV131 )
| ~ ~ ( in @ SY344 @ SV169 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY344 @ SV131 )
| ~ ~ ( in @ SY344 @ SV169 ) )
| ( in @ SY344 @ SV189 ) ) ) )
| ~ ( ~ ! [SY345: $i] :
~ ( ~ ( ~ ( in @ SY345 @ SV189 )
| ~ ( ~ ( in @ SY345 @ SV131 )
| ~ ~ ( in @ SY345 @ SV169 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY345 @ SV131 )
| ~ ~ ( in @ SY345 @ SV169 ) )
| ( in @ SY345 @ SV189 ) ) )
| ( SV189
= ( set_difference @ SV131 @ SV169 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1085]) ).
thf(1129,plain,
! [SV190: $i,SV170: $i,SV132: $i] :
( ( ( ~ ( subset @ SV132 @ SV170 ) )
= $true )
| ( ( ( in @ SV190 @ SV132 )
| ( subset @ SV132 @ ( set_difference @ SV170 @ ( singleton @ SV190 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1086]) ).
thf(1130,plain,
! [SV133: $i] :
( ( ( SV133 != empty_set )
| ! [SY277: $i] :
~ ( in @ SY277 @ SV133 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1087]) ).
thf(1131,plain,
! [SV133: $i] :
( ( ~ ! [SY278: $i] :
~ ( in @ SY278 @ SV133 )
| ( SV133 = empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1088]) ).
thf(1132,plain,
! [SV171: $i,SV134: $i] :
( ( ( subset @ SV134 @ SV171 )
= $false )
| ( ( ( set_union2 @ SV134 @ SV171 )
= SV171 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1089]) ).
thf(1133,plain,
! [SV191: $i,SV172: $i,SV135: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV135 @ SV172 )
| ~ ( subset @ SV172 @ SV191 ) ) )
= $true )
| ( ( subset @ SV135 @ SV191 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1090]) ).
thf(1134,plain,
! [SV136: $i,SV173: $i] :
( ( ~ ( ( SV173
!= ( powerset @ SV136 ) )
| ! [SY329: $i] :
~ ( ~ ( ~ ( in @ SY329 @ SV173 )
| ( subset @ SY329 @ SV136 ) )
| ~ ( ~ ( subset @ SY329 @ SV136 )
| ( in @ SY329 @ SV173 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1091]) ).
thf(1135,plain,
! [SV136: $i,SV173: $i] :
( ( ~ ( ~ ! [SY330: $i] :
~ ( ~ ( ~ ( in @ SY330 @ SV173 )
| ( subset @ SY330 @ SV136 ) )
| ~ ( ~ ( subset @ SY330 @ SV136 )
| ( in @ SY330 @ SV173 ) ) )
| ( SV173
= ( powerset @ SV136 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1091]) ).
thf(1136,plain,
! [SV174: $i,SV137: $i] :
( ( ~ ( disjoint @ ( singleton @ SV137 ) @ SV174 )
| ~ ( in @ SV137 @ SV174 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1092]) ).
thf(1137,plain,
! [SV138: $i,SV175: $i] :
( ( ~ ( ( SV175
!= ( singleton @ SV138 ) )
| ! [SY331: $i] :
~ ( ~ ( ~ ( in @ SY331 @ SV175 )
| ( SY331 = SV138 ) )
| ~ ( ( SY331 != SV138 )
| ( in @ SY331 @ SV175 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1093]) ).
thf(1138,plain,
! [SV138: $i,SV175: $i] :
( ( ~ ( ~ ! [SY332: $i] :
~ ( ~ ( ~ ( in @ SY332 @ SV175 )
| ( SY332 = SV138 ) )
| ~ ( ( SY332 != SV138 )
| ( in @ SY332 @ SV175 ) ) )
| ( SV175
= ( singleton @ SV138 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1093]) ).
thf(1139,plain,
! [SV176: $i,SV139: $i] :
( ( ( ~ ( in @ SV139 @ SV176 ) )
= $false )
| ( ( disjoint @ ( singleton @ SV139 ) @ SV176 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1094]) ).
thf(1140,plain,
! [SV192: $i,SV177: $i,SV140: $i] :
( ( ( ( singleton @ SV140 )
!= ( unordered_pair @ SV177 @ SV192 ) )
= $true )
| ( ( SV140 = SV177 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1095]) ).
thf(1141,plain,
! [SV178: $i,SV141: $i] :
( ( ( in @ SV141 @ SV178 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV141 ) @ SV178 )
= SV178 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1097]) ).
thf(1142,plain,
! [SV179: $i,SV142: $i,SV193: $i] :
( ( ~ ( ( SV193
!= ( set_intersection2 @ SV142 @ SV179 ) )
| ! [SY346: $i] :
~ ( ~ ( ~ ( in @ SY346 @ SV193 )
| ~ ( ~ ( in @ SY346 @ SV142 )
| ~ ( in @ SY346 @ SV179 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY346 @ SV142 )
| ~ ( in @ SY346 @ SV179 ) )
| ( in @ SY346 @ SV193 ) ) ) )
| ~ ( ~ ! [SY347: $i] :
~ ( ~ ( ~ ( in @ SY347 @ SV193 )
| ~ ( ~ ( in @ SY347 @ SV142 )
| ~ ( in @ SY347 @ SV179 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY347 @ SV142 )
| ~ ( in @ SY347 @ SV179 ) )
| ( in @ SY347 @ SV193 ) ) )
| ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1098]) ).
thf(1143,plain,
! [SV194: $i,SV180: $i,SV143: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV143 @ SV180 )
| ~ ( disjoint @ SV180 @ SV194 ) ) )
= $true )
| ( ( disjoint @ SV143 @ SV194 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1099]) ).
thf(1144,plain,
! [SV181: $i,SV144: $i,SV195: $i] :
( ( ~ ( ( SV195
!= ( unordered_pair @ SV144 @ SV181 ) )
| ! [SY348: $i] :
~ ( ~ ( ~ ( in @ SY348 @ SV195 )
| ( SY348 = SV144 )
| ( SY348 = SV181 ) )
| ~ ( ~ ( ( SY348 = SV144 )
| ( SY348 = SV181 ) )
| ( in @ SY348 @ SV195 ) ) ) )
| ~ ( ~ ! [SY349: $i] :
~ ( ~ ( ~ ( in @ SY349 @ SV195 )
| ( SY349 = SV144 )
| ( SY349 = SV181 ) )
| ~ ( ~ ( ( SY349 = SV144 )
| ( SY349 = SV181 ) )
| ( in @ SY349 @ SV195 ) ) )
| ( SV195
= ( unordered_pair @ SV144 @ SV181 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1100]) ).
thf(1145,plain,
! [SV196: $i,SV182: $i,SV145: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV145 @ SV182 )
| ~ ( subset @ SV145 @ SV196 ) ) )
= $true )
| ( ( subset @ SV145 @ ( set_intersection2 @ SV182 @ SV196 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1101]) ).
thf(1146,plain,
! [SV183: $i,SV146: $i] :
( ( ( subset @ ( singleton @ SV146 ) @ ( singleton @ SV183 ) )
= $false )
| ( ( SV146 = SV183 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1102]) ).
thf(1147,plain,
! [SV112: $i,SV151: $i] :
( ( ( SV151
!= ( union @ SV112 ) )
| ! [SY306: $i] :
~ ( ~ ( ~ ( in @ SY306 @ SV151 )
| ~ ! [SY237: $i] :
~ ~ ( ~ ( in @ SY306 @ SY237 )
| ~ ( in @ SY237 @ SV112 ) ) )
| ~ ( ~ ~ ! [SY238: $i] :
~ ~ ( ~ ( in @ SY306 @ SY238 )
| ~ ( in @ SY238 @ SV112 ) )
| ( in @ SY306 @ SV151 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1103]) ).
thf(1148,plain,
! [SV112: $i,SV151: $i] :
( ( ~ ! [SY309: $i] :
~ ( ~ ( ~ ( in @ SY309 @ SV151 )
| ~ ! [SY240: $i] :
~ ~ ( ~ ( in @ SY309 @ SY240 )
| ~ ( in @ SY240 @ SV112 ) ) )
| ~ ( ~ ~ ! [SY241: $i] :
~ ~ ( ~ ( in @ SY309 @ SY241 )
| ~ ( in @ SY241 @ SV112 ) )
| ( in @ SY309 @ SV151 ) ) )
| ( SV151
= ( union @ SV112 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1104]) ).
thf(1149,plain,
! [SV152: $i,SV113: $i] :
( ( ~ ( subset @ ( singleton @ SV113 ) @ SV152 )
| ( in @ SV113 @ SV152 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1105]) ).
thf(1150,plain,
! [SV152: $i,SV113: $i] :
( ( ~ ( in @ SV113 @ SV152 )
| ( subset @ ( singleton @ SV113 ) @ SV152 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1106]) ).
thf(1151,plain,
! [SV184: $i,SV153: $i,SV114: $i] :
( ( ( ~ ( ~ ( subset @ SV114 @ SV153 )
| ~ ( subset @ SV184 @ SV153 ) ) )
= $false )
| ( ( subset @ ( set_union2 @ SV114 @ SV184 ) @ SV153 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1107]) ).
thf(1152,plain,
! [SV155: $i,SV116: $i] :
( ( ~ ( subset @ SV116 @ SV155 )
| ! [SY313: $i] :
( ~ ( in @ SY313 @ SV116 )
| ( in @ SY313 @ SV155 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1109]) ).
thf(1153,plain,
! [SV155: $i,SV116: $i] :
( ( ~ ! [SY314: $i] :
( ~ ( in @ SY314 @ SV116 )
| ( in @ SY314 @ SV155 ) )
| ( subset @ SV116 @ SV155 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1110]) ).
thf(1154,plain,
! [SV156: $i,SV117: $i] :
( ( ( ~ ( subset @ SV117 @ SV156 ) )
= $true )
| ( ( ~ ( proper_subset @ SV156 @ SV117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1111]) ).
thf(1155,plain,
! [SV157: $i,SV118: $i,SV185: $i] :
( ( ~ ( ( SV185
!= ( set_union2 @ SV118 @ SV157 ) )
| ! [SY342: $i] :
~ ( ~ ( ~ ( in @ SY342 @ SV185 )
| ( in @ SY342 @ SV118 )
| ( in @ SY342 @ SV157 ) )
| ~ ( ~ ( ( in @ SY342 @ SV118 )
| ( in @ SY342 @ SV157 ) )
| ( in @ SY342 @ SV185 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1112]) ).
thf(1156,plain,
! [SV157: $i,SV118: $i,SV185: $i] :
( ( ~ ( ~ ! [SY343: $i] :
~ ( ~ ( ~ ( in @ SY343 @ SV185 )
| ( in @ SY343 @ SV118 )
| ( in @ SY343 @ SV157 ) )
| ~ ( ~ ( ( in @ SY343 @ SV118 )
| ( in @ SY343 @ SV157 ) )
| ( in @ SY343 @ SV185 ) ) )
| ( SV185
= ( set_union2 @ SV118 @ SV157 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1112]) ).
thf(1157,plain,
! [SV158: $i,SV119: $i] :
( ( ~ ( proper_subset @ SV119 @ SV158 )
| ~ ( ~ ( subset @ SV119 @ SV158 )
| ~ ( ( SV119 != SV158 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1113]) ).
thf(1158,plain,
! [SV158: $i,SV119: $i] :
( ( ~ ~ ( ~ ( subset @ SV119 @ SV158 )
| ~ ( ( SV119 != SV158 ) ) )
| ( proper_subset @ SV119 @ SV158 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1114]) ).
thf(1159,plain,
! [SV159: $i,SV120: $i] :
( ( ( ~ ( in @ SV120 @ SV159 ) )
= $true )
| ( ( ~ ( empty @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1115]) ).
thf(1160,plain,
! [SV160: $i,SV121: $i] :
( ( ~ ( subset @ SV121 @ ( singleton @ SV160 ) )
| ( SV121 = empty_set )
| ( SV121
= ( singleton @ SV160 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1116]) ).
thf(1161,plain,
! [SV160: $i,SV121: $i] :
( ( ~ ( ( SV121 = empty_set )
| ( SV121
= ( singleton @ SV160 ) ) )
| ( subset @ SV121 @ ( singleton @ SV160 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1117]) ).
thf(1162,plain,
! [SV122: $i,SV161: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV122 )
| ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV161 ) )
| ~ ( ~ ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV161 )
| ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV122 ) ) ) )
= $false )
| ( ( SV122 = SV161 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1118]) ).
thf(1163,plain,
! [SV186: $i,SV162: $i,SV123: $i] :
( ( ( ( singleton @ SV123 )
= ( unordered_pair @ SV162 @ SV186 ) )
= $false )
| ( ( SV162 = SV186 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1119]) ).
thf(1164,plain,
! [SV187: $i,SV164: $i,SV125: $i] :
( ( ( subset @ SV125 @ SV164 )
= $false )
| ( ( subset @ ( set_difference @ SV125 @ SV187 ) @ ( set_difference @ SV164 @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1121]) ).
thf(1165,plain,
! [SV126: $i,SV165: $i] :
( ( ( in @ SV165 @ SV126 )
= $false )
| ( ( in @ SV126 @ SV165 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1122]) ).
thf(1166,plain,
! [SV166: $i,SV128: $i] :
( ( ( SV128 != SV166 )
| ~ ( ~ ( subset @ SV128 @ SV166 )
| ~ ( subset @ SV166 @ SV128 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1123]) ).
thf(1167,plain,
! [SV166: $i,SV128: $i] :
( ( ~ ~ ( ~ ( subset @ SV128 @ SV166 )
| ~ ( subset @ SV166 @ SV128 ) )
| ( SV128 = SV166 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1124]) ).
thf(1168,plain,
! [SV167: $i,SV129: $i] :
( ( ~ ~ ( ~ ~ ( disjoint @ SV129 @ SV167 )
| ~ ! [SY321: $i] :
~ ~ ( ~ ( in @ SY321 @ SV129 )
| ~ ( in @ SY321 @ SV167 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1125]) ).
thf(1169,plain,
! [SV167: $i,SV129: $i] :
( ( ~ ~ ( ~ ~ ! [SY322: $i] :
~ ~ ( ~ ( in @ SY322 @ SV129 )
| ~ ( in @ SY322 @ SV167 ) )
| ~ ( disjoint @ SV129 @ SV167 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1126]) ).
thf(1170,plain,
! [SV188: $i,SV168: $i,SV130: $i] :
( ( ( subset @ SV130 @ SV168 )
= $false )
| ( ( subset @ ( set_intersection2 @ SV130 @ SV188 ) @ ( set_intersection2 @ SV168 @ SV188 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1127]) ).
thf(1171,plain,
! [SV169: $i,SV131: $i,SV189: $i] :
( ( ~ ( ( SV189
!= ( set_difference @ SV131 @ SV169 ) )
| ! [SY344: $i] :
~ ( ~ ( ~ ( in @ SY344 @ SV189 )
| ~ ( ~ ( in @ SY344 @ SV131 )
| ~ ~ ( in @ SY344 @ SV169 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY344 @ SV131 )
| ~ ~ ( in @ SY344 @ SV169 ) )
| ( in @ SY344 @ SV189 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1128]) ).
thf(1172,plain,
! [SV169: $i,SV131: $i,SV189: $i] :
( ( ~ ( ~ ! [SY345: $i] :
~ ( ~ ( ~ ( in @ SY345 @ SV189 )
| ~ ( ~ ( in @ SY345 @ SV131 )
| ~ ~ ( in @ SY345 @ SV169 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY345 @ SV131 )
| ~ ~ ( in @ SY345 @ SV169 ) )
| ( in @ SY345 @ SV189 ) ) )
| ( SV189
= ( set_difference @ SV131 @ SV169 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1128]) ).
thf(1173,plain,
! [SV190: $i,SV170: $i,SV132: $i] :
( ( ( subset @ SV132 @ SV170 )
= $false )
| ( ( ( in @ SV190 @ SV132 )
| ( subset @ SV132 @ ( set_difference @ SV170 @ ( singleton @ SV190 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1129]) ).
thf(1174,plain,
! [SV133: $i] :
( ( ( SV133 != empty_set )
= $true )
| ( ( ! [SY277: $i] :
~ ( in @ SY277 @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1130]) ).
thf(1175,plain,
! [SV133: $i] :
( ( ( ~ ! [SY278: $i] :
~ ( in @ SY278 @ SV133 ) )
= $true )
| ( ( SV133 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1131]) ).
thf(1176,plain,
! [SV191: $i,SV172: $i,SV135: $i] :
( ( ( ~ ( ~ ( subset @ SV135 @ SV172 )
| ~ ( subset @ SV172 @ SV191 ) ) )
= $false )
| ( ( subset @ SV135 @ SV191 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1133]) ).
thf(1177,plain,
! [SV136: $i,SV173: $i] :
( ( ( SV173
!= ( powerset @ SV136 ) )
| ! [SY329: $i] :
~ ( ~ ( ~ ( in @ SY329 @ SV173 )
| ( subset @ SY329 @ SV136 ) )
| ~ ( ~ ( subset @ SY329 @ SV136 )
| ( in @ SY329 @ SV173 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1134]) ).
thf(1178,plain,
! [SV136: $i,SV173: $i] :
( ( ~ ! [SY330: $i] :
~ ( ~ ( ~ ( in @ SY330 @ SV173 )
| ( subset @ SY330 @ SV136 ) )
| ~ ( ~ ( subset @ SY330 @ SV136 )
| ( in @ SY330 @ SV173 ) ) )
| ( SV173
= ( powerset @ SV136 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1135]) ).
thf(1179,plain,
! [SV174: $i,SV137: $i] :
( ( ( ~ ( disjoint @ ( singleton @ SV137 ) @ SV174 ) )
= $true )
| ( ( ~ ( in @ SV137 @ SV174 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1136]) ).
thf(1180,plain,
! [SV138: $i,SV175: $i] :
( ( ( SV175
!= ( singleton @ SV138 ) )
| ! [SY331: $i] :
~ ( ~ ( ~ ( in @ SY331 @ SV175 )
| ( SY331 = SV138 ) )
| ~ ( ( SY331 != SV138 )
| ( in @ SY331 @ SV175 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1137]) ).
thf(1181,plain,
! [SV138: $i,SV175: $i] :
( ( ~ ! [SY332: $i] :
~ ( ~ ( ~ ( in @ SY332 @ SV175 )
| ( SY332 = SV138 ) )
| ~ ( ( SY332 != SV138 )
| ( in @ SY332 @ SV175 ) ) )
| ( SV175
= ( singleton @ SV138 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1138]) ).
thf(1182,plain,
! [SV176: $i,SV139: $i] :
( ( ( in @ SV139 @ SV176 )
= $true )
| ( ( disjoint @ ( singleton @ SV139 ) @ SV176 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1139]) ).
thf(1183,plain,
! [SV192: $i,SV177: $i,SV140: $i] :
( ( ( ( singleton @ SV140 )
= ( unordered_pair @ SV177 @ SV192 ) )
= $false )
| ( ( SV140 = SV177 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1140]) ).
thf(1184,plain,
! [SV179: $i,SV142: $i,SV193: $i] :
( ( ~ ( ( SV193
!= ( set_intersection2 @ SV142 @ SV179 ) )
| ! [SY346: $i] :
~ ( ~ ( ~ ( in @ SY346 @ SV193 )
| ~ ( ~ ( in @ SY346 @ SV142 )
| ~ ( in @ SY346 @ SV179 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY346 @ SV142 )
| ~ ( in @ SY346 @ SV179 ) )
| ( in @ SY346 @ SV193 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1142]) ).
thf(1185,plain,
! [SV179: $i,SV142: $i,SV193: $i] :
( ( ~ ( ~ ! [SY347: $i] :
~ ( ~ ( ~ ( in @ SY347 @ SV193 )
| ~ ( ~ ( in @ SY347 @ SV142 )
| ~ ( in @ SY347 @ SV179 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY347 @ SV142 )
| ~ ( in @ SY347 @ SV179 ) )
| ( in @ SY347 @ SV193 ) ) )
| ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1142]) ).
thf(1186,plain,
! [SV194: $i,SV180: $i,SV143: $i] :
( ( ( ~ ( ~ ( subset @ SV143 @ SV180 )
| ~ ( disjoint @ SV180 @ SV194 ) ) )
= $false )
| ( ( disjoint @ SV143 @ SV194 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1143]) ).
thf(1187,plain,
! [SV181: $i,SV144: $i,SV195: $i] :
( ( ~ ( ( SV195
!= ( unordered_pair @ SV144 @ SV181 ) )
| ! [SY348: $i] :
~ ( ~ ( ~ ( in @ SY348 @ SV195 )
| ( SY348 = SV144 )
| ( SY348 = SV181 ) )
| ~ ( ~ ( ( SY348 = SV144 )
| ( SY348 = SV181 ) )
| ( in @ SY348 @ SV195 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1144]) ).
thf(1188,plain,
! [SV181: $i,SV144: $i,SV195: $i] :
( ( ~ ( ~ ! [SY349: $i] :
~ ( ~ ( ~ ( in @ SY349 @ SV195 )
| ( SY349 = SV144 )
| ( SY349 = SV181 ) )
| ~ ( ~ ( ( SY349 = SV144 )
| ( SY349 = SV181 ) )
| ( in @ SY349 @ SV195 ) ) )
| ( SV195
= ( unordered_pair @ SV144 @ SV181 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1144]) ).
thf(1189,plain,
! [SV196: $i,SV182: $i,SV145: $i] :
( ( ( ~ ( ~ ( subset @ SV145 @ SV182 )
| ~ ( subset @ SV145 @ SV196 ) ) )
= $false )
| ( ( subset @ SV145 @ ( set_intersection2 @ SV182 @ SV196 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1145]) ).
thf(1190,plain,
! [SV112: $i,SV151: $i] :
( ( ( SV151
!= ( union @ SV112 ) )
= $true )
| ( ( ! [SY306: $i] :
~ ( ~ ( ~ ( in @ SY306 @ SV151 )
| ~ ! [SY237: $i] :
~ ~ ( ~ ( in @ SY306 @ SY237 )
| ~ ( in @ SY237 @ SV112 ) ) )
| ~ ( ~ ~ ! [SY238: $i] :
~ ~ ( ~ ( in @ SY306 @ SY238 )
| ~ ( in @ SY238 @ SV112 ) )
| ( in @ SY306 @ SV151 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1147]) ).
thf(1191,plain,
! [SV112: $i,SV151: $i] :
( ( ( ~ ! [SY309: $i] :
~ ( ~ ( ~ ( in @ SY309 @ SV151 )
| ~ ! [SY240: $i] :
~ ~ ( ~ ( in @ SY309 @ SY240 )
| ~ ( in @ SY240 @ SV112 ) ) )
| ~ ( ~ ~ ! [SY241: $i] :
~ ~ ( ~ ( in @ SY309 @ SY241 )
| ~ ( in @ SY241 @ SV112 ) )
| ( in @ SY309 @ SV151 ) ) ) )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1148]) ).
thf(1192,plain,
! [SV152: $i,SV113: $i] :
( ( ( ~ ( subset @ ( singleton @ SV113 ) @ SV152 ) )
= $true )
| ( ( in @ SV113 @ SV152 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1149]) ).
thf(1193,plain,
! [SV152: $i,SV113: $i] :
( ( ( ~ ( in @ SV113 @ SV152 ) )
= $true )
| ( ( subset @ ( singleton @ SV113 ) @ SV152 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1150]) ).
thf(1194,plain,
! [SV184: $i,SV153: $i,SV114: $i] :
( ( ( ~ ( subset @ SV114 @ SV153 )
| ~ ( subset @ SV184 @ SV153 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV114 @ SV184 ) @ SV153 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1151]) ).
thf(1195,plain,
! [SV155: $i,SV116: $i] :
( ( ( ~ ( subset @ SV116 @ SV155 ) )
= $true )
| ( ( ! [SY313: $i] :
( ~ ( in @ SY313 @ SV116 )
| ( in @ SY313 @ SV155 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1152]) ).
thf(1196,plain,
! [SV155: $i,SV116: $i] :
( ( ( ~ ! [SY314: $i] :
( ~ ( in @ SY314 @ SV116 )
| ( in @ SY314 @ SV155 ) ) )
= $true )
| ( ( subset @ SV116 @ SV155 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1153]) ).
thf(1197,plain,
! [SV156: $i,SV117: $i] :
( ( ( subset @ SV117 @ SV156 )
= $false )
| ( ( ~ ( proper_subset @ SV156 @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1154]) ).
thf(1198,plain,
! [SV157: $i,SV118: $i,SV185: $i] :
( ( ( SV185
!= ( set_union2 @ SV118 @ SV157 ) )
| ! [SY342: $i] :
~ ( ~ ( ~ ( in @ SY342 @ SV185 )
| ( in @ SY342 @ SV118 )
| ( in @ SY342 @ SV157 ) )
| ~ ( ~ ( ( in @ SY342 @ SV118 )
| ( in @ SY342 @ SV157 ) )
| ( in @ SY342 @ SV185 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1155]) ).
thf(1199,plain,
! [SV157: $i,SV118: $i,SV185: $i] :
( ( ~ ! [SY343: $i] :
~ ( ~ ( ~ ( in @ SY343 @ SV185 )
| ( in @ SY343 @ SV118 )
| ( in @ SY343 @ SV157 ) )
| ~ ( ~ ( ( in @ SY343 @ SV118 )
| ( in @ SY343 @ SV157 ) )
| ( in @ SY343 @ SV185 ) ) )
| ( SV185
= ( set_union2 @ SV118 @ SV157 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1156]) ).
thf(1200,plain,
! [SV158: $i,SV119: $i] :
( ( ( ~ ( proper_subset @ SV119 @ SV158 ) )
= $true )
| ( ( ~ ( ~ ( subset @ SV119 @ SV158 )
| ~ ( ( SV119 != SV158 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1157]) ).
thf(1201,plain,
! [SV158: $i,SV119: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV119 @ SV158 )
| ~ ( ( SV119 != SV158 ) ) ) )
= $true )
| ( ( proper_subset @ SV119 @ SV158 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1158]) ).
thf(1202,plain,
! [SV159: $i,SV120: $i] :
( ( ( in @ SV120 @ SV159 )
= $false )
| ( ( ~ ( empty @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1159]) ).
thf(1203,plain,
! [SV160: $i,SV121: $i] :
( ( ( ~ ( subset @ SV121 @ ( singleton @ SV160 ) ) )
= $true )
| ( ( ( SV121 = empty_set )
| ( SV121
= ( singleton @ SV160 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1160]) ).
thf(1204,plain,
! [SV160: $i,SV121: $i] :
( ( ( ~ ( ( SV121 = empty_set )
| ( SV121
= ( singleton @ SV160 ) ) ) )
= $true )
| ( ( subset @ SV121 @ ( singleton @ SV160 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1161]) ).
thf(1205,plain,
! [SV122: $i,SV161: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV122 )
| ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV161 ) )
| ~ ( ~ ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV161 )
| ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV122 ) ) )
= $true )
| ( ( SV122 = SV161 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1162]) ).
thf(1206,plain,
! [SV166: $i,SV128: $i] :
( ( ( SV128 != SV166 )
= $true )
| ( ( ~ ( ~ ( subset @ SV128 @ SV166 )
| ~ ( subset @ SV166 @ SV128 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1166]) ).
thf(1207,plain,
! [SV166: $i,SV128: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV128 @ SV166 )
| ~ ( subset @ SV166 @ SV128 ) ) )
= $true )
| ( ( SV128 = SV166 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1167]) ).
thf(1208,plain,
! [SV167: $i,SV129: $i] :
( ( ~ ( ~ ~ ( disjoint @ SV129 @ SV167 )
| ~ ! [SY321: $i] :
~ ~ ( ~ ( in @ SY321 @ SV129 )
| ~ ( in @ SY321 @ SV167 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1168]) ).
thf(1209,plain,
! [SV167: $i,SV129: $i] :
( ( ~ ( ~ ~ ! [SY322: $i] :
~ ~ ( ~ ( in @ SY322 @ SV129 )
| ~ ( in @ SY322 @ SV167 ) )
| ~ ( disjoint @ SV129 @ SV167 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1169]) ).
thf(1210,plain,
! [SV169: $i,SV131: $i,SV189: $i] :
( ( ( SV189
!= ( set_difference @ SV131 @ SV169 ) )
| ! [SY344: $i] :
~ ( ~ ( ~ ( in @ SY344 @ SV189 )
| ~ ( ~ ( in @ SY344 @ SV131 )
| ~ ~ ( in @ SY344 @ SV169 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY344 @ SV131 )
| ~ ~ ( in @ SY344 @ SV169 ) )
| ( in @ SY344 @ SV189 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1171]) ).
thf(1211,plain,
! [SV169: $i,SV131: $i,SV189: $i] :
( ( ~ ! [SY345: $i] :
~ ( ~ ( ~ ( in @ SY345 @ SV189 )
| ~ ( ~ ( in @ SY345 @ SV131 )
| ~ ~ ( in @ SY345 @ SV169 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY345 @ SV131 )
| ~ ~ ( in @ SY345 @ SV169 ) )
| ( in @ SY345 @ SV189 ) ) )
| ( SV189
= ( set_difference @ SV131 @ SV169 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1172]) ).
thf(1212,plain,
! [SV170: $i,SV132: $i,SV190: $i] :
( ( ( in @ SV190 @ SV132 )
= $true )
| ( ( subset @ SV132 @ ( set_difference @ SV170 @ ( singleton @ SV190 ) ) )
= $true )
| ( ( subset @ SV132 @ SV170 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1173]) ).
thf(1213,plain,
! [SV133: $i] :
( ( ( SV133 = empty_set )
= $false )
| ( ( ! [SY277: $i] :
~ ( in @ SY277 @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1174]) ).
thf(1214,plain,
! [SV133: $i] :
( ( ( ! [SY278: $i] :
~ ( in @ SY278 @ SV133 ) )
= $false )
| ( ( SV133 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1175]) ).
thf(1215,plain,
! [SV191: $i,SV172: $i,SV135: $i] :
( ( ( ~ ( subset @ SV135 @ SV172 )
| ~ ( subset @ SV172 @ SV191 ) )
= $true )
| ( ( subset @ SV135 @ SV191 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1176]) ).
thf(1216,plain,
! [SV136: $i,SV173: $i] :
( ( ( SV173
!= ( powerset @ SV136 ) )
= $true )
| ( ( ! [SY329: $i] :
~ ( ~ ( ~ ( in @ SY329 @ SV173 )
| ( subset @ SY329 @ SV136 ) )
| ~ ( ~ ( subset @ SY329 @ SV136 )
| ( in @ SY329 @ SV173 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1177]) ).
thf(1217,plain,
! [SV136: $i,SV173: $i] :
( ( ( ~ ! [SY330: $i] :
~ ( ~ ( ~ ( in @ SY330 @ SV173 )
| ( subset @ SY330 @ SV136 ) )
| ~ ( ~ ( subset @ SY330 @ SV136 )
| ( in @ SY330 @ SV173 ) ) ) )
= $true )
| ( ( SV173
= ( powerset @ SV136 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1178]) ).
thf(1218,plain,
! [SV174: $i,SV137: $i] :
( ( ( disjoint @ ( singleton @ SV137 ) @ SV174 )
= $false )
| ( ( ~ ( in @ SV137 @ SV174 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1179]) ).
thf(1219,plain,
! [SV138: $i,SV175: $i] :
( ( ( SV175
!= ( singleton @ SV138 ) )
= $true )
| ( ( ! [SY331: $i] :
~ ( ~ ( ~ ( in @ SY331 @ SV175 )
| ( SY331 = SV138 ) )
| ~ ( ( SY331 != SV138 )
| ( in @ SY331 @ SV175 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1180]) ).
thf(1220,plain,
! [SV138: $i,SV175: $i] :
( ( ( ~ ! [SY332: $i] :
~ ( ~ ( ~ ( in @ SY332 @ SV175 )
| ( SY332 = SV138 ) )
| ~ ( ( SY332 != SV138 )
| ( in @ SY332 @ SV175 ) ) ) )
= $true )
| ( ( SV175
= ( singleton @ SV138 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1181]) ).
thf(1221,plain,
! [SV179: $i,SV142: $i,SV193: $i] :
( ( ( SV193
!= ( set_intersection2 @ SV142 @ SV179 ) )
| ! [SY346: $i] :
~ ( ~ ( ~ ( in @ SY346 @ SV193 )
| ~ ( ~ ( in @ SY346 @ SV142 )
| ~ ( in @ SY346 @ SV179 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY346 @ SV142 )
| ~ ( in @ SY346 @ SV179 ) )
| ( in @ SY346 @ SV193 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1184]) ).
thf(1222,plain,
! [SV179: $i,SV142: $i,SV193: $i] :
( ( ~ ! [SY347: $i] :
~ ( ~ ( ~ ( in @ SY347 @ SV193 )
| ~ ( ~ ( in @ SY347 @ SV142 )
| ~ ( in @ SY347 @ SV179 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY347 @ SV142 )
| ~ ( in @ SY347 @ SV179 ) )
| ( in @ SY347 @ SV193 ) ) )
| ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1185]) ).
thf(1223,plain,
! [SV194: $i,SV180: $i,SV143: $i] :
( ( ( ~ ( subset @ SV143 @ SV180 )
| ~ ( disjoint @ SV180 @ SV194 ) )
= $true )
| ( ( disjoint @ SV143 @ SV194 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1186]) ).
thf(1224,plain,
! [SV181: $i,SV144: $i,SV195: $i] :
( ( ( SV195
!= ( unordered_pair @ SV144 @ SV181 ) )
| ! [SY348: $i] :
~ ( ~ ( ~ ( in @ SY348 @ SV195 )
| ( SY348 = SV144 )
| ( SY348 = SV181 ) )
| ~ ( ~ ( ( SY348 = SV144 )
| ( SY348 = SV181 ) )
| ( in @ SY348 @ SV195 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1187]) ).
thf(1225,plain,
! [SV181: $i,SV144: $i,SV195: $i] :
( ( ~ ! [SY349: $i] :
~ ( ~ ( ~ ( in @ SY349 @ SV195 )
| ( SY349 = SV144 )
| ( SY349 = SV181 ) )
| ~ ( ~ ( ( SY349 = SV144 )
| ( SY349 = SV181 ) )
| ( in @ SY349 @ SV195 ) ) )
| ( SV195
= ( unordered_pair @ SV144 @ SV181 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1188]) ).
thf(1226,plain,
! [SV196: $i,SV182: $i,SV145: $i] :
( ( ( ~ ( subset @ SV145 @ SV182 )
| ~ ( subset @ SV145 @ SV196 ) )
= $true )
| ( ( subset @ SV145 @ ( set_intersection2 @ SV182 @ SV196 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1189]) ).
thf(1227,plain,
! [SV112: $i,SV151: $i] :
( ( ( SV151
= ( union @ SV112 ) )
= $false )
| ( ( ! [SY306: $i] :
~ ( ~ ( ~ ( in @ SY306 @ SV151 )
| ~ ! [SY237: $i] :
~ ~ ( ~ ( in @ SY306 @ SY237 )
| ~ ( in @ SY237 @ SV112 ) ) )
| ~ ( ~ ~ ! [SY238: $i] :
~ ~ ( ~ ( in @ SY306 @ SY238 )
| ~ ( in @ SY238 @ SV112 ) )
| ( in @ SY306 @ SV151 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1190]) ).
thf(1228,plain,
! [SV112: $i,SV151: $i] :
( ( ( ! [SY309: $i] :
~ ( ~ ( ~ ( in @ SY309 @ SV151 )
| ~ ! [SY240: $i] :
~ ~ ( ~ ( in @ SY309 @ SY240 )
| ~ ( in @ SY240 @ SV112 ) ) )
| ~ ( ~ ~ ! [SY241: $i] :
~ ~ ( ~ ( in @ SY309 @ SY241 )
| ~ ( in @ SY241 @ SV112 ) )
| ( in @ SY309 @ SV151 ) ) ) )
= $false )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1191]) ).
thf(1229,plain,
! [SV152: $i,SV113: $i] :
( ( ( subset @ ( singleton @ SV113 ) @ SV152 )
= $false )
| ( ( in @ SV113 @ SV152 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1192]) ).
thf(1230,plain,
! [SV152: $i,SV113: $i] :
( ( ( in @ SV113 @ SV152 )
= $false )
| ( ( subset @ ( singleton @ SV113 ) @ SV152 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1193]) ).
thf(1231,plain,
! [SV184: $i,SV153: $i,SV114: $i] :
( ( ( ~ ( subset @ SV114 @ SV153 ) )
= $true )
| ( ( ~ ( subset @ SV184 @ SV153 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV114 @ SV184 ) @ SV153 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1194]) ).
thf(1232,plain,
! [SV155: $i,SV116: $i] :
( ( ( subset @ SV116 @ SV155 )
= $false )
| ( ( ! [SY313: $i] :
( ~ ( in @ SY313 @ SV116 )
| ( in @ SY313 @ SV155 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1195]) ).
thf(1233,plain,
! [SV155: $i,SV116: $i] :
( ( ( ! [SY314: $i] :
( ~ ( in @ SY314 @ SV116 )
| ( in @ SY314 @ SV155 ) ) )
= $false )
| ( ( subset @ SV116 @ SV155 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1196]) ).
thf(1234,plain,
! [SV117: $i,SV156: $i] :
( ( ( proper_subset @ SV156 @ SV117 )
= $false )
| ( ( subset @ SV117 @ SV156 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1197]) ).
thf(1235,plain,
! [SV157: $i,SV118: $i,SV185: $i] :
( ( ( SV185
!= ( set_union2 @ SV118 @ SV157 ) )
= $true )
| ( ( ! [SY342: $i] :
~ ( ~ ( ~ ( in @ SY342 @ SV185 )
| ( in @ SY342 @ SV118 )
| ( in @ SY342 @ SV157 ) )
| ~ ( ~ ( ( in @ SY342 @ SV118 )
| ( in @ SY342 @ SV157 ) )
| ( in @ SY342 @ SV185 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1198]) ).
thf(1236,plain,
! [SV157: $i,SV118: $i,SV185: $i] :
( ( ( ~ ! [SY343: $i] :
~ ( ~ ( ~ ( in @ SY343 @ SV185 )
| ( in @ SY343 @ SV118 )
| ( in @ SY343 @ SV157 ) )
| ~ ( ~ ( ( in @ SY343 @ SV118 )
| ( in @ SY343 @ SV157 ) )
| ( in @ SY343 @ SV185 ) ) ) )
= $true )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1199]) ).
thf(1237,plain,
! [SV158: $i,SV119: $i] :
( ( ( proper_subset @ SV119 @ SV158 )
= $false )
| ( ( ~ ( ~ ( subset @ SV119 @ SV158 )
| ~ ( ( SV119 != SV158 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1200]) ).
thf(1238,plain,
! [SV158: $i,SV119: $i] :
( ( ( ~ ( ~ ( subset @ SV119 @ SV158 )
| ~ ( ( SV119 != SV158 ) ) ) )
= $false )
| ( ( proper_subset @ SV119 @ SV158 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1201]) ).
thf(1239,plain,
! [SV120: $i,SV159: $i] :
( ( ( empty @ SV159 )
= $false )
| ( ( in @ SV120 @ SV159 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1202]) ).
thf(1240,plain,
! [SV160: $i,SV121: $i] :
( ( ( subset @ SV121 @ ( singleton @ SV160 ) )
= $false )
| ( ( ( SV121 = empty_set )
| ( SV121
= ( singleton @ SV160 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1203]) ).
thf(1241,plain,
! [SV160: $i,SV121: $i] :
( ( ( ( SV121 = empty_set )
| ( SV121
= ( singleton @ SV160 ) ) )
= $false )
| ( ( subset @ SV121 @ ( singleton @ SV160 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1204]) ).
thf(1242,plain,
! [SV122: $i,SV161: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV122 )
| ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV161 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV161 )
| ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV122 ) ) )
= $true )
| ( ( SV122 = SV161 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1205]) ).
thf(1243,plain,
! [SV166: $i,SV128: $i] :
( ( ( SV128 = SV166 )
= $false )
| ( ( ~ ( ~ ( subset @ SV128 @ SV166 )
| ~ ( subset @ SV166 @ SV128 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1206]) ).
thf(1244,plain,
! [SV166: $i,SV128: $i] :
( ( ( ~ ( ~ ( subset @ SV128 @ SV166 )
| ~ ( subset @ SV166 @ SV128 ) ) )
= $false )
| ( ( SV128 = SV166 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1207]) ).
thf(1245,plain,
! [SV167: $i,SV129: $i] :
( ( ~ ~ ( disjoint @ SV129 @ SV167 )
| ~ ! [SY321: $i] :
~ ~ ( ~ ( in @ SY321 @ SV129 )
| ~ ( in @ SY321 @ SV167 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1208]) ).
thf(1246,plain,
! [SV167: $i,SV129: $i] :
( ( ~ ~ ! [SY322: $i] :
~ ~ ( ~ ( in @ SY322 @ SV129 )
| ~ ( in @ SY322 @ SV167 ) )
| ~ ( disjoint @ SV129 @ SV167 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1209]) ).
thf(1247,plain,
! [SV169: $i,SV131: $i,SV189: $i] :
( ( ( SV189
!= ( set_difference @ SV131 @ SV169 ) )
= $true )
| ( ( ! [SY344: $i] :
~ ( ~ ( ~ ( in @ SY344 @ SV189 )
| ~ ( ~ ( in @ SY344 @ SV131 )
| ~ ~ ( in @ SY344 @ SV169 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY344 @ SV131 )
| ~ ~ ( in @ SY344 @ SV169 ) )
| ( in @ SY344 @ SV189 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1210]) ).
thf(1248,plain,
! [SV169: $i,SV131: $i,SV189: $i] :
( ( ( ~ ! [SY345: $i] :
~ ( ~ ( ~ ( in @ SY345 @ SV189 )
| ~ ( ~ ( in @ SY345 @ SV131 )
| ~ ~ ( in @ SY345 @ SV169 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY345 @ SV131 )
| ~ ~ ( in @ SY345 @ SV169 ) )
| ( in @ SY345 @ SV189 ) ) ) )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1211]) ).
thf(1249,plain,
! [SV133: $i,SV197: $i] :
( ( ( ~ ( in @ SV197 @ SV133 ) )
= $true )
| ( ( SV133 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1213]) ).
thf(1250,plain,
! [SV133: $i] :
( ( ( ~ ( in @ ( sK18_SY278 @ SV133 ) @ SV133 ) )
= $false )
| ( ( SV133 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1214]) ).
thf(1251,plain,
! [SV191: $i,SV172: $i,SV135: $i] :
( ( ( ~ ( subset @ SV135 @ SV172 ) )
= $true )
| ( ( ~ ( subset @ SV172 @ SV191 ) )
= $true )
| ( ( subset @ SV135 @ SV191 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1215]) ).
thf(1252,plain,
! [SV136: $i,SV173: $i] :
( ( ( SV173
= ( powerset @ SV136 ) )
= $false )
| ( ( ! [SY329: $i] :
~ ( ~ ( ~ ( in @ SY329 @ SV173 )
| ( subset @ SY329 @ SV136 ) )
| ~ ( ~ ( subset @ SY329 @ SV136 )
| ( in @ SY329 @ SV173 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1216]) ).
thf(1253,plain,
! [SV136: $i,SV173: $i] :
( ( ( ! [SY330: $i] :
~ ( ~ ( ~ ( in @ SY330 @ SV173 )
| ( subset @ SY330 @ SV136 ) )
| ~ ( ~ ( subset @ SY330 @ SV136 )
| ( in @ SY330 @ SV173 ) ) ) )
= $false )
| ( ( SV173
= ( powerset @ SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1217]) ).
thf(1254,plain,
! [SV174: $i,SV137: $i] :
( ( ( in @ SV137 @ SV174 )
= $false )
| ( ( disjoint @ ( singleton @ SV137 ) @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1218]) ).
thf(1255,plain,
! [SV138: $i,SV175: $i] :
( ( ( SV175
= ( singleton @ SV138 ) )
= $false )
| ( ( ! [SY331: $i] :
~ ( ~ ( ~ ( in @ SY331 @ SV175 )
| ( SY331 = SV138 ) )
| ~ ( ( SY331 != SV138 )
| ( in @ SY331 @ SV175 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1219]) ).
thf(1256,plain,
! [SV138: $i,SV175: $i] :
( ( ( ! [SY332: $i] :
~ ( ~ ( ~ ( in @ SY332 @ SV175 )
| ( SY332 = SV138 ) )
| ~ ( ( SY332 != SV138 )
| ( in @ SY332 @ SV175 ) ) ) )
= $false )
| ( ( SV175
= ( singleton @ SV138 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1220]) ).
thf(1257,plain,
! [SV179: $i,SV142: $i,SV193: $i] :
( ( ( SV193
!= ( set_intersection2 @ SV142 @ SV179 ) )
= $true )
| ( ( ! [SY346: $i] :
~ ( ~ ( ~ ( in @ SY346 @ SV193 )
| ~ ( ~ ( in @ SY346 @ SV142 )
| ~ ( in @ SY346 @ SV179 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY346 @ SV142 )
| ~ ( in @ SY346 @ SV179 ) )
| ( in @ SY346 @ SV193 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1221]) ).
thf(1258,plain,
! [SV179: $i,SV142: $i,SV193: $i] :
( ( ( ~ ! [SY347: $i] :
~ ( ~ ( ~ ( in @ SY347 @ SV193 )
| ~ ( ~ ( in @ SY347 @ SV142 )
| ~ ( in @ SY347 @ SV179 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY347 @ SV142 )
| ~ ( in @ SY347 @ SV179 ) )
| ( in @ SY347 @ SV193 ) ) ) )
= $true )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1222]) ).
thf(1259,plain,
! [SV194: $i,SV180: $i,SV143: $i] :
( ( ( ~ ( subset @ SV143 @ SV180 ) )
= $true )
| ( ( ~ ( disjoint @ SV180 @ SV194 ) )
= $true )
| ( ( disjoint @ SV143 @ SV194 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1223]) ).
thf(1260,plain,
! [SV181: $i,SV144: $i,SV195: $i] :
( ( ( SV195
!= ( unordered_pair @ SV144 @ SV181 ) )
= $true )
| ( ( ! [SY348: $i] :
~ ( ~ ( ~ ( in @ SY348 @ SV195 )
| ( SY348 = SV144 )
| ( SY348 = SV181 ) )
| ~ ( ~ ( ( SY348 = SV144 )
| ( SY348 = SV181 ) )
| ( in @ SY348 @ SV195 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1224]) ).
thf(1261,plain,
! [SV181: $i,SV144: $i,SV195: $i] :
( ( ( ~ ! [SY349: $i] :
~ ( ~ ( ~ ( in @ SY349 @ SV195 )
| ( SY349 = SV144 )
| ( SY349 = SV181 ) )
| ~ ( ~ ( ( SY349 = SV144 )
| ( SY349 = SV181 ) )
| ( in @ SY349 @ SV195 ) ) ) )
= $true )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1225]) ).
thf(1262,plain,
! [SV196: $i,SV182: $i,SV145: $i] :
( ( ( ~ ( subset @ SV145 @ SV182 ) )
= $true )
| ( ( ~ ( subset @ SV145 @ SV196 ) )
= $true )
| ( ( subset @ SV145 @ ( set_intersection2 @ SV182 @ SV196 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1226]) ).
thf(1263,plain,
! [SV112: $i,SV151: $i,SV198: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV198 @ SV151 )
| ~ ! [SY350: $i] :
~ ~ ( ~ ( in @ SV198 @ SY350 )
| ~ ( in @ SY350 @ SV112 ) ) )
| ~ ( ~ ~ ! [SY351: $i] :
~ ~ ( ~ ( in @ SV198 @ SY351 )
| ~ ( in @ SY351 @ SV112 ) )
| ( in @ SV198 @ SV151 ) ) ) )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1227]) ).
thf(1264,plain,
! [SV151: $i,SV112: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV151 )
| ~ ! [SY352: $i] :
~ ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SY352 )
| ~ ( in @ SY352 @ SV112 ) ) )
| ~ ( ~ ~ ! [SY353: $i] :
~ ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SY353 )
| ~ ( in @ SY353 @ SV112 ) )
| ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV151 ) ) ) )
= $false )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1228]) ).
thf(1265,plain,
! [SV184: $i,SV153: $i,SV114: $i] :
( ( ( subset @ SV114 @ SV153 )
= $false )
| ( ( ~ ( subset @ SV184 @ SV153 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV114 @ SV184 ) @ SV153 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1231]) ).
thf(1266,plain,
! [SV155: $i,SV116: $i,SV199: $i] :
( ( ( ~ ( in @ SV199 @ SV116 )
| ( in @ SV199 @ SV155 ) )
= $true )
| ( ( subset @ SV116 @ SV155 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1232]) ).
thf(1267,plain,
! [SV116: $i,SV155: $i] :
( ( ( ~ ( in @ ( sK20_SY314 @ SV155 @ SV116 ) @ SV116 )
| ( in @ ( sK20_SY314 @ SV155 @ SV116 ) @ SV155 ) )
= $false )
| ( ( subset @ SV116 @ SV155 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1233]) ).
thf(1268,plain,
! [SV157: $i,SV118: $i,SV185: $i] :
( ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $false )
| ( ( ! [SY342: $i] :
~ ( ~ ( ~ ( in @ SY342 @ SV185 )
| ( in @ SY342 @ SV118 )
| ( in @ SY342 @ SV157 ) )
| ~ ( ~ ( ( in @ SY342 @ SV118 )
| ( in @ SY342 @ SV157 ) )
| ( in @ SY342 @ SV185 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1235]) ).
thf(1269,plain,
! [SV157: $i,SV118: $i,SV185: $i] :
( ( ( ! [SY343: $i] :
~ ( ~ ( ~ ( in @ SY343 @ SV185 )
| ( in @ SY343 @ SV118 )
| ( in @ SY343 @ SV157 ) )
| ~ ( ~ ( ( in @ SY343 @ SV118 )
| ( in @ SY343 @ SV157 ) )
| ( in @ SY343 @ SV185 ) ) ) )
= $false )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1236]) ).
thf(1270,plain,
! [SV158: $i,SV119: $i] :
( ( ( ~ ( subset @ SV119 @ SV158 )
| ~ ( ( SV119 != SV158 ) ) )
= $false )
| ( ( proper_subset @ SV119 @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1237]) ).
thf(1271,plain,
! [SV158: $i,SV119: $i] :
( ( ( ~ ( subset @ SV119 @ SV158 )
| ~ ( ( SV119 != SV158 ) ) )
= $true )
| ( ( proper_subset @ SV119 @ SV158 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1238]) ).
thf(1272,plain,
! [SV160: $i,SV121: $i] :
( ( ( SV121 = empty_set )
= $true )
| ( ( SV121
= ( singleton @ SV160 ) )
= $true )
| ( ( subset @ SV121 @ ( singleton @ SV160 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1240]) ).
thf(1273,plain,
! [SV160: $i,SV121: $i] :
( ( ( SV121 = empty_set )
= $false )
| ( ( subset @ SV121 @ ( singleton @ SV160 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1241]) ).
thf(1274,plain,
! [SV160: $i,SV121: $i] :
( ( ( SV121
= ( singleton @ SV160 ) )
= $false )
| ( ( subset @ SV121 @ ( singleton @ SV160 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1241]) ).
thf(1275,plain,
! [SV122: $i,SV161: $i] :
( ( ( ~ ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV122 )
| ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV161 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV161 )
| ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV122 ) ) )
= $true )
| ( ( SV122 = SV161 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1242]) ).
thf(1276,plain,
! [SV166: $i,SV128: $i] :
( ( ( ~ ( subset @ SV128 @ SV166 )
| ~ ( subset @ SV166 @ SV128 ) )
= $false )
| ( ( SV128 = SV166 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1243]) ).
thf(1277,plain,
! [SV166: $i,SV128: $i] :
( ( ( ~ ( subset @ SV128 @ SV166 )
| ~ ( subset @ SV166 @ SV128 ) )
= $true )
| ( ( SV128 = SV166 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1244]) ).
thf(1278,plain,
! [SV167: $i,SV129: $i] :
( ( ( ~ ~ ( disjoint @ SV129 @ SV167 ) )
= $true )
| ( ( ~ ! [SY321: $i] :
~ ~ ( ~ ( in @ SY321 @ SV129 )
| ~ ( in @ SY321 @ SV167 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1245]) ).
thf(1279,plain,
! [SV167: $i,SV129: $i] :
( ( ( ~ ~ ! [SY322: $i] :
~ ~ ( ~ ( in @ SY322 @ SV129 )
| ~ ( in @ SY322 @ SV167 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV129 @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1246]) ).
thf(1280,plain,
! [SV169: $i,SV131: $i,SV189: $i] :
( ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $false )
| ( ( ! [SY344: $i] :
~ ( ~ ( ~ ( in @ SY344 @ SV189 )
| ~ ( ~ ( in @ SY344 @ SV131 )
| ~ ~ ( in @ SY344 @ SV169 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY344 @ SV131 )
| ~ ~ ( in @ SY344 @ SV169 ) )
| ( in @ SY344 @ SV189 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1247]) ).
thf(1281,plain,
! [SV169: $i,SV131: $i,SV189: $i] :
( ( ( ! [SY345: $i] :
~ ( ~ ( ~ ( in @ SY345 @ SV189 )
| ~ ( ~ ( in @ SY345 @ SV131 )
| ~ ~ ( in @ SY345 @ SV169 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY345 @ SV131 )
| ~ ~ ( in @ SY345 @ SV169 ) )
| ( in @ SY345 @ SV189 ) ) ) )
= $false )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1248]) ).
thf(1282,plain,
! [SV133: $i,SV197: $i] :
( ( ( in @ SV197 @ SV133 )
= $false )
| ( ( SV133 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1249]) ).
thf(1283,plain,
! [SV133: $i] :
( ( ( in @ ( sK18_SY278 @ SV133 ) @ SV133 )
= $true )
| ( ( SV133 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1250]) ).
thf(1284,plain,
! [SV191: $i,SV172: $i,SV135: $i] :
( ( ( subset @ SV135 @ SV172 )
= $false )
| ( ( ~ ( subset @ SV172 @ SV191 ) )
= $true )
| ( ( subset @ SV135 @ SV191 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1251]) ).
thf(1285,plain,
! [SV136: $i,SV173: $i,SV200: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV200 @ SV173 )
| ( subset @ SV200 @ SV136 ) )
| ~ ( ~ ( subset @ SV200 @ SV136 )
| ( in @ SV200 @ SV173 ) ) ) )
= $true )
| ( ( SV173
= ( powerset @ SV136 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1286,plain,
! [SV173: $i,SV136: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV173 )
| ( subset @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV136 ) )
| ~ ( ~ ( subset @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV136 )
| ( in @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV173 ) ) ) )
= $false )
| ( ( SV173
= ( powerset @ SV136 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1253]) ).
thf(1287,plain,
! [SV138: $i,SV175: $i,SV201: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV201 @ SV175 )
| ( SV201 = SV138 ) )
| ~ ( ( SV201 != SV138 )
| ( in @ SV201 @ SV175 ) ) ) )
= $true )
| ( ( SV175
= ( singleton @ SV138 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1255]) ).
thf(1288,plain,
! [SV175: $i,SV138: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK22_SY332 @ SV138 @ SV175 ) @ SV175 )
| ( ( sK22_SY332 @ SV138 @ SV175 )
= SV138 ) )
| ~ ( ( ( sK22_SY332 @ SV138 @ SV175 )
!= SV138 )
| ( in @ ( sK22_SY332 @ SV138 @ SV175 ) @ SV175 ) ) ) )
= $false )
| ( ( SV175
= ( singleton @ SV138 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1256]) ).
thf(1289,plain,
! [SV179: $i,SV142: $i,SV193: $i] :
( ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $false )
| ( ( ! [SY346: $i] :
~ ( ~ ( ~ ( in @ SY346 @ SV193 )
| ~ ( ~ ( in @ SY346 @ SV142 )
| ~ ( in @ SY346 @ SV179 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY346 @ SV142 )
| ~ ( in @ SY346 @ SV179 ) )
| ( in @ SY346 @ SV193 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1257]) ).
thf(1290,plain,
! [SV179: $i,SV142: $i,SV193: $i] :
( ( ( ! [SY347: $i] :
~ ( ~ ( ~ ( in @ SY347 @ SV193 )
| ~ ( ~ ( in @ SY347 @ SV142 )
| ~ ( in @ SY347 @ SV179 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY347 @ SV142 )
| ~ ( in @ SY347 @ SV179 ) )
| ( in @ SY347 @ SV193 ) ) ) )
= $false )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1258]) ).
thf(1291,plain,
! [SV194: $i,SV180: $i,SV143: $i] :
( ( ( subset @ SV143 @ SV180 )
= $false )
| ( ( ~ ( disjoint @ SV180 @ SV194 ) )
= $true )
| ( ( disjoint @ SV143 @ SV194 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1259]) ).
thf(1292,plain,
! [SV181: $i,SV144: $i,SV195: $i] :
( ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $false )
| ( ( ! [SY348: $i] :
~ ( ~ ( ~ ( in @ SY348 @ SV195 )
| ( SY348 = SV144 )
| ( SY348 = SV181 ) )
| ~ ( ~ ( ( SY348 = SV144 )
| ( SY348 = SV181 ) )
| ( in @ SY348 @ SV195 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1260]) ).
thf(1293,plain,
! [SV181: $i,SV144: $i,SV195: $i] :
( ( ( ! [SY349: $i] :
~ ( ~ ( ~ ( in @ SY349 @ SV195 )
| ( SY349 = SV144 )
| ( SY349 = SV181 ) )
| ~ ( ~ ( ( SY349 = SV144 )
| ( SY349 = SV181 ) )
| ( in @ SY349 @ SV195 ) ) ) )
= $false )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1261]) ).
thf(1294,plain,
! [SV196: $i,SV182: $i,SV145: $i] :
( ( ( subset @ SV145 @ SV182 )
= $false )
| ( ( ~ ( subset @ SV145 @ SV196 ) )
= $true )
| ( ( subset @ SV145 @ ( set_intersection2 @ SV182 @ SV196 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1262]) ).
thf(1295,plain,
! [SV112: $i,SV151: $i,SV198: $i] :
( ( ( ~ ( ~ ( in @ SV198 @ SV151 )
| ~ ! [SY350: $i] :
~ ~ ( ~ ( in @ SV198 @ SY350 )
| ~ ( in @ SY350 @ SV112 ) ) )
| ~ ( ~ ~ ! [SY351: $i] :
~ ~ ( ~ ( in @ SV198 @ SY351 )
| ~ ( in @ SY351 @ SV112 ) )
| ( in @ SV198 @ SV151 ) ) )
= $false )
| ( ( SV151
= ( union @ SV112 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1263]) ).
thf(1296,plain,
! [SV151: $i,SV112: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV151 )
| ~ ! [SY352: $i] :
~ ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SY352 )
| ~ ( in @ SY352 @ SV112 ) ) )
| ~ ( ~ ~ ! [SY353: $i] :
~ ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SY353 )
| ~ ( in @ SY353 @ SV112 ) )
| ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV151 ) ) )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1264]) ).
thf(1297,plain,
! [SV114: $i,SV153: $i,SV184: $i] :
( ( ( subset @ SV184 @ SV153 )
= $false )
| ( ( subset @ SV114 @ SV153 )
= $false )
| ( ( subset @ ( set_union2 @ SV114 @ SV184 ) @ SV153 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1265]) ).
thf(1298,plain,
! [SV155: $i,SV116: $i,SV199: $i] :
( ( ( ~ ( in @ SV199 @ SV116 ) )
= $true )
| ( ( in @ SV199 @ SV155 )
= $true )
| ( ( subset @ SV116 @ SV155 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1266]) ).
thf(1299,plain,
! [SV116: $i,SV155: $i] :
( ( ( ~ ( in @ ( sK20_SY314 @ SV155 @ SV116 ) @ SV116 ) )
= $false )
| ( ( subset @ SV116 @ SV155 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1267]) ).
thf(1300,plain,
! [SV116: $i,SV155: $i] :
( ( ( in @ ( sK20_SY314 @ SV155 @ SV116 ) @ SV155 )
= $false )
| ( ( subset @ SV116 @ SV155 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1267]) ).
thf(1301,plain,
! [SV157: $i,SV118: $i,SV185: $i,SV202: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV202 @ SV185 )
| ( in @ SV202 @ SV118 )
| ( in @ SV202 @ SV157 ) )
| ~ ( ~ ( ( in @ SV202 @ SV118 )
| ( in @ SV202 @ SV157 ) )
| ( in @ SV202 @ SV185 ) ) ) )
= $true )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1268]) ).
thf(1302,plain,
! [SV185: $i,SV118: $i,SV157: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV185 )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV118 )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV157 ) )
| ~ ( ~ ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV118 )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV157 ) )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV185 ) ) ) )
= $false )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1269]) ).
thf(1303,plain,
! [SV158: $i,SV119: $i] :
( ( ( ~ ( subset @ SV119 @ SV158 ) )
= $false )
| ( ( proper_subset @ SV119 @ SV158 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1270]) ).
thf(1304,plain,
! [SV158: $i,SV119: $i] :
( ( ( ~ ( ( SV119 != SV158 ) ) )
= $false )
| ( ( proper_subset @ SV119 @ SV158 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1270]) ).
thf(1305,plain,
! [SV158: $i,SV119: $i] :
( ( ( ~ ( subset @ SV119 @ SV158 ) )
= $true )
| ( ( ~ ( ( SV119 != SV158 ) ) )
= $true )
| ( ( proper_subset @ SV119 @ SV158 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1271]) ).
thf(1306,plain,
! [SV122: $i,SV161: $i] :
( ( ( ~ ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV122 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV161 )
| ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV122 ) ) )
= $true )
| ( ( SV122 = SV161 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1275]) ).
thf(1307,plain,
! [SV122: $i,SV161: $i] :
( ( ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV161 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV161 )
| ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV122 ) ) )
= $true )
| ( ( SV122 = SV161 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1275]) ).
thf(1308,plain,
! [SV166: $i,SV128: $i] :
( ( ( ~ ( subset @ SV128 @ SV166 ) )
= $false )
| ( ( SV128 = SV166 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1276]) ).
thf(1309,plain,
! [SV128: $i,SV166: $i] :
( ( ( ~ ( subset @ SV166 @ SV128 ) )
= $false )
| ( ( SV128 = SV166 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1276]) ).
thf(1310,plain,
! [SV166: $i,SV128: $i] :
( ( ( ~ ( subset @ SV128 @ SV166 ) )
= $true )
| ( ( ~ ( subset @ SV166 @ SV128 ) )
= $true )
| ( ( SV128 = SV166 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1277]) ).
thf(1311,plain,
! [SV167: $i,SV129: $i] :
( ( ( ~ ( disjoint @ SV129 @ SV167 ) )
= $false )
| ( ( ~ ! [SY321: $i] :
~ ~ ( ~ ( in @ SY321 @ SV129 )
| ~ ( in @ SY321 @ SV167 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1278]) ).
thf(1312,plain,
! [SV167: $i,SV129: $i] :
( ( ( ~ ! [SY322: $i] :
~ ~ ( ~ ( in @ SY322 @ SV129 )
| ~ ( in @ SY322 @ SV167 ) ) )
= $false )
| ( ( ~ ( disjoint @ SV129 @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1279]) ).
thf(1313,plain,
! [SV169: $i,SV131: $i,SV189: $i,SV203: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV203 @ SV189 )
| ~ ( ~ ( in @ SV203 @ SV131 )
| ~ ~ ( in @ SV203 @ SV169 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV203 @ SV131 )
| ~ ~ ( in @ SV203 @ SV169 ) )
| ( in @ SV203 @ SV189 ) ) ) )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1280]) ).
thf(1314,plain,
! [SV189: $i,SV131: $i,SV169: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV189 )
| ~ ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
| ~ ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
| ~ ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 ) )
| ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV189 ) ) ) )
= $false )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1281]) ).
thf(1315,plain,
! [SV135: $i,SV191: $i,SV172: $i] :
( ( ( subset @ SV172 @ SV191 )
= $false )
| ( ( subset @ SV135 @ SV172 )
= $false )
| ( ( subset @ SV135 @ SV191 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1284]) ).
thf(1316,plain,
! [SV136: $i,SV173: $i,SV200: $i] :
( ( ( ~ ( ~ ( in @ SV200 @ SV173 )
| ( subset @ SV200 @ SV136 ) )
| ~ ( ~ ( subset @ SV200 @ SV136 )
| ( in @ SV200 @ SV173 ) ) )
= $false )
| ( ( SV173
= ( powerset @ SV136 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1285]) ).
thf(1317,plain,
! [SV173: $i,SV136: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV173 )
| ( subset @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV136 ) )
| ~ ( ~ ( subset @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV136 )
| ( in @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV173 ) ) )
= $true )
| ( ( SV173
= ( powerset @ SV136 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1286]) ).
thf(1318,plain,
! [SV138: $i,SV175: $i,SV201: $i] :
( ( ( ~ ( ~ ( in @ SV201 @ SV175 )
| ( SV201 = SV138 ) )
| ~ ( ( SV201 != SV138 )
| ( in @ SV201 @ SV175 ) ) )
= $false )
| ( ( SV175
= ( singleton @ SV138 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1287]) ).
thf(1319,plain,
! [SV175: $i,SV138: $i] :
( ( ( ~ ( ~ ( in @ ( sK22_SY332 @ SV138 @ SV175 ) @ SV175 )
| ( ( sK22_SY332 @ SV138 @ SV175 )
= SV138 ) )
| ~ ( ( ( sK22_SY332 @ SV138 @ SV175 )
!= SV138 )
| ( in @ ( sK22_SY332 @ SV138 @ SV175 ) @ SV175 ) ) )
= $true )
| ( ( SV175
= ( singleton @ SV138 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1288]) ).
thf(1320,plain,
! [SV179: $i,SV142: $i,SV193: $i,SV204: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV204 @ SV193 )
| ~ ( ~ ( in @ SV204 @ SV142 )
| ~ ( in @ SV204 @ SV179 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV204 @ SV142 )
| ~ ( in @ SV204 @ SV179 ) )
| ( in @ SV204 @ SV193 ) ) ) )
= $true )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1289]) ).
thf(1321,plain,
! [SV193: $i,SV142: $i,SV179: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV193 )
| ~ ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
| ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
| ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 ) )
| ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV193 ) ) ) )
= $false )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1290]) ).
thf(1322,plain,
! [SV143: $i,SV194: $i,SV180: $i] :
( ( ( disjoint @ SV180 @ SV194 )
= $false )
| ( ( subset @ SV143 @ SV180 )
= $false )
| ( ( disjoint @ SV143 @ SV194 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1291]) ).
thf(1323,plain,
! [SV181: $i,SV144: $i,SV195: $i,SV205: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV205 @ SV195 )
| ( SV205 = SV144 )
| ( SV205 = SV181 ) )
| ~ ( ~ ( ( SV205 = SV144 )
| ( SV205 = SV181 ) )
| ( in @ SV205 @ SV195 ) ) ) )
= $true )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1292]) ).
thf(1324,plain,
! [SV195: $i,SV144: $i,SV181: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK26_SY349 @ SV181 @ SV144 @ SV195 ) @ SV195 )
| ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV144 )
| ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV181 ) )
| ~ ( ~ ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV144 )
| ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV181 ) )
| ( in @ ( sK26_SY349 @ SV181 @ SV144 @ SV195 ) @ SV195 ) ) ) )
= $false )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1293]) ).
thf(1325,plain,
! [SV182: $i,SV196: $i,SV145: $i] :
( ( ( subset @ SV145 @ SV196 )
= $false )
| ( ( subset @ SV145 @ SV182 )
= $false )
| ( ( subset @ SV145 @ ( set_intersection2 @ SV182 @ SV196 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1294]) ).
thf(1326,plain,
! [SV112: $i,SV151: $i,SV198: $i] :
( ( ( ~ ( ~ ( in @ SV198 @ SV151 )
| ~ ! [SY350: $i] :
~ ~ ( ~ ( in @ SV198 @ SY350 )
| ~ ( in @ SY350 @ SV112 ) ) ) )
= $false )
| ( ( SV151
= ( union @ SV112 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1295]) ).
thf(1327,plain,
! [SV151: $i,SV112: $i,SV198: $i] :
( ( ( ~ ( ~ ~ ! [SY351: $i] :
~ ~ ( ~ ( in @ SV198 @ SY351 )
| ~ ( in @ SY351 @ SV112 ) )
| ( in @ SV198 @ SV151 ) ) )
= $false )
| ( ( SV151
= ( union @ SV112 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1295]) ).
thf(1328,plain,
! [SV151: $i,SV112: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV151 )
| ~ ! [SY352: $i] :
~ ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SY352 )
| ~ ( in @ SY352 @ SV112 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY353: $i] :
~ ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SY353 )
| ~ ( in @ SY353 @ SV112 ) )
| ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV151 ) ) )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1296]) ).
thf(1329,plain,
! [SV155: $i,SV116: $i,SV199: $i] :
( ( ( in @ SV199 @ SV116 )
= $false )
| ( ( in @ SV199 @ SV155 )
= $true )
| ( ( subset @ SV116 @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1298]) ).
thf(1330,plain,
! [SV116: $i,SV155: $i] :
( ( ( in @ ( sK20_SY314 @ SV155 @ SV116 ) @ SV116 )
= $true )
| ( ( subset @ SV116 @ SV155 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1299]) ).
thf(1331,plain,
! [SV157: $i,SV118: $i,SV185: $i,SV202: $i] :
( ( ( ~ ( ~ ( in @ SV202 @ SV185 )
| ( in @ SV202 @ SV118 )
| ( in @ SV202 @ SV157 ) )
| ~ ( ~ ( ( in @ SV202 @ SV118 )
| ( in @ SV202 @ SV157 ) )
| ( in @ SV202 @ SV185 ) ) )
= $false )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1301]) ).
thf(1332,plain,
! [SV185: $i,SV118: $i,SV157: $i] :
( ( ( ~ ( ~ ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV185 )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV118 )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV157 ) )
| ~ ( ~ ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV118 )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV157 ) )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV185 ) ) )
= $true )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1302]) ).
thf(1333,plain,
! [SV158: $i,SV119: $i] :
( ( ( subset @ SV119 @ SV158 )
= $true )
| ( ( proper_subset @ SV119 @ SV158 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1303]) ).
thf(1334,plain,
! [SV158: $i,SV119: $i] :
( ( ( SV119 != SV158 )
= $true )
| ( ( proper_subset @ SV119 @ SV158 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1304]) ).
thf(1335,plain,
! [SV158: $i,SV119: $i] :
( ( ( subset @ SV119 @ SV158 )
= $false )
| ( ( ~ ( ( SV119 != SV158 ) ) )
= $true )
| ( ( proper_subset @ SV119 @ SV158 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1305]) ).
thf(1336,plain,
! [SV122: $i,SV161: $i] :
( ( ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV122 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV161 )
| ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV122 ) ) )
= $true )
| ( ( SV122 = SV161 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1306]) ).
thf(1337,plain,
! [SV122: $i,SV161: $i] :
( ( ( ~ ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV161 )
| ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV122 ) )
= $false )
| ( ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV161 )
= $false )
| ( ( SV122 = SV161 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1307]) ).
thf(1338,plain,
! [SV166: $i,SV128: $i] :
( ( ( subset @ SV128 @ SV166 )
= $true )
| ( ( SV128 = SV166 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1308]) ).
thf(1339,plain,
! [SV128: $i,SV166: $i] :
( ( ( subset @ SV166 @ SV128 )
= $true )
| ( ( SV128 = SV166 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1309]) ).
thf(1340,plain,
! [SV166: $i,SV128: $i] :
( ( ( subset @ SV128 @ SV166 )
= $false )
| ( ( ~ ( subset @ SV166 @ SV128 ) )
= $true )
| ( ( SV128 = SV166 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1310]) ).
thf(1341,plain,
! [SV167: $i,SV129: $i] :
( ( ( disjoint @ SV129 @ SV167 )
= $true )
| ( ( ~ ! [SY321: $i] :
~ ~ ( ~ ( in @ SY321 @ SV129 )
| ~ ( in @ SY321 @ SV167 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1311]) ).
thf(1342,plain,
! [SV167: $i,SV129: $i] :
( ( ( ! [SY322: $i] :
~ ~ ( ~ ( in @ SY322 @ SV129 )
| ~ ( in @ SY322 @ SV167 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV129 @ SV167 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1312]) ).
thf(1343,plain,
! [SV169: $i,SV131: $i,SV189: $i,SV203: $i] :
( ( ( ~ ( ~ ( in @ SV203 @ SV189 )
| ~ ( ~ ( in @ SV203 @ SV131 )
| ~ ~ ( in @ SV203 @ SV169 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV203 @ SV131 )
| ~ ~ ( in @ SV203 @ SV169 ) )
| ( in @ SV203 @ SV189 ) ) )
= $false )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1313]) ).
thf(1344,plain,
! [SV189: $i,SV131: $i,SV169: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV189 )
| ~ ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
| ~ ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
| ~ ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 ) )
| ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV189 ) ) )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1314]) ).
thf(1345,plain,
! [SV136: $i,SV173: $i,SV200: $i] :
( ( ( ~ ( ~ ( in @ SV200 @ SV173 )
| ( subset @ SV200 @ SV136 ) ) )
= $false )
| ( ( SV173
= ( powerset @ SV136 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1316]) ).
thf(1346,plain,
! [SV173: $i,SV136: $i,SV200: $i] :
( ( ( ~ ( ~ ( subset @ SV200 @ SV136 )
| ( in @ SV200 @ SV173 ) ) )
= $false )
| ( ( SV173
= ( powerset @ SV136 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1316]) ).
thf(1347,plain,
! [SV173: $i,SV136: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV173 )
| ( subset @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV136 ) ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV136 )
| ( in @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV173 ) ) )
= $true )
| ( ( SV173
= ( powerset @ SV136 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1317]) ).
thf(1348,plain,
! [SV138: $i,SV175: $i,SV201: $i] :
( ( ( ~ ( ~ ( in @ SV201 @ SV175 )
| ( SV201 = SV138 ) ) )
= $false )
| ( ( SV175
= ( singleton @ SV138 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1318]) ).
thf(1349,plain,
! [SV175: $i,SV138: $i,SV201: $i] :
( ( ( ~ ( ( SV201 != SV138 )
| ( in @ SV201 @ SV175 ) ) )
= $false )
| ( ( SV175
= ( singleton @ SV138 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1318]) ).
thf(1350,plain,
! [SV175: $i,SV138: $i] :
( ( ( ~ ( ~ ( in @ ( sK22_SY332 @ SV138 @ SV175 ) @ SV175 )
| ( ( sK22_SY332 @ SV138 @ SV175 )
= SV138 ) ) )
= $true )
| ( ( ~ ( ( ( sK22_SY332 @ SV138 @ SV175 )
!= SV138 )
| ( in @ ( sK22_SY332 @ SV138 @ SV175 ) @ SV175 ) ) )
= $true )
| ( ( SV175
= ( singleton @ SV138 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1319]) ).
thf(1351,plain,
! [SV179: $i,SV142: $i,SV193: $i,SV204: $i] :
( ( ( ~ ( ~ ( in @ SV204 @ SV193 )
| ~ ( ~ ( in @ SV204 @ SV142 )
| ~ ( in @ SV204 @ SV179 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV204 @ SV142 )
| ~ ( in @ SV204 @ SV179 ) )
| ( in @ SV204 @ SV193 ) ) )
= $false )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1320]) ).
thf(1352,plain,
! [SV193: $i,SV142: $i,SV179: $i] :
( ( ( ~ ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV193 )
| ~ ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
| ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
| ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 ) )
| ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV193 ) ) )
= $true )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1321]) ).
thf(1353,plain,
! [SV181: $i,SV144: $i,SV195: $i,SV205: $i] :
( ( ( ~ ( ~ ( in @ SV205 @ SV195 )
| ( SV205 = SV144 )
| ( SV205 = SV181 ) )
| ~ ( ~ ( ( SV205 = SV144 )
| ( SV205 = SV181 ) )
| ( in @ SV205 @ SV195 ) ) )
= $false )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1323]) ).
thf(1354,plain,
! [SV195: $i,SV144: $i,SV181: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_SY349 @ SV181 @ SV144 @ SV195 ) @ SV195 )
| ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV144 )
| ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV181 ) )
| ~ ( ~ ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV144 )
| ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV181 ) )
| ( in @ ( sK26_SY349 @ SV181 @ SV144 @ SV195 ) @ SV195 ) ) )
= $true )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1324]) ).
thf(1355,plain,
! [SV112: $i,SV151: $i,SV198: $i] :
( ( ( ~ ( in @ SV198 @ SV151 )
| ~ ! [SY350: $i] :
~ ~ ( ~ ( in @ SV198 @ SY350 )
| ~ ( in @ SY350 @ SV112 ) ) )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1326]) ).
thf(1356,plain,
! [SV151: $i,SV112: $i,SV198: $i] :
( ( ( ~ ~ ! [SY351: $i] :
~ ~ ( ~ ( in @ SV198 @ SY351 )
| ~ ( in @ SY351 @ SV112 ) )
| ( in @ SV198 @ SV151 ) )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1327]) ).
thf(1357,plain,
! [SV151: $i,SV112: $i] :
( ( ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV151 )
| ~ ! [SY352: $i] :
~ ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SY352 )
| ~ ( in @ SY352 @ SV112 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY353: $i] :
~ ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SY353 )
| ~ ( in @ SY353 @ SV112 ) )
| ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV151 ) ) )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1328]) ).
thf(1358,plain,
! [SV157: $i,SV118: $i,SV185: $i,SV202: $i] :
( ( ( ~ ( ~ ( in @ SV202 @ SV185 )
| ( in @ SV202 @ SV118 )
| ( in @ SV202 @ SV157 ) ) )
= $false )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1331]) ).
thf(1359,plain,
! [SV185: $i,SV157: $i,SV118: $i,SV202: $i] :
( ( ( ~ ( ~ ( ( in @ SV202 @ SV118 )
| ( in @ SV202 @ SV157 ) )
| ( in @ SV202 @ SV185 ) ) )
= $false )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1331]) ).
thf(1360,plain,
! [SV185: $i,SV118: $i,SV157: $i] :
( ( ( ~ ( ~ ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV185 )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV118 )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV157 ) ) )
= $true )
| ( ( ~ ( ~ ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV118 )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV157 ) )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV185 ) ) )
= $true )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1332]) ).
thf(1361,plain,
! [SV158: $i,SV119: $i] :
( ( ( SV119 = SV158 )
= $false )
| ( ( proper_subset @ SV119 @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1334]) ).
thf(1362,plain,
! [SV158: $i,SV119: $i] :
( ( ( SV119 != SV158 )
= $false )
| ( ( subset @ SV119 @ SV158 )
= $false )
| ( ( proper_subset @ SV119 @ SV158 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1335]) ).
thf(1363,plain,
! [SV122: $i,SV161: $i] :
( ( ( ~ ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV161 )
| ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV122 ) )
= $false )
| ( ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV122 )
= $true )
| ( ( SV122 = SV161 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1336]) ).
thf(1364,plain,
! [SV122: $i,SV161: $i] :
( ( ( ~ ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV161 ) )
= $false )
| ( ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV161 )
= $false )
| ( ( SV122 = SV161 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1337]) ).
thf(1365,plain,
! [SV122: $i,SV161: $i] :
( ( ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV122 )
= $false )
| ( ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV161 )
= $false )
| ( ( SV122 = SV161 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1337]) ).
thf(1366,plain,
! [SV128: $i,SV166: $i] :
( ( ( subset @ SV166 @ SV128 )
= $false )
| ( ( subset @ SV128 @ SV166 )
= $false )
| ( ( SV128 = SV166 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1340]) ).
thf(1367,plain,
! [SV167: $i,SV129: $i] :
( ( ( ! [SY321: $i] :
~ ~ ( ~ ( in @ SY321 @ SV129 )
| ~ ( in @ SY321 @ SV167 ) ) )
= $false )
| ( ( disjoint @ SV129 @ SV167 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1341]) ).
thf(1368,plain,
! [SV167: $i,SV129: $i,SV206: $i] :
( ( ( ~ ~ ( ~ ( in @ SV206 @ SV129 )
| ~ ( in @ SV206 @ SV167 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV129 @ SV167 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1342]) ).
thf(1369,plain,
! [SV169: $i,SV131: $i,SV189: $i,SV203: $i] :
( ( ( ~ ( ~ ( in @ SV203 @ SV189 )
| ~ ( ~ ( in @ SV203 @ SV131 )
| ~ ~ ( in @ SV203 @ SV169 ) ) ) )
= $false )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1343]) ).
thf(1370,plain,
! [SV189: $i,SV169: $i,SV131: $i,SV203: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV203 @ SV131 )
| ~ ~ ( in @ SV203 @ SV169 ) )
| ( in @ SV203 @ SV189 ) ) )
= $false )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1343]) ).
thf(1371,plain,
! [SV189: $i,SV131: $i,SV169: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV189 )
| ~ ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
| ~ ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
| ~ ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 ) )
| ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV189 ) ) )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1344]) ).
thf(1372,plain,
! [SV136: $i,SV173: $i,SV200: $i] :
( ( ( ~ ( in @ SV200 @ SV173 )
| ( subset @ SV200 @ SV136 ) )
= $true )
| ( ( SV173
= ( powerset @ SV136 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1345]) ).
thf(1373,plain,
! [SV173: $i,SV136: $i,SV200: $i] :
( ( ( ~ ( subset @ SV200 @ SV136 )
| ( in @ SV200 @ SV173 ) )
= $true )
| ( ( SV173
= ( powerset @ SV136 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1346]) ).
thf(1374,plain,
! [SV173: $i,SV136: $i] :
( ( ( ~ ( in @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV173 )
| ( subset @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV136 ) )
= $false )
| ( ( ~ ( ~ ( subset @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV136 )
| ( in @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV173 ) ) )
= $true )
| ( ( SV173
= ( powerset @ SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1347]) ).
thf(1375,plain,
! [SV138: $i,SV175: $i,SV201: $i] :
( ( ( ~ ( in @ SV201 @ SV175 )
| ( SV201 = SV138 ) )
= $true )
| ( ( SV175
= ( singleton @ SV138 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1348]) ).
thf(1376,plain,
! [SV175: $i,SV138: $i,SV201: $i] :
( ( ( ( SV201 != SV138 )
| ( in @ SV201 @ SV175 ) )
= $true )
| ( ( SV175
= ( singleton @ SV138 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1349]) ).
thf(1377,plain,
! [SV175: $i,SV138: $i] :
( ( ( ~ ( in @ ( sK22_SY332 @ SV138 @ SV175 ) @ SV175 )
| ( ( sK22_SY332 @ SV138 @ SV175 )
= SV138 ) )
= $false )
| ( ( ~ ( ( ( sK22_SY332 @ SV138 @ SV175 )
!= SV138 )
| ( in @ ( sK22_SY332 @ SV138 @ SV175 ) @ SV175 ) ) )
= $true )
| ( ( SV175
= ( singleton @ SV138 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1350]) ).
thf(1378,plain,
! [SV179: $i,SV142: $i,SV193: $i,SV204: $i] :
( ( ( ~ ( ~ ( in @ SV204 @ SV193 )
| ~ ( ~ ( in @ SV204 @ SV142 )
| ~ ( in @ SV204 @ SV179 ) ) ) )
= $false )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1351]) ).
thf(1379,plain,
! [SV193: $i,SV179: $i,SV142: $i,SV204: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV204 @ SV142 )
| ~ ( in @ SV204 @ SV179 ) )
| ( in @ SV204 @ SV193 ) ) )
= $false )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1351]) ).
thf(1380,plain,
! [SV193: $i,SV142: $i,SV179: $i] :
( ( ( ~ ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV193 )
| ~ ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
| ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
| ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 ) )
| ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV193 ) ) )
= $true )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1352]) ).
thf(1381,plain,
! [SV181: $i,SV144: $i,SV195: $i,SV205: $i] :
( ( ( ~ ( ~ ( in @ SV205 @ SV195 )
| ( SV205 = SV144 )
| ( SV205 = SV181 ) ) )
= $false )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1353]) ).
thf(1382,plain,
! [SV195: $i,SV181: $i,SV144: $i,SV205: $i] :
( ( ( ~ ( ~ ( ( SV205 = SV144 )
| ( SV205 = SV181 ) )
| ( in @ SV205 @ SV195 ) ) )
= $false )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1353]) ).
thf(1383,plain,
! [SV195: $i,SV144: $i,SV181: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_SY349 @ SV181 @ SV144 @ SV195 ) @ SV195 )
| ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV144 )
| ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV181 ) ) )
= $true )
| ( ( ~ ( ~ ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV144 )
| ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV181 ) )
| ( in @ ( sK26_SY349 @ SV181 @ SV144 @ SV195 ) @ SV195 ) ) )
= $true )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1354]) ).
thf(1384,plain,
! [SV112: $i,SV151: $i,SV198: $i] :
( ( ( ~ ( in @ SV198 @ SV151 ) )
= $true )
| ( ( ~ ! [SY350: $i] :
~ ~ ( ~ ( in @ SV198 @ SY350 )
| ~ ( in @ SY350 @ SV112 ) ) )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1355]) ).
thf(1385,plain,
! [SV151: $i,SV112: $i,SV198: $i] :
( ( ( ~ ~ ! [SY351: $i] :
~ ~ ( ~ ( in @ SV198 @ SY351 )
| ~ ( in @ SY351 @ SV112 ) ) )
= $true )
| ( ( in @ SV198 @ SV151 )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1356]) ).
thf(1386,plain,
! [SV151: $i,SV112: $i] :
( ( ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV151 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY353: $i] :
~ ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SY353 )
| ~ ( in @ SY353 @ SV112 ) )
| ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV151 ) ) )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1357]) ).
thf(1387,plain,
! [SV151: $i,SV112: $i] :
( ( ( ~ ! [SY352: $i] :
~ ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SY352 )
| ~ ( in @ SY352 @ SV112 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY353: $i] :
~ ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SY353 )
| ~ ( in @ SY353 @ SV112 ) )
| ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV151 ) ) )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1357]) ).
thf(1388,plain,
! [SV157: $i,SV118: $i,SV185: $i,SV202: $i] :
( ( ( ~ ( in @ SV202 @ SV185 )
| ( in @ SV202 @ SV118 )
| ( in @ SV202 @ SV157 ) )
= $true )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1358]) ).
thf(1389,plain,
! [SV185: $i,SV157: $i,SV118: $i,SV202: $i] :
( ( ( ~ ( ( in @ SV202 @ SV118 )
| ( in @ SV202 @ SV157 ) )
| ( in @ SV202 @ SV185 ) )
= $true )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1359]) ).
thf(1390,plain,
! [SV185: $i,SV118: $i,SV157: $i] :
( ( ( ~ ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV185 )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV118 )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV157 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV118 )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV157 ) )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV185 ) ) )
= $true )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1360]) ).
thf(1391,plain,
! [SV158: $i,SV119: $i] :
( ( ( SV119 = SV158 )
= $true )
| ( ( subset @ SV119 @ SV158 )
= $false )
| ( ( proper_subset @ SV119 @ SV158 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1362]) ).
thf(1392,plain,
! [SV122: $i,SV161: $i] :
( ( ( ~ ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV161 ) )
= $false )
| ( ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV122 )
= $true )
| ( ( SV122 = SV161 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1363]) ).
thf(1393,plain,
! [SV122: $i,SV161: $i] :
( ( ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV122 )
= $false )
| ( ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV122 )
= $true )
| ( ( SV122 = SV161 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1363]) ).
thf(1394,plain,
! [SV122: $i,SV161: $i] :
( ( ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV161 )
= $true )
| ( ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV161 )
= $false )
| ( ( SV122 = SV161 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1364]) ).
thf(1395,plain,
! [SV129: $i,SV167: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK27_SY321 @ SV167 @ SV129 ) @ SV129 )
| ~ ( in @ ( sK27_SY321 @ SV167 @ SV129 ) @ SV167 ) ) )
= $false )
| ( ( disjoint @ SV129 @ SV167 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1367]) ).
thf(1396,plain,
! [SV167: $i,SV129: $i,SV206: $i] :
( ( ( ~ ( ~ ( in @ SV206 @ SV129 )
| ~ ( in @ SV206 @ SV167 ) ) )
= $false )
| ( ( ~ ( disjoint @ SV129 @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1368]) ).
thf(1397,plain,
! [SV169: $i,SV131: $i,SV189: $i,SV203: $i] :
( ( ( ~ ( in @ SV203 @ SV189 )
| ~ ( ~ ( in @ SV203 @ SV131 )
| ~ ~ ( in @ SV203 @ SV169 ) ) )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1369]) ).
thf(1398,plain,
! [SV189: $i,SV169: $i,SV131: $i,SV203: $i] :
( ( ( ~ ~ ( ~ ( in @ SV203 @ SV131 )
| ~ ~ ( in @ SV203 @ SV169 ) )
| ( in @ SV203 @ SV189 ) )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1370]) ).
thf(1399,plain,
! [SV189: $i,SV131: $i,SV169: $i] :
( ( ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV189 )
| ~ ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
| ~ ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
| ~ ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 ) )
| ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV189 ) ) )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1371]) ).
thf(1400,plain,
! [SV136: $i,SV173: $i,SV200: $i] :
( ( ( ~ ( in @ SV200 @ SV173 ) )
= $true )
| ( ( subset @ SV200 @ SV136 )
= $true )
| ( ( SV173
= ( powerset @ SV136 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1372]) ).
thf(1401,plain,
! [SV173: $i,SV136: $i,SV200: $i] :
( ( ( ~ ( subset @ SV200 @ SV136 ) )
= $true )
| ( ( in @ SV200 @ SV173 )
= $true )
| ( ( SV173
= ( powerset @ SV136 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1373]) ).
thf(1402,plain,
! [SV173: $i,SV136: $i] :
( ( ( ~ ( in @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV173 ) )
= $false )
| ( ( ~ ( ~ ( subset @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV136 )
| ( in @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV173 ) ) )
= $true )
| ( ( SV173
= ( powerset @ SV136 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1374]) ).
thf(1403,plain,
! [SV173: $i,SV136: $i] :
( ( ( subset @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV136 )
= $false )
| ( ( ~ ( ~ ( subset @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV136 )
| ( in @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV173 ) ) )
= $true )
| ( ( SV173
= ( powerset @ SV136 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1374]) ).
thf(1404,plain,
! [SV138: $i,SV175: $i,SV201: $i] :
( ( ( ~ ( in @ SV201 @ SV175 ) )
= $true )
| ( ( SV201 = SV138 )
= $true )
| ( ( SV175
= ( singleton @ SV138 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1375]) ).
thf(1405,plain,
! [SV175: $i,SV138: $i,SV201: $i] :
( ( ( SV201 != SV138 )
= $true )
| ( ( in @ SV201 @ SV175 )
= $true )
| ( ( SV175
= ( singleton @ SV138 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1376]) ).
thf(1406,plain,
! [SV175: $i,SV138: $i] :
( ( ( ~ ( in @ ( sK22_SY332 @ SV138 @ SV175 ) @ SV175 ) )
= $false )
| ( ( ~ ( ( ( sK22_SY332 @ SV138 @ SV175 )
!= SV138 )
| ( in @ ( sK22_SY332 @ SV138 @ SV175 ) @ SV175 ) ) )
= $true )
| ( ( SV175
= ( singleton @ SV138 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1377]) ).
thf(1407,plain,
! [SV175: $i,SV138: $i] :
( ( ( ( sK22_SY332 @ SV138 @ SV175 )
= SV138 )
= $false )
| ( ( ~ ( ( ( sK22_SY332 @ SV138 @ SV175 )
!= SV138 )
| ( in @ ( sK22_SY332 @ SV138 @ SV175 ) @ SV175 ) ) )
= $true )
| ( ( SV175
= ( singleton @ SV138 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1377]) ).
thf(1408,plain,
! [SV179: $i,SV142: $i,SV193: $i,SV204: $i] :
( ( ( ~ ( in @ SV204 @ SV193 )
| ~ ( ~ ( in @ SV204 @ SV142 )
| ~ ( in @ SV204 @ SV179 ) ) )
= $true )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1378]) ).
thf(1409,plain,
! [SV193: $i,SV179: $i,SV142: $i,SV204: $i] :
( ( ( ~ ~ ( ~ ( in @ SV204 @ SV142 )
| ~ ( in @ SV204 @ SV179 ) )
| ( in @ SV204 @ SV193 ) )
= $true )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1379]) ).
thf(1410,plain,
! [SV193: $i,SV142: $i,SV179: $i] :
( ( ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV193 )
| ~ ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
| ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
| ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 ) )
| ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV193 ) ) )
= $true )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1380]) ).
thf(1411,plain,
! [SV181: $i,SV144: $i,SV195: $i,SV205: $i] :
( ( ( ~ ( in @ SV205 @ SV195 )
| ( SV205 = SV144 )
| ( SV205 = SV181 ) )
= $true )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1381]) ).
thf(1412,plain,
! [SV195: $i,SV181: $i,SV144: $i,SV205: $i] :
( ( ( ~ ( ( SV205 = SV144 )
| ( SV205 = SV181 ) )
| ( in @ SV205 @ SV195 ) )
= $true )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1382]) ).
thf(1413,plain,
! [SV195: $i,SV144: $i,SV181: $i] :
( ( ( ~ ( in @ ( sK26_SY349 @ SV181 @ SV144 @ SV195 ) @ SV195 )
| ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV144 )
| ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV181 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV144 )
| ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV181 ) )
| ( in @ ( sK26_SY349 @ SV181 @ SV144 @ SV195 ) @ SV195 ) ) )
= $true )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1383]) ).
thf(1414,plain,
! [SV112: $i,SV151: $i,SV198: $i] :
( ( ( in @ SV198 @ SV151 )
= $false )
| ( ( ~ ! [SY350: $i] :
~ ~ ( ~ ( in @ SV198 @ SY350 )
| ~ ( in @ SY350 @ SV112 ) ) )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1384]) ).
thf(1415,plain,
! [SV151: $i,SV112: $i,SV198: $i] :
( ( ( ~ ! [SY351: $i] :
~ ~ ( ~ ( in @ SV198 @ SY351 )
| ~ ( in @ SY351 @ SV112 ) ) )
= $false )
| ( ( in @ SV198 @ SV151 )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1385]) ).
thf(1416,plain,
! [SV151: $i,SV112: $i] :
( ( ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV151 )
= $true )
| ( ( ~ ( ~ ~ ! [SY353: $i] :
~ ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SY353 )
| ~ ( in @ SY353 @ SV112 ) )
| ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV151 ) ) )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1386]) ).
thf(1417,plain,
! [SV151: $i,SV112: $i] :
( ( ( ! [SY352: $i] :
~ ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SY352 )
| ~ ( in @ SY352 @ SV112 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY353: $i] :
~ ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SY353 )
| ~ ( in @ SY353 @ SV112 ) )
| ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV151 ) ) )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1387]) ).
thf(1418,plain,
! [SV157: $i,SV118: $i,SV185: $i,SV202: $i] :
( ( ( ~ ( in @ SV202 @ SV185 ) )
= $true )
| ( ( ( in @ SV202 @ SV118 )
| ( in @ SV202 @ SV157 ) )
= $true )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1388]) ).
thf(1419,plain,
! [SV185: $i,SV157: $i,SV118: $i,SV202: $i] :
( ( ( ~ ( ( in @ SV202 @ SV118 )
| ( in @ SV202 @ SV157 ) ) )
= $true )
| ( ( in @ SV202 @ SV185 )
= $true )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1389]) ).
thf(1420,plain,
! [SV185: $i,SV118: $i,SV157: $i] :
( ( ( ~ ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV185 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV118 )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV157 ) )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV185 ) ) )
= $true )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1390]) ).
thf(1421,plain,
! [SV185: $i,SV118: $i,SV157: $i] :
( ( ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV118 )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV157 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV118 )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV157 ) )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV185 ) ) )
= $true )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1390]) ).
thf(1422,plain,
! [SV122: $i,SV161: $i] :
( ( ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV161 )
= $true )
| ( ( in @ ( sK17_SY318 @ SV161 @ SV122 ) @ SV122 )
= $true )
| ( ( SV122 = SV161 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1392]) ).
thf(1423,plain,
! [SV129: $i,SV167: $i] :
( ( ( ~ ( ~ ( in @ ( sK27_SY321 @ SV167 @ SV129 ) @ SV129 )
| ~ ( in @ ( sK27_SY321 @ SV167 @ SV129 ) @ SV167 ) ) )
= $true )
| ( ( disjoint @ SV129 @ SV167 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1395]) ).
thf(1424,plain,
! [SV167: $i,SV129: $i,SV206: $i] :
( ( ( ~ ( in @ SV206 @ SV129 )
| ~ ( in @ SV206 @ SV167 ) )
= $true )
| ( ( ~ ( disjoint @ SV129 @ SV167 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1396]) ).
thf(1425,plain,
! [SV169: $i,SV131: $i,SV189: $i,SV203: $i] :
( ( ( ~ ( in @ SV203 @ SV189 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV203 @ SV131 )
| ~ ~ ( in @ SV203 @ SV169 ) ) )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1397]) ).
thf(1426,plain,
! [SV189: $i,SV169: $i,SV131: $i,SV203: $i] :
( ( ( ~ ~ ( ~ ( in @ SV203 @ SV131 )
| ~ ~ ( in @ SV203 @ SV169 ) ) )
= $true )
| ( ( in @ SV203 @ SV189 )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1398]) ).
thf(1427,plain,
! [SV189: $i,SV131: $i,SV169: $i] :
( ( ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV189 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
| ~ ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 ) )
| ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV189 ) ) )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1399]) ).
thf(1428,plain,
! [SV189: $i,SV131: $i,SV169: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
| ~ ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
| ~ ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 ) )
| ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV189 ) ) )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1399]) ).
thf(1429,plain,
! [SV136: $i,SV173: $i,SV200: $i] :
( ( ( in @ SV200 @ SV173 )
= $false )
| ( ( subset @ SV200 @ SV136 )
= $true )
| ( ( SV173
= ( powerset @ SV136 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1400]) ).
thf(1430,plain,
! [SV173: $i,SV136: $i,SV200: $i] :
( ( ( subset @ SV200 @ SV136 )
= $false )
| ( ( in @ SV200 @ SV173 )
= $true )
| ( ( SV173
= ( powerset @ SV136 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1401]) ).
thf(1431,plain,
! [SV173: $i,SV136: $i] :
( ( ( in @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV173 )
= $true )
| ( ( ~ ( ~ ( subset @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV136 )
| ( in @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV173 ) ) )
= $true )
| ( ( SV173
= ( powerset @ SV136 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1402]) ).
thf(1432,plain,
! [SV173: $i,SV136: $i] :
( ( ( ~ ( subset @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV136 )
| ( in @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV173 ) )
= $false )
| ( ( subset @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV136 )
= $false )
| ( ( SV173
= ( powerset @ SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1403]) ).
thf(1433,plain,
! [SV138: $i,SV175: $i,SV201: $i] :
( ( ( in @ SV201 @ SV175 )
= $false )
| ( ( SV201 = SV138 )
= $true )
| ( ( SV175
= ( singleton @ SV138 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1404]) ).
thf(1434,plain,
! [SV175: $i,SV138: $i,SV201: $i] :
( ( ( SV201 = SV138 )
= $false )
| ( ( in @ SV201 @ SV175 )
= $true )
| ( ( SV175
= ( singleton @ SV138 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1405]) ).
thf(1435,plain,
! [SV175: $i,SV138: $i] :
( ( ( in @ ( sK22_SY332 @ SV138 @ SV175 ) @ SV175 )
= $true )
| ( ( ~ ( ( ( sK22_SY332 @ SV138 @ SV175 )
!= SV138 )
| ( in @ ( sK22_SY332 @ SV138 @ SV175 ) @ SV175 ) ) )
= $true )
| ( ( SV175
= ( singleton @ SV138 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1406]) ).
thf(1436,plain,
! [SV175: $i,SV138: $i] :
( ( ( ( ( sK22_SY332 @ SV138 @ SV175 )
!= SV138 )
| ( in @ ( sK22_SY332 @ SV138 @ SV175 ) @ SV175 ) )
= $false )
| ( ( ( sK22_SY332 @ SV138 @ SV175 )
= SV138 )
= $false )
| ( ( SV175
= ( singleton @ SV138 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1407]) ).
thf(1437,plain,
! [SV179: $i,SV142: $i,SV193: $i,SV204: $i] :
( ( ( ~ ( in @ SV204 @ SV193 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV204 @ SV142 )
| ~ ( in @ SV204 @ SV179 ) ) )
= $true )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1408]) ).
thf(1438,plain,
! [SV193: $i,SV179: $i,SV142: $i,SV204: $i] :
( ( ( ~ ~ ( ~ ( in @ SV204 @ SV142 )
| ~ ( in @ SV204 @ SV179 ) ) )
= $true )
| ( ( in @ SV204 @ SV193 )
= $true )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1409]) ).
thf(1439,plain,
! [SV193: $i,SV142: $i,SV179: $i] :
( ( ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV193 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
| ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 ) )
| ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV193 ) ) )
= $true )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1410]) ).
thf(1440,plain,
! [SV193: $i,SV142: $i,SV179: $i] :
( ( ( ~ ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
| ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
| ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 ) )
| ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV193 ) ) )
= $true )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1410]) ).
thf(1441,plain,
! [SV181: $i,SV144: $i,SV195: $i,SV205: $i] :
( ( ( ~ ( in @ SV205 @ SV195 ) )
= $true )
| ( ( ( SV205 = SV144 )
| ( SV205 = SV181 ) )
= $true )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1411]) ).
thf(1442,plain,
! [SV195: $i,SV181: $i,SV144: $i,SV205: $i] :
( ( ( ~ ( ( SV205 = SV144 )
| ( SV205 = SV181 ) ) )
= $true )
| ( ( in @ SV205 @ SV195 )
= $true )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1412]) ).
thf(1443,plain,
! [SV195: $i,SV144: $i,SV181: $i] :
( ( ( ~ ( in @ ( sK26_SY349 @ SV181 @ SV144 @ SV195 ) @ SV195 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV144 )
| ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV181 ) )
| ( in @ ( sK26_SY349 @ SV181 @ SV144 @ SV195 ) @ SV195 ) ) )
= $true )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1413]) ).
thf(1444,plain,
! [SV195: $i,SV144: $i,SV181: $i] :
( ( ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV144 )
| ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV181 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV144 )
| ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV181 ) )
| ( in @ ( sK26_SY349 @ SV181 @ SV144 @ SV195 ) @ SV195 ) ) )
= $true )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1413]) ).
thf(1445,plain,
! [SV151: $i,SV112: $i,SV198: $i] :
( ( ( ! [SY350: $i] :
~ ~ ( ~ ( in @ SV198 @ SY350 )
| ~ ( in @ SY350 @ SV112 ) ) )
= $false )
| ( ( in @ SV198 @ SV151 )
= $false )
| ( ( SV151
= ( union @ SV112 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1414]) ).
thf(1446,plain,
! [SV151: $i,SV112: $i,SV198: $i] :
( ( ( ! [SY351: $i] :
~ ~ ( ~ ( in @ SV198 @ SY351 )
| ~ ( in @ SY351 @ SV112 ) ) )
= $true )
| ( ( in @ SV198 @ SV151 )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1415]) ).
thf(1447,plain,
! [SV151: $i,SV112: $i] :
( ( ( ~ ~ ! [SY353: $i] :
~ ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SY353 )
| ~ ( in @ SY353 @ SV112 ) )
| ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV151 ) )
= $false )
| ( ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV151 )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1416]) ).
thf(1448,plain,
! [SV207: $i,SV151: $i,SV112: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV207 )
| ~ ( in @ SV207 @ SV112 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY353: $i] :
~ ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SY353 )
| ~ ( in @ SY353 @ SV112 ) )
| ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV151 ) ) )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1417]) ).
thf(1449,plain,
! [SV157: $i,SV118: $i,SV185: $i,SV202: $i] :
( ( ( in @ SV202 @ SV185 )
= $false )
| ( ( ( in @ SV202 @ SV118 )
| ( in @ SV202 @ SV157 ) )
= $true )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1418]) ).
thf(1450,plain,
! [SV185: $i,SV157: $i,SV118: $i,SV202: $i] :
( ( ( ( in @ SV202 @ SV118 )
| ( in @ SV202 @ SV157 ) )
= $false )
| ( ( in @ SV202 @ SV185 )
= $true )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1419]) ).
thf(1451,plain,
! [SV185: $i,SV118: $i,SV157: $i] :
( ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV185 )
= $true )
| ( ( ~ ( ~ ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV118 )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV157 ) )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV185 ) ) )
= $true )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1420]) ).
thf(1452,plain,
! [SV185: $i,SV118: $i,SV157: $i] :
( ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV118 )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV118 )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV157 ) )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV185 ) ) )
= $true )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1421]) ).
thf(1453,plain,
! [SV185: $i,SV118: $i,SV157: $i] :
( ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV157 )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV118 )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV157 ) )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV185 ) ) )
= $true )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1421]) ).
thf(1454,plain,
! [SV129: $i,SV167: $i] :
( ( ( ~ ( in @ ( sK27_SY321 @ SV167 @ SV129 ) @ SV129 )
| ~ ( in @ ( sK27_SY321 @ SV167 @ SV129 ) @ SV167 ) )
= $false )
| ( ( disjoint @ SV129 @ SV167 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1423]) ).
thf(1455,plain,
! [SV167: $i,SV129: $i,SV206: $i] :
( ( ( ~ ( in @ SV206 @ SV129 ) )
= $true )
| ( ( ~ ( in @ SV206 @ SV167 ) )
= $true )
| ( ( ~ ( disjoint @ SV129 @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1424]) ).
thf(1456,plain,
! [SV169: $i,SV131: $i,SV189: $i,SV203: $i] :
( ( ( in @ SV203 @ SV189 )
= $false )
| ( ( ~ ( ~ ( in @ SV203 @ SV131 )
| ~ ~ ( in @ SV203 @ SV169 ) ) )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1425]) ).
thf(1457,plain,
! [SV189: $i,SV169: $i,SV131: $i,SV203: $i] :
( ( ( ~ ( ~ ( in @ SV203 @ SV131 )
| ~ ~ ( in @ SV203 @ SV169 ) ) )
= $false )
| ( ( in @ SV203 @ SV189 )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1426]) ).
thf(1458,plain,
! [SV189: $i,SV131: $i,SV169: $i] :
( ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV189 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
| ~ ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 ) )
| ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV189 ) ) )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1427]) ).
thf(1459,plain,
! [SV189: $i,SV131: $i,SV169: $i] :
( ( ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
| ~ ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
| ~ ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 ) )
| ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV189 ) ) )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1428]) ).
thf(1460,plain,
! [SV173: $i,SV136: $i] :
( ( ( ~ ( subset @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV136 )
| ( in @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV173 ) )
= $false )
| ( ( in @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV173 )
= $true )
| ( ( SV173
= ( powerset @ SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1431]) ).
thf(1461,plain,
! [SV173: $i,SV136: $i] :
( ( ( ~ ( subset @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV136 ) )
= $false )
| ( ( subset @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV136 )
= $false )
| ( ( SV173
= ( powerset @ SV136 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1432]) ).
thf(1462,plain,
! [SV173: $i,SV136: $i] :
( ( ( in @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV173 )
= $false )
| ( ( subset @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV136 )
= $false )
| ( ( SV173
= ( powerset @ SV136 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1432]) ).
thf(1463,plain,
! [SV175: $i,SV138: $i] :
( ( ( ( ( sK22_SY332 @ SV138 @ SV175 )
!= SV138 )
| ( in @ ( sK22_SY332 @ SV138 @ SV175 ) @ SV175 ) )
= $false )
| ( ( in @ ( sK22_SY332 @ SV138 @ SV175 ) @ SV175 )
= $true )
| ( ( SV175
= ( singleton @ SV138 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1435]) ).
thf(1464,plain,
! [SV175: $i,SV138: $i] :
( ( ( ( sK22_SY332 @ SV138 @ SV175 )
!= SV138 )
= $false )
| ( ( ( sK22_SY332 @ SV138 @ SV175 )
= SV138 )
= $false )
| ( ( SV175
= ( singleton @ SV138 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1436]) ).
thf(1465,plain,
! [SV175: $i,SV138: $i] :
( ( ( in @ ( sK22_SY332 @ SV138 @ SV175 ) @ SV175 )
= $false )
| ( ( ( sK22_SY332 @ SV138 @ SV175 )
= SV138 )
= $false )
| ( ( SV175
= ( singleton @ SV138 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1436]) ).
thf(1466,plain,
! [SV179: $i,SV142: $i,SV193: $i,SV204: $i] :
( ( ( in @ SV204 @ SV193 )
= $false )
| ( ( ~ ( ~ ( in @ SV204 @ SV142 )
| ~ ( in @ SV204 @ SV179 ) ) )
= $true )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1437]) ).
thf(1467,plain,
! [SV193: $i,SV179: $i,SV142: $i,SV204: $i] :
( ( ( ~ ( ~ ( in @ SV204 @ SV142 )
| ~ ( in @ SV204 @ SV179 ) ) )
= $false )
| ( ( in @ SV204 @ SV193 )
= $true )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1438]) ).
thf(1468,plain,
! [SV193: $i,SV142: $i,SV179: $i] :
( ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV193 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
| ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 ) )
| ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV193 ) ) )
= $true )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1439]) ).
thf(1469,plain,
! [SV193: $i,SV142: $i,SV179: $i] :
( ( ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
| ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
| ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 ) )
| ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV193 ) ) )
= $true )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1440]) ).
thf(1470,plain,
! [SV181: $i,SV144: $i,SV195: $i,SV205: $i] :
( ( ( in @ SV205 @ SV195 )
= $false )
| ( ( ( SV205 = SV144 )
| ( SV205 = SV181 ) )
= $true )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1441]) ).
thf(1471,plain,
! [SV195: $i,SV181: $i,SV144: $i,SV205: $i] :
( ( ( ( SV205 = SV144 )
| ( SV205 = SV181 ) )
= $false )
| ( ( in @ SV205 @ SV195 )
= $true )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1442]) ).
thf(1472,plain,
! [SV195: $i,SV144: $i,SV181: $i] :
( ( ( in @ ( sK26_SY349 @ SV181 @ SV144 @ SV195 ) @ SV195 )
= $true )
| ( ( ~ ( ~ ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV144 )
| ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV181 ) )
| ( in @ ( sK26_SY349 @ SV181 @ SV144 @ SV195 ) @ SV195 ) ) )
= $true )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1443]) ).
thf(1473,plain,
! [SV195: $i,SV144: $i,SV181: $i] :
( ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV144 )
= $false )
| ( ( ~ ( ~ ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV144 )
| ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV181 ) )
| ( in @ ( sK26_SY349 @ SV181 @ SV144 @ SV195 ) @ SV195 ) ) )
= $true )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1444]) ).
thf(1474,plain,
! [SV195: $i,SV144: $i,SV181: $i] :
( ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV181 )
= $false )
| ( ( ~ ( ~ ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV144 )
| ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV181 ) )
| ( in @ ( sK26_SY349 @ SV181 @ SV144 @ SV195 ) @ SV195 ) ) )
= $true )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1444]) ).
thf(1475,plain,
! [SV112: $i,SV151: $i,SV198: $i] :
( ( ( ~ ~ ( ~ ( in @ SV198 @ ( sK28_SY350 @ SV151 @ SV112 @ SV198 ) )
| ~ ( in @ ( sK28_SY350 @ SV151 @ SV112 @ SV198 ) @ SV112 ) ) )
= $false )
| ( ( in @ SV198 @ SV151 )
= $false )
| ( ( SV151
= ( union @ SV112 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1445]) ).
thf(1476,plain,
! [SV151: $i,SV112: $i,SV208: $i,SV198: $i] :
( ( ( ~ ~ ( ~ ( in @ SV198 @ SV208 )
| ~ ( in @ SV208 @ SV112 ) ) )
= $true )
| ( ( in @ SV198 @ SV151 )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1446]) ).
thf(1477,plain,
! [SV151: $i,SV112: $i] :
( ( ( ~ ~ ! [SY353: $i] :
~ ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SY353 )
| ~ ( in @ SY353 @ SV112 ) ) )
= $false )
| ( ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV151 )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1447]) ).
thf(1478,plain,
! [SV151: $i,SV112: $i] :
( ( ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV151 )
= $false )
| ( ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV151 )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1447]) ).
thf(1479,plain,
! [SV207: $i,SV151: $i,SV112: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV207 )
| ~ ( in @ SV207 @ SV112 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY353: $i] :
~ ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SY353 )
| ~ ( in @ SY353 @ SV112 ) )
| ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV151 ) ) )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1448]) ).
thf(1480,plain,
! [SV185: $i,SV157: $i,SV118: $i,SV202: $i] :
( ( ( in @ SV202 @ SV118 )
= $true )
| ( ( in @ SV202 @ SV157 )
= $true )
| ( ( in @ SV202 @ SV185 )
= $false )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1449]) ).
thf(1481,plain,
! [SV157: $i,SV185: $i,SV118: $i,SV202: $i] :
( ( ( in @ SV202 @ SV118 )
= $false )
| ( ( in @ SV202 @ SV185 )
= $true )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1450]) ).
thf(1482,plain,
! [SV118: $i,SV185: $i,SV157: $i,SV202: $i] :
( ( ( in @ SV202 @ SV157 )
= $false )
| ( ( in @ SV202 @ SV185 )
= $true )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1450]) ).
thf(1483,plain,
! [SV185: $i,SV118: $i,SV157: $i] :
( ( ( ~ ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV118 )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV157 ) )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV185 ) )
= $false )
| ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV185 )
= $true )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1451]) ).
thf(1484,plain,
! [SV185: $i,SV118: $i,SV157: $i] :
( ( ( ~ ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV118 )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV157 ) )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV185 ) )
= $false )
| ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV118 )
= $false )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1452]) ).
thf(1485,plain,
! [SV185: $i,SV118: $i,SV157: $i] :
( ( ( ~ ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV118 )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV157 ) )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV185 ) )
= $false )
| ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV157 )
= $false )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1453]) ).
thf(1486,plain,
! [SV129: $i,SV167: $i] :
( ( ( ~ ( in @ ( sK27_SY321 @ SV167 @ SV129 ) @ SV129 ) )
= $false )
| ( ( disjoint @ SV129 @ SV167 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1454]) ).
thf(1487,plain,
! [SV129: $i,SV167: $i] :
( ( ( ~ ( in @ ( sK27_SY321 @ SV167 @ SV129 ) @ SV167 ) )
= $false )
| ( ( disjoint @ SV129 @ SV167 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1454]) ).
thf(1488,plain,
! [SV167: $i,SV129: $i,SV206: $i] :
( ( ( in @ SV206 @ SV129 )
= $false )
| ( ( ~ ( in @ SV206 @ SV167 ) )
= $true )
| ( ( ~ ( disjoint @ SV129 @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1455]) ).
thf(1489,plain,
! [SV189: $i,SV169: $i,SV131: $i,SV203: $i] :
( ( ( ~ ( in @ SV203 @ SV131 )
| ~ ~ ( in @ SV203 @ SV169 ) )
= $false )
| ( ( in @ SV203 @ SV189 )
= $false )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1456]) ).
thf(1490,plain,
! [SV189: $i,SV169: $i,SV131: $i,SV203: $i] :
( ( ( ~ ( in @ SV203 @ SV131 )
| ~ ~ ( in @ SV203 @ SV169 ) )
= $true )
| ( ( in @ SV203 @ SV189 )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1457]) ).
thf(1491,plain,
! [SV189: $i,SV131: $i,SV169: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
| ~ ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 ) )
| ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV189 ) )
= $false )
| ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV189 )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1458]) ).
thf(1492,plain,
! [SV189: $i,SV131: $i,SV169: $i] :
( ( ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 ) )
= $true )
| ( ( ~ ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
| ~ ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 ) )
| ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV189 ) ) )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1459]) ).
thf(1493,plain,
! [SV173: $i,SV136: $i] :
( ( ( ~ ( subset @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV136 ) )
= $false )
| ( ( in @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV173 )
= $true )
| ( ( SV173
= ( powerset @ SV136 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1460]) ).
thf(1494,plain,
! [SV173: $i,SV136: $i] :
( ( ( in @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV173 )
= $false )
| ( ( in @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV173 )
= $true )
| ( ( SV173
= ( powerset @ SV136 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1460]) ).
thf(1495,plain,
! [SV173: $i,SV136: $i] :
( ( ( subset @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV136 )
= $true )
| ( ( subset @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV136 )
= $false )
| ( ( SV173
= ( powerset @ SV136 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1461]) ).
thf(1496,plain,
! [SV175: $i,SV138: $i] :
( ( ( ( sK22_SY332 @ SV138 @ SV175 )
!= SV138 )
= $false )
| ( ( in @ ( sK22_SY332 @ SV138 @ SV175 ) @ SV175 )
= $true )
| ( ( SV175
= ( singleton @ SV138 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1463]) ).
thf(1497,plain,
! [SV175: $i,SV138: $i] :
( ( ( in @ ( sK22_SY332 @ SV138 @ SV175 ) @ SV175 )
= $false )
| ( ( in @ ( sK22_SY332 @ SV138 @ SV175 ) @ SV175 )
= $true )
| ( ( SV175
= ( singleton @ SV138 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1463]) ).
thf(1498,plain,
! [SV175: $i,SV138: $i] :
( ( ( ( sK22_SY332 @ SV138 @ SV175 )
= SV138 )
= $true )
| ( ( ( sK22_SY332 @ SV138 @ SV175 )
= SV138 )
= $false )
| ( ( SV175
= ( singleton @ SV138 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1464]) ).
thf(1499,plain,
! [SV193: $i,SV179: $i,SV142: $i,SV204: $i] :
( ( ( ~ ( in @ SV204 @ SV142 )
| ~ ( in @ SV204 @ SV179 ) )
= $false )
| ( ( in @ SV204 @ SV193 )
= $false )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1466]) ).
thf(1500,plain,
! [SV193: $i,SV179: $i,SV142: $i,SV204: $i] :
( ( ( ~ ( in @ SV204 @ SV142 )
| ~ ( in @ SV204 @ SV179 ) )
= $true )
| ( ( in @ SV204 @ SV193 )
= $true )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1467]) ).
thf(1501,plain,
! [SV193: $i,SV142: $i,SV179: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
| ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 ) )
| ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV193 ) )
= $false )
| ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV193 )
= $true )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1468]) ).
thf(1502,plain,
! [SV193: $i,SV142: $i,SV179: $i] :
( ( ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 ) )
= $true )
| ( ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
| ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 ) )
| ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV193 ) ) )
= $true )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1469]) ).
thf(1503,plain,
! [SV195: $i,SV181: $i,SV144: $i,SV205: $i] :
( ( ( SV205 = SV144 )
= $true )
| ( ( SV205 = SV181 )
= $true )
| ( ( in @ SV205 @ SV195 )
= $false )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1470]) ).
thf(1504,plain,
! [SV181: $i,SV195: $i,SV144: $i,SV205: $i] :
( ( ( SV205 = SV144 )
= $false )
| ( ( in @ SV205 @ SV195 )
= $true )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1471]) ).
thf(1505,plain,
! [SV144: $i,SV195: $i,SV181: $i,SV205: $i] :
( ( ( SV205 = SV181 )
= $false )
| ( ( in @ SV205 @ SV195 )
= $true )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1471]) ).
thf(1506,plain,
! [SV195: $i,SV144: $i,SV181: $i] :
( ( ( ~ ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV144 )
| ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV181 ) )
| ( in @ ( sK26_SY349 @ SV181 @ SV144 @ SV195 ) @ SV195 ) )
= $false )
| ( ( in @ ( sK26_SY349 @ SV181 @ SV144 @ SV195 ) @ SV195 )
= $true )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1472]) ).
thf(1507,plain,
! [SV195: $i,SV144: $i,SV181: $i] :
( ( ( ~ ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV144 )
| ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV181 ) )
| ( in @ ( sK26_SY349 @ SV181 @ SV144 @ SV195 ) @ SV195 ) )
= $false )
| ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV144 )
= $false )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1473]) ).
thf(1508,plain,
! [SV195: $i,SV144: $i,SV181: $i] :
( ( ( ~ ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV144 )
| ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV181 ) )
| ( in @ ( sK26_SY349 @ SV181 @ SV144 @ SV195 ) @ SV195 ) )
= $false )
| ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV181 )
= $false )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1474]) ).
thf(1509,plain,
! [SV112: $i,SV151: $i,SV198: $i] :
( ( ( ~ ( ~ ( in @ SV198 @ ( sK28_SY350 @ SV151 @ SV112 @ SV198 ) )
| ~ ( in @ ( sK28_SY350 @ SV151 @ SV112 @ SV198 ) @ SV112 ) ) )
= $true )
| ( ( in @ SV198 @ SV151 )
= $false )
| ( ( SV151
= ( union @ SV112 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1475]) ).
thf(1510,plain,
! [SV151: $i,SV112: $i,SV208: $i,SV198: $i] :
( ( ( ~ ( ~ ( in @ SV198 @ SV208 )
| ~ ( in @ SV208 @ SV112 ) ) )
= $false )
| ( ( in @ SV198 @ SV151 )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1476]) ).
thf(1511,plain,
! [SV151: $i,SV112: $i] :
( ( ( ~ ! [SY353: $i] :
~ ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SY353 )
| ~ ( in @ SY353 @ SV112 ) ) )
= $true )
| ( ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV151 )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1477]) ).
thf(1512,plain,
! [SV207: $i,SV151: $i,SV112: $i] :
( ( ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV207 )
| ~ ( in @ SV207 @ SV112 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY353: $i] :
~ ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SY353 )
| ~ ( in @ SY353 @ SV112 ) )
| ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV151 ) ) )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1479]) ).
thf(1513,plain,
! [SV185: $i,SV118: $i,SV157: $i] :
( ( ( ~ ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV118 )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV157 ) ) )
= $false )
| ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV185 )
= $true )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1483]) ).
thf(1514,plain,
! [SV185: $i,SV118: $i,SV157: $i] :
( ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV185 )
= $false )
| ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV185 )
= $true )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1483]) ).
thf(1515,plain,
! [SV185: $i,SV118: $i,SV157: $i] :
( ( ( ~ ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV118 )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV157 ) ) )
= $false )
| ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV118 )
= $false )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1484]) ).
thf(1516,plain,
! [SV185: $i,SV118: $i,SV157: $i] :
( ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV185 )
= $false )
| ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV118 )
= $false )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1484]) ).
thf(1517,plain,
! [SV185: $i,SV118: $i,SV157: $i] :
( ( ( ~ ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV118 )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV157 ) ) )
= $false )
| ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV157 )
= $false )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1485]) ).
thf(1518,plain,
! [SV185: $i,SV118: $i,SV157: $i] :
( ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV185 )
= $false )
| ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV157 )
= $false )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1485]) ).
thf(1519,plain,
! [SV129: $i,SV167: $i] :
( ( ( in @ ( sK27_SY321 @ SV167 @ SV129 ) @ SV129 )
= $true )
| ( ( disjoint @ SV129 @ SV167 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1486]) ).
thf(1520,plain,
! [SV129: $i,SV167: $i] :
( ( ( in @ ( sK27_SY321 @ SV167 @ SV129 ) @ SV167 )
= $true )
| ( ( disjoint @ SV129 @ SV167 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1487]) ).
thf(1521,plain,
! [SV129: $i,SV167: $i,SV206: $i] :
( ( ( in @ SV206 @ SV167 )
= $false )
| ( ( in @ SV206 @ SV129 )
= $false )
| ( ( ~ ( disjoint @ SV129 @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1488]) ).
thf(1522,plain,
! [SV169: $i,SV189: $i,SV131: $i,SV203: $i] :
( ( ( ~ ( in @ SV203 @ SV131 ) )
= $false )
| ( ( in @ SV203 @ SV189 )
= $false )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1489]) ).
thf(1523,plain,
! [SV131: $i,SV189: $i,SV169: $i,SV203: $i] :
( ( ( ~ ~ ( in @ SV203 @ SV169 ) )
= $false )
| ( ( in @ SV203 @ SV189 )
= $false )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1489]) ).
thf(1524,plain,
! [SV189: $i,SV169: $i,SV131: $i,SV203: $i] :
( ( ( ~ ( in @ SV203 @ SV131 ) )
= $true )
| ( ( ~ ~ ( in @ SV203 @ SV169 ) )
= $true )
| ( ( in @ SV203 @ SV189 )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1490]) ).
thf(1525,plain,
! [SV189: $i,SV131: $i,SV169: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
| ~ ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 ) ) )
= $false )
| ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV189 )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1491]) ).
thf(1526,plain,
! [SV189: $i,SV131: $i,SV169: $i] :
( ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV189 )
= $false )
| ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV189 )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1491]) ).
thf(1527,plain,
! [SV189: $i,SV131: $i,SV169: $i] :
( ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
= $false )
| ( ( ~ ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
| ~ ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 ) )
| ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV189 ) ) )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1492]) ).
thf(1528,plain,
! [SV173: $i,SV136: $i] :
( ( ( subset @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV136 )
= $true )
| ( ( in @ ( sK21_SY330 @ SV136 @ SV173 ) @ SV173 )
= $true )
| ( ( SV173
= ( powerset @ SV136 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1493]) ).
thf(1529,plain,
! [SV175: $i,SV138: $i] :
( ( ( ( sK22_SY332 @ SV138 @ SV175 )
= SV138 )
= $true )
| ( ( in @ ( sK22_SY332 @ SV138 @ SV175 ) @ SV175 )
= $true )
| ( ( SV175
= ( singleton @ SV138 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1496]) ).
thf(1530,plain,
! [SV179: $i,SV193: $i,SV142: $i,SV204: $i] :
( ( ( ~ ( in @ SV204 @ SV142 ) )
= $false )
| ( ( in @ SV204 @ SV193 )
= $false )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1499]) ).
thf(1531,plain,
! [SV142: $i,SV193: $i,SV179: $i,SV204: $i] :
( ( ( ~ ( in @ SV204 @ SV179 ) )
= $false )
| ( ( in @ SV204 @ SV193 )
= $false )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1499]) ).
thf(1532,plain,
! [SV193: $i,SV179: $i,SV142: $i,SV204: $i] :
( ( ( ~ ( in @ SV204 @ SV142 ) )
= $true )
| ( ( ~ ( in @ SV204 @ SV179 ) )
= $true )
| ( ( in @ SV204 @ SV193 )
= $true )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1500]) ).
thf(1533,plain,
! [SV193: $i,SV142: $i,SV179: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
| ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 ) ) )
= $false )
| ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV193 )
= $true )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1501]) ).
thf(1534,plain,
! [SV193: $i,SV142: $i,SV179: $i] :
( ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV193 )
= $false )
| ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV193 )
= $true )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1501]) ).
thf(1535,plain,
! [SV193: $i,SV142: $i,SV179: $i] :
( ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
= $false )
| ( ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
| ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 ) )
| ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV193 ) ) )
= $true )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1502]) ).
thf(1536,plain,
! [SV195: $i,SV144: $i,SV181: $i] :
( ( ( ~ ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV144 )
| ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV181 ) ) )
= $false )
| ( ( in @ ( sK26_SY349 @ SV181 @ SV144 @ SV195 ) @ SV195 )
= $true )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1506]) ).
thf(1537,plain,
! [SV195: $i,SV144: $i,SV181: $i] :
( ( ( in @ ( sK26_SY349 @ SV181 @ SV144 @ SV195 ) @ SV195 )
= $false )
| ( ( in @ ( sK26_SY349 @ SV181 @ SV144 @ SV195 ) @ SV195 )
= $true )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1506]) ).
thf(1538,plain,
! [SV195: $i,SV144: $i,SV181: $i] :
( ( ( ~ ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV144 )
| ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV181 ) ) )
= $false )
| ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV144 )
= $false )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1507]) ).
thf(1539,plain,
! [SV195: $i,SV144: $i,SV181: $i] :
( ( ( in @ ( sK26_SY349 @ SV181 @ SV144 @ SV195 ) @ SV195 )
= $false )
| ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV144 )
= $false )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1507]) ).
thf(1540,plain,
! [SV195: $i,SV144: $i,SV181: $i] :
( ( ( ~ ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV144 )
| ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV181 ) ) )
= $false )
| ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV181 )
= $false )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1508]) ).
thf(1541,plain,
! [SV195: $i,SV144: $i,SV181: $i] :
( ( ( in @ ( sK26_SY349 @ SV181 @ SV144 @ SV195 ) @ SV195 )
= $false )
| ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV181 )
= $false )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1508]) ).
thf(1542,plain,
! [SV112: $i,SV151: $i,SV198: $i] :
( ( ( ~ ( in @ SV198 @ ( sK28_SY350 @ SV151 @ SV112 @ SV198 ) )
| ~ ( in @ ( sK28_SY350 @ SV151 @ SV112 @ SV198 ) @ SV112 ) )
= $false )
| ( ( in @ SV198 @ SV151 )
= $false )
| ( ( SV151
= ( union @ SV112 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1509]) ).
thf(1543,plain,
! [SV151: $i,SV112: $i,SV208: $i,SV198: $i] :
( ( ( ~ ( in @ SV198 @ SV208 )
| ~ ( in @ SV208 @ SV112 ) )
= $true )
| ( ( in @ SV198 @ SV151 )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1510]) ).
thf(1544,plain,
! [SV151: $i,SV112: $i] :
( ( ( ! [SY353: $i] :
~ ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SY353 )
| ~ ( in @ SY353 @ SV112 ) ) )
= $false )
| ( ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV151 )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1511]) ).
thf(1545,plain,
! [SV207: $i,SV151: $i,SV112: $i] :
( ( ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV207 ) )
= $true )
| ( ( ~ ( in @ SV207 @ SV112 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY353: $i] :
~ ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SY353 )
| ~ ( in @ SY353 @ SV112 ) )
| ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV151 ) ) )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1512]) ).
thf(1546,plain,
! [SV185: $i,SV118: $i,SV157: $i] :
( ( ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV118 )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV157 ) )
= $true )
| ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV185 )
= $true )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1513]) ).
thf(1547,plain,
! [SV185: $i,SV118: $i,SV157: $i] :
( ( ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV118 )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV157 ) )
= $true )
| ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV118 )
= $false )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1515]) ).
thf(1548,plain,
! [SV185: $i,SV118: $i,SV157: $i] :
( ( ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV118 )
| ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV157 ) )
= $true )
| ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV157 )
= $false )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1517]) ).
thf(1549,plain,
! [SV206: $i,SV167: $i,SV129: $i] :
( ( ( disjoint @ SV129 @ SV167 )
= $false )
| ( ( in @ SV206 @ SV129 )
= $false )
| ( ( in @ SV206 @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1521]) ).
thf(1550,plain,
! [SV169: $i,SV189: $i,SV131: $i,SV203: $i] :
( ( ( in @ SV203 @ SV131 )
= $true )
| ( ( in @ SV203 @ SV189 )
= $false )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1522]) ).
thf(1551,plain,
! [SV131: $i,SV189: $i,SV169: $i,SV203: $i] :
( ( ( ~ ( in @ SV203 @ SV169 ) )
= $true )
| ( ( in @ SV203 @ SV189 )
= $false )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1523]) ).
thf(1552,plain,
! [SV189: $i,SV169: $i,SV131: $i,SV203: $i] :
( ( ( in @ SV203 @ SV131 )
= $false )
| ( ( ~ ~ ( in @ SV203 @ SV169 ) )
= $true )
| ( ( in @ SV203 @ SV189 )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1524]) ).
thf(1553,plain,
! [SV189: $i,SV131: $i,SV169: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
| ~ ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 ) ) )
= $true )
| ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV189 )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1525]) ).
thf(1554,plain,
! [SV189: $i,SV131: $i,SV169: $i] :
( ( ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 ) )
= $false )
| ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
| ~ ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 ) )
| ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV189 ) ) )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1527]) ).
thf(1555,plain,
! [SV179: $i,SV193: $i,SV142: $i,SV204: $i] :
( ( ( in @ SV204 @ SV142 )
= $true )
| ( ( in @ SV204 @ SV193 )
= $false )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1530]) ).
thf(1556,plain,
! [SV142: $i,SV193: $i,SV179: $i,SV204: $i] :
( ( ( in @ SV204 @ SV179 )
= $true )
| ( ( in @ SV204 @ SV193 )
= $false )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1531]) ).
thf(1557,plain,
! [SV193: $i,SV179: $i,SV142: $i,SV204: $i] :
( ( ( in @ SV204 @ SV142 )
= $false )
| ( ( ~ ( in @ SV204 @ SV179 ) )
= $true )
| ( ( in @ SV204 @ SV193 )
= $true )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1532]) ).
thf(1558,plain,
! [SV193: $i,SV142: $i,SV179: $i] :
( ( ( ~ ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
| ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 ) ) )
= $true )
| ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV193 )
= $true )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1533]) ).
thf(1559,plain,
! [SV193: $i,SV142: $i,SV179: $i] :
( ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 )
= $false )
| ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
| ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 ) )
| ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV193 ) ) )
= $true )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1535]) ).
thf(1560,plain,
! [SV195: $i,SV144: $i,SV181: $i] :
( ( ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV144 )
| ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV181 ) )
= $true )
| ( ( in @ ( sK26_SY349 @ SV181 @ SV144 @ SV195 ) @ SV195 )
= $true )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1536]) ).
thf(1561,plain,
! [SV195: $i,SV144: $i,SV181: $i] :
( ( ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV144 )
| ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV181 ) )
= $true )
| ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV144 )
= $false )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1538]) ).
thf(1562,plain,
! [SV195: $i,SV144: $i,SV181: $i] :
( ( ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV144 )
| ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV181 ) )
= $true )
| ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV181 )
= $false )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1540]) ).
thf(1563,plain,
! [SV112: $i,SV151: $i,SV198: $i] :
( ( ( ~ ( in @ SV198 @ ( sK28_SY350 @ SV151 @ SV112 @ SV198 ) ) )
= $false )
| ( ( in @ SV198 @ SV151 )
= $false )
| ( ( SV151
= ( union @ SV112 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1542]) ).
thf(1564,plain,
! [SV198: $i,SV112: $i,SV151: $i] :
( ( ( ~ ( in @ ( sK28_SY350 @ SV151 @ SV112 @ SV198 ) @ SV112 ) )
= $false )
| ( ( in @ SV198 @ SV151 )
= $false )
| ( ( SV151
= ( union @ SV112 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1542]) ).
thf(1565,plain,
! [SV151: $i,SV112: $i,SV208: $i,SV198: $i] :
( ( ( ~ ( in @ SV198 @ SV208 ) )
= $true )
| ( ( ~ ( in @ SV208 @ SV112 ) )
= $true )
| ( ( in @ SV198 @ SV151 )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1543]) ).
thf(1566,plain,
! [SV151: $i,SV112: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ ( sK29_SY353 @ SV151 @ SV112 ) )
| ~ ( in @ ( sK29_SY353 @ SV151 @ SV112 ) @ SV112 ) ) )
= $false )
| ( ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV151 )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1544]) ).
thf(1567,plain,
! [SV207: $i,SV151: $i,SV112: $i] :
( ( ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV207 )
= $false )
| ( ( ~ ( in @ SV207 @ SV112 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY353: $i] :
~ ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SY353 )
| ~ ( in @ SY353 @ SV112 ) )
| ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV151 ) ) )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1545]) ).
thf(1568,plain,
! [SV185: $i,SV118: $i,SV157: $i] :
( ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV118 )
= $true )
| ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV157 )
= $true )
| ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV185 )
= $true )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1546]) ).
thf(1569,plain,
! [SV185: $i,SV118: $i,SV157: $i] :
( ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV118 )
= $true )
| ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV157 )
= $true )
| ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV118 )
= $false )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1547]) ).
thf(1570,plain,
! [SV185: $i,SV118: $i,SV157: $i] :
( ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV118 )
= $true )
| ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV157 )
= $true )
| ( ( in @ ( sK23_SY343 @ SV157 @ SV118 @ SV185 ) @ SV157 )
= $false )
| ( ( SV185
= ( set_union2 @ SV118 @ SV157 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1548]) ).
thf(1571,plain,
! [SV131: $i,SV189: $i,SV169: $i,SV203: $i] :
( ( ( in @ SV203 @ SV169 )
= $false )
| ( ( in @ SV203 @ SV189 )
= $false )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1551]) ).
thf(1572,plain,
! [SV189: $i,SV131: $i,SV169: $i,SV203: $i] :
( ( ( ~ ( in @ SV203 @ SV169 ) )
= $false )
| ( ( in @ SV203 @ SV131 )
= $false )
| ( ( in @ SV203 @ SV189 )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1552]) ).
thf(1573,plain,
! [SV189: $i,SV131: $i,SV169: $i] :
( ( ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
| ~ ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 ) )
= $false )
| ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV189 )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1553]) ).
thf(1574,plain,
! [SV189: $i,SV131: $i,SV169: $i] :
( ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 )
= $true )
| ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
| ~ ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 ) )
| ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV189 ) ) )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1554]) ).
thf(1575,plain,
! [SV193: $i,SV142: $i,SV179: $i,SV204: $i] :
( ( ( in @ SV204 @ SV179 )
= $false )
| ( ( in @ SV204 @ SV142 )
= $false )
| ( ( in @ SV204 @ SV193 )
= $true )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1557]) ).
thf(1576,plain,
! [SV193: $i,SV142: $i,SV179: $i] :
( ( ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
| ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 ) )
= $false )
| ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV193 )
= $true )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1558]) ).
thf(1577,plain,
! [SV193: $i,SV142: $i,SV179: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
| ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 ) )
| ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV193 ) )
= $false )
| ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
= $false )
| ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 )
= $false )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1559]) ).
thf(1578,plain,
! [SV195: $i,SV144: $i,SV181: $i] :
( ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV144 )
= $true )
| ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV181 )
= $true )
| ( ( in @ ( sK26_SY349 @ SV181 @ SV144 @ SV195 ) @ SV195 )
= $true )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1560]) ).
thf(1579,plain,
! [SV195: $i,SV144: $i,SV181: $i] :
( ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV144 )
= $true )
| ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV181 )
= $true )
| ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV144 )
= $false )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1561]) ).
thf(1580,plain,
! [SV195: $i,SV144: $i,SV181: $i] :
( ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV144 )
= $true )
| ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV181 )
= $true )
| ( ( ( sK26_SY349 @ SV181 @ SV144 @ SV195 )
= SV181 )
= $false )
| ( ( SV195
= ( unordered_pair @ SV144 @ SV181 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1562]) ).
thf(1581,plain,
! [SV112: $i,SV151: $i,SV198: $i] :
( ( ( in @ SV198 @ ( sK28_SY350 @ SV151 @ SV112 @ SV198 ) )
= $true )
| ( ( in @ SV198 @ SV151 )
= $false )
| ( ( SV151
= ( union @ SV112 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1563]) ).
thf(1582,plain,
! [SV198: $i,SV112: $i,SV151: $i] :
( ( ( in @ ( sK28_SY350 @ SV151 @ SV112 @ SV198 ) @ SV112 )
= $true )
| ( ( in @ SV198 @ SV151 )
= $false )
| ( ( SV151
= ( union @ SV112 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1564]) ).
thf(1583,plain,
! [SV151: $i,SV112: $i,SV208: $i,SV198: $i] :
( ( ( in @ SV198 @ SV208 )
= $false )
| ( ( ~ ( in @ SV208 @ SV112 ) )
= $true )
| ( ( in @ SV198 @ SV151 )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1565]) ).
thf(1584,plain,
! [SV151: $i,SV112: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ ( sK29_SY353 @ SV151 @ SV112 ) )
| ~ ( in @ ( sK29_SY353 @ SV151 @ SV112 ) @ SV112 ) ) )
= $true )
| ( ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV151 )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1566]) ).
thf(1585,plain,
! [SV151: $i,SV112: $i,SV207: $i] :
( ( ( in @ SV207 @ SV112 )
= $false )
| ( ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV207 )
= $false )
| ( ( ~ ( ~ ~ ! [SY353: $i] :
~ ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SY353 )
| ~ ( in @ SY353 @ SV112 ) )
| ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV151 ) ) )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1567]) ).
thf(1586,plain,
! [SV189: $i,SV131: $i,SV169: $i,SV203: $i] :
( ( ( in @ SV203 @ SV169 )
= $true )
| ( ( in @ SV203 @ SV131 )
= $false )
| ( ( in @ SV203 @ SV189 )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1572]) ).
thf(1587,plain,
! [SV189: $i,SV131: $i,SV169: $i] :
( ( ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 ) )
= $false )
| ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV189 )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1573]) ).
thf(1588,plain,
! [SV189: $i,SV131: $i,SV169: $i] :
( ( ( ~ ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 ) )
= $false )
| ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV189 )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1573]) ).
thf(1589,plain,
! [SV189: $i,SV131: $i,SV169: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
| ~ ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 ) )
| ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV189 ) )
= $false )
| ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
= $false )
| ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1574]) ).
thf(1590,plain,
! [SV193: $i,SV142: $i,SV179: $i] :
( ( ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 ) )
= $false )
| ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV193 )
= $true )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1576]) ).
thf(1591,plain,
! [SV193: $i,SV142: $i,SV179: $i] :
( ( ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 ) )
= $false )
| ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV193 )
= $true )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1576]) ).
thf(1592,plain,
! [SV193: $i,SV142: $i,SV179: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
| ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 ) ) )
= $false )
| ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
= $false )
| ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 )
= $false )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1577]) ).
thf(1593,plain,
! [SV193: $i,SV142: $i,SV179: $i] :
( ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV193 )
= $false )
| ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
= $false )
| ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 )
= $false )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1577]) ).
thf(1594,plain,
! [SV151: $i,SV198: $i,SV112: $i,SV208: $i] :
( ( ( in @ SV208 @ SV112 )
= $false )
| ( ( in @ SV198 @ SV208 )
= $false )
| ( ( in @ SV198 @ SV151 )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1583]) ).
thf(1595,plain,
! [SV151: $i,SV112: $i] :
( ( ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ ( sK29_SY353 @ SV151 @ SV112 ) )
| ~ ( in @ ( sK29_SY353 @ SV151 @ SV112 ) @ SV112 ) )
= $false )
| ( ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV151 )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1584]) ).
thf(1596,plain,
! [SV207: $i,SV151: $i,SV112: $i] :
( ( ( ~ ~ ! [SY353: $i] :
~ ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SY353 )
| ~ ( in @ SY353 @ SV112 ) )
| ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV151 ) )
= $false )
| ( ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV207 )
= $false )
| ( ( in @ SV207 @ SV112 )
= $false )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1585]) ).
thf(1597,plain,
! [SV189: $i,SV131: $i,SV169: $i] :
( ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
= $true )
| ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV189 )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1587]) ).
thf(1598,plain,
! [SV189: $i,SV131: $i,SV169: $i] :
( ( ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 ) )
= $true )
| ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV189 )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1588]) ).
thf(1599,plain,
! [SV189: $i,SV131: $i,SV169: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
| ~ ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 ) ) )
= $false )
| ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
= $false )
| ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1589]) ).
thf(1600,plain,
! [SV189: $i,SV131: $i,SV169: $i] :
( ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV189 )
= $false )
| ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
= $false )
| ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1589]) ).
thf(1601,plain,
! [SV193: $i,SV142: $i,SV179: $i] :
( ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
= $true )
| ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV193 )
= $true )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1590]) ).
thf(1602,plain,
! [SV193: $i,SV142: $i,SV179: $i] :
( ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 )
= $true )
| ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV193 )
= $true )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1591]) ).
thf(1603,plain,
! [SV193: $i,SV142: $i,SV179: $i] :
( ( ( ~ ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
| ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 ) ) )
= $true )
| ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
= $false )
| ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 )
= $false )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1592]) ).
thf(1604,plain,
! [SV151: $i,SV112: $i] :
( ( ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ ( sK29_SY353 @ SV151 @ SV112 ) ) )
= $false )
| ( ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV151 )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1595]) ).
thf(1605,plain,
! [SV112: $i,SV151: $i] :
( ( ( ~ ( in @ ( sK29_SY353 @ SV151 @ SV112 ) @ SV112 ) )
= $false )
| ( ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV151 )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1595]) ).
thf(1606,plain,
! [SV207: $i,SV151: $i,SV112: $i] :
( ( ( ~ ~ ! [SY353: $i] :
~ ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SY353 )
| ~ ( in @ SY353 @ SV112 ) ) )
= $false )
| ( ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV207 )
= $false )
| ( ( in @ SV207 @ SV112 )
= $false )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1596]) ).
thf(1607,plain,
! [SV207: $i,SV151: $i,SV112: $i] :
( ( ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV151 )
= $false )
| ( ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV207 )
= $false )
| ( ( in @ SV207 @ SV112 )
= $false )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1596]) ).
thf(1608,plain,
! [SV189: $i,SV131: $i,SV169: $i] :
( ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 )
= $false )
| ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV189 )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1598]) ).
thf(1609,plain,
! [SV189: $i,SV131: $i,SV169: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
| ~ ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 ) ) )
= $true )
| ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
= $false )
| ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1599]) ).
thf(1610,plain,
! [SV193: $i,SV142: $i,SV179: $i] :
( ( ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
| ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 ) )
= $false )
| ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
= $false )
| ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 )
= $false )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1603]) ).
thf(1611,plain,
! [SV151: $i,SV112: $i] :
( ( ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ ( sK29_SY353 @ SV151 @ SV112 ) )
= $true )
| ( ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV151 )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1604]) ).
thf(1612,plain,
! [SV112: $i,SV151: $i] :
( ( ( in @ ( sK29_SY353 @ SV151 @ SV112 ) @ SV112 )
= $true )
| ( ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV151 )
= $true )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1605]) ).
thf(1613,plain,
! [SV207: $i,SV151: $i,SV112: $i] :
( ( ( ~ ! [SY353: $i] :
~ ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SY353 )
| ~ ( in @ SY353 @ SV112 ) ) )
= $true )
| ( ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV207 )
= $false )
| ( ( in @ SV207 @ SV112 )
= $false )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1606]) ).
thf(1614,plain,
! [SV189: $i,SV131: $i,SV169: $i] :
( ( ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
| ~ ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 ) )
= $false )
| ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
= $false )
| ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1609]) ).
thf(1615,plain,
! [SV193: $i,SV142: $i,SV179: $i] :
( ( ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 ) )
= $false )
| ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
= $false )
| ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 )
= $false )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1610]) ).
thf(1616,plain,
! [SV193: $i,SV142: $i,SV179: $i] :
( ( ( ~ ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 ) )
= $false )
| ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
= $false )
| ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 )
= $false )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1610]) ).
thf(1617,plain,
! [SV207: $i,SV151: $i,SV112: $i] :
( ( ( ! [SY353: $i] :
~ ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SY353 )
| ~ ( in @ SY353 @ SV112 ) ) )
= $false )
| ( ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV207 )
= $false )
| ( ( in @ SV207 @ SV112 )
= $false )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1613]) ).
thf(1618,plain,
! [SV189: $i,SV131: $i,SV169: $i] :
( ( ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 ) )
= $false )
| ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
= $false )
| ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1614]) ).
thf(1619,plain,
! [SV189: $i,SV131: $i,SV169: $i] :
( ( ( ~ ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 ) )
= $false )
| ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
= $false )
| ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1614]) ).
thf(1620,plain,
! [SV193: $i,SV142: $i,SV179: $i] :
( ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
= $true )
| ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
= $false )
| ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 )
= $false )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1615]) ).
thf(1621,plain,
! [SV193: $i,SV142: $i,SV179: $i] :
( ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 )
= $true )
| ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV142 )
= $false )
| ( ( in @ ( sK25_SY347 @ SV179 @ SV142 @ SV193 ) @ SV179 )
= $false )
| ( ( SV193
= ( set_intersection2 @ SV142 @ SV179 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1616]) ).
thf(1622,plain,
! [SV207: $i,SV151: $i,SV112: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ ( sK30_SY353 @ SV207 @ SV151 @ SV112 ) )
| ~ ( in @ ( sK30_SY353 @ SV207 @ SV151 @ SV112 ) @ SV112 ) ) )
= $false )
| ( ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV207 )
= $false )
| ( ( in @ SV207 @ SV112 )
= $false )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1617]) ).
thf(1623,plain,
! [SV189: $i,SV131: $i,SV169: $i] :
( ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
= $true )
| ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
= $false )
| ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1618]) ).
thf(1624,plain,
! [SV189: $i,SV131: $i,SV169: $i] :
( ( ( ~ ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 ) )
= $true )
| ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
= $false )
| ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1619]) ).
thf(1625,plain,
! [SV207: $i,SV151: $i,SV112: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ ( sK30_SY353 @ SV207 @ SV151 @ SV112 ) )
| ~ ( in @ ( sK30_SY353 @ SV207 @ SV151 @ SV112 ) @ SV112 ) ) )
= $true )
| ( ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV207 )
= $false )
| ( ( in @ SV207 @ SV112 )
= $false )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1622]) ).
thf(1626,plain,
! [SV189: $i,SV131: $i,SV169: $i] :
( ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 )
= $false )
| ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV131 )
= $false )
| ( ( in @ ( sK24_SY345 @ SV169 @ SV131 @ SV189 ) @ SV169 )
= $true )
| ( ( SV189
= ( set_difference @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1624]) ).
thf(1627,plain,
! [SV207: $i,SV151: $i,SV112: $i] :
( ( ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ ( sK30_SY353 @ SV207 @ SV151 @ SV112 ) )
| ~ ( in @ ( sK30_SY353 @ SV207 @ SV151 @ SV112 ) @ SV112 ) )
= $false )
| ( ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV207 )
= $false )
| ( ( in @ SV207 @ SV112 )
= $false )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1625]) ).
thf(1628,plain,
! [SV207: $i,SV151: $i,SV112: $i] :
( ( ( ~ ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ ( sK30_SY353 @ SV207 @ SV151 @ SV112 ) ) )
= $false )
| ( ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV207 )
= $false )
| ( ( in @ SV207 @ SV112 )
= $false )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1627]) ).
thf(1629,plain,
! [SV112: $i,SV151: $i,SV207: $i] :
( ( ( ~ ( in @ ( sK30_SY353 @ SV207 @ SV151 @ SV112 ) @ SV112 ) )
= $false )
| ( ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV207 )
= $false )
| ( ( in @ SV207 @ SV112 )
= $false )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1627]) ).
thf(1630,plain,
! [SV207: $i,SV151: $i,SV112: $i] :
( ( ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ ( sK30_SY353 @ SV207 @ SV151 @ SV112 ) )
= $true )
| ( ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV207 )
= $false )
| ( ( in @ SV207 @ SV112 )
= $false )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1628]) ).
thf(1631,plain,
! [SV112: $i,SV151: $i,SV207: $i] :
( ( ( in @ ( sK30_SY353 @ SV207 @ SV151 @ SV112 ) @ SV112 )
= $true )
| ( ( in @ ( sK19_SY309 @ SV112 @ SV151 ) @ SV207 )
= $false )
| ( ( in @ SV207 @ SV112 )
= $false )
| ( ( SV151
= ( union @ SV112 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1629]) ).
thf(1632,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[930,1631,1630,1626,1623,1621,1620,1612,1611,1608,1607,1602,1601,1600,1597,1594,1593,1586,1582,1581,1580,1579,1578,1575,1571,1570,1569,1568,1556,1555,1550,1549,1541,1539,1537,1534,1529,1528,1526,1520,1519,1518,1516,1514,1505,1504,1503,1498,1497,1495,1494,1482,1481,1480,1478,1465,1462,1434,1433,1430,1429,1422,1394,1393,1391,1366,1365,1361,1339,1338,1333,1330,1329,1325,1322,1315,1300,1297,1283,1282,1274,1273,1272,1254,1239,1234,1230,1229,1212,1183,1182,1170,1165,1164,1163,1146,1141,1132,1120,1108,1096,1081,1059,1028,1027,1026,1025,1024,984,982,939,938,937,936,935,934,933,932,931]) ).
thf(1633,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1632,890]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU158+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.15 % Computer : n002.cluster.edu
% 0.09/0.15 % Model : x86_64 x86_64
% 0.09/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.15 % Memory : 8046.5625MB
% 0.09/0.15 % OS : Linux 6.8.0-71-generic
% 0.09/0.15 % CPULimit : 300
% 0.09/0.15 % WCLimit : 300
% 0.09/0.15 % DateTime : Tue Oct 6 15:04:42 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.98/1.50
% 7.98/1.50 No.of.Axioms: 52
% 7.98/1.50
% 7.98/1.50 Length.of.Defs: 0
% 7.98/1.50
% 7.98/1.50 Contains.Choice.Funs: false
% 7.98/1.50 ..................................................
% 7.98/1.50
% 7.98/1.50 ********************************
% 7.98/1.50 * All subproblems solved! *
% 7.98/1.50 ********************************
% 7.98/1.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:52,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1632,loop_count:0,foatp_calls:1,translation:fof_full)
% 7.98/1.50
% 7.98/1.50 %**** Beginning of derivation protocol ****
% 7.98/1.50 % SZS output start CNFRefutation
% See solution above
% 7.98/1.51
% 7.98/1.51 %**** End of derivation protocol ****
% 7.98/1.51 %**** no. of clauses in derivation: 1598 ****
% 7.98/1.51 %**** clause counter: 1632 ****
% 7.98/1.51
% 7.98/1.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:52,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1632,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------